These models should not be taken seriously. They all have tiny sample sizes and a huge number of potential explanatory variables meaning that researchers can cherry pick to get whatever result they want. Re sample size, one model dates back to 1952. 1/ https://www.washingtonpost.com/news/powerpost/paloma/the-finance-202/2020/04/09/the-finance-202-the-coronavirus-economy-is-already-hurting-trump-s-reelection-chances-economists-say/5e8e45b588e0fa101a75e650/?p9w22b2p=b2p22p9w00098&tid=a_classic-iphone&no_nav=true

Presidential elections happen every 4 years meaning there are 17 data points through 2016. If you picked 17 uncorrelated time series variables at random and threw them into a regression along with a constant (intercept), you’d get a perfect fit. It would be meaningless. 2/

There are way more than 17 variables that matter to election outcomes. Thus, a valid time series model to predict presidential election outcomes does not exist. Even if there were a model that is a good and plausible explanation for past outcomes, 3/

the model changes over time. Where does a pandemic fit in your data from 1952 to 2016, or the increased polarization of the political parties, or the phenomenon of Donald Trump? If model parameters change over time, simple regression models are invalid. 4/

Economists have known for a long time that time series regressions can produce silly results because you can search for variables that seem to have explanatory power and you will be sure to find them. For example, swan migrations and sun spot activity seem to explain GDP. 5/

They don’t, of course, but the exercise shows that with lots of potential explanatory variables and few data points, it’s not hard to find seemingly statistically significant relationships. The WaPo article starts by saying an election model suggests the economic 6/

collapse could doom Trump’s re-election hopes. But later it cites another seemingly impressive model which draws the opposite conclusion. It has six explanatory variables and has correctly predicted the winner in every election since 1952. You could find many models 7/

with 17 observations and 6 variables (plus a constant) that get the sign of the vote margin right. And every one would be useless in predicting the outcome of the 2020 election. A much better, although still imperfect, approach is the kind of structural model 8/

that @FiveThirtyEight builds. They draw in lots more data—from polls across states and over time—and apply judgement, which adds additional informaton if it is well founded. This solves the small sample size problem. You still have to scrutinize the models and data carefully, 9/

but the results aren’t totally spurious. 10/10

Copying @jbernoff for his BS files.