Appendix A.1: Variable definitions, sources and summary statistics

Crime victimization: whether the respondent or household member has been a victim of assault or burglary in the last 5 years. Source: ESS.

Crime perception: dummy variable constructed using the feeling of safety when walking alone in local area after dark. Two definitions are used, with different degrees of stringency: very unsafe only, or unsafe and very unsafe. Source: ESS.

Immigration penetration: log(migrant/resident population), where migrant is defined as non-national, or born-abroad, or born in Europe or born outside Europe. Source: authors’ calculation using LFS data.

Financial Wealth: whether main source of income of respondent’s household is financial. Source: ESS.

Educational attainment, years of education, degree of urbanization of local area, age, gender, labour market status and political orientation. Source: ESS.

Share of immigrants by world flow area of origin in 2000 by region. Source: Eurostat Census.

Summary statistics are displayed in Table 10. The correlations between alternative measures of immigration penetration by region are reported in Table 11.

Table 10 Summary statistics, by country Full size table

Table 11 Correlations between alternative measures of % immigrants across European regions in 2002 Full size table

Appendix A.2: European regions in the sample

Our baseline sample consists of individuals residing in the period 2002-2008 in 16 western European countries, i.e. Austria, Belgium, Switzerland, Germany, Denmark, Spain, Finland, France, Greece, Ireland, Luxembourg, Netherlands, Norway, Portugal, Sweden and the UK, and 127 regions whose NUTS codes are the following:

AT11, AT12, AT13, AT21, AT22, AT31, AT32, AT33, AT34, BE1, BE2, BE3, CH01, CH02, CH03, CH04, CH05, CH06, CH07, DE1, DE2, DE3, DE4, DE5, DE6, DE7, DE8, DE9, DEA, DEB, DEC, DED, DEE, DEF, DEG, DK0, ES11, ES12, ES13, ES21, ES22, ES23, ES24, ES30, ES41, ES42, ES43, ES51, ES52, ES53, ES61, ES62, ES63, ES70, FI13, FI18, FI19, FI1A, FR1, FR2e, FR2w, FR3, FR4, FR5, FR6, FR7, FR8, GR11, GR12, GR13, GR14, GR21, GR22, GR23, GR24, GR25, GR30, GR41, GR42, GR43, IE01, IE02, LU0, NL11, NL12, NL13, NL21, NL22, NL23, NL31, NL32, NL33, NL34, NL41, NL42, NO01, NO02, NO03, NO04, NO05, NO06, NO07, PT11, PT15, PT16, PT17, PT18, SE11, SE12, SE21, SE22, SE23, SE31, SE32, SE33, UKC, UKD, UKE, UKF, UKG, UKH, UKI, UKJ, UKK, UKL, UKM, UKN.

Regional codes are NUTS 2 with the exception of Belgium, France, Germany, Denmark, Luxembourg and the UK whose regional codes are NUTS 1.

Note that for a small number of region ∖year combinations the ESS immigration share of non-nationals and those born outside Europe is missing whereas the LFS measure is not. This explains the discrepancy between the number of observations of the fixed effects regressions using LFS data in Table 3 and the SSIV regressions using both ESS and LFS data in Table 6.

When considering non-national immigrants, the ESS immigration penetration is missing for AT11 (2004), DE4 (2004), DE8 (2004 and 2008), DEB (2008), DEE (2002 and 2004), DEG (2008), ES1(2002), FI1A (2004 and 2008), NL11 (2002, 2006, 2008), NL12 (2002, 2006, 2008), NL13 (2002, 2006), NL21 (2006), PT18 (2006), SE32 (84), UKC (2002, 2008). When considering immigrants born outside Europe, the ESS immigration penetration is missing for AT11(2004), PT18(2002) and UKN (2002, 2008).

Appendix A.3: Monte Carlo simulations of attenuation bias from sampling error in immigration shares

We investigate the extent of attenuation bias in our setting by means of Monte Carlo simulations using an artificial population of 10 million individuals distributed across 100 regions. We assume a given share of immigration per region equal to 10 % (in the order of the average immigration share in our sample) that each period, and for four subsequent periods, like in our data, is subject to a random positive immigration shock that varies across regions plus a random positive shock common to all regions. The shock is generated from a uniform distribution designed so that the total immigration share increases from 10 to 13.7 % in four periods (i.e. we mimic the dynamics in the four biannual ESS waves that cover the 8 years period from 2002 to 2008).

We then construct a population model of crime victimization where the probability of being a crime victim is given by:

$$ crime_{rit}=\beta m_{rt}+{\upmu}_{r} + {\upmu}_{t} + \varepsilon_{it}, $$ (11)

where m r t is the resulting immigration share in each region and year, μ r is a set of regional fixed effects on victimization, assuming the 100 regions are characterized by different degrees of criminality and ranked from the safest to the most dangerous, μ t is a set of year random effects generated from a uniform distribution and ε i t is a normally distributed random disturbance with ε i t ∼N(0,0.05). We assume β=1 so that the resulting average probability to be a crime victim is equal to 20 % like in our data.

We then draw 500 random samples, using different sampling rates (from 1/10,000 to 30/100) and we estimate our fixed effects model (i.e. including region and year fixed effects) in each of the 500 random samples, producing an averaged estimated coefficient of interest \(\hat {\beta }\) and standard error across the 500 replications. Our aim is to check the extent of the attenuation bias for randomly drawn samples of different sizes, i.e. for region/year cells of different sizes.

Table 12 reports the findings of our Monte Carlo simulations where the average sample cell size used to calculate the immigration share varies with the sampling rate. Despite the average immigration share is very precisely estimated even for very low sampling rates, the attenuation bias can be large in fixed effects estimations when the sampling rate is low. Our simulations show that in presence of a unitary effect of immigration on crime at the population level we observe a 52 % bias when the sampling rate equals 5/1000 (average cell size of 522), 35 % bias when the sampling rate equals 1/100 (average cell size of 1043) and 15 % bias when the sampling rate equals 3/100 (average cell size of 3130). However, a positive, albeit biased, and statistically significant effect of immigration on crime is found even when the sampling rate is as low as 5/10,000 (average cell size of 52).

Table 12 Monte Carlo simulations of fixed effects model by sampling rate Full size table

Table 13 displays the average LFS cell sizes used to calculate the regional immigration share in each country and year. The latter varies between 2977 and 115,508 according to country, with a total average of 13,451. This indicates that our fixed effects estimates should identify a significant effect of immigration on crime victimization if present, and that the attenuation bias should not be too large in our data.

Table 13 Region/year cell size by country in LFS data Full size table

Table 14 presents the results of similar simulations performed adopting a SSIV specification where we use two alternative measures of the immigration share by region/year. The first (the instrumented immigration share, m 1 ) is obtained from a small sample analogous to the ESS sample, with sampling rates varying from 1/1000 (average cell size of 104) to 1/100 (average cell size of 1043). The second (the instrumenting immigration share, m 2 ) is obtained from a large sample analogous to the LFS sample, with sampling rates varying from 1/1000 to 10/100 (average cell size of 10,433) and reported by column.

Table 14 Monte Carlo simulations of SSIV model by sampling rate Full size table

Our SSIV model largely outperforms the fixed effects model, with a resulting very small attenuation bias even for very low sampling rates. When the m 1 sampling rate equals 1/1000 (average cell size of 104), the bias is consistently lower than 5 percent for m 2 sampling rates equal to or greater than 5/1000 (average cell size of 522). The bias is consistently lower that 1 % when the m 1 sampling rate is equal to or greater than 5/1000. In addition, the first stage coefficients are always positive and highly significant, especially when the m 2 sampling rate is equal to or greater than 3/1000 (average cell size of 313).

Appendix A.4: Additional tables

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