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Instrumental variables estimation of a generalized correlated random coefficients model

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  • Matthew Masten
  • Alexander Torgovitsky

Abstract

We study identification and estimation of the average treatment effect in a correlated random coefficients model that allows for first stage heterogeneity and binary instruments. The model also allows for multiple endogenous variables and interactions between endogenous variables and covariates. Our identification approach is based on averaging the coefficients obtained from a collection of ordinary linear regressions that condition on different realizations of a control function. This identification strategy suggests a transparent and computationally straightforward estimator of a trimmed average treatment effect constructed as the average of kernel-weighted linear regres-sions. We develop this estimator and establish its √n–consistency and asymptotic normality. Monte Carlo simulations show excellent finite-sample performance that is comparable in precision to the standard two-stage least squares estimator. We apply our results to analyze the effect of air pollution on house prices, and find substantial heterogeneity in first stage instrument effects as well as heterogeneity in treatment effects that is consistent with household sorting.

Suggested Citation

  • Matthew Masten & Alexander Torgovitsky, 2014. "Instrumental variables estimation of a generalized correlated random coefficients model," CeMMAP working papers 02/14, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:02/14
    DOI: 10.1920/wp.cem.2013.0214
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    1. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    Cited by:

    1. Iv'an Fern'andez-Val & Aico van Vuuren & Francis Vella, 2018. "Nonseparable Sample Selection Models with Censored Selection Rules," Papers 1801.08961, arXiv.org, revised Sep 2020.
    2. Stefan Hoderlein & Hajo Holzmann & Alexander Meister, 2015. "The triangular model with random coefficients," CeMMAP working papers 33/15, Institute for Fiscal Studies.
    3. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    4. Carolina Caetano & Juan Carlos Escaniano, 2015. "Identifying Multiple Marginal Effects with a Single Binary Instrument or by Regression Discontinuity," CAEPR Working Papers 2015-009, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    5. Iv'an Fern'andez-Val & Franco Peracchi & Aico van Vuuren & Francis Vella, 2018. "Selection and the Distribution of Female Hourly Wages in the U.S," Papers 1901.00419, arXiv.org, revised Jan 2022.
    6. Fernández-Val, Iván & van Vuuren, Aico & Vella, Francis, 2018. "Decomposing Real Wage Changes in the United States," IZA Discussion Papers 12044, Institute of Labor Economics (IZA).
    7. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    8. Fabian Dunker & Konstantin Eckle & Katharina Proksch & Johannes Schmidt-Hieber, 2017. "Tests for qualitative features in the random coefficients model," Papers 1704.01066, arXiv.org, revised Mar 2018.
    9. Fernández-Val, Iván & van Vuuren, Aico & Vella, Francis, 2018. "Nonseparable Sample Selection Models with Censored Selection Rules: An Application to Wage Decompositions," IZA Discussion Papers 11294, Institute of Labor Economics (IZA).

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