COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1885 Multiscale Adaptive Inference on Conditional Moment Inequalities Timothy B. Armstrong and Hock Peng Chan January 2013 This paper considers inference for conditional moment inequality models
using a multiscale statistic. We derive the asymptotic distribution of this test statistic
and use the result to propose feasible critical values that have a simple analytic
formula. We also propose critical values based on a modified bootstrap procedure and prove
their asymptotic validity. The asymptotic distribution is extreme value, and the proof
uses new techniques to overcome several technical obstacles. We provide power results that
show that our test detects local alternatives that approach the identified set at the best
possible rate under a set of conditions that hold generically in the set identified case
in a broad class of models, and that our test is adaptive to the smoothness properties of
the data generating process. Our results also have implications for the use of moment
selection procedures in this setting. We provide a monte carlo study and an empirical
illustration to inference in a regression model with endogenously censored and missing
data. |
