Bontempi M. E., Mammi I. (2015).

Implementing a strategy to reduce the instrument count in panel GMM. THE STATA JOURNAL, vol. 15, pp. 1075-1097 (ISSN 1536-867X).

Abstract:

The problem of instrument proliferation and its consequences overfitting of the endogenous explanatory variables, biased instrumental-variables and generalized method of moments estimators, and weakening of the power of the overidentification tests are well known. This article introduces a statistical method to reduce the instrument count. Principal component analysis is applied on the instrument matrix, and the principal-component analysis scores are used as instruments for the panel generalized method of moments estimation. This strategy is implemented through the new command pca2.