科学研究

Ruixuan LIU is an Associate Professor at the Chinese University of Hong Kong (CUHK) Business School. He received his PhD in Economics from University of Washington. His research is in the area of econometrics and data science. His recent works focus on nonparametric Bayesian inference and its applications to econometric models. His research work has been published on Econometrica, Journal of Econometrics, Econometric Theory and Quantitative Economics, etc. He won the 2018 Arnold Zellner Price (jointly with Yanqin Fan) for the best theoretical econometrics paper published by Journal of Econometrics between 2016 and 2017. He is currently an associate editor of Journal of Econometrics and Econometric Reviews.

This paper studies a quasi-Bayesian method that integrates frequentist estimation in the first stage with Bayesian inference in the second stage, motivated by structural discrete choice models using control function methodology to address endogeneity bias. In the first stage, a frequentist nonparametric approach estimates the control function, while the second stage employs a Bayesian approach to manage complex likelihood functions associated with the structural equation. We analyze the asymptotic properties of the quasi-posterior distributions from the second stage, demonstrating that the resulting quasi-Bayesian credible set lacks the desired coverage in large samples. However, the quasi-Bayesian point estimator remains consistent and asymptotically equivalent to a frequentist two-stage estimator. We also show that valid inference can be achieved by bootstrapping the quasi-posterior mean, accounting for first-stage estimation uncertainty.