Wavelet Instruments for Efficiency Gains in Generalized Method of Moment Models

We propose a simple computational method in the context of generalized method of moments for improving the efficiency of regression coefficient estimates. The gains in efficiency arise by incorporating additional moment conditions in the estimation framework based on maximal overlap wavelet packet transforms of the continuous explanatory variables. A major advantage of the proposed method is that it does not require additional exogenous auxiliary information but relies on wavelet packet transforms of the existing continuous explanatory variables. Based on existing theory, we provide theoretical arguments for the proposed methodology, for both linear and non-linear models, and demonstrate its advantages with both an empirical application concerning two brand demand models and a Monte Carlo simulation study.