Abstract: This paper is concerned with the estimation of a fixed effects panel data model that adopts a partially linear form, in which the coeffcients of some variables are restricted to be constant but the coeffcients of other variables are assumed to be varying, depending on some exogenous continuous variables. Moreover, we allow for the existence of endogeneity in the structural equation. Conditional moment restrictions on first differences are imposed to identify the structural equation. Based on these restrictions we propose a three stage estimation procedure. The asymptotic properties of these proposed estimators are established. Moreover, as a result of the first differences transformation, to estimate the unknown varying coeffcient functions, two alternative backfitting estimators are obtained. As a novelty, we propose a minimum distance estimator that, combining both estimators, is more effcient and achieves the optimal rate of convergence. The feasibility and possible gains of this new procedure are shown by estimating a Life-cycle hypothesis panel data model and a Monte Carlo study is implemented

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