Weak Identification in Low-Dimensional Factor Models with One or Two Factors - Cox, Gregory Fletcher (The Review of Economics and Statistics, 2026)
Abstract This paper describes how to reparametrize low-dimensional factor models with one or two factors to fit weak identification theory developed for generalized method of moments models. Some identification-robust tests, here called “plug-in” tests, require a reparametrization to distinguish weakly identified parameters from strongly identified parameters. The reparametrizations in this paper make plug-in tests available for subvector hypotheses in low-dimensional factor models with one or two factors. Simulations show that the plug-in tests are less conservative than identification-robust tests that use the original parametrization. An empirical application to a factor model of parental investments in children is included.