In any case, the largest partisan differences in income growth, by far, occur in the second year of each administration.
The link, by the way, answers many objections to his basic thesis. View this graph if you don’t already know the argument. The core claim is that Republican Presidents are better for the rich and Democratic Presidents are better for the poor, and to a striking degree.
I view the statistical significance of the Bartels result as stemming from monetary policy. Republicans are more willing to break the back of inflation and risk an immediate recession. Alternatively, it could be said that central bankers expect enough support for tough, anti-inflation decisions only from Republican Presidents. (Note that Jimmy Carter, who did support Volcker, is in fact the single Democratic outlier.) Note that without the monetary policy effect, only a few data points, mostly from very recent times, support the basic claim. Without the monetary policy effect, I do not think that statistical significance would remain. Furthermore other plausible channels for income inequality effects, such as tax and regulatory decisions, would not be concentrated in the second year of each administration. Monetary policy decisions would be. A recession, by generating more unemployment, hurts the poor the most in proportional terms.
So what does this all mean?
Inflation is good for the poor in the short run, since many poor are debtors. But inflation is bad for the poor in the long run. Just ask anyone who lived through the New Zealand inflation of the 1970s.
So Bartels could have entitled his key graph: "Democratic Presidents live for the short run and we need a Republican President every now and then."
Addendum: Even Paul Krugman wonders about the basic mechanism driving the result.