Nonparametric Instrumental Regression with Two-Way Fixed Effects

Abstract This paper proposes a novel estimator for nonparametric instrumental regression while controlling for additive two-way fixed effects. In particular, the Landweber–Fridman regularization, to overcome the ill-posed inverse problem in the nonparametric instrumental regression procedure, is combined with the local-within two-ways fixed effect estimator presented by Lee, Y., D. Mukherjee, and A. Ullah. (2019. “Nonparametric Estimation of the Marginal Effect in Fixed-Effect Panel Data Models.” Journal of Multivariate Analysis 171: 53–67). Compared to other estimators in this context, an appealing feature is its flexible applicability with respect to different panel model specifications, i.e. models comprising either individual, temporal, or two-way fixed effects. The estimator’s performance is tested on simulated data, where a Monte Carlo study reveals good finite sample behaviour. Confidence intervals are provided by applying the wild bootstrap.