Estimation and Inference for Hyperbolic Utility Concave Consumption Using Estimating Functions and Pivots

Hyperbolic absolute risk aversion (HARA) utility, (See is a more Carroll and Kimball, 1996), realistic alternative to the power utility used in consumption-based capital asset pricing models (CCAPM). We propose a new estimator for the HARA based on Godambe-Durbin “estimating functions” and small sigma asymptotics (SSA). This is an alternative to the generalized method of moments (GMM). Since the parameters of the HARA involve ratios of regression coefficients, the traditional inference based on the delta method is problematic. As in Vinod (1998) we use Godambe's pivot for inference on these parameters. As a scaled sum of scores this pivot is convenient for bootstraps and double bootstraps, and leads to a meaningful concave consumption function.