Heterogenous intertemporal elasticity of substitution and relative risk aversion: estimation of optimal consumption choice with habit formation and measurement errors

This paper investigates the existence and degree of variation across house holds and over time in the intertemporal elasticity of substitution (IES) and the coefficient of relative risk aversion (RRA) that is generated by habit forming preferences. To do so, we develop a new nonlinear GMM estimator to investigate the presence of habit formation in household consumption using data from the Panel Study of Income Dynamics. Our method accounts for classical measurement errors in consumption without parametric assumptions on the distribution of measurement errors. The estimation results support habit formation in food consumption. Using these estimates, we develop bounds for the expectation of the implied heterogenous intertemporal elasticity of substitution and relative risk aversion that account for measurement errors and compute asymptotically valid confidence intervals on these bounds. We find that these parameters display significant variation across households and over time.