Victory by association: Using electronic prediction markets to measure coattail effects
Stephen Travis May
Harvard College ‘09, email@example.com
In this paper, we study the magnitude of coattail effects in the 2008 election, or the impact of the presidential election on congressional elections. We utilize data from electronic prediction markets to measure these effects. In order to eliminate endogeneity biases in our analysis, we measure coattails by using the occurrence of a major event as an instrument. We select days in which major events occurred (such as presidential debates) that affected the presidential election without any direct effect on local elections. Since the shifts that occur on these days in congressional markets are due exclusively to coattails, we then measure the impact the exogenous events had on the congressional elections. We find strong coattail effects in House elections and insignificant effects in the overall Senate race. We then apply our methodology to the Minnesota Senate election, where we find strikingly strong coattail effects. We discuss these results in the context of our simple model of voting preferences.
As the cornerstone of democracy, elections play a critical role in the United States political system. Every four years, star candidates rise and fall, scandals emerge and disappear, and long campaigns are fiercely fought before settling on a winner. Pundits devise dozens of stories that “explain” what determined the winner, and television and radio talk shows will debate these theories for months. But to the academic empiricist, understanding an election is problematic. To understand the determinants of a specific election, the sample size is only one event—so how can we know whether John McCain would have fared better with a different vice-presidential candidate? To understand election determinants, political economists like Ray Fair have pooled the data of many elections and constructed models of very broad trends; yet because of the small sample size and the complexity of the variables impacting elections, these models yield only a few answers about what shapes elections in general, and much less about what shapes specific elections.
In this paper, we propose the use of a new tool for understanding elections: electronic prediction markets. These markets have been studied at length, with a broad theoretical and empirical consensus that they yield reasonably unbiased, efficient estimates of the probability that an event occurs. Instead of focusing on their efficiency, as most papers about electronic prediction markets have, we will instead assume that they are efficient. In this paper, we will begin to answer the following question: given that electronic prediction markets are efficient, what can they tell us about political institutions? We will provide a case study of the potential utility of this methodology in the example of coattail effects. While this paper yields interesting results, our focus is primarily methodological and aims to understand how the existence of a continuous metric of election probabilities can be useful for causal analysis.
Background on Electronic Prediction Markets
Electronic prediction markets are futures exchanges in which the value of an asset is tied to the outcome of a particular event. In a vote share market, traders bid in a continuous double auction for the optimal price that they will pay for a contract that pays $1 for every percentage point that a particular party receives. For example, in the 2000 election, George Bush received 47.9% of the vote, and thus the Republican contract paid off $47.90 at the end of the election. In a winner-take-all (WTA) election, traders bid on contracts for which candidate will win the election and receive $100 per share of the winning candidate held.
In a system with no transaction costs and risk neutrality, Wolfers and Zitzwitz (2004) show that the market price of the contract should equal the median market participant’s expected election outcome weighted by trading volume. Furthermore, Berg et al. (2001) show that the market price is a remarkably accurate short-term predictor of the real election outcome, consistently outperforming polls as a last-day prediction tool. In a follow-up study, Berg et al. (2003) find that electronic markets have exceptional long-term predictive abilities, and greatly outperform both polls and forecasting models.
The intuition behind these results is clear: traders are forced to “put their money where their mouth is,” and they are thus incentivized to be accurate. Since projection models and poll results are generally publically available, that information can be incorporated into the market price. Thus the market prediction should be at least as accurate as any type of publicly-known prediction mechanism, if not more so. Interestingly, this assumption does not depend on traders being a random sample of the population, as the market can incorporate information without all voters participating. As Berg et al. (2001) point out, market participants are far from a random sample; they tend to be wealthy, young, and highly-educated. Furthermore, the average trader in the market can be biased and trade based on his own bias; empirically, there is a small set of “marginal traders” who are the ultimate price-makers and hunt for arbitrage opportunities—and their probabilistic assumptions are quite accurate.
With this consensus of research demonstrating that prediction markets are accurate estimators, we intend to utilize the market results in this paper as a continuous set of election results—changing over the course of the election only as the expected outcome changes. Thus, we have a much more complete data set, with a continuous set of data points that can be evaluated in order to measure the importance of contextual events.
Background on Coattail Effects
In the paper, we apply electronic prediction markets to understand the interplay between national and local elections. While resting partially on local issues and candidate personalities, local elections are often a referendum on national political figures. Local elections are heavily correlated with national results, and many elections—such as the 2008 election—have the same party sweep to victory in the House, the Senate, and the presidency.
Some of this correlation is due to contextual shifts, such as macroeconomic changes or wars abroad. Other sources of correlation may be due to a demographic transition, leading to partisan realignment. A third part of the correlation comes from the presence of coattail effects, or the effect that a top-level candidate has on a local candidate. A popular presidential candidate can register new voters, drive partisan turnout and party-line voting, and change voter preferences on issues, leading to coattail effects that change the outcome of congressional elections.
Despite the intuitive nature of coattail effects, attempts at effectively quantifying these effects have generally floundered. Since elections are correlated for a wide variety of reasons, measuring basic correlation between elections is insufficient to establish coattail effects. The methodological obstacles to measuring coattail effects were pointed out by Miller (1955), who noted the simultaneity of decisions taking place in elections. Mondak (1990) asserted that “a growing consensus holds that the presidential vote does exert significant influence on congressional elections,” though he added that these analyses were set back by the “long–recognized difficulties associated with measuring political coattails.”
Two primary obstacles exist in measuring coattail effects. First, there is a highly limited sample size: there is only one presidential election every four years from which to draw data, and there are substantial contextual changes that occur over that time frame. To overcome the limited datasets, we use electronic prediction markets to assess the status of elections on a continual basis. A second obstacle is one of endogeneity: much of the correlation between candidates is due to agreement on issues and shifts in economic context, rather than coattail effects? In this paper, we measure coattail effects within the 2008 election by using exogenous changes in the presidential election (that do not directly affect congressional elections) as an instrument. We find substantial coattail effects in the House and insignificant effects in the Senate.
The paper is organized as follows: first, we describe a theoretical model for the existence of coattail effects; then, we propose an empirical methodology based on the electronic prediction market dataset; next, we analyze the results of this methodology; and finally, we provide concluding remarks and suggest areas for future research.
Modeling Coattail Effects
Despite the difficulties in measurement, there are intuitive reasons why coattail effects are likely to exist. First, voter registration and turnout are often driven by grassroots campaigns and excitement for a top-level candidate. If a presidential candidate is able to register millions of first-time voters, those voters are likely to vote in lower-level elections for the same party. Similarly, excitement about a top-level candidate can help drive party-line voting in some states, as voters that are ambivalent about lower-level elections choose out of simplicity and expediency to vote for a party generally rather than evaluating individual candidates. While these effects can help shift votes towards a popular presidential candidate’s party, a more subtle source of coattail effects shapes the median voter’s preferences directly in lower-level elections. The median voter, typically a swing voter who was planning to vote and does not make a straight party-line vote, may change her lower-level preferences based on a change in her perception of a top-level candidate; her preference for a particular presidential candidate informs her decision of which lower-level candidate to support.
To gain a better understanding of the impact of coattail effects on the election, we will consider a congressional election that is simultaneous with a presidential election. Define candidate C as a congressional candidate in the same party as presidential candidate J. The decision of whether to vote for candidate C can be modeled as:
XiC = 1 if Udif_C (Equation 1)
XiC = 0 if –Ū < Udif_C < Ū
XiC = –1 if Udif_C < –Ū
Where Udif_C = E[UiC]–E[UiC2]
XiC: vote cast by voter i for candidate C. Not voting counts as 0 votes, and voting against counts as a negative vote for the candidate.
UiC: utility voter i receives in the state of the world where candidate C wins
UiC2: utility voter i receives in the state of the world where candidate C’s opponent wins
Ū: absolute utility difference threshold that causes voter i to cast a vote.
Additionally, we can further expand these variables as:
E(UiC) = E(F(ii, viC)) (Equation 2)
ii = i(c, ti)
E(viC) = v(c, riC, pC, siC)
UiC: utility voter i receives in the state of the world where candidate C wins
viC: vector of expected agreement between voter i and candidate C’s decisions
ii: vector of weights of importance that a voter gives to particular issues
c: context of election
ti: voter i’s tastes
pC: personal characteristics of candidate C
riC: historical correlation between voter i and candidate C’s known beliefs
siC: signals of future agreement between voter i and candidate C
Under this model, a voter’s tastes (ti) and the election’s context (c) are the same in both the presidential and congressional elections, and are not affected by either candidate. Similarly, the personal characteristics of a candidate (pC) and the agreement between a voter and a candidate’s revealed beliefs (riC) are specific to a particular candidate, and we assume that they are not affected across elections. Instead, we model coattails as an informational phenomenon, with signaled beliefs (siC) as the source of coattail effects between the elections.
Intuitively, the model suggests that coattail effects occur as voters use presidential candidates as partial proxies for local, less-known candidates. Beyond any information known about the candidate personally, the candidate’s party affiliation is also visible to a voter—a strong signal of the candidate’s future decisions if elected. Mondak (1990) finds that voters without much knowledge of a political race may use their views of the presidential candidate in the same party as a factor in their votes. Given the time cost of information collection and the voter’s scarce budget of time, a typical voter spends only part of her time considering the election, and uses the presidential candidate as a proxy for the views of the local candidate. We formalize this view of election signaling as a simplified model:
siC = s(vij, wic) (Equation 3)
siC: signals of future agreement between voter i and candidate C
vij: vector of expected agreement between voter i and presidential candidate j’s decisions
wiC: relative strength of presidential views as a proxy for congressional candidate’s views
The extent that the voter expects to agree with the presidential candidate’s political decisions (vij) affects the voter’s expectation of how much she expects to agree with the lower-level candidate (vic). The importance of the presidential candidate as a proxy is given a weight (wic) that shows the extent to which the voter relies on the presidential candidate as a proxy (which in turn is affected by the perceived correlation between the presidential candidate and the local candidate as well as the relative amount known about the views of each). Assuming a candidate’s views are considered to be positively correlated with the presidential candidate of the same party, then ∂sic /∂vij > 0, implying that ∂Uic/ ∂vij > 0. Thus, the probability that the voter votes for candidate c increases with the voter’s expected degree of agreement with the presidential candidate (vij). Furthermore, the magnitude of impact of coattails on voter choice increases with weight, so ∂2Uic/ ∂vij∂wic > 0.
This model outlines a mechanism for why, ceteris paribus, a candidate’s popularity might be affected by a change in political popularity of the presidential candidate from the same party. Since a voter often knows more about a presidential candidate than about a local candidate, she uses the presidential candidate as a proxy for the local one – resulting in coattail effects.
The Problem with Traditional Measurement Approaches
For an observer trying to estimate the impact of coattail effects, many of the variables from Equations 1 and 3 are not directly observable; instead, what is observable is the median voter’s decision on the presidential election, Xij and their decision in the lower-level election Xic. Previous attempts at measurement, such as the C-Correlation approach, have effectively regressed lower-level election results directly on presidential election results, or Xic on Xij. Equation 3, however, demonstrates why this is problematic. The unobserved effect of context is a factor in both Xic and Xij, causing correlation without coattails.
To give a concrete example of this problem, in the 2008 election, negative events in the economy tended to shift voters’ views in ways that were favorable to Democrats in general. There was substantial correlation between local elections and the presidential election, but much of this relationship was due to the favorable context for Democratic policies that were shared among candidates. The correlation in such a case could not be attributed to coattails, since it was economic changes—rather than changes in the presidential election—that shaped the association between the two elections.
A New Empirical Methodology
Despite the intuitive theoretical justifications for coattail effects, attempts to measure the effects empirically have been hindered by both causality questions and a limited dataset. To overcome these obstacles, we propose an instrumental variable approach that uses data from electronic prediction markets. There are three steps to our methodology: first, we will broaden the dataset by turning to electronic prediction markets; second, we will select specific events where the presidential elections were exogenously affected without any direct effect on congressional elections; and finally, we will analyze the impact of these events on the congressional elections.
Step 1: Broadening the dataset
In order to broaden the dataset, we use electronic prediction market data for the 2008 election from the Iowa Electronic Markets. We track daily closing prices for Democrats in the winner-take-all (WTA) market for the presidential election and the seat gain WTA market for the House and Senate elections from August 26, 2008 (the date the congressional markets opened) until November 4, 2008 (Election Day). In these markets, House and Senate prices are aggregated total probabilities of the Democrats winning seats in each respective chamber rather than looking specifically at particular districts. Figures 1 and 2 show the association between weekly changes in presidential markets and changes in the House and Senate races, respectively. As expected, the figures demonstrate a clear correlation, from which we intend to isolate the coattail effects.
Due to light trading and large bid-ask spreads, we use weekly price changes for the congressional prices instead of daily changes. However, if we were to compare weekly prices for each, we would unintentionally include correlation that does not result from coattails by expanding our time horizon too greatly (for example, economic changes over that time period may affect both if the time horizon is too long). Thus, throughout this paper, we are generally comparing weekly congressional shifts with daily presidential shifts, assuming that any congressional price change that occurred in the preceding six days is in a random direction. We also remove from the dataset all periods in which there was no trading volume. Finally, we restrict the dataset to periods on which presidential candidate Barack Obama gained vote share as a proxy for an election event being positive. Summary statistics are shown in Table 1.
Step 2: Choosing events
In order to construct an instrument, we establish a binary variable dependent on whether or not there is a major shift that affects the presidential election without directly impacting lower-level elections. While some factors in the presidential election (such as economic context) are also major direct factors in lower-level elections, certain events only affect the presidential election directly. For example, a presidential debate—designed to influence public opinion about only the presidential candidates—would impact congressional outcomes exclusively through coattail effects. After analyzing major events in the election,  we select seven such events to set our binary variable equal to one:
8/23/08 – Obama selects Biden for VP
8/28/08 – Obama Acceptance Speech
8/29/08 – McCain selects Palin for VP
9/27/08 – Day after 1st debate
10/3/08 – Day after VP debate
10/8/08 – Day after 2nd debate
10/16/08 – Day after 3rd debate
To confirm that these events had a substantial effect on the presidential election, we compared prediction market price changes on major event days in which Obama’s market price for winning the presidency improved. As Figure 3 shows, the average gain in the presidential markets nearly doubles on the dates with major events.
Step 3: Measuring impact
Now that we have measured the impact of these events on the presidential elections, we turn to the congressional elections to gauge the impact that these major, exogenous events from the presidential election have on the congressional markets. Figure 3 shows a substantial effect of major presidential events on the congressional markets that increases average gains by a factor of eight in the Senate and a factor of four in the House.
To quantify this effect, we run a two-stage least squares regression using the presence of a major event as an instrument. As our first step, we regress changes in the probability of Obama winning on the presence of a major event on days where Obama gained popularity in the election:
Change_DemPres_WTA = α0 + α1 × MajorEvent + u (Equation 4)
Change_DemPres_WTA: daily price change for prediction market outcome of Obama winning presidency
Major_Event: binary variable equal to one on days with major presidential events
u: error term
We can now plug this result in to measure coattail effects. Equation 4 shows that the probability that a particular local candidate wins the median voter’s support is a function of candidate-specific effects (including the candidate likability and the agreement between the voter and the candidate’s revealed beliefs), time-specific contextual effects, and changes in the popularity of the party’s presidential candidate. In a naïve model regressing change in congressional probability on change in presidential probability directly, the error term would include both the candidate-specific effects and the time-specific contextual effects and would thus be correlated with the regressor. To overcome this problem with the naïve model, we instead use the predicted effect from Equation 4 as a regressor. Since we constructed MajorEvents to be uncorrelated with macroeconomic contextual changes and based exclusively on exogenous events in the campaign, its expected correlation with the error term is 0. Aggregating local elections into a metric of all ongoing congressional elections, this instrument enhances our model for a change in probability of the Democrats winning the election:
Change_DemCongress_WTA = (Equation 5)
β0 + β1 × Predicted_Change_DemPres_WTA + ε
Where Predicted_Change_DemPres_WTA = α0 + α1 × MajorEvent (with α0 and α1 from Equation 4)
Change_DemCongress_WTA: weekly price change for prediction market outcome of Democrats winning seats in Congress
Change_DemPres_WTA: daily price change for prediction market outcome of Obama winning presidency
ε: error term
Through the two-stage least squares outlined in Equation 4 and Equation 5, we observe the effect of an exogenous shift in presidential preferences on Congressional prediction markets, yielding an unbiased estimate of coattail effects as β1.
Results and Discussion
General results and discussion
Our results from the two-stage regression in Equations 4 and 5 are reflected in Table 2. The results display strong, significant coattail effects in the House election but weaker, insignificant results in the Senate. A 1% increase in Obama’s likelihood of winning is associated with a 2.1% increase in the Democrats winning the House, but only a 0.76% change in probability in the Senate. The coattail effect in the House election is quite strong, as an event occurring in the presidential election has a larger effect on candidates in the House than on the presidential candidates themselves.
The general model of coattail effects in Equation 3 helps explain the difference in magnitude of the effects in the House and Senate. One of the model’s core results is that a voter’s perception of the presidential candidate matters in congressional elections only to the extent that the presidential candidate’s views are a useful proxy for the congressional candidate’s views, or the magnitude of the variable wic. In an election where the median voter knows less about the candidate, coattail effects are expected to be stronger, since the party affiliation of the candidate carries more meaning. Typically, Senate candidates are better known than their House counterparts; since senators serve longer incumbencies, wield more personal power, spend more on their campaigns, and have broader constituencies, they generally capture a larger share of news coverage and political buzz. Thus, the median voter often knows more about the candidates in the Senate election than the candidates in the House election, and presidential views are more necessary as a proxy in the House election.
One of the more surprising results of this analysis is the amplification of effects across elections. A one percent change in the probability of Obama winning is transformed into a greater than one percent change in the probability of Democrats winning in the House election. We propose two hypotheses for why amplification exists: geographic influences and the self-fulfillment of predicted success. In these markets, changes in voting trends in different states are not equally important, as a vote shift in a non-swing state is not as meaningful as a vote in a swing state. The presidential swing states may vary from congressional swing states. Thus, a presidential announcement that “rallies the base” may have an amplified effect in states with close congressional elections but that are heavily leaning towards a particular party already in the presidential election.
An alternative hypothesis for amplification is that success is self-fulfilling, as the perception of being likely to win an election can increase the actual likelihood of winning. Campaign contributors, key politician endorsers, and even news editorial boards are often eager to support the winning side of an election and reap potential benefits of early support. A company’s executives may choose to donate to a campaign they expect will win in order to gain potential political goodwill, and they must base their decisions on probability estimates made weeks or months before an election. Since these acts of support may directly shift the outcome of an election (and likely have larger effects in elections where candidates are lesser known), success may have inertia that amplifies a small probability change into strong gains.
Case study: Minnesota
Turning from the general application of our model across all congressional and Senate elections in 2008, we now apply our model to one specific election: the 2008 Minnesota Senate election. Because of the perceived closeness of Minnesota’s election, the Iowa Electronic Markets introduced a market with reasonable trading volume that measured the vote share in state’s senatorial election. Table 3 shows the results of applying the instrumental variable regression from Equation 5 on Minnesota’s results. A 1% change in likelihood of Obama’s victory is associated with a 5.865% increase in the expected vote share for Franken (the Democratic candidate in this election).
The magnitude of the coattail effect is strikingly large, especially for a Senate race. The difference in effect between this election and other Senate elections is likely due to the extreme closeness of this race – a race that was ultimately decided by just a few hundred heavily-contested ballots. Thus the impact of any perceived political shift would be heavily amplified in this ultra-close election. Furthermore, Minnesota was not a heavy swing state in the presidential election, and ultimately voted by a substantial margin for Obama. Thus, events in the presidential election that resounded with liberal voters may have had a stronger effect on the Senate election outcome than the general election probabilities.
Limitations and further research
There are several limitations to these conclusions, and several questions are raised for further research. First, while this methodology could be generalized, we only used data from the 2008 elections in this analysis due to the limited history of electronic prediction markets for Congressional elections. As more elections occur and the use of electronic prediction markets expands, a broader analysis could be performed on the impact of coattail effects on elections and the determinants of the magnitude of the effects. In particular, the 2008 election was unique in recent elections because of the relative certainty of the eventual outcome for Senate and House control, as the probabilities that Democrats would control each chamber were over 90% for much of the period evaluated. Thus, an analysis performed in a year when both the presidential and congressional elections are expected to be close may yield different results.
As prediction markets continue to mature, another potential expansion would be to observe coattail effects on a state-by-state level. While state-by-state election details from electronic prediction markets were limited in the 2008 election, further expansion in market availability and trading volume would enable a study on state-specific coattail effects and determinants of the magnitude of coattails.
Finally, several assumptions were made in choosing to use electronic prediction market prices as proxies for probabilities of actual outcomes. First, we assumed that they are unbiased, reasonably accurate estimators, claims that are generally supported by both empirical and theoretical literature on prediction markets. A more subtle assumption is that changes in prediction market prices are due to events impacting the election directly, rather than merely changing perceptions of the candidates themselves by market participants. For example, an eloquent speech by a candidate would not only boost his chances in the election directly, it might also signal to prediction market participants that he will be similarly eloquent in the future—and traders will factor these future events into the market price. This effect would likely be particularly magnified early in an election, since market participants know less about the strategic and tactical competence of particular candidates. In order to mitigate this effect, we selected events for this study that occurred relatively late in the election and would likely have a primary effect of directly altering the election, such as the selection of a vice-presidential candidate. Furthermore, even if the market changes its perception of a candidate and incorporates information about future expected events because of one of the events we selected, as long as those future events also generate coattails, they will also be incorporated into congressional prediction markets, leaving our estimate unbiased.
Our results provide an intriguing insight into one of the major determinants of United States elections outcomes. Using electronic prediction market trading data, we find that coattail effects have a major impact on House elections, but a more limited impact on Senate elections. By using major exogenous shifts in the presidential election as an instrument, we isolate the coattail effects in the election and overcome causality concerns intrinsic to most past studies of empirical effects.
While this result generally confirms our intuitive expectations about coattail effects, the methodology provides an intriguing new way to study major factors shaping elections. Similar to coattail effects, many factors that intuitively have large effects on elections are difficult to show empirically, since elections occur only once every few years and substantial differences in context occur from election to election that complicate any attempts to hold multiple factors constant. By using market prices of a particular outcome as a proxy for the status of an election, electronic prediction markets promise to widely expand the data set available for analyzing election phenomena. Nonetheless, most literature on electronic prediction markets to date has been either theoretical in nature or an empirical measurement of the market’s predictive ability. By assuming the markets are in fact reasonably accurate (which most analysis supports), we use prediction markets as robust, real-time indicators of the status of an election. Our results indicate that – beyond their predictive value – prediction markets can also be a useful tool in isolating empirical effects in presidential elections and uncovering the determinants of political success.
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-  While a number of resources were used to select the largest events of the election, the Pew Research Center’s “Top 25 Events of 2008 Election” was particularly useful. In choosing events, we selected events that were clearly exogenous to the election and were confined to a discrete time period. While there were several other significant events in the Presidential election (such as Obama travelling to Europe), we specifically selected for events with measurable short-term effects. ↩