This thesis has three chapters. The first chapter studies new tests for the number of latent factors in factor models having a large cross-sectional dimension n and small time series dimension T, i.e., a short panel. These tests are based on the eigenvalues of variancecovariance matrices of asset returns, and rely on either an assumption of spherical errors, or instrumental variables for factor betas. The second chapter develops inferential tools for latent factor analysis in short panels. The pseudo maximum likelihood setting in short panels relies on a diagonal variance-covariance matrix of the errors without imposing sphericity nor Gaussianity. The chapter outlines the asymptotic distributions of the latent factor and error variance estimates as well as an asymptotically uniformly most powerful invariant (AUMPI) test for the number of factors based on the likelihood ratio statistic. The third chapter develops inference tools for the number of common latent factors between two short panels. The approach builds on general tests for the dimension of the intersection of two matrix column spaces, where each matrix is observed with noise. The test statistics are based on canonical correlations, and their asymptotic distributions are derived via perturbation methods.