estimating the electoral effects of voter turnoutfaculty.ucmerced.edu/thansford/articles/estimating...

American Political Science Review Vol. 104, No. 2 May 2010

doi:10.1017/S0003055410000109

Estimating the Electoral Effects of Voter TurnoutTHOMAS G. HANSFORD University of California, MercedBRAD T. GOMEZ Florida State University

This article examines the electoral consequences of variation in voter turnout in the United States.Existing scholarship focuses on the claim that high turnout benefits Democrats, but evidencesupporting this conjecture is variable and controversial. Previous work, however, does not account

for endogeneity between turnout and electoral choice, and thus, causal claims are questionable. Usingelection day rainfall as an instrumental variable for voter turnout, we are able to estimate the effectof variation in turnout due to across-the-board changes in the utility of voting. We re-examine thePartisan Effects and Two-Effects Hypotheses, provide an empirical test of an Anti-Incumbent Hypothesis,and propose a Volatility Hypothesis, which posits that high turnout produces less predictable electoraloutcomes. Using county-level data from the 1948–2000 presidential elections, we find support for eachhypothesis. Failing to address the endogeneity problem would lead researchers to incorrectly reject allbut the Anti-Incumbent Hypothesis. The effect of variation in turnout on electoral outcomes appearsquite meaningful. Although election-specific factors other than turnout have the greatest influence onwho wins an election, variation in turnout significantly affects vote shares at the county, national, andElectoral College levels.

There are two undercurrents to much of the liter-ature on voter turnout: a normative belief thathigh rates of voter participation are desirable,

and an empirical expectation that variation in voterturnout will have electoral consequences. To someextent, these undercurrents flow together. Althoughone might argue that high turnout is preferable forpurely expressive reasons, the typical normative claimasserts that increased levels of voter participation im-prove the quality of representation by reducing anybias that might result from dissimilarities between vot-ers and nonvoters. Assumed differences between thosewho vote and those who do not are also at the heartof the commonly hypothesized empirical relationshipbetween aggregate turnout and partisan vote share.As argued originally by the authors of The Ameri-can Voter (Campbell et al. 1960, 96–115), if nonvot-ers and occasional voters hold preferences that differfrom those of habitual (or core) voters, then variationin turnout is likely to have meaningful electoral im-plications. Higher turnout might advantage one partyover another, might advantage incumbents or perhaps

Thomas G. Hansford is Associate Professor of Political Science, Uni-versity of California–Merced, 5200 North Lake Road, Merced, CA95343 ([email protected]).

Brad T. Gomez is Assistant Professor of Political Science, FloridaState University, 536 Bellamy Building, Tallahassee, FL 32306([email protected]).

An earlier version of this article was presented at the AnnualMeeting of the American Political Science Association, Boston,MA, August 28–31, 2008. We wish to thank Robert Jackson, CarlKlarner, Michael Martinez, Steve Nicholson, Alex Whalley, and thereviewers and co-editors of the APSR for their constructive com-ments during the writing of this article. We also wish to thank ScottEdwards of EarthInfo, Inc., for his assistance with extracting thehistorical weather data, as well as Dave Cowen, Courtney Russell,and, especially, Lynn Shirley from the Department of Geographyat the University of South Carolina for their work and expertise inproducing GIS interpolations of the weather data. Last, we thankthe College of Arts and Science at the University of South Carolina,where this work commenced, for its generous financial support forthis project. All errors should be attributed to the authors alone.

their challengers, or might lead to greater volatility inthe electorate. In turn, each electoral implication fromhigher turnout is likely to result in significant policyconsequences.

Given the potential importance of the link betweenvoter turnout and electoral outcomes, the literature isreplete with studies testing the existence and natureof this relationship. Yet, for all the effort, scholarlywork has not produced an agreement about whetheran empirical association between turnout and electoraloutcomes actually exists, nor is there universal agree-ment regarding the causal mechanism that connects thetwo phenomena.

Almost all existing studies, for instance, have a par-tisan component—the most common conjecture beingthat Democratic candidates typically do better whenturnout is high. Some, however, hypothesize that thispartisan effect will be conditioned by the partisancomposition of the electorate (DeNardo 1980, 1986),whereas others find instead that this partisan effect maydepend on the presence of class cleavages (Martinezand Gill 2005). This debate over the causal nature of therelationship between turnout and partisan outcomesis fueled by mixed empirical evidence. Tests of thepartisan conjecture vary remarkably in their findings,with Radcliff (1994) and Erikson (1995) anchoring thepolar extremes of large partisan (i.e., pro-Democratic)turnout effects and no turnout effects, respectively.

An alternative to the partisan hypotheses is identi-fied by Grofman, Owen, and Collet (1999), who suggestthat higher turnout rates could be bad news for incum-bents. They note that high turnout “can arise if growingunpopularity of an incumbent leads to an increase invoters who seek to unseat him/her turning out at thepolls and/or if potential vulnerability of an incumbentto a successful challenge leads to a campaign by awell-financed challenger whose campaign succeeds inattracting more voters to the polls” (Grofman, Owen,and Collet 1999, 359). In this view, high turnout is likelyto correspond with decreased vote share for incumbent

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candidates or the incumbent party. This hypothe-sized connection between turnout and incumbency isa reasonable alternative (or perhaps complement) tothe partisan conjecture, but unfortunately it remainsuntested. Thus, there exists little scholarly agreementabout either the partisan consequences of high turnoutor its effect on incumbents in general.

One possible reason for the lingering questionsabout the effect of turnout on electoral outcomes isthat the empirical approaches typically used to as-sess the relationship allow for claims of correlationbut likely do not allow for claims of causation. Fromclassic treatments of the subject (e.g., Burnham 1965;DeNardo 1980) to more recent studies (e.g., Citrin,Schickler, and Sides 2003; Nagel and McNulty 2000),existing scholarship generally investigates the effect ofturnout on electoral outcomes using one of two ap-proaches. One set of studies uses survey data on votersand nonvoters to assess the degree to which the latterhold different preferences from the former and thuswould have altered the election in question if they hadvoted (e.g., Citrin, Schickler, and Sides 2003; Hightonand Wolfinger 2001; Martinez and Gill 2005). Anotherset typically regresses aggregate vote share data onaggregate turnout to assess the effect of turnout onpartisan outcomes (e.g., Erikson 1995; Nagel and Mc-Nulty 1996, 2000; Radcliff 1994).1 Establishing a causalrelationship between turnout and electoral outcomes—using either approach—is difficult because individualdecisions to vote, as well as aggregate turnout data,are likely endogenous to dependent variables involv-ing vote choice. To the extent that the endogeneityproblem exists, current analyses suffer from coefficientbias and cannot lead to causal claims. In the end,of course, it is the causal claim that most interestsscholars.

In an effort to assess the actual causal effect ofvariation in voter turnout on electoral outcomes, weemploy an instrumental variable approach that useselection day weather—rainfall, to be specific—as an in-strument for voter turnout. Election day rainfall is anattractive instrument because it predicts turnout andis exogenous to electoral outcomes. Moreover, we canexpect the causal effect of weather-induced variation inturnout to be similar to the general effect of variationin turnout (endogenous or exogenous) resulting fromuniformly distributed changes in the costs or benefitsof voting. Although our instrument is unlikely to illu-minate the causal effect of variation in voter turnoutdue to targeted mobilization (or suppression) effortsor idiosyncratic candidate characteristics, variation ofthe sort captured by our instrument is likely to com-pose a substantial portion of the total variation in voterturnout.

By using county-level data that extend longitudinallyfrom the 1948 to the 2000 U.S. presidential elections, wegain substantial leverage for our weather-based instru-

1 Other important studies not neatly fitting into our classificationinclude those that examine the effect of voter turnout on racial orethnic representation in local governments (Hajnal and Trounstine2005) and the allocation of federal money (Martin 2003).

mental variable design and, consequently, substantialleverage in uncovering the electoral consequences ofturnout variation in recent U.S. elections. Using thisapproach, we test two previously examined partisan hy-potheses: (1) increases in turnout enlarge the vote shareof Democratic candidates, and (2) this partisan effectis conditioned by the partisan composition of the elec-torate. We find substantial support for both hypotheses.In addition, we use the instrumental variable approachto test Grofman, Owen, and Collet’s (1999) previouslyuntested hypothesis: (3) increases in turnout decreasethe vote share of incumbent candidates/parties. We alsopropose and test a Volatility Hypothesis: (4) increasesin turnout lead to greater electoral volatility. We findsubstantial support for these latter hypotheses as well,revealing that by narrowly focusing on partisan out-comes, previous scholarship has overlooked two im-portant implications of higher turnout: anti-incumbentvoting and general electoral volatility. When we com-pare the instrumental variable estimates with ordinaryleast squares (OLS) estimates, it becomes apparentthat a failure to address the endogeneity in our modelwould lead researchers to incorrectly reject all but theAnti-Incumbent Hypothesis.

We conclude by reporting the results of a simulationthat varies turnout two percentage points above andbelow its observed levels. We find that this four-pointswing in turnout causes an average change of approx-imately 20 Electoral College votes per election. Thus,although election-specific factors other than turnouthave the greatest influence on who wins an election,variation in turnout appears to exert a significant effecton vote shares at the county, national, and ElectoralCollege levels.

THEORETICAL CONNECTION BETWEENTURNOUT AND ELECTORAL OUTCOMES

If voters and nonvoters have the same propensitiesto cast ballots for particular candidates or parties,then turnout levels should not affect who wins elec-tions. This strict condition, however, is unlikely to bemet in practice, meaning that variation in turnout willlikely result in potentially meaningful changes in elec-toral outcomes. Exactly how voters and nonvoters dif-fer becomes the crucial question (e.g., Highton andWolfinger 2001; Wolfinger and Rosenstone 1980), be-cause the nature of these differences will define thepolitical implications of turnout.

We outline the theory behind two well-establishedhypotheses regarding the effect of turnout on elec-toral outcomes, one previously proposed but untestedhypothesis, and one original hypothesis derived fromextant theory. Although our goal here is not to intro-duce a new, overarching theory of turnout effects fromwhich each hypothesis can be derived, it is theoreticallyplausible for all four hypotheses to work in consort,instead of in competition. This prospect suggests thatthe effects of turnout may be more multifaceted thanprevious scholarship has surmised.

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Electoral Effects of Voter Turnout May 2010

Partisan Effects and the“Two-Effects” Hypothesis

The hypotheses most often discussed in the literatureinvolve the partisan implications of voter turnout. Thetheoretical rationale positing a partisan bias to turnoutbegins from an assumption that the same socioeco-nomic factors that influence whether people vote alsocorrespond with partisan preferences. It is well estab-lished in the behavioral literature that U.S. voters tendto be better educated, wealthier, and older than non-voters, creating a socioeconomic bias in who turns outto vote (e.g., Leighley and Nagler 1992). These samesocial factors have also been fairly stable predictors ofsupport for the Republican Party and its candidates(Gelman et al. 2008). So, it is reasonable to assumethat those who are likely to vote are also more likelyto sympathize with Republican candidates than thosewho are not likely to vote. Elections in which onlyhigh probability voters turn out at the polls shouldexhibit the greatest pro-Republican bias. As turnoutrates increase—resulting from lower probability vot-ers casting ballots—this partisan bias should decrease.2Thus, the logic underlying the Partisan Effect Hypoth-esis corresponds with the conventional wisdom thatDemocratic candidates do better when turnout is high.3

Partisan Effect Hypothesis: Increases in turnout will lead toincreases in the Democratic candidate’s vote share.

In what is arguably the best known work on the effectof turnout on vote share, DeNardo (1980, 1986) con-cedes that Democrats will benefit from higher turnouton average, but argues that this effect is conditional.DeNardo contends that the electorate is composed oftwo types of voters: those who regularly vote (“corevoters”) and those who occasionally vote (“peripheralvoters”).4 Although core voters have strong partisanattachments, peripheral voters have much weaker par-tisan leanings and tend to be more vulnerable to short-term electoral forces. Consequently, peripheral votersare more likely to defect from their weakly held parti-san allegiances. As a result, the partisan composition ofan electorate will influence the partisan effect of higherturnout.5

As an extreme example, consider a county in whichevery registered voter identifies as a Democrat. In a

2 Pacek and Radcliff (1995, 138) note that “the strength of the rela-tionship between turnout and the (partisan) vote . . . depends uponthe extent to which party competition is structured along socioeco-nomic cleavages—in other words, upon the extent to which partiesrepresent the interests of specific social classes.” In such cases, “thelower-status citizens who are the natural constituency of left partiestend to vote at lower and more variable rates than the higher-statussupporters of center or right parties.”3 Burnham (1965) was one of the first to demonstrate empiricallythat support for the Democratic Party increases as one moves fromcore voters to perpetual nonvoters.4 The distinction between core and peripheral voters was originatedby Campbell (1966), building off Burnham’s (1965) earlier delin-eation of the “American political universe” into three groups: corevoters, occasional voters, and perpetual nonvoters.5 For a critique of DeNardo’s Two-Effects Hypothesis, see Tuckerand Vedlitz (1986).

low turnout election, core voters, who are likely tobe dedicated Democrats, are most likely to turn out,and the vote share for a Democratic candidate shouldbe close to 100%. In a high turnout election, whereperipheral voters with weaker commitments to theDemocratic Party are voting, a meaningful proportionof these added voters are likely to defect and vote forthe Republican. Thus, higher turnout in this countywill increase the vote share for the Republican candi-date. Of course, the underlying mechanism works in ex-actly the same way if we alternate the Republican andDemocratic labels in the given example. The point tobe made here is that high turnout does not necessarilybenefit the Democratic Party as the Partisan Effect Hy-pothesis (and conventional wisdom) suggests. As ourextreme example illustrates, the partisan compositionof an electorate will condition the effect of the levelof voter turnout if peripheral voters are more likely todefect than core voters.

Thus, DeNardo contends that turnout has “two ef-fects.” Higher turnout will generally help Democraticcandidates, but higher turnout also helps the minorityparty within an electorate. More precisely, the positivemarginal effect of turnout on Democratic vote shareshould decrease in size as the proportion of Democratsin the electorate increases. In Republican-dominatedelectorates, Democratic candidates will be particularlyhelped by higher turnout because both the introductionof more Democratic voters and weak Republican iden-tifiers will push Democratic vote share upward. Themore Democratic the electorate, the less helpful higherturnout will be for a Democratic candidate. In fact,in particularly Democratic electorates, higher turnoutcould increase the Republican candidate’s vote share.

Two-Effects Hypothesis: The more Republican an elec-torate, the more that increases in turnout will increaseDemocratic vote share. In particularly Democratic elec-torates, increases in turnout may decrease Democratic voteshare.

The Anti-incumbent Effect

Grofman, Owen, and Collet (1999) offer a third hy-pothesis involving the political implications of turnout.Although careful not to make a causal claim, they arguethat higher turnout will be associated with lower voteshare for the incumbent party.6 In our view, there aretwo plausible justifications for this expectation. First,the conditions that cause voters to reject the incumbentparty may also cause more voters to turn out at thepolls. A troubled economy or unpopular war effort,for example, may stimulate both higher turnout anda collective vote against the incumbent candidate or

6 In fairness, Jacobson (2004) alludes to a relationship betweenturnout and incumbency advantage. Yet, we choose to attribute thehypothesis to Grofman, Owen, and Collet (1999), who refer to it asthe “competition hypothesis” because Jacobson does not expresslyarticulate the relationship as a hypothesis. Other existing studies onthe effect of turnout control for incumbency effects on vote shares,but do not actually test whether increases in turnout benefit or hurtincumbents (Nagel and McNulty 1996; Radcliff 1994).

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party. In this situation, however, turnout and an anti-incumbent vote are associated, but the former does notcause the latter.

A second potential justification for this hypothe-sis builds on the assumption that core voters differfrom peripheral voters. Here, the operative differencebetween these groups is not partisan, ideological, orsocioeconomic. Instead, the assumption is that corevoters are on average more supportive of the govern-mental status quo than peripheral votes because theyplayed a more active role in establishing the statusquo in previous elections.7 By definition, occasionalvoters or perpetual nonvoters had a lesser hand inthe formation of the status quo. The more that thesevoters are involved in an election, the worse the in-cumbent party’s candidate will do. This justification forGrofman, Owen, and Collet’s (1999) hypothesis clearlydraws a causal arrow from turnout to the vote shareof the incumbent party’s candidate. Because we areinterested in causal claims about turnout, we rely onthis second rationale:

Anti-Incumbent Hypothesis: Higher turnout will decreasethe vote share of the incumbent party’s candidate.

The Volatility Effect

Because peripheral voters tend to possess weaker par-tisan attachments and weaker affinity toward incum-bents, it is likely to be more difficult to predict ex-actly how they will vote if and when they do cometo the polls. Consider DeNardo’s defection argument.He contends that peripheral voters are more likelyto defect from whatever partisan leanings they maypossess. If this is the case, one wonders what criteriaperipheral voters do rely on when making an electoralchoice. It is unlikely that peripheral voters vote basedon policy preferences or ideology. In fact, Highton andWolfinger (2001) find—relying on American NationalElection Study (ANES) data—that those who did notvote in the 1992 and 1996 elections were less likelyto view themselves ideologically, had weaker policyopinions, and were more likely to view themselves asindependents than those who did vote. Thus, not onlyare peripheral voters more likely to defect from theirweakly held partisan leanings, but they are also lesslikely to vote based on policy preferences or ideol-ogy. This suggests that DeNardo’s defection argumentcan be expanded beyond its original specification: pe-ripheral voters not only have weaker levels of partisanattachment, but they also generally have weakly heldpolitical attitudes that play a minimal role in determin-ing their vote. Consequently, we suspect that if thesetypical nonvoters actually do vote, their votes will be

7 It is also quite plausible that peripheral votes are generally lesstrustworthy of the political system, which would also cause them toexhibit anti-incumbent tendencies on those few occasions when theyvote. Political trust predicts incumbent vote share (Hetherington1999), but it is not clear whether individual-level trust increases voterturnout (see Levi and Stoker 2000).

less predictable than those cast by ideological partisanswith strong policy preferences.8

High levels of turnout result from occasional votersand some perpetual nonvoters heading to the polls.This, in turn, means that a larger proportion of theelectorate is nonideological, independent, and holdsweak policy preferences. If these additional voters areless predictable in terms of their vote choice, then highturnout elections ought to be less predictable in theaggregate than low turnout elections.

Volatility Hypothesis: As turnout increases, vote share willbecome less predictable.

CURRENT APPROACHES TO ESTIMATINGTURNOUT EFFECTS AND THE PROBLEMOF ENDOGENEITY

Scholars have employed two different strategies whenanalyzing the political implications of voter turnout.The first approach uses aggregate data and regressespartisan vote share on levels of voter turnout. The re-sults of these studies are quite mixed, with some findingstrong support for what we label partisan effects (e.g.,Radcliff 1994), some finding no support for partisaneffects (e.g., Erikson 1995), and others providing evi-dence for the Two-Effects Hypothesis (e.g., Nagel andMcNulty 1996, 2000).

The problem with this approach is that it assumesthat levels of voter turnout are exogenous to partisanvote share. Yet, it is likely that voter turnout is actu-ally endogenous. Downs’s (1957) seminal work on thelogic of voter turnout implies as much. First, Downs’scalculus of voting suggests that eligible voters decidewhether to vote based in part on the extent to whichone candidate is preferable (i.e., provides greater ex-pected benefits) to the other. If some segment of voterssees no (or little, if there is a cost to voting) differencein expected utility between the candidates, Downs’smodel predicts that it is rational for these voters toabstain (1957, 39). Of course, the relative utility of thecandidates also determines for whom a voter choosesto vote. In other words, a voter’s relative preferencesregarding the candidates, and thus the likely directionof the vote, affect his or her decision to vote in the firstplace.

A second way in which Downs’s logic suggests endo-geneity is via the perceived closeness of the election. Asthe perceived probability of a close election increases,the instrumental value of voting also increases andturnout levels should rise (Nicholson and Miller 1997).Moreover, in close elections, candidates and partiesalso have a greater incentive to mobilize voters, an-other possible source of higher turnout (Cox 1988).

8 Although not providing an explicit test of the Volatility Hypoth-esis, Petrocik (1981) argues that a “dramatic increase in the sizeof the electorate . . . will increase the proportion of psychologicallyuninvolved and uncommitted participants” (Petrocik 1981, 163–64).“An electorate composed of voters who rarely missed an election,”Petrocik (1981, 166) continues, “would be quite stable. In contrast, anelectorate composed of a large proportion of peripheral participantswould be more volatile.”

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Consequently, this could cause high turnout to appearto cause close elections when the reverse relationshipis more likely.

Although mobilization efforts may intensify dur-ing close elections, parties and candidates are likelyto engage in some mobilization efforts regardless ofthe expected closeness of the campaign (Rosenstoneand Hansen 1993). These mobilization efforts alonecould also contribute to the endogeneity problem. If,by example, the Republican Party’s mobilization ef-forts target Republicans in heavily Republican areas,while the Democratic Party targets Democrats in heav-ily Democratic areas, then high turnout might appearto favor the Republican candidate in Republican areasand the Democratic candidate in Democratic areas,even though turnout was boosted in these areas as afunction of anticipated vote share.

The second approach scholars have taken when an-alyzing the political implications of voter turnout isto use individual-level survey data to simulate whatwould have happened if nonvoters had decided to votein the election (e.g., Citrin, Schickler, and Sides 2003;Highton and Wolfinger 2001; Martinez and Gill 2005).The appeal of this approach is that researchers canuse data on the preferences of nonvoters to projecthow they might have voted. The problem, of course,is that these projections are not testable, and it is notnecessarily clear how to forecast what nonvoters woulddo at the polls. Moreover, there is still the issue ofendogeneity. For example, it is possible that nonvoterschose not to vote because there was not a candidatefor whom they wanted to vote. Assigning preferencesto these individuals may be presumptuous.

The main point here is that the decision to turn outcannot be simply assumed to be exogenous to votechoice. At both the individual and aggregate levels,turnout is likely endogenous to vote choice. If endo-geneity exists, then the coefficient estimates of existinganalyses are biased, and any attempt to infer a causalrelationship between turnout and the vote will be in-valid. In sum, prior work has not been able to providea clear, causal connection between level of turnout andelectoral outcomes.

AN INSTRUMENTAL VARIABLE APPROACHTO ESTIMATING TURNOUT EFFECTS

Instrumental variables regression analysis (IV) wasdeveloped explicitly for situations in which an inde-pendent variable is potentially endogenous.9 This ap-proach begins with the identification of a variable (orset of variables) that will serve as an instrument forthe endogenous variable. The endogenous indepen-dent variable is then regressed on the instrument(s),and the results of this regression are used to predictvalues of the endogenous variable. These predictedvalues are then included as an independent variablein the main model of interest. Proper identification ofthe IV model requires that the model of the endoge-nous “independent” variable must include a subset of

9 See Wooldridge (2002, chapter 5) for a useful overview of IV.

instruments that are excluded from the main model(consequently, we refer to such an instrument as an“excluded instrument”). Model identification also re-quires that there must be at least as many excludedinstruments as there are endogenous independent vari-ables in the main model. As long as the excluded in-struments are (1) uncorrelated with the error term inthe main equation (i.e., are exogenous to the depen-dent variable in the main model) and (2) correlatedwith the endogenous independent variable, then IVproduces consistent coefficient estimates of the effectof the endogenous independent variable on the depen-dent variable.

For our model, the primary task is to identify an ap-propriate instrument for aggregate voter turnout. Nosuch instrument has been recognized in the literature.One might assume that registration laws, such as closingdates, Motor Voter laws, and the like, might serve assuitable instruments for turnout, but none of these vari-ables is clearly exogenous to electoral outcomes.10 Webelieve that we have found a useful instrument for pur-suing an IV approach to estimating the effect of turnouton electoral outcomes—election day weather. Recentwork by Gomez, Hansford, and Krause (2007) vali-dates the long-held belief that bad weather on electionday is associated with lower levels of voter turnout, andbad weather is clearly exogenous to electoral outcomes.These properties suggest that election day rainfall—our operationalization of weather—should serve as asuitable excluded instrument for turnout. To deter-mine whether this instrument has sufficient explana-tory power, the econometric literature indicates thatan F-test statistic of at least 10 for an excluded instru-ment or set of excluded instruments should be obtainedfor the main equation estimates to be consistent (seeStaiger and Stock 1997). For each of our analyses, weprovide the relevant F-test statistic. Each F statisticclearly exceeds the threshold of 10, further validatingour choice of election day rainfall as an instrument forvoter turnout.11

Before proceeding, however, we must confront animportant issue at the nexus of theory and method.Although our weather-based instrument leverages ex-ogenous variation in voter turnout to identify the causaleffect of turnout on electoral outcomes, we need to con-sider the extent to which our IV approach will illumi-nate the electoral implications of endogenous sources

10 Changes in election law are unlikely to be randomly assigned.Poll taxes were adopted in the solidly Democratic South as a wayof sustaining the party’s electoral advantage. Motor Voter laws alsoappear to have been adopted for partisan reasons. Before Congressadopted the National Voter Registration Act of 1993, 19 states hadalready adopted such laws. Of these, 13 had Democratic majoritystate legislatures at the time of adoption. Given that it was widelyassumed that Motor Voter laws would benefit Democrats, we find ithard to claim that these laws—and others that might affect turnout—are sufficiently exogenous. See footnote 26 for details of an IV modelusing variation in the closing date for registration.11 Kleibergen and Paap’s (2006) rk Lagrange multiplier statistic alsoindicates that election day rainfall is a sufficiently powerful instru-ment to properly identify the IV model. We use Schaffer’s (2007)Stata module to calculate this statistic and estimate the IV modelspresented in Table 1.

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of variation in voter participation. After all, one mightask (1) whether “variation in the endogenous regressorrelated to [our] instrumental variable [has] the samecausal effect as variation unrelated to [our] instrument”(Dunning 2008, 291) and (2) whether the effect wecapture is politically relevant.

The first question presumes that turnout can be di-vided into two components, TO1 and TO2, where theformer includes all variation in turnout (exogenous andendogenous) that has the same effect on vote shares asthe variation exogenously determined by election dayweather, and the latter includes variation in turnoutthat has an alternative effect. The question is: howmuch variation is contained by each component? With-out additional instruments to allow us to test empiri-cally whether different components of the variation invoter turnout have similar or different effects on voteshares, we must rely on theory to answer this question(Dunning 2008, 301).

At one extreme, TO1 could consist only of weather-determined turnout. At the other, TO1 could con-tain turnout in its entirety, meaning that our IV es-timates represent the effect of any and all variationin turnout on electoral outcomes. Neither extreme isrealistic. Theoretically, the causal effect of weather-induced variation in turnout should be similar to theeffect of all variation in turnout (endogenous or ex-ogenous) resulting from uniformly distributed changesin the costs or benefits of voting that particularly alterthe turnout decisions of peripheral voters, who “sit thefence” between voting and staying home. This wouldinclude variation in turnout that results from any gen-eral change to the costs and benefits of voting that is notpolitically targeted (i.e., that does not target potentialvoters based on their likely vote choice) or determinedby the appeal of a specific candidate. Importantly, vari-ation of this type (i.e., nontargeted and non–candidate-generated variation) likely represents a significant por-tion of the overall variation in voter turnout. For in-stance, alterations in registration or voter identificationrequirements represent changes in costs that are metedout equally across all eligible voters, and thus should beconsidered within TO1. Research shows that changesin electoral laws are powerful predictors of aggregatevoter turnout (see Geys 2006; Rosenstone and Wolfin-ger 1978). Another important source of variation inturnout that should fall into TO1 is the closeness ofthe electoral contest (see Geys 2006). Because a closerace increases the probability that any one vote will beinfluential, all voters will experience a change in theircalculus of participation. These changes may be deter-minative for peripheral voters for whom a slight changein the benefits (or costs) of voting determines whetherthey turn out. Thus, a close race increases their turnoutjust as a sunny election day does. Expansive changes inthe information environment are likely to uniformly re-duce the cognitive costs (or increase the perceived ben-efits) of becoming engaged with and informed aboutthe political world (Berinsky 2005). Changes of thissort will affect the utility calculations of all voters andmay be pivotal in activating peripheral voters. Finally,mobilization efforts that are not politically targeted,

such as general get-out-the-vote (GOTV) appeals, canincrease turnout (e.g., Gerber and Green 2000). Theincrease in turnout resulting from these efforts is afunction of adding marginal voters (see Arceneauxand Nickerson 2009), who should behave in much thesame way as additional voters spurred on by a pleasantelection day. In sum, our IV estimates should capturethe causal effect of much of the politically interestingvariation in turnout, exogenous and endogenous.

Variation in voter turnout attributable to candidatecharacteristics or mobilization (or suppression) effortsthat target particular types of voters will likely havedifferent electoral effects, however. For example, ifthe presence of a particularly charismatic candidateon the ballot causes an increase in turnout, this in-crease may not have the same consequences as vari-ation in turnout generated by non–candidate-drivenchanges to the benefits or costs of voting. Similarly, if acandidate or party can effectively target and mobilizecore supporters, any resulting increase in turnout willprobably benefit that candidate or party, producing apotentially asymmetric effect on vote share. Of course,it is possible, if not likely, that the mobilization efforts ofone party may be counteracted by similar activities bythe opposition, indicating that increases in turnout dueto this mechanism may have little or no net effect onelectoral outcomes. Both types of influence on turnoutshould fall into TO2, meaning that we cannot infer thatour IV results apply to this type of variation in turnout.

Which type of determinant of turnout is of greaterimportance? Put differently, which is larger, TO1 orTO2? Again, we have no way to answer this questionempirically because the absence of an exogenous in-strument for TO2 makes a direct comparison impossi-ble. We do believe it important, though, that two of thebest systematic predictors of changes in aggregate-levelturnout—changes to registration requirements and theanticipated closeness of the election—should have elec-toral effects similar/to those revealed by our IV model.In short, our IV results should apply well beyondthe electoral consequences of truly exogenously de-termined variation in turnout, but may not encompassall possible sources of variation in turnout.

DATA

Our data set consists of observations from the nearly2,000 non-Southern counties in the continental U.S. foreach presidential election from 1948 to 2000.12 Ourunit of analysis is thus the county election dyad. Thislow level of aggregation is particularly useful given thatthe excluded instrument we use for turnout is rain onelection day. A larger unit of aggregation, such as thestate, would prevent an accurate measure of rainfall,potentially muting the correlation between weather

12 Because Alaska and Hawaii did not enter the union until 1959,and because Alaska records election data by election district ratherthan county, we excluded these states from the analysis. We alsoexcluded Oregon from our 2000 data because the state implementedan early voting program that resulted in nearly all votes being castbefore election day.

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and turnout, and would thus hurt the power of thiscritical instrument. The inclusion of a substantial num-ber of elections also guarantees a good deal of variationin election day weather.13

Studies examining turnout effects usually excludethe South. In our case, we exclude Southern coun-ties for three reasons.14 First, both voter turnout andpresidential vote share are problematic in Southernstates for the first half of our time span. Formal andinformal barriers to voting depressed turnout until fed-eral actions largely removed them. At the same timethat these barriers were being overcome, the Southexperienced a major partisan realignment, which maylead to a spurious relationship between turnout andelectoral outcomes (see Erikson 1995). This is quiteimportant. Erikson (1995) argues that previous studiesdemonstrating a correlation between turnout and thevote are primarily driven by political change in theSouth. He argues that when analyses are restricted tonon-Southern states there is “no evidence whatsoeverof a turnout effect on the vote” (Erikson 1995, 387).A second justification for restricting our data is thatregional third-party candidates garnered substantialelectoral support in the South during a few of our ear-lier elections, making it difficult to analyze two-partyvote share.15 Third, F tests reveal that rainfall doesnot have the same explanatory power when it comesto voter turnout in Southern counties, as it does fornon-Southern counties. In fact, for Southern counties,rainfall does not produce F statistics that meet the min-imum threshold for properly estimating an IV model.

The dependent variable in our initial analyses isthe percentage of the two-party vote received by theDemocratic presidential candidate.16 To measure ourexcluded instrument, rainfall on election day, we usethe National Climatic Data Center’s “Summary of theDay” data (made available by EarthInfo, Inc.). TheSummary of the Day data report various measuresof daily weather for more than 20,000 weather sta-tions located in the U.S. Despite the sizeable numberof meteorological observations, not all U.S. countieshave weather stations situated within their borders,whereas many counties have multiple weather stations.We therefore used a geographic information system(GIS) method known as Kriging to estimate electionday rainfall, in inches, for each county (see Childs2004).17 To provide a sense of what these rainfall data“look like,” Figure 1 presents rainfall maps for the 1996

13 See Gomez, Hansford, and Krause (2007) for details regardingthe distribution of the rainfall variable.14 We define a Southern county as a county located in one of theeleven states of the Confederacy.15 Erikson (1995) notes the additional problem that a few Southernstates did not have pledged Democratic slates of electors in the 1960and 1964 elections.16 County-level vote returns were gathered primarily from Congres-sional Quarterly’s “America Votes” series and Congressional Quar-terly’s “Voting and Elections” online module.17 Comparative diagnostics (against an inverse distance weightingfunction) indicated that “Universal Kriging with linear drift” pro-vides superior model fit for our data and thus was used to interpolateour data. Kriging assumes that the data follow a Gaussian distri-bution and determines the extent of spatial dependence between

and 2000 elections, the two most recent elections in ouranalysis.

It is likely that the behavioral effect of election dayrain depends on the typical weather conditions ex-perienced in a county on that day. For this reason,we also calculated the normal (average) rainfall foreach election date (ranging from November 2 to 9) foreach county using data from the entire 1948–2000 timespan. We then subtracted the county’s normal rainfallfrom the rainfall estimated to have occurred on eachrespective election day under analysis. By measuringRain as a deviation from its normal, we account fortypical regional variations in weather.18 As we discussin the previous section, this measure will serve as ourexcluded instrument for voter turnout.19

Two of the hypotheses we seek to test require addi-tional independent variables: partisan composition ofthe county and party of the incumbent president. Parti-san Composition is measured as the moving average ofthe two-party Democratic vote share (i.e., percentageof the two-party vote cast for the Democratic presiden-tial candidate) in the county in the three most recentelections. For county C in presidential election E, thisvariable equals the average of C’s Democratic voteshare in E-1, E-2, and E-3. The Two-Effects Hypothesisindicates that partisan composition conditions the ef-fect of turnout on Democratic vote share. We thereforeinclude the interaction of this variable with turnoutand expect a negative estimate for this multiplicativeterm (indicating that the more Democratic a county,the less that increases in turnout add to Democraticvote share). To include an interaction term involving an

observations via the construction of a semivariogram. The Krigingmethod is regarded as a best linear unbiased estimator for spatial data(Stein 1999). Thus, spatial predictions based disproportionately ondistant observations may exhibit a loss in efficiency, but they remainunbiased. With more than 20,000 weather station observations perelection day, this loss in efficiency is not a concern. Our county-levelestimates of rainfall represent an average of the rainfall on eachestimated surface unit (one unit = 4,000 square meters) in the county.In counties that experienced substantial intracounty variation inelection day rainfall, our county-level estimate may result in a lessefficient instrument in our IV model, but it is nonetheless unbiased.More details on these data and the GIS interpolation methodologycan be found in Gomez, Hansford, and Krause (2007, 653–55).18 The mean value for election day deviation from normal rainfall is.005. This variable ranges from a minimum of −.419 to a maximumof 2.63 (with a standard deviation of .208).19 We use only rainfall as our instrument for turnout because addingsnowfall (deviation from normal snowfall, specifically) generally de-creases the F statistics for the set of excluded instruments. The IVapproach requires that we include at least one exogenous, excludedinstrument for every endogenous variable in the main model. Addi-tional excluded instruments are useful if they increase explanatorypower, but this is not the case with snowfall. Snowfall may be weakerthan rain as an instrument because snow is much rarer than rain inany given county on election day. Snow cannot, for example, explaintemporal variation in turnout in most California counties because ithas not snowed on election day in these counties during our timespan (it has rained, however). If we include deviation from normalsnowfall as a separate excluded instrument, our results are similar tothose presented here. If we combine rainfall and snowfall into a singlemeasure of precipitation that represents the total water content of theprecipitation, our results are again similar to what we present here.If we simply add inches of rain to inches of snowfall, this measure ofprecipitation no longer successfully identifies the IV model.

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FIGURE 1. Estimated Rainfall during the 1996 and 2000 Elections

Notes: Estimated rainfall is in inches. The eleven states of the Southern Confederacy were excluded from the analyses presented in this paper but were used in the GIS interpolation of ourcounty-level rainfall estimates. Similarly, the state of Oregon, although shown here, was excluded from our 2000 data because the state used a vote-by-mail program that resulted in nearlyall votes being cast before election day, but was used for interpolation.

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endogenous variable, we need to create a second ex-cluded instrument.20 We thus include in our IV modelthe product of our rain variable and the partisancomposition measure as a second excluded instru-ment predicting the product of turnout and partisancomposition.21 This strategy provides us with consis-tent estimates of the conditioning influence of partisancomposition on the effect of turnout on vote shares.

Our incumbency variable is a dummy variable thatequals one if the incumbent president is a Republican.The Anti-Incumbent Hypothesis suggests that the can-didate of the same party as the incumbent presidentwill be hurt by higher turnout. To test this hypothesis,we need to interact the Republican Incumbent vari-able with turnout. We expect the coefficient estimateassociated with the interaction term to be positive (in-dicating that turnout increases Democratic vote sharewhen the incumbent is a Republican). Again, for ourIV model, we must create an instrument for this in-teraction term, so we use the product of rainfall andthe dummy variable for Republican incumbent as anadditional excluded instrument predicting the productof turnout and Republican incumbent. Note that thedummy variable indicating a Republican incumbent isnot included in the model on its own (as a constitutiveterm) because this effect is already accounted for byour inclusion of election-specific fixed effects, which wediscuss as follows. For a presentation of the three first-stage models (predicting turnout, turnout × partisancomposition, and turnout × Republican incumbent),as well as an alternative IV approach to incorporatinginteraction terms including an endogenous variable,see the Appendix.

There are obviously many other factors that may in-fluence a county’s Democratic vote share in any givenelection. Our strategy for controlling these other po-tential influences is to include fixed effects for bothcounties and elections. These fixed effects should ac-count for potential heterogeneity in the data and theaccompanying correlation of residuals, while providingus with conservative coefficient estimates for our vari-ables of interest.22 Given that the Volatility Hypothesisimplies heteroskedastic residuals, we estimate robuststandard errors. As we discuss later in some detail, we

20 Recent studies using interaction terms in an IV model in the sameway we do include Gabel and Scheve (2007) and Miguel, Satyanath,and Sergenti (2004).21 More precisely, we are using rain × partisan composition as anexcluded instrument for turnout × partisan composition.22 A Hausman test shows fixed effects to be more appropriate thanrandom effects. Fixed effects were also used in the first-stage modelspredicting turnout and the interaction terms involving turnout. Byincluding election-specific fixed effects, we control for short-term,election-specific effects, such as campaign effects, the state of theeconomy, etc. To ease presentation, we do not report any of thefixed effects. The election-specific effects reveal, however, that the1956 and 1984 elections were particularly good for the Republicancandidate (all else equal), whereas the 1964 and 1996 elections wereespecially good for the Democratic candidate. An examination of thecounty-specific fixed effects indicates that, on average, counties withsmall populations have fixed effects of a larger magnitude (positive ornegative), whereas counties with large populations (typically urbancounties) have small, often positive, fixed effects.

also consider the potential problem posed by spatialautocorrelation.

For the purpose of comparison, we also use OLSto estimate our model with actual turnout instead ofinstrumented turnout. Our measure of voter turnoutin each county is calculated by dividing the number ofvotes cast at the presidential level by the estimatedvoting age population.23 We provide these parallelmodel estimations in order to assess the consequencesof treating turnout as exogenous.

RESULTS

The results of the OLS and IV models explaining thetwo-party vote share of Democratic presidential can-didates are presented in Table 1. The first column inTable 1 presents the OLS estimates for the model whenactual, not instrumented, turnout is included as thekey independent variable. Based on these estimates,we would conclude that increases in turnout lead toincreases in Democratic vote share if there is a Re-publican incumbent. Thus, the OLS results supportthe Anti-Incumbent Hypothesis, but not the others.Of course, the OLS evidence in support of the Anti-Incumbent Hypothesis is itself suspect. If we had onlyestimated the OLS model, a skeptic would rightfullyquestion the causal connection between incumbencyand turnout. After all, it is quite possible that highturnout occurs because voters are dissatisfied withthe incumbent president’s performance. Davidson andMacKinnon’s (1993) endogeneity test reveals, as sus-pected, that the OLS estimates using actual turnoutsuffer from endogeneity.24 The OLS estimates are thusnot consistent, and the IV estimates we discuss beloware preferred.25

23 County-level voting age population was gathered from two pri-mary sources: the U.S. Census Bureau’s City and County Data Bookand the U.S. Census Bureau’s Web site.24 Davidson and MacKinnon’s (1993) test is based on a regressionof the dependent variable in the main equation on the residualsgenerated by the first-stage equations. The test is similar to the moretraditional Hausman test (sometimes referred to as the Wu-Hausmantest in the context of choosing between IV and OLS), with the im-portant exception that it is appropriate for panel data models withfixed effects.25 If we regress national Democratic vote share on raw nationalturnout for the 1832–2008 presidential elections, we find a positivebut statistically insignificant estimate for turnout. The potential prob-lem of endogeneity is apparent, however, when the vote share spreadbetween the winning and losing candidate is regressed on turnout.In this model, the estimate for turnout is negative and significant,indicating that as turnout increases the vote share gap between thecandidates decreases. It is likely that the causal arrow runs the otherdirection because both voters and elites seeking to mobilize votershave more at stake when elections are likely to be close. This formof endogeneity is likely muting any partisan effect.

If we regress national two-party vote share for the candidate ofthe incumbent president’s party on raw national turnout, we findthat turnout has a negative but statistically insignificant coefficient.The 1920 election appears to be a substantial outlier (perhaps due tothe preceding ratification of the Nineteenth Amendment), and if it isexcluded from the analysis, the estimate for turnout is negative andsignificant. These aggregate results regarding the Anti-IncumbentEffect are thus at least weakly consistent with those of our county-level IV model.

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TABLE 1. County-level Democratic Vote Share in Presidential Elections, 1948–2000

Actual Turnout Instrumented Turnout

OLS Estimate IV Estimate IV Estimate(Robust Stand. (Robust Stand. (Robust Stand.

Independent Variable Error) Error) Error)

Turnout −.066 .405∗ .397∗

(.020) (.242) (.231)Turnout × Partisan composition .001 −.011∗ −.012∗

(.000) (.004) (.004)Turnout × Republican incumbent .155∗ .469∗ .723∗

(.007) (.102) (.107)Partisan composition .595∗ 1.43∗ 1.48∗

(.029) (.231) (.231)State-election controls? No No YesN 27,401 27,401 27,401F test, all covariates 3,372∗ 2,901∗ 1,341∗

R 2 .798 .644 .588F test, excluded instruments for turnout — 24.0∗ 30.1∗

F test, excluded instruments for turnout × partisan comp. — 34.2∗ 34.1∗

F test, excluded instruments for turnout × Republican inc. — 50.7∗ 67.0∗

Notes: Fixed effects for counties and for election years are included in all models. Southern counties are excluded from theanalysis.∗p ≤ .05 (one-tailed test).

The second column of results in Table 1 presents theestimates for our fixed effects IV model.26 An initialexamination of these IV coefficient estimates and theirstandard errors reveals three tentative conclusions.27

First, when the partisan composition of a county is0% Democratic—a purely hypothetical condition—andthere is a Democratic president in office, the estimatedeffect of voter turnout is positive and (barely) statisti-cally significant. Thus, in the most Republican countyimaginable, increases in turnout lead to increases inDemocratic vote share. This conclusion is solely basedon the estimate for the constitutive turnout variable,

26 Election day rainfall is the best available instrument for turnoutbecause it (1) has sufficient explanatory power to identify the IVmodel and (2) is clearly exogenous to electoral outcomes. Yet, tofurther explore the robustness of our results, we replicated our IVresults using the length of time between the statewide closing datefor registration and election day as an instrument for turnout. Thisvariable has sufficient explanatory power when predicting turnout,but is NOT clearly exogenous to electoral outcomes. It should thus beviewed as an inferior instrument to election day rain. Identificationtests reveal that turnout × partisan composition is not sufficientlywell explained by the excluded instruments to identify the IV model.We therefore only include turnout and turnout × Republican incum-bent in this model. The IV estimate for turnout with this specificationis .095 (SE = .144) and the estimate for turnout × Republican in-cumbent is .421 (SE = .024). These results are quite consistent withthe IV results obtained using rainfall. As a somewhat rough test ofwhether the closing date might be endogenous to electoral outcomes,we tested whether changes to the closing date are predicted by whichparty controlled the legislature that adopted the change. Not surpris-ingly, this test suggests that Democratic legislatures are more likelyto push the closing date closer to election day.27 The standard errors in the IV model are considerably larger thanthose in the OLS model, but this is quite typical (Wooldridge 2002,86).

which captures the effect of turnout when the two con-ditioning variables equal zero. Of course, not muchshould be made of this particular result, given thatcounties are never 0% Democratic.

Second, the coefficient estimates from this IV modelalso indicate that the positive effect of turnout ona Democratic candidate’s vote share decreases as acounty becomes more Democratic in composition. Thisconditional relationship is indicated by the negativeand statistically significant estimate for the interac-tion term involving partisan composition. Accordingto DeNardo (1980, 1986), high levels of turnout meanthat more peripheral voters are voting. These votersare, by nature, more likely to defect from their looselyheld partisan ties, a tendency that benefits the minorityparty in the county. The IV results support both ofDeNardo’s “two effects”—increases in turnout simul-taneously help both Democrats and the minority partyin the electorate in question. To be sure, prior workhas provided evidence compatible with DeNardo’s hy-pothesis (Nagel and McNulty 1996, 2000), but this isthe first evidence that variation in turnout exerts thisconditional causal effect on vote share. It is importantto note that the OLS estimates presented in Column 1“miss” this effect.

A third inference to be drawn from these IV esti-mates is that turnout exerts a larger positive effect onDemocratic vote share when the incumbent presidentis a Republican. The positive and statistically significantestimate for the interaction term including the Repub-lican incumbent dummy variable reveals this effect.This finding supports the Anti-Incumbent Hypothesis,which is based on the assumption that marginal votersare less supportive of the incumbent party (i.e., party of

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FIGURE 2. Coefficient for Turnout, Conditional on Partisan Composition (Republican Incumbent)

Note: Coefficients and confidence intervals are generated by the IV results in the second column of Table 1.

the president in office) than dedicated voters. Accord-ing to this hypothesis, the positive effect of turnouton Democratic vote share should be conditioned bywhether the incumbent president is a Republican ora Democrat. Our evidence shows this to be the case.Although this particular result is also obtained withthe OLS model, these IV results provide greater con-fidence in the causal claim that higher turnout lowersvote share for the candidate of the incumbent’s party.

To gain a full picture of these IV results and a clearunderstanding of their implications for the hypothesestested, we computed the full range of conditional co-efficients and the accompanying conditional standarderrors in the IV model. Given the presence of thetwo interaction terms, the effect of voter turnout ona Democratic presidential candidate’s vote share is acombination of the coefficient estimates for the consti-tutive term and the two interaction terms. Specifically,the estimated effect (the conditional coefficient) ofvoter turnout is [.405 – (.011 × partisan composition) +(.469 × Republican incumbent)]. This can be fur-ther simplified by separately considering situationsin which the incumbent president is a Republicanand those in which the incumbent is a Democrat.With a Republican incumbent, the conditional coef-ficient for turnout is [(.405 + .469) – (.011 × partisancomposition)]. With a Democratic incumbent, the co-efficient is [.405 – (.011 × partisan composition)].

Figures 2 and 3 graphically illustrate the marginaleffect (i.e., coefficient) of turnout on Democratic voteshare, conditional on the partisan composition of thecounty. In Figure 2, the coefficients correspond to the

presence of a Republican incumbent, whereas the coef-ficients in Figure 3 are calculated with a Democratic in-cumbent. For both figures, partisan composition rangesfrom 10% to 90% Democratic, a range of values closelyapproximating the actual range found in our data.

When there is a Republican incumbent (a conditionthat is true in 7 of our 14 elections), turnout has apositive effect on Democratic vote share (i.e., the pointestimate for the coefficient is greater than zero) as longas the county in question is less than 80% Democratic.This effect is statistically significant for all values ofpartisan composition less than 60%.28 Put differently,increases in turnout generally help the Democraticcandidate when there is a Republican in office. Themagnitude of the effect is attenuated, though, by thepartisan composition of the county. The more Demo-cratic the county, the less that turnout helps the Demo-cratic candidate. This declining conditional marginaleffect (exhibited in Figure 2) is entirely consistentwith DeNardo’s Two-Effects logic and demonstratesthat changes in turnout do simultaneously help bothDemocrats and the minority party in the electorate.

Interestingly, when there is a Democratic incumbent,as shown in Figure 3, turnout never has a positive andstatistically significant effect on Democratic vote share.Turnout has a negative coefficient for all values of par-tisan composition higher than 36%, and these negativecoefficients are statistically significant when partisan

28 To perform these tests of statistical significance, we calculate theconditional coefficients and conditional standard errors (Brambor,Clark, and Golder 2006).

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FIGURE 3. Coefficient for Turnout, Conditional on Partisan Composition (Democratic Incumbent)

Note: Coefficients and confidence intervals are generated by the IV results in the second column of Table 1.

composition exceeds 62% Democratic. The decliningconditional marginal effect of turnout on Democraticvote share is, again, consistent with DeNardo’s the-sis; however, that turnout never enhances Democraticvote share under these conditions is surprising. Whenviewed in conjunction with the evidence in Figure 2,these results suggests that Democratic gains fromturnout are likely to occur only when the party doesnot control the presidency. Indeed, when a Democraticpresident is in office, his party is likely to experienceonly the harmful effects of increased turnout. Thisfinding suggests that DeNardo’s “two effects” may nottell the whole story; a “third effect,” incumbency, alsoconditions the relationship between turnout and voteshare.

As a further illustration of the results of the IVmodel, we plot predicted Democratic vote share byturnout. In Figures 4 and 5, three sets of predictedvote shares are presented: one for “toss-up” counties(partisan composition is 50% Democratic), one for Re-publican counties (partisan composition is 30% Demo-cratic), and one for Democratic counties (partisan com-position is 70% Democratic). The predicted vote sharesin Figure 4 are generated with Republican incumbentset at one, whereas in Figure 5 the predictions are basedon a Democratic incumbent.29

These figures again reveal the conditional relation-ship between turnout and partisan vote share. When

29 For Figure 4, the election-specific fixed effect is set at the averageeffect for elections in which there was a Republican incumbent. ForFigure 5, we use the average effect for the elections in which therewas a Democratic incumbent.

the incumbent president is a Republican, increases inturnout uniformly lead to a higher vote share for theDemocratic candidate. The increase is steepest in Re-publican counties, and the slope becomes less steep asthe size of the Democratic electorate increases. Givena Democratic incumbent, the direction of the effect ofturnout depends on the partisan composition of thecounty. Increases in turnout in Democratic countieshelp the Republican candidate, whereas increases inRepublican counties assist the Democratic candidate;however, as noted previously, this latter effect is notstatistically different from zero. In toss-up counties, themodel shows that high levels of turnout work againstthe Democrats.

Our IV results provide considerable support for allthree hypotheses tested thus far. When we look at val-ues of partisan composition and the partisanship of theincumbent president that lead to statistically significantturnout effects, we find a significant pro-Democraticeffect in 45% of the observations (county electiondyads) in our data and a significant pro-Republicaneffect in only 2% of the observations. We can thereforestate that when there is a significant turnout effect, itis generally pro-Democratic. This result is compatiblewith the Partisan Effect Hypothesis.30 Our analysis also

30 Given our strategy of pooling data from 14 presidential elec-tions, we implicitly assume that any turnout effects are, on average,constant over the 1948–2000 time span. To get a sense of how ourresults might change over time or are otherwise sensitive to particularelections, we employed a jackknife approach and estimated our IVmodel 14 times, while each time excluding one election. After each

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FIGURE 4. Effect of Turnout and Partisan Composition on Predicted Democratic Vote Share(Republican Incumbent)

Notes: Predicted values are generated by the IV model presented in the second column of Table 1. For the purposes of this figure,we define toss-up, Republican, and Democratic counties as ones in which (Democratic) partisan composition equals 50%, 30%,and 70%, respectively. The election-specific fixed effect is set at the average effect for elections in which there was a Republicanincumbent.

supports the Two-Effects Hypothesis. Although in-creases in turnout more often help the Democraticcandidate than the Republican candidate, the effectof turnout is clearly conditioned by the partisan com-position of an electorate (a county, in our data). Thereis also clear evidence of an anti-incumbent effect atwork. This is demonstrated by the fact that turnoutexerts a statistically significant and positive effect onDemocratic vote share for 95% of the observations inour data in which there is a Republican incumbent.

estimation, we calculated the average effect of turnout, meaning theeffect of turnout on Democratic vote share, while holding Republicanincumbent and partisan composition at their means. We then subtractthis average effect from the average effect found when all electionsare included. The resulting quantity tells us how much the inclusionof the election in question changes the average effect of turnout. Thisexamination reveals that the vast majority of the individual electionshave little influence over our results. The noteworthy exception isthe 1992 election. When this election is excluded, the average ef-fect of turnout increases considerably. This result suggests that, forwhatever reason (perhaps the presence of a significant third-partycandidate), the average effect of turnout in 1992 was considerablysmaller than in other elections. Interestingly, the exclusion of eitherthe 1996 or 2000 election leads to a slightly smaller average effectfor turnout, meaning that the two most recent elections in our dataactually exhibit somewhat larger than average turnout effects. Thereis little evidence that, 1992 aside, there has been a change in theeffect of turnout over our time period.

When there is a Democratic incumbent, turnout neverexerts a positive, significant pro-Democratic effect, re-gardless of the partisan composition of a county.31 Theonly significant effect that turnout has in this scenariois a pro-Republican effect in very Democratic counties.In sum, increases in turnout captured by our instrumentexert three effects: pro-Democratic, antimajority partyin the electorate, and anti-incumbent.32

31 Because there are only 14 presidential elections in our data, ourresults regarding the Anti-Incumbency Hypothesis could be sensitiveto an outlier election. Yet, this is not the case. We again used ajackknife procedure to see if any one election drives our results. Nomatter which election we exclude from our analysis, the estimate forturnout × Republican incumbent remains positive and statisticallysignificant.32 One might be concerned that particularly rainy days in our analysismight be exerting an undue influence. We assessed this possibility byestimating our model while excluding the rainiest observations (the40 county election dyads that experienced more than 1.5 inches ofrain above the average for that day). The inferences for the twointeraction terms remain the same. We then estimated our modelagain while excluding the 231 observations that experienced morethan one inch of rain above the daily average. Again, the inferencesremain the same. The only implication of excluding these rainiestobservations is that the estimate for turnout is no longer statisticallysignificant (it is only just barely significant in the IV model presentedin Table 1). This has little meaning, though, because this coefficientonly reveals the effect of turnout when there is a Democratic presi-dent and a county with a partisan composition of 0%. No such caseexists in reality.

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FIGURE 5. Effect of Turnout and Partisan Composition on Predicted Democratic Vote Share(Democratic Incumbent)

Notes: Predicted values are generated by the IV model presented in the second column of Table 1. For the purposes of this figure, wedefine toss-up, Republican, and Democratic counties as ones in which (Democratic) partisan composition equals 50%, 30%, and 70%,respectively. The election-specific fixed effect is set at the average effect for elections in which there was a Democratic incumbent.

Spatial Autocorrelation

We have been careful to account for election- andcounty-specific effects with our inclusion of fixed ef-fects for each. In fact, the county fixed effects also ac-count for any state effects that are constant over timebecause the county effects are simply disaggregatedstate effects. Yet it is possible that there are state-election dyadic-specific effects that are unaccountedfor in our model and thus lead to spatial autocorrela-tion, meaning that the residuals for the counties in agiven state in a given election year might not be inde-pendent from each other. Furthermore, as illustratedin Figure 1, our instrument, election day rainfall, isnot randomly distributed across counties in a givenelection. Neighboring counties are likely to experi-ence similar weather on any given day, and thus ourinstrument naturally exhibits spatial correlation. Con-sequently, despite the fact that we have 27,401 countyelections in our data, there is a danger that a few region-ally concentrated storms are influencing our results.This concern is heightened by the fact that if we excludefrom our analysis the two rainiest elections (1992 and2000), our instrument loses power, our model identifi-cation suffers, and the two key coefficient estimates areno longer statistically significant ( p = .089 and .093 withone-tailed tests, for turnout × partisan compositionand turnout × Republican incumbent, respectively),although each is in the hypothesized direction and

actually increases in magnitude.33 It is important tonote, however, that if we exclude either 1992 or 2000,the IV model is sufficiently identified, and the estimatesfor these two interaction terms are statistically signifi-cant and in the same direction as the results reportedin Table 1.

An analysis of the residuals from our IV modelreveals that they are not fully independent for thecounties in a given state in a given election—in otherwords, the residuals are spatially correlated.34 In gen-eral, there are a few possible ways to address the is-sue of spatial autocorrelation, although the IV contextmakes dealing with this problem a bit more compli-cated due to identification concerns. One straightfor-ward solution to any potential correlation of residualsfor counties within a given state for a given electionis to include state-election fixed effects (e.g., a fixedeffect for California in 1948, California in 1952, etc.)

33 The Kleibergen and Paap (2006) rk Lagrange multiplier statisticindicates that when we exclude these two elections, our IV model isinsufficiently identified.34 We calculated the global Moran’s I for the residuals for all fourcomponents of our IV model (the three first-stage models and thesecond-stage model). For a given county c for election e, we use aweight of 1 for every other county in c’s state in election e. Every othercounty in the data is then weighted at 0. With this weighting matrix,Moran’s I ranges from a low of .310 (for the turnout × partisancomposition first-stage model) to a high of .414 (for the second-stage,vote share model).

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in our IV model. Unfortunately, diagnostics indicatethat our IV model is no longer sufficiently identifiedwhen these additional fixed effects are included. Thesestate-election effects reduce the explanatory power ofour instrument in the first-stage models because rain-fall (or its absence) on any election day will be geo-graphically clustered.35 Even with the additional state-election fixed effects, the second-stage model resultsare somewhat consistent with the results presented inTable 1 because turnout × Republican incumbent hasa positive and significant coefficient (1.29, p = .011),whereas turnout × partisan composition has a neg-ative and insignificant coefficient (−.005, p = .163).These particular results must be treated with caution,however, due to the lack of sufficient identification. Itis possible that the identification problems we expe-rience due to the inclusion of these additional fixedeffects is further evidence that spatial autocorrelationis a concern here.

A common way to address the effect that spatial au-tocorrelation can have on the estimates of standard er-rors is to estimate robust standard errors that “cluster”on the grouping variable in question. However, cluster-ing is not straightforward when the grouping variable(state-election dyad) is different from the panel vari-able (county), which is our situation.36 Nonetheless,when these clustered standard errors are estimated,they are substantially larger than the robust standarderrors that do not cluster on state-elections, and theselarger standard errors would cause us to fail to rejectthe null hypotheses for all key independent variablesin the model (and all but two of the election dummyvariables). We are skeptical about the size of these stan-dard error estimates, though. These clustered standarderrors are just as large, if not larger, when they areclustered on states, instead of state-elections, despitethe fact there is no correlation of residuals within states(as compared to state-elections).

To attempt a blunt test of the consequences of spatialautocorrelation in our data, we aggregate our data tothe state level (reducing our N from 27,401 to 517). Bydefinition, these data cannot suffer from state-election

35 If a state is rainy on a particular election day, then the inclusionof the relevant state-election effect (which appears, as it must, in allthe first-stage models, as well as in the second-stage model) wipesout our instrument’s leverage in terms of explaining turnout in thecounties of this state compared to drier states. If a state is completelydry on election day, then the inclusion of the relevant state-electioneffect wipes out our instrument’s leverage for explaining turnout inthe counties of this state compared to those in wetter states. Allthat is left to identify the model are the state-elections in which ameaningful number of counties experienced rain and a meaningfulnumber did not.36 The specific routine we are using to estimate our model, xtivreg2(Schaffer 2007, implemented in Stata) does not allow panels to spanmultiple clusters (nor were we able to find any other existing routinethat allows this specification). This may be due to a lack of consensusregarding the proper degrees of freedom weighting when panelsare not encompassed by clusters (Schaffer personal correspondence,September 24, 2009). In pursuing this line of investigation, Jeff Lewiskindly created R code that estimates fixed effects IV models whileallowing for clustering on any grouping variable, regardless of panelvariable. The results discussed in this paragraph were obtained withthis code.

spatial autocorrelation because there is only one obser-vation for each state in each election. This higher levelof aggregation leads to insufficient identification for thetwo interaction terms in our model, but the constituentturnout variable is sufficiently identified to estimate anIV model of state-level Democratic vote share. In thismodel estimation, the effect of turnout is positive andstatistically significant, which is reassuringly consistentwith the average effect of turnout in the IV modelspresented in the second column of Table 1.

For our final and we believe most compelling effortto address the nonindependence of residuals for coun-ties in a given state and election year, we attempt todirectly control for various potential sources of spatialautocorrelation by including a wide variety of indepen-dent variables that should soak up much of the state-election effects. We identify and include four such typesof variable: state laws regarding registration/voting,statewide elections occurring at the same time as thepresidential election, expected closeness of the state inthe presidential election, and candidate connections tothe state.37 These variables might affect turnout and/orvote shares within a state in a particular election.

With these state-election–specific variables in place,we re-estimate our IV model (still including countyfixed effects and election fixed effects), and the re-sults for the variables of interest are presented in thefinal column of Table 1. An analysis of the residu-als for this model reveals that the inclusion of thesecontrols reduces, but does not eliminate, the spatialautocorrelation.38 After this reduction in spatial auto-correlation, the IV results remain robust, which givesus confidence that spatial autocorrelation is not drivingour results. For the rest of the article, we use the IVresults obtained without the inclusion of these addi-tional state-election variables because there may beendogeneity concerns with some of the variables in thesaturated model (e.g., registration requirements mightbe endogenous to vote shares). Furthermore, the re-sults for the more parsimonious model are somewhat

37 Specifically, we include dummy variables indicating whether thestate had a literacy test, poll tax, or Motor Voter law for the election inquestion. We also include the minimum number of days in advanceof the election by which a voter must register. To control for thepresence of other statewide contests, we include dummy variablesindicating whether a gubernatorial election or Senate election wasalso taking place. To control for both the expected closeness of thepresidential race in a given state for a given election and the state’s re-cent voting history/ideological orientation, we include a one-electionlag of state-level Democratic vote share and its square (a linear re-lationship between prior and contemporary vote shares can thus beaccommodated by this specification, as can a nonlinear relationshipin the first-stage models). We also include the mean Common Spacescore for the state’s U.S. House delegation as an additional mea-sure of the state’s ideological orientation at that point in time (seeHolbrook 1991). Finally, we also include dummies indicating whethereither of the parties’ presidential or vice presidential candidates werefrom the state in question. We then also interact these four dummieswith the voting age population of the state because there is evidencethat home state advantages are conditioned by the size of the state’spopulation (see Dudley and Rapoport 1989; Lewis-Beck and Rice1983).38 The Moran’s I statistics for the residuals decrease in size for allthree first-stage models and the second stage. For example, I for thesecond-stage model decreases by 12%.

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TABLE 2. Inferred Voting Patterns of Marginal Voters When aCounty’s Turnout Increases from 50% to 51%

Partisan Composition/Democratic Percentage of Additional Voters Difference fromVote Share at 50% Turnout Voting for Democratic Candidate Rest of Voters

Republican incumbent30% 57.7% +27.7%40% 62.1% +22.1%50% 66.5% +16.5%60% 70.9% +10.9%70% 75.3% +5.3%Democratic incumbent30% 33.8% +3.8%40% 38.2% −1.8%50% 42.6% −7.4%60% 47.0% −13.0%70% 51.4% −18.6%

Notes: These vote shares are calculated based on the IV results presented in column 2 of Table 1.For these calculations, the baseline turnout is set at 50%, and the baseline Democratic vote share isset equal to partisan composition (e.g., a partisan composition of 60% Democratic equals a baselinevote share of 60% Democratic).

more conservative in the sense that the conditionaleffects of turnout are smaller in magnitude.

Implications for the Aggregate Behaviorof Marginal Voters

To gain further information from our IV results, weuse the estimates presented in the second column ofTable 1 (i.e., those without the state-election controls)to simulate the voting patterns of the marginal vot-ers who may or may not vote in a given election. Forpurposes of illustration, we base our simulation on ahypothetical county in which the baseline turnout is50%. Although varying both the partisan identificationof the incumbent president and the partisan composi-tion of the county, we use our IV estimates to pre-dict the change in Democratic vote share based on aone percentage point increase in turnout (i.e., increas-ing turnout from 50% to 51%). Using this predictedchange and some basic algebra, we then determine howthis additional one percentage point worth of voters(i.e., marginal voters) voted. Table 2 presents thesepredicted Democratic vote shares for these marginalvoters.

The second column of Table 2 contains the simu-lated percentage of the additional marginal voters vot-ing for the Democratic candidate. The third columncontains the difference between this vote share forthe marginal voters and the vote share for the “core”50% who turned out (which, for the sake of simplicity,is assumed to be equal to the partisan compositionof the county; i.e., percentage Democratic). This sim-ulation reveals that when the partisan, antimajority,and anti-incumbent effects work together, there is amarked difference between the voting patterns of themarginal voters and the core voters, as we have de-fined them here. Specifically, when the hypothetical

county is highly Republican (only 30% Democratic)and there is a Republican incumbent, the vote sharefor the marginal voters is nearly 28 percentage pointsmore Democratic than that of the core voters. Typically,however, these three effects will not work together tothis extent, and thus, the differences in the aggregatevoting behavior of core and peripheral voters are usu-ally smaller, although often still quite impressive.

Several survey-based studies compare the votechoice of actual voters with predicted vote choices ofnonvoters. While these studies typically conclude thatchanges in voter turnout would only occasionally affectelection outcomes, they do report substantial differ-ences in the vote choices of voters and the predictedor self-reported likely votes of nonvoters. For example,from Highton and Wolfinger’s (2001) results, it can bederived that, in 1996, Clinton’s two-party vote sharewould have been 22.3 percentage points greater withnonvoters than voters. Teixeira (1992, 96) examinesseveral earlier presidential elections and finds that non-voters range from reporting likely vote shares that aresomewhat disproportionately Republican in the 1980sto reporting likely vote shares that are more than 12percentage points more Democratic than actual vot-ers in 1964. In their survey-based examination of thelikely votes of nonvoters in Senate elections, Citrin,Schickler, and Sides (2003) find that the difference inthe vote shares of voters and nonvoters ranged from ap-proximately 10 percentage points more for the Demo-cratic candidate to 5 percentage points more for theRepublican. As these studies reveal, the vote shareswings we report in Table 2 are not wildly out of linewith those obtained by surveys, even though some ofthe swings are quite dramatic. The advantage to oursimulations over the survey-based studies is that thesurveys take place after the election and, as Campbellet al. (1960, 112) speculate, nonvoters with weak parti-san ties are likely to simply report that they would have

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voted for the winner of the election. Furthermore, weuse a large number of elections while controlling forelection-specific effects. The survey-based studies tendto rely on data from a small number of elections, whichmakes it more difficult to separate out general turnouteffects from election-specific influences.

How Meaningful Are Turnout Effectsat the Aggregate Level?

Do our county-level results translate into impor-tant turnout effects at higher levels of aggregation?To address this question, we use the results of ourIV model (without state-election controls) to predictfor each election how Democratic vote share wouldhave changed in each non-Southern county based onchanges from the actual, observed level of turnout inthe county. Note that the effect of a change in turnoutin each county depends on the partisan composition ofthe county and the party of the incumbent president.Weighting each county by its number of voters, wethen aggregate these predicted changes in vote shareto determine the effect of uniform changes in turnout.These effects are aggregated at both the national leveland the state level. The former reveals the estimatedeffect of turnout on national vote share (excluding theSouth), whereas the latter is used to estimate the effectof turnout on Electoral College outcomes.

Through this aggregation process, we find that ourcounty-level effects have implications at the nationallevel. We simulate the change in national Democraticvote share based on a four percentage point swingin turnout (i.e., ranging turnout from two percentagepoints below the actual turnout for the election to twopercentage points above). Note that a four percent-age point variation in turnout is not unreasonable, andmay be viewed as conservative, given that national-level turnout has a much greater range than this overour 14 elections (ranging from 49.1% to 63.3%). Fur-thermore, prior research suggests that simple changesto voter registration requirements, for instance, couldlead to changes in national-level turnout that exceedfour percentage points (e.g., Rosenstone and Wolfinger1978). In his meta-analysis of aggregate-level turnoutstudies, Geys (2006) finds that a one standard deviationincrease in the closeness of an election leads to morethan half of a standard deviation increase in turnout.Again, our hypothetical variation in turnout appearsto be on the conservative side, given that Gey’s resultimplies that moving from one standard deviation belowthe mean closeness of an election to one standard de-viation above mean closeness would lead to more thana four percentage point swing in turnout (which has astandard deviation of 4.9% at the national level duringour time span). Based on our simulation, we find thata 4% swing in turnout leads to an average change inDemocratic vote share at the national level of just lessthan one percentage point.39

39 The magnitude and direction of the change in Democratic voteshare varies from election to election, depending on the party of

When we aggregate our results to the state level, wefind that varying turnout from two points above andbelow observed values causes an average change ofapproximately 20 Electoral College votes per election.In fact, in the 1948, 1960, and 1976 elections, at least50 Electoral College votes change. These are not triv-ial effects, especially considering that they exclude theElectoral College votes of Southern states. Althoughelection-specific factors other than turnout have thegreatest effect on who wins an election (Kaufman,Petrocik, and Shaw 2008, 147), it appears that varia-tion in turnout, at least the sort captured by our IVapproach, can exert an effect on vote shares at thecounty, national, and Electoral College level.

Testing the Volatility Hypothesis

The IV results presented in Table 1 suggest that highturnout elections are likely to have negative electoralconsequences for the majority party in an electorateand for the incumbent party in the White House. Assuch, high turnout elections may be quite disruptive.Our Volatility Hypothesis builds on this underlyinglogic and asserts that increases in turnout should leadto less predictable (i.e., more volatile) vote shares. Bybringing nontraditional voters into the electorate, theelectoral outcomes of high turnout elections shouldbe more variable. To test this proposition, we use thepredictability of Democratic vote share as the depen-dent variable in our final analysis. To measure this,we calculate the residuals from the IV model withoutstate-election controls (presented in the second columnof results in Table 1) and then square them. A largesquared residual indicates a county election dyad forwhich our model in Table 1 does a poor job of predict-ing Democratic vote share. Small squared residuals areassociated with more predictable data points.40

We again use the IV approach and regress thesesquared residuals on instrumented turnout, as well asthe county- and election-specific fixed effects.41 Be-cause our dependent variable and key independentvariable are predicted values, traditional standard er-rors cannot be used (Pagan 1984). We therefore boot-strap the standard errors associated with the coefficientestimates (Mooney and Duval 1993). These results arepresented in Table 3.

As suggested by the Volatility Hypothesis, the co-efficient estimate for instrumented turnout is posi-tive and statistically significant. Increases in turnoutcause larger residuals in our full vote share model.In other words, increases in turnout make the two-party vote share less predictable at the county level.

the incumbent president and over-time variation in our measure ofpartisan composition of the counties.40 The IV approach assumes that the excluded instrument (rainfall)is uncorrelated with the error term in the main model. Our Volatil-ity Hypothesis does not suggest that such a correlation is present.Instead, we hypothesize that increases in turnout (instrumented)causes increases in the variance of the error term.41 We cannot employ a conventional heteroskedastic regressionmodel because of the inclusion of an endogenous variable in bothmean and variance equations.

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TABLE 3. Volatility in County-level Democratic Vote Share in Presidential Elections, 1948–2000

Actual Turnout Instrumented TurnoutOLS Estimate IV Estimate

(Bootstrap Standard (Bootstrap StandardIndependent Variable Error) Error)

Turnout −.072 2.00∗

(.051) (.858)N 27,401 27,401Wald test for all covariates 832∗ 684∗

R 2 .029 .026F test for excluded instruments for turnout — 24.0∗

F test for excluded instruments for turnout × Partisan composition — 34.2∗

F test for excluded instruments for turnout × Republican incumbent — 50.7∗

Notes: The dependent variable for the OLS model is the squared residuals from the OLS model presented in Table 1. The dependentvariable for the IV model is the squared residuals from the IV model without the state-election controls presented in Table 1. Fixedeffects for counties and for election years are included in the model. Southern counties are excluded from the analysis.∗ p ≤ .05 (one-tailed test).

As turnout increases in a county, the fixed effect forthe county (the county-specific constant), the parti-san composition of the county, the fixed effect forthe election (the national election-specific constant),and, ironically, the turnout variable itself lose somepower to explain Democratic vote share. For a givenpresidential election, counties with higher turnoutwill deviate more from the national trend (capturedby the election-specific fixed effect) in that elec-tion, all else equal. For a given county, high turn-out elections are associated with a greater deviationfrom the mean Democratic vote share exhibited by thatcounty over the latter half of the twentieth century.

In sum, these results imply that the irregular vot-ers who contribute to high turnout event are less pre-dictable than regular voters. When these peripheralvoters do turn out, aggregate vote shares become lesspredictable. Importantly, the electoral volatility causedby increases in turnout is not detected by the stan-dard approaches to this problem. The OLS estimateobtained with actual turnout is not statistically distin-guishable from zero, suggesting that models that donot account for the endogenous relationship betweenturnout and vote share are unlikely to reveal the elec-toral volatility caused by higher turnout.

CONCLUSION

Political scientists have long pondered the electoralconsequences of voter turnout. Most have presumedthat in the United States, turnout serves as a lever forthe electoral fortunes of the Democratic Party. Theconventional wisdom is that Democratic vote sharerises with turnout, owing to an infusion of atypicalvoters—who tend to share a demographic profile withtraditional Democratic voters—into the electorate. Yetthe empirical evidence regarding the partisan conse-quences of turnout has been far from incontrovertible.Moreover, few scholars have looked beyond the parti-san implications to examine the effect of high turnout

on incumbency or electoral volatility in general. Ournovel approach to testing the electoral implications ofvariation in voter turnout yields two central contribu-tions.

First, we make a theoretical case for the endogenousrelationship between turnout and vote choice. We thendemonstrate empirically that aggregate turnout andaggregate electoral outcomes are endogenous. The factthat previous research has not accounted methodologi-cally for this endogeneity strikes us as surprising. Afterall, most observers recognize that voters sometimeschoose for whom they want to vote before they actu-ally decide whether to turn out to vote. This is true,for instance, whenever it is asserted that an emergent,perhaps charismatic, candidate is likely to bring newvoters to the polls. It is also the case when a non-voter decides to abstain because he or she perceivesthe choice as being a regrettable selection betweenTweedledum and Tweedledee.42 In cases such as these,or more axiomatically in Downs’s calculus of voting,the vote choice is conceived as preceding the decisionto go to the polls. By not accounting for the potentialendogeneity in the relationship between turnout andelectoral outcomes, the causal claims made in previousstudies must be treated with some skepticism.

Second, by leveraging a unique instrument for voterturnout, we are able to pin down the causal effect ofmuch of the variation in voter turnout on electoraloutcomes. As such, we believe that we provide thestrongest and clearest evidence to date of the politicalimportance of variation in turnout, at least variationof the sort captured by our instrument. Our empiricalresults present a more complex, nuanced view of theeffect of turnout on presidential elections. We show“four effects” to be at work. Democratic candidates,on average, are helped by higher turnout. The parti-san composition of the electorate and the party of the

42 In 1968, third-party presidential candidate George Wallace fa-mously asserted that the two major political parties were as close asTweedledum and Tweedledee.

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TABLE A1. First-stage Results: Predicting County-level Turnout, 1948–2000

Turnout × Turnout ModelTurnout Partisan Comp. Turnout × Rep. (No Instrumented

Independent Variable Model Model Incumb. Model Interactions)

Rain 2.35∗ 346∗ −.360 −1.02∗

(.854) (46.3) (.947) (.207)Rain × Partisan composition −.050∗ −7.32∗ −.047∗ —

(.017) (.977) (.019)Rain × Republican incumbent −1.96∗ −110∗ 1.05∗ —

(.401) (20.3) (.424)Partisan composition −.008 65.1∗ −.023∗ −.006

(.009) (.480) (.008) (.009)N 27,401 27,401 27,401 27,401F test (all covariates) 1,399∗ 3,805∗ 63,849∗ 1,584∗

F test (rain) — — — 24.2∗

F test (rain, rain × partisan comp., 24.0∗ 34.2∗ 50.7∗ —rain × rep. incumb.)

R 2 .227 .706 .963 .225

Notes: Cell entries are coefficient estimates (robust standard errors). Fixed effects for county and for election year are includedin all models. Southern counties are excluded from the analysis.∗p ≤ .05 (two-tailed test).

incumbent president condition this relationship, how-ever. Furthermore, we show that higher turnout resultsin greater levels of electoral volatility more generally.

In low turnout elections, where the electorate is com-prised primarily of core voters who possess relativelystrong and unwavering partisan attachments, electoraloutcomes reflect this underlying stability. Low turnoutelections tend to benefit Republican candidates on av-erage, a by-product of the GOP’s relative advantagewith core voters, who tend to be of a higher socioeco-nomic status than peripheral voters. Our results alsoindicate that low turnout tends to validate the statusquo because elections of this type significantly advan-tage the party of the incumbent president. Combined,these results suggest that the voters in low turnoutelections are likely to exert little “change” when theygo to the polls. Put differently, lower levels of turnoutmay yield representational bias in the electoral con-nection. Interestingly, this bias is not simply partisan innature because low turnout also produces a proincum-bent bias.

High turnout elections, in contrast, bring both coreand peripheral voters to the polls. Importantly, theinfusion of this latter group into the electorate maycontribute to outcomes that are both potentially dis-ruptive to the existing political order and less system-atically predictable. Peripheral voters are likely to pos-sess weak partisan or ideological attachments at bestand thus are more influenced by transient or idiosyn-cratic considerations. It appears the infusion of theseatypical or peripheral voters into the electorate hasconsequences for America’s political parties. Our find-ings conform to those hypothesized by DeNardo’s Two-Effects thesis. That is, although higher turnout benefitsDemocrats on average, the magnitude of those bene-fits is conditioned by the composition of the electorate

being brought to the polls. Indeed, in highly Demo-cratic electorates, high turnout may actually help theRepublicans, who benefit from weak partisans defect-ing from their Democratic attachments. In addition tothese partisan effects, we find that high turnout also hasa significant anti-incumbency effect. Peripheral votersnot only have weak partisan ties, but they may also beless likely to support the electoral status quo. Conse-quently, when the electorate expands with these voters,the incumbent party is fighting an uphill battle. Com-pared to their more participatory counterparts, infre-quent voters bring both change and noise when theygo to the polls. High turnout elections portend partisanchange, anti-incumbency tendencies, and generally lesspredictable consequences.

APPENDIX

The IV models presented in Table 1 treat three indepen-dent variables as endogenous: turnout, turnout × partisancomposition, and turnout × Republican incumbent. Thereare thus three first-stage models, one for each endogenousvariable. Following IV convention, each first-stage model in-cludes all three excluded instruments: rain, rain × partisancomposition, and rain × Republican incumbent. The first-stage estimates for the model without state-election controlsare presented in the first three columns of Table A1 .43

These estimates imply that the effect of rain on turnout isconditioned by Republican incumbent and partisan compo-sition. Note that despite the positive “main effect” for rain

43 The instrument (i.e., predicted values) for turnout has a mean of65.6 and a standard deviation of 9.2. The instrument for turnout ×partisan composition has a mean of 2,887 and a standard deviationof 751. The instrument for turnout × Republican incumbent has amean of 33.3 and a standard deviation of 33.7.

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TABLE A2. Alternative IV Approach toModeling County-level Democratic VoteShare in Presidential Elections, 1948–2000

Coefficient EstimateIndependent Variable (Bootstrap Standard Error)

Turnout .502∗

(.140)Turnout × Partisan −.002∗

composition (.001)Turnout × Republican .208∗

incumbent (.012)Partisan composition .821∗

(.034)N 27,401Wald test for all covariates 64,401∗

Notes: The model includes fixed effects for county andfor election year. Southern counties are excluded fromthe analysis. The standard errors are bootstrapped (500repetitions).∗p ≤ .05 (one-tailed test).

in the turnout model, the average conditional effect of rainon turnout is negative (−.85, based on the average valuesof conditioning variables). The key considerations when de-termining whether rainfall is a valid instrument for turnoutare (1) exogeneity and (2) explanatory power. We believethat it is safe to assume that rainfall is exogenous to votechoice, so we will not belabor the point. Does it have enoughexplanatory power? The econometric rule of thumb is thatan F statistic of 10 or greater indicates that an instrument (orset of instruments) has sufficient explanatory power for IVestimation (Staiger and Stock 1997). As reported in Tables 1and A1, our rainfall variable and associated interaction termsfar exceed this threshold.

To ensure that the conditional effect of rain on turnoutin the first stage of the IV model is not problematic for theestimation of the main model, we re-estimate the IV modelwhile employing a somewhat different strategy. We predictjust turnout in the first stage while including rain as instru-ment and excluding the interaction terms involving rain. Theresults of this alternative first stage are reported in the last col-umn of Table A1. Then, we multiply predicted turnout withRepublican incumbent and partisan composition, and includethese interactions in the main model. This approach forcesrain to have a constant, nonconditional effect on turnout inthe first stage. One disadvantage to this approach is that theestimated standard errors may not be correct in the secondstage, but this can be resolved by bootstrapping these second-stage standard errors. The results obtained by this alternativeIV strategy are presented in Table A2. These results are quitesimilar to those presented in Table 1, and the fundamentalinferences are the same. This indicates that allowing the effectof rain on turnout in the first stage to be conditional is notdeterminative of the ultimate conclusions drawn based onthe second-stage model of vote shares.

We then square the residuals from the model presentedin Table A2 and regress them on the alternative version ofpredicted turnout to retest our Volatility Hypothesis. Theseresults are presented in Table A3. The result is fundamentallysimilar to that presented in Table 2. Both IV strategies lead tothe conclusion that increases in voter turnout cause greatervolatility in presidential vote shares.

TABLE A3. Alternative IV Approach toModeling Volatility in County-levelDemocratic Vote Share in PresidentialElections, 1948–2000

Coefficient Estimate(Bootstrap Standard

Independent Variable Error)

Turnout 6.13∗

(1.28)N 27,401Wald test for all covariates 753∗

Notes: The dependent variable is the squared residualsfrom the model presented in Table A2. Fixed effects forcounties and for election years are included in the model.Southern counties are excluded from the analysis.∗ p ≤ .05 (one-tailed test).

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