Presenting joint distributions of income and wealth

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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 2007 1 / 36

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 2007 2 / 36

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 2007 3 / 36

Introduction Introduction Examine the joint distribution of income and wealth in selected countries. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 4 / 36

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 2007 4 / 36

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 2007 4 / 36

Introduction Why study the joint distribution? Informs us of the nature of the data. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 5 / 36

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 2007 5 / 36

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 2007 5 / 36

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 2007 6 / 36

Data LWS datasets analysed Canada (1999) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 7 / 36

Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 7 / 36

Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Italy (SHIW 2002) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 7 / 36

Data LWS datasets analysed Canada (1999) Germany (GSOEP 2002) Italy (SHIW 2002) Sweden (2002) Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 7 / 36

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 2007 7 / 36

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 2007 8 / 36

Data Issues in analysis Choose comparable but inclusive concept of net worth (nw2). Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 9 / 36

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 2007 9 / 36

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 2007 9 / 36

Data Sample sizes and outliers Canada Germany Italy Sweden United States Pre-shaving 15930 12692 7975 17953 4442 Post-shaving 14810 12108 7709 16846 3577 Difference 1120 584 266 1107 865 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 10 / 36

Data Pre-shave percentiles Percentiles Country 1 10 50 90 99 Income Canada 1826 9351 21307 41104 74271 Germany 2355 8915 18792 35664 68845 Italy 256 7143 16065 32476 65528 Sweden 3642 10540 18935 31455 52634 United States 345 7310 22029 53674 203430 Wealth Canada 19446 2921 27486 174641 832144 Germany 31332 0 25187 235754 768699 Italy 4611 543 84478 318035 1123966 Sweden 51148 11152 18447 145189 439580 United States 27435 3351 29267 325396 2777112 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 11 / 36

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 2007 12 / 36

Descriptive results Descriptive results Show marginal distributions. Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 13 / 36

Descriptive results Descriptive results Show marginal distributions. Study the bivariate distribution using: Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 13 / 36

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 2007 13 / 36

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 2007 13 / 36

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 2007 13 / 36

Descriptive results Density estimates: disposable income 0 100000 0 100000 Canada Germany Italy Sweden United States 5e 05 4e 05 Density 3e 05 2e 05 1e 05 0e+00 0 100000 0 100000 Disposable income 0 100000 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 14 / 36

Descriptive results Density estimates: net worth 0e+00 6e+05 0e+00 6e+05 Canada Germany Italy Sweden United States 1.5e 05 1.0e 05 Density 5.0e 06 0.0e+00 0e+00 6e+05 0e+00 6e+05 Net worth 0e+00 6e+05 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 15 / 36

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 2007 16 / 36

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 : 0.05 0.10 0.15 IncomeQG 2 WealthQG : 1 WealthQG : 2 0.05 0.10 0.15 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 : 4 0.05 0.10 0.15 Proportion 0.05 0.10 0.15 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 17 / 36

The multivariate distribution of wealth Income-wealth quartile groups 0.15 0.10 0.05 Canada Germany 0.15 0.10 0.05 Proportion 0.15 0.10 0.05 Italy Sweden 0.15 0.10 0.05 0.15 United States 0.10 0.05 1 1 1 2 1 3 1 4 2 1 2 2 2 3 2 4 3 1 3 2 3 3 3 4 4 1 4 2 4 3 4 4 Income wealth cell Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 18 / 36

The multivariate distribution of wealth Income-wealth median-based groups Country 0.00 0.10 0.20 0.00 0.10 0.20 omeb : 0.5 med omeb : 0.5 med omeb : 0.5 med omeb : 0.5 med althb : 0.5 medthb : 0.5 1 methb : 1 1.5 me althb : 1.5 media United States Sweden Italy Germany Canada meb : 0.5 1 meb : 0.5 1 meb : 0.5 1 meb : 0.5 1 me althb : 0.5 medthb : 0.5 1 methb : 1 1.5 me althb : 1.5 media United States Sweden Italy Germany Canada meb : 1 1.5 meb : 1 1.5 meb : 1 1.5 meb : 1 1.5 me althb : 0.5 medthb : 0.5 1 methb : 1 1.5 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 : 0.5 1 methb : 1 1.5 me althb : 1.5 media United States Sweden Italy Germany Canada 0.00 0.10 0.20 0.00 0.10 0.20 Proportion Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 19 / 36

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 2007 20 / 36

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 2007 21 / 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 2007 22 / 36

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 2007 23 / 36

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 2007 24 / 36

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 2007 25 / 36

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 2007 26 / 36

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 2007 27 / 36

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 2007 28 / 36

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 2007 28 / 36

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 2007 28 / 36

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 2007 28 / 36

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 2007 28 / 36

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 2007 28 / 36

Regression results Regression results: share of variance explained 0.10 0.15 0.20 0.25 0.30 0.35 DisposableIncome NetWorth United States Sweden Italy Germany Canada 0.10 0.15 0.20 0.25 0.30 0.35 R 2 in regression Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 29 / 36

Regression results Regressions results: disposable income Coefficient estimates and confidence intervals Canada 20000 Germany Italy 20000 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: 50 70 Age: 30 50 20000 20000 Coefficient estimates 20000 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 30 / 36

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: 50 70 Age: 30 50 1e+05 3e+05 1e+05 3e+05 Coefficient estimates 1e+05 3e+05 Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 31 / 36

Regression results Residual standard deviation of disposable income Regression residuals United States Sweden Country Italy Germany Canada 0.25 0.30 0.35 0.40 0.45 0.50 Residual standard deviation of disposable income Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 32 / 36

Regression results Residual standard deviation of net worth Regression residuals United States Sweden Country Italy Germany Canada 20000 40000 60000 80000 100000 Residual standard deviation of net worth Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 33 / 36

Regression results Residual correlation of disposable income and net worth Regression residuals United States Sweden Country Italy Germany Canada 0.25 0.30 0.35 0.40 0.45 0.50 Residual correlation of disposable income and net worth Jäntti, Sierminska, Smeeding (LIS, LWS) Income and wealth July 2007 34 / 36

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 2007 35 / 36

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 2007 36 / 36

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 2007 36 / 36

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 2007 36 / 36

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