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Nonparametric Estimation Of Homogeneous Functions

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  • Tripathi, Gautam
  • Kim, Woocheol

Abstract

Consider the regression y = f(x) + e ' where E (e | x) = 0 and the exact functional form of f is unknown, although we do know that it is homogeneous of known degree r. Using a local linear approach we examine two ways of nonparametrically estimating f: (i) a direct or numeraire approach, and (ii) a projection based approach. We show that depending upon the nature of the conditional variance var (E | x), one approach may be asymptotically better than the other. Results of a small simulation experiment are presented to support our findings.
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Suggested Citation

  • Tripathi, Gautam & Kim, Woocheol, 2003. "Nonparametric Estimation Of Homogeneous Functions," Econometric Theory, Cambridge University Press, vol. 19(04), pages 640-663, August.
  • Handle: RePEc:cup:etheor:v:19:y:2003:i:04:p:640-663_19
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    Cited by:

    1. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    2. Lewbel, Arthur & Linton, Oliver, 2003. "Nonparametric estimation of homothetic and homothetically separable functions," LSE Research Online Documents on Economics 2066, London School of Economics and Political Science, LSE Library.
    3. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.
    4. Haag, Berthold R. & Hoderlein, Stefan & Pendakur, Krishna, 2009. "Testing and imposing Slutsky symmetry in nonparametric demand systems," Journal of Econometrics, Elsevier, vol. 153(1), pages 33-50, November.

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