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Statistica Sinica 31 (2021), 981-1003

EFFICIENT NONPARAMETRIC THREE-STAGE
ESTIMATION OF FIXED EFFECTS VARYING
COEFFICIENT PANEL DATA MODELS

Juan M. Rodriguez-Póo and Alexandra Soberón

Universidad de Cantabria

Abstract: This study estimates a fixed effects panel data model that adopts a partially linear form: the coefficients of some variables are restricted to be constant, but the coefficients of other variables are assumed to vary depending on some exogenous continuous variables. Moreover, we allow for endogeneity in the structural equation. Conditional moment restrictions are imposed on the first-differences to identify the structural equation. Based on these restrictions, we propose a three-stage estimation procedure, and establish the asymptotic properties of these proposed estimators. Moreover, from the first-differences transformation, we obtain two alternative backfitting estimators to estimate the unknown varying coefficient functions. As a novel contribution, we propose a minimum distance estimator that combines both estimators and, thus, is more efficient and achieves the optimal rate of convergence. The feasibility and benefits of this new procedure are shown by estimating a life-cycle hypothesis panel data model and implementing a Monte Carlo study.

Key words and phrases: Endogeneity, fixed effects, functional-coefficient models, generalized F-test, instrumental variables, panel data.

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