Estimating the elasticity of intertemporal substitution: Is the aggregate financial return free from the weak instrument problem?

The elasticity of intertemporal substitution (EIS) is one of the key parameters in the Economics and Finance literature. It is usually estimated by means of the consumer's Euler Equation using an instrumental variable approach, and the estimates are usually zero or close to zero. Nevertheless, such attempts present two major problems: first, the use of weak instruments, and second, the absence of a rate of return that is representative of the agent's asset portfolio. The latter has been addressed by using the return of a synthetic mutual fund (SMF), which is a weighted combination of the returns of all assets held by the average household. The use of SMF returns led to EIS estimates of about 0.2 for the US economy. In this paper, we first investigate whether the EIS estimates using the SMF returns for the US suffer from the weak instrument problem. Next, we conduct robustness analyses using different estimators and instrument sets. Our findings show that estimates using SMF returns are plagued by weak instruments, but in some cases partially robust estimators were able to deliver a positive and statistically significant EIS estimate. Furthermore, we found that the Treasury Bill return does not suffer from weak instruments, but the EIS is not precisely estimated and seems to be close to zero.