Mobility, taxation and welfare

Transcription

1 Mobility, taxation and Abdelkrim Araar Sami Bibi Jean-Yves Duclos September 3, 2008 Mobility, taxation and SCW / 29

2 permanent incomes taxation Mobility, taxation and SCW / 29

3 permanent incomes permanent incomes taxation Income mobility has at least two potential impacts. The first is to make the distribution of permanent incomes potentially more equal than the distribution of periodic incomes. Cross sectional measures can behave quite differently to longitudinal measures due to economic mobility. (E.g.: cross sectional inequality may rise, while permanent incomes inequality falls.) Friedman (1962): a society in which everyone remains in the same position year after year can almost certainly be declared worse than a mobile society with identical cross-sectional inequality. Mobility, taxation and SCW / 29

4 permanent incomes taxation The second impact is to cause individual-level due to the time variability of individual incomes. This generates a cost if individuals would prefer their incomes to be distributed as equally as possible across time. Gittleman and Joyce (1996): a preference for retaining one s position in the distribution makes mobility less desirable. The paper is concerned with the impact of the dynamics of income across individuals and across time. Mobility, taxation and SCW / 29

5 taxation permanent incomes taxation The paper also investigates the impact of taxation on income dynamics. This impact depends upon the aversion to individual income variability across periods and on the preference towards equalization of permanent incomes across individuals. Both components can be expected to be qualitatively improved by a redistributive tax system: The precise quantitative impact depends on the distribution of market incomes and on the structure of the tax system. We illustrate this using the Canadian Survey of Labor and Income Dynamics (SLID). Mobility, taxation and SCW / 29

6 Permanent incomes EDEI incomes Post-tax EDEI Social Mobility, taxation and SCW / 29

7 Permanent incomes EDEI incomes Post-tax EDEI Social Let x and y stand for pre- and post-tax income, respectively, with F x,y (, ) as their joint distribution function. The marginal distributions are denoted as F x ( ) and F y ( ) Index individuals by their characteristics ω, of which the distribution function is F ω ( ). F t ω ( ) is the distribution of income t (with t equal to x or to y), conditional on individual ω. Mobility, taxation and SCW / 29

8 Permanent incomes Permanent incomes EDEI incomes Post-tax EDEI Social The permanent pre-tax income of an individual with characteristic ω is given by: and the permanent post-tax income by x(ω) = zdf x ω (z) (1) y(ω) = zdf y ω (z) (2) Periodic utility function given by U ɛ (t): U ɛ (t) = { t 1 ɛ, for ɛ 1, 1 ɛ ln (t), for ɛ =1. (3) where ɛ 0 is a parameter of risk aversion. Mobility, taxation and SCW / 29

9 EDEI incomes Permanent incomes EDEI incomes Post-tax EDEI Social Let χ(ω; ɛ) be the pre-tax equally distributed equivalent income (EDEI) for individual ω: χ(ω; ɛ) =U 1 ɛ ( ) U ɛ (z)df x ω (z). (4) χ(ω; ɛ) is in general lower than x(ω) to allow for aversion to periodic income variability. Define γ(ω; ɛ) analogously as the post-tax EDEI for individual ω: γ(ω; ɛ) =U 1 ɛ ( ) U ɛ (z)df y ω (z). (5) Mobility, taxation and SCW / 29

10 Post-tax EDEI Permanent incomes EDEI incomes Post-tax EDEI Social Further, define ξ(ω; ɛ) as the post-tax EDEI for individual ω, estimated applying the variability in pre-tax incomes on permanent post-tax incomes, y(ω): ( ) χ(ω; ɛ) ξ(ω; ɛ) =y(ω) x(ω) For a proportional tax system, we have ξ(ω; ɛ) =γ(ω; ɛ). (6) Mobility, taxation and SCW / 29

11 Social We measure social over the distribution of individual EDEI; thus, Permanent incomes EDEI incomes Post-tax EDEI Social W χ(ɛ) (ρ) =U 1 ρ ( ) U ρ (χ(ω; ɛ))df ω (ω) (7) W γ(ɛ) (ρ) and W ξ(ɛ) (ρ) are defined accordingly. ρ is the aversion to between-individual inequality in EDEI. Mobility, taxation and SCW / 29

12 Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and Mobility, taxation and SCW / 29

13 Welfare and permanent incomes Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and W x (ρ) and W y (ρ) are the EDEI of permanent pre-tax and post-tax incomes: W x (ρ) =U 1 ρ W y (ρ) =U 1 ρ ( ( ) U ρ (x(ω))df ω (ω), (8) ) U ρ (y(ω))df ω (ω). (9) W x (ρ) and W y (ρ) are the EDEI of periodic incomes: W x (ρ) =U 1 ρ ( ) U ρ (z)df x (z), (10) W y (ρ) =U 1 Mobility, taxation and SCW / 29 ρ ( ) U ρ (z)df y (z). (11)

14 Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and Define M x (ɛ; ρ) =W χ(ɛ) (ρ) W x (ρ) (12) as the net effect of mobility on pre-tax social. This can be decomposed into two components: W χ(ɛ) (ρ) W x (ρ) (13) = W χ(ɛ) (ρ) W x (ρ) }{{} (14) (Mx(ɛ;ρ) 0: 1 effect of ) + W x (ρ) W x (ρ) }{{} (15) (Mx(ρ) 0: 2 equalization of permanent pre-tax incomes) (16) Mobility, taxation and SCW / 29

15 Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Whenever ɛ = ρ, the negative effect is exactly counterbalanced by the positive effect of the equalization of permanent incomes, so that Mx 1(ɛ; ɛ) = M x 2 (ɛ) and M x (ɛ; ɛ) =M y (ɛ; ɛ) =0. The net social impact of income mobility will be positive if equalization of permanent incomes dominates in periodic income (when ρ>ɛ). Taxation and Mobility, taxation and SCW / 29

16 Variability of post-tax income Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and The cost of variability in post-tax income, namely, M 1 y (ɛ; ρ), can be decomposed as: W γ(ɛ) (ρ) W y (ρ) }{{} (17) (<0: cost of mobility in post-tax incomes) = W ξ(ɛ) (ρ) W y (ρ) }{{} (18) (<0: initial of pre-tax periodic incomes) + W γ(ɛ) (ρ) W ξ(ɛ) (ρ) }{{} (>0: fall in periodic variability due to tax system) (19) Mobility, taxation and SCW / 29

17 Taxation and mobility Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and Both aspects of mobility can be expected to be qualitatively improved by a redistributive tax system. 1. A progressive tax system reduces the variability of periodic incomes around permanent incomes. 2. A progressive tax system makes distribution of permanent post-tax incomes more equal than the distribution of permanent pre-tax incomes. Mobility, taxation and SCW / 29

18 Impact of taxation on mobility Let the impact of the tax system on mobility be expressed as Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and ΔM(ɛ; ρ) =M y (ɛ; ρ) M x (ɛ; ρ) =ΔM 1 (ɛ; ρ)+δm 2 (ρ). (20) which is the difference in the impact of mobility before and after tax. ΔM 1 (ɛ; ρ) shows the effect of taxation on ΔM 2 (ρ) shows the effect of taxation on permanent income inequality. Mobility, taxation and SCW / 29

19 Taxation and Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and W χ(ɛ) (ρ) is the EDEI of the distribution of pre-tax individual permanent incomes corrected for the cost of income variability. Let Γ(ɛ; ρ) =W γ(ɛ) (ρ) W χ(ɛ) (ρ) be the total effect of. Γ(ɛ =0;ρ) is the effect of taxation on the distribution of permanent incomes. We then have: Theorem 1 With degrees ɛ and ρ of aversion to income variability across time and to income inequality across individuals, respectively, the policy effectiveness of the tax system is given by Γ(ɛ; ρ) = (W y (ρ) W x (ρ)) + ΔM 1 (ɛ; ρ)+δm 2 (ρ) = Γ(0;ρ)+ΔM 1 (ɛ; ρ). (21) Mobility, taxation and SCW / 29

20 Welfare and permanent incomes Variability of post-tax income Taxation and mobility Impact of taxation on mobility Taxation and W y (ρ) W x (ρ) is the social effect of the tax system on periodic incomes; ΔM 1 (ɛ; ρ) is the effect of the tax system on the cost of income variability; ΔM 2 (ρ) is the effect of the tax system on the cost of permanent income inequality; The extent to which the tax system is judged improving will then depend upon its ability 1) to equalize the distribution of periodic incomes; 2) to reduce the cost of income variability; and 3) to reduce the cost of permanent income inequality. Mobility, taxation and SCW / 29

21 taxation taxation on social Mobility, taxation and SCW / 29

22 taxation taxation Let Λ(ɛ; ρ) =W γ(ɛ) (ρ) W x (ρ) be the total effect of mobility and. Corollary 1 variability across time and to income inequality across individuals, respectively, the combined effect of mobility and taxation is given by With degrees ɛ and ρ of of aversion to income Λ(ɛ; ρ) = M x (ɛ; ρ)+γ(ɛ; ρ) (22) = M x (ɛ; ρ)+m 1 (ɛ; ρ)+γ(0;ρ). (23) For a progressive tax system: Γ(ɛ; ρ) is positive. The sign of M x (ɛ; ρ) depends on whether the cost of Mobility, taxation and SCW / 29

23 SLID data Results: mobility and with Canadian data taxation Mobility, taxation and SCW / 29

24 SLID data SLID data Results: mobility and taxation We use panel data from the Canadian Survey of Labor and Income Dynamics (SLID) to assess the combined impact of taxation and mobility in Canada. Pre-tax-and-benefit income ( market income ) includes wages and salaries, self-employment income, private pensions and investment income. Post-tax-benefit income ( disposable income ) is market income plus transfers minus taxes. Transfers include federal and provincial child and family allowances, old age security pensions and guaranteed income supplement, employment insurance benefits, social assistance benefits, and various tax credits. Taxes include both provincial and federal personal income taxes. The panel runs from 1996 to 2001 and comprises about Mobility, taxation and SCW / 29

25 Results: mobility and SLID data Results: mobility and taxation The impact of mobility on social is summarized in Table 1. The cost of mobility in pre-tax income (Mx 1 (ɛ; ρ)) ranges from 2.26 to percent of pre-tax mean income. The tax system reduces considerably the time variability of incomes; for instance, the cost (M 1 y (ɛ; ρ)) is more than halved for ɛ = ρ =0.6. The variability of periodic incomes is decreased significantly by the tax system: mobility contributes less to the equalization effect of permanent post-tax incomes than of pre-tax incomes. The net effect of mobility on social is dominated by mobility s benefit for ɛ<ρand by its cost for ɛ>ρ. Mobility, taxation and SCW / 29

26 Table 1: The effect of mobility on social in pre- and post-tax incomes in Canada, Pre-tax income Post-tax income Effect of taxation on mobility ɛ ρ M 1 x (ɛ; ρ) M 2 x (ρ) M 1 y (ɛ; ρ) M 2 y (ρ) ΔM 1 (ɛ; ρ) ΔM 2 (ρ) ΔM(ɛ; ρ) , Mobility, taxation and SCW / 29

27 taxation SLID data Results: mobility and taxation Turn now to the social effects of the tax system shown in Tables 2 and 3: Tax equalization of the periodic variability of incomes: drop in the cost of income variability since W ξ(ɛ) (ρ) is always greater than W γ(ɛ) (ρ). Tax equalization of permanent incomes: Table 3 shows that Γ(0; ρ) can reach up to percent of mean income when ρ =0.9. Following Corollary 1, the redistributive benefit of the tax system may be enhanced, decreased, or even outdone by the effect of mobility on pre-tax incomes. Table 3 shows that the net effect of both mobility and taxation on social is usually positive. Mobility, taxation and SCW / 29

28 Table 2: The impact of taxation and mobility on social in pre- and post-tax incomes in Canada, Levels of social Pre-tax income Post-tax income ɛ ρ W x (ρ) W x (ρ) W χ(ɛ) (ρ) W y (ρ) W y (ρ) W γ(ɛ) (ρ) W ξ(ɛ) (ρ) Mobility, taxation and SCW / 29

29 Table 3: The impact of taxation and mobility on social Changes in social ɛ ρ Γ(ɛ; ρ) M x (ɛ; ρ) Λ(ɛ; ρ) Mobility, taxation and SCW / 29