Empirical tests of real estate market efficiency

Journal of Real Estate Finance and Economics, 4:297-313 (1991) �9 1991 Kluwer Academic Publishers

Empirical Tests of Real Estate Market Efficiency

KARL L. GUNTERMANN Arizona Realtors Professor of Real Estate, Arizona State University, Tempe, AZ 85287-3706

STEFAN C. NORRBIN Assistant Professor of Economics, Florida State University, Tallahassee, FL 32306

Abstract

Recent empirical research using real estate data has supported the weak and semi-strong forms of the efficient markets hypothesis. Previous studies have not included an estimate of expected appreciation into the tests of market efficiency, thus raising a question about the reliability of the results. We first use a market model to test for market efficiency with results similar to those reported by others. We next use a dynamic multiple indicator, multiple cause (DYMIMIC) model, which extracts a vector of expected appreciation from the price data, to test market efficiency. This approach produces superior results and a stronger conclusion about the efficiency of housing markets. The results indicate limited adjustment delays which can be explained by the existence of high transactions and search costs.

Keywords: Efficient markets hypothesis, real estate market efficiency, housing market efficiency, DYMIMIC model and real estate, DYMIMIC model and housing market efficiency

The common perception of real estate markets is that they are less efficient than financial markets. This would seem to be especially true for the housing market where many properties trade only infrequently, making it difficult for participants to determine "correct" prices. The unique characteristics of real property and the local orientation of the market, which require specialized knowledge of the factors that affect r isk and return, also may

contribute to inefficiency. Furthermore, transaction and financing costs as well as tax consid- erations make it difficult to exploit potentially profitable opportunities even if they can be identified.

There is a growing literature testing for market efficiency using real estate databases. Previous researchers have taken one of two approaches when testing for market efficiency.

Gau (1984, 1985), Rayburn, Devaney, and Evans (1987), Mclntosh and Henderson (1989), and Case and Shiller (1989) primari ly use a forecasting approach, where an inability to predict future prices is interpreted as evidence supporting market efficiency. Linneman (1986), and Guntermann and Smith (1987) use a market model approach analogous to earlier tests of efficiency in securities markets. These studies generally find some evidence of market inefficiency but typically conclude that trading rules or strategies cannot be developed to earn abnormal rates or return either because of high transaction and information costs or because of the difficulty of accurately forecasting real estate prices.

298 KARL L. GUNTERMANN AND STEFAN C. NORRBIN

1. Expected appreciation in EMH tests

The efficient markets hypothesis holds that changes in expectations are immediately capital- ized into asset prices. While changes in price may result in windfall gains or losses to cur- rent owners, investors purchasing after expectations have changed should expect to earn only a normal, risk-adjusted rate of return in an efficient market. Therefore, a market is defined to be weak-form efficient if it is not possible to earn an abnormal rate of return by making investment decisions based on historical information such as price data.

One difficulty in conducting weak-form EMH tests is that expectations are unobservable, yet the ex-post price data used require the assumption that they correctly reflect changes in expectations. This means that any test of market efficiency involves a comparison between actual rates of return and the rates that would be expected in an efficient market. To conduct such a test requires specifying (at least implicitly) an assumption about the expected return. Given that an assumption such as this is necessary, tests of market efficiency are unavoidably joint tests of the expectation assumption as well. Rejecting the null hypothesis about market efficiency implies either that the market is inefficient or that the assumption about expected returns is incorrect.

Tests of market efficiency using the market model are based on the implicit assumption that factors such as inflation rate changes would affect all returns similarly. Hence, a comparison is made of relative returns across real estate markets or neighborhoods (or census tracts) within a local market. The efficiency test involves the cross-sectional correlation of residuals from the market model over time. A finding of no correlation is correctly interpreted as evidence supporting market efficiency, while a finding of significant correlations over time may or may not indicate inefficiency as discussed above.

From a conceptual standpoint the forecasting approach for testing market efficiency may be superior to the market model approach but it is subject to potentially serious statistical problems. In an efficient market past price changes should be of no value in predicting future price changes. The efficiency test in this case typically involves regressing changes in an index of real estate prices (or rates of return) on its own lagged values where significant relationships are interpreted as evidence of market inefficiency. Case and Shiller (1989) point out that spurious serial correlation may suggest market inefficiency when there actually is none. Their solution is to divide their data into two parts and regress a change in the value of the index from one sample on lagged changes in the index constructed from the other half of the data.

Hamilton and Schwab (1985) have published the only efficient markets test that attempts to account for expected appreciation in property values. They used a forecasting model with annual Housing Survey data from 49 metropolitan areas for the years 1974-1976 to test whether expected appreciation (-rent/value) correctly reflects all available information. They find that past appreciation rates are not reflected in expectations and conclude that participants in the housing market fail to include valuable information when forming expectations about future appreciation. However, the short period covered by their data make it unclear that their conclusions can be generalized to other time periods.

The research reported here is a weak form test of the EMH presented in two empirical sections. In the first section we use local market transactions data to calculate a quarterly rate of return series over 12 years. These data are used to test for market efficiency using a

REAL ESTATE MARKET EFFICIENCY 299

combination of the market model and forecasting approaches. We find evidence of inefficiency in certain census tracts for lags up to six quarters. These results appear to be at odds with published research on market efficiency but are consistent with other evidence of inefficiency which may not be exploitable due to transaction and other costs.

In the second empirical section, we use the dynamic multiple-indicator multiple-cause (DYMIMIC) model, a recent estimation methodology developed by Engle and Watson (1981) and Watson and Engle (1983). This model estimates an underlying unobserved component based on the observable data available. Previously, the model has been used by Engle, Lilien, and Watson (1985) to estimate the capitalization rate in housing. In addition, several authors--for example, Norrbin and Schiagenhauf (1988)--have used the model to estimate unobserved cyclical components of macroeconomic fluctuations. Since expected appreciation can be considered an unobserved variable which is signalled by the observed transactions price, it should be possible to estimate such an observed variable if one allows for the differing property characteristics in different transactions. This test of market efficiency might be superior since it estimates quarterly expected appreciation simultaneously with being sensitive to different property characteristics. The residual terms for each equation in the DYMIMIC model should be free of the expected appreciation component that may confound the results of previous EMH tests. These residuals can then be tested for serial dependence.

2. Data and methodology

The database used in the empirical analyses contains information on 9,340 transactions of single-family houses in Lubbock, Texas, for the period from January 1970 through Sep- tember 1981.1 The data are from 20 of the 35 census tracts in Lubbock which contained 71 percent of the housing units as of the 1970 census. 2 Descriptive statistics of the data are presented in table 1.

During the 1970-1981 time period the Lubbock and West Texas economies were in a generally favorable growth situation, and the outlook for the future was positive. Nationally, inflationary expectations changed substantially in response to oil embargoes, budget deficits, and shifts in monetary policy. While the trend of price indexes was upward, there were substantial variations in inflation rates during this period, undoubtedly reflecting substantial revisions in expectations in both directions. Hence, this should be an interesting period to test for housing market efficiency.

Efficient markets tests require a time series of rates of return. While this is relatively easy to obtain in financial markets with continuous trading in homogeneous assets, there is neither continuous trading nor are assets homogenous in real estate markets. This problem typically is addressed by deriving an index of prices from the real estate database for use in the efficiency tests. Only Linneman (1986) took steps to ensure that the rate of return series reflected a homogenous asset over time although Gau (1984, 1985) attempted to hold quality constant in the selection of his sample.

Our approach is to calculate a quarterly rate of return series using the mean price per square foot of transactions in each census tract? The data cover 47 quarters from 1970-I through 1981-III which yields 46 rates of return beginning with 1970-II. Since the composition of houses sold is likely to vary over a long period of time, the calculated rates of return


Table 1. Mean values for selected house characteristics for 20 census tracts in Lubbock, Texas, 1970 Q1 through 1981 III.

Central Evap. Fire- Financing Air Air place FHA VA ASUM

Census Lot Tract 1 N Price Size Age Baths Front (Percent) (Percent)

1.00 91 $24,085 1,309 8.7 2.3 70.1 26.3 36.3 26.3 42.9 18.7 6.6 3.00 221 12,766 1,001 19.2 1.3 55.5 5.0 28.5 5.4 66.5 10.0 3.2 4.02 537 33,397 1,644 6.7 3.0 68.3 54.4 39.7 65.7 25.3 20.1 3.5 4.03 287 36,273 1,769 9.9 3.2 76.7 42.9 45.3 3 2 . 1 26.1 11.5 4.5

13.00 117 12,588 1,030 28.9 1.4 52.6 6.0 50.4 2.6 52.1 13.7 3.4 14.00 240 20,614 1,341 30.0 1.7 60.2 17.1 39.6 1 8 . 8 45.4 14.2 2.5 15.00 292 25,918 1,512 26.3 1.9 63.5 30.1 40.8 21.6 43.8 7.5 2.4 16.01 125 36,193 1,836 15.0 3.0 76.8 48.0 47.2 46.4 14.4 9.6 10.4 16.02 248 20,185 1,324 20.4 1.6 63.3 16.1 49.6 12.5 45.6 13.3 4.0 17.02 561 29,748 1,526 6.2 2.9 64.4 48.5 38.5 56.1 30.5 12.1 6.1 17.03 309 31,247 1,515 8.1 2.9 66.6 41.4 48.9 52.8 28.5 10.0 2.6 18.01 470 19,780 1,243 16.9 2.0 62.8 13.0 57.4 9.8 42.1 12.1 3.4 18.02 1 , 2 6 8 47,578 1,843 2.1 3.2 69.1 81.8 10.9 86.4 12.9 9.2 8.1 19.01 341 27,472 1,740 17.7 2.7 72.4 40.2 42.8 34.3 27.6 11.4 1.8 19.02 1 , 0 2 3 48,718 2,096 5.4 3.3 74.2 85.4 12.5 90.7 6.6 6.7 8.9 20.00 321 23,976 1,420 20.6 2.0 65.1 32.1 43.6 1 5 . 9 38.0 9.7 4.0 21.00 1 , 3 2 4 38,175 1,731 5.8 3.0 69.1 78.2 18.3 68.8 21.6 9.6 6.5 22.00 964 30,549 1,539 9.5 2.7 66.8 53.4 33.1 53.9 32.8 11.7 6.2 23.00 270 17,678 1,185 20.0 1.5 59.8 13.0 47.4 5.9 48.1 10.7 1.1 24.00 341 15,367 1,102 17,5 1.5 59.2 10.6 45.6 3.6 60.1 9.7 1.2

Overall 9,340 $33,148 1,614 10.6 2.7 67.3 52.7 31.3 52.0 28.5 10.8 5.4

11970 Census tracts. Note: Price is the contract selling price; size is the total square footage of a house based on exterior dimensions; age is the chronological age in years at the time of sale; baths is the number of baths in a typical house; lot front is in feet and is a proxy for site area since most lots have a standard depth; central air and fireplace are the percentage of houses with each; FHA, VA, and ASUM represnt the proportion of transactions that used FHA, VA, or assumption financing.

reflect the heterogeneity of the underlying assets and are inappropriate for a market efficiency

test without some adjustment. For this reason, the vector of rates of return in each census tract is regressed on the mean quarterly changes in the values of a set of property characteristics typical ly used in hedonic models. 4 The result is a series of residuals for each census tract that have been adjusted for differences in property characteristics that could have affected the raw rates of return.

Regression results for this model are presented in table 2. The model is estimated sepa- rately for each census tract to allow the coefficients to vary across different parts of the city. The fairly high R 2 and number of significant variables in most census tracts are indi- cations that the raw rates of return reflect very different assets across time. The results for individual variables or census tracts are of no particular interest and will not be discussed in detail. Residuals for each census tract should reflect actual appreciation rates and a ran- dom error term, since a change variable for t ime was not included in the model.

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Use of the residuals in a market model test of market efficiency carries with it the assumption that expected appreciation rates are the same in all census tracts. While an assumption of equal expected appreciation might be appropriate in financial market tests of efficiency, it is less plausible in the housing market. Differences in expected appreciation across census tracts might exist due to differences in the age of desirability of neighborhoods or other factors. Hence, evidence of inefficiency would have to be interpreted carefully since it may merely reflect the divergence of expected appreciation in a census tract from the market average.

We calculate the average value of the residuals from the first regression by quarter across all census tracts and subtract that series from the residuals for each census tract. If the housing market is efficient, there should be no pattern in the resulting series of excess returns that would allow an investor to earn an abnormal return. We are interested in testing whether an investor could identify one or more census tracts where historical data could be used to earn an abnormal return and interpret this as evidence of market inefficiency. This is different than the approach taken by Guntermann and Smith (1987) who attempted to identify systematic abnormal returns across all cities in their database for specific years and lag intervals.

2.1. Market model results

We test for market efficiency by regressing the contemporaneous excess returns in each census tract on their own lagged excess returns for lags up to six quarters: The results for the 15 census tracts with at least one significant lagged variable are presented in table 3. The significant lagged relationships in 12 of the 15 census tracts occurred during the first two quarters and may reflect the errors-in-variable problem discussed by Gau (1984, p. 311) or the situation described by Guntermann and Smith (1987, p. 38). 6 In this study the rates of return are calculated based on the mean price per square foot each quarter. An unusual transaction may influence the rate of return in a given quarter and show up as a spurious correlation in the first or second lags. For this reason it is more appropriate to focus on the three census tracts (4.02, 14.00, and 16.01) with a persistent pattern of significant lags over five or six quarters. 7

The results for these census tracts suggest inefficiency consistent with an adaptive expectations explanation of the market. The negative coefficients are an indication that high (or low) prices and rates of return in one period lead to a correction in the opposite direction that takes several quarters to work out. Since short sales are not possible in the housing market, an investor could capitalize on this information only by investing when prices are too low and selling during the next peak in the cycle. These results suggest that the market is moving toward correct prices which would eliminate excess returns but that for periods longer than one year excess returns are possible.

One possible explanation for these results is an extension of the errors-in-variables/spurious correlation discussion presented earlier. The significant correlations may be partly a function of differences in the variances of the excess returns across census tracts. This should be noted, in particular for census tract 16.01, and may reflect the relatively small number of observations in that census tract (see Appendix). This appears to be less of a concern in the other two census tracts.


Table 3. Census tracts exhibiting evidence of significant abnormal returns based on lagged quarterly excess returns (dependent variable--contemporaneous excess return)?

Census Tract Intercept Lag 1 Lag 2 Lag 3 Lag 4 Lag 5 Lag 6 R 2

3.00 0.1 -0.49** -0.15 -0.18 -0.25 0.02 -0.24 .37 (0.4) (-2.9) (-0.7) (-0.8) ( - 1.2) (0.1) ( - 1.2)

4.02 -0.00 -0.45** -0.54** -0.53** -0.31" -0.39** -0.34** .35 (0.0) (-2.8) (-3.2) (-2.8) ( - 1.7) (-2.3) (-2.1)

4.03 0.01 -0.39** -0,15 -0.15 -0.02 -0.08 -0.23 .22 (0.04) (-2.3) (0.8) (-0.8) (-0.1) (-0.4) (-1.4)

14.00 0.00 -0.67** -0.55** -0.59** -0.44** -0.38* -0.24 .36 (0.2) (-4.0) (-2.8) (-3.0) (-2.2) (-2.0) (-1.5)

15.00 0.00 -0.43** -0.20 0.03 0.00 -0.15 -0.18 .17 (-0.0) (-2.4) (-1.0) (0.2) (0.0) (-0.8) (-1.0)

16.01 -0 .3 -0.77** -0.84** -0.82** -0.81"* -0.69** -0.42** .56 (-1.9) (-4.9) (-5.1) (-4.4) (-3.3) (-4.4) (-2.8)

16.02 0.00 -0.45* -0.12 -0.18 -0.21 0.18 0.01 .30 (0.4) (-2.6) (-0.7) (-1.1) (-1.2) (1.0) (0.1)

17.02 -0.00 -0.06 -0.46** -0.11 -0.17 0.01 -0.44* .34 (-0.1) (-0.4) (-2.9) (-0.6) ( - 1.0) (0.1) (-2.7)

17.03 0.01 -0.43** -0.10 -0.25 -0.42** -0.31" 0.05 .34 (1.5) (-2.7) (-0.6) (-1.6) (-2.7) (-1.9) (0.4)

18.02 0.00 -0.40** -0.62** -0.21 -0.29 -0.07 0.23 .30 (0.9) (-2.3) (-3.2) ( - 1.0) ( - 1.3) (-0.4) ( - 1.3)

19.01 0.00 -0.43** -0.25 -0.40** -0.33* -0.27 -0.13 .23 (0.2) (-2.5) ( - 1.4) (-2.3) ( - 1.9) ( - 1.5) (-0.7)

19.02 0.00 -0.45** -0.27 -0.20 -0.07 -0.24 -0.05 .22 (0.0) (-2.6) (-1.4) (-1.0) (-0.3) (-1.2) (-0.3)

21.00 0.00 -0.47* -0.28 -0.26 -0.12 -0.19 0.06 .23 (0.0) (-2.6) ( - 1.5) ( - 1.2) ( - 0.7) ( - 1.3) (0.4)

22.00 -0.00 -0.47** -0.33* -0.28 -0.06 -0.12 -0.18 .26 (0.1) (-2.9) ( - 1.8) ( - 1.5) (-0.3) (-0.7) ( - 1.2)

24.00 -0.00 -0.40** -0.52** -0.22 -0.20 -0.02 -0.14 .24 (-0.3) (-2.3) (-2.7) (-1.1) (-1.0) (-0.1) (-0.8)

tExcess returns are calculated by subtracting the average quarterly residuals from census tract's residual. (t-ratios are in parentheses.)

*Significant at the .10 level. **Significant at the .05 level.

the first regression from each

A final explanat ion for these results, consistent wi th market efficiency, has to do with

the assumpt ion o f equal expected apprec ia t ion across census tracts inherent in the use o f

the market model . The housing market may be efficient with the observed pattern of signifi-

cant lags providing ev idence of different rates o f expected apprecia t ion in those census


tracts that was not accounted for in calculating the excess returns. However, a regression of lagged on contemporaneous residuals without adjusting for a market effect produces approximately the same results as those presented in table 3, including four census tracts with significant lags for four to six quartersY

The empirical results reported here support inefficiency within a local housing market, but the findings must be qualified by possible methodological or statistical problems. Hence, it is not possible to make a clear-cut statement that investors could earn abnormal returns by investing in certain areas within the housing market, ignoring transaction and search costs. A key factor is expected appreciation which cannot be explicitly modeled in either the market model or forecasting techniques used in the efficiency tests. The DYMIMIC technique described in the next section estimates expected appreciation reflected in the transactions data simultaneously with adjusting for changing property characteristics over time. The resulting residuals from this approach should provide for a more definitive test of market efficiency whose results can be compared to those from the more traditional approaches.

3. DYMIMIC model

The previous section tested market efficiency in a two-step process by first estimating the residuals while controlling for changing housing characteristics and then testing the serial dependence of the excess of this residual over the market average. The DYMIMIC process can provide two improvements. First, efficiency will be increased by estimating the two parts jointly, and second an unobserved market rate of return can be calculated, which does not rely on the market average as a proxy. If one sector has an excessive return relative to the other sectors then the market average would be upwardly biased. A more accurate market return would give less weight to the sector with an excessive return since it does not co-move with the others. The DYMIMIC technique uses a form of factor analysis which can extract the underlying co-movement between the sectors, disregarding outliers of the type mentioned above. Therefore, the excess return over the market rate can be more accurately estimated, since the market rate will more accurately reflect the underlying market return. Once these residuals are estimated, we can test the serial dependence of the excess return to each housing vector.

To clearly identify the method and procedure, we begin by constructing a simple multivariate time series model. Let RORit be the one-period return in census tract i, and AXit be the change in the vector of characteristics of the census tract. Then the model would be:

RORit = fJiA Xit -1- eit. (1)

This hedonic equation does not, however, take into account the proportion of return to vector i which reflects the market return to housing investments. Returns in an efficient market should equalize, although a level adjustment might be necessary due to the particular composition of the market. The market return should reflect the present value of the expected appreciation to housing investment at+ k and the implicit rental flow, rt+k, where k is the time-period in question. The present value of rent and expected appreciation A~ at discount rate c can be expressed by:


~-] j I "y i ( r t+k ) -~ at+k 1 (2) "yiAt = (1 + C) k (1 + c) - - - - - - - -~ "

k=0

A t should be constant across census tracts except for a level adjustment ~/i which equalizes the relative rental rates between census tracts. Since the price each time period reflects the present value of expected appreciation and rent, the rate of return would be affected by the change in At, or the housing market rate of return.

RORit = ,yiAAt q- t3iAXit q- eit (3)

where eit represents the excess return in time t in sector i. This return is the variable of interest.

Equation (3) cannot be estimated using standard econometric techniques, due to the unobservable variable A t. In the first part of the article the above complication was solved by replacing A A t by:

I

Z (RORi, - ~iAXit)/I i=1

where I is the total number of sectors. However, such a proxy can be biased if one or more sectors are inefficient and uncorrelated with other sectors. In this part of the article we choose to use a factor analysis type estimation technique by Engle and Watson (1981) called Dymamic Multiple Indicator--Multiple Cause (DYMIMIC). The DYMIMIC model is based on one or more vectors of unobserved variables, in this case the change in market return. This variable then drives an "indicator" of the unobservable variable, in this case the return to the individual sector. This "indicator" can also be driven by exogenous variables, in this case housing characteristics, and by a disturbance term, which in our case is the excess return on sector i. The indicator equation is represented by equation (3). This equation can then be estimated using a maximum likelihood estimation of the type suggested by Dempster, Laird, and Rubin (1977). Details of the algorithm for the DYMIMIC model can be found in Watson and Engle (1983). This technique has been applied to housing data by Engle, Lilien, and Watson (1985).

The intuition behind the estimation technique is as follows. I f the market return AA t were observable, then equation (3) could be estimated. Furthermore, if the coefficients /3 i were known, then signal extraction techniques could be used to estimate the AA t and the information matrix. Combining these two processes, we have an iterative algorithm. The first step finds the ~i estimates based on initial values of AAt, and the second step estimates the AA t based on the sample moment matrices. When this process is repeated to convergence, it can be shown to satisfy the first-order conditions for maximization of the likelihood function. Using this approach we can follow the same testing procedure as in the first part of the article. The data set is identical, but the system is now extended to allow for an unobservable variable, the expected market appreciation.


3.1. DYMIMIC model results

The regression results are presented in table 4. The DYMIMIC model is estimated jointly and the results are very similar to those in table 2. The variable estimated for the expected market appreciation rate (EXPAPP) is significant in 12 of the 20 sectors, indicating the importance of the expected market appreciation rate in the individual sectors. The remaining residuals for each census tract will reflect excess appreciation rates over the expected market rate. 9

We test for market efficiency by regressing the contemporaneous excess returns in each census tract on their own lagged excess returns for lags up to six quarters. The results for the 14 census tracts with at least one significant lagged variable are presented in table 5. The results are similar to those presented earlier in table 3.

However, evidence for the superiority of the DYMIMIC model can be seen by examining results for the three census tracts that showed evidence of inefficiency with the market model test (4.02, 14.00, and 16.01). The significant six-quarter lag for census tract 4.02 has been reduced to two quarters, which may reflect the spurious correlation problem discussed earlier. The significant lag in census tract 14.00 has been reduced from five to four quarters. Only census tract 16.01 continues to show persistent evidence of inefficiency with a significant lag for quarters one through five.

These results suggest that, in general, the housing market moves fairly rapidly toward equilibrium. In six of the census tracts the adjustment occurs without any lag, while in most of the other census tracts it occurs within two or three quarters, assuming that the significant lags are not spurious. One census tract provides evidence of the potential for excess returns over a prolonged period of time and, hence, market inefficiency. The per- sistence of possible excess returns suggests that transaction and search costs must be large relative to the potential gains.

4. Conclusion

Market efficiency typically has been tested using either a market model or forecasting approach. Since it has not been possible until now to estimate expected appreciation, findings of inefficiency using ex-post data do not rule out the possibility that real estate markets are efficient exante. Adjusting for expected appreciation prior to carrying out efficiency tests increases the likelihood that the results of those tests are correct.

In the first empirical section, housing data are used to conduct an intramarket test of the efficient markets hypothesis using the market model. The evidence supports inefficiency since there is serial correlation of the residuals in at least three sectors for up to six quarters. However, transaction and search costs are ignored so it is not clear that it would be profitable to exploit perceived areas of inefficiency. These findings and conclusions are consistent with other real estate studies that have used the market model.

In the second empirical section, the DYMIMIC model is used to estimate an expected appreciation series as part of the adjustment process to control for heterogeneous property characteristics. Serial correlation of the residuals to test for efficiency produced results superior to those obtained with the market model. If significant lagged correlations in some

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(-

1.5

0)

(-0,

42)

(-1.

59)

(-3

.51

) (2

.74)

(-

0.16

) (0

.61)

CH

GV

A

0.02

0.

17,*

-0

,009

-0

.02

-0

.02

-0

.07

0.

03

0.10

"*

0.09

0.

09

(0.5

5)

2.98

(-

0.36

) (-

0.6

6)

(-0.

52)

(-0.

93)

(0.5

8)

(1.8

9)

(1.4

4)

(1.5

6)

CH

GA

SUM

0.

02

0.23

* -0

.01

0.03

0.

04

-0.3

5**

0.05

-0

.02

-0.0

8 -0

.10

(0

.52)

1.

78

(-0.

16)

(0.7

1)

(0,9

7)

(-3.

82)

(0.5

9)

(-0.

13)

(-0.

75)

(-0.

37)

EX

PAPP

0.

003

0.00

1 0.

001

-0.0

05**

-0

,004

**

0.00

5*

0.00

4**

-0.0

07**

0.

008*

* -0

.004

(1

.63)

(0

..19)

(0

,91)

(-

3.00

) (-

4.03

) (1

.83)

(2

.42)

(-

3.47

) (3

.40)

(-

1.17

)

R 2

.71

.55

.36

.55

.77

.76

.78

.65

.76

.69

>

1197

0 ce

nsus

tra

cts

num

bers

for

Lub

bock

, T

exas

. 2V

alue

s for

the

vari

able

s C

HG

SIZ

E,

CH

GA

GE

, C

HG

BA

TH

S, a

nd C

HG

FRO

NT

are

the

perc

enta

ge c

hang

es in

the

mea

n va

lues

of s

ize,

age

, an

d so

on,

fro

m q

uart

er

to q

uart

er e

xpre

ssed

in

deci

mal

for

m.

The

rem

aini

ng v

aria

bles

are

dum

my

vari

able

s an

d th

e va

lue

of th

e ch

ange

var

iabl

e is

the

dif

fere

nce

in t

he m

ean

valu

es f

rom

qu

arte

r to

qua

rter

exp

ress

ed a

s a

deci

mal

. (t

-rat

ios

are

in p

aren

thes

es.)

*S

igni

fica

nt a

t th

e .1

0 le

vel.

**Si

gnif

ican

t at

the

.05

lev

el.


Table 5. Census tracts exhibiting evidence of significant abnormal returns based on quarterly excess returns from DYMIMIC model (dependent variable--contemporaneous excess return). ~

Census Tract Intercept Lag 1 Lag2 Lag3 Lag4 Lag 5 Lag6 R 2

3.00 0.00 -0.57** -0.36* -0.30 -0.27 -0.01 0.19 .33 (0.1) (-3.2) (-1.7) (-1.3) (-1.2) (-0.03) (-1.1)

4.02 0.00 -0.44** -0.46** -0.26 -0.02 -0.15 -0.20 .31 (-0.1) (-2.6) (-2.3) (-1.2) (-0.1) (-0.8) (-1.2)

13.00 -0.00 -0.47** -0.37* -0.26 -0.09 -0.19 -0.38** .31 (-0.1) (-2.9) (-2.0) (-1.3) (-0.5) (-1.0) (-2.2)

14.00 0.00 -0.54** -0.47** -0.52** -0.33* -0.28 -0.15 .29 (0.3) (-3.2) (-2.5) (-2.7) (-1.7) (-1.5) (-0.9)

15.00 -0.00 -0.44** -0.22 -0.01 -0.01 -0.13 -0.16 .17 (-0.0) (-2.5) (-1.2) (-0.1) (-0.1) (-0.7) (-0.9)

16.01 -0.01 -0.64** -0.67** -0.62** -0.44** -0.52** -0.22 .41 (-1.0) (-3.8) (-3.7) (-3.1) (-2.2) (-2.9) (-1.4)

17.02 0.00 -0.22 -0.49** 0.37** -0.21 -0.23 -0.39** .32 (0.0) (-1.4) (-3.1) (-2.1) (-1.2) (-1.4) (-2.4)

17.03 0.00 -0.36** -0.05 -0.23 -0.44** -0.15 -0.08 .29 (1.5) (-2.3) (-0.4) (-1.4) (-2.8) (-1.0) (0.5)

18.02 0.00 -0.42** -0.70** -0.29 -0.35 -0.14 -0.25 .34 (1.3) (-2.4) (-3.7) (-1.4) (-1.6) (-0.8) (-1.5)

19.01 0.00 -0.28* -0.15 -0.36** -0.35** -0.06 -0.09 .22 (0.3) ( - 1.7) (-0.9) (-2.2) (-2.1) (-0.4) (-0.5)

19.02 -0.00 -0.39** -0.42** -0.22 -0.18 -0.36* -0.11 .26 (-0.2) (-2.3) (-2.2) (-1.1) (-0.9) (-1.9) (-0.6)

21.00 0.00 -0.73** -0.49** -0.51"* -0.30 -0.24* -0.10 .39 (1.5) (-4.2) (-2.4) (-2.3) (-1.6) (-1.8) (-0.8)

22.00 0.00 -0.53** -0.24 -0.24 -0.11 -0.13 -0.07 .27 (0.5) (-3.2) (-1.3) (-1.3) (-0.6) (-0.7) (-0.0)

24.00 -0.00 -0.36** -0.66** 0.31 -0.32* -0.10 -0.23 .33 (-0.3) (-2.1) (-3.7) (-1.5) (-1.7) (-0.5) (-1.4)

~Excess returns are calculated by subtracting the average quarterly residuals from the first regression from each census tract's residual. (t-ratios are in parentheses.)

*Significant at the .10 level. **Significant at the .05 level.


s e c t o r s d u r i n g t h e f i r s t t w o l agged q u a r t e r s a r e n o t s p u r i o u s , t h e resu l t s s u g g e s t a fa i r ly

r a p i d a d j u s t m e n t o f t he m a r k e t t o w a r d s e q u i l i b r i u m . In o n l y 1 o f t h e 20 s e c t o r s d i d s ign i f i -

c a n t l agged c o r r e l a t i o n s o c c u r for f ive qua r t e r s . T h e p e r s i s t e n c e o f a po t en t i a l l y exp lo i t ab l e

s i t ua t ion s u g g e s t s tha t t r a n s a c t i o n a n d s e a r c h c o s t s m u s t b e l a r g e re la t ive to t h e p o t e n t i a l

e x c e s s r e t u r n s .

Notes

1. Most of the data were obtained from appraisal sources. Multiple listing service (MLS) data are included for the period of October 1975 through September 1978, which overlaps with the appraisal data except for a four-quarter period when the only available data were from the MLS.

2. Three of the excluded census tracts were very small while a fourth exclusively contained Texas Tech Univer- sity. The remaining 11 census tracts were excluded primarily because the limited number of transactions made it impossible to develop a reliable quarterly time series of dam. There is a significant racial and geographic difference between the two groups of census tracts because of the highly segregated nature of the city. The 20 included census tracts are 94 percent white while 11 excluded census tracts average 57 percent black or Hispanic (9 of the 11 average 69 percent minority) and are located on the northeast and east side of the city.

3. The number of transactions per census tract per quarter range from 2.0 (census tract 1.00) to 28.0 (census tract 21.00) with the average approximately 6.5 per census tract per quarter. In a few cases in each census tract, data were missing either completely for a quarter or for a specific variable. Mean values for the census tract for the four preceding and four succeeding quarters were used to generate data for the missing values.

4. The Lubbock data reflect a strong relationship between price and property characteristics. It is not unusual for size to explain over 70 percent of the variation in price within a census tract and for the standard heronic price model to yield an R 2 about 90 percent. Therefore, changes in property characteristics rather than neighborhood or other demographic factors are likely to account for most of the variation in rates of return over time.

5. Regression rather than correlation analysis is used to allow for the cumulative or interactive effect of lagged variables on the dependent variable. Preliminary correlations of the residuals, or excess returns in the residuals, for present and lagged periods by census tract produced results consistent with market efficiency since the only pattern of significant correlations involved lags of one period. A one-period lag was found in 15 of the 20 census tracts and in tests on the combined pool of residuals. A significant, negative one-period coefficient could be explained by an errors-in-variable problem where an incorrect or abnormal price (and, hence, rate of return) in one period is corrected in the following period. See Gau (1984, p. 311).

6. Census tracts 17.02, 17.03, and 19.01 have significant coefficients for the first or second lagged period and then for consecutive quarters after a several-quarter gap. This may be evidence of sustained excess returns but the discontinuity makes any interpretation hazardous.

7. There is nothing special about the choice of a six-quarter period. Preliminary analysis did not reveal a pattern of significant lagged relationships for more than six quarters in any of the census tracts.

8. Census tracts 14.00 and 16.01 had significant lags for, respectively, four and six quarters, while census tract 4.02 had significant lags only the first two quarters. In addition, census tracts 17.02 and 22.00 had significant lags of four and five quarters, respectively.

9. The expected market appreciation rate is here modeled as being dependent on changes in money (M1), changes in mortgage interest rates, and the real price of oil. These variables are included to improve the efficiency of the expected appreciation measure but not to identify the variable. The M 1 and interest rate variables enter as marginally signficant while the real oil price enters as insignificant. These results are available on request from the authors.


Appendix: Variance of the Excess Returns in Census Tracts with Statistically Significant Lagged Variables

Census Tract I N Variance of Excess Returns

3.00 221 0.0154 4.02 537 0.0033 4.03 287 0.0125

14.00 240 0.0068 15.00 292 0.0109 16.01 125 0.0128 16.02 248 0.0047 17.02 561 0.0013 17.03 309 0.0018 18.02 1,268 0.0012 19.01 341 0.0029 19.02 1,023 0.0012 21.00 1,324 0.0008 22.00 964 0.0020 24.00 341 0.0052

1Census tracts 1.00, 13.00, 18.01, 20.00, and 23.00 had no significant coefficients for lagged variables.

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Documents

Empirical tests of real estate market efficiency