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Identification and estimation in a correlated random coefficients binary response model

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  • Stefan Hoderlein

    () (Institute for Fiscal Studies and Boston College)

  • Robert Sherman

    (Institute for Fiscal Studies)

Abstract

We study identification and estimation in a binary response model with random coefficients B allowed to be correlated with regressors X. Our objective is to identify the mean of the distribution of B and estimate a trimmed mean of this distribution. Like Imbens and Newey (2009), we use instruments Z and a control vector V to make X independent of B given V. A consequent conditional median restriction identifies the mean of B given V. Averaging over V identifies the mean of B. This leads to an analogous localise-then-average approach to estimation. We estimate conditional means with localised smooth maximum score estimators and average to obtain a vn-consistent and asymptotically normal estimator of a trimmed mean of the distribution of B. The method can be adapted to models with nonrandom coefficients to produce vn-consistent and asymptotically normal estimators under the conditional median restrictions. We explore small sample performance through simulations, and present an application.

Suggested Citation

  • Stefan Hoderlein & Robert Sherman, 2012. "Identification and estimation in a correlated random coefficients binary response model," CeMMAP working papers CWP42/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:42/12
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    1. repec:eee:csdana:v:114:y:2017:i:c:p:130-145 is not listed on IDEAS
    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. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random Coefficients in Static Games of Complete Information," Boston College Working Papers in Economics 835, Boston College Department of Economics.
    4. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.

    More about this item

    Keywords

    Heterogeneity; Correlated Random Coefficients; Endogeneity; Binary Response Model; Instrumental Variables; Control Variables; Conditional Median Restrictions;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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