the prince and the pauper:

The Prince and the Pauper:

Movement of Children Up and Down the Canadian Income Distribution

Peter Burton and Shelley PhippsDalhousie University

P. Burton and S. Phipps Dalhousie University

Acknowledgements

Lihui Zhang, for excellent research assistance

Atlantic Research Data Centre for access to the data


Introduction

Use Statistics Canada’s National Longitudinal Survey of Children and Youth (NLSCY) to study family income for a cohort of Canadian children between 1994 and 2004

Children 0 to 7 in 1994; 10 to 17 in 2004Longest panel of data yet available in CanadaLinks to sense of self, aspirations, well-being?


Five questions:

1. What happens to the level of family income as children grow up?

2. What happens to income inequality among children?

3. How much movement up and down the distribution takes place?

4. What are characteristics associated with being ‘stuck at the bottom’ or ‘secure at the top’ of the distribution?

5. What are the correlates of moving up or down the distribution?


DataNLSCY representative of Canadian child

populationInterviews every 2 years (6 cycles,

spanning 10 years)Use information provided by the ‘person

most knowledgeable’ about the childSelect 7,163 children with complete

income and family size dataLongitudinal weights; bootstrap for

complex survey design


Question 1. Trends in Income Levels?

Expect real growth, on average◦Parental life-cycle (finish education, gain

seniority with higher wages and more job security)

◦Mothers returning to paid work and/or increasing paid hours

But, odds of parental divorce also increase


Changes in family characteristics

Family sizeProbability of living in lone parent familyPaid work participation and hours of

participation‘High hours’ (greater than 80 per week for

two-parent families; greater than 40 for lone-parent families)


Changing Family Composition

1994 1996 1998 2000 2002 2004

Child Age Range0-7 2-9 4-11 6-13 8-15 10-17

Percent Lone Parent

14.3 15.5 14.9 16.8 19.0 20.4Mean Household Size

4.2 4.3 4.4 4.4 4.3 4.2


Paid Work in Two-Parent Families

1994 1996 1998 2000 2002 2004

Child Age Range0-7 2-9 4-11 6-13 8-15 10-17

Percent Two-Earner 55.7 71.4 76.2 79.8 79.6 83.8Mean Weekly Paid Hours (Mother + Father hours) 59.1 65.4 68.5 70.1 70.9 73.1


Paid Work Participation in Lone-Parent Families

1994 1996 1998 2000 2002 2004

Child Age Range 0-7 2-9 4-11 6-13 8-15 10-17

Percent with Paid Work

41.1 66.5 75.4 81.7 84.2 84.8Mean Paid Hours in Lone-parent families

14.1 23.3 26.3 30.7 32.1 32.8


Two parents more than 80 hours; lone parent more than 40 hours

1994 1996 1998 2000 2002 20040

5

10

15

20

25

30

35

40

18.3

22.4

27.4

31.9 32.935.5

% with ‘High

Hours’


Measure of Family Income‘Person most knowledgeable’ about the

child reports incomePre-tax annual income from all sources

including government transfersAdjust for differences in need for families

of different size using Luxembourg Income study ‘equivalence scale’ (square root of family size)

Actual income of $80,000 for family of 4 means ‘equivalent income’ of $40,000


Mean equivalent family income, in 2004 dollars

1994 1996 1998 2000 2002 20040

5000

10000

15000

20000

25000

30000

35000

40000

45000

29918 3070634373

37403 38082 38276


Is income growth the same at all points in the distribution?

Compute mean equivalent income in each year for each income decile

Decile cut points defined using the NLSCY (i.e., families with children)

1994 1996 1998 2000 2002 20040

20,000

40,000

60,000

80,000

100,000

120,000


Are children at the top ‘pulling ahead’ of those at the bottom?

Real growth in all decilesConsiderable inequality among children,

but ratio of mean income in top decile to mean income in bottom decile 9.42 in 1994; 9.39 in 2004


Question 2. Trends in Inequality?

Inequality among children would be expected to increase over time as some parents ‘make it’ in the labour market while others fall behind

On the other hand, some families may catch up as mothers increase paid hours


Compute standard measures of income inequality for each year for our cohort of children

Choose measures sensitive to different parts of the distribution (CV is sensitive to the top; Gini to the middle and Atkinson to the bottom)

Also compute all measures using six-year average income


Measures of Income Inequality

1994 1996 1998 2000 2002 2004

Long-run

Average Income

Coefficient of variation 0.679 0.788 0.753 0.801 0.716 0.701 0.622

Gini coefficient 0.334 0.345 0.328 0.339 0.325 0.321 0.293

Atkinson (eps =2) 0.335 0.340 0.317 0.314 0.326 0.328 0.247

Theil 0.188 0.214 0.196 0.214 0.189 0.186 0.150


Key findingsNo obvious trend in annual income inequality

for this cohort of children◦High-end sensitive CV shows highest inequality in

middle years◦Low-end sensitive Atkinson shows lowest inequality

in middle years

Inequality among children less than in population over-all; these inequality measures slightly higher because for pre-tax income


Annual versus ‘permanent’ income inequality

Inequality of six-period income lower than inequality in any particular year

True for all measures of inequality and regardless of comparison year


Theil Decomposition

Theil index allows de-composition of total inequality into ‘within group’ inequality plus ‘between group’ inequality

In our application, ‘within group’ is for the same child across six cycles; ‘between group’ is permanent income across different children

De-composition suggests inequality of ‘permanent income’ about 75 percent of total


Question 3. Are the Same Children Always at the Bottom (or Top) of the Income Distribution?What percent of children who start in

bottom quintile in 1994 are again in bottom quintile in 2004?

What percent of children who start in top quintile in 1994 are again in top quintile in 2004?

Considerable ‘stickiness’ of position evident


1994 to 2004 Transition Matrix

Bottom Quintile 2004

2nd Quintile 2004

3rd Quintile 2004

4th Quintile 2004

Top Quintile 2004


0.51 0.25 0.14 0.06 0.04

2nd Quintile 1994

0.26 0.28 0.25 0.14 0.07

3rd Quintile 1994

0.12 0.25 0.30 0.23 0.10

4th Quintile 1994

0.07 0.14 0.22 0.34 0.24

Top Quintile 1994

0.03 0.08 0.08 0.24 0.58


Transition Matrix for Children of Immigrants


2nd Quintile 2004

3rd Quintile 2004

4th Quintile 2004

Top Quintile 2004


0.67 0.15 0.07 0.07 0.05

2nd Quintile 1994

0.18 0.31 0.34 0.07 0.10

3rd Quintile 1994

0.12 0.39 0.22 0.16 0.10

4th Quintile 1994

0.14 0.08 0.23 0.35 0.19

Top Quintile 1994

0.02 0.06 0.11 0.23 0.58


‘Lenses’

What happens during intervening years?

How many children ever exposed to a position of low income?

How many children always (in all six cycles) in a position of low income?


0 10 20 30 40 50 60 70 80 90100

0

10

20

30

40

50

60

70

80

90

100

26.1

42.2

54.3

65.1

73.9

81.987.8

92.997.0

100.0

0.01.3

4.79.9

16.6

24.2

34.8

46.5

60.9

78.2

100.0

Figure 2. Relative Income "Lens"

Always Below

Ever Below

Equivalent Income Percentile

Percentof Children

Link


Key points from lenses

More children ‘ever’ exposed to low income than cross-sectional data suggest (42 percent were ‘ever’ in bottom quintile)

Only about 5 percent ‘always’ in the bottom quintile, but this group of great policy relevance

Links to social exclusion?Note: children of immigrants especially

likely to be ‘stuck’ at bottom


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

0.0

40.0

63.6

80.9

92.5

100.0

0.03.9

15.5

33.5

60.3

100.0

0.0

54.5

73.5

86.9

95.1100.0

0.0

9.1

22.7

42.3

64.3

100.0

Relative Income Lenses, Immigrants and NonIm-migrants

Immigrant, Always Below

Immigrant, Ever Below

NonImmigrant, Always Below

NonImmigrant, Ever Below


Percentof Children


Question 4a. Characteristics of Children ‘Exposed to’ or ‘Stuck’ at BottomEstimate probit models of the correlates of

‘ever’ and ‘always’ being in the bottom quintile

Dependent variable uses full six-cycle historyExplanatory variables ‘starting point risks’

(1994 values):◦Region◦Age, education, ethnicity, immigrant, marital and

employment/student status of parent◦Age of child and number of siblings


‘Ever’ Bottom Quintile

‘Always’ Bottom Quintile

Child age-0.017(0.013)

-0.047**

(0.020)

Number of siblings0.147***

(0.034)0.164**

(0.067)

Lone mother1.300***

(0.100)1.051***

(0.133)

Pmk Age-0.293***

(0.092)-0.002(0.012)

Pmk non-white0.168

(0.182)0.574*

(0.294)

Pmk Immigrant0.460***

(0.123)0.315

(0.264)

Pmk no paid hours0.651***

(0.067)0.922***

(0.157)




Region

Atlantic 0.377***

(0.081)0.766***

(0.156)

Quebec 0.201**

(0.089)0.374**

(0.180) Manitoba/Saskatchewan

0.284***

(0.092)0.084

(0.229)

Alberta 0.054(0.115)

-0.038(0.291)

BC 0.244**

(0.101)0.165

(0.232)




Pmk Education Less than High School

0.681***

(0.111)0.253

(0.198) Some Post-Secondary

-0.191**

(0.089)-0.204(0.193)

University -0.293***

(0.092)-0.411*

(0.236)

Pmk student -0.063(0.120)

-0.630***

(0.243)


Key results from probit regressions for ‘ever’ in bottom quintile:In order of size of association, a child is at

greatest risk of ‘ever’ being at the bottom of the distribution for his/her cohort if he/she:◦Lives in a lone-mother family ◦Parent has less than high-school education◦Parent has no paid hours◦Parent is an immigrant◦Family lives in Atlantic Canada


Key results from probit regressions for ‘always’ in bottom quintile:In order of size of association, a child is at

greatest risk of ‘always’ being at the bottom of the distribution for his/her cohort if he/she:◦Lives in a lone-parent family◦Has a parent with no paid work◦Lives in the Atlantic region◦Has a parent who is non-white


Simulated Probability of Always Being in the Bottom Quintile

Base Lone Parent Pmk Unpaid Atlantic Non-white0

0.5

1

1.5

2

2.5

3

3.5

4


Question 4b: Characteristics of Children ‘Exposed to’ or ‘Secure’ at the Top

Repeat probit analyses with 2 new dependent variables; same explanatory variables

Results mostly symmetric


Question 5. Which characteristics are associated with movements up or down?Estimated conditional logit models of

movements into or out of the bottom quintile (14,790 movements in/out of bottom; 12,864 movements in/out top)

Procedure excludes children who never move in or out

Explanatory variables are now ‘changes’ (so ethnicity and immigrant status dropped)


Key results from conditional logit modelsIn order of size of association, the most important changes associated with moving into or out of the bottom quintile are:◦Divorce/re-marriage of parents◦Regional migration◦Changes in employment status of parent◦Parent finishing or returning to school◦Change in number of siblings

See odds ratios


Bottom Quintile Top QuintileRegion Atlantic 4.108* 0.200 Quebec 1.205 0.049 Man/Sask 10.684*** 0.634 Alberta 2.530 1.815 BC 5.319* 1.102Pmk Education Less than High School 1.048 1.075 Some Post-Secondary 0.893 1.339 University 0.686** 1.881***

Lone parent 17.017*** 0.052***

Pmk student 1.561** 0.710**

Number of siblings 1.304*** 0.542***

Pmk no paid hours 2.539*** 0.335***


Fixed Effects Estimates of Change in Percentile RankNot just ‘in or out’ of top/bottom, but ‘how

far’ up or down the relative income distribution does child move with particular change in co-variate?

Estimate fixed effects models for change in percentile position

Coefficient Standard Error Atlantic -11.810*** 2.183 Quebec -4.044 3.641 Manitoba/Saskatchewan -10.005*** 2.515 Alberta -3.972 2.813 BC -2.642 2.837 Less than High School -1.094 (0.950) Some Post-Secondary 0.788 (0.602) University 2.724*** (0.630)Lone parent -22.360*** (0.739)Pmk student -3.571*** (0.626)Number of siblings -2.827*** (0.283)Pmk no paid hours -7.062*** (0.489)


Key points:

Largest movements up/down the distribution associated with changes in marital status; regional migration


Conclusions

Use longitudinal data tracking a cohort of Canadian children from 1994 to 2004 (from ages 0 to 7 until ages 10 to 17)

Real growth at all points in income distribution; no trends in inequality as this cohort of children grows up

Lower measured inequality of ‘permanent income’

75 percent of inequality is attributable to ‘permanent income’


Considerable beginning to end of period ‘stickiness’ of relative income position

Only 5 percent ‘always’ in bottom quintile, but this is a group of particular policy concern

But, more exposure to low income than cross-sectional data suggest

Parental marital and employment status, region of residence and ethnicity key correlates of relative income position

Largest movements up/down the distribution associated with change in parental marital status and regional migration


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

0.0 1.34.7

9.9

16.6

24.2

34.8

46.5

60.9

78.2

100.0

26.1

42.2

54.3

65.1

73.9

81.987.8

92.997.0

Relative Income Lenses: Actual

Ever Below

Always Below


Percent of Children


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

0.1 0.4 1.64.7

11.8

26.2

53.1

0.0

46.9

73.8

88.2

95.398.4 99.6 99.9

Relative Income Lenses: Actual, Random

Ever Below

Always Below

Random Ever Below

Random Always Below


Percent of Children


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

40

0

10

20

30

40

50

60

70

80

90

100

60

0.1 0.4 1.64.7

11.8

26.2

53.1

0.0

46.9

73.8

88.2

95.398.4 99.6 99.9

Relative Income Lenses: Actual, Random, Max and Min

Ever Below

Always Below

Random Ever Below

Random Always Below

Max Ever Below

Max Always Below = Min Ever Below

Min always Below


Percent of Children

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the prince and the pauper:

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