TIME SERIES OF ELECTION FORECASTS AND EVENTS

Figure 1 shows a time series of 2020 IEM forecasts with total contract volumes.Footnote ⁵ The upper panel shows Trump’s forecasted two-party vote share and probability of winning the popular vote. Trump’s VS/vote-share forecast generally has fallen between 45% and 50%, only rising above 50% for 14 days in April. Trump’s WTA/probability forecast peaked on February 26, 2020, at 47.4%; fell dramatically between then and March 25; hovered between 35% and 40% until May 31; dropped rapidly until July 5; and then became quite volatile. Figure 2 compares this forecast probability to incumbent candidates in previous IEM markets. Through press date, Trump’s winning probability fell significantly lower than other previous incumbent candidates, regardless of the number of days remaining before Election Day.

Figure 1 IEM Forecasts, Contract Volume, and Significant Price Movements Identified Using the Berg-Penny-Rietz Method

Figure 2 WTA Forecasts for Trump and Previous Incumbent Candidates

No other candidate faced a first-term impeachment, a global pandemic, an economic shutdown, and massive protests. Did these events affect Trump’s reelection chances?

Figure 1 tags significant, sustained WTA price changes using Berg, Penney, and Rietz’s (Reference Berg, Penney and Rietz2015) procedure. Politically significant events include the Mueller Report release (April 18, 2019), the impeachment vote (December 18, 2019) and trial (January 16–February 5, 2020), and the CARES Act (March 27, 2020). None of these events led to significant, sustained price movements. Five major Federal Reserve actions between March 15 and March 26, 2020, led to no significant daily changes and a total (insignificant) drop of 1.8 percentage points. These outcomes may have already been priced into the market. Having little effect, the worst quarterly GDP contraction ever recorded (−32.9% annualized) also was likely priced in when released on July 30, 2020. Significant events related to racial justice include Ahmaud Arbery killed (February 23, 2020), Breonna Taylor killed (March 12, 2020), George Floyd killed (May 25, 2020), Capitol Hill Autonomous Zone established (June 11, 2020), Rayshard Brooks killed (June 12, 2020), and Jacob Blake shot (August 23, 2020). Given their random nature, it is unlikely that these events were priced into the market. There were no significant, sustained WTA price movements according to the Berg-Penney-Rietz (Reference Berg, Penney and Rietz2015) procedure on any of these days.

Figure 3 shows the forecast of Trump’s winning probability versus (scaled) levels of the S&P500 stock market index, new seasonally adjusted jobless claims, and US COVID-19 cases.Footnote ⁶ In early March, Trump’s chances fell as the S&P500 crashed and COVID-19 led to economic shutdown in mid-March. However, although jobless claims rose dramatically in March through May, Trump’s chances varied little. His chances also changed little as the stock market recovered during the second quarter.

Figure 3 WTA Forecasts for Trump Versus Scaled Levels of the S&P500, New Seasonally Adjusted Jobless Claims, and New COVID-19 Cases

Trump’s chances fell again when civil rights protests began in earnest (May 26, 2020) and weekly average COVID-19 cases began rising again in mid-May through late July. Volatility increased dramatically after July 6, with six significant price movements in 29 days as states reopened; protests continued; federal law enforcement “surged” in US cities; new COVID-19 cases began decreasing; and companies reported Phases I and II clinical-trial results, moving into Phase III. Trump’s largest WTA gains occurred when biotech firm Moderna, Inc., published successful Phase I results on July 15 (+9.1¢, +45%) and when Russia announced October vaccination plans on August 2 (+6.4¢, +30%). Overall, Trump’s reelection chances appear to be more affected by protests and the pandemic than economic outcomes or individual political events.

CONFIDENCE INTERVALS AROUND FORECASTS

Events during this reelection cycle may lead to unusual uncertainty about the forecast. Sampling theory cannot assess the uncertainty in IEM forecasts because the IEM is not a random poll. We estimated forecast vote-share uncertainty using several methods (see details in the online appendix). We emphasize that considerable uncertainty remains.

First, at each horizon (i.e., days to the election), we use the standard deviation in forecast errors from previous presidential VS markets. Figure 4, panel A, shows the forecasted Republican vote share with one standard deviation confidence interval (CI) estimated from previous markets. This benchmarks the uncertainty inherent in the forecast distribution if this election has forecast errors similar to previous elections.

Figure 4 Republican Vote-Share Forecasts and Estimated Uncertainty

Notes: Panel A shows ±1 standard deviation CIs from previous vote-share markets. Panel B shows ±1 time-series standard deviation CIs. Panel C shows ±1 implied volatility standard deviation CIs. Panel D shows 16th to 84th percentile ranges using the Berg-Geweke-Rietz (Reference Berg, Geweke and Rietz2010) method.

Second, we assess uncertainty using the evolution of VS prices in the current market. If the market is efficient, VS forecasts should follow a random walk. Assuming this is true, we forecast the distribution of the random walk t-days in the future (i.e., Election Day). Figure 4, panel B, shows the forecasted Republican vote share with ± 1 standard deviation CIs assuming a random walk. Forecast volatility increases after large swings in VS prices and slowly erodes as the horizon falls. Overall, it shows much larger uncertainty than the first method. Current VS price changes reveal more uncertainty at this point in the election cycle than historical errors would suggest.

The third method integrates the information in the two IEMs, assuming consistent pricing across them. At each horizon, the VS market reveals the mean of a forecast vote-share distribution and the WTA market reveals a point on the distribution (p>0.5). This allows us to parameterize a log-odds normal forecast vote-share distribution and estimate its standard deviation. Figure 4, panel C, shows the forecasted Republican vote share with the resulting ±1 standard deviation CIs. We see significantly more uncertainty than in the first method, again suggesting greater uncertainty than observed in the past. Furthermore, it is more variable than the second method, which suggests that there is more to the uncertainty than the evolution of vote-share prices alone indicates.

The fourth method applies Berg, Geweke, and Rietz’s (Reference Berg, Geweke and Rietz2010) nonparametric approach to estimate the entire forecast distribution. Figure 4, panel D, shows forecast vote shares with 16th through 84th percentiles of the numerically estimated distributions (approximately ±1 standard deviation for a normal distribution). Closer to the first method, this shows significantly less uncertainty than the second and third methods, with more stable uncertainty estimates. On 77% of the days through August 26, 2020, the Berg-Geweke-Rietz forecasted distributions show two peaks: one (less likely) with Trump winning the popular vote by a small margin and one (more likely) with Trump losing by a large margin. Figure 5 illustrates a typical example. Shifting weight between these two distinct possibilities may drive the current elevated uncertainty about the vote share.

Figure 5 Sample Two-Party Vote-Share Distribution on August 2, 2020, Using the Berg-Geweke-Rietz (Reference Berg, Geweke and Rietz2010) Method

On August 26, 2020, the forecasted Republican vote share was 49.95% from the VS market alone, with a median of 48.36% according to the Berg-Geweke-Rietz forecasted distribution. At this 69-day horizon, ±2 standard deviation CIs were 42.84% to 57.06% using historical errors, 32.87% to 67.04% using the time-series method, 49.75% to 50.15% using implied volatility, and approximately 43.47% to 53.33% using the Berg-Geweke-Rietz method. Overall, considerable uncertainty remains in that all ±2 standard deviation CIs overlap 50% vote share.