Root-$n$ Asymptotically Normal Maximum Score Estimation
Nan Liu, Yanbo Liu, Yuya Sasaki, Yuanyuan Wan
TLDR
This paper presents a method for maximum score estimation that achieves root-$n$ asymptotic normality using strictly concave surrogate score functions.
Key contributions
- Introduces strictly concave surrogate score functions for maximum score estimation.
- Achieves root-$n$ convergence and normal limiting distribution for binary choice models.
- Characterizes primitive conditions required for these improved asymptotic properties.
- Simulation studies validate the root-$n$ convergence and asymptotic normality.
Why it matters
The original maximum score method has theoretical and practical limitations. This work provides a significant theoretical advancement by enabling standard statistical inference for a powerful class of models, making them more practical for econometric applications.
Original Abstract
The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges at a slower-than-root-$n$ rate to a nonstandard limiting distribution. We investigate conditions under which strictly concave surrogate score functions can be employed to achieve identification through a smooth criterion function. This criterion enables root-$n$ convergence to a normal limiting distribution. While the conditions to guarantee these desired properties are nontrivial, we characterize them in terms of primitive conditions. Extensive simulation studies support, the root-$n$ convergence rate, the asymptotic normality, and the validity of the standard inference methods.
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