A strategy to reduce the count of moment conditions in panel data GMM

The problem of instrument proliferation and its consequences (overfitting of endogenous variables, bias of estimates, weakening of Sargan/Hansen test) are well known. The literature provides little guidance on how many instruments is too many. It is common practice to report the instrument count and to test the sensitivity of results to the use of more or fewer instruments. Strategies to alleviate the instrument proliferation problem are the lag-depth truncation and/or the collapse of the instrument set (the latter being an horizontal squeezing of the instrument matrix). However, such strategies involve either a certain degree of arbitrariness (based on the ability and the experience of the researcher) or of trust in the restrictions implicitly imposed (and hence untestable) on the instrument matrix. The aim of the paper is to introduce a new strategy to reduce the instrument count. The technique we propose is statistically founded and purely datadriven and, as such, it can be considered a sort of benchmark solution to the problem of instrument proliferation. We apply the principal component analysis (PCA) on the instrument matrix and exploit the PCA scores as the instrument set for the panel generalized method-of-moments (GMM) estimation. Through extensive Monte Carlo simulations, under alternative characteristics of persistence of the endogenous variables, we compare the performance of the Difference GMM, Level and System GMM estimators when lag truncation, collapsing and our principal component-based IV reduction (PCIVR henceforth) are applied to the instrument set. The same comparison has been carried out with two empirical applications on real data: the first replicates the estimates of Blundell and Bond [1998]; the second exploits a new and large panel data-set in order to assess the role of tangible and intangible capital on productivity. Results show that PCIVR is a promising strategy of instrument reduction.