  We propose confidence regions for the parameters of incomplete models with
exact coverage of the true parameter in finite samples. Our confidence region
inverts a test, which generalizes Monte Carlo tests to incomplete models. The
test statistic is a discrete analogue of a new optimal transport
characterization of the sharp identified region. Both test statistic and
critical values rely on simulation drawn from the distribution of latent
variables and are computed using solutions to discrete optimal transport, hence
linear programming problems. We also propose a fast preliminary search in the
parameter space with an alternative, more conservative yet consistent test,
based on a parameter free critical value.
