Looking far in the Past: Revisiting the growth-returns nexus with non-parametric tests

Looking far in the past: Revisiting the growth-returns nexus with non-parametric tests Ekaterini Panopoulou∗Nikitas Pittis†Sarantis Kalyvitis‡ March 2006 Abstract In this paper we reexamine the linkages between output growth and real stock price changes for the G7 countries using a battery of non-parametric procedures to account for the impact of long-lagged observations. We find that correlation between growth and returns is detected at larger horizons than those typically employed in parametric studies. The major feedbacks emerge from stock price changes to growth within the first 6 to 12 months, but we show that significant feedbacks may last for up to two or three years. Our evidence also suggests that the correlation patterns differ substantially between the countries at hand when the sectoral share indices are considered. JEL classification: C14, G10, O51. Keywords: real stock price changes, output growth, long-run covariance matrix. Acknowledgments: We are grateful to A. Antzoulatos, D. Malliaropulos, M. Michail, M. Roche and participants in the 2005 ASSET Conference and the 4th HFAA Conference for helpful comments and suggestions. Financial support under the “PYTHAGORAS II” project co-financed by the European Social Fund and the Greek Ministry of National Education and Religious Affairs is gratefully acknowledged. The usual disclaimer applies. ∗(corresponding author) Department of Economics, National University of Ireland Maynooth, Co.Kildare, Republic of Ireland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax: 00353 1 7083934. †Department of Banking and Financial Management, University of Piraeus, Karaoli & Dimitriou 80, Pireus, 18534, Greece. e-mail: n[email protected] ‡Department of International and European Economic Studies, Athens University of Economics and Business, Patision Str 76, Athens 10434, Greece. e-mail: skaly[email protected] 1. Introduction What is the interaction between the goods market and the stock market? This relationship has attracted considerable empirical research over the last thirty years.1Early contributions, beginning with the work by Goldsmith (1969), assessed the positive relationship between stock returns and economic growth. Subsequent studies by, among others, Bosworth (1975), Hall (1978), Fama (1981, 1990), Schwert (1990) and Estrella and Mishkin (1998), have focused on the US and strongly indicate that the stock market index can serve as a reliable leading indicator in the US economy. This conclusion reflects the view, put forward by Morck et al. (1990), that the stock market is largely a ‘sideshow’, which simply mirrors ‘news’ about anticipated developments in firms’ future payouts and output growth. Moreover, some spotty evidence in the relevant literature suggests that there is also a negative -though weakrelationship between current output and future stock prices in the US (see Park, 1997, McQueen and Roley, 1993). This behavior might be triggered by the reaction of stock market participants to other macroeconomic variables closely linked to output, such as employment and inflation, which are negatively related to future earnings and business conditions.2 In general, the empirical studies have relied almost exlusively on single-equation or multivariate vector autoregressive (VAR) and panel models to investigate the relationship between output growth and stock price changes. However, single equations or finite-order multivariate models may be too restrictive to represent the true autocovariance structure of a given multiple time series for several reasons. First, although the process assumed may be wide sense stationary and purely non-deterministic, it will fail to have an autoregressive representation if some of 1The theoretical relationship between these sectors have been founded by Brainard and Tobin (1968) who pointed out that capital formation and, consequently, output growth are triggered when the market values new capital higher than its replacement cost (q-theory of investment). Hayashi (1982) has reinforced this finding by showing that under certain assumptions the stock market valuation of firms can be encapsulated in the neoclassical investment model with adjustment costs and serve as the main determinant for investment and output growth. Lettau and Ludvigson (2002) have shown that in the presence of a time-varying risk premium the q-theory implies that a change in expected returns alters future stock prices and the cost of capital, thus triggerring a change in investment over longer horizons. An alternative transmission channel involves consumption, and consequently wealth and output, which may rise after an increase in stock prices generated by optimistic expectations of future dividends or, alternatively, by a fall in interest rates (Parker and Julliard, 2005). These links may be more intense in the case of a financial crisis (Bosworth, 1975). From a fiscal policy point of view, Blanchard (1981) has shown that after an expansionary policy shock, asset prices change as a result of anticipated changes in real interest rates and profitability, thus affecting wealth and spending, and spurring a rise in supply and equilibrium output. 2Another possible explanation for this pattern may be that it reflects countercyclical macroeconomic policy through the reaction function of monetary authorities. For instance, in a period of unanticipated recession the Fedmayreactbyreducinginterestrates,thusinducing a rise in stock prices, as investors find the stock market more profitable. On the other hand, a rise in output growth is usually considered as a sign of future inflation, which affects negatively future growth and returns, and policymakers may respond by raising interest rates which, in turn reduces the future cash flows of firms. 1 the roots of the Laurent expansion of its moving average representation lie on the unit circle. Second, the process may admit a representation of infinite order, which implies that its finite approximation may give misleading results in common size samples.3Third, when parametric models are employed in which output growth is explained by lagged and contemporaneous stock price changes, as in Fama (1981, 1990) and Barro (1990), it is implicitly assumed that the latter are weakly exogenous to the parameters of interest, thus resulting in inconsistent and/or inefficient estimators if this assumption fails to hold. Finally, the problem of approximating the true data generation process by, say, a finite-order VAR may be particularly acute when data on stock returns are employed. The work by Fama and French (1988) and Poterba and Summers (1988) suggests the presence of transitory components in stock prices with returns showing positive autocorrelation over short periods (reflecting e.g. the well-known momentum effect, as in Jegadeesh, 1990), but negative autocorrelation over longer periods (due e.g. to mean reversion to fundamentals). In view of such an autocovariance structure the use of a finite-order VAR, or any other approximating parametric model, becomes questionable.4 The purpose of this study is to reinvestigate systematically this bivariate relationship by using non-parametric tests of long-run correlation between growth and stock returns for the G-7 countries. To remedy potential caveats associated with the use of standard parametric techniques in the empirical investigation of the growth-returns nexus, we estimate the longrun covariance matrix of the two series via kernel-based estimation techniques, which involve only the choice of a kernel and a bandwidth parameter to estimate the covariance matrix of the process that equals the spectral density of the process at frequency zero.5Based then 3Luetkepohl and Poskitt (1996) discuss the problems that arise in causality testing by fitting finite VAR models to infinite-order processes. The authors prove that the use of standard Wald tests for Granger-causality can indeed be justified under more general regularity conditions, but in small samples these tests tend to reject the null hypothesis of no causality more often than indicated by asymptotic significance levels. Additional reasons that may produce misleading inferences in testing for causality within VARs are related to the time heterogeneity properties of the vector process under consideration. For instance, if the process does admit a finite-order VAR representation, but contains unit roots and exhibits cointegration, then some estimated coefficients of the VAR(p) model converge to nonstandard limiting distributions with a faster rate than T1/2. In such a case, testing for Granger causality requires prior knowledge of the number and location of unit roots in the system. See, for example, Sims et al. (1990), and Toda and Phillips (1993). 4To our knowledge, the only study that has attempted to tackle with this issue by use of a non-parametric technique is Hassapis (2003), who has applied the Andrews (1991) procedure to estimate the long-run covariance matrix of output growth and financial variables. The author investigates the relationship between Canadian and U.S. financial market variables and Canadian growth and finds that as the number of autocovariances that are assigned a non-zero weight increases, the feedback from selected Canadian or U.S. financial variables (including stock prices) to future Canadian output growth increases. 5These methods were first proposed by Parzen (1957) and Priestley (1962). Contributions to the covariance estimation literature include among others White (1984), Newey and West (1987, 1994), Andrews (1991), Robinson (1991) and B.E. Hansen (1992). 2 on the derivation of a normal asymptotic approximation of the spectral density matrix of the process, we are able to derive the asymptotic distribution of the long-run correlation coefficient between the series at hand and test for its significance. The aggregate correlation coefficient can be further decomposed into the contemporaneous and temporal cross correlation, in order to facilitate the analysis of the covariance pattern between growth and returns. We use the non-parametric methodology proposed by Hong (2001) to perform hypothesis testing. The test is based on the residual cross-correlation function of the series and is robust to distributional assumptions, which are likely to be important here since the variables at hand typically exhibit both autocorrelation and/or conditional volatility effects. We utilize monthly data from the G-7 countries to investigate the bivariate relationship between stock price changes and industrial output growth in the context of these non-parametric methodologies. Until now, existing studies (including, among others, Barro, 1990, Fama, 1990, and Schwert, 1990), have focused in the impact of current and lagged stock prices on future output in the US, whereas fewer studies have investigated this pattern in other developed economies, like Canada (Barro, 1990), Japan, Germany and the UK (Mullins and Wadhwani, 1989), and the G-7 countries (Choi et al., 1999). In line with the empirical literature on the issue, our objective is not to test alternative theories on the determination of the growth-returns nexus, but rather to employ a recently developed general econometric framework to reinvestigate the direction of causality and the strength of the correlation patterns between real stock price changes and output growth for the G-7 countries.6 In contrast to the bulk of the literature that has established that the major feedbacks emerge from stock returns to growth within the first six to twelve months, our findings indicate that the effect may last for up to two or three years. In particular, our results indicate a positive correlation between stock returns and growth in the G-7 countries (with the exception of Italy). Decomposing this long-run correlation to allow for contemporaneous and temporal feedbacks, we 6There are several reasons why this relationship might be different between developed countries (Mauro, 2003, Binswanger, 2004). First, the size of some G-7 economies is relatively small compared to the US and the production of several large firms that are listed in domestic stock markets takes place abroad, which renders them less sensitive to anticipated developments in domestic real activity. Also, the degree of openess in European economies and in Canada is a lot higher than in Japan and the U.S. and, consequently, foreign disturbances may have weakened the association between domestic stock returns and the real sector of the economy. Moreover, in countries where the stock market regulations are of English origin the growth-returns link should be higher because managers are less protected from shareholders and, hence, less able to pursue e.g. investment strategies in the case of a negative market sentiment. In addition, these economies share some common characteristics, such as greater possibility of takeovers, lower gearing ratios, and smaller role of employees in decision making. 3 find that the long-run correlation is mainly triggered by the feedbacks from stock price changes to future output growth with the strongest feedbacks occurring for US, Japan, Germany, and the UK. The most interesting finding is that when the number of autocovariances that are assigned a non-zero weight increases, the feedback from stock price changes to output growth increases, reaching a peak at a range between eighteen to twenty-four months, whereas weaker effects may last up to thirty-six months. On the other hand, with the exception of the UK we do not find any evidence of substantial correlation running from output growth to stock returns. As regards the correlation patterns from sectoral indices we establish that there are large variations across sectors and countries with substantial information encountered in distant lags as well. Our main contention is thus that there are valid grounds for expecting the growth-returns nexus to be one with long-term impacts. Hence, these findings complement and extend those reported by Fama (1990), Schwert (1990), Barro (1990), Choi et al. (1999) and other authors who have reported that there is a strong positive link between stock returns and future industrial production that reaches its maximum at a forecast interval of approximately 6 to 12 months, depending on the horizon of returns. Our approach suggests that stock prices are correlated with upward movements in industrial production at longer intervals as well, while useful information is also contained in the sectoral stock price indices. Hence, the non-parametric methodologies utilized here seem to provide additional information about the effect of the financial on the real sector of the economy that can be obtained by examining the past behavior of the stock price changes at horizons that are unlikely to be captured by parametric single-equation or multivariate regressions. Finally, our approach suggests that the finding of a negative correlation between output growth and future stock price changes, reported by Park (1997) and McQueen and Roley (1993) for the US economy, is mainly driven by the negative association of US output growth with future changes in the Basic Industries and the Consumer Goods share indices. However, with few exceptions this association is not broadly supported by aggregate or sectoral data from other developed economies. The rest of the paper is structured as follows. Section 2 outlines the non-parametric procedures used for the empirical estimation of the growth-returns relationship and section 3 describes the data at hand. Sections 4 and 5 present and comment the empirical results for the G-7 countries. Section 6 concludes the paper. 4 2. Non-parametric tests for the growth-returns correlation Consider the ‘long-run’ correlation coefficient between output growth, yt,and real stock returns, xt. The long-run covariance matrix Ωof the process Zt=[yt,x t]>is defined as: Ω≡   ωyy ωxy ωxy ωxx   =lim T→∞ T−1 T X i=1 T X j=1 E(ZiZ> j)(1) In practice, only a fraction of the sample autocovariances is used to estimate the asymptotic variance Ω,by employing a class of kernel estimators and the selection of a bandwidth parameter, M, with the estimator of Ωgiven by: ˆ ΩT= T X j=−T k(j/M)ˆ Γ(j)(2) where ˆ Γ(j)=          1 T T P t=j+1 (ZtZT t−j)for j≥0, 1 T T P t=−j+1 (Zt+jZT t)for j<0          ,and k(·)is a real-valued kernel.7The estimator b Ωis a consistent estimator of Ωfor unconditionally fourthor eighth-order stationary random variables, and for any given bandwidth {M}, such that M→∞and M/T1/2→0. More importantly, this long-run covariance matrix given by (2) is equal to 2πtimes the spectral density matrix evaluated at zero, an analogy which enables us to utilise the relevant asymptotic theory for spectral density estimation. Specifically, under certain regularity conditions, these nonparametric spectral density estimators have been shown to approximate the normal distribution.8The elements of b Ωare jointly normally distributed and this joint distribution enables us to derive the asymptotic distribution for the long-run correlation coefficient estimate between the two series of interest, ytand xt,defined as ˆρxy ≡ˆωxy √ˆωxx ˆωyy ,with ˆρxy normally distributed as 7Here, we employ the Quadratic Spectral (QS) kernel that gives a non-zero weight to all the sample cross correlations and is best with respect to an Asymptotic Truncated Mean Square Error (ATMSE) criterion in the class Kas proved by Andrews (1991). The author, in an extensive Monte Carlo study, reports cases where the kernel estimators of Ωyield confidence intervals whose coverage probabilities are too low. This problem is not associated with a poor choice of a specific kernel or bandwidth parameter and is particularly severe when there is considerable temporal dependence in the data. In such a case, data filtering before estimating Ωmay yield more accurately sized test statistics than standard kernel estimators; see Andrews and Monahan (1992). In the context of the present study, however, such a data prewhitening is unecessary since both stock price changes and output growth exhibit strong mean reverting properties. 8See Grenander and Rosenblatt (1953), Anderson (1971), and Priestley (1981). Sufficient regularity conditions for obtaining such a result is that Zt= ∞ S j=0 ψjεt−j,where εtis an i.i.d. process with (E(εt)=0,E(ε2 t)< ∞,E(ε4 t)<∞,and ∞ S j=0  ψj <∞. 5 follows (see the Appendix for the detailed derivation): rT M(ˆρxy −ρxy)∼N³0,¡1−ρ2 xy¢2´(3) An advantage of this methodology is that the long-run covariance matrix can be decomposed into the contemporaneous covariance matrix Gand the temporal covariance matrix Λ (or Λ>), i.e. Ω=G+Λ+Λ>where G≡   gyy gxy gxy gxx   =E(Z0Z> 0)and Λ≡   λyy λyx λxy λxx   = ∞ P k=1 E(Z0Z> k). This, in turn, implies that the long-run correlation coefficient ρxy can be decomposed as: ρxy =µgxy √ωxxωyy¶+µλyx √ωxxωyy¶+µλxy √ωxxωyy¶≡cxy +ryx +rxy (4) Relationship (4) expresses the long-run coefficient, ρxy,as the sum of the contemporaneous correlation coefficient, cxy, the temporal correlation coefficient, ryx, describing feedbacks from past output growth to current real stock returns (yt→xt), and the temporal correlation coefficient rxy that describes feedbacks of the opposite direction (xt→yt). While we are able to exploit the asymptotic normality of the estimator of the two-sided long-run covariance matrix and derive the relevant distribution for the long-run correlation coefficient, formal hypothesis testing on the basis of the contemporaneous correlation coefficient, cxy, and the temporal correlation coefficients, rxy and ryx is not feasible. The main reason is that asymptotic normal approximations for the respective components of the spectral density matrix are not available, since the off-diagonal elements of the one-sided long-run covariance matrix can not be expressed in terms of periodograms. To circumvent the lack of formal hypothesis testing on the decomposed correlation coefficients, we indirectly investigate their significance by testing for the existence of causal relations in the mean of two series in the context of the non-parametric method put forward by Hong (2001). In particular, consider again the bivariate stationary and ergodic stochastic process Zt=[yt,x t]>. The test is based on the sample cross-correlations function of the standardized residuals and involves two stages. In the first stage, we estimate univariate time-series models for both the series under scrutiny and in the second stage, we calculate the sample cross-correlations of the standardized residuals of output growth and real stock returns, buyt and 6 buxt respectively.9The sample cross-correlation function of uyt and uxt (bτx,y(k))isgivenby: bτx,y(k)≡b Cx,y(k) qb Cx,x(0) b Cy,y(0) (5) where b Cx,y(k)= T−1PT t=k+1[buytbuxt−k],k=0 T−1PT t=−k+1[buyt+kbuxt],k<0 is the sample cross-covariance, b Cx,x(0), b Cy,y(0) are the sample variances of the stock returns and output growth, respectively and Tisthesamplesize. Theteststatistic,Q, proposed by Hong (2001) is given by the following formula: Q=TPT−1 j=1 k2(j/M)∗bτ2 x,y(j)−C1T(k) p2∗D1T(k)(6) where C1T(k)=PT−1 j=1 (1 −j T)∗k2(j/M),D1T(k)=PT−1 j=1 (1 −j T)∗(1 −j+1 T)∗k4(j/M) and k(j/M)is a weighting function.10 Under the null hypothesis of no causality and some appropriate regularity conditions, the Q-test follows asymptotically a N(0,1) distribution.11 This methodology allows for bivariate conditional mean specification and includes the case of infinite unconditional variance, which is often encountered in empirical studies on stock returns. Testing for the significance of the contemporaneous correlation coefficient between two series is performed by employing the typical sample correlation coefficient, which is also asymptotically normal (Anderson, 1971); assuming that the true value of the correlation coefficient is q,the correlation coefficient estimator is then distributed as bqx,y →N³q, (1−q2)2 T´. 3. Data To gauge this empirical relationship between output growth and stock returns, we use existing measures of output and real composite and sectoral stock price changes for the G-7 countries. Our data set is monthly and covers the period from January 1973 to August 2003. As a measure of the growth rate of output we use the industrial production index (seasonally adjusted) from Thomson Financial (obtained by Datastream). Following Fama (1990) and other authors, real stock price changes are obtained by use of Datastream-calculated composite and sectoral indices, appropriately adjusted for the inflation rate of the countries under consideration. So, apart from the total market aggregate index and the total non-financial market index, 9In our study, we employ the typical ARMA(p,q)-GARCH(1,1) models, the correct order of which is determined by means of the Akaike information criterion. 10In the present study, we use the QS kernel. 11Notice that the Q−test is an one-sided test and upper-tailed critical values should be used. 7 the following sectoral indices are employed: Financial, Basic Industries, General Industries, Cyclical Services, Non-Cyclical Services, Information Technologies, Cyclical Consumer Goods, Non-cyclical Consumer Goods, Utilities.12 4. Empirical evidence In this section we apply the non-parametric techniques outlined above to examine the empirical relationship between growth and stock returns. We emphasize that, following Fama (1990), Schwert (1990) and others, we do not try to discriminate among various theoretical hypotheses. Instead, we implement the estimation and testing strategy outlined in section 2 to investigate non-parametrically the strength and the direction of correlation between real stock price changes and output growth for the G-7 countries. 4.1. Long-run correlation between growth and returns We begin the empirical analysis with the estimates of the long-run correlation between growth and stock returns. The first column in the upper part of Table 1 reports the relevant figures for the aggregate market returns at the highest bandwidth examined (36 months). This choice of bandwidth, i.e. the number of autocovariances that are assigned a non-zero weight, represents one tenth of our sample and ensures that the majority of the effects have been taken into account. With the exception of Italy, estimates of the long-run correlation range from 0.488 (Japan) to 0.656 (UK). The second column reports the standard deviation of the point estimates of the long-run correlation based on (3). As was shown in the previous section, the variances of the point estimates are inversely related to the true value of the long-run correlation coefficients. Accordingly, Italy has the lower long-run correlation and thus exhibits the higher standard deviation of the respective estimate. The next column reports the respective figures for all the countries. In this respect, the long-run correlation of the rest of the countries is found to be significantly different from zero.13 Not surprisingly, the only country for which we cannot reject the null hypothesis of zero long-run correlation is Italy.14 Inthesamemode,we 12The Datastream codes for the corresponding stock market indices are the following: TOTMKXX, TOTLFXX, BASICXX, GENINXX, CYSERXX, NCYSRXX, ITECHXX, UTILSXX, CYCGDXX, NCYCGXX, where XX stands for the country code, i.e. CN (Canada), FR (France), BD(Germany), IT (Italy), JP (Japan), UK and US. In the same mode, the Consumer Price Index code is the XXI66...CE and the Industrial Production code is XXI64...F. All the reported results were obtained by programs written in E-views 4.1 and are available from the authors upon request. 13These tests are performed based on the asymptotic approximation of the distribution of the zero long-run correlation, which is shown to be standard normal. 14In principle, we could also calculate the range of bandwidths over which we reject the null hypothesis of a zero 8 by Stock and Watson, 2003). It is likely that a subsantial portion of information is lost by the need to estimate parsimonious single-equation and multivariate parametric models, which in turn reduces their forecasting ability. Hence, although the evidence presented here can only be interpreted tentatively in terms of forecasting ability, there is some indication that some predictive content could be found if larger lags of stock price changes are utilized in parametric specifications aiming at predicting output in the G-7 countries. Themethodemployedherecanalsobeappliedto other cases in which parametric methods leave empirical questions open. For instance, Thoma and Gray (1998) claim that, contrary to the view popularly held in the literature, financial variables (money supply and interest rates) do not provide any predictive power for future industrial growth. The authors note that, given that the predictive power of parametric models should be evaluated in out-of-sample forecasting, much of their power is the outcome of specific outliers. The non-parametric empirical strategy used here can be extended to the estimation and hypothesis testing for the long-run covariance structure between monetary variables and real activity. Another promising route for further research involves the links between domestic and international stock portfolios and future output. Dumas et al. (2003) point out that an open question in the study of international financial markets is whether stock markets correlations across countries can be explained by economic fundamentals. Empirical findings on this issue have not been universally conclusive (see Smith, 1999) and the present methodology could shed some light on the links between variations in international aggregate or sectoral stock market links and underlying economic variables. 15 Appendix: Asymptotic distribution of the long-run correlation coefficient Here we derive the asymptotic distribution of the long-run correlation coefficient ˆρxy.Given that the covariance between any two elements of the spectral density matrix, for example (a, b) and (c, d),isequaltofacfbd +fadfbc, we obtain the following asymptotic distribution for the elements of b Ω: rT M       ˆωxx −ωxx ˆωyy −ωyy ˆωxy −ωxy       ∼N       0,       2ω2 xx 2ω2 xy 2ωxxωxy 2ω2 xy 2ω2 yy 2ωyyωxy 2ωxxωxy 2ωyyωxy ωxxωxy +ω2 xy             (A1) In order to derive the asymptotic distribution of the long-run correlation coefficient ˆρxy ≡ ˆωxy pˆωxx ˆωyy we apply the delta method with the transformation vector Jequal to the partial derivatives of ρxy with respect to ωxx,ωyy and ωxy: J=·∂ρ ϑωxx ∂ρ ϑωyy ∂ρ ϑωxy ¸ Specifically, we get that: ∂ρ ϑωxx = ∂µωxy √ωxxωyy¶ ϑωxx =−ωxy 2ω2 xx√ωxxωyy ∂ρ ϑωyy = ∂µωxy √ωxxωyy¶ ϑωyy =−ωxy 2ω2 yy√ωxxωyy ∂ρ ϑωxy = ∂µωxy √ωxxωyy¶ ϑωxy =1 √ωxxωyy Setting QtheasymptoticvarianceoftheΩmatrix in (A1), the asymptotic variance of the long-run correlation coefficient is calculated as follows: P=JQJ0 16 After some simple algebra, we have: P=(ω2 xy −ωxxωyy)2 ω2 xxω2 yy =(ρ4 xy +1−2ρ2 xy)=(ρ2 xy −1)2(A2) It follows from (A1) and (A2) that: rT M£ˆρxy −ρxy¤∼N³0,¡1−ρ2 xy¢2´ which is equation (3) in the text. 17 References Anderson T.W., 1971, The Statistical Analysis of Time Series,Wiley,NewYork. 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Long-run correlation estimates between output growth (y) and stock price changes (x) Country Long-Run Correlation Standard Deviation t-stat Ho: ρxy =0 t-stat Ho: ρxy =ρ Contemporaneous correlation Temporal correlation x → y Temporal correlation y → x Sample period: 1973-2003 Canada 0.556 0.221 2.536 -0.203 (ρ=0.6) 0.041 0.353 0.162 France 0.564 0.219 2.536 -0.201 (ρ=0.6) 0.116 0.362 0.086 Germany 0.491 0.243 2.219 -0.040 (ρ=0.5) -0.021 0.451 0.061 Italy 0.194 0.309 0.862 -0.034 (ρ=0.2) -0.033 0.190 0.037 Japan 0.488 0.244 2.216 -0.041 (ρ=0.5) -0.022 0.476 0.034 UK 0.656 0.183 2.988 -0.158 (ρ=0.7) 0.116 0.422 0.118 US 0.583 0.211 2.641 -0.083 (ρ=0.6) -0.018 0.498 0.103 Sample period: 1989-2003 Canada 0.575 0.210 2.005 -0.130 (ρ=0.6) 0.001 0.278 0.296 France 0.549 0.219 1.918 -0.254 (ρ=0.6) 0.090 0.321 0.138 Germany 0.412 0.260 1.439 -0.374 (ρ=0.5) -0.131 0.424 0.119 Italy 0.371 0.271 1.296 0.562 (ρ=0.2) 0.084 0.285 0.002 Japan 0.275 0.289 0.961 -0.957 (ρ=0.5) -0.030 0.348 -0.043 UK 0.565 0.214 1.974 -0.844 (ρ=0.7) 0.033 0.368 0.164 US 0.648 0.182 2.264 0.239 (ρ=0.6) -0.020 0.395 0.273 Notes: The bandwidth for the 1973-2003 period is 36 months and for the 1989-2003 period is 18 months; see section 2 in text for details. Table 2A. Hypothesis testing for temporal correlation: from stock price changes to output growth Q-test Country/Bandwidth 3 6 9 12 18 24 30 36 48 Canada No No No No Yes** Yes** Yes** Yes** Yes** France No No No No No No No No No Germany No No Yes** Yes** Yes** Yes** Yes** Yes** Yes** Italy Yes* Yes** Yes* No No No No No No Japan Yes** Yes** Yes* No No No No No Yes* UK No No Yes* Yes** Yes** Yes* No No No US Yes** Yes** Yes** Yes** Yes** Yes** Yes** Yes** Yes** Table 2B. Hypothesis testing for temporal correlation: from output growth to stock price changes Q-test Country/Bandwidth 3 6 9 12 18 24 30 36 48 Canada No No No No No No No No No France No No No No No No No No No Germany No No No No No No No No No Italy No No No No No No No No No Japan No No No No No No No No No UK No No No Yes** Yes** Yes** Yes** Yes** Yes** US No No No No No No No No No Notes: Q-test denotes the Hong (2001) test; see section 2 for details.* denotes statistical significance at the 5% level and ** at the 1% level. Table 3. Hypothesis testing for contemporaneous correlation Country Contemporaneous correlation qxy t-stat Ho: qxy =0 Canada 0.103 1.947 France 0.099 1.877 Germany 0.005 0.095 Italy 0.039 0.734 Japan 0.041 0.774 UK 0.059 1.128 US -0.017 -0.317 Notes: qxy denotes the Anderson (1971) test; see section 2 for details. .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Total market index .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Total non-financial market index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Financial index -.1 .0 .1 .2 .3 5 10 15 20 25 30 35 cxy ryx rxy Basic industries index .0 .1 .2 .3 5 10 15 20 25 30 35 cxy ryx rxy General industries index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Cyclical services index -.1 .0 .1 .2 .3 .4 .5 5 10 15 20 25 30 35 cxy ryx rxy Non-cyclical services index .0 .1 .2 .3 5 10 15 20 25 30 35 cxy ryx rxy Information technology index -.1 .0 .1 .2 .3 5 10 15 20 25 30 35 cxy ryx rxy Utilities index -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 cxy ryx rxy Cyclical consumer goods index Figure 1 CANADA: Decomposed long-run correlation coefficient between output growth and stock price changes -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Total market index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Total non-financial market index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Financial index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Basic industries index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy General industries index -.2 -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Cyclical services index -.1 .0 .1 .2 .3 .4 .5 5 10 15 20 25 30 35 cxy ryx rxy Non-cyclical services index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Information technology index -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 cxy ryx rxy Cyclical consumer goods index -.1 .0 .1 .2 .3 .4 5 10 15 20 25 30 35 cxy ryx rxy Non-cyclical consumer goods index Figure 2 FRANCE: Decomposed long-run correlation coefficient between output growth and stock price changes