Republicans are expected to win the White House under two economic models that have accurately forecast presidential elections for decades.

A third model run by Moody’s Analytics predicts Democrats will win the White House, in part because of President Obama’s rising approval rating.

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The three models are being challenged like never before by the presence of GOP presidential front-runner Donald Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE, whose campaign has shaken up politics.

Trump’s fights with Ted Cruz Rafael (Ted) Edward CruzLoeffler calls for hearing in wake of Netflix's 'Cuties' Health care in the crosshairs with new Trump Supreme Court list 'Parks and Rec' cast members hosting special reunion to raise money for Wisconsin Democrats MORE and his other GOP rivals have electrified his supporters but have turned off other voters. A Washington Post-ABC poll last week found that 67 percent of registered voters held an unfavorable view of the outspoken billionaire. That has given hope to Democrats that even with a weakened Hillary Clinton Hillary Diane Rodham ClintonHillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers The Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters FBI chief says Russia is trying to interfere in election to undermine Biden MORE as their nominee, their party could cruise to victory.

“As economists this is a very unusual election and there’s a lot more uncertainty introduced this time around that could upset the balance and the historical relationship of how marginal voters vote,” said Dan White, an economist with Moody’s Analytics who oversees the firm’s monthly election model.

Ray Fair, a Yale professor who launched his model in 1978, told The Hill that while all elections include unruly features that an economic model can’t pick up, “this one seems particularly unusual.”

“If there’s any time in which personalities would trump the economy it would be this election,” Fair said.

Fair’s model has correctly forecast all but three presidential races since 1916 but was wrong in 2012, when it predicted a narrow loss for Obama to Mitt Romney.

It relies on just three pieces of information: per capita growth rate of gross domestic product in the three quarters before an election, inflation over the entire presidential term and the number of quarters during the term growth per capita exceeds 3.2 percent.

Given the sluggish economy, his model doesn’t show enough growth under Obama to predict a Democratic win in the election. In his most recent forecast from January, his model predicted a 45.66 percent share of the presidential vote for the Democratic candidate, less than the 49 percent it predicted in 2012.

The other two models, unlike Fair’s, consider the incumbent president’s approval rating. In both cases, Obama’s improving favorability helps his party’s chances of winning the White House. But only one of those models predicts a Democratic win.

Emory University’s Alan Abramowitz, whose model has correctly predicted every outcome since 1992, forecasts a Republican win.

It measures the incumbent president's job-approval rating by the end of June of the election year; the economy's growth during the first half of year, especially during the second quarter; and how long the incumbent party has been in the White House.

By this methodology, the Democratic candidate can expect to receive 48.7 percent of the vote — with Obama's approval rating at 50 percent — according to his most recent calculation.

But since that prediction, Obama’s approval rating has ticked up to 52 percent.

Moody’s arrives at a similar result, but one that is better for Democrats.

That model, which hasn’t missed an election since it was created in 1980, awards Electoral College votes to each party based on state-by-state outcomes. The most important economic variable is income growth by state, including job and wage growth, hours worked and the quality of the jobs being created in the two years leading up to an election. The model also factors in home and gasoline prices on a state level, as well as presidential approval numbers.

The Moody’s equation also includes an additional dummy variable that penalizes Democrat incumbents, stemming from the theory that Democrats and Democrat-leaning independent voters are more likely to switch sides and vote for a Republican candidate than vice versa.

Moody’s latest model, set for release this week, shows that the Democratic nominee would take 332 electoral votes compared to 206 for the Republican nominee.

The main driver of the change was the president's approval rating, a first-time variable added into the model this year, White said.

The president's approval rating has risen 3 percentage points since the first model was released in August.

White says the unruly GOP primary may be helping Obama.

“The gains lately could be construed as a reflection of what a mess the primary process has become in recent weeks,” he said. Trump, who has high unfavorable ratings among some voter groups, could be giving Obama’s approval rating a boost.

Abramowitz told The Atlanta-Journal Constitution last week that “all the noise being made by the presidential campaign, especially by the Republican campaign, has taken attention away from what may turn out to be more significant for the general election — Barack Obama Barack Hussein ObamaThe Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon Trump appointees stymie recommendations to boost minority voting: report Obama's first presidential memoir, 'A Promised Land,' set for November release MORE’s rising approval rating.”

His research has found that the president’s approval rating is an essential predictor of the election results even when the president is not on the ballot, and Obama's has risen to its highest level in many months.

White said that one of the most frequently asked questions he gets is whether a Trump variable could be added into the model to test out how his brand of fireworks factors in.

No way, he said.

“The model doesn’t know or care if there are two or 10 candidates,” he said. “It knows the economics and whether marginal swing voters will keep the incumbent party in or not.”

In fact, their models are designed to sweep away the effects of boisterous personalities and the usual ebbs and flows of a long presidential campaign season and instead track specific economic factors that voters deem most important.

Justin Wolfers, an economics professor at the University of Michigan and senior fellow at the Brookings Institution who has researched the reliability of economic models, said that while every election is different the “point of the statistical models is to try to find the underlying similarity across all of them.”

“So the logic that says that these models should have worked over the past few decades also says that they should work in this election cycle, too,” he told The Hill.

“There's no reason to think the models should do better or worse in 2016,” he said.