  This study develops a framework for testing hypotheses on structural
parameters in incomplete models. Such models make set-valued predictions and
hence do not generally yield a unique likelihood function. The model structure,
however, allows us to construct tests based on the least favorable pairs of
likelihoods using the theory of Huber and Strassen (1973). We develop tests
robust to model incompleteness that possess certain optimality properties. We
also show that sharp identifying restrictions play a role in constructing such
tests in a computationally tractable manner. A framework for analyzing the
local asymptotic power of the tests is developed by embedding the least
favorable pairs into a model that allows local approximations under the limits
of experiments argument. Examples of the hypotheses we consider include those
on the presence of strategic interaction effects in discrete games of complete
information. Monte Carlo experiments demonstrate the robust performance of the
proposed tests.
