Immigration and Crime: Making Sense of Multiple Patterns*

Giulio Zanella† January 2009

The paper of Alonso, Garupa, Perera, and Vazquez (2008; henceforth AGPV), tackles a thorny issue, the relation between immigration and crime in host countries. Despite being at least as old as the large migration waves of the 19th and early 20th centuries to the United States (Moehling and Morrison Piehl 2007), this issue is bound to become increasingly important as migration costs and economic barriers between countries continue to fall while substantial cross-country differences in earning opportunities persist. Unlike the United States, where immigration is an old and (in many respects) special phenomenon, most European countries have only recently begun experiencing a positive net migration rate. In some cases – Spain being the most prominent – such flows are so large and the speed of the process so high that public opinion, and hence many politicians, have come to associate immigration and crime across the board and in a causal sense.1 How can we assess whether this is actually the case? Any investigation of the relation between immigration and crime is limited by the available measures of the two phenomena. Measuring crime is tricky because only a fraction of committed crimes are known by the police and reported to judicial authorities. Of these, only some actually lead to an arrest, and only a fraction of arrested persons are eventually convicted; thus,

convicted ≤ arrested ≤ reported ≤ committed.

While these different measures tend to coincide for certain crimes (homicide is the most obvious example), in general there may be a substantial bias in comparing the crime rate across time and space using smaller subsets (e.g., arrests versus convictions. These would include, respectively, measures of the efficiency and of the resources available to the police and the judicial system. For instance, if the police get tougher on crime then we may well observe an increase in the number of arrested persons even if the crime rate is actually decreasing. Similarly, if the police are more *

Based on the discussion of “Immigration and Crime in Spain, 1999–2006”, by Garupa et al., at the FEDEA Workshop on Immigration, Madrid, October 16-17, 2008. I have benefited much from conversations with Paolo Buonanno. † Department of Economics, University of Siena, Italy. 1 Martinez and Lee (2000) survey sociological theories, opinion polls, and almost a century of descriptive evidence from the United States. They conclude that, although there are theoretical reasons to expect a positive relation between immigration and crime and although public opinion clearly believes this is the case, the available evidence is inconclusive at best.

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efficient in small than in large metropolitan areas, then a person who looks only at the arrest rate might wrongly conclude that there is more crime in a small town than in a large city. Using the largest observable dataset—typically, crimes reported by the police—minimizes such bias. Measuring immigration is equally tricky owing to the presence of illegal immigrants. Thus, if one computes the crime rate of natives and foreigners based on official immigration flows, then the crime rate of foreigners will be upward biased. Probably, the best that one can do is to include an estimate of illegal immigrants in the denominator. Barring measurement issues, from a purely statistical viewpoint the association between immigration and crime is, in principle, a mechanical consequence of decreasing migration costs. These imply that, in all rich countries, immigrants have fallen in quality relative to the native population. By “quality” I mean the level of a set of characteristics statistically associated with crime, such as age, education, and skills. Since quality is positively correlated with income (i.e., young, less educated, low-skill individuals tend to be poorer), it follows that falling migration costs imply decreasing average quality of immigrants (Hatton and Williamson 2007). As a consequence, although the data put together by AGPV show a considerable gap between the crime rates of natives and immigrants, conditioning on socioeconomic characteristics tends to reduce this difference. This pattern is observed in other European countries for which crime statistics are disaggregated by nationality. However, a very different pattern is observed in the United States. Field evidence analyzed by sociologist Robert Sampson (2008) suggests that (i) recent U.S. immigration is associated with lower propensity to violence and (ii) cities where immigrants concentrate are actually becoming safer more rapidly than other cities. This is known as the “Latino paradox”, a negative correlation between immigration and crime – although the evidence extends beyond immigrants of Hispanic origin. Spain illustrates yet a different pattern, which I label “Spain’s exceptionalism”. According to Eurostat data, foreign-born residents per 1,00 inhabitants increased by an astonishing factor of almost 4 between 1999 and 2006, and the total number of crimes reported to the police increased by “only” about 9% during the same period. I say “only” because this figure makes Spain a clear outlier in Europe, as illustrated in Figure 1. Cross-country comparison of crime statistics is, of course, problematic in itself because of differences between criminal codes and between systems of deterrence. Yet Figure 1 suggests that if there is a positive relation between immigration and crime in Europe, then the effect in Spain was relatively mild. The two panels of Figure 2 compare crime and foreign-born rates in these same countries in 1999 and 2006.

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Figure 1. Dynamics of immigration and crime in Europe, 1999–2006

Growth rate of total crime per 1,000 inhabitants 0 .2 .4 .6

Cyprus

Slovenia

Austria

Spain

Portugal

Sweden France Germany

-.2

Italy Ireland

UK Malta

Nether. Hungary Finland Denmark Czech R

0

1 2 3 Growth rate of foreign-born population per 1,000 inhabitants

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Source: Eurostat.

Figure 2. Immigration and crime in Europe, 1999 vs. 2006

Source: Eurostat.

How can we make sense of these multiple patterns? Clearly, there is more than the mechanical relation induced by falling migration costs and socioeconomic characteristics. This is where economic theory is needed. 3

Consider the following toy model. The world population inhabits J different countries j = 1,…, J. Each individual is endowed with a unit of time and is characterized by a set of socioeconomic characteristics (such as age, gender, education, nationality, skills) lying in Θ. An individual with characteristics θ ∈Θ has legal and illegal earning opportunities in country j. Work and crime yield, respectively, wages wj(θ ) and sj(θ ) per unit of time. The probability of apprehension and the associated punishment are denoted by πj and pj(θ ), respectively. Punishment depends on individual characteristics because some of its components (e.g., deportation) apply only to certain types of individuals (e.g., foreigners). Time is divisible and can be allocated either to legal work or crime. There are gains from specialization, but these gains are decreasing. That is, t units of time devoted to a certain activity yield tα effective units, where α∈(0,1). I assume risk neutrality in order to emphasize the role of the interaction between country and individual characteristics. The expected payoff of crime (C) to individual θ in country j is (1)

E Cj (θ ) = (1 − π j ) s j (θ ) − π j p j (θ ) ,

and an individual solves (2)

{

}

max t α E Cj (θ ) + (1 − t )α w j (θ ) . t, j

That is, an individual chooses a country and the time to devote to legal and criminal activities. The optimal share of time devoted to crime by individual θ conditional on living in country j, which is a measure of the conditional (on θ ) crime rate in that country, is −1

(3)

⎛ ⎛ w (θ ) ⎞1 /(1−α ) ⎞ j ⎟ . ⎟ t j (θ ) = ⎜⎜1 + ⎜ C ⎟ ⎜ E (θ ) ⎟ ⎠ ⎝ ⎝ j ⎠

Therefore, the value to individual θ of living in country j is (4)

v j (θ ) = t j (θ )α E Cj (θ ) + (1 − t j (θ ))α w j (θ ) .

Given E Cj (θ ) , it can be shown that v j (θ ) is an increasing convex function of wj(θ ); similarly, given

wj(θ ), it is an increasing convex function of E Cj (θ ) . Assuming that (4) is single-peaked with respect to j and ignoring migration costs, an individual of type θ will live in country (5)

j (θ ) = arg max v j (θ ) . j

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This is an extremely simplified, partial equilibrium model in which most key objects are exogenous and crime is just another type of economic activity (i.e., with no economic or social consequences). Yet it helps make an important point clear: immigration to a country or regions within a country, equation (5), and crime, equation (3), are simultaneously determined. This means that regressing the crime rate on the immigration rate would be misleading, which is why AGPV devote so much effort to instrumenting the immigration rate. There are objective difficulties in finding valid instruments in administrative data. For instance, AGPV use lags, and Bianchi, Buonanno, and Pinotti (2008) use the immigration flows in the rest of the continent (Europe in this case) as a measure of supply shocks. Although these are sensible approaches, such instruments allow identification only under restrictive assumptions. Therefore, simultaneity is the source of a fundamental identification problem, one from which there is no easy way out. Ideally, one would like to exploit “natural” occurrences unrelated to the fundamentals (which include the fundamentals in the home country) of at least this very simple model. Finding such instruments presents a challenge but is potentially rewarding. The model suggests that cross-country differences in crime depend in a non-separable way on differences in legal earning opportunities, deterrence, and the distribution of individual characteristics. Quite crucially, such differences depend on the quality of the match between individual and country characteristics. This is the interesting aspect because even in this toy model the local distribution of immigrants’ characteristics is endogenously determined and depends on the characteristics of the host country relative to alternative countries – including one’s home country. It is the quality of this match that determines the relation between immigration and crime. Suppose that, for a low-skilled individual θ 0 , w j (θ 0 ) is low everywhere while E Cj (θ 0 ) is large in some host country 0 relative to the home country. Then we are likely to observe a positive relation between immigration and crime in country 0. However, suppose there exist a type θ1 and a host country 1 for which w1 (θ1 ) is relatively large. In this case the relation between immigration and crime will be weaker in country 1. This seems to describe “Spain’s exceptionalism”, with Spanish Americans as the θ1 type. Immigrants from Spanish America constitute a large share of overall recent immigration to Spain, and they are linguistically and to some extent culturally assimilated. As such, they can be expected to perform better in the labor market and so to have a lower t1 (θ1 ) , as per equation (3). By combining information on the origin of immigrants to Spain with the results from shift-share decomposition reported by AGPV, we confirm that immigrants from Latin America (the vast majority of individuals who move to Spain from America) actually had a negative impact on the crime rate in Spain between 1999 and 2006. This result is summarized in Table 1.2

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Because of data limitations, the share of new immigrants in the first column refers to males of all ages whereas figures in the second column refers to males in the age range 20–50. However, I claim that the ensuing distortion is minimal.

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Table 1. Origin of recent male immigrants to Spain and their contribution to crime, 1999–2006

Origin Europe America Africa Asia

Share of new immigrants 41.8% 33.8% 18.5% 5.8%

Contribution to new crimes 29.2% -1.4% 69.3% 6.5%

Source: Eurostat and AGPV’s shift-share analysis.

Consider a third pair ( θ 2 , 2) such that w2 (θ 2 ) is large relative to the home country and E C2 (θ 2 ) is very low and possibly negative—for instance, because punishment includes deportation. Then the relation between immigration and crime may well be downward sloping. This case is consistent with the “Latino paradox” from a purely economic perspective. Being deported from the United States has a large opportunity cost for a Mexican immigrant, given the gap between the two countries in low-skill wages. Far from providing (or even sketching) a rigorous analysis, the toy model I suggested here indicates a potentially fruitful research direction. From a policy viewpoint, it emphasizes that a government can minimize the impact of immigration on crime, if any, via policies directed at obtaining a highquality pool of immigrants relative to country characteristics, which are themselves an object of choice in equilibrium. An additional important piece of descriptive evidence produced by AGPV is that the crime rate of native Spaniards has moved in the same direction as the crime rate of immigrants to Spain: roughly two thirds of the additional crimes committed in Spain between 1999 and 2006 are accounted for by the increased share of foreigners; one third is accounted for by the increased crime rate of natives. Similarly, Sampson (2008) finds that the “Latino paradox” is associated with a decline in crime among whites and blacks in the 1990s. An obvious explanation is that there is no structural relation between immigration and crime: rather, there is something that affects the overall crime rate as well as particular socioeconomic groups in relation to their economic incentives. An alternative explanation is that there are externalities in criminal activities, as suggested by economic models of crime, e.g. Sah (1991). If the overall crime rate increases, the deterrence system is congested in the short run and the probability of apprehending any single individual decreases. Thus, the expected payoff of crime increases. In sum, AGPV deserve a lot of credit for putting together a large amount of interesting Spanish data from different sources. A closer look at these data and at data from other European countries and the United States reveals the existence of different patterns relating immigration and crime that will be best understood in the context of a unifying general equilibrium model—for instance, one along the lines of Burdett, Lagos, and Wright (2004). Such a model, in turn, should be able to answer many interesting quantitative policy questions.

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References [1] Alonso, C., N. Garupa, M. Perera and P. Vazquez (2008). “Immigration and Crime in Spain, 1999–2006.” Fundación de Estudios de Economía Aplicada, Documento de Trabajo 2008-43. [2] Bianchi, M., P. Buonanno, and P. Pinotti (2008). “Do Immigrants Cause Crime?” Paris School of Economics, Working Paper No. 2008-05. [3] Burdett, K., R. Lagos, and R. Wright (2004). “An On-the-Job Search Model of Crime, Inequality, and Unemployment.” International Economic Review, 45(3):681–706. [4] Hatton, T., and J. Williamson (2007). Global Migration and the World Economy: Two Centuries of Policy and Performance. Cambridge, MA: MIT Press. [5] Martinez, R., and M. Lee (2000). “On Immigration and Crime.” In Gary LaFree (ed.) Criminal Justice 2000: The Changing Nature of Crime, vol. 1, pp. 485–524. Washington, DC: National Institute of Justice. [6] Moehling, C., and A. Morrison Piehl (2007). “Immigration and Crime in Early 20th Century America.” NBER Working Paper No. 13576. [7] Sah, R. (1991). “Social Osmosis and Patterns of Crime.” Journal of Political Economy, 94:1272–95. [8] Sampson, R. (2008). “Rethinking Crime and Immigration.” Contexts, 7:28–33.

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