Review of Economic Studies · 2018 · Matias D. Cattaneo、Michael Jansson、Xinwei Ma
中文摘要
我们研究了在进入两步估计程序的第一步估计中包含大量协变量的含义。我们发现，当所包含的协变量数目相对于样本量的平方根而言“很大”时，会出现一阶偏误，从而使标准推断程序失效。我们表明，刀切法能够一致地估计这一“大量协变量”偏误，从而给出一个新的自动偏误校正两步点估计量。刀切法还能一致地估计原始两步点估计量的标准误。在推断方面，我们发展了一种有效的偏误校正后自助法近似，它考虑了刀切法偏误校正所引入的额外变异性。我们发现，刀切法偏误校正点估计量与自助法偏误校正后推断在模拟中表现优异，相较于对包含大量协变量并不稳健的常规两步点估计量与推断程序，带来了重要的改进。我们将结果应用于一系列不同的处理效应、政策评估及其他应用微观经济学情境。特别地，我们详细讨论了生产函数与边际处理效应的估计。
Abstract
We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first-order bias emerges when the number of included covariates is “large” relative to the square-root of sample size, rendering standard inference procedures invalid. We show that the jackknife is able to estimate this “many covariates” bias consistently, thereby delivering a new automatic bias-corrected two-step point estimator. The jackknife also consistently estimates the standard error of the original two-step point estimator. For inference, we develop a valid post-bias-correction bootstrap approximation that accounts for the additional variability introduced by the jackknife bias-correction. We find that the jackknife bias-corrected point estimator and the bootstrap post-bias-correction inference perform excellent in simulations, offering important improvements over conventional two-step point estimators and inference procedures, which are not robust to including many covariates. We apply our results to an array of distinct treatment effect, policy evaluation, and other applied microeconomics settings. In particular, we discuss production function and marginal treatment effect estimation in detail.