US PRESIDENTIAL ELECTIONS

In words, the presidential election model can be summarized in the following way

(Lewis-Beck and Rice Reference Lewis-Beck and Rice1984, 7):

(1) $${\rm{Presidential\ Vote}} = {\rm{Political\ Popularity}} + {\rm{Economic\ Growth}}$$

where the Presidential Vote = the two-party share of the national popular vote for the president’s party, Economic Growth = the GNP growth in the first two quarters of the election year, and Political Popularity = the job approval rating for the president in the July Gallup Poll.

This political economy model essentially views the election as a referendum on how well the president has handled economic and non-economic issues. Other things being equal, the better the performance on these two dimensions, the better his or her party will do. Estimating the model with ordinary least squares (OLS) across the post-World War II period yields these results:

(2) $$\eqalign{ & {\rm{Vote}} = 37.50 + .26 * {\rm{Popularity}} + 1.17 * {\rm{Growth}} \cr & \left( {14.83} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {4.45} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {2.04} \right) \cr}$$

To forecast the 2016 presidential election, we simply plug in the appropriate values of Popularity and Growth. Based on data reported as of August 26, 2016. Popularity = 51 and Growth = .20, which yields the following point estimate:

(3) $${\rm{Vote}} = 37.50 + .26\left( {51} \right) + 1.17\left( {.20} \right) = {\rm{51}}{\rm{.0}}\,\% \,{\rm{of\ the\ popular\ two - party\ vote\ for\ the\ Democrat}}{\rm{.}}$$

How accurate do we expect this forecast to be? First, over the time series of elections, it correctly picked the winning party 14 out of 17 times (missing only 1960, 1968, and 1976), or 83% of the time, based on our out-of-sample testing (table 1). To examine out-of-sample error, we ran a series of jackknife tests. That is, taking each year in turn, we dropped it from the data, re-estimated the model, then predicted that out-of-sample year and examined the forecasting error. We found seven elections with a negative error greater than -1.0. Because our forecast is 51.0, if it has an error greater than -1.0, we would forecast a victory for the wrong party. This translates into a 41% chance that this forecast would be wrong (i.e., 7/17 = .41), leaving a 59% chance that this forecast of a Democratic victory is correct. Such a high level of uncertainty, barely greater than 50/50, suggests that the race will be won or lost by a very small margin of the popular vote. Put another way, it will be a squeaker, too close to call at any meaningful distance before the election itself.

Table 1

Presidential Election Predictions with the Political Economy Model

CONGRESSIONAL ELECTIONS

We have also been forecasting US House and Senate elections since the early 1980s (Lewis-Beck and Rice Reference Lewis-Beck and Rice1984; Reference Lewis-Beck and Rice1985), with occasional “improved” updates as well (Lewis-Beck and Tien Reference Lewis-Beck and Tien2010; Reference Lewis-Beck and Tien2015). For our 2016 congressional forecasts, we also make a return to our original efforts, expressed for the House as follows:

(4) $${\rm{House\ Seat\ Change}} = {\rm{Political\ Popularity}} + {\rm{Economic\ Conditions}} + {\rm{Midterm\ Status}}$$

where House Seat Change = number of seats lost or gained by the president’s party, Political Popularity = the job approval rating for the president in the June Gallup Poll, economic conditions = growth rate of real disposable income over the first two quarters of the election year, Midterm Status = 0 for presidential election years and = 1 for midterm election years.

Thus, for the House forecast, we also employ a political economy model based on a classic referendum model, rooted in strong theory. That is, electoral success for the incumbent in House elections depends on how well the president and his or her party have handled economic and non-economic issues, conditioned on whether it is a midterm. Estimating (OLS) the model in the post-war period yields the following:

(5) $$\eqalign{ & {\rm{House\ Seat\ Change}} = - 44.97 + .82 * {\rm{Popularity}} + 4.95 * {\rm{Income}} - 28.3 * {\rm{Midterm}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\rm{ - }}3.39} \right)\,\,\,\,\,\,\,\,\,\,\left( {3.27} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {2.88} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( { - 4.39} \right) \cr}$$

$${\rm{R}} - {\rm{squared}} = {\rm{.59,}}\,{\rm{Adj}}{\rm{.\ R - squared}} = {\rm{.55}}\,{\rm{Root\ mean\ squared\ error}} = 18.34$$

$${\rm{Durbin - Watson}} = 1.86{\rm{,\ N}} = {\rm{34\ elections}}\,\left( {{\rm{1948 - 2014}}} \right)\,{\rm{and\ the\ other\ notation\ is\ as\ with\ Eq.2.}}$$

To use this equation to forecast the 2016 House elections, we plug in the appropriate values (as of July 29, 2016), producing the following seat change estimate:

(6) $$\eqalign{ & {\rm{House\ Seat\ Change}} = - 44.97 + .82\left( {53} \right) + 4.95\left( {.83} \right) - 28.3\left( 0 \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\rm{3\ seat\ gain\ for\ the\ Democrats}}{\rm{.}} \cr}$$

How certain is it that Republicans will retain their House majority after the 2016 elections? The model prediction would have to be off by at least 27 seats for the Democrats to regain the House majority. Only once in the model’s time series has it missed by more than that amount (1948). Thus, the model certainty that Republicans will retain their House majority is 97%.

Senate elections, we argue, also respond to the same economic and non-economic evaluations of the president, in the context of certain cyclical factors. In other words, Senate elections are referenda on how well the president has been handling the economy and political issues, conditioned on the political calendar. Only one-third of the Senate seats are up for election every two years. Thus, how many seats the president’s party has up for election, plus the midterm status, also influence Senate election outcomes. In words, our Senate forecast reads as follows:

(7) $${\rm{Senate\ Seat\ Change}} = {\rm{Popularity}} + {\rm{Economy}} + {\rm{Midterm\ Status}} + {\rm{Seats\ Exposed}}$$

where Senate Seat Change = number of seats lost or gained by the president’s party; Seats Exposed = number of seats the president’s party has up for reelection; the other variables are as defined in equation 6. The estimated (OLS) model yields the following results:

(8) $$\eqalign{ & {\rm{Senate}} = 2.88 + .14 * {\rm{Popularity}} + .89 * {\rm{Income}} - 2.52 * {\rm{Midterm}} - .70 * {\rm{Seats Up}} \cr & \,\,\,\,\,\,\,\,\,\left( {.98} \right)\,\,\,\,\,\,\,\,\,\,\,\left( {3.40} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {3.17} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( { - 2.44} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( { - 5.75} \right) \cr}$$

R-squared = .68, Adj. R-squared = .63, Root mean squared error = 2.92

Durbin-Watson = 1.85, N = 34 elections (1948-2014) and the other notation is as with Eq.2.

$$R-squared = .76\,Adj. R-squared = .73\,Root\,Mean Squared Error = 2.84$$

$$Durbin - Watson = 2.36\,N = 17\,elections, 1948 - 2012\,Figures in parentheses = t-ratios\,Asterisk indicates statistical significance = .05,\,one - tail.$$

All variables are statistically significant at the 0.05 level, one-tail. This means that the president’s party can expect to pick up one additional seat for every seven points added to the president’s approval rating, ceteris paribus. A better economy, as measured by personal disposable income, also yields additional seats on an almost one-to-one basis (.89). Further, the president’s party is disadvantaged in midterm years, with an expected loss of two and one-half seats. Moreover, for every additional 10 seats it has up for reelection, it can expect to lose seven seats, holding all else constant.

What does this mean for Senate control in 2016? Obama’s June approval rating is 53%, disposable personal income change over the election year has been .83, and the Democrats have 10 seats exposed in this presidential election year (using data reported as of July 29, 2016). This yields a forecasted gain of four seats for the Democrats, which is exactly what the Democrats need to give them majority party control of the Senate (assuming the Democrats win the presidency and the vice-president then votes with the Democrats). But, if the forecast of four Democratic seats turns out to be three instead (3 - 4 = -1) then Republicans retain control of the Senate. Therefore, if the model is off by one seat (-1) Senate control stays with the Republicans. In the 34 elections in the time series, it has produced an error greater than -1 a total of 13 times (13/34 = .38). Thus, the certainty of this forecast of Democratic control of the Senate is only 62%. Again, barely better than a coin flip.