The robustness of Okun's law: Evidence from OECD countries

JIM LEE Texas A &M University-Corpus Christi

Corpus Christi, Texas

The Robustness of Okun's Law: Evidence from OECD Countries

This paper evaluates the robustness of the Okun relationship based on postwar data for 16 OECD countries. While Okun's law is statistically valid for most countries, the quantitative as opposed to qualitative esttmates are far from uniform. Estimates are also sensitive to the choiee of models, including the first-difference and the "gap" specifications, the relevant data for the latter are constructed alternatively from the HP filter, the Beveridge-Nelson decomposition procedure, and the Kalman filter based on the NAIRU framework. There is mixed evidence of asymmetric behavior, but strong evidence of structural breaks occurring around the 1970s, after which time most countries began to experience a smaller output loss associated with higher unemployment.

1. Introduction Okun's law is commonly measured by the correlation between varia-

tions in unemployment and real output over the business cycle. Okun (1970) suggested that a one-percentage point change in the unemployment rate is associated with an approximately three-percentage change in output in the opposite direction. This rule of thumb is regarded as a benchmark for policy- makers to measure the cost of higher unemployment. Recent economic developments, however, have raised challenges to the three-to-one ratio as an empirical regularity.

The decade following the oil shocks in the 1970s was witness to persistently high joblessness and low output growth in the U.S. These turmoils have led some economists (see Evans 1989; Gordon 1984) to believe that output and unemployment dynamics have undergone structural change. Prominent explanations for such developments include rising female labor- force participation, productivity and wages slowdown, and corporate restructuring (e.g., Juhn, Murphy and Top 1991; Weiner 1993). These developments have further contributed to skepticism (e.g., Friedman 1988; Altig, Fitzgerald and Rupert 1997) about the robustness of Okun's law. More specifically, Hsing (1991), Prachowny (1993), and Sheehan and Zahn (1980) observe that job losses associated with a given amount of output reduction have tended to increase through time. More recent estimates by Gordon (1998) and Mankiw (1994) further suggest that Okun's rule of thumb is closer to two than three.

Journal of Macroeconomics, Spring 2000, Vol. 22, No. 2, pp. 331~356 Copyright © 2000 by Louisiana State University Press 0164-0704/2000/$1.50

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Despite the amount of attention to Okun's law, the bulk of empirical literature draws conclusions from U.S. data. A few exceptions include studies by Paldam (1987), Kaufman (1988), and Nickell (1997) who, however, illustrate substantial disparity in the output-unemployment trade-off across developed countries. Similar findings are found in other case studies. In particular, Hamada and Kurosaka (1984) report an Okun coefficient estimate of nearly 30 for Japan. Attfield and Silverstone (1998), on the other hand, report a relatively smaller estimate of about 1.45 for the U.K.

While the U.S. economy has continued to improve over the past decade, many other industrialized, particularly European, countries have experienced persistently high and volatile unemployment rates. Many economists (e.g., Bean 1994; Blanchard and Summers 1986; and Layard, Nickell and Jackman 1994) regard these developments as a structural rather than a cyclical phenomenon. Recent advances in understanding the workings of European labor market institutions set the stage for our investigation into the issue of whether Okun's law remains valid overseas.

Against the backdrop of recent global developments, this paper em- pirically investigates whether the properties of Okun's law, both statistical and quantitative, have altered. This question is explored using postwar time- series data for 16 OECD countries. The data sample allows us to shed light on the nature of Okun's law from an international perspective. Tests for structural instability over time are performed using Andrews' (1993) procedure, which assumes no a priori information about the timing of plausible structural change.

Another contribution of this paper is an evaluation of model robustness. We compare estimates from the two broad classes of specifications originally suggested by Okun ( 1 9 7 0 ) ~ e first-difference model and the "gap" model. For the "gap" approach, we further present results based on three leading data decomposition procedures, namely the Hodrick-Prescott (HP, 1997) filter, the Beveridge-Nelson (BN, 1981) method, and the Kalman filter incorporating the NAIRU framework. In effect, this paper differs from the existing literature that draws inferences primarily from a single model. The sensitivity of model estimates is further explored by: (1) extending the first-difference model to an error-correction framework, and (2) taking into account possible asymmetries in the output-unemployment relationship.

The remainder of the paper proceeds as follows: Section 2 describes the data sample and presents the alternative model specifications. Section 3 reports the empirical results and Section 4 concludes.

2. Data and Model Specifications The Data Sample

The Okun relationship is examined using annual data for 16 OECD countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France,

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The Robustness o f Okun's Law: Evidence f r o m O E C D Countries

Germany, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the United Kingdom, and the United States. 1 Except for Germany, the sample period runs from 1955 to 1996. In the case of Germany, the sample begins in 1960 in order to avoid a possible structural break in 1959 associated with the inclusion of the Saar region.

The theoretical foundation underlying the reduced-form cyclical relationship between real output and unemployment was initially laid out by Oknn (1970). z He further suggested two alternative approaches for estima- t ion--a first-difference and a "gap" model. Since Okun, model specifications for estimating the output-unemployment trade-off are equally divided in the literature. The first-difference form, as employed by Mankiw (1994), among others, represents a convenient way to achieve stationarity in data containing a unit root. The "gap" approach, as followed by Gordon (1984) and Hsing (1991), for example, aims at providing inferences on time series behavior over the business cycle. To provide a balanced treatment of the issue at hand, we therefore consider both approaches.

The Difference Model This method expresses the output (yt) and unemployment (ut) vari-

ables in first differences:

Ayt = ~o - ~lAut + ~ , t = 1, . . . , T , (1)

where A is a difference operator and at is a white-noise disturbance term. The parameter 130 is an intercept term capturing the mean growth rate, and 131 is commonly known as the Okun coefficient. The preceding specification, however, suffers from a major drawback. Attfield and Silverstone (1997) point out that if the output arid unemployment series not only are individ- ually integrated as I(1) but also are together cointegrated, then Equation (1) is misspecified. They further show that in contrast to Prachowny's (1993) estimate of 0.67 based solely on differenced data, the Okun coefficient es-

ZData axe obtained from various issues of OECD Main Economic Indicators. The real GDP data are in log form and premultiplied by 100. The German data refer to western Germany. Following previous studies (e.g., Kuttner 1994; Weiner 1993), the CPI is used to measure inflation. Oil-price data are obtained from the International Price Index database of the Bureau of Labor Statistics.

2The specification in which the unemployment variable appears as an explanatory variable is consistent with the production theory that output depends on the amount of labor employed (see Okun 1970; Prachowny 1993; and Sheehan and Zahn 1980). In contrast, Gordon (1998), among others, uses output as the explanatory variable. General conclusions based on the latter specification are qualitatively the same as those reported here. Furthermore, no lagged terms are specified because of the use of rather low (annual) data frequency and, in most cases, lagged terms are statistically insignificant.

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timate for the U.S. is in fact over 2.0 when a cointegrating relation is also included. In Section 3 below, therefore, we also report results which incor- porate information about long-rnn dynamics.

The "Gap" M o d e l

The second approach to estimating Okun's law is based on the notion of the "gap" between actual and eqnihbrium output and the "gap" in unemployment in the expression:

y , - y~* = - 1 3 1 ( u , - u * ) + ~ , , (9,)

where y* represents the potential or trend level of output such that Yt - Y* - y~ captures the cyclical level of output (output gap); and u* correspondingly represents the natural rate of unemployment such that u t - u * ~ u7 captures the eychcal unemployment rate (unemployment gap). In contrast to Equation (1), Equation (2) requires information about unemployment and output trends, which are directly unobservable. There is, unfortunately, no universal agreement on the proper procedure that generates these trend series.

Okun (1970) reported that based on U.S. data over the period 1947- 60, either specification (1) or (2) delivers an estimate of around 3 for 131. For the "gap" equation, he used linear trends to measure the potential output level and the natural rate of unemployment. More recent evidence, however, supports that both variables are integrated such that applying deterministic trends might result in misleading inferences. Accordingly, we focus on estimation results that take the possible existence of stochastic trends into consideration. To further overcome criticisms of any individual techniques in estimating the stochastic trends y* and u*, we consider three alternative methods--the HP filter, the BN filter, and an unobserved component framework estimated with the Kalman filter. They are discussed in turn.

The HP filter is a two-sided moving average filter that decomposes an integrated time series x~ into a stochastic trend (x*) and a cyclical (x~) component by minimizing the variance of the cyclical component subject to a penalty for variations in the second difference of the trend component. The optimization problem is based on the expression

T

E [(Xt - - Xt*) 2 ~- ~(/~Xt*÷l - - A~t*)2] , (3) t=l

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where L is a parameter controlling the smoothness of x*, 3 and the cyclical component in xt can be written as

x~ --- ~, - ~ . (4)

Intuitively, the solution to Equation (3) provides a mapping from x¢ to x* with the relevant "gap" data series xf determined residually based on Equa- tion (4).

The HP filter is a widely used method for discerning business cycle dynamics. For instance, Giorno et al. (1995) apply this filter to extract trend and cyclical components from output data. King, Stock and Watson (1995) use HP filtered data to explore the Phillips curve relationship between inflation and unemployment over the business cycle frequency. Despite its popularity, however, recent studies demonstrate that the HP filter may potentially lead to spurious inferences. King and Rebelo (1993) show that the dynamics of HP filtered data can differ remarkably from those based on difference operations or other detrending methods. Moreover, Cogley and Nason (1995) reveal that this method can generate business cycle dynamics even if none are present in the underlying data. Given these perspectives, we also consider other detrending methods.

The second approach to decomposing an I(1) series into a stochastic trend and a cyclical component is suggested by Beveridge and Nelson (1981). To illustrate this data decomposition procedure, we first assume that x t is I(1) and Ax~ is stationary. According to the Wold decomposition, Axt can be expressed as

~L% t : ]t o -1- f,D t -t- ~/lf.0t_i q- y2f.0t_2 -}- . . . . (5)

where 7is are parameters and ot is a serially uncorrelated random innova- tion. We further define Et(xt+j) as thej th period ahead expectation of xt at period t such that

Et(xt+j) = xt + Et Axt+ i , (6)

where Et(xt) = xt. Based on Equations (5) and (6), the trend component x* under the BN approach can be written as

aThe smoothing parameter is set to )~ = 400, which corresponds to an 8-year duration of the business cycle. See King and Rebelo (1993) for further discussions on the properties of the univariate HP filter.

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Jet ~ = ~t -t- E Et(~lo "~ Z ~ t + i ) , (7) i=1

and the cyclical component x~ can be recovered using Equation (4). Essen- tially, x* is characterized as the infinitely long-run forecast of xt based on information through period t. Attfield and Silverstone (1998) apply this procedure to construct cychcal output and unemployment data for the U.K. Procedures similar to the BN method have also been employed by Evans (1989) and King et al. (1991) to construct the trend components of aggregate time series.

In contrast to the ad hoc nature of the HP and BN filters, the next approach utilizes the Phillips curve relationship to identify output and unemployment gaps. According to the Phillips curve, inflation varies with deviations of the output level from its potential level or, equivalently, deviations of the unemployment rate from its natural rate. Given this framework, the trend components of output and unemployment, which are further assumed to follow random walks with drift, are obtained in light of an unobserved component approach.

According to Gordon (1997), King, Stock and Watson (1995), and Too- tell (1994), the unobserved trend component of either the output or unemployment series xt can be identified within an expectations-augmented Phillips curve model:

~ = 0~,_~ + ~,(x,_, - x~*_,) + ~ q~z,_~ + v , , (8) i=1 i=0 i=0

where nt represents inflation, zt is a variable controlling for the influence of supply shocks, and v t is a disturbance term. The lagged inflation terms capture an adaptive expectations process.

Equation (8) states that unexpected inflation is related to cychcal output (unemployment), which is the output level (unemployment rate) below (above) its full-employment level. All else equal, if inflation exceeds its ex- pected level, output (unemployment rate) must be higher (lower) than the full-employment level, and vice versa. In other words, x* is consistent with a steady level of inflation in the absence of supply shocks. Knttner (1994) and Watson (1986) apply this method to extract historical potential output levels for the U.S. A similar model is also used by Clark (1989), Jaeger and Parkinson (1994), and Gordon (1997) to model the U.S. natural unemployment series.

Our preliminary analysis suggests that the inflation data for most countries, as measured by the change in the log level of the Consumer Price

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Index (CPI), are nonstationary in levels. Accordingly, we express the inflation variable in first-difference form. Furthermore, based on the Akaike Infor- mation Criterion (AIC), we determine that the lag length is m = 2. The inclusion of two lags is also sufficient to remove all significant autoeorrelation from the residuals. Supply shocks are measured by log levels of the world crude oil price (oilp). Unit-root test results (not reported here) further suggest that this series is appropriately expressed in second differences, and only the contemporaneous value enters Equation (8). Finally, the AIC further supports that the lag length for the unemployment variable varies between 0 and i depending on the country sample. 4

Given the preceding parameterizations, time-varying estimates of x* are updated using the Kalman filter. The system of updating equations can be more conveniently illustrated in state-space form. In a special case where m = 2, n = 0 and p = 0, the measurement and transition equations of the state-space representation can be written, respectively, as

Arc t = Cx* + D Z t + vt ; (9)

x* = ~ + x * i + Tit; (10)

where

Z t = [Ant_i, Ant_2, xt, A2oilpt] ' ,

C = -qb0,

D = [0 l, 02, qb0, %].

The errors vt and ~t are assumed to be mutually uncorrelated and i.i.d. normal with variances c~ and ~ respectively. Equation (10) depicts the unobserved state variable x* as a random walk with drift captured by g.

The Kalman filtering algorithm updates the system (9)-(10), particularly x*, based on the maximum likelihood (ML) method described fully in Hamilton (1994, Chapter 3). More specifically, the covariance matrix of the parameter estimates is approximated by summing over the outer products of the gradients of the log-likelihood function for each data observation and taking the inverse of this sum. The ML estimation requires that all disturbance terms in the system be i.i.d. Gaussian, the condition of which may not be satisfied in practice given the historical behavior of our data, particularly

4The lag order p = 0 for Australia, Belgium, Canada, Germany, Italy, Japan, Spain, Swit- zerland, the U.K. and the U.S.; andp = 1 for the remainder of the sample.

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inflation. For this reason, a quasi-ML procedure, as suggested by Hamilton (1994), is used to deliver consistent and asymptotically normal parameter estimates even when the Gaussian assumption is violated.

An advantage of the preceding data decomposition method is its link to a prominent macroeconomic benchmark known as the NAIRU, which stands for the Non-Accelerating Inflation Rate of Unemployment. This unobserved component approach, nonetheless, is not without its criticisms. Most notably, recent estimates by Staiger, Stock and Watson (1997) suggest that, largely due to the extent of supply shocks, the degree of model uncertainty around any estimate of the NAIRU can be so high to make it practically meaningless for forecasting short-run dynamics.

In an attempt to assess the robustness of Okun coefficient estimates without espousing one particular approach over another, we consider all data transformation methods described above. The four approaches can be broadly grouped into three classes. The first class includes the first-difference model, which rests on the variables' unit-root properties while obviating the need to model their stochastic trend components. As shown in Section 3 below, the first-difference model will further be extended to an error-correction framework. Based on a "gap" specification, the remaining three models are designed to produce the trend components for the historical data of output and unemployment. The HP and BN filters belong to one particular class of data decomposition procedures that emphasize the dynamic difference between the trend and the cyclical component in light of the univariate behavior of time series. Finally, framed within an unobserved component model, the Kahnan filtering procedure draws heavily on theoretical restric- tions associated with the NAIRU.

Data Representations As an initial step of the econometric work, we examine the appropriate

specifications of the unemployment and out-put data. As shown in Table 1, the Augmented Dickey-Fuller (ADF) t-test statistics demonstrate strong evidence of a unit root in the data series of the 16 OECD countries. These results imply that using a linear function to proxy the trend component, as in Okun (1970), may potentially lead to biased estimates for the unemployment-output trade-off.

Perron (1989), however, argues that the presence of structural change may lead to spurious inferences of unit roots in characterizations of the level of series. To explore the possibility of stationarity along a broken trend, we employ Zivot and Andrews' (1992) minimum ADF-t (rain-t) procedure. As reported in Table 1, the min-t statistics reveal evidence of broken-trend stafionarity for the output data from Japan and Switzerland. Both trend breaks occur around the 1973 oil shock, whose timing is in line with Perron's

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TABLE 1. Unit-Root Test Statistics

Real G D P Unemploymen t

Count ry A D F - t Min-t A D F - t Min-t

Austral ia - 1.01 - 3.64 (1972) - 1.77 - 2.45 (1985) Austr ia - 0.83 - 4.35 (1976) - 1.79 - 3.42 (1981) Belgium - 0 . 7 4 - 4 . 1 0 (1973) - 1 . 9 2 - 3 . 0 5 (1980) Canada - 1 . 3 2 - 4 . 1 4 (1976) - 2 . 1 3 - 4 . 5 0 (1982) Denmark - 0 . 5 2 - 3 . 8 0 (1969) - 1 . 9 6 - 3 . 4 5 (1974) F in land - 1.66 - 2.62 (1972) - 2.17 - 4.04 (1989) France - 0.29 - 3.84 (1976) - 2.42 - 3.37 (1970) Germany - 2 . 0 1 - 3 . 3 1 (1970) - 2 . 3 5 - 4 . 2 4 (1981) I taly - 0 . 9 5 - 2 . 1 3 (1968) - 2 . 1 0 - 4 . 7 3 (1981) Japan - 0.54 - 6.01"(1972) - 2.75 - 3.67 (1974) Nether lands - 0.49 - 3.42 (1968) - 2.07 - 6.34"(1981) Norway - 2.56 - 3.'77 (1983) - 1.03 - 3.54 (1980) Sweden - 0 . 9 2 - 2 . 5 9 (1970) - 2 . 0 8 - 4 . 1 4 (1989) Switzerland - 1.72 - 6.25"(1975) - 2.45 - 4.56 (1989) U.K. - 1 . 8 2 - 4 . 6 8 (1980) - 1 . 8 3 - 4 . 5 8 (1980) U.S. - 1 . 9 8 - 3 . 8 3 (1974) - 2 . 3 0 - 3 . 6 5 (1975)

NOTE: The sample period for all countries is 1955-96, except that for Germany, which is 1960-96. *denotes significance at the 0.01 level. ADF statistics are t-values for a in regression

3 , . .

of the form: Ax t = 3o + ~lt + o~xt 1 + ~ j = l (~iAxt-i + et' Mm-t stahstics are computed using sequential regressions over i < TB < T based on the equation: Ax t = 50 + 31t + 62DU~ + 5aDTt + axt 1 + ~ a 1 6 A x t j + e~ where the dummy variables" DUt = 1 and - 9 = ~ / ,

D T t = t - TB for t > TB and 0 otherwise, and TB denotes the period at which a possible trend break occurs. Critical values for the ADF-t statistics are given by Davidson and Mac- Kinnon (1993), and those for min-t are given by Zivot and Andrews (i992). Periods corresponding to min4 statistics are indicated in parentheses.

findings. F o r unemployment , only the data for the Nether lands supports the b roken- t rend alternative.

Given the above test results, first differencing is appl ied to all data series except for the three cases in which b roken- t rend stationarity has been found, s Fo r the latter, data are fi t ted to a b roken- t r end model in the form

of Zivot-Andrews (1992) regression. This method proceeds as follows. First, let T~B be the per iod at which a t r end break has been identif ied such that we earl specify a d u m m y variable DU e which is equal to 1 for t > T~B and 0

STo maintain compatibility, in the case where either file output or unemployment variable has been found stationary along a broken trend, a linear trend is applied to the other variable as well prior to model estimation.

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otherwise; and another dummy variable DTt which is equal to t - T~B for t > T~B and 0 otherwise. The first dummy variable captures a possible level shift in a linear trend, while the second dummy variable captures a possible change in the slope of the trend. Next, we fit those three time series identified with trend breaks to an equation of the form:

xt = 80 + 8it + 6BDUt + 83DTt + e t , (ii)

where 8i are parameters. Estimates for the residual term et are then treated as the relevant broken-trend stationary data, which will replace the first- differenced data in subsequent estimations.

3. Estimation Results Benchmark Estimates

This section presents the empirical results for Okun's law based on the alternative models described in Section 2. More specifically, we compare results from first-differenced data with those based on the "gap" approach. For the latter, the relevant cyclical data are obtained alternatively from a broken linear trend (for Japan, Switzerland, and the Netherlands), the HP and BN filters, and a NAIRU model estimated with the Kalman filter. The Newey-West (1987) procedure is used to produce consistent estimates of variance-covariance matrices and, thus, t-statistics.

Table 2 displays the estimation results of interest. There are some interesting observations. First, the Okun coefficient estimates are qualitatively similar across different models. Except for Italy (Kalman filter), 131 is statistically significant at the conventional levels for most countries. Second, there are apparent disparities in the quantitative estimates across countries, ranging from below one for Italy to above four for Japan. The highest estimate of 12.6 for Japan (Kalman filter) is comparable with the figure reported by Hamada and Kurosaka (1984). This anomaly reflects substantially high institutional rigidity in Japanese labor markets, due particularly to lifetime job security.

The markedly low/~2's for some European countries, particularly Italy and Sweden, may be attributed to increased variability in their unemployment and output data since the 1970s. Together with recent global economic developments, this observation further implies the possibility of structural instability in the Okun regressions. To formally test for parameter constancy, we implement the Quandt Likelihood Ratio (QLR) test, which has been modified by Andrews (1993). Under the assumption of one a priori unknown breakpoint, the QLR statistic is the maximum value of sequential Wald-type statistics, each of which tests for a possible structural break at a period within

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the estimation sample. Essentially, the Wald tests compare the sum-of- squared residuals of two subsample estimations separated by a possible breakpoint.

As reported in Table 2, the QLR statistics yield strong evidence of structural instability in the Okun relationship. The null hypothesis of parameter constancy is uniformly rejected for data obtained from the Kalman filter. By comparison, the cross-country evidence of structural instability is weaker under the first-difference specification than under the alternative "gap" models. In particular, the rather weak evidence of structural change for the U.S. is consistent with the standard Chow test results reported by Weber (1995).

The periods (k) associated with the maximum QLR statistics indicate the locations of most dominant structural breaks. In contrast to Perron's (1989) findings, many break dates displayed in Table 2 do not coincide with the timing of the major oil shock in 1973. Instead, breakpoints spread over the intermediate range of the sample periods. Structural breaks before the 1980s can be associated with structural changes in labor markets, as observed by Jaeger and Parkinson (1994) and Kaufman (1988).

The bottom row of Table 2 displays cross-country means of the Okun coefficient estimates under different models. By comparison, the smallest mean of around two is delivered by the first-difference model, while the Kalman filter produces the largest mean of 2.64. The two univariate data decomposition methods--the HP and BN filters--appear to yield similar estimates not only on average but also for individual countries. Overall, these findings can be interpreted as evidence that the detrending method is crucial to inferences about economic relations over the business cycle.

Error Correction Model Attfield and Silverstone (1997) point out that if output and unemploy-

ment are cointegrated, then the Okun regression in the form of Equation (1) is misspecified. From this perspective, this section evaluates the robustness of estimates with first-differenced data by reestimating the Okun coefficient within an error-correction framework which takes into account information about cointegrating relations.

To reestimate the Okun coefficient~ we apply the maximum-likelihood method to a vector error-correction model (VECM):

q

AZt = M + ~, F~AZ~_~ + HZt_I + Ct, (12) ~=1

where Zt = [Yto ut]', M is a 2 X i vector of intercepts, Fi is a 2 X 2 parameter

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matrix, and ~t is a 2 x 1 vector of disturbances. Long-run relations are captured by the matrix 17 = aqb' where a and qb are 2 X r matrices of rank r -< 2, and qb is the matrix of cointegration vectors such that qb'Zt are called cointegrating relations. If the rank of II is r, then there are r eointegration vectors for Zt.

As Attfield and Silverstone (1997) point out, Equation (12) also admits a "gap" representation in the form of an error-correction mechanism. By construction, if unemployment and output are cointegrated, then they will tend to return to equilibrium once disturbed by shocks. The parameters in F~ trace out the temporary dynamics. In light of the AIC, we include one autoregressive lag (i.e., q = 1) in the VECM system for all countries. The particular parameters of interest are: (1) F12 (the second element in the first row of F) which captures the relationship between lagged unemployment and current output in the short run, and (2)17I~'s (the upper row elements in 17) which trace the adjustment of output toward the long-run equilibrium.

For those output and unemployment series that have been identified as I(1) processes, we proceed to test for cointegration. More specifically, we employ Johansen (1988), and Johansen and Juselius' (1990) two reduced- rank methods, which are based on estimates for the eointegration matrix 17I in (19.). The first test is based on the maximum eigenvalue (?~l~ax) statistic, which tests the null hypothesis that the rank of II is r against the alternative that the rank is r + 1. The second test is based on the trace 0~t . . . . ) statistic, which tests the null hypothesis that the rank of II is less than or equal to r against a more general alternative. Test statistics in Table 3 indicate that the null hypothesis o f r = 0 is rejected for most countries with I(1) data except Norway. Therefore, we conclude that with one exception, output and unemployment share at least one cointegrating relation.

Table 3 presents some parameter estimates for the VECM in (12), which are obtained using the ML method along with the imposition of cointegrating ranks identified. 6 Except for Belgium, Italy and Sweden, estimates for Fm are fairly close to the estimates for the corresponding Okun coefficient 131 in Table 2. It is, however, important to distinguish that, in line with the conventional practice, the error-correction model in (12) admits lagged relationships, while only a contemporaneous relationship enters the first- difference Equation (1). The similarity between the 131 estimates in Table 2 and the F12 estimates in Table 3 can be attributed to two factors: First, estimates of the short-run relationship between output and unemployment

6Stock and Watson (1993) suggest an alternative estimation procedure based on dynamic ordinary least-squares. Estimation results, nonetheless, were found to be similar to those reported here.

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are not particularly sensitive to the presence of their long-run comovements; and second, substantial persistence exists in the unemployment data, as ev- idenced in Table 1.

In contrast to the short-run estimates, the estimates for the coefficient on the lagged unemployment rate (II12) are statisticallyinsignificant for many countries. This reflects little output response to the deviation from secular movements in unemployment. Only data from Belgium, France, and the U.K. yield estimates for H12 that are significant at the 5% level or better. These results complement the conclusion that the omission of the cointegrating relation IIZt_ 1 does not entail severe bias in estimating the Okun coefficient, as found in Attfield and Silverstone (1997). The cross-sectional mean of the estimates is 1_80, which is nonetheless below those means in Table 2. Moreover, the estimates for the coefficient 1711 appear to support the importance of an error-correction mechanism in many OECD countries' output series.

Based on a model similar to (12), Attfield and Silverstone (1997, 1998) estimate the Okun relationship for the U.S. and the U.K. using postwar quarterly data. By comparison, their estimate of 1.45 for the U.K. is comparable with our estimate of 1.47. For the U.S., on the other hand, our estimate of 1.88 is somewhat lower in absolute value than their estimates between 2.0 and 2.3. Such a discrepancy may be attributed to differences in the sample period and/or data frequency. Our estimate is, nonetheless, much closer to theirs than to Prachowny's (1993) estimate of 0.67, which is obtained in pure first-difference form.

For comparison purposes, we further test for structural instability in the estimated VECMs. This is done by performing Hansen and Juselius' (1995) test based on the models' maximized log-likelihood values computed recursively period by period over a subsample of 1965-96. The null hypothesis of parameter constancy is rejected if the plot of the recursive log- likelihood values crosses the 95% confidence bounds. The results lend strong support against structural stability for most countries except Austria and Canada. The last column of Table 3 displays periods corresponding to the widest gaps between the 95% boundaries and the log-likelihood series. Evidently, most structural breaks take place around the 1973 oil shock. It is, however, important to recognize that these break periods, which reflect structural changes in error-correction relations, conflict with those in Table 2, which reflect breaks in first-differenced data.

Asymmetric Effects Conventional wisdom holds that economic contractions are sharper

and steeper whereas expansions are more gradual. There is also a large body of evidence supporting that maeroeconomic time series exhibit nonlinear or

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asymmetric behavior over various phases of the business cycle. For example, Neft~i (1984) demonstrates that the U.S, unemployment rate has experienced much sharper increases during downswings than declines during up- swings. Using alternative estimation methods, Brunner (1997) finds similar asymmetric features in U.S. real GNP data.

Motivated by these stylized facts, we investigate whether estimates of the Okun coefficient are sensitive to the possible existence of asymmetries. To dais end, we augment the Okun equations by allowing for different effects between non-negative and negative values in the unemployment data. More formally, we rewrite Equation (1) as

a y t = ~o - (~31+IltAut + + f 3 f I ~ a u t ) + e t , (13)

where I l t is the Heaviside indicator function such that

[1 if A u t > - O It+t= to if A u t < 0 ;

I~ = {~ ifAut < 0 if A u t > 0 "

The analogous specification for the "gap" form in Equation (2) can be expressed as

+ + Yt - Y* = - [[31I~t (ut - u*) + [3f I ~ (ut - u*)] + e~, (14)

where I2t is the corresponding Heaviside indicator function such that

[ l i f ( u t - u * ) > - 0 12+= 10 if (u t u*) < 0 ; {~if(u~-u*)<0 I~t = if (u t u*) > O '

Separate Okun coefficient estimates for non-negative ( - 13i ~ ) and negative (-13~-) values in the unemployment series are reported in Table 4. The last column at each panel also reports 9~2 statistics for testing the existence of asymmetries, as represented by inequality between ( - 1 ~ ) and ( - 13i-). Overall, the evidence of asymmetries is mixed. In first-difference form, only Finland, Japan, and the U.S. show evidence that the Okun coefficient is significantly higher in absolute term for decreases in the unemployment rate than for increases. Surprisingly, the opposite effect appears to hold for Canada, France, and the Netherlands.

Parameter estimates using the "gap" models reveal a similar theme in

346

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Jim Lee

the sense that the extent of asymmetries varies remarkably across countries. By comparison, the HP filter generates the least evidence of asymmetries. Furthermore, as displayed at the bottom of Table 4, the cross-sectional means reveal a discernible contrast in estimates between the first-difference model and the "gap" models. For the first-difference model, coefficient estimates are comparable between unemployment series of opposite signs. According to the "gap" models, estimates are overall higher for negative than positive gaps, suggesting that the Okun coefficient is higher during contractions than expansions.

It is noteworthy that the evidence of asymmetric effects is not statistically significant for the U.S. based on the "gap" models. Consistent with Mills' (1995) findings, there is also little evidence of asymmetries in the U.K. data. Finally, while our findings are far from conclusive, varying evidence of asymmetries across countries may be attributed to structural differences among labor markets, which will be further addressed below.

Structural Change In light of the strong evidence of parameter instability shown in Table

1, we reestimate the Okun coefficients by taking into account identified structural breaks. 7 For countries identified with a structural break occurring at period k, we create a dummy variable Dr(k) such that the Okun Equations (1) and (2) are expressed, respectively, as

a y t = 13o - 131Aut + 132Dt(re) - 13a[Dt(fe) " Aut] + 4 ; (15)

Yt - y* = -131(ut - u*) - 132Dt(f~)

- 133[Dt(/~)' (ut - u*)] + a t ; (16)

where Dt(]~) = i for t >/~ and 0 otherwise. The parameters 132 and 133 capture the effects of plausible structural change. By construction, the Okun coefficient is 131 before the break and 131 + 133 afterwards.

Coefficient estimates based on regressions augmented with the dummy variable are presented in Table 5. All estimates are statistically significant at the conventional levels. The Okun coefficient (131 + 133) estimates for subperiods after structural breaks are overall lower in absolute values than those (131) for subperiods before. This indicates that a given change in the unemployment rate corresponds to a smaller change in the output level

7Sinee estimates in the first-difference model seem to be rather insensitive to the presence of cointegrafion, we do not report results for the VECM that takes structural breaks into consideration.

348

L..... L-... ~.~ ~ c.~ L-... ~.,,-~ . ~ ,,_{ ~,~ , ~ ~,~ ~:~ ~:~ ~..~ ~ L ~-

~,~ ,,_1 ,,_] ~-._ , ~ ~:~ ~-.~ L..... ~::~ , ~ 'L--... ~::~ c-~ "~, @'~

~ ~ ~ ~ ~ 1 ~ 1 ~ I I I I I I I I I I I I

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jim Lee

in more recent subperiods, supporting earlier findings by Hsing (1991), and Sheehan and Zahn (1980).

The coefficient 132 represents a shift in the intercept. For the first- difference model in (15), more specifically, the magnitude of 132 reflects a change in output growth between subperiods. Table 5 shows that most estimates enter with a negative sign, indicating lower output growth rates in the last two decades. The corresponding estimates under the alternative "gap" models, on the other hand, represent intertemporal differences in the output gap rather than in the average output growth rate. There is evidence to support some fundamental changes in the nature of the business cycle over recent decades.

Taken together, the OECD data confirm that Okun's law is valid from an international perspective in the sense of statistical significance in the estimates of the output-unemployment relationship. Substantial evidence, however, supports that the quantitative as opposed to qualitative estimates are unstable over recent decades. Despite the primary attention to U.S. data in the existing literature, there is anecdotal evidence of heterogeneity across countries. This latest finding provides motivation for our investigation into the issue whether the estimate for the U.S. earl indeed be used as a benchmark for characterizing other economies.

Table 6 reports F-test results for the null hypothesis that for a given sampled country i, the Okun relationship, as depicted by Equation (15) or, equivalently, Equation (16), is equal to that for the U.S. The test statistics show mixed results across different models. The evidence against the null hypothesis of no qualitative difference in the Okun relationship is much weaker under the HP filter than the other three models. Nonetheless, the F-tests for Denmark, Japan, and Switzerland are statistically significant at the conventional levels across all four models.

Two major patterns emerge from the results in Tables 5 and 6. First, there is an overall reduction in the output-unemployment trade-offin recent decades. For the U.S., in particular, such evidence echoes structural changes to industries and labor markets, as observed by Evans (1989), Gordon (1984), Juhn, Murphy and Topel (1991) and Weiner (1993), among others. Second, the Okun coefficient estimates for many European countries, particularly European Union members, are markedly lower than those for the U.S. s What then contributes to such disparity? This finding can be associated with the substantially high and persistent unemployment rates experienced by those countries since the early 1980s when a global-wide disinflation began. The consensus among economists (e.g., Bean 1994; Blanehard and Summers

SOut of the 15 members, the EU states within our sample are: Austria, Belgium, Denmark, Finland, France, Germany, Italy, the Netherlands, Sweden, and the U.K.

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TABLE 6. F-Test Results

Country First Difference Kalman Filter HP Filter BN Filter

Australia 1.39 3.45" 1.05 1.36 Austria 1.77"* 5.64" 1.04 1.35 Belgium 2.74* 3.28* 1.g4 1.86"* Canada 1.62"** 2,77" 1.13 1.39 Denmark 2.32* 2.71' 1.58"** 2.37** Finland 3.30* 1.18 1.33 1.99 France 1.14 1.86"* 0.34 0.44 Germany 2.15"* 1.72"** 1.42 1.70 Italy 3.69* 1.48 1.18 1.41 Japan a 3.90* 18.31" 1.92"* 2.49** Netherlands a 2.96* 4.03* 1.10 1.43 Norway 2.05** 1.83"* 1.35 1.75"** Sweden 2.53* 9.62* 1.30 1.82"** Switzerland a 5.09* 15_97" 2.92* 4.08* U.K. 2.53* 2.00** 0.96 1.84"** U.S. 0.00 0.00 0.00 0.00

NOTE: *, **, and *** denote rejection of the null hypothesis that the Okun coefficient for country i is equal to that for the U.S. at the 0.01, 0.05, and 0.1 levels, respectively. "denotes a broken-trend model which replaces the first-difference model with residuals in estimating Equa- tion (8).

1986; and Layard, Niekell and Jackman 1994) is that the bulk of European unemployment, whose rates were more than twice that of the U.S. during the past decade, is structural rather than cyclical.

The persistently poor unemployment performance among many Eu- ropean countries reflects relatively high rigidities of their labor markets. Nickell (1997), and Nickell and Bell (1996) attribute this phenomenon to the downward inflexibility of real wages due to high unionization, generous long-term unemployment benefits, and poor educational standards at the lower end of labor markets. Ljungqvist and Sargent (1996, 1998) further assert that Europe's welfare and social insurance programs have made its labor markets more difficult to cope with changing economic conditions in association with restructuring from manufacturing to service industries and adoption of new technologies.

4. Conclusion An extensive body of research supports that labor markets and indus-

trial structures in developed countries have evolved in new ways such that

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Jim Lee

the relationship between output and unemployment, commonly known as Oknn's law, deserves reexamination. In this paper, this relationship has been reevaluated based on postwar data for 16 OECD countries. We have also presented comparative results under the first-difference model and the "gap" specification. For the latter, the relevant data are constructed alternatively from the HP filter, the BN decomposition method, and the Kalman filter based on the NAIRU framework. Several findings emerge from our empirical exercise. First, the data sample generally supports the validity of Okun's law in the sense of statistical significance in parameter estimates. Beyond this, however, the results are not as robust as those reported originally by Oknn (1970). Quantitative estimates differ remarkably across countries as well as across alternative detrending methods.

The robustness of estimation results has further been explored by: (1) extending the first-difference model to an error-correction framework, and (2) allowing for asymmetric effects. Whereas the Okun coefficient estimates appear not to be particularly sensitive to the inclusion of eointegrating relation between unemployment and output, evidence of asymmetries varies across countries.

There is also substantial disparity between the estimates for the U.S. and other OECD countries. Although this paper offers no direct explanations for the lower Oknn coefficient estimates, or varying patterns of asymmetries, for many European countries than for the U.S., such macroeconomic evidence can be interpreted as the consequences of relatively high rigidities among European labor markets.

Besides cross-country heterogeneity, the OECD data reveal strong evidence of structural change in the Okun relationship. Most countries experienced a smaller output loss associated with a given increase in unemployment in recent decades. This finding of varying estimates across both time and countries implies that any rule-of-thumb, such as Okun's law, should be applied with caveat. Adding to such uncertainty is the sensitivity of empirical results to how the data of interest are constructed. In particular, there are marked differences in inferences between first-differenced data and those constructed under the "gap" approach, particularly the BN filter. These results essentially highlight the difficulties of distinguishing between long-term trends and cyclical fluctuations in economic time series. From this perspective, inferences based on a single model specification, as in many previous studies, should be interpreted with caution. On the other hand, our empirical results also complement the existing literature (e.g., King and Rebelo 1993; Cogley and Nason 1995; and Canova 1998) which reveals sizable distortion- ary effects of certain data detrending methods on evaluating macroeeonomic models.

352


Received'. June 1998 Final version: August 1999

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The robustness of Okun's law: Evidence from OECD countries