Testing for Granger causality between stock prices and ...

1 Munich Personal RePEc ArchiveTesting for Granger causality betweenstock prices and economic growthForesti, Pasquale2006 Online Paper No. 2962, posted 26 Apr 2007 UTCT esting for Granger causality between StockPrices and Economic ForestiApril 26, 2007 AbstractThis paper has focused on the relationship between stock marketprices and growth. A Granger - causality analysis has been carried outin order to assess whether there is any potential predictability powerof one indicator for the other. The conclusion that can be drawn isthat stock market prices can be used in order to predict growth, butthe opposite it is not IntroductionFor years, practitioners have analyzed the relationship between the growthofa Nation (in GDP growth) and the stock market. In particular, the questionabout the forecasting power of the stock prices for the economic growth hasbeen very who support the market power argue that the stock market con-tains information about the future economic growth.

2 Thus, stock pricesreflect expectations about profitability, and profitability is assumed to belinked with economic activities. If the economy is expected to go in to agrowing phase the stock market will predict this, bidding up the prices ofstock since future earnings are supposed to rise. Campbell (1989) relatesstock market to real economy through the fundamental valuation of equity :StockPrice= j=1 ExpectedDividendst+j(1+k)jwherek(assumed to be constant) is the rate at which the dividendsare discounted. According to this equation it is possible to state that thestock prices are directly related to future profitability, that is supposed to berelated with the real economy. Since this model gives great importance toexpectations, it has to be considered that investors do not always anticipatecorrectly the returns. Thus sometimes the stock market will mislead thedirection of the element that supports the stock market predictability is the wealth effect.

3 When the stock market rises, investors are willing to spendmore because they are more wealthy, so the economy expands. On the otherside if the stock prices declines, investors are less wealthy and spend less, sothe economic growth , fundamental variation models and the wealth effect, bothsuggest that the stock market predicts economy, although it can be arguedthat the causations are are also critics to these theories. One of these is related to theexpectations and the fact that they are subject to human error. MoreoverPearce (1983) and Campbell (1989) point out that the stock market hasgenerated false signals in previous years, hence more evidence of this pre-dictability capacity is paper is structured as follows. Section 2 provides an overview of themethodology that has been used. In section 3 a description of the data andtheir preliminary analysis is presented. Section 4 reports the results of theempirical analysis.

4 Section 5 concludes the MethodologyGranger (1969) proposed a time-series data based approach in order to de-termine causality . In theGranger-sense xis a cause ofyif it is useful inforecastingy1. In this framework useful means thatxis able to increasethe accuracy of the prediction ofywith respect to a forecast, consideringonly past values 1:Assuming to have an information set twith the form (xt,..xt j,yt,..yt i), we say thatxtisGranger causalforytwrt. tifthe variance of the optimal linear predictor ofyt+h, based on t, has smallervariance than the optimal linear predictor ofyt+hbased only on lagged valuesofyt, for anyh. Thus,x Granger -causes yif and only if 21(yt:yt j,xt i)< 22(yt:yt j), withjandi= 1,2,3,..nand 2representing the variance ofthe forecast are three different types of situation in which aGranger-causalitytest can be applied: In a simple Granger - causality test there are two variables and theirlags.

5 In a multivariate Granger - causality test more than two variables areincluded, because it is supposed that more than one variable can influ-ence the results. Finally Granger - causality can also be tested in a VAR framework, inthis case the multivariate model is extended in order to test for for thesimultaneity of all included empirical results presented in this paper are calculated within a sim-ple Granger - causality test in order to test whether stock prices Grangercause economic growth and vice rate of real values of Standard and Poor s Composite index (SP)is used as an indicator for stock prices , while changes in economic growth aremeasured by the rate of growth of real GDP. Thus, according to Mahdaviand Sohrabian (1989), the following two equations can be specified(GDP)t= +m i=1 i(GDP)t i+n j=1 j(SP)t j+ t(1)1 This idea is consistent with the notion that the cause precedes theeffects but cannotbe applied to the contemporaneous values (SP)t= +p i=1 i(SP)t i+q j=1 j(GDP)t j+ t(2)Based on the estimated OLS coefficients for the equations (1) and (2)four different hypotheses about the relationship between GDP and SP canbe formulated:1.

6 UnidirectionalGranger-causalityfrom SP to GDP. In this case Stockprices increase the prediction of the economy but not vice versa. Thus nj=1 j6= 0 and qj=1 j= UnidirectionalGranger-causalityfrom GDP to SP. In this case thegrowth rate of the economy increases the prediction of the stock Pricesbut not vice versa. Thus nj=1 j= 0 and qj=1 j6= Bidirectional (or feedback) causality . In this case nj=1 j6= 0 and qj=1 j6= 0, so in this case the growth rate of the economy increasesthe prediction of the stock prices and vice Independence between GDP and SP. In this case there is noGranger-causalityin any direction, thus nj=1 j= 0 and qj=1 j= by obtaining one of these results it seems possible to detect thecausality relationship between stock prices and the economic growth of Data AnalysisThe totality of the data that we are going to analyze was taken from Econ-stats, from the Standard and Poor s website and from Datastream.

7 Thecountry that has been chosen for this empirical test has been the UnitedStates, with nominal values made real through the use of the Implicit GDPP rice Deflator anchored to the year 2000. Standard s and Poor index hasbeen chosen as the indicator of the stock market this paper a wider range of data than the ones analyzed in previouspapers in the literature has been used, and the time series are given all theway to the end of 2005. A quarterly frequency has been used, since it isthe most logical given the need to observe changes in GDP over time. Thetwo series, obtained in real values, have been manipulated to work with thegrowth ratios 1: Scatter plots for GDP growth and SP growthFigure 1 shows how just a quick view on the data can support a positiverelation between the two variables (in percentages of growth). The analysis inthis paper will show in formal terms what kind of relation can be hypothesizedon these two Empirical Analysis and ResultsThe first step in this analysis concerns the stationarity of the GDP andSP series.

8 Granger causality requires that the series have to be covariancestationary, so an Augmented Dickey-Fuller test has been calculated. For allof the series the null hypothesisH0of non stationarity can be rejected at a5% confidence , since the Granger - causality test is very sensitive to the number oflags included in the regression, both theAkaike (AIC)andSchwarzInfor-mation Criteria have been used in order to find an appropriate number that these requirements have been satisfied, Granger - causality testsare computed. Taking equation (1) as an example, the two steps procedurein Testing whetherSPcausesGDPis as regressed on its past values excludingSPin the is called the restricted regression, from which we obtain the re-stricted sum of squared 2: Plots of the GDP growth series on the right, and of the SP growthseries on the left Thus, a second regression is computed including the laggedSP. Thisis called the unrestricted regression from which the unrestricted sum ofsquared residuals is statistics is defined asF=[(SSRr SSRu)n][SSRuT (m+n+1)](3)whereSSRrandSSRuare the two sums of squared residuals related tothe restricted and unrestricted form of the equation; the elements that formthe degrees of freedom areT, that is the number of observations whilenandmare the number of lags as it can be seen from (1).

9 The same procedure isused in order to test for the inverse Granger - causality relation in (2).It is important that the data are covariance stationary in order to performany kind of such regression, given the key of interpretation that we are lookingfor. For this the ADF test has been performed. This is a classic choice inliterature and very strong test against unit roots. It is worth emphasizingthat the two series that we are working with are already growth patterns,therefore we expect them to be I(0).The result reflects the I(0) stateof thevariables. It is also possible to see this result from the graphs above, thatshow the rates of growth of the two series. Indeed the plots show covariancestationary compatible eye patternsSince the series are covariance stationary we can proceed to checking for the number of lags to input in the model. The Granger causality test issensitive to this kind of formatting of the model, and it is therefore importantto choose and information criterion to base the decision on the number oflags to apply to the two series in the regressions to follow.

10 For this purpose6we have analyzed a large range of lags both for the referring to the GDPand for the one referring to the Standard and Poor value. Many previousworks use the criterions of Akaike and Schwarz to formulate these optimal values arem= 2 andn= 7 formdefined as the lag of the GDPseries andnthe lag applied for the SP , the results of Granger causality for equations (1) and (2) are rep-resented in table 1 and 2. The tables report the results corresponding todifferent regressions, in order to have a comparison of the different regres-sions values ofFstatistic suggest thatSPGranger-causes GDP2,and GDPdoes not cause SP. Thus, it can be argued that past values ofSPcontributeto the prediction of the present value ofGDPeven with past values by the single regressions it can be showed that also with 5 lags muchof the coefficients have positive sign and with an acceptable significance it has to be taken in account that the level ofR2is low, remindingthat past rates of SP could have a limited ability for the prediction the equation (2) the associatedFtests give the opposite result, in factthere seems to be no Granger - causality from past values ofGDPfor futurevalues ofSP.