# Nonparametric Derivative Estimation for Related-Effect Panel Data

*Myoung-jae Lee* and
*Yasushi Kondo*

No A5-1, 10th International Conference on Panel Data, Berlin, July 5-6, 2002 from International Conferences on Panel Data

**Abstract:**
In a "fixed-effect" panel data model with a nonparametric regression function \rho(x_{it}), the usual first-differencing yields a nonparametric regression function \mu(x_{it},x_{i,t+1}) with the restriction \mu(x_{it},x_{i,t+1}) = \rho(x_{i,t+1}) - \rho(x_{it}). Although \mu(x_{it},x_{i,t+1}) can be easily estimated nonparametrically with a kernel method, it is not clear that how to identify and estimate \partial\rho(x_{it})/\partial x_{it} (and \rho(x_{it})) using a kernel method, and this task becomes more difficult when a time-invariant variable c_i enters \rho(x_{it}). In this paper, we propose a kernel estimator that is a linear combination of partial derivative estimators for \partial\mu(x_{it},x_{i,t+1},c_i)/\partial x_{i,t+1} and \partial\mu(x_{it},x_{i,t+1},c_i)/\partial x_{i,t}, prove its consistency for \partial\rho(x_{it})/\partial x_{it} and derive the asymptotic distribution. An extensive Monte Carlo study is presented. Also multiple periods longer than two and mixed continuous/discrete regressor cases are considered to enhance the applicability.

**Keywords:** nonparametrics; partial derivatives; panel data; related-effect. (search for similar items in EconPapers)

**Date:** 2002-06

**New Economics Papers:** this item is included in nep-ecm

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**Persistent link:** https://EconPapers.repec.org/RePEc:cpd:pd2002:a5-1

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