A Derivative Based Estimator for Semiparametric Index Models

Abstract

This paper proposes a semiparametric estimator for single- and multiple-index models. It provides an extension of the average derivative estimator to the multiple index model setting. The estimator uses the average of the outer product of derivatives and is shown to be root-N consistent and asymptotically normal. Unlike the average derivative estimator, our estimator still works in the single-index setting when the expected derivative is zero (symmetry). Compared to other estimators for multiple index models, the proposed estimator has the advantage of ease of computation. While many econometric models can be regarded as multiple index models with known number of indices, our estimator in addition provides for a natural framework within which to test for the number of indices required.

Keywords: Semiparametric estimation, index models, average derivatives, outer product of derivatives, rank testing