The regression line, that is.

John’s post on “the ‘formidable campaign’ narrative” offers some apt words of caution regarding one popular explanation for the president’s reelection. Alas, that’s a bit like trying to bail out the ocean with a bucket. There’s always more ocean; and there are always more plausible-sounding special explanations for Obama’s victory–including demographic shifts, early ads, clever micro-targeting, and a fortuitous storm, among many others. Some of them may even have merit. But what all of them have in common is that they are superflous. In 2012, as in 2008, Obama’s electoral performance was quite consistent with what might have been expected on the basis of political fundamentals. Perhaps the president deserves some sort of award for his unmatched fidelity to the “laws” (irony intended) of political science.

We have lots of distinct but broadly consistent statistical analyses of presidential election outcomes. My own favorite is based on just two factors: the income growth rate in the second and third quarters of the election year and the incumbent party’s tenure in office. The figure above combines these two factors by relating election outcomes to *tenure-adjusted* income growth, which simply subtracts 1.29 from the actual income growth rate for each consecutive term (beyond the first) that the incumbent party has held the White House. Details of the regression analysis appear after the jump.

Statistical analyses of this sort provide useful benchmarks for interpreting the result of any specific presidential election. For example, the 2012 election outcome (which appears almost exactly in the center of the figure) fits the historical pattern of post-war presidential election results splendidly; Obama’s popular vote margin was 3.8%, while his expected margin (based on the preliminary tabulations of real disposable income currently available from the Bureau of Economic Analysis) was 4.6%. (Subsequent revision of the income figures may push the 2012 data point to the left or right, but is unlikely to move it far from the regression line.) The 2008 election outcome (near the lower-left corner of the figure) was also quite consistent with the historical pattern; McCain trailed Obama in the popular vote by 7.3 percentage points—slightly *better* than expected, given the dismally low −0.8% mid-year income growth rate and eight years of “incumbent fatigue” due to George W. Bush.

Perhaps we need a Political Science Balanced Budget Act as a constraint on election interpretation. Anyone who wants to believe that Obama’s “formidable campaign” (or whatever) won him more votes than an ordinary campaign would have won should feel free to do so, but should be required to propose some equally plausible source(s) of vote *losses* to balance the ledger. You can’t just add a positive number to 4.6 (or whatever analogous baseline figure you prefer) and get 3.8.

Meanwhile, the scatterplot should also underline the point that not every election is as typical as both of Obama’s have been. From the perspective of this or any other model, future elections will produce some surprising landslides (like Eisenhower’s in 1956) and some surprising defeats (like Humphrey’s in 1968 and Ford’s in 1976). While it may well be that “the findings of the political science canon were largely confirmed by the 2012 election,” that is no guarantee that they will be largely confirmed again next time. (Certainly the canon is not being enriched so quickly that we are in danger of running out of surprises anytime soon.) As Neal Beck put it many years ago in a related context, “We Should Be Modest.”

Finally, on the subject of next time, this analysis suggests that any income growth at all is likely to be sufficient for reelection when a party has held the White House for only four years. (Indeed, the only incumbent party candidate in more than a century to have lost under that circumstance was Jimmy Carter, who ran for reelection in the midst of an election-year recession more severe than the Republicans’ in 2008.) That was a lucky thing for Democrats in 2012. But now things get harder. Holding the White House again in 2016–regardless of who the competing candidates turn out to be–will probably require a significantly more robust election-year economy than last year’s. On that score alone, Any Republican should, for now, be considered a modest favorite.

The figure above is derived from the following very simple regression analysis:

*Incumbent Party Margin* = 9.93 + 5.48 × *Income Growth* – 1.76 × *Years in Office*.

*Incumbent Party Margin* represents the incumbent party’s national popular vote margin in percentage points. *Income Growth* is measured by the change in real disposable personal income per capita in the second and third quarters of the election year (Q14 and Q15 of the president’s term), also in percentage points. *Years in Office* is a counter indicating how long the incumbent party has held the White House. The regression parameters are estimates based on data from the 17 presidential elections since the end of World War II.

This is an updated version of a regression model first proposed by Chris Achen and me in a 2004 paper entitled “Musical Chairs: Pocketbook Voting and the Limits of Democratic Accountability.” (We were interested in the implications of voters’ apparent focus on income growth over a very short time-horizon, just a fraction of the election year.) Including the three additional presidential elections that have occurred since then improves the fit of the model slightly, but leaves the parameter estimates essentially unchanged–unusual luck in this sort of exercise.

This very simple regression model “explains” more than three-quarters of the observed variation in election outcomes, with an average discrepancy in the incumbent party’s vote *share* of less than 3 percentage points. (The adjusted R-squared statistic is .77 and the standard error of the regression is 5.10. The standard errors of the regression parameter estimates are 2.46, 0.92, and 0.29, respectively; thus, they are easily “statistically significant” by conventional standards.)

It seems worth stressing that this regression model is not intended as an election forecasting tool. The relevant data on income growth are not available soon enough to be useful for forecasting; and in any case, an analysis aiming merely to maximize predictive accuracy would focus on state-by-state rather than national results, and would incorporate additional information such as contemporaneous polling data–which seems to me to take us outside the realm of “political fundamentals,” and to provide a less useful baseline for most analyses of campaign effects.