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June 08, 2012 10:19 AM Interpreting a Before-After Change as a Causal Effect: Campaign Spending and the Wisconsin Election

By Andrew Gelman

John quotes Seth Masket’s claim that it didn’t matter that the Republican outspent the Democrat by 7-1 in the recent governor recall election in Wisconsin. Masket writes:

Walker and Barrett faced each other less than two years ago. Walker beat Barrett by five points back then, after raising $11 million to Barrett’s $6 million. That is, Walker raised 65% of the funds raised by the Republican and Democratic candidates that year and he won 53% of the two-party vote. This week, Walker raised about 88% of the funds raised by the two candidates and he won—wait for it—54% of the two-party vote.
So there’s your money effect, folks. Go from a 2:1 money advantage to a 7:1 money advantage, and it could increase your vote share by a full percentage point! Woo hoo!

I really really really don’t like this sort of snappy “woo hoo” reply. Nor do I like the subtle minimization of the effect (note how Masket writes “it could …”, thus implicitly taking the 1 percentage point as an upper bound rather than an estimate of the effect).

There’s been a lot of research showing that money matters in campaigns, but more so in nonpartisan contests such as referenda and less so in highly partisan contexts. I think that’s the way to address such questions. Not by taking a single before-after comparison and treating it as a causal effect. That’s just sloppy.

That said, the numbers from a rematch election are relevant, as long as you don’t step off the cliff by taking the before-after difference and interpreting it as a causal effect. Masket criticizes a news report for saying that “this is the biggest story in the campaign so far: Money matters.” We already know that money matters, so you could argue that the news reporter is overinterpreting this one election—-but I really don’t like this idea of directly interpreting a before-after difference as a causal effect. As political scientists, I think we should be a bit more careful with our snappy rejoinders.

[Cross-posted at The Monkey Cage]

Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University.