President Obama’s Strongest Support is from High Marginal Tax Rate States

President Obama’s strongest support in last week’s election was from states that have the highest marginal tax rates for the top earners in their states.  The average top marginal tax rate in the states (and Washington DC) that President Obama won is 6.24% while the average top marginal rate in the states that Mitt Romney won is 4.92%.

In addition, a simple regression of President Obama’s percentage margin of victory (or loss) against the top marginal tax rate in a state indicates that each one percentage point increase in a state’s marginal tax increased the President’s margin of victory by 3.35%.  This means the higher the marginal tax rate paid by top earners for the state income tax, the greater the support for President Obama.  The following graph shows the relationship between the margin of victory and top marginal tax rates.  The regression relationship is statistically significant.  (The t-statistic on the marginal tax rate variable is 2.92.)

There are, of course, other important factors influencing election outcomes.  But it appears that the President’s strongest supporters and the base of the Democratic party tend to live and work in states that have the highest marginal income tax rates.  The Republican party and the President’s opposition live and work in states with lower marginal tax rates.  Both sides have been elected to come back to Washington and work on a solution to avert the fiscal cliff and achieve some type of Federal income tax reform.  A key area of disagreement is about the top marginal tax rate for the highest income earners.  A compromise on this issue may be difficult to achieve given the policy preferences and philosophies of each party’s base.

Note: the top state marginal tax rates used in this analysis are from the Tax Foundation.

Nate Silver’s Value Added and Systematic Forecast Errors

Nate Silver had a very good night on November 6th.  He forecast that President Obama would win 313 electoral votes and was within 5.7% of the 332 electoral votes received by the President.  He proved to be more accurate than many individual pollsters.  Silver bases his projections on state poll averages, national polls, “state fundamentals” and trends in polls.  Anyone could have forecast the election outcome in at least 35 states, so the best way to understand Silver’s contribution is to focus on states where the election was expected to be close.  Both state poll averages and Silver’s projections underestimated President Obama’s strength in swing states, but Silver’s 538 model had substantially less systematic bias than state poll averages.

Nate Silver has brought statistical analysis of elections to the masses (or at least to the readers of the New York Times).  His blog makes it clear that when an average of polls prior to the election shows a candidate has a 55-45 advantage, it doesn’t mean that she will lose 45% of the time.  It means instead that she will almost certainly win the election.  Poll averages improve the precision of forecasts because errors due to sampling variation are decreased.  More importantly, the 538 model incorporates “state fundamentals” and poll trends to improve the precision of  forecasts. 

Consider the following comparison of state poll averages, Silver’s projections and election outcomes in 11 states that were expected to close on election day:

State State Poll Avg. Silver’s Projection Election Outcome
Colorado DEM:  1.9 DEM:  2.5 DEM:  4.7
Florida REP:    0.7 D/R:    0.0 DEM:  0.9
Iowa DEM:  2.6 DEM:  3.2 DEM:  5.6
Michigan DEM:  4.7 DEM:  7.1 DEM:  9.5
Nevada DEM:  3.6 DEM:  4.5 DEM:  6.6
New Hampshire DEM:  2.6 DEM:  3.5 DEM:  5.8
North Carolina REP:    1.9 REP:    1.7 REP:    2.2
Ohio DEM:  3.0 DEM:  3.6 DEM:  1.9
Pennsylvania DEM:  4.6 DEM:  5.9 DEM:  5.2
Virginia DEM:  1.3 DEM:  2.0 DEM:  3.0
Wisconsin DEM:  4.3 DEM:  5.5 DEM:  6.7

Notice that in every one of these states Silver’s 538 model predicted that the President would outperform the polls.  Although this infuriated many conservatives Silver was correct, on average.  The President’s vote share in the states listed above was 2.0 percentage points higher than forecasted by poll averages.  The President even out-performed Silver’s forecast by receiving 1.1 percent more of the votes cast than predicted by the 538 model.  This occurred despite the fact that Mitt Romney exceeded Silver’s expectations in North Carolina, Ohio and Virginia. 

The standard deviation of the forecast error was 1.7% for state poll averages and 1.4% for Silver’s model (about 18% lower) in the eleven swing states listed above.  Thus in the states where the election was contested Silver’s simulations were slightly more accurate than a simple average of state polls.  However, the most important contribution of the 538 model in 2012 was that it substantially reduced the systematic underestimate of President Obama’s vote share from 2.0% to 1.1%.

The systematic gap between vote totals and state polls has little to do with sampling variation and more to do with mis-estimation of voter enthusiasm and turnout.   While averages of state polls provide more efficient forecasts than individual polls in a given election there will be systematic errors across states because of the difficulty in forecasting voter turnout and assessing voter enthusiasm.  Based on the past four presidential elections the systematic poll gap favors Democrats in some elections and Republicans in others and is likely to be similar in magnitude to the 2.0% difference observed in 2012.  If the 2.0% systematic gap in poll forecasts had favored Mitt Romney on Tuesday he would have received 266 electoral votes and lost the presidency by less than 5,000 votes in New Hampshire.

Nate Silver simulations are valuable when they reduce the magnitude of the systematic gap between state poll averages and election outcomes as they did in 2012.  His work correctly identified that polls were underestimating President Obama’s support even though the 538 model also contained systematic bias.  This source of forecast error can’t be reduced by taking more polls but can be mitigated somewhat by supplementing poll averages with additional information.

Nate Silver and the Accuracy of Late Presidential Polls

In my blog post yesterday I explained why Nate Silver’s projection that President Obama has more than an 85% chance of winning the election tomorrow might be inaccurate.  Yesterday Mr. Silver listed 60 state poll averages over the three presidential elections from 2000 to 2008 in his New York Times blog.  The average state on his list had been the subject of between 6 and 7 late polls leading up to the election.  The average prediction error, the difference between the actual election outcome and the average of state polls, was about one-quarter of a percentage point averaged across all states and all years.  The margin of error, or 95% confidence interval, for the prediction error in a single state and election was plus or minus 6.38%.  Averages of state polls are accurate, on average, but can be widely inaccurate from one state/election to the next.

Mitt Romney needs to win the bulk of swing states in order to reach 270 electoral votes.  This is more difficult to do if unexpected election outcomes are statistically independent across states.  For example, if nine swing states are toss-ups and the challenger needs to win at least seven of them to win the electoral college, the challenger will lose 91% of the time with statistical independence across states.  If however, success in one state is correlated with success in another, the challenger’s likelihood of winning can be much different from 9%.   Everyone, including Nate Silver, knows that election surprises are correlated across states.   Nationwide differences in voter enthusiasm, turnout, late deciding voters and under-represented voters can all make prediction errors positively correlated across states.  For Mitt Romney to win tomorrow the nationwide component of the prediction error in polls must break his way and be large enough for him to carry the bulk of the swing states.

Nate Silver believes his model has accurately captured the true correlation in prediction errors, or unexpected election outcomes, across states and polls in 2012.  This is a very difficult task because: (1) we won’t know the 2012 prediction errors until the election is over, (2) polls differ in their methodology and possible biases and (3) correlations in prediction errors among states and polls in previous elections need not hold today.  Mr. Silver is savvy enough to recognize that regardless of the election outcome his statement that Mitt Romney is more than a 6:1 longshot will be hard to refute.   By late tomorrow, however, it will be easier to evaluate his prediction that the President will win 307 electoral votes.

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