Wald, QLR, and score tests when parameters are subject to linear inequality constraints

• Published in: Journal of econometrics Vol. 235; no. 2; pp. 2005 - 2026
• Main Authors: Fan, Yanqin, Shi, Xuetao
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2023
• Subjects: algorithms; Bonferroni-type correction; class; econometrics; Extremum estimation; Implicit nuisance parameter; Mincer earnings regression; Monte Carlo method; Polytope projection; Random coefficients model; Uniform inference; Implicit nuisance parameter; C12; Uniform inference; Polytope projection; Mincer earnings regression; Extremum estimation; C18; Bonferroni-type correction; Random coefficients model
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2023.02.009

This paper develops Wald-type, QLR, and score-type tests for linear equality constraints in a general class of extremum estimation problems where the parameter space is characterized by a finite number of linear equality and inequality constraints. We show that the asymptotic null distributions of the Wald and QLR statistics are discontinuous in an implicit nuisance parameter and propose an algorithm to identify it. In contrast, the asymptotic null distribution of the score statistic is not discontinuous in any model parameter but depends on a polytope projection. We present an algorithm based on the Fourier–Motzkin elimination to compute such a projection. We study the consistency and local power properties of the three tests. Finally, we present numerical results of our tests’ finite sample performance from a Monte Carlo study and conduct an empirical illustration of a Mincer earnings regression.