Informational Content of Special Regressors in Heteroskedastic Binary Response Models

47 Pages Posted: 22 Apr 2013 Last revised: 17 May 2013

See all articles by Songnian Chen

Songnian Chen

Hong Kong University of Science & Technology (HKUST) - Department of Economics

Shakeeb Khan

Duke University - Department of Economics

Xun Tang

University of Pennsylvania - Department of Economics; Rice University - Department of Economics

Date Written: April 16, 2013

Abstract

We quantify the identifying power of special regressors in heteroskedastic binary regressions with median-independent or conditionally symmetric errors. We measure the identifying power using two criteria: the set of regressor values that help point identify coefficients in latent payoffs as in (Manski 1988); and the Fisher information of coefficients as in (Chamberlain 1986). We …find that for median-independent errors, requiring one of the regressors to be "“special" (in a sense similar to (Lewbel 2000)) does not add to the identifying power or the information for coefficients. Nonetheless it does help identify the error distribution and the average structural function. For conditionally symmetric errors, the presence of a special regressor improves the identifying power by the criterion in (Manski 1988), and the Fisher information for coefficients is strictly positive under mild conditions. We propose a new estimator for coefficients that converges at the parametric rate under symmetric errors and a special regressor, and report its decent performance in small samples through simulations.

Keywords: Binary regression, heteroskedasticity, identi…fication, information, median independence, conditional symmetry

Suggested Citation

Chen, Songnian and Khan, Shakeeb and Tang, Xun, Informational Content of Special Regressors in Heteroskedastic Binary Response Models (April 16, 2013). Economic Research Initiatives at Duke (ERID) Working Paper No. 144, PIER Working Paper No. 13-021, Available at SSRN: https://ssrn.com/abstract=2254970

Songnian Chen

Hong Kong University of Science & Technology (HKUST) - Department of Economics ( email )

Clear Water Bay
Kowloon, Hong Kong
China

Shakeeb Khan (Contact Author)

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

Xun Tang

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-7409 (Phone)
215-573-2057 (Fax)

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States

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