Exact Testing of Many Moment Inequalities Against Multiple Violations

2019/04/29 by Nick Koning, Koning, Nick, Paul Bekker +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Statistics Theory (math.ST) #econ.EM #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1904.12775

arxiv created 2020/06/08 · arxiv updated 2020/06/09

Abstract

This paper considers the problem of testing many moment inequalities, where the number of moment inequalities (p) is possibly larger than the sample size (n). Chernozhukov et al. (2019) proposed asymptotic tests for this problem using the maximum t statistic. We observe that such tests can have low power if multiple inequalities are violated. As an alternative, we propose novel randomization tests based on a maximum non-negatively weighted combination of t statistics. We provide a condition guaranteeing size control in large samples. Simulations show that the tests control size in small samples (n = 30, p = 1000), and often has substantially higher power against alternatives with multiple violations than tests based on the maximum t statistic.

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