stock prices and inflation

The Journal of Financial Research. Vol. XXIV, NO.4. Pages 587-602. Winter 2001

STOCK PRICES AND INFLATION

Ali Anari and James KolariTexas A&M University

Abstract

Numerous empirical studies establish that inflation has a negative shortrun effect on stock returns but few studies report a positive, long-run Fisher effectfor stock returns. Using stock price and goods price data from six industrialcountries, we show that long-run Fisher elasticities ofstock prices with respect togoods prices exceed unity and range from 1.04 to 1.65, which tends to support theFisher effect. We also find that the time path of the response of stock prices to ashock in goods prices exhibits an initial negative response, which turns positiveover longer horizons. These results help reconcile previous short-run and long-runempirical evidence on stock returns and inflation. Also, they reveal that stockprices have a long memory with respect to inflation shocks, such that investorsshould expect stocks to be a good inflation hedge over a long holding period.

JEL Classification: G12

I. Introduction

The ability ofstock prices to maintain their purchasing power as a long-runhedge against inflation' is the subject of extensive research in empirical finance.Fisher's (1930) proposition states that the expected rate of return is composed of a

Financial support is gratefully acknowledged from both the Center for International Business Studiesand the Real Estate Center in the Lowry Mays Graduate School of Business at Texas A&M University. Thisarticle received the Best Paper Award in Investments at the 1999 annual meetings of the SouthwesternFinance Association. Also, it was presented at 1999 Financial Management Association Internationalconferences in Barcelona, Spain, and Orlando, Florida. We are thankful for comments from participants atthose conferences, especially Scott Hein, Deryl Martin, Diana Harrington, Leigh Riddick, Joe Smolira,Benton Gup, Richard Stehle, Seppo Pynnonen, and Tom Berglund, in addition to helpful comments fromanonymous referees.

'As observed by Bodie (1976), "inflation hedge" has alternative definitions. One definition is that thepossibility ofa negative real rate of return on investment is reduced or eliminated. A second definition is thatthe real return is independent ofthe inflation rate. Our article is consistent with this second alternative, whichBodie explains as follows: "Economic theorists have long considered common stocks an inflation hedge ...because stocks represent ownership of physical capital whose real value is assumed to be independent of therate of inflation. This independence implies that a ceteris paribus change in the rate of inflation should beaccompanied by an equal change in the nominal rate ofreturn on equity. Indeed, this view is most commonlyexpressed in looser terms as a positive correlation between the nominal rate of return on equity and the rateof inflation" (1976, p. 460).

587

588 The Journal of Financial Research

real return plus an expected rate of inflation. Applying this proposition to commonstocks, several empirical studies find the anomalous result that returns are inverselyrelated to expected and unexpected inflation (e.g., see Geske and Roll (1983)). 2 Jaffeand Mandelker (1976) also report a negative relation between annual stock returnsand concurrent rates of inflation over short sample periods but a positive relationover the much longer period 1875-1970. The latter positive, long-run inflation effectis confirmed by Boudoukh and Richardson (1993), who examine stock returns andinflation using one-year and five-year holding-period returns during 1802-1990 inthe United States and the United Kingdom. Thus, although numerous studies reportevidence on the negative short-run effect of inflation on stock returns, only twostudies find a positive, long-run Fisher effect for stocks.

A problem in estimating the long-run Fisher effect is that stock rates ofreturn and inflation rates are calculated using first differences of stock prices andgoods prices, respectively, which eliminates long-run information crucial to itsmeasurement. In this respect, many writers acknowledge that their findings reflectonly a short-run relation. For example, based on data for 1953-72, Bodie (1976)concludes that stock returns and inflation were negatively related in the short run.

One approach to overcoming this problem and capturing long-run inflationeffects is to use long holding-period returns and long sample periods of 100 to 200years, as Boudoukh and Richardson (1993) and Jaffe and Mandelker (1976)successfully demonstrate. An alternative approach to this problem is to use levelsofstock prices and goods prices, rather than stock returns and inflation rates. Hendry(1986, p. 54) observes that, when a time series is differenced, long-run informationcontained in the levels of the variables is lost (e.g., see Juselius (1991)). Granger(1986) and Engle and Granger (1987) compare series in levels versus series in firstdifferences. Relevant to our purpose, they make clear that first-differenced variablesthat are integrated of order zero, or 1(0), such as stock returns and inflation rates,have only limited memory ofpast behavior. By contrast, variables that are integratedof order one, or 1(1), such as levels of stock prices and goods prices, have aninfinitely long memory (i.e., an innovation will permanently affect the process). Inthis context, it makes sense to estimate the long-run Fisher effect using stock pricesand goods prices. Previous studies that use one-year and five-year holding-periodstock returns capture some but not all long-run inflation information in stock prices.

In this article we contribute further evidence on the long-run Fisher effectfor stocks by using stock prices and goods prices. Consistent with Engle andGranger (1987), this approach allows us to fully use long-run information containedin the levels ofthe variables, as opposed to focusing on partial long-run informationcontained in selected holding periods. Additionally, by using levels rather than firstdifferences, we avoid using data over long historical periods, in which the accuracyand relevance of the data series can be compromised. We examine monthly time

2As we discuss later, several theories are advanced to explain the negative relation between stockreturns and inflation (e.g., see Geske and Roll (1983) and Stulz (1986».

Stock Prices and Inflation 589

series ofstock price indexes and goods price indexes for six industrialized countries(United States, Canada, United Kingdom, France, Germany, and Japan) from 1953to 1998. Because stock prices and goods prices are nonstationary series, we employcointegration methods to estimate Fisher coefficients.' In brief, our estimates ofthelong-run elasticities ofstock prices with respect to inflation generally exceed 1 andrange from 1.04 to 1.65, which tends to support the Fisher effect. Because stockprices and goods prices have an infinitely long memory, we also estimate theresponse ofstock prices to a shock in goods prices over a forecast horizon oftwentyyears. These analyses reveal the time path of the relation between stock prices andgoods prices. In this regard, the initial responses of stock prices in all six countriesare negative and thereafter become positive and permanent. These findings areconsistent for the most part with the empirical studies that document negative shortrun but positive long-run inflation effects on stock returns. They also are consistentwith Fisher's finding of long-distributed lag effects of inflation for bonds in theUnited States and United Kingdom. Thus, these results help reconcile previousshort-run and long-run empirical evidence on stock returns and inflation. Moreover,they reveal that stock prices have a long memory for inflation shocks, such thatinvestors should expect stocks to be a good inflation hedge over a long holdingperiod.

II. Theoretical and Empirical Framework

The Fisher relation for common stocks is specified in terms of rates ofreturn and inflation rates. In this section we respecify this relation in terms of stockprices and goods prices.

The strong form of the Fisher hypothesis as derived by Darby (1975) andCarrington and Crouch (1987) can be written as:

(1)

where It is the nominal interest rate at time t, R~ is the expected real rate of interest,1t~ is the expected rate of inflation, and T is the marginal tax rate on investmentincome. The tax-adjusted coefficients of this equation are expected to exceed 1

'Ely and Robinson (1997) employ the Johansen maximum likelihood estimator (MLE) to examine thelong-run relations between stock prices and goods prices for sixteen industrialized countries. Theyincorporate measures of money supply and economic output (i.e., industrial production and real grossdomestic product) into the analyses because oftheir potential effect on the relation between stock prices andinflation. However, they do not conduct bivariate tests of the long-run Fisher relation between stock pricesand inflation and, therefore, do not report Fisher elasticities. Also, a recent working paper by Hein andMercer (1999) applies MLE to U.S. stock price and goods prices. These studies provide support for ourempirical approach.


because 0 < T < 1. Assuming the cross-product term can be ignored, the semistrongform of the Fisher hypothesis is:

(2)

Although investors adjust their expectations of inflation for bonds andstocks in the same way, testing the Fisher hypothesis for stocks involves a majormeasurement problem not encountered with bonds. The nominal return on stocks,unlike short-term bonds with promised coupon and par payments, is not known. Forthe estimation of nominal stock returns, expectations about future stock prices arenecessary. Ignoring dividends, ifS~ is expected stock price in period I and St-l is thestock price in period I-I (both in natural logarithm form), then equation (2) forstock prices is written as:

(3)

Assuming the expected real stock return for period I is equal to real stock return inperiod I-I, the expected stock return can be written as:

Denoting P, as the natural logarithm ofa goods price index (e.g., the consumer priceindex, or CPI), 1C can be written as the first difference ofP; such that equation (4)becomes a model of distributed lags for expected stock prices and goods prices."

Because stock prices are a component of the index of leading economicindicators in the United States and in many other countries, it is reasonable toassume that market participants take into consideration the history of stock pricesin forming inflationary expectations. Define S, = S~ + US t and P, = P~ + UPt,S whereUS t and UPt are unexpected movements in stock prices and goods prices, respectively.Given a long tradition of employing distributed lag models of inflationaryexpectations, it is reasonable to assume that the dynamic relation between stockprices and goods prices can be specified as a vector autoregressive (VAR) model.Consider a vector X = (S P), where Sand P are as defined earlier. The dynamicrelation between Sand P is written in the following reduced-form VAR model:

'The relation between levels of stock prices and inflation can be traced to a homogenous money demandfunction, where demand for real money is specified as a function of real wealth (including stock holdings)and interest rates.

'This transformation implies 1t;= n, + U1t,. According to MacDonald and Murphy (1989), substitutingthis expression for1t~ into equation (3) likely invokes an error-in-variables problem. However, they note that,if the time series is cointegrated (as in the present article), any bias in the estimate of the coefficients of themodel are asymptotically negligible.

Stock Prices and Inflation

n

X t = C + L Ak~-k + Ut ,k=l

591

(5)

where C is a 2x 1 vector of constants, Ak are 2x2 matrices of coefficients to beestimated, and vector ut represents the unexpected movements in Sand P. It isassumed that E(ut) = 0 and E(utu' J = 0 when v * t. By choosing the order n of theVAR to be large enough, the residual serial correlation problem is avoided.

Using a Choleski decomposition of the covariance matrix, the VAR modelis used to investigate the effect of unexpected movements in P on stock prices.However, the VAR model cannot provide information about the long-run relationbetween stock prices and inflation. For the estimation of the long-run relation, weemploy Johansen's (1991a) full information maximum likelihood estimator (MLE).Crowder and Wohar (1999) demonstrate the usefulness of this technique in theestimation of long-run Fisher effects for Treasury and municipal bonds.

Johansen (1991a) shows that the VAR model in equation (5) can be writtenas the following vector error-correction (VEC) model:

where T, and II are 2x2 matrices, and k is the lag order. The rank of matrix P givesthe number ofcointegrating vectors, which are long-run relations between Sand P.If 0 < rank ofmatrix II < 2, there is one cointegrating relation. In this case the termIIX;-k is written as:

II~_k = eg'~-k' (7)

where the term g'X;-k represents the long-term relation between Sand P, and e is theerror-correction coefficient or the speed of adjustment reflecting the speed ofconvergence to equilibrium. If there exists a long-run relation between Sand P,equation (6) can be written for stocks as:

n-l n-l

tJ..St = L aktJ..St_k + L bktJ..Pt-k + e(St_l - c - dPt-1) , (8)k=l k=l

where the summation terms represent the short-run relation between stock prices andgoods prices, the error-correction term e represents the speed ofadjustment ofstockprices to unexpected changes in inflation, and the term in parentheses is the vectorof deviations from the long-run relation between stock prices and goods prices.After normalizing the latter long-term vector by the level ofstock prices, we get thefollowing long-run equation:


(9)

If the variables are in log terms, the coefficient d in this equation is the elasticity ofstock prices with respect to goods prices, otherwise known as the Fisher coefficient.

Johansen (199la) provides a test for determining the rank of matrix IT, orthe number of cointegrating (long-run) relations between the variables. Becauseincluding a linear trend (i.e., a constant in the error-correction representation withinor outside the matrix IT) is important, we conduct a sequential trace test for the jointdetermination of the number of cointegrating vector(s) as well as the linear trend(Johansen (1991b)).

Johansen's method can be applied to time-series variables that are 1(1).Thus, it is necessary to pretest variables before they can be used to estimate long-runrelations. For this purpose we employ the augmented Dickey-Fuller (ADF) (1979,1981) unit root test.

III. Data and Empirical Results

Data

We use monthly data series for six national stock price indexes: S&P 500(United States), TSE300 Composite (Canada), FTSE100 (United Kingdom),SBF250 (France), DAX (Germany), and Nikkei (Japan), denoted as SUS, SCN,SUK, SFR, SGR, and SJP, respectively." For an index of goods prices, we use theCPls for the six countries, denoted as CUS, CCN, CUK, CFR, CGR, and CJP,respectively. The sample period begins in January 1953 and ends in December 1998(a total of 564 monthly observations). All variables are transformed into naturallogarithms. An anonymous referee suggested using international data, which enablescomparative analyses to check the robustness of the results. In this regard, there issome concern about the power of tests to detect cointegration for different samplesizes. Based on the literature on this subject (e.g., see Hakkio and Rush (1991) andJunttila (2001)), we infer that our sample sizes are sufficiently large to providereliable cointegration tests. Also, testing several models for multiple countriesallows the consistency of the estimated test statistics to be observed.

During the sample period, the stock indexes in the six countries experiencedgrowth rates that outstripped the growth rate of the corresponding CPIs. During1953-99, SUS, SCN, SDK, SFR, SGR, and SJP increased by 4,238.7 percent,1,973.9 percent, 2,932.7 percent, 5,644.5 percent, 4,974.4 percent, and 2,932.7percent, respectively, whereas CUS, CCN, CUK, CFR, CGR, and CJP increased by518.0 percent, 553.7 percent, 1,504.2 percent, 957.5 percent, 260.8 percent, and

"These market indexes are composed of the following numbers of stocks: SUS (n = 500), SeN (n =

300), SUK (n = 100), SFR (n = 250), SGR (n = 30), and SJP (n = 225).


TABLE 1. Augmented Dickey-Fuller (ADF) Unit Root Tests.

593

Variable ADF Statistics Variable ADF Statistics

SUS 0.54 LlSUS -9.27SCN -0.23 LlSCN -9.29SUK -0.12 LlSUK -10.94SFR -0.39 LlSFR -5.68SGR -1.71 LlSGR -9.59SJP -1.93 LlSJP -9.77CUS -0.39 LlCUS -4.41CCN 0.16 LlCCN -5.00CUK 0.16 LlCUK -6.22CFR -0.67 LlCFR -5.91CGR -0.30 LlCGR -8.78CJP -1.82 LlCJP -8.845% critical value -2.87 -2.87

Note: In this table SUS, SCN, SUK, SFR, SGR, and SJP are logarithms ofstock prices for the United States,Canada, the United Kingdom, France, Germany, and Japan, respectively, and CUS, CCN, CUK, CFR, CGR,and CJP are the consumer price indexes for these respective countries. The corresponding variables in firstdifferences are denoted as LlSUS, LlSCN, LlSUK, LlSFR, LlSGR, LlSJP, LlCUS, LlCCN, LlCUK, LlCFR,LlCGR, and LlCJP. The augmented Dickey-Fuller (ADF) procedure tests for stationarity using the regression

n

Sx, = Il + pX'~l + L 0;Llx,~; + e"i=!

where !!.xt-! is the first difference of Xt-!, and n is number oflags so that e, is empirically white noise. TheADF test statistic is the pseudo r-statistic associated with p. As the test statistics suggest, at the 5 percentsignificance level all series are nonstationary in level but stationary after first differencing.

580.6 percent, respectively. Thus, casual observation suggests stock prices arepositively correlated with goods prices over the long run.

Long-Run Analyses

We first test whether the twelve time series are nonstationary. To determinethe stationarity properties of the series, we use the ADF unit root test. Table 1presents the results of these tests for levels as well as first differences of thevariables. For each of the series examined, the test statistics suggest the levels ofseries are not stationary but the first differences (prefixed with ~) ofthe series arestationary (i.e., the null hypothesis of an 1(1)process cannot be rejected but the nullhypothesis of an 1(2) process can be rejected). Hence, all series are integrated oforder one and can be tested for cointegration in the Johansen system.

Because Johansen tests are performed within a VAR framework, and theresults from VARs are sensitive to the lag length (Hafer and Sheehan (1991»,attention should be paid to lag length. Because the data are monthly, and based on


TABLE 2. Cointegration Tests Based on Johansen's Trace Test.

Likelihood RatioHypothesized No. of 5% CriticalCointegrating Vectors U.S Canada U.K. France Germany Japan Value

None 24.43 23.68 21.94 29.40 32.39 20.49 19.96At most one 2.93 5.22 5.85 2.76 5.41 6.67 9.24

Note: In this table SUS, SCN, SUK, SFR, SGR, and SJP are logarithms ofstock prices for the United States,Canada, the United Kingdom, France, Germany, and Japan, respectively, and CUS, CCN, CUK, CFR, CGR,and CJP are the consumer price indexes (CPI) for these respective countries. The corresponding variablesin first differences are denoted as tlSUS, tlSCN, tlSUK, tlSFR, tlSGR, tlSJP, tlCUS, tlCCN, tlCUK, tlCFR,tlCGR, and tlCJP. The table provides the results from Johansen's trace test to determine the number ofcointegrating vector(s)-that is, the number oflong-run relations between a stock price index and CPI in agiven country. Because there are two variables in each test (i.e., the stock price index and CPI), the numberofcointegrating vector(s) can be 0, I, or 2. For each test the first line tests whether there is no cointegratingvector. If the test statistics in the first line for each stock index are larger than the 5 percent critical value, wereject the hypothesis ofno cointegration and accept that there is at least one cointegrating relation. Then weproceed to the second line and test the hypothesis ofat most one cointegrating vector. If the test statistic inthe second line for each stock index is smaller than the 5 percent critical value, we accept there is onecointegrating relation between the stock price index and CPr. The tests show there is one cointegratingrelation between each pair of stock price index and CPr.

lag-selection tests using the Sims (1980) criterion/ we introduced twelve monthlylags in the Johansen system. Applying the MLE approach, we show in Table 2results from Johansen's trace test to determine whether a long-term relation existsbetween each pair of stock prices and goods prices (CPI). We start with the nullhypothesis that there is no cointegrating relation, and if this hypothesis cannot beaccepted, we test the hypothesis that there is at most one cointegrating vector.Because there are two variables in each model-the respective stock price index andthe CPI-we test whether the number of cointegrating vectors is zero, one, or two.The test provides evidence of cointegration where there is only one cointegratingvector. The test also determines whether to include the constant term within oroutside the cointegrating vectors. As Table 2 shows, the results suggest the existenceof one cointegrating vector (or long-run relation) between each pair of stock price

7The Sims (1980) test statistic is

where :E, and :E. are restricted and unrestricted covariance matrices, respectively; M is the number ofobservations; and C is a correction factor for small samples. The test is asymptotically distributed as a X'statistic with degrees of freedom equal to the number of restrictions. In selecting the order ofa VAR model,the log-likelihood ratio statistic tests the hypothesis that the order ofthe VAR is n against the alternative thatit is n+1. We initially select a maximum order of twenty-four monthly lags. This order is high enough toallow us to select an optimal lag based on a selected criterion. The Sims tests suggest using lags of orderthirteen or more. We find that the results obtained using longer lag lengths are not significantly different witha lag order of twelve months.


TABLE 3. Long-Run Relations Between Stock Prices and Goods Prices Based on the FullInformation Maximum Likelihood Estimator (MLE).

595

Speed ofStock Index Long-Run Equation Adjustment

Terms in Equation (9): c d e

United States SUS -0.46 + 1.62tCUS -0.01--(0.6) (6.6) (4.5)

Canada SCN 2.76 + 1.17tCCN -0.03(9.3) (15.5) (4.1)

United Kingdom SUK 1.85-- + 1.19tCUK -0.02--(4.3) ( 11.6) (3.3)

France SFR 2.44-- + 1.04CFR -0.03--(6.7) (12.4) (4.85)

Germany SGR 2.84-- + 1.18CGR -0.01--(2.3) (4.5) (3.6)

Japan SJP 2.09-- + 1.65tCJP -0.02--(2.3) (8.3) (3.4)

Note: In this table SUS, SCN, SUK, SFR, SGR, and SJP are logarithms ofstock prices for the United States,Canada, the United Kingdom, France, Germany, and Japan, respectively, and CUS, CCN, CUK, CFR, CGR,and CJP are the consumer price indexes (CPI) for these respective countries. For each country the tableshows the long-run relation between the stock price index and CPI using monthly data as specified inequation (9). The signs ofthe estimated d coefficients for the CPI in the equations are all positive and supportthe long-run Fisher effect. Because all the variables are in logarithms, the coefficient of CPI is the elasticityof the stock price with respect to the CPr. For instance, the first equation shows that for the United States,a 1 percent increase in the CPI is expected to result in a 1.62 percent increase in the S&P index over the longrun. The absolute values of z-statistics are shown in parentheses, in which the null hypothesis is that theestimated coefficient is zero. Moreover, a cross (t) indicates failure to accept the null hypothesis (at the 5percent significance level) that the Fisher coefficient is less than or equal to 1 and instead acceptance of thealternative hypothesis that it is greater than 1. The term e is the speed of adjustment, which is the rate ofconvergence to the long-run equilibrium relation.

--Significantly different from zero at the 5 percent level.

index and CPI. Because results are similar across several countries, we infer thecointegration tests are robust.

Based on equation (9), Table 3 reports the MLE estimates of long-runrelations between stock prices and the CPI for the sample period. As shown in Table3, the estimated Fisher coefficients (d) range from 1.04 to 1.65: United States =

1.62, Canada = 1.17, United Kingdom = 1.19, France = 1.04, Germany = 1.19, andJapan = 1.65. Because all variables are in logarithm, the coefficient for CPI (d) ineach equation shows the elasticity of the stock price with respect to inflation. Forinstance, the estimated coefficient 1.62 for the United States means that for every1 percent increase in CPI, the S&P 500 is expected to increase by 1.62 percent over


the sample period. The United States and Japan experienced large stock price indexincreases in the 1980s and 1990s, respectively, which likely explains their higherFisher coefficient estimates relative to the other countries. In view ofcomments byan anonymous reviewer, the lower Fisher coefficients for Canada, the UnitedKingdom, France, and Germany provide more conservative estimates of howinflation affects stock price indexes in the long run. As shown in Table 3, t-tests forwhether the estimated Fisher coefficient estimates are less than or equal to unityversus greater than unity indicate that (at the 5 percent significance level) estimatesfor the United States, Canada, the United Kingdom, and Japan are greater than unity,but estimates for France and Germany are less than or equal to unity. Results for theformer countries support Darby's tax-adjusted version ofthe Fisher effect specifiedin equation (2), whereas results for the latter countries do not support Darby.

In Table 3 the estimates of the speed-of-adjustment coefficients (e) liebetween 0.01 and 0.03, which means it takes a long time for stock prices to returnto their long-run relation following an unexpected movement in goods prices. Theseresults support the impulse response function findings, to be discussed shortly.

Jaffe and Mandelker (1976) estimate a long-run elasticity coefficient of0.50(i.e., not statistically different from one) using annual stock returns and inflationrates for 1875-70. Subsequently, Boudoukh and Richardson (1993) employ oneand five-year holding-period returns for stocks for 1802-90, as well as for 1870-90and 1914-90. Based on estimates from various instrumental variable models, theone-year relations generally were negative in sign but not significant. However, thefive-year relations yielded positive and significant coefficients ranging from 0.38to 2.12, with most coefficients exceeding 1. Because our Fisher coefficients rangefrom 1.04 to 1.65, they are more consistent with those reported by Boudoukh andRichardson than those reported by Jaffe and Mandelker. Hein and Mercer (1999)perform similar MLE tests of U.S. stock market index prices and consumer pricesfor 1953-92. They report Fisher coefficients that are significantly greater than 1,ranging from 1.26 to 2.19. We infer that our Fisher coefficient estimates are withinthe range obtained by other researchers using different periods, empirical methods,and data series.

Time Path ofthe Relation Between Stock Prices and Goods Prices

Previous researchers report a negative short-run but positive long-runrelation between stock returns and inflation. In the previous section we focus on thelong-run relation but do not address the short-run relation between stock prices andgoods prices. We now turn to the timing of these two inflation effects. The longmemory of information contained in stock prices and goods prices enables us toinvestigate the time path ofthe response ofstock prices to an unpredicted movementin goods prices. For this purpose we use the VAR models of stock prices and goodsprices estimated in the previous section.

Figure I shows the responses of the stock price indexes to unexpectedmovements (i.e., innovations or shocks) in the CPI generated from the VAR models


United States Canada000,--------------_,

o 0

20 40 60 80 100120140160180200220240Forecast honzon months

004

o 02

20 40 60 80 100120140160180200220240

Forecast honz o n months

United Kingdomo 081-r----:O'--------------,

FranceoOll;----------------,

004

002

o 0

-0 04

,\

~ -002\·~-

§0.

0)

~

20 40 60 '80 10012014016018020022'0240Forecast honzons months

o 0

o 08:-r-Ge::..::..::rm~a:::n;;:y _, Japano08:-r--:.---------------,

o 06

o 04

o OE

004

-0 04

o 02

00 -,_ " ~

~,oozl'~,,--"c0.~

0)

~

20406080100120140160180200220240Forecas t honzons months

o 02

Figure I. Graph of the Impulse Response Functions Illustrating the Responses of Stock PriceIndexes to a One-Standard-Deviation Shock in the Consumer Price Index Using MonthlyData for 1953-98.

over a forecast horizon of240 months (twenty years), as well as their bands ofplusor minus two standard errors. The impulse response functions reveal the wayanunexpected movement in the goods price index affects the stock price index over


time." As Figure I shows, the initial, short-run responses of all six stock priceindexes to a one-standard-deviation positive shock in consumer prices are negative.The negative, short-run relation between stock returns and inflation rates in manypast studies of the Fisher effect can be attributable to this negative response.

After a transitory period of negative shocks to stock prices, as shown inFigure I, the impulse functions for all six countries return to zero and thereafterbecome positive and permanent in the long run. The similarity of the impulseresponse functions across the six countries implies the results are robust to differentgrowth rates of stock price and goods price indexes.

Table 4 reports the impulse response functions' estimates (illustrated inFigure I) and their corresponding t-statistics. The t-statistics are derived based on ananalytic method for estimating variances of impulse functions suggested byHamilton (1994, p. 336). As shown, the initial negative responses ofstock prices toa shock in goods prices are statistically significant. After these initial negativeresponses, stock prices respond positively and significantly to inflation over longertime horizons for all six countries' stock price indexes. Again, the initial negativeresponses of the stock price indexes are consistent with previous empirical studiesthat document the negative short-run effect of inflation (see also Ely and Robinson(1997) for a discussion of theoretical explanations).

After the initial negative reaction, the responses become positive and exhibita permanent long-run relation. This positive long-run inflation effect on stock pricesis consistent with previously cited research by Jaffe and Mandelker (1976) as wellas by Boudoukh and Richardson (1993). Nichols (1976) proposes that long-runforces would eventually overwhelm short-run processes (i.e., the positive effect ofinflation on asset prices takes considerable time to offset the capital loss associatedwith an increase in inflation expectations). Our finding that it takes a long time forinflation to be fully reflected in stock prices is also consistent with Fisher. Thelongevity of inflation effects led Fisher to invent distributed lag models. Heexamined interest and inflation rate series for the United Kingdom and United Statesin 1820-24 and 1890-27, respectively, and found that interest rates follow pricechanges with long distributed lags of about fifteen to thirty years. Inhis words, "Itseems fantastic, at first glance, to ascribe to events which occurred last century anyinfluence affecting the rate of interest today" (1930, p. 428). Our results using thelong-run information contained in stock prices and goods prices indicate these longdistributed lag effects of inflation exist for stocks also.

'Because the estimated impulse response functions may be sensitive to order in the Choleski methodof orthogonalization of the covariance matrix, we estimate impulse response functions using two orders ofthe variables. In the first case we order stock price first followed by CPI, and in the second case we orderCPI first followed by stock prices. We find that changing the order of the variables has no effect on theestimated impulse response functions.


TABLE 4. Impulse Response Functions and Their r-Values.

ForecastHorizon:Month United States Canada United Kingdom France Germany Japan

6 -0.29 -0.65 -1.17 -2.00 -0.85 -0.20(0.81) (1.69) (2.29)** (3.99)** (1.80)** (0.40)

12 -1.16 -0.58 -1.55 -2.76 -1.49 -1.04(3.40)** (1.46) (2.56)** (4.51)** (2.28)** (1.60)

18 -1.46 -0.64 -1.70 -3.26 ~ 1.87 -1.37(3.36)** (1.28) (2.30)** (4.35)** (2.22)** (1.64)

24 -1.74 -0.53 -1.47 -3.23 -2.01 -1.38(3.40)** (0.94) (1.79) (3.93)** (2.07) (1.48)

30 -1.90 -0.33 -1.15 -3.00 -1.93 -1.19(3.24)** (0.55) (1.36) (3.47)** (1.90) (1.23)

36 -1.97 -0.12 -0.74 -2.69 -1.69 -0.89(3.02)** (0.19) (0.90) (3.02)** (1.64) (0.91)

42 -1.98 0.13 -0.31 -2.34 -1.38 -0.54(2.78)** (0.21) (0.39) (2.57)** (1.38) (0.56)

48 -1.92 0.37 0.12 -1.99 -1.03 -0.19(2.51)** (0.64) (0.16) (2.13)** (1.09) (0.20)

54 -1.81 0.61 0.52 -1.65 -0.69 0.13(2.24)** (1.09) (0.74) (1.72) (0.78) (0.14)

60 -1.66 0.83 0.90 -1.32 -0.37 0.41(1.96)** (1.56) (1.32) (1.35) (0.45) (0.45)

66 -1.48 1.03 1.23 -1.00 -0.09 0.64(1.67) (2.05)** (1.86) (1.01) (0.11) (0.73)

72 -1.26 1.21 1.52 -0.70 0.16 0.83(1.39) (2.54)** (2.36)** (0.70) (0.23) (0.97)

78 -1.03 1.36 1.77 -0.42 0.38 0.98(1.11) (2.98)** (2.79)** (0.42) (0.57) (1.19)

84 -0.78 1.49 1.98 -0.15 0.55 1.09(0.83) (3.32)** (3.15)** (0.15) (0.92) (1.39)

90 -0.53 1.60 2.16 0.10 0.69 1.17(0.56) (3.53)** (3.45)** (0.10) (1.26) (1.57)

96 -0.27 1.70 2.30 0.34 0.80 1.23(0.29) (3.62)** (3.68)** (0.35) (1.61) (1.72)

102 -0.02 1.77 2.42 0.56 0.88 1.27(0.02) (3.60)** (3.83)** (0.61) (1.96)** (1.86)

108 0.23 1.83 2.51 0.77 0.95 1.30(0.25) (3.52)** (3.91)** (0.86) (2.30)** (1.97)**

114 0.48 1.88 2.59 0.97 0.99 1.32(0.52) (3.40)** (3.94)** (1.13) (2.61)** (2.06)**

120 0.71 1.92 2.64 1.16 1.03 1.32(0.79) (3.28)** (3.91)** (1.42) (2.87)** (2.12)**

126 0.94 1.95 2.69 1.33 1.05 1.32(1.06) (3.16)** (3.84)** (1.71) (3.06)** (2.16)**

132 1.15 1.97 2.72 1.50 1.06 1.32(1.34) (3.04)** (3.76)** (2.03)** (3.18)** (2.18)**

138 1.34 1.98 2.74 1.65 1.07 1.31(1.62) (2.94)** (3.66)** (2.35)** (3.23)** (2.19)**

144 1.52 1.99 2.76 1.79 1.07 1.30(1.90) (2.85)** (3.56)** (2.68)** (3.24)** (2.19)**

(Continued)


TABLE 4. Continued.

ForecastHorizon:Month United States Canada United Kingdom France Germany Japan

150 1.69 2.00 2.77 1.93 1.07 1.29(2.17)-- (2.77)-- (3.48)-- (2.99)-- (3.22)-- (2.18)--

156 1.84 2.00 2.77 2.05 1.06 1.28(2. 42)-- (2.70)-- (3.39)-- (3.28)-- (3.18)-- (2.17)--

162 1.98 2.00 2.77 2.16 1.06 1.27(2.65)-- (2.65)-- (3.32)-- (3.51)-- (3.14)-- (2.16)--

168 2.10 1.99 2.77 2.27 1.05 1.26(2.84)-- (2.60)-- (3.26)-- (3.67)-- (3.10)-- (2.14)--

174 2.20 1.99 2.77 2.37 1.05 1.24(2.97)-- (2.56)-- (3.20)-- (3.75)-- (3.08)-- (2.13)--

180 2.29 1.98 2.76 2.46 1.04 1.23(3.04)-- (2.52)-- (3.16)-- (3.75)-- (3.06)-- (2.11)--

186 2.37 1.98 2.76 2.54 1.03 1.22(3.06)-- (2.49)-- (3.12)-- (3.70)-- (3.05)-- (2.10)--

192 2.44 1.97 2.75 2.62 1.03 1.21(3.03)-- (2.47)-- (3.09)-- (3.61)-- (3.04)-- (2.09)--

198 2.50 1.96 2.74 2.69 1.02 1.20(2.97)-- (2.45)-- (3.07)-- (3.49)-- (3.04)-- (2.08)--

204 2.54 1.96 2.74 2.75 1.01 1.19(2.87)-- (2.44)-- (3.05)-- (3.35)-- (3.04)-- (2.06)--

210 2.58 1.95 2.73 2.80 1.01 1.18(2.77)-- (2.42)-- (3.03)-- (3.22)-- (3.05)-- (2.05)--

216 2.60 1.94 2.72 2.85 1.00 1.16(2.65)-- (2.41)-- (3.02)-- (3.08)-- (3.06)-- (2.04)--

222 2.62 1.93 2.71 2.90 1.00 1.15(2.54)-- (2.40)-- (3.01)-- (2.96)-- (3.07)-- (2.03)--

228 2.63 1.93 2.70 2.94 0.99 1.14(2.43)-- (2.40)-- (3.00)-- (2.84)-- (3.08)-- (2.02)--

234 2.64 1.92 2.70 2.97 0.99 1.13(2.32)-- (2.39)-- (2.99)-- (2.73)-- (3.10)-- (2.00)--

240 2.64 1.91 2.69 3.00 0.98 1.12(2.23)-- (2.39)-- (2.99)-- (2.62)-- (3.11)-- (2.00)--

Note: This table shows the response of the stock price indexes to a one-standard-deviation positive shockin the consumer price index and their corresponding z-values, As the table shows, the initial responses arenegative and become positive and statistically significant in the long run.

--Significant at the 5 percent level.

IV. Summary and Conclusions

Numerous empirical studies establish that inflation has a negative short-runeffect on stock returns but few studies report a positive, long-run Fisher relation. Aproblem in measuring the long-run Fisher effect using stock returns and inflationrates is that these variables are based on first differences of stock prices and goods


prices, respectively, which eliminates long-run information in their time series. Thisproblem is overcome by some researchers who use long holding-period returns andlong sample periods. An alternative approach, employed here, is to use stock pricesand goods prices so that the long-run information contained in these variables isused to estimate the long-run Fisher effect. In this regard, we examine monthly stockprice indexes and goods price indexes for six industrialized countries for 1953-98using cointegration methods.

Our estimates of the long-run Fisher elasticities of stock prices for goodsprices range from 1.04 to 1.65 across the six countries. Except for France andGermany, the Fisher coefficient estimates are significantly greater than one andtherefore support Darby's tax version ofthe Fisher effect. For France and Germany,the empirical results support the Fisher hypothesis, with estimated coefficients nearunity. Consistent with previous studies ofshort-run inflation effects on stock returns,we find an initial, negative response of stock prices to an inflation shock in all sixcountries. Beyond the initial, negative transitory period, the long-run relationbetween stock prices and goods prices is positive and permanent in all cases. Thus,our results help reconcile previous short-run and long-run empirical evidence onstock returns and inflation. Moreover, they reveal that stock prices have a longmemory with respect to shocks in goods prices, which implies investors shouldexpect stocks to be a good inflation hedge over a long holding period.

References

Bodie, Z., 1976, Common stocks as a hedge against inflation, Journal ofFinance 31, 459-70.Boudoukh, J. and M. Richardson, 1993, Stock returns and inflation: A long-horizon perspective, American

Economic Review 83, 1346-55.Carrington, S. and R. Crouch, 1987, A theorem on interest rate differentials, risk and anticipated inflation,

Applied Economics 19, 1675-83.Crowder, W. 1. and M. E. Wohar, 1999, Are tax effects important in the long-run Fisher relationship?,

Journal ofFinance 54, 307-17.Darby, M., 1975, The financial and tax effects of monetary policy on interest rates, Economic Inquiry 13,

266-76.Dickey, D. A. and W. A. Fuller, 1979, Distribution of the estimators for autoregressive time series with a

unit root, Journal ofthe American Statistical Association 74, 427-31.___ , 1981, The likelihood ratio statistics for autoregressive time series with a unit root, Econometica

49, 1057-72.Ely, D. P. and K. J. Robinson, 1997, Are stocks a hedge against inflation: International evidence using a

long-run approach, Journal ofInternational Money and Finance 16, 141-67.Engle, R. F. and C. W. J. Granger, 1987, Cointegration and error-correction: Representation, estimation, and

testing, Econometrica 55, 251-76.Fisher, I., 1930, The Theory ofInterest (Macmillan, New York).Geske, R. and R. Roll, 1983, The fiscal and monetary linkages between stock returns and inflation, Journal

ofFinance 38, 1-33.Granger, c., 1986, Developments in the study of cointegrated economic variables, Oxford Bulletin of

Economics and Statistics 48, 213-28.Hafer, R. and R. Sheehan, 1991, Policy inference using VAR models, Economic Inquiry 29, 44-52.Hakkio, C. S. and M. Rush, 1991, Cointegration: How short is the long run?, Journal ofInternational Money

and Finance 10,571-81.


Hamilton, J. D., 1994, Time Series Analysis (Princeton University Press, Princeton, NJ).Hein, S. E. and J. M. Mercer, 1999, Comovements of stock prices and consumer goods prices, Working

paper presented at the 1999 Southern Finance Association conference.Hendry, D., 1986, Econometric modelling with cointegrated variables: An overview, Oxford Bulletin of

Economics and Statistics 48, 51-63.Jaffe, 1. and G. Mandelker, 1976, The "Fisher effect" for risky assets: An empirical investigation, Journal

ofFinance 31, 447-58.Johansen, S., 1991a, Estimation and hypothesis testing of cointegration vectors in Gaussian vector

autoregressive models, Econometrica 59,1551-80.____ , 1991b, The role of the constant term in cointegration analysis of non-stationary variables,

Discussion paper, University of Copenhagen.Junttila, J., 2001, Testing an augmented Fisher hypothesis for money market rates in Finland, Journal of

Macroeconomics 23, forthcoming.Juselius, K., 1991, Long-run relations in a well-defined statistical model for the data generating process:

Cointegration analysis of the PPP and UIP relations between Denmark and Germany, in 1. Gruber,ed.: Econometric Decision Models:New Methods ofModeling and Applications (Springs Verlag,Berlin).

MacDonald, R. and P. D. Murphy, 1989, Testing for the long run relationship between nominal interest ratesand inflation using cointegration techniques, Applied Economics 21, 439-47.

Nichols, D. A., 1976, Discussion, Journal ofFinance 31, 483-87.Sims, c., 1980, Macroeconomics and reality, Econometrica 48,1-48.Stulz, R. M., 1986, Asset pricing and expected inflation, Journal ofFinance 41,209-23.

stock prices and inflation

Documents