Inference in partially identified panel data models with interactive fixed effects

This paper develops methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. We consider the case where the number of cross-sectional units (N) is large and the number of time series periods (T).as well as the number of unobserved common factors (R) are fixed. Under some normalization rules, wecan concentrateout thelarge dimen-sional parameter vector of factor loadings and specify a set of conditional moment restriction that are involved with only the finite dimensional factor parameters along with the infinite dimensional nonpara-metric component. For a conjectured restriction on the parameter, we consider testing the null hypothesis that the restriction is satisfied by at least one element in the identified set and propose a test statistic based on a novel martingale difference divergence (MDD) measure for the distance between a conditional expectation object and zero. We derive the limiting distribution of the resultant test statistic under the null and show that it is divergent at rate-N under the global alternative based on the U-process theory. To obtain the critical values for our test, we propose a version of multiplier bootstrap and establish its asymptotic validity. Simulations demonstrate the finite sample properties of our inference procedure. We apply our method to study Engel curves for major nondurable expenditures in China by using a panel dataset from the China Family Panel Studies (CFPS).