摘要翻译：
本文考察了差中差及相关估计量的有效性是否依赖于函数形式。我们给出了一个新的刻画：平行趋势假设在结果的所有严格单调变换下成立当且仅当一个更强的“平行趋势”型条件对未处理潜在结果的累积分布函数成立。该条件满足当且本质上仅当群体可以被划分为一个有效随机分配治疗的亚组和一个未治疗的潜在结果分布随时间稳定的剩余亚组。我们进一步表明，如果不施加函数形式限制或不施加识别未治疗潜在结果的全部分布的假设，就不可能构造任何对治疗后(ATT)的平均治疗效果一致（或无偏）的估计量。我们的结果表明，希望指出ATT的研究人员应该证明以下其中之一是合理的：(i)为什么治疗是随机分配的，(ii)为什么选择的功能形式在排除其他功能形式时是正确的，或者(iii)推断未经治疗的潜在结果的整个反事实分布的方法。
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英文标题：
《When Is Parallel Trends Sensitive to Functional Form?》
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作者：
Jonathan Roth and Pedro H. C. Sant'Anna
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最新提交年份：
2021
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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：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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英文摘要：
  This paper assesses when the validity of difference-in-differences and related estimators depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger "parallel trends"-type condition holds for the cumulative distribution function of untreated potential outcomes. This condition is satisfied if and essentially only if the population can be partitioned into a subgroup for which treatment is effectively randomly assigned and a remaining subgroup for which the distribution of untreated potential outcomes is stable over time. We show further that it is impossible to construct any estimator that is consistent (or unbiased) for the average treatment effect on the treated (ATT) without either imposing functional form restrictions or imposing assumptions that identify the full distribution of untreated potential outcomes. Our results suggest that researchers who wish to point-identify the ATT should justify one of the following: (i) why treatment is as-if randomly assigned, (ii) why the chosen functional form is correct at the exclusion of others, or (iii) a method for inferring the entire counterfactual distribution of untreated potential outcomes.
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PDF链接：
https://arxiv.org/pdf/2010.04814