Divided Landscapes of Economic Opportunity: The Canadian Geography of Intergenerational Income Mobility DATA APPENDIX REPLICATING THE RESULTS USING ONLY THE AGE COHORTS 16 TO 19 YEARS OF AGE IN 1986 Miles Corak University of Ottawa Miles Corak, all rights reserved. June 2017 This is an appendix to the paper Divided Landscapes of Economic Opportunity: The Canadian Geography of Intergenerational Income Mobility, offering information replicating all the tables and figures in the original paper using a subset of the original sample, those 16 to 19 years of age in 1986, the year in which the Census geography is defined. This is intended to examine the robustness of the results to a data quality issue highlighted in the data appendix attached to the paper. The possibility of geographic mobility may imply that some children may not be ascribed the geography of the region where they lived as teenagers if the algorithm creating the data links them to their parents when they are older. The original paper and all supplementary information is available at MilesCorak.com/Equalityof-Opportunity. The table and figure numbers in this appendix correspond to those in the original paper, including eight additional tables offering direct comparisons of each of the following eight intergenerational mobility statistics. Income mobility Regression to the mean in parent-child incomes 1. Absolute α j least squares estimate of intercept 2. Relative β j least squares estimate of slope 3. Average income Ȳ j average permanent income of parents Rank Mobility Percentile rank-rank regression 4. Absolute a j least squares estimate of intercept 5. Relative b j least squares estimate of slope Directional mobility Cells of qunitile transition matrix 6. Rags to riches P 1,5 conditional probability of top income 7. Intergenerational low income P 1,1 conditional probability of bottom income 8. Intergenerational privilege P 5,5 conditional probability of top income 1
Table 2: Number of children born between 1963 and 1970: weighted and unweighted Intergenerational Income Data sample sizes compared to estimates from the 1986 Census Administrative Data 1986 Census Ratio weighted Province / Territory Weighted Unweighted Total to Census Newfoundland and Labrador 41,600 30,900 Prince Edward Island 7,800 5,850 Nova Scotia 50,050 38,250 New Brunswick 41,950 32,450 Quebec 334,900 244,350 Ontario 462,400 378,650 Manitoba 54,800 43,250 Saskatchewan 55,000 38,500 Alberta 122,750 88,600 British Columbia 136,700 101,600 Yukon 1,400 850 Northwest Territories, Nunavut 3,300 1,800 Canada 1,312,600 1,005,000 Note: All numbers are rounded to the nearest 50. Table 3: Intergenerational income mobility: absolute income mobility, relative income mobility, and average parental community income Absolute Relative Average Province / Territory mobility mobility income (α j ) (β j ) (Ȳj) Newfoundland and Labrador 8.62 0.186 28,635 Prince Edward Island 8.75 0.173 31,439 Nova Scotia 8.45 0.193 34,383 New Brunswick 8.45 0.196 32,482 Quebec 8.67 0.183 38,309 Ontario 8.67 0.188 43,178 Manitoba 6.85 0.350 36,550 Saskatchewan 7.80 0.273 39,116 Alberta 8.64 0.197 47,137 British Columbia 8.66 0.180 45,029 Yukon 9.08 0.144 40,871 Northwest Territories, Nunavut 8.48 0.190 29,845 Canada 8.48 0.203 40,808 Note: First two columns are least squares estimates. 2
Table 4: Intergenerational rank mobility: absolute rank mobility, relative rank mobility, and the estimated percentile rank for a child raised by the average parents in the bottom half of the income distribution At 38 to 45 years of age At 31 and 32 years of age Province / Territory Absolute Relative Expected Absolute Relative Expected (a j ) (b j ) Rank (a j ) (b j ) Rank Newfoundland and Labrador 35.7 0.278 42.7 33.2 0.277 40.1 Prince Edward Island 35.4 0.257 41.8 35.3 0.239 41.3 Nova Scotia 32.4 0.253 38.7 32.0 0.249 38.2 New Brunswick 31.4 0.288 38.6 31.1 0.286 38.2 Quebec 36.5 0.252 42.8 36.9 0.240 42.9 Ontario 40.9 0.227 46.6 43.4 0.215 48.8 Manitoba 30.4 0.335 38.8 29.9 0.320 37.9 Saskatchewan 40.1 0.253 46.4 37.7 0.236 43.6 Alberta 44.2 0.209 49.4 41.1 0.203 46.2 British Columbia 39.5 0.184 44.1 39.9 0.185 44.5 Yukon 41.5 0.174 45.9 38.5 0.176 42.9 Northwest Territories, Nunavut 32.1 0.312 39.9 31.4 0.283 38.5 Canada 38.1 0.246 44.2 38.4 0.240 44.4 Source: Least squares estimates using Statistics Canada, Intergenerational Income Data as described in text. 3
(a) Children of bottom one and of bottom fifth percentile parents 5 Percentage of children (%) 4 3 2 1 Bottom percentile parents Fifth percentile parents 0 0 10 20 30 40 50 60 70 80 90 100 (b) Children of top percentile parents 10 Percentage of children (%) 8 6 4 2 0 0 10 20 30 40 50 60 70 80 90 100 Child's income rank in adulthood (percentile) Figure 1: Intergenerational Directional Mobility: Percentile ranks of children raised by bottom ranking and top ranking parents 4
Table 5: Intergenerational directional mobility based on selected transition probabilities: rags to riches, intergenerational cycle of poverty, and the intergenerational cycle of privilege Rags to riches Cycle of poverty Cycle of privilege Province / Territory (P 1,5 ) (P 1,1 ) (P 5,5 ) (P 3,3 ) Newfoundland and Labrador 0.089 0.318 0.297 0.199 Prince Edward Island 0.097 0.283 0.270 0.229 Nova Scotia 0.071 0.353 0.256 0.223 New Brunswick 0.065 0.356 0.259 0.216 Quebec 0.090 0.297 0.295 0.237 Ontario 0.145 0.284 0.352 0.209 Manitoba 0.074 0.429 0.293 0.239 Saskatchewan 0.143 0.289 0.341 0.217 Alberta 0.186 0.255 0.376 0.199 British Columbia 0.126 0.305 0.256 0.223 Yukon 0.134 0.302 0.282 0.224 Northwest Territories, Nunavut 0.095 0.405 0.373 0.169 Canada Source: Selected entries from the quintile transition matrix calculated using Statistics Canada, Intergenerational Income Data. 0.35 0.35 0.30 0.30 0.25 0.25 Rags to Riches 0.20 0.15 Rags to Riches 0.20 0.15 0.10 0.10 0.05 0.05 0.00 0.00 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 (a) Cycle of Privilege (b) Cycle of Poverty Figure 2: Rags to riches mobility across Census Divisons and its correlation with intergenerational cycles of privilege and poverty, as measured with quintile transition probabilities 5
70,000 Average income is higher for children 60,000 Average child adult income 50,000 40,000 30,000 20,000 10,000 Average income is higher for parents 10,000 20,000 30,000 40,000 50,000 60,000 70,000 Average parent income in each Census Division (2014 constant dollars) Figure 3: Average incomes of parents and children in each of 266 Census Divisions 6
60 Expected percentile rank of children 50 40 30 20 10 Canada Parents in the top half Parents in the bottom half Parents in the bottom fifth 0 50 100 150 200 250 266 Census Divisions ordered from lowest to highest rank mobility for bottom half children Figure 4: Expected rank outcomes for children from top half, bottom half, and bottom fifth parents by Census Division 7
Probability of moving to the top quintile for men and women having bottom quintile parents 0.20 or more 0.15 to 0.20 0.10 to 0.15 0.05 to 0.10 0.025 to 0.05 less than 0.025 Figure 5: Rags to riches mobility: Census Divisions classified according to the probability that children of bottom quintile parents have adult incomes in the top quintile 8
Table 6: Income and rank mobility statistics for the Census Divisons with a probability of moving from the bottom to the top quintile of less than five percent Number Income mobility Rank Mobility Census Division of Absolute Relative Average Absolute Relative children (α j ) (β j ) Parent Income (a j ) (b j ) Central Coast Regional District BC 150 6.5 0.308 27,055 8.1 0.519 Stikine Region BC 50 5.4 0.433 36,594 7.7 0.519 Division No. 19 MB 600 6.0 0.349 10,567 7.2 0.496 Kitikmeot Region NT 250 10.0 0.005 20,582 25.7 0.087 Brome QC 800 8.0 0.236 33,486 27.1 0.359 Charlevoix-Ouest QC 800 9.5 0.100 27,316 40.6 0.154 Charlevoix-Est QC 1,150 8.8 0.165 30,921 34.8 0.233 Division No. 22 MB 1,550 2.4 0.752 27,512 8.4 0.677 Frontenac QC 1,450 9.0 0.140 27,686 33.7 0.240 L Islet QC 1,250 9.3 0.117 23,482 34.4 0.250 Iles-de-la-Madeleine QC 1,300 8.8 0.157 27,820 31.3 0.253 Huntingdon QC 700 8.0 0.231 26,975 27.5 0.311 Sunbury County NB 1,050 7.6 0.279 33,760 27.1 0.363 Yamaska QC 950 8.7 0.171 29,184 32.1 0.286 Hants County NS 2,100 8.7 0.165 31,151 31.6 0.206 Gaspe-Ouest QC 750 8.6 0.178 24,159 32.0 0.265 Division No.8 MB 650 5.5 0.480 23,169 28.2 0.348 Division No. 21 MB 1,250 5.3 0.485 36,737 21.8 0.454 Shelburne County NS 1,000 8.9 0.139 29,612 30.8 0.208 Gaspe-Est QC 2,000 8.4 0.199 29,814 29.8 0.301 Kings County NS 3,000 8.5 0.188 31,898 29.7 0.288 Division No.7 MB 3,600 5.6 0.453 32,633 16.9 0.506 Carleton County NB 1,500 8.9 0.141 25,954 29.5 0.263 Queens County NB 700 9.1 0.128 24,816 32.5 0.189 Division No.3 MB 2,350 8.4 0.203 28,889 31.7 0.280 Division No. 23 MB 350 4.1 0.572 36,789 14.5 0.442 Maskinonge QC 1,400 8.4 0.202 27,427 32.2 0.271 Skeena-Queen Charlotte Regional District BC 1,100 6.5 0.350 43,210 18.1 0.388 Note: Census Divisions are ranked from lowest to highest transition probability conditional on being less than 0.05. Numbers are rounded to nearest 50. 9
Table 7: Income and rank mobility statistics for the Census Divisons with a probability of moving from the bottom to the top quintile of at least twenty percent Number Income mobility Rank Mobility Census Division of Absolute Relative Average Absolute Relative children (α j ) (β j ) Parent Income (a j ) (b j ) Dufferin County ON 1,900 9.3 0.132 38,977 46.0 0.158 Division No. 13 AB 3,150 9.4 0.127 31,878 49.1 0.131 Division No.7 AB 2,050 9.2 0.151 40,006 46.8 0.192 Division No. 16 AB 3,400 7.7 0.288 50,554 41.2 0.286 Division No.2 SK 1,450 8.6 0.210 43,268 49.2 0.152 Division No. 18 AB 850 7.2 0.335 37,542 36.8 0.344 Division No.8 AB 6,000 9.2 0.153 41,778 49.4 0.146 Division No. 19 AB 3,800 9.0 0.172 39,917 50.3 0.176 York Regional Municipality ON 19,550 8.9 0.172 52,644 45.5 0.185 Division No. 14 MB 700 9.1 0.142 36,501 43.8 0.138 Halton Regional Municipality ON 15,600 9.3 0.136 55,733 47.7 0.163 Division No. 14 AB 750 9.9 0.079 42,568 51.4 0.111 Division No.10 AB 4,300 9.5 0.118 36,764 49.7 0.144 Division No. 13 SK 1,550 9.0 0.173 40,226 52.4 0.118 Note: Census Divisions are ranked from lowest to highest transition probability conditional on being at least 0.20. Numbers are rounded to nearest 50. 10
Probability of staying in the bottom quintile for men and women having bottom quintile parents 0.40 or higher 0.35 to 0.40 0.30 to 0.35 0.25 to 0.30 0.20 to 0.25 less than 0.20 Figure 6: Intergenerational cycles of low income: Census Divisions classified according to the probability that children of bottom quintile parents have adult incomes in the bottom quintile 11
Table 8: Income and rank mobility statistics for the Census Divisons with a 40 percent or higher chance that children of bottom quintile parents will be bottom quintile adults Number Income mobility Rank Mobility Census Division of Absolute Relative Average Absolute Relative children (α j ) (β j ) Parent Income (a j ) (b j ) Squamish-Lillooet Regional District BC 900 6.8 0.343 40,112 27.9 0.296 Kootenay Boundary Regional District BC 1,600 8.1 0.237 47,042 37.2 0.235 Brome QC 800 8.0 0.236 33,486 27.1 0.359 Alberni-Clayoquot Regional District BC 1,700 7.9 0.237 45,402 31.6 0.228 Annapolis County NS 1,200 8.5 0.179 29,696 29.1 0.223 Territoire-du-Nouveau-Quebec QC 1,350 6.7 0.363 35,045 31.7 0.278 Stikine Region BC 50 5.4 0.433 36,594 7.7 0.519 Sunbury County NB 1,050 7.6 0.279 33,760 27.1 0.363 Haliburton County ON 650 8.5 0.188 27,629 32.1 0.289 Division No.8 MB 650 5.5 0.480 23,169 28.2 0.348 Division No.3 AB 1,800 6.8 0.361 36,163 32.9 0.327 Baffin Region NT 650 9.3 0.087 21,323 29.8 0.240 Division No.1 MB 850 5.7 0.463 30,904 28.3 0.375 Keewatin Region NT 350 9.2 0.111 21,146 36.1 0.166 Division No. 18 MB 1,350 5.8 0.442 20,515 24.2 0.404 Kitikmeot Region NT 250 10.0 0.005 20,582 25.7 0.087 Kitimat-Stikine Regional District BC 2,350 6.3 0.385 42,757 23.7 0.369 Manitoulin District ON 700 5.1 0.505 21,006 23.1 0.395 Mount Waddington Regional District BC 650 7.2 0.309 46,701 33.9 0.253 Skeena-Queen Charlotte Regional District BC 1,100 6.5 0.350 43,210 18.1 0.388 Division No. 21 MB 1,250 5.3 0.485 36,737 21.8 0.454 Division No.7 MB 3,600 5.6 0.453 32,633 16.9 0.506 Division No. 18 SK 1,350 6.3 0.352 20,618 16.5 0.426 Central Coast Regional District BC 150 6.5 0.308 27,055 8.1 0.519 Kenora District ON 3,050 3.1 0.699 35,482 16.7 0.548 Division No. 23 MB 350 4.1 0.572 36,789 14.5 0.442 Division No. 22 MB 1,550 2.4 0.752 27,512 8.4 0.677 Division No. 19 MB 600 6.0 0.349 10,567 7.2 0.496 Note: Census Divisions are ranked from lowest to highest transition probability conditional on being at least 0.40. Numbers are rounded to nearest 50. 12
Table 9: Income and rank mobility statistics for the Census Divisons with a less than 20 percent chance that children of bottom quintile parents will be bottom quintile adults Income mobility Rank Mobility Census Division Number of Absolute Relative Average Absolute Relative children (α j ) (β j ) Parent Income (a j ) (b j ) Montmorency No. 2 QC 400 9.5 0.113 37,813 45.6 0.133 Division No. 13 SK 1,550 9.0 0.173 40,226 52.4 0.118 Division No. 14 AB 750 9.9 0.079 42,568 51.4 0.111 Division No. 19 AB 3,800 9.0 0.172 39,917 50.3 0.176 Division No.3 SK 1,050 9.8 0.083 39,847 46.9 0.150 Division No.2 SK 1,450 8.6 0.210 43,268 49.2 0.152 Division No.10 AB 4,300 9.5 0.118 36,764 49.7 0.144 Division No.8 AB 6,000 9.2 0.153 41,778 49.4 0.146 Note: Census Divisions are ranked from lowest to highest transition probability conditional on being less than 0.20. 0 5 10 15 Figure 7: Preferred Dendrogram illustrating the grouping of 266 Census Divisions into two clusters, based on Complete linkage with Euclidean-Based Distance 13
Figure 8: The landscape of us and them: Census Divisions clustered into two groups based upon similarities between all eight intergenerational mobility measures 14
Table 10: Does the Manitoba border matter? Estimates from Linear probability models of whether Census Divisions are within the province of Manitoba (1) (2) (Intercept) 0.086 0.086 (0.016) (0.015) Absolute income mobility 0.306 0.228 (0.437) (0.431) Relative income mobility 0.134 0.049 (0.407) (0.401) Absolute rank mobility 0.106 0.117 (0.107) (0.105) Relative rank mobility 0.006 0.019 (0.060) (0.060) Bottom to bottom mobility 0.008 0.027 (0.041) (0.040) Bottom to top mobiility 0.034 0.026 (0.036) (0.036) Top to top mobility 0.032 0.022 (0.023) (0.023) Parent mean income 0.057 (0.019) R 2 0.207 0.235 Adj. R 2 0.186 0.211 Num. obs. 266 266 RMSE 0.254 0.250 Note: Boldface indicates a p-value of less than 0.05. All regressors are standardized. 15
Census Division Clusters (determined by Hierarchical Agglomorative Clustering) 1 2 3 4 Figure 9: The divided landscape of intergenerational income mobility: four clusters of Census Divisions as determined by agglomoarative hierarchial clustering 16
Probability of intergenerational low income 0.5 0.4 0.3 50,000 Number of Children in bottom quintile families 10,000 0.2 1,000 0.1 5 10 15 20 25 30 35 40 Poverty rate in the parent's generation (Percent of population in the Census Division below the LICO) Figure 10: The relationship between the intergenerational cycle of low income and Census Division poverty rates 17
Table 11: Correlates of intergenerational income mobility: correlation coefficients based on Census Divisons weighted by number of children Income mobility Rank mobility Directional mobility Absolute Relative Average Absolute Relative Rags to Cycle of Cycle of Census Division Characteristic income income income rank rank riches poverty privilege (α j ) (β j ) (Ȳj) (a j ) (b j ) (P 1,5 ) (P 1,1 ) (P 5,5 ) Poverty rate (below low income cut-off) -0.062 0.033-0.393-0.338 0.283-0.407 0.226-0.208 Gini coefficient (parent incomes) -0.324 0.326-0.198-0.271 0.446-0.065 0.326 0.265 Parents between 25th and 75th percentiles 0.316-0.328-0.102 0.077-0.236-0.162-0.235-0.14 Parent incomes at 50th to 25th percentile -0.637 0.618-0.348-0.461 0.546-0.199 0.57-0.042 Parent incomes at 75th to 50th percentile -0.433 0.404-0.502-0.471 0.504-0.323 0.423-0.128 Parent incomes at 90th to 50th percentile -0.316 0.293-0.381-0.389 0.449-0.253 0.337-0.011 Parent incomes at 99th to 50th percentile 0.021 0.005 0.18 0.111 0.101 0.26-0.019 0.516 Less than high school -0.218 0.171-0.808-0.358 0.188-0.386 0.232-0.502 Lone parents -0.068 0.062 0.193-0.161 0.198-0.119 0.251 0.154 Not born in Canada 0.197-0.15 0.638 0.492-0.322 0.597-0.207 0.57 English mother tongue -0.055 0.071 0.192 0.232-0.175 0.38 0.01 0.188 French mother tongue 0.068-0.092-0.274-0.285 0.186-0.462-0.007-0.288 Parents not married -0.075 0.073 0.431-0.017 0.088 0.129 0.255 0.295 Population 0.126-0.087 0.428 0.273-0.076 0.363-0.09 0.546 Population 25 years and older 0.121-0.084 0.412 0.26-0.07 0.347-0.081 0.532 Parents filing in french 0.07-0.093-0.245-0.272 0.173-0.446-0.01-0.269 Moved to Census division 0.083-0.069 0.331 0.252-0.259 0.319-0.173 0.117 Moved to Census sub division 0.126-0.098 0.499 0.364-0.309 0.464-0.216 0.293 Employment in manufacturing 0.267-0.284-0.079 0.035-0.126-0.089-0.117-0.058 Employment in primary sector -0.252 0.252-0.459-0.074 0.057-0.041 0.034-0.24 Employment in top ten 3-digit SICs -0.325 0.301-0.53-0.313 0.251-0.291 0.251-0.38 Note: Column entries are weighted correlation coefficients. Census Division characteristics are derived from administrative tax data and the 1986 Canadian Census. 18
Estimate using only 16 to 19 year olds in 1986 10 8 6 4 2 2 4 6 8 10 Estimate using all cohorts Figure 11: Estimates of asbsolute income mobility in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 19
0.8 Estimate using only 16 to 19 year olds in 1986 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 Estimate using all cohorts Figure 12: Estimates of relative income mobility in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 20
Estimate using only 16 to 19 year olds in 1986 60,000 50,000 40,000 30,000 20,000 10,000 10,000 20,000 30,000 40,000 50,000 60,000 Estimate using all cohorts Figure 13: Estimates of average parent income in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 21
Estimate using only 16 to 19 year olds in 1986 50 40 30 20 10 10 20 30 40 50 Estimate using all cohorts Figure 14: Estimates of absolute rank mobility in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 22
Estimate using only 16 to 19 year olds in 1986 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 Estimate using all cohorts Figure 15: Estimates of relative rank mobility in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 23
Estimate using only 16 to 19 year olds in 1986 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 Estimate using all cohorts Figure 16: Estimates of rages to riches movement in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 24
Estimate using only 16 to 19 year olds in 1986 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 Estimate using all cohorts Figure 17: Estimates of intergenerational cycles of poverty in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 25
0.6 Estimate using only 16 to 19 year olds in 1986 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 Estimate using all cohorts Figure 18: Estimates of intergenerational cycles of privilege in each of 266 Census Divisions using all available data compared to the subset 16 to 19 years old in 1986 26