更改

The synthetic control method tries to offer a more systematic way to assign weights to the control group. It typically uses a relatively long time series of the outcome prior to the intervention and estimates weights in such a way that the control group mirrors the treatment group as closely as possible. In particular, assume we have ''J'' observations over ''T'' time periods where the relevant treatment occurs at time <math>T_{0}</math> where <math>T_{0}<T.</math> Let  

The synthetic control method tries to offer a more systematic way to assign weights to the control group. It typically uses a relatively long time series of the outcome prior to the intervention and estimates weights in such a way that the control group mirrors the treatment group as closely as possible. In particular, assume we have ''J'' observations over ''T'' time periods where the relevant treatment occurs at time <math>T_{0}</math> where <math>T_{0}<T.</math> Let  

The synthetic control method tries to offer a more systematic way to assign weights to the control group. It typically uses a relatively long time series of the outcome prior to the intervention and estimates weights in such a way that the control group mirrors the treatment group as closely as possible. In particular, assume we have J observations over T time periods where the relevant treatment occurs at time T_{0} where T_{0}<T. Let  

The synthetic control method tries to offer a more systematic way to assign weights to the control group. It typically uses a relatively long time series of the outcome prior to the intervention and estimates weights in such a way that the control group mirrors the treatment group as closely as possible. In particular, assume we have J observations over T time periods where the relevant treatment occurs at time T_{0} where T_{0}<T. Let  

综合控制方法试图为控制组的权重分配提供一种更加系统的方法。它通常使用一个相对较长的时间序列的结果之前的干预和估计权重的方式，控制组镜像治疗组尽可能接近。特别地，假设我们在 t 时间段有 j 观测值，在 t {0} < t 时相应的处理发生在 t {0} < t 时。让

综合控制方法试图为控制组的权重分配提供一种更加系统的方法。它通常使用一个相对较长的时间序列的结果之前的干预和估计权重的方式，控制组镜像治疗组尽可能接近。特别地，假设我们在 t 时间段有 j 观测值，在 t {0} < t 时相应的处理发生在 t {0} < t 时。让

【翻译】合成对照方法试图用一种更加系统的方法为控制组分配权重。它通常采用干预之前相对比较长时间段内的多个时间序列，估计一组权值使得对这些时间序列的输出进行加权后得到的控制组时间序列尽可能去拟合治疗组的时间序列。特别地，假设我们在时间段T里总共有J个观测值，其中T_{0}，T_{0}<T代表治疗组发生的时间段。让

 

 

【翻译】合成对照方法试图用一种更加系统的方法为控制组分配权重。它通常采用干预之前相对比较长时间段内的多个时间序列，估计一组权值使得对这些时间序列的输出进行加权后得到的控制组时间序列尽可能去拟合治疗组的时间序列。特别地，假设我们在总共T个时间段里有J个观测量（单位），其中一个单位接受了治疗，相应的治疗发生在T_{0}时间段，且T_{0}<T。让

:<math>\alpha_{it}=Y_{it}-Y^N_{it},</math>

: \alpha_{it}=Y_{it}-Y^N_{it},

:\alpha_{it}=Y_{it}-Y^N_{it},

为单位 i 的在时间 t 的治疗效果，其中 Y^N_{it} 是未经治疗的结果。不失一般性，如果单位1接受了相应的治疗，只有在 t > T_{0} 时段的 Y^N_{1t} 没有被观察到。我们的目标是估计(\alpha_{1T_{0}+1} ... ... \alpha_{1T})。

be the treatment effect for unit i at time t, where Y^N_{it} is the outcome in absence of the treatment. Without loss of generality, if unit 1 receives the relevant treatment, only Y^N_{1t}is not observed for t>T_{0}. We aim to estimate (\alpha_{1T_{0}+1}......\alpha_{1T}).

Imposing some structure

Imposing some structure

Imposing some structure

Imposing some structure

强加一些结构

强加一些结构