Stock-Market Participation, Intertemporal Substitution, and Risk-Aversion

Many of the empirical rejections of the consumption CAPM can be explained by the fact that the marginal rate of substitution between present and future consumption, which in the standard model functions as the pricing kernel for all assets for which a consumer is not at a corner, seems to vary too little to be consistent with sensible values of the parameters. Moreover, when one considers more than one asset at a time, one typically gets strong rejections of the overidentifying restrictions implied by the model. The failure seems to be both in terms of unconditional and conditional moments. Two recent papers Attanasio et al., 2002 [henceforth ABT]; Vissing-Jorgensen, 2002 [henceforth VJ] have shown that, if one focuses on the consumption of individuals participating in the stock market, one does not reject some implications of the model. In particular, both VJ and ABT find that, using the consumption of stockholders, conditional Euler equations lead to sensible preference parameters and, in the case of ABT, fail to reject the overidentifying restrictions even when considering two assets (stocks and bonds) at the same time. While these results constitute a first empirical success, they do not necessarily constitute a solution to the equity premium puzzle. As argued by Robert E. Hall (1988) and Attanasio and Guglielmo Weber (1989), the estimates of the coefficient on the interest rate in a loglinearized Euler equation should be interpreted as the elasticity of intertemporal substitution (EIS) and can only be informative about the degree of risk-aversion under more restrictive assumptions (CRRA utility). In this paper we argue that considering the consumption growth of stockholders and two asset returns not only yields values of the EIS that are plausible, but also helps explain the equity premium puzzle. The evidence we have on the consumption, income, and portfolios of stockholders is consistent with fairly plausible values of the coefficient of relative risk-aversion when using the preference specification of Larry G. Epstein and Stanley E. Zin (1991). We use three Euler equations, one for each of the two assets considered, and one for the household’s total wealth portfolio, whose return will be denoted as Rm. Rm is, in principle, an unobservable variable in that it depends on the returns on all assets an individual consumer holds, including human capital. In this paper, we specify the conditional expected return to human capital as a linear function of the conditional expected returns to stocks and bonds. We suggest a novel approach to estimating the coefficients in this function based on conditional Euler equations for stockholders with two asset returns on the right-hand side. Then, considering unconditional moments, we estimate the risk-aversion of stockholders using the log-linearized equation for the equity premium from Epstein-Zin utility also explored by John Y. Campbell (1996). Unlike Campbell, our preferred approach does not substitute out consumption. Furthermore, we emphasize the importance of allowing for bonds in households’ portfolios as well as not restricting the conditional expected human-capital return to equal that of stocks.