THE INFLATION-OUTPUT VARIABILITY TRADE-OFF:OECD EVIDENCE

JIM LEE*

This article employs a multivariate GARCH model to empirically estimate apossible trade-off between output variability and inflation volatility in light ofOECD data over the 1984±2001 period. Statistical support for the hypothesizedvolatility trade-off is equivocal across countries. The mixed findings can beassociated with central banks' varying monetary policy responses to exogenousshocks. The trade-off estimates are also found to be consistent with earlier studiesthat reveal different degrees of central bank commitment to price vis-aÁ-vis outputstability. (JEL E30, E58, C32)

I. INTRODUCTION

Earlier policy debates emphasized inflation-output trade-offs in levels, but the focus todayis on the choice between the variability of infla-tion and the variability of output. Followingthe seminal work of Taylor (1979, 1993,1994), it is now standard to express a centralbank's objective as an expected loss functionconsisting of both inflation variability and out-put variability with different relative weights.Accordingly, if policy makers aim at loweringinflation to a predetermined target over time,then inflation will be less variable and outputwill inevitably exhibit larger fluctuations.

Methodologically, the bulk of existing stud-ies concerning the output-inflation volatilitytrade-off rely on simulations with calibratedmodels. Despite the popularity of this new pol-icy trade-off as an expositional tool in explain-ing the choices confronting policy makers, itsempirical value remains questionable for tworeasons. First, as pointed out by Walsh (1998),because there is no consensus regarding whichmodel best represents the economy, those stud-ies inevitably lead to disagreements about thetrue trade-off faced by policy makers. Second,the volatility trade-off frontier is traced out in

light of a series of `̀ optimal'' policy rules, eachof which is simulated in a stable and optimalcondition over a long time horizon. Cecchettiet al. (2001), however, find varying degrees ofpolicy inefficiency in practice among centralbanks. For these reasons, the empirical signifi-cance of these simulation-based studies islimited.

Another distinguishing feature of previousstudies is their focus on the long run. One rea-son for the scarcity of empirical studies on theshort-run volatility dynamics of inflation andoutput is that volatility behavior is not directlyobservable. A few exceptions include Lee(1999, 2002), who uses a bivariate generalizedautoregressive conditional heteroscedasticity(GARCH) model to estimate the conditionalvariances of inflation and output. Based ondata for the United States, his model showssupport for an inflation-output volatilitytrade-off in the short run. The first objectiveof the present study is to extend this line of workto other countries. Given data availability,a sample of 22 Organisation for EconomicCo-operation and Development (OECD)members has been selected.

ABBREVIATIONS

GARCH: Generalized Autoregressive Conditional

Heteroscedasticity

IT: Inflation Targeting

OECD: Organisation for Economic Co-operation

and Development

VAR: Vector Autoregression

*This is a revision of a paper presented at the WesternEconomic Association International Pacific Rim Confer-ence, Taipei, Taiwan, 9±12 January 2003. The authorthanks two anonymous referees for helpful comments.

Lee: Professor of Economics, Texas A&M UniversityÐCorpus Christi, Corpus Christi, TX 78412.Phone 1-361-825-5831, Fax 1-361-825-5609, E-mailjlee@cob.tamucc.edu

344

Contemporary Economic Policy DOI: 10.1093/cep/byh025(ISSN 1074-3529) # Western Economic Association International 2004Vol. 22, No. 3, July 2004, 344±356 No Claim to Original U.S. Government Works

The GARCH approach has two majoradvantages over the conventional measure ofvolatility, such as moving standard deviationsand squared residual terms in vector auto-regressions (VARs). The first advantage isthat conditional volatility, as compared tounconditional volatility, better represents per-ceived uncertainty (e.g., Grier and Perry, 2000),which is of particular interest to policy makers.The second advantage is that the GARCHmodel offers insights into the hypothesizedvolatility relationship in both the short runand the long run. Whereas time-varying con-ditional variances reveal volatility dynamics inthe short run, the model also generates a long-run measure of the output-inflation covariancethat will be helpful in evaluating monetarypolicy trade-offs, as will be illustrated in acomparison study in section IV.

As Fuhrer (1997), and Cecchetti andEhrmann (1999) point out, the output-inflation volatility trade-off relationship canbe affected by many factors, including thestructure of the economy and the centralbank's policy toward inflation stability. Sincethe early 1980s, central banks around theworld, including the Federal Reserve, havegiven particular attention to price stability.Many of them have now adopted proceduresthat explicitly target low or zero inflation.Against this background, the second objectiveof this article is to provide measures of centralbanks' commitment to price vis-aÁ-vis outputstability that are comparable to some recentstudies.

The remainder of the article is organized asfollows.ThenextsectiondescribestheGARCHestimation model and sample data. The thirdsection discusses the estimation results. Thefourth section compares regression-based infer-ences on central bank behavior with the find-ings of some recent studies. The final sectioncontains a summary and conclusion.

II. METHODOLOGY

A. Estimation Model

The hypothesized volatility trade-off rela-tionship is explored in light of a bivariateGARCH( p, q) process governing output andinflation.1 For convenience, this author

pursues a GARCH(1,1), which is the mostpopular representation in the literature. Toillustrate the model, let yt� [ y1t y2t]

0 be a2� 1 vector containing the output andinflation variables in a conditional meanequation as

yt�h� et, et�N�0,Ht� 8t� 1, . . . ,T ,�1�

where h� [h1 h2]0 is a 2�1 vector of constantterms capturing the unconditional means of thetwo time series, and et� [e1t e2t]

0 is a vector ofresiduals with a corresponding 2�2 condi-tional variance-covariance matrix Ht.

The GARCH(1,1) process for Ht can beexpressed as:

Ht � G 0G� A0Htÿ1A� B0etÿ1e0tÿ1B,�2�

where G is a 2� 2 lower-triangular matrixwith three constant terms, and the other 2� 2matrices of free parameters are {A}ij�aij, and{B}ij� bij 8i, j� 1, 2. Similar to G, A isrestricted to be a lower-triangular matrixsuch that a12� 0. By restricting all the termson the right-hand side of the equation in qua-dratic form, equation (2) guarantees a positivedefinite Ht. The GARCH process is a naturalgeneralization of the ARCH model such thatthe two conditional variances are a functionnot only of past errors but also of past con-ditional variances. Moreover, equation (2)allows for own and cross-effects in the con-ditional variances through the off-diagonalcoefficients in B. The lagged variance termaccounts for persistence in Ht that is commonlyfound in macroeconomic and financial timeseries.

The system of conditional mean and con-ditional variance-covariance equations, ascaptured by equations (1) and (2), is estimatedusing the maximum-likelihood method inwhich the (concentrated) likelihood functionis written as

L�Q� �XT

t�1

Lt�Q��3�

� ÿ�1=2�XT

t�1

�log jHt�Q�j

� e0t�Q�Hÿ1t �Q�et�Q��,

1. See Engle and Kroner (1995) for a discussion ofmultivariate GARCH models and alternative estimationmethods.

LEE: OECD INFLATION-OUTPUT VARIABILITY TRADE-OFF 345

where Q is the vector of all parameters forestimation. This procedure requires that et bestandardnormal.Aswillbeshown, theassump-tion of normality is violated for the majorityof data series, especially for inflation. In thislight, we employ Bollerslev and Wooldridge's(1992) quasi-maximum-likelihood procedure,which produces consistent parameter estimatesthat are robust to nonnormality.

B. Data

Empirical lessons are drawn from monthlyOECD data spanning the period between 1984and 2001.2 Even though gross domesticproduct may serve as a better measure ofaggregate output, industrial production isused instead because of its availability in themonthly frequency, which effectively yieldsmore (three times) data points than the corre-sponding quarterly observations. The inflationvariable is measured by the month-to-monthchange in the price level, as measured by thefirst difference of the log of the Consumer PriceIndex.

The data specification should be consistentwith the recent theoretical literature in which acentral bank is assumed to achieve output (zerooutput gap) and price (zero inflation) stability.The common practice treats the output vari-able as the percent deviation of output fromits trend or potential level. For each country,Baxter and King's (1995) low-pass filter is usedto filter out the low-frequency component, orlong-term trend, in industrial production.3

As Figure 1 illustrates, the filtered output seriesevidently fluctuate along a zero mean.

In comparison with the `̀ great inflation'' ofthe 1970s, the sample period is associated withan extended period of overall declining infla-tion as well as increased output stability acrossOECD countries. Along with the FederalReserve, an increasing number of centralbanks around the world began to pay closeattention to price stability. By the mid-1990s,many countries would have instituted aprocedure explicitly targeting low or zero infla-tion. Figure 2 illustrates, the inflation series donot appear to have stationary means such thatthe conditional mean equation (1) might result

in misleading inferences. In this light, the articleapplies the low-pass filter to the inflation datain the same manner as to the output data.The dashed lines in Figure 2 display the low-frequency components, which represent esti-mated time-varying inflation means.4 Inflationtends to decline across countries beginningin the mid-1980s. For some countries, theinflation trend appears to pick up modestly inthe late 1990s. Given these observations, itmakes sense to filter out the low-frequencycomponents in the inflation data beforeGARCH estimations.

Tables 1 and 2 show some descriptive statis-tics for the filtered output and inflation series ofthe 22 OECD countries over the observationperiod 1984±2001. The data means are all closeto zero as a result of the detrending processes.The variances, by contrast, vary considerablyacross countries. The output varianceranges from 0.061 (United States) to 0.669(Luxembourg), where the inflation varianceranges between 0.038 (United States) and1.574 (Greece). These figures echo a majorobservation in Figures 1 and 2: Although out-put and inflation tend to move together acrosscountries, the extents of their variations differsubstantially.

Tables 1 and 2 also display test statisticsfor skewness, kurtosis, and the Jarque-Berac2 test for normality. The null hypothesisof normality is rejected for the majority ofdata series. The skewness and kurtosis testsfurther indicate that many series have fattails and/or sharper central peaks than the stan-dard normal distribution. The two tables alsoshow results for Engle's (1983) Lagrange multi-plier test for ARCH with 20 lags. Clearly,conditional heteroscedasticity exists in bothoutput and inflation series. The evidence ofARCH in high order offers support for aGARCH process instead of ARCH. In parti-cular, given its popularity and parsimony, aGARCH(1,1) model is selected to representthe conditional variance process.5 The finding

2. All data are taken from the OECD Main EconomicIndicators.

3. The data are insensitive to the use of filteringmethod. For example, the Hodrick and Prescott (1997)filter produces virtually the same trend line for every indus-trial production series.

4. Instead of the low-pass filter, the author also esti-mated the time-varying means (captured by the interceptterm) in inflation using alternatively a moving-average pro-cedure, the Kalman filter, and a Fourier-series approxima-tion suggested by Becker et al. (2002). The results arenonetheless the same as those with the low-pass filter.

5. The author further tested for misspecificationin the GARCH(1,1) model based on Wooldridge's(1991) method and ARCH tests. Although not reportedhere, these diagnostic tests revealed scant evidence ofmisspecification.

346 CONTEMPORARY ECONOMIC POLICY

FIGURE 1

Detrended Industrial Production

FIGURE 2

Inflation

of nonnormality also supports the use ofBollerslev and Wooldridge's (1992) quasi-maximum-likelihood method as alreadyoutlined.

III. ESTIMATION RESULTS

Table 3 displays the estimation results forthe conditional variance-covariance equation(2) using OECD data. The table is divided intothree sets of columns, each of which displaysparameter estimates in a particular matrix.More specifically, the first set, which spansbetween the second and fourth columns,displays parameter estimates in G; the secondpanel, which spans between the fifth andseventh columns, displays parameter estimatesin A; and the third panel, which spans betweentheeighthto eleventhcolumns, displays param-eter estimates in B. As a result of the filteringprocesses, the estimates for the conditionalmean equation (1) are statistically insignificantand are therefore not reported here to con-serve space.

The left part of Table 3 reports the param-eter estimates in G. The diagonal elements

in G, g11 and g22, provide information regardingthe unconditional output and inflation var-iances over the estimation period. As expected,countries that have a relatively high out-put variance (e.g., Denmark, Ireland, andLuxembourg) tend to have relatively high g11

estimates. Similarly, countries with a relativelyhigh inflation variance (e.g., Greece, Australia,and New Zealand) tend to have a relativelyhigh g22 estimate. The third column shows esti-mates for the lower-corner parameter of G, g21,which lends to the measure of unconditionalcovariance between output and inflation. Ofspecific interest are the signs of the estimates,which indicate the directions of covariationbetween output and inflation variances.Twelve of the 22 countries yield a significantand negative estimate, which indicates anegative unconditional covariance over theentire estimation period. On the other hand,such countries as the United States and NewZealand have a significant and positive esti-mate, which is consistent with the observationthat both output variability and inflation varia-bility tended to decline across the observationperiod (see Figures 1 and 2).

TABLE 1

Descriptive Statistics for Industrial Production, 1984±2001

Country Mean Variance Skewness Kurtosis Jarque-Bera ARCH

Australia 0.006 0.103 ÿ0.059 0.220 0.545 144.241*

Austria 0.005 0.214 0.060 0.293 0.877 78.082*

Belgium 0.005 0.169 ÿ0.461 3.003 86.356* 58.363*

Canada 0.009 0.140 ÿ0.235 ÿ0.466 3.824 139.327*

Denmark 0.011 0.418 ÿ0.436 1.531 27.183* 68.871*

Finland 0.014 0.306 ÿ0.095 ÿ0.480 2.334 118.750*

France 0.001 0.076 ÿ0.431 ÿ0.055 6.514** 123.917*

Germany 0.001 0.188 ÿ1.059 5.267 281.953* 111.016*

Great Britain ÿ0.005 0.081 0.015 0.950 7.913** 91.755*

Greece 0.001 0.289 ÿ1.569 9.876 939.588* 16.200***

Ireland 0.029 0.640 0.116 1.575 22.180* 51.512*

Italy 0.001 0.164 ÿ0.274 ÿ0.309 3.460 93.857*

Japan 0.025 0.248 ÿ0.068 ÿ0.300 0.950 119.783*

Luxembourg 0.007 0.669 ÿ0.612 1.389 29.963* 59.833*

Netherlands 0.015 0.260 0.387 1.272 19.405* 77.888*

New Zealand 0.003 0.074 0.105 ÿ0.413 1.879 126.263*

Norway ÿ0.001 0.318 ÿ1.135 2.936 120.515* 50.041*

Portugal 0.000 0.322 ÿ0.041 0.159 0.280 87.287*

Spain ÿ0.002 0.200 ÿ0.235 0.216 2.333 124.952*

Sweden 0.012 0.322 0.205 0.617 4.796*** 75.722*

Switzerland 0.000 0.178 ÿ0.421 ÿ0.271 6.860** 149.779*

United States 0.021 0.061 ÿ0.241 0.298 2.805 146.461*

Note: *, **, and *** denote statistical significance at the 0.01, 0.05, and 0.1 levels, respectively.

LEE: OECD INFLATION-OUTPUT VARIABILITY TRADE-OFF 349

The middle section of Table 3 reportsthe parameter estimates in A. These threeparameters depict the extents to which the cur-rent levels of conditional variances are corre-lated with their past levels. In particular, thediagonal elements, a11 and a22, are the keyelements in capturing the degrees of persistencein conditional variances. The level of persis-tence in the conditional variance of output ismeasured by a11� b11, and the level of persis-tence in the conditional variance of inflation ismeasured by a22� b22. It is apparent that thesum of the diagonal elements in A and B arefairly close to unity in many cases, implyingthat the effect of any shock tends to last fora long period of time.

Column six of Table 3 displays the estimatesfor the off-diagonal element of A, a21, whichcaptures the extent to which inflation volatilityis correlated with lagged output volatility. Anegative estimate supports the presence of aninflation-output volatility trade-off. Thirteenout of the 22 estimates are statistically signifi-cant with a negative sign. The negative estimatefor the United States is in line with the recentfindings in Lee (1999, 2002). Conversely,

Sweden has a positive estimate, meaning thathigher output volatility is followed by higher(instead of lower) inflation volatility. Overall,the size of the a21 estimate varies widely acrosscountries.

The right portion of Table 3 reports theparameter estimates in B. These parametersreveal the extents to which the conditional var-iances of output and inflation are correlatedwith past squared innovations (i.e., deviationsfrom output trend and deviations from infla-tion mean). The diagonal elements, b11 and b22,measure how these innovations are transmittedinto ARCH effects, whereas the off-diagonalelements measure how the innovation in onevariable generates ARCH effects in anothervariable. The majority of estimates are statis-tically significant at the 0.1 level or higher. Thepositive signs reflect the destabilizing effect ofan economic shock.

The off-diagonal elements, b12 and b21,depict how the conditional variance of onevariable is correlated with the past squaredinnovation of another variable. More specifi-cally, b12 captures the extent to which a one-period lagged inflation shock explains current

TABLE 2

Descriptive Statistics for Inflation, 1984±2001

Country Mean Variance Skewness Kurtosis Jarque-Bera ARCH

Australia ÿ0.003 0.443 1.809 3.841 243.601* 55.304**

Austria ÿ0.008 0.142 0.134 1.132 11.844* 118.372*

Belgium 0.006 0.067 0.265 0.303 3.260 83.142**

Canada 0.004 0.082 2.198 17.558 2866.515* 48.731***

Denmark 0.002 0.127 0.870 6.042 345.917* 49.615***

Finland 0.005 0.094 0.758 1.158 31.869* 70.642**

France 0.004 0.038 0.114 0.607 3.675 62.550**

Germany 0.004 0.069 1.384 4.548 248.004* 48.852***

Great Britain 0.003 0.193 1.261 4.883 264.243* 49.445***

Greece 0.000 1.574 ÿ0.091 ÿ0.260 0.879 131.711*

Ireland 0.004 0.246 1.696 2.490 154.983* 104.673*

Italy 0.002 0.039 0.160 1.425 18.665* 63.153***

Japan 0.002 0.185 0.630 2.290 59.770* 50.099***

Luxembourg 0.001 0.135 ÿ0.400 9.203 746.750* 119.234*

Netherlands 0.000 0.134 ÿ0.196 0.415 2.847 91.555*

New Zealand 0.006 0.857 3.513 21.934 4641.544* 46.307***

Norway 0.008 0.123 0.514 0.006 9.231* 87.367**

Portugal ÿ0.003 0.303 0.188 6.113 328.175* 81.925*

Spain ÿ0.002 0.139 1.417 5.978 382.967* 49.080***

Sweden 0.001 0.267 1.699 5.646 379.880* 49.954***

Switzerland 0.004 0.078 0.326 0.578 6.641** 79.743*

United States 0.004 0.038 0.113 0.512 2.739 75.569***

Note: *,**, and *** denote statistical significance at the 0.01, 0.05, and 0.1 levels, respectively.

350 CONTEMPORARY ECONOMIC POLICY

TABLE 3

Estimation Results for GARCH(1,1), 1984±2001

Estimated Coefficients

C A B

Country g11 g21 g22 a11 a21 a22 b11 b21 b12 b22

Australia 0.031**(2.18)

ÿ 0.129*(5.38)

0.036***(1.69)

0.741*(5.96)

ÿ 0.214*(4.72)

0.714**(2.63)

0.081*(9.65)

0.052(1.15)

ÿ 0.651*(4.68)

0.352(0.61)

Austria 0.004*(4.12)

ÿ 0.592**(1.95)

0.003*(3.69)

0.296*(2.79)

ÿ 0.05***(1.65)

0.873*(3.36)

0.120***(1.73)

0.098(0.82)

0.075***(1.76)

0.118*(6.49)

Belgium 0.126**(2.36)

ÿ 0.307(0.42)

0.014*(11.40)

0.260**(2.02)

ÿ 0.317(1.30)

0.789*(7.99)

0.422*(3.16)

0.014(0.17)

ÿ 0.049(0.94)

0.070*(2.91)

Canada 0.017*(3.55)

ÿ 0.086***(1.89)

0.034*(4.54)

0.864**(2.75)

ÿ 0.638***(1.71)

0.509*(8.13)

0.059*(10.17)

0.279(1.62)

0.213**(2.06)

0.348(1.32)

Denmark 0.320*(3.23)

ÿ 0.560*(7.44)

0.055*(6.17)

0.224*(3.31)

0.922(0.06)

0.538*(9.18)

0.454*(3.12)

0.161**(2.13)

0.062**(2.36)

ÿ 0.059**(2.13)

Finland 0.126*(5.00)

ÿ 0.298*(4.92)

0.003*(7.48)

0.447*(3.68)

ÿ 0.454**(2.47)

0.369**(2.39)

0.314*(8.91)

0.037(0.27)

ÿ 0.029(1.06)

0.202*(2.96)

France 0.027*(2.85)

ÿ 0.095*(3.26)

0.003*(3.76)

0.326*(4.51)

ÿ 0.020(1.07)

0.941(0.86)

0.508*(7.16)

0.065(0.65)

0.033(1.31)

0.245*(2.92)

Germany 0.120**(2.41)

ÿ 0.101**(2.36)

0.004*(3.44)

0.204*(3.00)

0.126(1.28)

0.899**(2.29)

0.631*(4.86)

0.058(0.66)

0.048(0.91)

0.046**(2.15)

Great Britain 0.015*(3.05)

0.072*(3.08)

0.001*(6.64)

0.716*(6.95)

ÿ 0.120***(1.63)

0.609(1.11)

0.242*(3.58)

0.034(0.78)

ÿ 0.124**(1.85)

0.049(1.60)

Greece 0.062**(2.48)

ÿ 0.238*(4.39)

0.085**(2.61)

0.130*(4.28)

ÿ 0.255*(3.29)

0.201*(3.26)

0.458*(4.10)

0.177*(4.03)

ÿ 0.510(1.43)

0.086(1.18)

Ireland 0.187*(8.77)

ÿ 0.310*(3.46)

0.017*(4.19)

0.326*(5.73)

ÿ 0.411*(3.24)

0.921*(3.67)

0.301*(3.42)

ÿ 0.299**(1.88)

0.066***(1.70)

0.056**(2.49)

Italy 0.009**(2.12)

0.080(1.00)

0.008*(5.33)

0.469*(12.36)

0.288(0.85)

0.007(0.91)

0.204**(2.50)

0.171(0.84)

0.081(1.09)

0.166**(1.92)

Japan 0.098*(2.85)

ÿ 0.160*(6.32)

0.012*(3.49)

0.372*(9.70)

ÿ 0.139***(1.66)

0.875(1.30)

0.566*(11.32)

0.015(0.19)

ÿ 0.009(0.32)

0.015**(2.39)

Luxembourg 0.092*(4.06)

ÿ 0.092**(1.72)

0.083**(2.26)

0.478*(13.74)

0.161(0.57)

0.397*(6.23)

0.174**(1.88)

0.027(0.17)

0.134**(2.59)

1.170*(5.87)

continued

LE

E:

OE

CD

INF

LA

TIO

N-O

UT

PU

TV

AR

IAB

ILIT

YT

RA

DE

-OF

F351

TABLE 3 continued

Estimated Coefficients

C A B

Country g11 g21 g22 a11 a21 a22 b11 b21 b12 b22

Netherlands 0.096*(3.48)

ÿ 0.090(0.37)

0.064***(1.74)

0.391*(2.94)

ÿ 0.862*(3.70)

0.240*(8.73)

0.168*(3.24)

ÿ 0.008(0.04)

0.007(0.06)

0.134(1.48)

New Zealand 0.010**(2.86)

0.140*(6.75)

0.086*(3.36)

0.157**(2.31)

0.027(0.14)

0.641*(12.03)

0.608*(5.38)

0.012(0.82)

0.311(1.21)

0.462*(4.32)

Norway 0.051**(2.48)

0.184**(2.26)

0.109**(2.12)

0.103*(12.85)

ÿ 0.608***(1.62)

0.243*(3.08)

0.243*(2.98)

0.059**(1.87)

0.192**(2.09)

0.035***(1.72)

Portugal 0.019**(2.21)

ÿ 0.111(0.93)

0.010**(2.48)

0.769*(4.19)

ÿ 0.045***(1.72)

0.814*(5.77)

0.183*(5.23)

0.142**(2.09)

ÿ 0.027(1.00)

0.058**(2.19)

Spain 0.063*(3.18)

ÿ 0.239(1.38)

0.006*(3.39)

0.153**(2.80)

ÿ 0.073(0.93)

0.221*(0.12)

0.457*(8.99)

ÿ 0.129(0.27)

0.008(0.61)

0.024*(3.44)

Sweden 0.137*(3.01)

0.094(0.46)

0.170*(3.69)

0.167**(2.76)

0.148**(2.37)

0.824*(5.12)

0.755(0.89)

ÿ 0.277*(2.73)

0.504**(1.86)

0.093*(2.43)

Switzerland 0.061**(2.31)

ÿ 0.086**(2.68)

0.107**(1.88)

0.014**(2.64)

0.520(1.26)

0.034***(1.86)

0.872*(12.17)

ÿ 0.017(0.36)

ÿ 0.023(0.42)

0.063(0.55)

United States 0.007**(1.98)

0.064*(4.93)

0.013**(3.23)

0.024**(2.73)

ÿ 0.298*(3.81)

0.289*(5.91)

0.936*(21.11)

0.079**(2.35)

0.155**(1.97)

0.190*(4.58)

Notes: All estimations are based on equation (2): Ht � G0G� A0Htÿ1A� B0etÿ1e0tÿ1B, where et is obtained from equation (1): yt � h� et, where yt � �y1t y2t�0 which represents avector of detrended industrial production series and demeaned inflation series. Equations (1) and (2) are estimated simultaneously using the quasi-maximum-likelihood method over theperiod 1984±2001. Absolute t-statistics are indicated in parentheses. *, **, and *** denote statistical significance at the 0.01, 0.05, and 0.1 levels, respectively.

35

2C

ON

TE

MP

OR

AR

YE

CO

NO

MIC

PO

LIC

Y

output volatility. The parameter b21, on theother hand, captures the extent to which aone-period lagged output shock explainscurrent inflation volatility. The estimates offermixed support for any cross-effects in eitherdirection. Only the United States and Norwayhave significantly positive estimates for bothoutput and inflation shocks.

Overall, in contrast to earlier findings (forexample, Lee, 1999, 2002) for the UnitedStates, the OECD data lend mixed supportto the hypothesized volatility trade-offrelationship. It is nevertheless noteworthythat Table 3 provides information regardingvolatility dynamics in both the short run andthe long run. The parameter a21 captures theshort-run (time-varying) dynamic relationshipbetween inflation and output conditionalvariances, whereas the parameter g21 capturestheir long-run relationship in light of theirunconditional covariance throughout theentire estimation period. Not surprisingly,many countries that have a negative a21

(short-run) estimate also have a negative g21

(long-run) estimate. The exceptions are theUnited States and Norway, which experiencedlower volatility in both output and inflation inthe 1990s than in the 1980s.

To further evaluate the significance ofshort-run dynamics in the covariance betweeninflation and output, this author followsBollerslev (1990) and performs likelihoodratio tests on restricting the cross-effectsbetween the conditional variances of inflationand output to zero, that is, a21� b12� b21� 0.The resulting statistics are distributed as c2(3).As shown in Table 4 the null hypothesis of nocross-effects is rejected at the 1% level or betterin most cases. In other words, although it is ofinterest to make long-run inferences on thevariances of output and inflation and theircovariance, their short-run variations shouldnot be overlooked.

These findings on volatility trade-offs maybe compared with previous studies using dif-ferent approaches. Most relevant is the work ofCecchetti and Ehrmann (1999), and Cecchettiet al. (2001), who find a link between theoutput-inflation volatility trade-off and ameasure of central bank commitment to infla-tion stability across countries. In the followingsection, the article attempts to compare theirfindings on central bank behavior with thoseimplied by the current estimated GARCHmodel.

IV. A COMPARISON WITH RECENT STUDIES

As in many recent monetary policy±oriented studies, the output-inflation volatilitytrade-off relationship can be interpreted as anoutcome of a central bank's optimal decision-making process. In particular, Cecchetti andEhrmann (1999), and Cecchetti et al. (2001)highlight the role that a central bank'spreference for price vis-aÁ-vis output stabilityaffects, such a trade-off.

To illustrate this line of reasoning, theauthor assumes that central bankers seek sta-bilization in output ( yt) and inflation (pt)around their targets. In a simple one-periodsetting, the objective can be formulated inthe form of a quadratic loss function:

E�q�pt ÿ p�t �2 � �1ÿ q��yt ÿ y�t �2�,�4�

where E denotes mathematical expectations,and pt* and yt* denote the target levels for pt

TABLE 4Likelihood Ratio Tests

for Cross Effects

Country c2(3)

Australia 87.94*

Austria 8.68**

Belgium 7.44***

Canada 19.24*

Denmark 9.58**

Finland 14.40*

France 8.14**

Germany 7.12***

Great Britain 11.92*

Greece 25.30*

Ireland 44.14*

Italy 29.30*

Japan 10.94**

Luxembourg 17.92*

Netherlands 6.66***

New Zealand 13.30*

Norway 38.86*

Portugal 6.58***

Spain 16.16*

Sweden 8.80**

Switzerland 17.16*

United States 33.54*

Notes: The likelihood ratio testsare applied to testing a21 � b12 �b21 � 0 in equation (2). *,**, and***indicate that the null hypothesis isrejected at the 0.01, 0.05, and 0.1levels, respectively.

LEE: OECD INFLATION-OUTPUT VARIABILITY TRADE-OFF 353

and yt, respectively. The parameter q capturesthe policy makers' preference for output stabi-lity relative to price stability or their aversion toinflation volatility. If they care only about pricestability, then q� 1. Conversely, if they careonly about output stabilization, then q� 0.

Following Cecchetti and Ehrmann (1999),the central bank's problem can be solved byfirst assuming that the dynamics of outputand inflation are governed by the followingprocesses:

yt � ÿl�rt ÿ dt� � st,�5�

pt � ÿ�rt ÿ dt� ÿ wst,�6�

where rt is the interest rate instrument con-trolled by the central bank, and dt and st repre-sent aggregate demand and aggregate supplyshocks, respectively. The parameter l is theratio between the responses of output and infla-tion to a monetary policy shock and can beinterpreted as the inverse of the slope of aggre-gate supply.

Given this stylized representation of theeconomy, the optimal policy response todemand and supply shocks can be expressedin a linear rule as

rt � ÿdt � jst,�7�

where j represents the central bank's reactionto supply shocks. This simple policy reactionfunction implies that the central bank totallyoffsets aggregate demand shocks. The responseto supply shocks, however, involves trade-offs. Policy responses are contingent on the eco-nomic structure captured by the slope of theaggregate supply curve (1/l), the impact of thesupply shock on inflation (w), along with policymakers' preference to output stability relativeto price stability (q).

Given the above setup, the optimal policyrule implies a trade-off between output varia-bility and inflation variability, which can beexpressed precisely as

s2y=s2

p � �q=l�1ÿ q��2:�8�

Such a volatility trade-off is directly related toq. If q� 0, which means that policy makers careonly about output stability, then s2

y=s2p � 0.

Conversely, if q� 1, which means that policymakers care only about price stability, then

s2y=s2

p � 1. Other than q, the shape of thevolatility trade-off also depends on the slopeof the aggregate supply curve (1/l).

The third column of Table 5 displaysthe estimates for l that are reported inCecchetti and Ehrmann (1999, tables 2and 3), and Cecchetti et al. (2001, table 2).Their observation period, which spans between1984 and 1997, is comparable to the currentone. Because l is the inverse aggregate supplyslope, a high value indicates a flat aggregatesupply curve, and a low value indicates asteep aggregate supply curve. A relatively flataggregate supply curve is found for Australia,France, Germany, Italy, and Switzerland,whereas a relatively steep aggregate supply

TABLE 5

Estimate for l and q

Inflationu

Country Targeting l Simulation Estimation

Australia IT (93:2) 4.65 0.81 0.80

Austria 0.22 0.50 0.19

Belgium 0.13 0.43 0.11

Canada IT (91:4) 1.80 0.75 0.66

Denmark 0.70 0.61 0.48

Finland IT (93:2) 3.76 0.96 0.81

France 6.15 0.95 0.82

Germany 5.72 0.94 0.82

Great Britaina IT (92:9) 2.57 0.97

Greece 1.75

Ireland 2.83 0.94 0.73

Italy 4.89 0.91

Japan 1.09 0.84 0.64

Luxembourg 1.15

Netherlands 2.03 0.84 0.49

New Zealand IT (90:4) 0.67 0.53

Norway 1.45

Portugala 0.58 0.53 0.49

Spain IT (94:4) 1.22 0.67 0.72

Sweden IT (93:1) 2.35 0.86 0.82

Switzerland 5.08 0.92 0.82

United States 1.10 0.74

Mean:

All countries 2.36 0.77 0.59

IT 2.43 0.83 0.69

Non-IT 2.32 0.73 0.54

aEstimates for l and simulation-based q are fromCecchetti et al. (2001); all others are from Cecchettiand Ehrmann (1999). Estimation-based q estimates arederived from estimating the GARCH model in thisarticle. The periods in which inflation targeting began arelisted in parentheses.

354 CONTEMPORARY ECONOMIC POLICY

curve is found for Austria, Belgium, Denmark,New Zealand, and Portugal.

The fourth column of Table 5 presents theestimates for q, which are obtained from thetwo studies by dividing the average outputresponse by the average inflation response toa monetary policy shock over a three-year hori-zon. Policy shocks are measured by interestrate innovations of a VAR model that resem-bles the system of equations (5)±(7). As indi-cated, a smaller value of q implies that centralbankers care more about output volatility, anda value closer to 1 implies that they are morecommitted to the inflation objective. Accord-ing to these simulation-based studies, manycountries with a relatively high q estimate aremembers of the European Union, includingFinland, France, Germany, Great Britain,Ireland, and Switzerland.

The last column of Table 5 displaysGARCH-based measures for q. A reasonableapproximation for the long-run volatilitytrade-off is the steady-state equivalent of g21

in light of the estimated first-order parametersof the variance-covariance matrix in equation(2). For each country, the author solves for q byusing the estimate for l in previous studies andequating the left-hand side of equation (9) tothe long-run covariance measure given theparameter estimates reported in Table 3. Coun-tries with a positive instead of negative measureof g21 (i.e., no volatility trade-off) are omitted.It is apparent that the estimates tend to besomewhat lower than their simulation-basedcounterparts. However, the countries thatyield a relatively high q based on GARCHestimation are also those that have a relativelyhigh q based on simulations. A high correlationindeed exists between these two sets of cross-sectional data. Their simple correlation coeffi-cient is 0.92.

Cecchetti and Ehrmann (1999) andCecchetti et al. (2001) use cross-country datato discern the effect of inflation targeting (IT).As indicated in the second column of Table 5, 7out of the 22 countries in the sample haveadopted monetary policy that explicitly targetsinflation. They conclude that a country's shiftto inflation targeting should theoretically moveits position along an output-inflation vari-ability trade-off. In contrast to this conjecture,they find a modestly higher mean q estimate forIT countries than non-IT countries. As shownat the bottom of Table 5, their mean q estimateis 0.83 for IT countries as compared to 0.73 for

non-IT countries. The GARCH-based resultstells a similar story.

V. SUMMARY AND CONCLUSION

This article attempted to investigate thetrade-off between output variability andinflation variability in light of recent OECDdata. In contrast to the earlier simulation-based literature, a GARCH model is used toshed light on the hypothesized trade-off rela-tionship in both the short run and the long run.

There is some (though not pervasive) statis-tical evidence in support of an output-inflationvolatility trade-off. Estimates are statisticallymeaningful for about half of the country sam-ple. The size of the trade-off also varies widelyacross countries. The current literature attrib-utes variation in the volatility trade-off to dif-ferent economic structures, as captured by theaggregate supply curve, as well as differentlevels of central bank commitment to pricestability.

Based on GARCH estimations, this articledrew inferences on central banks' commitmentto price vis-aÁ-vis output stability. The estimatesare comparable to earlier simulation-basedestimates presented by Cecchetti and Ehrmann(1999) and Cecchetti et al. (2001). Some of thediscrepancy between the estimates under thetwo alternative approaches can be explainedin part by inefficiency in monetary policyimplementation. The evidence of time-varyingconditional variances of output and inflationas well as their covariance further highlights theimportance of evaluating monetary policy overthe short-run horizon.

REFERENCES

Baxter, M., and R. G. King. `̀ Measuring Business Cycles:Approximate Band-Pass Filters for Economic TimeSeries.'' National Bureau of Economic ResearchWorking Paper No. 5022, 1995.

Becker, R., W. Enders, and S. Hurn. `̀ A General Test forTime Dependence in Parameters.'' University ofAlabama Working Paper No. 01-02-5, 2002.

Bollerslev, T. `̀ Modelling the Coherence in Short-RunNominal Exchange Rates: A Multivariate General-ized ARCH Mode.'' Review of Economics and Statis-tics, 72(3), 1990, 498±505.

Bollerslev, T., and J. M. Wooldridge. `̀ Quasi MaximumLikelihood Estimation of Dynamic Models withTime Varying Covariance.'' Econometric Review,11(2), 1992, 143±72.

Cecchetti, S. G., and M. Ehrmann. `̀ Does Inflation Target-ing Increase Output Volatility? An InternationalComparison of Policymakers' Preferences and

LEE: OECD INFLATION-OUTPUT VARIABILITY TRADE-OFF 355

Outcomes.'' National Bureau of Economic ResearchWorking Paper No. 7426, 1999.

Cecchetti, S. G., A. Flores-Lagunes, and S. Krause. `̀ HasMonetary Policy Become More Efficient? A Cross-Country Analysis.'' Ohio State University WorkingPaper, 2001.

Cecchetti, S. G., M. M. McConnell, and G. Perez-Quiros.`̀ Policymakers' Revealed Preferences and the Out-put-Inflation Variability Tradeoff: Implications forthe European Systems of Central Banks'' OhioState University Working Paper, 2001.

Engle, R. F. `̀ Estimates of the Variance of U.S. InflationBased upon the ARCH Model.'' Journal of Money,Credit, and Banking, 15(3), 1983, 266±301.

Engle, R. F., and K. F. Kroner. `̀ Multivariate Simulta-neous Generalized ARCH.'' Econometric Theory,11(1), 1995, 122±50.

Fuhrer, J. C. `̀ Inflation/Output Variance Trade-offs andOptimal Monetary Policy.'' Journal of Money, Credit,and Banking, 29(2), 1997, 214±34.

Grier, K. B., and M. J. Perry. `̀ The Effects of Real andNominal Uncertainty on Inflation and OutputGrowth: Some GARCH-M Evidence.'' Journal ofApplied Econometrics, 15(1), 2000, 45±58.

Hodrick, R., and E. C. Prescott. `̀ Post-War U.S.Business Cycle: An Empirical Investigation.''

Journal of Money, Credit and Banking, 29(1), 1997,1±16.

Lee, J. `̀ The Inflation and Output Variability Tradeoff:Evidence from a GARCH Model.'' EconomicsLetters, 62(1), 1999, 63±67.

ÐÐÐ.`̀ The Inflation-Output Variability Tradeoff andMonetary Policy: Evidence from a GARCHModel.'' Southern Economic Journal, 69(1), 2002,261±90.

Taylor, J. B. `̀ Estimation and Control of MacroeconomicModel with Rational Expectations.'' Econometrica,47(5), 1979, 1267±86.

ÐÐÐ.`̀ Discretion versus Policy Rules in Practice.''Carnegie-Rochester Conference Series on PublicPolicy, 39, 1993, 195±214.

ÐÐÐ.`̀ The Inflation/Output Variability Trade-off Revis-ited,.'' in Goals, Guidelines, and Constraints FacingMonetary Policymakers,, Federal Reserve Bank ofBoston Conference Series no. 38, 1994, 21±38.

Walsh, C. E. `̀ The New Output-Inflation Trade-off.''Federal Reserve Bank of San Francisco, EconomicLetter, No. 98-04, 1998.

Wooldridge, J. `̀ On the Application of Robust,Regression-Based Diagnostics to Models of Conditional Meansand Conditional Variances.'' Journalof Econometrics,47(1), 1991, 5±46.

356 CONTEMPORARY ECONOMIC POLICY