Statistical Modeling, Causal Inference, and Social Science

Darcy Kelley sends along a link to this site, Make My Vote Matter, in which you can enter two different addresses where you might vote, and it will tell you in which (if any) of these addresses has elections that are predicted to be close. The site is aimed at students; according to the site, they can register to vote at either their home or school address.

David Weakliem writes:

Thomas Edsall has a piece in which he cites a variety of work saying that Democratic and Republican voters are increasingly divided by values. He’s particularly concerned with “authoritarianism,” which is an interesting issue, but one I’ll save for another post. What I want to talk about here is the idea that the recent rise in political polarization is the result of a rise of “cultural and lifestyle politics” at the expense of economic issues. The reasoning is that it’s easier to compromise on economics, on which you can split the difference, than on cultural issues, which involve principles of right and wrong. The idea that culture has been displacing economics as the main axis of political conflict been around for about fifty years—it was first proposed in response to the developments of the late 1960s and early 1970s. I think it has value (although with some qualifications which I discuss in this paper), but I don’t see how it can explain the rising polarization of the last decade or so. In that time, the single most divisive issue in American politics has probably been the Affordable Care Act. This is basically an economic policy, and a very complicated one involving a lot of technical issues—that is, exactly the kind of issue where it seems you could make deals, offering a concession here in return for getting something there. The second most divisive issue has probably been the combination of bailouts, tax changes, and stimulus spending that gave birth to the Tea Party: another complicated set of economic policies that seemed to offer lots of room for compromise. Meanwhile, some leading cultural issues have faded. For example, same-sex marriage is widely accepted—even people who aren’t enthusiastic about it have mostly given up the fight. Another example involves drugs: a consensus seems to be developing in favor of legalizing and regulating marijuana, and the rise in opioid abuse has been treated as a public health problem rather than producing a “moral panic.”

What I think these examples show is that both economic and cultural issues can be more or less “moralized.” There was a period in the middle of the 20th century when leading politicians of both left and right accepted the basic principles of the welfare state and government intervention to maintain high employment. But that consensus had not been around before then, and it isn’t around now. Now issues that were once part of what Seymour Martin Lipset called “the politics of collective bargaining” are part of the “culture wars.”

This is an excellent point. Weakliem should have a regular column in the New York Times.

A couple months ago I wrote about party balancing in the midterm elections and pointed to the work of Joe Bafumi, Bob Erikson, and Chris Wlezien.

Erikson recently sent me this note on the upcoming midterm elections:

Donald Trump’s tumultuous presidency has sparked far more than the usual interest in the next midterm elections as a possible midcourse correction. Can the Democrats can win back the House of Representatives and possibly even the Senate in 2018? This short essay presents some observations about midterm elections and congressional elections generally, followed by some considerations relevant toward understanding the upcoming 2018 midterm verdict. Most of my [Erikson’s] remarks would be commonplace among seasoned congressional election scholars. Please note, however, that I tout a theory of ideological balancing in elections, that remains controversial in some quarters.

As soon as it became clear that Donald Trump would become the next president of the United States, it became almost certain that the Democrats would gain seats in the House (and possibly the Senate) in 2018. For the past 32 midterm elections going back to 1878, in all but three instances (1934, 1998, 2002) the out-party gained seats. In all but two instances (1926, 2002), the out-party gained in terms of vote percentage. So we have a sort of law of politics. Why? One factor is that when presidents have coattails, these coattails are withdrawn at midterm. But winning presidents often lack coattails. Another factor is that unpopular presidents (e.g., Trump) see their party receive the greatest punishment at midterm. But on average presidents are not uniquely unpopular at midterm. So there must be something more.

Further, it is not just that the presidential party’s vote and seat margins decline at midterm. The presidential party also suffers in terms of its level of support. Each major party performs worse at midterm when it does not hold the presidency. If the goal of a congressional party is to do well at midterm, it should lose the presidency.

The mechanism that drives midterm loss is ideological balancing, a theory best elaborated by Alberto Alesina and Howard Rosenthal in the 1990s. The election of a president tilts the direction of national policy to the left or the right of the median voter, depending on the party of the winner. The way for the median voter (and voters generally) to make the ideological correction at midterm is by voting into office more from the opposition party.

One challenge to balance theory as the explanation for near-universal midterm loss, however, is that presidential elections are often predictable in advance. Knowing the presidential winner, presidential-year voters could balance in advance by casting congressional ballots for the party they expected to lose the presidency. Certain winners, however, are likely to have coattails that also carry their ticket-mates into office via straight-ticket voting. In large and predictable presidential wins, coattails work but are offset by presidential-year balancing. At midterm, withdrawn coattails lead to midterm loss. In other words, coattails and balancing work in tandem to account for nearly universal midterm loss.

An interesting circumstance is when perceptions of the likely presidential winner are wrong. In 1948, everyone “knew” that Thomas Dewey would defeat President Harry Truman. But, as everyone knows, Truman won in a huge upset. What is less well known is that Truman’s Democrats gained a whopping 75 House seats in 1948, arguably because people were voting Democratic for Congress to block “President Dewey.” The 2016 election provided an analogue. Plausibly, many who thought Hillary Clinton would win voted Republican for Congress to block, thus accounting for the Democrats’ surprisingly feeble performance at the congressional level in 2016.

It is arguable that balancing also works in the reverse direction. In 2016, for instance, the fact that the Republicans seemed to have a firm hold on Congress may have led some to put their thumb on the scale for Clinton over Trump for the presidency. In 1994 and 2010, Republican congressional triumphs could have made it easier for Bill Clinton and Barack Obama to win reelection two years later. In retrospect, maybe Harry Truman was reelected in 1948 because his campaign against the “do-nothing” Republican Congress was surprisingly effective. (As side evidence, we can see a pattern involving gubernatorial and presidential elections. When a party wins a close gubernatorial election at midterm, it becomes more likely to lose the state in the presidential election two years later. Based on the statistical evidence—via regression discontinuity—that implies this regularity, one could actually project that if the Republicans had counterfactually lost all the governor races they won in 2010, Romney could have defeated Obama in 2012.)

So what about the 2018 midterms? What can we say beyond the casual evidence that there may be a Democratic wave coming this Fall? First, we should believe the generic ballot polls. Properly interpreted, generic ballot polls are more predictive of House midterm elections than presidential polls are of presidential election outcomes. Based on post-WWII history, the way to predict the November vote from polls in mid-spring is roughly to take the vote margin in live-interview polls and cut it in half and then add four points to the out-party. By this measure, the current expectation is that the Democrats should win about 54 percent of the vote. As a statistical prediction, forecasting the midterm vote from regressing the House vote on generic ballot margins plus party control has a smaller expected error (RMSE) than the comparable prediction of presidential elections based on early presidential polls. Generic polls predict, and early in the campaign (e.g. spring of the election year) one should also factor in party control. Survey respondents apparently do not consider party control much until the approach of Election Day.

So the chances of the Democrats winning a sizeable majority of the vote for the House are quite good. The question is whether that is enough to win most seats. From gerrymandering (both natural and induced by Republican state legislatures), the terrain tilts in favor of the Republicans. For instance, in 2016, for districts where the two parties each ran a candidate for the House, the average Democratic vote was only 1.5 percentage point less than Hillary Clinton’s percent of the local two-party vote. In other words, the vote margin nationally was a virtual even split. Yet the Republicans won a decisive plurality of 47 seats.

A natural but wrong way to predict the 2018 seat division is to take the 2016 vote in all districts and project a uniform swing of the two-party vote. By this (wrong) uniform swing method, a projected 54 percent of the vote would yield a pathetic 12 seat pickup. The Democrats would need an unrealistic 55.8 percent of the vote to win the required 23 new seats. The task of winning the House would be nearly impossible.

We can see the error in uniform-swing forecasting by applying the uniform swing retrospectively to the two most recent surge elections. If in 2006 the Democrats knew in advance exactly how much their national vote would increase, the uniform-swing heuristic would lead them to predict a gain of only 16 seats rather than their actual yield of 30 seats! If in 2010 the Republicans had known in advance what their gain in the vote margin would be, their expectation would be 48 seats gained, rather than their actual yield of 63 new Republican seats.

Where uniform swing goes awry is the failure to account for party effort being strategic. The “wave-party” (Democrats in 2006, Republicans in 2010) had put little effort in the previous election in those districts where its best shot would have been a close loss. Thus, the wave-party started with few obvious pickups from close misses from the pre-wave election. Instead, the wave party wins new seats where the non-wave-party seemed safe based on prior voting, but where a combination of surging partisan winds plus wave-party effort made them vulnerable. Similarly, for 2018, a combination of a Democratic surge and a Democratic effort could make the difference in many seemingly safe Republican districts.

But what about gerrymandering, one might ask. The Democrats did regain the House in 2006 with about the same vote margin that is projected for 2018. They did so despite a gerrymander based on the 2000 Census that was only marginally less harmful than the gerrymander facing the Democrats of 2018, based on the 2010 election. Further, when a wave is extreme—as if a 100 year flood, the gerrymander can backfire by upending party control where the gerrymander is designed to protect against all—except maybe a 100 year flood. The 2006 election provides a lesson. Democrats could have picked up 10 additional seats (beyond their total of 30) if the 2006 vote (not 2004 in a uniform swing) had been one percentage point more Democratic everywhere. That is, there were 10 seats the Republicans barely hung on with less than 51.0 percent of the vote.

There is one major change that has overtaking recent congressional elections that adds to uncertainty about predicting 2018. This is the growing nationalization of congressional elections; district partisanship now takes on increased importance at the expense of the candidates’ personal vote. (Partisan polarization plus party control of Congress being in play increasingly dominates congressional attention to local issues). This trend has several ramifications.

On the one hand, the more partisanship determines outcomes, the stronger is the bias from the Republican gerrymander if the national vote is close. On the other hand, nationalizing elections offers two temporary advantages to the Democrats. First, the incumbency advantage seems to have largely disappeared in very recent elections.5 With more Republican than Democratic incumbents, this decline takes away from Republican incumbents the insulation of a strong incumbency advantage. Second, the “swing ratio,” the increment of seats won per increment of the national vote, should steepen as candidates lose control of their fates. Thus 2018 election could see a sharper partisan shift in Democratic seats per increments in Democratic votes than previously considered normal.

One final uncertainty about 2018 concerns who will vote and especially, voter turnout among the young. Prior to this century, age differences in partisan voting were relatively minimal, so it mattered little if the youth vote did not show up at midterm. In the 2010 and 2014 midterms, the combination of balancing plus the missing (mainly Democratic) youth vote worked together to create the overwhelming Republican success. The balancing argument works for the Democrats in 2018. But will the Democrats’ younger voters vote in sufficient numbers to make a difference?

References

Alberto Alesina and Howard Rosenthal. 1995. Partisan Politics, Divided Government and the Economy. Cambridge University Press.

Robert S. Erikson. 2016. Congressional Elections in Presidential Years: Presidential Coattails and Strategic Voting. Legislative Studies Quarterly. 41: 551-572.

Robert S. Erikson, Olle Folke, and James Snyder. 2015. Is there a Gubernatorial Helping Hand? Journal of Politics. 77: 491-504.

Joseph Bafumi, Robert S. Erikson, and Christopher Wlezien. 2010, Balancing, Generic Polls, and Midterm Congressional Elections. Journal of Politics. 72: 705-719.

Very helpful. I’ll just add one clarification regarding factors that are not directly mentioned in the model.

What about campaigning and candidate quality? That’s gotta make a difference, and we’ve heard a lot about these factors in some recent primary elections.

First off, we’d expect individual campaigning and individual features of the candidates to be more important in the primary than in the general election: General elections have just two candidates are more predictable and more determined by partisanship, in contrast to primaries, which can have multiple candidates with the same party and similar political ideologies; so in primaries it’s more important to differentiate yourself personally and communicate your existence and your positions to the voters.

That said, campaigning and candidate quality can make a difference in the general election—just ask that Republican who lost the Senate race in Alabama last year.

So, how do these factors fit into Erikson’s story? They come into the model in two ways. Most obviously, there’s the error term. The predictions have a lot of uncertainty, both at the national level and for individual races, and some of that comes down to who’s running, what resources they have, and how they campaign. The other way that campaigning and candidate quality come in is that they are affected by expectations: in a year where there everyone expects a swing toward the Democrats—and we’ve been expecting this for the past year, if not more—this motivates more people to run on the Democratic side and provides less incentives for Republicans to run. And of course it’s easier to run a strong campaign when public opinion is on your side. So campaigning and candidate quality are implicitly in the model, in that they partly explain how it is that the lead in the polls transfers into votes.

Beyond this there are further complications, as Erikson indicated with his comment about party effort being strategic.

To put it another way, the fact that outcomes are somewhat predictable based on data available a year before the election does not imply that candidates and campaigns don’t make a difference. What’s happening is that: (a) in expectation, the difference that will be made by campaigns and candidates is implicitly included in the predictions, and (b) the model’s predictions do have some uncertainty, and that uncertainty includes variation in candidate and campaign effectiveness, as well as uncertainty about national voting trends.