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A Kernelization-Based Approach to Nonparametric Binary Choice Models

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  • Guo Yan

Abstract

We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its computational efficiency. For instance, even when assuming a normal error distribution as in probit models, commonly used sieves for approximating an unknown function of covariates can lead to a large-dimensional optimization problem when the number of covariates is moderate. Our approach, motivated by kernel methods in machine learning, views certain reproducing kernel Hilbert spaces as special sieve spaces, coupled with spectral cut-off regularization for dimension reduction. We establish the consistency of the proposed estimator for both the systematic function of covariates and the distribution function of the error term, and asymptotic normality of the plug-in estimator for weighted average partial derivatives. Simulation studies show that, compared to parametric estimation methods, the proposed method effectively improves finite sample performance in cases of misspecification, and has a rather mild efficiency loss if the model is correctly specified. Using administrative data on the grant decisions of US asylum applications to immigration courts, along with nine case-day variables on weather and pollution, we re-examine the effect of outdoor temperature on court judges' "mood", and thus, their grant decisions.

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  • Guo Yan, 2024. "A Kernelization-Based Approach to Nonparametric Binary Choice Models," Papers 2410.15734, arXiv.org.
  • Handle: RePEc:arx:papers:2410.15734
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    References listed on IDEAS

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    1. Anthony Heyes & Soodeh Saberian, 2022. "Correction to "Temperature and Decisions: Evidence from 207,000 Court Cases" and Reply to Spamann," American Economic Journal: Applied Economics, American Economic Association, vol. 14(4), pages 529-533, October.
    2. Antonio Merlo & Áureo de Paula, 2017. "Identification and Estimation of Preference Distributions When Voters Are Ideological," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(3), pages 1238-1263.
    3. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    4. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    5. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, January.
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