  We develop inferential tools for latent factor analysis in short panels. The
pseudo maximum likelihood setting under a large cross-sectional dimension n and
a fixed time series dimension T relies on a diagonal TxT covariance matrix of
the errors without imposing sphericity nor Gaussianity. We outline the
asymptotic distributions of the latent factor and error covariance estimates as
well as of an asymptotically uniformly most powerful invariant (AUMPI) test for
the number of factors based on the likelihood ratio statistic. We derive the
AUMPI characterization from inequalities ensuring the monotone likelihood ratio
property for positive definite quadratic forms in normal variables. An
empirical application to a large panel of monthly U.S. stock returns separates
month after month systematic and idiosyncratic risks in short subperiods of
bear vs. bull market based on the selected number of factors. We observe an
uptrend in the paths of total and idiosyncratic volatilities while the
systematic risk explains a large part of the cross-sectional total variance in
bear markets but is not driven by a single factor. Rank tests show that
observed factors struggle spanning latent factors with a discrepancy between
the dimensions of the two factor spaces decreasing over time.
