标题： 在双重差分设计中是否应针对预趋势检验进行调整？ 显示英文标题

标题： Should We Adjust for the Test for Pre-trends in Difference-in-Difference Designs?

摘要： 差异-差异（DiD）设计中的常见做法是在处理分配之前检查平行趋势，但典型的估计和推断并未考虑这一检验已经进行的事实。我分析了在通过（即未被拒绝）平行前期趋势检验的条件下，传统DiD估计量的性质。当DiD设计有效且前期趋势检验确认这一点时，典型DiD估计量是无偏的，但传统的标准误差过于保守。此外，在平行趋势下，存在一个比传统DiD估计量更有效的无偏估计量。然而，当总体中存在非零前期趋势但我们未能拒绝平行前期趋势的假设时，DiD估计量相对于总体DiD系数通常是偏的。此外，如果趋势是单调的，则在合理的假设下，条件带来的偏差会加剧相对于真实处理效应的偏差。我提出了考虑平行趋势检验的新估计和推断程序，并在蒙特卡洛模拟中将其性能与传统估计量进行了比较。 显示英文摘要

摘要： The common practice in difference-in-difference (DiD) designs is to check for parallel trends prior to treatment assignment, yet typical estimation and inference does not account for the fact that this test has occurred. I analyze the properties of the traditional DiD estimator conditional on having passed (i.e. not rejected) the test for parallel pre-trends. When the DiD design is valid and the test for pre-trends confirms it, the typical DiD estimator is unbiased, but traditional standard errors are overly conservative. Additionally, there exists an alternative unbiased estimator that is more efficient than the traditional DiD estimator under parallel trends. However, when in population there is a non-zero pre-trend but we fail to reject the hypothesis of parallel pre-trends, the DiD estimator is generally biased relative to the population DiD coefficient. Moreover, if the trend is monotone, then under reasonable assumptions the bias from conditioning exacerbates the bias relative to the true treatment effect. I propose new estimation and inference procedures that account for the test for parallel trends, and compare their performance to that of the traditional estimator in a Monte Carlo simulation.