Optimal Mirrleesian Income Taxation with Tax Avoidance

Transcription

1 Optimal Mirrleesian Income Taxation with Tax Avoidance Daniel Moncayo January 30, 2014

2 Introduction People have more than one way to respond to taxation. The labor supply elasticity alone can t explain taxpayer s responses to changes in marginal taxes. Striking evidence of avoidance responses to tax changes in that time frame: - Burman, Clausing and O Hare (1994) - Increases in marginal taxes on capital gains effective January, 1987, caused a 700% increase in capital gain realizations the month of December, 1986, compared to the previous and following years. - Maki(1996) and Scholz(1994) - There was a large shift from no-longer-deductible consumer interest, into a still-deductible mortgage or home equity loans. - MacKie-Mason(1990,1997) - There was a large shift from C-Corporations to S-Corporations. - Gordon and Slemrod (1988)- In 1983, the US collected approximately zero tax revenue from taxes levied on capital income.

3 Introduction Considerable effort has been placed to estimate an elasticity of taxable income with respect to marginal taxes. This composite elasticity measures the labor response to taxation as well as tax avoidance responses. This is very difficult to measure. In fact, we have no idea of the size of the Tax Gap. The previous facts can t be analyzed using the classic Mirrleesian model. This model only allows one way for agents to reduce their taxable income. There are no formal models that include information asymmetries and moral hazard into the analysis of both labor and avoidance responses to taxation, or a normative analysis of optimal marginal taxes.

4 What am I doing? Extend the classic Mirrleesian framework to include general tax avoidance opportunities. The model takes into account the structure of the tax system before finding the optimal tax policy ( Third Best ). Prove a Non-Falsification theorem for the optimality of a discrete tax system. The theorem does not need any restricting assumptions on the functional form of costs of tax avoidance. Characterization of optimal tax system, taxing limitations, and individual responses to taxation.

5 Results Tax avoidance opportunities for the agents set upper limits on income redistribution. When loopholes and avoidance channels are abundant, negative marginal taxes at the top collect more tax revenue and increase expected welfare. Soft cap on marginal taxes for high income individuals.

6 Mechanism design approach Given a distribution of ability/wages, find the constrained optimal allocation of consumption and labor effort by solving a social planner s problem: Solve for the MRS between consumption and labor effort for each type of agent. Use these optimality conditions to solve the model numerically. If the constrained optimal allocation is individually incentive compatible, then it can be implemented in a environment where agents self-report their labor effort by enacting marginal taxes and lump sum transfers: Equalize the MRS of the individual s maximization problem with that of the social planner s problem. Match the consumption and labor effort levels using lump sum transfers.

7 Economic Environment and Preferences Agents can be of two ability-types, θ {θ L, θ H } Ability is private information. F (θ),the distribution of ability across the population is known: f (θ H ) = π, f (θ L ) = (1 π) Preferences and production technology: for i = 1, 2: W (c i, l i ) = U(c i ) V (l i ) y i = θ i l i

8 Tax Avoidance g(y, x) is the cost of employing the least expensive tax avoidance channel at an agent s disposal by reporting x i 0 while earning y i 0: g(y, x) = min {h(y, x), r(y, x), e(y, x), s(y, x),...} g : R 2 + R +, and g(z, z) = 0 for any z R + - x is the reported income - g(y, x) is known. - y is realized income (private information).

9 Tax Avoidance Taxes can only be levied on reported income, x. Consumption for i {H, L}: c reported i = x i T (x i ) c private i = (y i x i ) g(y i, x i ) c i = y i g(y i, x i ) T (x i )

10 Social Planner s problem The Social Planner is uncertain about agents private productivity, but knows the ability distribution across the population. The Social Planner will maximize total expected utility, subject to a set of incentive compatibility constraints and a feasibility constraint.

11 Social Planner s problem The social planner solves, for i {H, L}: max π W (c H, l H ) + (1 π) W (c L, l L ) c i,l i s.t c i = y i g(y i, x i ) T (x i ) y i = θ i l i Feasibility Constraint & Incentive Constraints

12 Social Planner s problem Plugging in for consumption and labor: max y i,x i,t (x i ) π[u(y H g(y H, x H ) T (x H )) V (y H /θ H )] +(1 π)[u(y L g(y L, x L ) T (x L )) V (y L /θ L )]

13 Social Planner s problem Plugging in for consumption and labor: max y i,x i,t (x i ) π[u(y H g(y H, x H ) T (x H )) V (y H /θ H )] +(1 π)[u(y L g(y L, x L ) T (x L )) V (y L /θ L )] Feasibility constraint: ReportedConsumption {}}{ π[x H T (x H )] + (1 π)[x L T (x L )] = or πt (x H ) + (1 π)t (x L ) = 0 ReportedIncome {}}{ πx H + (1 π)x L

14 Social Planner s problem Incentive Compatibility Constraints: 1 Report Constraint:Agents don t misreport their income by reporting the other agent s income, for i j: U(y i g(y i, x i ) T (x i )) V (y i /θ i ) U(y i g(y i, x j ) T (x j )) V (y i /θ i )

15 Social Planner s problem Incentive Compatibility Constraints: 2 Labor Constraint:Agents don t mimic to be the other type s labor choice, and report their income correctly for i j: U(y i g(y i, x i ) T (x i )) V (y i /θ i ) U(y j g(y j, x j ) T (x j )) V (y j /θ i )

16 Social Planner s problem Incentive Compatibility Constraints: 3 Double Deviation Constraint:Agents don t mimic to be the other type s labor choice and misreport their income, for i j: U(y i g(y i, x i ) T (x i )) V (y i /θ i ) U(y j g(y j, x i ) T (x i )) V (y j /θ i )

17 Social Planner s problem Incentive Compatibility Constraints: 1 Report Constraint:Agents don t misreport their income by reporting the other agent s income, for i j: U(y i g(y i, x i ) T (x i )) V (y i /θ i ) U(y i g(y i, x j ) T (x j )) V (y i /θ i ) 2 Labor Constraint:Agents don t mimic to be the other type s labor choice, and report their income correctly for i j: U(y i g(y i, x i ) T (x i )) V (y i /θ i ) U(y j g(y j, x j ) T (x j )) V (y j /θ i ) 3 Double Deviation Constraint:Agents don t mimic to be the other type s labor choice and misreport their income, for i j: U(y i g(y i, x i ) T (x i )) V (y i /θ i ) U(y j g(y j, x i ) T (x i )) V (y j /θ i )

18 Non-Falsification Non-Falsification theorem Let Γ = { yi, xi, T (xi ) } be the solution to the social planner s problem. i=h,l Then for i {H, L}, yi = xi g(yi, xi ) = 0. Proof(sketch) Suppose there is an optimal allocation which involves income falsification Γ = {y i, x i, T (x i )} i=h,l. There is always a welfare enhancing lump sum transfer T (x i ) so that: - The agent with the false report is indifferent between tax avoidance and truthfully reporting. - T (xi ) > T (x i ) No functional form restrictions! Greatly simplifies the problem by eliminating one decision variable.

19 Simplifying the problem Corollary 1 (Redistributive Limits) If y i = x i for i {H, L}, then the labor constraint is reduced to: T (y i ) T (y j ) g(y i, y j ) for i j. This sets a upper bound on possible taxation alternatives, and restricts the social planner s ability to redistribute income.

20 Simplifying the problem Corollary 2 (Single deviation constraint dominance) If the condition in Corollary 1 is satisfied, then the labor constraint dominates the double deviation constraint for every choice of y i.

21 Simplifying the problem Corollary 3 (Downward Binding Constraints) 1 When non-falsification holds, and the objective function is concave, then T (y H ) 0 and T (y L ) 0, and the report constraint for the low ability type agents never bind. T (y l )/(π) g(y L, y H ) 2 The single crossing property guarantees that only the high ability type agent s labor constraint bind.

22 Social Planner s problem The social planner solves, for i {H, L}: max π [ U ( y H T (y H ) ) V ( )] [ ( y H /θ H + (1 π) U yl T (y L ) ) V ( )] y L /θ L y i,t (y i ) s.t. [λ] πt (y H ) + (1 π)t (y L ) = 0 [γ] [µ] g(y H y L U ( y H T (y H ) ) V ( ) y H /θ H T ( (y H ) T (y L U yl T (y L ) ) V ( ) y L /θ H

23 A tale of two costs Assume that the utility function is quasi-linear W (c i, l i ) = c i V (l i ).

24 A tale of two costs Assume that the utility function is quasi-linear W (c i, l i ) = c i V (l i ). Assume the cost of avoidance is a fixed proportion of sheltered income η y H y L.

25 A tale of two costs Assume that the utility function is quasi-linear W (c i, l i ) = c i V (l i ). Assume the cost of avoidance is a fixed proportion of sheltered income η y H y L. Under these assumptions the two incentive constraints can be written as: (y H y L ) [V (y H /θ H V (y L /θ H )] T (y H ) T (y L ) η y H y L T (y H ) T (y L )

26 A tale of two costs (yh yl) [V (yh/θh) V (yl/θh)] η(yh yl) yl y H yh ˆ Figure: Incentive constraints with quasi-linear utility, θ H = 11, θ L = 10

27 A tale of two costs The constraints can be written as a cost of avoidance for the agents { Cost }} { { Benefit }} { y H y L }{{} (V (y H /θ H ) V (y L /θ H )) T (y H ) + T (y L ) }{{} = χ labor 0 Consumption Labor η y H y L T (y H ) + T (y L ) }{{}}{{} Cost Benefit = χ report 0

28 Solution The solution to the social planner s problem Γ = ( y H, y L, T (y H ), T (y L )) satisfies the Kuhn-Tucker necessary conditions: 1 γ > 0, µ = 0, and the report constraint binds, but the labor constraint does not - Region 1 2 γ > 0, µ > 0, and the report and labor constraint bind - Region 2 3 γ = 0, µ = 0, and the labor constraint binds, but the report constraint does not - Region 3 4 γ = 0, µ = 0,does not satisfy optimality conditions.

29 Solution There is a closed form solution for marginal taxes in each constrained region. If g y H (0, 1) and g y L ( 1, 0) and they exists at the optimum: 1 Region 1 : ( MRS H = 1 + (1 π)g y U ) L H U H 1 = (1 τ H ) > 1 ) MRS L = 1 + πg y L (1 U H U = (1 τ L ) < 1 L

30 Solution There is a closed form solution for marginal taxes in each constrained region. If g y H (0, 1) and g y L ( 1, 0) and they exists at the optimum: 2 Region 2: MRS H = MRS L = ( 1 + (1 π)g y (1 π µ)πu L H 1 π µ 1 π µ V H θ L V L θ H (π+µ)(1 π)u H ) 1 > 1 [ 1 + πg y L (1 (π+µ)(1 π)u H (1 π µ)πu L )] < 1

31 Solution There is a closed form solution for marginal taxes in each constrained region. If g y H (0, 1) and g y L ( 1, 0) and they exists at the optimum: 1 Region 1 : 2 Region 2: MRS H = MRS L = ( MRS H = 1 + (1 π)g y U ) L H U H 1 = (1 τ H ) > 1 ) MRS L = 1 + πg y L (1 U H U = (1 τ L ) < 1 L ( 1 + (1 π)g y (1 π µ)πu L H 1 π µ 1 π µ V H θ L V L θ H (π+µ)(1 π)u H ) 1 > 1 [ 1 + πg y L (1 (π+µ)(1 π)u H (1 π µ)πu L )] < 1

32 Solution There is a closed form solution for marginal taxes in each constrained region. If g y H (0, 1) and g y L ( 1, 0) and they exists at the optimum: 3 Region 3: MRS H = 1 1 π µ MRS L = 1 π µ V H < 1 θ L V L θ H

33 Solution There is a closed form solution for marginal taxes in each constrained region. If g y H (0, 1) and g y L ( 1, 0) and they exists at the optimum: 2 Region 2: MRS H = MRS L = 3 Region 3: ( 1 + (1 π)g y (1 π µ)πu L H 1 π µ 1 π µ V H θ L V L θ H (π+µ)(1 π)u H ) 1 > 1 [ 1 + πg y L (1 (π+µ)(1 π)u H (1 π µ)πu L MRS H = 1 1 π µ MRS L = 1 π µ V H < 1 θ L V L θ H )] < 1

34 Solution There is a closed form solution for marginal taxes in each constrained region. If g y H (0, 1) and g y L ( 1, 0) and they exists at the optimum: 1 Region 1 : 2 Region 2: MRS H = MRS L = 3 Region 3: ( MRS H = 1 + (1 π)g y U ) L H U H 1 = (1 τ H ) > 1 ) MRS L = 1 + πg y L (1 U H U = (1 τ L ) < 1 L ( 1 + (1 π)g y (1 π µ)πu L H 1 π µ 1 π µ V H θ L V L θ H (π+µ)(1 π)u H ) 1 > 1 [ 1 + πg y L (1 (π+µ)(1 π)u H (1 π µ)πu L MRS H = 1 1 π µ MRS L = 1 π µ V H < 1 θ L V L θ H )] < 1

35 Numerical Exercises Functional form for Utility: U(c) V (l) = c1 γ 1 1 γ α l σ σ - σ = 3 - the elasticity of labor supply is ɛ c = 1 1 σ = α = to match the average percentage of hours that are spent on work from the NLSY - γ = 1.5 Functional form for the cost of tax avoidance: θ i will be represented by hourly wages. η y H y L

36 Welfare and MRS 1.8 γ=0 and µ(θ H )>0 γ>0 and µ(θ H )=0 γ>0, µ(θ H )> W W L 1.2 W H ω H (η) ω L (η) η RC η IC η

37 Income and Consumption y L y H T(y H ) T(y L ) c H c L 5 0 γ=0 and µ(θ H )>0 γ>0, µ(θ H )>0 γ>0 and µ(θ H )= η RC η IC η

38 Indifference avoidance costs γ=0 and µ(θ H )> η e 0.64 γ>0 and µ(θ H )> η γ>0 and µ(θ H )= θ, θ L =10

39 Conclusions 1 In the case of the US, the Federal Government uses marginal tax brackets to collect income tax revenue. In such system, the taxpayer s behavior to minimize their tax burden depends on these discrete tiers. Individuals must deviate in their income report, or labor market choices by an amount large enough to place them in a lower income bracket. Thus, a discrete model captures relevant characteristics of the environment where individuals make decisions about tax avoidance. 2 Where there is information asymmetry and moral hazard, and individuals have tax avoidance opportunities: Three constrained regions, which inform empirical observations about the elasticity of taxable income to changes in marginal taxes Negative marginal taxes can collect larger revenues and increase welfare where tax avoidance opportunities are abundant. Soft cap on marginal taxes for high income individuals.

40 Future Work Tax payers have different costs of tax avoidance. Voluntary percentage for wages and salaries is 99.5%, but only 41.4% for self-employment income (IRS s Taxpayer Compliance Measurement Program). Welfare and tax incidence depends on tax avoidance opportunities. We observe tax avoidance in the real world, at the optimum this model does not have any tax avoidance. Working on a model with positive tax avoidance.