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This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research
Volume Title: Econometric Models of Cyclical Behavior, Volumes 1 and2
Volume Author/Editor: Bert G. Hickman, ed.
Volume Publisher: NBER
Volume ISBN: 0-870-14232-1
Volume URL: http://www.nber.org/books/hick72-1
Publication Date: 1972
Chapter Title: An Analysis of the Forecasting Properties of U.S. Econometric Models
Chapter Author: Michael K. Evans, Yoel Haitovsky, George I. Treyz,Vincent Su
Chapter URL: http://www.nber.org/chapters/c2790
Chapter pages in book: (p. 949 - 1158)
AN ANALYSIS OF THEFORECASTING PROPERTIES OFU.S. ECONOMETRIC MODELSMICHAEL K. EVANS • Chase Econometric
Associates, Inc.YOEL HAITOVSKY • Hebrew UniversityGEORGE I. TREYZ University of Massachusettsassisted by VINCENT SU
1 GENERAL INTRODUCTION
IN A recent study for the National Bureau of Economic Research,Victor Zarnowitz tabulated and analyzed the records of a great manybusiness forecasts.' Zarnowitz' study, while instructive and informa-tive, for the most part excluded forecasts made with econometricmodels. However, the record should be enlarged to include thesemodels as well. Techniques of model-building have improved, andthird generation computers have removed nearly all the drudgery ofeconometric forecasting. Consequently, such forecasts have recentlyproliferated.
As recently as 1963, the only econometric forecasts issued on aregular basis were prepared by the Research Center for QuantitativeEconomics at the University of Michigan. Today such forecasts arecomputed by the Econometric and Forecasting Unit of the Wharton
NOTE: The authors would like to thank the members of the National Bureau of Eco-nomic Research seminar for their helpful comments, Victor Zarnowitz for his carefulreading and criticism of an earlier draft, and Malcolm Burns, C. Richard Hathaway,Robert Gonter, and Leon W. Taub for their assistance in replicating the forecasts ofthe various econometric models. We would like to express our gratitude to GeorgeGreen, Albert A. Hirsch, and Maurice Liebenberg for the information they providedfor the OBE Model. While all of the authors are jointly responsible for the study, itshould be noted that Michael K. Evans and George I. Treyz have primary responsibilityfor calculating the results of the Wharton-EFU and Evans Models, and Yoel Haitovsky,assisted by Vincent Su, has primary responsibility for the ORE Model calculations.
Victor Zarnowitz, An Appraisal of Short-Term Economic Forecasts, NationalBureau of Economic Research, Occasional Paper No. 104.
949
950 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
School, the Office of Business Economics of the Department ofCommerce, and several large private corporations. In addition, theFederal Reserve Board-MIT Model is nearly completed, and even thelarge-scale Brookings Model has been reestimated for possible use inshort-term prediction. Since this method of forecasting has grownrapidly, it certainly deserves further examination.
The analysis of the forecasting record of econometric modelscan be undertaken in a manner quite different from the procedure usedby Zarnowitz. Noneconometric forecasts are not based on a definablealgorithm or methodology which enables the ex post examiner to de-termine in what respects the forecasts might have been changed if theforecaster had possessed more accurate information on various exog-enous developments. Econometric forecasts, however, are based ona definite model and explicitly incorporate the exogenous estimates offuture values. Thus, while it is possible to analyze the ex ante record ofeconometric and noneconometric forecasts in the same way, the ex-plicit statement of assumptions by the econometric forecaster enablesus to add an extra dimension to the analysis of econometric forecasts.
The obvious alternative to examining ex ante econometric fore-casts is to replicate the exact method of solution used by the forecaster,then finding out how his forecast would have been affected had he usedthe cx post values for the exogenous variables. Despite the superficialattraction of this method, it has become apparent to us that the ex postforecast is not the only test for an econometric forecaster. We havefound that detailed appraisal of both the ex ante and the ex post fore-casts, as well as other types of forecasts and simulations, is necessaryif we wish to obtain a penetrating analysis of the current state of theart of econometric forecasting.
Those unfamiliar with econometric forecasting may believe thatall econometric forecasts are made using the model as a "black box"of equations, coefficients, and solution algorithms into which the fore-caster enters his best exogenous estimates and then awaits the single,definitive answer. This description is not true, however, for the moresophisticated econometric forecasts. The judgment that is used whenforecasts are made with the Wharton and OBE Models is substantialand can be broken into three basic categories.
FORECASTING PROPERTIES OF U.S. MODELS • 951
First, judgment is used to select the values for future exogenousvariables. The forecaster must make informed guesses about the pathof fiscal and monetary policy during the period to be predicted. Hemust also estimate economic activity in the foreign sector and in anyother sectors which are exogenous to the model. Similar estimatesmust also be done, of course, by the noneconometric forecaster, butusually not in such explicit detail.
Second, the constants of individual equations are changed toincorporate various factors. They can be changed to reflect informationabout future exogenous developments not included in the model (suchas a strike, a credit crunch, or unusual weather conditions). Constantsare altered to incorporate structural changes that have occurred in thereal world, but which are not included in the estimated function. Simi-larly, they are adjusted to reflect unexplained short-run patterns ofcyclical behavior or autocorrelation of the residuals. In addition, con-stants are shifted to recognize substantive data revisions in the levelof certain series.
The method used for adjusting the constant terms will be quitedifferent, depending on the source of error. In the case of extraneousinformation, the explicit adjustment would be entered in the constantterm for the duration of the disturbance, and would then return to itsprevious value. In other cases, the forecaster would use some weightedaverage of residuals (predicted-actual) for a number of past periods.For data revision, a reasonable alternative to reestimation of the wholemodel with revised data—if the new revisions are small—is to adjustthe constant terms. This assumes that the alterations of the slope co-efficients due to the revisions are small, relative to those of the inter-cepts. Since some of these methods are explained in the following sec-tions, we shall not discuss them here in detail.
Finally, the forecaster may change some of the decisions he hasmade about constant adjustments or exogenous variables if preliminaryforecasts with these assumptions lead to a forecast for some variablesthat is out of the range of his a priori concept of a reasonable forecast.2
2Any forecaster will know the multipliers in his model. Thus, he may modify his "exog-enous assumptions" so that the forecast will be in line with his a priori ideas of a reason-able forecast, even if he has decided never to alter these assumptions once the prelimi-nary forecast is made.
952 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
The first quarter that is "forecast" is the current quarter. Since thisfirst-quarter forecast is made midway through the quarter to be fore-cast, some of this a priori information is available from interim reportsfor important economic series, such as employment, consumer prices,and investment anticipations. Other a priori restrictions may come froman implicit model used by the forecaster. Such a model may includequalitative information that is not adequately reflected in quantitativeindicators. It must be made clear that using these unstated restrictionsis not the same as predetermining the forecast values for all variables.Such restrictions are ranges, and are more important for some variablesthan for others. They are much the same as the a priori views econo-mists use in deciding whether a regression coefficient is reasonable ornot.
The three above adjustments of the model, sometimes known as"fine tuning," have been criticized for destroying the objective natureof econometric forecasting and precluding direct tests of the predictiveefficacy of such models. But they preclude only a test with a strawman — an econometric model which has never been adjusted. Theremay be some interest in examining how well these nonadjusted modelsperform, and various summary statistics for these experiments arepresented later in this study. These results should not be confusedwith forecasts made by econometricians. They may, however, be re-garded as forecasts made by econometric models. A major part of thisstudy is devoted to explaining that these two concepts can be quitedifferent from each other, sometimes bearing little resemblance. Thisis a separate problem which cannot be analyzed in comparisons ofjudgmental forecasts; some of the methodological implications of thisdifference are explored next.
Virtually every econometric forecast involves some judgment,even if it is estimating only the totally exogenous part of the fiscalpolicy (such as defense spending or change in tax rates). It is unlikelythat a totally endogenous econometric model would be a very usefultool. Such a model would be able to issue only one forecast at anygiven time, regardless of projected changes in government policy. Ifgovernment expenditures were to double or triple, or even if there werea conflagration or holocaust such that only the computer making the
FORECASTING PROPERTIES OF U.S. MODELS • 953
forecast were to be saved, the prediction would not change.:3 In thisstudy we plan to exclude such models—if, indeed, any do exist—andto treat only those econometric models which involve some degree ofjudgment.
The degree to which econometric methods are used for forecastingin a model depends in part on the relative size of the exogenous sector.In thelimiting case, everything would be exogenous; in this case, itwould coincide with the pure judgmental forecasts. Most econometricmodels contain consumption and investment sectors which are bothendogenous, although in some cases consumer and producer durablesare predicted by survey data within the over-all framework of an econ-ometric model. In the government sector, most (or all) expendituresare exogenous; endogenous revenue functions are estimated but theydepend on exogenous tax-rates. There is usually an endogenous mone-tary sector which depends on certain key exogenous variables, suchas unborrowed reserves or the discount rate. Foreign income andprices are almost always exogenous because they depend primarilyon events which are independent of this economy. In models of theUnited States, the agricultural sector is usually treated exogenously,both because it is affected mainly by exogenous variables such as theweather and government farm policy, and because it is quantitativelyunimportant. While there are some minor variations from this broadoutline, it serves as a general guideline for the type of econometricmodels which will be considered.
Given the sort of econometric model outlined above, its forecast-ing record will depend on the estimation structure of the individualequations, the interaction of these equations in a simultaneous solution,and cumulation of error in successive quarters of forecast. Forecastingrecords compiled from such a system—without adjustment, but withthe actual values of the exogenous variables —can be easily tabulated
It is true that certain types of forecasts, such as the National Bureau leading indica-tors, and various types of anticipations and intentions surveys, give only one forecastat any given time. However, these methods of forecasting presumably have advantagesnot found in the econometric models, such as simplicity and inclusion of exogenousinformation not easily predicted by econometric methods. It would seem a great mis-allocation of resources to estimate complex econometric models which then did not havethe flexibility to issue alternative forecasts which reflect policy decisions.
954 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
and analyzed. As we have already stated, this kind of record may notbe very meaningful, although for future prediction one would generallyprefer a model with a better forecasting record (as defined on this basis)to a model with a poorer one.
The question of how well econometricians forecast, given thatthey have developed a certain model, depends both on their ability tojudge future exogenous events correctly and on their success at "fine-tuning" the model. One might want to separate these effects; this isdone with the empirical results presented in this study. Errors in pre-dicting exogenous variables are generally less offensive than errors inthe model itself.4 For example, consider two forecasts, both of whichhave understated GNP by $10 billion. The first forecast uses a poorguess at exogenous variables; if the correct ex post values wereinserted, the forecast would be correct. The second forecast containsall the correct exogenous variables but nevertheless it is still in errorby $10 billion. Most neutral observers would consider the first forecastas the better of the two, even though the actual error was identical.Furthermore, if a third forecast were correct only because it used theincorrect exogenous values, and was found to contain an error of $10billion when the actual ex post values were supplied, some might arguethat this forecast is also inferior to the first one. In many cases, thismay be true. For example, the 10 per cent surcharge which went intoeffect in July, 1968, was widely assumed to be effective during theentire year by those forecasting a year ahead in late 1967. A forecastwhich underestimated the level of 1968 GNP by only the amountdirectly attributable to the delay in the surcharge would have been abetter one than a forecast which was actually correct but assumed nosurcharge.
The above example notwithstanding, it may be an unrealisticprocedure to enter the correct exogenous values in an ex ante forecastand claim that this is the forecast which would have been released ifthe correct values of the exogenous variables were known. For in-stance, if the model had been tuned with the expectation of no sur-charge, such a forecast might be quite different from one prepared withthe expectation of the surcharge and only a change in the slope-
We assume that the model-builder will try to find the exogenous variable which iseasiest to predict in any given class of variables imparting equal predicting information.
FORECASTING PROPERTIES OF U.S. MODELS 955
coefficient of the tax function. The fine-tuning of the individual equa-tions might have been considerably different for these two forecasts.
In addition, one must consider the interaction of the actual fore-casts with government policy. It is possible that monetary and fiscalpolicy will be partially determined by ex ante forecasts when suchmodels predict undesirable economic developments. In these cases,the forecasts might be incorrect because of incorrect values of the exog-enous variables, but this could in no way be considered a poor fore-cast. In such instances, the econometric model would have performedone of the most important tasks for which it is designed. Thus, theentire question of errors in predicting exogenous variables is one whichcontains many problems of interpretation, and should, in any event,be analyzed separately from other forecasting errors.
If we wanted to evaluate ex post forecasts for many models, wewould have to control the exogeneity in the various models. As anextreme example of a good conditional forecast due to a high de-pendence on exogenous variables, consider the extremely simplemodel GNP = pX, where p and X are both exogenous. It is clear thatthe conditional forecasts from this "model," i.e., with the exogenousvalues known, would always be perfect. However, such a model wouldbe of no use for forecasting. This particular example is clearly un-realistic, and is not representative of econometric models. Yet, it wouldbe possible to construct a model in which all sectors of aggregate de-mand and supply were closely tied to exogenous variables. The tend-ency away from this sort of model-making suggests that these types ofresults are not really very useful, and we do not consider them in thisstudy.
It should be emphasized that the primary purpose of our study isto uncover the various sources of error inherent in ex ante forecasts,and to suggest alternative methods of adjustment, estimation, andspecification of the models which might systematically improve theirforecasts. Our work is not intended to be a comparison of the predic-tive records of various models, or to be a study aimed at establishingthat one model is "better" than the others. Because each econometricmodel has so many of its own unique characteristics, it is not possibleto treat each set of forecasts anonymously, as was done by Zarnowitzin his study. Thus, each model considered in this study is prominently
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identified, and its fundamental characteristics are discussed. This isdone with a view to providing the reader with a better background forunderstanding the results which follow, rather than as an invitation toinvidious comparisons.
2 THE MODELS INCLUDED IN THIS STUDY
A. THE CHOICE OF MODELS USED
At the outset of this study, our impression was that there were inexistence a fairly large number of econometric models which might beincluded and analyzed. However, upon closer examination, and uponapplication of various criteria to prospective models, we found thatthe alleged list was much smaller than we had expected. The fourcriteria which were used are as follows:
First, the forecasts should be made with a structural econometricmodel. This study is not concerned with purely extrapolative tech-niques, even if they are formal and very sophisticated.
Second, the models included must have reasonably long true exante forecasting records.
Third, the particular versions of the model used for specific exante forecasts, the exogenous assumptions, and the constant adjust-ments associated with these forecasts, must currently exist. In addition,it is necessary that the ex ante forecasts can be reproduced, and thatvariations on these forecasts can be performed using alternativeassumptions.
Fourth, the models and forecasts must be on a quarterly basis.While we recognize that annual models may be as useful in forecastingand policy analysis as are quarterly models, the method of analysisused in this study would not be applicable.
After applying these criteria and requiring, in addition, that theproprietors of any given model agree to cooperate with this project, itwas found that only two models could be included: the WhartonEconometric Forecasting Unit (Wharton-EFU) Model and the Officeof Business Economics (OBE) Model. The Evans Model (which was
FORECASTING PROPERTIES OF U.S. MODELS • 957
estimated at Brown University but was used for forecastingby theWharton School for two years) is treated as a subset of the Wharton-EFU Model, as will now be explained.
B. THE WHARTON SCHOOL AND EVANS MODELS
The initial model in this collection was estimated by M. K. Evansas part of his unpublished doctoral dissertation.5 Forecasts from thismodel were first made in early 1963; they were genuine ex ante fore-casts, in that the first-quarter figures were not yet known, but they werenot circulated publicly. These forecasts were made without adjustingthe constant terms for any of the equations, owing to a certain naiveteof the forecaster at that time, which led him to believe that econometricmodels should not need any adjustments.6 This model was improvedby Evans and L. R. Klein during the summer of 1963, and regularquarterly forecasts were started at that time. The model underwentcontinuous revision until the beginning of 1964, when a stabilizedversion was used for prediction for several quarters. A slightly revisedversion was used for the fall 1964—summer 1965 predictions.
In August, 1965, the national income data were completelyrevised, and it was found that the old model, even with some patch-work, was no longer relevant. A completely new model was estimatedby Messrs. Evans and Klein, and was first used for forecasting pur-poses at the end of 1965. While the new model was being constructed,no forecasts were made, leaving a two-quarter break in an otherwisecontinuous series of predictions. This version was slightly refinedearly in 1966 and the revised version was used through the spring of
At that time, an enlarged monetary sector was added, but theremaining equations were unchanged. This model was used for fore-casting through the end of 1968, at which time it was supplanted by arevised and updated version. All these various versions are referred to
M. K. Evans, "A Quarterly Postwar Model of the United States Economy," un-published doctoral dissertation, Brown University, 1964.
6 Experience shows that this sort of naivete is typical of many newcomers to the"business" of econometric forecasting.
version is found in M. K. Evans and L. R. Klein, The Wharton EconometricForecasting Model, University of Pennsylvania, 1968.
958 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
as the Wharton Model in this study, except in those tables where theEvans Model is explicitly accorded separate treatment.
Before proceeding to the empirical record, it may be useful todescribe some of the characteristics of the Wharton Models. In spiteof the multiplicity of models actually estimated, there are certain basicfeatures which have remained unchanged throughout all versions.
The models have grown in size from approximately 30 to 50 sto-chastic equations, but the primary emphasis is still centered on theaggregate demand equations in general, and the investment sector inparticular. The consumption sector has separate equations for autosand other durables, and treats nondurables and services in a singleequation. In that equation, the ratio of nondurables and services topersonal disposable income is a function of the lagged dependent ratioand percentage changes in income. Nonauto durables are a function ofincome, relative prices, and previous stocks. The specification of theautomobile equation has changed somewhat because of its poor per-formance in initial predictions. Income, relative prices, previous stocks,and the rate of unemployment have always been important variables,but the lag structure has been modified. A money-stock variable repre-senting general credit conditions has been replaced by a variable forspecific changes in consumer credit regulations, and a dummy variablefor supply shortages was added later.
Fixed business investment and inventory investment have alwaysbeen disaggregated into the manufacturing and nonmanufacturingsectors. Fixed business investment in manufacturing is a function ofoutput, cash flow and capital stock in that sector, and the long-terminterest rate. In earlier versions of the model, the "inverted W" dis-tribution was used;8 separate output terms were included withaverage lags of 1 and 2 quarters, and 5 and 6 quarters. All other vari-ables entered the function only with the longer (5—6 quarter) lag. Later,this formulation was modified by introducing the Almon lag structurefor all independent variables, plus a modifications term—representedby capacity utilization—which is lagged one quarter. In early versionsof the model, investment was positively related to the change in the
8 For a discussion of this distribution, see M. K. Evans, "A Study of Industry Invest-ment Decisions," Review of Economics and Statistics, Vol. 49, No. 2 (May, 1967),pp. 151—64.
FORECASTING PROPERTIES OF U.S. MODELS • 959
wholesale price level and negatively related to the variability of re-tained earnings, but these terms were later dropped. The independentvariables in the nonmanufacturing fixed-business-investment functionwere, originally, the change in the wholesale price level, total salesoriginating in the private sector, and the long-term interest rate. Thefunction included the change in sales with a short lag, and the level ofsales with a longer (5 quarter) lag. The wholesale price level was laterdropped, and the Almon lag structure introduced, but the other inde-pendent variables are unchanged. Early versions of the model includedan endogenous function for farm investment, which depended on farmprices, farm income, and farm capital stock. This equation was laterdropped (since all of the independent variables were exogenous), and
investment was further subdivided into equationsfor regulated and commercial investment.
The inventory investment functions have changed very little. Forthe manufacturing-sector equation, sales, lagged inventory stocks,change in unfilled orders, a dummy variable for steel strikes, andchanges in the wholesale price level have been the dependent vari-ables. In later versions, the wholesale price level term was dropped,and the lag structure on sales and unfilled orders was slightly modified.For the nonmanufacturing (trade) sector, the change in manufacturingoutput, change in the wholesale price level, purchases of consumerdurables, and lagged inventory stocks are the independent variables.There has been virtually no change in this function. A farm inventoryinvestment function, in which the independent variables were the farmprice level and lagged inventory investment, was subsequently droppedfrom the model.
Investment in residential construction contains elements of supplyas well as demand, since in the short run the amount of constructionput in place measures the amount of housing built, rather than bought.Thus, cost variables, such as the ratio of the price of new housing rela-tive to a rent index, and a variable representing the availability of credit— which is the spread between the long- and short-term interest rates —have always been important. In addition, disposable income has aminor role. Some early attempts to include population and the stock ofhousing as long-run variables were not continued in more recent ver-sions of the model. The change in the money stock was, at one time,
960 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
included as a general credit variable. This, too, was subsequentlydropped, although it might have helped predict housing in late 1966.
The early versions of the model treated the foreign sector com-pletely exogenously. This omission was rectified in the post-1965models, when three import equations and an export equation wereadded. In the import sector, imports of food depend on per capitaincome and relative prices. Imports of crude materials and semi-manufactured goods depend on sales and inventory investment in themanufacturing sector, and on relative prices. Imports of other goodsand services depend on personal disposable income and relative prices.Exports depend on an index of world trade and on the price of exportsrelative to the price of world trade. In the last two equations, the de-pendent variable is also included on the right-hand sid'e of the equa-tions, with an average lag of the past four quarters.
It is in the supply side that the older and newer models differsubstantially. In the Evans Model, corporate profits were determineddirectly, as a function of national income, capacity utilization, and(with a negative relationship) lagged capacity utilization. Wage incomewas thus determined as a residual, which precluded the need for equa-tions explaining employment, hours worked, or wage rates. Unemploy-ment was estimated directly, as a function of capacity utilization,instead of being calculated implicitly as the residual between laborforce and total employment.
Later versions of the model followed the approach set forth byKlein in his earlier work, with an expansion to the two-sector approach.Output originating in the manufacturing sector is a function of utilizedlabor (defined as employment times hours worked per week), utilizedcapital stock (defined as total manufacturing capital stock times anindex of capacity utilization), and a nonlinear trend representing tech-nological improvement. Maximum output in the manufacturing sectorcan then be made a function of total—rather than utilized—labor andcapital in that sector. The ratio between actual and maximum outputin manufacturing is then defined as the index of capacity utilization.The nonmanufacturing-sector function is the same, except that nodistinction is made between total and utilized capital stock. Further-more, the concept of capacity utilization is not defined for the non-manufacturing sector.
FORECASTING PROPERTIES OF U.S. MODELS • 961
Hours worked in the manufacturing sector are a function of thelevel of output, the change in output, capacity utilization, and the wagerate. The positive relation with output, and the negative relation withthe wage rate, represent the tendency of employers to use more laborwhen demand grows, but to reduce the length of the work week asovertime wages grow. In addition, the wage rate may represent a sub-stitution on the part of workers of more leisure for more overtime pay.The change in output and capacity-utilization terms represent thebuffer-stock nature of hours; in the short run, employers prefer tochange the length of the workweek rather than the number of em-ployees. Hours in the nonmanufacturing sector do not fluctuate cycli-cally but, rather, follow a general downward trend. Only the wage rateand a marginally significant capacity-utilization term are included inthat equation.
The manufacturing wage-rate function, estimated in annual firstdifferences, is a function of previous changes in the consumer pricelevel and the spread between the over-all unemployment rate and the"prime group" unemployment rate (calculated as the unemploymentrate for males aged 25—34). There is a nonlinear relationship betweenthese two rates; they are almost the same during recession, but inbooms the prime-group rate falls below 2 per cent, while the over-allrate stays at a much higher level. Thus, the nonlinearity inherent inPhillips-curveanalysis is included by using the spread between thesetwo rates. An additional equation in the system tracks the nature ofthe nonlinearity between these two rates. The nonmanufacturing wagerate follows the manufacturing wage rate; it includes a separate termfor the change in consumer prices, but not for the tightness of the labormarket.
The factor-share equations are similar for both models and are, inany case, quite straightforward. Taxes are a function of the income onwhich they are levied, transfer payments depend on the unemploymentrate and a time trend (for increased coverage), and depreciation allow-ances for the various sectors depend on the relevant capital stocks.Dividends are a function of after-tax profits and lagged dividends, andinventory valuation adjustment is a function of changes in the whole-sale price level, in the post-1965 models, equations are also providedfor unincorporated business income and for rental and interest income;
962 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
these variables were not needed in earlier versions of the model be-cause personal income was then calculated directly as national incomeless corporate savings plus transfer payments. Both models containequations explaining output originating in the manufacturing sector asa function of various components of aggregate demand. They alsoinclude an equation in which unfilled orders is a function of sales,changes in government defense purchases, dummy variables for theKorean War, and (in earlier versions) fixed investment and the laggedlevel of orders.
The price functions have undergone the greatest changes in thevarious models, although the wholesale price level has continued tobe the central price variable in the model. In the earliest model, changesin the wholesale price level were a linear function of the level of capac-ity utilization and the money stock, and a nonlinear function of changesin capacity utilization. Other price levels were then related to thewholesale price level and to specific variables important to particularsectors. Later the money stock was dropped and various dummy vari-ables were added for the Korean War period. In the post-I 965 ver-sions, levels instead of changes were estimated, unit labor costswere added as the main independent variable, capacity utilizationwas retained but the nonlinear terms were dropped (for lack of em-pirical evidence), and the lagged dependent variable was also included.Other sectoral price levels still depended on the wholesale price leveland on other specific factors, i.e., the price of food, of nondurables andservices, and the ratio of investment to GNP for the capital-goodssector. It might be noted that in the post-1968 versions (not used forempirical results here), these equations have again been substantiallychanged. The equations have been estimated for the period 1954—1967so that the periods of price controls during the Korean War could beomitted, annual percentage first differences are used, nonlinearitiesnear full employment have again been found to be important, normalunit labor costs have been included successfully in the wholesale priceequation, and sector price levels also depend directly on unit laborcosts.
Until very recently, the monetary sector consisted of two equa-tions. The short-term interest rate was a function of the discount rateand the lagged short-term rate (later, a term including the required
FORECASTING PROPERTIES OF U.S. MODELS • 963
reserve ratio was included, and after that, the free reserve ratio wasadded), and the long-term rate was a function of the short-term rateand the lagged long-term rate. In the 1968 version of the model, equa-tions have been added for the three components of the money stock. Inthese equations, the ratio of money to a weighted average of GNPdepends on differential rates of interest. A time deposit rate has alsobeen added, and the equations for the short and long rates have beensomewhat modified.
The brief description above is, of course, not intended to conveyall of the theoretical and empirical specifications that serve as back-ground for the estimation of the models and for the areas of future im-provement, these being discussed in other publications.9 It should,however, convey some of the flavor of these models and provide thereader with a useful background for interpreting the statistical resultsof the next three sections.
C. THE OFFICE OF BUSINESS ECONOMICS MODEL
This model will not be described here, since its outline and acomplete equation specification are included in another paper preparedfor this Conference.1° However, it may be useful to sketch the develop-ment of this model after 1966, since several different versions havebeen used to make the forecasts. All of the various respecifications ofthe OBE Model are based on the May, 1966, published version, whichcontained 36 stochastic equations. (See the paper by Green, Lieben-berg, and Hirsch, present volume.)
Only those versions of the model which were used for makingforecasts during the last three quarters of 1967 and during 1968 will beused. All efforts to replicate the forecasts prior to 1967.2 proved to beunsuccessful. There are, basically, three different models to be con-sidered:
(a) The 1967.2 version is quite similar to the 1966 published
See Evans and Klein, op. cit., and M. K. Evans, Macroeconomic Activity: Theory,Forecasting and Control. New York, Harper & Row, 1969.
10 Maurice Liebenberg, Albert A. Hirsch, and Joel Popkin, "A Quarterly EconometricModel of the United States: A Progress Report," Survey of Current Business, May,1966, pp. 13—39.
964 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
version, the major addition being the inclusion of an employmentequation. The price and wage equations were also reestimated.
(b) The 1967.3 version incorporated substantial changes. Thewage rate, civilian labor force, and compensation of employees equa-tions were respecified. This had a significant effect on price determina-tion, since prices are determined primarily as a markup over unit laborcosts.
(c) Further substantial changes were made in the 1968.1 version.The number of stochastic equations was increased to 56, with thenumber of variables now totaling 170. The monetary sector was greatlyenlarged, and equations for new orders, unfilled orders, and shipmentswere introduced. All the consumption and investment functions wererestructured and reestimated. The merchandise import equation waschanged to include production, capacity utilization, and prices as in-dependent variables. The price equations were again respecified andreestimated. in the 1968.3 version of the model, several equationswere reestimated with the revised July, 1968, data, but very few re-specifications occurred in either that model or in the 1968.4 version.In the forecasts for 1968.1 and 1968.2, the endogenous equations forfixed nonresidential investment were suppressed for the two quartersof forecasting, and were replaced by realization functions for antici-pated investment expenditures from the OBE investment anticipation.survey. The endogenous equations were used for the final quarter ofthe forecasts.
3 HOW WELL DO ECONOMETRIC MODELSFORECAST
A. GENERAL METHODOLOGY
In this section, we will confine our investigation to sampleperiod simulations and ex post mechanical forecasts. Thus, we willbe examining the predictive efficacy of econometric models in theunrealistic situation where all of the revised values of the lagged vari-ables are known, and where the future values of the exogenous van-
FORECASTING PROPERTIES OF U.S. MODELS 965
ables are also known. This procedure is designed to isolate the amountof forecast error that is due to the model alone. We are testing how wellthe model would forecast in the absence of any interaction betweenthe forecaster and the model, and in the absence of any uncertaintyabout the values of exogenous variables.
Each model was simulated over both its sample period (with minorexceptions to be noted later) and the postsample period through 1968.In most cases, simulations were calculated six quarters ahead fromeach starting date. Each six-quarter forecast uses observed values oflagged endogenous variables before the starting date, while using inter-nally generated endogenous variables for all values after that date. Inall cases, the actual values of the exogenous variables are used, sincewe want to isolate the effect of incorrect exogenous values on fore-casting error and to discuss this effect at a later point.
In the first set of simulations, we did not adjust the constant termsof the equations. These simulations were carried out to show thesample-period performance of the model itself. They do not reflect theprocedure that was used for ex ante forecasting. In particular, theyneglect the constant term adjustments which are incorporated in mostex ante forecasts. We then examined the actual adjustments used dur-ing the six-year cx ante forecasting record of the Wharton Models tosee if any systematic rules for adjustment could be found. While, aswill become apparent later, no single rule explains all of the adjust-ments which were made, it was found that the following mechanicalrule explains the adjustments best: for all equations where the de-pendent variable is not expressed as a first difference (quarterly orannually), add the average of the single-equation residuals for the lasttwo quarters to the constant term in the equation.t' This rule was alsoused in the analogous simulation of the OBE Model. This method ofmaking adjustments is referred to as "AR (average residual) constantadjustments" in all of the following tables.
If the equation disturbances are autocorrelated, but it is thoughtthat the structure of the equation has not changed, the forecaster canoften take advantage of the information imparted by recent residualsin another way. The appropriate procedure for a first-order auto-
" In the Wharton-EFIJ Model, the equation for the change in unfilled orders wastreated as if it were not a first-difference equation.
966 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
regressive scheme of the disturbances is given by Goldberger as:'2A — T— pj
where A, is the correction applied to the ith equation, p, is the auto-correlation coefficient of the residuals of the ith equation, t is the latestobserved date previous to the generation of the forecast, and is theobserved single-equation residual for this date.'3
Goldberger's procedure has been refined by George Green, whocalculates a modified correction factor as:14
AG —
_________
—2
On purely theoretical grounds one might prefer to use a second-orderauto-regressive scheme for computing the correction factor.15 How-ever, this procedure was also tried by George Green for the OBEModel and was not found to be superior to the simpler first-order cor-rection. The purpose of additional Green refinement is to eliminate anoveradjustment which might ensue from an exceptionally large resid-ual in the latest observed quarter. Forecasts and simulations for whichthe type adjustments were applied are referred to as "GO (Gold-berger-Green) constant adjustments" in all of the following tables.
In addition to reporting the simulation results up to six quartersahead, we have calculated statistics for simulations one year ahead.These are the root mean square (RMS) statistics computed from theforecasting errors of the various simulations—one, two, three, andfour quarters ahead. These forecasts are obtained by simple averagingof the forecasts over a four-quarter period. This statistic is reported in
12 Arthur S. Goldberger, "Best Linear Unbiased Prediction in the Generalized LinearRegression Model," Journal of the American Statistical Association, Vol. 57, No. 2(June, 1962), PP. 369—375.
13 Goldberger developed his formula for single equation estimates rather than formodel forecasts. Also, his et is the last sample-period residual. However, the spirit of hisdevelopment is not violated by our simple extensions.
14 An alternative procedure would be to calculate
T eu +AW+T) = 1 + Pi
for example, Guy H. Orcutt, "A Study of the Autoregressive Nature of theTime Series Used for Tinbergen's Model of the Economic Systems of the U.S., 19 19—1932," Journal of the Royal Statistical Society (Series B), Vol. 10, No. 1, pp. 1—45.
FORECASTING PROPERTIES OF U.S. MODELS 967
order to facilitate comparisons with annual forecasts. It is not sur-prising that occasionally the one year ahead forecasts have a smallerRMS error than the one quarter ahead forecasts. Evidently, many ac-tual short-run fluctuations not captured by the model are canceledwhen averaged over a longer period.
Two bench mark (or standard of comparison) statistics are alsocomputed for each of the reported variables. These are the so called"naive forecasts." Two naive models were computed. The first, whichis termed here Naive Model I is the "no change" forecast, i.e.,
=
where F- stands for the forecast of the ith variable and R, stands forthe "realized" (observed) value of the ith variable.
The second is the "same change" naive model (Naive Model II),which is
= + TX —
that.is, the trend in the last two observed quarters is extrapolated for Tperiods.
The RMS statistics for the various simulations are then dividedby the corresponding RMS of Naive Model I. The purposeof the newstatistic is twofold: (a) the performance of the forecasting procedureunder investigation can be easily compared to the "no change" fore-cast. A value larger than unity for the new statistic immediately cau-tions the reader that the model forecast performance was inferior evento the simplest of all extrapolations; (b) the division by Naive ModelI RMS can be viewed in some sense as a normalization procedure, nor-malizing for the erratic behavior of the series in the periodunder investigation.
We have followed standard procedure in reporting the RMS errorfor all these different simulations. In addition, we have decomposed themean square error (= (RMS)2) into the Theil inequality coefficients.We have
UM=(F—R)2US = — SR)2
and
968 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
UC = 2(1 — rFR)SPSR
where F, R, SR, and rFR are respectively the means and standarderrors of the simulated and realized values and the correlation coeffi-cient between them over the period covered in the tables.
UM, US, and UC are called by the "partial coefficient ofinequality due to unequal central tendency, to unequal variation, andto imperfect covariation, respectively." This breakdown provides ad-ditional information about the source of the forecasting inaccuracies.
B. THE WHARTON-EFU MODEL
The version of the Wharton-EFU Model used for the sample pe-riod simulations is the one listed in The Wharton Econometric Fore-casting Model. This model was estimated with data including the July,1965 revision of the national income accounts for the sample period1948.1—1966.4. The Wharton-EFU Model has two separate operatingsystems: the standard version and the anticipations version. In the an-ticipations version, equations for purchases of consumer durables,plant and equipment expenditures, and residential construction are ex-panded to include terms for the Survey Research Center index of con-sumer attitudes, the OBE-SEC investment anticipations, and housingstarts lagged one quarter, respectively. Since the anticipations var-iables are not generated endogenously, this version can be used toforecast only one or two quarters ahead.
In this section, simulations with both systems of the Wharton-EFU Model are presented, although the emphasis is on the standardversion. Sample period simulations were carried out for six-quarterintervals, beginning in 1953.1, and the model was then restarted foreach quarter through 1963.3. The 1963.4 simulation was calculated foronly five quarters so that it would still end within the sample period;similarly, the 1964 simulations were generated for four, three, two, andone quarters. The starting date of 1953.1 was chosen even though thesample period extends from 1948.1 to 1964.4. The Korean War yearsare excluded from these simulations, because they include economicfluctuations not adequately captured by an econometric model whichis designed primarily for forecasting the post-I 964.4 period. As cur-
'6H. Theil, Economic Forecast and Policy. Amsterdam, North-Holland, 1961, p. 35.
FORECASTING PROPERTIES OF U.S. MODELS • 969
rently written, the solution program for the Wharton-EFU Model willnot converge to a reasonable answer (e.g., unemployment greater thanzero) for more than one quarter ahead during some of the Korean Warperiods.
As stated earlier, the sample period simulations presented hereuse revised values for the lagged variables and the actual values of allexogenous variables. In addition, the parameters of the three tax func-tions are changed whenever there is a corresponding change in the taxlaws. The parameters of each tax function are usually estimated byleast squares during the duration of any tax law. In some cases, wherethere were only a few observations, simple inspection sufficed for de-termining the parameters.
In addition to the types of simulations already described in Sec-tion 3A, one additional set of simulations was calculated for theWharton-EFU Model. These simulations, which are described in muchgreater detail in Section 5, are called Regression on Simulated Val-ues, or ROS coefficients. Very briefly, the model is first estimated bystandard methods (in this case, two-stage least squares with principalcomponents) and parameter estimates are obtained. The system is thensolved for each quarter to obtain simulation values. The coefficients, arethen reestimated using the complete system solution values for the un-lagged endogenous variables that appear on the right-hand side of eachequation in place of their actual values. The parameter estimates thusobtained are used to resimulate the model for six-quarter periods, andit is these statistics which are reported in the lowest quadrant of Ta-bles 3.1 through 3.10.
We consider the sample period results first. While it would besuperfluous to comment on each set of entries individually, a few gen-eral comments are in order. First, it can be noted that all the errors areuncomfortably large. In particular, the $6.8 billion RMS error inpredicting GNP only one quarter ahead is only slightly lower thanthe actual change of $8.1 billion given by Naive Model I for the sameperiod. Similarly unimpressive results are reported for the other var-iables included in these tables.'7 Furthermore, the constant adjust-
These summary statistics were originally calculated for seventeen variables. How-ever, in the interests of reducing the number of tables here, we have chosen toanalyze only five variables: GNP, consumption, and investment in current dollars, GNPin constant dollars, and unemployment. Summary statistics for the other variables areavailable on request.
TAB
LE 3
.1
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
0 (I) 0
.91
r 0
Sam
ple
Perio
d Si
mul
atio
ns fo
r GN
P in
. Cur
rent
Dol
lars
, Wha
rton-
EFU
Mod
el S
tand
ard
Ver
sion
A. N
o C
onst
ant A
djus
tmen
ts
S rn r) 0 z 0 rn -1 C)
RM
S6.
758.
207.
708.
178.
1910
.02
6.20
5.11
5.70
UM
.50
.81
.18
.20
4.61
8.13
1.67
2.11
US
.23
.60
0.00
.47
2.42
4.02
.55
UC
44.8
065
.83
59.1
166
.08
73.7
988
.25
RM
S (%
Err
or)
1.47
1.77
1.67
1.78
1.98
2.22
RM
S/R
MS
(Nai
ve I)
.83
.54
.35
.29
.29
.25
.34
MSE
45.5
667
.24
59.2
966
.75
80.8
210
0.40
38.4
4(o
f com
pone
nts)
20.5
825
.14
25.6
128
.87
33.4
6
B.
GG
Con
stan
t Adj
ustm
ents
RM
S6.
11U
M Us
Uc
RM
S (%
Err
or)
RM
S/R
MS
23.8
929
.47
1.11
1.23
.63
26.1
132
.49
37.2
518
.96
16.9
8
8.14
8.28
8.59
9.18
9.83
6.62
.10
0.00
.14
.01
1,83
3.63
0.00
.40
.35
0.00
.94
1.75
37.2
365
.86
68.0
773
.78
81.5
091
.25
1.39
1.74
1.80
1.86
1.99
2.15
(Nai
ve1)
.75
.53
.38
.30
.27
.25
.37
MSE
37.3
366
.26
68.5
673
.79
84.2
796
.63
43.8
2£M
SE (o
f com
pone
nts)
15.7
823
.43
25.6
329
.15
33.5
136
.95
C. A
R C
onst
ant A
djus
tmen
tsR
MS
6.87
9.29
9.92
11.0
712
.92
14.0
28.
415.
156.
17U
M2.
835.
704.
235.
028.
188.
451.
913.
46U
S1.
04.7
7.4
91.
476.
188.
25.1
3.0
4U
C43
.44
79.8
393
.69
116.
0515
2.57
179.
8524
.48
34.5
7R
MS
(% E
rror
)1.
492.
032.
182.
442.
863.
091.
121.
34R
MS/
RM
S (N
aive
I).8
4.6
1.4
5.3
9.3
8.3
5.4
7.6
3.4
1M
SE47
.20
86.3
098
.41
122.
5416
6.93
196.
5670
.72
26.5
238
.07
IMSE
(of c
ompo
nent
s)17
.21
31.3
645
.47
57.5
173
.17
65.2
411
.66
17.8
7
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
sR
MS
5.26
8.22
10.0
011
.79
13.9
815
.30
8.30
UM
1.33
5.27
7.40
10.7
015
.81
22.9
4U
S.2
2.1
4.2
0.6
94.
106.
32Z
UC
26.1
262
.16
92.4
012
7.61
174.
5320
4.83
RM
S (%
Err
or)
1.14
1.80
2.19
2.58
3.06
3.35
RM
S/R
MS
(Nai
ve 1
).6
5.5
4.4
6.4
2.4
1.3
8.4
6M
SE27
.67
67.5
710
0.00
139.
0019
5.44
234.
0768
.89
(of c
ompo
nent
s)12
.75
25.3
636
.04
48.9
864
.21
75.8
40
IR
MS
8.13
15.2
421
.87
28.1
734
.07
39.8
317
.78
Nai
ve II
RM
S5.
9012
.05
18.9
526
.57
33.1
139
.40
15.4
1
0 rTl
U) S
TAB
LE 3
.2
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
rn > 0
Sam
ple
Perio
d Si
mul
atio
ns fo
r Con
sum
ptio
n, W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on"C . rn 0 z 0 rn r) 0 C — C) r
A.
No
Con
stan
t Adj
ustm
ents
RM
S3.
944.
334.
144.
224.
614.
983.
452.
883.
09U
M.2
8.2
4.5
51.
254.
596.
05.0
1.0
1U
S0.
00.0
40.
000.
00.1
3.1
7.1
1.3
3U
C15
.24
18.4
716
.59
16.5
616
.53
18.5
88.
179.
21R
MS
(% E
rror
)1.
321.
441.
371.
391.
521.
66.9
51.
02R
MS/
RM
S (N
aive
I).8
7.5
0.3
3.2
6.2
3.2
0.3
3.6
4.3
6M
SE15
.52
18.7
517
.14
17.8
121
.25
24.8
011
.90
8.29
9.55
(of c
ompo
nent
s)8.
239.
669.
3510
.05
11.4
513
.06
5.15
5.99
B.
GG
Con
stan
t Adj
ustm
ents
RM
S3.
804.
454.
414.
42-
4.67
4.84
3.65
UM
.47
.30
.30
.63
2.65
3.45
US
.03
.09
.10
.03
.05
.04
UC
13.9
419
.41
19.0
518
.88
19.1
119
.95
RM
S (%
Err
or)
1.25
1.46
1.45
1.44
1.53
1.59
RM
S/R
MS
(Nai
ve 1
).8
4.5
2.3
5.2
7.2
3.2
0.3
5M
SE14
.44
19.8
019
.45
19.5
421
.81
23.4
313
.32
£MSE
(of c
ompo
nent
s)7.
209.
7310
.06
10.7
611
.90
12.7
2
C. A
R C
onst
ant A
djus
tmen
tsR
MS
4.17
4.97
5.38
5.81
6.66
6.95
4.58
2.96
3.34
UM
1.27
1.51
1.39
1.65
43.
093.
14.8
0.9
3U
S.6
1.3
7.3
7.7
422.
612.
75.1
00.
00U
C15
.51
22.8
227
.18
31.3
6037
.86
42.4
17.
8610
.22
RM
S (%
Err
or)
1.42
1.68
1.82
1.98
2.29
2.38
1.01
1.12
RM
S/R
MS
(Nai
ve I)
.92
.58
.43
.35
.33
.29
.44
.65
.39
MSE
17.3
924
.70
28.9
433
.756
43.5
648
.30
20.9
78.
7611
.15
(of c
ompo
nent
s)8.
2215
.59
27.9
534
.02
41.3
425
.61
5.15
7.64
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
sR
MS
3.50
4.47
5.36
6.21
7.33
7.85
4.57
UM
1.21
1.86
2.47
3.20
5.75
7.33
US
.48
.20
.29
.58
2.31
2.53
UC
10.5
617
.92
25.9
734
.78
45.6
751
.71
RM
S (%
Err
or)
1.19
1.50
1.79
2.07
2.46
2.64
RM
S/R
MS
(Nai
ve I)
.77
.52
.43
.38
.36
.33
.44
MSE
12.2
519
.98
28.7
338
.56
53.7
361
.62
20.8
8(o
f com
pone
nts)
6.96
12.3
918
.90
25.4
732
.27
36.2
80
Nai
veI R
MS
4.54
8.64
12.6
316
.54
20.2
924
.06
10.3
0N
aive
II R
MS
3.00
5.17
.8.
0410
.43
13.0
615
.61
5.63
0 r Cl) . -4
TAB
LE 3
.3Sa
mpl
e Pe
riod
Sim
ulat
ions
for I
nves
tmen
t, W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on\0 rn C
.) 0 0 rn — — 0
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
S
4.48
4.92
1.35
.41
1.06
.73
5.37 .0
3.2
311
.83
20.0
217
.66
23.0
728
.58
5.56
7.20
6.97
.92
.75
.54
13.8
423
.04
20.0
714
.51
24.2
116
.73
28.8
419
.60
B. G
G C
onst
ant A
djus
tmen
ts
7.63
3.11
8.12
.50
3.56
8.79
.49
.50
1.85
2.46
.62
1.20
7.20
9.01
4.66
5.35
RM
S3.
724.
805.
903.
54U
M1.
401.
91.3
1U
S.6
11.
11.0
7U
C34
.43
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
.53
MSE
34.8
112
.53
(of c
ompo
nent
s)11
.06
13.9
621
.46
RM
S2.
974.
464.
755.
135.
515.
923.
57U
M.0
7.1
8.7
3.4
3.0
2.0
6U
S.2
91.
142.
041.
65.7
4.4
0U
C8.
4618
.57
19.7
924
.23
29.6
034
.59
RM
S (%
Err
or)
4.36
6.60
7.41
7.95
8.32
8.81
RM
S/R
MS
(Nai
ve I)
.73
.70
.57
.52
.51
.51
.54
MSE
8.82
19.8
922
.56
26.3
130
.36
35.0
512
.74
IMSE
(of c
ompo
nent
s)7.
6012
.37
13.9
216
.50
19.3
821
.99
C r'i C ri C.) I
.77
.56
9.67
12.6
712
.54
9.50
C. A
R C
onst
ant A
djus
tmen
tsR
MS
3.17
4.79
4.93
5.67
6.88
7.76
4.00
2.65
3.39
UM
.43
1.74
1.02
1.29
1.89
2.29
.32
1.02
US
.01
0.00
.29
.32
.05
0.00
.01
.03
UC
9.61
21.2
022
.99
30.5
445
.39
57.9
36.
6910
.44
RM
S (%
Err
or)
4.67
7.13
7.43
8.41
9.96
11.1
93.
835.
01R
MS/
RM
S (N
aive
1)
.78
.75
.60
.58
.63
.66
.60
.65
.53
MSE
10.0
524
.30
32.1
547
.33
60.2
216
.00
7.02
11.4
9(o
f com
pone
nts)
7.99
14.3
215
.27
20.5
528
.10
35.2
76.
068.
82
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
sR
MS
2.44
4.07
4.68
5.53
6.66
7.45
3.66
UM
0.00
.81
1.14
1.86
2.57
3.99
US
.21
.31
.61
.55
.18
0.00
UC
5.74
15.4
420
.15
28.1
741
.60
51.5
1R
MS
(% E
rror
)3.
596.
127.
098.
199.
6910
.80
RM
S/R
MS
(Nai
ve I)
.60
.64
.57
.56
.61
.64
.55
MSE
5.95
16.5
621
.90
30.5
840
.35
55.5
013
.39
(of c
ompo
nent
s)4.
7811
.17
14.1
519
.40
26.6
833
.22
-0 11
Nai
veI R
MS
4.05
6.36
8.27
9.88
10.3
611
.72
6.57
Nai
ve II
RM
S5.
089.
3414
.00
19.2
123
.49
28.2
710
.31
0 .
TAB
LE 3
.4S
Sam
ple
Perio
d Si
mul
atio
ns fo
r GN
P in
Con
stan
t Dol
lars
,W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on
.A
ntic
ipat
ion
Ver
sion
:Q
uarte
rsA
head
One
Yea
rQ
uarte
rs A
head
12
34
56
Ahe
ad1
2
A. N
o C
onst
ant A
djus
tmen
tsR
MS
UM
Us
UC
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve 1
)M
SE
6.53
0.00 .2
542
.39
1.41 .9
842
.64
1.32
RM
S/R
MS
(Nai
ve I)
.92
7.54
7.55
0.00
.34
.62
2.74
56.2
353
.92
1.64
1.66
.62
.44
56.8
557
.00
8.96
10.6
32.
259.
275.
8611
.75
2.00
2.37
.42
.42
B. G
G C
onst
ant A
djus
tmen
ts
12.0
66.
1712
.22
16.2
9
2.69 .4
2.4
480
.28
113.
0014
5.44
7.79
7.89
8.84
10.2
211
.40
6.54
.36
.11
.78
4.41
6.31
.18
.44
1.89
6.23
9.09
60.1
461
.70
75.4
893
.81
114
.56
1.69
1.73
1.95
2.26
2.52
.64
.46
.41
.41
.40
.47
MSE
37.5
860
.68
62.2
578
.15
104.
4512
9.96
42.7
7
38.0
6
4.90
5.20
.24
.16
.02
.30
23.7
426
.58
1.05
1.19
.73
.43
24.0
027
.04
72.1
791
.98
116.
93
rn 0 z 0 — C.) 0 rn r 0 r r rn
RM
SU
M Us
UC
RM
S (%
Err
or)
6.13 .6
9.5
636
.33
C. A
R C
onst
ant A
djus
tmen
tsR
MS
7.06
9.18
9.74
11.2
713
.41
14.8
58.
465.
516.
49U
M4.
446.
744.
464.
836.
655.
293.
314.
55U
S2.
642.
532.
093.
569.
3511
.47
1.00
.76
UC
42.7
675
.00
88.3
211
8.62
163.
8320
3.76
20.0
536
.81
RM
S (%
Err
or)
1.54
2.03
2.16
2.51
2.97
3.26
1.21
1.44
RM
S/R
MS
(Nai
ve 1
)1.
06.7
5.5
7.5
3.5
3.5
2.6
1.8
3.5
3M
SE49
.84
84.2
794
.87
127.
0117
9.83
220.
5271
.57
30.3
642
.12
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
s0
RM
S5.
348.
3810
.01
11.8
313
.99
15.3
88.
48U
M2.
396.
538.
0210
.50
14.4
816
.79
US
1.00
1.19
1.50
2.80
7.83
10.8
8U
C25
.12
62.5
090
.68
126.
6517
3.41
208.
87R
MS
(% E
rror
)1.
211.
852.
222.
623.
083.
37R
MSI
RM
S (N
aive
1)
.83
.68
.59
.55
.56
.54
.61
MSE
28.5
170
.22
100.
2013
9.95
195.
7223
6.54
71.9
1H
Nai
veI R
MS
6.68
12.2
517
.11
21.4
125
.12
25.5
813
.79
Nai
ve II
RM
S5.
4511
.78
19.0
526
.97
34.1
040
.24
16.5
0
0 r . \0
TAB
LE 3
.5
Sam
ple
Perio
dS
imul
atio
nfo
r the
Une
mpl
oym
ent R
ate,
Wha
rton-
EFU
Mod
el S
tand
ard
Ver
sion
00
Ant
icip
atio
nV
ersi
on:
.Q
uarte
rs1
23
Ahe
ad 45
One
Yea
r6
Ahe
adQ
uarte
rs A
head
12
C) 0 z
A. N
o C
onst
ant A
djus
tmen
ts
MSE
1.18
1.74
1.77
2.10
2.62
3.06
1.19
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
01.
20C
)
C)
C) > rn0 rn C) 0 r 1/)
RM
S1.
391.
451.
401.
571.
781.
941.
211.
25U
M.4
3.4
9.6
2.8
51.
281.
49.3
8U
S.3
2.2
3.0
7.0
5.0
6.1
0.2
8U
C1.
181.
381.
271.
561.
832.
17.9
0R
MS
(% E
rror
)29
.84
29.6
729
.09
32.1
835
.54
38.4
926
.92
RM
S/R
MS
(Nai
veI)
2.77
1.60
1.15
1.11
1.18
1.27
1.27
2.48
MSE
1.93
2.10
1.96
2.46
3.17
3.76
1.46
1.56
B.
GG
Con
stan
t Adj
ustm
ents
RM
S1.
091.
321.
331.
451.
621.
751.
09U
M.0
8.1
4.1
7.3
1.6
0.8
0U
S.0
6.1
1.0
8.0
8.1
1.1
4U
C1.
0423
.81
2.18
1.49
26.3
81.
46
1.52
1.71
1.91
26.4
438
.39
31.4
01.
101.
021.
07
2.12
34.1
61.
151.
14
.43
.12
.89
24.0
91.
321.
44
C. A
R C
onst
ant A
djus
tmen
tsR
MS
1.16
1.54
1.61
1.71
1.83
1.86
1.34
1.01
1.22
UM
.08
.13
.08
.07
.08
.07
.06
.09
US
.02
.12
.18
.28
.37
.34
0.00
.01
UC
1.24
2.12
2.33
2.57
2.90
3.05
.96
1.39
RM
S (%
Err
or)
25.7
231
.04
30.4
931
.14
33.6
034
.72
23.5
126
.45
RM
S/R
MS
(Nai
ve I)
2.29
1.69
1.32
1.21
1.21
1.22
1.41
2.01
1.35
MSE
1.34
2.37
2.59
2.92
3.35
3.46
1.79
1.02
1.49
D. A
R C
onst
ant A
djus
tmen
ts a
rid R
OS
Coe
ffic
ient
sR
MS
.98
1.43
1.69
1.85
1.99
2.01
1.37
UM
.05
.13
.14
.16
.21
.24
Us
0.00
.04
.23
.46
.63
.57
UC
.91
1.87
2.49
2.80
3.12
3.23
RM
S (%
Err
or)
21.8
729
.70
32.8
434
.63
37.5
638
.13
RM
S/R
MS
(Nai
ve!)
1.94
1.58
1.39
1.31
1.32
1.32
1.44
MSE
.96
2.04
2.86
3.42
3.96
4.04
1.87
— mN
aive
I R
MS
.50
.91
1.22
1.41
1.51
1.52
.95
Nai
ve II
RM
S.4
51.
071.
802.
543.
213.
801.
62C C C
', S '.0 -.4 '.0
TAB
LE 3
.6
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
A. N
o C
onst
ant A
djus
tmen
ts
RM
S (%
Err
or)
1.47
RM
S/R
MS
(Nai
ve I)
.73
11.7
716
.17B
. GG
Con
stan
t Adj
ustm
ents
15.7
595
.68
178.
6912
6.06
7.81
14.7
971
.79
.50
11.7
315
.34
.58
10.3
9.2
52.
1435
.01
70.5
211
4.19
146.
4512
1.67
105.
551.
971.
861.
471.
28.3
3.2
4.1
6.1
213
8.53
261.
4724
8.06
218.
7413
7.59
107.
95£M
SE (o
f com
pone
nt)
92.4
315
4.20
161.
5216
6.23
153.
6414
7.75
0 rn
Ex P
ost F
orec
asts
for G
NP
in C
urre
nt D
olla
rs, W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on00 0 S rn C) 0 z 0 — C)
34.1
333
.71
8.29
2.77
.28
3.09
1.37
2.16
.78
1.88
.37
1.52
.24
1.33
.16
.12
RM
S22
.00
24.6
311
.29
14.8
712
.09
10.6
314
.76
23.8
227
.32
UM
404.
9248
1.46
162.
2263
.99
9.76
.45
524.
0968
5.47
US
.08
.01
22.2
726
.30
UC
44.6
791
.66
128.
3415
6.76
136.
2311
2.54
21.0
134
.90
RM
S (%
Err
or)
3.05
3.48
RM
S/R
MS
(Nai
ve 1
).3
81.
48.8
6M
SE48
3.73
606.
8429
8.86
221.
0414
6.08
113.
0021
7.85
567.
3374
6.67
(of c
ompo
nent
)24
1.12
265.
1518
8.86
173.
9416
4.06
151.
9126
4.84
293.
89
RM
S10
.62
UM
:
US
7.84
12.2
6U
C
.27
112.
78M
SE
0 C)
C)
— C) r > 6
2.02 .51
C. A
R C
onst
ant A
djus
tmen
tsR
MS
8.13
11.9
215
.35
17.3
217
.40
20.7
510
.63
6.85
8.08
UM
22.8
738
.08
43.5
942
.60
16.3
53.
4422
.76
35.8
4U
S1.
197.
1117
.67
31.8
078
.41
141.
22.4
74.
70U
C42
.04
96.9
017
4.36
225.
5820
8.00
285.
9023
.69
24.7
5R
MS
(% E
rror
)1.
041.
491.
912.
152.
132.
48.8
91.
00R
MS/
RM
S (N
aive
I).5
1.3
8.3
3.2
8.2
3.2
3.2
7.4
3.2
6M
SE66
.10
142.
0923
5.62
299.
9830
2.76
430.
5611
2.99
46.9
265
.29
(of c
ompo
nent
)51
.55
73.4
710
8.74
136.
5315
2.54
188.
7545
.83
54.9
3..T
1
D.
AR
Con
stan
t Adj
ustm
ents
and
RO
S C
oeff
icie
nts
rnR
MS
6.80
11.5
614
.84
17.4
818
.27
20.8
310
.72
UM
26.5
958
.00
67.8
364
.16
33.0
411
.28
US
.97
5.08
8.37
12.5
331
.38
81.1
4U
C18
.68
70.5
514
4.02
228.
8626
9.37
341.
47R
MS
(% E
rror
).8
81.
461.
872.
202.
262.
49R
MS/
RM
S (N
aive
I).4
2.3
7.3
2.2
8.2
4.2
4.2
7M
SE46
.24
133.
6322
0.22
305.
5533
3.79
433.
8911
4.91
(of c
ompo
nent
)45
.78
74.0
210
6.52
136.
4013
2.53
187.
19
Nai
ve I
RM
S16
.06
31.6
547
.11
61.8
475
.68
88.5
338
.32
Nai
ve H
RM
S5.
5111
.16
16.1
824
.14
32.7
839
.89
15.2
1
0 rn U, S Co -I
TAB
LE 3
.7
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
RM
S
Us
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
MSE
(of c
ompo
nent
)
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
.84
A. N
o C
onst
ant A
djus
tmen
ts
B. G
G C
onst
ant A
djus
tmen
ts
65.2
911
0.46
122.
5411
8.81
1.69
77.9
810
6.29
(of c
ompo
nent
)25
.23
58.4
465
.29
65.8
558
.63
54.4
6
3.37
3.51
276.
2330
2.75
108.
2511
4.97
Ex P
ost F
orec
asts
for C
onsu
mpt
ion,
Wha
rton-
EFU
Mod
el S
tand
ard
Ver
sion
00 I'.)
UM
UC
14.5
514
.60
12.4
511
.38
10.4
78.
8310
.31
16.6
217
.40
160.
9115
7.18
97.7
375
.48
61.5
539
.66
52.4
168
.55
28.8
024
.74
16.3
96.
5511
.65
12.1
921
.22
21.7
921
.93
31.2
740
.91
47.4
536
.41
26.1
311
.29
14.5
02.
892.
892.
452.
252.
031.
52.7
9.4
6.3
2.2
421
1.64
213.
1915
5.03
129.
4970
.32
109.
6265
.14
rn 0 z 0 C) 0 rTl
C,) 0 p.
11 C)
C) r — >
RM
SU
M Us
UC
.18
.46
1.74
.94
MSE
95.3
993
.39
76.6
954
.44
8.08
10.5
111
.07
10.9
08.
498.
847.
5537
.14
70.2
572
.05
66.9
538
.75
39.2
48.
1513
.41
14.0
18.
334.
7216
.25
20.0
026
.80
36.4
843
.53
23.6
122
.66
1.59
2.07 .5
72.
18 .41
2.14 .3
01.
83 .22
72.0
8
1.68 .18
78.1
5.3
357
.00
6
C. A
R C
onst
ant A
djus
tmen
tsR
MS
5.61
7.48
9.81
11.3
511
.47
14.0
06.
904.
856.
09U
M8.
1520
.42
30.7
041
.61
30.9
229
.99
8.80
20.6
2U
S2.
089.
2917
.90
29.1
156
.96
91.5
31.
587.
79U
C21
.24
26.2
447
.64
58.1
043
.68
74.4
813
.14
8.68
RM
S (%
Err
or)
1.14
1.47
1.93
2.22
2.20
2.65
.99
1.19
RM
S/R
MS
(Nai
ve 1
).5
9.4
1.3
6.3
2.2
7.2
8.3
0.5
1.3
3M
SE31
.47
55.9
596
.24
128.
8213
1.56
196.
0047
.61
23.5
237
.09
ZMSE
(of c
ompo
nent
)17
.83
27.7
746
.81
62.9
974
.87
97.4
814
.65
20.4
5
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
sR
MS
5.59
7.69
9.54
11.0
011
.32
13.7
46.
84U
M7.
6615
.75
20:3
824
.91
28.9
831
.45
US
1.31
4.32
6.17
8.41
23.7
355
.46
UC
12.4
814
.40
22.4
429
.43
46.1
982
.17
RM
S(%
Err
or)
1.14
1.53
1.89
2.17
2.19
2.61
RM
S/R
MS
(Nai
ve I)
.59
.42
.35
.31
.26
.27
.30
MSE
21.4
534
.31
57.2
279
.05
98.8
716
9.08
46.7
8(o
f com
pone
nt)
18.7
831
.89
49.0
062
.75
70.7
396
.11
0N
aive
I RM
S9.
5718
.68
27.0
135
.81
48.1
950
.31
22.3
0N
aive
II R
MS
5.64
8.50
13.0
316
.04
19.9
821
.83
8.28
0 0 . 00
TAB
LE 3
.8
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
A. N
o C
onst
ant A
djus
tmen
tsR
MS
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
MSE
(of c
ompo
nent
)
UC
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
MSE
13.9
617
.10
172.
6924
6.56
10.9
912
.26
11.3
333
.49
11.8
214
.38
2.28
2.16
122.
0114
4.74
11.8
510
.34
91.3
947
.16
3.99
.16
9.92
8.66
1.20
.92
83.3
969
.26
8.72
7.96
13.6
63.
78.1
6.7
258
.84
7.32
6.65
.67
.59
76.0
963
.35
57.8
952
.42
B. G
O C
onst
ant A
djus
tmen
ts
11.4
025
.80
40.9
7
69.0
613
2.94
122.
3211
1.30
83.5
465
.77
10.5
913
.76
8.55
8.42
17.6
31.
382.
24
66.7
4
17.1
8
14.6
112
.75
14.4
62.
17
Ex P
ost F
orec
asts
for i
nves
tmen
t, W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on00
UM Us
UC
44.9
659
.69
62.2
6
195.
0129
2.31
140.
3410
7.01
172.
2826
7.79
RM
SU
M Us
rn C) 0 z 0 M — 0 rn 0 C)
C)
— C) 0
8.31
11.5
355
.51
102.
562.
15
11.0
677
.89
3.46
4.58
7.08
1.36
10.5
553
.97
1.12
56.2
18.
82 .93
9.77
1.46
9.14
23.5
81.
3558
.60
7.64 .71
9.30
1.12
8.11
7.66
2.17
55.9
46.
75 .60
112.
1418
9.26
295.
1513
2.19
150.
43
8.17
1.07
(of c
ompo
nent
)55
.78
77.8
972
.44
69.8
958
.65
51.7
4
C. A
R C
onst
ant A
djus
tmen
tsR
MS
4.80
6.83
8.31
9.59
10.1
011
.26
5.38
4.60
4.92
UM
8.53
9.19
8.56
6.62
1.63
.26
7.85
7.97
Us
.11
.33
.07
0.00
.61
0.00
0.00
.53
UC
14.4
037
.13
60.4
385
.35
99.7
712
6.53
13.3
115
.71
RM
S (%
Err
or)
4.19
5.86
7.03
8.05
8.54
9.40
3.97
4.18
RM
S/R
MS
(Nai
ve I)
.78
.86
.84
.85
.78
.83
.70
.75
.62
MSE
23.0
446
.65
69.0
691
.97
102.
0112
6.79
28.9
421
.16
24.2
1£M
SE (o
f com
pone
nt)
29.0
440
.80
54.6
662
.88
66.0
278
.33
26.5
029
.58
D.
AR
Con
stan
t Adj
ustm
ents
and
RO
S C
oeff
icie
nts
RM
S3.
976.
478.
129.
8010
.68
11.3
65.
47U
M6.
8612
.10
12.4
09.
133.
310.
00U
S0.
000.
00.0
6.1
9.2
3.5
2U
C8.
9029
.76
53.4
786
.72
110.
5212
8.53
RM
S (%
Err
or)
3.52
5.60
6.91
8.29
9.12
9.56
RM
S/R
MS
(Nai
ve 1
).6
5.8
2.8
2.8
7.8
3.8
4.7
1M
SE15
.16
41.8
665
.93
96.0
411
4.06
129.
0529
.92
(of c
ompo
nent
)22
.61
36.8
649
.78
62.8
150
.00
77.9
1
Nai
ve I
RM
S6.
137.
919.
9011
.28
12.9
513
.53
7.63
Nai
ve II
RM
S8.
7314
.25
20.2
125
.09
32.2
437
.98
10.3
4
0 ru r . 00
TAB
LE 3
.9
\0 00 0\ S
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
0 r C',
B. G
G C
onst
ant A
djus
tmen
ts
66.3
010
3.77
129.
1310
8.91
MSE
83.3
612
3.31
122.
5416
9.78
215.
8030
5.20
55.9
5
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
1.01
Ex P
ost F
orec
asts
for G
NP
in C
onst
ant D
olla
rs, W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on
A. N
o C
onst
ant A
djus
tmen
ts
r71
C) 0 z 0 — C)
8.55
41.3
32.
561.
90
80.2
010
6.38
129.
1911
4.55
2.33 .8
9
60.9
2
1.67 .4
32.
11 .42
2.45 .41
RM
S17
.18
15.5
811
.10
14.0
616
.52
19.4
88.
8519
.04
17.4
9U
M24
5.34
162.
414.
4313
.67
97.5
422
1.01
337.
4427
2.05
US
.22
12.2
954
.87
62.7
95.
43U
C95
.73
19.6
433
.53
RM
S (%
Err
or)
2.87
2.86
2.63
RM
S/R
MS
(Nai
veI)
.43
.41
2.10
1.00
MSE
295.
2324
2.82
123.
1019
7.72
273.
0137
9.53
78.3
236
2.52
305.
93
RM
S60
.17
46.7
2
17.4
77.
48U
M16
1.60
US
46.8
5U
C96
.72
1.67 .6
41.
67 .43
1.96 .3
92.
19 .37
2.58 .3
8.3
5
11.1
056
.33
6.66
9.13
51.7
83.
6731
.21
1.36
11.0
79.
09 9.68
0 C)
C)
— C) 0
14.6
913
.03
2.61
38.0
3
C. A
R C
onst
ant A
djus
tmen
tsR
MS
6.83
9.83
12.6
514
.18
13.9
817
.08
8.75
5.57
6.22
UM
11.6
613
.43
7.04
1.00
7.04
36.7
611
.79
12.4
2U
S.3
7.5
81.
603.
020.
000.
00.4
3.2
3U
C34
.62
82.6
215
1.38
197.
0518
8.40
18.8
026
.04
RM
S (%
Err
or)
1.03
1.47
1.89
2.12
2.09
2.51
.85
.93
RM
S/R
MS
(Nai
ve I)
.75
.56
.49
.43
.35
.38
.41
.61
.36
MSE
46.6
596
.63
160.
0220
1.07
195.
4429
1.73
76.5
631
.02
38.6
9
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
s0
RM
S5.
559.
4012
.18
14.6
315
.34
17.6
08.
91U
M13
.89
24.1
216
.32
5.14
1.41
23.8
5U
S.2
2.7
94.
4511
.34
9.41
4.34
UC
16.6
963
.45
127.
5819
7.56
224.
4928
1.57
RM
S (%
Err
or)
.84
.41
1.83
2.20
2.30
2.60
RM
S/R
MS
(Nai
ve I)
.61
.54
.47
.44
.38
.39
.41
MSE
30.8
088
.36
148.
3521
4.04
235.
3130
9.76
79.3
8-1
Nai
veI R
MS
9.06
12.4
425
.72
33.3
639
.91
45.6
121
.27
Nai
ve II
RM
S4.
949.
6213
.64
20.2
127
.32
33.4
612
.64
C 0 rn r . 00
TAB
LE 3
.10
00 00 U
Ant
icip
atio
nV
ersi
on:
Qua
rters
Ahe
adO
neY
ear
Qua
rters
Ahe
ad1
23
45
6A
head
12
B. G
G C
onst
ant A
djus
tmen
ts
Ex P
ost F
orec
asts
for t
he U
nem
ploy
men
t Rat
e, W
harto
n-EF
U M
odel
Sta
ndar
d V
ersi
on
A. N
o C
onst
ant A
djus
tmen
ts
t!1 C) 0 z 0 z — 0 rTl 0 C)
C) — C)
rTl 0
RM
S1.
171.
28.9
01.
081.
291.
41.7
51.
151.
31U
M.4
0.6
8.0
2.6
01.
501.
89.5
41.
14U
S.4
3.5
3.5
0.4
0.0
6.0
4.3
0.2
6U
C.5
3.4
3'.2
8.1
7.1
0.0
6.4
7.3
2R
MS
(% 'E
rror
)30
.38
33.3
223
.70
29.0
534
.47
37.6
729
.87
34.0
2R
MS/
RM
S (N
aive
I)6.
364.
132.
182.
052.
132.
242.
146.
264.
23M
SE1.
361.
64.8
11.
171.
661.
99.5
61.
321.
72
RM
S.8
9.8
8.9
81.
181.
421.
54.8
8U
M.1
2.0
2.2
5.7
51.
742.
14U
S.5
0.6
2.6
1.5
5.2
0.1
7U
C.1
7.1
3.1
0.0
9'.0
7.0
6R
MS
(% E
rror
)22
.89
22.1
025
.67
31.8
438
.45
41.5
1R
MS/
RM
S (N
aive
I)4.
852.
832.
372.
242.
352.
452.
15M
SE.7
9.7
7.9
61.
392.
022.
37.7
7
C. A
R C
onst
ant A
djus
tmen
tsR
MS
1.04
1.13
1.15
1.01
.85
.85
1.02
.94
.88
UM
.24
.10
.07
.07
.29
.38
.25
.11
US
.63
.96
1.00
.70
.22
.12
.48
.54
UC
.21
.22
.25
.25
.21
.22
.15
.12
RM
S (%
Err
or)
26.9
429
.07
29.8
026
.67
22.3
422
.39
24.1
622
.25
RM
S/R
MS
(Nai
ve I)
5.69
3.64
2.78
1.92
1.40
1.34
2.91
5.14
2.83
MSE
1.08
1.28
1.32
1.02
.72
.72
1.04
.88
.77
D. A
R C
onst
ant A
djus
tmen
ts a
nd R
OS
Coe
ffic
ient
sR
MS
.94
.99
1.06
.99
.87
.81
.95
UM
.20
.03
.01
.02
.16
.24
US
.52
.77
.91
.70
.34
.18
UC
.16
.18
.20
.26
.26
.24
RM
S (%
Err
or)
24.3
925
.15
27.1
525
.70
23.0
421
.41
RM
S/R
MS
(Nai
ve I)
5.14
3.18
2.57
1.87
1.44
1.28
2.71
MSE
.88
.98
1.12
.98
.76
.66
.90
Nai
ve I
RM
S.1
8.3
1.4
1.5
3.6
1.6
3.3
5N
aive
II R
MS
.19
.38
.51
.63
.84
1.01
.354
C 0 rn r 00
990 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
ments do not seem to affect the results very much. The simulationswith AR adjustments are almost uniformly worse than the no-constant-adjustment results, the only exception being investment one quarterahead. The results using the GG adjustments are slightly better, but thedifference, in most cases, is quite small. It can also be noted that whilethe performance of the AR continues to deteriorate relative to the no-constant-adjustments simulations as the forecast span increases, theGG adjustments tend to perform about the same relative to no-con-stant-adjustments for all quarters. One would expect that by six quar-ters, these latter types of adjustments would disappear for the mostpart, and the results should be similar to no-adjustments in any case.
The anticipations version does indicate a substantial improvementfor the two quarters for which the figures are available. The ROScoefficients are significantly better for the first quarter but rapidly losethis advantage, becoming the worst of the four methods by the time sixquarters have passed. The comparison with the naive models showsthat all of the simulations perform much better than either of the naivemodels. It is interesting to .note that for four of the five variables chosenfor these tables, Naive Model I (no change) has a smaller RMS errorthan Naive Model II (same change); this finding is reversed only for therelatively stable consumption series.
The decomposition of error shows the same pattern in virtually allcases. Almost the entire error is due to imperfect covariation; there isvery little systematic error due to bias in the mean values or cyclicalbehavior. Theil states that "if the forecaster's ability does not allowhim to attain perfection, the desirable distribution of inequality over thethree sources is UM = Us = 0, Uc = l."18 The Wharton pattern verynearly fits this description. However, the errors themselves are largeenough so that little comfort can be drawn from these results.
The forecast period (1965.1—1968.4) results are quite different.The forecasts with no constant adjustments are clearly the worst. Forall variables, the error increases from the first to the second quarterand then declines for the rest of the six-quarter period. The RMSerrors for GNP for the first two quarters are $22.0 and $24.6 billion,which compares unfavorably with the RMS of actual changes of $16.1and $31.6 billion, and even more unfavorably with RMS errors of
Theil, op. cit., p. 37. In Theil's notation, UM, US and UC correspond toUS/MSE and UC/MSE respectively, where MSE = UM + US + UC.
FORECASTING PROPERTIES OF U.S. MODELS • 991
Naive Model II, $5.5 and $11.2 billion, respectively. It is clear that theWhartoñ-EFU Model cannot be used to make short-term forecasts out-side the sample period without some kind of adjustments. It should benoted, however, that after six periods, the RMS error is only $10.6billion, and there are similar declines for the other numbers reported inthese tables. By this time, Naive Models I and II have RMS errors of$88.6 and $39.9 billion respectively, so that the no-constant-adjust-ment forecasts appear in a much more favorable light.
The constant adjustments do make quite a difference in the forecastperiod. The AR adjustments lead to forecasts which are relativelymuch better for the first two quarters. Their relative advantage beginsto decline thereafter, so that by the sixth quarter these forecasts aremuch worse than no-constant-adjustments for GNP in current prices,consumption, and investment. For GNP in constant prices and unem-ployment, the AR adjustments continue to have smaller errors for thefull six-quarter period.
Since the AR adjustments give relatively good performance in thefirst two quarters, and the no-constant-adjustment forecasts do betterfor the remaining periods, it should be expected that the GG adjust-ments would perform best for all six quarters. With a few exceptions,this is exactly what does happen. For GNP in current dollars, the GGadjustments are substantially better than no-constant-adjustments butslightly worse than AR adjustments for the first.three quarters; for theremaining three quarters, they are the best. The consumption pattern isidentical to GNP. A similar pattern is observed for investment, withthe changeover coming at the fourth quarter; the no-constant-adjust-ment forecasts are slightly better than the GG adjustments thereafter.For constant dollar GNF, the changeover comes in the third period.The pattern is reversed for unemployment, where the GO adjustmentsare best for three quarters, and the AR adjustments are better there-after.
A few other brief items might be mentioned. When none of theconstant terms are adjusted, the anticipations version performs evenmore poorly than the standard version. With the AR adjustments, theanticipations are slightly better for all variables listed. The ROS co-efficients have the best one-quarter forecasting record for all variablesexcept unemployment (for which GO adjustments are slightly better)but deteriorate rapidly, and perform no better than the AR coefficients
992 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
by the end of six quarters. This time the decomposition of error showsa more interesting pattern. The large errors in the first two quarters aredue primarily to large components in UM, but by six quarters almostthe entire error is due to imperfect covariation. Thus, the early quarterforecasts are bad not only because of their large magnitude, but be-cause they are badly biased in addition.
In spite of the fact that the errors tend to diminish over time for theno-constant-adjustment version, and in spite of the fact that the size ofthe error is considerably diminished by introducing various constantadjustments, the level of error is still too high to be satisfactory whenthese mechanical methods are used. In particular, it is hard to accept aRMS error in predicting unemployment one quarter ahead of 0.89%(using the method of constant adjustment which gives, the smallesterror) when compared to RMS errors of 0.18% and 0.19% for NaiveModels I and II, respectively.
In addition to these tables, we present several diagrams for keyvariables. These diagrams might be called complete forecasting ac-curacy diagrams, because they show all the simulation results from oneto six quarters superimposed on the actual path of the variable. Morethan any summary statistic, these diagrams reveal how well the modelis performing. All graphs include the period from 1953.1 to 1968.4 andare based on both sample-period simulations, and cx post forecastsusing the Wharton-EFU Model.
We have not calculated sample-period statistics for the EvansModel, relying instead on the figures gathered for the Wharton-EFUModel. We have, however, evaluated mechanical ex post forecasts forthe published version of the Evans Model.19 These simulated forecastswere made for the period 1963.1 through 1965.2. The later forecastscannot be made for the full six quarters because of the data revisionthat occurred in the third quarter of 1965. In Table 3.11, we presentthe predicted values minus the actual ones for GNP in constant dol-lars for each of the simulated forecasts that were made.
These results can be compared with Table 3.12, where the errorsfor sample-period forecasts of the Wharton-EFU Model are given. Theaverage absolute errors are not directly comparable, because the Evans
19 Michael K. Evans, "Multiplier Analysis of a Postwar Quarterly U.S. Model and aComparison with Several Other Models," Review of Economic Studies, Vol. 33, No. 4,pp. 337—60.
FORECASTING PROPERTIES OF U.S. MODELS • 993
TABLE 3.11
Published Evans Model: Accuracy of Mechanical Ex Post GNP Forecasts,1963.1—1965.2
Residuals (Predicted — Actual)
QuarterStarting Point 1 2 3 4 5 6
1963.1 0.9 3.4 3.2 3.4 2.0 7.21963.2 4.7 3.8 3.0 1.7 6.7 11.21963.3 0.7 0.2 0.8 5.7 10.0 11.21963,4 2.6 3.1 9.4 12.1 12.2 0.41964.1 —0.5 5.8 9.8 9.8 —2.5 1.61964.2 10.8 13.5 14.0 —0.5 3.81964.3 6.4 9.0 —1.4 3.41964.4 9.9 1.0 8.01965.1 —2.9 8.11965.2 9.0
Root mean-squareerror . 6:2 6.7 7.6 6.6 7.3 7.8
TABLE 3.12
Wharton-EFU Model Predicted Minus Actual in MechanicalEx Post GNP Forecasts with No Constant Adjustment
Starting Point 1 2Quarters Ahead
3 4 5 6
1963.1 4.8 2.8 1.3 —0.1 —3.3 3.71963.2 6.0 2.9 0.4 2.9 3.0 —1.61963.3 3.0 0.6 —2.8 2.1 —2.0 2.71963.4 0.4 —3.2 2.8 —0.8 3.3 —9.21964.1 —6.3 —1.1 —3.1 0.3 —11.5 —9.81964.2 0.4 —4.4 1.2 —10.0 —8.51964.3 —4.7 —1.3 —12.7 —11.61964.4 1.8 —13.6 —11.51965.1 —13.9 —10.31965.2 —13.1
Root mean-squareerror 7.1 6.2 6.3 6.0 6.3 6.4
994 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
Model errors are based on ex post forecasts, while the Wharton-EFUfigures are based on sample-period simulations. More interesting is thelack of a direct correspondence between these errors, even when werecognize that different models and different data bases have been used.This difference would seem to indicate that mechanical forecast errorsare very sensitive to the slight modification of models, and that theactual modifications and adjustments which are made are, in fact, quitesignificant.
C. THE ORE MODEL
The sample-period simulations and ex post forecasting record forthe OBE Model are treated much the same way as is the Wharton-EFU Model, with three exceptions: (a) the comparison of sampleperiod against cx post forecast for the same model was not ready forthe Conference and, therefore, only the sample-period results are pre-sented; (b) for the same reason, the complete forecasting accuracydiagrams for OBE are missing from the text; and (c) there are no ex-periments with ROS coefficients for the OBE Model. The sample-period simulations are 1953.2 to 1966.4; and in each case, six-quartersimulations were generated by the methods described earlier. Thecomplete forecasting accuracy diagrams for the OBE Model from1953.3 to 1969.3 are presented immediately following the sample-period tables. The heavy line indicates actual data.
In general, the sample-period simulations results are slightly betterfor the OBE Model than for the Wharton-EFU Model.20 If we con-sider the simulation results for current-dollar GNP with no constantadjustments, the first-quarter OBE RMS error of $4.6 billion is sub-stantially better than the Wharton-EFU error of $6.8 billion. However,the difference narrows by six quarters, when the figures are $8.9 and$10.0 billion, respectively. The comparison is much the same for con-sumption and investment, with almost no difference by the sixth quar-
20 should be emphasized that the sample simulation periods of the Wharton-EFUModel and the OBE Model are not identical. In particular, the Wharton-EFU sampleperiod does not include the years 1965 and 1966. These years were noted for beingtrend dominated, as is clearly exhibited by the difference between the RMS of the NaiveModels in Wharton and OBE simulation periods.
FORECASTING PROPERTIES OF U.S. MODELS 995
ter. The gap is considerably larger, in favor of OBE, for constant-dollarGNP; and for unemployment, the gap between the two model simu-lations steadily widens in favor of OBE.
The finding that the OG adjustments are better than the AR ad-justments is borne out by the OBE Model also, and is, in fact, some-what stronger for that model. For all the variables compiled here, theGG adjustments are better than AR adjustments in the first quarterand continue to improve their relative performance throughout thesix-quarter simulations. It can also be noted that the GG adjustmentsare superior to no-constant-adjustments for all variables in all quarters,except for unemployment in the fourth quarter and constant-dollarGNP in the last three quarters. This is a somewhat stronger showingfor the GG adjustments than is the case with the Wharton-EFUModel. However, it should be stressed that in almost all cases thedifferences are rather small and, as would be expected, are almostnonexistent for the last three quarters.
As in the Wharton-EFU Model, there is an exceptionally per-sistent pattern to the decomposition of error; both UM and US aresmall relative to UC. This is especially true for the shorter timeperiods. Thus, most of the inaccuracy in the forecasts is accounted forby the fact that the realized and simulated values do not move to-gether, rather than by the fact that the average values and the vari-ances of the two differ. This is related to Suits's argument that aquarterly model should be judged according to its ability to accountfor quarter-to-quarter variations.21 A model does not necessarily de-serve to be called quarterly only because it is estimated with quar-terly data and can generate quarterly forecasts. The decomposition oferror does show that the major weakness of the models lies preciselyin tracking these fluctuations. The fact that, in most cases, the one-year-ahead simulations had smaller errors than the average of the one-to-four-quarter simulations is another indication of the same phe-nomenon.
It is somewhat surprising that the AR adjustments, which did notperform well relative to the other methods, were the most successful
21 D. B. Suits and 0. R. Sparks, "Consumption Regressions with Quarterly Data,"in J. S. Duesenberry et al., eds., The Brookings Quarterly Econometric Model of theUnited States. Chicago, Rand McNally and Co., 1965.
TAB
LE 3
.13
\0
.
Qua
rter
sA
head
One
Yea
r1
23
45
6A
head
C5.
171.
14 .06
25.4
9
.23
26.6
9
Sam
ple
Perio
d Si
mul
atio
ns fo
r GN
P in
Cur
rent
Dol
lars
, OB
E M
odel
No
Con
stan
t Adj
ustm
ents
rn 0 z 0 -l — 0 r U) C — C)
RM
S•
4.62
6.48
7.69
8.24
8.52
8.96
UM
.25
1.23
2.50
5.21
9.64
14.9
8us
.01
.14
.39
.38
.16
.02
UC
21.0
540
.67
56.2
462
.27
62.7
865
.28
RM
S (%
Err
or)
.84
1.53
2.17
2.47
2.60
2.79
RM
S/R
MS
(Nai
ve I)
.49
.36
.29
.24
.20
72.5
8.1
8M
SE21
.31
42.0
459
.12
67.8
6.8
0.27
£MSE
(of c
ompo
nent
s)14
.47
20.0
225
.14
28.8
532
.42
36.6
5
GG
Con
stan
t Adj
ustm
ents
RM
S.
3.63
5.43
6.94
7.77
8.35
8.91
UM
.15
.94
2.00
4.14
7.55
11.6
4U
S.1
7.2
2.3
2.5
01.
97U
C12
.88
28.3
2.45
.81
55.7
861
.34
65.7
9R
MS
(% E
rror
).5
81.
181.
872.
23.
2.42
•2.
59R
MS/
RM
S (N
aive
I).3
8.3
0.2
6.2
2'.2
0.1
8M
SE•
13.1
929
.48
48.1
360
.43
69.7
9•
79.4
0(o
f com
pone
nts)
8.96
14.8
520
.38
24.8
129
.47
34.7
8
5.86
1.23
1.06
32.1
0
.26
34.3
9
AR
Con
stan
t Adj
ustm
ents
RM
S3.
725.
847.
869.
8611
.60
13.0
86.
20U
M.0
5.6
81.
592.
834.
085.
311.
00U
s.,.0
2.2
31.
001.
651.
812.
35.5
5U
C13
.75
33.1
659
.14
92.8
012
8.66
163.
4136
.93
RM
S (%
Err
or)
.61
2.88
4.90
7.43
10.1
612
.63
RM
S/R
MS
(Nai
ve I)
.39
.32
.30
.28
.27
.26
.28
MSE
13.8
234
.06
61.7
397
.28
134.
5517
1.08
38.4
8(o
f com
pone
nts)
11.1
220
.47
29.0
239
.36
50.9
263
.27
Nai
ve I
RM
S9.
4818
.18
26.5
734
.75
42.5
449
.99
21.7
5U
M55
.91
227.
4951
7.61
931.
2314
55.6
620
74.2
335
0.81
US
10.8
339
.31
82.6
413
8.90
200.
5826
5.17
55.8
5U
C23
.17
63.7
210
5.61
137.
5315
3.47
159.
4466
.20
RM
S (%
Err
or)
3.18
11.2
923
.38
38.8
857
.05
77.7
2R
MS/
RM
S (N
aive
I)1.
001.
001.
001.
001.
001.
001.
00M
SE89
.91
330.
5270
5.86
1207
.66
1809
.71
2498
.85
472.
86(o
f com
pone
nts)
27.4
473
.21
143.
1323
2.43
332.
7644
9.30
Nai
vell
RM
S5.
2910
.86
16.9
423
.50
29.5
034
.93
13.6
7U
M.0
8.7
82.
7810
.52
27.5
149
.79
2.84
US
.08
1.15
5.60
8.19
9.04
15.1
21.
73U
C27
.77
278.
5153
3.64
833.
9211
55.5
118
2.32
RM
S (%
Err
or)
1.22
5.29
12.9
124
.72
38.4
952
.51
RM
S/R
MS
(Nai
ve I)
.56
.60
.64
.68
.69
.70
.62
MSE
27.9
411
8.04
286.
8955
2.36
870.
4712
20.4
318
6.89
(of c
ompo
nent
s)34
.48
92.9
119
1.25
352.
3051
5.06
733.
89
TAB
LE 3
.14
00
Qua
rters
Ahe
adO
neY
ear
12
34
56
Ahe
ad
Sam
ple
Perio
d Si
mul
atio
ns fo
r Con
sum
ptio
n, O
BE
Mod
elS 0 z 0 — 0 rn 0 C.)
C.) — 0
No
Con
stan
t Adj
ustm
ents
RM
S2.
933.
744.
394.
775.
125.
353.
48U
M.2
6.8
41.
462.
373.
765.
50.9
2U
S.2
3.1
0.0
2.0
10.
00.0
2.0
1U
C8.
1213
.03
17.8
320
.38
22.4
323
.12
11.2
0R
MS
(% E
rror
).8
41.
231.
742.
082.
362.
53R
MSJ
RM
S (N
aive
I).5
5.3
6.2
9.2
3.2
0.1
8.2
7M
SE8.
6113
.98
19.3
122
.75
26.2
028
.64
12.1
3£M
SE (o
f com
pone
nts)
4.47
6.37
8.14
9.51
11.2
912
.84
.O
GC
onst
ant A
djus
tmen
tsR
MS
2.54
3.30
4.08
4.57
5.03
5.29
3.15
UM
.11
.61
1.22
2.06
3.24
4.61
.79
US
.14
.20
.21
.19
.14
.16
.18
UC
6.18
10.0
515
.18
18.6
321
.93
23.2
68.
94R
MS
(% E
rror
).6
5.9
71.
511.
892.
262.
44R
MS/
RM
S (N
aive
I).4
7.3
2.2
7.2
2.2
0.1
8.2
4M
SE6.
4310
.87
16.6
120
.88
25.3
228
.02
9.91
IMSE
(of c
ompo
nent
s)3.
535.
317.
258.
7610
.79
12.5
5
AR
Con
stan
t Adj
ustm
ents
RM
S2.
683.
744.
986.
207.
558.
803.
97U
M0.
00.2
1.5
91.
071.
451.
95.4
4U
S'0
.00
0.00
.08
.15
.06
.05
.14
UC
7.19
13.7
524
.15
37.2
555
.45
75.3
915
.15
RM
S (%
Err
or)
.68
2.46
4.51
7.03
10.4
713
.95
RM
S/R
MS
(Nai
ve I)
.50
.36
.32
.30
.30
.29
.31
MSE
7.20
13.9
624
.82
38.4
756
.96
77.4
015
.73
(of c
ompo
nent
s)4.
227.
6412
.33
17.5
724
.17
32.3
3
Nai
ve I
CR
MS
5.38
10.3
715
.37
20.3
825
.30
29.9
912
.73
UM
20.9
886
.07
194.
8435
0.11
547.
9678
1.73
134.
29U
S2.
4910
.08
21.8
239
.53
60.4
781
.79
16.2
8U
C5.
5211
.30
19.4
625
.78
31.7
236
.13
11.5
8R
MS
(% E
rror
)2.
408.
7919
.04
32.9
550
.10
69.7
7R
MS/
RM
S (N
aive
I)1.
001.
001.
001.
001.
001.
001.
00M
SE28
.99
107.
4523
6.12
415.
4264
0.15
899.
6516
2.15
(of c
ompo
nent
s)12
.91
42.9
892
.04
157.
5823
8.45
332.
26
Nai
ve II
RM
S3.
175.
187.
8010
.24
12.6
515
.00
6.28
UM
.0.
00.1
4.2
91.
475.
409.
78.4
3U
S.0
6.1
81.
561.
72.3
8.6
0.3
5U
C9.
9626
.46
58.9
110
1.75
154.
3121
4.72
38.6
7R
MS
(% E
rror
).7
82.
295.
269.
3714
.66
20.4
1R
MS/
RM
S (N
aive
I).5
9.5
0.5
1.5
0.5
0.5
0.4
9M
SE10
.03
26.7
860
.76
104.
9416
0.08
225.
1039
.45
(of c
ompo
nent
s)9.
2123
.73
50.5
384
.91
127.
4017
5.56
TAB
LE 3
.15
Sam
ple
Perio
d Si
mul
atio
ns fo
r Inv
estm
ent,
OB
E M
odel
Qua
rters
12
3
Ahe
ad 45
6
One
Yea
rA
head
. rn 0 z C -R C-)
.
RM
SU
MU
S
3.34 .0
4.0
1
No
4.51
0.00 .1
3
Con
stan
t Adj
ustm
ents
5.12
5.33
.06
.38
.22
.17
5.38
1.14 .0
3
5.59
2.21 .1
.0
3.79
0.00
1.05
UC
RM
S (%
Err
or)
RM
S/R
MS
(Nai
ve I)
MSE
11.1
017
.62
.81
11.1
5
20.2
431
.41
.70
20.3
6
25.9
727
.84
39.7
542
.12
.60
.51
26.2
428
.39
27.8
042
.01 .46
28.9
6
28.9
643
.83
.43
31.2
7
13.3
2
.55
14.3
7(o
f com
pone
nts)
9.21
12.4
515
.49
17.6
819
.43
22.1
1
GG
Con
stan
t Adj
ustm
ents
RM
S2.
483.
594.
374.
795.
155.
633.
04U
M.0
2•
.09
.20
.54
1.21
2.08
.06
US
.30
.53
.82
1.22
1.86
3.11
.13
UC
5.82
12.2
718
.07
21.2
023
.46
26.5
19.
02R
MS
(% E
rror
)11
.23
23.7
933
.14
35.8
536
.64
39.5
8R
MS/
RM
S (N
aive
I).6
0.5
6.5
1.4
6.4
4.4
3.4
4M
SE6.
1412
.89
19.0
922
.96
26.5
331
.71
9.21
(of c
ompo
nent
s)5.
128.
9312
.22
14.9
017
.38
20.7
8
AR
Con
stan
t Adj
ustm
ents
RM
S2.
653.
974.
835.
596.
306.
913.
66tIM
.07
.29
.51
.79
1.12
1.36
.25
US
.27
.77
1.88
3.13
4.37
5.71
.55
UC
6.65
14.7
020
.99
27.3
134
.20
40.7
312
.59
RM
S (%
Err
or)
13.5
164
.46
86.4
910
6.22
127.
7514
4.69
RM
S/R
MS
(Nai
ve I)
.64
.62
.57
.54
.54
.53
53M
SE7.
0015
.76
23.3
731
.23
39.6
947
.80
13.3
9(o
f com
pone
nts)
6.62
12.2
515
.68
20.3
724
.99
28.6
8
Nai
ve I
0R
MS
4.10
6.43
8.51
10.3
.511
.73
13.0
56.
85U
M1.
697.
0416
.59
29.8
846
.39
64.4
711
.20
US
.49
1.08
2.51
4.33
6.65
9.60
1.15
U.C
14.6
633
.24
53.3
772
.96
84.5
296
.34
34.5
5R
MS
(% E
rror
)33
.47
84.3
814
0.81
194.
9623
3.56
272.
07R
MS/
RM
S (N
aive
I)1.
001.
001.
001.
001.
001.
001.
00M
SE16
.84
41.3
672
.47
107.
1613
7.56
170.
4146
.90
(of c
ompo
nent
s)13
.67
28.1
447
.08
68.4
385
.31
105.
260
-N
aive
IIR
MS
8.86
16.4
924
.40
32.7
340
.29
48.2
020
.59
UM
.63
2.87
5.69
9.50
13.5
319.52
3.99
US
.29
19.3
294
.12
262.
4254
1.01
949.
1758
.42
UC
77.5
224
9.80
495.
5679
9.44
1068
.42
1354
.80
361.
59R
MS
(% E
rror
)235.12
1020.43
2134.83
3654.38
5140.97
6296.73
RMS/RMS
(Nai
ve 1
)2.
162.
562.
873.
163.
433.
693.
00M
SE78
.44
271.
9959
5.37
1071
.36
1622
.97
2323
.48
424.
00(o
f com
pone
nts)
23.8
966
.09
134.
0825
5.56
369.
5053
0.82
TAB
LE 3
.16
C
Qua
rters
Ahe
adO
neY
ear
12
34
56
Ahe
ad
RM
SU
MU
sU
CR
MS
(% E
rror
)R
MS/
RM
S (N
aive
I)M
SE
3.07
4.43
0.00
.06
.02
.02
9.38
19.5
3.4
2.8
6.4
2.3
39.
4019
.60
5.48
6.11
.24
.85
.06
.35
29.6
836
.17
1.28
1.51
.28
.25
29.9
837
.37
6.69
7.34
1.94
3.14
1.34
3.71
41.4
147
.09
1.69
1.91
.22
.21
44.7
053
.94
4.08 .1
9.0
616
.41
.25
16.6
6
Sam
ple
Perio
d Si
mul
atio
ns fo
r GN
P in
Con
stan
t Dol
lars
, OB
E M
odel
rn 0 z 0 —
RM
S3.
675.
005.
896.
366.
747.
22U
M0.
00.1
1.4
21.
352.
954.
66U
S.0
4.3
7.6
3.4
1.0
3.3
6U
C13
.42
24.5
433
.63
38.7
542
.45
47.0
5R
MS
(% E
rror
).5
61.
011.
391.
601.
751.
95R
MSI
RM
S (N
aive
1).5
0.3
7.3
0.2
6.2
3.2
1M
SE(o
f com
pone
nts)
13.4
612
.63
25.0
316
.05
34.6
819
.58
40.5
021
.98
45.4
323
.86
52.0
626
.52
C
4.52 .2
2.7
1C
19.5
1.< C
.)
.28
20.4
4>
GG
Con
stan
t Adj
ustm
ents
(of c
ompo
nent
s)7.
9012
.34
16.2
319
.19
21.9
525
.62
AR
Con
stan
t Adj
ustm
ents
RM
S3.
335.
056.
447.
899.
1910
.10
5.05
UM
.01
.14
.41
1.06
1.97
2.59
.43
Us
0.00
0.00
.02
.31
1.30
2.93
.13
UC
11.1
025
.35
41.0
160
.88
81.0
996
.58
24.8
9R
MS
(% E
rror
).5
02.
283.
605.
347.
088.
17R
MS/
RM
S (N
aive
I).4
6.3
7.3
3.3
2.3
1.2
9.3
1M
SE11
.11
25.4
941
.44
62.2
584
.37
102.
1025
.45
(of c
ompo
nent
s)9.
9017
.53
23.4
929
.65
36.2
142
.00
Nai
ve I
0R
MS
7.30
13.5
919
.39
24.8
629
.94
34.7
215
.88
UM
21.7
990
.03
210.
4238
6.59
610.
0986
9.39
145.
34U
s5.
2319
.86
42.1
474
.02
113.
0415
6.96
31.3
7U
C26
.22
74.8
912
3.29
157.
5617
3.42
178.
8575
.47
RM
S (%
Err
or)
2.14
7.19
14.0
722
.26
31.2
541
.06
RM
S/R
MS
(Nai
ve I)
1.00
1.00
1.00
1.00
1.00
1.00
1.00
MSE
53.2
418
4.78
375.
8561
8.17
896.
5512
05.2
025
2.18
(of c
ompo
nent
s)21
.56
50.8
794
.08
145.
1819
8.58
259.
570
Nai
veII
RM
S7.
5015
.33
24.1
834
.03
43.7
053
.42
19.9
9U
M.8
54.
2811
.48
29.4
062
.96
106.
569.
96U
s2.
8320
.54
76.2
516
4.70
284.
6347
7.58
43.7
2U
C52
.55
210.
0949
7.05
964.
2515
62.5
222
69.6
234
6.08
RM
S (%
Err
or)
2.87
12.2
230
.84
61.2
210
0.08
146.
29R
MS/
RM
S (N
aive
I)1.
031.
131.
251.
371.
461.
541.
25M
SE56
.24
234.
9258
4.77
1158
.35
1910
.11
2853
.76
399.
76£M
SE (o
f com
pone
nts)
269.
2410
43.6
623
88.2
143
07.4
167
84.7
799
42.3
9
TAB
LE 3
.17
Sam
ple
Perio
d Si
mul
atio
ns fo
r the
Une
mpl
oym
ent R
ate,
OB
E M
odel
Qua
rters
Ahe
adO
neY
ear
12
34
56
Ahe
ad
RM
SU
M Us
UC
.R
MS
RM
S/M
SE
(% E
rror
)R
MS
(Nai
veI)
IMSE
(of c
ompo
nent
s)
RM
S
S C z C rn 0 rn 0 C.)
C.)
— C-) rn 6
.42
.57
.64
.67
.66
.67
.51
:
0.00
.oi
.02
.04
0.00
.01
.01
.02
.02
.02
.02
0.00
.17
.31
.40
.42
.40
.38
.25
66.4
812
0.59
146.
1716
3.64
170.
0717
6.12
.87
.65
.58
.53
.51
.51
.57
.18
.41
.44
.44
.44
.25
0.•0
O0.
00.0
.00
0.00
0.00
.0.o
0
GG
Con
stan
t Adj
ustm
ents
.35
.67
•.66
.65
.49
0.00
.01
.01
.02
0.00
0.00
.03
.03
.04
0.00
.12
.42
.40
.36
.24
(% E
rror
)15
6.53
.
160.
5515
8.39
RM
S (N
aive
1).5
4.5
1.4
9.5
5.4
1.4
5.4
4.4
2.2
4(o
f com
pone
nts)
0.00
0.00
0.00
0.00
0.00
0.00
UM Us
UC
.R
MS
RM
S/M
SE
.54
0.00 .0
1.2
810
6.48 .6
2.2
9
.64
0.00 .0
2.3
913
6.07 .5
749
.06
.72 .12
AR
Con
stan
t Adj
ustm
ents
RM
S.4
0.6
7.9
01.
081.
201.
26.7
1U
M0.
000.
00.0
1.0
2.0
4.0
6.0
1U
S0.
000.
000.
000.
000.
000.
00.0
2U
C.1
5.4
5.8
01.
151.
381.
52.4
9R
MS
(% E
rror
)56
.67
286.
5951
3.70
827.
8311
12.5
912
89.8
3R
MS/
RM
S (N
aive
1)
.82
.77
.81
.87
.93
.96
.79
MSE
.16
.45
.81
1.17
1.43
1.58
.52
£MSE
(of c
ompo
nent
s)0.
000.
000.
000.
000.
000.
00
Naj
vet
RM
S.4
8.8
71.
121.
251.
291.
31.8
9U
M0.
000.
000.
000.
00.0
1.0
10.
00U
S0.
000.
000.
000.
000.
000.
00.0
2U
C.2
3.7
51.
241.
561.
661.
71.7
7°
RM
S(%
Err
or)
114.
2829
3.74
400.
8149
8.27
549.
1158
7.24
RM
S/R
MS
(Nai
ve I)
1.00
1.00
1.00
1.00
1.00
1.00
1.00
MSE
.24
.75
1.24
1.56
1.67
1.72
.79
(of c
ompo
nent
s)0.
000.
000.
000.
000.
000.
000
Nai
veII
RM
S.4
21.
001.
652.
302.
883.
431.
31U
M0.
000.
00.0
1.0
3.0
7.1
3.0
1U
S.0
4.3
0.8
91.
863.
325.
27.7
1U
C.1
3.7
01.
823.
424.
926.
351.
00R
MS
(% E
rror
)74
.03
336.
2482
4.31
1720
.49
3032
.79
4675
.53
RM
S/R
MS
(Nai
ve I)
.87
1.15
1.48
1.84
2.23
2.61
1.47
—M
SE
.18
.99
2.72
5.31
8.32
11.7
61.
72(o
f com
pone
nts)
0.00
0.00
0.00
0.00
0.00
0.00
1006 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3.1
Gross National Product— Forecasts with No Constant Adjustments
Billion dollars
1953 '56 '58 '60 '62 '64 '66 '68
FORECASTING PROPERTIES OF
CHART 32
U.S. MODELS • 1007
Gross National Product—Forecasts with AR Constant AdjustmentsBillion dollars
1008 S ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3.3
—
Gross National Product—Forecasts with No COnstant Adjustments
1953 '60 '62 '64 '66 168
Billion 1958 dollars750
'56 '58
FORECASTING PROPERTI ES
CHART 3.4
OF U.S. MODELS • 1009
Gross National Product—Forecasts with AR Constant A
1953 '56 '58 '60 '62 '64 '66 '68
Billion 1958 dollars751
1010 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3.5
GNP Implicit Price Deflator— Forecasts with AR Constant Adjustments
(1957-59 100)1.25
FORECASTING PROPERTIES OF U.S. MODELS • 1011
CHART 3.6
Consumption—Forecasts with AR Constant Adjustments
1953 '56 '58 '60 '62 '64 '66 '68
Billion dollors550
1012 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3.7
Gross Private Domestic Investment—Forecasts with AR ConstantA djustmenrs
1953 '56 '58 '60 '62 '64 '66 '68
Billion dollars140
a z C.)
C', z C)
Pt a Pt
5:
-a 0
C
1014 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3.9
Gross National Product—Forecasts with No Constant Adjustments
dollarswoo
900
800 —
700 -
600 —
500 -
400 -
I I f I I I I I I I I I
I I I I I I I I I I I I I I
1953 '55 '57 '59 '61 '63 '65 '67 '69
C
300
FORECASTING PROPERT!ES OF U.S. MODELS • 1015
CHART 3.10Gross National Product— Forecasts with AR Constant Adjustments
BilliOn dollars1,000
900
800-
700-
600 -
500 -
400-
1 I I I I 1 I I I I
I I I I I I I I I I I I
1953 '55 '57 '59 '61 '63 '65 '67 '69300
1016 ECONOMETRIC MODELS OF CYCLICAL BEHAVJOR
CHART 3.11
Gross National Product—Forecasts with GG Constant Adjustments
Billion dollars1poo -
900 -
800 -
700 -
600
500
400 —
I I I I I I I I I
0
3001953 '55 '57 '59 '61 '63 '65 '67 '69
_I I I It_I I I_I I I I
FORECASTING PROPERTIES OF U.S. MODELS • 1017
CHART 3.12Gross National Product— Forecasts with No Constant Adjustments
Billion 1958 dollars750
700-
650 -
600 —
550 -
500
450
400
I I I r F I --
I .1 I I I I I. I I I I155 '59 '63 '65 '67 '69
C
350
1018 . ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3113
I I I I I I I I I I I I I I
Gross National Product—Forecasts with AR Constant Adjustments
Gillion 1958 dollars750
700 -
650 -
600 -
550 —
500 -
450 -
400 -
350 I I I I I I I I I I I I I
1953 '57 '59 '61 '63 '65 '67 '69
FORECASTING PROPERTIES OF U.S. MODELS • 1019
CHART 3.14
Gross National Product—Forecasts with GG Constant Adjustments
1958 dollars750
700 -
650 -
600
550
500 —
450 —
400
I— I I I I I I I F I
I I I I I I I I I I I I I
'55 '57 '59 '61 '63 '65 '67 '69
0B-
3501953
1020 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
Billion dollars
CHART 3.15
Consumption—Forecasts with No Constant Adjustments
I I I I I I I I I
0
600 —
550 —
500 -
450 —
400 -
350 —
300 —
250 —
200 — I I I I I I I I I I I t___I I
1953 '55 '57 '59 '61 '63 '65 '67 '69
FORECASTING PROPERTIES OF U.S. MODELS 1021
dollar
CHART 3.16Consumption—Forecasts with AR Constant Adjustments
I I I I I I I I I I I I I I I I600
550 -
500
450 -
400 -
350 -
300 -
250 -
200 — I I J I
1953 '55 '57 '59 '61 '63 '65 '67 '69
1022 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
CHART 3.17Consumption — Forecasts with G G Constant A djustments
Billion dollars600
550 -
500 -
450 -
400 -
350 -
300 -
250 -
I I I I I I I I I I I I I
El
I I I I I I I I I I I I
1953 '59 '61 '63 '65 '67 '69
0
200
FORECASTING PROPERTIES OF U.S. MODELS 1023
CHART 3.18Gross Private Domestic Investment—Forecasts with No Constant
Billion dollars
A djustments
130—
120 —
11
100-
90 —
80 -
70
60
50
I I —t I I I I I I I
I I I I I I t I I
1953 '55 '57 '59 '61 '63 '65 '67 '6940
AU
im
()0
00
00
0I
II
II
U'
C)
2.
m-
0(
zU
'0 —
-.4
0
(C
,)(0
0
—
'-4
— 0—
.U
i
-4C
..,
I
II
-4 00
0
UI
UI
-J U'
C C 0 rn H — rn C,' 0 C 0 rn C,' .
0(f
l-4
'.00
00.
00
0 0I
II
II
II
0-a N 0
0—
o 0. 0 0
C') C
-J (0I
II
II
I
C
(J1
01 ()J
01 (7'
01 01 (.0
-S -4
w ()J
U,
-J
CD r C,
CO C CD 3 0 'C Ct
— 0 . 0 z C 0 0 r) — r 0
FORECASTING PROPERTIES OF U.S. MODELS ' 1027
I I I I I I I I I I
IJ
CHART 3.22Unemployment Rate—Forecasts with AR Constant Adjustments
Per cent unemployed9—
8—
7
6
5
4
3
2
______ ____
I I I I I I I I I I I I I I I I
1953 '55 '57 '59 '61 '63 '65 '67 '69
1028 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
S
7
6
5
4
3
CHART 3.23
Unemployment Rate—Forecasts with GG Constant Adjustments
2'61 '63 '65 '67 '69
in getting the forecasts on the right track. The component of bias(UM) is consistently smaller for the AR adjustments than for anyother method. This was true for all of the simulations from one to sixquarters. The US component remains small in almost all cases and onlyoccasionally exceeds 10 per cent of the total mean square error.
For the largest component of error, UC, the GG adjustmentsusually produce the lowest values; but with very few exceptions theno-constant-adjustments simulations improve their relative position,and in some cases, even become superior to the GG adjustments as
Per cent unemployed9
I I I I I I I I I I I I
9
/
1953 '55 '57 '59I I I t I I I I I I I I I I
FORECASTING PROPERTIES OF U.S. MODELS •. 1029
the time span lengthens. The AR adjustments remain inferior to theother two methods for the UC component as well.
In addition, it might be noted that for almost all variables in bothmodels, the simulation performance improves substantially, com-pared to the naive models,. as the time span increases. This is, per-haps, the one encouraging note about these econometric models to bedrawn from this section: even if there are cases where the model is un-able to track the short-run fluctuations, it is capable of returning tothe actual path over a longer period.
In summary, the. sample-period statistics for both models showlittle difference between no-constant-adjustments, AR adjustments,GG adjustments, and (for the Wharton-EFU Model) ROS coeffi-cients with AR adjustments; There is a slight tendency for the GGadjustments to give superior simulation results in the sample period.In the forecast period, it was found that the constant adjustments doreduce forecast errors substantially. In all cases, however, the errorsare large relative to the actual change in GNP and its components.One is left with the conclusion that mechanical adjustment of econo-metric models does not lead to satisfactory predictive performance.It is this point which will be analyzed in detail in the next section.
4 HOW WELL DO ECONOMETRICIANS FORECAST
AS WE have already stated, the sample-period simulations and. expost forecasts presented in the previous section are not very im-pressive. If these are compared to the average of all noneconometricforecasts made at year-end,22 the results are still less so. The RMSerror of these forecasts for prediction of GNP one year ahead is $8.1billion during the period 1959-1968. Recall that this figure may becompared with RMS errors one year ahead ranging from $10.6 to$14.8 billion—depending on the method of constant adjustment—for the Wharton-EFU Model during its ex post forecasting period.
22 are tabulated near the end of each calendar year by the Federal ReserveBank of Philadelphia.
1030 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
Similar results have led many economists to conclude that econo-metric models do not forecast very well. On the basis of the resultsbrought forth in the previous section, we are not in a position to con-tradict them.
However, it was stressed at the beginning of this study that com-parisons with forecasts generated by econometric models which havenot been adjusted (or have been adjusted using only mechanical rulesof thumb) are not to be confused with forecasts which have actuallybeen issued. Fine-tuning of the model (i.e., adjustment on the basisof judgment) is a very important step in forecasting for the WhartonModel. For comparison, the publicly circulated23 ex ante forecasts ofthe Wharton Model for the period 1963—1968 have had a root meansquare error of $3.5 billion for GNP one quarter ahead, and $9.1 bil-lion for an average of four quarters ahead. The Wharton year-end fore-casts for one year ahead, which are directly comparable with the Phila-delphia FRB figure of $8.1 billion, were considerably better than theWharton average one year ahead forecast, and have had a RMS errorof only $4.3 billion. The RMS error for the true ex ante forecast issubstantially smaller than the RMS error of both the sample-periodsimulations and the cx post forecasts.
We now consider in more detail the various types of forecastswhich were calculated. Our first step was to obtain exact replica-tions of the existing cx ante forecasts, which were then used as acomparison with other types of predictions. As has mentionedin Section II, we have a complete record of the various Wharton andOBE Model forecasts, and of all of the exogenous inputs. However, wecould not always find a complete record of all of the constant adjust-ments or of all of the values of the lagged variables. It was not alwayseasy to obtain the exact lagged values used at the time of prediction,because preliminary (or even guessed) data were often used, particu-larly for the one-quarter lags. After some experimentation, we wereusually able to duplicate the forecast solution exactly. However, in afew cases this did not prove to be possible. Many of the early calcu-lations were done by hand on a desk calculator, and some shortcuts
23These forecasts are now published in Business Week and The Wharton Quarterly.However, in the first two years, these forecasts were restricted to subscribers of theWharton-EFU forecasting service.
FORECASTING PROPERTIES OF U.S. MODELS • 1031
and rounding errors were found when these forecasts were redupli-cated. In these cases, we made further small adjustments in the con-stant terms of the equations which seemed .to contain errors untilexact replication of the entire forecast was obtained within a toler-ance of .1 percent.
It should be mentioned at this point that Wharton Model predic-tions for each quarter usually contain a set of different forecastswhich depend on various guesses about monetary and fiscal policyover the forecast period. However, one particular solution is alwaysdesignated as the control solution, meaning that this solution con-tained their best guesses about future exogenous variables, and is theone which was publicly issued as their best forecast.
In almost all cases, we used the control solution in the tableswhich follow in this section (Tables 4.1A through 4.15P). How-ever, there are two major exceptions to this rule which should bestated. First, the Wharton Model forecasters were consistentlywrong about the date of implementation of the 1968 surcharge. Atfirst, it was thought that this would be enacted in late 1967; later, itwas believed that the surcharge would be in effect by April, 1968.Thus, the control solution forecasts made in 1967.4 and 1968.1 arefar too low in the first few quarters, because they assumed that thesurtax would be imposed at an earlier date than it actually was. Inthese cases, we have analyzed the results with the alternative solu-tion — no surcharge — but have included in the summary tables thesurcharge forecasts as well. The second exception is related to thegreat automobile strike of early 1968, which never occurred. TheWharton forecasters had what they considered good reason to be-lieve that there would be a severe strike at GM, which would takeplace during the first quarter of 1968. Accordingly, they built thisassumption into their official year-end forecasts (made in 1967.4),which were released to Business Week, and were tabulated by theFederal Reserve Bank of Philadelphia. By it becamemuch clearer that there would be no such automobile strike, so theforecasts were again revised; the revised version was circulated onDecember 18, 1967. We have used this revised version for the 1967.4forecast, although it is not the one which was officially released earlierin the quarter.
.1032 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
It was necessary to use a somewhat different procedure for theOBE forecasts. The Office of Business Economics does not releaseits forecasts to the public; they are intended only for restricted cir-culation within certain sectors of the federal government. In addi-tion, no one set of forecasts were identified as preferred solutions be-fore .1968.2. Instead, the model is used. to test the effect of variousalternative monetary and fiscal policies on the economy. In somecases, in considering the OBE it is possible to identify a "most widelycirculated" forecast,24 but in these predictions, the forecasters wererestricted by having to use official government budget figures, whichwere known to be out of date. It is not surprising that these exogenousassumptions gave very poor forecasts. There seemed to be no worth-while purpose in using such forecasts in this study, since they arenot a true indication of the forecasting efficacy of the OBE Model.Instead, for the 1967.2, 1967.3, and 1968.1 forecasts, they chose theforecasts containing the set of exogenous variables which, accordingto their memory, seemed to include the most probable set of exoge-nous variables at that time. There, was only one version for 1967.4that was a "serious forecast." The 1968.2—1968.4 forecasts weredesignated .as preferred forecasts internally at OBE, but were notverified as such outside that office. The OBE forecasts that were• se-lected at an ex post date, rather than being true control solutions,should be regarded as selected ex ante forecasts. For this reason, thereader is cautioned against comparing the Wharton and OBE records.Another reason why the summary results should not be compared isthat they encompass different forecast periods.
After we had succeeded in duplicating the cx ante forecasts, weinserted the actual values of all the exogenous variables,25 but didnot change any of the constant adjustments or lagged values. These
24There is a substantial difference between a control solution and a most ,widelycirculated forecast. In the former case, the forecaster ,enters his best guesses about fu-ture exogenous values; in the latter case, the forecaster may be restricted to using un-realistic values for exogenous variables, although this need not occur.
25 Unfortunately, the term actual needs to be severely qualified. In order to keep theex ante and ex post forecasts on' a comparable basis, we used preliminary estimates ofall lagged variables. If we were to use revised figures for the values of the exogenousvariables during the forecast period, there might be an inconsistency in the data. Thechange between G1..1 (on a preliminary basis) and G1 (on a revised basis) would be muchgreater than the actual difference. In order to minimize such problems, we have calcu-lated realized as preliminary plus actual revised
FORECASTING PROPERTIES OF U.S. MODELS 1033
are called ex post forecasts with actual adjustments. The comparisonof these two tests should enable us to examine how much of the fore-cast error is due to erroneous guesses about future values of the exoge-nous variables. Both of these forecasts are properly compared withpreliminary data, which is defined as the most recent lagged value ofGNP (or any other variable) available at the time of the forecast, plusthe actual change in GNP during the forecast period. In this case, theactual values are taken from the July, 1969, issue of the Survey of Cur-rent Business for the Wharton tables, and from the May, 1969, issuefor the OBE tables.
We also calculated both ex ante and ex post forecasts, using thetwo methods of constant adjustments — average residual of the pasttwo quarters (AR) and that residual multiplied by powers of theautocorrelation coefficient (GG)—which were used for the sample-period simulations and for the ex post forecasts in Section 3. Inaddition, we calculated both ex ante and ex post forecast with no-constant-adjustments. For the Wharton-EFU Model we added expost forecasts with AR adjustments where the coefficients were esti-mated by the ROS (regression simulated values) method. The re-sults are presented in Tables 4.1—4.5 for the Wharton-EFU Model,1966.1—1968.4; in Tables 4.6—4.10 for the Evans Model, 1964.1—1965.2;26 and in Tables 4.11—4.15 for the OBE Model, 1967.2—1968.4.27 In addition, the results for constant-dollar GNP for thesemodels are portrayed on the familiar forecast-realization diagrams inCharts 4.1—4.8.
The principal results to be drawn from these tables can be sum-marized as follows:
1. With very few exceptions, the Wharton true ex ante fOrecastsare superior to the ex post forecasts with the original constant adjust-
26 Although the Evans Model was used for true ex ante forecasting during 1963, theseearly forecasts could not be replicated, due in part to a data base which was largely drawnfrom sources other than the Survey of Current Business. In addition, sincethere are noformal records of constant adjustments for the Evans Model, only the actual ex anteforecasts and the ex post forecasts calculated by substituting in the correct values of theexogenous variables are given. While this results in a much briefer treatment, a good dealof the analysis based on the results of the other two models cannot be extended to includethe Evans Model.
27 In initial calculation, it has been determined that there is anerror in the ex post ARforecasts of 67.3 and 67.4. Since the data set is such that it is not feasible to regeneratethe calculation, these two forecasts are deleted from all tables.
TAB
LE 4
.IA
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter o
f For
ecas
t0
1967
.176
9.7
1967
.277
6.1
1967
.379
5.0
1967
.4*8
059
806.
7
6.7
764.
72.
577
1.1
2.5
787.
30.
1 0.9
810.
5
1.7
758.
1—
2.5
769.
1—
5.2
787.
6
4.7
808.
5
—4.
576
3.2
—4.
978
0.1
2.7
795.
5
776.
1—
10.4
780.
6—
12.4
791.
6
—10
.380
2.2
13.1
763.
07.
077
3.6
—0.
979
2.5
—3.
680
5.8
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
Wha
rton
Mod
el, G
NP
in C
urre
nt D
olla
rs. C) 0 z C — C)
—17
.6
1966
.170
7.9
—9.
171
6.3
—0.
771
8.2
1.2
705.
6—
11.4
710.
0—
7.0
717.
019
66.2
727.
61.
273
9.1
12.7
739.
513
.172
5.1
—1.
372
5.6
—0.
872
7.9
1966
.374
8.6
4.2
744.
40.
073
6.4
—8.
072
6.8
C)
1966
.475
7.9
—1.
575
1.1
—8.
374
3.7
—15
.773
2.6
—26
.8
—4.
975
0.8
—12
.2
1968
.1*8
28.8
751.
976
0.5
r
7.5
744.
4
2.0
1.1
759.
4
—1.
3—
6.3
829.
12.
382
8.7
1.9
815.
1—
11.7
794.
2—
32.6
840.
713
.982
6.8
1968
.284
6.6
—4.
184
0.1
—10
.684
9.4
—37
.484
7.9
—2.
885
0.7
1968
.386
1.3
—8.
085
5.7
—13
.686
3.0
866.
3—
3.0
869.
319
68.4
884.
1—
2.8
866.
7—
20.2
871.
3—
15.6
837.
7—
49.2
883.
4—
3.5
886.
9A
FE*
*37
AFE
3.8
6.8
7.5
21.6
5.4
813.
383
2.0
—37
.3
13.2
825.
0
(I, z C) 0 'I, 0 'TI F 0 tn I- 'I)
1966
.119
66.2
1966
.319
66.4
1967
.119
67.2
1967
.319
67.4
720.
674
1.6
762.
176
7.0
780.
279
6.1
816.
1*8
151
832.
9
—10
.273
3.1
2.6
758.
92.
975
7.8
4.1
760.
2
7.9
778.
95.
678
1.6
7.9
800.
0—
9.9
7.9
828.
8
Seco
nd Q
uarte
r of F
orec
ast
2.3
731.
00.
271
7.1
19.9
753.
914
.973
7.8
—1.
474
4.7
—14
.573
5.4
—2.
774
6.2
—16
.773
7.5
6.6
766.
4—
5.9
759.
6—
8.9
778.
4—
12.1
774.
1—
8.2
802.
0—
6.2
795.
2
725.
5—
5.3
730.
8—
1.2
743.
74.
773
9.0
—23
.8—
25.4
768.
977
2.4
9.7
759.
29.
576
2.9
—12
.778
7.6
15.3
772.
3—
16.4
800.
29.
779
0.5
3.8
825.
00.
081
2.9
—12
.183
8.2
(con
tinue
d)
NO
TES
(Tab
les 4
.1 th
roug
h 4.
10):
*T
hese
fore
cast
s wer
e or
igin
ally
issu
ed a
s con
trol s
olut
ions
but
are
not
incl
uded
in th
e an
alys
is. S
ee te
xt fo
r exp
lana
tion.
AFE
is a
bsol
ute
aver
age
fore
cast
err
or.
AR
adj
ustm
ents
are
the
aver
age
resi
dual
of t
he p
revi
ous t
wo
perio
ds. S
ee te
xt, S
ectio
n 3A
, for
fulle
r dis
cuss
ion.
GO
adj
ustm
ents
are
the
aver
age
resi
dual
s of t
he p
revi
ous t
wo
perio
ds m
ultip
lied
by th
e po
wer
s of t
he a
utoc
orre
latio
nco
effic
ient
. See
text
, Sec
tion
3A, f
or fu
ller d
iscu
ssio
n.
RO
S m
eans
the
vers
ion
of th
e m
odel
est
imat
ed w
ith R
OS
(reg
ress
ion
on si
mul
ated
val
ues)
coe
ffic
ient
s. Se
e te
xt, S
ec-
tion
5, fo
r ful
ler e
xpla
natio
n.
"Ex
post
with
act
ual a
djus
tmen
ts"
fore
cast
s are
mad
e by
repl
acin
g th
e ex
ant
e va
lues
of t
he e
xoge
nous
var
iabl
es a
nd th
eex
ant
e ta
x-eq
uatio
n sl
ope
and
inte
rcep
ts w
ith th
e ap
prop
riate
real
ized
val
ues.
In th
e ca
se o
f the
exo
geno
us v
aria
bles
,th
e re
vise
d ch
ange
is a
dded
to th
e la
gged
val
ue. T
he ta
x fu
nctio
ns a
re a
djus
ted
to re
flect
new
tax
law
s and
gro
wth
of
stat
e an
d lo
cal t
ax c
olle
ctio
ns.
TAB
LE 4
.1A
(con
tinue
d)
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
.w
ith A
Rw
ith G
Gw
ith N
ow
ith A
ctua
lR
ealiz
edFo
reca
stFo
reca
stA
djus
tmen
tsA
djus
tmen
tsA
djus
tmen
tsA
djus
tmen
tsPr
eim
i-W
as M
ade
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror n
ary
Val
ue
Seco
nd Q
uarte
rof
Fore
cast
(con
tinue
d)
rn C) 0 z 0
1968
.1*8
393
—10
.984
6.4
—3.
8
AFE
**7
7A
FE
845.
3—
4.9
823.
3
7.0
10.2
839.
1
13.3
24.6
778.
5—
10.7
792.
6—
13.6
813.
9—
13.5
9.2
tn I 0
1968
.1*8
485
—19
.485
8.4
—9.
585
5.0
—12
.983
5.6
—32
.382
9.5
—38
.485
9.8
—8.
186
7.9
S
1968
.2..
856.
4—
12.0
841.
3—
27.1
843.
8—
24.6
812.
3—
56.1
856.
4—
12.0
868.
419
68.3
873.
8—
11.6
859.
3—
26.1
861.
4—
24.0
835.
3—
50.1
879.
2—
6.2
885.
4
1966
.173
3.7
—9.
774
3.9
Third
0.5
Qua
rter o
f For
ecas
t—
6.1
730.
3—
13.1
743.
50.
174
3.4
1966
.275
5.6
1.8
771.
117
.376
1.1
7.3
751.
5—
2.3
763.
29.
475
3.8
1966
.377
0.5
7.8
768.
45.
775
6.3
—6.
475
2.9
—9.
878
4.9
22.2
762.
719
66.4
778.
46.
277
4.7
2.5
761.
7—
10.5
761.
1—
11.1
782.
710
.577
2.2
1967
.178
5.2
—4.
078
9.0
—0.
277
8.5
—10
.778
9.7
0.5
789.
219
67.2
809.
23.
079
2.6
—13
.679
3.8
—12
.481
0.0
3.8
806.
219
67.3
824.
0—
3.4
808.
5—
18.9
813.
6—
13.8
826.
8—
0.6
827.
419
67.4
*845
.2—
3.2
852.
54.
11—
9.3
837.
3—
111.
183
3.3
—15
.186
6.1
17.7
848.
4
0 m C,, C C)
C)
— C)
1968
.286
2.4
—22
.184
2.6
—41
.983
9.0
—45
.583
0.2
—54
.386
4.9
—19
.688
4.5
AFE
*A
FE
7.2
12.3
15.7
18.1
9.3
Four
th Q
uarte
r of F
orec
ast
1966
.174
5.8
—12
.475
6.0
—2.
274
7.5
—10
.774
2.5
—15
.776
0.0
2.4
758.
219
66.2
768.
511
.278
6.2
28.9
773.
516
.276
6.5
9.2
787.
630
.375
7.3
1966
.378
0.4
8.4
777.
25.
276
6.1
—5.
976
4.7
—7.
380
1.3
29.3
772.
019
66.4
788.
9—
0.2
788.
3—
0.8
776.
7—
12.4
777.
8—
11.3
790.
91.
878
9.1
1967
.179
3.9
—11
.079
7.1
—7.
879
0.3
—14
.679
2.8
—12
.179
6.8
—8.
180
4.9
1967
.282
8.3
2.9
807.
9—
17.5
812.
7—
12.7
815.
2—
10.2
841.
816
.482
5.4
1967
.383
8.1
—12
.782
0.7
—30
.183
0.1
—20
.783
0.8
—20
.085
0.6
—0.
285
0.8
1967
.4*8
52.2
—13
.985
6.5
—9.
684
1.6
—24
.584
2.3
—23
.884
0.9
—25
.286
2.8
—3.
386
6.1
1968
.1*8
56.6
—27
.486
5.5
—18
.586
1.9
—22
.184
4.9
—39
.184
2.2
—41
.886
3.2
—20
.888
4.0
AFE
**1
1.1
AFE
9.7
15.5
17.3
17.0
12.5
0Fi
fth Q
uarte
r of F
orec
ast
1966
.175
3.2
—8.
576
1.5
—0,
275
1.3
—10
.475
1.7
—10
.078
0.6
18.9
761.
719
66.2
775.
79.
178
8.2
21.6
773.
74.
177
4.0
7.4.
802.
246
.676
6.6
1966
.379
1.0
2.1
785.
9—
3.0
778.
1—
10.8
777.
0—
11.9
813.
524
.678
8.9
1966
.480
2.5
—2.
380
2.1
—2.
779
3.6
—11
.279
5.7
—9.
180
3.1
—1.
780
4.8
1967
.181
6.4
—7.
781
2.6
—11
.581
11.0
—13
.181
4.3
—9.
882
8.1
4.0
824.
1
(con
tinue
d)
00 . C z 0 — C.) 0 ci) C
Fifth
Qua
rter o
f For
ecas
t (co
ntin
ued)
1967
.4*8
555
—26
.586
7.3
—14
.985
4.5
—27
.785
7.8
—24
.485
7.7
—24
.5
Sixt
h Q
uarte
r of F
orec
ast
0.2 8.7
761.
877
8.9
—9.
2—
4.6
761.
777
9.6
793.
2—
11.4
787.
3—
17.3
787.
3
16.0
848.
8
—12
.2
1966
.481
9.4
—4.
681
8.0
—6.
081
2.1
—11
.981
4.4
—9.
683
0.6
6.6
824.
0
>
TAB
LE 4
.IA(c
oncl
uded
)
Qua
rter
Rep
rodu
ced
Lx A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
r
1967
.283
9.1
—9.
781
8.6
—30
.282
7.7
—21
.182
9.6
—19
.286
4.8
1967
.385
2.7
—15
.883
1.7
—36
.884
4.1
—24
.484
4.8
—23
.785
2.6
—15
.986
8.5
870.
088
2.2
AFE
8.8
16.7
14.9
.14
.517
.5
1966
.176
2.3
—8.
777
1.2
—9.
379
6.4
28.3
768.
119
66.2
782.
1—
1.4
792.
2—
3.9
813.
229
.778
3.5
1966
.379
9.0
—5.
6—
17.3
824.
820
.280
4.6
0
1967
.1•8
34.8
—12
.782
8.6
—18
.983
0.8
—16
.783
4.7
—12
.885
4.3
6.8
847.
519
67.2
842.
0—
24.5
823.
5—
43.0
835.
5—
31.0
837.
1—
29.4
861.
0—
5.5
866.
519
67.3
867.
4—
17.2
846.
5—
38.1
861.
2—
23.4
862.
1—
22.5
860.
5—
24.1
884.
6A
FE10
.718
.016
.315
.017
.3
Fore
cast
One
Yea
r Ahe
ad19
66.1
727.
0—
10.3
737.
3—
1.8
733.
5—
5.6
723.
8—
15.3
734.
7—
4.4
737.
319
66.2
748.
33.
876
3.8
19.3
757.
012
.574
5.2
0.7
755.
010
.574
4.5
1966
.376
5.4
5.9
744.
4—
15.1
736.
4—
23.1
744.
9—
14.6
776.
717
.275
9.5
1966
.477
3.0
2.1
768.
5—
2.4
757.
0—
13.9
752.
2—
18.7
776.
65.
777
0.9
1967
.178
2.2
—0.
178
2.4
0.1
773.
3—
9.0
770.
4—
11.9
787.
55.
278
2.3
1967
.280
2.4
3.5
788.
3—
10.6
788.
2—
10.7
786.
6—
12.3
808.
19.
219
8.9
1967
.381
8.3
—1.
480
4.1
—15
.680
8.4
—11
.380
4.9
—14
.881
8.0
—1.
781
9.7
1967
.4*8
296
—6.
783
7.1
0.8
830.
0—
6.3
828.
2—
8.1
820.
6—
15.7
842.
36.
083
6.3
1968
.1*8
43.3
—13
.984
9.8
—7.
484
7.7
—9.
582
9.7
—27
.581
7.6
—39
.685
6.2
—1.
085
7.2
AFE
*53
3.9
8.9
13.5
15.9
6.7
c 0 r -a C
TAB
LE 4
.1P
C rn z 0 rn 0 rn 0 C)
rn 0
Com
paris
on o
f Ex
Post
For
ecas
ts, W
harto
n M
odel
, GN
P in
Cur
rent
Dol
lars
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
NO
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
ErrO
rV
alue
Firs
t Qua
rter o
f For
ecas
t19
66.1
724.
2—
5.3
719.
3—
10.2
708.
0—
21.5
720.
8—
8.7
729.
519
66.2
746.
53.
273
7.5
—5.
872
5.4
—17
.974
2.8
—0.
574
3.3
1966
.375
5.6
—0.
374
8.8
—7.
173
9.2
—16
.775
3.6
—2.
375
5.9
1966
.476
8.3
—2.
476
4.6
755.
3—
15.4
766.
4—
4.3
770.
7
1967
.176
9.3
.—
4.9
769.
1—
5.1
763.
4—
10.8
771.
8—
2.4
774.
219
67.2
771.
0—
12.5
775.
3—
8.2
770.
5—
13.0
772.
5—
11.0
.78
3.5
1967
.379
0.9
—9.
579
0.0
—10
.478
2.7
—17
.779
0.9
—9.
580
0.4
1967
.480
5.1
800.
8—
15.3
790.
7—
25.4
809.
8—
6.3
1968
.184
0.6
5.3
834.
6—
0.7
819.
4—
15.9
836.
41.
183
5.3
1968
.283
6.1
4.4
853.
7—
5.0
835.
5—
23.2
858.
3—
0.4
858.
719
68.3
860.
4—
16.0
851.
7—
20.4
836.
0—
40.4
863.
1—
13.3
876.
419
68.4
880.
3—
12.2
867.
4—
25.1
850.
0—
42.5
—9.
789
2.5
.A
FE.
5.8
.
.Se
cond
Qua
rter
of F
orec
ast
1966
.173
3.9
—4.
472
9.7
—13
.672
0.0
—23
.373
2.4
—10
.974
3.3
1966
.276
2.2
6.3
747.
5—
8.4
737.
3—
18.6
757.
11.
275
5.9
7.2
10.0
21.7
1966
.377
3.5
2.8
762.
4—
8.3
754.
0—
16.7
768.
9—
1.8
770.
719
66.4
785.
010
.877
7.7
3.5
769.
9—
4.3
783.
39.
177
4.2
1967
.177
8.8
—4.
777
9.6
—3.
977
5.1
—8.
478
0.5
—3.
078
3.5
1967
.277
5.6
—24
.878
4.6
—15
.878
1.2
—19
.277
6.3
—24
.180
0.4
1967
.379
6.5
—19
.679
6.6
—19
.579
0.4
—25
.780
0.5
—15
.681
6.1
1967
.483
5.4
0.1
827.
6—
7.7
817.
9—
17.4
833.
1—
2.2
835.
3
1968
.185
9.8
1.1
849.
2—
9.5
834.
8—
23.9
855.
8—
2.9
858.
719
68.2
863.
1—
13.3
849.
0—
27.4
832.
9—
43.5
863.
8—
12.6
876.
419
68.3
868.
6—
23.9
857.
0—
22.5
843.
9—
48.6
869.
1—
23.4
892.
5
AFE
10.2
12.7
22.7
9.7
Third
Qua
rter o
f For
ecas
t19
66.1
756.
20.
374
7.1
—8.
874
4.1
—11
.874
8.0
—7.
975
5.9
1966
.277
8.1
7.4
764.
4—
6.3
761.
3—
9.4
772.
72.
077
0.7
1966
.379
0.9
16.7
781.
47.
277
9.2
5.0
788.
414
.277
4.2
1966
.412
.379
0.1
6.6
789.
66.
179
7.9
14.4
783.
5
1967
.178
2.9
—17
.578
8.9
—11
.579
0.8
—9.
678
5.3
—15
.180
0.4
1967
.278
2.5
—33
.679
7.6
—18
.580
0.1
—16
.078
4.7
—31
.481
6.1
1967
.382
6.3
—9.
083
0.1
—5.
283
0.7
—4.
682
2.6
—12
.783
5.3
1967
.485
9.0
0.3
854.
3—
4.4
852.
2—
6.5
855.
5—
3.2
858.
7
1968
.185
7.5
—18
.985
0.8
—25
.684
6.7
—29
.786
1.1
—15
.387
6.4
1968
.286
6.9
—25
.685
8.4
—34
.185
4.2
—38
.386
8.5
—24
.089
2.5
AFE
14.2
12.8
13.7
14.0
(con
tinue
d)
TAB
LE 4
.1P
(con
clud
ed)
1967
.283
2.4
—26
.386
1.5
2.8
864.
25.
5
-S P1 C z C P1 C P1
C', 0 r) -I
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Four
th Q
uarte
r of F
orec
ast
.
1966
.177
3.5
2.8
764.
6—
6.1
763.
3—
7.4
764.
6—
6.1
770.
719
66.2
795.
921
.778
3.0
8.8
782.
28.
079
2.2
18.0
774.
219
66.3
803.
820
.379
5.6
12.1
795.
411
.980
5.4
21.9
783.
519
66.4
803.
83.
480
0.7
0.3
802.
62.
280
8.6
8.2
800.
4
1967
.179
0.6
—25
.580
3.1
—13
.080
7.1
—9.
079
5.8
—20
.381
6.1
1967
.281
0.7
—24
.683
3.5
—1.
883
7.4
2.1
805.
3—
30.0
835.
319
67.3
851.
4—
7.3
860.
31.
686
2.7
4.0
845.
9—
12.8
858.
719
67.4
856.
3—
20.1
855.
8—
20.6
856.
8—
19.6
861.
9—
14.5
876.
4
1968
.186
3.1
—29
.486
1.0
—31
.586
1.0
—31
.586
6.2
—26
.389
2.5
AFE
17.2
1966
.178
9.0
.
14.8
782.
5
Fifth
Qua
rter
8.3
of F
orec
ast
783.
29.
078
2.7
8.5
•
774.
219
66.2
810.
527
.079
9.0
15.5
799.
215
.780
9.5
26.0
783.
519
66.3
813.
513
.180
6.4
6.0
806.
86.
481
7.4
17.0
800.
419
66.4
816.
0—
0.1
815.
6—
0.5
818.
01.
982
3.0
6.9
816.
1
1967
.181
7.5
—17
.883
6.1
0.8
840.
082
5.8
—32
.985
8.7
10.6
10.6
16.5
4.7
815.
3—
20.0
835.
3
1967
.385
0.3
—26
.186
2.1
—14
.386
3.3
—13
.185
3.3
—23
.187
6.4
1967
.486
7.1
—25
.486
8.1
—24
.486
8.3
—24
.287
1.0
—21
.589
2.5
AFE
18.8
9.1
10.1
19.5
Sixt
h Q
uarte
rof F
orec
ast
1966
.180
3.4
19.9
798.
114
.679
9.1
15.6
799.
516
.078
3.5
1966
.281
8.7
18.3
807.
97.
580
8.7
8.3
820.
019
.680
0.4
1966
.382
6.2
10.1
819.
73.
682
0.3
4.2
832.
416
.381
6.1
1966
.484
3.8
8.5
845.
09.
784
7.6
12.3
844.
28.
983
5.3
1967
.184
0.4
—18
.386
3.7
5.0
867.
38.
683
6.5
—22
.285
8.7
1967
.283
0.8
—45
.686
4.2
—12
.286
7.0
—9.
483
1.9
—44
.587
6.4
1967
.385
9.5
—33
.087
3.2
—19
.387
5.6
—16
.986
1.6
—30
.989
2.5
zA
FE
22.0
10.3
10.8
22.6
Fore
cast
One
Yea
r Ahe
ad19
66.1
746.
9—
2.9
740.
1—
9.7
733.
8—
16.0
741.
4—
8.4
749.
819
66.2
770.
69.
675
8.1
—2.
975
1.5
—9.
576
6.2
5.2
761.
019
66.3
780.
99.
977
2.0
1.0
766.
9—
4.1
779.
08.
077
1.0
1966
.478
8.2
6.0
783.
21.
077
9.3
—2.
978
9.0
6.8
782.
2
1967
.178
0.4
—5.
678
5.1
—0.
978
4.1
—1.
978
3.3
—2.
778
6.0
1967
.278
4.9
—23
.979
7.7
—11
.179
7.3
—11
.578
4.7
—24
.180
8.8
1967
.381
6.2
—11
.481
9.2
—8.
481
6.6
—11
.081
4.9
—12
.782
7.6
1967
.483
8.9
—7.
783
4.6
—12
.082
9.4
—17
.284
0.0
—6.
684
6.6
1968
.185
5.2
—10
.584
8.9
—16
.884
0.4
—25
.385
4.8
—10
.986
5.7
AFE
9.7
7.0
11.0
9,4
TAB
LE 4
.2A
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
Wha
rton-
EFU
Mod
el, C
onsu
mpt
ion
— C C) 0 z 0 rn
1966
.144
5.5
1966
.245
9.2
1966
.347
0.8
1966
.447
5.2
—5.
2.4
47.2
3.5
462.
92.
646
7.8
2.0
471.
7
—3.
544
7.9
7.2
462.
2—
0.4
461.
9—
1.5
465.
7
—2.
844
3.7
6.5
457.
3—
6.3
456.
2—
12.0
—7.
545
8.7
—14
.547
0.3
477.
5
—4.
745
0.7
2.2
455.
72.
146
8.2
4.3
473.
2
5.1
480.
90.
549
1.1
1.1
496.
6
—3.
850
2.7
6
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
.
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
.A
djus
tmen
tsA
djus
tmen
tsA
djus
tmen
ts.
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
,Er
ror
Val
ueEr
ror
nary
Val
ue
Firs
t Qua
rter o
f For
ecas
t—
7.0
446.
01.
645
7.9
0 r19
67.1
483.
93.
048
1.3
0.4
475.
9—
5.0
469.
3—
11.6
486.
019
67.2
488.
1—
3.0
485.
2.
—5.
948
3.0
—8.
147
7.3
—13
.8.
491.
619
67.3
497.
91.
349
0.1
—6.
549
0.5
—6.
148
3.5
—13
.149
7.7
1967
.4*5
02.4
—0.
3
.50
2.8
0.1
504.
21.
550
3.2
0.5
494.
1—
8.6
498.
9
1968
.1*5
14.6
—4.
8.
.
514.
9—
4.5
513.
8—
5.6
506.
4—
13.0
493.
3—
26.1
519.
60.
219
68.2
526.
9—
0.6
521.
7—
5.8
527.
1—
0.4
504.
3—
23.2
527.
4—
0.1
1968
.353
5.4
—6.
852
7.2
—15
.053
7.5
—4.
719
68.4
548.
61.
753
5.7
—11
.254
8.7
1.8
AFE
**2
.9A
FE2.
95.
46.
4'
16.2
2.6
530.
9—
11.3
537.
751
1.3
—9.
2—
30.9
514.
5—
32.4
519.
452
7.5
542.
254
6.9
Seco
nd Q
uarte
r of F
orec
ast
1966
.145
3.4
—1.
445
5.9
1.1
454.
90.
145
1.2
—3.
645
4.4
—0.
445
4.8
1966
.246
8.2
3.2
473.
28.
247
0.3
5.3
465.
80.
846
7.3
2.3
465.
019
66.3
477.
86.
347
4.9
3446
6.9
—4.
646
3.0
—8.
547
8.6
7.1
471.
519
66.4
480.
40.
847
7.0
—2.
646
8.2
—11
.446
4.3
—15
.348
2.3
2.7
479.
619
67.1
489.
3—
0.5
488.
3—
1.5
480.
5—
9.3
476.
3—
13.5
490.
81.
048
9.8
1967
.249
6.5
—0.
549
0.1
—6.
948
7.1
—9.
948
3.7
—13
.350
0.6
3.6
497.
019
67.3
505.
52.
049
6.6
—6.
949
7.0
—6.
549
2.1
—11
.449
9.3
—4.
250
3.5
1967
.4*5
069
—13
.851
8.7
—2.
051
3.3
—7.
451
1.4
—9.
350
4.6
—16
.152
1.4
0.7
520.
7
1968
.1*5
19.7
—9.
452
5.3
—3.
852
2.9
—6.
251
2.4
—16
.750
3.2
—25
.953
0.6
1.5
529.
119
68.2
530.
6—
11.5
520.
1—
22.0
520.
0—
22.1
505.
0—
37.1
530.
6—
11.5
542.
119
68.3
540.
0—
7.8
529.
5—
18.3
528.
6—
19.2
516.
3—
31.5
542.
6—
5.2
547.
8A
FE*
5.2
AFE
3.6
7.7
10.4
16.1
3.7
Third
Qua
rter o
f For
ecas
t0
1966
.146
1.8
—2.
346
3.6
—0.
546
1.3
—2.
845
9.4
—4.
646
3.3
—0.
846
4.1
1966
.247
7.2
8.9
481.
713
.447
7.3
9.0
474.
56.
247
8.1
9.8
468.
319
66.3
483.
55.
648
1.1
3.2
47.3
.1—
4.8
471.
448
5.4
7.5
477.
919
66.4
—1.
648
3.8
—4.
747
4.9
—13
.647
4.2
—14
.348
8.2
—0.
348
8.5
1967
.149
1.7
—4.
049
1.7
—4.
048
45—
11.2
483.
3—
12.4
494.
2—
1.5
495.
719
67.2
'502
.6—
1.3
495.
249
3.0
492.
150
4.2
0.3
503.
919
67.3
509.
2—
12.3
500.
1—
21.4
501.
2—
20.3
499.
2—
22.3
514.
2—
7.2
521.
5—
(con
tinue
d)
TAB
LE 4
.2A
(con
tinue
d)
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rea
lized
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rA
djus
tmen
tsPr
elim
i-V
alue
Erro
r nar
y V
alue
Third
Qua
rter o
f For
ecas
t (co
ntin
ued)
1967
.4*5
263
—3.
153
0.8
0.4
520.
9—
9.5
519.
5—
10.9
516.
1—
14.3
1968
.1*5
258
—17
.953
2.3
—11
.452
8.3
—15
.451
8.2
—25
.551
4.1
—29
.653
7.6
—10
.152
3.3
—24
.452
0.6
—27
.151
4.7
—33
.0
5.8
10.5
13.6
15.5
535.
24.
853
0.4
AFE
1966
.119
66.2
1966
.319
66.4
1967
.119
67.2
1967
.319
67.4
470.
048
5.3
490.
149
0.8
0\ a C) 0 z 0 a r) 0 a 0 C)
C)
C) a a 0
2.6
471.
610
.649
1.6
3.3
487.
1—
3.6
488.
6
528.
0—
15.7
543.
753
8.3
—9.
454
7.7
Four
th Q
uarte
r of F
orec
ast
4.2
469.
11.
746
7.7
0.3
16.9
486.
411
.748
4.2
9.5
0.3
479.
2—
7.6
478.
4—
8.4
—5.
848
0.1
—14
.348
0.2
—14
.2
496.
8—
5.8
496.
3—
6.3
490.
5—
12.1
490.
7—
11.9
514.
7—
7.2
504.
8—
17.1
504.
3—
17.6
504.
2—
17.7
517.
7—
13.5
507.
3—
23.9
509.
9—
21.3
508.
6—
22.6
*529
3—
15.7
5.7
-
6.0
467.
414
.347
4.7
6.3
486.
8—
0.7
494.
4
—6.
350
2.6
1.6
521.
9—
5.1
531.
2
473.
448
9.0
493.
149
3.7
496.
352
3.5
526.
1
534.
9—
10.1
522.
7—
22.3
522.
3—
22.7
520.
4—
24.6
532.
5—
12.5
545.
0
1968
.1*5
322
—17
.153
8.7
—10
.653
2.9
—16
.452
3.9
—25
.452
1.2
—28
.153
3.5
—15
.854
9.3
AFE
*8.
8A
FE7.
512
.614
.915
.37.
6
Fifth
Qua
rter
of F
orec
ast
1966
.147
4.3
0.5
475.
92.
147
3.3
—0.
547
3.1
—0.
748
2.3
8.5
473.
819
66.2
490.
67.
049
4.4
10.8
489.
05.
448
8.6
5.0
496.
613
.048
3.6
1966
.349
6.6
3.9
493.
30.
648
5.4
—7.
348
4.5
—8.
250
0.9
8.2
492.
719
66.4
499.
1—
2.2
496.
0—
5.3
488.
3—
13.0
488.
6—
12.7
499.
7—
1.6
501.
3
1967
.150
9.7
—10
.950
4.8
—15
.850
1.1
—19
.550
1.5
—19
.151
5.3
—5.
352
0.6
1967
.252
0.0
—11
.651
0.1
—21
.551
0.8
—20
.851
0.2
—21
.453
4.2
2.6
531.
619
67.3
525.
6—
20.2
511.
7—
34.1
515.
3—
30.5
514.
0—
31.8
526.
5—
19.3
545.
819
67.4
*534
0—
16.6
542.
6—
8.0
530.
6—
20.0
531.
4—
19.2
529.
9—
20.7
539.
7—
10.9
550.
6
AFE
8.0
13.8
14.5
15.0
8.7
rn
Six
thQ
uarte
r of F
orec
ast
1966
.148
1.3
—1.
448
2.9
0.2
480.
5—
2.2
480.
2—
2.5
490.
98.
248
2.7
1966
.249
5.3
5.8
498.
18.
649
3.2
3.7
493.
03.
553
0.6
14.1
489.
519
66.3
502.
12.
549
8.5
—1.
149
1.6
—8.
049
1.7
—7.
950
5.1
5.5
499.
619
66.4
508.
7—
10.6
505.
5—
13.8
499.
0—
20.3
500.
0—
19.3
514.
6—
4.7
519.
3
1967
.151
8.3
—12
.O51
3.0
—17
.351
1.1
—19
.251
2.5
—17
.852
6.8
—3.
553
0.3
1967
.252
2.1
—24
.151
2.7
—33
.551
4.6
—31
.651
4.7
—31
.553
1.1
—15
.154
6.2
1967
.353
3.3
—18
.151
9.6
—31
.852
4.2
—27
.252
3.6
—27
.853
2.4
—19
.055
1.4
AFE
10.6
15.2
16.0
15.8
10.0
(con
tinue
d)
0 00T
AB
LE4.
2A (c
oncl
uded
)
0 z C — 0 r71 r (/) 0 — (-)
t-n > 0
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
-F
orec
ast
One
Yea
r Ahe
ad19
66.1
457.
6—
1.6
459.
50.
345
8.3
—cL
945
5.5
—3.
746
4.2
5.0
459.
219
66.2
472.
46.
547
7.3
11.4
474.
08.
147
0.4
4.5
473.
07.
146
5.9
1966
.348
0.5
4.4
467.
8—
8.3
461.
9—
14.2
467.
2—
8.9
481.
15.
047
6.1
1966
.448
3.3
—0.
648
0..2
—33
472.
2—
11.7
469.
3—
14.6
485.
41.
548
3.9
1967
.149
0.4
—1.
848
9.4
—2.
848
2.8
—9.
447
9.9
—12
.349
1.8
—0.
449
2.2
1967
.250
0.4
—3.
049
3.8
—9.
649
1.8
—11
.648
9.3
—14
.150
4.9
1.5
503.
419
67.3
507.
5—
5.7
498.
5—
14.7
499.
6—
13.6
495.
8—
17.4
509.
3—
3.9
513.
219
67.4
*516
.2—
8.5
521.
8—
2.9
515.
2—
9.5
514.
1—
10.6
508,
8—
15.9
522.
0—
2.7
524.
7
1968
.1*5
23.0
—12
.352
7.8
—7.
552
4.5
—10
.951
5.2
—20
.250
7.9
—27
.452
7.9
—7.
553
5.3
*49
.
AFE
3.7
7.9
11.1
13.2
.
3.8
TAB
LE 4
.2P
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
Adj
ustm
ents
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alU
eEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ue
•Fi
rst Q
uarte
rof
For
ecas
t19
66.1
452.
2—
5.6
450.
1—
7.7
444.
6—
13.2
448.
7—
9.1
457.
819
66.2
464.
72.
845
9.4
—2.
545
3.3
—8.
646
1.4
—0.
546
1.9
1966
.347
0.6
—0.
646
6.5
—4.
746
1.3
—9.
946
8.4
—2.
847
1.2
1966
.447
8.2
3.7
475.
91.
447
0.0
—4.
547
7.1
2.6
474.
5
1967
.147
8.0
—2.
947
8.4
—2.
547
3.9
—7.
047
9.1
—1.
848
0.9
1967
.248
0.2
—9.
648
3.6
—6.
247
8.7
—11
.148
0.7
—9.
148
9.8
1967
.349
2.9
—2.
849
2.2
—3.
548
5.4
—10
.349
2.7
—3.
049
5.7
1967
.449
8.4
—4.
249
5.4
—7.
248
7.5
—15
.150
1.5
—1.
150
2.6
1968
.151
8.2
—2.
451
4.5
—6.
150
4.5
—16
.151
6.6
—4.
052
0.6
1968
.253
3.3
3.0
526.
9—
3.4
515.
4—
14.9
531.
41.
053
0.3
1968
.353
0.5
—14
.452
4.1
—20
.851
4.3
—30
.653
0.6
—14
.354
4.9
1968
.454
4.3
—6.
453
4.2
—16
.552
2.3
—28
.454
4.7
—6.
055
0.7
AF
E4.
96.
914
.14.
6
Com
paris
on o
f Ex
Post
For
ecas
ts, W
harto
n M
odel
, Con
sum
ptio
n
C C.) > '4)
— z C.) C ru — U) 0 F ¶1) 0 tTl r '4, S C
(con
tinue
d)
TAB
LE 4
.2P
(con
tinue
d)
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
S 0 — C) 0 Cl) 0 — 0
Seco
nd Q
uarte
r of F
orec
ast
C) 0 z
1966
.145
9.3
—2.
645
5.6
—6.
345
1.7
—10
.245
4.7
—7.
246
1.9
1966
.247
2.2
1.0
464.
7—
6.5
460.
7—
10.5
460.
4—
2.8
471.
219
66.3
480.
05.
547
4.4
—0.
147
0.9
—3.
647
7.8
3.3
474.
519
66.4
485.
14.
248
1.3
0.4
477.
5—
3.4
485.
24.
348
0.9
1967
.148
2.0
—7.
848
3.3
—6.
548
0.6
—9.
248
3.4
—6.
448
9.8
1967
.248
3.7
—12
.048
9.1
—6.
648
6.2
—9.
548
3.8
—11
.949
5.7
1967
.349
4.5
—8.
149
3.8
—8.
848
9.5
—13
.149
7.0
—5.
650
2.6
1967
.451
6.4
—4.
251
1.8
—8.
850
6.4
—14
.251
6.1
—4.
552
0.6
1968
.152
8.4
—1.
952
2.9
—7.
451
5.9
—14
.452
7.8
—2.
553
0.3
1968
.252
9.9
—15
.052
1.7
—23
.251
4.1
—30
.852
9.7
—15
.254
4.9
1968
.353
6.0
—14
.752
8.5
—22
.252
2.5
—28
.453
5.4
—15
.355
0.7
AFE
1966
.146
7.7
—3.
546
4.0
Third
Qua
rter
—7.
2
of F
orec
ast
462.
5—
8.7
462.
2—
9.0
471.
219
66.2
481.
26.
747
3.9
—0.
647
2.5
—2.
047
7.9
3.4
474.
519
66.3
487.
06.
148
2.0
1.1
480.
8—
0.1
486.
55.
648
0.9
1966
.449
0.0
10.2
486.
8—
3.0
485.
8—
4.0
492.
12.
348
9.8
7.0
8.8
r C)
13.4
7.2
1967
.148
5.1
—10
.648
8.7
—7.
048
8.6
—7.
148
6.7
—9.
049
5.7
1967
.248
5.2
—17
.449
3.2
—9.
449
2.8
—9.
848
7.0
—15
.65.
02.6
1967
.351
2.4
—8.
251
2.5
—8.
151
1.2
—.9
.451
1.1
—9.
552
0.6
1967
.452
8.2
—2.
152
4.4
—5.
952
2.2
—8.
152
8.6
—1.
753
0.3
1968
.152
4.6
—20
.352
0.4
—24
.551
7.7
—27
.252
6.2
—18
.754
4.9
1968
.253
4.4
—16
.452
7.9
—22
.852
5.3
—25
.453
4.4
—16
.355
0.7
AFE
9.2
9.0
10.2
9.1!
Fou
rth
Qua
rter
ofFo
reca
st19
66.1
477.
02.
547
3.4
—1.
047
2.5
—2.
047
1.7
—2.
847
4.5
1966
.248
8.5
7.6
481.
50.
648
1.0
0.1
486.
45.
548
0.9
1966
.349
2.7
2.9
488.
4—
1.4
488.
0—
1.8
494.
24.
448
9.8
1966
.449
5.5
—0.
249
3.3
—2.
449
3.4
—2.
349
8.4
2.7
495.
7
1967
.148
7.0
—15
.649
3.8
—8.
849
4.8
—7.
849
0.7
—11
.950
2.6
1967
.250
1.8
—18
.851
3.3
—7.
351
3.7
—6.
949
9.9
—20
.752
0.6
1967
.352
4.7
—5.
652
6.7
—3.
652
6.4
—3.
952
3.7
—6.
653
0.3
1967
.452
4.8
—20
.152
2.7
—22
.252
2.0
—22
.952
7.8
—17
.154
4.9
rTl
1968
.152
9.7
—21
.052
7.7
—23
.052
6.9
—23
.853
1.2
—19
.555
0.7
AFE
10.5
7.8
7.9
10.1
-c C
,,
Fift
hQ
uarte
r of F
orec
ast
019
66.1
482.
61.
748
0.0
—0.
947
9.6
—1.
347
8.6
—2.
348
0.9
.
1966
.249
5.4
5.6
488.
6—
1.2
488.
0—
1.8
494.
4—
4.6
489.
819
66.3
499.
33.
649
4.8
—0.
949
4.0
—1.
750
1.2
5.5
495.
719
66.4
500.
9—
1.7
499.
3—
3.3
499.
2—
3.4
505.
83.
250
2.6
(con
tinue
d)
TAB
LE 4
.2P
(con
clud
ed)
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
.A
djus
tmen
tsA
djus
tmen
tsA
djus
tmen
tsA
djus
tmen
tsR
evis
edW
as M
ade
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ue
0. rn 0 z 0 — C.) 0 'I) 0 C
.)Q
uarte
r of F
orec
ast
(con
tinue
d)
11.2
7.4
1967
.119
67.2
1967
.319
67.4
502.
751
1.3
522.
453
3.4
—17
.9—
19.0
—22
.5—
17.3
512.
252
5.5
524.
853
0.9
—8.
4—
4.8
—20
.1
—19
.8
512.
652
4.7
523.
252
8.9
—8.
0—
5.6
—21
.7—
21.8
502.
850
9.7
524.
053
6.0
—17
.8—
20.0
—20
.9—
14.7
520.
653
0.3
544.
955
0.7
AFE
.
1966
.119
66.2
1966
.319
66.4
•
489.
850
0.7
504.
751
6.6
. 0.0 5.0
2.1
—4.
0
487.
749
4.1
500.
451
5.5
Sixt
hQ
uarte
r—
2.1
—1.
6—
2.2
—5.
1
of F
orec
ast
487.
949
4.4
500.
551
6.3
—1.
9—
1.3
—2.
l—
4.3
•
486.
850
0.0
508.
551
8.0
—3.
04.
3. 5.9
—2.
6
489.
849
5.7
502.
652
0.6
8.2
11.2
1967
.151
3.1
—17
.252
5.1
—5.
252
6.0
—4.
351
3.3
—17
.053
0.3
1967
.250
8.8
—36
.152
5.1
—19
.852
5.4
—19
.550
9.3
—35
.654
4.9
1967
.352
9.9
—20
.853
2.9
—17
.853
3.0
—17
.753
1.2
—19
.555
0.7
AFE
12.2
7.7
7.3
12.6
Fore
cast
One
Yea
r Ahe
ad19
66.1
464.
0—
2.3
460.
7—
5.6
457.
8—
8.5
459.
3—
7.0
46.3
1966
.247
6.6
4.5
469.
8—
2.3
466.
8—
5.3
471.
5—
0.6
472.
119
66.3
482.
53.
447
7.8
—1.
347
5.2
—3.
948
1.7
2.6
479.
119
66.4
487.
22.
048
4.3
—0.
948
1.6
—3.
648
8.2
3.0
485.
2
1967
.148
3.0
—9.
248
6.0
—6.
248
4.4
—7.
848
4.9
—7.
349
2.2
1967
.248
7.7
—14
.449
4.8
—7.
349
2.8
—9.
348
7.8
—14
.350
2.1
1967
.350
6.1
—6.
250
6.3
—6.
050
3.1
—9.
250
6.1
—6.
251
2.3
1967
.451
6.9
—7.
751
3.5
—11
.150
9.5
—15
.151
8.5
—6.
152
4.6
1968
.152
5.2
—11
.452
1.3
—15
.351
6.2
—20
.452
5.4
—11
.253
6.6
AFE
6.7
6.2
9.2
6.4
—
TA
BLE
4.3A
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
Wha
rton-
EFU
Mod
e!, I
nves
tmen
t
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Lx A
nte
with
AR
with
OG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter o
f For
ecas
t
. 8 z 0 rn 0 r 0 — rn 0
1966
.110
9.5
—2.
211
6.3
4.6
117.
86.
110
8.9
—2.
810
9.9
—1.
811
1.7
1966
.211
4.9
0.0
122.
8—
7.9
124.
09.
111
4.4
—0.
511
4.5
—0.
411
4.9
1966
.311
7.9
3.2
116.
51.
811
3.0
—1.
710
7.8
—6.
911
7.3
2.6
114.
719
66.4
118.
0—
3.6
114.
4—
7.2
110.
2—
11.4
104.
2—
17.5
119.
1—
2.5
121.
6
1967
.111
3.9
8.5
110.
75.
310
7.2
1.8
104.
9—
0.5
114.
79.
110
5.4
1967
.210
9.7
4.9
107.
12.
310
5.1
0.3
103.
2—
1.6
111.
76.
910
4.8
1967
.311
2.1
—0.
711
0.9
—1.
910
9.1
—3.
710
7.1
—5.
711
2.0
—0.
811
2.8
1967
.4*1
13.6
—2.
611
4.7
—1.
511
6.8
0.6
113.
7—
2.5
108.
0—
8.2
114.
3—
1.9
116.
2
1968
.1*1
257
8.9
.
9.0
121.
85.
011
5.6
—1.
210
6.9
--9.
912
8.0
11.2
116.
819
68.2
126.
3.—
0.3
125.
4—
1.2
128.
31.
710
7.9
—18
.712
7.0
0.4
126.
619
68.3
122.
7—
2.5
123.
3—
1.9
125.
40.
210
7.1
—18
.112
5.2
012
5.2
1968
.412
8.2
—5.
712
1.9
—12
.012
3.6
—10
.310
6.0
—27
.912
7.8
—6.
113
3.9
AFE
*3.
2A
FE3.
54.
34.
59.
93.
6
Seco
nd Q
uarte
r of F
orec
ast
1966
.111
1.0
—5.
612
0.7
4.1
119.
42.
810
9.6
—7.
011
2.4
—4.
211
6.6
1966
.211
5.9
3.8
128.
015
.912
6.1
14.0
114.
52.
411
6.0
3.9
112.
119
66.3
120.
6—
0.7
119.
0—
2.3
111.
7—
9.6
105.
5—
15.8
121.
50.
212
1.3
1966
.411
5.9
6.9
112.
33.
310
3.2
—5.
897
.0—
12.0
117.
28.
210
9.0
1967
:111
3.9
12.7
113.
111
.910
5.1
3.9
101.
40.
211
6.9
15.7
101.
2
1967
.211
7.1
4.0
108.
0—
5.1
104.
8—
8.3
102.
7—
10.4
120.
87.
711
3.1
1967
.311
8.4
0.0
109.
2—
9.2
108.
8—
9.6
105.
8—
12.6
116.
2—
2.2
118.
4
1967
.4*1
16.1
3.8
122.
510
.212
2.7
10.4
118.
15.
811
1.5
—0.
812
0.8
8.5
112.
3C
)
1968
.1*1
266
2.6
128.
54.
512
4.6
0.6
113.
0—
11.0
102.
7—
21.3
132.
98.
912
4.0
1968
.212
6.3
1.1
123.
1—
2.1
121.
6—
3.6
100.
6—
24.6
125.
20.
012
5.2
1968
.312
6.5
—7.
412
0.9
—13
.011
9.2
—14
.710
1.2
—32
.712
9.1
—4.
813
3.9
AFE
*4.
4A
FE5.
27.
18.
112
.75.
8
Third
Qua
rter o
f For
ecas
t19
66.1
112.
3—
1.5
120.
26.
411
5.7
1.9
111.
1—
2.7
114.
91.
111
3.8
1966
.211
7.9
—0.
812
8.5
9.8
123.
14.
411
6.5
—2.
212
0.6
1.9
118.
719
66.3
120.
311
.612
0.6
11.9
113.
95.
211
1.6
2.9
123.
114
.410
8.7
1966
.411
5.1
10.3
114.
29.
410
5.5
0.7
104.
90.
111
7.4
12.6
104.
8
1967
.111
8.8
9.1
108.
7—
1.0
107.
2—
2.5
108.
8—
0.9
121.
111
.410
9.7
1967
.211
7.8
—0.
810
9.3
—9.
311
1.2
—7.
411
2.3
—6.
311
7.4
—1.
211
8.6
1967
.311
7.8
3.3
109.
3—
5.2
111.
2—
3.3
112.
3—
2.2
117.
42.
911
4.5
—
(con
tinue
d)
TAB
LE 4
.3A
(con
tinue
d)0
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
OG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Was
Mad
e V
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsPr
elim
i-V
alue
Erro
r nar
y V
alue
L,I
Third
Qua
rter o
f For
ecas
t (co
ntin
ued)
121.
72.
211
8.1
—1.
4
122.
911
8.1
116.
7
0.3
—15
.8
—2.
8
113.
511
1.2
13l.5
—9.
1—
22.7
12.0
111.
210
5.5
—11
.4—
28.4
5.9
126.
412
2.2
3.8
11.7
C.) 0 z C 0 m C,) 0 ,.rl
C.) 0
127.
47.
911
9.5
1968
.1*
123.
0—
0.4
126.
94.
312
2.6
1968
.212
2.2
—11
.713
3.9
A,F
E*5.
4A
FE6.
17.
1
Fou
rth
Qua
rter
1966
.11
12.9
—7.
5
.
120.
419
66.2
120.
214
.110
6.1
1966
.312
0.8
16.3
104.
519
66.4
116.
23.
111
3.1
1967
.111
0.1
—5.
011
5.1
1967
.211
2.7
—2.
111
4.8
1967
311
8.5
—3.
212
1.7
1967
.4*1
23.2
5.1
122.
54.
411
8.2
0.1
115.
7—
2.4
115.
8—
2.3
122.
94.
811
8.1
120.
813
1.1
120.
511
7.3
6.0
of F
orec
ast
0.4
25.0
16.0 4.2
114.
912
3.8
114.
210
9.2
7.3
—5.
517
.7 9.7
113.
2
111.
711
9.4
113.
0
—1.
9
—8.
713
.3 8.5
—3.
9
110.
810
8.9
107.
8—
4.0
117.
412
4.5
126.
510
9.5
—3.
018
.4
—7.
31
1•.1
—12
.8
—3.
6
109.
7
113.
2—
2.7
22.0
118.
1
114.
1—
8.5
—5.
4—
0.7
5.0
112.
7
114.
712
6.7
—2.
4
—7.
011
.912
5.3
3.6
1968
.1*1
210
—10
.312
4.0
—7.
312
1.0
—10
.311
3.0
18.3
112.
7—
18.6
120.
7—
10.6
131.
3A
FE*
7.4
AFE
7.0
8.3
8.4
7.6
9.1
Fifth
Qua
rter
of F
orec
ast
1966
.111
2.9
5.1
118.
811
.011
1.5
3.7
112.
85.
011
9.8
12.0
107.
819
66.2
17.6
127.
325
.411
8.6
16.7
119.
918
.012
7.4
25.5
101.
919
66.3
122.
39.
512
2.1
9.3
116.
63.
811
6.1
3.3
129.
016
.211
2.8
1966
.411
6.7
—2.
01
0.1
112.
3—
6.4
113.
5—
5.2
118.
80.
111
8.7
1967
.111
5.7
4.5
115.
64.
411
3.0
1.8
115.
54.
311
8.0
6.8
111.
219
67.2
124.
72.
711
2.6
—9.
411
6.4
—5.
611
8.3
—3.
713
4.9
12.9
122.
019
67.3
120.
80.
5ilO
.6—
9.7
116.
5—
3.8
118.
2—
2.1
120.
30.
012
0.3
1967
.4*1
17.2
—9.
612
1.0
—5.
811
8.1
—8.
711
6.8
—10
.011
7.9
—8.
911
9.3
—7.
512
6.8
C)
*6.4
AFE
6.0
9.8
6.5
6.3
10.1
Sixt
hQ
uart
er o
f For
ecas
t
1966
.1,
-11
2.3
8.7
118.
514
.911
1.9
8.3
112.
89.
212
7.7
24.1
103.
619
66.2
118.
48.
212
4.7
14.5
117.
16.
911
8.4
8.2
128.
117
.911
0.2
1966
.312
2.1
3.7
121.
43.
011
6.5
—1.
911
6.1
—2.
313
0.3
11.9
118.
419
66.4
120.
45.
612
1.5
6.7
116.
01.
211
6.8
2.0
123.
99.
111
4.8
C19
67.1
120.
62.
211
8.4
..0
.011
7.5
—0.
911
9.6
.1.2
128.
510
.111
8.4
1967
.212
1.5
0.9
110.
6—
10.0
115.
9—
4.7
117.
1—
3.5
127.
56.
912
0.6
1967
.312
1.8
—7.
211
1.4
—17
.611
8.5
—10
.511
9.6
—9.
411
8.4
—10
.612
9.0
AFE
5.2
9.5
4.9
5.1
12.9
(con
tinue
d)
TAB
LE 4
.3A
(con
clud
ed)
"I 00
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
e V
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Fore
cast
One
Yea
r Ahe
ad19
66.1
111.
4—
4.2
119.
53.
911
6.9
1.3
110.
3—
5.3
113.
6—
2.0
11.5
.619
66.2
117.
24.
312
7.6
14.7
124.
211
.311
6.2
3.3
118.
96.
011
2.9
1966
.311
9.9
7.6
119.
26.
911
3.2
0.9
109.
4—
2.9
122.
19.
811
2.3
1966
.411
6.3
4.2
114.
52.
410
7.0
—5.
110
3.9
—8.
211
7.9
5.8
112.
1
1967
.111
4.1
6.1
111.
43.
410
6.8
—1.
210
6.2
—1.
811
6.3
8.3
108.
019
67.2
114.
31.
510
8.8
—4.
010
8.3
—4.
510
8.0
—4.
811
9.1
6.3
112.
819
67.3
116.
7—
0.2
109.
5—
7.4
110.
5—
6.4
111.
0—
5.9
117.
70.
811
6.9
1967
.4*1
19.2
2.7
121.
75.
211
9.8
3.3
116.
4—
0.1
111.
6—
4.9
122.
35.
811
6.5
1968
.1*1
24.0
0.4
126.
32.
712
2.6
—1.
111
3.8
—9.
91O
6.9
—16
.712
7.0
3.3
123.
6
3.5
AFE
4.0
5.2
4.5
6.0
5.0
C z 0 -4 C) 0
TAB
LE 4
.3P
Com
paris
on o
f Ex
Post
For
ecas
ts, W
harto
n M
odel
, inv
estm
ent
(con
tinue
d)
0 r) C,,
— z C 0 rn C,,
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Firs
t Qua
rter
of F
orec
ast
1966
.111
6.6
—0.
911
2.1
—5.
410
5.1
—12
.411
6.8
—0.
711
7.5
1966
.212
1.9
—0.
511
5.9
—6.
510
8.4
—14
.012
1.4
—1.
012
2.4
1966
.311
8.4
—1.
211
3.2
—6.
410
6.9
—12
.711
8.5
—1.
111
9.6
1966
.411
9.8
—6.
411
5.4
—10
.810
9.9
—16
.311
9.3
—6.
912
6.2
1967
.111
2.1
—1.
510
8.2
—5.
410
5.2
—8.
411
4.0
0.4
113.
619
61.2
106.
2—
3.2
104.
3—
5.1
102.
7—
6.7
107.
7—
1.7
109.
419
67.3
111.
6—
6.1
108.
8—
8.9
106.
5—
11.2
111.
7—
6.0
117.
719
67.4
113.
9—
9.4
110.
2—
13.1
106.
1—
17.2
115.
8—
7.5
123.
3
1968
.112
3.1
3.7
117.
8—
1.6
110.
2—
9.2
120.
91.
511
9.4
1968
.212
9.2
2.6
121.
5—
5.1
111.
2—
15.4
126.
3—
0.3
126.
619
68.3
122.
2—
3.0
114.
7—
10.5
105.
5—
19.7
125.
20.
012
5.2
1968
.412
4.7
—9.
211
7.1
—16
.810
8.0
—25
.912
7.0
—6.
913
3.9
AFE
4.0
8.0
14.1
2.8
.
TAB
LE 4
.3P
(con
tinue
d)
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
S0 0 rn C) 0 z 0 -I C)
Sec
ond
Qua
rter
of F
orec
ast
1966
.111
8.4
—4.
011
0.3
—12
.110
3.7
—18
.711
6.5
—5.
912
2.4
1966
.212
3.1
3.5
112.
5—
7.1
105.
2—
14.4
121.
51.
911
9.6
1966
.319
66.4
122.
412
1.2
—3.
87.
611
3.1
113.
2—
13.1
—0.
410
7.0
107.
9—
19.2
—5.
712
0.2
119.
7—
6.0
6.1
126.
211
3.6
1967
.111
3.4
4.0
108.
3—
1.1
105.
4—
4.0
114.
24.
810
9.4
C)
1967
.210
5.4
—12
.310
5.3
—12
.410
3.8
—13
.910
6.4
—11
.311
7.7
1967
.310
9.4
—13
.910
6.7
—16
.610
3.7
—19
.611
1.3
—12
.012
3.3
1967
.411
8.6
—0.
811
1.9
—7.
510
6.5
—12
.911
7.1
—2.
311
9.4
1968
.119
68.2
1968
.3
127.
612
5.7
121.
1
1.0
0.5
—12
.8
118.
111
3.3
111.
1
—8.
5—
11.9
—23
.8
109.
110
2.6
100.
9
—17
.5—
22.6
—33
.0
124.
512
7.3
122.
4
—2.
12.
1—
11.5
126.
612
5.2
133.
9
AFE
5.8
10.4
16.5
6.0
Third
Qua
rter
of F
orec
ast
1966
.112
0.1
0.5
111.
7—
7.9
109.
9—
9.7
117.
5—
2.1
119.
619
66.2
125.
3—
0.9
114.
9—
11.3
112.
5—
13.7
123.
2—
3.0
126.
219
663
124.
210
.611
5.1
1.5
113.
3—
0.3
122.
38.
711
3.6
1966
.412
2.7
13.3
115.
05.
611
4.5
5.1
123.
113
.711
3.6
1967
.111
2.6
—5.
110
9.6
—8.
111
0.8
—6.
911
3.8
—3.
911
7.7
1967
.210
4.7
—18
.610
7.5
—15
.810
9.8
—13
.510
5.9
—17
.412
3.3
1967
.311
3.6
—5.
811
3.1
—6.
311
4.5
—4.
911
1.7
—7.
711
9.4
1967
.412
6.0
—0.
612
0.9
—5.
812
0.3
—6.
312
2.5
—4.
112
6.6
1968
.112
2.1
—3.
111
4.4
—10
.811
2.2
—13
.012
5.2
0.0
125.
219
68.2
121.
2—
12.7
111.
3—
22.6
108.
5—
25.4
123.
6—
10.3
133.
9
AF
E7.
19.
69.
97.
1
Fou
rth
Qua
rter
of F
orec
ast
1966
.112
3.4
—2.
811
4.6
—11
.611
3.9
—12
.312
0.0
—6.
212
6.2
1966
.212
7.1
13.5
116.
63.
011
5.7
2.1
125.
411
.811
3.6
1966
.312
6.7
17.3
117.
78.
311
7.2
7.8
127.
217
.810
9.4
1966
.412
3.4
5.7
116.
3—
1.4
117.
3—
0.4
125.
67.
911
7.7
1967
.111
2.6
—10
.711
2.0
—11
.311
4.5
—8.
811
4.8
—8.
512
3.3
1967
.210
8.8
—10
.611
5.1
—4.
311
8.2
—1.
210
6.3
—13
.111
9.4
1967
.312
2.1
—4.
512
4.0
—2.
612
6.3
—0.
311
7.9
—8.
712
6.6
1967
.411
9.6
—5.
611
6.2
—8.
911
7.4
—7.
812
3.5
—1.
712
5.2
tTI
1968
.111
8.6
—15
.311
2.5
—21
.411
2.6
—21
.312
1.4
—12
.513
3.9
APE
9.6
8.1
6.9
9.8
Fifth
Qua
rter
of F
orec
ast
1966
.112
4.3
10.7
116.
52.
911
7.2
3.6
122.
28.
611
3.6
1966
.213
0.1
20.7
120.
210
.812
0.6
11.2
130.
120
.710
9.4
1966
.312
7.8
10.1
119.
31.
611
9.8
2.1
130.
012
.211
7.7
1966
.412
4.3
1.0
118.
5—
4.8
120.
4—
2.9
127.
23.
912
3.3
— 0(c
ontin
ued)
1966
.412
8.9
9.5
123.
612
8.9
9.5
119.
4
0\ . rn C.) 0 z 0 0 C (I, 0 C)
C)
TAB
LE 4
.3P
(con
clud
ed)
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Fifth
Qua
rter o
f For
ecas
t (co
ntin
ued)
1967
.111
6.2
—3.
211
8.3
—1.
112
1.1
1.7
115.
1—
4.3
119.
419
67.2
116.
6—
10.0
125.
8—
0.8
128.
62.
011
2.4
—14
.212
6.6
1967
.311
6.1
—9.
112
0.0
—5.
212
2.3
—2.
911
8.8
—6.
412
5.2
1967
.411
7.9
—16
.011
5.7
—18
.211
7.3
—16
.612
0.5
—13
.413
3.9
AFE
10.1
5.7
5.4
10.5
..
Sixt
hQ
uarte
rof
Fore
cast
1966
.112
6.9
14.4
119.
512
6.2
16.8
109.
419
66.2
130.
913
.212
1.0
132.
615
.011
7.7
1966
.312
9.3
6.0
120.
713
2.2
8.9
123.
3
C) I
10.1
120.
13.
312
1.2
10.7 3.5
—2.
612
0.8
—2.
54.
212
4.9
5.5
1967
.112
4.5
—2.
112
8.1
1.5
130.
13.
512
1.4
—5.
212
6.6
1967
.211
0.5
—14
.712
1.5
—3.
712
16—
L611
2.8
—12
.412
5.2
1967
.311
3.9
—20
.011
8.6
—15
.312
0.5
—13
.411
5.9
—18
.013
3.9
AFE
11.4
5.8
5.8
12.3
Fore
cast
One
Yea
r Ahe
ad19
66.1
119.
6—
1.8
112.
1—
9.3
108.
1—
13.3
117.
7—
3.7
121.
419
66.2
124.
33.
911
4.9
—5.
511
0.4
—10
.012
2.8
2.4
120.
419
66.3
122.
95.
711
4.7
—2.
511
1.1
—6.
112
2.0
4.8
117.
219
66.4
121.
74.
011
4.9
—2.
811
2.4
—5.
312
1.9
4.2
117.
7
1967
.111
2.6
—3.
410
9.5
—6.
510
8.9
—7.
111
4.2
—1.
811
6.0
106.
2—
11.2
108.
0—
9.4
108.
6—
8.8
106.
5—
10.9
117.
419
67.3
114.
1—
7.6
113.
1—
8.6
112.
7—
9.0
113.
1—
8.6
121.
719
67.4
119.
5—
4.1
114.
8—
8.8
112.
5—
11.1
119.
7—
3.9
123.
60
1968
.112
2.8
—3.
411
5.7
—10
.511
1.0
—15
.212
3.0
—3.
212
6.2
AFE
5.0
7.1
9.5
4.8
TAB
LE 4
.4A
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
Wha
rton-
EFU
Mod
el, G
NP
in C
onst
ant D
olla
rs
Firs
t Qua
rter o
f For
ecas
t
C 0 z 0 0 ru Cl, C — (-)
tTl
1968
.1*6
900
AFE
*
690.
30.
81.
169
0.4
3.0
1.2
680.
3—
8.9
663.
3—
25.9
699.
710
.568
9.2
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
1966
.163
0.9
—6.
063
6.4
—0.
563
7.9
1.0
629.
1—
7.8
632.
6—
4.3
636.
919
66.2
639.
60.
864
8.7
9.9
649.
210
.463
7.8
—1.
063
9.7
0.9
638.
819
66.3
653.
03.
664
9.8
0.4
643.
6—
5.8
636.
0—
13.4
654.
75.
364
9.4
1966
.465
5.2
—2.
065
0.6
—6.
664
4.6
—12
.663
5.6
—21
.665
9.7
2.5
657.
2
1967
.165
9.9
—4.
565
7.7
2.3
652.
2—
3.2
646.
0—
9.4
666.
911
.565
5.4
1967
.266
2.3
1.1
659.
3—
1.9
657.
8—
3.4
652.
9—
8.3
666.
45.
266
1.2
1967
.367
8.3
6.2
671.
4—
0.7
672.
40.
366
6.0
—6.
167
3.7
1.6
672.
119
67.4
*678
.00.
967
7.9
0.8
683.
26.
168
2.0
4.9
671.
1—
6.0
673.
1—
4.0
677.
1
1968
.269
9.8
—2.
469
6.7
—5.
570
4.4
2.2
675.
8—
26.4
700.
9—
1.3
702.
219
68.3
702.
8—
6.5
701.
1—
8.2
706.
9—
2.4
682.
3—
27.0
705.
1—
4.2
709.
319
68.4
716.
9—
0.8
705.
2—
12.5
708.
7—
9.0
681.
2—
36.5
715.
3—
2.4
717.
7
AFE
3.0
4.7
5.3
15.8
4.5
Seco
nd Q
uarte
r of F
orec
ast
1966
.163
8.6
—4.
264
5.9
3.1
644.
41.
663
6.1
—6.
764
2.6
—0.
264
2.8
1966
.264
6.7
2.7
659.
115
.165
5.7
11.7
644.
00.
064
8.4
4.4
644.
019
66.3
660.
83.
565
8.8
1.5
650.
2—
7.1
644.
7—
12.6
668.
110
.865
7.3
1966
.465
8.1
2.5
656.
10.
564
6.3
—9.
364
1.3
—14
.366
6.2
10.6
655.
6
1967
.166
4.6
5.2
668.
89.
465
9.8
0.4
655.
8—
3.6
671.
512
.165
9.4
1967
.267
5.2
6.2
665.
9—
2.8
665.
0—
3.7
662.
8—
5.9
677.
18.
466
8.7
1967
.368
0.4
12.8
677.
3—
0.3
681.
64.
067
7.5
—0.
167
6.5
—1.
167
7.6
1967
.4*6
81.1
5.8
696.
0—
9.1
695.
78.
869
4.7
7.8
686.
3—
0.6
698.
611
.768
6.9
1968
.1*6
945
—7.
270
0.5
—1.
270
0.5
—1.
268
6.7
—15
.067
4.6
—27
.171
2.0
10.3
701.
719
68.2
701.
1—
8.1
693.
3—
15.9
696.
1—
13.1
676.
7—
32.5
699.
1—
10.1
709.
219
68.3
707.
7—
7.3
703.
1—
11.9
704.
8—
10.2
689.
1—
25.9
708.
9—
6.1
715.
0A
FE*
5.9
AFE
5.7
6.4
7.6
12.9
7.8
Third
Qua
rter o
f For
ecas
t19
66.1
647.
0—
1.0
651.
13.
164
7.0
—1.
064
4.8
—3.
265
4.6
6.6
648.
019
66.2
655.
43.
566
4.9
13.0
658.
16.
265
2.8
0.9
661.
69.
765
1.9
1966
.366
4.4
8.7
664.
79.
065
8.7
3.0
658.
52.
867
9.1
23.4
655.
719
66.4
664.
78.
766
6.5
6.9
659.
4—
0.2
661.
82.
267
1.8
12.2
659.
6
1967
.166
4.7
—2.
267
3.9
7.0
668.
21.
367
0.3
3.4
668.
21.
366
6.9
1967
.268
2.2
8.0
672.
7—
1.5
675.
71.
567
8.5
4.3
678.
74.
567
4.2
1967
.369
3.3
5.9
681.
7—
5.7
689.
82.
469
1.6
4.2
692.
65.
268
7.4
— C
(con
tinue
d)-
TAB
LE 4
.4A
(con
tinue
d)
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
e V
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Four
th Q
uarte
rof
For
ecas
t
C (ID C C)
— C) > 0
1967
.166
9.4
1967
.269
4.6
1967
.370
2.7
1967
.4*7
049
—3.
067
8.7
10.6
683.
52.
869
0.1
1.5
6.3
677.
3—
0.5
691.
6—
9.8
702.
5
4.9
681.
17.
669
5.1
2.6
704.
9
8.7
669.
211
.170
1.0
5.0
708.
8
—3.
267
2.4
17.0
684.
08.
969
9.9
Third
Qua
rter o
f For
ecas
t (co
ntin
ued)
S rn C) 0 0 rn C
1967
.4*7
038
4.4
708.
08.
670
1.9
2.5
703.
84.
470
2.6
3.2
716.
316
.969
9.4
1968
.1*6
960
—12
.770
3.9
—4.
870
2.4
—6.
369
3.4
—15
.369
2.6
—16
.170
2.2
—6.
570
8.7
1968
.270
1.2
—13
.769
2.0
—22
.969
2.2
—22
.769
2.5
—22
.470
0.4
—14
.571
4.9
AFE
6.2
7.8
5.8
6.3
10.1
1966
.165
4.5
—1.
465
7.6
1.7
653.
1—
2.8
652.
5—
3.4
665.
910
.065
5.9
1966
.266
2.2
11.9
672.
422
.166
4.5
14.2
661.
611
.367
3.9
23.6
650.
319
66.3
669.
710
.066
9.1
9.4
665.
55.
866
6.5
6.8
689.
830
.165
9.7
1966
.466
9.9
2.8
675.
38.
267
0.7
3.6
674.
06.
967
4.0
6.9
667.
1
707.
00.
670
1.3
—5.
170
6.1
—0.
370
6.8
0.4
704.
5—
1.9
706.
4
1968
.1*6
98.2
—16
.270
4.9
—9.
570
4.3
—10
.169
9.5
—14
.970
0.8
—13
.670
1.2
—13
.271
4.4
AFE
5.8
8.1
4.6
7.5
12.8
Fifth
Qua
rter
of F
orec
ast
1966
.165
8.2
3.9
658.
64.
365
3.9
—0.
465
8.0
3.7
679.
425
.165
4.3
1966
.266
4.8
10.5
669.
515
.266
1.2
6.9
664.
510
.268
3.4
29.1
654.
319
66.3
675.
48.
267
4.6
7.4
673.
86.
667
5.2
8.0
695.
528
.366
7.2
1966
.467
8.0
5.4
685.
012
.468
4.2
11.6
688.
115
.567
8.7
6.1
672.
6
1967
.168
4.7
2.5
689.
97.
769
3.8
11.6
698.
015
.869
1.9
9.7
682.
219
67.2
699.
63.
169
0.1
—6.
470
2.4
5.9
705.
28.
771
5.1
18.6
696.
519
67.3
711.
54.
669
7.0
—9.
971
2.8
5.9
715.
28.
370
1.6
—5.
370
6.9
1967
.4*7
026
—9.
571
1.2
—09
708.
6—
3.5
716.
74.
671
8.6
6.5
706.
7—
5.4
712.
1
AFE
4.9
8.4
6.7
9.6
16.0
ni
Six
th Q
uart
er o
f For
ecas
tni
1966
.166
3.3
5.0
663.
35.
066
0.6
2.3
663.
85.
568
9.0
30.7
658.
319
66.2
666.
95.
166
9.2
7.4
663.
11.
266
6.2
4.4
686.
124
.36.
61.8
1966
.367
9.0
6.3
677.
64.
967
9.7
7.0
681.
99.
269
9.8
27.1
672.
719
66.4
688.
35.
969
6.3
698.
215
.870
1.8
19.4
698.
015
.668
2.4.
1967
.169
5.3
0.6
701.
06.
370
8.3
13.6
712.
417
.770
9.1
14.4
694.
719
67.2
.699
.l—
4.4
69.1
.8—
11.7
706.
93.
470
9.4
5.9
702.
90.
470
3.5
1967
.371
8.5
5.9
705.
.5—
7.1
724.
011
.472
6.7
14.1
704.
1—
8.5
712.
6
AFE
4.7
8.0
7.8
10.9
17.3
(con
tinue
d)
00
TA
BLE
4.4A
(con
clud
ed)
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
e V
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Fore
cast
One
Yea
r Ahe
ad19
66.1
642.
7—
3.2
647.
71.
864
5.6
—0.
364
0.6
—5.
364
8.9
3.0
645.
919
66.2
650.
94.
766
1.2
15.0
656.
810
.664
9.0
2.8
655.
99.
764
6.2
1966
.366
1.9
6.4
660.
65.
165
4.5
—1.
065
1.4
—4.
167
2.9
17.4
655.
519
66.4
661.
92.
166
2.1
2.3
655.
2—
4.6
653.
1—
6.7
667.
98.
165
9.8
1967
.166
4.6
1.1
669.
76.
266
4.3
0.8
663.
3—
0.2
.668
.95.
466
3.5
1967
.267
8.5
6.5
670.
3—
1.7
672.
50.
567
2.3
0.3
680.
88.
867
2.0
1967
.368
8.6
4.4
680.
1—
4.1
686.
52.
368
5.0
0.8
687.
93.
768
4.2
1967
.4*6
919
—0.
569
7.2
4.8
695.
53.
169
6.6
4.2
691.
7—
0.7
698.
15.
769
2.4
1968
.1*6
94.6
—8.
9.
699.
9—
3.6
.
699.
5—
4.0
690.
0—
13.5
682.
8—
20.7
703.
80.
370
3.5
*4.2
AFE
4.0
4.8
4.2
4.6
6.9
TAB
LE 4
.4P
Com
paris
on o
f Ex
Post
For
ecas
ts, W
harto
n M
odel
, GN
P in
Con
stan
t Dol
lars
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Firs
t Qua
rter
of F
orec
ast
1966
.164
2.4
—6.
766
3.5
—10
.662
9.2
—19
.963
9.3
—9.
864
9.1
1966
.265
9.2
4.2
651.
8—
3.2
641.
5—
13.5
656.
01.
065
5.0
1966
.366
0.1
—0.
165
4.3
—5.
964
6.0
—14
.265
8.4
—1.
866
0.2
1966
.466
9.0
0.9
666.
2—
1.9
658.
3—
9.8
667.
3—
0.8
668.
119
67.1
663.
1—
3.4
663.
4—
3.1
658.
6—
7.9
665.
5—
1.0'
666.
519
67.2
660.
0—
10.5
664.
3—
6.2
660.
4—
10.1
661.
5—
9.0
670.
519
67.3
672.
3—
5.7
672.
2—
5.8
666.
2—
11.8
672.
3—
5.7
678.
019
67.4
676.
2—
7.3
673.
0—
10.5
664.
6—
18.9
680.
4—
3.1
683.
5
1968
.169
9.0
5.7
694.
81.
568
2.5
—10
.869
5.2
1.9
693.
319
68.2
712.
16.
370
5.4
—0.
469
1.1
—14
.770
7.8
2.0
705.
819
68.3
698.
8—
14.0
692.
4—
20.4
680.
0—
32.2
701.
2—
11.6
712.
819
68.4
711.
1—
7.4
700.
7—
17.8
686.
5—
32.0
713.
3—
5.2
718.
5
AFE
6.0
7.3
16.3
4.4
0 z 0 0 Cl, 0 I, 0
(con
tinue
d)
TAB
LE 4
.4P
(con
tinue
d)
Third
Qua
rter
of F
orec
ast
1966
.468
6.5
16.0
684.
614
.168
6.0
15.5
688.
417
.967
0.5
. tTl
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
.A
djus
tmen
tsA
djus
tmen
tsA
djus
tmen
tsR
evis
edW
as M
ade
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Val
ue
Seco
nd Q
uarte
rof
For
ecas
t
0 z 0 ru —
1966
.119
66.2
1966
.319
66.4
1967
.119
67.2
1967
.319
67.4
650.
266
6.8
614.
668
0.7
668.
666
0.5
671.
669
8.0
—4.
86.
66.
514
.2
—1.
9—
17.5
—11
.9 4.7
643.
965
5.9
666.
267
6.2
.
671.
267
0.4
674.
469
4.5
—11
.1—
4.3
—1.
99.
7
0.7
—7.
6—
9.1
—1.
2
637.
864
8.7
660.
267
1.2
669.
066
9.3
671.
268
8.5
—17
.2—
11.5
—7.
94.
7
—1.
5—
8.7
—12
.4—
4.8
644.
766
2.6
670.
667
9.3
669.
966
1.0
675.
269
5.4
—10
.3 2.4
2.5
12.8
—0.
6—
17.0
—8.
32.
1
655.
066
0.2
668.
166
6.5
670.
567
8.0
683.
569
3.3
0 C)
1968
.119
68.2
"19
68.3
••
710.
570
2.8
701.
4
4.7
—10
.0—
17.1
705.
369
5.6
696.
0
—O
.5
—17
.2—
22.5
696.
268
5.7
688.
2•
—9.
6—
27.1
—30
.3
707.
270
4.0
701.
7
1.4
—8.
8—
16.8
705.
871
2.8
718.
5
AFE
.9.
17.
812
.3.
7.5
1966
.166
0.1
—0.
165
5.3
—4.
965
5.2
—5.
065
3.3
—6.
966
0.2
1966
.267
9.2
11.1
670.
62.
566
9.9
1.8
674.
96.
866
8.1
1966
.368
6.8
20.3
680.
814
.268
0.3
13.8
684.
818
.366
6.5
1967
.166
7.9
—10
.167
6.1
—1.
967
9.5
1.5
669.
9—
8.1
678.
019
67.2
661.
6—
21.9
677.
7—
5.8
681.
8—
1.7
663.
6—
20.0
683.
519
67.3
693.
70.
470
1.3
8.0
704.
110
.868
9.8
—3.
569
3.3
1967
.471
3.3
7.5
714.
48.
671
5.2
9.4
710.
24.
470
5.8
1968
.170
0.1
—12
.770
0.3
—12
.570
0.1
—12
.770
3.7
—9.
171
2.8
1968
.270
2.5
—16
.070
2.5
—16
.070
2.9
—15
.570
4.0
—14
.571
8.5
AFE
11.6
8.9
8.8
11.0
Four
th Q
uarte
r of F
orec
ast
1966
.167
3.7
5.6
670.
12.
067
1.1
3.0
666.
4—
1.7
668.
119
66.2
691.
625
.168
4.8
18.3
685.
418
.968
8.8
22.3
666.
519
66.3
694.
624
.169
0.3
19.8
691.
220
.769
6.2
25.7
670.
519
66.4
689.
111
.169
0.2
12..2
693.
215
.269
3.2
15.2
678.
0
1967
.167
0.0
—13
.568
4.4
0.9
689.
25.
767
4.2
—9.
368
3.5
1967
.268
3.0
—10
.370
6.4
13.1
711.
418
.167
7.6
—15
.769
3.3
1967
.371
0.6
4.8
723.
717
.972
7.7
21.9
705.
6—
0.2
705.
819
67.4
702.
6—
10.2
708.
3—
4.5
711.
2—
1.6
707.
7—
5.1
712.
8
1968
.170
1.8
—16
.770
7.5
—11
.071
0.2
—8.
370
4.3
—14
.271
8.5
AFE
13.5
11.1
12.6
12.2
Fifth
Qua
rter o
f For
ecas
t19
66.1
684.
317
.868
3.6
17.1
686.
019
.467
9.4
12.9
666.
519
66.2
700.
630
.169
5.8
25.3
697.
226
.770
0.2
29.7
670.
519
66.3
698.
720
.769
6.1
18.1
697.
319
.370
2.1
24.1
678.
019
66.4
694.
511
.069
8.8
15.3
702.
118
.570
0.4
16.9
683.
50
(con
tinue
d)
TAB
LE 4
.4P
(con
clud
ed)
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
Rea
lized
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
. rn C) 0 z 0 rn — C) 0 rn 0
Fifth
Qua
rter
of F
orec
ast (
cont
inue
d)
714.
821
.573
0.7
24.9
720.
57.
771
9.6
1.1
17.4
687.
169
1.9
704.
371
1.7
1967
.269
7.9
—7.
972
7.0
21.2
1967
.370
1.2
—11
.671
7.7
4.9
1967
.470
8.7
—9.
871
7.4
—1.
1
AFE
14.0
15.0
1966
.169
3.6
23.1
694.
423
.969
6.5
26.0
690.
620
.167
0.5
1966
.270
3.3
25.3
699.
621
.670
1.1
23.1
704.
626
.667
8.0
1966
.370
4.6
21.1
703.
119
.670
4.2
20.7
709.
926
.468
3.5
1966
.471
4.8
21.5
721.
328
.072
4.2
30.9
714.
120
.869
3.3
—6.
2
—13
.9—
8.5
—6.
8
14.9
Sixt
h Q
uarte
rof
Fore
cast
693.
370
5.8
712.
871
8.5
C) 0
1967
.170
6.2
0.4
730.
624
.873
4.5
28.7
702.
1—
3.7
705.
819
67.2
689.
1—
23.7
721.
99.
172
5.6
12.8
690.
5—
22.4
712.
819
67.3
706.
5—
12.0
725.
77.
272
9.4
10.9
708.
0—
10.5
718.
5
AFE
18.2
19.2
21.9
18.6
Fore
cast
One
Yea
r Ahe
ad19
66.1
656.
6—
1.5
658.
20.
164
8.3
—9.
865
0.9
—7.
265
8.1
1966
.267
4.2
11.8
665.
73.
366
1.3
—1.
167
0.6
8.2
662.
419
66.3
679.
012
.767
2.9
6.6
669.
43.
167
7.5
11.2
666.
319
66.4
681.
310
.667
9.3
8.6
677.
16.
468
2.0
11.3
670.
7tn
1967
.166
7.4
—7.
267
3.7
—0.
967
4.0
—0.
666
9.8
—4.
867
4.6
1967
.266
6.2
—15
.167
9.7
—1.
668
0.7
—0.
666
5.9
—15
.468
1.3
1967
.368
7.0
—3.
169
2.9
2.8
692.
32.
268
5.7
—4.
469
0.1
1967
.469
7.5
—1.
369
7.5
—1.
369
4.8
—4.
069
8.4
—0.
469
8.8
1968
.170
2.8
—4.
870
1.9
—5.
769
7.2
—10
.470
2.6
—5.
070
7.6
AFE
7.5
3.4
4.2
7.5
0 0 rn r (I, .
-JT
AB
LE4.
5A
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
Wha
rton-
EFU
Mod
el, U
nem
ploy
men
t
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GO
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter o
f For
ecas
t
0 z 0 rn C) 0 tn C,, C C)
— C)
— C
1966
.13.
980.
184.
801.
004.
710.
914.
180.
383.
880.
083.
8019
66.2
3.63
—0.
233.
66—
0.20
4.07
0.21
3.82
—0.
043.
54—
0.32
3.86
1966
.33.
82—
0.02
5.40
1.56
4.32
0.48
5.20
1.36
3.68
—0.
16.3
.84
1966
.44.
090.
324.
710.
945.
231.
465.
872.
103.
95'0
.18
'3.7
7
1967
.14.
210.
382.
94—
0.89
3.98
0.15
5.05
1.22
3.72
—0.
113.
8319
67.2
4.09
0.16
4.30
0.37
5.06
1.13
5.92
1.99
4.11
0.18
3.93
1967
.33.
63—
0.30
3.99
0.06
4.87
0.94
6.34
2.41
3.82
—0.
113.
9319
67.4
*4.1
80.
25.
.
4.17
0.24
3.12
—0.
814.
180.
256.
232.
304.
220.
293.
93
1968
.1*3
.61
0.04
3.60
0.03
6.71
3.14
•5.
171.
60'7
.54
3.97
2.67
—0.
903.
5719
68.2
3.47
—0.
133.
47—
0.13
4.01
0.41
7.25
3.65
3.27
—0.
333.
6019
68.3
4.25
0.65
4.25
0.65
4.54
0.94
6.88
3.28
3.53
—0.
073.
6019
68.4
3.80
0.40
3.80
0.40
5.44
2.04
7.47
4.07
4.01
0.61
3.40
AFE
*0.
26.
AFE
0.25
0.84
0.87
2.23
0.27
Seco
nd Q
uarte
r of F
orec
ast
1966
.13.
74—
0.09
4.15
0.32
3.95
0.12
4.03
0.20
3.49
—0.
343.
8319
66.2
3.29
—0.
542.
75—
1.08
3.17
—0.
663.
59—
0.24
3.16
—0.
673.
8319
66.3
3.89
0.18
5.44
1.73
4.83
1.12
5.57
1.86
3.18
—0.
533.
7119
66.4
4.53
0.73
5.26
1.46
6.26
2.45
6.83
3.03
4.24
0.44
3.80
1967
.14.
010.
052.
77—
1.19
4.34
0.38
5.17
1.21
4.28
0.32
3.96
1967
.23.
55—
0.48
4.35
0.32
5.33
1.30
5.92
1.89
3.67
—0.
364.
0319
67.3
3.19
—0.
744.
390.
465.
371.
446.
542.
613.
85—
0.08
3.93
1967
.4*4
.21
3.32
—0.
282.
86—
0.74
4.24
0.64
5.93
2.33
2.91
—0.
693.
60C
)
1968
.1*3
650.
083.
36—
0.21
6.39
2.82
5.69
2.12
7.73
4.16
2.25
—1.
323.
5719
68.2
3.79
0.19
5.40
1.80
5.47
1.87
8.28
4.68
3.25
—0.
353.
6019
68.3
4.36
0.96
5.30
1.90
5.35
1.95
7.49
4.09
3.78
0.38
3.40
AFE
*0.
42A
FE0.
401.
251.
272.
390.
49—
Thi
rdQ
uarte
r of F
orec
ast
019
66.1
3.42
—0.
383.
900.
103.
78—
0.02
3.71
—0.
092.
91—
0.89
3.80
1966
.23.
13—
0.57
2.59
—1.
113.
19—
0.51
3.46
—0.
242.
83—
0.87
3.70
1966
.33.
840.
105.
631.
894.
921.
185.
091.
353.
06—
0.68
3.74
1966
.44.
310.
384.
890.
965.
651.
725.
501.
574.
880;
953.
93
1967
.14.
170.
112.
81—
1.25
4.15
0.09
4.25
0.19
4.78
0.72
4.06
1967
.23.
82—
0.21
4.59
0.56
5.32
1.29
5.30
1.27
4.14
0.11
4.03
1967
.33.
32—
0.28
4.64
1.04
5.44
1.84
5.84
2.24
3.16
.—
0.44
3.60
(con
tinue
d)
TAB
LE 4
.5A
(con
tinue
d)
Third
Qua
rter o
f For
ecas
t (co
ntin
ued)
. 0 z 0 m — 0
1967
.119
67.2
1967
.319
67.4
4.04
—0.
023.
60—
0.10
3.26
—0.
34*4
260.
66
2.96
—1.
104.
310.
614.
651.
05
3.84
—0.
224.
570.
885.
161.
56
3.61
—0.
454.
340.
645.
261.
66
5.08
1.02
3.31
—0.
392.
23—
1.37
4.06
370
3.60
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GO
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
C
1967
.4*3
710.
113.
26—
0.34
3.20
—0.
404.
470.
875.
231.
632.
09—
1.51
3.60
1968
.1*4
190.
623.
700.
136.
753.
185.
9623
96.
743A
72.
84—
0.73
3.57
1968
.24.
461.
066.
252.
856.
853.
457.
574.
173.
91O
il3.
40A
FE*
0.38
AFE
0.36
1.33
1.33
1.59
0.74
1966
.13.
12—
0.55
3.68
Four
th0.
01
Qua
rter
3.57
of F
orec
ast
—0.
103.
40—
0.27
2.35
—1.
423.
6719
66.2
2.95
—0.
782.
31—
1.42
2.99
—0.
743.
11—
0.62
2.59
—1.
143.
7319
66.3
3.88
0.01
5.86
1.99
5.00
1.13
4.92
1.05
3.27
—0.
603.
8719
66.4
4.01
—0.
024.
450.
424.
900.
874.
550.
524.
91—
.88
4.03
0 0 'TI
C.) — rn
4.36
0.76
3.98
0.38
5.07
1.47
5.38
1.78
3.21
—0.
393.
60
1968
.1*4
.64
1.27
4.24
0.87
7.17
3.80
6.16
2.79
6.43
3.06
3.75
0.38
3.37
AFE
*0.
42A
FE0.
381.
191.
081.
120.
84
Qua
rter
of F
orec
ast
1966
.13.
44—
0.26
4.05
0.35
3.93
0.23
3.59
—0.
112.
06—
1.64
3.70
1966
.22.
98—
0.88
2.56
—1.
303.
28—
0.58
3.13
—0.
732.
84—
1.02
3.86
1966
.33.
81—
0.16
6.25
2.28
4.76
0.79
4.80
0.83
3.09
—0.
883.
9719
66.4
3.73
—0.
304.
160.
134.
140.
113.
94—
0.09
4.96
0.93
4.03
1967
.13.
56—
0.17
2.64
—1.
093.
05—
0.68
2.88
—0.
854.
220.
483.
7319
67.2
3.81
0.11
4.26
0.56
4.13
0.43
4.08
0.38
2.70
—1.
003.
7019
67.3
3.22
—0.
385.
581.
984.
811.
214.
941.
342.
77—
0.83
3.60
1967
.4*4
791.
394.
390.
994.
190.
794.
941.
545.
291.
893.
470.
073.
40
AFE
0.41
1.06
0.69
0.78
0.86
Sixt
hQ
uart
er o
f For
ecas
t
1966
.13.
54—
0.29
4.22
0.39
4.00
0.17
3.61
—0.
221.
76—
2.07
3.83
1966
.23.
05—
0.91
2.88
—1.
083.
51—
0.45
3.22
—0.
742.
66—
1.30
3.96
1966
.33.
96—
0.01
6.61
2.64
4.82
0.85
4.90
0.93
3.20
—0.
773.
9719
66.4
3.35
—0.
353.
930.
233.
59—
0.11
3.48
—0.
223.
920.
223.
70
1967
.13.
03—
0.70
2.20
—1.
532.
39—
1.34
2.21
—1.
523.
13—
0.60
3.73
1967
.24.
390.
694.
510.
814.
130.
434.
17—
.47
3.52
—0.
183.
7019
67.3
3.64
0.24
4.80
1.40
4.80
1.40
4.96
1.56
3.50
0.10
3.40
AFE
0.46
1.15
0.67
0.81
0.75
(con
tinue
d)
00
TA
BLE
4.5A
(con
clud
ed)
0 z 0 r 0 0
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
e V
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Fore
cast
One
Yea
r Ahe
ad19
66.1
3.56
—0.
214.
130.
364.
000.
233.
830.
063.
15—
0.62
3.77
1966
.23.
25—
0.53
2.82
—0.
963.
35—
0.43
3.49
—0.
293.
03—
0.75
3.78
1966
.33.
850.
065.
581.
794.
770.
895.
191.
403.
29—
0.50
3.79
1966
.44.
230.
354.
820.
945.
511.
635.
681.
804.
490.
613.
88
1967
.14.
100.
132.
87—
1.10
4.08
0.10
4.52
0.55
4.46
0.49
3.97
1967
.2—
0.16
4.38
0.46
5.07
1.15
5.37
1.45
3.80
—0.
123.
9219
67.3
3.35
—0.
414.
410.
655.
211.
455.
992.
233.
26—
0.50
3.76
1967
.4*4
.09
0.41
3.77
0.09
3.29
—0.
394.
490.
815.
692.
013.
10—
0.58
3.68
1968
.1*4
.02
0.50
3.72
0.20
6.75
3.23
5.75
2.23
7.11
3.59
2.88
—0.
643.
52
AFE
*030
.
0.23
1.09
0.99
1.48
0.53
TAB
LE 4
.5P
Com
paris
on o
f Ex
Post
For
ecas
ts, W
harto
n M
odel
, Une
mpl
oym
ent
(con
tinue
d)
C C rTl
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
in W
hich
with
AR
with
GG
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
1966
.12.
46—
1.3
.
Firs
t Qua
rter
2.68
—1.
1
of F
orec
ast
3.37
—0.
42.
76—
1.0
3.80
1966
.21.
69—
2.1
2.08
—1.
72.
70—
1.1
1.93
—1.
93.
8319
66.3
2.08
—1.
72.
30—
1.5
2.76
—1.
02.
25—
1.6
3.80
1966
.41.
92—
1.7
2.00
—1.
72.
68—
1.0
2.04
—1.
63.
67
1967
.13.
43—
0.3
3.30
—0.
43.
9502
3.31
—0.
43.
7019
67.2
4.79
1.0
4.50
0.7
5.37
1.5
4.79
1.0
3.83
1967
.33.
61—
0.3
3.93
0.0
5.16
1.2
3.64
—0.
33.
9319
67.4
3.84
—0.
14.
280.
35.
741.
83.
61—
0.3
3.93
1968
.12.
99—
0.6
3.16
—0.
45.
201.
63.
18—
0.4
3.60
1968
.22.
29—
1.3
2.62
—1.
04.
901.
32.
49—
1.1
3.60
1968
.33.
09—
0.5
3.29
—0.
35.
141.
53.
02—
0.6
3.60
1968
.42.
97—
0.4
2.97
—0.
44.
781.
42.
88—
0.5
3.40
AFE
.0.
940.
791.
170.
89
TAB
LE 4
.5P
(con
tinue
d)
Qua
rter
Ex P
ost
Ex P
ost
Exin
Whi
chw
ith A
Rw
ith G
OEx
Pos
t RO
S
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
with
No
with
AR
Rea
lized
Was
Mad
eV
alue
Erro
rV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rR
evis
edV
alue
Seco
nd Q
uarte
r of F
orec
ast
C z C tTI
1966
.119
66.2
1966
.319
66.4
1967
.119
67.2
1967
.3
2.39
1.90
1.95
2.30
4.49 5.37
4.27
—1.
4—
1.9
—1.
7—
1.4
0.7
1.4
0.3
2.81
2.50
2.28
2.44
4.09
4.55
4.36
—1.
0—
1.3
—1.
4—
1.3
0.3
0.6
—0.
4
3.45
3.14
2.86
3.17
4.84
5.46
—0.
4—
0.7
—0.
8—
0.5 1.0
1.5
2.95
2.29
2.27
2.40
4.48
5.44
—0.
9—
1.5
—1.
4—
1.3
0.7
1.5
3.83
3.80
3.67
3.70
3.83
3.93
1967
.4
1968
.119
68.2
1968
.3
2.95
2.95
2.58
2.78
—0.
7
—.0
.7—
1.0
—0.
8
3.32
3.32
2.75
3.16
—0.
3
—0.
3—
0.8
—0.
4
5.59
4.84 4.84
4.90
1.7
1.2 1.2
1.3
4.12
3.03
3.03
2.77
0.2
—0.
6
—0.
6—
0.8
3.93
3.60
3.60
3.60
z 6
1968
.43.
64—
0.2
3.56
1.2
5.54
5.64
1.9
2.2
2.85
3.73
—0.
80.
33.
60
AFE
3.40
1966
.119
66.2
2.41
—1.
42.
03—
1.6
2.60
—1.
22.
61—
1.2
3.01
—0.
83.
802.
32—
1.3
3.67
1966
.32.
27—
1.4
2.22
—1.
52.
32—
1.4
2.40
—1.
33.
7019
66.4
3.22
—0.
63.
02—
0.8
3.19
—0.
63.
10—
0.7
3.83
1967
.15.
051.
14.
030.
14.
360.
45.
041.
13.
9319
67.2
5.87
1.9
4.34
0.4
4.86
0.9
5.92
2.0
3.93
1967
.33.
34—
0.3
2.84
—0.
83.
52—
0.1
3.55
—0.
13.
6019
67.4
2.13
—1.
51.
94—
1.7
2.88
—1.
72.
33—
1.3
3.60
1968
.13.
22—
0.4
2.84
—0.
84.
240.
63.
07—
0.5
3.60
1968
.23.
620.
23.
17—
0.2
4.67
1.3
3.58
0.2
3.40
Four
th Q
uarte
r of F
orec
ast
019
66.1
2.34
—1.
32.
28—
1.4
2.07
—1.
62.
82—
0.8
3.67
1966
.22.
44—
1.3
2.25
—1.
42.
08—
1.6
2.53
—1.
23.
7019
66.3
3.06
—0.
82.
71—
1.1
2.64
—1.
22.
90—
0.9
3.83
1966
.43.
59—
0.3
3.02
—0.
92.
99—
0.9
3.29
—0.
63.
93
1967
.15.
511.
63.
76—
0.2
3.96
0.0
5.37
1.4
3.93
1967
.24.
891.
32.
53—
1.1
2.98
—0.
65.
331.
73.
6019
67.3
2.32
—1.
31.
22—
2.4
1.73
—1.
92.
66—
0.9
3.60
1967
.42.
81—
0.8
2.10
—1.
52.
77—
0.8
2.59
—1.
03.
60
1968
.13.
880.
52.
84—
0.6
3.90
0.5
3.73
0.3
3.40
AFE
1.02
1.18
1.01
0.98
Fifth
Qua
rter o
f For
ecas
t19
66.1
2.52
—1.
22.
23—
1.5
2.04
—1.
72.
81—
0.9
3.70
1966
.22.
80—
1.0
2.48
—1.
42.
40—
1.4
2.77
—1.
13.
8319
66.3
3.11
—0.
82.
61—
1.3
2.66
—1.
32.
82—
1.1
3.93
1966
.43.
66—
0.3
2.78
—1.
2.2
.90
—1.
03.
30—
0.6
3.93
.00
(con
tinue
d)
00 rTl
C) 0 z 0
TA
BLE
4.5P
(con
clud
ed)
Qua
rter
Ex P
ost
Ex P
ost
Ex P
ost
Ex P
ost R
OS
Rea
lized
in W
hich
with
AR
with
GO
with
No
with
AR
Rea
lized
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Rev
ised
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Fifth
Qua
rter
ofFo
reca
st (c
ontin
ued)
0.73
1.55
1967
.14.
661.
12.
31—
1.3
2.70
—0.
94.
921.
33.
6019
67.2
3.94
0.3
1.15
—2.
51.
84—
1.8
4.49
0.9
3.60
1967
.32.
82—
0.8
1.57
—2.
02.
25—
1.3
2.73
—0.
93.
6019
67.4
3.15
—0.
32.
21—
1.2
3.02
—0.
42.
95—
0.5
3.40
AFE
0.91
-Si
xth
Qua
rtero
f For
ecas
t19
66.1
3.01
—0.
82.
63—
1.2
2.55
—1.
33.
16—
0.7
3.83
1966
.22.
92—
1.0
2.56
—1.
42.
60—
1.3
2.84
—1.
13.
93•
1966
.33.
18—
0.8
2.59
—1.
32.
75—
1.2
2.88
—1.
13.
9319
66.4
2.82
—0.
81.
74—
1.9
1.99
—1.
62.
84—
0.8
3.60
1.22
1967
.13.
640.
01.
07—
2.5
1.57
—2.
04.
050.
53.
6019
67.2
4.40
0.8
1.55
—2.
02.
24—
1.4
4.52
0.9
3.60
1967
.33.
25—
0.1
2.04
—1.
42.
62—
0.8
3.14
—0.
33.
40
AFE
0.61
1.67
1.37
0.77
Fore
cast
One
Yea
r Ahe
ad19
66.1
2.40
—1.
372.
59—
1.18
2.87
—0.
902.
88—
0.89
3.77
1966
.22.
01—
1.74
2.26
—1.
492.
59—
1.16
2.26
—1.
493.
7519
66.3
2.34
—1.
412.
37—
1.38
2.64
—1.
112.
45—
1.30
3.75
1966
.42.
75—
1.03
2.62
—1.
163.
00—
0.78
2.70
—1.
083.
78
1967
.14.
620.
783.
79—
0.05
4.27
0.43
4.55
0.71
3.84
1967
.25.
231.
413.
980.
164.
660.
845.
371.
553.
8219
67.3
3.38
—0.
383.
08—
0.68
4.00
0.24
3.49
—0.
273.
7619
67.4
2.93
—0.
932.
91—
0.95
4.05
0.19
2.89
—0.
973.
86
1968
.13.
26—
0.29
3.04
—0.
514.
540.
993.
25—
0.30
3.55
AFE
1.03
0.84
0.73
0.95
CI) C C r (I) 00
TABLE 4.6Comparison of Ex Ante and Ex Post Forecasts,
Evans Model, GNP in Current Dollars
Quarterin Which Reproduced Ex Post with Actual RealizedForecast Ex Ante Forecast Adjustments Preliminary
Was Made Value Error V alue Error Value
First Quarter of Forecast1964.1 609.4 0.6 605.9 —2.9 608.81964.2 620.4 1.8 618.9 0.3 618.61964.3 632.6 4.2 634.3 5.9 628.41964.4 636.6 2.0 637.2 2.6 634.6
1965.1 649.3 0.5 645.2 —3.6 648.81965.2 659.2 1.2 659.3 1.3 658.0
AFE 1.7 2.8
Second Quarter of Forecast1964.1 623.0 4.4 618.1 —0.5 618.61964.2 632.3 3.9 629.7 1.3 628.41964.3 644.8 10.2 648.8 14.2 634.61964.4 649.3 0.5 640.4 —8.4 648.8
1965.1 664.8 6.8 664.2 6.2 658.0
AFE 5.2 6.1
Third Quarter of Forecast1964.1 636.5 8.1 630.7 2.3 628.41964.2 641.7 7.1 639.2 4.6 634.61964.3 656.0 7.2 659.0 10.2 648.81964.4 659.9 1.9 655.1 —2.9 658.0
AFE 6.1 5.0
Fourth Quarter of Forecast1964.1 647.9 13.3 640.3 5.7 634.61964.2 651.5 2.7 647.4 —1.4 648.81964.3 669.2 11.2 676.6 18.6 658.0
AFE 9.1 8.6
Forecast One Year A head1964.1 629.2 6.6 623.7 1.1 622.61964.2 636.4 3.8 633.8 1.2 632.61964.3 650.6 8.2 654.6 12.2 642.4
AFE 6.2 4.8
TABLE 4.7
Comparison of Ex Ante and Ex Post Forecasts,Evans Model, Consumption
Quarterin Which Reproduced Ex Post with Actual RealizedForecast Ex Ante Forecast Adjustments Preliminary
Was Made Value Error V alue Error Value
First Quarter of Forecast1964.1 385.9 —4.1 385.1 —4.9 390.01964.2 392.9 —3.2 392.3 —3.8 396.11964.3 403.9 —0.7 403.9 —0.7 404.61964.4 407.3 0.8 406.2 —0.3 406.5
1965.1 417.3 —0.8 415.2 —2.9 418.11965.2 421.7 —1.3 421.5 —1.5 423.0
AFE 1.8 2.4
Second Quarter of Forecast1964.1 395.4 —0.7 393.7 —2.4 396.11964.2 402.0 —2.6 400.3 —4.3 404.61964.3 411.2 4.7 412.1 5.6 406.51964.4 416.6 —1.5 413.9 —4.2 418.1
1965.1 424.2 1.2 423.4 0.4 423.0
AFE 2.1 3.4
Third Quarter of Forecast1964.1 404.1 —0.5 401.6 —3.0 404.61964.2 407.8 1.3 406.0 —0.5 406.51964.3 417.4 —0.7 419.6 1.5 418.11964.4 423.9 0.9 420.8 —2.2 423.0
AFE 0.8 1.8
Fourth Quarter of Forecast1964.1 411.1 4.6 408.0 1.5 406.51964.2 414.3 —3.8 413.3 —4.8 418.11964.3 424.7 1.7 428.6 5.6 423.0
AFE 3.4 4.0
Forecast One Year Ahead1964.1 399.1 —0.2 397.1 —2.2 399.31964.2 404.2 —2.1 402.9 —3.4 406.31964.3 414.3 1.3 416.0 3.0 413.0
AFE 1.2 2.8
TABLE 4.8
Comparison of Ex Ante and Ex Post Forecasts,Evans Model, In vestment
Quarterin Which Reproduced Ex Post with Actual RealizedForecast Ex Ante Forecast . Adjustments Preliminary
Was Made Value Error Value Error Value
First Quarter of Forecast1964.1 88.8 2.9 88.0 2.1 85.91964.2 91.8 4.6 91.3 4.1 87.21964.3 91.8 4.5 92.0 4.7 87.31964.4 91.5 1.1 93.3 2.9 90.4
1965.1 93.6 —1.1 93.9 —0.8 94.71965.2 96.4 2.1 97.1 2.8 94.3
AFE 2.7 2.9
Second Quarter of Foreëast1964.1 90.9 3.7 89.2 2.0 87.21964.2 93.6 6.3 93.0 5.7 87.31964.3 94.9 4.5 95.8 5.4 90.41964.4 93.8 —0.9 90.5 —4.2 94.7
1965.1 99.8 5.5 100.2 5.9 94.3
AFE 4.;2 4.6
Third Quarter of Forecast1964.1 94.2 6.9 92.6 5.3 87.31964.2 96.2 5.8 95.5 5.1 90.41964.3. 98.1. 3.4 99.4 4.7 94.7
95.9 1.6 93.6. —0.7 94.3.
AFE 4.4 4.0
Fourth Quarter of Forecast1964.1 97.1 6..7 94.7 4.3 90.41964.2 98.5 3.8 98.0 4.3 94.71964.3 102.2 7.9 104.1 9.8 94.3
AFE 6.1 6.2
Forecas•t One, Year Ahead1964.1 92.7 SM 91.1 3.4 87.71964.2 95.0 5.1 94.4 4.5 89.91964.3 96.7 5.1 97.8, 61 91.6
AFE 5.0 4.7
TABLE 4.9
Comparison of Ex Ante and Ex Post Forecasts,Evans Model GNP in Constant Dollars
Quarterin Which Reproduced Ex Post with Actual RealizedForecast Ex Ante Forecast Adjustments Preliminary
Was Made Value Error Value Error Value
First Quarter of Forecast1964.1 508.3 0.3 505.5 —2.5 508.01964.2 515.3 1.8 514.9 1.4 513.51964.3 523.2 3.6 524.8 5.2 519.61964.4 523.5 0.8 524.4 1.7 522.7.
1965.1 532.2 0.0 528.7 —3.5 532.21965.2 539.0 2.3 537.1 0.4 536.7
AFE 1.5 2.4
Second Quarter of Forecast1964.1 517.4 3.9 514.3 0.8 513.51964.2 520.8 1.2 519.5 —0.1 519.61964.3 531.1 8.4 534.2 11.5 522.71964.4 531.7 —0.5 524.5 —7.7 532.2
1965.1 542.7 6.0 540.3 —3.6 536.7
AFE 3.9 4.7
Third Quarter of Forecast1964.1 526.0 6.4 522.7 3.1 519.61964.2 528.6 5.9 527.4 4.7 522.71964.3 537.7 5.5 539.7 7.5 532.21964.4 538.2 1.5 532.7 —4.0 536.7
AFE 4.8 4.8
Fourth Quarter of Forecast1964.1 532.8 10.1 528.4 5.7 522.71964.2 534.5 . 2.3 531.8 —0.4 532.21964.3 545.8 9.1 549.8 13.1 536.7
AFE 7.2 6.4
Forecast. One Year Ahead1964.1 521.1 5.2 517.7 1.8 515.91964.2 524.8 2.8 523.4 1.4 522.019643 534.4 6.6 537.1 9.3 527.8
AFE 4.8 4.1
TABLE 4.10
Comparison of Ex Ante and Lx Post Forecasts,Evans Model, Unemployment Rate
Quarterin Which Reproduced Ex Post with Actual RealizedForecast Ex Ante Forecast Adjustments Preliminary
Was Made Value Error Value Error Value
First Quarter of Forecast1964.1 5.60 0.17 5.65 0.22 5.431964.2 5.33 0.03 5.37 0.07 5.301964.3 5.07 0.00 5.02 —0.05 5.071964.4 5.00 —0.03 5.00 —0.03 5.03
1965.1 4.80 —0.03 5.00 0.17 4.831965.2 4.60 —0.13 5.39 0.66 4.73
AFE 0.06 0.20
Second Quarter of Forecast1964.1 5.53 0.23 5.70 0.40 5.301964.2 5.11 0.04 5.20 0.13 5.071964.3 4.73 —0.30 4.57 —0.46 5.031964.4 4.90 0.07 5.08 0.25 4.83
1965.1 4.50 —0.23 4.63 —0.10 4.73
AFE 0.17 0.27
Third Quarter of Forecast1964.1 5.37 0.30 5.60 0.53 5.071964.2 4.94 —0.09 5.05 0.02 5.031964.3 4.55 —0.28 4.29 —0.54 4.831964.4 4.70 —0.03 5.00 0.27 4.73
AFE 0.17 0.34
Fourth Quarter of Forecast1964.1 5.27 0.24 5.58 0.55 5.031964.2 4,85 0.02 5.03 0.20 4.831964.3 4.43 —0.30 3.95 —0.78 4.73
AFE 0.19 0.51
Forecast One Year Ahead1964.1 5.44 0.24 5.63 0.43 5.201964.2 5.05 0.00 5.16 0.11 5.051964.3 4.69 —0.22 4.45 —0.46 4.91
AFE 0.15 0.33
TAB
LE 4
.IIA
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
OB
E M
odel
, GN
P in
Cur
rent
Dol
lars
(con
tinue
d)
0 r) Cl) -3 -4 z C) 0 rn (I) C F Cl) C r (I) 00
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
OG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter o
f For
ecas
t19
67.2
774.
11.
877
9.6
7.3
776.
03.
777
7.1
4.8
773.
91.
677
2.3
1967
.379
2.3
2.1
793.
33.
179
7.7
7.5
803.
413
.278
6.4
—3.
879
0.2
1967
.480
4.7
—2.
180
2.5
—4.
381
1.5
4.6
818.
711
.880
2.1
—4.
880
6.9
1968
.182
7.4
—0.
082
4.1
—3.
382
7.4
—0.
083
1.8
4.3
834.
46.
982
7.5
1968
.284
6.6
—2.
384
1.4
—7.
584
5.9
—3.
084
6.7
—2.
285
1.1
2.1
849.
019
68.3
860.
9—
7.9
860.
0—
8.8
857.
3—
11.5
853.
6—
15.2
863.
3—
5.6
868.
919
68.4
884.
4—
2.9
882.
0—
5.3
882.
6—
4.7
879.
8—
7.5
880.
6—
6.8
887.
4
AFE
2.8
5.7
5.1
8.5
4.5
:Se
cond
Qua
rter o
f For
ecas
t19
67.2
788.
81.
479
4.5
7.1
793.
66.
279
3.6
6.2
783.
8—
3.6
787.
419
67.3
812.
46.
581
4.4
8.5
823.
517
.683
1.8
25.9
797.
8—
9.9
805.
919
67.4
827.
90.
881
6.6
—10
.483
1.1
4.0
841.
114
.083
3.4
6.3
827.
1
1968
.183
5.3
—13
.883
7.2
—11
.984
1.8
—7.
384
7.0
—2.
184
9.2
0.0
849.
219
68.2
860.
3—
6.7
849.
7—
17.3
858.
0—
9.0
857.
3—
9.7
867.
20.
186
7.1
1968
.386
9.0
—16
.286
2.5
—22
.786
0.0
—25
.285
6.4
—28
.886
8.1
—17
.288
5.3
AFE
7.6
13.1
11.6
14.5
6.2
Third
Qua
rter o
f For
ecas
t
Four
th Q
uarte
r of F
orec
ast
\0 . 0 z 0 tTl
— C) 0 r 0 C)
C)
— C)
1967
.219
67.3
852.
519
67.4
857.
94.
784
9.8
—8.
985
3.2
2.0
863.
5—
13.6
867.
715
.786
9.6
0.8
874.
4
818.
121
.884
7.9
7.5
875.
4
—5.
282
3.3
0.1
847.
88.
586
6.9
1968
.185
4.5
—29
.186
2.7
—20
.986
5.7
—17
.987
0.0
—13
.686
7.2
—16
.588
3.7
AFE
14.3
12.2
11.5
14.3
7.6
TAB
LE 4
.1IA
(con
clud
ed)
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Was
Mad
e V
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsPr
elim
i-V
alue
Erro
r nar
y V
alue
1967
.383
3.5
7.4
832.
86.
784
3.6
17.5
850.
124
.082
1.5
—4.
682
6.1
1967
.484
5.6
—3.
183
4.5
—14
.284
9.3
0.5
856.
98.
185
8.7
9.9
848.
8
1968
.184
6.1
—21
.185
1.5
—15
.785
5.6
—11
.686
0.5
—6.
786
4.1
—3.
286
7.3
1968
.286
8.3
—15
.185
5.0
—28
.486
7.1
—16
.386
4.7
—18
.786
9.7
—13
.888
3.5
AFE
10.1
14.5
1 1.
513
.67.
5
ru — 0
Fifth
Qua
rter o
f For
ecas
t19
67.2
840.
8—
4.2
845.
019
67.3
864.
7—
1.1
864.
5—
1.3
882.
716
.888
9.4
23.5
867.
11.
286
5.9
1967
.487
0.3
—12
.986
7.2
—16
.088
3.0
—0.
288
9.8
6.5
885.
21.
988
3.3
AFE
7.1
8.7
8.5
15.0
2.4
Sixt
h Q
uarte
r of F
orec
ast
1967
.286
1.9
—1.
286
3.1
1967
.388
2.9
0.6
.880
.0—
2.2
903.
220
.990
9.9
27.6
879.
0—
3.3
882.
3
AFE
0.6
2.3
20.9
27.6
2.3
Fore
cast
One
Yea
r Ahe
ad19
67.2
793.
2—
3.3
796.
519
67.3
822.
75.
2.82
2.6
5.1
832.
114
.683
8.8
21.2
813.
44.
181
7.5
1967
.483
4.1
—3.
382
6.7
—10
.683
9.9
2.5
10.3
842.
45.
083
7.4
1968
.184
0.9
—16
.084
3.9
—13
.084
7.7
—9.
285
2.4
—4.
585
3.7
3.2
856.
9
AFE
8.2
9.6
8.8
12.1
5.2
C,) 0 rn r C,) . C
1092 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
TABLE 4.IIPComparison of Ex Post Forecasts, OBE Model,
GNP in Current Dollars
Quarter Ex Post Ex Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
First Quarter of Forecast1967.2 788.8 8.6 789.7 9.5 787.6 7.4 780.21967.3 791.0 —4.3 789.4 —5.9 795.31967.4 809.3 —1.7 809.2 —1.8 811.0
1968.1 837.7 6.5 835.8 4.6 833.5 2.3 831.21968.2 856.5 3.6 856.2 3.3 847.8 —5.1 852.91968.3 868.5 —2.5 861.1 —9.9 856.4 —14.6 871.01968.4 878.0 —9.4 879.3 —8.1 877.1 —10.3 887.4
AFE 6.1 5.9 6.8
Second Quarter of Forecast1967.2 814.7 19.4 807.3 12.0 803.5 8.2 795.31967.3 803.7 —7.3 803.4 —7.6 811.01967.4 826.3 —4.9 829.1 —2.1 831.2
1968.1 859.0 6.1 850.3 —2.6 847.1 —5.8 852.91968.2 876.9 5.9 874.9 3.9 862.7 —8.3 871.01968.3 875.4 —12.0 862.8 —24.6 858.4 —29.0 887.4
AFE 10.9 9.2 10.2
Third Quarter of Forecast1967.2 839.3 28.3 826.6 15.6 821.7 10.7 811.01967.3 820.1 —11.1 821.3 —9.9 831.21967.4 842.7 —10.2 847.1 —5.8 852.9
1968.1 879.0 8.0 863.0 —8.0 860.2 —10.8 871.01968.2 883.6 —3.8 886.1 —1.3 873.2 —14.2 887.4
AFE 13.4 9.2 10.3
FORECASTING PROPERTIES OF U.S. MODELS • 1093
TABLE 4.1IP (concluded)
Quarter Ex Post Ex Post Ex Postin Which with AR with GO with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
Fourth Quarter of Forecast1967.2 860.1 28.9 845.7 14.5 839.3 8.1 831.21967.3 840.3 —12.6 841.1 —11.8 852.91967.4 858.6 —12.4 862.9 —8.1 871.0
1968.1 887.5 0.1 865.5 —21.9 863.2 —24.2 887.4
AFE 14.5 15.3 13.0
Fifth Quarter of Forecast1967.2 880.4 27.5 865.8 12.9 858.0 5.1 852.91967.3 860.9 —10.1 860.8 —10.2 871.01967.4 868.5 —18.9 872.2 —15.2 887.4
AFE 27.5 14.0 10.2
Sixth Quarter of Forecast
1967.2 899.0 28.0 884.7 13.7 876.0 5.0 871.01967.3 875.4 —12.0 874.6 —12.8 887.4
AFE 28.0 12.8 8.9
Forecast One Year Ahead1967.2 825.8 20.4 817.4 13.0 813.1 8.6 804.41967.3 813.8 —8.7 813.8 —8.7 822.51967.4 834.3 —7.2 837.1 —4.4 841.5
1968.1 865.8 5.2 853.7 —6.9 851.0 —9.6 860.6
AFE 1.2.8 9.0 7.8
TAB
LE 4
.12A
Com
paris
on o
f Ex
A n
te F
orec
asts
, for
OB
E M
odel
, Con
sum
ptio
n Ex
cept
Hou
sing
Ser
vice
s in
Con
stan
t Dol
lars
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter o
f For
ecas
t—
5.0
362.
7—
1.1
368.
00.
637
2.6
Seco
nd Q
uarte
r of F
orec
ast
rn 0 z 0 rn — C) 0 rn Cl) 0 C)
C) r — C) > r m > — 0
1967
.236
6.9
1967
.337
4.2
1967
.437
7.6
—0.
636
5.6
4.4
371.
5—
1.7
373.
2
—1.
936
6.8
1.7
372.
9—
6.1
375.
9
—0.
736
7.9
3.1
374.
1—
3.4
377.
6
0.3
364.
74.
337
2.7
—1.
737
8.2
—2.
936
7.6
2.9
369.
8—
1.2
379.
4
1968
.137
7.4
—3.
537
7.1
—3.
838
2.7
1.7
385.
54.
537
9.1
—1.
938
1.0
1968
.238
4.0
—2.
737
8.9
—7.
838
7.2
0.4
389.
32.
538
4.9
—1.
938
6.8
\0
1967
.236
3.3
—4.
036
2.3
—4.
636
3.9
—3.
436
3.8
—3.
636
7.4
1967
.336
9.9
1.9
366.
80.
036
8.1
0.1
369.
31.
336
8.0
1967
.437
1.1
1.4
370.
32.
937
3.2
3.5
371.
01.
336
9.7
1968
.137
6.7
—2.
437
4.6
—4.
537
8.1
—1.
038
1.4
2.2
376.
637
9.2
1968
.238
2.1
2.5
378.
7—
0.8
384.
75.
138
8.4
8.8
383.
03.
437
9.6
1968
.338
2.7
—5.
438
5.4
—2.
738
5.9
—2.
238
6.0
—2.
138
2.9
—5.
338
8.2
1968
.439
1.6
3.3
390.
01.
739
2.5
4.2
391.
73.
439
1.4
3.1
388.
3
AFE
3.0
2.4
2.9
3.4
2.9
1968
.338
3.9
—3.
038
5.7
—1.
238
7.4
0.4
387.
20.
238
4.3
—2.
738
7.0
AFE
2.7
3.8
1.6
2.3
2.3
Third
Qua
rter o
f For
ecas
t19
67.2
371.
11.
736
8.8
—0.
537
1.6
2.2
372.
32.
936
7.4
—2.
036
9.4
1967
.338
0.6
1.1
376.
8—
2.6
378.
6—
0.8
379.
90.
437
7.2
—2.
337
9.5
1968
.138
2.8
1.6
377.
8—
3.3
380.
7—
0.4
382.
61.
438
4.7
3.5
381.
219
68.2
379.
2—
8.9
380.
4—
7.7
387.
2—
0.9
389.
61.
438
1.6
—6.
638
8.2
1968
.338
5.8
0.2
379.
1—
6.4
388.
83.
238
9.8
4.2
386.
30.
738
5.6
AFE
2.7
4.2
1.6
2.1
3.2
Four
th Q
uarte
r of F
orec
ast
1967
.237
1.8
—7.
337
9.1
1967
.338
5.9
4.6
380.
9—
0.3
382.
81.
538
3.8
2.5
385.
03.
738
1.3
1967
.438
6.1
—2.
238
3.2
—5.
138
4.9
—3.
438
6.1
—2.
238
8.2
388.
4
1968
.138
0.8
—6.
138
3.0
—3.
939
0.7
3.7
392.
85.
838
2.7
—4.
338
7.0
AFE
4.4
.22.
93.
53.
9
Fifth
Qua
rter o
f For
ecas
t19
67.2
378.
1—
2.8
380.
919
67.3
389.
30.
838
4.1
—-4
.338
6.5
—1.
938
7.4
—1.
039
0.1
1.6
388.
519
67.4
389.
01.
838
5.9
—1.
238
8.4
1.2
389.
42.
239
1.3
4.1
387.
2
AFE
1.3
2.9
1.6
1.7
2.8
(con
tinue
d)
TAB
LE 4
.12A
(con
clud
ed)
('1 0 z 0 z C) 0 cn 0 C)
— C)
C- til > 0
Qua
rter
Rep
rodu
ced
in W
hich
Ex A
nte
Fore
cast
Fore
cast
Was
Mad
e V
alue
Erro
r
Ex A
nte
Ex A
nte
Ex A
nte
with
AR
with
GG
with
No
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Val
ueEr
ror
Val
ueEr
ror
Val
ueEr
ror
Ex p
ost
with
Act
ual
Rea
lized
Adj
ustm
ents
Prel
imi-
Val
ueEr
ror n
ary
Val
ue
Six
th Q
uart
er o
f For
ecas
t
1967
.219
67.3
393.
05.
738
7.4
0.1
390.
53.
239
1.2
3.9
383.
5—
4.6
388.
139
4.3
7.0
387.
3
AFE
5.7
0.1
3.2
3.9
5.8
For
ecas
t One
Yea
r A
head
1967
.219
67.3
377.
73.
019
67.4
379.
5—
0.2
374.
1—
0.5
375.
60.
937
6.5
1.8
376.
2—
3.5
378.
6—
1.1
379.
90.
2
367.
0—
5.2
370.
937
6.1
1.5
374.
638
0.5
0.8
379.
7
1968
.137
8.6
—5.
237
8.8
—5.
038
4.7
0.8
387.
43.
538
0.0
—3.
838
3.8
AFE
2.9
3.1
1.0
1.8
2.8
FORECASTING PROPERTIES OF U.S. MODELS • 1097
TABLE 4..12P
Comparison of Ex Post Forecasts, OBE Model, ConsumptionExcept Housing Services in Constant Dollars
Quarter Ex Post Ex Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
First Quarter of Forecast1967.2 363.0 —5.8 366.2 —2.6 367.4 —1.4 368.81967.3 377.8 370.7 1.7 367.1 —1.9 369.01967.4 385.7 374.0 3.2 372.2 1.4 370.8
1968.1 373.3 —7.2 375.9 —4.6 377.6 —2.9 380.51968.2 383.0 0.7 387.0 4.7 384.8 2.5 382.31968.3 387.6 —1.9 385.7 —3.8 383.9 —5.6 389.51968.4 389.4 1.1 392.2 3.9 391.4 3.1 388.3
AFE 5.8 3.5 2.7
Second Quarter of Forecast1967.2 361.7 —7.3 367.6 —1.4 368.6 —0.4 369.01967.3 384.3 372.7 1.9 370.9 0.1 370.81967.4 392.3 375.7 —4.8 375.4 —5.1 380.5
1968.1 375.1 —7.2 377.1 —5.2 378.1 —4.2 382.31968.2 385.3 —4.2 388.4 —1.1 386.3 —3.2 389.51968.3 389.9 1.6 386.9 —1.4 385.9 —2.4 388.3
APE 5.1 2.6 2.6
Third Quarter of Forecast1967.2 361.1 —9.7 370.4 —0.4 371.4 0.6 370.81967.3 388.8 375.8 —4.7 375.3 —5.2 380.51967.4 400.9 380.9 —1.4 381.7 —0.6 382.3
1968.1 377.9 —11.6 379.7 —9.8 380.3 —9.2 389.51968.2 387.6 —0.7 389.9 1.6 388.2 —0.1 388.3
AFE 7.3 3.6 3.1
(continued)
1098 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
TABLE 4.12P (concluded)
Quarter Ex Post Ex Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
Fourth Quarter of Forecast
1967.2 360.0 —20.5 373.3 —7.2 374.3 —6.2 380.51967.3 395.9 382.5 0.2 382.5 0.2 382.31967.4 408.7 385.4 —4.1 386.5 —3.0 389.5
1968.1 379.9 —8.4 381.5 •—6.8 382.3 —6.0 388.3
AFE 14.5 4.6 3.9
Fifth Quarter of Forecast
1967.2 360.2 —22.1 377.6 —4.7 378.4 —3.9 382.31967.3 401.1 387.9 —1.6 387.9 —1.6 389.51967.4 416.2 389.6 1.3 390.6 2.3 388.3
AFE —22.1 2.5 2.6
Sixth Quarter of Forecast
1967.2 359.6 —29.9 380.8 —8.7 381.5 —8.0 389.51967.3 392.8 4.5 392.6 4.3 388.3
AFE —29.9 6.6 6.1
Forecast One Year Ahead1967.2 361.5 —10.7 369.4 —2.8 370.5 —1.7 372.21967.3 375.5 —0.1 374.0 —1.6 375.61967.4 379.,1 —1.6 379.0 —1.7 380.7
1968.1 376.6 —8.4 378.6 —6.5 379.6 —5.4 385.1
AFE 9.6 2.8 2.7
TAB
LE 4
.13A
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
OB
E M
odel
, inv
estm
ent i
n C
onst
ant D
olla
rs
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GO
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
1967
.292
.12.
2
Firs
t Qua
rter o
f For
ecas
t
96.2
6.3
92.2
2.3
92.3
2.4
89.8
—0.
189
.919
67.3
94.7
1.3
96.7
3.3
95.1
1.7
95.1
1.7
94.0
0.6
93.4
1967
.496
.4—
8.2
96.6
—8.
097
.5—
7.1
97.2
—7.
496
.4—
8.3
104.
7
1968
.110
5.1
5.3
103.
53.
710
2.2
2.4
100.
40.
610
4.9
5.1
99.8
1968
.210
3.6
—3.
010
4.3
—2.
398
.7—
7.9
96.2
—10
.410
4.7
—2.
010
6.7
1968
.310
3.7
—0.
810
4.4
—0.
110
0.7
—3.
899
.7—
4.8
103.
2—
1.4
104.
619
68.4
109.
0—
4.0
108.
4—
4.6
106.
2—
6.8
101.
9—
11.1
108.
8—
4.3
113.
1
AFE
3.6
4.1
4.6
5.5
1.7
1967
.292
.30.
3Se
cond
Qua
rter o
f For
ecas
t97
.45.
494
.62.
694
.12.
194
.02.
092
.019
673
97.9
—3.
710
0.3
-—1.
310
2.9
1.2
102.
91.
294
.7—
7.0
101.
719
67.4
102.
71.
298
.1—
3.3
103.
72.
210
6.3
4.8
101.
4—
0.1
101.
5
'TI C C)
C', -I z C) 0 -1 ITI
U, 0 'TI
C) 0 0 C',
(con
tinue
d)'0
TAB
LE 4
.13A
(con
clud
ed)
Qua
rter
Rep
rodu
ced
Lx A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
e V
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alU
eEr
ror n
ary
Val
ue
.
—2.
910
2.8
—l L
i
4.8
Four
th Q
uarte
r of F
orec
ast
1.2
105.
10.
8
—
100.
398
.510
7.3
1967
.410
4.1
—1.
610
3.1
—2.
610
7.3
1.5
107.
11.
310
6.3
0.5
105.
8
r'i C C — C tTl C
1968
.110
3.3
—2.
210
4.0
—1.
510
2.5
—3.
010
3.9
—1.
610
5.2
—0.
410
5.6
1968
.210
4.0
—1.
110
3.2
—1.
996
.7—
8.4
94.9
—10
.210
5.5
0.3
105.
219
68.3
102.
8—
9.0
100.
1—
11.7
96.9
—14
.995
.7—
16.i
102.
5—
9.4
111.
9
AFE
3.0
4.3
5.4
6.0
3.2
Third
Qua
rter
of F
orec
ast
1967
.295
.5—
4.7
99.7
—0.
599
.9—
0.3
98.4
—1.
898
.9—
1.4
1967
.310
1.4
2.9
103.
04.
510
3.5
5.0
103.
95.
498
.0—
0.5
1967
A10
5.3
—1.
910
0.2
—7.
010
5.9
—1.
310
6.9
—0.
310
6.7
—0.
6
1968
.110
1.1
—1.
210
1.6
—2.
410
4.6
0.5
104.
10.
010
4.1
1968
.210
1.3
100.
7—
11.7
93.5
—18
.991
.9—
20.5
102.
9—
9.6
112.
5
AFE
.5.
15.
75.
82.
4
1967
.296
.3—
0.8
97.1
1968
.198
.3—
13.0
101.
2—
10.1
100.
9—
10.4
104.
8—
6.5
102.
4—
9.0
111.
4
AFE
5.1
4.7
4.3
2.9
2.8
Qua
rter o
f For
ecas
t
1967
.210
2.8
—0.
110
2.9
1967
.310
2.8
0.0
107.
04.
210
8.1
5.3
107.
64.
810
2.9
0.1
102.
819
67.4
103.
8—
9.2
104.
0—
9.0
107,
8—
5.2
107.
4—
5.6
106.
9—
6.2
113.
1
AFE
4.7
6.7
5.3
5.3
2.1
Sixt
hQ
uart
er o
f For
ecas
t
1967
.210
1.9
0.5
101.
419
67.3
103.
6—
6.4
107.
9—
2.1
110.
0—
0.0
109.
2—
0.8
104.
0—
6.1
110.
1z
AF
E6.
52.
20.
10.
93.
30
For
ecas
tO
ne Y
ear A
head
1967
.294
.8—
3.9
94.8
1967
.399
.80.
210
1.4
1.9
101.
72.
210
1.8
2.3
97.6
1.9
99.5
1967
.410
2.2
—2.
699
.5—
5.2
103.
6—
1.1
104.
4—
0.3
102.
72.
110
4.8
o
1968
.110
2.0
—3.
210
2.9
—2.
210
1.8
—3.
310
3.5
—1.
710
4.2
1.0
105.
2
AFE
2.1
3.2
2.3
1.5
0 rn r S -I -I
1102 • ECONOMETRIC. MODELS OF CYCLICAL BEHAVIOR
TABLE 4.13P
Comparison of Ex Post Forecasts, OBE Mode!, Investment inConstant Dollars
Quarter Ex Post Ex Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
First Quarter of Forecast1967.2 100.8 1.0 99.9 0.1 100.1 0.3 99.81967.3 95;8 1.5 95.1 0.8 94.31967.4 101.2 4.8 99.8 3.4 96.4
1:968.1 104.8 0.1 102.0 —2.7 99.2 —5.5 104.71968.2 108.6 7.1 103.1 1.6 100.5 —1.0 101.51968.3 107.4 0.1 102.6 —4.7 103.0 —4.3 107.31968.4 108.2 2.4 106.4 0.6 102.4 —3.4 105.8
AFE 2.1 23 2.7
Second Quarter of Forecast1967.2 100.7 64 103.0 8.7 102.6 8.3 94.31967.3 100.6 4.2 99.8 3.4 96.41967.4 105.0 0.3 104.5 —0.2 104.7
1968.1 108.0 6.5 102.3 0.8 100.4 —1.1 101.51968.2 113.2 5.9 101.9 —5.4 97.4 —9.9 107.31968.3 109.0 3.2 102.3 —3.5 1019 —3.9 105.8
AFE 5.5 3.8 4.5
Third Quarter of Forecast1967.2 100.1 3.7 106.4 10.0 105.1 8.7 96.41967.3 102.1 —2.6 101.9 —2.8 104.71967.4 107.2 5.7 108.1 6.6 101.5
1968.1 107.7 0.4 102.1 —5.2 102.1 —5.2 107.31968.2 113.5 7.7 99.8 —6.0 96.0 —9.8 105.8
AFE 3.9 5.9 6.6
FORECASTING PROPERTIES OF U.S. MODELS • 1103
TABLE 4.13P (concluded)
Quarter Ex Post Ex Post Ex Postin Which with AR with GO with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
Fourth Quarter of Forecast
1967.2 94.3 —10.4 105.3 0.6 102.9 —1.8 104.71967.3 104.7 3.2 104A 2.9 101.51967.4 107.7 0.4 108;7 1.4 107.3
1968.1 106.4 102.2 —3.6 1031 —2.6 105.8
AFE 5.5 1.9 21
Fifth Quarter of Forecast90.4 —11.1 105.7 4.2. 102.5 1.0 101.5
1967.3 106.9 —0.4 106.2 —1.1 107.31967.4 110.0 4.2 1.10.3 4.5 105.8
AFE —11.1 2.9 2.2
Sixth Quarter of Forecast1967.2 88.0. —19.3 106.4 —0.9 102.8. —4.5 1.07.31967.3 —19.3 110.3 4.5 109.3 . 3.5 105.8
AFE 2.7 4.0
Forecast. One Year Ahead1967.2 99.0 0.3 103.7 5.0 102.7 4.0 98.71967.3 100.8 1.6 100.3 1.1 99.21967.4 105.3 2.9 105.3 2.8 102.4
19.68.1 106.8 1.9 102.2_2•5
101.3 —3.5 104.8
AFE 1.1 3.0 2.9
TAB
LE 4
.14A
S
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GO
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter
of F
orec
ast
0 ..r1
1967
.266
0.5
1967
.367
4.4
1967
.467
7.6
—0.
166
4.3
3.3
675.
0—
0.5
677.
4
3.6
661.
83.
967
3.9
—0.
768
1.2
1.1
663.
12.
867
7.5
3.0
684.
9
2.4
660.
76.
467
0.5
6.7
675.
1
0.0
660.
7—
0.6
671.
1—
3.1
678.
2
Sec
ond
Qua
rter
of F
orec
ast
1967
.469
2.5
3.4
685.
5—
3.5
692.
73.
669
8.9
9.8
694.
55.
468
9.1
— I 0
Com
paris
on o
f Ex
Ant
e Fo
reca
sts,
OB
E M
odel
, GN
P in
Con
stan
t Dol
lars
0 z C -l — C C,)
1.9
3.3
1968
.169
0.8
0.3
687.
8—
2.6
690.
0—
0.4
692.
92.
469
5.3
4.8
690.
519
68.2
699.
1—
1.2
695.
8—
4.5
697.
4—
2.9
697.
1.
—3.
270
1.8
1.4
700.
419
68.3
703.
7—
6.8
703.
9—
6.6
701,
9—
8.6
700.
8—
9.7
705.
8—
4.8
710.
619
68.4
718.
90.
571
7.3
—1.
071
8.3
—0.
071
7.5
—0.
871
6.!
—2.
371
8.4
AFE
2.4
1967
.266
7.5
0.4
671.
74.
667
1.2
4.1
671.
84.
766
2.4
—4.
766
7.1
1967
.368
4.9
7.6
686.
18.
868
8.0
10.7
693.
115
.867
4.9
—2.
467
7.3
2.7
4.6
1968
.169
2.6
—8.
569
3.6
—7.
569
8.0
—3.
170
2.5
1.3
701.
20.
070
1.2
1968
.270
3.9
—5.
369
6.8
—12
.469
9.7
—9.
569
8.8
—10
.470
8.4
—0.
970
9.3
1968
.370
5.4
—11
.270
1.0
—15
.670
1.0
—15
.669
9.6
—17
.070
5.5
—11
.271
6.7
AFE
6.1
8.8
7.8
9.9
4.1
Third
Qua
rter
of F
orec
ast
1967
.267
7.3
4.0
679.
86.
568
3.0
9.7
682.
89.
566
8.6
—4.
767
3.3
1967
.369
7.3
9A69
6.4
8.2
698.
610
.470
1.5
13.3
689.
71.
568
8.2
1967
.470
2.5
2.7
694.
0—
5.7
702.
12.
370
5.9
6.1
708.
58.
769
9.8
019
68.1
695.
7—
14.3
698.
1—
11.9
705.
1—
4.9
710.
10.
070
7.2
—2.
971
0.1
1968
.270
5.5
—9.
869
6.3
—19
.070
0.5
—14
.868
9.6
—25
.770
6.4
—9.
071
5.4
AFE
8.0
10.3
8,5
10.9
5.4
C)
Fou
rth
Qua
rter
of F
orec
ast
019
67.2
682.
3—
1.9
684.
219
67.3
707.
28.
370
5.0
6.1
707.
99.
070
9.6
10.7
704.
96.
069
8.9
1967
.470
6.6
—2.
070
3.9
—4.
771
0.1
1.4
712.
43.
771
5.0
6.3
708.
7
1968
.169
7.9
—18
.270
3.3
—12
.871
1.3
—4.
871
6.4
0.2
705.
8—
10.4
716.
2
AFE
9.6
7.9
5.1
4.9
6.2
(con
tinue
d)
TAB
LE 4
.14A
(con
clud
ed)
C z C C r r 0
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
e V
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Fifth
Qua
rtero
f For
ecas
t
1967
.269
6.7
1.8
694.
919
67.3
711.
23.
471
1.8
4.0
716.
38.
571
.7.8
10.0
712.
85.
070
7.8
1967
.471
1.8
—2.
971
1.3
—3.
471
6.9
2.1
718.
73.
971
7.8
3.0
714.
8
AFE
3;2
3.8
5.3
7.0
3.3
Sixt
h Q
uarte
r of F
orec
ast
1967
.271
0.0
6.2
703.
819
67.3
718.
84.
971
8.2
4.3
724.
710
.872
5.3
11.4
717.
43.
571
3.9
AFE
4.9
4.3
10.8
11.4
4.9
Fore
cast
One
Yea
r Ahe
ad19
67.2
.
668.
5—
2.8
671.
319
67.3
691.
07.
169
0.7
6.8
692.
18.
269
5.5
11.6
685.
01.
168
3.9
1967
.469
4.8
0969
0.2
—3.
769
6.6
2.6
700.
66.
669
8.3
4.4
693.
9
1968
.169
4.3
—10
.269
5.7
—8.
770
1:1
—3.
370
5.5
1.0
702.
4—
2.1
704.
5
AFE
6.1
6.4
4.7
6.4
2.8
FORECASTING PROPERTIES OF MODELS • 1107
TABLE 4.14P
Comparison of Ex Post Forecasts,' OBE Model,GNP in Constant Dollars
Quarter Ex Post Lx Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
First Quarter of Forecast1967.2 684.2 15.0 685.8 16.6 687.6 18.4 669.21967.3 675.7 0.1 674.5 —1.1 675.61967.4 683.5 1.7 683.6 1.8 681.8
1968.1 692.6 —0.1 694.1 1.4 694.0 1.3 692.71968.2 705.1 1.7 704.8 1.4 699.7 —3.7 703.41968.3 710.7 —1.6 705.4 —6.9 704.0 —8.3 712.31968.4 714.4 —4.0 715.8 —2.6 715.6 —2.8 718.4
AFE 4.5 4.4 5.3
Second Quarter of Forecast1967.2 683.6 8.0 690.5 14.9 691.9 16.3 675.61967.3 ' 683.4 1.6 6833 1.5 681.81967.4 696.3 3.6 698.1 5.4 692.7
1968.1 700.7 —2.7 700.9 —2.5 700.6 —2.8 703.41968.2 714.4 2.1 708.6 —3.7 702.0 —10.3 712.31968.3 712.5 —5.9 705.2 —13.2 703.9 —14.5 718.4
AFE 4,7 6.6 8.5
Third Quarter of Forecast1967.2 686.0 4.2 698.7 16.9 699.5 17.7 681.81967.3 695.1 2.4 696.3 3.6 692.71967.4 706.9 3.5 710.1 6.7 703.4
1968.1 707.5 —4.8 708.0 —4.3 708.6 —3.71968.2 715.1 —3'.3 707.1 —11.3 701.7 —16.7 718.4
AFE 4.1 7.7 9.7
(continued)
1108 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
TABLE 4.14P (concluded)
Quarter Ex Post Ex Post Ex Postin Which with AR with OG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
Fourth Quarter of Forecast
1967.2 687.9 —4.8 708.0 15.3 707.9 15.2 692.71967.3 708.0 4.6 708.8 5.4 703.41967.4 716.2 3.9 719.0 6.7 712.3
1968.1 707.4 —11.0 709.3 —9.1 710.6 —7.8 718.4
AFE —7.9 8.2 8.8
Fifth Quarter of Forecast
1967.2 688.9 —14.5 716.4 13.0 715.6 12.2 703.41967.3 719.0 6.7 719.3 7.0 712.31967.4 721.8 3.4 723.6 5.2 718.4
AFE —14.5 7.7 8.1
Sixth Quarter of Forecast
1967.2 691.6 —20.7 725.5 13.2 724.2 11.9 712.31967.3 725.7 7.3 725.5 7.1 718.4
AFE —20.7 10.3 9.5
Forecast One Year Ahead1967.2 685.5 5.7 695.8 16.0 696.8 17.0 679.81967.3 690.6 2.3 690.8 2.5 688.31967.4 700.8 3.3 702.7 5.2 697.5
1968.1 702.1 —4.6 703.1 —3.4 703.5 —3.2 706.7
AFE 5.2 6.3 7.0
TAB
LE 4
.15A
Com
paris
on o
f Lx
Ant
e Fo
reca
sts,
OB
E M
odel
, Une
mpl
oym
ent R
ate
p.11 C P1
C)
— C P1
P1 C 0 P1
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GO
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Adj
ustm
ents
Prel
imi-
Was
Mad
eV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
rV
alue
Erro
r nar
y V
alue
Firs
t Qua
rter o
f For
ecas
t19
67.2
3.9
0.0
3.7
—0.
13.
8—
0.0
4.5
0.6
3.9
0.0
3.9
1967
.33.
80.
04.
10.
33.
80.
03.
7—
0.0
3.8
0.0
3.8
1967
.44.
00.
14.
00.
13.
4—
0.4
3.3
—0.
54.
10.
23.
9
1968
.13.
70.
04.
00.
34.
20.
54.
40.
73.
70.
03.
719
68.2
3.6
0.0
3.6
0.0
3.2
—0.
33.
1—
0.4
3.6
0.0
3.6
1968
.33.
70.
13.
70.
13.
80.
23.
60.
03.
70.
13.
619
68.4
3:7
0.3
3.7
0.3
3.7
0.3
3.7
0.3
3.8
0.4
3.4
AFE
0.1
0.2
0.3
0.4
0.1
Seco
nd Q
uarte
r of F
orec
ast
1967
.24.
00.
13.
7—
0.1
3.7
—0.
14.
91.
04.
20.
33.
919
67.3
3.7
—0.
03.
90.
13.
6—
0.1
3.3
—0.
44.
10.
33.
819
67.4
4.0
0.4
4.2
0.6
3.5
—0.
03.
2—
0.3
4.0
0.4
3.6
(con
tinue
d)-a
TAB
LE 4
.15A
(con
clud
ed)
rTl 0 2 0 rn — C)
Qua
rter
Rep
rodu
ced
Ex A
nte
Ex A
nte
Ex A
nte
Ex P
ost
in W
hich
Ex A
nte
with
AR
with
GG
with
No
with
Act
ual
Rea
lized
Fore
cast
Fore
cast
Was
Mad
e V
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsV
alue
Erro
rA
djus
tmen
tsPr
elim
i-V
alue
Erro
r nar
y V
alue
Sec
ond
Qua
rter
of F
orec
ast (
cont
inue
d)
S
1968
.23.
70.
13.
70.
13.
2—
0.3
3.2
—0.
33.
60.
03.
619
68.3
3.8
0.4
3.8
0.4
4.0.
0.6
0.6•
3.9
0.5
3.4
AFE
0.3
0.4
0.4
0.7
0.3
..
Third
Qua
rter o
fFor
ecas
t
1967
.23.
90.
03.
7—
0.1
3.5
—0.
35:
11.
24.
50.
63.
919
67.3
3.5
0.0
3.7
0.2
3.3
—0.
13.
1—
0.3
•4.
00.
53.
519
67.4
,3.
80.
34.
30.
83.
4—
0.0
3.1
•—
0.3
3.6
0.1
3.5
1968
.14.
10.
54.
50.
94.
71.
14.
50.
94.
00.
43.
,619
68.2
3.8
0.4
3.9
0.5
3.3
—0.
03.
3—
0.0
3.9
0.5
3.4
AFE
0.2
0.5
0.4
0.6
.0.
4,
,Fo
urth
Qua
rter o
fFor
ecas
t.
•
1967
.2•
4.5
0.9
3.6
1967
.33.
3—
0.0
3.6
0.2
3.1
—0.
22.
9—
0.4
3.7
0.3
3.4
1967
.43.
80.
34.
30.
83.
3—
0.1
3.1
—0.
33.
50.
03.
5
0 'I) 0 C)
C)
— r 0
1968
.14.
20.
84.
61.
24.
81.
44.
51.
14.
10.
73.
4
AFE
0.4
0.7
0.6
0.7
0.5
Fifth
Qua
rter o
f For
ecas
t19
67.2
4.5
0.9
3.6
1967
.33.
3—
0.0
3.5
0.1
3.0
—0.
32.
8—
0.5
3.6
0.2
3.4
1967
43.
80.
54.
31.
03.
30.
03.
1—
0.1
3.7
0.4
3.3
AFE
0.3
0.6
0.2
0.4
0.5
0S
ixth
Qua
rter o
f For
ecas
t19
67.2
4.3
0.7
3.6
1967
.33.
20.
03.
50.
32.
8—
0.3
2.7
—0.
40.
53.
2z
AF
E0.
00.
30.
40.
50.
6
Fore
cast
One
Yea
r Ahe
ad19
67.2
4.3
0.5
3.8
1967
.33.
6—
0.0
3.9
0.2
3.5
—0.
13.
3—
0.3
3.9
0.3
3.6
1967
.43.
90.
34.
20.
63.
4—
0.1
3.2
—0.
33.
80.
23.
6
1968
.14.
00.
44.
40.
84.
61.
04.
50.
94.
00.
4.
3.6
(I)
AP
E0.
20.
50.
50.
60.
50 r I —
1112 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
TABLE 4.15P
Comparison of Ex Post Forecasts, OBE Model, Unemployment
Quarter Ex Post Ex Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
First Quarter of Forecast1967.2 2.3 —1.6 3.2 —0.7 4.0 0.1 3.91967.3 4.5 0.6 4.5 0.6 3.91967.4 4.3 0.4 4.3 0.4 3.9
1968.1 3.9 0.2 4.5 0.8 4.8 1.1 3.71968.2 3.6 0.0 2.4 —1.2 2.5 —1.1 3.61968.3 3.6 0.0 3.8 0.2 3.7 0.1 3.61968.4 3.8 0.4 3.8 0.4 3.7 0.3 3.4
AFE 0.6 0.6 0.5
Second Quarter of Forecast1967.2 2.0 —1.9 3.1 —0.8 4.3 0.4 3.91967.3 5.0 1.1 5.1 1.2 3.91967.4 4.8 1.1 4.8 1.1 3.7
1968.1 4.0 0.4 5.1 1.5 5.2 1.6 3.61968.2 3.4 —0.2 1.9 —1.7 2.3 —1.3 3.61968,3 3.6 0.2 4.1 0.7 4.1 0.7 3.4
AFE 0.7 1.1 1.1
Third Quarter of Forecast1967.2 2.1 —1.8 3.2 —0.7 4.8 0.9 3.91967.3 5.2 1.5 5.2 1.5 3.71967.4 4.9 1.3 4.7 1.1 3.6
1968.1 4.0 0.4 5.3 1.7 5.3 1.7 3.61968.2 3.4 0.0 1.6 —h8 2.1 —1.3 3.4
AFE 0.7 1.4 1.3
FORECASTING PROPERTIES OF U.S. MODELS • 1113
TABLE 4.15P (concluded)
Quarter Ex Post Ex Post Ex Postin Which with AR with GG with No RealizedForecast Adjustments Adjustments Adjustments Revised
Was Made Value Error Value Error Value Error Value
Fourth Quarter of Forecast
1967.2 2.5 —1.2 3.3 —0.4 5.2 1.5 3.71967.3 5.1 1.5 .5.0 1.4 3.61967.4 4.9 1.3 4.7 1.1 3.6
1968.1 4.1 0.7 5.5 2.1 5.4 2.0 3.4
AFE 0.9 1.3 1.5
Fifth Quarter of Forecast
1967.2 2.8 —0.8 3.3 —0.3 5.5 1.9 3.61967.3 4.8 1.2 4.8 1.2 3.61967.4 4.8 1.4 4.7 1.3 3.4
AFE .0.8 1.0 1.5
Sixth Quarter of Forecast
1967.2 3.2 —0.4 3.3 —0.3 5.7 2.1 3.61967.3 4.7 1.3 4.7 1.3 3.4
AFE 0.4 0.8 1.7
Forecast One Year Ahead
1967.2 2.3 —L5 3.2 —0.6 4.6 0.8 3.81967.3 5.0 1.3 5.0 1.3 3.71967.4 4.8 1.1 4.7 1.0 3.7
1968.1 4.0 0.5 5.1 1.6 5.2 1.7 3.5
AFE 1.0 1.1 1.2
CH
AR
T 4.
1
Fore
cast
vs.
Rea
lizat
ion
Wha
rton
Mod
el w
ith A
ctua
l Con
stan
t Adj
ustm
ents
(GN
P. B
illio
n /9
58 D
olla
rs)
Rea
lizat
ion
Rea
lizat
ion
. 0 z 0 — C) 0 0 C)
C) r — C) C
•F
irst q
uart
er o
f for
ecas
to
Sec
ond
quar
ter
of fo
reca
stx
Thi
rd q
uart
er o
f for
ecas
ta
Fou
rth
quar
ter
of fo
reca
st
For
ecas
tF
orec
ast
720
700
680
660
640
640
660
680
700
720
640
660
-68
070
072
0
CH
AR
T 4.
2
For
ecas
tvs
. Rea
lizat
ion
Wha
rton
Mod
e! w
ith A
R C
onst
ant A
djus
tmen
ts(G
NP.
Bill
ion
1958
Dol
lars
)
Rea
lizat
ion
0 rn r) 0, — z C C rn 'I, C "1 0 til 0, S
For
ecas
t
•F
irst q
uart
er o
f for
ecas
t0
Sec
ond
quar
ter
of fo
reca
stX
Thi
rd q
uart
er o
f for
ecas
ta
Fou
rth
quar
ter
of fo
reca
st
For
ecas
t
640
660
680
700
720
640
660
680
700
720
CH
AR
T 4.
3Fo
reca
st v
s. R
ealiz
atio
nW
harto
n M
odel
with
GG
Con
stan
t Adj
ustm
ents
(GN
P: B
illio
n 19
58 D
olla
rs)
640
Rea
lizat
ion
Rea
lizat
ion
r C) 0
•F
irst q
uart
er o
f for
ecas
to
Sec
ond
quar
ter
of fo
reca
stx
Thi
rd q
uart
er o
f for
ecas
tF
ourt
h qu
arte
r of
fore
cast
For
ecas
tF
orec
ast
720
700
680
660
640
640
660
680
700
720
660
680
700
720
C fTl > z C
.) 0 -f fri
cit 0 C. 0 fri
ci,
CH
AR
T 4.
4Fo
reca
st v
s. R
ealiz
atio
nW
harto
n M
odel
with
No
Con
stan
t Adj
ustm
ents
(GN
P: B
illio
n 19
58 D
olla
rs)
•F
irst q
uart
er o
f for
ecas
to
Sec
ond
quar
ter
of fo
reca
st
For
ecas
tF
orec
ast
Thi
rd q
uart
er o
f for
ecas
ta
Fou
rth
quar
ter
of fo
reca
st
680
Rea
lizat
ion
640
680
Rea
lizat
ion
680
660
660
680
Rea
lizat
ion
740
660
680
720
740
-I -a — 00 . C) 0 z 0 rn C) 0 rn (I, 0 C)
C) I- — C) > 0
CH
AR
T
Fore
cast
vs.
Rea
lizat
ion
OB
E M
odel
with
Act
ual C
onst
ant A
djus
tmen
ts(G
NP:
Bill
ion
1958
Dol
lars
)
Firs
t qua
rter
of f
orec
ast
x T
hird
qua
rter
of f
orec
ast
Fou
rth
quar
ter
of fo
reca
sto•
Sec
ond
quar
tero
f for
ecas
t
For
ecas
tF
orec
ast
740
720
700
700
720
700
Rea
lizat
ion
CH
AR
T 4.
6
Fore
cast
vs.
Rea
lizat
ion
OB
E M
odel
with
AR
Con
stan
t Adj
ustm
ents
(GN
P: B
illio
n 19
58 D
olla
rs)
•F
irst q
uart
er o
f for
ecas
to
Sec
ond
quar
ter
of fo
reca
stx
Thi
rd q
uart
er o
f for
ecas
tA
Fou
rth
quar
ter
of fo
reca
st
0 C)
U, z 0 -f f's U, 0 0 f's 5- U'
For
ecas
tF
orec
ast
660
680
700
Rea
lizat
ion
720
740
700
Rea
l cat
ion
For
ecas
t
720
700
680
660
Rea
'izat
ion
Rea
lizat
ion
— C z 0 — 0 C m I- (I,
C C.)
C.) C) > > 6
CH
AR
T 4.
7Fo
reca
st v
s. R
ealiz
atio
nO
BE
Mod
e!w
ithG
G C
onst
ant A
djus
tmen
ts(G
NP:
Bill
ion
1958
Dol
lars
)
•F
irst q
uart
er o
f for
ecas
tx
Thi
rd q
uart
er o
f for
ecas
to
Sec
ond
quar
ter
of fo
reca
stA
Four
thqu
arte
r of
fore
cast
740
For
ecas
t
660
680
700
720
740
660
680
700
720
740
660
680
CH
AR
T 4.
8
Fore
cast
vs.
Rea
lizat
ion
OB
E M
odel
with
No
Con
stan
t Adj
ustm
ents
720
(GN
P: B
illio
n 19
58 D
olla
rs)
740
For
ecas
tX T
hird
qua
rter
of f
orec
ast
Fou
rth
quar
ter
of fo
reca
st
Rea
lizat
ion
0 O (I) — C) 0 0 C 0 (1)
Firs
t qua
rter
of f
orec
ast
oof
fore
cast
700
Rea
lizat
ion
660
680
700
S
720
740
1122 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
ments but utilizing the actual values of the exogenous variables. TheOBE results show no advantage for either method.
2. For both the Wharton and OBE forecasts, about half of the exante forecasts with mechanical adjustments have smaller error than therespective ex post forecasts.
3. The GG adjustments are considerably better than any othermechanical adjustments (including no constant adjustments) for theOBE Model, but no one mechanical method is definitely superior forthe Wharton-EFU Model.
4. The true ex ante forecasts are much better than any of the exante forecasts generated by mechanical methods for both the Wharton-EFU and OBE Models.
We consider first, points 4 and 3; and then, points 1 and 2. Thefourth point is easily explained and provides substantive evidencq forthe widespread belief that there is a considerable amount ofof econometric models when they are used for true ex ante forecasiing.This finding in large part explains why errors of the true ex ante fbre-casts are so much smaller than corresponding sample-period
It is not possible to draw any definite conclusions about,,the thirdpoint, since the two models present conflicting evidence. In view of thecomments in the previous section, one would expect that/Ic GG ad-justments would provide the best results of any of the meth-ods which were tried. In this respect, the OBE Model results agreewith a priori reasoning, but the Wharton-EFU Mod/el results do not.Closer examination of the results reveals a rather peculiar pattern. Forthe shorter period forecasts (one or two quarters), when the AR andGG adjustments should be most similar, the AR' adjustments usuallygive a smaller error. However, for the longer time spans, when the GGadjustments are quite small, the latter give the better fo,recasts. Inother words, in the first two periods very large adjustments are needed— almost the full amount of the residuals — while in later periods almostno adjustments are needed. There is no unique explanation for this di-chotomy, but it does agree with the decomposition of error analysisdiscussed in the previous section. At that point, it was shown that forthe sample period and ex post simulations, the Wharton-EFUModel was unable to track minor fluctuations in the first few periods,
FORECASTING PROPERTIES OF U.S. MODELS • 1123
although it did much better in staying close to the actual values forlonger periods.
We shall next consider the first conclusion. It was originally thoughtthat the subjective adjustment of constants was in large part a methodof offsetting bad guesses for the exogenous variables. For example,suppose that the econometric forecaster expects government expend-itures for the next quarter to increase by $5 billion; inserting this as-sumption in the model generates a $15 billion increase in GNP for thenext quarter. However, given his "feeling" about the economy, but-tressed by additional information about orders, construction starts, andso on, the forecaster thinks that $10 billion will be a better estimate.This would lead to a downward adjustment in the constant terms of theconsumption and investment functions until the GNP forecast is re-duced to a $10 billion increase. Later, the actual figures reveal thatgovernment expenditures increased by only $2 billion; the rise in GNPis in fact $10 billion. Since most econometric models have impact mul-tipliers for government purchases of 1.5 to 2.0, this would reduce theincrease in GNP which was predicted ex post to about $5 billion. If theadditional constant adjustments had not been made, the ex post fore-cast would have shown an increase of about $10 billion. In this case, cxpost forecasts would be inferior to the cx ante forecasts when the exante
a conjecture; there may be other rea-sons why the ex ante forecasts are better than the ex post forecasts forthe Wharton Model. If we introduce the evidence summarized in thesecond conclusion, that conjecture must be rejected, for the ex anteforecasts are superior to the ex post forecasts in almost half the cases,even when the same method of constant adjustment is used. This ispotentially a much more damaging argument against the use of econo-metric models for forecasting and policy analysis than is the first con-clusion. Even if we eschew all judgment in the adjustment of the con-stant terms, the forecast error increases almost as often as it decreaseswhen we introduce the correct values of the exogenous variables intothe solution. The first conclusion could be explained by offsetting er-rors; the forecaster is able to gauge the change in the economy ac-curately for the next one or two quarters, so he offsets his bad guesses
1124 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
for the values of the exogenous variables by adjusting the rest of themodel. With mechanical (or no) constant adjustments, this is no longeran admissible procedure. Inserting the correct exogenous values oftenpushes the solution farther away from the true value. This might occureither because the actual data series are faulty, or because the fiscalpolicy multipliers are overstated in the Wharton-EFU and OBEModels. Each of these possibilities will be considered in turn.
The only exogenous variables for which the differences betweenestimated and actual values make much difference are government ex-penditures, tax rates, and monetary policy variables (discount rate andfree reserve ratio). Of these, only ex post figures for government ex-penditures are likely to be subject to distortion in reporting. In par-ticular, defense spending may be entered in the National Income Ac-counts as inventory investment while the goods are being produced,becoming government purchases only when they are finished and aretransferred to the military authorities. While the same problem alsoexists for producers' durable equipment, it is not as serious a problembecause the quarterly fluctuations are not as acute.
To illustrate this problem, consider a situation where the govern-ment orders an additional $10 billion of military hardware. We makethe extreme assumption that all of this equipment is ordered at thesame time, and that it all takes exactly one year to complete, at whichtime it is delivered to the government. Work progresses on this equip-ment steadily during the year. There are two polar positions for present-
-ing this in the national income accounts.
Case I:$2.5 $2.5 $2.5 $2.5 —$10.0
0.0 0.0 0.0 0.0 $10.0Casc' II:
0.0 0.0 0.0 0.0 0.0$2.5 $2.5 $2.5 $2.5 0.0
The net increase in GM? in each quarter is the same for both cases. Inthe final quarter, the only activity occurring is the transfer of finished
• goOds from the manufacturer to the government. However, if one istrying to predict the level of government expenditures, it makes a greatdifference whether Case I or Case II accounting methodology is used.
FORECASTING PROPERTIES OF U.S. MODELS • 1125
If the forecaster is in our hypothetical Period 4 (above), if he istrying to predict Period 5, and if he knows that Case I is being used, itis then a simple matter to make an adjustment of —$ 10 billion to theinventory investment equation. However, one is usually not sure howmuch of recent movements in inventory investment is due to changesin semifinished defense goods. Thus the adjustment may be only par-tial, or may not be made at all. In the case of mechanical constant ad-justments, it has been noted earlier that no adjustment is made for theinventory investment equations at all. In this case, an adjustmentbased on the previous residuals would lead to an even larger error. Ifthe ex ante forecaster does not foresee the large rise in then hisprediction of Gd would be understated by $10 billion, but his estimateof GNP (assuming no other errors) would be perfect. However, if heuses the ex post figures and raises Gd by $10 billion without includi.ngoffsetting constant adjustments elsewhere in the model, the GNP pre-diction is almost sure to be overstated. This is what appears to havehappened, particularly in the first two quarters in 1967, when govern-ment defense expenditures rose $8.5 billion and manufacturing inven-tory investment dropped $8.1 billion (total LII, dropped $17.5 billion).
With respect to the other possibility for the superior performanceof the ex ante forecasts mentioned above, there is some evidence tosuggest that the early quarter government expenditure (and tax) mul-tipliers are overstated by the Wharton-EFU Model. The first-quarterchange in constant-dollar GNP, due to a $1 billion change in constant-dollar government expenditure, is $2.0 billion. In an updated version ofthe model, this multiplier is reduced to about 1.6.28 Furthermore, theOBE Model, the FRB-MIT Model, the Brookings Model, and theMichigan Model all have impact multipliers of about 1.5 for govern-ment purchases. However, even these multipliers may be overstated,as explained in the next section. The Wharton forecasters may havecompensated for this deficiency in their models by choosing exogenousvalues that would yield forecasts in line with their good a priori view ofa reasonable forecast, or the good ex ante results may have been causedby random occurrences, in a small sample.
These results are reported in M. K. Evans, "Computer Simulations of Non-LinearEconometric Models," in T. H. Naylor, ed., The Design of Computer Simulation Ex-periments. New York, John Wiley & Sons, Inc., 1969.
1126 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
5 AN ANALYSIS OF PROCEDURES FOR MINIMIZINGEX ANTE FORECAST ERROR
WE SHALL examine four techniques that might be used to reduce fore-cast error. The methods that we will examine are: (a) the introductionof judgment during the forecasting process, (b) the adjustment of equa-tions on the basis of previous residuals, (c) the use of new estimatingprocedures to reduce forecast error for complete system solutions, and(d) the use of alternative specifications and estimating procedures toreduce error propagation within a simultaneous model. It will be seenthat both the third and fourth sources of error stem from a commonproblem.
A. THE INTRODUCTION OF JUDGMENT DURING THE FORECASTINGPROCESS
We shall consider three ways that judgment can be used in theforecasting process after the model has been specified and estimated,and after the preliminary lagged values have been collected. The fore-caster first exercises his judgment when he chooses the values of theexogenous variables, again when he adjusts the constant terms of theequations, and again when he modifies these decisions on the basis ofpreliminary forecasts. We shall consider each of these problems in turn.
In order to make an econometric forecast, one must project thevalues for the exogenous variables. We can see, in Table 4.1, thatforecasts of constant-dollar GNP when actual values of the exogenousvariables were used are not any better than results achieved when theguessed values were employed. Since it is obvious that a forecasterwould benefit from future information, we must conclude that somefactors tend to offset the inherent advantage that cx post data shouldhave in tracking the actual path of the economy. The method used inthe National Income Accounts in reporting government expenditure(which was explained in Section 4) is clearly one such factor.
When we specify an equation we cannot include every conceivablevariable as an explanatory variable. Thus, only a priori reasonablevariables are included in our specification of an econometric equation.
FORECASTING PROPERTIES OF U.S. MODELS • 1127
This procedure will not bias the values of the coefficients in our equa-tion as long as the omitted variables are not correlated with an includedvariable. When the econometrician is making a forecast, he may havesome information about an excluded variable which is pertinent to thedetermination of the dependent variable. He may also have some know-ledge of the coefficient that relates changes in the excluded variable tochanges in the dependent variable. Examples of special extraneousevents would include the 1964 automobile strike, the 1965 dock strike,and the 1966 credit crunch. Evidence that reflects on whether or notextraneous constant adjustments, taken alone, improved forecast per-formance, can be seen by comparing the ex post forecasts with theactual constant adjustments to those with mechanical constant adjust-ments (see Tables 4.1—4.5 and 4.11—4.15). The ex post forecastswith the actual adjustments are only superior to mechanicallyadjusted forecasts about one-half of. the time. Thus, there is no strongevidence that constant adjustments made a major contribution to fore-cast accuracy.
Econometricians have been rejecting preliminary specificationsand substituting other maintained hypotheses on the basis of prelim-inary coefficient estimation ever since econometric model-buildingstarted. The method of introducing a priori information before makingestimates has not been utilized by practicing econometricians. Instead,econometricians have continued to select equations on the basis ofreasonableness. Likewise, it appears that econometric forecasters havesubjected their forecasts to the test of "reasonableness" before makingthem official. That this check on forecasts has improved forecast per-formance can be seen clearly in the superiority, of the ex ante resultsover the ex post results.
It appears that the most significant way in which judgment hasbeen used to improve the forecasts that would have been made, had themodels been used mechanically, consists of adjusting the exogenousassumptions and constant terms in such a way that the final forecast isa compromise between the econometricians' a priori idea of what areasonable forecast would be, and the forecast that would have emergedif the exogenous variables and constants had been chosen without re-gard to the effect of such guesses on the forecast values of the endoge-nous variables.
1128 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
B. THE ADJUSTMENT OF EQUATIONS ON THE BASIS OF PREVIOUSRESIDUALS
Ex post forecasts with both the regular and the anticipations ver-sion of the Wharton-EFU Model show a reduction of error in one- andsometimes two-quarter forecasts when AR adjustments are made onthe basis of past residual values. The relative advantage of the adjustedforecast is lost for three or more quarters.
The results shown in the tables in Section IV suggest that one ob-tains the best ex post forecasts by multiplying the residuals by powersof the autocorrelation coefficient, and that the use of the same residualfor four or more quarters may be too rigid and unrealistic. With fewexceptions, the ex ante results support this position.
C. THE USE OF NEW ESTIMATING PROCEDURES TO REDUCEFORECAST ERROR FOR COMPLETE SYSTEM SOLUTIONS
We can examine the error for an individual equation in four dif-ferent situations. We can distinguish between the fit in the sample pe-riod and in the forecast period, and we can differentiate between theerror when the dependent variable in the equations is determined usingthe observed values of the explanatory variables and when it isfound using the complete system solution values of these variables.The situation can be pictured as follows:
Sample ForecastPeriod Period
Observed explanatory endoge-nous variables 2 1
System-determined explanatoryendogenous variables 3 4
The econometrician who wanted to minimize the sum of squarederror in Quadrant 2 would use. ordinary least squares (OLS) as hisestimation technique. Widespread recognition of the inconsistency in-troduced by OLS estimates has led to the belief that they probably
FORECASTING PROPERTIES OF U.S. MODELS • 1129
yield results inferior to the consistent estimating techniques in Quad-rant 1. Since in actual forecasts the values of the endogenous ex-planatory variables are, of course, unknown, we should be concernedprimarily with minimizing error in Quadrants 3 and 4. To accomplishthis, we must calculate regression equations where the explanatoryvariables are system-determined values rather than actual observations.
Another related problem which arises is the buildup of error overtime. Classical methods of estimation do not take into account thesituation where error buildup is introduced into the equation becausethe lagged dependent variable is used as an independent variable.Some method is needed which not only reduces the dependence on si-multaneous variables, but which does not overstate the importance oflagged dependent variables in complete system solutions.
Such a method has been worked out by Cooper and Jorgenson29and extended by L. R. Klein;30 the idea was mentioned at an earlierdate by Houthakker, and was reported by Theil.31 Klein refers to themethod as iterative TSLS; we call it ROS (regression on simulatedvalues). The essence of the method is to regress the equations on sim-ulated values of the simultaneous and lagged dependent variables,instead of either actual values or TSLS-calculated values.
Informally, the five-step procedure that we used to find and testthe ROS coefficients can be described as follows:
1. The coefficients in the model were estimated using TSLS withprincipal components as the exogenous instruments. These coeffi-cients are the same coefficients that have been published for the Whar-ton-EFU Model.
2. Sample-period forecasts were calculated one quarter ahead foreach point in the sample period. These forecasts were made using theAR constant adjustments mentioned earlier.
3. The forecast values for each of the endogenous variables wereused as explanatory variables for ordinary least squares regressions in
29 R. L. Cooper and D. W. Jorgenson, "The Predictive Performance of QuarterlyEconometric Models of the U.S.," Working Paper in Mathematical Economics andEconometrics, No. 113, University of California, Berkeley, August, 1967.
3° Lawrence R. Klein, An Essay on the Theory of Economic Prediction. Helsinki,American Book Store, 1968.
H. Theil, Econo,nic Forecasts and Policy. Amsterdam, North-Holland PublishingCo., 1958, 1st edition only.
1130 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
this step. This regression of the observed dependent variables on the"forecast" explanatory variables was performed for all equations inwhich the dependent variable was one of the main components of ag-gregate demand.
4. The new coefficients were used in the model, and sample-period simulations one quarter ahead were made, using the same rule-of-thumb constant adjustments.
5. The average absolute errors and the root mean-squared errorsof the predictions in the forecast period — using the new coefficients —were compared to forecast errors using the old coefficients. The error,measured either way, was lower using the ROS than the TSLS coeffi-cients for GNP and almost all of the other important variables.
As can be seen from this description, our approach was onlypartial. We did not reestimate the complete model; we did not estimatelagged dependent-variables by this method; and we did not iterate toobtain fully consistent estimates. Formally, we can extend this methodto include the dynamic situation where lagged variables are also esti-mated in this same scheme. The exposition here follows L. R. Klein(op. cit., pp. 69—70).
Consider the general linear model
+ = et
First, let us estimate A, and E by the standard method of TSLS, usingprincipal components as the exogenous instruments if the number ofexogenous variables is large relative to the number of degrees offreedom.
We can then obtain elements as a solution of the general model
+ = 0
We stress that the are complete system solution values.We may solve the model for the complete sample period without
restarting, but, in general, we are interested in solving at most pperiods at a time. We would then obtain complete system solutionvalues . . . where the first subscript indicates the particular
FORECASTING PROPERTIES OF U.S. MODELS • 1131
quarter in which the solution starts (e.g., 1955.1), and the second sub-script, the number of quarters ahead the solution is carried. For prac-tical purposes, we would have p 4 in the Wharton Models.
Having obtained these we can now reestimate the whole sys-tem of equations
p0
and obtain a new set of parameter estimates: A and B. The processmay be continued until convergence is reached, defined as
nfl (n—i )A nfl (n—i)AB—B
(n—1)fl < (n—1)fl <A, B
where is some predesigned level of tolerance and nA represents thenth iteration of estimation.
The theory for this class of estimation has not yet been developed,and the solution algorithm has never been fully tested, in particular, it
nflis not clear whether asymptotically the A, B are of the limited-information or full-information class of estimation. While they takeinto account all the information in the system, they do not do so in theusual manner of full-information methods. (No attention is paid tointercorrelation of residuals from different equations.) Also, Theilsuggests that this method does not converge, and some preliminarycalculations on Klein Model I also suggest this. In Table 5.11, theoriginal coefficients are compared with the ROS coefficients.
The mean square error of the aggregate demand componentsof current dollar GNP in the sample period (1953.1—1964.4), using thecomplete system solution values of the explanatory variables andmechanical constant adjustments, was $12.75 billion for the ROScoefficients, compared with $17.21 billion for the TSLS coefficients.In the forecast period, the values were $45.78 and $51.55 billion,respectively. This suggests that single equation forecast error in thefirst quarter might be significantly reduced using some variation of theROS coefficient estimation method.
1132 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
D. THE USE OF ALTERNATIVE SPECIFICATIONS AND ESTIMATINGPROCEDURES TO REDUCE ERROR PROPAGATION WITHIN A SIMUL-TANEOUS MODEL
The error of forecast for an aggregate variable such as GNP occursnot only because each component of the aggregate variable cannot bepredicted exactly, but also because errors in individual equationsreverberate throughout the system and reinforce or cancel out eachother. In the limiting case, where no equation has any individual equa-tion error, the simultaneous solution for the system will yield therealized values and there will be no error propagation. On the otherhand, a forecast error in any equation in the system will cause allother simultaneously determined variables to be in error, unless thereis an offsetting errorelsewhere in the system.
If the forecast of a particular variable is relatively unreliable underthe restrictions of the model, a regression on the predicted values ofthis variable will lead to a smaller coefficient than was the case withthe original TSLS coefficients. Conversely, a variable that is predictedbetter under the restrictions of the model than in the first stage ofTSLS will have a larger weight under the ROS procedure than it hadunder the TSLS procedure.
The shifting weight in the equations from those variables that arenot predicted reliably to those that are can easily be seen in Table 5.1.In general, the shift is from eñdogenous to lagged variables. Particularlydramatic shifts away from variables that are not reliably predicted inthe Wharton-EFU Model can be seen by looking at the reduced impor-tance of unemployment under the ROS procedure in the car equation,and at the reduction of the importance of in the nonmanufacturinginventory investment equation.
It can be seen from Table 5.1 that the principal effect of reesti-mating the model using ROS coefficients is to decrease the amount ofsimultaneity. This appears to reduce forecast error substantially byrelying less on those simultaneously determined variables which can-not be predicted accurately. We now present additional evidence thatforecast error might also be reduced by diminishing the propagation oferror in simultaneously determined models.
Before we look at propagation, we might reasonably ask whether
TABLE 5.1
Comparison of ROS Coefficients with TSLS Coefficients(The ROS coefficients are written, in above the TSLS coefficients in these
selected equations from. the Wharton-EFU Model.)
.2405— 0.29101. = 0.2273 - 0.4590 [(v) + .75 + .50 + .25 (v)]
+ .70051 C+ 0.7232 (ns)
(0.0512) i—'
—8.61 + 0.1086 — 0.01082. Cna=1L52+ 0.1570Y— 0.0574Kna1
(0.0274) (0.025 1)
1.26+ .1143 Tr — 7.64 P — 0.017 — 2.4403. Ca48.54+ 0.1346 (Y__)_ 54.19 0.430Un
(0.0228) (10.20) Pc (0.175) (0.458)
+ 1.710 — 0.0484+ 1.835Cr— 0.0744K
(0.478) (0.0180)
58.63 + 0.0237 — 45.83 + 1.4447. = 58.26 + 0.0249Y — + 1.433(1,, —
(0.0033) (4.76) (0.282)
—25.03 + 0.1276 — 0.1849 + 0.26809. =—14.94 + — 0.1 17311,l_2 +
(0.0456) (0.0476) (0.0634)
+ 0.03 14 + 34.54+ + 4.0A3(p,1 —
(0.0686) (11.82)
.0127+ 0.0060 0.004410. —= 0.0117+ 0.0064 —— 0.0041 —
(0.0013) N (0.00 15) Pi
2.47 + 0.0348 + 0.0605 — 1.3711. F.m, = 3.51 + + 0.0960M,, —
(0.0022) (0.0194)
—2.83,+ 0.0287 — 1.73 + 0.612112. ± 0.0293Y— 1.97 0.6014
(0.0073) (1.48) rn (0.1109) i='
—26.25+ 0.1132 + 23.88 + 0.620013. Fe=38.88+ 34.33 0.4663 (Fe)_i
(0.0128) (4.78) (0.0534) 4
1134 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
the errors in single equations are related to each other. This can betested by utilizing the well-known theorem that the sum of the squarederror of random variables is equal to the squared error of the sum ofthe variables when all of these variables are independent. Thus, we canfind out if there is a significant difference between the sum of thesquared error of the individual equation residuals and the squared errorof the sum of these residuals.
In the first part of Table 5.2, we can see that in most cases thereis a slight negative relationship among the errors in single equations.There is a very large negative relationship for the TSLS's in the fore-cast period, and a pronounced but smaller negative relationship for theROS in the forecast period. Yet, due to the simultaneous nature of aneconometric model, we should expect that in any complete systemforecast, the errors for many of the variables will have the same sign.For example, since Cna, and Ca are all positively dependent ondisposable income, a forecast of disposable income that is too high willcause Cna, and Ca all to be too high; this will, in turn, increase theerror in the forecast of disposable income. Thus, as long as we look atforecasts for the entire system, we may find a positive correlation oferrors. In the lower half of Table 5.2, it can be seen that the mean-squared error for individual variables is lower for the lower level ofaggregation. This is true whether we use forecasts with or withoutanticipations equations, with or without constant adjustments, or withor without ROS coefficients. It should be noted that the positive corre-lation of forecast error is less in the simulations using ROS coefficientsthan in other forecasts. This is especially significant when we noticethat the single-equation errors showed less of a tendency to cancel outeach other for ROS in the forecast period than they did for TSLS.This suggests that the ROS coefficients tend to reduce the propagationof error.
The propagation of error seems to cause 28 per cent of the errorin the 1965—1968 TSLS forecast, thus offsetting the 83 per cent re-duction that we might have anticipated when looking at the single-equation results. Comparing the 1953.1—1964.4 record of the no-constant-adjustment simulations with the regular and anticipationsversions, it can be seen that almost all of the difference in forecast
FORECASTING PROPERTIES OF U.S. MODELS • 11 35
error of GNP can be attributed to the smaller propagation of error inthe anticipations version.
This result might be anticipated a priori, because the ROS coeffi-cients give smaller weight to endogenous explanatory variables thando the TSLS coefficients; and because the addition of anticipationsvariables to consumption and investment equations reduces interde-pendence within the equation system. This reduced interdependence
TABLE 5.2Mean Square Error in Current Dollars at Different Levels ofAggregation
for Various Methods of Calculation(One Quarter Ahead Only)
Sum ofMSE of
Indi-vidual
Demand Ratio toMethod of Calculating Equa- MSE of Column
Time Period Predicted Values tions GNP One
Single-Equation Residuals1948.3—1964.4 TSLS—Regular 13.4 11.2 0.841948.3—1964.4 ROS—Regular 15.7 15.0 0.961953.1—1964.4 ROS—Regular 12.3 14.4 1.171953.1—1964.4 TSLS—Regular 11.2 10.8 0.961965.1—1968.4 TSLS—Regular 82.2 13.6 0.171965.1—1968.4 ROS—Regular 88.0 49.2 0.56
Systems Forecasts1953.1—1964.4 TSLS— AR Adjustments— Regular 17.21 47.20 2.741953.1—1964.4 ROS—AR Adjustments— Regular 12.75 27.67 2.171953.1—1964.4 TSLS — AR Adjustments — Anticipa-
tions 11.66 26.52 2.271953.1—1964.4 TSLS — No Constant Adjustments —
Anticipations 18.96 26.11 1.381953.1—1964.4
1953.1—1964.4
TSLS — No Constant Adjustments —Regular
TSLS—GG Adjustments— Regular20.5815.78
45.5637.33
2.212.37
1965.1—1968.4 ROS—AR Adjustments—Regular 45.78 46.24 1.011965.1—1968.4 AR Adjustments— Regular 51.55 66.10 1.28
1136 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
means that an error in one equation has less tendency to reverberatethrough the system than it does when all of the equations are closelydependent on each other. While the ROS coefficients give poorerresults for each individual equation, they give better results for com-plete system solutions.
We now return to our earlier surmise that impact multipliers ofeconometric models are generally overstated. While TSLS removesbias asymptotically, there is little question that much of this bias re-mains when we are working with short sample periods with strong timetrends, and are using instruments which explain well over 90 per centof the variance of the exogenous variables. The ROS coefficients areone step more removed from the stochastic disturbances that causesuch bias than TSLS estimators are. Thus, the ROS coefficients areless likely to reflect small-sample bias than are TSLS estimates, andmay give us a more accurate estimation of impact multipliers than weget from a model estimated by TSLS.
The calculations reported in Sections v-c and V-D, while clearlyof a tentative and experimental nature, do suggest that forecasting ac-curacy could be improved if simultaneous equation systems were es-timated by methods which removed more of the small-sample bias thando TSLS and other k-class limited-information estimators. By doingso, one would obtain better estimates of the structural parameters ofthe system as well. While such methods would lower single-equationmeasures of goodness of fit and t-ratios, they would probably givegreater insight into the true structure of the economy, and would resultin better models for both forecasting and policy-simulation purposes.
6 CONCLUSION
OUR analysis of the forecasting properties of the Wharton and the OBEeconometric models supports six major conclusions:
1. The first two quarters of forecast for both models are signifi-cantly improved by including mechanical constant adjustments basedon single-equation residuals of previous periods. This result holds for
FORECASTING PROPERTIES OF U.S. MODELS 1i37
both methods of constant adjustment that we used in this study, andcorroborates the logical argument that constant adjustments will im-prove forecasts if models are mis-specified and have autocorrelated re-siduals. Specifically, when the Wharton Model is used without adjust-ment, the errors for GNP and its major components in the first twoquarters of forecast are almost twice as large as the first two quartersof simulation error when this error is measured as root mean squareper cent error, or as root mean square error divided by the root meanerror of a no-change forecast. This difference disappears in longer fore-casts.
2. The true ex ante forecasts are significantly better than other exante forecasts for virtually all variables and all time periods for theWharton Models, and for most of the variables and time periods forthe OBE Models. The true ex ante forecasts differ from the other exante forecasts only because the constant adjustments actually used bythe forecasters were included, instead of either no-constant-adjustmentor a mechanical adjustment based on previous single-equation residuals.These actual adjustments differed from the other adjustments becausethey included judgment in addition to previous residuals. This judg-ment was based on information about events that would affect endog-enous variables but which was not included in the specification ofindividual equations, and also on the forecaster's a priori expectationsof what was a reasonable prediction. The fact that the true ex anteforecasts are better than the mechanical ex ante forecasts suggests thatthe use of judgment in adjusting the constant terms appreciably im-proved the Wharton and OBE forecasts.
3. The Wharton true ex ante forecasts are better than ex postforecasts with the same constant adjustments. The OBE cx post fore-casts were no better or no worse than the ex ante forecasts. For bothmodels, the ex ante forecasts with mechanical constant adjustmentsare better than the ex post forecasts with the same adjustments inalmost half of the cases. The superiority of the Wharton true ex anteforecasts over the ex post forecasts where the actual ex ante constantadjustments are used was contrary to our expectations. One wouldexpect that when realized values were sUbstituted for the estimatedvalues of the exogenous variables, forecasts would be improved if
1138 ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
the structure of the model is correct. We tried to explain the observedsuperiority of the true ex ante forecast as follows: after the forecasterselected the values of the exogenous variables, his preliminary fore-cast may have been out of line with his a priori forecast for the currentquarter and for the next quarter. He may then have reconsidered someof the constant adjustments in order to make his forecast reasonable.if we now substitute the realized values of the exogenous variables,this will lead to a forecast not in line with either a forecast by the modelor a forecast based entirely on a priori notions. But this explanationdoes not explain the superiority of mechanically adjusted ex ante toex post forecasts in almost half of the cases. This can be explained byincorrect reporting of government expenditures in the national incomeaccounts, or by the overstatement of the degree of simultaneity andshort-run fiscal multipliers, which leads to our next point.
4. Closer analysis of both the sample-period simulations and exante and cx post forecast errors suggests that these errors might havebeen reduced if the fiscal multipliers estimated by the models weresmaller, and if the monetary multipliers were larger. Since fiscal var-iables tend to enter all the models covered here as simultaneous deter-minants of GNP, and monetary variables enter through the laggedstructure, this suggests that the degree of simultaneity in the models isoverstated, and that the contribution of the lagged variables is under-stated. This hypothesis is strengthened by the finding that there issubstantial propagation of error in the system: the mean square errorof total GNP is much larger than the mean square error of the sum ofthe individual aggregate demand components. Part of this problem maybe caused by faulty estimation techniques. This would be consistentwith recent findings that the results obtained by using two-stage leastsquares are virtually indistinguishable from those obtained with or-dinary least squares for macromodels of the size used in this study.
5. Most of the ex post forecast error generated when mechanicalconstant adjustments are used is due to imperfect covariation, ratherthan to imperfect central tendency or unequal variation. Thus, theerrors in the forecasts are due primarily to random fluctuations,rather than to consistent errors in forecasting trends or cyclical fluc-tuations. In addition, it should be noted that the annual forecast error
FORECASTING PROPERTIES OF U.S. MODELS • 1139
for GNP is substantially smaller than the sum of the absolute value ofthe first four quarters of error. This indicates that in spite of the quar-terly nature of the models, they may be best suited for predicting annual,rather than quarterly, movements.
6. In order to mitigate some of these difficulties, we tried a methodof estimation which we called ROS (regression on simulated values).In using this method, one estimates the complete model a first time bythe usual methods, and then uses the complete system solution values,instead of the observed values of the independent endogenous variablesto reestimate the coefficients. It is found that this method reduces theaverage forecast error for the first two quarters, and also reduces thesize of the impact multipliers, the degree of simultaneity, and thepropagation of error. However, the errors using the ROS coefficientsare slightly larger than the other methods for later quarters, whichmight indicate that the ROS coefficients will be most useful if they areestimated with complete system solution values for lagged, as well ascurrent, values.
This study has shown that econometricians have had a better fore-casting record to date than an analysis of the econometric models thatthey used would have led us to predict. Our results offer no substan-tive evidence that the same econometricians, forecasting without the"benefit" of an econometric model, would have done any better or anyworse in their predictions. This recognition of the limitations of currentmodels need not lead to pessimism about the future development of ac-curate econometric forecasting models. With a finer understanding ofhow changes in monetary and fiscal policy actually influence economicactivity, closer attention to the short-run specifications and lag adjust-ments of the system, possible improvements in the National IncomeAccounts, and refinement of existing estimation and forecasting tech-niques, the next few years could offer substantial advances in the artand the science of econometric forecasting.
1140 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
DISCUSSION
H. 0. STEKLERSTATE UNIVERSITY OF NEW YORK
IN READiNG this paper by Evans, Haitovsky, and Trey.z, I am onceagain impressed by the vast amount of detailed manipulation that isrequired before an econometric model can be used to make economicforecasts. The OBE and Wharton School econometricians are to becomplimented for keeping such meticulous records that this recon-struction of the forecasting record of their model could be undertaken.The task of reconstructing the forecasting record of econometricmodels and then comparing the accuracy of these predictions againstnaive standards and judgmental forecasts is essential. It is preciselythrough such analyses that we learn about the relative advantages ofthe various approaches. Subsequently, the profession can select thefavored forecasting approach, or approaches, or it may choose to com-bine the several techniques in some fashion.
Econometricians have long known, and the authors again remindus, that models cannot be used in a mechanistic manner. A priori in-formation about events which the model cannot be expected to pre-dict should be, and has been, incorporated into these models. Theconstant terms of equations must frequently be adjusted; and theauthors' discussion of alternative techniques which might be used is ofgeneral interest.
While there are mechanistic rules for adjusting constants whichmight be followed, we are told that "no single rule explains all of theadjustments which were made" to the constant terms of the WhartonModel. We can thus infer that sometimes the constants were adjustedin an ad hoc fashion. This finding reveals the extent to which forecastsobtained from an econometric model are a blend of judgmental andeconometric techniques.
However, the fact that constant adjustments are made should notbe entirely considered a virtue. The necessity for making these adjust-ments indicates that the model is not a completely accurate represen-tation of the economy. Such adjustments might be required if therewere systematic errors, which are obvious indications of structural
FORECASTING PROPERTIES OF U.S. MODELS • 1141
inaccuracies, or if it were constantly necessary to incorporate informa-tion about exogenous events, such as strikes. If these exogenous eventsoccurred periodically, and if they had an economic impact on auto-mobile sales, inventories, and so forth, it might be more appropriate toreestimate the relevant equations by including a "strike variable" thanto make the constant adjustments.
I seem, also, to have a major philosophical difference with thethree authors of this paper about the appropriate criteria to be used inevaluating the forecasting accuracy of econometric models. I' believethat such an evaluation should be based on the model's ex post pre-dictions.• Although the authors present these ex post results, theyindicate that the ex ante predictions are the more relevant forecasts.There is an obvious interaction between a model and the econometri-cians who issue the actual forecasts; and they argue (1) that forecast-ing with an econometric model involves judgment, (2) that a modelmust be "fine-tuned" before a prediction is issued, and (3) that no oneuses unadjusted econometric models to make forecasts. Therefore,they say, one should determine how well econometric models cumeconometricians performed.
I disagree with this view. Since econometric models are subjectto inaccuracies, it might be just as appropriate to determine how wellthe econometricians would have done had they ignored the model andrelied solely on their judgment. Only the ex post approach allows oneto distinguish between the ability of the analyst in estimating the pre-determined variables, and that of the model in simulating the economy.
The entire 'rationale behind evaluating the forecasting record ofalternative approaches and different models is to select the techniquewhich is superior. The profession is less interested in knowing whichman had the best batting average. On the other hand, some judg-mental adjustments are obviously useful and necessary in generatingforecasts. It is, therefore, appropriate to examine the ex post forecastsfor which mechanical constant adjustments have been made. Theauthors have developed this measure, and I will use it in evaluating thepredictive usefulness of the econometric models which are discussed inthis paper.
While I argue that it is necessary to use ex post forecasts in orderto evaluate properly the accuracy of econometric models qua
1142 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
casting technique, I recognize, too, that there are no ex post judg-mental predictions. Since it is necessary to compare the accuracy ofjudgmental and econometric techniques, ex ante judgmental andeconometric forecasts must be examined. Rather than comparing thepredictive record of econometricians and judgmental forecasters, Iwould like to suggest an alternative approach which will compare therelative accuracy of the two techniques.
If judgmental forecasts are to be compared with econometric pre-dictions, in order to be consistent the ex ante econometric forecastsmust be utilized as the basis of comparison. Moreover, both sets of exante forecasts must utilize the same assumption about exogenousevents. The two types of forecasts should have been made at the sametime, using the same data. In addition, the estimates of the exogenousvariables which are used in the model should be those of the judg-mental forecaster whose procedures are being compared with themodel.1 The difference in the two sets of forecasting errors nowmeasures the relative accuracy of the techniques.
Any different procedure would yield results failing to reflect therelative forecasting accuracy of the two approaches. It should, how-ever, be noted that the accuracy of a model can only be judged relativeto that of a specific forecaster. Just as some models or forecasters out-perform other models or forecasters, the performance of a particularmodel might be more accurate than the record of some judgmental fore-casters and inferior to that of others. Consequently, to obtain a validcomparison of the accuracy of the two techniques,this procedure wouldhave to be repeated a number of times — for different forecasters anddifferent models.
Turning aside from this philosophical difference, I would like tocomment on some of the methodology used in the study under con-sideration. There is as yet no agreement about the best method forevaluating multiperiod predictions. In this paper, the levels of economicvariables which are forecast quarters in advance are compared withthe actual levels observed in those quarters. While it is not incorrect touse this approach in evaluating multiperiod forecasts, there is one dan-
A mechanical constant-adjustment method would, of course, be incorporated intothe model. If the judgmental forecaster takes into account the impact of some exog-enous variable not considered by the model, an adjustment must also be made for thisfactor.
FORECASTING PROPERTIES OF U.S. MODELS • 1143
ger which must be recognized. It is possible that the level predictionsmade n quarters in advance were identical to the actual levels observedin that quarter; but that accuracy could have resulted from underes-timates of the changes in the firstj quarters, followed by overestimatesin the remaining n —j quarters.2 It is for this reason that I prefer toexamine the intraperiod quarterly changes.3 In fact, the results wiltshow that neither the OBE nor Wharton Model tracked quarterlychanges very well, but both do return to the path.
There is also no agreement about the preferred naive standard withwhich multiperiod predictions should be compared. The authors use anappropriate naive standard which is based upon a form of the secondNaive Model =
= + (j + —
j0,l...nThis is not an overly severe standard and some auto-regressive schemebased on n lags might have been preferred. I would prefer that thespecifications of this lag structure be chosen in advance, rather thanseeking out that structure which maximizes R2.
Another possible difficulty involved in the paper is that the errorsof all forecasts made n quarters in advance are averaged and tabulatedwith an average of all the forecast errors made n — 1 and n + I quar-ters in advance. I have previously noted that such a procedure may in-troduce biases should observations be missing for some quarters. Ibelieve that it is appropriate to compare the errors only of those quar-ters which had common forecasts made n and n + 1 quarters in ad-vance.5
2 It should be remembered that policies which are based on forecasts would not beinvariant with respect to the time pattern of the errors.
This approach, however, requires that we decide how to measure the predicted andactual changes. It turns out that for multiperiod forecasts there may be a differencebetween the methodology used to measure the ex ante predicted changes and that uti-lized to obtain the ex post predicted changes. In the first case, it is = — in thesecond instance, it may be either — A1_1 or Pg_1.
If the naive standard = + — Xr_2) j = 0. 1 . . . n were used, therewould be a downward bias in a period of growth. If changes are analyzed, then an ap-propriate standard might be
H. 0. Stekler, "An Evaluation of Quarterly Judgmental Economic Forecasts,"Journal of Business, XLI (July, 1968), pp. 329—339.
1144 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
A point on the data which is used in this study is also in order. Inanalyzing the forecasts of the Wharton Model, the published cx anteforecasts—which are generated from preliminary data (and even es-timates, in some cases)—are compared with the actual changes, whichare derived from the revised figures available in 1969. This may be aninappropriate procedure because the inputs to the forecasts are notrevised, whereas the outcome and actual data are. There may be norelationship between the state of the economy which was assumed toexist at the time that the forecast was prepared, and that which thecurrently available figures reveal as actually having existed. Conse-quently, it is possible that an ex ante forecast accurately predicted thecurrently available GNP data, but that the forecast was based on as-sumptions which did not reflect actuality; the prediction may have beenright for the wrong reasons. It is even possible that these ex ante fore-casts would become more and more accurate as the National Incomedata are revised.6 This method of analyzing the forecasts may, in fact,provide a clue to a finding that our authors have difficulty explaining.
The authors compare the Wharton cx ante predicted changes withthe actual changes now recorded in the National Income Accounts.They then replace the estimates of the exogenous variables with valueswhich they call actual values. At the same time, the lagged predeter-mined variables are left unchanged, generating a set of datainconsistent. The forecasts generated from these data are called ex postwith preliminary lags; the ex ante forecasts are superior. I believe thatthe implied changes in the predetermined variables should also havebeen revised in order to achieve consistency. Then, if the ex ante fore-casts had still been superior, we could have concluded that the in-adequate estimates of all of these variables more than offset all of theerrors in the model.
The other results of this study are quite revealing. For the periodof fit, the no-change or same-change Naive Model has lower errorsthan do the cx post predictions — with constant adjustments —made onequarter in advance, for the following variables: GNP, real GNP, Con-sumption; and for all six quarters: unemployment. The errors of the expost extrapolations beyond the sample period are also larger than the
6 The ex ante forecasts may also be compared with either the preliminary or the reviseddata, but this point is not discussed.
FORECASTING PROPERTIES OF U.S. MODELS • 1145
errors of these naive standards: GNP (1, 2 quarters in advance), C (1,2), 1(1, 2, 3), GNP, real (1, 2), unemployment (1—6).
The OBE forecasts are not compared with naive data, and com-parisons with the Wharton Model should not be made because differentperiods are involved.
Furthermore, when the National Income data were revised in1965, the econometricians at the Wharton School discovered that theirprevious model no longer adequately represented the economy. Theauthors also indicated that "mechanical forecast errors were verysensitive to slight modifications of models." Given this great sensitivityto revisions in the data and model adjustments, it is appropriate toquestion the degree to which a model adequately describes an economy.This query could then cause one to question whether econometricmodels are useful for short-run forecasting.
I believe that the accuracy of economic forecasts can only beimproved by using systematic analytical techniques which can bereplicated. Then the source of forecast errors can be determined andeliminated. Econometric models can obviously fulfill this role, and it is,therefore, the task of the econometrician to improve the quality of hismodels. The authors suggest a new estimating procedure, calledregression on predictions, which, in this case, has reduced the size ofthe ex post forecast errors. Unfortunately, these errors still seem to belarger than those obtained from the naive standard (Tables 3.2Aand 3.2).
In closing, I want to indicate that the usefulness of an econometricmodel does not depend solely on its ability to forecast aggregateeconomic activity one or two quarters in the future. Furthermore, weshould all recognize that analyses of the forecasting properties ofmodels are new and difficult tasks, for many problems are still Un-resolved; and we should thank Messrs. Evans, Haitovsky, and Treyzfor this pioneering effort.
1146 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
A. J. KarchereINTERNATIONAL BUSINESS MACHINES CORPORATION
THOSE of us who forecast with econometric models should be gratefulto the authors of this paper for the labor that went into it, and for thecandor with which they report the results. Their primary purpose is todiscover the sources of error in the ex ante forecasts and to suggestmethods for improving them.
Their fundamental conclusion is that models forecast very badly,indeed, but that econometricians using econometric models forecastwith an accuracy that compares favorably with forecasts made byother methods. They find themselves on the horns of an uncomfortabledilemma. At one point, they argue that forecasts made by the unaidedefforts of a model are not very meaningful. Elsewhere, they offer sug-gestions for improving the forecast accuracy of models. The mainconcrete proposal for improving the forecast performance of models isa new method of estimation, which they call "regression on simulatedvalues" (ROS).
I do not believe that they have a satisfactory explanation of whythe models they report on have behaved so badly. As a consequence, Ithink that their understanding of model adjustment is not clear, andthat their prescription for improvement in models is unsatisfactory.Moreover, it appears to me that a major improvement in the specifica-tion of models to reduce simulation errors will be required before thepotential benefits of ROS can be realized.
The forecast errors made by a linear simultaneous econometricmodel depend on the inverse of the matrix of coefficients of the simul-taneous variables (the multipliers); the size and sign distribution of thevector of errors of the stochastic functions; and the matrix of coeffi-cients of the lagged endogenous variables. In a nonlinear model, thesame general statement would hold, but we could not be precise in ourstatement of the algebra involved. It is, of course, true that there is anintimate relationship between these sources of error. But I suspectthat the major problem stems from the errors made by the individualstochastic functions, given correct independent variables for thosefunctions (single-equation errors); that a substantial number of thesingle-equation forecast errors have means significantly different from
PROPERTIES OF U.S. MODELS • 1147
zero; and that the variance is significantly different from the varianceof the sample-period residuals.
The Theil decomposition of the mean-square errors reported bythe authors tends to support the notion that an important source ofthe poor model forecasts are mean forecast errors which are signifi-cantly different from zero. The decomposition of the simulation errorsof both the OBE and Wharton Models indicates that almost all of theerror results from imperfect covariation between the simulated andactual values. The contribution to simulation errors from unequalcentral tendency is virtually zero. This is what we should expect in asimulation of a model where the mean single-equation errors in thatmodel are zero. The results for, the ex po'st forecasts are quite different.With no constant adjustment, almost all the error in the first twoquarters results from unequal central tendency. The importance ofthis factor diminishes as the span of the forecast increases but this, Isuspect, results from the errors made in the earlier quarters of theforecast, which affect the later forecasts through distributed lags.
I do not claim to have a definitive answer regarding the mainsource of forecast error in the Wharton Model, but I will present someevidence that makes my hypothesis — that it is single-equation errors —seem plausible.
On the basis of an educated guess about where the Wharton Modelwas having major trouble, I made calculations using seven of the sto-chastic in the model. The functions examined were: (1)consumer expenditure on durables except cars, (2) consumer expendi-ture on cars, (3) manufacturing investment, (4) regulated and mining-industry investment, (5) commercial and other investment, (6) nonfarmhousing, (7) manufacturing inventory-investment. (See List of Vari-ables, pp. 1157—1158.)
The purpose of my calculations is to determine the single-equationforecast errors that would be made by these functions on the assump-tion that the independent variables were correct for 1965-I to 1968-I V.The results are given in Table 1. Positive errors mean that actual valuesare greater than forecast. It is evident that the errors in this group offunctions are predominantly positive and that they are large. The sumof the errors is positive in every quarter shown in the table. The meanof the sum is $9.1 billion. The Wharton Model multiplier of government
1148 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
TABLE 1
Wharton Model Single-Equation Forecast Errors(billion 1958 dollars)
Cna Ca 'pm 'Pr 'PC 'h Sum
1965.1 1.9 2.8 .8 .2 .9 1.3 —1.6 6.31965.2 1.5 .6 .4 .1 1.2 1.2 —1.9 3.11965.31965.4
1.12.5
.3—.5
1.11.3°
.3
.81.32.0
1.31.0
1.41.2
6.88.3
1966.1 3.9 .1 2.0 1.5 1.3 1.0 0 9.81966.2 4.2 —2.8 1.1 1.7 3 —.4 1.9 6.01966.3 5.1 —2.1 .9 1.1 2.6 —1.8 3.8 9.61966.4 4.8 —1.9 .2 1.5 1.2 —3.7 6.0 11.91967.1 4.4 —4.4 —.3 1.0 2.1 —3.9 4.3 3.21967.2 5.0 —1.8 —.8 1.7 1.5 —2.3 2.4 5.71967.3 5.2 —2.2 —1.4 2.0 1.6 —.3 .4 5.31967.4 5.9 —.1 —1.5 3.0 1.9 1.1 1.5 11.81968.1 5.4 —.8 —1.3 4.4 3.6 —.2 —1.6 9.51968.2 6.1 —.6 —1.9 3.0 1.0 1.6 2.1 11.31968.3 7.1 3.6 —1.2 3.1 .8 .7 3.7 17.81968.4 6.9 3.8 —1.0 4.9 —.2 2.1 2.3 18.8
purchases on constant-dollar GNP is approximately two. I would guessthat this is about the multiplier on these errors. It more than accountsfor the average one-quarter-ahead forecast errors of the model, andone would therefore conclude that there are counteracting single-equation errors elsewhere in the model.
We generally assume that forecasts made with econometric func-tions have errors whose mean is zero and variance not significantlydifferent from the variance of the sample-period residuals. Table 2compares the variance of the forecast errors to the variance of theperiod-of-fit residuals, and gives the mean error of the forecast for theseven functions whose forecast errors are shown in Table I. The statis-tics calculated indicate that the mean of the forecast error is signifi-cantly different from zero at the 5 per cent level for four of the sevenfunctions. In six of the seven cases, the variance of the forecast isgreater than the variance of the sample-period residuals; and in five ofthose cases, the difference is significant at the 5 per cent level.
FORECASTING PROPERTIES OF U.S. MODELS • 1149
These results have wider implications than the question of whetherwe can expect to get reasonably accurate forecasts from a medium-size simultaneous econometric model. They raise the issue of whetherwe can expect to get reasonably accurate forecasts from aggregateeconometric functions with existing econometric estimation and testprocedures. It may be, of course, that these functions in the WhartonModel are exceptionally poor, but I do not believe that this is the case.I suspect that the literature is filled with econometric functions whoseforecast properties are as bad as these.
The two functions in the set of seven which behaved particu-larly poorly are those for consumer expenditure on durables exceptcars, and regulated and mining-industry investment. The calculationsreported in Table 3 were made to find out what went wrong with theforecast of consumer expenditure on durables except cars, and Table5 contains a similar set of calculations for regulated and mining-industry investment.
The consumption function was computed for the period 1965-I—1968-IV (using OLS for obvious reasons) and compared with an OLSfunction for the sample period of the Wharton Model. Table 4 con-tains the ex post forecast from the Wharton Model TSLQ function,a similar forecast from the OLS function, and the residuals from anOLS function fit over the period 1965-I—1968-IV. When looking at
TABLE 2A nalysis of Single-Equation Forecast Errors
Ratio of Variance, Fore-cast Error to Residuals a Mean Forecast Error
Mean t(]5)Cna F(15,64) = 3.79 4.44 9.70Ca F(15,60) = 3.21 —0.36 0.64'pm F(15,6fl= 3.29 0.09 0.29'Pr F(15,61)6.67 1.89 5.33'PC F(15,58) = 0.72 1.45 6.54
F(l5,61)= 2.69 —0.08 —0.17Jim F(15,60) 1.88 1.61 2.90
a Variance corrected for degrees of freedom.
1150 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
TABLE 3Consumer Expenditure on Durables Except Cars
(1948-IT—i 964-IV)
StandardMean Deviation Correlation Matrix
Y K Cna
Y 307.39 51.23 1.0Kna_i 256.24 56.22 0.996 1.0Cna 22.07 5.05 0.979 0.968 1.0
SE d
(OLS) C,ia = —14.07 + 0.1855Y —(2.079) (0.027) (0.024)
.963 0.97 1.24
(TSLS) +(0.0274) (0.025 1)
.965 0.94 1.29
(1965-1—1968-IV)
StandardMean Deviation Correlation Matrix
Y K Cna
V 467.25 24.97 1.0Kna_i 440.97 42.01 0.986 1.0Cna 40.96 3.32 0.981 0.958 1.0
R2 SE d
(OLS) Cna = 29.22 + 0. 1765Y — 0.0279Kna_i(8.887) (0.042) (0.025)
.960 0.67 1.14
Table 4, it is hard to avoid remarking on the power of the least squaresfit during the sample period, and the contrast between the residualsand the forecasts.
Returning now to Table 3 to find out what produced the astonish-ing contrast, the source appears to be a modest change in the coeffi-cients—principally the coefficient for a compensating
FORECASTING PROPERTIES OF U.S. MODELS • 1151
change in the constant. Remembering the formula
— r13 — r12r23 S1b132—
— '23
examine Table 3. You will find little difference in S1/S3 in the twoperiods, and the changes in the intercorrelation matrix hardly appear tobe large. However, it turns out, when the arithmetic is done, that whatappears to be a very small change in the correlation coefficient betweenthe independent variables Y and Kna_j (from 0.996 in the 1948-Il—1964-IV period, to 0.986 in the 1965-I—1968-IV period) has an over-whelming effect on changing the coefficient of Kna_i.
We all pay lip service to the problems of multicollinearity, butthese results indicate that we should, perhaps, think again. Economictheory leads us to look for, and to assume, stability in the relationships
TABLE 4Consumer Expenditure on Durables Except Cars
(Constant Prices)(billion dollars)
ForecastTSLQ
ErrorsOLS Residuals
1965.1 1.9 1.5 0.21965.2 1.5 1.2 —0.51965.3 1.1 .5 —1.31965.4 2.5 1.8 —0.41966.1 3.9 3.4 0.71966.2 4.2 3.9 0.71966.3 5.1 4.8 1.11966.4 4.8 4.7 .51967.1 4.4 4.3 —0.31967.2 5.0 5.0 01967.3 5.2 5.2 —0.21967.4 5.9 6.0 0.2
• 1968.1 . 5.4 5.5 —0.71968.2 6.1 6.3 —0.31968.3 7.1 7.4 .31968.4 6.9 7.3 —0.2
1152 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
between dependent and independent variables. Indeed, this is what wemean by structure. However, there is generally nothing in economictheory that leads us to expect stability in the relationships betweenindependent variables. Yet, the arithmetic we use to calculate thecoefficients of a function imposes, as a requirement for stability of thestructure, that there be stability in the relationship between inde-pendent variables. This is a particularly serious matter when the cor-relation between the independent variables is as high as it is in thisfunction.
Let us turn back now to ask whether there is anything in thestatistics calculated for the sample period that would cause us to expectbad forecasts from this function. There were some indications. Al-though the signs of the coefficients were right; the standard errors ofthe coefficients satisfactory; R2 was high and Se was low. The Durbin-Watson statistic was suspicious—an indication of the long runs presentin the residuals. This, along with the .996 intercorrelation of the in-dependent variables, should (employing hindsight) have raised doubtsabout the forecasting properties of the function.
Much of what was said about the function for consumer durablesexcept cars applies, also, to the function for regulated and mining-in-dustry investment. The data are shown in Tables 5 and 6. There is onemajor difference, however, which is that the 1965-1—1968-TV functionbears very little resemblance to the 1948-111—1964-TV function. Theintercorrelation matrix indicates that there were major shifts in therelationships between the dependent and independent variables, aswell as high, and changing, intercorrelation between the independentvariables. As in the case of the other function, the low Durbin-Watsonstatistic reflects the presence of runs, and the intercorrelation matrixcontains a suggestion of future forecast difficulties.
Where does this kind of examination take us? I have concludedthat we have to be as careful as we possibly can in our examination ofthe statistics calculated for the sample period—with a particular con-cern for runs in the residuals and multicollinearity — but that this initself is not enough. Estimation by minimizing sums of squares is avery powerful device for fitting data: The assumptions that we makewhen using the fits for forecasting—particularly zero mean and con-stant variance—must be tested empirically. This can be done by suc-
(con
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FORECASTING PROPERTIES OF U.S. MODELS • 1155
cessive ex post forecasts beyond the period of fit. The statistical prop-erties of the forecast could then be calculatedfrom the expostforecasts.The span of the ex post forecasts should be the span we need for exante forecasting.
At this point, we can begin to discuss intelligent interaction be-tween the econometrician and the model. The authors report on elab-orate experiments with constant adjustments for the sample period andfor ex post forecasts, and conclude that they get an improvement inboth cases for the first two quarters; and thereafter, deterioration. Theexperiment with constant adjustments over the sample period suggeststo me that they have missed the main point. The single-equation resultsgiven in Table I indicate that the need for constant adjustment arisesfrom the necessity of correcting forecasts from functions which have anexpected mean error of the forecast that is not zàro. Over the sampleperiod, the constant adjustment is a crude adjustment for autocorre-
TABLE 6Regulated and Mining-Industry investment
(Constant Prices)(billion dollars)
Forecast Residuals
1965.1 .2 .21965.2 .1 01965.3 .3 —.31965.4 .8 —.21966.1 1.5 .11966.2 1.7 .21966.3 1.1 —.11966.4 1.5 .41967.1 1.0 —.21967.2 1.7 .21967.3 2.0 —.51967.4 3.0 —.21968.1 4.4 1.11968.2 3.0 —.51968.3 3.1 —.71968.4 4.9 .5
1156 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
lation in a set of residuals whose mean error is zero. In these circum-stances, there is little point in constant adjustment over the sampleperiod. Moreover, if the real problem in forecasting with econometricmodels is change in the structure, for one reason or another, an auto-regressive function of residuals from the sample period will then pro-vide only marginal help in improving the accuracy of the forecast. Theadjustment to the single-equation forecast errors should, I believe, bemade from the properties of the successive ex post forecasts referredto above.
The authors report an improvement in ex post forecasts one quar-ter ahead for current and constant-dollar GNP, through the use ofROS. They point out that their results come from a partial applicationof the ROS procedure, and express the opinion that ROS holds prom-ise for further improvement. The application of ROS was partial, be-cause they did not use model-solution values for lagged dependentvariables. The authors propose a method for doing this, followingLawrence Klein.' The reasoning used to justify ROS suggests the fol-lowing extension on the method that they and Klein propose. If weassume that the model solution is carried ahead a maximum of fourquarters, the following four sets of regressions could be carried out foreach element of Each set would be used to create a model appro-priate to the span of the forecast.
(1) and A'
(2) Yt, and X
(3) andXA A A A(A\ V V* V* V*' t+4' t+2, an
Where the Y's are endogenous current and lagged variables, andthe X's are exogenous variables.
is the solution value for each element of one quarter aheadfrom the model, estimated by TSLQ; and is the solution valuefor each element of one quarter ahead from the model, estimatedby ROS. is solution value for each element of two quarters
Lawrence R. Klein, An Essay on the Theory of Economic Prediction. Helsinki, TheAcademic Book Store, 1968, pp. 69—70.
FORECASTING PROPERTIES OF U.S. MODELS • 1157
ahead, using the same model; and is obtained from solution of themodel developed from equation (3). If the processes of iterative esti-mation and model solution converge, then
The authors suspect that this procedure will, not converge and alsopoint out that the method would lead to lower measures of goodness-of-fit and t-ratios. As a matter of fact, it is. reasonable to suppose thatif ROS were extended to the lagged endogenous variables, the regres-sions might, in some cases, explain very little. It is my guess that amajor effort to improve the simulations of the Wharton Model shouldbe undertaken prior to engaging in ROS experiments. It is reasonableto suppose that better simulations would also enhance the probabilityof getting convergence in the ROS iterative process.
In conclusion, the authors have provided us with ample evidencethat econometric models need substantial improvement. The simula-tion errors reported are not satisfactory, and we cannot expect a modelto forecast more accurately than it simulates. Moreover, the authorsreport that forecast errors are substantially worse than simula-tion errors.
They suggest ROS as an avenue for improvement, but it seemslikely that improved simulation properties will be required beforesubstantial benefits will result from ROS. I have suggested that thecritical problem is the need to contain the model forecast errors withinthe boundaries suggested by the simulations. To accomplish this, itwill, I believe, be necessary to pay more attention to single-equationex post forecast errors over the span we intend to forecast. In par-ticular, we should attempt to specify functions that have satisfactorycx post forecast-error properties. When we are not successful in ac-complishing this, we should use the characteristics of the single-equa-tion ex post forecast errors to adjust the single-equation ex ante fore-casts.
LIST OF VARIABLES
C,ia Purchases of consumer durables except automobiles and parts,billions of 1958 dollars
Ca Purchases of automobiles and parts, billions of 1958 dollars
11158 • ECONOMETRIC MODELS OF CYCLICAL BEHAVIOR
Manufacturing investment in plant and equipment, billions of1958 dollars
'pr Regulated and mining investment in plant and equipment, bil-lions of 1958 dollars
'PC Plant and equipment investment in commercial and other in-dustries, billions of 1958 dollarsInvestment in nonfarm residential construction, billions of1958 dollarsInvestment in manufacturing inventories, billions of 1958 dol-lars, arbitrary origin
Y Personal disposable income, billions of 1958 dollarsKna Stock of consumer durables except automobiles, billions of
1958 dollarsZ Final sales in the private sector, billions of 1958 dollars
Kr Stock of regulated and mining-industry investment, billions of1958 dollars
A. Distributed lag weightsMoody's average yield on bonds
