When Is Parallel Trends Sensitive to Functional Form?
研究了双重差分法中平行趋势假设何时依赖于结果变量的函数形式，给出了该假设对所有严格单调变换都成立的条件，并提出了可检验的假说检验。
This paper assesses when the validity of difference‐in‐differences 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 for parallel trends to be insensitive to functional form 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. These conditions have testable implications, and we introduce falsification tests for the null that parallel trends is insensitive to functional form.