Presenting joint distributions of income and wealth
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1 Presenting joint distributions of income and wealth Markus Jäntti 1 Eva Sierminska 2 Timothy M Smeeding 3 1 Luxembourg Income Study 2 Luxembourg Wealth Study 3 Syracuse University LWS Conference Rome July 2007 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
2 Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
3 Introduction Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
4 Introduction Introduction Examine the joint distribution of income and wealth in selected countries. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
5 Introduction Introduction Examine the joint distribution of income and wealth in selected countries. Exploratory analysis to compare nature of association across countries. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
6 Introduction Introduction Examine the joint distribution of income and wealth in selected countries. Exploratory analysis to compare nature of association across countries. Use common definitions (limits number of countries) and comparative units. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
7 Introduction Why study the joint distribution? Informs us of the nature of the data. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
8 Introduction Why study the joint distribution? Informs us of the nature of the data. Wealth and income clearly related, but possibly in quite different ways. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
9 Introduction Why study the joint distribution? Informs us of the nature of the data. Wealth and income clearly related, but possibly in quite different ways. May reveal interesting differences that could be related to institutional and sectoral differences across countries. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
10 Data Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
11 Data LWS datasets analysed Canada (1999) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
12 Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
13 Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Italy (SHIW 2002) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
14 Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Italy (SHIW 2002) Sweden (2002) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
15 Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Italy (SHIW 2002) Sweden (2002) United States (SCF 2001) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
16 Data Income and wealth variables Variable Symbol LWS definition Disposable income dispincome lis dpi = grossincome taxes Gross income grossincome giw Taxes taxes inctax + contrib Net worth networth nw2 = wealth debt Wealth wealth tfa1 + tnf2 Debt debt td Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
17 Data Issues in analysis Choose comparable but inclusive concept of net worth (nw2). Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
18 Data Issues in analysis Choose comparable but inclusive concept of net worth (nw2). Focus on non-outlier observations: retain the observations where both net worth and disposable income is within the inner 98 percent of the values. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
19 Data Issues in analysis Choose comparable but inclusive concept of net worth (nw2). Focus on non-outlier observations: retain the observations where both net worth and disposable income is within the inner 98 percent of the values. Express all money values in terms of international US dollars in 2002 prices use domestic deflator and PPP for actual individual consumption. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
20 Data Sample sizes and outliers Canada Germany Italy Sweden United States Pre-shaving Post-shaving Difference Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
21 Data Pre-shave percentiles Percentiles Country Income Canada Germany Italy Sweden United States Wealth Canada Germany Italy Sweden United States Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
22 Descriptive results Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
23 Descriptive results Descriptive results Show marginal distributions. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
24 Descriptive results Descriptive results Show marginal distributions. Study the bivariate distribution using: Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
25 Descriptive results Descriptive results Show marginal distributions. Study the bivariate distribution using: Quartile-group cross-tabulations. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
26 Descriptive results Descriptive results Show marginal distributions. Study the bivariate distribution using: Quartile-group cross-tabulations. Bands of income related to median (< 50%, 50% 100%, 100% 150%, > 150% of median). Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
27 Descriptive results Descriptive results Show marginal distributions. Study the bivariate distribution using: Quartile-group cross-tabulations. Bands of income related to median (< 50%, 50% 100%, 100% 150%, > 150% of median). Bivariate density estimates. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
28 Descriptive results Density estimates: disposable income Canada Germany Italy Sweden United States 5e 05 4e 05 Density 3e 05 2e 05 1e 05 0e Disposable income Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
29 Descriptive results Density estimates: net worth 0e+00 6e+05 0e+00 6e+05 Canada Germany Italy Sweden United States 1.5e e 05 Density 5.0e e+00 0e+00 6e+05 0e+00 6e+05 Net worth 0e+00 6e+05 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
30 The multivariate distribution of wealth Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
31 The multivariate distribution of wealth Income-wealth quartile groups Country United States Sweden Italy Germany Canada United States Sweden Italy Germany Canada United States Sweden Italy Germany Canada United States Sweden Italy Germany Canada IncomeQG : 1 IncomeQG : 1 IncomeQG : 1 IncomeQG : 1 WealthQG : 1 WealthQG : 2 WealthQG : 3 WealthQG : 4 : IncomeQG 2 WealthQG : 1 WealthQG : IncomeQG : 2 IncomeQG : 2 IncomeQG : 2 WealthQG : 3 WealthQG : 4 IncomeQG : 3 IncomeQG : 3 IncomeQG : 3 IncomeQG : 3 WealthQG : 1 WealthQG : 2 WealthQG : 3 WealthQG : 4 IncomeQG : 4 IncomeQG : 4 IncomeQG : 4 IncomeQG : 4 WealthQG : 1 WealthQG : 2 WealthQG : 3 WealthQG : Proportion Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
32 The multivariate distribution of wealth Income-wealth quartile groups Canada Germany Proportion Italy Sweden United States Income wealth cell Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
33 The multivariate distribution of wealth Income-wealth median-based groups Country omeb : 0.5 med omeb : 0.5 med omeb : 0.5 med omeb : 0.5 med althb : 0.5 medthb : methb : me althb : 1.5 media United States Sweden Italy Germany Canada meb : meb : meb : meb : me althb : 0.5 medthb : methb : me althb : 1.5 media United States Sweden Italy Germany Canada meb : meb : meb : meb : me althb : 0.5 medthb : methb : me althb : 1.5 media United States Sweden Italy Germany Canada meb : 1.5 media meb : 1.5 media meb : 1.5 media meb : 1.5 media althb : 0.5 medthb : methb : me althb : 1.5 media United States Sweden Italy Germany Canada Proportion Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
34 The multivariate distribution of wealth Joint distribution of income and net worth Non-parametric density estimates: Canada Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
35 The multivariate distribution of wealth Joint distribution of income and net worth Non-parametric density estimates: Germany Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
36 The multivariate distribution of wealth Joint distribution of income and net worth Non-parametric density estimates: Italy Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
37 The multivariate distribution of wealth Joint distribution of income and net worth Non-parametric density estimates: Sweden Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
38 The multivariate distribution of wealth Joint distribution of income and net worth Non-parametric density estimates: United States Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
39 The multivariate distribution of wealth Joint distribution of income and wealth Canada and Germany relative to the US Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
40 The multivariate distribution of wealth Joint distribution of income and wealth Italy and Sweden relative to the US Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
41 Regression results Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
42 Regression results Bivariate regressions of income and wealth Simple bivariate regressions relate disposable income and net worth to selected covariates: dispincome = f dpi (age, education, fam. struct) + ɛ dpi networth = f nw (age, education, fam. struct) + ɛ nw [ ] ([ ] [ ]) (1) ɛdpi 0 σ 2 N, dpi ρσ dpi σ nw 0 ɛ nw σ 2 nw Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
43 Regression results Bivariate regressions of income and wealth Simple bivariate regressions relate disposable income and net worth to selected covariates: Report: dispincome = f dpi (age, education, fam. struct) + ɛ dpi networth = f nw (age, education, fam. struct) + ɛ nw [ ] ([ ] [ ]) (1) ɛdpi 0 σ 2 N, dpi ρσ dpi σ nw 0 ɛ nw σ 2 nw Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
44 Regression results Bivariate regressions of income and wealth Simple bivariate regressions relate disposable income and net worth to selected covariates: Report: dispincome = f dpi (age, education, fam. struct) + ɛ dpi networth = f nw (age, education, fam. struct) + ɛ nw [ ] ([ ] [ ]) (1) ɛdpi 0 σ 2 N, dpi ρσ dpi σ nw 0 ɛ nw Share of variation accounted for by f ( ) σ 2 nw Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
45 Regression results Bivariate regressions of income and wealth Simple bivariate regressions relate disposable income and net worth to selected covariates: Report: dispincome = f dpi (age, education, fam. struct) + ɛ dpi networth = f nw (age, education, fam. struct) + ɛ nw [ ] ([ ] [ ]) (1) ɛdpi 0 σ 2 N, dpi ρσ dpi σ nw 0 ɛ nw Share of variation accounted for by f ( ) Regression coefficients σ 2 nw Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
46 Regression results Bivariate regressions of income and wealth Simple bivariate regressions relate disposable income and net worth to selected covariates: Report: dispincome = f dpi (age, education, fam. struct) + ɛ dpi networth = f nw (age, education, fam. struct) + ɛ nw [ ] ([ ] [ ]) (1) ɛdpi 0 σ 2 N, dpi ρσ dpi σ nw 0 ɛ nw Share of variation accounted for by f ( ) Regression coefficients Standard deviations σ dpi, σ nw σ 2 nw Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
47 Regression results Bivariate regressions of income and wealth Simple bivariate regressions relate disposable income and net worth to selected covariates: Report: dispincome = f dpi (age, education, fam. struct) + ɛ dpi networth = f nw (age, education, fam. struct) + ɛ nw [ ] ([ ] [ ]) (1) ɛdpi 0 σ 2 N, dpi ρσ dpi σ nw 0 ɛ nw Share of variation accounted for by f ( ) Regression coefficients Standard deviations σ dpi, σ nw Correlation ρ σ 2 nw Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
48 Regression results Regression results: share of variance explained DisposableIncome NetWorth United States Sweden Italy Germany Canada R 2 in regression Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
49 Regression results Regressions results: disposable income Coefficient estimates and confidence intervals Canada Germany Italy SwedenUnited State Intercept Fam: sng, no kids Fam: sng parent Fam: other Fam: cpl, no kids Covariate Educ: Unknown Educ: Medium Educ: High Age: 70 Age: Age: Coefficient estimates Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
50 Regression results Regressions results: net worth Canada 1e+05 3e+05 Germany Italy 1e+05 3e+05 SwedenUnited State Intercept Fam: sng, no kids Fam: sng parent Fam: other Fam: cpl, no kids Covariate Educ: Unknown Educ: Medium Educ: High Age: 70 Age: Age: e+05 3e+05 1e+05 3e+05 Coefficient estimates 1e+05 3e+05 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
51 Regression results Residual standard deviation of disposable income Regression residuals United States Sweden Country Italy Germany Canada Residual standard deviation of disposable income Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
52 Regression results Residual standard deviation of net worth Regression residuals United States Sweden Country Italy Germany Canada Residual standard deviation of net worth Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
53 Regression results Residual correlation of disposable income and net worth Regression residuals United States Sweden Country Italy Germany Canada Residual correlation of disposable income and net worth Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
54 Concluding comments Outline 1 Introduction 2 Data 3 Descriptive results 4 The multivariate distribution of wealth 5 Regression results 6 Concluding comments Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
55 Concluding comments Concluding comments Substantial differences in the range of variation, even after shaving the data. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
56 Concluding comments Concluding comments Substantial differences in the range of variation, even after shaving the data. US has much greater variation that the rest. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
57 Concluding comments Concluding comments Substantial differences in the range of variation, even after shaving the data. US has much greater variation that the rest. The association between income and wealth also greatest in the United States. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July / 36
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