Altruism, Incomplete Markets, and Tax Reform Luisa Fuster, Ayse Imrohoroglu, Selahattin Imrohoroglu Presented by Cagri S. Kumru Sydney Macro Reading Group
September 2007
Optimal Tax Structure
Judd (1985) and Chamley (1986) Ramsey approach in the standard one sector growth model with complete markets. Zero capital income tax rate DO NOT DISTORT CAPITAL ACCUMULATION
Aiyagari (1995) Ramsey approach in the standard one sector growth model with incomplete markets Optimal to tax capital income to prevent over-accumulation of capital because of self-insurance.
Optimal Tax Structure
Erosa and Gervais (2002) Pure OLG with complete markets Ramsey solution calls for nonzero capital income taxation Tax rate vary over the life cycle to enhance e¢ ciency in the face of age-varying earnings and savings pro…le.
Imrohoroglu (1998), Garriga (2003), Conesa, Kitao, and Kruger (2006) To tax capital income might be optimal.
Quantifying the Impact of Tax Reform
Auerbach and Kotliko¤ (1987) G.E. OLG model with complete markets Signi…cant capital deepening when the tax base is changed from a 15% income tax to 20.1% wage tax or 17.6% consumption tax. Welfare loss with a switch to wage taxation Welfare gain with a switch to consumption tax
Imrohoroglu (1988) G.E. OLG model with incomplete markets. Positive capital tax maximizes long run welfare
Auerbach, Kotliko¤, Smetters, and Walliser (2001) Despite long run gains in output and average welfare, certain group experience welfare losses.
General Objective & Methodology
Examine the welfare impact of various tax reform proposals
General Objective & Methodology
Examine the welfare impact of various tax reform proposals G. E. pure life-cycle & dynastic OLG models with incomplete markets
General Objective & Methodology
Examine the welfare impact of various tax reform proposals G. E. pure life-cycle & dynastic OLG models with incomplete markets Long-run equilibrium & an equilibrium transition to a new balanced growth path
Speci…c Questions
1
What are the welfare e¤ects of changing the current U.S. tax code on individuals taking into account the transitional e¤ects.
2
What are the characteristics of households that bene…t or lose from tax reform?
Two Models
Dynastic Model: altruistically linked households Pure Life-cycle Model: pure life-cycle agents
Two Models Technology
Cobb-Douglas production function Yt = Ktα (At Nt )1
α
Factor prices rˇt = αKtα ω t = (1
1
( A t Nt ) 1
α
α)Ktα (At Nt )
(1) α
(2)
Two Models Social Security and Fiscal Policy
Pay As You Go (PAYG) social security system Social security system is self-…nancing. τ s is social security tax rate
G : an exogenously given level of government expenditures Financed by labor income, capital income, and consumption taxes
G = τ c C + τ n ωN + τ k rK
Two Models Demographics and Endowments
Every period t a generation of individuals is born. Maximum possible age: 2T An individual’s lifetime support overlaps during the …rst T periods with that of his parents. An individual’s lifetime support overlaps during the last T periods with that of his children.
Individuals are endowed with one unit of time. Mandatory retirement age is R.
Permanent lifetime labor ability shock: z 2 Z = fH, Lg Altruistic model: Π(z 0 , z ) = [π ij ], i, j 2 fH, Lg,where π ij = Prfz 0 = j jz = i g
Two Models Demographics and Endowments
The labor productivity of an individual of ability z and age j: ε j ( z ) e u j (z ) Permanent labor ability shock a¤ects three features of an individual’s lifetime opportunities: 1
an individual’s life expectancy, ψj (z )
2
age-e¢ ciency pro…le fεj (z )g2T j =1
3
the stochastic process for the uninsurable idiosyncratic productivity shock, uj (z ). There are no private insurance markets for longevity risk and permanent and temporary labor income shocks.
Two Models Demographics and Endowments
The size of cohort 1 with ability z, relative to that of cohort (T + 1): µ1 (z ) = λ(z )(1 + n)T Relative size of other generations: µ i +1 ( z ) =
ψi (z ) µi (z ) , i = 1, ..., 2T (1 + n )
1.
Two Models Dynastic Model: Households’Decision Problem
Individuals derive utility from the lifetime utility of their parents and children. Following Laitner (1992), assume that parents and children have the same objective function during the periods their lives overlap The parent and children constitute a single decision unit, household. the parent of age T + 1, and his m = (1 + n)T adult children of age 1.
A household lasts T period or until the parent and the children have died. A dynasty is a sequence of households that belong to the same family line.
Two Models Dynastic Model: Households’Decision Problem
Households are heterogenous with respect to their asset holdings, age, abilities, and their composition. There are three types of households: Type I household: only children Type II household: only parent Type III household: both parent and children
The budget constraint facing an age-j household:
[φs (h)cs ,j + φf (h)cf ,j ](1 + τ c ) + (1 + g )aj = [1 + r (1 τ k )aj 1 + ej (h, e¯f , zf , zs , us , uf ) + [φs (h) + φf (h)]ξ (3) Households face borrowing constraints, aj
0, 8j.
Two Models Dynastic Model: Households’Decision Problem
A household chooses a sequence of consumption, leisure, and asset holdings given a set of …scal parameters and prices The state of a household: x = (a, h, e¯f , e¯s , zf , zs , uf , us )
Two Models Dynastic Model: Households’Decision Problem
The household’s decision problem: 2 4
Vj ( x ) =
max
f[φs (h)u (cs ,j , ls ,j ) + φf (h)u (cf ,j , lf ,j )]
fcs ,cf ,ls ,lf ,a 0 g ~ + βV j +1 (a0 , h, e¯f0 , e¯s0 , zf , zs , uf , us )
subject to budget and borrowing constraints, where 2
3
3
5 (4)
3
6 7 ∑ 6 7 h 0 =1 6 7 V j +1 (x ) = 6Vj +1 (a0 , h0 , e¯f0 , e¯s0 , zf , zs , uf0 , us0 ) for j < T ;7 6 7 4 5 ψT (zs )(1 + n)T Efzs0 ,uf0 ,us0 /zs ,us g 0 0 0 0 0 V1 (a , 3, e¯s , 0, zs , zs , uf , us ) for j = T . ~
0
χj (h, h0 ; zf , zs )Efuf0 ,us0 /uf , us g
Two Models: Pure Life-cycle model: Individual’s decision problem
The budget constraint for an individual of age j
( 1 + τ c ) cj + ( 1 + g ) a j = [ 1 + r ( 1
τ k )]aj
1
+ ej (e¯ , z, u ) + ξ (5)
The state of an individual: x = (a, e¯ , z, u ) The individual’s decision problem: ~
Wj (x ) = maxfu (c, l ) + βWj +1 (a0 , e¯ 0 , z, u )g fc ,l ,a 0 g
subject to budget and liquidity constraints.
Two Models Stationary Equilibrium and Transition
1
Given …scal policy, factor prices, and lump-sum transfers, households’decision rules solve households’decision problems.
2
Factor prices are competitive.
3
Aggregate values of capital stock, labor input, and consumption are derived from individuals’choices.
4
Government’s budget and the budget of the social sec. system are balanced.
5
Final goods and factor markets clear.
Calibration Period Utility Function
u (c, l ) =
(c 1
υ l v )1 υ
1
γ
1
Calibration List of Parameters
Quantitative Findings Comparison
Similarities Precautionary saving motives against the uninsurable income risk and mortality risk
Di¤erences In the dynastic framework: Perfect family insurance Perfect sharing of di¤erences in tax incidences Save to leave bequests and to give intervivos transfers
The same …scal reform may deliver di¤erent results depending on the choice of the framework.
Quantitative Findings Main Results
Dynastic model: The dynastic links work as an informal redistribution mechanism to deliver some of the future gains to current generations. Life-cycle model: Since individuals do not have any generational links, they are worse o¤ in reforms where most of gains realized in the future.
Long-Run E¤ects of Tax Reform Altruistic Model
G = τ c C + τ n ωN + τ k rK τ e¤ = (τ c + τ n + τ s )/(1 + τ c ) Eliminating the tax on saving encourages faster capital accumulation. Larger increase in the capital stock if the reform is …nanced by consumption tax.
Long-Run E¤ects of Tax Reform Pure Life-Cycle Model
The steady state welfare declines with the …rst reform in line with previous results in Auerbach et al (1983) and Imrohoroglu (1998). The di¤erential impact of consumption and labor taxation on capital acc. is quantitatively less important in a dynastic framework.
Transition and Welfare E¤ects (TWE) Main Results
Higher consumption tax primarily hurts the retirees and older cohorts Higher wage tax hurts the younger and poorer individuals Third reform get the widest support in the dynastic framework Dynasties can redistribute future gains to the current generation through bequests and inter-vivos transfers.
The …rst reform get the widest support in the life cycle model Middle age and older individuals who constitute more than 50% of population support the reform
TWE: Switch to Higher Wage Taxation Transitional Paths
TWE: Switch to Higher Wage Taxation Transitional Paths
TWE: Switch to Higher Wage Taxation Transitional Paths
TWE: Switch to Higher Wage Taxation Welfare E¤ects
TWE: Switch to Higher Wage Taxation Welfare E¤ects
TWE: Switch to Higher Wage Taxation Welfare E¤ects
TWE: Switch to Higher Consumption Taxation Welfare E¤ects
TWE: Switch to Higher Consumption Taxation Welfare E¤ects
TWE: Switch to Higher Consumption Taxation Welfare E¤ects
TWE: Elimination of Income Taxation Transitional Paths
TWE: Elimination of Income Taxation Transitional Paths
TWE: Elimination of Income Taxation Welfare E¤ects
TWE: Elimination of Income Taxation Welfare E¤ects
TWE: Elimination of Income Taxation Welfare E¤ects
TWE: Elimination of Income Taxation Welfare E¤ects
Conclusion
In both cases, eliminating the capital income tax by raising the labor income tax hurts the younger generations who may also be facing borrowing constraints.
Conclusion
In both cases, eliminating the capital income tax by raising the labor income tax hurts the younger generations who may also be facing borrowing constraints. When a higher consumption tax is used to eliminate all of income taxation, long run gains are highest in both models.
Conclusion
In both cases, eliminating the capital income tax by raising the labor income tax hurts the younger generations who may also be facing borrowing constraints. When a higher consumption tax is used to eliminate all of income taxation, long run gains are highest in both models. In both cases, the increased consumption tax hurts the retirees the most.
Conclusion
In both cases, eliminating the capital income tax by raising the labor income tax hurts the younger generations who may also be facing borrowing constraints. When a higher consumption tax is used to eliminate all of income taxation, long run gains are highest in both models. In both cases, the increased consumption tax hurts the retirees the most. In the altruistic model, the family serves as a very e¤ective insurance mechanism.
Conclusion
A majority of the individuals are better o¤ transitioning from the benchmark …scal policy toward the reformed steady-state where there is no income taxation.
Conclusion
A majority of the individuals are better o¤ transitioning from the benchmark …scal policy toward the reformed steady-state where there is no income taxation. The dynastic links work as an informal redistribution mechanism to deliver some of the future gains to current generations.
Conclusion
A majority of the individuals are better o¤ transitioning from the benchmark …scal policy toward the reformed steady-state where there is no income taxation. The dynastic links work as an informal redistribution mechanism to deliver some of the future gains to current generations. In the life cycle model, individuals do not have any generational links and this backward transfer is not possible.
Conclusion
A majority of the individuals are better o¤ transitioning from the benchmark …scal policy toward the reformed steady-state where there is no income taxation. The dynastic links work as an informal redistribution mechanism to deliver some of the future gains to current generations. In the life cycle model, individuals do not have any generational links and this backward transfer is not possible. As a result, life cycle individuals are worse o¤ when income taxation is eliminated and replaced by a consumption tax.
