Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Making the Case for a Low Intertemporal Elasticity of Substitution

Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Making the Case for a Low Intertemporal Elasticity of Substitution

Article excerpt

1 Introduction

One of the most important margins in intertemporal decision making is the response of expected consumption growth to a change in the expected interest rate.

Empirical evidence from macroeconomic data about the magnitude of the intertemporal elasticity of substitution (IES) is mixed.

Simple and intuitive arguments for a large IES are provided by two sets of facts that we will refer to as the levels facts and difference facts. The levels facts are closely related to the risk-free rate puzzle discussed by Weil (1989). He points out that it is difficult to reconcile empirical observations about the average level of risk free returns and the average level of consumption growth with the intertemporal Euler equation when the maintained level of risk aversion is large and the discount factor is less than one. The observation that low risk aversion is required to account for the average level of risk free returns can also be stated in terms of the IES. Under the assumption of time additive preferences the IES is the inverse of the risk aversion coefficient and only high values of the IES can be reconciled with data on the average level of consumption growth and the real risk-free interest rate. Guvenen (2006), for instance, derives a lower bound on the IES of about 0.7 using data on consumption growth and real returns using U.S data.

A second set of observations that has been used to argue that the IES is large concerns cross-country differences in consumption growth and real returns. Lucas (1990) observes that a small IES implies that a permanent one percentage difference in the growth rate of consumption is associated with larger proportionate variations in the real return on capital. He goes on to argue that it is hard to reconcile a value of the IES as low as 1/2 with the small differences in measured real returns on capital across different countries. We will subsequently refer to this observation as the difference facts.

Perhaps the most influential empirical evidence in favor of a low value of the IES is provided by Hall (1988). He estimates the IES using U.S. data on aggregate consumption and interest rates. The resulting estimates of the IES are close to zero and sometimes even negative. Hall (1988) concludes that the value of the IES is probably 0.2 or lower. Low estimated values of the IES have been documented in more recent research as well. Campbell (2003) finds evidence of a low IES in a variety of countries and Yogo (2004) estimates the IES to be 0.2 for the U.S. using an estimation strategy that controls for weak instruments. (1)

This paper makes two contributions. First, we provide two distinct ways to reconcile a low value of the true IES with the empirical evidence that it is large. Our resolutions arise in a model in which all agents have identical preferences and the same access to asset markets. These results do not necessarily imply that the IES is low. The model can also account for the same macroeconomic evidence with a high IES. This motivates our second contribution which is to provide empirical evidence that the true value of the IES is low. We make this case by confronting respectively the maintained hypothesis of a high value of the IES and the maintained hypothesis of a low IES with the regression-based evidence that the IES is low. An encompassing test indicates that the maintained hypothesis of a low IES (0.35 or lower) is consistent with the regression based evidence but that the maintained hypothesis of a large value of the IES of e.g. 1.5 is inconsistent with this evidence.

Agents in our model have Epstein and Zin (1989) (see also Weil (1990)) preferences and growth is endogenous. Epstein-Zin preferences are convenient because they allow us to make a meaningful distinction between intertemporal substitution and risk aversion. One parameter determines the IES or the desired response of expected consumption growth to an increase in the expected interest rate. …

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