We propose a methodology for constructing valid confidence regions
in incomplete models with latent variables satisfying moment equality restrictions.
These include moment equality and inequality models with latent variables. The
confidence regions are obtained by inverting tests based on the characterization of
the identified set derived in Ekeland, Galichon, and Henry (2010). A valid bootstrap approximation of the distribution of the test statistic is derived under mild
conditions and the confidence regions are shown to have correct asymptotic size.