Jimmy Greene, Nelba Marquez-Greene, parents of Sandy Hook Elementary School shooting victim Ana Marquez-Greene, shown in the large photograph, and Nicole Hockley, right, mother of victim Dylan Hockley, during a news conference at Edmond Town Hall in Newtown, Conn, Jan. 14, 2013. AP One year on from the Connecticut shootings and the “gun-control paradox” still reigns in U.S. politics. In the wake of the murder of the 20 children and six staff at Sandy Hook Elementary School, the response from President Barack Obama was quick and unequivocal: new regulations on guns were an imperative.

As it turned out, even a modest effort to strengthen background checks on private sales at gun shows and online failed on April 17 when the Senate did not pass the Manchin-Toomey amendment. What is puzzling is that all polls at the time showed overwhelming public support for this regulation. For example, a CBS News/New York Times poll carried out in Jan. 2013 found that 92% of Americans supported an expansion of background checks. Similar figures were found in other polls carried out in April 2013. As Obama put it: “How can something have 90% support and yet not happen?”

Our research tries to explain what appears to be a failure of democracy. We study how electoral incentives might lead politicians to take a pro-gun stance, in line with the interests of a minority of the electorate.

Model behaviour

To this purpose, we formulate a simple theoretical model in which politicians vote on a “primary” and a “secondary” policy issue. We see the primary issue as one that a majority of voters cares relatively more about, such as the level of public spending. The secondary issue is meant to capture gun control, a policy that a minority cares more intensely about. However, citizens have only one vote to make their representatives accountable on a bundle of policy issues.

Politicians may then pander to the minority on the secondary issue, without losing too much support from the majority. The model demonstrates that understanding politicians’ decisions on gun control requires taking into account not only the direction of voters’ preferences, but also their intensity.

The model delivers three main testable predictions. First, politicians should be more likely to take a pro-gun stance at the end of their terms, when their policy choices have a bigger impact on their re-election prospects. Second, politicians who are in favour of gun regulations and are concerned with re-election are likely to “flip-flop” on gun control since they face a tension between their policy preferences and their re-election prospects. Finally, the proximity of an election should have no impact on the voting behaviour of politicians who are against gun regulations and/or are not concerned about re-election.

We brought these predictions to the data by analysing the determinants of votes on gun regulations that have been cast in the Senate since the early 1990s. In particular, we examined whether proximity to elections affected voting behaviour on gun control, exploiting the fact that senators serve six-year terms and that one third of them is up for re-election every two years. For any given vote, the staggered structure of the Senate allows us to compare the behaviour of senators belonging to three different “generations” — who will be up for re-election at different times.

Election flip-flop

Our results confirm that senators who are closer to re-election are significantly more likely to vote pro-gun. We find that only Democratic senators flip-flop on gun control, while Republican are always more pro gun and do not change their voting behaviour throughout their terms. The effect is also sizeable: in the last two years of their term, the probability that Democratic senators vote pro gun increases by between 15.3% and 18.9%.

We have included a wealth of controls to account for characteristics of legislators (including different party affiliation, gender, age, and contributions received from gun-rights and gun-control lobbies). We also catered for different characteristics of states (their different violent crime rates, for example, and the number of subscriptions to gun magazines as a proxy for the overall pro-gun stance of voters in the state).

In order to illustrate our results, we can use our estimates to calculate the average probability that a senator will vote the way the gun lobby wants: or “pro gun”. These calculations distinguish between Democrats and Republicans and also the time left until their re-election. Senators in Generation 1 are the farthest away from the ballot while those in Generation 3 face re-election within two years. The graph below reports these probabilities (the circles and triangles) along with their confidence intervals (the bars, representing the range of values that contain the true probability).

The circles and triangles are the predicted probabilities of different generations of senators, while the bars represent their 95% confidence interval. CEPR

Visually, it is clear that the voting behaviour of Republican senators does not change during their time in office since the probabilities illustrated by the “triangles” are not changing across generations. Instead, the predicted probability of a pro-gun vote increases dramatically for Democratic senators who are close to re-election — which is why the “circle” for the third generation reaches a much higher probability compared to the first two generations.

In order to verify whether the pro-gun effect of election proximity is driven by re-election motives, we also look at the voting behaviour of senators who aren’t intending to stand for re-election or those with very safe seats. In line with our third theoretical prediction, election proximity has no impact on the voting behaviour of these senators.

Money also talks

Obviously, financial pressure from lobby groups can also contribute when a politician’s vote differs from the preferences of the majority. Our results confirm that senators who receive larger amounts of campaign contributions from gun-rights lobbies are more likely to take a pro-gun stance. Still, even after controlling for the contributions received by individual senators throughout their terms, we find that they are still more likely to vote pro gun when they are closer to facing re-election. The power of gun-rights lobbies like the NRA may not only lie in their deep pockets, but also in the fact that their members are single-issue voters.

Our results can help to understand why Congress has not introduced stricter gun regulations in the wake of the tragedy in Connecticut, despite overwhelming public support. The gun-control paradox can be explained by the fact that an intense minority prevails over an apathetic majority.