The Information Content of Implied Probabilities to Detect Structural Change

Abstract

This paper proposes Pearson-type statistics based on implied probabilities to detect structural change. The class of generalized empirical likelihood estimators (see Smith (1997)) assigns a set of probabilities to each observation such that moment conditions are satisfied. These restricted probabilities are called implied probabilities. Implied probabilities may also be constructed for the standard GMM (see Back and Brown (1993)). The proposed test statistics for structural change are base on the information content in these implied probabilities. We consider cases of structural change with unknown breakpoint which can occur in the parameters of interest or in the overidentifying restrictions used to estimate these parameters. The test statistics considered here have good size and power properties.