Migrant crime in Germany, redux

Interesting results, but wrong methods for the research question

This new study is making the rounds, also in the English speaking world (e.g. Reuters):

Higher proportion of migrants does not mean more crime, German institute says

BERLIN, Feb 18 (Reuters) - An higher proportion of foreigners in Germany does not lead to a higher crime rate, a research institute said on Tuesday, five days ahead of an election in which violent attacks linked to migrants have pushed security to the top of the agenda.

In an analysis of police statistics from 2018 to 2023, the Ifo institute found "no correlation between an increasing proportion of foreigners in a district and the local crime rate", researcher Jean-Victor Alipour said, adding that this also applied to refugees.

Immigration and security issues have dominated campaigning ahead of the February 23 election, especially after a series of violent incidents in recent weeks, with polls showing the centre-right CDU/CSU bloc leading followed by the far right.

Last week, an Afghan immigrant ploughed his car into a crowd in Munich, injuring over 30 people, two of whom later died. Prosecutors suspect he was motivated by Islamist ideology.

In their analysis, Ifo took into account that foreigners appear in crime statistics more frequently than would correspond to their share of the population. The reason for this is that migrants are more likely to move to urban centres with a structurally higher crime rate, even among Germans, the institute said.

At this point, it's all over the world: Turkey, Spain, MSN Singapore, and more.

So let's dive in and see what's up. It's a report by a German institute called IFO (Ifo Institute - Leibniz Institute for Economic Research at the University of Munich). They published a German-language 12-page report called Steigert Migration die Kriminalität? Ein datenbasierter Blick (Does migration increase crime? A data-based look). Their own summary is (from German):

Foreigners are overrepresented in the police crime statistics (PKS) compared to their share of the population. This fuels concerns that migration endangers security through a supposedly higher tendency of foreigners to commit crime. This article analyzes data from the PKS (2018-2023) by district and discusses existing findings from research on the impact of immigration on crime. The results show that the higher crime rate among foreigners is mainly explained by location-specific factors, such as their concentration in metropolitan areas with a high crime density. Their demographics (younger and more male), on the other hand, play a lesser role. In the period 2018-2023, no connection can be proven between a change in the regional proportion of foreigners and the local crime rate. The results are consistent with findings from international research: (refugee) migration has no systematic influence on crime in the host country. Finally, we discuss measures to prevent crime among migrants and to reduce misconceptions about migrants and migration.

It appears thus to be an exercise in the ecological fallacy. Using aggregate data of political units trying to infer causality at the individual level. We already know, and they already say, that foreigners are over-represented in the crime statistics. Instead of using person-level data to investigate controls for age, sex, location etc., they use administrative division aggregate statistics. This is not guaranteed to work because if various controls are correlated with migrant related factors, this leads to under- or over-correction. One can end up with the Everest fallacy -- controlling for altitude, mount Everest is not really cold, but actually warm (I am wondering if someone actually did this regression somewhere). What they seek to explain or find out is:

Foreigners are overrepresented in the police crime statistics (PKS).1 In 2023, there were 57 foreign suspects for crimes (excluding residence violations) per 1,000 foreign residents. For Germans, however, there were only 19 (see Figure 1). Even after deducting suspects without German residence, the rate of foreign suspects remains almost three times higher. The discrepancy has existed for over a decade - despite declining crime.

Here's their first model findings:

(Images are translated to English by Google Translate image translation.)

We see that across the administrative units (Kreisen, I think there are about 400 of them, these are about equivalent to US counties), the migrants are younger and have slightly more men than women (54% vs. German 49%). The age difference will make a large difference since most crime is committed by younger people, but the sex difference is too small to have much effect. To see the latter, you can assume that men are e.g. 3 times more criminal than women. If we arbitrarily set men's crime rate to 3 and women to 1, the German average rate will be 0.49*3+0.51*1 = 1.98. If Germans instead had 54% male like migrants, their crime rate would be 0.54*3+0.46*1 = 2.08, or 5% higher. A trivial difference compared to the observed 3x difference. They furthermore show that there are positive relationships between the logged versions of various variables like the proportion of foreigners and the German crime rate. I don't think they should use log transformations here, but they said they did it for making terms interpretable in terms of percentage changes, a common economist approach. Their main results which the headlines are based on are these:

The X axis is the log proportion of foreigners and the Y is log of the total crime rate in that area. They have a slope of 0.41. Then they add a bunch of controls for the second plot:

• Male %

• Mean age

• Log of German crime rate

• Total unemployment rate

Their outcome is again the total crime rate. Now the relationship has gone away, in fact, it is a bit negative (about p=0.05). So can we conclude from this that non-Germans are really not more prone to crime? Not really. Not only did they control for the German crime rate, but even the total unemployment rate, which is also based on the non-Germans. These are no ordinary foreigners after this control, but a strange statistical concoction that is hard to interpret. Better is their next idea:

Here they seem to split the data by year, thus 6x their dataset (6x more dots in the plot than above). The slope is now 0.30, from 0.41 above. This decline suggests random errors in the variables since crime rates for small aggregate units are inaccurately estimated (the same rare event statistics problem I just wrote about). In their second plot, they seem to add fixed effects for years and the units. What this does is to check whether the units that increased their foreigner % the most in those 5-6 years (from 2018 to 2023) saw an increase in the crime rate. They did not (slope -0.03). This is a better design than above as fixed effects do not risk indirectly over-controlling for other correlated variables not used in the model. This finding suggests immigrants are not more crime prone, but rather that specific areas just have high crime no matter who lives there. We know this to be true and false to some extent. Urban areas always have more crime, as of course, it is easier to commit crimes when there are more potential targets nearby (if you live in a forest alone, you can't really commit many crimes). However, no one sane would believe that if we decreed that the population of a city should be changed from German pensionists to Syrians, the crime rate would remain constant (that is what their model implies). Furthermore, because the time-span is so short (~5 years of change), other correlated changes can affect the results. If crime prone immigrants tend to move into areas where low-crime Germans also move into, then nothing will be seen. Similarly, because they group all foreigners into the same category, if many relatively low-crime French people move into some border town lowering its crime rate, this will cause a negative relationship to be seen.

Insofar as the data they have are concerned, the first set of results are uninterpretable and useless, and the latter are more reasonable but leaves some worries still. However, strange is just that they didn't just adjust the data directly. It is possible to calculate the crime rate (suspect rate actually) for groups by country of origin or citizenship directly from the German government statistics. One can also get their age and sex composition. Using these, one can compute the expected crime rate seen in each group if they in fact had the same age- and sex-dependent crime rate as Germans. This produces a correction factor one can adjust the crime rates with. If they remain over-represented after this direct correction, then age and sex composition cannot explain the criminality. I did this already in 2017 (Immigrant crime in Germany 2012-2015), and these are the results:

As it turns out, adjusting for age and sex doesn't matter much for the differences between origin groups (r = 0.96) in Germany nor Denmark (r's = 0.95-0.98). However, it reduces the crime rate ratios. A typical problematic origin group is Nigeria, which is 6 times over-represented in the 2012-2015 data, but only about 3 times over-represented when age and sex adjusted. Typically, the ratio is inflated by about 2x due to the age and sex composition for the German data (in Danish data, it was close to the same). As such, the overall crime rate of foreigners being 3x is about 1.5x when adjusted for age and sex properly. The Danish statistics agency also supplies age and sex specific counts of crimes, so it is possible to compare the direct method to the subsetting method. These produced almost the same result (r = 0.98), so we know this method works. By the way, here are the Norwegian results, subset to only males age 15-24. This leaves no possibility of sex-confounding and very little age-confounding, yet the results remain:

In conclusion, the problems with the study are the following:

1. They use administrative units of analysis, whereas they should have used origin-groups or person-level data instead for the research question they wanted to answer. This leaves their regression open to problems with over-controlling (their first model), and untested assumptions for the fixed effects approach (2nd model). This is on top of the attempt to infer causality at individual level from aggregate data.

   1. Their insufficient statistical presentation make it hard to see where the first model goes wrong.

2. They group all foreigners into the same category, whereas we know that there are stark differences between origin groups. Japanese migrants have a crime rate of about 0.25x of the German rate, but Algerians were more than 10x over-represented.

3. The use of the German category is problematic because many foreigners convert their citizenship into German, and thus count as German in most government statistics. This creates systematic bias in this variable that has unpredictable effects on results. It's possible that some areas see a continued influx of foreigners but at the same rate as the already residing foreigners convert citizenships to German. The result is that there appears to be no change in foreigner%, whereas it is increasing. They should not have used citizenship data if possible.

   1. "The term foreigner includes persons without German citizenship, including stateless persons and persons with unclear nationality." We know from other countries that the most problematic groups are those more eager to convert to Western citizenship, creating systematic bias in the citizenship data.

4. Their use of log values make the results harder not easier to interpret.