Specification testing for conditional moment restrictions under local identification failure

• 成果类型: Article
• 署名作者: Dovonon, Prosper; Gospodinov, Nikolay
• 署名单位: Universite de Montreal; Concordia University - Canada; Universite de Montreal; Federal Reserve System - USA; Federal Reserve Bank - Atlanta
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE2242
• 发表日期: 2024
• 页码: 849-891
• 关键词: GMM; conditional moment restrictions; test for overidentifying restrictions; local and global identification; first-order local identification failure; second-order local identification; U-statistics; strong mixing dependence; Robustness

摘要

In this paper, we study the asymptotic behavior of specification tests in conditional moment restriction models under first-order local identification failure with dependent data. More specifically, we obtain conditions under which the conventional specification test for conditional moment restrictions retains its standard normal limit when first-order local identification fails but global identification is still attainable. In the process, we derive some novel intermediate results that include extending the first- and second-order local identification framework to models defined by conditional moment restrictions, establishing the rate of convergence of the GMM estimator and characterizing the asymptotic representation for degenerate U-statistics under strong mixing dependence. Importantly, the specification test is robust to first-order local identification failure regardless of the number of directions in which the Jacobian of the conditional moment restrictions is degenerate and remains valid even if the model is first-order identified.