The Stock Market as a Leading Indicator- An Application of Grange

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Te Park Place Economist

Volume 4 | Issue 1 Article 13

1996

Te Stock Market as a Leading Indicator: AnApplication of Granger Causality

Brad Comincioli '95

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Recommended CitationComincioli '95, Brad (1996) "Te Stock Market as a Leading Indicator: An Application of GrangerCausality," Te Park Place Economist: Vol. 4

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The Stock Market as a Leading Indicator:An Application of Granger CausalityBrad Comincioli

L INTRODUCTIONThe stock market has traditionally beenviewed as an indicator or "predictor" of the

economy. Many believethat arge decreases instock prices are reflective of a hturerecession, whereas large increases in stockprices suggest future economic growth.

The stock market as an indicator ofeconomic activity, however, does not gowithout controversy. Skeptics point to thestrong economic growth that followed the1987 stock market crash as reason to doubtthe stock market's predictive ability. Giventhe controversy that surrounds the stockmarket as an indicator of h r e economicactivity, it seems relevant to further researchthis topic.

Theoretical reasons for why stock pricesmight predict economic activity include thetraditional valuation model of stock prices andthe "wealth effect." The traditional valuationmodel of stock prices suggests that stockprices reflect expectations about the futureeconomy, and can therefore predict theeconomy. The "wealth effect" contends thatstock prices lead economic activity by actuallycausing what happens to the economy.The purpose of this paper, then, is toevaluate stock prices as a leading indicator ofeconomic activity. Time-series analysis andthe notion of "Granger causality" are used inthis project to estimate relationships betweenstock prices and the economy, and to see ifthey are consistent with theory.In this paper, we will explore the followingquestions. First, does the stock market leadthe real economy, in the sense that variation inits past values explains some of the variation inthe real economy? Second, does the stock

market "Granger-cause" the real economy, inwhich casepast values of stock prices improvethe prediction of hture economic activity?And third, does the real economy "Granger-cause" the stock market, in that past values ofeconomic activity improve the prediction ofthe stock market?11. CAN THE STOCK MARKETPREDICTECONOMICACTIVITY?

The question of whether the stock marketcan predict the economy has been widelydebated. Those who support the market'spredictive abiity arguethat the stock market isforward-looking, and current prices reflect thefuture earnings potential, or profitability, ofcorporations. Since stock prices reflectexpectations about profitability, andprofitabiity is directly linked to economicactivity, fluctuations in stock prices arethought to lead the direction of the economy.If the economy is expected to enter into arecession, for example, the stock market willanticipate this by bidding down the prices ofstocks.

The "wealth effect" is also regarded assupport for the stock market's predictiveability. Pearce (1983) argues that sincefluctuations in stock prices have a diect effecton aggregate spending, the economy can bepredicted fiom the stock market. When thestock market is rising, investors are morewealthy and spend more. As a result, theeconomy expands. On the other hand, if stockprices are declining, investors are less wealthyand spend less. This results in slowereconomic growth.

Critics, however, point to a number ofreasons not to trust the stock market as an


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FIGURE 1:Does the Stock Market Predict the Economy?s S&PSOO and Real GDP

1970:IQ-l994:IIXQ5500 ^

ir,,0OI4500 4

cw- i03500 3e3000 P,n2500

a2me un tm tm ua ws uu mt ISM

indicator of future economic activity. Someargue that the stock market has previouslygenerated "false signals" about the economy,and therefore, should not be relied on as aneconomic indicator. The 1987 stock marketcrash is one example in which stock pricesMsely predicted the direction of the economy.Instead of entering into a recession whichmany were expecting, the economy continuedto grow until the early 1990's (see FIGURE1)-Another reason why skeptics do not trustthe stock market as an indicator of theeconomy isbecause of investors' expectations.Critics reason that expectations about futureeconomic activity are subject to human error,which in many cases causes stock prices todeviate from the "real" economy. Sinceinvestors do not always anticipate correctly,stockprices will sometimesincrease before theeconomy enters into recession and decreasebefore the economy expands. As a result, thestock market will often mislead the directionof the economy.

Even when stock prices do precedeeconomicactivity,a question that arises is howmuch lead or lag time should the market beallowed. For example, do decreases in stockprices today signal a recession in six months,

one year, two years, or will a recession evenoccur? An examination of historical datayields mixed results with respect to the stockmarket's predictive ability. Douglas Pearce(1983) found support for stock prices leadingthe direction of the economy. His studydiscovered that fiom 1956-1983, stock pricesgenerally started to decline two to fourquarters before recessionsbegan. Pearce alsofound that stock prices began to rise in allcases before the beginning of an economicexpansion, usually about midway through thecontraction.

Other studies have found evidence thatdoes not support the stock market as a leadingeconomic indicator. A study by Peek andRosenberg (1988), for example, indicates thatbetween 1955and 1986, out of eleven cases inwhich the Standard and Poor's CompositeIndex of 500 stocks (S&P500) declined bymore than 7 percent (the smallest pre-recession decline in the S&P500), only sixwere followed by recessions. Furthennore, astudy conducted by Robert J. Barro (1989)found that stock prices predicted threerecessions for the years 1963, 1967, and 1978,that did not occur.


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IILWHY TOCK PRlCESMIGHT LEADTHEECONOMY

One theoretical reason why stock pricesmight lead economic activity is based on thetraditional equity valuation model shownbelow (Brealeyand Myers 1988):m

Stock Price = Emected Profitability1= 1 (k + 1)'

where profitability is the expected amount ofcorporate earnings, and k is the rate at whichprofitability is discounted. It is usuallyassumed that k is constant.

According to this equation, stock pricesequal the present value of a company'sexpected fbture profits. If profitability isexpected to increase (holding k constant), theprice of the stock will increase. Conversely, ifinvestors are expecting a firm's profits todecline in the fbture, then the price of thestockwill decrease in value.

Since a firm's profits are directly linked tothe behavior of the real economy, stock priceswill be affected by expectations about thefbture economy. For example, if investorsexpect the economy to enter into recession,then expected profits will be d i s h e d andstock prices will decrease in value. On theother hand, if investors anticipate economicgrowth, then expected profitswill improve andstock prices will increase. Thus, investorshave an interest in predicting the &re realeconomy. And, if they are somewhatsuccessll in their predictions, then stock pricemovements will lead the direction of theeconomy.An issue to point out here is how investorsform their expectations. There are a numberof models that attempt to explain howexpectations are fonned (see, for example,DeBondt and Thaler 1985, and Pearce andRoley 1985). Such models include theadaptive expectations model and the rationalexpectations model. ' Adaptive expectationsmodels suggest that expectations are

-rmincioli

developed through past experience, whereasrational expectations models pose thatexpectations are fonned using all currentinformation that is available. Although thesemodels are not the focus of this paper, it isimportant to understand that stock prices arehighly dependent on investors' expectations.To some extent, these models assume thatexpectations arise out of experience orhistorical data. A change in recent experience,then, can cause investors to change theirexpectations about the &re real economy,which then causes them to bid up or down theprices of stocks. To the extent that thesemodels are true, the economy may also leadthe stock market.The "wealth effect" &om fluctuations instock prices is another theoretical argumentfor why stock prices might lead the economy.Traditional macroeconomic models oftenassume that consumption depends not just onincome, but also on wealth. Increases anddecreases in stock prices raise and lowerwealth, which in turn raise and loweraggregate consumption. And, becauseconsumption is a large part of the economy,changes in the real economy are observed.

In summary, according to findarnentalvaluation models, stock prices depend onexpectations about the &re economy.Therefore, expected changes in the realeconomy cause the values of stock prices.According to the wealth effect, however,changes in stock prices cause the variation inthe real economy. It is important to point outthat, while the causation in the two theories isdifferent, both theories suggest that the stockmarket predicts the economy.IV.DATA

The sampledata cover the period 1970:IQ-1994:IIIQ and contain a total of 99 quarterlyobservations. The variable that is used tomeasure movements in stock prices is thequarterly percent change in the Standard and


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me Park Place Economist, v. 4Poor's Composite Index of 500 stocks(SP500). The reason for choosing theS&P500 rather than other stock indexes isbecause it is a fairly representative measure ofthe stock market. Other indexes such as theDow Jones Industrial Average, whichmeasures the performance of only 30 blue-chipcompanies, are less representative. The factthe S&P500 Index is a "value-weighted" asopposed to a "price-weighted" index isanother reason this index was chosen. Onefinalreason for choosing the S&PSOO Index isbecause it is included as one of the twelvecomponents in the Department of Commerce'sindex of leading economic indicators.

The variable used to measure changes inreal economic activity is the quarterly percentchange of real Gross Domestic Product(GDP). In using real values of GDP, the year. 1987 is used as the base year for the implicitprice deflator. Other studies utilized percentchanges in the Index of Industrial Productionas their proxy for economic growth, but didnot indicate that it was a better measure ofeconomic activity.V. TESTING FOR GRANGERCAUSALITY

The procedure for testing statisticalcausality between stock prices and theeconomy is the direct "Gqinger-causality" testproposed by C. J. Granger in 1969. Grangercausality may have more to do withprecedence, or prediction, than with causationin the usual sense. It suggests that while thepast can causdpredict the future, the futurecannot causdpredict the past.

According to Granger, X causes Y if thepast values of X can be used to predict Y moreaccurately than simply using the past values ofY. In other words, if past values of Xstatistically improve the prediction of Y, thenwe can conclude that X Granger-causes" Y.It should be pointed out that given thecontroversy surrounding the Granger causalitymethod, our empirical results and conclusionsdrawn fiom them should be considered assuggestive rather than absolute. This isespecially important in light of the "falsesignals" that the stock market has generated inthe past.Our first step in testing for "Granger

causality" is to determine whether there is atrend in our sample data. An importantassumption in any time-series analysis is thatthe variables being tested are stationary.Figure 1 demonstrates how this assumption isviolated. During the period 1970-1994, bothReal GDP and the S&PSOO Index follow anupward trend. In order to eliminate the trend,we form percent changes in the two variablesand then examine if the two are stationary (seeFIGURE 2). Since the two variables do notappear to have a trend, we reason that thepercent changes are stationary and proceedwith the Granger test.Our next step in testing for "Grangercausality" is to test whether a relationshipexists between stock prices and the economy.In order for causality to hold true, arelationship must already exist between thevariables being tested. For example, ifX wasnot related to Y, then how could X possiblycause the variation in Y?


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FIGURE 2: Testing for Stationarity

./.Change in Real GDP197oa~-i99rrnq

..................................................................

96 Changein S&P 500197olQ-l994mQ

-To determine whether a relationship existsbetween stock prices and the economy, we

regress %GDP on past values of %SP500,lagged back 6 quarters:

The results of this regression indicate thatstock prices are positively related to theeconomy when lagged as much as three

quarters (seeFIGURE 3). Moreover, stockprices lagged one quarter areboth positive andstatistically significant at the .O 1 level. As adt,e conclude that there is a relationshipbetween past values of stock prices and theeconomy. Thus, the results &om thisregression suggest that past values of stockprices do lead economic behavior, but thisdoes not imply that stock prices "Granger-cause"the economy. Formal tests of causalityare exhibited later in the paper.


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FIGURE 3:Dependent Variable = %GDP. .Variable Estimated Coefficient T-St-

1. %SP500., .0359 3.0233***2. %SPSOO, .0167 1.40763. %SP5OO4 .0158 1.31234. %SP50O4 .03385. %SP500., .07946. %SP5OO4 .6757Adjusted R2= .0779* Significant at .10 level** Sig d can t at -05level*** Significant at .O1 level

To test causality between %SPSOO and%GDP and its direction the following two

equations are specified:

t t

(1) %GDP, = a,, + a, (%GDPIa +z bi (%SPSOO)aCI C1The steps in testing whether stock prices"Granger cause" the economy (equation 1)areas follows. First, we regress %GDP on pastvalues of %GDP, but do not include thelagged %SPSOO terms. This is the restrictedregression. After we run the regression, weobtain the restricted sum of squares, RSS,.Second, we run he regression and includethe lagged %SP500 terms. This is theunrestricted regression. After we run this

regression, we obtain the unrestricted residualsum of squares, RSS,.The null hypothesis is 4 = 0 for all values

of i. In other words, the lagged %SP500terms do not belong in the regression. To testthis hypothesis, the F-test is applied, as shownbelow:

If the F-value exceeds the critical F-valueat the chosen level of significance, the nullhypothesis is rejected, in which case the laggedS&P 500 variable belongs in the regression.This would imply that stock prices "Granger


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cause" or improve the prediction of theeconomy. We then use the same steps forequation 2 to test whether the economy"Granger-causes" stock prices.Based on the results fkom equations 1 and2, four possibilities representing possiblecausal relationships between %GDP and%SPSOO maybe formulated, which are definedbelow:

(1) The stock market "Granger-causes"economic activity if stock prices improve theprediction of the economy, and the economydoes not improve the prediction of stockprices (bi+Oand d,=O).

(2) The economy "Granger causes" thestock market if the economy improves theprediction of stock prices, and stock prices donot improve the prediction of the economypi=ond 4+0).(3)A feedback relationship exists betweenstock prices and the economy when stockprices "Granger cause" the economy, and then,the economy "Granger causes" stock prices(bpo and di*O).

(4) independence is indicated when nocausal relationships are found between stockprices and the economy (bi=O and 4=O).V.RESULTS

The results of Granger tests for equations1 and 2 are presented in FIGURE 4. In thistable, the two columns represent therelationship which was being tested. Incolumn 1, we test whether stock prices predictthe economy, and in column 2, we testwhether the economy predicts stock prices.Separate regressions were run for all values ofk (1 to 6), and the F-statistics, along with theirprob-values, were calculated from the results.Each value of k represents the maximum laglength in the regression. For both %GDP and%SP500 amaximum lag length of six quarterswas tried. Past studies attempted a maximumlag length of eight quarters, but the authorsreported that longer lag orders did not changethe basic results in any significant way(Mahdavi and Sohrabian).

FIGURE 4(1) Does %SP500 predict %GDP? (2) Does %GDP predict %SP500?k F-Statistic Prob-Value F-Statistic Prob-Value .

1 9.4083 .0028*** .I557 .69405.1949 .0073*** .6131 .5439

3 2.82834 1.76985 1.17876 1.2743* Significantat .10 level** Significant at .05 level*** Significant at .O1 level


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As can be seen in figure 4, the F-statisticsused to test causality in equation 1 aresigdicant for lagged quarters 1, 2, and 3.These results indicate that stock prices do"Granger cause" economic activity whenlaggedorders of 1,2, and 3 are used. That is,past values of %SPSOO significantly contributeto the prediction of current %GDP even in thepresence of past values of GDP.

In equation 2, however, the results showthat the F-statistics are not sufficient to rejectthe null hypothesis in any of the laggedquarters. Past values of %GDP do notsignificantly contribute to the prediction ofcurrent %SPSOO. Therefore, the economydoes not "Granger-cause7' the stock market.In sum, the results of the Granger-causalitytests indicate a causal relationship betweenstock prices and the economy. Moreover, theresults reveal that stock prices do "Granger-cause7' economic activity, but the economydoes not "Granger-cause" stock prices.VI. EXPLANATIONS FORCAUSALITY RELATIONSHIP

THE

The results suggest that stock prices do"Granger cause" economic activity. That is,the stockmarket does predict the economy. Itis important, therefore, to review the theoriesthat are consistent with the stock market as aleading economic indicator.

One possible explanation for why stockprices predict the economy is that stock pricesactually cause what happens to the economy.This would be consistent with the wealtheffect. According to this argument,fluctuations in stock prices raise and lowerwealth, which in turn, raises and lowersaggregate consumption. As a result, economicactivity is affected or "caused" by fluctuationsin the stock market.

Another possible explanation for whystock prices "Granger cause" economicactivity is that the stock market is forward-looking. If investors are truly forward-

!eEconomist, v. 4looking, then stock prices reflect expectationsabout filture economic activity. If a recessionis anticipated, for example, then stock pricesreflect this by decreasing in value. Since theresults indicate that the stock mark& improvesthe prediction of economic activity, and if weassume that the stock market is forward-looking, then investors' expectations about thefbture economy are fairly accurate.Furthermore, since the economy does notpredict stock prices, expectations about thefbture economy are not being formed bysimply looking at past values of GDP, which issuggested by the adaptive expectations model.For the adaptive expectations model to holdtrue, past values of GDP would have to"Granger cause" stock prices.It is important to note that we do notknow how investors are forming theirexpectations. There are a number of factorswhich influence investors' expectations thatour model does not account for. We do knowfrom the results, however, that they are notbeing derived by simply looking at the pasttrend in the economy to form expectationsabout future economic activity.VIL SUMMARY AND CONCLUSION

The purpose of this paper was to evaluatethe stock market as a leading economicindicator and explore causal relationshipsbetween stock prices and the economy. Thisproject used fonnal tests of causalitydevelopedby C. J. Granger and quarterlyU.S.data for the period 1970:IQ-1994:mQ toinvestigate the relationship between thegrowth rate in stock prices and the growth rate. -in the economy.

Our results indicated a "causal"relationship between the stock market and theeconomy. We found that while stock pricesGranger-caused economic activity, no reversecausality was observed. Furthermore, wefound that statistically significant lag lengthsbetween fluctuations in the stock market and


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changes in the real economy are relativelyshort. The longest significant lag lengthobserved from the results was three quarters.One issue that needs further exploration isthe actual reason for the causality relationshipbetween the stock market and economicactivity. Is the causality relationship moreconsistent with the wealth effect or with theforward-looking nature of the stock market?The results fiom this project are consistentwith both the wealth effect and the forward-looking nature of the stock market, but do notprove either.Another possibiity for future research is toW e r valuate where expectations about thefuture economy are coming from. Our resultsreveal that expectations for future economicactivity are not simply formed by looking atthe past trend in the economy as the adaptiveexpectations model would suggest.Expectations are being formed in other ways,but how?In conclusion, the results of this projectreveal that the stock market does help predictthe h r e conomy. Although it may not besurprising to find that fluctuations in economicactivity may be preceded by changes in stockprices, our finding that changes in GDP are"Granger-caused" by changes in stock pricesis important in that it provides additionalsupport fo r the leading economic role of thestock market.

REFERENCESAbdullah,Dewan A and Hayworth, Steven C."Macroeconomics of Stock PriceFluctuations." Quarterly Journa l ofBusiness and Economics, Winter 1993,32: 50-63.Bosworth, Barry. "The Stock Market and theEconomy." Brookings Papers on

Economic Activity, 2: 1975: 257-290.

Brealey, Richard A. and Myers, Stewart C.Principles of Corporate Finance, 1988:49-55.Campbell,Harvey R "Forecasts of Economic

Growth from the Bond and StockMarkets." Financial Amlysts Journal,SeptemberIOctober 1989: 3 8-45.Carlson, Keith M. "Monthly EconomicIndicators: A Closer Look at theCoincident Index." Fed eral Reserve Bankof St. Louis Review, November 1985: 20-30.Comincioli, Brad. "The Relationship Betweenthe Stock Market and theMacroeconomy." unpublished projectconducted in 1994.DeBondt, Werner F. M. and Thaler,Richard."Does the Stock Market Overreact?"Journa l of Finance, July 1985: 793-805.Fama, Eugene F. "Efficient Capital Markets:A Review of Theo'y and EmpiricalWork."

J1 of Finance, May 1970: 383-417.Fama, Eugene F. "Efficient Capital Markets:

11." Jaurn al of Finance, December 19911575-1617.Gorton, Gary. "Forecasting W ith the Indexof Leading Economic Indicators."FeCeral Reserve Bank of Philadelphia,NovemberDecember 1982: 15-27.Granger, C. J. "Investigating CausalRelationships by Econometrics Modelsand Cross Spectral Methods."Econometrics, Vol. 37, 1969: 425-435.Heathcotte, Bryan and Apilado, Vincent P.

"The Predictive Content of Some LeadingEconomic Indicators for Future StockPrices." Jo umal of F inanc ia l an d


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TItePark Place Economist, v. 4QuantitativeAnalysis, March 1974: 247-258.

Keane, Simon M. "The Efficient MarketHypothesis on Trial." Financial AnalystsJ mmaI , March/April 1986: 58-63.Mahdavi, Saeid and Sohrabian, Ahmad. "TheLink Between the Rate of Growth ofStock Prices and the Rate of Growth of

GNP in the United States: A GrangerCausality Test." American Econom ist,Fall 1991: 41-48.Pearce, Douglas K. and Roley, V. Vance.

"Stock Prices and Economic News."Journal of B&nes, January 1985: 49-67.

Pearce, Douglas K. "Stock Prices and theEconomy." Federal Reserve Bank ofXansas C iy Economic Review, November1983: 7-22.

Ratti, Ronald A. "A Descriptive Analysis ofEconomic Indicators." Federal ReserveBank of St. Louis Review, January 1985:14-24.

Sims, Christopher A "Money, Income, andCausality." American Economic Review,September 1972: 540-552.Urnstead, David A. "Forecasting Stock

Market Prices." Jaumalof Finance, May1977: 427-441.

- -Brad Comiaeioli ('95) was an Economics major v%h a m&r in Business Administration. Thispaperwaswrittenfor his ResearchHonors project. Currently, Brad works as a claims representativeat StateFarm;he plans to pursue an MBA in the f h r e o f k i h t e a career asan investment manageror portfolio manager.

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The Stock Market as a Leading Indicator- An Application of Grange