INFERENCE IN PARTIALLY IDENTIFIED PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS
针对带有内生性和交互固定效应的部分识别非参数面板数据模型，提出基于鞅差散度量的检验统计量，用于推断参数约束是否被识别集中至少一个元素满足，并应用于中国家庭追踪调查数据研究恩格尔曲线。
In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric 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 measure for the distance between a conditional expectation object and zero. We derive a tight asymptotic distributional upper bound for the resultant test statistic under the null and show that it is divergent at rate- N under the global alternative. 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.