Synthetic control method: Difference between revisions

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{{Short description|Type of statistical data method}}

[[File:SCMGermany.png|thumb|right|Comparison of per-capita GDP in West Germany before and after the 1990 German reunification and the hypothetical one if the reunification had not taken place.<ref name="ajps">{{cite journal |last1=Abadie |first1=Alberto |last2=Diamond |first2=Alexis |last3=Hainmueller |first3=Jens |date=February 2015 |title=Comparative Politics and the Synthetic Control Method |journal=American Journal of Political Science |volume=59 |issue=2 |pages=495–510 |doi=10.1111/ajps.12116 |authorlink1=Alberto Abadie}}</ref>|260x260px]]

The '''synthetic control method''' is an econometric method used to evaluate the effect of large-scale interventions. It was proposed in a series of articles by [[Alberto Abadie]] and his coauthors.<ref name=":0">{{Cite journal |lastlast1=Abadie |firstfirst1=Alberto |last2=Gardeazabal |first2=Javier |date=2003 |title=The Economic Costs of Conflict: A Case Study of the Basque Country |url=https://pubs.aeaweb.org/doi/10.1257/000282803321455188 |journal=American Economic Review |language=en |volume=93 |issue=1 |pages=113–132 |doi=10.1257/000282803321455188 |issn=0002-8282}}</ref><ref>{{Cite journal |lastlast1=Abadie |firstfirst1=Alberto |last2=Diamond |first2=Alexis |last3=Hainmueller |first3=Jens |date=2010 |title=Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’sCalifornia's Tobacco Control Program |url=http://www.tandfonline.com/doi/abs/10.1198/jasa.2009.ap08746 |journal=Journal of the American Statistical Association |language=en |volume=105 |issue=490 |pages=493–505 |doi=10.1198/jasa.2009.ap08746 |issn=0162-1459}}</ref><ref name=":1">{{Cite journal |last=Abadie |first=Alberto |date=2021 |title=Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects |journal=Journal of Economic Literature |language=en |volume=59 |issue=2 |pages=391–425 |doi=10.1257/jel.20191450 |issn=0022-0515 |doi-access=free |hdl-access=free |hdl=1721.1/144417}}</ref> A synthetic control is a weighted average of several units (such as regions or companies) combined to recreate the trajectory that the outcome of a treated unit would have followed in the absence of the intervention. The weights are selected in a data-driven manner to ensure that the resulting synthetic control closely resembles the treated unit in terms of key predictors of the outcome variable.<ref name=":0" /> Unlike [[difference in differences]] approaches, this method can account for the effects of [[confounder]]s changing over time, by weighting the control group to better match the treatment group before the intervention.<ref name=he>{{cite journal|last1=Kreif|first1=Noémi|last2=Grieve|first2=Richard|last3=Hangartner|first3=Dominik|last4=Turner|first4=Alex James|last5=Nikolova|first5=Silviya|last6=Sutton|first6=Matt|title=Examination of the Synthetic Control Method for Evaluating Health Policies with Multiple Treated Units|journal=Health Economics|date=December 2016|volume=25|issue=12|pages=1514–1528|doi=10.1002/hec.3258|pmid=26443693|pmc=5111584}}</ref> Another advantage of the synthetic control method is that it allows researchers to systematically select comparison groups. It has been applied to the fields of [[economics]],<ref>{{cite journal |last1=Billmeier |first1=Andreas |last2=Nannicini |first2=Tommaso |date=July 2013 |title=Assessing Economic Liberalization Episodes: A Synthetic Control Approach |journal=Review of Economics and Statistics |volume=95 |issue=3 |pages=983–1001 |doi=10.1162/REST_a_00324 |s2cid=57561957}}</ref> [[political science]],<ref name="ajps" /> [[health policy]],<ref name="he" /> [[criminology]],<ref>{{cite journal|last1=Saunders|first1=Jessica|last2=Lundberg|first2=Russell|last3=Braga|first3=Anthony A.|last4=Ridgeway|first4=Greg|last5=Miles|first5=Jeremy|title=A Synthetic Control Approach to Evaluating Place-Based Crime Interventions|journal=Journal of Quantitative Criminology|date=3 June 2014|volume=31|issue=3|pages=413–434|doi=10.1007/s10940-014-9226-5|s2cid=254702864 }}</ref> and others.

The synthetic control method combines elements from [[Matching (statistics)|matching]] and [[difference-in-differences]] techniques. Difference-in-differences methods are often-used policy evaluation tools that estimate the effect of an intervention at an aggregate level (e.g. state, country, age group etc.) by averaging over a set of unaffected units. Famous examples include studies of the employment effects of a raise in the [[Minimum wage in the United States|minimum wage]] in New Jersey fast food restaurants by comparing them to fast food restaurants just across the border in [[Philadelphia]] that were unaffected by a minimum wage raise,<ref name="CardKrueger">{{cite journal |last1=Card |first1=D. |authorlink=David Card |first2=A. |last2=Krueger |authorlink2=Alan Krueger |year=1994 |title=Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania |journal=[[American Economic Review]] |volume=84 |issue=4 |pages=772–793 |jstor=2118030 }}</ref> and studies that look at [[crime rates]] in southern cities to evaluate the impact of the [[Mariel boat lift|Mariel Boatlift]] on crime.<ref>{{cite journal |last=Billy |first=Alexander |year=2022 |title=Crime and the Mariel Boatlift |url=https://www.sciencedirect.com/science/article/pii/S0144818822000503 |journal=[[International Review of Law and Economics]] |volume=72 |issue= |pages=106094 |doi=10.1016/j.irle.2022.106094 |s2cid=219390309 |via=Science Direct}}</ref> The control group in this specific scenario can be interpreted as a [[Weighted arithmetic mean|weighted average]], where some units effectively receive zero weight while others get an equal, non-zero weight.

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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 |jstor=44511197 |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> -->