Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities
提出了两种数据驱动方法，用于非参数工具变量模型的最优估计和推断，包括自适应选择筛维度和构建一致置信带，并应用于估计企业出口弹性的国际贸易模型。
Abstract We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least-squares estimators. When implemented with this choice, estimators of both the structural function h0 and its derivatives (such as elasticities) converge at the fastest possible (i.e. minimax) rates in sup-norm. The second is for constructing uniform confidence bands (UCBs) for h0 and its derivatives. Our UCBs guarantee coverage over a generic class of data-generating processes and contract at the minimax rate, possibly up to a logarithmic factor. As such, our UCBs are asymptotically more efficient than UCBs based on the usual approach of undersmoothing. As an application, we estimate the elasticity of the intensive margin of firm exports in a monopolistic competition model of international trade. Simulations illustrate the good performance of our procedures in empirically calibrated designs. Our results provide evidence against common parameterizations of the distribution of unobserved firm heterogeneity.