Optimal Maximin GMM Tests for Sphericity in Latent Factor Analysis of Short Panels

Abstract

We derive optimal maximin tests for parametric hypotheses in short panels with latent common factors. We rely on a Generalized Method of Moments setting with optimal weighting under a large cross-sectional dimension n and a fixed time series dimension T. We outline the asymptotic distributions of the estimators as well as the asymptotic maximin optimality of the Wald, Lagrange Multiplier, and Likelihood Ratio-type tests. The characterisation of optimality relies on finding the limit Gaussian experiment in strongly identified GMM models under a block-dependence structure and unobserved heterogeneity. We reject sphericity of idiosyncratic errors in an empirical application to a large cross-section of U.S. stocks, which casts doubt on the validity of routinely applying Principal Component Analysis to short panels of monthly financial returns.

Joint paper with Alain-Philippe Fortin, Patrick Gagliardini, Olivier Scaillet.