Weak Identification in Low-Dimensional Factor Models with One or Two Factors

TL;DR

This paper develops reparameterization techniques for low-dimensional factor models with one or two factors, enabling the use of identification-robust tests and improving their performance.

Contribution

It introduces reparameterizations that facilitate plug-in tests for weak identification in simple factor models, expanding their applicability.

Findings

Plug-in tests are less conservative than original tests.

Reparameterizations enable subvector hypothesis testing.

Simulations confirm improved test performance.

Abstract

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.