Permanent and temporary components of stock prices: evidence from assessing macroeconomic shocks.

• Author: Gallagher, Liam A.

1. Introduction

   This paper examines the interaction between macroeconomic shocks and stock price movements, from both a theoretical and an empirical perspective.

   The mean reversion and predictability of stock returns is probably the most well researched topic in the empirical literature on financial economics, dating back at least to Cowles and Jones (1937). Numerous empirical studies have been unable to reject the hypothesis that returns are unpredictable and that stock prices follow a random-walk, or martingale, process (e.g., Granger and Morgenstern 1963; Fama 1965, 1970; Le Roy 1982). In the past decade, however, various studies have challenged this conventional view and reexamined the predictability of stock returns: Contrary to the random-walk hypothesis, recent empirical evidence has lent strong support to the hypothesis of mean reversion in stock prices.

   The influential work of Fama and French (1988) reports impressive findings that U.S. stock prices are mean reverting (i.e., contain a slowly decaying temporary component) and induce returns characterized by a large negative autocorrelation process for long return horizons of several years. Moreover, Fama and French show that between 25% and 45% of the variation of three- to five-year U.S. stock returns appears to be predictable from past returns. The Fama and French study has been corroborated by a number of other studies that report similar findings that stock returns contain large predictable components (Lo and Mackinaly 1988, 1989; Poterba and Summers 1988; Frennberg and Hansson 1993; Cochrane 1994; Lee 1995).

   In this paper, the information contained in macroeconomic variables is used to investigate whether stock prices contain a temporary component and are, therefore, mean reverting. In order to illustrate and identify the relationship between macroeconomic and financial time series, we outline a simple log-linear macro model with overlapping nominal wage contracts and a real stock price determination equation. Apart from the inertia introduced by overlapping contracts, the model is essentially neoclassical and Fisherian in structure and allows reasonably complex dynamics. (1) We use this model to demonstrate a number of issues.

   First, we show that changes in log real stock prices may be serially correlated even under the assumption of fully efficient markets in the sense that there are no profitable arbitrage opportunities between current and expected stock price movements. Second, we show how the temporary and permanent components of stock price movements may be related to aggregate macroeconomic supply and demand disturbances. In particular, in the context of the same macro model, we show that aggregate demand shocks have only temporary effects on real stock prices, while supply shocks may affect the level of real stock prices permanently. These results are not specific to the particular model analyzed, however, and apply to any standard macro model with a long-run vertical supply curve and short-run nominal inertia.

   We then go on to investigate the size and significance of this mean-reverting component in U.S. stock prices, for the January 1949 through December 1997 (1949:1-1997:12) period, by placing appropriate structural restrictions on a vector autoregressive system in real stock prices and consumer prices, corresponding to a long-run vertical aggregate supply curve framework in which, in line with our illustrative macro model, only aggregate supply shocks have a long-run effect on real stock prices. In contrast, in Lee (1995), the interpretation of the shocks is not based on an underlying macroeconomic model. A further contribution to the literature of this paper is to examine the sensitivity of the mean-reverting (temporary) component to the choice of variable to extract the temporary component from the vector autoregressive analysis. This complements Lee (1995), who uses dividends to extract the temporary component. We elicit the temporary component of U.S. stock prices using consumer prices, interest rate, output , the wage rate, and consumption. Further, we investigate the robustness of the results to the periodicity of the data.

   The remainder of the paper is set out as follows. The next section provides a brief overview of the literature of mean reversion in stock prices. Section 3 outlines a simple macro model with overlapping nominal wage contracts and shows how aggregate macroeconomic supply and demand disturbances may be related to the temporary and permanent components of stock price movements. Section 4 outlines the econometric method used to decompose real stock prices into temporary and permanent components. The data, preliminary tests, and the empirical findings for U.S. stock prices are reported in section 5. Section 6 concludes the study.

2. Mean Reversion in Stock Prices

   The essence of the mean-reversion hypothesis is that stock prices contain a temporary component. Thus, the market value of stocks deviates from the fundamental value but will revert to its mean. There exists a number of competing theories that explain the deviation of the actual market prices of stocks from their fundamental values, including noise trading (De Long et al. 1990), fads (Shiller 1984), speculative bubbles (Blanchard and Watson 1982), and limits of arbitrage (Shleifer and Vishny 1997). Furthermore, since stock prices that deviate from fundamentals in a highly persistent way may look as if they are following a random walk, arbitrageurs would find it difficult to detect such a deviation (Summers 1986; Cuthbertson 1996). Studies of mean reversion and the associated predictable component of stock prices tend to rely on one of two related testing methodologies: the test of autoregression on multiperiod returns (the regression-based test; Fama and French 1988) and the variance-ratio test (Cochrane 1988 ; Cochrarie and Sbordone 1988; Poterba and Summers 1988; Lo and MacKinlay 1988). More recently, vector autoregressive analysis has also been used to identify the permanent and temporary components of stock prices (e.g., Cochrane 1994; Lee 1995; Cuthbertson, Hayes, and Nitzsche 1997).

   The regression-based and variance-ratio tests of mean reversion have been subject to recent criticism. Kim, Nelson, and Startz (1991) suggest that mean reversion is a feature of the pre-World War II environment but not the postwar environment. Moreover, there is evidence of poor small-sample performance of the test statistics. The small-sample problem arises because, even though the sample period may be very large, the number of nonoverlapping return observations is necessarily small, and therefore there is not much independent information in the return series. Thus, the reliability of inferences drawn from individual point estimates of long-horizon autocorrelations has recently been questioned (Richardson and Stock 1989; Jegadeesh 1990; Kim, Nelson, and Startz 1991; Mankiw, Romer, and Shapiro 1991; Richardson 1993). The difficulty in drawing inferences from t-statistics based on overlapping data arises because the approximating asymptotic distributions perform poorly and long-horizon t-statistics tend to ove rstate the degree of mean reversion. Using an alternative asymptotic distribution theory for statistics involving multiyear returns, Richardson and Stock (1989) and Richardson (1993) show that empirical inference does not easily reject the hypothesis of no mean reversion--the number of significant negative autocorrelations at long return horizons is reduced substantially. Mankiw, Romer, and Shapiro (1991) find only moderate evidence against the random-walk hypothesis. In fact, Cecchetti, Lam, and Mark (1990) and Richardson (1993) show that the U-shaped pattern is consistent with stock prices following a random-walk process.

   An alternative perspective on the mean-reversion literature is given by Cochrane (1994) and Lee (1995). They argue that univariate estimation of stock prices will not reject the random-walk hypothesis for short autoregressions (e.g., AR(1)) and that mean reversion is evident in univariate analysis only from long return horizons. However, evidence from mean reversion in stock prices comes when one isolates a transitory multivariate shock.

   Cochrane (1994) estimates a vector autoregression (VAR) of annual changes in the natural logarithm of stock prices and changes in the natural logarithm of dividends for the 1927-1988 period. Furthermore, since stock prices and dividends are cointegrated, the (one-period lag of the) natural logarithm of the dividend/price ratio is included in the VAR. Two shocks on stock prices (and dividends) are isolated--a dividend ("permanent") shock causes stock prices to move immediately to their long-run values, and a price ("temporary") shock has only a transitory effect on stock prices. Furthermore, the temporary shock is persistent with a half life of about five years. The size of the transitory component is large and consistent with the long return horizon analysis--some 57% of the variance of returns is explained by temporary shocks.

   Employing a restricted two-variable autoregression involving stock price-dividend spreads and real stock prices, Lee (1995) reports similar results for quarterly data. The distinguishing feature of Lee (1995) is that permanent and temporary shocks to stock prices are identified using the present value hypothesis (i.e., a stationary dividend/price ratio) and assuming dividends to be a nonstationary, I(1) process. Lee (1995) estimates a restricted bivariate VAR of the price-dividend spread and stock returns and identifies the temporary and permanent shocks to stock prices by restricting the long-run response of the temporary shock to stock prices to equal zero. The permanent and temporary shocks are attributed to the dividend series--the random-walk component generates the permanent innovations (shocks), and the stationary component generates the temporary innovations. The two...