We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given observable factors, the criterion checks whether the errors are weakly cross-sectionally correlated or share at least one unobservable common factor (interactive effects). A general version allows to determine the number of omitted common factors also for time-varying structures. The empirical analysis runs on ten thousand US stocks from January 1968 to December 2011. For monthly returns, we select time-invariant specifications with at least
four financial factors, and a scaled three-factor specification. For quarterly returns, we cannot select macroeconomic models without the market factor.

Keywords : large panel, approximate factor model, asset pricing, model selection, interactive fixed effects.

JEL : C12, C13, C23, C51, C52, C58, G12.