The authors appreciate the editor as well as the associate editor of Economic Modelling, and two anonymous referees for their valuable comments and suggestions. The authors also thank Hongbin Li at Stanford University for his insightful advice. This work was carried out with the aid of the Fundamental Research Funds for the Central Universities, Zhongnan University of Economics and Law (2722022EK022). The research funding of Wuhan Polytechnic University (2022RZ004) is also gratefully acknowledged. All remaining errors belong to the authors.