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Nonparametric Derivative Estimation for Related-Effect Panel Data

Author

Listed:
  • Myoung-jae Lee

    () (Department of Economics, Sungkyunkwan University)

  • Yasushi Kondo

    () (Faculty of Economics, Toyama University)

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.

Suggested Citation

  • Myoung-jae Lee & Yasushi Kondo, 2002. "Nonparametric Derivative Estimation for Related-Effect Panel Data," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 A5-1, International Conferences on Panel Data.
  • Handle: RePEc:cpd:pd2002:a5-1
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    1. repec:cup:etheor:v:10:y:1994:i:1:p:172-97 is not listed on IDEAS
    2. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1989. "The Revenues-Expenditures Nexus: Evidence from Local Government Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(2), pages 415-429, May.
    3. Wooldridge, Jeffrey M., 1997. "Multiplicative Panel Data Models Without the Strict Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 13(05), pages 667-678, October.
    4. Koenker, Roger & Machado, José A.F. & Skeels, Christopher L. & Welsh, Alan H., 1994. "Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation," Econometric Theory, Cambridge University Press, vol. 10(01), pages 172-197, March.
    5. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    6. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
    7. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-362, March.
    8. repec:cup:etheor:v:13:y:1997:i:5:p:667-78 is not listed on IDEAS
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    Keywords

    nonparametrics; partial derivatives; panel data; related-effect.;

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