We derive optimal maximin tests for parametric hypotheses in short panels with latent common factors. We rely on a Generalized Method of Moments (GMM) 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 characterization of optimality relies on paths of triangular arrays of probability distributions to delineate the tangent space, the Local Asymptotic Normality (LAN) of the parametric and nonparametric components via slicing, and 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.

Keywords: Latent factor analysis, Generalized Method of Moments, maximin test, Gaussian experiment, fixed effects, panel data, sphericity, large n and fixed T asymptotics, equity returns.

JEL: C12, C23, C38, C58, G12.