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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" />
Synthetic controls have been used in a number of empirical applications, ranging from studies examining natural catastrophes and growth,<ref>{{cite journal |last1=Cavallo |first1=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 |s2cid=16038784 |url=http://www.economics.hawaii.edu/research/workingpapers/WP_10-6.pdf }}</ref> or civil conflicts and growth,<ref>{{cite journal |last1=Costalli,|first1=S. |last2=Moretti |first2=L. |last3=Pischedda |first3=C. |year=2017 |title=The Economic Costs of Civil War: Synthetic Counterfactual Evidence and the Effects of Ethnic Fractionalization. |journal=[[Journal of Peace Research]] |volume=54 |issue=1 |pages=80–98 |doi=10.1177/0022343316675200 |s2cid=151363517 |url=https://www.jstor.org/stable/44511197}}</ref> studies that examine the effect of vaccine mandates on childhood immunization,<ref>{{cite journal |last1=Li |first1=Ang. |last2=Toll |first2=Mathew. |title=Removing conscientious objection: The impact of 'No Jab No Pay' and 'No Jab No Play' vaccine policies in Australia |journal=Preventive Medicine |date=2020 |volume=145 |page=106406 |doi=10.1016/j.ypmed.2020.106406 |issn=0091-7435 |pmid=33388333 |s2cid=230489130 |url=https://www.sciencedirect.com/science/article/abs/pii/S0091743520304370}}</ref> and studies linking political murders to house prices.<ref>{{cite journal |last1=Gautier |first1=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 |s2cid=190624 }}</ref>
<!-- THE CITATION AT THE END OF THIS SENTENCE IS FOR A PAPER ABOUT "synthetic cohort models" (a.k.a. "pseudo-panel approach," using repeated cross-sections), WHICH IS NOT THE SAME AS "synthetic control": Yet, despite its intuitive appeal, it may be the case that synthetic controls could suffer from significant finite sample biases.<ref>{{cite journal |last=Devereux |first=P. J. |year=2007 |title=Small-sample bias in synthetic cohort models of labor supply |journal=[[Journal of Applied Econometrics]] |volume=22 |issue=4 |pages=839–848 |doi=10.1002/jae.938 }}</ref> -->
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