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 $h_0$ 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 $h_0$ 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.

翻译：我们提出了两种数据驱动方法，用于工具变量非参数模型的最优估计与推断。第一种方法针对一类流行的筛分两阶段最小二乘估计量，给出了筛分维度的数据驱动选择。当采用该选择时，结构函数$h_0$及其导数（如弹性）的估计量在超模范数下以最快可能（即极小化极大）速率收敛。第二种方法用于构建$h_0$及其导数的统一置信带（UCBs）。我们的UCBs保证在一般数据生成过程类别上的覆盖概率，并以极小化极大速率收缩（可能仅相差一个对数因子）。因此，与基于通常欠平滑方法的UCBs相比，我们的UCBs渐近更有效。作为应用，我们利用国际贸易垄断竞争模型估算了企业出口集约边际的弹性。仿真实验验证了我们的方法在经验校准设计中的良好表现。研究结果对未观测企业异质性分布的常见参数化假设提出了质疑。