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.

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, G1.