Politico Economic Consequences of Rising Wage Inequality

Transcription

1 Politico Economic Consequences of Rising Wage Inequality Dean Corbae Pablo D Erasmo Burhan Kuruscu University of Texas at Austin and University of Maryland February 8, 2010

2 Increase in Wage Inequality (PSID) Coefficient of Variation Hourly Wage Rate Year

3 Decrease in Median To Mean Wages (PSID) Median to Mean Ratio of Hourly Wage Rate Year

4 Increase in Redistribution (CBO) Normalized Effective Federal Tax Rate by Quintile for Young Year Definition of ETR

5 Question What are the quantitative implications of rising wage inequality and declining median to mean wages for changes in effective tax rates by quintiles in the U.S.?

6 What we do Apply the sequential majority voting equilibrium concept of Krusell, Quadrini and Rios Rull (1997) in a neoclassical growth model with no aggregate uncertainty but uninsurable, idiosyncratic risk. With incomplete markets, rising wage dispersion generates more individual consumption dispersion and an increased role for government insurance (transfer) programs. Quantitative Exercise: contrast equilibrium effective tax rates by income quintile in a low inequality regime versus those of a high inequality regime.

7 Environment Unit measure of ex-ante identical, infinitely lived hhs. Preferences: E [ t=0 βt u(c t, n t )], where u(c t, n t ) = 1 ] [c t χ n1+1/ν 1 γ t (1) 1 γ 1 + 1/ν Each hh is subject to an uninsurable, idiosyncratic labor productivity shock ɛ t which evolves according to a markov process Π(ɛ t+1 = ɛ ɛ t = ɛ). Technology: Y t = Kt α Nt 1 α where uppercase letters denote aggregate variables and capital depreciates at rate δ. Government taxes capital and labor income at the same proportional rate, τ t, consumes G t and provides lump-sum transfers T t.

8 Aggregates Joint distn of capital and earnings across agents denoted Γ t (k, ɛ) with law of motion Γ t+1 = H(Γ t, τ t ). Aggregate capital stock K t = k t dγ t (k, ɛ) and aggregate labor N t = n t ɛ t dγ t (k, ɛ). Perfect competition in factor markets implies r t w t = αkt α 1 Nt 1 α δ = (1 α)kt α Nt α. Government budget constraint: G t + T t = τ t [r t K t + w t N t ]. Law of motion for taxes given by: τ t+1 = Ψ(Γ t, τ t )

9 Recursive Representation of hh problem s.t. V (k, ɛ; Γ, τ) = max c,n,k b u(c, n) + β ɛ Π(ɛ ɛ)v (k, ɛ ; Γ, τ ) (2) c + k = k + [r(k)k + nw(k)ɛ] (1 τ) + T Γ = H(Γ, τ) τ = Ψ(Γ, τ) The solution to the individual s problem: n = η(k, ɛ; Γ, τ), c = q(k, ɛ; Γ, τ) and k = h(k, ɛ; Γ, τ).

10 Definition RCE (taxes given) Definition (RCE). Given Ψ(Γ, τ), a Recursive Competitive Equilibrium is a set of functions {V, η, q, h, Γ, H, r, w, T } such that: (i) Given (Γ, τ, H, Ψ), the functions V ( ), η( ), q( ) and h( ) solve the hh s problem in (2); (ii) Prices are competitively determined. (iii) The resource constraint is satisfied q(k, ɛ; )dγ(k, ɛ) + G + K = K α N 1 α + (1 δ)k; (iv) The government budget constraint is satisfied (v) H(Γ, τ) is given by Γ (k, ɛ ) = 1 {h(k,ɛ;γ,τ)=k }Π(ɛ ɛ)dγ(k, ɛ).

11 Evaluating alternative tax choices Consider a one period deviation where τ is set arbitrarily while all future tax rates are still given by Ψ. HH s problem is given by s.t. Ṽ (k, ɛ, Γ, τ, τ ) = max u(c, n) + βe c,n,k ɛ ɛ [V (k, ɛ, Γ, τ )] (3) b c + k = k + [r(k)k + nw(k)ɛ] (1 τ) + T Γ = H (Γ, τ, τ ) where H denotes law of motion for Γ induced by the deviation, while all future distns evolve using H. Figure k Future V is given by soln to hh problem in (2) of the defn of RCE.

12 Evaluating alternative tax choices (cont.) Policy outcomes evolution of the wealth distribution (both on and off the equilibrium path). Γ = H (Γ, τ, τ ) ( Γ = H H (Γ, τ, τ ), τ ) [ ( Γ = H H H (Γ, τ, τ ), τ ) (, Ψ H (Γ, τ, τ ), τ )]... Aiyagari and Peled (1995, JEDC) restricted off-the-equilibrium outcomes to be steady states. Assumed Γ = Γ (τ ). Similar to Krusell and Smith (1998 JPE) we approximate the distribution with a finite set of moments (mean and median matter). Functions

13 Definition PRCE (Endogenous Taxes) A Politico-Economic Recursive Competitive Equilibrium: (i) {V, η, q, h, H, Ψ, r, w, T } satisfies the definition of a RCE; (ii) For each τ, {Ṽ, ñ, q, h} solves (3) and is a RCE with continuation values satisfying (i); (iii) in individual state (k, ɛ) i, hh i s most preferred tax policy τ i satisfies τ i = ψ(k, ɛ, Γ, τ) = arg max Ṽ ((k, ɛ) i, Γ, τ, τ ); (4) τ (iv) the policy outcome function τ m = Ψ(Γ, τ) satisfies I {(k,ɛ):τ i τ m }dγ(k, ɛ) 1 2 and I {(k,ɛ):τ i τ m }dγ(k, ɛ) 1 2. If preferred tax rates are sorted and the median chosen out of that set, then the median tax rate is preferred to any other feasible tax rate in a pairwise vote by all agents provided Ṽ is single peaked over τ.

14 0.5 ψ(k,ε 1 ;Γ,τ) ψ(k,ε 2 ;Γ,τ) 0.45 ψ(k,ε 3 ;Γ,τ) ψ(k,ε 4 ;Γ,τ) ψ(k,ε 5 ;Γ,τ) 0.4 ψ(k,ε;γ,τ) wealth (k) Figure: Most Preferred Tax Rate. Return

15 28 k median, ε 1 29 k median, ε 2 k median, ε 3 k median, ε 4 30 k median, ε 5 Indirect Utility τ Figure: Single Peaked Preferences Ṽ ((k, ɛ)i, Γ79, τ79, τ ).

16 Definition: Steady State Equilibrium. Definition (SSPRCE). A Steady State PRCE is a PRCE which satisfies Γ = H(Γ, τ ) and τ = Ψ(Γ, τ ).

17 Sequential Utilitarian Planner sequentially chooses a future tax rate to maximize aggregate welfare: Ψ u (Γ, τ) = arg max Ṽ (k, ɛ, Γ, τ, τ )dγ(k, ɛ). τ with all continuation values evaluated according to the equilibrium function (e.g. τ = Ψ un (Γ, τ )).

18 Median Voter with commitment One time median voting: Median voter chooses a constant future tax rate: Ψ O (Γ, τ) = arg max τ Ṽ ((k, ɛ) m, Γ, τ, τ ) with all continuation values evaluated according to the identity function (e.g. τ = Ψ(Γ, τ ) = τ Γ, τ ). This restricts only the evolution of tax rates - the evolution the distn is still given by H(Γ, τ). It is still necessary to compute the entire transition (of prices) to evaluate each possible tax change. Transitions Γ = H (Γ, τ, τ ) ( Γ = H H (Γ, τ, τ ), τ ) [ ( Γ = H H H (Γ, τ, τ ), τ ), τ ]

19 Parametrization Table: Preferences and Technology Parameters. Parameter Value Discount Factor β 0.96 Preferences γ 1 ν 0.3 χ 100 Borrowing Constraint b 0 Capital Share α 0.36 Depreciation Rate δ 0.06

20 Parametrization: Labor Productivity Since tax data is for quintiles, we let wɛ i be average wage of individuals in quintile i. We use the PSID data to calibrate the levels and obtain the annual mobility matrices for 1978/79 (the low inequality regime) and 1995/96 (the high inequality regime). Matrices Selection Criterion (similar to Heathcote, Storesletten and Violante (2006)): restrict our sample to all hh heads who are between ages 20 and 59 with annual hours less than 5096 who are in the sample for both 1978/79 and 1995/96. Selection criterion yields an increase in the coefficient of variation from 0.93 in 1979 to 1.19 in 1996 while the median to mean ratio declines from 0.87 to More Tests

21 Mobility and Inequality Interpretation Autoregressive representation of the data log(ɛ t+1 ) = ρ log(ɛ t ) + u t+1, where u t+1 is iid mean zero and variance given by (1 ρ 2 )σ 2 where σ 2 var(log(ɛ t+1 )). Table: Autoregressive Representation % ρ σ This suggests that mobility, as measured by ρ, has risen slightly while inequality, as measured by σ 2, has risen substantially.

22 Government Parameters Government Parameters: G includes spending like defense and social security transfers. G 1979 /Y 1979 = 14.3% and G 1996 /Y 1996 = 12.3%. Transfers are distributed as income tax credit Υ and pure transfers T f T = Υ + T f = φt + (1 φ)t (5) Letting I = (rk + wɛ)dγ(k, ɛ), effective tax rates are: e = τi Υ I + T f. (6) We choose φ = 0.01 to match the ratio of total EITC to GDP in 1996 (φt/y ).

23 Good Approximation to a Progressive Tax System The model s simple assumption of a constant marginal tax rate and lump-sum transfer implies the effective tax rate in (6) is progressive (i.e. increases with income). Then the effective tax rate in (6) for quintile q can be re-written as e q = a + b where a = τ and b = ( τt f + Υ ). 1 I q + T f, (7) That is, a system with a constant marginal tax rate a and a fixed deduction b.

24 Good Approximation to a Progressive Tax System (cont.) Following Krueger and Perri (2005) we can regress effective tax rate data on I q + T f for each quintile in a given year t to yield estimates of â t and b t Table: Estimated Tax System YearEstimates â t bt R (0.017) (536) (0.017) (551) The high R 2 leads Krueger and Perri to state the progressive tax system... is almost perfectly approximated by a tax system with a constant marginal tax rate and a fixed deduction (our lump sum transfer).

25 Answer: Effective Tax Rates by Income Quintile Effective Tax Rates % quintile Data quintile quintile quintile quintile Seq. Median Voter quintile quintile quintile quintile Seq. Utilitarian quintile quintile quintile

26 Decomposition of Effective Tax Changes Due Only to changes in income With a progressive tax system, a change in the wage process could induce a change in effective tax rates by itself. Using estimates from the data we can compute a counterfactual e q,inc 1996 = â b 1979 /(I q T f 1979 ). Using the model, we can compute a counterfactual SSRCE for the 1996 wage parameterization using the 1979 tax rate τ 79 Take ratio of counterfactual to total % in effective tax rates: Income Quintiles K-P Estimates Sequential Utilitarian quintile 1 56% 72% 101% quintile 2 39% 60% 99% quintile 4 35% 57% 100% quintile 5 29% 62% 101%

27 Tax Choice Heterogeneity Previous models without uninsurable idiosyncratic uncertainty (e.g. Krusell and Rios Rull (1999)) predict 100% and 0%. Agents with lower wealth than median voter Agents with higher wealth than median voter % Fraction of agents (%) % 38% Fraction of agents (%) % 0 voting for higher taxes than median voter voting for lower taxes than median voter 0 voting for higher taxes than median voter voting for lower taxes than median voter

28 Mobility vs Inequality Changes in mobility (i.e changes in ρ): We compare the main results of our model with commitment to one where we solve for an equilibrium using E 1979 and Π 1996 (σ 2 remains virtually unchanged but ρ decreases by 2.6%). Changes in inequality (i.e changes in σ 2 ): We compare the results with one where we solve for an equilibrium using Π 1979 and E 1996 (ρ remains constant, but σ 2 increases by 33%). Income Quintiles Total % % from mobility % from inequality quintile quintile quintile quintile

29 Normative Findings: The Value of Commitment In a given environment, how much are agents willing to pay for commitment? We find taxes are lower with commitment than without Commitment is more valuable in high wage inequality regimes. Table: Welfare Value of Commitment Mechanism Environment W (%) Median Voter Low Inequality (1979) High Inequality (1996) Utilitarian Low Inequality (1979) High Inequality (1996) 0.356

30 Median Voter with commitment One time median voting: Median voter chooses a constant future tax rate: Ψ O (Γ, τ) = arg max τ Ṽ ((k, ɛ) m, Γ, τ, τ ) with all continuation values evaluated according to the identity function (e.g. τ = Ψ(Γ, τ ) = τ Γ, τ ). This restricts only the evolution of tax rates - the evolution the distn is still given by H(Γ, τ). It is still necessary to compute the entire transition (of prices) to evaluate each possible tax change. Transitions Γ = H (Γ, τ, τ ) ( Γ = H H (Γ, τ, τ ), τ ) [ ( Γ = H H H (Γ, τ, τ ), τ ), τ ] return

31 Transitions to Steady State 2.5 τ = 0.18 τ = 0.25 τ = τ = τ = 0.40 τ = Aggregate Capital (K) Time Periods Figure: Transitions at initial steady state τ Return

32 The Value of Commitment. Fraction of Agents (%) ε 1 ε 2 ε 3 ε 4 ε Consumption Equivalent λ (%) return

33 Conclusion First paper to incorporate idiosyncratic uncertainty without arbitrary restrictions on off-the-equilibrium-path behavior into a dynamic, incomplete markets model where taxes are chosen by a median voter. Despite a one dimensional tax choice (necessary for median voter results), our progressive tax system fits the data well. Sequential median voter model is able to predict roughly half of the increase in redistribution to households in the lowest wage quintiles as a consequence of exogenous changes in the wage process. Since the mobility matrices we construct from the data underestimate the coefficient of variation of wages, it is not surprising that we underpredict redistribution.

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35 The effective tax rate measures the percentage of household income going to the federal government from taxes. The income measure is comprehensive household income, which comprises pretax cash income plus income from other sources. Pretax cash income is the sum of wages, salaries, self-employment income, rents, taxable and nontaxable interest, dividends, realized capital gains, cash transfer payments, and retirement benefits plus taxes paid by businesses (corporate income taxes; the employer s share of Social Security, Medicare, and federal unemployment insurance payroll taxes); and employees contributions to 401(k) retirement plans. Other sources of income include all in-kind benefits (Medicare, Medicaid, employer-paid health insurance premiums, food stamps, school lunches and breakfasts, housing assistance, and energy assistance). Households with negative income are excluded from the lowest income category but are included in totals. Return

36 0.1 h(k,ε 3 ;Γ,τ,τ =0.1825) k h(k,ε 3 ;Γ,τ,τ = ) k 0.05 h(k,ε 3 ;Γ,τ,τ = ) k h(k,ε 3 ;Γ,τ,τ = ) k h(k,ε;γ,τ,τ ) k wealth (k) Figure: Decision rules over wealth for different levels of τ. Return

37 Transitions to Steady State 2.5 τ = 0.18 τ = 0.25 τ = τ = τ = 0.40 τ = Aggregate Capital (K) Time Periods Figure: Transitions at initial steady state τ Return

38 Utilitarian with commitment One time utilitarian solution: Planner chooses a future constant tax rate to maximize aggregate welfare: Ψ uc (Γ, τ) = arg max Ṽ (k, ɛ, Γ, τ, τ )dγ(k, ɛ). τ with all continuation values evaluated according to the identity function (e.g. τ = Ψ(Γ, τ ) = τ Γ, τ ). Again, still necessary to compute transition as above. return

39 Effective Tax Rates by Income Quintile Effective Tax Rates Quintiles Normalized % Q1 (lowest) Q Data Q3 (middle) Q Q5 (highest) quintile One-time Median Voter quintile quintile quintile Average level quintile One-time Utilitarian quintile quintile quintile return

40 Income Inequality by Income Quintiles: Data vs Model Table: Income Inequality by Income Quintiles Measures (hh s sorted by Income Quintile) Data Model Ratio Average Income to Middle Quintile Top 10% to Middle Quintile First Quintile (Lowest) to Middle Quintile Second Quintile to Middle Quintile Fourth Quintile to Middle Quintile Fifth Quintile (Highest) to Middle Quintile Gini Wealth return

41 Equilibrium Functions Law of motion of aggregate capital, function H K = a 0 + a 1 K + a 2 z m + a 3 τ (8) Law of motion of median total resources, function J z m = b 0 + b 1 K + b 2 z m + b 3 τ (9) Law of motion of taxes, function Ψ τ = d 0 + d 1 K + d 2 z m + d 3 τ (10) where z i = k + [r(k)k + w(k)ɛ i ] (1 τ) + T Return

42 Computed Equilibrium: Final SS. Variable K z τ Constant (3.45e-08) (6.10e-05) (2.87e-05) K (9.41e-07) (1.66e-04) (9.20e-05) z -1.21e (1.34e-07) (2.36e-04) (1.30e-04) τ -7.15e e e-02 (6.73e-08) (1.19e-04) (4.97e-05) R Table: Equilibrium Laws of Motion Return

43 Median is important Variable K τ Constant (9.17e-07) (1.35e03) K (2.93e-07) (4.44e-04) τ -7.88e (4.12e-06) (6.10e-03) τ K 5.50e (1.31e-03) (2.00e-03) R Table: Imperfect Equilibrium Laws of Motion the goodness of fit (measured by R 2 ) falls substantially for the law of motion of taxes (10). Return

44 Wage Process 1978/79 Table: Transition Matrix for ɛ 1 ɛ 3 ɛ 3 ɛ 4 ɛ 5 ɛ 1 (2.60) ɛ 2 (9.01) ɛ 3 (13.42) ɛ 4 (18.52) ɛ 5 (35.43) Return

45 Wage Process 1995/96 Table: Transition Matrix for ɛ 1 (1.75) ɛ 2 (7.92) ɛ 3 (11.90) ɛ 4 (17.03) ɛ 5 (35.98) Return

46 Preferred Tax Rates Summarize the tax choice of a typical agent as follows: 1. ψ(k, ɛ, Γ, τ) is decreasing in ε; i.e. hh s with lower wages choose higher taxes. 2. ψ(k, ɛ, Γ, τ) is decreasing in k; i.e. hh s with lower wealth choose higher taxes. 3. There may be hh s with different wealth and wages who choose the same taxes. Return