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Instrumental variables estimation of a generalized correlated random coefficients model

Author

Listed:
  • Matthew Masten

    (Institute for Fiscal Studies and Duke University)

  • Alexander Torgovitsky

    (Institute for Fiscal Studies and University of Chicago)

Abstract

We study identi?cation and estimation of the average treatment effect in a correlated random coefficients model that allows for ?rst stage heterogeneity and binary instruments. The model also allows for multiple endogenous variables and interactions between endogenous variables and covariates. Our identi?cation 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 identi?cation 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 vn–consistency and asymptotic normality. Monte Carlo simulations show excellent ?nite-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 ?nd substantial heterogeneity in ?rst 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 CWP02/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:02/14
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    File URL: http://www.cemmap.ac.uk/wps/cwp021414.pdf
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    References listed on IDEAS

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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, January.
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    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. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    4. 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.
    5. 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, IZA Network @ LISER.
    6. 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.
    7. 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.
    8. Fernández-Val, Iván & van Vuuren, Aico & Vella, Francis, 2018. "Decomposing Real Wage Changes in the United States," IZA Discussion Papers 12044, IZA Network @ LISER.
    9. Dylan Balla-Elliott, 2023. "Identifying Causal Effects in Information Provision Experiments," Papers 2309.11387, arXiv.org, revised Jan 2026.
    10. 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.

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