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平均处理效应 (Average Treatment Effect, ATE)是在随机实验、政策干预评估和医学实验中用于比较治疗或干预的一种测量方法。平均处理效应测量分配给处理单位和控制单位之间的平均结果的差异。在随机实验或者实验研究中，平均处理效应可以通过比较样本在处理单元和未处理单元的平均结果进行估计获得。然而，平均处理效应通常被理解为研究人员希望知道的一个因果参数 (即一个总体的估计或属性) ，定义时不参考试验设计或估计过程。观察性研究和随机赋值的实验性研究设计可能使得以多种方式进行平均处理效应估计。

平均处理效应 (Average Treatment Effect, ATE)是在随机实验、政策干预评估和医学实验中用于比较治疗或干预的一种测量方法。平均处理效应测量分配给处理单位和控制单位之间的平均结果的差异。在随机实验或者实验研究中，平均处理效应可以通过比较样本在处理单元和未处理单元的平均结果进行估计获得。然而，平均处理效应通常被理解为研究人员希望知道的一个因果参数 (即一个总体的估计或属性) ，定义时不参考试验设计或估计过程。观察性研究和随机赋值的实验性研究设计可能使得以多种方式进行平均处理效应估计。

== General definition ==

== 通用定义 General definition ==

Originating from early statistical analysis in the fields of agriculture and medicine, the term "treatment" is now applied, more generally, to other fields of natural and social science, especially [[psychology]], [[political science]], and [[economics]] such as, for example, the evaluation of the impact of public policies. The nature of a treatment or outcome is relatively unimportant in the estimation of the ATE—that is to say, calculation of the ATE requires that a treatment be applied to some units and not others, but the nature of that treatment (e.g., a pharmaceutical, an incentive payment, a political advertisement) is irrelevant to the definition and estimation of the ATE.

Originating from early statistical analysis in the fields of agriculture and medicine, the term "treatment" is now applied, more generally, to other fields of natural and social science, especially [[psychology]], [[political science]], and [[economics]] such as, for example, the evaluation of the impact of public policies. The nature of a treatment or outcome is relatively unimportant in the estimation of the ATE—that is to say, calculation of the ATE requires that a treatment be applied to some units and not others, but the nature of that treatment (e.g., a pharmaceutical, an incentive payment, a political advertisement) is irrelevant to the definition and estimation of the ATE.

虽然实验确保了潜在结果以及所有协变量在处理组和对照组中的等价分布，但是在观察性研究中，情况并非如此。在观察性研究中，处理组单位并不是随机分配和受人为控制，因此处理单位的分配可能取决于未观测到或不可观测的因素。观察到的因素可以在统计学上加以控制(例如，通过回归或匹配) ，但是任何关于平均处理效应的估计都可能与不可观察因素混淆，这些因素影响了哪些单位接受了处理，哪些单位没有接受处理。

虽然实验确保了潜在结果以及所有协变量在处理组和对照组中的等价分布，但是在观察性研究中，情况并非如此。在观察性研究中，处理组单位并不是随机分配和受人为控制，因此处理单位的分配可能取决于未观测到或不可观测的因素。观察到的因素可以在统计学上加以控制(例如，通过回归或匹配) ，但是任何关于平均处理效应的估计都可能与不可观察因素混淆，这些因素影响了哪些单位接受了处理，哪些单位没有接受处理。

== Formal definition ==

== 正式定义 Formal definition ==

In order to define formally the ATE, we define two potential outcomes : <math>y_{0}(i)</math> is the value of the outcome variable for individual <math>i</math> if they are not treated, <math>y_{1}(i)</math> is the value of the outcome variable for individual <math>i</math> if they are treated. For example, <math>y_{0}(i)</math>  is the health status of the individual if they are not administered the drug under study and <math>y_{1}(i)</math> is the health status if they are administered the drug.

In order to define formally the ATE, we define two potential outcomes : <math>y_{0}(i)</math> is the value of the outcome variable for individual <math>i</math> if they are not treated, <math>y_{1}(i)</math> is the value of the outcome variable for individual <math>i</math> if they are treated. For example, <math>y_{0}(i)</math>  is the health status of the individual if they are not administered the drug under study and <math>y_{1}(i)</math> is the health status if they are administered the drug.

如果我们能观察到一个大型代表性样本中每个个体的<math> y _ {1}(i) </math> 和 <math> y _ {0}(i) </math> ，我们可以简单地通过取样本中 <math> y _ {1}(i)-y _ {0}(i) </math> 的平均值来估计平均治疗效果。然而，我们不能同时观察每个个体的<math> y _ {1}(i)、y _ {0}(i) </math>，因为每个个体不能同时被处理和不被处理。例如，在药物例子中，我们只能观察到个体接受过药物治疗的<math> y _ {1}(i) </math> 和个体未接受药物的 <math> y _ {0}(i) </math> 。这是研究学者在评估治疗效果时面临的主要问题，并因此引发了大量估计技术的研究。

如果我们能观察到一个大型代表性样本中每个个体的<math> y _ {1}(i) </math> 和 <math> y _ {0}(i) </math> ，我们可以简单地通过取样本中 <math> y _ {1}(i)-y _ {0}(i) </math> 的平均值来估计平均治疗效果。然而，我们不能同时观察每个个体的<math> y _ {1}(i)、y _ {0}(i) </math>，因为每个个体不能同时被处理和不被处理。例如，在药物例子中，我们只能观察到个体接受过药物治疗的<math> y _ {1}(i) </math> 和个体未接受药物的 <math> y _ {0}(i) </math> 。这是研究学者在评估治疗效果时面临的主要问题，并因此引发了大量估计技术的研究。

== Estimation ==

== 估计 Estimation ==

Depending on the data and its underlying circumstances, many methods can be used to estimate the ATE. The most common ones are:

Depending on the data and its underlying circumstances, many methods can be used to estimate the ATE. The most common ones are:

* 工具变量估计 Instrumental Variables Estimation

* 工具变量估计 Instrumental Variables Estimation

== An example ==

== 示例 An example ==

Consider an example where all units are unemployed individuals, and some experience a policy intervention (the treatment group), while others do not (the control group). The causal effect of interest is the impact a job search monitoring policy (the treatment) has on the length of an unemployment spell: On average, how much shorter would one's unemployment be if they experienced the intervention? The ATE, in this case, is the difference in expected values (means) of the treatment and control groups' length of unemployment.

Consider an example where all units are unemployed individuals, and some experience a policy intervention (the treatment group), while others do not (the control group). The causal effect of interest is the impact a job search monitoring policy (the treatment) has on the length of an unemployment spell: On average, how much shorter would one's unemployment be if they experienced the intervention? The ATE, in this case, is the difference in expected values (means) of the treatment and control groups' length of unemployment.

考虑一个例子，所有单位都是失业个体，对一些个体给与政策处理（处理组），其余的不做任何处理(控制组) 。需要计算工作监督政策(治疗)对失业期的因果影响: 平均来说，如果监督个体寻找工作（给与处理），该个体的失业期会缩短多少？在这种情况下，平均处理效应是处理组和对照组的失业时间长度的期望值(平均值)差异。

考虑一个失业群体，对一些个体给与政策干预（处理组），其余的不做任何处理(控制组) 。现需要计算求职监控政策(干预)对失业期长短的影响: 平均来说，如果对个体进行求职监控（给与干预），失业期会缩短多少？在这种情况下，平均处理效应是处理组和对照组的失业时间长度的期望值(平均值)差异。

A positive ATE, in this example, would suggest that the job policy increased the length of unemployment. A negative ATE would suggest that the job policy decreased the length of unemployment. An ATE estimate equal to zero would suggest that there was no advantage or disadvantage to providing the treatment in terms of the length of unemployment. Determining whether an ATE estimate is distinguishable from zero (either positively or negatively) requires statistical inference.

A positive ATE, in this example, would suggest that the job policy increased the length of unemployment. A negative ATE would suggest that the job policy decreased the length of unemployment. An ATE estimate equal to zero would suggest that there was no advantage or disadvantage to providing the treatment in terms of the length of unemployment. Determining whether an ATE estimate is distinguishable from zero (either positively or negatively) requires statistical inference.

== Heterogenous treatment effects ==

== Heterogenous treatment effects ==

Some researchers call a treatment effect "heterogenous" if it affects different individuals differently (heterogeneously).  For example, perhaps the above treatment of a job search monitoring policy affected men and women differently, or people who live in different states differently.

Some researchers call a treatment effect "heterogenous" if it affects different individuals differently (heterogeneously).  For example, perhaps the above treatment of a job search monitoring policy affected men and women differently, or people who live in different states differently.

看待异质治疗效果的一种方法是将研究数据进行分组(例如，男性和女性，或者按地区) ，看看平均治疗效果是否因子组而异。每个子组的 ATE 被称为“条件平均治疗效应”(CATE) ，也就是说，每个子组的 ATE 被称为条件平均治疗效应，以子组内的成员为条件。

一种异质处理效应的研究方法是将研究数据进行分组(例如，按照男、女性别，或者按区域) ，比较平均治疗效果在子组内的效应差异。每个子组的平均处理效应被称为“条件平均治疗效应”(Cnditional Average Treatment Effect,CATE) ，也就是说，每个子组的 平均处理效应被称为条件平均治疗效应，以子组内的成员为条件。