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Identification and estimation in a correlated random coefficients binary response model

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  • Stefan Hoderlein
  • Robert Sherman

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 √n-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 √n-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 42/12, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:42/12
    DOI: 10.1920/wp.cem.2012.4212
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    References listed on IDEAS

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