Abstract. 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 pro-
pose a fast preliminary search in the parameter space with an alternative, more
conservative yet consistent test, based on a parameter free critical value.

Abstract:
We show that the identification problem for a class of dynamic panel logit models with fixed effects has a connection to the truncated moment problem in mathematics. We use this connection to show that the sharp identified set of the structural parameters is characterized by a set of moment equality and inequality conditions. This result provides sharp bounds in models where moment equality conditions do not exist or do not point identify the parameters. We also show that the sharp identified set of the non-parametric latent distribution of the fixed effects is characterized by a vector of its generalized moments, and that the number of moments grows linearly in T. This final result lets us point identify, or sharply bound specific classes of functionals, without solving an optimization problem with respect to the latent distribution. We illustrate our identification result with several examples, and an empirical application on modeling children’s respiratory conditions.

Abstract:
Quantile regression is a method that allows to access the effect of predictors on the conditional quantile of the response in a regression framework. In this talk, we will present some recent theoretical and methodology developments for quantile regression in a panel data setting where repeated observations on individuals are available. On the theory side, we will discuss conditions that guarantee unbiased asymptotic normality of quantile regression with individual-specific intercepts and common slopes. From a methodological standpoint, we will discuss approaches to relax the common slope assumption and allow for groups of individuals that share the same slopes while leaving the intercepts unrestricted.