Comparative Politics and the Synthetic Control Methodjhain/Paper/AJPS2015a.pdfComparative Politics and the Synthetic ... a systematic way to choose comparison units in comparative

Comparative Politics and the Synthetic ControlMethod

Alberto Abadie Harvard University and NBERAlexis Diamond International Finance CorporationJens Hainmueller Stanford University

In recent years, a widespread consensus has emerged about the necessity of establishing bridges between quantitative andqualitative approaches to empirical research in political science. In this article, we discuss the use of the synthetic controlmethod as a way to bridge the quantitative/qualitative divide in comparative politics. The synthetic control method providesa systematic way to choose comparison units in comparative case studies. This systematization opens the door to precisequantitative inference in small-sample comparative studies, without precluding the application of qualitative approaches.Borrowing the expression from Sidney Tarrow, the synthetic control method allows researchers to put “qualitative flesh onquantitative bones.” We illustrate the main ideas behind the synthetic control method by estimating the economic impactof the 1990 German reunification on West Germany.

Starting with Alexis de Toqueville’s Democracy inAmerica, comparative case studies have becomeclosely associated with empirical research in po-

litical science (Tarrow 2010). Comparative researchersbase their studies on meticulous description and anal-ysis of the characteristics of a small number of selectedcases, as well as of their differences and similarities. Bycarefully studying a small number of cases, comparativeresearchers gather evidence at a level of granularity thatis difficult if not impossible to incorporate in quantita-tive studies, which tend to focus on larger samples butemploy much coarser descriptions of the sample units.1

However, large-sample quantitative methods are some-times adopted because they provide precise numericalresults, which can be compared across studies, and be-cause they are better adapted to traditional methods ofstatistical inference.

Alberto Abadie is Professor of Public Policy, John F. Kennedy School of Government, Harvard University, 79 John F. Kennedy Street,Cambridge, MA 02138 (alberto˙[email protected]). Alexis Diamond, International Finance Corporation, 2121 Pennsylvania Avenue,NW, Washington, DC 20433 ([email protected]). Jens Hainmueller is Associate Professor, Department of Political Science and GraduateSchool of Business, Stanford University, 616 Serra Street, Stanford, CA 94305 ([email protected]).

We thank Neal Beck, Anthony Fowler, John Gerring, Adam Glynn, Danny Hidalgo, Kosuke Imai, Gary King, Hermann Maier, TeppeiYamamoto, the editor, and four anonymous reviewers for helpful comments on earlier versions of this article. The title of thisarticle pays homage to Lijphart (1971), one of the earliest and most influential studies on the methodology of the comparativemethod in political science. Companion software developed by the authors (Synth package for MATLAB, R, and Stata) is available athttp://www.stanford.edu/ �jhain. The data used in this study can be downloaded for purposes of replication from the AJPS Data Archiveon Dataverse (http://dvn.iq.harvard.edu/dvn/dv/ajps).

1See Lijphart (1971), Collier (1993), Mahoney and Rueschemeyer (2003), George and Bennett (2005), and Gerring (2004, 2007) for carefultreatments of case study research in the social sciences.

As a result of a recent and important methodolog-ical debate (Beck 2010; Brady and Collier 2004; Georgeand Bennett 2005; King, Keohane, and Verba 1994; Ra-gin 1987; Tarrow 1995), a widespread consensus hasemerged about the necessity of establishing bridges be-tween the quantitative and the qualitative approaches toempirical research in political science. In particular, therehave been calls for the development and use of quan-titative methods that complement and facilitate qual-itative analysis in comparative studies (Gerring 2007;Lieberman 2005; Sekhon 2004; Tarrow 1995, 2010). Atthe other end of the methodological spectrum, a re-cent strand of the quantitative literature is advocating forresearch designs that, like Mill’s Method of Difference,carefully select comparison units to reduce biases in ob-servational studies (Card and Krueger 1994; Rosenbaum2005).

American Journal of Political Science, Vol. 59, No. 2, April 2015, Pp. 495–510

C©2014, Midwest Political Science Association DOI: 10.1111/ajps.12116

495

496 ALBERTO ABADIE, ALEXIS DIAMOND, AND JENS HAINMUELLER

In this article, we discuss how synthetic control meth-ods (Abadie, Diamond, and Hainmueller 2010; Abadieand Gardeazabal 2003) can be applied to complementand facilitate comparative case studies in political sci-ence. Following Mill’s Method of Difference, we focus ona study design based on the comparison of outcomes be-tween units representing the case of interest, defined bythe occurrence of a specific event or intervention that isthe object of the study, and otherwise similar but unaf-fected units. In this design, comparison units are intendedto reproduce the counterfactual of the case of interest inthe absence of the event or intervention under scrutiny.2

The selection of comparison units is a step of cru-cial importance in comparative case studies because us-ing inappropriate comparisons may lead to erroneousconclusions. If comparison units are not sufficiently sim-ilar to the units representing the case of interest, thenany difference in outcomes between these two sets ofunits may merely reflect disparities in their characteristics(Geddes 2003; George and Bennett 2005; King, Keohane,and Verba 1994). The synthetic control method providesa systematic way to choose comparison units in com-parative case studies. Formalizing the way comparisonunits are chosen not only represents a way of system-atizing comparative case studies (as advocated, amongothers, by King, Keohane, and Verba 1994), but it also hasdirect implications for inference. We demonstrate thatthe main barrier to quantitative inference in compara-tive studies comes not from the small-sample nature ofthe data, but from the absence of an explicit mechanismthat determines how comparison units are selected. Bycarefully specifying how units are selected for the com-parison group, the synthetic control method opens thedoor to the possibility of precise quantitative inference incomparative case studies, without precluding qualitativeapproaches to the same data set.

One distinctive feature of comparative political sci-ence is that the units of analysis are often aggregate enti-ties, such as countries or regions, for which suitable singlecomparisons often do not exist (Collier 1993; George andBennett 2005; Gerring 2007; Lijphart 1971). The syntheticcontrol method is based on the premise that, when the

2See Fearon (1991) for an early discussion of the role of counterfac-tuals to assess causal hypotheses in political science. It is important,however, to recognize that comparative politics is “a river of manycurrents” (Hall 2003, 374), and researchers may have motivationsfor selecting cases other than the construction of counterfactuals(Collier and Mahoney 1996; Hall 2003). For example, researchersmay select cases in order to examine causal mechanisms throughwithin-case methods such as process tracing (George and Bennett2005) or causal process observations (Collier, Mahoney, and Sea-wright 2004). We do not intend to criticize these approaches, as inour view our proposal is complementary to existing methods.

units of analysis are a few aggregate entities, a combi-nation of comparison units (which we term “syntheticcontrol”) often does a better job of reproducing the char-acteristics of the unit or units representing the case ofinterest than any single comparison unit alone. Moti-vated by this consideration, the comparison unit in thesynthetic control method is selected as the weighted aver-age of all potential comparison units that best resemblesthe characteristics of the case of interest.

Relative to regression-based comparative case stud-ies, the synthetic control method has important advan-tages. Using a weighted average of units as a compari-son precludes the type of model-dependent extrapolationthat regression results are often based on (King and Zeng2006). Below we show that a regression estimator canalso be expressed as a weighted average of comparisonunits, with weights that sum to one. However, regressionweights are not restricted to lie between zero and one,allowing extrapolation. Moreover, in contrast to regres-sion analysis techniques, the synthetic control methodmakes explicit the contribution of each comparison unitto the counterfactual of interest. This allows researchersto use quantitative and qualitative techniques to analyzesimilarities and differences between the unit or units rep-resenting the case of interest and the synthetic control.

We apply the synthetic control method to estimatethe economic impact of the 1990 German reunificationon West Germany. This example illustrates the potentialgains derived by using synthetic controls in compara-tive case studies. We show that no single country is ableto closely approximate the values of economic growthpredictors for West Germany before the reunification.However, a weighted average of a few OECD countries,namely, Austria, the United States, Japan, Switzerland,and the Netherlands, provides a very close approxima-tion to West Germany prior to 1990. We also show that,in this example, a regression-based analysis relies on ex-trapolation to construct a comparison unit, whereas thesynthetic control method avoids extrapolation. Our re-sults suggest that reunification had a pronounced nega-tive effect on West German income, with gross domesticproduct (GDP) per capita being reduced by about 1,600U.S. dollars per year on average over the 1990–2003 pe-riod (approximately 8% of the 1990 baseline level). Thefindings are robust across a series of placebo studies andsensitivity checks.

In this section, we have briefly described the syntheticcontrol method and motivated the use of this method incomparative case studies. Relative to small-sample stud-ies, the synthetic control method helps in the selection ofcomparison cases and opens the door to quantitative in-ference. Relative to large-sample regression-based studies,

COMPARATIVE POLITICS AND THE SYNTHETIC CONTROL METHOD 497

the synthetic control method avoids extrapolation biasesand allows a more focused description and analysis of thesimilarities and differences between the case of interestand the comparison unit.

The rest of the article is organized as follows. Thenext section describes the synthetic control estimator,provides a formal comparison between this estimator anda conventional regression estimator, discusses inferentialtechniques, and provides recommendations for empiricalpractice. We then present an empirical application wherewe apply the synthetic control method to the study ofthe economic effects of the 1990 German reunification inWest Germany. The last section concludes. Data sourcesfor the empirical example are provided in an appendix.

Synthetic Control Method forComparative Case Studies

Suppose that there is a sample of J + 1 units (e.g., coun-tries) indexed by j , among whom unit j = 1 is the caseof interest and units j = 2 to j = J + 1 are potentialcomparisons.3 Borrowing from the medical literature, wewill say that j = 1 is the “treated unit,” that is, the unitexposed to the event or intervention of interest, and unitsj = 2 to j = J + 1 constitute the “donor pool,” that is,a reservoir of potential comparison units. Studies of thistype abound in political science (Gerring 2007; Tarrow2010). Because comparison units are meant to approx-imate the counterfactual of the case of interest withoutthe intervention, it is important to restrict the donor poolto units with outcomes that are thought to be driven bythe same structural process as for the unit representingthe case of interest and that were not subject to structuralshocks to the outcome variable during the sample pe-riod of the study. In the application explored later in thisarticle, we investigate the effects of the 1990, German re-unification on the economic prosperity in West Germany.In this example, the case of interest is West Germany in1990 and the set of potential comparisons is a sample ofOECD countries.

We assume that the sample is a balanced panel, that is,a longitudinal data set where all units are observed at thesame time periods, t = 1, . . . , T .4 We also assume that

3For expositional simplicity, we focus on the case where only oneunit is exposed to the event or intervention of interest. This isdone without a loss of generality. In cases where multiple units areaffected by the event of interest, our method can be applied to eachaffected unit separately or to an aggregate of all affected units.

4This is typically the case in political science applications, wheresample units are large administrative entities like nation-states

the sample includes a positive number of preinterventionperiods, T0, as well as a positive number of postinterven-tion periods, T1, with T = T0 + T1. Unit 1 is exposed tothe intervention of interest (the “treatment”) during pe-riods T0 + 1, . . . , T , and the intervention has no effectduring the pretreatment period 1, . . . , T0. The goal ofthe study is to measure the effect of the intervention ofinterest on some postintervention outcome.

As stated above, the preintervention characteristicsof the treated unit can often be much more accurately ap-proximated by a combination of untreated units than byany single untreated unit. We define a synthetic control asa weighted average of the units in the donor pool. That is,a synthetic control can be represented by a (J × 1) vectorof weights W = (w2, . . . , wJ +1)′, with 0 ≤ w j ≤ 1 forj = 2, . . . J and w2 + · · · + wJ +1 = 1. Choosing a par-ticular value for W is equivalent to choosing a syntheticcontrol. Following Mill’s Method of Difference, we pro-pose selecting the value of W such that the characteristicsof the treated unit are best resembled by the characteristicsof the synthetic control. Let X1 be a (k × 1) vector con-taining the values of the preintervention characteristicsof the treated unit that we aim to match as closely as pos-sible, and let X0 be the k × J matrix collecting the valuesof the same variables for the units in the donor pool. Thepreintervention characteristics in X1 and X0 may includepreintervention values of the outcome variable.

The difference between the preintervention charac-teristics of the treated unit and a synthetic control isgiven by the vector X1 − X0W. We select the syntheticcontrol, W∗, that minimizes the size of this difference.This can be operationalized in the following manner. Form = 1, . . . , k, let X1m be the value of the m-th variable forthe treated unit and let X0m be a 1 × J vector containingthe values of the m-th variable for the units in the donorpool. Abadie and Gardeazabal (2003) and Abadie, Dia-mond, and Hainmueller (2010) choose W∗ as the valueof W that minimizes:

k∑m=1

vm(X1m − X0mW)2, (1)

where vm is a weight that reflects the relative importancethat we assign to the m-th variable when we measurethe discrepancy between X1 and X0W.5 It is of crucial

or regions, for which data are periodically collected by statisti-cal agencies. We do not require, however, that the sample periodsare equidistant in time.

5More formally, let ‖ · ‖ be a norm or seminorm in Rk . One

example is the Euclidean norm, defined as ‖u‖ = √u′u for any

(k × 1) vector u. For any positive semidefinite (k × k) matrix,V , ‖u‖ = √

u′Vu defines a seminorm. The synthetic control


importance that synthetic controls closely reproduce thevalues that variables with a large predictive power on theoutcome of interest take for the unit affected by the inter-vention. Accordingly, those variables should be assignedlarge vm weights. In the empirical application below, weapply a cross-validation method to choose vm.

Let Yjt be the outcome of unit j at time t. In ad-dition, let Y1 be a (T1 × 1) vector collecting the post-intervention values of the outcome for the treated unit.That is, Y1 = (Y1 T0+1, . . . , Y1 T )′. Similarly, let Y0 be a(T1 × J ) matrix, where column j contains the post-intervention values of the outcome for unit j + 1. Thesynthetic control estimator of the effect of the treatmentis given by the comparison of postintervention outcomesbetween the treated unit, which is exposed to the interven-tion, and the synthetic control, which is not exposed to theintervention, Y1 − Y0W∗. That is, for a postinterventionperiod t (with t ≥ T0), the synthetic control estimator ofthe effect of the treatment is given by the comparison be-tween the outcome for the treated unit and the outcomefor the synthetic control at that period:

Y1 t −J +1∑j=2

w∗j Yjt .

The matching variables in X0 and X1 are meant tobe predictors of postintervention outcomes. These pre-dictors are themselves not affected by the intervention.Critics of Mill’s Method of Differences rightfully pointout that the applicability of the method may be limitedby the presence of unmeasured factors affecting the out-come variable as well as by heterogeneity in the effects ofobserved and unobserved factors. However, using a linearfactor model, Abadie, Diamond, and Hainmueller (2010)argue that if the number of preintervention periods in thedata is large, matching on preintervention outcomes (i.e.,on the preintervention counterparts of Y0 and Y1) helpscontrol for unobserved factors and for the heterogene-ity of the effect of the observed and unobserved factorson the outcome of interest. The intuition of this result isstraightforward: Only units that are alike in both observedand unobserved determinants of the outcome variable aswell as in the effect of those determinants on the outcomevariable should produce similar trajectories of the out-

W∗ = (w∗2 , . . . , w

∗J +1)′ is selected to minimize ‖X1 − X0W‖, sub-

ject to 0 ≤ w j ≤ 1 for j = 2, . . . J and w2 + · · · + wJ +1 = 1. Typ-ically, V is selected to weight covariates in accordance to their pre-dictive power on the outcome (see Abadie, Diamond, and Hain-mueller 2010; Abadie and Gardeazabal 2003). If V is diagonal withmain diagonal equal to (v1, . . . , vk), then W∗ is equal to the valueof W that minimizes Equation (1). Because W∗ is invariant to scalechanges in (v1, . . . , vk), these weights can always be normalized tosum to one.

come variable over extended periods of time. Once it hasbeen established that the unit representing the case of in-terest and the synthetic control unit have similar behaviorover extended periods of time prior to the intervention,a discrepancy in the outcome variable following the in-tervention is interpreted as produced by the interventionitself.6

Computation of synthetic controls can be done usingfreely available software scripts that we have written forR, MATLAB, and Stata.7

Comparison to Regression

Constructing a synthetic comparison as a linear combi-nation of the untreated units with coefficients that sumto one may appear unusual. However, here we show thata regression-based approach also uses a linear combina-tion of the untreated units with coefficients that sum toone as a comparison, albeit implicitly. In contrast to thesynthetic control method, the regression approach doesnot restrict the coefficients of the linear combination thatdefine the comparison unit to be between zero and one,therefore allowing extrapolation outside the support ofthe data.

The proof of this assertion is as follows. A regression-based counterfactual of the outcome for the treated unit inthe absence of the treatment is given by the (T1 × 1) vectorB ′ X1, where B = (X0 X ′

0)−1 X0Y ′0 is the (k × T1) matrix

of regression coefficients of Y0 on X0.8 As a result, theregression-based estimate of the counterfactual of interestis equal to Y0Wreg, where Wreg = X ′

0(X0 X ′0)−1 X1. Let �

be a (J × 1) vector of ones. The sum of the regressionweights is �′Wreg. Assume that, as usual, the regressionincludes an intercept, so the first row of X0 is a vector ofones.9 Then (X0 X ′

0)−1 X0� is a (k × 1) vector with the firstelement equal to one and all the rest equal to zero. The

6In this respect, the synthetic control method combines the syn-chronic and diachronic approaches outlined in Lijphart (1971).As pointed out by Gerring (2007), this approach is close inspirit to comparative historical analysis methods (Mahoney andRueschemeyer 2003; Pierson and Skocpol 2002).

7In Stata, the script can be installed by typing ssc installsynth, replace,which downloads the software from the Statis-tical Software Components (SSC) archive. InR, the software is avail-able as the Synth package from the Comprehensive R Archive Net-work at http://CRAN.R-project.org/package=Synth. The R pack-age is also described in detail in Abadie, Diamond, and Hainmueller(2011). MATLAB code is available on the authors’ websites.

8That is, each column r of the matrix B contains the regressioncoefficients of the outcome variable at period t = T0 + r on X0.

9It is easy to extend the proof to the more general case where theunit vector, �, belongs to the subspace of R

J +1 spanned by the rowsof [X1 X0].


reason is that (X0 X ′0)−1 X0� is the vector of coefficients

of the regression of � on X0. Because � is a vector ofones and because the first row of X0 is also a vectorof ones, the only nonzero coefficient of this regressionis the intercept, which takes a value equal to one. Thisimplies that �′Wreg = �′ X ′

0(X0 X ′0)−1 X1 = 1 (because the

first element of X1 is equal to one).That is, the regression estimator is a weighting esti-

mator with weights that sum to one. However, regressionweights are unrestricted and may take on negative val-ues or values greater than one. As a result, estimates ofcounterfactuals based on linear regression may extrap-olate beyond the support of comparison units. Even ifthe characteristics of the case of interest cannot be ap-proximated using a weighted average of the character-istics of the potential controls, the regression weightsextrapolate to produce a perfect fit. In more technicalterms, even if X1 is far from the convex hull of thecolumns of X0, regression weights extrapolate to produceX0Wreg = X0 X ′

0(X0 X ′0)−1 X1 = X1.

Regression extrapolation can be detected if theweights Wreg are explicitly calculated, because it resultsin weights outside the [0, 1] interval. We do not know,however, of any previous article that explicitly computesregression weights, and we are also unaware of previousresults interpreting regressions as weighting estimatorswith weights that sum to one. Because regression weightsare not calculated in practice, the extent of extrapola-tion produced by regression techniques is typically hid-den from the analyst. In the empirical section below, weprovide a comparison between the unit synthetic controlweights and the regression weights for the German re-unification example. For that example, we show that theregression-based counterfactual relies on extrapolation.Extrapolation is, however, unnecessary in the context ofour German reunification example. We show that thereexists a synthetic control that closely fits the values of thecharacteristics of the units and that does not extrapolateoutside of the support of the data.10

10While using weights that sum to one and fall in the [0, 1] in-terval prevents extrapolation biases, interpolation biases may besevere in some cases, especially if the donor pool contains unitswith characteristics that are very different from those of the unitrepresenting the case of interest. To reduce interpolation biases,we recommend restricting the donor pool to units that are sim-ilar to the one representing the case of interest. In addition, the‖X1 − X0W‖ objective function for the weights could be comple-mented with penalty terms that incorporate the discrepancies incharacteristics between the unit representing the case of interestand the units with positive weights in the synthetic control. Suchpenalty terms can also be useful to select a synthetic control whenminimization of ‖X1 − X0W‖ has multiple solutions, because X1

falls in the convex hull of the columns of X0.

Inference with the Synthetic ControlMethod

The use of statistical inference in comparative case stud-ies is difficult because of the small-sample nature of thedata, the absence of randomization, and the fact thatprobabilistic sampling is not employed to select sampleunits. These limitations complicate the application of tra-ditional approaches to statistical inference.11 However,by systematizing the process of estimating the counter-factual of interest, the synthetic control method enablesresearchers to conduct a wide array of falsification exer-cises, which we term “placebo studies,” that provide thebuilding blocks for an alternative mode of qualitative andquantitative inference. This alternative model of infer-ence is based on the premise that our confidence that aparticular synthetic control estimate reflects the impactof the intervention under scrutiny would be severely un-dermined if we obtained estimated effects of similar oreven greater magnitudes in cases where the interventiondid not take place.

Suppose, for example, that the synthetic controlmethod estimates a sizable effect for a certain interven-tion of interest. Our confidence about the validity of thisresult would dissipate if the synthetic control method alsoestimated large effects when applied to dates when the in-tervention did not occur (Heckman and Hotz 1989). Werefer to these falsification exercises as “in-time placebos.”These tests are feasible if there are available data for a suf-ficiently large number of time periods when no structuralshocks to the outcome variable occurred. In the exampleof the next section, we consider the effect of the 1990 Ger-man reunification on per capita GDP in West Germany.The German reunification occurred in 1990, but we havedata from 1960 and thus can test whether the methodproduces large estimated effects when applied to datesbefore the reunification. If we find estimated effects thatare of similar or larger magnitude than the one estimatedfor the 1990 reunification, our confidence that the effectestimated for the 1990 reunification is attributable to re-unification itself would greatly diminish. In that case, theplacebo studies would suggest that synthetic controls donot provide good predictions of the trajectory of the out-come in West Germany in periods when the reunificationdid not occur. Conversely, in the empirical section below,we find a very large effect for the 1990 German reunifica-tion, but no effect at all when we artificially reassign thereunification period in our data to a date before 1990.

11See Rubin (1990) for a description of the different modes ofstatistical inference for causal effects.


Another way to conduct placebo studies is to reas-sign the intervention not in time, but to members of thedonor pool. We refer to these tests as “in-space placebos.”Here the premise is that our confidence that a sizablesynthetic control estimate reflects the effect of the in-tervention would disappear if similar or larger estimatesarose when the intervention is artificially reassigned tounits not directly exposed to the intervention.

A particular implementation of this idea consists ofapplying the synthetic control method to estimate placeboeffects for every potential control unit in the donor pool.This creates a distribution of placebo effects against whichwe can then evaluate the effect estimated for the unit thatrepresents the case of interest. Our confidence that a largesynthetic control estimate reflects the effect of the in-tervention would be undermined if the magnitude of theestimated effect fell well inside the distribution of placeboeffects. As in traditional statistical inference, a quantitativecomparison between the distribution of placebo effectsand the synthetic control estimate can be operationalizedthrough the use of p-values. In this context, a p-value canbe constructed by estimating in-space placebo effects foreach unit in the sample and then calculating the fractionof such effects greater than or equal to the effect estimatedfor the treated unit. Notice that this inferential exercisereduces to classical randomization inference when theintervention is randomized (Rosenbaum 2005). In theabsence of randomization, the p-value still has an inter-pretation as the probability of obtaining an estimate atleast as large as the one obtained for the unit representingthe case of interest when the intervention is reassigned atrandom in the data set. Notice that the inferential meth-ods outlined in this section do not produce confidenceintervals or posterior distributions, and that the inferen-tial exercises (and associated p-values) are restricted tothe question of whether or not the estimated effect of theactual intervention is large relative to the distribution ofplacebo effects. In the empirical section below, we showthat the synthetic control estimate for West Germany isvery large relative to the distribution of placebo estimatesfor the countries in the donor pool.

Limitations of the Approach and SomeRecommendations for Empirical Practice

The synthetic control method facilitates comparative casestudies in instances when no single untreated unit pro-vides a good comparison for the unit affected by the treat-ment or event of interest. This is often the case when thetreatment affects large aggregates like regions or coun-tries, so a limited number of untreated units are available.

In this section, we discuss requirements and limitations ofthe method and provide recommendations for empiricalpractice.

Constructing a donor pool of comparison units re-quires some care. First, units affected by the event orintervention of interest or by events of a similar natureshould be excluded from the donor pool. In addition,units that may have suffered large idiosyncratic shocks tothe outcome of interest during the study period shouldalso be excluded if such shocks would have not affectedthe treated unit in the absence of the treatment. Finally,to avoid interpolation biases, it is important to restrictthe donor pool to units with characteristics similar tothe treated unit. Another reason to restrict the size of thedonor pool and consider only units similar to the treatedunit is to avoid overfitting. Overfitting arises when thecharacteristics of the unit affected by the intervention orevent of interest are artificially matched by combiningidiosyncratic variations in a large sample of unaffectedunits. The risk of overfitting motivates our adoption ofthe cross-validation techniques applied in the empiricalsection below.

The applicability of the method requires a sizablenumber of preintervention periods. The reason is thatthe credibility of a synthetic control depends upon howwell it tracks the treated unit’s characteristics and out-comes over an extended period of time prior to the treat-ment. We do not recommend using this method when thepretreatment fit is poor or the number of pretreatmentperiods is small.12 A sizable number of postinterventionperiods may also be required in cases when the effect ofthe intervention emerges gradually after the interventionor changes over time.

The Economic Cost of the 1990German Reunification

In this section, we apply the synthetic control method toestimate the impact of the 1990 German reunification,one of the most significant political events in postwarEurope. After the fall of the Berlin Wall on November 9,1989, the German Democratic Republic and the FederalRepublic of Germany officially reunified on October 3,1990. At that time, per capita GDP in West Germany wasabout three times higher than in East Germany (Lipschitzand McDonald 1990). Given the large income dispar-ity, the integration of both countries after 45 years of

12See Abadie, Diamond, and Hainmueller (2010) for a related dis-cussion.


separation called for political and economic adjustmentsof unprecedented complexity and scale. The 1990 Germanreunification therefore provides an excellent case study toexamine the economic consequences of political integra-tion. As Burda and Hunt (2001, 1) put it, “it is difficultto find a more dramatic episode of economic disloca-tion in peacetime during the twentieth century than thatassociated with the reunification of Germany.”

Many studies have examined the consequences of thereunification (see Burda and Hunt 2001; Heilemann andRappen 2000; and Sinn 2002 for reviews), but most ofthem focus on the consequences for (the former) EastGermany and the convergence between the East and WestGerman economy. The question of what the economiccosts are for West Germany has received less attention inthe literature. And while many argue that the economicimpact of reunification on the West German economyhas been negative, the magnitude of this effect remainsunknown (e.g., Canova and Ravn 2000; Heilemann andRappen 2000; Meinhardt et al. 1995). In particular, to ourknowledge no study has rigorously estimated the impactof reunification on West German per capita GDP usinga comparative case study analysis. Here we fill this gapand construct a synthetic West Germany as a weightedaverage of other advanced industrialized countries cho-sen to resemble the values of economic growth predictorsfor West Germany prior to the reunification. The syn-thetic West Germany is meant to replicate the (counter-factual) per capita GDP trend that West Germany wouldhave experienced in the absence of the 1990 reunification.We then estimate the effect of the reunification by com-paring the actual (with reunification) and counterfactual(without reunification) per capita GDP series for WestGermany.13

Data and Sample

We use annual country-level panel data for the period1960–2003. The German reunification occurred in 1990,giving a preintervention period of 30 years. Our sampleperiod ends in 2003 because a roughly decadelong periodafter the reunification seems like a reasonable limit on thespan of plausible prediction. Recall that the synthetic WestGermany is constructed as a weighted average of poten-tial control countries in the donor pool. Our donor poolincludes a sample of 16 OECD member countries: Aus-

13Additionally, one could also try to estimate the effect of reunifi-cation on East Germany. However, concerns about the quality ofthe official East German statistics before the German reunificationrender this a questionable endeavor. See Lipschitz and McDonald(1990).

tralia, Austria, Belgium, Denmark, France, Greece, Italy,Japan, the Netherlands, New Zealand, Norway, Portugal,Spain, Switzerland, the United Kingdom, and the UnitedStates.14

We provide a list of all variables used in the analysis inthe data appendix, along with data sources. The outcomevariable, Yjt , is the real per capita GDP in country j attime t. GDP is Purchasing Power Parity (PPP)-adjustedand measured in 2002 U.S. dollars (USD, hereafter). Forthe pre-reunification characteristics in X1 and X0, werely on a standard set of economic growth predictors:per capita GDP, inflation rate, industry share of valueadded, investment rate, schooling, and a measure of tradeopenness (see the appendix for details). For each variable,we checked that the German data refer exclusively to theterritory of the former West Germany.15 We experimentedwith a wide set of additional growth predictors, but theirinclusion did not change our results substantively.

Constructing a Synthetic Version of WestGermany

Using the techniques described in the methodologicalsection above, we construct a synthetic West Germanywith weights chosen so that the resulting synthetic WestGermany best reproduces the values of the predictorsof per capita GDP in West Germany in the prereuni-fication period. We use a cross-validation technique tochoose the weights vm in Equation (1). We first dividethe pretreatment years into a training period from 1971to 1980 and a validation period from 1981 to 1990. Next,using predictors measured in the training period, we se-lect the weights vm such that the resulting synthetic con-trol minimizes the root mean square prediction error

14To construct this sample, we started with the 23 OECD membercountries in 1990 (excluding West Germany). We first excludedLuxembourg and Iceland because of their small size and becauseof the peculiarities of their economies. We also excluded Turkey,which had in 1990 a level of per capita GDP well below the othercountries in the sample. We finally excluded Canada, Finland, Swe-den, and Ireland because these countries were affected by profoundstructural shocks during the sample period. Ireland experienced arapid Celtic Tiger expansion period in the 1990s. Canada, Finland,and Sweden experienced profound financial and fiscal crises at thebeginning of the 1990s. It is important to note, however, that whenincluded in the sample, these four countries obtain zero weightsin the synthetic control for West Germany. Therefore, our mainresults are identical whether or not we exclude these countries.

15For that purpose, when necessary, our data set was supplementedwith data from the German Federal Statistical Office (StatistischesBundesamt).


TABLE 1 Synthetic and Regression Weights for West Germany

Synthetic Regression Synthetic RegressionCountry Control Weight Weight Country Control Weight Weight

Australia 0 0.12 Netherlands 0.09 0.14Austria 0.42 0.26 New Zealand 0 0.12Belgium 0 0 Norway 0 0.04Denmark 0 0.08 Portugal 0 −0.08France 0 0.04 Spain 0 −0.01Greece 0 −0.09 Switzerland 0.11 0.05Italy 0 −0.05 United Kingdom 0 0.06Japan 0.16 0.19 United States 0.22 0.13

Notes: The synthetic weight is the country weight assigned by the synthetic control method. The regression weight is the weight assignedby linear regression. See text for details.

(RMSPE) over the validation period.16 Intuitively, thecross-validation technique selects the weights vm thatminimize out-of-sample prediction errors. Finally, we usethe set of vm weights selected in the previous step and pre-dictor data measured in 1981–90 to estimate a syntheticcontrol for West Germany. The vm weights chosen by thecross-validation indicate that the most important predic-tors (in order from highest to lowest weight) are GDPper capita (0.442), investment rate (0.245), trade open-ness (0.134), schooling (0.107), inflation rate (0.072), andindustry share (0.001).17 We estimate the effect of the Ger-man reunification on per capita GDP in West Germany asthe difference in per capita GDP levels between West Ger-many and its synthetic counterpart in the years followingthe reunification.

Table 1 shows the weights of each country in the syn-thetic version of West Germany. The synthetic West Ger-many is a weighted average of Austria, the United States,Japan, Switzerland, and the Netherlands with weights de-creasing in this order. All other countries in the donorpool obtain zero weights. As a comparison, Table 1 also

16The RMSPE measures lack of fit between the path of the outcomevariable for any particular country and its synthetic counterpart.The pre-1990 RMSPE for West Germany is defined as

RMSPE =⎛⎝ 1

T0

T0∑t=1

⎛⎝Y1t −

J +1∑j=2

w∗j Yjt

⎞⎠

2⎞⎠

1/2

.

The RMSPE can be analogously defined for other countries or timeperiods.

17Our results are robust to alternative procedures to choose vm. Inparticular, Abadie and Gardeazabal (2003) and Abadie, Diamond,and Hainmueller (2010) chose vm so that the resulting syntheticcontrol best approximates the preintervention path of the outcomevariable. For the German reunification example, this way to choosevm produces results that are almost identical to the results that weobtain using the cross-validation technique used in this article.

TABLE 2 Economic Growth Predictor Meansbefore German Reunification

West Synthetic OECDGermany West Germany Sample

GDP per capita 15808.9 15802.2 8021.1Trade openness 56.8 56.9 31.9Inflation rate 2.6 3.5 7.4Industry share 34.5 34.4 34.2Schooling 55.5 55.2 44.1Investment rate 27.0 27.0 25.9

Notes: GDP per capita, inflation rate, trade openness, and industryshare are averaged for the 1981–90 period. Investment rate andschooling are averaged for the 1980–85 period. The last columnreports a population-weighted average for the 16 OECD countriesin the donor pool.

reports the weights that regression analysis employs im-plicitly when applied to the same data (these weights arebacked out using the formulas presented in the method-ological section above). By construction, both sets ofweights sum to one. The two sets of weights show somesimilarities. For example, Austria receives the highestweight in both approaches. Overall, however, the weightsare very different. For example, the regression weights forJapan and Austria are much closer in values than theirsynthetic control counterparts. Moreover, regression as-signs negative weights to four of the 16 control units inthe donor pool: Greece (–0.09), Italy (–0.05), Portugal (–0.08), and Spain (–0.01). As discussed previously, negativeweights indicate that regression relies on extrapolation.

Table 2 compares the prereunification characteristicsof West Germany to those of the synthetic West Germany,and also to those of a population-weighted average ofthe 16 OECD countries in the donor pool. Overall, theresults in Table 2 suggest that the synthetic West Germany


FIGURE 1 Trends in per Capita GDP: WestGermany versus Rest of the OECDSample

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Reunification

provides a much better comparison for West Germanythan the average of our sample of other OECD countries.The synthetic West Germany is very similar to the actualWest Germany in terms of pre-1990 per capita GDP, tradeopenness, schooling, investment rate, and industry share.Compared to the average of the OECD countries, the syn-thetic West Germany also matches West Germany muchcloser on the inflation rate. Because West Germany hadthe lowest inflation rate in the sample during the prereuni-fication years, this variable cannot be perfectly fitted us-ing a combination of the comparison countries. Figure 1shows that before the German reunification, West Ger-many and the OECD average experienced different pathsin per capita GDP. However, in the next section, we willshow that a synthetic control can accurately reproducethe pre-1990 per capita GDP path for West Germany.

One of the central points of this article is that the syn-thetic control method provides the qualitative researcherwith a quantitative tool to select or validate comparisonunits. In our analysis, Austria, the United States, Japan,Switzerland, and the Netherlands emerge, in this order,as potential comparisons to West Germany. Regressionanalysis fails to provide such a list. In a regression analy-sis, typically all units contribute to the regression fit, andthe contribution of units with large positive regressionweights may be counterbalanced by the contributions ofunits with negative weights. In this example, the syntheticcontrol involves a combination of five countries. Below weshow how researchers can construct, if desired, syntheticcontrols that use a smaller number of countries.

FIGURE 2 Trends in per Capita GDP: WestGermany versus Synthetic WestGermany

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Reunification

The Effect of the 1990 Reunification

Figure 2 displays the per capita GDP trajectory of WestGermany and its synthetic counterpart for the 1960–2003period. The synthetic West Germany almost exactly re-produces the per capita GDP for West Germany duringthe entire prereunification period. This close fit for theprereunification per capita GDP and the close fit that weobtain for the GDP predictors in Table 2 demonstratethat there exists a combination of other industrializedcountries that reproduces the economic attributes of WestGermany before the reunification. That is, it is possible toclosely reproduce economic characteristics of West Ger-many before the 1990 reunification without extrapolatingoutside of the support of the data for the donor pool.

Our estimate of the effect of the German reunifica-tion on per capita GDP in West Germany is given by thedifference between the actual West Germany and its syn-thetic version, visualized in Figure 3. We estimate that theGerman reunification did not have much of an effect onWest German per capita GDP in the first two years imme-diately following reunification. In this initial period, percapita GDP in the synthetic West Germany is even slightlylower than in the actual West Germany, which is broadlyin line with arguments about an initial demand boom(see, e.g., Meinbardt et al. 1995). From 1992 onward,however, the two lines diverge substantially. While percapita GDP growth decelerates in West Germany, for thesynthetic West Germany per capita GDP keeps ascendingat a pace similar to that of the prereunification period.


FIGURE 3 Per Capita GDP Gap between WestGermany and Synthetic WestGermany

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−400

0−2

000

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0040

00

Year

Gap

in P

er C

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)

Reunification

The difference between the two series continues to growtowards the end of the sample period. Thus, our resultssuggest a pronounced negative effect of the reunificationon West German income. We find that over the entire1990–2003 period, per capita GDP was reduced by about1,600 USD per year on average, which amounts to ap-proximately 8% of the 1990 baseline level. In 2003, percapita GDP in the synthetic West Germany is estimatedto be about 12% higher than in the actual West Germany.

One valid concern in the context of this study is thepotential existence of spillover effects. In particular, itis possible that the German reunification had effects onper capita GDP in countries other than Germany. Notice,however, that the limited number of units in the syntheticcontrol allows the evaluation of the existence and direc-tion of potential biases created by spillover effects. For ex-ample, if the German reunification had negative spillovereffects on the per capita GDP of the countries includedin the synthetic control, then the synthetic control wouldprovide an underestimate of the counterfactual per capitaGDP trajectory for West Germany in the absence of thereunification and, therefore, an underestimate of the neg-ative effect of the reunification on per capita GDP in WestGermany. On the other hand, if the German reunificationhad positive effects in the economies included in the syn-thetic control, this would exacerbate the negative effect ofthe synthetic control estimates. Notice also that spillovereffects on countries not included in the synthetic controldo not affect the synthetic control estimates.

FIGURE 4 Placebo Reunification 1975–Trendsin per Capita GDP: West Germanyversus Synthetic West Germany

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Placebo Reunification

Placebo Studies

To evaluate the credibility of our results, we conductplacebo studies where the treatment of interest is reas-signed in the data to a year other than 1990 or to coun-tries different from West Germany. We first compare thereunification effect estimated above for West Germany toa placebo effect obtained after reassigning the Germanreunification in our data to a period before the reunifica-tion actually took place. A large placebo estimate wouldundermine our confidence that the results in Figure 2 areindeed indicative of the economic cost of reunificationand not merely driven by lack of predictive power.

To conduct this placebo study, we rerun the modelfor the case when reunification is reassigned to the mid-dle of the pretreatment period in the year 1975, about15 years earlier than reunification actually occurred. Weuse the same out-of-sample validation technique to com-pute the synthetic control, and we lag the predictors vari-ables accordingly for the training and validation period.Figure 4 displays the results of this “in-time placebo”study. The synthetic West Germany almost exactly repro-duces the evolution of per capita GDP in the actual WestGermany for the 1960–1975 period. Most importantly,the per capita GDP trajectories of West Germany and itssynthetic counterpart do not diverge considerably duringthe 1975–1990 period. That is, in contrast to the actual1990 German reunification, our 1975 placebo reunifica-tion has no perceivable effect. This suggests that the gapestimated in Figure 2 reflects the impact of the German


FIGURE 5 Ratio of Postreunification RMSPE to PrereunificationRMSPE: West Germany and Control Countries

Portugal

Denmark

France

Netherlands

Japan

United Kingdom

Austria

Switzerland

Belgium

Australia

Spain

United States

New Zealand

Italy

Greece

Norway

West Germany

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

5 10 15

Postperiod RMSPE / Preperiod RMSPE

reunification and not a potential lack of predictive powerof the synthetic control.18

An alternative way to conduct placebo studies is toreassign the treatment in the data to a comparison unit.In this way, we can obtain synthetic control estimates forcountries that did not experience the event of interest.Applying this idea to each country in the donor poolallows us to compare the estimated effect of the Ger-man reunification on West Germany to the distributionof placebo effects obtained for other countries. We willdeem the effect of the German reunification on West Ger-many significant if the estimated effect for West Germanyis unusually large relative to the distribution of placeboeffects.

Figure 5 reports the ratios between the post-1990RMSPE and the pre-1990 RMSPE for West Germany andfor all the countries in the donor pool. Recall that RM-

18We have computed similar in-time placebo studies where wereassign in our data the German reunification to the years 1970and 1980, respectively, and the results are similar to the results for1975 shown here.

SPE measures the magnitude of the gap in the outcomevariable of interest between each country and its syntheticcounterpart. A large postintervention RMSPE is not in-dicative of a large effect of the intervention if the syntheticcontrol does not closely reproduce the outcome of interestprior to the intervention. That is, a large postinterventionRMSPE is not indicative of a large effect of the interven-tion if the preintervention RMSPE is also large. For eachcountry, we divide the postreunification RMSPE by itspre-reunification RMSPE.19 In Figure 5, West Germanyclearly stands out as the country with the highest RM-SPE ratio. For West Germany, the postreunification gapis about 16 times larger than the prereunification gap. Ifone were to pick a country at random from the sample,the chances of obtaining a ratio as high as this one wouldbe 1/17 0.059.

19By taking the ratio between the post-1990 RMSPE, and the pre-1990 RMSPE, we avoid having to discard countries with pre-1990per capita GDP values that cannot be approximated with a syntheticcontrol. See Abadie, Diamond, and Hainmueller (2010).


FIGURE 6 Leave-One-Out Distribution of theSynthetic Control for West Germany

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West GermanySynthetic West GermanySynthetic West Germany (leave-one-out)

Robustness Test

In this section, we run a robustness check to test thesensitivity of our main results to changes in the countryweights, W∗. Recall from Table 1 that the synthetic WestGermany is estimated as a weighted average of Austria,the United States, Japan, Switzerland, and the Nether-lands, with weights decreasing in this order. Here weiteratively reestimate the baseline model to construct asynthetic West Germany omitting in each iteration oneof the countries that received a positive weight in Table 1.By excluding countries that received a positive weight wesacrifice some goodness of fit, but this sensitivity checkallows us to evaluate to what extent our results are drivenby any particular control country.

Figure 6 displays the results and reproduces Figure2 (solid and dashed black lines) while also incorporat-ing the leave-one-out estimates (gray lines). This figureshows that the results of the previous analysis are fairlyrobust to the exclusion of any particular country fromour sample of comparison countries. The leave-one-outsynthetic control that shows the smallest effect of the re-unification is the one that excludes the United States. Eventhis estimate is fairly large in substantive terms: Per capitaGDP over the 1990–2003 period is reduced by about 630USD per year on average, approximately 3% of the 1990baseline level. In 2003, per capita GDP in this syntheticWest Germany is estimated to be about 7% higher thanin the actual West Germany. The other leave-one-outsynthetic controls show either a very similar or slightly

larger effect compared to the results of the previousanalysis.

Reducing the Number of Units in aSynthetic Control

Recall again that the synthetic West Germany in Figure 2is a weighted average of five control countries: Austria, theUnited States, Japan, Switzerland, and the Netherlands.Comparative researchers, however, typically choose a verysmall number of cases, with the aim of meticulously de-scribing and analyzing the characteristics and outcomesof each of those cases. As a result, in many instances, com-parative researchers may favor sparse synthetic controls,that is, synthetic controls that involve a small number ofcomparison countries. Reducing the number of units inthe synthetic control may, nonetheless, impact the extentto which the synthetic control is able to fit the character-istics of the unit of interest. In this section, we examinethe trade-off between sparsity and goodness of fit in thechoice of the number of units that contribute to the syn-thetic control for West Germany.

In order to investigate this trade-off, we constructsynthetic controls for West Germany, allowing only com-binations of four, three, two, and a single control country,respectively.20 Table 3 shows the countries and weightsfor the sparse synthetic controls. For this example, thecountries contributing to the sparse versions of the syn-thetic control for West Germany are subsets of the setof five countries contributing to the synthetic controlin the baseline specification.21 Austria retains the largestweight in all instances, whereas the United States, Japan,and Switzerland are second, third, and fourth in terms oftheir synthetic control weights.

Table 4 compares economic growth predictors ofWest Germany, synthetic West Germany, the sparse ver-sions of synthetic West Germany, and the OECD sample.This table documents the sacrifice in terms of goodnessof fit resulting from a reduction in the number of coun-tries, l , allowed to contribute to the synthetic control.

20More precisely, for l = 4, 3, 2, 1, and for all possible combina-tions of l control countries, we choose the one that produces thesynthetic control unit that minimizes the loss defined in Equation(1). To reduce computational complexity, we used the weights vm

obtained for the baseline model instead of attempting to recalculatethese weights for the many different combinations of l countries.

21Also, each subset of countries in Table 3 is nested by any othersubset containing a larger number of countries. This is not im-posed in our analysis, as we consider all possible combinations ofcountries among the 16 countries in the donor pool, and it maynot necessarily be the case for other applications.


TABLE 3 Synthetic Weights from Combinations of Control Countries

Synthetic Combination Countries and W-Weights

Five control countries Austria USA Japan Switzerland Netherlands0.42 0.22 0.16 0.11 0.09

Four control countries Austria USA Japan Switzerland0.56 0.22 0.12 0.10

Three control countries Austria USA Japan0.59 0.26 0.15

Two control countries Austria USA0.76 0.24

One control country Austria1

Notes: Countries and W-weights for synthetic control are constructed from the best-fitting combination of five, four, three, and twocountries, as well as one country. See text for details.

TABLE 4 Economic Growth Predictor Means before the German Reunification for Combinations ofControl Countries

Synthetic West GermanyWest Number of countries in synthetic control OECD

Germany 5 4 3 2 1 Sample

GDP per capita 15808.9 15802.2 15800.9 15492.9 15580.9 14817.0 8021.1Trade openness 56.8 56.9 55.9 52.5 61.5 74.6 31.9Inflation rate 2.6 3.5 3.6 3.6 3.8 3.5 7.4Industry share 34.5 34.4 34.6 34.8 34.3 35.5 34.2Schooling 55.5 55.2 57.6 57.7 60.7 60.9 44.1Investment rate 27.0 27.0 27.2 26.8 25.6 26.6 25.9

Notes: GDP per capita, inflation rate, and trade openness are averaged for the 1981–1990 period. Industry share is averaged for the1981–1990 period. Investment rate and schooling are averaged for the 1980–1985 period.

Overall, relative to the baseline synthetic control with fivecountries, the decline in goodness of fit is moderate forl = 4, 3, 2. The “matching”case of l = 1, where the syn-thetic West Germany is Austria, produces a much worsegoodness of fit relative to l > 1, with substantial discrep-ancies in the per capita GDP and trade openness variables.However, even the matching case, with l = 1, representsa large improvement in terms of goodness of fit rela-tive to the comparison unit consisting of the population-weighted average of the OECD sample.

Figure 7 shows the per capita GDP path for West Ger-many and the sparse synthetic controls with l = 4, 3, 2, 1.With the exception of the matching case (l = 1), thesparse synthetic controls in Figure 7 produce results thatare very similar to the baseline result in Figure 2. However,using a single country, Austria, as a comparison providesa much poorer fit to the pre-1990 per capita GDP path

for West Germany.22 This analysis illustrates the poten-tial gains from using combinations of countries ratherthan single countries as comparison cases in comparativeresearch.23

22For example, at the time of the German reunification, the percapita GDP in Austria was about 7% lower than that of West Ger-many.

23The comparison between Austria and West Germany in the lowerright panel of Figure 7 comes close to a difference-in-differencesdesign, with Austria having a lower per capita GDP than WestGermany during the pre-1990 period, but a fairly similar trend inthis variable. In this comparison, we see that the Austrian per capitaGDP surpassed the West German per capita GDP a few years afterthe reunification, even when it had been consistently lower for atleast 30 years prior to the reunification. Therefore, this comparisonalso suggests a negative effect of the German reunification in WestGermany. See Abadie, Diamond, and Hainmueller (2010) for adiscussion of the relationship between the synthetic control andthe difference-in-differences estimator.


FIGURE 7 Per Capita GDP Gaps between West Germany and Sparse Synthetic Controls

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Conclusion

There is a widespread consensus among political method-ologists about the necessity to integrate and exploit com-plementarities between qualitative and quantitative toolsfor empirical research in political science. However, someof the efforts in this direction have been denounced byqualitative methodologists as attempts to impose quan-titative templates on qualitative research that disregardor do not make use of the many genuine advantages ofqualitative research (Brady and Collier 2004; George andBennett 2005). The synthetic control method discussedin this article falls in between the qualitative and quan-

titative methodologies and provides a potentially usefultool for researchers of both traditions. On the one hand,the synthetic control method provides a systematic way toselect comparison units in quantitative comparative casestudies. In this way, as in Card and Krueger (1994) andRosenbaum (2005), the synthetic control method bringsto quantitative studies the careful selection of cases that isdone in qualitative analysis. In addition, by explicitly spec-ifying the set of units that are used for comparison, themethod does not preclude but facilitates detailed qualita-tive analysis and comparison between the case of interestand the set of comparison units selected by the method.That is, the synthetic control method can be used to guide


the selection of comparison units in qualitative studies,allowing what Tarrow (1995) calls “qualitative inferencewith quantitative bones.”

Appendix

The data sources employed for the application are as fol-lows:

� GDP per Capita (PPP, 2002 USD). Source: OECDNational Accounts (retrieved via the OECDHealth Database). Data for West Germany wasobtained from Statistisches Bundesamt 2005(Arbeitskreis “Volkswirtschaftliche Gesamtrech-nungen der Lander”) and converted using PPPmonetary conversion factors (retrieved from theOECD Health Database).

� Investment Rate: Ratio of real domestic invest-ment (private plus public) to real GDP. The dataare reported in five-year averages. Source: Barro,Robert Joseph, and Jong-wha Lee. 1994. “DataSet for a Panel of 138 Countries.” Available athttp://www.nber.org/pub/barro.lee/.

� Schooling: Percentage of secondary school at-tained in the total population aged 25 and older.The data are reported in five-year increments.Source: Barro, Robert Joseph, and Jong-wha Lee.2000. “International Data on Educational Attain-ment: Updates and Implications.” CID WorkingPaper No. 42, April 2000 – Human Capital Up-dated Files.

� Industry: industry share of value added. Source:World Bank WDI Database 2005 and Statistis-ches Bundesamt 2005.

� Inflation: annual percentage change in consumerprices (base year 1995). Source: World Develop-ment Indicators Database 2005 and StatistischesBundesamt 2005.

� Trade Openness: Export plus imports as percent-age of GDP. Source: World Bank: World Devel-opment Indicators CD-ROM 2000.

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