Abstract
Summary We provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component analysis in the presence of missing data. We show that the resulting estimators are consistent in large panels, but suffer from approximation and shrinkage biases. We correct these biases using matching and difference-in-differences approaches. Numerical examples and an empirical application to the effect of election day registration on voter turnout in the US illustrate the properties and usefulness of our methods.
Highlights
Nonseparable models are useful to capture multidimensional unobserved heterogeneity, which is an important feature of economic data
We develop an approach to estimate nonseparable models from panel data based on homogeneity restrictions and low-rank factor approximations
We provide more examples of models covered by Assumption 2.1 below
Summary
Nonseparable models are useful to capture multidimensional unobserved heterogeneity, which is an important feature of economic data. We develop an approach to estimate nonseparable models from panel data based on homogeneity restrictions and low-rank factor approximations. The two-way procedure is related to several recent proposals, such as the matching approach of Imai and Kim (2019) to estimate causal effects from panel data and the blind regression of Li et al (2017) for matrix completion The difference with these proposals is in the information used to match the observations. In contemporaneous and independent work, Chernozhukov et al (2020) have developed an alternative rotation-debiasing method that can be applied to make inference on heterogenous treatment effects in low-rank models This method consists of the application of iterative least squares to the left and right singular vectors of the matrix-completion estimator. All the proofs of the theoretical results are gathered in the Appendix
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