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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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    Cited by:

    1. Fernández-Val, Ivan & van Vuuren, Aico & Vella, Francis, 2024. "Nonseparable sample selection models with censored selection rules," Journal of Econometrics, Elsevier, vol. 240(2).
    2. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    3. 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.
    4. 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).
    5. Dylan Balla-Elliott, 2023. "Identifying Causal Effects in Information Provision Experiments," Papers 2309.11387, arXiv.org, revised Jan 2026.
    6. 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).
    7. 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.
    8. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    9. 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.
    10. Fabian Dunker & Konstantin Eckle & Katharina Proksch & Johannes Schmidt-Hieber, 2017. "Tests for qualitative features in the random coefficients model," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 225, Courant Research Centre PEG.

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