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摘要翻译：
在差中差设计中，通常的做法是在治疗分配之前检查平行趋势，然而典型的估计和推断并没有考虑到这种测试已经发生的事实。我分析了传统的DiD估计器的性质，条件是通过了（即没有拒绝）平行前趋势的测试。当DiD设计有效且预趋势检验证实时，典型的DiD估计量是无偏的，但传统的标准误差过于保守。另外，在平行趋势下，存在一种替代的无偏估计，它比传统的DiD估计更有效。然而，当总体存在非零前趋势，但我们未能拒绝平行前趋势假设时，DiD估计量通常相对于总体DiD系数有偏差。此外，如果趋势是单调的，那么在合理的假设下，条件作用的偏差会加剧相对于真实治疗效果的偏差。我提出了新的估计和推断过程，说明了平行趋势的检验，并在蒙特卡罗模拟中比较了它们与传统估计器的性能。
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英文标题：
《Should We Adjust for the Test for Pre-trends in Difference-in-Difference
Designs?》
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作者：
Jonathan Roth
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最新提交年份：
2018
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/1804.01208
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