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Nonparametric Estimation and Identification in Non-Separable Models Using Panel Data

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  • Ben Deaner

Abstract

We present non-parametric identification results for panel models in the presence of a vector of unobserved heterogeneity that is not additively separable in the structural function. We exploit the time-invariance and finite dimension of the heterogeneity to achieve identification of a number of objects of interest with the panel length fixed. Identification does not require that the researcher have access to an instrument that is uncorrelated with the unobserved heterogeneity. Instead the identification strategy relies on an assumption that some lags and leads of observables are independent conditional on the unobserved heterogeneity and some controls. The identification strategy motivates an estimation procedure based on penalized sieve minimum distance estimation in the non-parametric instrumental variables framework. We give conditions under which the estimator is consistent and derive its rate of convergence. We present Monte Carlo evidence of its efficacy in finite samples.

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  • Ben Deaner, 2018. "Nonparametric Estimation and Identification in Non-Separable Models Using Panel Data," Papers 1810.00283, arXiv.org.
  • Handle: RePEc:arx:papers:1810.00283
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    File URL: http://arxiv.org/pdf/1810.00283
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    References listed on IDEAS

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    1. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    2. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    3. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    4. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    5. 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.
    6. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    7. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
    8. repec:cup:etheor:v:34:y:2018:i:03:p:659-693_00 is not listed on IDEAS
    9. repec:oup:restud:v:85:y:2018:i:3:p:1824-1851. is not listed on IDEAS
    10. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    11. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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