Logs with zeros? Some problems and solutions
含零值时如何取对数？若干问题与解决办法AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
本页为预印本版本；arXiv 收录、作者填写的期刊信息以及作者既有发表经历，都不单独证明本篇已接收。作者发表记录按 OpenAlex 身份与完整姓名、本站覆盖期刊 ISSN 及正式卷期核对，只展示已核实例，档案仍可能误合并。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要直接讨论平均处理效应的定义、识别和解释，以及广延与集约边际的因果效应。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
含零值时如何取对数？若干问题与解决办法
- 研究问题
- 当结果变量可取零且处理影响从零到非零的变化时，类对数变换的平均处理效应为何依赖计量单位，应如何解释和替代？
- 方法与思路
- 作者分析结果变量重新缩放对类对数效应的影响，提出三个性质不可兼得的结果，并讨论水平效应和分开分析两种边际。
- 材料陈述的贡献
- 摘要称类对数效应不宜解释为近似百分比效应，并指出个体效应平均、单位不变与点识别三者不能同时满足。
- 阅读关注点
- 应核对任意幅度效应与三难结果的条件、广延和集约边际如何定义，以及 Poisson 回归、校准与 Lee 界分别回答什么问题。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未完整给出不可能性条件，替代方法的识别要求也须逐项核实。
原文摘要
When studying an outcome $Y$ that is weakly-positive but can equal zero (e.g. earnings), researchers frequently estimate an average treatment effect (ATE) for a "log-like" transformation that behaves like $\log(Y)$ for large $Y$ but is defined at zero (e.g. $\log(1+Y)$, $\mathrm{arcsinh}(Y)$). We argue that ATEs for log-like transformations should not be interpreted as approximating percentage effects, since unlike a percentage, they depend on the units of the outcome. In fact, we show that if the treatment affects the extensive margin, one can obtain a treatment effect of any magnitude simply by re-scaling the units of $Y$ before taking the log-like transformation. This arbitrary unit-dependence arises because an individual-level percentage effect is not well-defined for individuals whose outcome changes from zero to non-zero when receiving treatment, and the units of the outcome implicitly determine how much weight the ATE for a log-like transformation places on the extensive margin. We further establish a trilemma: when the outcome can equal zero, there is no treatment effect parameter that is an average of individual-level treatment effects, unit-invariant, and point-identified. We discuss several alternative approaches that may be sensible in settings with an intensive and extensive margin, including (i) expressing the ATE in levels as a percentage (e.g. using Poisson regression), (ii) explicitly calibrating the value placed on the intensive and extensive margins, and (iii) estimating separate effects for the two margins (e.g. using Lee bounds). We illustrate these approaches in three empirical applications.