The Growth of Family Earnings Inequality in Canada, 1980-2005

The Growth of Family Earnings Inequality in Canada, 1980-2005

Yuqian Lu

Business and Labour Market Analysis

Statistics Canada

René Morissette

Business and Labour Market Analysis

Statistics Canada

Tammy Schirle

Department of Economics

Wilfrid Laurier University

ABSTRACT

In this study we document recent trends in family earnings inequality using data from the

Canadian Census and provide insight into the various factors that drive changes in the family earnings distribution. Over the period 1980-1995 we observe substantial increases in family earnings inequality. In contrast, we find some decrease in inequality occurred over the period 1995-2005 although the earnings of the richest 1% of families increased substantially. We use semi-parametric decomposition methods (following Dinardo, Fortin and Lemieux 1996) to show that increases in the employment rates of men and women and increases in their educational attainment will tend to have equalizing effects on the income distribution. We also show that increases in the returns to higher education, increases in assortative mating, and increases in the proportion of families headed by single parents drove increases in family earnings inequality. Overall, changes in family composition and family characteristics appear to be among the most important factors underlying changes in the family earnings distribution since 1980, with changes in family characteristics having a strong equalizing impact.

I.

Introduction

Along with many OECD countries, Canada has experienced important changes in its earnings structure since the early 1980s (Gottschalk and Smeeding, 1997). Over the period 1980-2005, there has been a substantial increase in family earnings inequality in

Canada. Family earnings at the bottom of the distribution have stagnated while those at the top have displayed remarkable growth. Such inequality often places greater pressure on Canada’s tax and transfer system, as efforts are made to produce a socially acceptable distribution of family income while minimizing disincentives to work.

The purpose of this paper is to document recent trends in family earnings inequality using

Canadian data and provide some insight into the various factors that drive changes in the family earnings distribution. Our study most closely follows the work of Fortin and

Schirle (2006), who had investigated various factors affecting family earnings inequality in Canada over the period 1982-1997. Using data from the Survey of Consumer

Finances, they found that the 90-10 differential increased by 12 log points. Using the decomposition methods of Dinardo, Fortin and Lemieux (1996) they found the bulk of this increase could be explained by changes in the wage structure of men and women over the 1980s and 1990s. A decrease in the proportion of married couples explained an increase in the 50-10 differential while increases in female labour force participation to some extent offset that increase. Increased assortative mating and an increasing proportion of families headed by unmarried women also contributed to the increase in family earnings inequality. Daly and Valetta (2006) find similar results for the United

States.

Using more recent data from the Canadian Census, we re-examine these results for the

1980-2005 period. Using the Census allows us to measure changes in the tails of the income distribution more accurately than other Canadian data sources. Frenette et al

(2007) have made the case that important changes in the income distribution (both market income and after tax income) have been in the tails and that use of other data sets will miss some of those changes.

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We find that a break in the trend in family earnings inequality occurred in the mid-1990s.

Over the period 1980-1995, we observe substantial increases in inequality representing large increases in income for the top half of the earnings distribution relative to the bottom end of the earnings distribution. In contrast, we find that several measures of family earnings inequality actually decreased over the period 1995-2005. Families in the bottom 10% of the earnings distribution made the greatest gains while middle incomes were relatively stagnant and modest gains were made by families in the top 10% of the earnings distribution. Interestingly, the earnings of the richest 1% of families increased substantially so that inequality measures sensitive to redistribution toward the very top of the family earnings distribution actually increased substantially. Saez and Veall (2005) have also observed large growth in wages and salaries in the top percentile of the income distribution, as the income share of the top 1% of families soared after 1995 in both

Canada and the United States. U.S. Evidence from Lemieux, Macleod and Parent (2006) would suggest a growing incidence of performance pay has driven a large part of this growth in earnings at the top of the distribution.

The break in inequality trends affords us the opportunity to verify the robustness of our methods and results in examining the factors that affect the family earnings distribution.

Similar to the results of previous studies, we find that changes in family composition reflecting an increasing proportion of lone parent families and families without kids will drive increases in family earnings inequality. Evidence from the entire 1980-2005 period demonstrates this was one of the most important factors driving increased inequality.

Over the 1980-1995 period, large increases in men’s returns to education were a key factor driving the large increases in family earnings inequality. In the 1995-2005 period, however, men’s returns to education stagnated and continued increases in women’s returns to education became a more important driving force to raise inequality. Increases in women’s employment rates have had important equalizing effects while increases in assortative mating have had important disequalizing effects.

Of course, we do not attempt to claim that we fully explain all changes in inequality over the past several decades. We do not, for instance, examine the importance of changes in unionization rates which Dinardo, Fortin and Lemieux (1996) have shown to be an

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important factor in explaining increased earnings inequality over the 1980s in the US.

We do not examine the role of policy interventions such as taxation or regulations in the labour market. Nor do we examine the role of technological change and global outsourcing. Rather we focus our attention on some key labour market outcomes and characteristics of families.

In the next section, we describe the data used to measure Canadian family earnings over the period 1980-2005. We then describe trends in family earnings inequality over this period. We also document how changes in various factors may have affected family earnings inequality. After providing the results of our decomposition we provide some concluding remarks.

II.

Data and Measurement

For this analysis, we use data from the Canadian Census, 1981-2006, which provides detailed information on income and work experience in the previous calendar year and demographic characteristics of Canada’s population. We are using the 20% sample

Census files and focus on the years 1981, 1996, and 2006 (income years 1980, 1995, and

2005).

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We adopt the ‘census family’ definition used in Census. A family refers to a married or common-law couple (of opposite sex) with or without children, or a lone parent of any marital status with at least one child living in the same dwelling. The term child refers to never-married sons or daughters who are living with their parent(s). We treat all other individuals as one-person families.

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1

Public use microdata files for the Canadian Census are based on samples of 2-3% of the population enumerated in the census.

2

Basically, we adopt the “census family” definition used in the pre-2001 Canadian Censuses. We re-group a same sex partner family into two one-person families, or the reference person as a lone-parent if they have children. There are about 4% of such families in our sample in 2005.

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For consistency with the previous studies in the area, we restrict our samples to families in which head of the family is aged 16 to 64.

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In addition, families have to be living in private households and family heads are Canadian residents with no self-employment income. We exclude: a) couples (with or without children) where husbands and wives both have zero earnings, b) lone-parent families in which the mother or father has no earnings, and c) single individuals with no earnings. Sample weights are used for all estimations.

Family earnings are defined as the sum of wage and salary earnings from all family members older than age 15. Recognizing the economies of scale in consumption that can be achieved in larger households, we adjust our earnings measure to compare families of different sizes. The method for adjustment is very straightforward and is commonly used in the literature: we generate an “equivalent” earnings measure by dividing family earnings by the square root of the family size.

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All the income measures are converted to

2002 Canadian dollars.

Finally, we define a family head as participating “in the labour market” if he/she has positive wages and salaries. We only include in our sample those families with at least one family head in the labour market. The family head is defined as “working full-time” if his or her usual working hours per week are 30 hours or more.

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3

Similar to the definition in Karoly and Burtless (1995), we treat both husband/male partner and wife/female partner as heads of a family, and label them as the “male head” and “female head”. As such there are two heads in coupled families and one head for lone parent families or single individuals.

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For example, see Fortin and Schirle (2006), Daly and Valetta (2006), and Karoly and Burtless (1995).

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This indicator is based on a variable for the “full time weeks or part time weeks worked in previous year” so that this variable represents the hours worked in the same year for which earnings are reported.

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Trends in Family Earnings Inequality, 1980-2005

To summarize the changes in the equivalent family earnings distribution, Figure 1 provides an index of median earnings and earnings inequality measures over the period

1980-2005. Figure 2 provides the 1980, 1995 and 2005 densities of log equivalent family earnings. Measures of equivalent family earnings and earnings inequality can be found in

Table 1.

In the early 1980s and early 1990s, family earnings inequality rose by all measures. The

Gini coefficient increased by 15% from 1980-1995. The log of the ratio of the 90 th percentile to the 10 th

percentile (the 90-10 differential) increased from 1.79 in 1980 to

2.21 in 1995, an increase of more than 23%. The 50-10 differential, which captures movements in the lower half of the family earnings distribution, largely drove this increase in inequality as it increased by 28%. The 90-50 differential also increased as the earnings of the richest families increased faster than the earnings of middle income families, but not to the same extent. The 90-50 differential increased by 13%. Similar trends in family earnings inequality for this period are found in Fortin and Schirle (2006) and similar trends in family market income are found in Frenette et al. (2007). These trends can also be seen in Figure 2. From 1980 to 1995, the distribution of log equivalent family earnings shows a substantial widening of the distribution as the middle and upper end of the distribution have shifted out.

After 1995, the distribution of family earnings moves very differently. The Gini coefficient increases only slightly over this period, by only 2%. We actually observe a fairly substantial reduction in the 90-10 differential due to a narrowing of the bottom half of the distribution. The 50-10 differential falls by nearly 7 percent between 1995 and

2005 as median incomes have stagnated while the lowest incomes (at the 10 th

percentile) have seen some modest increase. Family earnings at the top end of the distribution, however, have continued to increase resulting in a modest increase in the 90-50 differential. It is the incomes at the very top of the distribution, however, that have shown the most movement resulting in a 7% increase in the 99-50 differential.

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What has been driving these more recent changes in the family earnings distribution? In the following sections, our goal is to determine what factors underlie the changes in the income distribution in each of these two periods.

III.

Trends in Labour Market Outcomes and Family Characteristics

One of the most interesting developments in the labour market over the past several decades that we would expect to affect the family earnings distribution has been the substantial increase in women’s employment rates. In our sample, women’s employment rates have climbed steadily from 72% in 1980 to 84% in 1995 and 90% in 2005 (Table

2).

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The largest increases were observed among married women with children. In 1980 only 59% of these women were working. In 2005, 85% of these women were working.

Of all family types, couples with children represent the largest portion of families. This trend in women’s employment should then have important impacts on the family earnings distribution, particularly if the increases in employment rates have not occurred evenly across the distribution. In contrast, men in our sample became slightly less likely to be employed over time, with employment rates at 99% in our 1980 sample and 97% in our

2005 sample.

Not only were women more likely to be working, they were also more likely to work full time. In 1980, 53% of women in our sample worked full time. The corresponding percentage rose to 71% in 2005. These trends in part reflect the falling elasticity of women’s labour supply with respect to their own wages and their husbands’ wages on the intensive and extensive margins since the early 1980s (see Blau and Kahn, 2007 and

Morissette and Hou, 2008). Again, men experienced quite different patterns. In 1980,

94% of them worked full time. Their full-time employment rate fell to 90% in 1995 and has remained steady at 91% over 1995-2005. The results of Fortin and Schirle (2006) suggest that increases in women’s participation had an equalizing effect on the family

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Employment in our sample, by construction, is higher than in the general population. In 1980, 79.7% of men and 52.6% of women age 15 to 64 were employed. In 2005, 76.7% of men and 68.3% of women age

15 to 64 were employed. (CANSIM II series V2461483 and V2461693.)

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earnings distribution over the 1980s and 1990s. As women’s cross-wage labour supply elasticities fall, however, we might expect changes in their labour supply to offset disequalizing effects of changes in the male wage structure to a lesser extent than they did in the past.

The wages of women have also climbed steadily over this period. In our sample of families, median earnings of women rose by 25% from 1980-1995 and then rose an additional 4% from 1995-2005. This increase reflects in part the increase in educational attainment of women. In 1980, 40% of women in our sample had not completed high school and only 8% had completed university. By 1995, only 21% had not completed high school and this rate fell to only 12% in 2005. At the same time, 16% of women in

1995 and 23% of women in 2005 had completed university.

The wage structure of women also changed over this period. Returns to education are one of the most important components of the wage structure. Boudarbat, Lemieux and

Riddell (2006) have suggested that returns to university education for women increased modestly over the period 1980-2000. Fortin and Schirle (2006) suggest the changes in female wage structure explained a large portion (nearly 1/3) of the increase in family earnings inequality over the 1980s and early 1990s.

Men, on the other hand, actually experienced some decline in real earnings over this period.

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From 1980 to 1990, median annual earnings of men fell by 4%. Despite some recovery in the early 1990s, men’s median earnings fell after 1995. Although they also enjoyed increases in educational attainment over the period 1980-2005, the changes are not quite as stark as they were for women. For example, the portion of men that do not complete high school fell from just under 38% in 1980 to 15% in 2005, a 23 percentage point drop, which is less than the 28% percentage point drop among women. Changes in men’s wage structure would explain the observed decline in earnings. Boudarbat,

Lemieux and Riddell (2006) have provided Canadian evidence of substantial increases in the returns to university education in the late 1990s. However, there were only modest

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The declines in men’s earnings explain some portion of the reduced unconditional gender earnings differential. In our sample, women’s median earnings in 1980 were only 50% of men’s. By 1995, women earned 60% of men’s earnings and this ratio increased further to 65% in 2005.

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increases in the returns to post-secondary education and no increase in the return to high school completion. Fortin and Schirle (2006) found that the changes in men’s wage structure that led to the decline in men’s earnings in the 1980s explained a large portion of the increase in family earnings inequality. While we might expect more recent changes in men’s earnings to impact inequality measures, such disequalizing effects would be moderated by the increasing share of family earnings earned by women. At the same time, any effects of changes to women’s wage structure will be strengthened as women’s wages form a larger share of family earnings.

The relative importance of changes to men’s and women’s wages for explaining family earnings inequality depends on the nature of family formation and the extent to which that has changed over time. Consider that couples (with and without kids) represent the largest share of families in Canada. Over time there has been a trend to increased assortative mating as highly educated individuals have become more likely to marry each other. In Table 3 we summarize this trend among dual earner couples with children in our sample, presenting cross-tabulations of husbands’ and wives’ earnings deciles in

1980, 1995, and 2005. The table indicates an increase in assortative mating over the

1980-1995 period and a small decrease in assortative mating from 1995 to 2006.

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In

1995, women in the top deciles of earnings were obviously more likely to be married to men in the same earning deciles. Similarly, men and women in the bottom deciles were more likely to be married to each other in 1995 than 1980. Furthermore, for example, fewer men in the top (10 th

) earnings decile were married to women in the lowest decile.

Such trends are expected to increase family earnings inequality. From 1995 to 2005, women in the bottom deciles of earnings are slightly less likely to be married to men in the same decile and there were very few changes in the likelihood of matching among the top decile men and women.

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Trends in assortative mating can be summarized as the sum of the diagonal in each set of crosstabulations, representing the total portion of couples representing individual married to someone in the same earning decile. In 1980, this portion was 11.2%, rising to 13.8% in 1995 and then to 13.7% in 2005.

When we add cells adjacent to the diagonal, the corresponding statistics are 29.9% in 1980, 35.0 in 1995 and 35.9% in 2005. Tabulations for dual earner couples without children (so that women are less constrained in terms of labour market opportunities), have higher rates of assortative mating. In 1980

14.1% of couples represented those in the same earnings decile. This increased to 16.1% in 1995 and then falls to 15.2% in 2005.When we add cells adjacent to the diagonal, the corresponding statistics are 36.4% in

1980, 39.9% in 1995 and 38.9% in 2005.

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Other general trends in family composition may also be important. There has been a steady increase in the portion of families represented by lone parents, from just over 6% in 1980 to 11% in 2005. We would expect this to increase family earnings inequality over time as these families tend to be dominated by women at the lower end of the earnings distribution. We also see a marked increase in the percentage of single individuals

(which includes those divorced) and a slight increase in the relative importance of couples without kids. Relative to those with kids, couples without kids are less constrained in terms of their choices in the labour market and may represent households in the upper end of the earnings distribution. Conversely, single individuals tend to have relatively low earnings. Hence, the growing importance of both groups is expected to further increase inequality.

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In the following sections we examine these changes in labour market outcomes and family characteristics to determine the extent to which they can account for changes in the family earnings distribution. Given the different trends over the two periods (1980-

1995 and 1995-2005), we examine these two periods separately. In the next section, we summarize the decomposition methods used and subsequently discuss our results.

IV.

Decomposition Methods

We use the decomposition methods developed by Dinardo, Fortin and Lemieux (1996), closely following the work of Fortin and Schirle (2006). The methods used here allow us to separately identify the contribution of each factor we consider to observed changes in the family earnings distribution and inequality measures. We are considering changes to

(i) men’s likelihood of employment, (ii) men’s wage structure, (iii) women’s likelihood of employment, (iv) women’s wage structure, (v) assortative mating, (vi) family composition, and (vii) family characteristics (such as educational attainment). A thorough description of the methodology used can be found in Fortin and Schirle (2006).

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In 2005, equivalent earnings of single men (women) averaged $36,927 ($30,776), compared to $44,386 for couples with kids, $50,507 for couples without kids and $22,338 ($34,284) for lone-mothers (fathers).

The corresponding numbers for 1980 were $32,928, $25,483, $32,781, $41,519, $18,515 and $32,692.

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In this section, we provide only a summary of the methods and their intuitive interpretation with details provided in the Appendix.

In the first decomposition we construct a series of counterfactual densities that represent the density of log equivalent family earnings that would have prevailed in 1995 had each of the explanatory factors remained as in 1980. The decomposition is sequential in that once the 1995 density has been adjusted for a factor, that factor remains adjusted in the remaining stages of the decomposition.

The estimation of the counterfactual densities that would have prevailed in 1995 had our first factor – men’s likelihood of employment – not changed since 1980, ultimately requires adjusting the weights placed on each family so that the likelihood of employment in the adjusted sample is the same as the likelihood of male employment in the 1980 sample (see the appendix for details). The first counterfactual density and all inequality statistics describing the counterfactual density are estimated using these new sample weights.

In the second stage of the decomposition we create a counterfactual density that would have prevailed in 1995 had men’s likelihood of employment and their wage structure not changed since 1980. To do this, we estimate men’s log weekly earnings in each year

1980 and 1995 using a simple linear model represented by y

Mt

= X t

β t

+

ε t

(1)

The vector of characteristics (X t

) includes a quadratic in age, and dummy variables indicating education, years since immigration, province of residence, and full-time work status. Men’s 1995 log weekly earnings are adjusted by applying the 1980 parameter estimates (

β

80

) to men’s 1995 characteristics and adding the residuals from the 1995 earnings regression. That is, y

MX95

β

80

= X

95

β

80

+

ε

95

(2)

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These estimates are then used to adjust the family earnings of all families with a male head that is employed by replacing the male head’s contribution to family earnings in

1995 with the counterfactual earnings amount represented by (2). This revised family earnings and the previously revised weights are then used to estimate the counterfactual density representing the density that would have prevailed had men’s wage structure not changed after 1980.

The remaining stages of the decomposition are similar in nature. In the third stage, we estimate a counterfactual density that would have prevailed in 1995 had female employment rates (and the previously adjusted factors) not changed since 1980. In the fourth stage we further adjust for changes in the female wage structure in a manner corresponding to our adjustment in men’s wage structure. In the fifth stage we adjust for changes in assortative mating, then family composition and then finally family characteristics. Details of methods used to adjust the sample weights in each of these stages are provided in the appendix.

The primary order decomposition outlined above is repeated to decompose the changes in the log equivalent family earnings distribution between 1995 and 2005. Each stage is examined the same way, beginning with the 2005 density and estimating the counterfactual 2005 density that would have prevailed had men’s employment rates not changed since 1995.

As the decomposition results may be sensitive to the order in which factors are adjusted, we repeat the decomposition taking each factor into account in the reverse order. That is, in the first stage we estimate a counterfactual density that would have prevailed in 1995 had the family characteristics not changed since 1980. We then adjust for family composition, assortative mating, female wage structure, female employment, male wage structure, and male employment. Again, details of the procedures used to create the densities can be found in the appendix.

V.

Results

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In this section we present the results of the decomposition, focussing on the primary order decompositions for 1980-1995 and 1995-2005 first. We then briefly discuss the reverse order decomposition results, the results based on a more restricted sample (age

25-54), and the decomposition results for 1980-2005.

A.

Primary order decomposition results

The results of the 1980-1995 decomposition are provided in Tables 4 and 5 and Figure 3.

Corresponding results for the 1995-2005 decompositions are found in Tables 6 and 7 and

Figure 4. Figures 3 and 4 provide a graphical representation of each counterfactual density that is estimated in the decomposition, plotted with the density from the previous stage. Tables 4 and 6 provide the distribution statistics that describe the resulting densities. In Tables 5 and 7 we use that information to derive the relative contribution of each explanatory factor to the changes in the inequality statistics.

Over the period 1980-1995, we observed large increases in inequality by all measures

(Panel A of Table 4). We begin by looking at the contribution of changes to men’s employment rates. Recall that men’s employment rates fell slightly over the period 1980-

1995. Looking at the primary order decomposition distribution statistics in Table 4

(Panel B), the results suggest that if men’s employment rates had remained at the higher rates we observe in 1980, the 1995 inequality measures would have been lower. Thus, the reduction in employment rates over the period 1980-1995 had a disequalizing effect, acting to drive up family earnings inequality. Graphically (Figure 3a) we can see that the reduction in men’s participation led to some families moving into the lower end of the family earnings distribution. That is, relative to the 1995 observed density, the counterfactual density representing the distribution that would have prevailed had men’s employment rates not changed after 1980 would have more families near the mode and slightly fewer in the lower tail. Overall, the reduction in men’s employment explains only a modest portion of the increase in inequality – accounting for 5% of the increase in the 90-10 differential and 9% of the 90-50 differential (Table 5).

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Over the period 1995-2005 we had seen a reversal in the trends for men’s employment rates, increasing very slightly over the period. The 1995-2005 decomposition results suggest this had an equalizing effect on the distribution of family earnings – if employment rates had not risen, inequality measures would have been slightly higher.

While not as obvious in Figure 4a, if men’s employment rates had remained at 1995 levels, there would have been fewer families located at the mode of the distribution and more families in the lower end of the distribution. These small changes had a modest effect, suggesting that 9% of the decrease in the 90-10 differential is due to this factor.

There is a larger equalizing effect on the 90-50 differential as increases to men’s employment rates push up the 50 th

percentile while having little effect on the 90 th percentile.

Turning to changes in the male wage structure, our estimates suggest that if the male wage structure had remained as in 1980, all inequality measures would have been substantially lower in 1995. Graphically (in Figure 3B) we can see that men’s wage structure changed from 1980 to 1995 such that the entire distribution was driven leftward with all family incomes slightly lower by 1995. The fall in incomes was not evenly felt by all families. Counteracting the general decline in earnings, there was an increase in the return to education particularly for the highest education levels (see the second column of Table 8). As such, incomes at the top end of the distribution did not fall as far as incomes at the bottom of the distribution. Consistent with Aydemir and Skuterud

(2005), we also find larger wage penalties for recent immigrants by 1995, whose families are typically in the lower end of the earnings distribution. These changes in the wage structure were one of the most important factors in explaining the increase in inequality over the 1980-1995 period, explaining 22% in the 90-10 differential and 37% of the 90-

50 differential.

Over the period 1995-2005 we see some different changes in the male wage structure and their effect on inequality. The decomposition results suggest that if the male wage structure had not changed after 1995, inequality would have been slightly higher in 2005.

That is, changes in the male wage structure had equalizing effects. The key difference is that the return to university education did not increase much after 1995 while the return

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to some post-secondary education (which would include for instance many trade certificates) continued to increase slightly.

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Overall, these changes did not have a large impact, explaining only 2% of the decrease in the 90-10 differential.

Our results confirm the importance of changes in women’s employment as an explanatory factor for changes in the family earnings distribution. Women’s employment rates increased steadily over the period 1980-2005. The 1980-1995 suggest that if women’s employment rates had not increased we would have seen more inequality by

1995. Graphically, we can see how this affects different parts of the family earnings distribution in Figure 3C. Here, if women’s employment rates remained as in 1980, we would have seen more families in the lower end of the income distribution rather than in the middle. Since this brought up the bottom half of the distribution and didn’t affect the top half as much, we see the largest equalizing effects in the 90-50 and 99-50 differentials. Similar and slightly larger relative effects are seen over the period 1995-

2005, where the increases in women’s employment raised incomes in the bottom half of the distribution.

Changes to the female wage structure from 1980-1995 had effects similar to the changes in male wage structure. Women enjoyed larger increases in the returns to education than men did (see the fourth and fifth columns of Table 8) and this drove a modest portion of the increase in inequality as those with the highest level of education enjoyed the largest increases in returns. The results suggest we can explain 11% of the increase in the 90-10 differential, 11%of the increase in the 50-10 differential and 14% of the increase in the

90-50 differential.

The changes to the female wage structure are slightly different from men’s in the 1995-

2005 period, with distinct effects on inequality. While changes to men’s wage structure drove some of the decrease in inequality from 1995-2005, changes to women’s wage structure continued to have disequalizing effects - had women’s wage structure not

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Morissette (2008) shows that wage growth was fairly strong in the lower vingtiles in Alberta between

1997 and 2007, thereby suggesting that strong increases in the price of commodities after the early 2000s might have boosted the demand for lower-skilled workers in some industries such as mining and oil in some provinces.

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changed after 1995, all inequality measures would have been lower. The key difference between men and women is that women’s returns to education continued to increase substantially – particularly for those with university degrees – over the 1995-2005 period.

This would drive up family incomes at the top end of the distribution. The wage penalties for recent female immigrants also continued to increase substantially, exacerbating the effect on inequality.

Between 1980 and 1995, a higher degree of assortative mating appears to have had important disequalizing effects, driving 10% of the increase in the 90-10 differential, 9% of the 50-10 differential, and 15% of the 90-50 differential. Graphically, we can see in

Figure 3E how families were effectively pulled out of the middle of the income distribution and redistributed to the tails. Between 1995 and 2005, we actually observe a slight decline in the degree of assortative mating, particularly in the lower deciles of dual earner couples.

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The lower intensity of assortative mating drives 7% of the reduction in the 90-10 and 50-10 differentials. At the top end of the family earnings distribution, the changes in assortative mating have a moderate effect, explaining 15% of the 1995-2005 increase in the 90-50 differential and 2% of the increase in the 99-50 differential. This would relate to the slightly higher degree of assortative mating among married couples with kids in the very top earning deciles.

The results of the next stage of the decomposition demonstrate the importance of family composition for the distribution of family earnings. The steady increase in the proportion of families headed by lone parents, coupled with the increasing proportion of families without kids, drove increases in inequality over both periods 1980-1995 and 1995-2005.

In the 1980-1995 period, the changes in family composition created an overall increase in dispersion of family earnings – 20% of the 90-10 differential, 21% of the 50-10 differential, and 16% of the 90-50 differential are explained. In the 1995-2005 period, family composition appears to have the greatest impact on the top end of the distribution, explaining 63% of the (relatively small) increase in the 90-50 differential.

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The degree of assortative mating (measured as the sum of the diagonal in Table 3) falls from 13.78 to

13.73 for couples with kids and 16.13 to 15.22 for couples without kids. There appears to be reduced concentration along the diagonal among those in the lower deciles while there appears to be some increased concentration among those with kids in the upper deciles.

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Finally, we examine the role of changes in family characteristics. In the 1980-1995 period we find that changes in family characteristics had an equalizing effect, as measured inequality would have been substantially higher by 1995 had these characteristics not changed. The large increases in men’s and women’s education, the increasing likelihood of women to work full time, and the aging of the population worked to increase earnings generally, with the largest effects on the bottom half of the family earnings distribution (see Figure 3G). These trends continued in the 1995-2005 period, preventing family earnings inequality from rising further.

To summarize, the decomposition results have identified the extent to which various factors will affect the distribution of family earnings. Increases in men’s employment rates tend to reduce inequality by improving the lot of families in the lower end of the distribution. Increasing returns to education tend to favour families in the top half of the distribution, raising inequality. Increases in women’s employment rates will tend to reduce inequality while increased assortative mating, an increasing portion of single parent families, and an increasing portion of families without kids will tend to increase inequality.

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Recent changes in family characteristics, including increases in educational attainment and population aging, tend to reduce inequality.

B.

Robustness of the results

The results of the reverse order decompositions are nearly identical to the results of the primary order decompositions. An interesting difference in results for family composition and assortative mating point to the difficulty in separating the effects of factors that might not be entirely independent decisions. In the 1980-1995 decomposition, the effects of assortative mating on the 90-10 differential are much smaller when changes to family composition have already been accounted for. In the

1995-2005 decomposition, the effect of family composition is not as large when

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It is worth noting that the decomposition methods we use may overestimate (underestimate) the equalizing impact of increases in women’s employment rates. This would happen if women are better

(poorer) substitutes for low skilled male workers than they are for high skilled male workers. If so, increases in women’s employment rates would put downward pressures on the wages of low skilled men to a greater (lesser) extent than they would for high skilled men, thereby increasing (decreasing) male earnings inequality. Increases in male earnings inequality due to increases in female labour supply have been documented in Acemoglu et al. (2004) for the period surrounding World War II.

16

assortative mating has not yet been accounted for. Overall, we can be confident that both these factors are important but we can not be confident we have separately identified the magnitudes of these effects.

We repeated the decomposition for the period 1980-2005. Overall, inequality increased over the period. The resulting inequality statistics from the decomposition are presented in Table 9, and are very similar to the results for the 1980-1995 decomposition. This would be expected, given the large shift in the distribution of family earnings over 1980-

1995 relative to the shift from 1995-2005.

We also repeated the 1980-2005 decomposition using a more restricted sample, only including those families whose heads are between ages 25 and 54. The results are very similar, confirming that changes in university enrolments or retirements are not driving the results. Changes in family composition remains a key factor in explaining the overall increase in inequality, as changes to the wage structure have large effects on the family earnings distribution and increases in women’s employment rates have important equalizing effects.

VI.

Concluding Remarks

Between 1980 and 2005, family earnings inequality rose substantially in Canada. While family earnings at the 10 th

percentile were no higher in 2005 than they were in 1980, those at the 90 th

percentile grew by roughly 25% while those at the 99 th

percentile increased by a remarkable 48%.

In this paper, we examined the degree to which changes in the wage structure, changes in employment rates, changes in patterns of family formation as well as changes in family characteristics account for this increase. We find that both changes in the wage structure and changes associated with patterns of family formation (i.e. changes in family composition and changes in assortative mating) contributed to the growth of family earnings inequality since the early 1980s. Overall, changes in family composition and

17

family characteristics were among the most important factors underlying changes in the family earnings distribution since 1980, with changes in family characteristics having a strong equalizing impact.

As Canada—like many OECD countries— is currently experiencing an economic slowdown, one important and difficult question is whether the growth in family earnings inequality will continue in subsequent years or will come to a halt. Several factors could fuel the growth in family earnings inequality or, conversely, restrict it. It is conceivable that the growth in the relative importance of single individuals and lone-parent families might slow down in the years to come. Likewise, young well educated women, who have outnumbered young well educated men in recent years in Canada, could well start

“marrying down”, i.e. getting married with less educated male partners.

13

Both factors might plausibly restrict the growth of family earnings inequality.

Conversely, increases in the worldwide supply of low skilled workers partly associated with China’s and India’s economic growth could widen the wage gap between low skilled workers and high skilled workers in subsequent years (Fehr et al. 2008). Finally, the current economic slowdown could partly erase the earnings growth that blue collar workers enjoyed in recent years in Canada as a result of booming employment in sectors such as construction, mining, oil and gas extraction. This could also contribute to increasing family earnings dispersion.

13

In 1992, just over 56% of university degrees were granted to women. In 2002, just under 60% of university degrees were granted to women and that rate has remained steady since 2002. (Based on authors tabulations from CANSIM II series V31212549 AND V31212550.)

18

References

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Political Economy

112, 497–551

Aydemir, Abdurrahman and Mikal Skuterud. (2005). “Explaining the deteriorating entry earnings of Canada's immigrant cohorts, 1966 - 2000.”

Canadian Journal of

Economics

, vol. 38, No. 2 (May 2005), 641-672.

Boudarbat, Brahim, Thomas Lemieux and Craig Riddell (2006). “Recent trends in wage inequality and the wage structure in Canada.” in Dimensions of Inequality in

Canada, ed. David A. Green and Jonathan R. Kesselman. Vancouver: UBC Press.

273-306.

Blau, Francine, and Lawrence Kahn (2007). “Changes in the labour supply behaviour of married women: 1980-2000.” Journal of Labour Economics , vol. 25 no. 3, 393-

438.

Daly, Mary C. and Robert G. Valetta (2006). “Inequality and Poverty in United States:

The Effects of Rising Dispersion of Men's Earnings and Changing Family

Behaviour.”

Economica

, Volume 73, No. 289, February 2006 , 75-98.

Dinardo, John, Nicole M. Fortin and Thomas Lemieux (1996). “Labor Market

Institutions and the Distribution of Wages, 1973-1992: A Semiparametric

Approach.”

Econometrica

, vol. 64 no. 5. 1001-1044.

Karoly, Lynn A., and Gary Burtless (1995). “Demographic Change, Rising Earnings

Inequality, and the Distribution of Personal Well-Being, 1959-1989.”

Demography , Vol. 32, No. 3. 379-405.

Fehr, Hans, Sabine Jokisch, and Lawrence J. Kotlikoff (2008). “Dynamic Globalization and Its Potentially Alarming Prospects for Low-Wage Workers.” NBER Working

Paper no. 14527.

Frenette, Marc, David Green and Kevin Milligan (2007) “ The tale of the tails: Canadian

Income Inequality in the 1980s and 1990s” Canadian Journal of Economics , Vol.

40, No. 3 (August 2007), 734-764.

Fortin, Nicole and Tammy Schirle (2006) “Gender Dimensions of Changes in Earnings

Inequality in Canada” in Dimensions of Inequality in Canada, ed. David A. Green and Jonathan R. Kesselman. Vancouver: UBC Press. 307-346

Gottschalk, Peter and Timothy Smeeding (1997) “Cross-national comparison of earnings and income inequality,”

Journal of Economic Literature

35(2), 633-687.

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Lemieux, Thomas (2007). “The Changing Nature of Wage Inequality.” NBER Working

Paper no. 13523.

Lemieux, Thomas, W. Bentley Macleod and Daniel Parent (2006). “Performance Pay and

Wage Inequality.” Manuscript, University of British Columbia.

Morissette, Rene (2008). “Earnings in the last decade.” Perspectives on Labour and

Income

, Statistics Canada Catalogue no. 75-001-X, February 2008, 12-24.

Morissette, Rene and Feng Hou (2008) “Does the labour supply of wives respond to husbands’ wages? Canadian evidence from micro data and grouped data.”

Canadian Journal of Economics

, vol. 41, no. 4, 1185-1210.

Saez, Emmanuel and Michael R. Veall (2005). “The Evolution of High Incomes in

Northern America: Lessons from Canadian Evidence.”

American Economic

Review

, vol. 95, no. 3, 831-849.

20

130

125

120

115

110

105

100 log 99/50 log 90/50 log 90/10 log 50/10

Median

95

1980 1985 1990 1995 2000 2005

Year

Figure 1: Summary measures for equivalent family earnings (1980=100).

Note: Authors’ tabulations based on the Canadian Census (20% sample). See text for sample description .

21

.7

.6

.5

.2

.1

.4

.3

2005

1995

1980

.0

8 9 10 11 12

Log equivalent family earnings

Figure 2: Densities of log equivalent family earnings, 1980, 1995, and 2005

Note: Kernel density estimates based on the Canadian Census (20% sample). See text for sample description .

22

.5

.4

.3

.2

.7

.6

.1

.0

8

1995

Male employment

9 10 11

A

12

.7

.6

.5

.4

.3

.2

.1

.0

8

Male employment

Male wage structure

9 10 11

B

12

Male wage structure

Female employment

.5

.4

.3

.7

.6

Female employment

.7

.6

.5

.4

.3

.2

.1

.2

.1

.0

.0

8 9 10 11 12 8 9 10 11 12

Figure 3: Decomposition results 1980-1995: 1995 densities of log equivalent family earnings adjusted in each stage of the decomposition (2002 dollars) Note: The densities presented are the counterfactual densities that result from the primary order decomposition. The 1995 density of log equivalent earnings is adjusted for changes in male employment since 1980, then male wage structure, female employment, female wage structure, assortative mating, family composition, and family characteristics.

23

.5

.4

.3

.2

.1

.7

.6

Female wage structure

Assortative mating E

.7

.6

.5

.4

Assortative mating

Family composition F

.3

.2

.1

.0

8 9 10 11 12

.0

8

.7

9 10 11 12

.7

.6

Family composition

Family characteristics

G

.6

.5

1980


1995

H

.5

.4

.3

.4

.3

.2

.2

.1

.1

.0

.0

8 9 10 11 12 8 9 10 11 12

Figure 3 (continued): Decomposition results 1980-1995: 1995 densities of log equivalent family earnings adjusted in each stage of the decomposition (2002 dollars) Note: The densities presented are the counterfactual densities that result from the primary order decomposition. The 1995 density of log equivalent earnings is adjusted for changes in male employment since 1980, then male wage structure, female employment, female wage structure, assortative mating, family composition, and family characteristics.

24

.5

.4

.7

.6

.3

.2

.1

2005

Male employment

A

.3

.2

.1

.7

.6

.5

.4

Male employment

Male wage structure

B

.0

8 9 10 11 12

.0

8

.7

9 10 11 12

.7

.6

Male wage structure

Female employment

C

.6

.5

Female employment


D

.5

.4

.4

.3

.3

.2

.1

.2

.1

.0

.0

8 9 10 11 12 8 9 10 11

Figure 4: Decomposition results 1995-2005: 2005 densities of log equivalent family earnings adjusted in each stage of the

12 decomposition (2002 dollars) Note: The densities presented are the counterfactual densities that result from the primary order decomposition. The 2005 density of log equivalent earnings is adjusted for changes in male employment since 1995, then male wage structure, female employment, female wage structure, assortative mating, family composition, and family characteristics.

25

.7

.6

.5

.4

.3

.2

.1

.0

8


Assortative mating

.7

Assortative mating

Family composition

.6

E F

.5

.4

.3

.2

.4

.3

.2

.1

.7

.6

.5

9 10 11

.1

12

.0

8

.7

9 10 11 12

Family composition


G

.3

.2

.1

.6

.5

.4

1995


2005

H

.0

.0

8 9 10 11 12 8 9 10 11 12

Figure 4 (continued): Decomposition results 1995-2005: 2005 densities of log equivalent family earnings adjusted in each stage of the decomposition (2002 dollars) Note: The densities presented are the counterfactual densities that result from the primary order decomposition. The 2005 density of log equivalent earnings is adjusted for changes in male employment since 1995, then male wage structure, female employment, female wage structure, assortative mating, family composition, and family characteristics.

26

Table 1: Distribution Statistics, Equivalent Family Earnings

1980 1985 1990 1995 2000 2005

Mean

Percentiles

99 th

90 th

50

10 th th

Standard deviation log 99/50 log 90/50 log 90/10 log 50/10

Gini coefficient

32787 32265

1.145 1.198

0.633 0.669

1.790 1.990

1.157 1.321

.328 .351

34612

1.230

0.670

1.967

1.297

.352

37792

1.317

0.720

2.205

1.485

.378

37922 39896

94817 97536 108118 126151 134543

56818 57479 61754 69448 68134 72175

30180 29433

9485 7857

21817 23272

31607

8640

25570

33801

7653

31237

33062 34443

8386 9217

39275 42194

1.404 1.407

0.723 0.740

2.095 2.058

1.372 1.318

.383 .384

Notes: Authors’ tabulations from the Canadian Census (20% sample). See text for sample description. All amounts are in 2002 Canadian dollars.

27

Table 2: Family Characteristics 1980-2005

1980 1985 1990 1995 2000 2005

Family composition (%)

Couple, without kids

Couple, with kids

Lone parent

Single (includes divorced)

Male head

Average age

Less than HS

High school

Some post-secondary

University +

Employment rate* (%)

18.8

46.5

6.4

28.3

18.5

45.0

7.3

29.1

19.1

42.2

7.9

30.8

18.5

41.7

8.8

31.1

19.2

39.0

9.7

19.6

34.8

11.0

32.1 34.6

38.6

39.2

39.6

40.6

41.6 42.5

37.5

23.0

27.0

12.5

98.7

34.2

23.3

28.5

14.1

97.7

28.6

26.0

30.1

15.4

97.7

24.4

25.7

32.6

17.4

96.4

21.2

25.0

14.9

24.0

34.5 39.8

19.4 21.2

96.5 97.0


Couple, with kids

Working full-time** (%)

97.3

98.7

94.3

95.4

97.7

91.8

95.5

97.7

92.9

92.8

96.3

89.8

93.1 93.8

96.5 96.9

90.8 91.2

Median annual earnings*** 41091 39683 39541 42602 40571 40969

21.0 20.4 19.9 20.4 21.1 21.1

Female head

Average age 37.0

37.6

38.2

39.3

40.4 41.3

40.3

35.3

27.0

21.6

18.1 12.0

Less than HS

High school

Some post-secondary

University +

25.9

25.8

8.0

26.4

28.1

10.3

29.5

30.8

12.8

28.1

34.2

16.0

26.3

36.2

19.4

26.4

38.7

23.0

Employment rate* (%)


Couple, with kids

71.9

76.0

59.4

76.7

78.0

66.2

84.0

83.1

76.7

84.4

82.8

77.4

87.1

84.3

89.8

86.0

81.3 84.7

Working full-time** (%) 53.2

55.7

63.9

62.3

67.2 70.8

Median annual earnings*** 20455 20635 22959 25547 26205 26681

Immigrants (%) 19.8

19.2

18.9

19.9

20.9 21.2

Notes: Authors’ tabulations from the Canadian Census (20% sample). See text for sample description.

*A person is employed if they worked positive weeks in the year and have positive wages.

**A person who worked 30 or more hours per week is defined as full-time.

*** 2002 constant dollars, conditional on having positive wages and weeks worked

28

Table 3a: Assortative Mating Measures: Proportion of dual earner couples with kids

Male Earnings

Decile 1 2 3 4

Female Earnings Decile

5 6 7 8 9 10

1.24

1.05

0.94

0.91

0.95

0.92

0.98

0.93

0.94

0.93

1.11

1.02

0.95

1.00

0.95

0.96

0.96

0.93

0.92

0.88

1.15

1.24

1.14

1.08

1.02

0.98

1.00

0.94

0.93

0.86

0.90

1.27

1.17

1.05

1.03

0.96

0.91

0.85

0.80

0.72

0.78

1.26

1.20

1.12

1.03

1.07

1.02

0.89

0.84

0.77

0.71

0.94

1.21

1.15

1.11

1.06

1.11

0.97

0.92

0.83

0.67

0.67

0.99

1.17

1.10

1.13

1.12

1.08

1.07

1.01

1.37

1.34

1.16

1.03

1.04

0.83

1.07

0.62

0.82

0.70

0.99

1.48

1.20

1.05

1.07

0.87

1.14

0.63

0.82

0.74

0.87

1.48

1.37

1.29

1.25

1.07

1.38

0.73

0.94

0.89

0.66

0.75

1.21

1.00

1.09

0.83

1.12

0.63

0.77

0.68

0.66

0.75

1.20

1.31

1.28

1.04

1.43

0.76

0.96

0.88

0.59

0.61

0.71

1.23

1.26

1.03

1.44

0.78

1.08

0.99

0.59

0.57

0.67

0.77

1.29

1.27

1.61

0.91

1.28

1.24

1.34

1.35

1.11

1.06

0.98

0.89

0.86

0.82

0.73

0.66

1.05

1.37

1.22

1.11

1.07

0.96

0.91

0.84

0.80

0.67

0.85

1.23

1.25

1.16

1.09

1.02

0.97

0.90

0.82

0.72

0.75

0.94

1.29

1.17

1.16

1.06

1.03

0.97

0.88

0.76

0.62

0.76

1.04

1.21

1.21

1.10

1.11

1.03

1.04

0.89

0.60

0.67

0.79

1.06

1.23

1.15

1.20

1.17

1.12

1.02

0.55

0.57

0.67

0.81

1.01

1.14

1.31

1.33

1.31

1.30

Note: The degree of assortative mating, measured as the sum of the diagonal, is 11.7, 13.78 and 13.73 in 1980, 1995, and 2005 respectively.

0.53

0.42

0.47

0.55

0.69

0.76

0.99

1.37

1.78

2.42

0.51

0.43

0.45

0.54

0.64

0.67

1.44

1.02

1.72

2.35

0.67

0.56

0.61

0.66

0.89

1.03

1.13

1.18

1.46

1.80

29

Table 3b: Assortative Mating Measures: Proportion of dual earner couples without kids

Male Earnings

Decile

1980 1

2

1 2 3 4

Female Earnings Decile

5 6 7 8 9 10

6

7

1.41

1.54

1.05

1.26

0.85

0.82

0.86

0.78

0.71

0.82

1.08

1.61

1.17

1.40

0.97

0.92

0.85

0.81

0.69

0.66

0.92

1.36

1.16

1.53

1.02

1.01

1.00

0.83

0.70

0.64

0.92

1.16

1.49

1.87

1.33

1.37

1.29

1.24

1.09

0.88

0.47

0.52

0.56

1.00

0.77

0.78

0.79

0.78

0.72

0.55

0.64

0.64

0.63

1.29

1.05

1.10

1.17

1.21

1.15

1.08

0.65

0.58

0.51

0.91

0.91

1.28

1.23

1.32

1.30

1.31

1995 1

2

5

6

10

4

5

9

10

1.09

1.80

1.36

1.13

1.02

0.98

0.72

0.74

0.72

0.64

1.22

1.61

1.36

1.10

0.99

0.89

0.84

0.73

0.69

0.57

0.86

1.35

1.33

1.16

0.98

0.99

0.74

0.73

0.66

0.58

1.01

1.36

1.43

1.20

1.05

0.98

0.90

0.81

0.74

0.63

0.78

0.94

1.57

1.22

1.16

1.15

0.91

0.89

0.79

0.60

0.77

0.98

1.36

1.22

1.17

1.03

0.98

0.94

0.80

0.64

0.68

0.80

0.96

1.46

1.21

1.24

0.97

1.04

0.90

0.74

0.68

0.83

1.08

1.29

1.19

1.18

1.11

1.01

0.90

0.74

0.62

0.72

0.79

1.15

1.64

1.36

1.20

1.31

1.14

0.92

0.64

0.69

0.88

1.11

1.34

1.22

1.12

1.07

1.07

0.87

0.54

0.59

0.63

0.81

1.10

1.58

1.11

1.28

1.20

1.06

0.61

0.62

0.70

0.86

1.10

1.36

1.27

1.22

1.20

1.07

0.50

0.51

0.54

0.62

0.73

1.13

1.38

1.34

1.45

1.33

0.54

0.52

0.63

0.66

0.86

1.07

1.42

1.51

1.39

1.41

0.46

0.40

0.40

0.43

0.56

0.75

0.77

1.31

1.86

2.78

Note: The degree of assortative mating, measured as the sum of the diagonal, is 14.11, 16.13 and 15.22 in 1980, 1995, and 2005 respectively.

0.52

0.43

0.45

0.47

0.63

0.70

0.91

1.28

1.83

2.77

0.60

0.53

0.40

0.64

0.58

0.76

1.07

1.33

1.69

2.40

30

Table 4: Decomposition Results 1980-1995: Inequality Statistics deviation

1980

1995

1.790 1.157 0.633 1.145 0.852 0.328

2.205 1.485 0.720 1.317 1.071 0.378

B. Primary Order Decomposition

Male employment 2.184 1.472 0.713 1.305 1.061 0.375

Male wage structure 2.095 1.415 0.680 1.252 1.038 0.364

Female employment 2.131 1.436 0.695 1.280 1.047 0.369

Female wage structure 2.085 1.402 0.683 1.267 1.033 0.365

Assortative mating 2.043 1.372 0.670 1.247 1.019 0.360

Family composition 1.959 1.302 0.657 1.236 0.989 0.352

Family characteristics 2.189 1.494 0.695 1.251 1.067 0.371

C. Reverse Order Decomposition


Family composition

Assortative mating


Female employment

2.388 1.642 0.746 1.314 1.130 0.392

2.306 1.569 0.737 1.313 1.111 0.388

2.303 1.580 0.722 1.298 1.103 0.383

2.258 1.544 0.714 1.283 1.088 0.379

2.308 1.577 0.732 1.316 1.109 0.387

Male wage structure

Male employment

2.257 1.547 0.710 1.279 1.089 0.379

2.246 1.539 0.707 1.276 1.086 0.377

Note: Calculated using the Canadian Census (20% sample). The inequality statistics in panels B and C represent the counterfactual distribution of log equivalent family earnings that would have prevailed in

1995 had each factor remained as in 1980. See text for details.

31

Table 5: Decomposition Results 1980-1995: Changes in inequality measures deviation

Total Change 0.415 0.328

A. Primary Order Decomposition

0.087

0.172

Effect of:

Male employment

Male wage structure

Female employment

0.021 0.013

(5.1) (4.1)

0.090 0.057

(21.6) (17.5)

0.008

(8.6)

0.032

(37.2)

0.012

(6.9)

0.054

(31.1)

-0.037 -0.022

-0.015

-0.028

-(8.8) -(6.6)

Female wage structure 0.047 0.035

-(17.1)

0.012

-(16.3)

0.013

Assortative mating

Family composition

(11.2) (10.6)

0.042 0.029

(10.1) (8.9)

0.084 0.070

(20.2) (21.4)

(13.5)

0.013

(14.6)

0.014

(15.9)

(7.6)

0.019

(11.3)

0.012

(6.7)

Family characteristics -0.230 -0.192

-0.038

-0.015

Unexplained

-(55.4) -(58.5)

0.399 0.337

-(43.9)

0.062

-(8.8)

0.106

(96.1) (102.7) (71.2) (61.5)

0.219 0.050

0.010 0.003

(4.7) (6.0)

0.022 0.011

(10.2) (22.1)

-0.008 -0.005

-(3.9) -(9.9)

0.013 0.004

(6.1) (8.5)

0.015 0.005

(6.8) (10.0)

0.030 0.007

(13.5) (14.9)

-0.078 -0.019

-(35.6) -(37.8)

0.215 0.043

(98.0) (86.2)



Family composition

Assortative mating


Female employment

-0.183 -0.157

-(44.0) -(47.8)

0.082 0.074

(19.9) (22.4)

0.003 -0.012

(0.8) -(3.6)

0.045 0.036

-0.026

-(29.6)

0.009

(10.2)

0.015

(16.9)

0.008

0.002

(1.4)

0.001

(0.7)

0.015

(8.7)

0.015

(10.8) (11.1) (9.7) (9.0)

-0.050 -0.033

-0.018

-0.033

Male wage structure

Male employment

-(12.1) -(10.0) -(20.3) -(19.2)

0.051 0.030

(12.4) (9.0)

0.011 0.008

0.022

(25.0)

0.003

0.036

(21.1)

0.004

Unexplained

(2.6) (2.4)

0.456 0.382

(109.8) (116.4)

(3.2)

0.074

(84.9)

-0.059 -0.014

-(27.0) -(27.5)

0.020 0.004

(8.9) (8.5)

0.007 0.004

(3.3) (8.4)

0.016 0.004

(7.2) (8.8)

-0.022 -0.008

-(9.9) -(15.8)

0.021 0.008

(9.4) (16.7)

0.003 0.001

(2.0)

0.131

(1.5) (2.2)

0.234 0.049

(76.2) (106.6) (98.7)

Note: Calculated using the Canadian Census (20% sample). The effect of each explanatory factor indicates how much of the total change is attributed to that factor. Percent of the total change is in parentheses.

“Unexplained” is the residual not accounted for by all other factors.

32

Table 6: Decomposition Results 1995-2005: Inequality Statistics

A. Initial Estimates

1995

2005

B. Primary Order Decomposition

2.205

2.058

Male employment

Male wage structure

Female employment


Assortative mating

2.072

2.075

2.085

2.065

Family composition



2.070

2.022

2.062

1.485

1.318

1.328

1.332

1.334

1.320

1.327

1.292

1.322

0.720

0.740

0.743

0.743

0.750

0.745

0.742

0.730

0.740

1.317

1.407

1.411

1.413

1.429

1.420

1.418

1.410

1.392

deviation

1.071

0.950

0.955 0.386

0.955 0.386

0.961 0.389

0.953 0.386

0.953 0.386

0.934 0.381

0.947 0.382

0.378

0.384


Family composition

Assortative mating


Female employment

2.117

2.108

2.118

2.099

2.112

1.369

1.360

1.371

1.356

1.367

0.748

0.748

0.746

0.743

0.745

1.398

1.408

1.406

1.396

1.398

0.966 0.387

0.964 0.387

0.966 0.387

0.959 0.385

0.964 0.386

Male wage structure

Male employment

2.114

2.116

1.365

1.366

0.749

0.750

1.406

1.407

0.964 0.387

0.965 0.388



33

Table 7: Decomposition Results 1995-2005: Changes in Inequality Measures deviation

Total Change -0.147

-0.167

0.020

0.090

A. Primary Order Decomposition

-0.005 -0.002

Male employment

Male wage structure

Female employment


Assortative mating

Family composition

-0.014

(9.4)

-0.003

(1.8)

-0.010

(6.8)

0.019

-(13.2)

-0.004

(3.0)

0.048

-0.010

(6.1) -(18.6)

-0.003

(1.9)

-0.003

(1.6)

0.015

-(8.7)

-0.007

(4.4)

0.035

-0.004

0.000

(2.2)

-0.007

-(37.0)

0.005

(24.8)

0.003

(14.9)

0.012


-(32.5) -(21.2)

-0.040

-0.031

(62.9)

-0.009

(27.3)

Unexplained

(18.4) -(47.8)

-0.163

0.019

-0.004

-(4.3)

-0.002

-(2.0)

-0.017

-(18.5)

0.009

(10.3)

0.002

(1.9)

0.008

(8.9)

0.018

(19.9)

0.075

(4.1) -(25.3)

0.001 0.000

-(0.5) -(5.5)

-0.006 -0.003

(4.7) -(52.6)

0.008 0.003

-(6.4) (44.7)

-0.001 0.000

(0.4) (6.9)

0.020 0.005

-(16.4) (82.0)

-0.014 -0.001

(11.3) -(20.7)

-0.124 0.004

(97.3) (97.5) (98.6) (83.7) (102.7) (70.5)

B. Reverse Order Decomposition

Family characteristics -0.059

-0.051

-0.008

Family composition

(40.0)

0.009

(30.5) -(40.1)

0.010

0.000

0.009

(9.9)

-0.010

Assortative mating

-(6.4)

-0.010

-(5.8)

-0.012

-(1.0)

0.002

-(10.6)

0.001


(6.8) (7.0) (8.0) (1.6)

Female employment

Male wage structure

0.019

-(12.8)

0.015

-(9.0)

0.004

(18.9)

0.010

(10.8)

-0.013

-0.010

-0.003

-0.001

(8.9) (6.2) -(14.1) -(1.5)

Male employment

-0.002

(1.5)

0.002

-0.004

-0.008

-(1.1) -(20.6) -(9.3)

-0.002

-0.001

-0.001

-0.001

(1.2) (0.7) -(3.1) -(0.6)

Unexplained

(60.7)

-0.119

0.030

(71.5) (151.9)

0.090

(99.7)

-0.016 -0.002

(12.9) -(41.1)

0.002 0.000

-(1.9) -(6.9)

-0.002 0.000

(1.6) -(0.9)

0.007 0.002

-(5.9) (41.2)

-0.006 -0.002

(4.7) -(27.2)

0.000 -0.001

(0.1) -(19.4)

-0.001 0.000

(0.6) -(4.5)

-0.106 0.009

(87.9) (158.8)

Note: Calculated using the Canadian Census (20% sample). The effect of each explanatory factor indicates how much of the total change is attributed to that factor. Percent of the total change is in parentheses.

“Unexplained” is the residual not accounted for by all other factors.

34

Table 8: Regression Results

Male log weekly wages

1980 1995 2005

Age squared

Years since immigration

Female log weekly wages

1980

Education

High school

Some post-secondary

University +

0.13

0.19

0.40

Age 0.08

0.13

0.23

0.50

0.09

0.12

0.26

0.52

0.09

0.16

0.31

0.60

0.05

0.18

0.37

0.69

0.22

0.39

0.75

-0.0008

-0.0009

-0.0009

-0.0005

-0.0008 -0.0007

Immigrated <6 years

Immigrated 6-10 years



Immigrated >20 years

-0.26

-0.16

-0.07

-0.05

-0.01

Full-time 0.51

Province (Newfoundland and Labrador omitted )

Prince Edward island -0.16

Nova Scotia

New Brunswick

-0.06

-0.03

Quebec 0.04

Ontario 0.08

Manitoba 0.01

Saskatchewan 0.05

Alberta 0.20

British Columbia 0.20

Yukon 0.27

Northwest Territories and Nunavut 0.18

Constant 4.38

Not significantly different from zero at 1% MB

-0.49

-0.31

-0.21

-0.14

-0.04

0.77

-0.12

-0.08

-0.06

-0.03

0.11

-0.06

-0.05

0.06

0.13

0.14

0.24

3.73

MB

-0.51

-0.31

-0.27

-0.19

-0.04

0.89

-0.15

-0.07

-0.07

-0.03

0.15

-0.02

0.03

0.23

0.10

0.12

0.30

3.60

-0.21

-0.09

-0.02

-0.02

0.01

0.64

-0.08

-0.08

-0.06

0.11

0.04

0.01

0.07

0.14

0.17

0.28

0.22

4.44

-0.37

-0.21

-0.15

-0.09

-0.01

0.02

-0.04

-0.03

0.26

0.44

PEI

-0.43

-0.25

-0.19

-0.13

0.00

0.05

0.02

0.03

0.23

0.57

Imm>20

NB

Note: Estimates based on the Canadian Census (20% sample). See text for sample description. The regression results used in the decompositions may use revised weights.

The resulting coefficients are not substantially different.

35

Table 9: Decomposition Results 1980-2005: Inequality Statistics

90-10 50-10 90-50 99-50 Standard deviation

A. Initial Estimates

1980 1.790 1.157

2005 2.058 1.318

B. Primary order decomposition

Male employment 2.049 1.312

Male wage structure 1.985 1.280

Female employment 2.023 1.297


Assortative mating 1.941 1.244

Family composition 1.832 1.167

Family characteristics 2.025 1.321

C. Reverse order decomposition

0.633

0.740

0.736

0.705

0.726

0.712

0.697

0.665

0.704

1.145

1.407

1.405

1.359

1.409

1.394

1.372

1.349

1.326

0.852

0.950

0.945

0.925

0.940

0.919

0.913

0.871

0.938

0.328 1.790

0.384 2.058

0.383 2.049

0.372 1.985

0.382 2.023

0.376 1.962

0.371 1.941

0.359 1.832

0.373 2.025

Family characteristics 2.233 1.448

Family composition 2.190 1.415

Assortative mating 2.177 1.419


Female employment 2.164 1.400

Male wage structure 2.107 1.370

Male employment 2.102 1.367

0.785

0.775

0.759

0.737

0.764

0.737

1.443

1.459

1.439

1.409

1.431

1.390

1.008

0.995

0.990

0.966

0.986

0.966

0.401 2.233

0.399 2.190

0.395 2.177

0.387 2.103

0.395 2.164

0.386 2.107

0.736

1.388

0.964

0.386 2.102



36

Table 10: Decomposition Results 1980-2005, Heads Age 25-54: Inequality Statistics deviation

1980 1.598

2005 1.895

B. Primary order decomposition

1.014

1.196

0.614

0.700

1.111

1.357

0.786 0.311

0.891 0.364

Male employment 1.883

Male wage structure 1.830

Female employment 1.870

Female wage structure 1.830

Assortative mating 1.793

Family composition 1.662

Family characteristics 1.801

C. Reverse order decomposition

1.186

1.161

1.179

1.152

1.136

1.039

1.156

0.697

0.668

0.691

0.679

0.657

0.623

0.645

1.352

1.310

1.365

1.348

1.319

1.297

1.260

0.887 0.363

0.868 0.353

0.885 0.363

0.870 0.359

0.860 0.352

0.808 0.337

0.861 0.346

Family characteristics 1.967

1.256

0.711

1.356

0.919 0.368

Family composition

Assortative mating

1.951

1.920

1.236

1.223

0.715

0.697

1.393

1.367

0.915 0.372

0.907 0.366


Female employment

1.877

1.936

1.199

1.238

0.679

0.698

1.340

1.353

0.892 0.360

0.911 0.367

Male wage structure 1.892

1.214

0.678

1.322

0.895 0.360

Male employment 1.890

1.213

0.677

1.321

0.894 0.359

Note: Calculated using the Canadian Census (20% sample). The main sample is restricted to heads age 25-

54. The inequality statistics in panels B and C represent the counterfactual distribution of log equivalent family earnings that would have prevailed in 2005 had each factor remained as in 1980. See text for details.

37

Table 11: Summary of the effects of each factor on family earnings inequality

Increase in men’s employment rates

Increase in returns to higher education for men

Overall effect on inequality measures

Reduces inequality

Increases inequality

Increase in women’s employment rates Reduces inequality

Increase in returns to higher education for women Increases inequality

Increase in assortative mating

Increase in lone-parent families

Increase in education levels, aging population



Reduces inequality

38

Appendix –

Derivation of the counterfactual densities in each stage of the decomposition

In this section we provide a more formal and detailed exposition of the methods used in each stage of the decomposition. The methods and this description closely Fortin and

Schirle (2006) which, in turn, closely follows the description in Dinardo et at. (1996).

We are interested in the distribution of log equivalent family earnings ( y

) at two points in time ( t

=0,1). Treat each family observation as a vector made up of the family’s log equivalent family earnings ( y ), the male head’s employment status ( E

M

), the female head’s employment status (

E

F

), the degree of assortative mating in the family (

A

), family composition (

C

), the vector of family characteristics (

X

) that may be partitioned as the male head’s characteristics ( X

M

), and the female head’s characteristics ( X

F

), and a date t .

Each family observation belongs to the joint distribution

F(y, E

M

, E

F

, A, C, X, t; β

Mt

, β

Ft

) characterized by the population parameters describing the structure of men’s earnings

( β

Mt

) and women’s earnings ( β

Ft

). The joint distribution of log equivalent family earnings and attributes at one point in time is the conditional distribution

F(y, E

M

, E

F

, A, C, X | t,

β

Mt

, β

Ft

)

.

The density of log equivalent family earnings at one point in time f t

(y) can be written as the integral of the density of log equivalent family earnings conditional on the set of family attributes, given the structure of men’s and women’s earnings at that point in time.

Consider the density at time t =1, which we can write as f

1

( y )

= dF

∫∫∫∫ dF

(

(

E

A

M

| f

C

|

(

E

, y

F

|

X

,

E

, t

M

A

,

A

,

C

|

C

,

E

,

X

F

, A , C , X ; t

β

M

X

=

, t

EM dF

|

1

) (

EF

C

, A

|

, C , X

X

, t

=

=

C

|

1 ,

X t

β dF

F

1

) (

=

1

)

=

E

F

1 dF

)

|

(

X

A

,

|

C t

X

,

M

X

,

X

,

F t

EF |

=

A , C

1

) , X

=

1

)

(A1)

In our first set of decompositions, this would represent the 1995 density of log equivalent family earnings. We then estimate a set of counterfactual densities that involve different

“datings” for the explanatory variables E

M

, E

F

, A, C, X and the structure of men’s and women’s earnings (

β

Mt

, β

Ft

).

In the first stage of the decomposition, we want to create the counterfactual density of log equivalent family earnings f

C 1

( y

)

= dF

∫∫∫∫ dF

(

(

E

A

M

| f

C

|

(

E

, y

F

|

X

,

E

, t

M

A

,

A

,

C

| C ,

E

,

X

F

,

A

,

C

,

X

; t

β

M

X

=

, t

EM dF

|

1

) (

EF

C

,

A

,

C

|

X

,

X

,

= t

C

=

|

1 ,

0

X

) t

β

F dF

=

1

)

(

=

E

1

F dF

)

|

(

X

A

,

|

C

, t

X

M

X

, X

,

F t

EF

|

=

A

,

C

1

) ,

X

=

1

)

(A2) which represents the density of log equivalent earnings that would have prevailed in time t =1 had the employment of men remained as it was in time t =0, all other family attributes

39

are at their t =1 levels, and workers are paid according to the t =1 wage structure. We can create this counterfactual density by adjusting the actual density described in (1) as follows: f

C

1

( y

)

= ∫∫∫∫

ψ dF

EM

(

E

| EF

F dF

(

A

|

, f

|

A

C

(

, C

A

,

,

, y

X

|

E dF

M

(

,

E

E

M

C

X

,

, t

X

A

|

C

,

F

,

A

,

C

,

X

, t

X

EF

|

|

=

A

E

, C

F

,

A

,

=

C

1

)

,

1

, X

) (

C

|

; t

β

M

X

X

,

, t t

=

EM

C

|

1 ,

X

| t

β

F

=

1

)

=

1

EF , A , C , X dF

)

=

(

X

1

)

| t

X

M

,

X

F

=

1

)

(A3) where

ψ

EM | EF , A , C , X

(

E

M

,

E

F

,

A

,

C

,

X

)

= dF dF

(

(

E

E

M

M

|

E

F

,

A

,

C

,

X

, t

EM | EF , A , C , X

|

E

F

,

A

,

C

,

X

, t

EM | EF , A , C , X

=

=

0

1

)

)

(A4) is a reweighting function that represents the changes that have occurred between time t =0 and time t

=1 in male employment. As employment status takes on values of 0 or 1, the reweighting function can be stated as

ψ

EM | EF , A , C , X

( E

M

, E

F

, A , C , X )

=

+

E

( 1 m

−

Pr

Pr

(

(

E

E m

E m

)

=

1 | m

=

Pr

Pr

(

(

1

E

E

| m

E m

E

F

F

=

=

,

,

0

0

A

,

A ,

|

|

E

E

C

C

F

F

,

,

,

,

X

X

A

,

A ,

,

, t t

C

EM

EM

C ,

,

|

|

X

EF

EF

X

,

,

,

,

A t

A t

,

C

, C

,

EM

,

EM

X

|

X

|

EF

EF

=

=

,

,

A

A

0

1

)

)

,

C

, C

,

,

X

X

=

=

0

1

)

) (A5)

We estimate the above probabilities using a probit model in which the latent variable determining a man’s employment is a function of his age, age squared, education, immigration status, province of residence, and an indicator for the presence of children in the family. The predicted reweighting function is then multiplied by the weights of each observation for which a male head is present.

14

If it were the case that the conditional probability of men to work increased between time t =0 and time t =1 then we would be placing less weight on those families for which

E

M

=1 and more weight on those families for which

E

M

=0. As such, the first counterfactual income distribution statistics will reflect men’s employment status in time t =0.

In the second stage of the decomposition, we modify the counterfactual density for changes in the wage structure of men. That is, we want to estimate

14

When a male head is not present, the reweighting function is set equal to 1.

40

f

C 2

( y

)

= ∫∫∫∫

ψ dF

EM

(

E

|

EF

F dF

(

A

|

, f

|

A

C

(

,

C

,

, y

A

,

X

|

C

X

,

E dF

M

(

,

E

E

M

, t

X

A | C

, t

, X

F

,

A

,

C

,

X

EF

|

|

=

A

E

, C

F

,

A

,

=

C

1

)

,

1

, X

) (

C

|

; t

β

X

X

M

,

, t t

=

EM

C |

0 ,

X

| t

EF

=

β

,

F

A

1

)

,

C

=

,

X

1 dF

)

=

(

X

1

)

| t

X

M

, X

F

=

1

)

(A6)

We first estimate male log weekly earnings in each time period. The econometric model used to describe log weekly earnings is simply y

Mt

= X t

β t

+ ε t

(A7)

Where X includes a quadratic in age, indicators for education, years since immigration, province of residence, and full-time vs. part-time work status. To adjust for the changes in wage structure, we apply the time t=0 parameter estimates to the time t=1 characteristics of men who are employed and add the residual of the t=1 male log weekly earnings regression. That is, y

MX1 β 0

= X

1

β

0

+ ε

1

(A8)

The observed log equivalent family earnings at time t=1 is y

1

= log (Y

M1

+Y

F1

+ υ

1

) – log (F

1

) (A9) where

Y

M1

is the male head’s earnings,

Y

F1 is the female head’s earnings,

υ

1 represents the earnings of any other family members, and

F

1 represents the number of family members.

To create a counterfactual value of log equivalent family earnings at time t=

1, we replace the observed male earnings in (9) with

Y

Mc2

= exp (y

MX1 β 0

+ l

M1

) (A10)

Where l

M1

is the log of weeks worked by the male head. The resulting log equivalent family incomes, with the revised weights produced in the first stage, are used to estimate the counterfactual densities and inequality statistics for the second stage of the decomposition.

The next two stages of the decomposition, adjusting women’s employment and women’s wage structure, follow the same procedures as above. At the fourth stage of the decomposition we have the counterfactual density

41

f

C 4

( y

)

=

ψ

∫∫∫∫

EM

|

EF

ψ

EF | dF

A , C

(

A

|

,

, f

A

,

C

X

C

( dF

,

, y

X

X

|

E dF

(

E

F

M

(

E

,

|

E

, t

A | C ,

M

X

F

A

,

|

,

A

,

E

F

,

C

,

A

,

X

=

C

1

,

X

,

) ( t

EF

C

C

;

|

|

, t

β

X

A , C

X

M

,

,

X

, t t

=

C |

0 ,

=

EM

1

) |

EF

X t

=

β

,

F

A

1

)

,

C

=

,

X

0 dF

)

=

(

X

1

)

| t

X

M

, X

F where the reweighting function introduced can be written as

ψ

EF | A , C , X

(

E

F

,

A

,

C

,

X

)

=

+

E

( 1

F

−

Pr

Pr

(

(

E

E

F

E

F

)

=

1 |

F

=

Pr

Pr

(

(

1

E

E

|

F

F

A ,

A

,

=

=

C

C

0

0

,

,

|

|

X

X

A

,

A

,

,

, t t

C

EF

EF

C

,

,

|

|

A

X

X

, C

A , C

,

,

,

, t

X

X t

EF

=

=

EF |

| A , C

A , C

,

0

1

)

)

,

X

X

=

1

)

=

=

0

1

)

)

(A11)

(A12)

In the fifth stage of the decomposition, we adjust the density of log equivalent family earnings for the changes in assortative mating. Here, we create the counterfactual f

C 5

( y

)

=

ψ

∫∫∫∫

EM | EF

ψ

ψ

EF |

A

|

C

,

X

A , C f

,

,

A , C

X dF

(

, y dF

(

X

|

E dF

(

E

F

M

(

E

,

|

E

M

A

,

A

|

C

,

X

,

F t

|

,

C

A

A

,

E

,

F

|

C

X

,

X

,

C

,

X

; t

β

M

=

0 ,

,

A

, t

=

C

,

X

,

EF | A , C dF

,

1

) (

X

C t

=

EM

1

)

| EF

|

X

, t

β

, t

F

A , C

C

|

=

X

, X

0

=

)

=

1

)

1

) dF

(

X

| t

X

M

,

X

F

=

1

)

(A13) where

ψ

A | C , X

(

A

,

C

,

X

)

= dF dF

(

(

A

A |

|

C

,

C ,

X

X

,

, t

A | C , X t

A | C , X

=

=

0

1

)

)

(A14)

Represents the changes that have occurred in assortative mating over time. Following

Fortin and Schirle (2006), assortative mating is described by the likelihood of a husband in earnings decile i to be married to a wife in earnings decile j

. Using this description, the reweighting function may be written as

ψ

A | C , X

(

A

,

C

,

X

)

=

+

S

10 ∑ m =

1

( 1

−

I m n

10 ∑

=

1

I n

S

) m

10 ∑

=

1

I m

Pr

Pr

(

( i i n

10 ∑

=

1

I

= m

, n

= m

,

Pr

Pr

(

( i i j j

=

=

=

= n n m , m

,

|

| j j

C

,

C

,

=

=

X n

X n

|

, t

A

|

C

,

X

, t

A | C , X

| C ,

C

,

=

=

0

1

)

)

X , t

A | C , X

X

, t

A | C , X

=

=

0

1

)

) (A15) where S =1 if there are children present in the family and S =0 otherwise. I m

is an indicator function that takes on a value of 1 if i=m and zero otherwise and similarly for

I n

. The probabilities in (A15) are estimated based on the cross-tabulation of husbands’ and wives’ earnings deciles, separately for couples with and without children (presented in

Table 3). The resulting reweighting function is multiplied by the weights on each

42

observation and these new weights are used to estimate the counterfactual density and inequality statistics.

In the sixth stage of the decomposition, we create the counterfactual density f

C 6

( y

)

=

ψ

ψ

ψ

A

∫∫∫∫

EM

EF

| C

|

, X f

A

| EF

, C

,

, X

A , C , X dF dF

(

E

F dF

( y

(

A

|

E

|

M

(

C

,

,

E

|

E

M

X

F

A ,

,

| t

,

C

A

A

,

E

,

F

| C ,

X

,

C

X

,

X

; t

β

M

=

0 , t

,

A , C , X , t t

=

EF

1

| A

)

ψ

, C

C

,

|

X

X

=

EM

1

) | EF dF

(

C

,

β

|

F

A , C

=

X

, X

,

0 t

)

=

C | X

1

)

=

1

) dF

(

X

| t

X

M

, X

F

=

1

)

(A16) where

ψ

C | X

(

C

,

X

)

= dF dF

(

(

C

C

|

|

X , t

C | X

X

, t

C

|

X

=

=

0

1

)

)

(A17) reflects changes in family composition (

C

) over time.

We describe families as belonging to one of four categories – married with kids, married without kids, lone parents, and single without kids. The reweighting function in (A17) can then be written as

ψ

C

|

X

(

C

,

X

)

= s

4 ∑

=

1

I s

Pr

Pr

(

(

C

C

= s | X , t

C | X

= s

|

X

, t

C | X

=

=

0

1

)

)

(A18)

Where

I s is an indicator taking on a value of 1 when family type

C=s

and zero otherwise.

The probabilities used to estimate (A18) are found using a multinomial logit model, such that

Pr(

C = s

|

X

, t

C | X

= t

)

= exp(

X st

β st

)

1

+ j

4 ∑

=

1 exp(

X jt

β jt

)

(A19)

For this model,

X st

represents a subset of family characteristics, including the major earner’s age, age squared, and indicators for education, years since immigration and province of residence.

In the last stage of the decomposition we account for changes in family characteristics.

We create the counterfactual density

43

f c 7

( y

)

=

ψ

ψ

ψ

∫∫∫∫

EM

EF

A | C

|

,

|

EF

A , C

X f

,

,

A

X

( y

,

C dF

, dF

(

X

|

E dF

(

E

F

M

(

E

,

|

E

M

A

,

A

|

C

,

X

,

F t

|

,

E

C

A |

A

,

,

F

C ,

X

C

X

,

,

X

; t

β

M

=

0 , t

,

A

,

C

,

X

, t t

EM

=

1

) |

EF

=

EF |

1

)

A , C

ψ

,

C |

X

X dF

(

C

,

β

|

F

A

,

C

=

X

,

X

, t

0

)

=

C | X

1

)

=

1

)

ψ

X dF

(

X

| t

X

M

, X

F

=

1

)

(A20) where

ψ

X

(

X

)

= dF dF

(

(

X

X

| t

X

| t

X

=

=

0

1

)

)

(A21) reflects changes in characteristics over time.

Using Bayes’ rules we can restate the reweighting function in (A21) as

ψ

X

(

X

)

=

Pr( t

X

Pr( t

X

=

1 )

=

0 )

Pr( t

X

Pr( t

X

=

0

=

1 |

|

X

X

)

)

. (A22)

The conditional probabilities in (A22) are estimated by pooling together the time t

=0 and t

=1 samples and then using a probit model with year as the binary dependent variable and the characteristics of the major earner (age, age squared, and indicators for education, years since immigration and province of residence) as the covariates

X

. The unconditional probabilities are the weighted shares of each of the t

=0,1 samples in the pooled sample.

As in Fortin and Schirle (2006) the primary order decomposition implicitly assumes that demand factors come first, followed by family formation factors, and supply factors come last. We also perform the reverse order decomposition that places the supply factors first.

That is, consider rewriting the density of log equivalent family earnings as f

1

R

( y

)

= dF

∫∫∫∫

( dF

X

(

A

|

| f

C

,

E

(

F y

|

A

,

,

X

E

M

,

C

,

E

F

,

, t

A

,

E

M

E

F

, t

X

A | EF , EM

,

E

M

; t

β

M

| C

=

, A

1

, EF , EM

) (

E

=

F

=

1 ,

1

) t

β dF

F (

=

C

| E

M

, t

1

EF

|

|

)

A

,

EM

E

=

F

1

,

)

E

M dF

,

( t

C | A , EF

E

M

, t

, EM

EM

=

=

1

)

1

)

(A23)

The procedure is conceptually the same, except that the reweighting functions are defined a bit differently. In the final stage of the reverse order decomposition, represented by the counterfactual density

44

f

C

R

7

( y

)

=

ψ

ψ

ψ

ψ

∫∫∫∫ f

( y

|

X

,

(

C

,

A

,

E

F

,

E

M

; t

β

M

=

1 , t

β

F

=

X

C |

| C

A | EF

EF

A

|

,

, A

EM

, EF

EF

, EM

, EM

, EM dF dF dF

(

E dF

(

C

(

A

F

|

|

X

E

|

E

F

|

A

,

M

,

,

C

E

E t

,

EF

F

M

A ,

,

,

E t

|

EM

E

F

, E

M

, t

X | C

M

A |

, t

C |

EF

=

,

1

)

EM

ψ

A ,

=

EF ,

1

)

EM

EM dF

, A

=

, EF

1

) , EM

(

E

M

, t

1

)

=

EM

1

)

=

1

)

(A24) where the reverse order’s first stage reweighting function can be derived as a function of other reweighting functions. That is,

ψ

X | C , A , EF , EM

=

ψ

EM | EF

ψ

, A , C , X

ψ

C | A , EF , EM

ψ

EF | A , C , X

ψ

A | EF , EM

ψ

A | C , X

ψ

EF | EM

ψ

C | X

ψ

EM

X

From (A25), the reweighting functions in the numerator were defined in the primary order decomposition methods. Included in the denominator, we define the second stage reweighting function (similarly defined as in (A18)) as

ψ

C | A , EF , EM

(

C

,

A

,

E

F

,

E

M

)

= s

4 ∑

=

1

I s

Pr

Pr

(

(

C

C

= s

|

=

A

,

E

F

,

E

M

, t

C | A , EF , EM s

|

A

,

E

F

,

E

M

, t

C | A , EF , EM

=

=

0

1

)

)

(A26)

The conditional probabilities for each of the four family types are estimated using a multinomial logit model, with the employment status of the female and male head as covariates.

15

The reverse order’s third stage reweighting function that accounts for changes in assortative mating is defined (in a similar manner as A15) as

ψ

A | C , X

(

A

,

E

F

,

E

M

)

=

10 ∑ m =

1

I m n

10 ∑

=

1

I n

Pr

Pr i

( i

(

=

= m

, m

, j j

= n

|

E

F

= n

|

E

F

,

,

E

M

E

M

,

, t

A | EF , EM t

A | EF , EM

=

=

0

1

)

)

(A27)

The probabilities in (A27) are estimated based on the cross-tabulation of husbands’ and wives’ earnings deciles. Unlike the primary order decomposition reweighting function, we do not do this separately for those with kids and without.

In the fourth and sixth stage, we adjust the density for wage structure of women and men.

This follows the same procedure as in the primary order decomposition.

The fifth stage of the reverse order decomposition applies the reweighting function

15

We were unable to find a satisfactory way of conditioning on assortative mating, particularly the impossibility of coding this for single individuals. For employment status, if no male head is present, the observation is coded as not employed and similarly for families with no female head present.

45

ψ

EF | EM

( E

F

, E

M

)

=

+

E

F

( 1

−

Pr

Pr

(

(

E

E

F

E

F

)

=

1 |

F

=

Pr

Pr

(

(

1

E

E

|

F

F

E

E

M

M

=

=

,

,

0

0 t t

EF | EM

|

|

EF | EM

E

M

E

M

,

, t

=

=

0

1

)

)

EF

|

EM t

EF | EM

=

=

0

1

)

) (A28) to capture changes in women’s employment. The conditional probabilities are estimated based on a simple probit model of married/cohabiting women with their husbands’ employment status as the only covariate. For single women, the reweighting function is set to one as all single women must be employed to be part of our sample.

The last reweighting function is defined as

ψ

EM

(

E

M

)

= E

M

Pr

Pr

(

(

E

E

M

M

=

1

=

1 |

| t

EM t

EM

=

=

0

1

)

)

+

( 1

− E

M

)

Pr

Pr

(

(

E

E

M

M

=

=

0

0

| t

EM

| t

EM

=

=

0

1

)

)

(A29)

The probabilities in (A29) are simply the employment rates of males in each time period t

=0,1.

46

The Growth of Family Earnings Inequality in Canada, 1980-2005

The Growth of Family Earnings Inequality in Canada, 1980-2005

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The Growth of Family Earnings Inequality in Canada, 1980-2005

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