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    Immigration, Low Income and Income Inequality in Canada: What's New in the 2000s?

    Immigration, Low Income and Income Inequality in Canada: What's New in the 2000s?

    by Garnett Picot and Feng Hou
    Social Analysis and Modelling Division, Statistics Canada

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    Abstract

    This paper documents changes in low-income and high-income rates and in family-income inequality among immigrants and Canadian-born persons over the 1995-to-2010 period. In addition, it estimates the extent to which declining low-income rates among immigrants were attributable to changing compositional characteristics over this period, and the direct role that immigration played in low-income and income-inequality trends in Canada. Both national and regional results are presented. There are four major findings. First, in contrast to the 1980s and 1990s, immigrant low-income rates declined in the 2000s. The decline was particularly evident in the western regions, but was not observed in Toronto. However, because low-income rates also declined among the Canadian-born through the 2000s, immigrants’ low-income rates relative to the Canadian-born remained high in most regions. Manitoba and Saskatchewan were exceptions in this regard. Second, changes in immigrant characteristics and selection programs accounted for about one-third of the decline in low-income rates among recent immigrants. Again, this varied by region. Third, while rising immigrant low-income rates accounted for virtually all of the increase in the national low-income rate over the 1980s and 1990s, immigrants accounted for little of the decline in the national low-income rate during the 2000s. Immigrants also accounted for little of the rise in the high-income rate observed between 1995 and 2010. Fourth, immigration contributed very little to national trends in either family-income inequality or family-earnings inequality since the mid-1990s.

    Executive summary

    During the 1980s and 1990s, immigration was associated with the rise in low-income rates and family-income inequality in Canada. Over the 2000s, there were significant changes in the labour market and in immigrant selection. This paper focuses on the direct effect of immigration on the change in low income and family-income inequality over the 1995-to-2010 period. The paper outlines recent trends in low-income rates and income inequality for both the Canadian-born and immigrants. The low-income rate in Canada fell during the 2000s. Was this driven in part by changes in economic outcomes among immigrants? Inequality increased considerably in the late 1990s. Did immigration contribute to this increase?

    This paper uses Statistics Canada’s Longitudinal Administrative Databank (LAD) as the primary data source. The LAD is a random, 20% sample of the T1 Family File, which is a yearly cross-sectional file of all taxfilers and their families. Immigrants who have entered Canada since 1980 can be identified in this file. Furthermore, information based on immigrant landing records, such as education at entry, age at entry, intended occupation, gender, family status, whether the immigrant speaks English or French at entry, and immigrant class are included in the LAD file for immigrants. All immigrants who filed a return at any time during their tenure in Canada are included in the study sample. The low-income status in this study is based on a fixed low-income measure, defined as the average of one-half of the median adult-equivalent adjusted family incomes in 1995, 2000, 2005 and 2010. The income in each year is reported in 2010 constant dollars, i.e., is adjusted for inflation over the 1995-to-2010 period.

    Low-income rates among immigrants declined significantly over the 2000s, although their relative (to the Canadian-born) low-income rates did not improve. There were three regional exceptions to this general pattern: immigrant low-income rates did not fall in Toronto as in other regions during the 2000s; low-income rates did not fall among the Canadian-born in Toronto as in other regions during the 2000s; and rates among immigrants decreased the fastest in Manitoba and Saskatchewan, where relativerates among recent immigrants fell back to around 1.2 times those of the Canadian-born, levels of relative rates not seen since the early 1980s.

    At the national level, changes in immigrant characteristics—notably rising educational attainment and changing source regions—accounted for about one-third of the decline in the low-income rate among recent immigrants (in Canada five years or less) during the 2000s. The effect of compositional changes differed across regions. Changes in immigrant characteristics and entry programs accounted for between one-fifth and one-half of the decrease in low-income rates among recent immigrants, depending on the region.

    Declining immigrant low-income rates contributed little to the fall in low-income rates among the general population in Canada during the 2000s. Unlike the 1990s, when rising immigrant population shares and low-income rates accounted for most of the increase in low-income rates in Canada, the decrease in the rates during the 2000s was driven primarily by falling rates among the Canadian-born.

    High-income rates rose between 1995 and 2010 among both immigrants and the Canadian-born, although they were higher among the latter group. Immigration contributed little to the increase in the overall high-income rate in Canada over that period.

    Both family-income inequality and family-earnings inequality increased in Canada from 1990 to 2010, but the majority of the rise occurred during the late 1990s. The paper concludes that for Canada as a whole, immigration contributed little to the increase of the late 1990s in either income or earnings inequality. Family income and earnings inequality rose among the immigrant population during the late 1990s, as it did among the Canadian-born, but the immigrant population did not contribute disproportionately to the overall increase. There was little increase in income inequality in the 2000s.

    1 Introduction

    During the 1980s and 1990s, immigration had a significant negative effect on low-income rates and family-income inequality in Canada. The rise in immigration levels during that period were accompanied by concerns about immigrants’ declining economic outcomes. While low-income rates among the Canadian-born fell through the 1990s, they rose among immigrants. As a result, rising immigrant low-income rates accounted for virtually all of the increase in the national low-income rate during that period (Picot and Hou 2003). Immigration had an effect on family-income inequality as well. One study found that as much as one-half of the small rise in inequality during the early 1990s was associated with the immigrant population (Moore and Pacey 2003). The effect was most pronounced in the large cities where the immigrant population grew most. The preceding papers were concerned with the effect of immigration on the low income and inequality of the total Canadian population (immigrants plus the Canadian-born) due to rising shares of immigrants and their worsening economic outcomes. In this paper, this is referred to as the direct effect of immigration on low income and family-income inequality.

    There is another body of literature that focuses on the effect of immigration on the wages and the wage distribution of domestically-born workers (in our case the Canadian-born). Rising shares of immigrants in the Canadian population can potentially affect the wages of the Canadian-born. This can affect low-income rates, as earnings are the largest component of income for most families. It can also influence wage inequality among the Canadian-born. In this paper, this is referred to as the indirect effect of immigration on low income and inequality. The international literature on this topic is quite extensive, but only a small number of Canadian papers exist. The international literature tends to find that immigration has only a very small effect on the wages of domestic workers, whether positive or negative (Longhi, Nijkamp and Poot 2009;  European Economic Association 2012; Card 2009).

    In this context, it seems likely that the indirect effect of immigration on low income or family-income inequality among the Canadian-born population would be quite small. However, the direct effect of a rising share of immigrants in the population, combined with relatively poor economic outcomes of many recent immigrants, can significantly affect low-income and inequality levels for the total population in Canada. In the United States, Card (2009) found that immigration had little effect on wage inequality among the American-born (i.e., the indirect effect), while the direct effect on inequality was larger, although still not dramatic. This direct effect would be most pronounced in cities and regions where immigrants constitute a large share of the population.

    This paper briefly discusses the indirect effect of immigration and examines in detail the direct effect of immigration on the change in low income and family-income inequality over the 1995-to-2010 period. Recent trends in low-income rates and income inequality for both the Canadian-born and immigrants are outlined: the Canadian low-income rate fell during the 2000s, and whether this was driven in part by changes in economic outcomes of immigrants is explored. The rise in Canadian income inequality was concentrated in the late 1990s, and this paper looks at whether immigration contributed to this increase. The two preceding questions are the central focus of this paper, with results produced at the national and provincial levels and for major metropolitan areas.

    The primary data source used in this study is Statistics Canada’s Longitudinal Administrative Databank (LAD). The LAD is a random, 20% sample of the T1 Family File, which is a yearly cross-sectional file of all taxfilers and their families. Individuals selected for the LAD are linked across years to create a longitudinal profile of each individual. Since the early 1990s, approximately 95% of working-age Canadians filed tax returns. Immigrants who have entered Canada since 1980 can be identified in this file. Furthermore, information based on immigrant landing records, such as education at entry, age at entry, intended occupation, gender, family status, whether the immigrant speaks English or French at entry, and immigrant class are included in the LAD file for immigrants. All immigrants who filed a return at any time during their tenure in Canada are included in the sample.

    2 Immigration and low-income rates in Canada

    2.1 Low-income trends in Canada

    This paper is concerned with trends, and in particular the change in the low-income rate between 1995 and 2010. Low-income rates are very cyclically sensitive, rising in recessions and falling in expansions. To assess longer-term trends—abstracting from cyclical variation—focus is put on the years of 1981, 1989, 2000 and 2007. The low-income rate most commonly reported by Statistics CanadaNote 1 fell during the 1980s, from 11.6% in 1981 to 10.2% in 1989 (Chart 1). Over the 1990s the low-income rate rose marginally, reaching 12.5% by 2000. A significant decline followed during the 2000s, as the rate fell to 9.1% in 2007. The low-income rate rose marginally during the 2008-to-2009 recession and fell again to 8.8% by 2011. It is conceivable that improvements in the low-income rate among immigrants contributed to the falling low-income rate in Canada during the 2000s.

    Chart 1

    Description for chart 1

    The trends in low-income rates in Canada can differ depending on the data source, definition of income, and low-income cut-offs that are used. The trends based on the Longitudinal Administrative Databank (LAD) are similar to those reported above from the survey data, although the levels are quite different for a number of reasonsNote 2 (Table 1). The administrative data suggest that the low-income rate fell by about one-third between 1995 and 2010, while the survey data suggest a 39% drop. Some of this decline would be due to business cycle effects, notably the improvement in the economy between 1995 and 2000. Both the administrative and the survey data show that about one-third of the overall decline between 1995 and 2010 occurred during the expansion of the late 1990s. This is likely the normal decline in low-income rates observed over the last part of a business cycle. But the decline in the low-income rate during the 2000s is likely due at least in part to other factors, possibly including declining immigrant low-income rates.

    2.2 Trends in immigrant low-income rates

    Using census data, before-tax income, and the low-income cut-offs (LICOs), Picot and Hou (2003) found that both absolute and relative (to the Canadian-born) low-income rates among immigrants rose through the 1980s and 1990s (abstracting from business cycle fluctuations). This increase was observed not only among recent immigrants (those in Canada for less than five years), but also among immigrants in Canada for 6 to 10 and 11 to 15 years. Indeed, low-income rates increased by roughly 50% among each of these groups. This was evident across all education, age and language groups, but was concentrated primarily among immigrants from Asia, Africa and Southern and Eastern Europe. The trends among immigrants in Canada for more than 15 years closely resembled those observed among the Canadian-born population. In relative terms, low-income rates among recent immigrants increased from 1.4 to 2.5 times that of the Canadian-born population between 1980 and 2000 (Chart 2).

    Chart 2

    Description for chart 2

    Since 1995, low-income rates among immigrants and the total population have been declining. Among recent immigrants, the after-tax low-income rates using a fixed low-income measure (LIM)Note 3 fell from 45.7% to 31.9% between 1995 and 2010, a decline of one-third (Table 2). But, as noted above, there was a substantial decline in the low-income rate among the total population over this period. The comparison groupNote 4 used in this study, consisting mainly of the Canadian-born, also saw its low-income rate fall by roughly one-third, from 18.6% to 12.5%. Hence, there was little change in the relative low-income ratio among recent immigrants, which remained about 2.6 times that of the Canadian-born in 2010 (Chart 3). The rate for the comparison group (largely Canadian-born) acts as a control for business cycle and policy changes that can affect the low-income rate of all groups. Over the study period, the income distribution shifted significantly to the right for all these groups, although recent immigrants were more likely to locate at the bottom of the income distribution than other groups in both 2000 and 2010 (Charts A.1 and A.2, Appendix A).

    Chart 3

    Description for chart 3

    Over the 1995-to-2010 period, declines in the absolute low-income rates of immigrants in Canada for 6 to 10 years and 11 to 15 years were also observed (23% and 12% declines respectively) (Chart 2), although the relative low-income ratios of these groups rose marginally (Chart 3).

    Since both immigrant shares of the population and economic outcomes differ across regions, the low-income trend data are provided for the regions of Canada as well as the larger cities in Appendix Table A.1. The trends in low-income rates in most regions generally reflect those reported at the national level above. That is to say, absolute rates fell somewhat over the 2000s, but relative rates remained more or less stable, particularly for recent immigrants. However, there are a few exceptions to this observation. In Toronto, low-income rates did not decline significantly among immigrants during the 2000s, and did not fall among the Canadian-born (i.e., the comparison group). Toronto was the only region/city that did not experience an improvement in low-income rates among immigrants or the Canadian-born during that decade.

    The other major exceptions were Manitoba and Saskatchewan. Through the 2000s, they experienced significant increases in the number of immigrants admitted through the Provincial Nominee Program. The share of the population consisting of recent immigrants doubled in both provinces (Table A.1), although remaining well below that observed in Montreal, Toronto and Vancouver. These two provinces also experienced the most rapid decline in low-income rates among immigrants over the 2000s, and were the only two regions where recent immigrants’ relative (to the Canadian-born) low-income rates fell significantly. In Manitoba, low-income rates among recent immigrants declined by 40% over the 2000s to 16.3%, well below rates in most other regions (Table A.1). The rate fell by 50% in Saskatchewan. In both provinces, the relative low-income ratios fell back to around 1.2, levels not seen in Canada since the early 1980s. In Alberta and British Columbia, the low-income rates among immigrants declined significantly during the 2000s, but the relative rates remained in the 1.9 to 2.4 range by 2010, suggesting no real improvement beyond what was observed for the population as a whole, and well above relative levels observed in earlier decades.

    2.3 Did the rates among recent immigrants decline because of changing programs and immigrant characteristics?

    The immigrant selection system changed significantly over the 2000s. The Immigration and Refugee Protection Act introduced in 2002 altered the points system used to select federal skilled workers. As a result, the educational attainment of new immigrants increased, their “intended” occupational distribution moved somewhat away from engineers and information technology workers towards other occupations, their language skills improved, and the distribution of source regions shifted substantially. These changes in composition tended to increase the average earnings of federal skilled-worker principal applicants entering the country after 2004 (CIC 2010).

    The other major compositional shift was the expansion of the Provincial Nominee Program (PNP), particularly in Manitoba and Saskatchewan. Employers play a larger role in selection in this program than in the Federal Skilled Worker Program (FSWP); hence more immigrants entered Canada with a job in place. The result was that during the first few years after entering Canada, PNP immigrants had, on average, higher earnings than those entering under the FSWP. However, federal skilled workers’ earnings surpassed those in the PNP after about five years, likely due to their higher educational attainment levels (CIC 2011).

    The statistics on recent immigrants reflect the compositional shifts outlined above. Between 2000 and 2010, the proportion with a university degree increased from 31% to 42%, and, among recent immigrants whose mother tongue was not English, the share able to speak English increased from 48% to 59%.Note 5 Nationally, the proportion entering through the PNP increased from virtually zero in 2000 to 7% in 2010. This effect was strongest in Manitoba and Saskatchewan, where the shares entering via the PNP rose from 4% to 66% and from 0% to 49%, respectively.

    The compositional shifts in immigrant characteristics and programs of entry may have been partly responsible for the decline in low-income rates over the 2000s, particularly among recent immigrants (in Canada for less than five years), the group on which this section focuses.

    With a regression decomposition approach,Note 6 the extent to which the decline in the low-income rate was associated with changes in characteristics can be assessed—notably age, educational attainment, source region, knowledge of an official language and family status—or changes in the share entering the country under various programsNote 7—including the PNP and FSWP, and as family class and refugees. The decomposition is carried out for Canada and its regions and cities, and for two time periods—1995 to 2000 and 2000 to 2010. This paper focuses on the latter period,Note 8 but briefly reports the results for 1995 to 2000.

    During the economic expansion that occurred between 1995 and 2000, low-income rates among recent immigrants in Canada fell by 6.3 percentage points. The changing composition of recent immigrants contributed 1.9 points (or about 30%) of the decline. Changing education, age and family composition were the main factors underlying this composition effect (Table 2). During the 2000-to-2010 period particularly, of the 7.5-percentage-point decline in the low-income rate among recent immigrants in Canada, one-third (or 2.5 points) was associated with the changing composition of recent immigrants (Table 2). Rising educational attainment and changing source regions were the major contributors to the composition effect, together accounting for 1.7 of the 2.5-percentage-point drop associated with the compositional shift. Changing admission class did not have a large effect, accounting for only roughly 3% (0.2/7.5, Table 2) and at most 13%Note 9 of the total decline at the national level.

    Changes in immigration selection varied by province during the 2000s, as these jurisdictions played a more active policy role than during previous periods. Some provinces embraced the PNP, others did not. Furthermore, immigrant landings moved somewhat away from Toronto and Vancouver towards other regions (Bonikowska, Hou and Picot 2014). As a result, changes in composition and immigrant class varied by region, as did their effect on low-income rates. Compositional changes accounted for between one-fifth and one-half of the decrease in low-income rates in the regions and cities, and the specific factors responsible for these compositional affects varied among jurisdictions.

    In that regard, the three large cities remained the destination for most recent immigrants. In Toronto, low-income rates among recent immigrants did not fall over the 2000s. However, Montreal experienced a significant decline of 9.6 percentage points, half of which was associated with compositional changes. The most significant contributing factors included rising educational attainment levels and changes in admissions programs (Table 2), notably an increasing share of immigrants admitted via the FSWP, which increased from 39% to 57%. Furthermore, Vancouver saw a substantial 12.4-percentage-point drop in the low-income rates of recent immigrants, but only about 10% of it (1.2 points) was associated with compositional changes. In Vancouver, the share of immigrants entering through the federal skilled worker class fell from one-half to one-third and the shares entering through the family class and PNP rose. This shift in admission classes tended to put upward pressure on the low-income rate. However, this was offset by shifts in source region and rising educational attainment, which put downward pressure on the rate (Table 2). Overall, across the three largest immigrant-receiving cities, the effect of compositional changes on low-income rates varied significantly.

    This variability was also evident across regions that saw larger immigrant in-flows through the 2000s. Saskatchewan posted the largest decline in low-income rates among recent immigrants (16.5 percentage points). About one-third of this appears to be associated with changing immigrant composition, driven primarily by shifts in source regions. Results for Manitoba are unclear because of the unusually large 'joint change,' which makes it impossible to separate the effects of changing admission categories from other factors.Note 10 Alberta and the Atlantic region also registered declines in low-income rates among recent immigrants. Compositional changes accounted for almost one-half of the decline in the Atlantic region, driven mainly by changes in admission class and source region, and for about one-third in Alberta, driven mainly by changes in admission class and rising educational attainment.

    In summary, compositional changes—including changes in admission class and characteristics—did not play the dominant role in the decline in the low-income rates among recent immigrants over the 2000-to-2010 period, but played a significant part. The specific factors driving the compositional effect varied by region.

    However, the decline in immigrant low-income rates may have contributed to the fall in the Canadian rates during the 2000s, just as they accounted for much of the rise in the 1990s.

    2.4 The contribution of immigration to the decline in low-income rates in Canada during the 2000s

    The direct effect of immigration on the aggregate low-income rate can be driven by two factors: a change in the share of immigrants in the population, and a change in their low-income rate. To determine a group’s contribution to the change in the aggregate low-income rate in Canada or in a region, the following formula is used:

    %contribution=[ r i,y2 * S i,y2 r i,y1 * S i,y1 ]*100/[ R y2 R y1 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai yjaiaayIW7caaMi8UaaGjcVlaadogacaWGVbGaamOBaiaadshacaWG YbGaamyAaiaadkgacaWG1bGaamiDaiaadMgacaWGVbGaamOBaiabg2 da9maadmaabaGaamOCamaaBaaaleaacaWGPbGaaiilaiaayIW7caWG 5bGaaGOmaaqabaGccaGGQaGaam4uamaaBaaaleaacaWGPbGaaiilai aayIW7caWG5bGaaGOmaaqabaGccqGHsislcaWGYbWaaSbaaSqaaiaa dMgacaGGSaGaaGjcVlaadMhacaaIXaaabeaakiaacQcacaWGtbWaaS baaSqaaiaadMgacaGGSaGaaGjcVlaadMhacaaIXaaabeaaaOGaay5w aiaaw2faaiaayIW7caGGQaGaaGymaiaaicdacaaIWaGaai4lamaadm aabaGaamOuamaaBaaaleaacaWG5bGaaGOmaaqabaGccqGHsislcaWG sbWaaSbaaSqaaiaadMhacaaIXaaabeaaaOGaay5waiaaw2faaaaa@73AF@

    where r i,y1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OCamaaBaaaleaacaWGPbGaaiilaiaayIW7caWG5bGaaGymaaqabaaa aa@3E1D@  and r i,y2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OCamaaBaaaleaacaWGPbGaaiilaiaayIW7caWG5bGaaGOmaaqabaaa aa@3E1E@  are the low-income rates for immigrant group i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@  in year 1 and year 2, S i,y1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam 4uamaaBaaaleaacaWGPbGaaiilaiaayIW7caWG5bGaaGymaaqabaaa aa@3DFE@  and S i,y2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam 4uamaaBaaaleaacaWGPbGaaiilaiaayIW7caWG5bGaaGOmaaqabaaa aa@3DFF@  are immigrant group i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@ ’s shares of the population in the corresponding years, and R y1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuamaaBaaaleaacaWG5bGaaGymaaqabaaaaa@3ACE@  and R y2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuamaaBaaaleaacaWG5bGaaGOmaaqabaaaaa@3ACF@  are the low-income rates for the population as a whole in year 1 and year 2.

    The contribution of each group can be further decomposed into three components, namely: (1) the change in the group’s low-income rates, S i,y1 *[ r i,y2 r i,y1 ]*100/ [ R y2 R y1 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa83uamaaBaaaleaacaWFPbGaa8hlaiaa=LhaieaacaGFXaaabeaa kiaa=PcadaWadaqaaiaa=jhadaWgaaWcbaGaa8xAaiaa=XcacaWF5b Gaa4Nmaiaa=bcaaeqaaOGaa83eGiaa=bcacaWFYbWaaSbaaSqaaiaa =LgacaWFSaGaa8xEaiaa+fdaaeqaaaGccaGLBbGaayzxaaGaa8Nkai aa+fdacaGFWaGaa4hmaiaa=9cacaWFGaWaamWaaeaacaWFsbWaaSba aSqaaiaa=LhacaGFYaaabeaakiaa=bcacaWFtaIaa8hiaiaa=jfada WgaaWcbaGaa8xEaiaa+fdaaeqaaaGccaGLBbGaayzxaaaaaa@5739@ ; (2) the change in the group’s population share, r i, y1 *[ S i,y2 S i, y1 ]*100/ [ R y2 R y1 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8NCamaaBaaaleaacaWFPbGaa8hlaiaa=bcacaWF5bacbaGaa4xm aaqabaGccaWFQaWaamWaaeaacaWFtbWaaSbaaSqaaiaa=LgacaWFSa GaaGjcVlaa=LhacaGFYaGaa8hiaaqabaGccaWFtaIaaGPaVlaaykW7 caWFtbWaaSbaaSqaaiaa=LgacaWFSaGaa8hiaiaa=LhacaGFXaaabe aaaOGaay5waiaaw2faaiaa=PcacaGFXaGaa4hmaiaa+bdacaWFVaGa a8hiamaadmaabaGaa8NuamaaBaaaleaacaWF5bGaa4NmaaqabaGcca WFGaGaa83eGiaa=bcacaWFsbWaaSbaaSqaaiaa=LhacaGFXaaabeaa aOGaay5waiaaw2faaaaa@5C62@ ; (3) and the joint change in the group’s low-income rates and population share [ S i, y2 S i,y1 ]*[ r i, y2 r i, y1 ]*100/ [ R y2 R y1 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaam WaaeaaieGacaWFtbWaaSbaaSqaaiaa=LgacaWFSaGaa8hiaiaa=Lha ieaacaGFYaGaa8hiaaqabaGccaWFtaIaaGPaVlaaykW7caWFtbWaaS baaSqaaiaa=LgacaWFSaGaa8xEaiaa+fdaaeqaaaGccaGLBbGaayzx aaGaa8NkamaadmaabaGaa8NCamaaBaaaleaacaWFPbGaa8hlaiaa=b cacaWF5bGaa4Nmaiaa=bcaaeqaaOGaa83eGiaa=bcacaWFYbWaaSba aSqaaiaa=LgacaWFSaGaa8hiaiaa=LhacaGFXaaabeaaaOGaay5wai aaw2faaiaa=PcacaGFXaGaa4hmaiaa+bdacaWFVaGaa8hiamaadmaa baGaa8NuamaaBaaaleaacaWF5bGaa4NmaaqabaGccaWFGaGaa83eGi aa=bcacaWFsbWaaSbaaSqaaiaa=LhacaGFXaaabeaaaOGaay5waiaa w2faaaaa@63C6@ .

    2.4.1 The effect of recent immigration on low-income rates

    The low-income rates of recent immigrants are typically much higher than those of the Canadian-born, and hence a change in their population share can alter the overall rate. For that reason, the focus here is on recent immigrants.

    The share of recent immigrants in the national population rose marginally through the 2000s, from 2.9% to 3.3%. However, there was considerable variability across regions and cities, with shares decreasing in Toronto and Vancouver but rising in Manitoba, Saskatchewan and Alberta (Table A.1).

    At the national level, recent immigrants contributed very little to the overall decline in the low-income rate between 2000 and 2010, accounting for only 2% (Table A.2). Indeed, it was only in Vancouver that recent immigration played a significant role in the decline in low-income, accounting for about one-half of the 3.5-percentage-point decrease observed in that city. This effect was due to both declining low-income rates among recent immigrants and a decline in their share of the city’s population. Interestingly, countervailing trends were evident in Manitoba. Although low-income rates declined significantly among recent immigrants in that province, putting downward pressure on the overall rate, the share of the provincial population comprised of recent immigrants increased considerably, putting upward pressure on the rate. The end result was that immigration pushed up the provincial low-income rate by only about 0.2 percentage points.

    Nonetheless, looking at the national, regional or provincial and municipal levels, recent immigration generally had little to do with the decline in low-income rates observed over the 2000s. The same conclusion holds when one looks beyond recent immigrants and considers the effect of immigrants with 1 to 15 years of tenure in Canada. Using this broader categorization, immigration accounted for only 7% of the decline in the national low-income rate over the 2000s, and for virtually none of the decline between 1995 and 2000. Likewise, immigration had little direct effect on low-income rates in most regions. Again, however, the major exception was Vancouver, where three-quarters of the decline in the low-income rate over the 2000s was associated with both falling low-income rates among immigrants and their declining share of the population. Montreal witnessed a similar but much-less dramatic pattern, with immigration accounting for about 15% of the 2.9-percentage-point decline in that city’s low-income rate.

    3 Immigration and high-income rates in Canada

    A focus on income inequality, the ultimate goal of this paper, requires an analysis of changes across the entire income distribution, not just the bottom. In recent years there has been much debate regarding the increased concentration of income at the top of the distribution. This section concentrates on the top of the income distribution. It mirrors the low-income analysis presented in the previous section. The high-income cutoff used here is twice the median adult-equivalent-adjusted income. The median is the average observed over the years 1995, 2000, 2005 and 2010. The high-income cutoff is held fixed over time, so the analysis uses a fixed (not relative) high-income cutoff.

    The proportion of population in Canada with “high family income”Note 11 rose rapidly between 1995 and 2010, from 6.7% to 16.1% (Table 3). This increase was observed among immigrants as well. Along with a declining share in “low income” as noted in the previous section, a rising share of immigrants found themselves with high income. This suggests a shift to the right in the income distribution among all groups, immigrants as well as the Canadian-born. Charts A.1 and A.2 (Appendix A) demonstrate this shift between 2000 and 2010. These charts also indicate the higher share of immigrants than Canadian-born in “low income” and a lower share with high income, particularly among the recent immigrants.

    Not surprisingly, the high-income rate among immigrants, while increasing, is much lower than among the Canadian-born. In 2010, 4.6% of “recent” immigrants made it into the high-income category, compared to 9.6% of immigrants in Canada for 11 to 15 years, and 17% of the Canadian-born.Note 12

    Just as the last section examined whether immigration contributed to the decline in the Canada-wide low-income rate during the 2000s, this section examines whether immigration contributed to the increase in the high-income rate observed between 1995 and 2010. Immigrants could affect this rate either because their share of the population was declining, or because their high-income rates were increasing at a faster rate than that of the Canadian-born. Table 3 suggests that neither of these events occurred. The same method as in the previous section on low income is used to determine the contribution of immigration to the rise in the high-income rate. Just as in the last section, immigration contributed little to the increase. Only from 1% to 2% of the increase in the high-income rate can be ascribed to changes in the immigrant population.

    The trend in the “high-income” rate in Canada, as measured here, was very similar between the immigrant and Canadian-born population between 1995 and 2010, although more Canadian-born found themselves in that category.

    4 Immigration and family-income inequality

    4.1 Recent trends in family-income inequality in Canada

    To assess the effect of immigration on income inequality, inequality trends in Canada are first reviewed. A number of recent papers have addressed the issue of family-income inequalityin Canada. Fortin et al. (2012) and Frenette, Green and Milligan (2007) focus on overall inequality, while Veall (2012) concentrates on changes at the top of the income distribution. These papers report income inequality trends and discuss possible explanations and policy implications.

    Based on the survey data reported by Statistics Canada, family-income inequality as measured by the Gini coefficient fell marginally during the 1980s, increased significantly during the 1990s—mostly during the last half of the decade—and changed little during the 2000s (Chart 4).Note 13 Frenette, Green and Milligan (2007) stress the role of the tax-transfer system in preventing the rise in income inequality during the 1980s in the face of rising market earnings inequality. But the tax-transfer system could not repeat this feat in the 1990s, and family-income inequality rose under the pressure of rising market earnings inequality. Nonetheless, the inequality-reducing effect of the tax-transfer system was greater in 2000 than in the 1980s.

    Moore and Pacey (2003) examine the direct effect of immigration on family-income inequality. Based on their findings, it was estimated that approximately one-half of the quite small increase in inequality over the 1980-to-1995 period was associated with immigration. Most of this effect was observed in the 1990-to-1995 period.

    This analysis focuses on the period between 1995 and 2010 using taxation data. Adult-equivalent-adjustedNote 14 after-tax family income is used to assess income inequality. Family income is 'adult-equivalent-adjusted' to account for differences in family size among groups. The individual is the unit of analysis, since the adult-equivalent income is really a measure of the economic resources available to each individual in the family (a per capita measure). This measure of family income is ascribed to each member of the family. In calculating income inequality, the adult-equivalent-adjusted income is top-coded at $1,000,000.Note 15

    Chart 4

    Description for chart 4

    Are taxation data representative of overall trends? Just as with low-income data, different data sources provide different levels of inequality, but the trends are quite similar. Inequality levels tend to be higher in census and taxation data than in survey data,Note 16 mainly because surveys tend to miss some low and high incomes reported in both taxation and census data (Frenette, Green and Picot 2004; Frenette, Green and Milligan 2007). This results in lower inequality levels in the survey data.

    But the trends examined in this study over the 1995-to-2010 period are very similar to those in the taxation and survey data (Table 4). According to the after-tax income in survey data, most of the increase observed over the three decades occurs between 1995 and 2000. Of the 0.031-point increase in the Gini observed in the survey data between 1980 and 2010, 0.024 points, or about three-quarters of it, occurred between 1995 and 2000. The taxation data show a similar 0.025-point increase during this period, while the census data with estimated after-tax incomeNote 17 show very little increase. Income inequality typically rises in recessions, as it did in the early 1980s and 1990s, and therefore might be expected to fall in economic expansions. But this did not occur in the late 1990s’ expansion, and this period instead displayed the largest rise income inequality in the past three decades. Between 2000 and 2010, the survey data show no increase in the Gini, and the taxation data only display a small 0.004-point rise. Comparable data from the census are not available for this period. Overall, the trends over the 2000s observed in the taxation data (used here) and the survey data are very similar.

    4.2 Inequality among the immigrant population

    There are two basic findings regarding income inequality among immigrants that are germane to this analysis. First, levels of inequality tend to be marginally higher among the immigrant population than among the Canadian-born.Note 18 For example, in 2010, the Gini was 0.362 among the comparison group (mostly Canadian-born), and between 0.384 and 0.387 among immigrants in Canada for 1 to 15 years (Appendix Table A.4). This means that any increase in the immigrant’s share of the population will exert upward pressure on family-income inequality overall. Second, inequality among immigrants increased over the 1995-to-2000 period, just as it did for the Canadian-born. Similar to the trend among the Canadian-born, most of this increase was during the 1995-to-2000 period (Table A.4). This suggests that whatever pressures increased inequality among the Canadian-born may have also been applied to the immigrant population.

    4.3 Assessing immigrant contribution to changing aggregate family-income inequality

    Any group may have a direct effect on rising aggregate inequality for three possible reasons: (1) the level of inequality within the group may rise; (2) the level of income inequality among groups may rise;Note 19 or (3) a group’s share of the population may increase, and if that group’s level of inequality is above-average, as it often is for recent immigrants, this will contribute to rising inequality. In the analysis, the total population is divided into four groups: (1) the Canadian-born plus long-term immigrants;Note 20 (2) immigrants in Canada for 5 years or less (recent immigrants); (3) immigrants in Canada for 6 to 10 years; and (4) immigrants in Canada for 11 to 15 years.

    The selected income indexes are decomposed to answer two questions. First, to what extent did each group contribute to the rise in family-income inequality in Canada over the reference period? And second, to what extent was this contribution due to (a) increasing inequality within the group; (b) the group’s rising share of the total population; and (c) increased inequality among groups (i.e., increased difference in mean family incomes among groups)?

    While the Gini coefficient is the most commonly used inequality index, there are many others. In this analysis three decomposable indexes of inequality are used: the squared coefficient of variation ( C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@ ), the Theil, and the mean log deviation (Allison 1978; Jenkins 1999). More than one index is used because the value of some indexes are susceptible to movements at the top of the income distribution, while others are affected more by changes in income at the bottom. Such measures are taken to ensure that the findings are robust across the entire income distribution. The C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@  is affected more by income movements at the top of the distribution, where much of the action has been located over the past couple of decades. While both the mean log deviation and the Theil indexes are sensitive to changes at the lower end of income distribution, the mean log deviation is more so (Allison 1978; Jenkins 1999).

    The change in inequality is decomposed as measured by C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@ , Theil and the mean log deviation over the 1995-to-2000 and the 2000-to-2010 periods. The focus is on the 1995-to-2000 period, since inequality increased most during this period. An algebraic description of this decomposition technique is presented in Appendix B.

    Using these three decomposable indexes, the result of the analysis is straightforward, and all three indexes provide similar answers (Tables A.5, A.6, and A.7). Over the 1995-to-2000 period, during which most of the rise in inequality in Canada was concentrated, very little of the increase was associated with immigrant groups. Virtually all of the increase was due to increasing inequality within the comparison group (mostly Canadian-born).

    For instance, inequality as measured by Theil index rose from 0.214 to 0.256 for the total population between 1995 and 2000, and remained more or less constant to 2010 at that level (Table A.4). Thus, the 0.042 changein the index value is decomposed. While the share of immigrants (with less than 15 years tenure) increased from 7.2% to 8.2%, the difference in inequality between immigrants and the Canadian-born was not sufficient to result in a major contribution. The increase in the share of immigrants accounted for only 0.001 of the 0.042 increase. The rise in inequality within the immigrant groups accounted for 0.002 of the total increase, while the change in between-group inequality contributed virtually nothing to the change (Table A.6). Overall, the immigrant groups accounted for about 0.002 of the 0.042 rise, or about 5%. This is about what might be expected since these immigrant groups accounted for about 7% of the population. They did not disproportionately contribute to the rise in inequality.

    When the same analysis is conducted using the C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@  index, immigrant groups accounted for about 4% of the increase in inequality (Table A.5). Immigrants’ contribution to the change in the mean log deviation was larger than the changes in the other two indexes, about 26% (Table A.7). This is likely because the mean log deviation is most sensitive to changes in the bottom income distributions where immigrants are more likely to be concentrated.

    Using all three indexes, the vast majority—between 88% and 97%—of the increase in inequality from 1995 to 2000 was associated with the rising inequality within the comparison group, which includes the Canadian-born and longer-tenured immigrants. This is also what might be expected since they accounted for the majority of the population.

    But this result may not hold for all regions. In cities where immigrants constitute a large share of the population, did immigrants account for a disproportionately large share of the rise in income inequality in the late 1990s?

    The Theil index was used to examine regional differences. In Toronto, the rise in inequality between 1995 and 2000 was somewhat larger than for Canada as a whole, increasing 0.072 points, or about 28%, compared to 20% for Canada. Virtually none of this increase was associated with the immigrant population, and fully 97% by rising inequality within the Canadian-born population (Table A.6). A similar story holds for Vancouver, where none of the rise in the 0.055-point increase in inequality (or 22%) was concentrated among the immigrant groups. Results are similar for Montreal, which experienced a much smaller increase of only 0.020 points (or 9%) in inequality.

    5 Immigration and family-earnings inequality

    The tax and transfer system both reduce inequality at any given point and time, and can potentially affect inequality trends over time. This was observed in the 1980s, for example, when earnings inequality was rising, but after the tax and transfer system redistributed some income, after-tax, after-transfer income inequality changed little. It may be that earnings-based inequality trends—before taxes and transfers—in Canada have been affected by immigration, even if such an effect is not observed when income is measured post tax and transfer, as in the previous section. To determine if this is the case, we replicate some of the previous sections analysis using family earnings, rather than after-tax, after-transfer family income.

    As with family-income inequality, and based on the Gini, family-earnings inequality rose between 1995 and 2010, and most of the increase occurred during the late 1990s, although it increased marginally in the early 2000s. The family-earnings Gini for Canadians with positive family earnings rose from 0.420 in 1995 to 0.439 in 2000, and then to 0.447 in 2005. The other three indexes (the log deviation, Theil and C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@ ) tell a similar story; most of the increase occurred in the late 1990s, with some rise in the early 2000s.

    Family-earnings inequality also rose among the immigrant population in Canada for less than 15 years, but the rise was observed more equally between the late 1990s and early 2000s. Little increase was observed in the late 2000s.

    Did immigration contribute to the rise in family-earnings inequality in Canada? The answer is essentially no. The study’s focus is on the Theil index, the one used most often in the previous section. The Theil index increased from 0.324 in 1995 to 0.371 in 2000, an increase of 0.047. Of this increase, only 0.002 (or about 4%) is ascribed to changes in the immigrant population. These changes could include a rise in between-group inequality, a rise in within-group inequality or a change in immigrants’ share of the population. None of these possibilities occurred to a sufficient degree to significantly affect family-earnings inequality in Canada. Similarly, over the 2000-to-2010 period, when there was a much smaller increase of 0.007 in the Theil index, immigration accounted for none of this very small increase.

    6 The indirect effect of immigration on wage inequality

    As noted in the introduction, increasing shares of immigrants can potentially affect the wages of the Canadian-born. This effect can vary across the wage distribution, thereby affecting wage inequality. The international literature suggests that the effect of immigration on wages can be positive or negative, but, in general, it is very small (Kerr and Kerr 2011; Longi, Nijkamp and Poot 2006, 2009; Okkerse 2008; European Economic Association 2012). But this effect can vary among countries depending on the type of immigrants entering the country, notably their occupational skills and education, and the country’s industrial structure.

    In Canada, few papers have addressed this issue. Aydemir and Borjas (2007) find a negative effect of immigration on the wages of the Canadian-born. Overall a 10% immigration-induced increase in the labour supply, which is a very large supply increase, reduces wages of the Canadian-born by 3% to 4%. Immigration increases labour supply by perhaps 0.7% to 0.8% per year in Canada, which might reduce wages of the Canadian-born by around 0.3% according to this study. The negative wage effect is greater among the more highly educated since the immigration-induced labour supply increase is concentrated among this education group. Hence, Aydemir and Borjas conclude that by negatively affecting the wages of highly educated Canadians more than the less-educated (where the immigration effect may raise wages), immigration tended to reduce wage inequality.Note 21

    But by how much? Between 1980 and 2000, wages fell by 2.2% among university graduates and by 16.2% among high school graduates (Table 4 in Aydemir and Borjas 2007). Hence, wage inequality rose across education groups; between-group inequality increased. Using the results from a series of simulations that Aydemir and Borjas produce, one can roughly estimate the wage change that might have occurred over the 20-year period in the absence of immigration. Wages among the highly educated would have increased by 4% to 8% (instead of a 2% decrease), and among high school graduates it would have fallen by 17% to 20% (rather than 16%). Hence, in the absence of immigration, the income gap between the more- and less-educated would have increased more than it did, and inequality across education groups would have risen more than what was actually observed. In short, immigration might have reduced between-group inequality somewhat. But it is important to remember that changes in overall inequality are also determined by within-group inequality. Within-group inequality among the highly educated Canadian-born could increase if immigration effects were concentrated among those who were located near the bottom of the within-group income distribution. This outcome seems quite possible, since, on average, better-educated immigrants earn less than their non-immigrant counterparts, and hence may compete more with non-immigrants at the bottom of the within-group wage distribution. This possible increase in within-group inequality could offset to some unknown extent the immigration effect that results in a decline in between-group inequality, and may lead to a small total indirect effect of immigration on income inequality among the Canadian-born. Thus, it seems likely that the kinds of effects found by Aydemir and Borjas would have had some effect, but not a large indirect effect on total wage inequality.

    Tu (2010) used a methodology similar to that of Aydemir and Borjas, but applied it at both a national and sub-national level, and over a different time period (the 1990s). He finds no evidence of a negative effect of immigration on the wages of the Canadian-born, and in some specifications, a small positive effect. The zero or small effects found by Tu would have small effects on wage inequality.

    Card (2009) provides an in-depth examination of the immigration effect on the wage distribution of the native-born in the United States (referred to here as the indirect effect of immigration). He notes that the answer depends on a number of factors, including the extent to which immigrants and the native-born with similar education levels are perfect substitutes and hence are competing directly with one another. Card (2009) and a number of other papers (Ottaviano and Peri 2012; Manacorda, Manning and Wadsworth 2012) determine that immigrants and the native-born are imperfect substitutes, and that new immigrants, in particular, likely compete more with other immigrants, especially the recently arrived, than with the native-born. Hence, immigration-induced wage effects may be more evident among other immigrants than among native-born workers.

    Overall, Card concludes that in the United States the effect of immigration on native-born wage inequality is very small. Card argues that if the educational distributions of immigrants and the native-born are similar, there will be little effect. Accordingly, the immigration effect may be larger in Canada because educational distributions of immigrants and the native-born are more dissimilar in Canada than the United States—immigrants are more highly educated in Canada, and less-educated than the native-born in the United States.Note 22 Hence the downward pressure is more likely on the wages of the highly educated in Canada, since immigrants are overrepresented among this group. However, on balance, given the international and Canadian evidence, Card’s general conclusion likely applies to Canada as well, although additional research is needed to reach a more definitive conclusion.

    7 Conclusion

    This paper asks if immigration contributed to the decline in low-income rates in Canada during the 2000-to-2010 period. Low-income rates among immigrants declined over the 2000s, although their relative (to the Canadian-born) low-income rates did not improve. There was little progress in reversing the significant run-up in relative low-income ratios during the 1980s and 1990s. There were three regional exceptions to this general pattern: immigrant low-income rates did not fall in Toronto as in other regions during the 2000s (nor did rates among the Canadian-born), and rates among immigrants declined the fastest in Manitoba and Saskatchewan, where relative rates among recent immigrants fell back to around 1.2 times that of the Canadian-born, levels of relative rates not seen since the early 1980s.

    Policies and practices regarding immigrant selection changed significantly during the 2000s, with the introduction of the Immigration and Refugee Protection Act in 2002, and the expansion of the Provincial Nominee Program (PNP) in Manitoba and Saskatchewan. These and other changes altered both the characteristics of entering immigrants and the programs of entry (i.e., immigrant class). These changes tended to increase entry earnings, and may have contributed to the fall in low-income rates observed among recent immigrants (in Canada for less than five years). This paper concludes that, at the national level, changes in immigrant characteristics—notably rising educational attainment and changing source regions—accounted for about one-third of the decline in the low-income rate among recent immigrants (in Canada five years or less) during the 2000s. Changing admission class did not have a significant effect nationally. At the regional level, changes in selection policies and practices over the 2000s varied tremendously as some provinces embraced the PNP more than others. Furthermore, the change in the number of recent immigrants in the population also varied by region due to a decentralization of entering immigrants away from Toronto towards the western regions in particular. As a result, the effect of compositional changes also differed by province. Changes in immigrant characteristics and entry program accounted for between one-fifth and one-half of the decrease in low-income rates among recent immigrants depending on the region.

    Declining immigrant low-income rates contributed little to the fall in low-income rates among the general population in Canada during the 2000s. Unlike the 1990s, when rising immigrant shares and rates accounted for most of the increase in low-income rates in Canada, the decrease in the rates during the 2000s was driven primarily by falling rates among the Canadian-born. The only exception was Vancouver, where three-quarters of the decline in the city’s low-income rates was associated with both rapidly falling rates among immigrants and their declining share of the population.

    Family-income inequalityincreased in Canada from 1990 to 2010, but the majority of the rise occurred during the late 1990s. Using three decomposable inequality indexes, the paper concludes that, for Canada as a whole, immigration contributed little to the increase of the late 1990s. This null result held for the three largest cities as well. Family-income inequality rose among the immigrant population during the late 1990s, as it did among the Canadian-born, but the immigrant population did not contribute disproportionately to the overall increase. There was little increase in family-income inequality in the 2000s.

    A rising immigrant share of the population could also affect the wages and wage distribution of the Canadian-born. The international literature tends to suggest that the effect is generally small, whether positive or negative. If this immigration effect varies across the earnings distribution, then it can also indirectly change earnings inequality among the Canadian-born, and hence low-income rates and family-income inequality. While no original research is presented in this paper, a review of the extensive international literature along with the few Canadian papers that address this issue suggests that this effect is likely small.

    Appendix A: Tables

    Chart A1

    Description for chart A.1

    Chart A2

    Description for chart A.2

    Appendix B: Decomposing the squared coefficient of variation, Theil and mean log deviation indexes

    This paper decomposes the three inequality indexes to  assess the contribution of each of four groups to the change over time in the index. The four groups used here are immigrants in Canada for 1 to 5 years, 6 to 10 years, or 11 to 15 years, and the remainder of the Canadian population, although this approach can be used for groups defined in any way. Following is the algebraic development of this decomposition.

    At a given time point, the C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@  can be written as the sum of two terms: one is attributable to within-group income inequality, P i C V i 2 R i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuocbiGaa8huamaaBaaaleaacaWFPbaabeaakiaa=neacaWFwbWa aSbaaSqaaiaa=LgaaeqaaOWaaWbaaSqabeaaieaacaGFYaaaaOGaa8 NuamaaDaaaleaacaWGPbaabaGaaGOmaaaaaaa@4208@ , the second is attributable to between-group inequality, P i ( R i 2 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuocbiGaa8huamaaBaaaleaacaWFPbaabeaakmaabmaabaGaa8Nu amaaDaaaleaacaWGPbaabaGaaGOmaaaakiabgkHiTiaabgdaaiaawI cacaGLPaaaaaa@418F@ , where P i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8huamaaBaaaleaacaWFPbaabeaaaaa@3A03@  is the population share of group i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@  (in our study, i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@  =1 to 4), C V i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa83qaiaa=zfadaqhaaWcbaGaamyAaaqaaiaaikdaaaaaaa@3B8E@  is the C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@  for group i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@ , and R i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8NuamaaBaaaleaacaWFPbaabeaaaaa@3A05@  is the ratio of the mean income of group i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@  to the mean income of the total population.

    By straightforward algebraic manipulation, thechange in C V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefe KCPfgBaGqbaiaa=neacaWFwbWaaWbaaSqabeaacaWFYaaaaaaa@3C89@  over two time points can be decomposed into four terms.

    ΔC V 2  = Δ P i ( C V i 2 R i 2 + R i 2 1 ) + ΔC V i 2 P i R i 2  + Δ R i 2 P i ( C V i 2 1 ) +jointchanges. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu iLdqecbiGaa83qaiaa=zfadaahaaWcbeqaaiaabkdaaaGccaqGGaGa eyypa0JaaeiiaiabggHiLJqaaiaa+r5acaWFqbWaaSbaaSqaaiaa=L gacaWFGaaabeaakmaabmaabaGaa83qaiaa=zfadaWgaaWcbaGaa8xA aaqabaGcdaahaaWcbeqaaiaabkdaaaGccaWFsbWaaSbaaSqaaiaa=L gaaeqaaOWaaWbaaSqabeaacaqGYaaaaOGaey4kaSIaa8NuamaaBaaa leaacaWFPbaabeaakmaaCaaaleqabaGaaeOmaaaakiabgkHiTiaabg daaiaawIcacaGLPaaacaqGGaGaey4kaSIaaeiiaiabggHiLlabfs5a ejaa=neacaWFwbWaaSbaaSqaaiaa=LgaaeqaaOWaaWbaaSqabeaaca qGYaaaaOGaa8huamaaBaaaleaacaWFPbGaa8hiaaqabaGccaWFsbWa a0baaSqaaiaadMgaaeaacaaIYaaaaOGaaeiiaiabgUcaRiaabccacq GHris5cqqHuoarcaWFsbWaa0baaSqaaiaadMgaaeaacaaIYaaaaOGa a8huamaaBaaaleaacaWFPbGaa8hiaaqabaGcdaqadaqaaiaa=neaca WFwbWaaSbaaSqaaiaa=LgaaeqaaOWaaWbaaSqabeaacaqGYaaaaOGa eyOeI0IaaeymaaGaayjkaiaawMcaaiaabccacqGHRaWkcaWGQbGaam 4Baiaa=LgacaWFUbGaa8hDaiaayIW7caaMi8UaaGjcVlaadogacaWG ObGaamyyaiaad6gacaWGNbGaamyzaiaadohacaGGUaaaaa@829B@

    The first term is the contribution of changes in the population shares among groups; the second term is the contribution of changes in within-group inequality; the third term is the contribution of changes in between-group income inequality; and the fourth term is the joint changes of population shares, within-group inequality, and between-group inequality. The joint change term includes Δ P i ΔC V i 2 R i 2 +Δ P i C V i 2 Δ R i 2 + P i ΔC V i 2 Δ R i 2 +Δ P i ΔC V i 2 Δ R i 2 +Δ P i Δ R i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuUaeuiLdqecbiGaa8huamaaBaaaleaacaWFPbGaa8hiaaqabaGc cqqHuoarcaWGdbGaamOvamaaDaaaleaacaWGPbaabaGaaGOmaaaaki aa=jfadaqhaaWcbaGaamyAaaqaaiaaikdaaaGccqGHRaWkcqGHris5 cqqHuoarcaWFqbWaaSbaaSqaaiaa=LgacaWFGaaabeaakiaadoeaca WGwbWaa0baaSqaaiaadMgaaeaacaaIYaaaaOGaeuiLdqKaa8Nuamaa DaaaleaacaWGPbaabaGaaGOmaaaakiabgUcaRiabggHiLlaa=bfada WgaaWcbaGaa8xAaiaa=bcaaeqaaOGaeuiLdqKaam4qaiaadAfadaqh aaWcbaGaamyAaaqaaiaaikdaaaGccqqHuoarcaWFsbWaa0baaSqaai aadMgaaeaacaaIYaaaaOGaey4kaSIaeyyeIuUaeuiLdqKaa8huamaa BaaaleaacaWFPbaabeaakiabfs5aejaadoeacaWGwbWaa0baaSqaai aadMgaaeaacaaIYaaaaOGaeuiLdqKaa8NuamaaDaaaleaacaWGPbaa baGaaGOmaaaakiabgUcaRiaayIW7caaMi8UaaGjcVlaayIW7cqGHri s5cqqHuoarcaWFqbWaaSbaaSqaaiaa=LgaaeqaaOGaeuiLdqKaa8Nu amaaDaaaleaacaWGPbaabaGaaGOmaaaaaaa@80A0@ . The joint change is generally very small.

    The same approach can be used with the Theil index. At a given time point, the Theil index T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8hvaaaa@38F1@  can be expressed as the sum of two terms: P i T i R i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuocbiGaa8huamaaBaaaleaacaWFPbGaa8hiaaqabaGccaWFubWa aSbaaSqaaiaa=LgaaeqaaOGaa8NuamaaBaaaleaacaWFPbaabeaaaa a@4030@ , the component representing within-group income inequality, and P i ln( R i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuocbiGaa8huamaaBaaaleaacaWFPbGaa8hiaaqabaGccaqGSbGa aeOBamaabmaabaGaa8NuamaaBaaaleaacaWGPbaabeaaaOGaayjkai aawMcaaaaa@41B2@ , the component representing between-group income inequality, where P i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8huamaaBaaaleaacaWFPbaabeaaaaa@3A03@  and R i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8NuamaaBaaaleaacaWFPbaabeaaaaa@3A05@  are defined the same as the above, T i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8hvamaaBaaaleaacaWFPbaabeaaaaa@3A07@  is the Theil index for group  i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaaaa@3906@ .

    The change in T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8hvaaaa@38F1@  over two time points can be decomposed into four terms.

    ΔT = Δ P i R i ( T i +ln R i )+Δ T i P i R i +[ Δ P i R i ( T i +ln R i )+Δln R i P i ( R i +Δ R i ) ]  +jointchanges. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabe aacqqHuoarieGacaWFubGaaeiiaiabg2da9iaabccacqGHris5cqqH uoarcaWGqbWaaSbaaSqaaiaadMgaaeqaaOGaa8NuamaaBaaaleaaca WFPbaabeaakmaabmaabaGaa8hvamaaBaaaleaacaWFPbaabeaakiaa bUcacaaMi8UaaGjcVlaabYgacaqGUbGaa8NuamaaBaaaleaacaWFPb aabeaaaOGaayjkaiaawMcaaiabgUcaRiabggHiLlabfs5aejaa=rfa daWgaaWcbaGaa8xAaaqabaGccaWGqbWaaSbaaSqaaiaadMgaaeqaaO Gaa8NuamaaBaaaleaacaWFPbaabeaakiabgUcaRmaadmaabaGaeyye IuUaeuiLdqKaamiuamaaBaaaleaacaWGPbaabeaakiaa=jfadaWgaa WcbaGaa8xAaaqabaGcdaqadaqaaiaa=rfadaWgaaWcbaGaa8xAaaqa baacbaGccaGFRaGaa4hBaiaa+5gacaWFsbWaaSbaaSqaaiaa=Lgaae qaaaGccaGLOaGaayzkaaGaey4kaSIaeyyeIuUaeuiLdqKaa4hBaiaa +5gacaWFsbWaaSbaaSqaaiaa=LgaaeqaaOGaamiuamaaBaaaleaaca WGPbaabeaakmaabmaabaGaa8NuamaaBaaaleaacaWFPbaabeaakiab gUcaRiabfs5aejaa=jfadaWgaaWcbaGaa8xAaaqabaaakiaawIcaca GLPaaaaiaawUfacaGLDbaacaqGGaaabaGaey4kaSIaaGPaVlaadQga caWGVbGaa8xAaiaa=5gacaWF0bGaaGjcVlaayIW7caWGJbGaamiAai aadggacaWGUbGaam4zaiaadwgacaWGZbGaaeOlaaaaaa@8DD0@

    The first term is the contribution of changes in the population shares among groups; the second term is the contribution of changes in within-group inequality; the third term is the contribution of changes in between-group income inequality; and the fourth term is the joint changes of population shares, within-group inequality, and between-group inequality. The joint change term includes

    T i Δ P i Δ R i Δ T i Δ P i R i + Δ T i P i Δ R i + Δ T i Δ P i Δ R i +Δ P i Δ R i ln( R i )+ Δ P i R i Δln( R i ) + Δ P i R i Δln( R i ) + Δ P i Δ R i Δln( R i ). MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabe aacqGHris5ieGacaWFubWaaSbaaSqaaiaa=LgaaeqaaOGaaGjcVlab fs5aejaa=bfadaWgaaWcbaGaa8xAaaqabaGccaaMi8UaeuiLdqKaam OuamaaBaaaleaacaWGPbaabeaakiaabUcacaqGGaGaeyyeIuUaeuiL dqKaa8hvamaaBaaaleaacaWFPbaabeaakiaayIW7cqqHuoarcaWFqb WaaSbaaSqaaiaa=LgaaeqaaOGaamOuamaaBaaaleaacaWGPbaabeaa kiabgUcaRiaabccacqGHris5cqqHuoarcaWFubWaaSbaaSqaaiaa=L gaaeqaaOGaa8huamaaBaaaleaacaWFPbaabeaakiaayIW7cqqHuoar caWGsbWaaSbaaSqaaiaadMgaaeqaaOGaey4kaSIaaeiiaiabggHiLl abfs5aejaa=rfadaWgaaWcbaGaa8xAaaqabaGccaaMi8UaeuiLdqKa a8huamaaBaaaleaacaWFPbaabeaakiaayIW7cqqHuoarcaWGsbWaaS baaSqaaiaadMgaaeqaaOGaey4kaSIaeyyeIuUaeuiLdqKaa8huamaa BaaaleaacaWFPbaabeaakiaayIW7cqqHuoarcaWGsbWaaSbaaSqaai aadMgaaeqaaOGaaeiBaiaab6gadaqadaqaaiaadkfadaWgaaWcbaGa amyAaaqabaaakiaawIcacaGLPaaacqGHRaWkcaqGGaGaeyyeIuUaeu iLdqKaa8huamaaBaaaleaacaWFPbaabeaakiaadkfadaWgaaWcbaGa amyAaaqabaGccqqHuoarcaqGSbGaaeOBamaabmaabaGaamOuamaaBa aaleaacaWGPbaabeaaaOGaayjkaiaawMcaaaqaaiabgUcaRiaabcca cqGHris5cqqHuoarcaWFqbWaaSbaaSqaaiaa=LgaaeqaaOGaamOuam aaBaaaleaacaWGPbaabeaakiabfs5aejaabYgacaqGUbWaaeWaaeaa caWGsbWaaSbaaSqaaiaadMgaaeqaaaGccaGLOaGaayzkaaGaaeiiai abgUcaRiaabccacqGHris5cqqHuoarcaWFqbWaaSbaaSqaaiaa=Lga aeqaaOGaaGjcVlabfs5aejaadkfadaWgaaWcbaGaamyAaaqabaGccq qHuoarcaqGSbGaaeOBamaabmaabaGaamOuamaaBaaaleaacaWGPbaa beaaaOGaayjkaiaawMcaaiaac6caaaaa@B2DC@

    At a given time point, the mean log deviation, L MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8htaiaayIW7aaa@3A7A@ , can be written as the sum of two terms: P i L i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuocbiGaa8huamaaBaaaleaacaWFPbGaa8hiaaqabaGccaWFmbWa aSbaaSqaaiaa=LgaaeqaaOGaaGjcVdaa@3FD0@ , the component representing within-group income inequality; and P ln( R i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuocbiGaa8huamaaBaaaleaacaqGPbGaaeiiaaqabaGccaqGSbGa aeOBamaabmaabaGaa8NuamaaBaaaleaacaWFPbaabeaaaOGaayjkai aawMcaaaaa@41B2@ , the component representing between-group income inequality, where L i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8htamaaBaaaleaacaWFPbaabeaaaaa@39FF@  is the income inequality index for group i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8xAaiaayIW7aaa@3A97@ . The change in L MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi Gaa8htaaaa@38E9@  over two time points can be decomposed into four terms:

    ΔL=Δ P i [ L i +ln( R i ) ]+Δ L i P i +Δln( R i ) P i jointchanges. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu iLdqecbiGaa8htaiaa=1dacqGHris5cqqHuoarcaWFqbWaaSbaaSqa aiaa=LgacaWFGaaabeaakmaadmaabaGaa8htamaaBaaaleaacaWFPb aabeaakiabgUcaRiaabYgacaqGUbWaaeWaaeaacaWFsbWaaSbaaSqa aiaa=LgaaeqaaaGccaGLOaGaayzkaaaacaGLBbGaayzxaaGaae4kai abggHiLlabfs5aejaadYeadaWgaaWcbaGaamyAaaqabaGccaWFqbWa aSbaaSqaaiaa=LgacaWFGaaabeaakiaabUcacqGHris5cqqHuoarca qGSbGaaeOBamaabmaabaGaa8NuamaaBaaaleaacaWFPbaabeaaaOGa ayjkaiaawMcaaiaa=bfadaWgaaWcbaGaa8xAaiaa=bcaaeqaaOGaae 4kaiaabccacaWFQbGaa83Baiaa=LgacaWFUbGaa8hDaiaa=bcacaWF JbGaa8hAaiaa=fgacaWFUbGaa83zaiaa=vgacaWFZbGaa8Nlaaaa@6C55@

    The joint change term includes Δ L i Δ P i  +Δ P i Δln( R i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yeIuUaeuiLdqecbiGaa8htamaaBaaaleaacaWFPbGaa8hiaaqabaGc cqqHuoarcaWFqbWaaSbaaSqaaiaa=LgaaeqaaOGaaiiOaiabgUcaRi abggHiLlabfs5aejaa=bfadaWgaaWcbaGaa8xAaiaa=bcaaeqaaOGa euiLdqKaaeiBaiaab6gadaqadaqaaiaa=jfadaWgaaWcbaGaa8xAaa qabaaakiaawIcacaGLPaaaaaa@4F6F@ .


    Notes

    Date modified: