Set inference in latent variables models

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 et al. (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.