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Semiparametric Estimation of Correlated Random Coefficient Models without Instrumental Variables

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  • Samuele Centorrino
  • Aman Ullah
  • Jing Xue

Abstract

We study a linear random coefficient model where slope parameters may be correlated with some continuous covariates. Such a model specification may occur in empirical research, for instance, when quantifying the effect of a continuous treatment observed at two time periods. We show one can carry identification and estimation without instruments. We propose a semiparametric estimator of average partial effects and of average treatment effects on the treated. We showcase the small sample properties of our estimator in an extensive simulation study. Among other things, we reveal that it compares favorably with a control function estimator. We conclude with an application to the effect of malaria eradication on economic development in Colombia.

Suggested Citation

  • Samuele Centorrino & Aman Ullah & Jing Xue, 2019. "Semiparametric Estimation of Correlated Random Coefficient Models without Instrumental Variables," Papers 1911.06857, arXiv.org.
    • Handle: RePEc:arx:papers:1911.06857
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    References listed on IDEAS

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    9. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, vol. 79(2), pages 185-191, May.
    10. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    11. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
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    13. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
    14. Hoyt Bleakley, 2010. "Malaria Eradication in the Americas: A Retrospective Analysis of Childhood Exposure," American Economic Journal: Applied Economics, American Economic Association, vol. 2(2), pages 1-45, April.
    15. David Cutler & Winnie Fung & Michael Kremer & Monica Singhal & Tom Vogl, 2010. "Early-Life Malaria Exposure and Adult Outcomes: Evidence from Malaria Eradication in India," American Economic Journal: Applied Economics, American Economic Association, vol. 2(2), pages 72-94, April.
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    Cited by:

    1. Kien C. Tran & Mike G. Tsionas, 2022. "Instrumental Variables Estimation without Outside Instruments," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(3), pages 489-506, September.

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