The Republican candidates for president are vigorously debating who is most likely to throw out and keep out undocumented immigrants. New research suggests that doing so would be bad electoral politics.

The conventional wisdom is that Democrats benefit from immigration. A new paper by Anna Maria Mayda, Giovanni Peri and Walter Steingress shows that this is true, at least on average. Larger numbers of immigrants who acquire citizenship (and can thus vote) increase election returns for Democratic candidates across different types of U.S. elections.

Yet increases in the share of non-citizen migrants are correlated with higher Republican vote shares. They argue that this is so because native voters become increasingly attracted to Republican candidates when the share of undocumented migrants in their state increases.

Mayda, Peri and Steingress derive their findings from a nationwide analysis of population changes and voting returns in U.S. states between 1994 and 2012. It is difficult to measure variation in undocumented migrants. After all, the undocumented aren’t easy to count and they selectively flock to places for reasons that may be correlated with electoral politics. The authors use a clever set of instruments to deal with these issues, including varying levels of apprehensions at the U.S.-Mexico border.

A new paper by Nicole Baerg, Julie Hotchkiss and Myriam Quispe-Agnoli measures variation in undocumented migration more directly at the county level across the state of Georgia between 1990 and 2010. They use self-reported Social Security numbers that workers give to their employer to collect and pay taxes on their wages. They then check whether employees are reporting valid or invalid Social Security numbers and use the results to estimate the number of unauthorized immigrants across counties.

Despite the different methodology, time span and geographic focus the substantive findings are the same, increases in the undocumented population are associated with more Republican votes. Baerg, Hotchkiss, and Quispe-Agnoli estimate that in counties that are in the top half of the distribution for shares of unauthorized, a one percent increase in the unauthorized as a share of the population increases the share of votes going to Republicans by 1.5 percentage points.

Similarly, scholars have found that localities with higher levels of immigration also had larger vote shares for right-wing parties in Italy and Austria (both studies used instrumental variables to deal with endogeneity issues). Immigrants have a hard time acquiring citizenship in these countries, regardless of whether they are documented or undocumented. Thus the effect of immigration on native voters likely outweighs the effects of increased immigrant voting.

The recent German state-elections illustrate the same point. On March 13, 2016, German voters went and cast their ballots in three state elections, in Baden-Württemberg, Rhineland-Palatinate and Saxony-Anhalt. Even before the election, the media attributed the election as a “political referendum’‘ on immigration and refugees. The outcome of the election is considered a landslide victory for the AfD, Germany’s right-wing, anti-immigrant, populist party, as well as a severe electoral reprimand for the CDU — Chancellor Merkel’s party.

There is some anecdotal evidence that proximity to refugee camps was correlated with increased vote shares for the AfD. For example, electoral support for the AfD was 15 percent across the state of Baden-Württemberg. Yet this was much higher in electoral districts that are located around the Benjamin Franklin Village, an old U.S. army installation that was refitted to host refugees. In Schoenau, the AfD got 30.1 percent of the vote and in Vogelstang and Waldhof, the AfD got 28.8 and 25.9 percent of the vote respectively. Still, this warrants more systematic analysis.

All of this research suggests, then, that from an electoral perspective, Republican candidates should raise the salience of the issue of undocumented workers — but do little about it when they come into office.

Nicole Rae Baerg is an assistant professor in the department of political science at the University of Mannheim. She works on fiscal and monetary policy as well as topics relating to immigration.