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合成对照 (查看源代码)

2022年3月18日 (五) 10:22的版本

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【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
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【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结果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
    
: \alpha_{it}=Y_{it}-Y^N_{it},
 
: \alpha_{it}=Y_{it}-Y^N_{it},
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Imposing some structure
 
Imposing some structure
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Imposing some structure
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:<math>Y^N_{it}=\delta_{t}+\theta_{t}Z_{i}+\lambda_{t}\mu_{i}+\varepsilon_{it}</math>
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and assuming there exist some optimal weights <math>w_2, \ldots, w_J</math> such that
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:<math>Y_{1t} = \Sigma^J_{j=2} w_{j}Y_{jt}</math>
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强加一些结构
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for <math>t\leqslant T_{0}</math>, the synthetic controls approach suggests using these weights to estimate the counterfactual
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: <math>Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}</math>
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for <math>t>T_{0}</math>. So under some regularity conditions, such weights would provide estimators for the treatment effects of interest. In essence, the method uses the idea of matching and using the training data pre-intervention to set up the weights and hence a relevant control post-intervention.<ref name=":0">{{cite journal |last=Abadie |first=A. |authorlink=Alberto Abadie |first2=A. |last2=Diamond |first3= J. |last3=Hainmüller |year=2010 |title=Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program |journal=[[Journal of the American Statistical Association]] |volume=105 |issue=490 |pages=493–505 |doi=10.1198/jasa.2009.ap08746 }}</ref>
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:
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【翻译】
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:Imposing some structure Y^N_{it}=\delta_{t}+\theta_{t}Z_{i}+\lambda_{t}\mu_{i}+\varepsilon_{it}
   −
强加一些结构
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and assuming there exist some optimal weights w_2, \ldots, w_J such that
   −
:<math>Y^N_{it}=\delta_{t}+\theta_{t}Z_{i}+\lambda_{t}\mu_{i}+\varepsilon_{it}</math> 
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:Y_{1t} = \Sigma^J_{j=2} w_{j}Y_{jt}
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for t\leqslant T_{0}, the synthetic controls approach suggests using these weights to estimate the counterfactual
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:Y^N_{it}=\delta_{t}+\theta_{t}Z_{i}+\lambda_{t}\mu_{i}+\varepsilon_{it}  
+
:Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}
 +
for t>T_{0}. So under some regularity conditions, such weights would provide estimators for the treatment effects of interest. In essence, the method uses the idea of matching and using the training data pre-intervention to set up the weights and hence a relevant control post-intervention.
    +
:
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强加一些结构
 
: y ^ n { it } = delta { t } + theta { t } z { i } + lambda { t } mu { i } + varepsilon { it }
 
: y ^ n { it } = delta { t } + theta { t } z { i } + lambda { t } mu { i } + varepsilon { it }
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  −
and assuming there exist some optimal weights <math>w_2, \ldots, w_J</math> such that
  −
  −
and assuming there exist some optimal weights w_2, \ldots, w_J such that
  −
   
假设存在一些最优权重 w _ 2，ldots，w _ j 使得
 
假设存在一些最优权重 w _ 2，ldots，w _ j 使得
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:y {1 t } = Sigma ^ j { j = 2} w { j } y { jt }
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对于 t _ {0} ，综合控制方法建议使用这些权重来估计反事实
   −
:<math>Y_{1t} = \Sigma^J_{j=2} w_{j}Y_{jt}</math>
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:Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}
   −
:Y_{1t} = \Sigma^J_{j=2} w_{j}Y_{jt}  
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for t>T_{0}.因此，在一定的正则性条件下，这种权重可以作为利息处理效果的估计量。本质上，该方法采用了匹配的思想，并利用训练数据进行干预前的权重设置，从而得到干预后的相应控制。
 +
:
   −
: y {1 t } = Sigma ^ j { j = 2} w { j } y { jt }
     −
for <math>t\leqslant T_{0}</math>, the synthetic controls approach suggests using these weights to estimate the counterfactual
+
【翻译】
   −
for t\leqslant T_{0}, the synthetic controls approach suggests using these weights to estimate the counterfactual
+
强加一些结构
−
 
  −
对于 t _ {0} ，综合控制方法建议使用这些权重来估计反事实
      +
: <math>Y^N_{it}=\delta_{t}+\theta_{t}Z_{i}+\lambda_{t}\mu_{i}+\varepsilon_{it}</math>
 +
对于<math>t\leqslant T_{0}</math>，假设存在一些最优权重<math>w_2, \ldots, w_J</math>，使得
 +
:<math>Y_{1t} = \Sigma^J_{j=2} w_{j}Y_{jt}</math>
 +
而对于<math>t>T_{0}</math>，合成对照方法建议使用这些权重来估计反事实
 
:<math>Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}</math>  
 
:<math>Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}</math>  
−
for <math>t>T_{0}</math>. So under some regularity conditions, such weights would provide estimators for the treatment effects of interest. In essence, the method uses the idea of matching and using the training data pre-intervention to set up the weights and hence a relevant control post-intervention.<ref>{{cite journal |last=Abadie |first=A. |authorlink=Alberto Abadie |first2=A. |last2=Diamond |first3= J. |last3=Hainmüller |year=2010 |title=Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program |journal=[[Journal of the American Statistical Association]] |volume=105 |issue=490 |pages=493–505 |doi=10.1198/jasa.2009.ap08746 }}</ref>
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因此，在一定的正则性条件下，此类权重可以作为我们所关心的治疗效果的估计量。 本质上，该方法使用匹配的思想，并利用干预前的训练数据计算权重，进而能够计算干预后的相关控制组数据。<ref name=":0" />  
   −
:Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}
  −
for t>T_{0}. So under some regularity conditions, such weights would provide estimators for the treatment effects of interest. In essence, the method uses the idea of matching and using the training data pre-intervention to set up the weights and hence a relevant control post-intervention.
  −
  −
:Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}
  −
for t>T_{0}.因此，在一定的正则性条件下，这种权重可以作为利息处理效果的估计量。本质上，该方法采用了匹配的思想，并利用训练数据进行干预前的权重设置，从而得到干预后的相应控制。
      
Synthetic controls have been used in a number of empirical applications, ranging from studies examining natural catastrophes and growth,<ref>{{cite journal |last=Cavallo |first=E. |first2=S. |last2=Galliani |first3=I. |last3=Noy |first4=J. |last4=Pantano |year=2013 |title=Catastrophic Natural Disasters and Economic Growth |journal=[[Review of Economics and Statistics]] |volume=95 |issue=5 |pages=1549–1561 |doi=10.1162/REST_a_00413  |url=http://www.economics.hawaii.edu/research/workingpapers/WP_10-6.pdf }}</ref> and studies linking political murders to house prices.<ref>{{cite journal |last=Gautier |first=P. A. |first2=A. |last2=Siegmann |first3=A. |last3=Van Vuuren |year=2009 |title=Terrorism and Attitudes towards Minorities: The effect of the Theo van Gogh murder on house prices in Amsterdam |journal=[[Journal of Urban Economics]] |volume=65 |issue=2 |pages=113–126 |doi=10.1016/j.jue.2008.10.004 }}</ref>  
 
Synthetic controls have been used in a number of empirical applications, ranging from studies examining natural catastrophes and growth,<ref>{{cite journal |last=Cavallo |first=E. |first2=S. |last2=Galliani |first3=I. |last3=Noy |first4=J. |last4=Pantano |year=2013 |title=Catastrophic Natural Disasters and Economic Growth |journal=[[Review of Economics and Statistics]] |volume=95 |issue=5 |pages=1549–1561 |doi=10.1162/REST_a_00413  |url=http://www.economics.hawaii.edu/research/workingpapers/WP_10-6.pdf }}</ref> and studies linking political murders to house prices.<ref>{{cite journal |last=Gautier |first=P. A. |first2=A. |last2=Siegmann |first3=A. |last3=Van Vuuren |year=2009 |title=Terrorism and Attitudes towards Minorities: The effect of the Theo van Gogh murder on house prices in Amsterdam |journal=[[Journal of Urban Economics]] |volume=65 |issue=2 |pages=113–126 |doi=10.1016/j.jue.2008.10.004 }}</ref>  
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综合控制已经被应用于许多实证研究中，从研究自然灾害和经济增长，到研究政治谋杀与房价之间的联系。
 
综合控制已经被应用于许多实证研究中，从研究自然灾害和经济增长，到研究政治谋杀与房价之间的联系。
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【翻译】
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合成对照已经被应用于许多实证研究中，从研究自然灾害和经济增长，到研究政治谋杀与房价之间的联系。
    
==References==
 
==References==
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