Criminal convictions and immigrant background 1973–2017 in Sweden – have differences increased or declined?

ABSTRACT This study investigates Swedish conviction trends by individuals’ immigrant background for the period 1973–2017. The central research question is whether relative differences in conviction levels have increased, declined or remained unchanged over recent decades. This question is examined in part using a traditional cross-sectional approach, and in part using a cohort-based approach. All results are presented by gender, and results for the cohort-based approach also by holding socioeconomic background constant. The results show that conviction levels have decreased, to a greater extent among men than among women, irrespective of immigrant background. The level of overrepresentation among those born in Sweden to foreign-born parents has increased somewhat, while the overrepresentation of those born abroad has decreased towards the end of the period examined.


Introduction
Numerous Nordic studies have shown that individuals of foreign background, as a rule including both foreign-born individuals and those born in Sweden with foreign-born parents (hereafter labelled 'the second generation'), are over-represented among those registered for crime (see e.g. Hällsten et al., 2013;Klement, 2020;Skardhamar et al., 2014). A number of Swedish studies have found the risk for conviction among persons of foreign background to be approximately twice that of individuals born in Sweden to two Swedish-born parents. In studies that have not exclusively focused on immigrant background and crime, but that have also been able to capture between-group differences in levels of resources, the over-representation tends to be lower (Brå, 2019). The differences are also significantly smaller in research focused on self-reported offending, which primarily describes involvement in less serious offences among teenagers. In Swedish selfreport studies from more recent years, for example, youths of foreign background do not generally appear to be more involved in offending (Vasiljevic et al., 2020).
A recent review of Danish studies on immigration and crime concludes that the levels of overrepresentation differ depending on type of study (Klement, 2020). The variation between studies is inter alia due to differences in study populations, definitions of foreign background and the types of register data and crime outcomes analysed. In concrete terms, the difficulties comparing results from different studies means that analyses have rarely been able to draw more precise conclusions about whether levels of overrepresentation, either in general or for different groups or offence types, have varied over time.
The nature of immigration to Scandinavia has shifted over the past five decades. Stated briefly, until the 1970s migration to Sweden was dominated by labour and familyreunification migration from the other Nordic countries and southern Europe (SCB, 2016). From the 1990s, there has instead been a clear increase in refugee migration from non-European countries. In the Nordic public debate, this change in migration patterns is often linked to increases in crime and an alleged increase of the overrepresentation in crime among individuals of foreign background (Estrada, 1999:131ff). During recent decades, political parties such as the Danish People's Party, the Norwegian Progress Party, the Finns Party and the Sweden Democrats have recorded significant electoral successes, and linking migration and crime have undoubtedly been an important element in the rhetoric of these parties (see e.g. Rydgren, 2004). In recent years, alleged negative developments in Sweden in particular have attracted substantial interest in Scandinavia and have even given rise to a new concept -'the Swedish condition' (e.g., Lokland & Nilsson, 2018).
Although the political debate has emphasized a negative view of crime trends linked to immigration, research remains unclear regarding how levels of overrepresentation in crime among persons of foreign background have developed. The aim of this tudy was to analyse Swedish conviction trends by individuals' immigrant background for the period 1973-2017. All results will be presented by gender, a factor that has to date been missing from the published Nordic research (see below for a more detailed discussion). Given the significance of between-group differences in crime (Bäckman et al., 2020), the lack of studies that have been able to combine analyses of immigrant and other factors such as socioeconomic background over time is also problematic. This is a knowledge gap not only in Scandinavia but also in other parts of the world, since such analyses require the linking of different data sets that are rarely available over significant periods of time.
The article's central research question is whether differences in conviction levels for those of foreign background have increased, declined or remained unchanged over recent decades. The results are presented in two blocks which correspond to two subquestions relating to the longitudinal trend of between-group differences in the criminal conviction rate. These questions are examined in part using a traditional cross-sectional approach, and in part a cohort-based approach: (1) What are the long-term trends when the population is grouped on the basis of immigrant background and gender? We present the between-group differences for the period 1973-2017. This analysis is conducted using a traditional cross-sectional design in which conviction levels are compared on the basis of 1-year periods of time at risk for conviction for all offences, theft offences, violent offences and drug offences.
(2) What trends do we see for groups based on immigrant background and gender when we follow individuals over time, and also examine the most frequently convicted individuals, who account for a large proportion of registered crime? This analysis proceeds from a cohort-based approach, in which we focus on the cumulative risk for conviction for a 10-year period from age 15 to 24. The cohort design allows us to examine the significance of the individuals' childhood conditions. In this section we are therefore able to present time series for levels of overand underrepresentation while holding socioeconomic background constant, by looking at trends in the lowest income strata. Data availability considerations mean that this analysis is conducted for the period 1990-2017.

Previous research
It is well-established within Nordic criminology that immigrants, and also their children, are at higher risk of offending. The literature includes a range of different explanations for this overrepresentation (for reviews, see e.g., Beckley et al., 2017;Hällsten et al., 2013;Skardhamar et al., 2014). Stated briefly, three different categories of explanations are usually emphasized. The first involves factors related to which individuals migrate to the country, with the assumption being that conditions in the country of origin lead to a selection with regard to which individuals emigrate. Lenke (1983Lenke ( /2009), for example, argued that the overrepresentation in offending among Finnish migrants in Sweden during the 1970s was linked to the fact that many of those who migrated from Finland to Sweden at the time were socioeconomically disadvantaged. However, more recent studies from both Sweden and the Netherlands suggest that conditions in the country of origin play a subordinate role by comparison with the living conditions experienced by migrants in the destination country (Beckley, 2013;Bovenkerk & Fokkema, 2016). A slightly different aspect of selection relates to the reasons for migration, for example, whether migrants are refugees or labour-market migrants (Andersen et al., 2017). In this regard, there has been a substantial shift in Sweden, where an increasingly large proportion of immigrants are comprised of persons seeking asylum. It is currently unclear what effect this compositional shift has had on levels of overrepresentation in crime. The second, and dominant, category of explanations focuses on the differences in levels of resources that exist between foreign-born individuals and their descendants, as compared to natives. The central factor here is quite simply that the fundamental causes of crime are found in the circumstances that condition the individual life course. There are a large number of studies showing that differences in levels of involvement in crime are reduced if an analysis is able to control for differences in individuals' childhood and current living conditions (see Hällsten et al., 2013 for a review). Thirdly, research indicates that part of the overrepresentation is linked to discriminatory practices on the part of the police and criminal justice system. International research has shown, for example, that non-white individuals are at significantly higher risk of being stopped by the police without having committed an offence (see Mulinari, 2020 for a review). Exactly how great the significance of discrimination is for the patterns noted in crime statistics, and whether this has changed over time, is a very difficult question to answer however. At present, we are not aware of any Nordic research that has examined this issue.

The trend in levels of overrepresentation
Few Swedish studies have analysed changes in the between-group differences over time.
One recent study has employed the Swedish School Survey on Crime to examine the trends in self-reported offending for different groups based on immigrant background (Vasiljevic et al., 2020). During the period 1999-2017, the proportion of students who report having engaged in offending has declined in all groups, irrespective of background. It is notable, however, that the decline has been strongest among foreign-born youths. In 2017, foreign-born 16-year-olds reported lower levels of offending than youths born in Sweden to Swedish-born parents. As regards studies based on register data, a study restricted to persons aged 15-44, found that for individuals of foreign background, the risk of being registered as a crime suspect was roughly double that of native Swedes during the period 2013-2017 (Adamsson 2020). Comparisons with previous studies conducted in the same way indicate that this level of excess risk has remained relatively stable since the beginning of the 2000s. These comparisons also show that the trend has differed somewhat between foreign-born persons and the second-generation immigrants, with the level of excess risk declining somewhat for the former group but increasing somewhat for the latter (Adamsson 2020).
Nordic researchers have published a small number of studies analysing crime trends with a focus on immigrant background and changes in the level of overrepresentation (see also Klement, 2020;Brå, 2019 for recent reviews). Andersen et al. (2011) show that among men in Denmark, the excess risk for conviction over the course of a year is greatest for children of immigrants from non-Western countries, and thereafter for persons born abroad in these same countries. Viewed in relation to 'Danes', the excess risk for these groups, taking age differences into consideration, has declined over time, however, from 3.0 at the beginning of the 1990s, to less than 2.5 in 2006 (Andersen et al., 2011, p. 16). The study, which is based on register data for a large sample of men aged 15-45, presents levels of overrepresentation and their development over time both with and without controls for age and socioeconomic composition. The level of overrepresentation declines over time both with and without the inclusion of controls. The study does not present trends for female offenders.
Boesen Pedersen et al. (2017) have analysed trends for the subsequent period (2006--2014) using partly different methods and groups. This analysis shows that the number of suspects aged 10-17 has undergone a general decline in Denmark. The decline is also substantial (slightly over 40%) among youths labelled 'the most criminal' (individuals suspected of more than three serious offences between the ages of 10 and 17). When the authors divide the youths into groups on the basis of immigrant background, only small differences can be seen over time. The central finding was thus that youth crime has declined among youths of 'Danish background', among 'second-generation Danes' and also among persons born abroad. However, the decline was somewhat weaker in the second generation than among persons born abroad. The report does not present changes over time in the number of individuals in the different groups, but only the distribution of crime suspects. Among the two categories of youths of immigrant background there is some change in the level of overrepresentation. While this declines for youths born outside Denmark (from 4.5 to 3.2 times), it increases somewhat (from 3.5 to 4.0) for second generation Danes. The report does not present the results relating to immigrant background separately by gender.
A recent Norwegian study also shows that the level of overrepresentation among the children of immigrants has increased between 1992-2015 (Andersen et al., 2017). The analysis is based on cases that the police have cleared and submitted for prosecution, and the study includes controls for age and gender composition, but does not present results separately for men and women. The study shows that the level of overrepresentation among immigrants has declined since the millennium. This is the case for immigrant groups of both European and non-European background and for both violent and theft offences. The decline in the level of overrepresentation is primarily due to a stronger decline among foreign-born individuals by comparison with the remainder of the population (ibid: 55).
Viewed in combination, existing Nordic studies show that levels of overrepresentation among foreign-born individuals have not increased over recent decades. Instead, some findings indicate declining differences. In addition, we see a pattern whereby the least positive trend, and thus an increased level of excess risk, is found in relation to the children of immigrants, i.e. the second generation. In the small number of studies that include controls for socioeconomic differences, the levels of excess risk decline considerably, which is not unexpected, since individuals of foreign background more often grow up in relatively disadvantaged conditions (see also Hällsten et al., 2013). Finally, the Nordic research we have identified does not present information on the extent to which the trends over time among groups from different background categories differ for men and women, respectively.

Data, operationalizations and methods
It is well-established that convictions data of the kind on which this article is based are problematic in the sense that only a small proportion of the offences actually committed result in a conviction. This indicates that any assessment of patterns relating to offenders' background characteristics that are identified using official crime statistics must consider the fact that such patterns reflect differences between different social groups in both offending propensities and societal reactions/detection risks (McAra, 2016;Nilsson et al., 2017: 589 f.). Statistics on convictions at the level of the individual are administered by the Swedish National Council for Crime Prevention, and cover the period from 1973 to the present. These statistics present the conviction decisions made by prosecutors (summary sanction orders and waivers of prosecution) and county court judgements involving a finding of guilt. Summary fines issued by the police or the customs service are not included. A conviction may include decisions relating to several different offences.
The convictions register does not include data on the offenders' immigrant or social background, nor their living conditions at the time of the conviction. Such descriptions thus require the data to be linked to other registers, as has been the case in this study.
The population in our database is comprised of all individuals aged 0-75 who were registered as resident in Sweden on December 31 during any of the years 1968-2016 (described in more detail in Bäckman et al., 2020). This means, for example, that tourists and asylum seekers who had not yet been granted residence permits and registered as residents are not included. The study's database includes a total of approximately 15 million individuals.

Convictions data
For all individuals in the study population, a so-called micro-data excerpt from the convictions register was provided for the period 1973-2017. Year is defined by year of conviction. Since the age of criminal responsibility is 15 in Sweden, we have complete convictions data for the cohorts born from 1958 onwards. In total, almost 2 million individuals from our population have been convicted, in a total of just over 5 million convictions. The proportion of convictions that include more than one offence has remained relatively stable at approximately 30% throughout the period examined.
The offence type is based on the offence stated in the conviction. Each conviction decision may relate to a number of offences (e.g., theft and drug offences). We have included all the offences specified in each conviction, and thus not only the principal offence.

Data on immigrant and social background
In order to describe the convicted individuals' demographic and socioeconomic background characteristics, and also to identify the total population during each year of the study period, we have made use of a number of different registers.

Operationalizations and analytical methods
The crime outcomes that we analyse in the article are convictions for all offences, theft offences ( By following individuals over time, we have also been able to look at their total involvement in crime from the age of criminal responsibility (15) to age 24. We distinguish those individuals who have been convicted at least once during this ten-year period (which corresponds to the most criminally active period of the life course, e.g., Hirschi & Gottfredson, 1983; for a Swedish example see Sivertsson, 2018), and a smaller group whom we label repeat offenders. Given the substantial differences between the convictions frequencies of men and women, this group is comprised of individuals with two or more convictions among the women and at least four convictions among the men. Based on these thresholds, the proportion of repeat offenders among the men varies between 2.6 (for those aged 24 in 2009) and 4.6 (1990) per cent during the period 1990-2017 (i.e. cohorts born 1966-1993), while the corresponding figures for women are 0.9 (1999) and 1.6 (1993) percent. When we look to the number of convictions accumulated by individuals between the ages of 15 and 24 the analysis only includes those individuals who have been registered as resident in Sweden throughout this period. This selection is necessary for being able to create our indicator of socio-economic background (based on parents' incomes) when the individuals are at 15-17 years of age. This also renders more homogenous groups with immigrant background than in the cross-sectional part of the study. For example, it is reasonable to assume that we with this selection to a lesser degree include labour force immigrants.
We have created an immigrant background variable that differentiates between four groups: a) Native: born in Sweden to at least one Swedish-born parent; b) Second generation: born in Sweden to foreign-born parents; c) Immigrants from Western countries: born in Europe, the USA, Canada, Australia or New Zealand; d) Immigrants from non-western countries: born in some other country. This categorization is similar to that used in the Nordic studies described earlier. In those cases where there is only information for one parent among the Swedish-born, this parent's birth country has been used in the categorization. In our concluding analyses, we combine those born abroad into a single group (Immigrants).
Our measure of socioeconomic background is based on parental income data. Since we lack information on parental income for older individuals, these analyses are restricted to cohorts born 1966-1993. On the basis of the distribution of the parents' combined work income when an individual was aged 15, 16 and 17 we have created variables that categorize the individuals' families during childhood into deciles, where Decile 1 refers to the 10% from families with the lowest incomes. We have then examined the situation when each individual was aged 15-17 1 and categorized those who grew up in a family that was in Decile 1 for two of these 3 years as 'low income'. This is a relatively 'stringent' measure of low socioeconomic status. Growing up in a low-income family as defined here probably also involves a strong likelihood of having experienced other resource deficiencies and social problems. We know from previous research that different problematic conditions during childhood tend to cluster (see e.g., Bäckman & Nilsson, 2011).
The article's analyses are presented in the form of descriptive statistics. The ambition is to provide an overview of the trends over a substantial period of time.
The results are presented in two sections. In the first section we present conviction trends per 100,000 individuals in each immigrant background category and by gender, and also the trends for each category relative to those for natives (i.e. what is commonly labelled the level of overrepresentation). Since the age distribution varies substantially between the different groups, we have standardized our results for age by weighting the data so that all groups have the same age distribution as the native population. For reasons of space, the presentation of results for the separate offence types is restricted to showing levels of overrepresentation. In the second results section we use a cohort-approach to describe prevalence levels for birth-cohorts born 1966-1993. Since we measure involvement in crime in the ages 15-24 this corresponds to the period 1990-2017. In this section we also present the measures that identify the small group who have been convicted repeatedly during their youth, and socioeconomic background.

Cross-sectional analysis -conviction trends by immigrant background 1973-2017
Figure 1a presents convictions per 100,000 for men by immigrant background with controls for between-group age differences. As expected, the level of convictions is lower for natives than for the other groups, throughout the period examined. The overarching pattern for the trend over time is that the level of convictions has declined markedly for all four groups, i.e. irrespective of immigrant background. Among men born abroad, convictions increased during the 1970s and the highest convictions levels were noted at the beginning of the 1980s. For both groups of foreign-born men and for the second generation, the conviction levels have declined by half by comparison with the 1970s. Previous studies (see above) have found the second generation to have fewer convictions than those born abroad. As can be seen in Figure 1b, this pattern has changed since 2006. Since the beginning of the 1980s, the level of overrepresentation has increased continuously for this group, while for those born abroad, it has declined since the millennium. It is important to note that these differing trends are not due to an increase in convictions among the second-generation males, but rather to the level of convictions in this group having declined less markedly than that of the other groups examined.
Among women, the pattern is slightly different (Figure 2a-b). Firstly, the level of convictions does not decline as substantially as among the men. For second-generation women, the level of convictions remains stable until 2009 and then declines. A similar pattern is seen among native women. Among the foreign-born women the trend is very different, however. Here levels of convictions first increase during the 1970s and 1980s. During the 1990s we see the start of a powerful decline which then continues throughout the period until 2017. It is notable that this decline means that secondgeneration women, as was the case among the men, have become the group with the highest level of convictions. Among the women, however, this group's level of overrepresentation has been more stable over time (Figure 2b). Finally, among the women too we see that the level of overrepresentation in convictions for foreign-born individuals was greatest around the beginning of the 1990s and lowest during the years since 2010.
The conviction trends for theft, violent and drug offences differ markedly both in Sweden and many other Nordic and European countries (see Bäckman et al., 2020). While theft convictions have declined substantially, and are the crime type that has driven the general trends presented above, convictions for violence have remained relatively stable and drug convictions have increased considerably. Figure 3a-f presents the relative trends in convictions by immigrant background for these three offence categories with native men and women as the reference category.
A long-term decline in convictions for theft offences started in Sweden in the mid-1980s and occurred irrespective of immigrant background (see Bäckman et al., 2020, p. 57). The level of overrepresentation is similar for both groups of foreign-born men and is greatest in the mid-1980s and at the end of the 1990s (Figure 3a). For secondgeneration men there is a gradual increase in the level of overrepresentation. It is important here to bear in mind that the underlying pattern behind this trend is that theft convictions among second-generation men have declined more slowly than theft convictions among native men. The picture is more complex for violent offences ( Figure  3b). Since the mid-1980s, the trends for the two Swedish-born groups have followed one another. This means that the increased overrepresentation noted among secondgeneration men (see Figure 1b), is not due to convictions for violent crime. Among foreign-born men from non-Western countries, the difference in conviction levels compared to the Swedish-born reference group is greatest during the period 1980-2000, when the risk for conviction is approximately 3.5 times as high. During the period since the year 2000, the level of overrepresentation has declined markedly. In the other group of foreign-born men, the level of overrepresentation has declined from just over 2.5 times at the beginning of the 1990s to 1.5 times in the mid-2010s.
The trend for drug crime is interesting since this is an offence type for which policing measures in the form of 'stop and search' play an important role for the trend in convictions. During the 1970s, the actual levels of convictions for drug offences were very low by comparison with the period since the year 2000 for all the groups examined (see Bäckman et al., 2020, p. 57). One important reason for the increase is that in 1993, the police were given increased powers to test for possession and drug use by means of blood and urine testing. It is notable that this increase in the use of police controls initially appears to affect convictions for all groups of men irrespective of immigrant background; thus, for men during the period 1994-2005, levels of overrepresentation appear relatively stable (Figure 3c). During the past 10 years, the excess risk for being convicted for drug crime among foreign-born men has declined in relation to both groups of Swedish-born men. This means that the increase in convictions for drug offences has been more notable among the male children of immigrants than among immigrant men. This is also part of the explanation for why the total convictions level of Swedish-born men of foreign background has shifted to a higher level than that of the foreign-born men (Figure 1).
Among women, the trends differ from those presented for men in a number of important ways. Among foreign-born women, there has been a powerful decline in convictions for theft since the beginning of the 1990s.The level of overrepresentation among women born in non-Western countries has declined from over 5 times at the beginning of the 1990s to 2.0 times by the end of the period examined (Figure 3d). The trend is very different for second-generation women. This group begins the period with the same level of convictions as the reference group, but is then characterized by an excess risk for conviction that increases gradually throughout more or less the entire period examined.
Levels of excess risk for violent crime have decreased for all groups of foreign background (Figure 3e). During the 1990s, the average level of overrepresentation was 2.6 times for both female children of immigrants and women born in non-Western countries. For those born in western countries the level of overrepresentation was 2.1 times that of women born in Sweden. During the 2010s, the corresponding levels of excess risk for conviction were around 2.0 for the two former groups. At the end of the period examined there is hardly any overrepresentation of foreign-born women from Western countries. It should be noted that since convictions for violent offending are uncommon among women, the highly fluctuating levels of Figure 3e should be interpreted with some caution. 2 Among immigrants from non-western countries, for example, no women were convicted of violent offences in certain years. These years have been excluded from the presentation.
There is also an increase in convictions for drug offences among women in general, particularly after 1993 ( Figure 3f). However, by contrast with the trends among men, foreign-born women are those with the lowest conviction rates, while Swedish-born women are those at greatest risk of conviction. There is an overrepresentation of secondgeneration women, which is most marked during the second half of the 1990s (2.5 times) and then declines successively after the year 2000 to a level of 1.4 times. This means that the increase in convictions for drug offences is most marked among native women.

Cohort analysis -cumulative convictions to age 24 by immigrant and socioeconomic background
In this section, we supplement our descriptive analysis and provide a more detailed picture by focusing on cumulative conviction frequencies to age 24 for the cohorts born between 1966 and 1993.
Table 1a-b shows the development, in terms of percentages and relative risk ratios, of offenders with at least one conviction and repeat offenders stratified by immigrant background and gender, and presented by four-year grouped cohorts. Seen over the period as a whole, immigrants and the second generation have a higher risk of being convicted for a crime than natives. This is true for both males and females and regardless of conviction category. Furthermore, we cannot see the pattern noted earlier, whereby the level of overrepresentation for second-generation men passes that of those born abroad. Instead, Immigrants have a slightly higher excess risk compared to the second generation over the full period. However, the difference between these two groups declines successively and at the end of the period examined, the percentages with at least one conviction virtually identical. 3 As regards the trend for the small but highly active group of men with four or more convictions to age 24, we can see that here too, second-generation men move up to draw level with the men who were born abroad. The excess risk for immigrant men lies at close to three times at the beginning and end of the period examined, but is   somewhat higher among those that reached age 24 during the mid-1990s to the mid-2000s (i.e. cohorts born 1970-1981). The corresponding excess risk for secondgeneration men increases from around two at the beginning of the period to three at the end. Underlying this trend is a general decline in the percentages of the population with several convictions. The increase in the excess risk among second-generation men is thus due the fact that the decline in this group is slightly weaker than that in the other two groups of men.
The patterns for women with at least one conviction and for those with two or more convictions are similar, although at very different levels. In both of these groups, the level of overrepresentation among women of foreign background declines, starting with cohorts born in the late 1970s. If we look to the small group of women with repeated convictions, for example, the level of overrepresentation among those born abroad was 3.2 times for cohorts born 1974-1977, declining to 1.7 times in the youngest group. Overall, among the women, we see a decline in the differences between the different immigrant background groups in both absolute and relative terms.

Trends among immigrant background groups within the low-income category
In the final stage of our analysis we examine the distribution of convictions across immigrant background groups among those within the low-income category. This involves a simple but informative control for the significance of differences in childhood and living conditions between the immigrant background groups. Thus, Table 2a-b presents the percentages of individuals with at least one and at least four convictions to age 24 for men and women from low-income families by the three different immigrant background groups, and presented by four-year grouped cohorts.
Beginning with the men, we now see much smaller differences over the whole period, as compared to the levels of overrepresentation presented above. In the three oldest cohort groups, native men lie at a level below that of the other two groups. Thereafter, the differences are small and fairly stable. This is the case both for those with at least one conviction and for those with at least four convictions. In the group that is of most interest from a crime policy perspective, i.e. the small group of repeat offenders, there is, however, still an excess risk for second-generation men in the youngest cohorts of around 1.3-1.7 times, and for immigrant men of around 1.1-1.3 times.
Turning to the women, here too we see that the levels of excess risk are greatly affected by the fact that the analysis is limited to those who have grown up in low-income families. Once again, we see that the level of overrepresentation declines and that it converges in cohorts born in the late 1970s and later. It is notable that among those women who have grown up in the most disadvantaged families, we see that during the period since the millennium the lowest levels are found among those who were born abroad. This is particularly salient with regard to repeat offenders in the youngest cohort group where there is a 50% lower risk of being convicted at least twice in the immigrant population compared to the native population. 4 Table 2. a-b. Men (a) and women (b) from low-income background born between 1966 and 1993 followed between ages 15 and 24 (i.e. who reached age 24 in the years 1990-2017) by grouped birth cohort, immigrant background and number of convictions. Prevalence (%), relative risks (RR) and grouped cohort size (N).

Concluding discussion
Despite the large number of studies that have examined offending among immigrants in Scandinavia since the 1970s, none have been able to describe longer term trends in the level of overrepresentation. In this article, we have shown that among men, the level of convictions for crime has declined irrespective of the individuals' immigrant background. The overarching trend over the past 40 years, as shown by a traditional cross-sectional analysis, is primarily characterized by a similarity in the trends between persons born abroad and those born in Sweden. In spite of this, when we study the relative trends it is clear that the level of overrepresentation has changed in certain respects. For men born abroad, the levels of overrepresentation are lower during the 2010s than they were during the 1990s and at the beginning of the 2000s, irrespective of whether they were born in Western or non-Western countries, and not least with regard to convictions for violent crime. It is also notable that this pattern of declining overrepresentation is confirmed by a study based on the Swedish self-report surveys conducted among students enrolled in 9 th grade (15-16 years old) during the period 1999-2017 (Vasiljevic et al., 2020). Previous Swedish studies have found conviction levels to be higher for immigrants than for the second generation. This pattern differs from that noted in studies from other countries, and has been interpreted as a positive result of integration, with children who are born and grow up in Sweden being assumed to have more similar life chances irrespective of background (see e.g. Von Hofer et al., 1998). The time series presented in this article show that this situation has changed, and that the pattern is no longer found during the 2010s, at least as regards the risk for conviction. This means that the second generation constitutes the group for whom the trend in convictions has been the least positive. When we focus on different offence types, it is clear that young secondgeneration men have experienced a powerful increase in convictions for drug offences, which is an important part of the reason why this group is at higher risk for conviction than foreign-born men at the end of the period examined. In addition, their convictions for theft offences have declined less than those of native men, which contributes to the increased level of excess risk. It may also be noted that the trend has been fairly similar for immigrants from both Western and non-Western countries.
It is also notable that our results are similar to those reported in neighbouring Scandinavian countries (see e.g. Andersen et al., 2011:16;Andersen et al., 2017). In this regard, the accusations in the Nordic political debate of a special 'Swedish condition' regarding immigration and crime trends seems inaccurate. However, the available Scandinavian studies all use different operationalizations of key indicators and also differ in their methods of analysis. As was recently noted by Klement (2020), this makes it difficult to compare studies both within and between countries. A comparative study covering a substantial period of time based on a common method and comparable data would therefore be very useful.
Previous Swedish and Nordic research has rarely studied trends in immigrant background and crime over time among women, and we therefore know little about whether the trend in levels of overrepresentation among women follows that seen among men. Among foreign-born women, convictions have declined over time, whereas conviction levels among Swedish-born women have remained relatively unchanged. The decline in differences between the conviction levels of Swedish and foreign-born women over the past 25 years is particularly marked in relation to theft offences. Further, there is an interesting difference with regard to drug offences, where we see a considerably lower risk for conviction among foreign-born women compared to those born in Sweden. However, the change in the societal reaction to drug offences from around 1993 has produced an increased number of convictions for drug offences among women, irrespective of immigrant background. Further, in the same way as among the men, the trend is least positive for the second-generation women, and here too, the increase in convictions for drug offences is striking. Since the Scandinavian studies of which we are aware have not studied trends among women, we cannot know whether our Nordic neighbours have experienced similar or different trends.
The second part of our results section presented findings from cohort-based analyses focused on the risk for convictions over a ten-year period, which also identified the small group of individuals who were convicted repeatedly. In these analyses we have been able to link individuals to their parents in order to account for the impact of socioeconomic background. Over the period 1990-2017, there has been a decrease in the proportion of men who had been convicted several times by age 24. This decline is somewhat less marked among second-generation men, which has rendered an increase of the excess risk from 2 to 3 for this group relative to native men during the period examined. Among women, we see a potential decline in the size of these between-group differences, with a gentle increase over the course of the period for native women at the same time as there is a decline in the proportion of women of immigrant background with two or more convictions, primarily during the 1990s. However, due to small numbers these patterns should be interpreted with some caution.
We know from previous research that there are substantial differences in socioeconomic conditions between the different immigrant background groups (see e.g. Hällsten et al., 2013;Andersen et al., 2017). We would therefore expect to find a large part of the overrepresentation in convictions among those born abroad and in the second generation, both in general, and particularly in relation to repeatedly registered offending, to be linked to these socioeconomic differences. The difference by comparison with previous studies is that we have been able to follow how this relationship has developed over time. We can see that within the low-income category, the differences in levels of convictions between the immigrant background categories have declined over time for both men and women. The differences are particularly small in cohorts born in the late 1970s and later. Following this control for the individuals' socioeconomic conditions during childhood, there is virtually no overrepresentation during the 2010s for foreign-born men in relation to native men. Among the foreignborn women, the overrepresentation has instead become an underrepresentation. It should here be borne in mind, however, that our indicator of low-income background is a relatively 'stringent' measure. Having lived in a household in which the adults were counted among the 10 per cent of the population with the lowest work-related incomes in two of three years involves a relatively powerful selection with regard to resource deficiencies and thus probably also an accumulation of other social problems. It is likely that this selection is more powerful in the native population than among those born abroad, since a larger proportion of the latter group are counted among those with low incomes. The relationships between these different factors constitute an important area for future research.
The reduction we have shown in the level of overrepresentation for foreign-born individuals, irrespective of the region from which they have migrated, may appear surprising given that there have been simultaneous increases in levels of inequality and residential segregation. The composition of the group of foreign-born individuals has also shifted over time both with regard to country of origin and reason for migration. A larger proportion is now comprised of refugees from non-Western countries. It is therefore difficult to relate the trends we have described to factors related to changing selfselection among immigrants. How then might the trends be understood?
In order to understand the similarities in conviction trends between the different groups, not least with regard to theft offences, explanations focused on the opportunity structure are of course important (Farrell et al., 2015). Measures that reduce the opportunities for crime affect different groups irrespective of their immigrant background.
Differences between the different immigrant background groups in living conditions and resources has been linked to differences in crime (e.g., Hällsten et al., 2013;Andersen et al., 2017). Increasing inequalities may also be assumed to mean that any deteriorations, or improvements, that have occurred in relation to childhood conditions and life chances have not been evenly distributed across all groups in society. We have shown that the children of immigrants constitute one of the groups characterized by a less positive conviction trend. We know from previous research that this group has also experienced less positive trends in terms of parents' economic resources (Bäckman et al., 2020:83 f). An interpretation that would view increased inequality as a mechanism underlying increased differences in criminal convictions is however made more difficult by the fact that we see a quite different trend among individuals born abroad, among whom the size of the excess risk for conviction has instead declined. In order to better understand these trends, which may appear somewhat contradictory, would require more detailed analyses than those presented in this article. This might, for example, involve looking more closely at how the composition of the different groups has changed over time, among other things with regard to social background, reasons for migration, individual resources and the significance of residential segregation.
Interpretations of our results are of course also complicated by the fact that trends in convictions are not only a consequence of offending behaviour but also of society's reactions to crime and the public´s inclination to report crime. If for example, the police choose to direct their control measures at socially disadvantaged areas, the detection risk will increase more for those who spend time in these areas (Irwin et al., 2013;McAra, 2016;Schclarek Mulinari, 2020). As a means of approaching this issue, we have in the current study utilized the fact that theft, violence and drug offences come to the attention of the justice system in different ways, and we view drug offences in particular as an offence for which convictions are greatly affected by the focus of policing measures. On the basis of self-report surveys of young people of different immigrant background, between-group differences in drug use appear to be relatively small (Brå, 2018), while at the same time this study shows there are substantial differences in conviction levels. This might be due to a policing effect, with young men of foreign background being at greater risk than other groups of being stopped by the police on suspicion of drug crime. Although our study cannot measure differences in the risk of being stopped by the police, two points may be noted. Firstly, the trend in convictions for drug offences appears relatively similar, irrespective of immigrant background group since the legislative change of 1993. This suggests that all groups have been affected by the increase in police controls in relation to drug offending. Secondly, it is clear that the increase in convictions for drug crime constitutes one explanation for the increased level of the overrepresentation of the second generation as compared to persons born abroad. A closer examination of the trends across different sociodemographic groups in the risk for being subject to police controls, and for then being registered for crime, would be very useful.
Finally, it should be noted that there was a major wave of immigration at the end of the period we have examined, largely as a consequence of the war in Syria (SCB, 2018). To what extent this has produced new conditions and by extension a shift in the risk for offending is something this article has not been able to capture. What we can say on the basis of our study, however, is that despite the fact that we include a long observation period characterized by substantial changes in the level and composition of immigration to Sweden, we see no major changes in the level of excess risk for conviction among those of immigrant background. The level of overrepresentation among second-generation immigrants has increased somewhat, while the overrepresentation of those born abroad has decreased towards the end of the period examined. At the general level, however, conviction levels have decreased, to a greater extent among men than among women, irrespective of immigrant background. This is something that was previously unknown, and that may surprise many, given the public debate in Scandinavia, where crime trends are often linked to increased immigration (see eg. Estrada, 1999;Rydgren, 2004).