  This paper describes how to reparameterize 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 reparameterization to distinguish weakly identified
parameters from strongly identified parameters. The reparameterizations 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
parameterization. An empirical application to a factor model of parental
investments in children is included.
