Attendees hold signs as they listen to speakers during a rally to mark the fifth anniversary of the Supreme Court's Citizens United decision at Lafayette Square in Washington last year. (Drew Angerer/Getty Images)

Tilman Klumpp is an associate professor of economics at the University of Alberta. Hugo M. Mialon is an associate professor of economics at Emory University. Michael A. Williams is a director at the economics consulting firm Competition Economics LLC.

In January 2010, the Supreme Court issued its decision in Citizens United v. FEC. In this landmark ruling, the court held that the First Amendment prohibits the government from restricting independent political expenditures by corporations and labor unions. Proponents hailed the decision as a victory for free speech, while opponents — including both remaining 2016 Democratic presidential candidates — have criticized the court for opening the floodgates to unprecedented amounts of money in U.S. elections.

As the country gets set to elect its next president, along with 435 representatives, 34 senators and thousands of state and local office holders, what do we know about the effects of independent political spending in elections? Quite a bit, it turns out, if we look in the right places. Those places are the states.

Unlike the federal government, some states never restricted independent political expenditures and were, therefore, unaffected by the Citizens United decision. Other states had restricted such expenditures and were forced to remove the restrictions after the ruling. In a study that will be published in a forthcoming issue of the Journal of Law and Economics, we analyzed data from more than 38,000 state legislative races between 2000 and 2012, in both groups of states. Our objective was to figure out what impact, if any, Citizens United had on who gets elected to state legislative office. In states that previously banned corporate and union expenditures, we found that Citizens United shifted the odds of electoral success detectably and in a clear direction: from Democratic to Republican candidates.

Many things determine who wins on Election Day, and simple correlations don’t automatically indicate causal effects. States that were forced to lift their bans on independent expenditures may have elected more Republicans in 2010, but this surge could have been caused by a reaction to the passage of the Affordable Care Act, the recession or any other issue on voters’ minds at the time. And while states with independent expenditure bans may have elected more Democrats before 2010 than did states without such bans, this does not necessarily have anything to do with how the states regulated election finance. There are many reasons some states vote differently from others, including historical, cultural and demographic differences.

So how can we isolate the effect of a specific factor such as Citizens United? Enter John Snow, a British doctor and epidemiologist who, in 1855, pioneered a statistical approach called difference-in-differences. Never mind that Snow was concerned with a very different public policy issue — the effect of water contamination on cholera rates. His technique applies equally well in our setting. Here’s how it works.

First, we calculated the difference in the percentage of state legislative elections won by Republican candidates before and after 2010 in states that previously restricted independent spending. This difference measures the combined effect of Citizens United as well as that of Obamacare, the recession and any other factor on electoral outcomes. In estimating this effect, we controlled for as many known variables as we could, including how much money a candidate’s campaign raised directly from donors. We then computed the same difference for states that did not restrict independent spending. This difference measures the effect of Obamacare, the recession, etc., but not Citizens United. Lastly, we took the difference between the first and the second numbers. This final difference represents the effect of the factor we know was present in the first group of states but not the second: Citizens United.

With this approach, we found that the chance of Republican candidates winning state legislative seats increased by about four percentage points on average as a result of Citizens United, and by 10 or more percentage points in several states. The decision also made it more difficult to unseat Republican officeholders, cementing the already strong financial advantage of political incumbents, and reduced the number of Democratic candidates who ran for office. Finally, the data provide evidence that Citizens United discouraged ordinary people from making monetary contributions to candidates’ campaigns, an effect feared by critics of the decision early on.

What does this mean for the future? Corporate- and union-backed super PACs and other groups are expected to pour hundreds of millions of dollars into this year’s federal and state races. Given this staggering magnitude, independent political expenditures are sure to receive renewed scrutiny by politicians and the public in the years to come — and may, perhaps, one day be revisited by the Supreme Court. The saliency of the issue stems from the belief that unlimited outside spending in elections, even if protected by the First Amendment, affects outcomes. The evidence shows that such effects are measurable and real.