arXiv 21 Oct 2024 · Econometrics
arXiv:2410.15734 · PDF · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Anthony Heyes and Soodeh Saberian (2019) Temperature and decisions: evidence from 207,000 court cases | 0.971 | 12 | 3 | 92% |
| 2 | Xiaohong Chen (2007) Large sample sieve estimation of semi-nonparametric models | 0.874 | 6 | 4 | 67% |
| 3 | Schölkopf, Bernhard and Alexander J. Smola (2002) Learning with kernels | 0.811 | 4 | 2 | 100% |
| 4 | A. Ronald Gallant and Douglas W. Nychka (1987) Semi-nonparametric maximum likelihood estimation | 0.794 | 8 | 4 | 50% |
| 5 | Victor M. Fenton and A. Ronald Gallant (1996) Convergence rates of SNP density estimators | 0.794 | 6 | 3 | 50% |
| 6 | Victor M. Fenton and A. Ronald Gallant (1996) Qualitative and asymptotic performance of SNP density estimators | 0.737 | 3 | 2 | 100% |
| 7 | Heyes, Anthony and Saberian, Soodeh (2022) Correction to “Temperature and Decisions: Evidence from 207,000 Court Cases” and Reply to Spamann | 0.737 | 3 | 2 | 100% |
| 8 | Rosa L. Matzkin (1992) Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models | 0.737 | 3 | 2 | 100% |
| 9 | Charles A. Micchelli and Yuesheng Xu and Haizhang Zhang (2006) Universal kernels. | 0.644 | 2 | 2 | 100% |
| 10 | Singh, Rahul (2022) Kernel methods for unobserved confounding: Negative controls, proxies, and instruments | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 51 scored citations.