In Unequal Democracy, Bartels undertakes to prove that this is not merely a statistical fluke. Bartels argues that the dramatic increase in income inequality over the past 50 years is a direct result of the policies of Republican presidents, not impersonal (or inevitable) market forces.
After reading the book, I'm still not 100% persuaded, but not because Bartels' case was weak—it wasn't. To the contrary, it was a tour de force: cogent, methodical, data-driven, and statistically sophisticated. I just don't think there's enough data to arrive at a definitive answer. Specifically, I think monetary policy played a big role in income growth rates over the past 50 years; we simply don't have enough data to tease out the effects of monetary policy on income growth.
However, Bartels' argument was much more convincing than I expected. For my money, the most convincing piece of evidence was the fact that almost the entire difference in income growth under Democratic vs. Republican presidents occurs during the second year of each administration (the year you would expect a president's policies to start having an effect). Here's the chart Bartels provides:

As you can see, Democratic presidents have consistently produced extremely strong income growth in their second ("honeymoon") year, while Republican presidents have consistently produced extremely weak income growth in their second year. Moreover, this doesn't merely reflect a cyclical pattern in income growth, because it holds in honeymoon years with and without partisan turnover.
That's remarkable. Income growth during the first, third, and fourth years of each administration was virtually identical, regardless of party. This implies that presidents have little impact on income growth in those years, but substantially affect income growth in the second year of their administrations. The fact that Democrats have systematically produced higher-than-average income growth in the second year of their administrations, and Republicans have systematically produced lower-than-average income growth in the second year of their administrations, strongly suggests that the difference is attributable to the president's party affiliation.
The book is an absolute treasure trove of interesting statistical findings like this, many of them based on original work. Not all the evidence in the book is favorable for the Democrats either—for example, Bartels finds that both Democratic and Republican senators are completely unresponsive to the preferences of low-income constituents. This makes Bartels' argument all the more credible.
Highly recommended.