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THE JOURNAL OF FINANCE • VOL, LI. NO, 2 • JUNE 1996

Oil and the Stock Markets

CHARLES M. JONES and GAUTAM KAUL*

ABSTRACT

We test whether the reaction of international stock markets to oil shocks can bejustified by current and future changes in real cash fiows and/or changes in expectedreturns. We find that in the postwar period, the reaction of United States andCanadian stock prices to oil shocks can be completely accounted for by the impact ofthese shocks on real cash flows alone. In contrast, in both the United Kingdom andJapan, innovations in oil prices appear to cause larger changes in stock prices thancan be justified by subsequent changes in real cash flows or by changing expectedreturns.

THE DEPENDENCE OF THE world economy on oil was again reflected in the inter-national reaction to Iraq's occupation of Kuwait. The maneuvers by Iraq toraise the world price of oil late in July 1990 and its invasion of Kuwait lessthan a week later led to a near doubling of oil prices (from $16.10 to $30.00 perbarrel) in the second half of 1990. In fact, the 1990 oil price rise is comparableto even the notorious OPEC price hikes of 1973-1974 and 1979-1980.

There are two distinguishing features of oil in the postwar world economy.First, oil is a major resource that has been (and continues to be) extensivelyused around the world. For example. Figure 1 shows that even as late as 1988,energy expenditures as a proportion of gross national product were as high as8.03 percent in the United States. The relative share of petroleum productsalone was a nontrivial 3.7 percent of GNP. Second, oil price hikes in thepostwar era appear to be dominated by shocks "exogenous" to the rest of theworld economy. For example, Hamilton (1983, 1985) conducts a detailed anal-ysis of oil price changes in the United States and concludes that ". . . theparticular timing of changes in nominal crude oil price reflects largely exoge-nous developments speciflc to the petroleum sector." (italics added) In fact,based on his statistical and qualitative analyses, Hamilton argues that wemust give a causal interpretation to the correlation between oil prices andmacroeconomic phenomena. Similarly, the critical importance of oil to other

* Princeton University and the University of Michigan, respectively. We thank Hank Bessem-binder (the discussant at the AFA), Stephen Brown, John Campbell, Jennifer Conrad, KennethFrench, Thomas George, Campbell Harvey, Victor Ng, Jonathan Paul, Nejat Seyhun, SteveSlezak, and participants in the finance seminar at The University of Michigan and the AmericanFinance Association Meetings at Boston, and especially an anonymous referee and the editor,Steve Buser, for their helpful comments and suggestions. We thank Kenneth French for providingsome Japanese data. We also thank Patti Lamparter and Stacy Ferry for preparing the manu-script. Partial funding for this project is provided by the School of Business Administration, TheUniversity of Michigan,

463

464 The Journal of Finance

1988

Figure 1. Share of Energy and Related Products in Gross National Product for theUnited States, 1970-1988. Annual U.S. energy expenditures (solid line) and expenditures onpetroleum products (dashed line) as proportions ofthe gross national product.

countries is amply demonstrated in the studies by Helliwell, Sturm, Jarrett,and Salou (1986) and Rasche and Tatom (1981).

Given the importance of oil to the world economy, it is surprising that littleresearch has been conducted on the effects of oil shocks on the stock market.^In this article, we conduct a detailed investigation of the effects of changes inoil prices on stock prices during the postwar period. Our main contribution isthat we gauge whether the stock market rationally evaluates the impact of oilshocks on the economy. The peculiar characteristics of oil shocks, that is, theirGranger-precedence with respect to other economic phenomena and theirobvious importance to the world economy, provides us a unique opportunity toassess the stock market's ability to (rationally) evaluate the causal real effectsof events that "exogenously" perturb the economy.^

Our detailed investigation of the reaction of the U.S. stock market to oilshocks shows that stock prices rationally reflect the impact of news on currentand future real cash flows. We flnd no evidence of fads and/or market overre-action. While the Canadian stock market also appears to react rationally to oilshocks, the experiences of Japan and the United Kingdom are different. We areunable to completely explain these stock markets' reactions to oil price changeswithin the context of a rational asset pricing framework; oil shocks in Japanand the United Kingdom lead to changes in stock prices that appear to besubstantially greater than can be justified by the effects of these shocks onsubsequent real cash flows. Our attempts to account for changing expected

' Notable exceptions are a few recent studies that use oil prices as one of many risk factors thatmay be priced in the stock markets (see Chen, Roll, and Ross (1986), Ferson and Harvey (1993),and Hamao (1988)). The economic relevance of oil shocks is also refiected in their apparentsignificant importance in explaining the postwar negative relation between stock returns andinflation (see Hess and Lee (1994) and Kaul and Seyhun (1990)).

^ We use the term Granger-precedence in the Granger (1969) causality sense. The expressionthat oil price changes Granger-precede implies that they are not Granger-caused by other vari-ables in the system. Of course, if oil price changes are also weakly exogenous, then they will be"strongly exogenous" with respect to the variables in the system (see Engle, Hendry, and Richard(1983)),

Oil and the Stock Markets 465

returns also cannot help explain the effect of oil shocks on either stock market.Measurement errors in inflation and/or oil price variables and, more impor-tantly, in our proxies for expected real cash flows also do not appear to affectour analysis. Therefore, we conclude that in the case of Japan and the UnitedKingdom either: (a) oil price shocks impact expected stock returns in a waythat is not captured by our proxies for expected returns, or (b) these stockmarkets overreact to oil price shocks.

The remainder of this article is organized as follows. Section I contains adiscussion ofthe theoretical basis for our tests ofthe rationality of stock prices.This section also contrasts our study with numerous recent attempts to gaugethe efficiency of stock markets. Section II contains an analysis ofthe post-warexperience of the United States, Canada, Japan, and the United Kingdom.Section III contains a brief summary and conclusions.

I. Oil Shocks and the Rationality of the Stock MarketWe motivate our tests of whether stock prices react rationally, or overreact,

to changes in oil prices using the standard cash-flow/dividend valuation model.Following Campbell (1991), the log real return on a stock in period t, RS,, canbe expressed as (see also Campbell and Shiller (1988))

^ , . - ( E , - E , _ I ) S P^RS,., (1)j=0 j=l

where E, denotes the expectation formed at time t, C, is the log ofthe real cashflow in period t, and p is a parameter close to but less than one.

Equation (1) simply states that stock retums vary through time due tochanges in expected and unexpected returns. The unexpected return in periodt has two sources of variation: (a) changes in current and expected future cashflows (given by the second term on the right hand side of equation (1)), and (b)changes in expected future returns (the last term in equation (1)).

A, Oil Shocks and Stock PricesOur test ofthe rationality ofthe stock market is based on equation (1) and

uses the effects of oil shocks to gauge whether stock prices overreact to newinformation that has real consequences for the economy. We gauge whetherthe reaction of stock prices to an oil shock can be fully explained by the effectsof the latter on current and future real cash flows and/or current and futurechanges in expected returns. Specifically, we estimate a regression ofthe form:

RS, = E,_,(RS,) + (E, - E,_i) 2

(2)

+ i f ,OIU_, + 7,,


where OIL, is the percentage change in oil prices in period t, and k is somearbitrarily chosen parameter.

The basic implication ofthe rationality ofthe stock market for equation (1)is that the coefficients ofthe oil price variables, 6^s, should be jointly indistin-guishable from zero. This follows because, given equation (1), oil shocks arerelevant for changes in stock prices only to the extent that they affect currentand future real cash flows and/or expected returns. (Of course, oil shocks areclearly not the sole determinants of cash flows or returns.) Conversely, how-ever, if the stock market overreacts to oil shocks, then the joint insigniflcanceof dgS should be rejected.

It is important to note that lagged oil price variables are included in equation(2) because past oil shocks could affect current expected retums (E(_i(RSf) inequations (1) and (2)). Of course, if expected returns are constant then the flrst(and third) term of (1) and (2) would disappear and, therefore, any correlationbetween stock returns, RS,, and lagged oil price variables would be directevidence of market inefficiency. Given the growing evidence of time-variationin expected returns (see, for example, Fama and French (1989), Fama (1990),Keim and Stambaugh (1986), and Schwert (1990)), it appears natural to designour tests based on equation (2), which allows for oil shocks to affect expectedstock returns.

B. A Comparison to Previous Studies

In recent years there have been numerous studies which argue that stockprices not only reflect changes in current and future cash flows and expectedreturns, but are also determined by speculative dynamics, that is, fads, inves-tor sentiment, and/or overreaction to news. Many researchers claim that thestrong predictability of stock returns over various horizons is evidence of suchfads. In an attempt to gauge whether the predictability of stock returns isrational, several recent studies test whether imposing a "factor structure" onreturns (using Capital Asset Pricing Model (CAPM) or a more general assetpricing model like the Arbitrage Pricing Theory (APT)) can eliminate or ex-plain their predictability. If factors and/or their associated risks can explainthe predictability of stock returns then the market is rational, and vice versa(see, for example. Cutler, Poterba, and Summers (1991), Fama and French(1989), Ferson and Harvey (1991), Ferson and Korajczyk (1995), Morck, Shle-ifer, and Vishny (1990), and Sentana and Wadhwani (1991)).

For illustrative purposes, consider the basic approach adopted by Ferson andKorajczyk (1995), who estimate a regression similar to:

L k

^i> = a.o + E a^pZ^t-x + S (iijFjt + u^ (3)

where Rj, is the excess return on a security (portfolio), ^^/-i is the value ofthe predetermined variable p at time ( - 1, and F ^ is the value of factoryin month t.


If the stock market is rational (irrational) then we should be unable to reject(accept) the joint hypothesis that a, and a,^s are equal to zero in equation (3)for all assets. The problem with such an approach is that since irrationality isa valuation problem, the use of endogenous flnancial variables (or functionsthereof) to determine the rationality (or irrationality) of stock prices may notlead to convincing inferences. In particular, the predictor variables, Zpf_i,which are typically past stock returns, dividend yields, treasury bill returns,etc., are endogenous valuation variables with no (theoretically) establishedcausal real effects on the economy or the stock market. Therefore, the corre-lation(s) between these variables and stock retums, R,,, could be entirelydriven by common fads. More importantly, the factors, F,,, on the right-handside of equation (3), are also usually endogenous valuation variables (such asthe market return, the default spread, the term spread, etc.), or functionsthereof, and can therefore be subject to the same fads that potentially infectthe left-hand side (portfolio) returns in equation (3). Consequently, it mayeventually be impossible to distinguish rational from irrational stock-pricemovements using such an approach.

We attempt to circumvent some ofthe drawbacks of previous studies. First,note that we consider the impact of oil price changes, which econometricallyprecede (or Granger-cause) virtually all economic time series. These oil shockshave documented economically significant real effects on the economy and areunlikely to suffer from fads because they are dominated by a few sharpmovements induced by "exogenous" events such as wars and OPEC embargoes(see Hamilton (1983, 1985), Hess and Lee (1994), and Kaul and Seyhun(1990)).^ Unlike previous studies, therefore, we study the causal effects ofeconomically important events like oil shocks on the economy and real cashflows, and we gauge the stock market's ability to evaluate the impact of theseshocks.

To determine whether the stock market's response is rational (irrational),we adopt a two-step approach that should, at least partially, circumvent theproblems associated with earlier studies. In the first step, we abstract frompotential changes in expected returns and test whether the effect of oil shockson stock returns can be completely explained by real measures of cash flows inequation (2). The major advantage of using current and future real cash flowvariables alone is that if their inclusion in equation (2) is sufficient to neutral-ize the effects of oil shocks on stock returns (i.e., render Qg = 0 Vs), then we canconclude that the stock market is efficient. This conclusion follows because,unlike the "factors" used in most previous studies (see equation (3)), real cashflow measures are unlikely to suffer from fads. Conversely, however, if realcash flow measures are unable to "explain" the effects of oil shocks on stockreturns, we cannot conclude that the stock market is inefficient. Changes in

^ Ideally we would like to measure "real supply shocks," However, due to data availabilityconsiderations, we use oil price changes to proxy for supply shocks. Given the exogenous causes formost major oil price changes in the postwar period, it may be reasonable to presume that oil pricesare not subject to fads (or at least not the fads that potentially infect the stock market).


expected returns could also help explain the effects of oil price changes on stockprices. Therefore, our second step in explaining the effects of oil shocks onstock returns involves conditioning stock returns on these shocks, real cashflows, and expected return variables. However, a major problem with account-ing for changes in expected returns is that well-accepted proxies for them —theterm spread, the default spread, dividend yields, etc., —are all financial vari-ables that could be subject to the same fads as stock returns. Consequently, asin previous studies that impose a factor structure on asset returns, our secondstep in explaining the effects of oil shocks on stock prices suffers from prob-lems; any correlation between real stock returns and proxies of expectedreturns could be spurious and fad-driven. Nevertheless, our two-step proce-dure of separately evaluating the impacts of real cash flow variables andchanging expected returns could provide new insights into the rationality ofthe stock-valuation process.

II. The Evidence

A. Data Description

We study the experiences of four countries—the United States, Canada,Japan, and the United Kingdom—to gauge the effects of oil shocks on differenteconomies. The effects of oil shocks are likely to vary considerably acrossdifferent countries depending on their production and consumption of oilreserves. For example, ceteris paribus, net exporters (importers) of oil arelikely to benefit (suffer) from the several price hikes in the postwar period. Ananalysis ofthe experience of different countries is also important to gauge theability of various stock markets to rationally assess the impact of unpredict-able "events." Apart from studying the United States, the experiences ofCanada, Japan, and the United Kingdom should provide a wide variety ofevidence for countries in different parts ofthe globe, with presumably differentinstitutional and regulatory environments. The speciflc choice of innovationsin oil prices as the "event" is justified by the findings of Hamilton (1983, 1985),Helliwell, Sturm, Jarrett, and Salou (1986) and Rasche and Tatom (1981), whoshow that oil shocks have permanent detrimental effects on output in mostcountries.

The empirical analysis is limited to the postwar period largely because ofdata availability considerations. The sources ofthe data and a description ofthe particular variables used in our empirical analysis are presented in Ap-pendix A. Therefore, here we briefly describe only some ofthe more importantfeatures ofthe data. Since we are interested in determining the real impact ofoil prices on stock markets, we use real stock returns throughout our analysis(although we do check the sensitivity of our results to the use of nominal stockreturns). We measure the real rate of return on common stock, RS,, as thedifference between the continuously compounded return on a country's marketindex (e.g., S&P 500 for the United States) and the inflation rate calculatedusing the consumer price index. We measure oil prices using the producer price


indices for oil, which vary slightly across the countries: the index for theUnited States is for fuels and related products and power; for Canada andJapan the indices measure prices of petroleum and coal products, while theseries for the United Kingdom measures all fuel prices. To measure oil-priceshocks, we first calculate the percentage change in oil prices and then pre-whiten these series. The prewhitening is conducted to remove any serialcorrelation induced by the averaging of nonsynchronously measured compo-nents ofthe overall price index (see Working (I960)). This procedure has theadvantage of removing any spurious statistical significance of lagged oil pricevariahles in estimates of equation (2).

Our measure of aggregate cash flows is the (seasonally adjusted) index ofindustrial production (IIP). We calculate the growth rate of output (or equiv-alently the percentage change in real cash flows) as the first difference of thelogarithm of the index, and denote it by IP,. We use quarterly data on allvariables as a compromise hetween the measurement errors in monthly dataand the lack of sufficient annual observations. Finally, Granger (1969)-causal-ity tests for all countries reveal that, with the exception of the United King-dom, oil prices Granger-precede both stock retums and output. These resultsconfirm Hamilton's (1983, 1985) conclusion that the episodic volatility of oilprices in the postwar period may be regarded (at least statistically) as exoge-nous events vis a vis the rest of the world economy.*

B. Rationality ofthe Stock Market: The Case of Cash Flows

We evaluate the rationality of the stock market in two distinct steps; firstallowing for the effects of oil shocks on real cash flows alone, followed by ananalysis that also accounts for potential variations in expected returns inducedby changes in oil prices. Before testing for rationality using a regressionsimilar to equation (2), we establish two important empirical facts: (a) stockreturns in all countries are correlated with current and future changes inexpected cash flows, and (b) oil shocks have a signiflcant impact on each ofthefour stock markets under consideration. Specifically, we estimate the followingtwo regressions:

s=0

and

(5)

'' Detailed evidence on the causality tests can be obtained from the authors.

470 The Journal ofFinanee

To test for the significance of the relations in equations (4) and (5), weconduct two sets of tests on the slope coefficient of each regression: an F-test ofwhether the sum ofthe slope coefficients is zero, and an F-test for the hypoth-esis that each of the slope coeflicients is zero. The first test, therefore, testswhether the net effect of a variable is statistically significant, while the secondone tests for the significance ofthe effects of individual independent variables.Under the assumption that the independent variables are mutually uncorre-lated, the two tests should provide identical inferences unless the signs of thecoefficients are not the same. We also report the (adjusted) R^ ofthe regres-sions as a measure ofthe overall strength ofthe various relations. Finally, duelargely to sample size considerations, we use four leads and/or lags in estimat-ing regressions (4) and (5).

It is important to note that in equation (4), we use actual future realizationsof industrial production, rather than expected values as dictated by theory (seeequation (2)). In Appendix B we show that the ordinary least squares (OLS)estimator ofthe coefficient ofthe actual future growth rate of production willbe inconsistent and biased toward zero, and the R'^ of a regression usingrealized future growth rates will provide a lower bound on the "true" explan-atory power of the independent variables. More importantly, measurementerrors in the cash flow variables also have implications for our tests of therationality ofthe stock market (see discussion below).

The estimates of regression (4) are reported in Table I.' The evidence showsthat stock returns have a strong positive relation with current and future cashflows in all four countries. Both the null hypotheses for the cash-flow coeffi-cients, that is, E*=o/5is ^ 0 and ^^^ = 0 Vs, are strongly rejected; bothF-statistics have p-values equal to zero in most cases, with the highest p-valuebeing 0.005. The ^^'s of the regressions range between 10 percent and 18percent. These results are particularly noteworthy because the use of actual(versus expected) cash flows leads to bias toward zero in the coefficients and anattenuation in the R^s of estimates of regression (4).^

Table II contains estimates of regression (5) that measure the effects, if any,of oil shocks on stock returns. The only difference in the formats of Tables I andII is that we report more hypothesis tests conducted on the regression coeffi-cients in the latter. We report two sets of F-statistics for tests of both the

•''All reported 7^-statistics have not been corrected for heteroskedasticity since White's (1980)specification tests could not reject the null hypotheses of homoskedasticity for virtually all theestimated regressions. We nevertheless also calculate heteroskedasticity-adjusted x^ statistics forthe significance ofthe slope coefficients of all regressions ((4) and (5) and (6)). These tests do notsignificantly alter our inferences.

''Previous researchers find that future output explains much larger proportions (up to 60percent] of retum variations of longer (one year} returns compared to shorter (monthly, quarterly)returns (see, for example, Fama (1981,1990), Kaul (1987), and Schwert (1990)). The same patternis revealed by the R s of equation (4) when estimated over different horizons. This differenceprobably occurs because information about cash flows is spread over many periods and henceaffects stock returns of many previous periods (see Fama (1990)). Consequently, quarterly cashflow variables contain more "noise" lin a relative sense) than do corresponding annual variables.


Table I

Regression Analysis of the Relation Between Real Stock Returnsand Real Cash Flows Using Quarterly Data for the United States,

Canada, Japan, and the United KingdomThis table contains estimates of regression (4):

R S , -

where RS, = real stock retum in quarter t measured as the difference between the continuouslycompounded nominal stock return, S,, calculated from a country's stock market index and theinflation rate, I,, computed as the logarithmic difference in the consumer price index (CPI); andIP, = growth rate of industrial production in quarter t calculated as the logarithmic difference inthe (seasonally adjusted) index of industrial production. The hypotheses tests, H^ and Hy, areconducted using standard F-statistics; the p-values of these statistics are reported in parentheses.

Country a^ 2,*=oPia ^^ H,: 2 J ^ )3,» = 0 H,: 8,. = 0 Vs

United States -0.008 1.835 0.174(1947-1991)Canada -0.016 1.853 0.174(1960-1991)Japan: -0.008 2.618 0.180(1970-1991)United Kingdom: -0.013 3.730 0.104(1962-1991)

21.651(0.000)12.588(0.001)14.618(0.000)13.925(0.000)

8.158(0.000)5.961

(0.000)4.476

(0.001)3.585

(0,005)

summed and individual coefficients. The first set of tests for each basic hy-pothesis (Hi and H3) include all current and lagged coefficients. To distinguishthe current versus lagged effects of oil shocks on stock returns, we also reportF-tests (see H2 and H4) which consider only the lagged coefficients. Theseparation of the lagged from the contemporaneous oil effects helps us deter-mine the relative importance of these two effects on stock returns and conse-quently also provides some idea ofthe effects of oil shocks on current expectedversus unexpected returns (see equations (1) and (2)).

The evidence in Table II shows that oil price hikes in the postwar periodhave had a significant, and (on average) detrimental effect on the stock marketof each country. Unlike the stock return-cash flow relation, and presumablydue to varying dependence of the countries on oil, there is a substantialdifference in the extent of detrimental effects of oil on the different stockmarkets. For example, the negative impact of oil-price hikes is most dramaticin the case of Japan. The p-values for all F-tests are less than 0.004, and theR^ is over 25 percent! In contrast, the relation between oil shocks and stockreturns is much weaker for Canada, with only the sum of the d^^s beingsignificantly different from zero at conventional significance levels and a lowR^ (about 3 percent).

The results for both the United States and the United Kingdom, althoughnot as extreme as Japan or Canada, show the substantial negative impact of oil


Table II

Regression Analysis of the Effects of Oil Shocks on Real StockRetums Using Quarterly Data for the United States, Canada, Japan,

and the United KingdomThis table contains estimates of regression (5):

RS, - 0 2 + 2 fli.OIL,-,. +

where RS, = real stock return in quarter ( measured as the difference between the continuouslycompounded nominal stock return. S , calculated from a country's stock market index and theinflation rate, I,, computed as the logarithmic difference in the consumer price index (CPI); andOIL, = prewhitened percentage change in the oil price in quarter t computed as the logarithmicdifference in the producer price indices for fuels and related products and power for the UnitedStates, for petroleum and coal products for Canada and Japan, and for fuel for the UnitedKingdom. All hypotheses tests, Hj through H4, are conducted using standard F-statistics; thep-values of these statistics are reported in parentheses.

Country

United States(1947-1991)Canada(1960-1991)Japan(1970-1991)United Kingdom(1962-1991)

" 2

0.008

0.002

0.019

0.003

^ 4 a

-1.009

-0.992

-1.531

-1,107

R^

0.069

0.028

0,260

0,122

S^-o ei«=o

12.323(0.001)6.911

(0.009)17,475(0.000)5.366

(0.023)

7.732(0.006)6.434

(0,013)8.985

(0.004)0.327

(0,569)

9,,. = 0 Vs fi

3.529(0.005)1,672

(0.147)6.563

(0.000)4.071

10.002)

11, - 0 Vs > 0

2.905(0.023)1.904

(0.115)6.352

(0.000)0.948

(0.439)

shoeks on stock retums. Finally, with the exception ofthe United Kingdom,stock returns of each country are negatively affected by both current andlagged oil price variables. In regressions of current stock returns on lagged oilprice variables alone, we also find that the latter have a statistically significanteffect on the former, again with the sole exception ofthe United Kingdom. Wedo not report estimates of these regressions; they provide identical inferencesto the ones based on estimates in Tahle II heeause changes in oil prices areprewhitened."^ It is important to emphasize that, to the extent that all maero-economic variables (including oil prices) contain measurement errors, the"true" effects of oil shocks on stock returns are likely to he even stronger.Specifically, the arguments in Appendix B for the attenuation of the R^s ofregression (4) because of (ohvious) measurement errors in real cash flowvariables also applies to estimates of regression (5) if oil prices are alsomeasured with error.

' Although we do not report the results for hrevity, we also find that oil shocks have had asignificant negative impact on the current and future cash flows of each ofthe four countries in thepostwar period.


The evidence of statistically significant lagged effects of oil prices on stockreturns suggests that either (a) oil shocks induce some variation in expectedstock retums, or (b) the stock markets are inefficient. One intriguing aspect ofthe results for all countries, except the United Kingdom, is that the magni-tudes of the effects of oil price changes at lags 2 and 3 (and even at lag 4 forCanada) are usually larger than the effect of contemporaneous oil pricechanges on stock returns.^ At first glance, this may suggest that the stockmarkets are inefficient hecause the current oil price variable should have alarger effect than past oil price variables on current stock returns. From (1)note that in an efficient market past oil shocks can only affect the currentexpected return component, E^.^CS,), of returns, while the contemporaneousoil shock affects all future expected stock returns, (E,-E(_i) X7=i p^^RS^^j.This line of reasoning, however, may be misleading because the estimatedcoefficient of the contemporaneous oil price variable in equation (5), âo.reflects not only the effects ofthe current oil shock on all future expected stockreturns but also the (conceivably opposite) effects of the shock on all futurechanges in real cash flows. In fact, there is some evidence to suggest that pastoil prices proxy for expected returns in the United States and Canada (seeSection II.C and footnote 9 for details).

However, given the nontrivial nature ofthe effects of current versus laggedoil price changes on stock returns, without a more explicit model for stockreturns {both expected and unexpected) we cannot determine whether theestimates of equation (5) in Table II conclusively imply that the stock marketsare efficient, or vice versa. Since developing such a model is beyond the scopeof this paper, we study the combined effects of oil price changes (past andcurrent) on stock returns and test whether this effect can be rendered insig-nificant by conditioning stock returns on real cash-flow and/or expected returnvariables.

To directly gauge whether the significant negative effects of oil shocks onreal cash flows are correctly evaluated by the stock market, we estimate anappropriately parameterized version of model (3), which we rewrite as:

RS, = Q3 + X e2,0IL,_, + S )32jPr.,s + V3f (6)s=0 s=0

If the stock market rationally reflects the effects of oil shocks on current andanticipated future cash flows, then the slope coefficients of the oil price vari-ables in equation (6), flgsS, should be jointly indistinguishable from zero usingboth the F-tests proposed earlier. Also, comparisons ofthe estimates of (6) withestimates of equations (4) and (5) result in some interesting inferences. The

^ Tbe estimated coefficients of tbe contemporaneous oil price variable, ffô. a"cl the four laggedoil price variables, flî to 824, in (5) are: -0,272, -0,063, -0,343, -0.362, and 0,031 (for the UnitedStates); -0,089, -0.223, -0,064, -0,373, and -0.244 (for Canada); -0.555, 0,065, -0.261,-0.838, and 0.057 (for Japan); and -0.124, 0.059, -0,020, -0.117, and -0.092 (for tbe UnitedKingdom).


difference between the ^^s of regressions (6) and (4) provides an economicmeasure ofthe extent of overreaction (or irrational response) of stock prices tooil shocks conditional on expected returns being constant. Similarly, a com-parison ofthe 0^ coefficients in equations (5) and (6) reveals the extent to whichcurrent and future cash flows neutralize the effects of oil shocks on stockreturns.

Measurement errors entailed in the use of actual versus expected real cashflows in equation (6), however, could lead to problems in interpreting theregression estimates. In Appendix B we show that if current and/or lagged oilshocks are correlated with "true" expected cash flows, measurement errors inactual cash flows will (a) bias the coefficients of oil price changes away fromzero; and (b) spuriously accentuate the difference between the R^s of regres-sions (6) and (4). Consequently, measurement errors in real cash flows used inequation (6) may lead to a rejection ofthe null hypothesis of market efficiencyeven when the market is efficient. If, therefore, we find that inclusion of actualfuture cash flows in equation_(6) renders the oil effects insignificant, and thereis no difference between the R^s of equations (4) and (6), we can conclude thatthe stock market rationally evaluates the impact of oil shocks. Conversely, ifthe oil effects remain significant in equation (6) and there is a substantialdifference between the R^s of regressions (4) and (6), then the market may ormay not be efficient depending upon the extent of measurement errors in cashflows and/or the extent to which oil shocks affect expected returns. Therefore,in Section III.A we conduct an investigation ofthe potential effects of mea-surement errors on our tests.^

Estimates of regression (6) are reported in Table III. The evidence for theUnited States and Canada provides support for the hypothesis that the stockmarkets of both these countries correctly assess the impact of oil shocks. First,note that all F-tests conducted on the oil price coefficients, the &2sS in equation(6), cannot reject the hypothesis that these coefficients individually or collec-tively, whether lagged or contemporaneous, are indistinguishable from zero.The lowest p-value for all the hypotheses tests is 0.123 for the United Statesand 0.427 for Canada. Second, the estimate of 2 1 o 2s in regression (6) is lessthan half (one-third) its magnitude in regression (5) for the United States(Canada). On the other hand, the estimated effects ofthe cash flow variablesare only marginally altered by the inclusion of oil price variables, and for boththe United States and Canada these effects remain strongly significant (see H5and Hg). Finally, the R^s of regressions (6) and (4) are virtually identical for theUnited States—17.7 percent versus 17.4 percent—and for Canada the R^ ofregression (6) is actually slightly less than the R^ of regression (4).

The experiences of Japan and the United Kingdom, however, provide a sharpcontrast to the United States and Canadian results. Perhaps the most star-tling evidence is for Japan over the 1970-1991 period. Both Hj: 2s=o 2s = 0and H3: 82s = 0 Vs in equation (6) are rejected at conventional levels of

^ In Appendix B we show that if oil prices also contain measurement errors, then the effects oferrors in real cash flows on our analysis will actually be mitigated.


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significance, potentially implying that the stock market does not rationallyreact to oil shocks. And the hypothesis tests conducted only on lagged values ofthe oil variable, Hg and H4, have p-values of 0.072 and 0.002. Also note thatSs=o 2.- in (6) is -1.042, which remains large relative to 2 s .o ls = -1.531 inequation (5). Even conditional on future cash flows, therefore, a one percentincrease in oil prices leads to a one percent decrease in real stock returns. Onthe other hand, there is a significant decrease in the effect of future cash flowvariables in (6) compared to (4); 2^ =0 ^2, = 1.719 in equation (6) compared to2s=o ^1.. = 2.618 in equation (4), although these effects remain statisticallysignificant (see H5 and Hg). The ohvious inability of real cash-flow measures toexplain the effects of oil shocks on the Japanese stock market is best reflectedin the substantial increase in the R"^ of (6) relative to (4); the increase from 18to 33 percent is over 80 percent!

The estimate of regression (6) for the United Kingdom also shows that theeffects of oil shocks on stock returns are not completely accounted for by thereal cash flow variables. The sum ofthe ggS in equation (6) remains relativelylarge in absolute magnitude (-0.606 versus -1.107 in regression (5)), al-though (unlike Japan) there is only a contemporaneous effect of oil shocks onstock returns. Similar to the Japanese experience, however, the increase in theR^ of (6) relative to (4) is also over 80 percent. Therefore, the experiences ofJapan and the United Kingdom suggest that the volatility in postwar stockprices generated by oil shocks cannot be explained by the impact of theseshocks on real cash flows. And this conclusion appears to be robust to mea-surement errors in oil prices and real cash-flow variables (see Section III.A).

C. Rationality ofthe Stock Markets: Variations in Cash Flows andExpected Returns

The preceding empirical analysis has been conducted without accounting forany changes in expected returns induced by oil price changes. Given thegrowing evidence of time-varying expected returns (see, for example, Famaand French (1989), Fama (1990), Keim and Stambaugh (1986), and Schwert(1990)), we need to account for the potential effects of oil shocks on expectedreturns. However, a major problem with accounting for changes in expectedreturns is that well-accepted proxies for expected returns—the term spread,the default spread, dividend yields, etc., —are themselves financial variables.Therefore, any correlation between real stock returns and proxies of expectedreturns could be spurious and fad-driven. This problem is unlikely to be ofsignificance for the United States and Canada, because in these countries theinclusion of future cash flow variables is sufficient to eliminate the effects of oilshocks on stock returns, in spite of measurement errors in the cash flowvariables. Also, Fama (1990) shows that current and future growth rates ofreal output subsume most ofthe information contained in the expected returnvariables (see also Schwert (1990)). Since real output is unlikely to be subjectto fads, any correlation between ex ante expected retums (and shocks to

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The case of Japan and the United Kingdom, however, is more complicated.Our evidence for both countries shows that the response of stock prices to oilshocks cannot be justified by current and future real cash flows. If conditioningon ex ante expected returns and changes in expected returns eliminates theeffects of oil shocks, it may not imply that these stock markets are efficient; thecorrelation between proxies of expected returns and stock returns may bepartly or entirely fad-induced. If, however, in spite of the inclusion of theseproxies the effects of oil shocks on stock returns remain significant, the evi-dence would be consistent with market overreaction, although changes inequilibrium expected returns not captured by our proxies and/or measurementerrors in real cash flows cannot be completely ruled out as sources of any"excess" volatility generated by oil shocks.

In order to gauge the role of changing expected returns, we estimate thefollowing regression for all four countries:

+ ^4,, (7)

where X,, are well-accepted proxies for expected returns and shocks to expectedreturns (see, for example, Fama (1990) and Schwert (1990)), that is, X , =DYf_i = dividend yield measured at time t - 1, the average of monthlydividend yields on the country's market index for the past twelve months,X21 = DEF, 1 = default spread measured at time ^ - 1, the difference betweenthe annual yield on a portfolio of corporate bonds (CBY, 1) and the yield on aportfolio of long-term govemment bonds (GBY,_i), X3, = TERM^.i = termspread measured at time t - \, the difference between the annual yield on aportfolio of long-term government bonds (GBY^.i) and the yield on a short-term Treasury bill (TBY,_j), X4, = SDEF, = shocks to the default spread attime t, the residual from a first order autoregressive model for DEF,, andXs, =STERM, = shock to the term spread at time t, the residual from a first orderautoregressive model for TERM,. The data are obtained from the Citihasedatabase for the United States, and from Financial Statistics (an OECDpublication) for the other countries (see Appendix A for details).

Before analyzing the estimates of equation (7), we briefly discuss the rela-tions between stock returns and the expected return variables, X,,. Estimatesof the regressions of RS, on X,, alone (not reported) show strong evidence oftime variation in expected returns in all countries. The ^^s of these regressionsrange between three and 16 percent. The F-statistics for the joint significanceof the a,s have p-values of less than 0.01 for all countries except the UnitedKingdom. In spite of the strong relation between the X s and real stockreturns, however, the information in these proxies for expected returns istypically subsumed by the real cash flow variables (IPs) for all countries, withthe sole exception of Japan. This evidence is similar to the findings of Fama


(1990) and is consistent with the production-hased asset pricing model ofCochrane (1990) in which expected returns depend on expected output growthand unexpected retums are dependent on unexpected output growth.

Estimates of regression (7) are reported in Table IV. The format of this tableis similar to Table III; the only difference between the estimates reported inthe two tables is the inclusion of expected return variables, X ,, in the latterregressions. Since we are only interested in the combined importance of theX,,s, we do not report the d, coefficients (see equation (7)) but instead report ani^-statistic that evaluates their joint significance. Finally, the numbers inparentheses in the R^ column are the R^s of regressions (not reported) thatproject stock retums on the expected return, X ,, and the real cash flow, /P,,variables alone. The differences in the two sets of .R s provide a measure oftheextent of overreaction, once stock retums are conditioned on real cash flow andexpected retum variables.

The results in Table IV show that'the effects of oil shocks are eliminated bythe inclusion ofthe real cash flow and expected return variables for the UnitedStates and Canada, which is not surprising given that current and future cashflows alone are sufficient to account for the effects of oil shocks in bothcountries.^" The results for Japan and the United Kingdom, however, remainpuzzling. Conditioning onX^^s does eliminate the significance ofthe combinedeffect of all oil variables for Japan (see H2 and H3); but the hypotheses tests onthe individual coefficients of the oil variables, whether contemporaneous orlagged, continue to have low p-values. The p-values for H4 and H5 are 0.058and 0.032. The continued significance of oil shocks is also reflected in thedifference in R'^s of 0.361 versus 0.303; that is, the oil variables add nontrivialexplanatory power to regressions of stock returns on both cash flow andexpected return variables. The Japanese evidence is therefore consistent withthe findings of French and Poterba (1991) who are unable to isolate eitherchanges in required returns or growth expectations that are large enough toexplain recent Japanese stock price movements. The experience ofthe UnitedKingdom is even more perplexing than the case of Japan. Inclusion of theexpected return variables has virtually no effect on the significance of the(contemporaneous) oil variable, and the difference in ^^s of 0.236 versus 0.151remains large.

Clearly, measurement errors in future cash flow variables could explain theapparent "excess" volatility generated by the postwar oil shocks in the UnitedKingdom and Japan. However, attempts to account for the effects of measure-ment errors (see discussion in Section 111.B) again have virtually no impact onthe results reported in Table IV.

'" However, there is evidence that oil shocks affect expected retums on stocks. For example, themere inclusion ofthe expected return variahles (that is, without the cash flow variahles in (71),eliminates the individual and combined effects of the lagged oil price variables in the UnitedStates and Canada.


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III. Additional Issues

Our results show that the effects of oil shocks on the U.S. and Canadianstock markets can be eonipletely explained by their effects on contemporane-ous and future real cash flows. In the ease of Japan and the United Kingdom,however, real cash flows and expected return proxies cannot explain thedetrimental effects of oil shocks on their respective stock markets. In thissection, we address some potential biases that may be present in our empiricalanalyses.

A. The Impact of Measurement Errors

Measurement errors plague virtually any empirical analysis. However, theuse of macroeconomic data, and particularly the use of actual versus expectedfuture real cash flows, makes our inferences particularly vulnerable to sucherrors.

A.I. Measurement Errors in Inflation

From an eeonomie perspective, it is obvious that the real impaet of oil shockson stock markets should be gauged by regressing real stock retums on proxiesfor oil shocks. Consequently, in our entire empirieal analysis we use real stockreturns, RS(, measured as the difference between nominal stock returns andthe inflation rate, that is RS^ = S^- I^ (see Appendix A and Section II. A). Notethat random measurement errors in our measures of inflation (first differencesin the logarithm of the consumer price index) should cause no biases in theregression estimates because RS, is the dependent variable in all our tests.However, since oil price shocks are also measured using nominal price series,some potential biases may be induced in estimates of the regression coeffi-cients of oil price variahles in equations (4), (6), and (7).

To determine the potential implications ofthe use of real stock returns in ouranalysis, we reestimate all the regressions and conduct all hypotheses testsusing nominal stock returns, S,. For brevity, we do not report the results,whieh are qualitatively similar to those reported in the paper. For all thecountries, use of nominal stock returns attenuates the measured effects of oilshoeks on the stock markets, but it also attenuates the statistical relationbetween stock returns and real cash flows. Consequently, it is not surprisingthat our main inferences remain quahtatively unchanged. Most importantly,our puzzling inability to explain the strong negative effects of oil shocks on theJapanese and the U.K. stoek markets has virtually no relation to the use of realstock returns in the empirical analysis.

A.2. Measurement Errors in Oil Prices

Since oil prices used in this study are producer price indices, the constituentprices of which are sampled, they may contain measurement errors. However,if these measurement errors exhibit classical properties (that is, are randomand uncorrelated with the other variables used in the analysis), the measured


effects of oil shoeks in regression estimates of equation (5) will actually un-derestimate the true effects of these shocks on stock returns (see Appendix B).Hence, the strong negative impact of oil shocks on the Japanese and the U.K.stoek markets shown in Table II, which we are unable to explain using realcash flows and expected returns, actually underestimate the true effects ofthese shocks on the two stock markets.

We explicitly attempt to deal with one particular effect of measurementerrors on the oil price indices. Working (I960} shows that the average ofnonsynehronously sampled components of an index can lead to serial correla-tion in the first differences of the index. Consequently, our entire analysis isbased on prewhitened first differences of the (logarithm) of oil price indices,where the prewhitening is accomplished by fitting parsimonious time-seriesmodels to the first differences and using the residuals from these empiricalmodels as the proxies for oil shocks.

A.3. Measurement Error in Cash Flows

In Appendix B we show that measurement errors in future cash flow vari-ables will bias the eoefEieient(s) of real cash flows in regression (4) toward zero.More importantly, however, these errors will affect our main inferences aboutthe rationality of stock markets that are based on regression (6). Specifically,we show that coefficients of oil, 02s, i ^ estimates of (6) will be biased away fromzero, and the difference between the R'^s of regressions (6) and (4) will bemagnified, even under the null hypothesis that 62^ = 0 Vs. The same effectswill be observed for the estimated coefficients of oil shocks and the .R s ofregression (7). Therefore, measurement errors could he the cause of our inabil-ity to explain the effects of oil shocks on the stock markets of Japan and theUnited Kingdom. However, in Appendix B we also show that if both real eashflows and oil prices contain measurement errors, then the effects of measurementerrors in real eash flows on our analysis will be mitigated. Nevertheless, since ourreal eash flow measures surely contain measurement errors (because we useactual versus expected variables), we concentrate on the biases caused by them.

To evaluate the potential impact of measurement errors in real cash flows onestimates of equations (6) and (7), we first use the innovative approach of Kothariand Shanken (1992) to purge these regressions ofthe effects of measurementerrors. Specifically, we estimate the following augmented versions of (6) and (7):

, + 2 (^2siPt.s + 2 r2.RS,+, + TJ3,, {6a)s=0 s=0 s=l

and

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Note that future realized stock returns are included as additional regressorsin (6a) and (7a) because they are proxies for the measurement errors in thefuture realized cash flow variables used in (6) and (7). In an efficient market,information about future real cash flows is revealed after time t, and shouldtherefore be reflected in stoek prices after the time interval {t - 1, t} (see alsoequation (4)). Thus retums over the future four quarters are chosen as proxiesfor the measurement errors in the realized future cash flow variahles used inequations (6) and (7). In each case, a single augmented regression ofthe form(6a) or (7a) is used because a two-stage procedure of regressing real cash flows(IPs) on real stock returns (to purge the measurement errors) and then usingthe estimated residuals in equations (6) or (7) would lead to biased estimatesofthe eoefficients of real cash flows and potentially misleading standard errors(see Kothari and Shanken (1992)).

For brevity, we do not report the detailed estimates of regressions (6a) and(7a). Our results for the United States and Canada show that estimates of 62sin (6a) and 6^ in (7a), individually and jointly, are again indistinguishable fromzero. This is not surprising, because even without any corrections for measure-ment errors, the effects of oil shocks are insignificant in estimates of equations(6) and (7). The surprising and important evidence, however, is that theinferences for the United Kingdom and Japan based on equations (6a) and (7a)also remain largely unaltered. For both countries, the 62^^. and 8,s remain,either individually and/or jointly, significantly different from zero. Also, thedifferences in the R^s of regressions (6a) and (4) are quite similar to thedifferences inR^s of regressions (6) and (4) in Table III, as are the differencesin the R^s in the R^ column of Table IV constructed based on estimates of (7a).

To confirm the robustness of our results based on equation (6a), we alsocalculate the extent of measurement error(s) in realized cash flows (i.e., IPs)needed to explain the apparent "exeess" volatility in the Japanese and the U.K.stoek markets (see appendix for details). Based on annual estimates of equa-tions (4) and (6), we show that the extent of noise to variation in "true"expected real eash flows would have to be to the order of 1.38 and 1.22 forJapan and the United Kingdom. Therefore, between 55 and 60 percent ofthevariation in realized real cash flows would have to be "unexpected." Theseestimates appear to be quite high, especially given the estimates of regression(6a) and (7a) and the fact that annual stock returns alone can predict largeproportions ofthe variation in future annual real eash flow variables (see, forexample, Fama (1990)). Finally, note that measurement errors in real eashflow variables may not play an important role in our analysis because currentand lagged oil price variables already have a significant impaet on currentstock returns without the inclusion of these variables (see estimates of equa-tion (5) in Table II).

Our results therefore suggest that measurement errors alone cannot explainthe apparent "exeess" volatility in stock returns in the United Kingdom andJapan, at least in tests that condition stock returns on oil shocks and real cashflow variables alone.


B. Sensitivity to Subperiod Analysis

Due to data availability considerations, the sample periods for the fourdifferent countries analyzed in this study cover substantially different timeperiods. The U.S. sample covers the entire postwar period, while Japan coversonly the post-1970 period and the Canadian and the U.K. samples include thepost-1960 period.

To uneover the sensitivity of our inferences to the use of different periods, weestimate all regressions for all countries for the same 1970-1991 period. Weestimate all regressions separately for each eountry, and we also estimate allof them jointly using a Seemingly Unrelated Regression model (see Zeilner(1962)). The results are qualitatively similar to those reported in the paper. Wedo not further subdivide our sample because this would lead to statisticallyunreliable evidence sinee the 1970-1991 quarterly data already contain lessthan 100 ohservations.

IV. Conclusion

In this article, we show that changes in oil priees that Granger-precede mosteconomic series have a detrimental effeet on output and real stock retums inthe United States, Canada, Japan, and the United Kingdom during the post-war period. More importantly, the Granger-precedence of oil prices and the useof real eash flow variables provides a natural opportunity to test whether theworld's stock markets are rational or they overreact to new information. Theevidence suggests that the U.S. and Canadian stock markets are rational: thereaction of stock prices to oil shocks can be completely accounted for by theirimpact on current and expected future real cash flows alone. In contrast,however, the evidence for Japan and the United Kingdom is puzzling. In bothcountries, we are unable to explain the effects of oil price shocks on stockreturns using changes in future cash flows and/or finaneial variables that areoften used to proxy for changes in expected retums. These results appear to berobust to measurement errors in oil priees, inflation, and real cash flowvariables used in this study. We also find it difficult to envision a rationalmodel in which oil shocks change expected returns in a way that is unrelatedto future cash flows, as well as default spreads, term premia, and otherexpected return variables used in our study. Consequently, we conclude thatthe postwar oil shoeks appear to have generated volatility in the Japanese andU.K. stock markets that is in "excess" of what can be explained by existingrational models.

Appendix A

Data Sources and Description

This appendix contains a detailed description ofthe various sources of dataused in this study. We also describe the specific transformations conducted onthe raw data to obtain the variahles used in the empirieal analysis.


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Appendix B

Econometric Consequences of Errors in Variables

In this appendix we discuss the econometric consequences of using aciua/, inlieu of expected, changes in future cash flows in our regressions. For conve-nience, assume that all variables have zero means, and let y = current realstock returns, x = expected change in future cash flows, and z - currentchange in oil prices, where x = yz + T} (i.e., expected change in future cashflows ispartly determined by the current change in oil prices). Though oil pricechanges are assumed to be measured without error, expected future cash flows(x) are unobservable and are proxied by actual changes, X - x + u, where u =unexpected component of future cash flows given all current information. Theuse of actual versus future cash flows in our regressions not only biases theOLS coefficient estimator of expected cash flows, but it also biases the coeffi-cient estimator of oil price changes in the multiple regression (6) and thedifference in the ff^s of regressions (4) and (6), which is our measure of theextent of excess volatility generated by oil shocks.

To simplify our econometric analysis, we do not use multiple leads and lagsof variables as in (4)-(6). Instead we assume that x measures all futureexpected cash flows, and z contains all information about oil price changesrelevant to current changes in stock prices. Speciflcally, let us suppose that the"true" relation between stock returns and expected changes in cash flows isgiven by

y = fix + s (Bl)

Since x is unobservable, in (Bl) we replace x by X = x + u, i.e.,

y = ^X + e = ^{x + u) + e. (B2)

Under the assumption that expected stock returns are constant throughtime, Cov(e, u) = 0 and the OLS ^ suffers from the well-known errors invariables bias toward zero (see Greene (1993)):

plim(/3)1 +

It can also be shown that the R^ of regression (B2) will be downward biased. Asin the case of the bias in ^, the downward bias in the R^ depends on the ratioo^/o^. Also, it is important to note that this "errors in variables" analysisapplies to any simple regression in which the regressor is measured with error.Specifically, if oil prices are measured with error, then in equation (5) theestimated effects of oil shocks on stock returns will be attenuated, and the R^of this univariate regression will also be downward biased.


Now consider the simplified version ofthe regression of real stock returns onactual future changes in cash flows and current changes in oil prices, under theassumption that oil prices are measured without errors (see equation (6)):

y = eoz + dy(x + u) + h. (B3)

It can be shown for this special case that, given x = yz + T),

and

plim(0i) = 2/ 2- (B5)

From equation (B5) it is clear that the OLS estimator of the coefficient ofchanges in future cash flows in the multiple regression (B3) is also biasedtoward zero as in the simple regression (B2). However, the bias in Q-^ will belarger than the bias in ^j unless 7 = 0 (i.e., unless x and z are orthogonal).More importantly, however, (B4) implies that even under the null hypothesisof BQ = 0, the OLS estimator BQ will be biased away from zero. (Note that if thestock market is efficient the true coefficient of oil price changes in (B3) or (6)will be zero.) Again, the strength of the bias will depend on the relationbetween the true expected changes in future cash flows, x, and current changesin oil prices, z. In our case, 7 < 0, therefore 6Q will be negative, and its absolutevalue will be larger the more the noise in measured X (i.e., the larger is o^)and/or the stronger the relation between x and y (i.e., the smaller is o^). Notethat this analysis applies to current and lagged oil price variables as long asthe oil variable is correlated with the future output variable(s).

Also, the difference in R'^s between regressions (B2) and (B3) will be positive.Using plim(^), and rearranging (Bl) and (B2), we can write the variances ofthe disturbances of regressions (B2) and (B3) as:

and

Var(e) = Varfa) + /3'

Var(h) = Var(e) +

(B6)

(B7)

Since of > CT^, Var(e) > Var(h), and thus adding the additional variable zdoes increase the R of regression (B3) relative to regression (B2). Note thatthis occurs even under the null hypothesis that oil price changes do not affectstock returns once the latter are conditioned on expected changes in futurecash flows X. Hence, since x is measured with error, we will tend to falselyreject the null hypothesis of an efficient stock market because plim(0o) "^ 0 andthe R^ of regression (B3) is greater than the R"^ of regression (B2). A similar


econometric analysis applies to regression (7) under the assumption that bothoil prices and expected return proxies are measured without error.

However, if oil price shocks are also measured with error, the biases notedabove will be attenuated. Specifically, suppose that oil price changes aremeasured with error u, so that we observe Z = z + v. Then the estimatedregression of stock returns on oil shocks and real cash flows becomes

y = Boiz + v) + e^ix + u) + h. (B8)

where the measurement error v has variance of, and is independent of all othervariables. The measurement error v is simply an additional source of noise inregression (B3), in which only cash flows are measured with error. A conse-quence of this additional "noise" is that the coefficient of the mismeasuredvariable is driven toward zero in the usual way. That is,

1 - (TKCT'^ + CTI)

p l i m ( 0 o ) = ^ p l i m ( e o ) , k ^ l + - ^ , - 2 , 2 v ( B 9 )

More importantly, the bias in the estimator of 0, in equation (B5) is similarlymitigated:

yo-f.plim(ei) = plim{e,) + plimieo),, 2 ^ 2v

K[O--f- (T)

Thus, additional measurement error in oil shocks partially reverses the effectsof errors in measuring expected cash flows. To the extent that oil prices aremeasured with error, measurement errors become a less likely source for thesignificance of oil shocks in regression (6).

Potential Importance of Measurement Errors for Japan and theUnited Kingdom

Note that the difference in the R'^s of (B2) and (B3) is a function of unknownparameters j3, of, o^, and o^. This difference will be zero under the nullhypothesis of no overreaction if (a) there is no measurement error in X, i.e.,o = 0, and/or (b) if J: and z are orthogonal, i.e., 0 ^ cr . Our evidence clearlysuggests that neither of these two conditions is met, and therefore the extentof the upward bias in the difference in R^s remains an empirical issue. Al-though we do not know each of the unknown parameters (3, of, o^, and rr?,, wecan use the OLS point estimates of p, a , dj- (i.e., of + af^), and of to calculatethe degree of measurement error in expected versus actual cash flow changes(i.e., d^) that could "explain" the observed differences in R^s of regressions (4)and (6).

In order to be consistent with the above econometric analysis, and given thatwe use four quarters of lead and/or lag variables in equations (4) and (6), weuse annual estimates of (B2) and (B3) to calculate the o^s that would berequired to explain the large differences in R% observed for Japan and the


United Kingdom. We find that the extent of noise in actual cash flows relativeto the "true" value of expected cash flows, that is, afjo^, has to be very large toexplain the differences in observed R'^s for both Japan and the United King-dom. Specifically, ofja^ for Japan and the United Kingdom are 1.38 and 1.22,respectively, implying that the variance of the noise in actual future cash flowsis substantially greater than the variance of expected cash flows. These esti-mates suggest that the extent of excess volatility generated by oil shocks inJapan and the United Kingdom is unlikely to be spuriously driven by statis-tical biases induced by measurement errors (see Section U1.B).

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