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. ( 2018 ) 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 a novel randomization test based on a maximum non-negatively weighted combination of t statistics.  Simulations show that the test controls size in small samples (n = 30, p = 1000), and often has substantially higher power against alternatives with multiple violations  .
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 .
R
2018
2019
R
a novel randomization test
novel randomization tests
A
We provide a condition guaranteeing size control in large samples.
R
test controls
tests control
A
than tests based on the maximum t statistic