Synthetic Control Methods for Comparative Case
Social scientists are often interested in the effects of events or policy interventions that take place at an aggregate level and affect aggregate entities, such as firms, schools, or geographic or administrative areas (countries, regions, cities, etc.). To es- timate the effects of these events or interventions, researchers often use comparative case studies. In comparative case stud- ies, researchers estimate the evolution of aggregate outcomes (such as mortality rates, average income, crime rates, etc.) for a unit affected by a particular occurrence of the event or interven- tion of interest and compare it to the evolution of the same ag- gregates estimated for some control group of unaffected units. Card (1990) studies the impact of the 1980 Mariel Boatlift, a large and sudden Cuban migratory influx in Miami, using other cities in the southern United States as a comparison group. In a well-known study of the effects of minimum wages on employ- ment, Card and Krueger (1994) compare the evolution of em- ployment in fast food restaurants in New Jersey and its neigh- boring state Pennsylvania around the time of an increase in New Jersey’s minimum wage. Abadie and Gardeazabal (2003) esti- mate the effects of the terrorist conflict in the Basque Country on the Basque economy using other Spanish regions as a com- parison group.
Comparing the evolution of an aggregate outcome (e.g., state-level crime rate) between a unit affected by the event or intervention of interest and a set of unaffected units requires only aggregate data, which are often available. However, when data are not available at the same level of aggregation as the outcome of interest, information on a sample of disaggregated units can sometimes be used to estimate the aggregate outcomes of interest (like in Card 1990 and Card and Krueger 1994).
Given the widespread availability of aggregate/macro data (e.g., at the school, city, or region level), and the fact that many policy interventions and events of interest in the social sciences take place at an aggregate level, comparative case study re- search has broad potential. However, comparative case study research is limited in the social sciences by two problems that affect its empirical implementation. First, in comparative case studies there is typically some degree of ambiguity about how comparison units are chosen.
Researchers often select compar- ison groups on the basis of subjective measures of affinity be- tween affected and unaffected units. Second, comparative case studies typically employ data on a sample of disaggregated units and inferential techniques that measure only uncertainty about the aggregate values of the data in the population. Un- certainty about the values of aggregate variables can be elimi- nated completely if aggregate data are available. However, the availability of aggregate data does not imply that the effect of the event or intervention of interest can be estimated without error. Even if aggregate data are employed, there remains un- certainty about the ability of the control group to reproduce the counterfactual outcome trajectory that the affected units would have experienced in the absence of the intervention or event of interest. This type of uncertainty is not reflected by the stan- dard errors constructed with traditional inferential techniques for comparative case studies.
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