Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Politico Economic Consequences of Rising Wage Inequality Dean Corbae
Pablo D’Erasmo
Burhan Kuruscu
University of Texas at Austin
June 7, 2008
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Increase in Wage Inequality (PSID) 1.3
Coefficient of Variation Hourly Wage Rate
1.2
1.1
1
0.9
0.8
1970
1975
1980
1985
1990
1995
Year
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Decrease in Median To Mean Wages (PSID) 0.94
Median to Mean Ratio of Hourly Wage Rate
0.92
0.9
0.88
0.86
0.84
0.82
0.8
0.78
0.76
1970
1975
1980
1985
1990
1995
Year
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Increase in Redistribution (CBO) Normalized Effective Federal Tax Rate by Quintile for Young 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
1980
1985
1990 Year
1995
2000
Definition of ETR
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
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.?
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
What we do
I
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.
I
With incomplete markets, rising wage dispersion generates more individual consumption dispersion and an increased role for government insurance (transfer) programs.
I
Quantitative Exercise: contrast equilibrium effective tax rates by income quintile in a low inequality regime versus those of a high inequality regime.
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Environment I
Unit measure of ex-ante identical, infinitely lived hhs.
I
P∞ Preferences: E [ t=0 β t u(ct , nt )], where 1+1/ν
u(ct , nt ) =
i1−γ 1 h n ct − χ t 1−γ 1 + 1/ν
(1)
I
Each hh is subject to an uninsurable, idiosyncratic labor productivity shock t which evolves according to a markov process Π(t+1 = 0|t = ).
I
Technology: Yt = Ktα Nt1−α where uppercase letters denote aggregate variables and capital depreciates at rate δ.
I
Government taxes capital and labor income at the same proportional rate, τt , consumes Gt and provides lump-sum transfers Tt .
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Aggregates I
Joint distn of capital and earnings across agents denoted Γt (k, ) with law of motion Γt+1
I
I
= H(Γt , τt ). R Aggregate capital stock Kt = kt dΓt (k, ) and aggregate labor R Nt = nt t dΓt (k, ). Perfect competition in factor markets implies rt wt
I I
= αKtα−1 Nt1−α − δ = (1 − α)Ktα Nt−α .
Government budget constraint: Gt + Tt = τt [rt Kt + wt Nt ] . Law of motion for taxes given by: τt+1
Politico Economic Consequences of Rising Wage Inequality
=
Ψ(Γt , τt ) Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Recursive Representation of hh problem V (k, ; Γ, τ ) =
max 0
c,n,k ≥−b
u(c, n) + β
X
Π(0 |)V (k 0 , 0 ; Γ0 , τ 0 )
(2)
0
s.t. c + k0 Γ0 τ0
= k + [r(K)k + nw(K)] (1 − τ ) + T = H(Γ, τ ) = Ψ(Γ, τ )
The solution to the individual’s problem: n = η(k, ; Γ, τ ), c = q(k, ; Γ, τ ) and k 0 = h(k, ; Γ, τ ). Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
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 Z q(k, ; ·)dΓ(k, ) + G + K 0 = K α N 1−α + (1 − δ)K; (iv) The government budget constraint is satisfied (v) H(Γ, τ ) is given by Z Γ0 (k 0 , 0 ) = 1{h(k,;Γ,τ )=k0 } Π(0 |)dΓ(k, ).
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Evaluating alternative tax choices I
Consider a one period deviation where τ 0 is set arbitrarily while all future tax rates are still given by Ψ.
I
HH’s problem is given by Ve (k, , Γ, τ, τ 0 ) =
max
c,n,k0 ≥−b
u(c, n) + βE0| [V (k 0 , 0 , Γ0 , τ 0 )]
(3)
s.t. c + k0 Γ
I
0
= k + [r(K)k + nw(K)] (1 − τ ) + T e (Γ, τ, τ 0 ) = H
˜ denotes law of motion for Γ induced by the deviation, where H while all future distns evolve using H. Figure k0 Future V is given by soln to hh problem in (2) of the defn of RCE.
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Evaluating alternative tax choices (cont.) I
Policy outcomes ⇔ evolution of the wealth distribution (both on and off the equilibrium path). Γ0 Γ00 Γ000
I
I
e (Γ, τ, τ 0 ) = H e (Γ, τ, τ 0 ) , τ 0 = H H h i e (Γ, τ, τ 0 ) , τ 0 , Ψ H e (Γ, τ, τ 0 ) , τ 0 = H H H ...
Aiyagari and Peled (1995, JEDC) restricted off-the-equilibrium outcomes to be steady states. Assumed Γ00 = Γ∗ (τ ∗ ). Similar to Krusell and Smith (1998 JPE) we approximate the distribution with a finite set of moments (mean and median matter). Functions
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
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 0 , {Ve , n e, qe, e h} solves (3) and is a RCE with continuation values satisfying (i); (iii) in individual state (k, )i , hh i0 s most preferred tax policy τ i satisfies τ i = ψ(k, , Γ, τ ) = arg max V˜ ((k, )i , Γ, τ, τ 0 ); 0 τ
(4)
(iv) the policy outcome function τ m = Ψ(Γ, τ ) satisfies Z Z 1 1 i m and I{(k,):τ i ≤τ m } dΓ(k, ) ≥ . I{(k,):τ ≥τ } dΓ(k, ) ≥ 2 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 Ve is single peaked over τ 0 . Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
0.5 ψ(k,ε1;Γ,τ) ψ(k,ε2;Γ,τ) ψ(k,ε3;Γ,τ)
0.45
ψ(k,ε4;Γ,τ) ψ(k,ε5;Γ,τ)
ψ(k,ε;Γ,τ)
0.4
0.35
0.3
0.25
0.2
0
1
2
3
4
5
6
7
wealth (k)
Figure: Most Preferred Tax Rate. Return Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
−28 kmedian , ε1 kmedian , ε2 kmedian , ε3
−29
kmedian , ε4 kmedian , ε5
Indirect Utility
−30
−31
−32
−33
−34
−35
0.2
0.25
0.3
τ′
0.35
0.4
0.45
0.5
Figure: Single Peaked Preferences V˜ ((k, )i , Γ79 , τ79 , τ 0 ).
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Definition: Steady State Equilibrium.
Definition (SSPRCE). A Steady State PRCE is a PRCE which satisfies Γ∗ = H(Γ∗ , τ ∗ ) and τ ∗ = Ψ(Γ∗ , τ ∗ ).
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Parametrization
Table: Preferences and Technology Parameters.
Parameter Discount Factor Preferences
Borrowing Constraint Capital Share Depreciation Rate
Politico Economic Consequences of Rising Wage Inequality
β γ ν χ b α δ
Value 0.96 1 0.3 100 0 0.36 0.06
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Parametrization: Labor Productivity I
Since tax data is for quintiles, we let wi be average wage of individuals in quintile i.
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
I
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.
I
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 0.79. More Tests
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Parametrization: Labor Productivity (cont.) I
Autoregressive representation of the data log(t+1 ) = ρ log(t ) + ut+1 , where ut+1 is iid mean zero and variance given by (1 − ρ2 )σ 2 where σ 2 ≡ var(log(t+1 )). Table: Autoregressive Representation
ρ σ2 I
1979 0.77 0.75
1996 0.75 1.01
%∆ −2.6 35.0
This suggests that “mobility”, as measured by ρ, has risen slightly while “inequality”, as measured by σ 2 , has risen substantially.
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Government Parameters I
Government Parameters: G includes spending like defense and social security transfers. G1979 /Y1979 = 14.3% and G1996 /Y1996 = 12.3%.
I
Transfers are distributed as income tax credit Υ and pure transfers Tf T = Υ + T f = φT + (1 − φ)T (5)
I
The “effective tax rate” is: R τ (rk + w)dΓ(k, ) − Υ e= R . (rk + w)dΓ(k, ) + T f
I
(6)
We choose φ = 0.01 to match the ratio of total EITC to GDP in 1996 (φT /Y ).
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Progressive Tax System I
Equation (6) implies that the effective tax rate in our model increases with income.
I
R Let (rk + nw)dΓq (k, ) = I q be the pre-tax, pre-transfer average income for quintile q. The effective tax rate for quintile q can be written as 1 , (7) eq = a + b · q I + Tf where a = τ and b = − τ T f + Υ .
I
A system with a constant marginal tax rate a and a fixed deduction b.
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Progressive Tax System I
Following Krueger and Perri we regress effective tax rate data on pre-tax, post-transfer average income for each quintile in a given year t, yielding estimates of b at and bbt Table: Estimated Tax System
YearEstimates 1979 1996
I
b at 0.2672
bbt −3059
(0.017)
(536)
0.2725
−3667
(0.017)
(551)
R2 0.92 0.94
The high R2 leads Krueger and Perri to state “the progressive tax system used in the last section (which is similar to ours) is almost perfectly approximated by a tax system with a constant marginal tax rate and a fixed deduction.”
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Answer: Effective Tax Rates by Income Quintile Effective Tax Rates Data
Seq. Median Voter
Seq. Utilitarian definition
Politico Economic Consequences of Rising Wage Inequality
quintile quintile quintile quintile quintile quintile quintile quintile quintile quintile quintile quintile
1 2 4 5 1 2 4 5 1 2 4 5
1979 0.499 0.823 1.116 1.383 0.578 0.878 1.084 1.194 0.560 0.870 1.065 1.212
1996 0.320 0.776 1.117 1.454 0.491 0.848 1.113 1.271 0.498 0.851 1.109 1.261
%∆ -35.91 -5.76 0.05 5.08 -15.04 -3.48 2.60 6.43 -11.01 -2.17 1.52 4.05
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
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Positive Findings
Conclusion
Decomposition of Effective Tax Changes Due Only to changes in income I
I
With a progressive tax system, a change in the wage process could induce a change in effective tax rates by itself. Using the data we can compute f q ). + T1979 a1979 + bb1979 /(I1996 eq,inc 1996 = b
I
I
From the model we compute SS RCE for 1996 wage parameterization using τ79 Take ratio of counterfactual to total %∆ in effective tax rates: Income Quintiles quintile 1 quintile 2 quintile 4 quintile 5
K-P Estimates 56% 39% 35% 29%
Politico Economic Consequences of Rising Wage Inequality
Sequential 72% 60% 57% 62%
Utilitarian 101% 99% 100% 101%
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Tax Choice Heterogeneity I
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
100
100
90
90
80
80
91 %
70 62%
60
50 38%
40
Fraction of agents (%)
Fraction of agents (%)
70
60
50
40
30
30
20
20
10
10
0
voting for voting for higher taxes lower taxes than median than median voter voter
Politico Economic Consequences of Rising Wage Inequality
0
9%
voting for voting for higher taxes lower taxes than median than median voter voter
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Mobility vs Inequality I
Changes in mobility (i.e changes in ρ): We compare main results of our model with one where we solve for an equilibrium using E1979 and Π1996 (σ 2 remains virtually unchanged but ρ decreases by 2.6%).
I
Changes in inequality (i.e changes in σ 2 ): We compare the results with one where we solve for an equilibrium using Π1979 and E1996 (ρ remains constant, but σ2 increases by 33%).
Income Quintiles quintile 1 quintile 2 quintile 4 quintile 5
Total %∆ -11.83 -2.34 1.65 4.25
Politico Economic Consequences of Rising Wage Inequality
%∆ from mobility -2.03 -0.33 0.28 0.87
%∆ from inequality -11.03 -2.34 1.61 3.86
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Conclusion I
The median voter model generates I
I
I
less change in redistribution in response to the rise in wage inequality than in the data; more redistribution than a utilitarian model or one with commitment after the increase in inequality.
To better match the data on redistribution across quintiles and the level of effective taxes may necessitate more progressivity in the tax schedule. tax system I
I I
I
For instance, agents could vote over the degree of progressivity ω in marginal tax τ˜(I) = τ I ω , a variant of Gouveia and Strauss (1994); currently our model has ω = 0 and people choose τ ; in the proposed case, τ could be calibrated to match the average effective tax rate; computationally this adds another fixed point problem in τ .
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Politico Economic Consequences of Rising Wage Inequality
Parametrization
Positive Findings
Conclusion
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
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
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
0.1 h(k,ε3;Γ,τ,τ′=0.1825) − k h(k,ε3;Γ,τ,τ′=0.25306) − k h(k,ε3;Γ,τ,τ′=0.28833) − k
h(k,ε;Γ,τ,τ′)−k
0.05
h(k,ε3;Γ,τ,τ′=0.32361) − k
0
−0.05
−0.1
0
2
4
6 wealth (k)
8
10
12
Figure: Decision rules over wealth for different levels of τ 0 . Return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Transitions to Steady State 2.5 τ′ = 0.18 τ′ = 0.25 τ′ = τ = 0.3415 τ′ = 0.40 τ′ = 0.47
Aggregate Capital (K)
2
1.5
1
0
10
20
30
40
50 60 Time Periods
70
80
90
100
Figure: Transitions at initial steady state τ Return Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Utilitarian with No-commitment
I
Planner sequentially chooses a future tax rate to maximize aggregate welfare: Z Ψu (Γ, τ ) = arg max Ve (k, , Γ, τ, τ 0 )dΓ(k, ). 0 τ
with all continuation values evaluated according to the equilibrium function (e.g. τ 00 = Ψun (Γ0 , τ 0 )). Return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Median Voter with commitment I
One time median voting: Median voter chooses a constant future tax rate: ΨO (Γ, τ ) = arg max Ve ((k, )m , Γ, τ, τ 0 ) 0 τ
with all continuation values evaluated according to the “identity” function (e.g. τ 00 = Ψ(Γ0 , τ 0 ) = τ 0 ∀Γ0 , τ 0 ). I
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 Γ0 Γ00 Γ000
e (Γ, τ, τ 0 ) = H e (Γ, τ, τ 0 ) , τ 0 = H H h i e (Γ, τ, τ 0 ) , τ 0 , τ 0 = H H H
return Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Utilitarian with commitment
I
One time utilitarian solution: Planner chooses a future constant tax rate to maximize aggregate welfare: Z uc Ψ (Γ, τ ) = arg max Ve (k, , Γ, τ, τ 0 )dΓ(k, ). 0 τ
I
with all continuation values evaluated according to the “identity” function (e.g. τ 00 = Ψ(Γ0 , τ 0 ) = τ 0 ∀Γ0 , τ 0 ). Again, still necessary to compute transition as above.
return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Effective Tax Rates by Income Quintile Effective Tax Rates
Data
One-time Median Voter
One-time Utilitarian
Quintiles Q1 (lowest) Q2 Q3 (middle) Q4 Q5 (highest) quintile 1 quintile 2 quintile 4 quintile 5 Average level quintile 1 quintile 2 quintile 4 quintile 5
Normalized 1979 0.4997 0.8233 1 1.1165 1.3839 0.614 0.893 1.071 1.163 0.338 0.602 0.889 1.075 1.173
%∆ 1996 0.320 0.776 1 1.117 1.454 0.541 0.873 1.089 1.212 0.331 0.538 0.871 1.090 1.216
-35.91 -5.76 0 0.05 5.08 -11.83 -2.34 1.65 4.25 2.08 -10.53 -1.96 1.37 3.66
return Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Income Inequality by Income Quintiles: Data vs Model Table: Income Inequality by Income Quintiles
Measures (hh’s sorted by Income Quintile) 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
Data 1.34 4.43 0.30 0.65 1.41 3.16 0.80
Model 1.24 2.80 0.46 0.74 1.35 2.63 0.51
return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Equilibrium Functions I
Law of motion of aggregate capital, function H K 0 = a0 + a1 K + a2 zm + a3 τ
I
Law of motion of median total resources, function J 0 zm = b0 + b 1 K + b 2 z m + b3 τ
I
(8)
(9)
Law of motion of taxes, function Ψ τ 0 = d 0 + d 1 K + d 2 zm + d 3 τ
(10)
where zi = k + [r(K)k + w(K)i ] (1 − τ ) + T Return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Computed Equilibrium: Final SS. Variable
K0
z0
τ0
Constant
0.14 (3.45e-08) 0.94 (9.41e-07) -1.21e-02 (1.34e-07) -7.15e-02 (6.73e-08)
0.15 (6.10e-05) 0.16 (1.66e-04) 0.73 (2.36e-04) 8.07e-03 (1.19e-04)
0.37 (2.87e-05) -0.04 (9.20e-05) 0.12 (1.30e-04) -3.36e-02 (4.97e-05)
0.999
0.998
0.948
K z τ
R2
Table: Equilibrium Laws of Motion Return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Median is important Variable
K0
τ0
Constant
0.15 (9.17e-07) 0.92 (2.93e-07) -7.88e-02 (4.12e-06) 5.50e-03 (1.31e-03)
0.29 (1.35e03) 0.12 (4.44e-04) 0.21 (6.10e-03) -0.15 (2.00e-03)
0.999
0.867
K τ τK
R2
Table: Imperfect Equilibrium Laws of Motion I
the goodness of fit (measured by R2 ) falls substantially for the law of motion of taxes (10).
Return Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Wage Process 1978/79
Table: Transition Matrix for 1978-1979.
1
(2.60) 2 (9.01) 3 (13.42) 4 (18.52) 5 (35.43)
1 0.732 0.165 0.038 0.034 0.029
3 0.189 0.553 0.188 0.050 0.019
3 0.048 0.222 0.527 0.160 0.041
4 0.015 0.048 0.190 0.556 0.193
5 0.015 0.009 0.055 0.198 0.716
Return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Wage Process 1995/96
Table: Transition Matrix for 1995-1996.
1 (1.75) 2 (7.92) 3 (11.90) 4 (17.03) 5 (35.98)
1 0.731 0.145 0.055 0.040 0.029
2 0.148 0.558 0.207 0.045 0.036
3 0.051 0.219 0.505 0.191 0.033
4 0.033 0.056 0.208 0.575 0.126
5 0.034 0.021 0.022 0.147 0.774
Return
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
The Value of Commitment. 10
ε1
9
ε2 ε3
Fraction of Agents (%)
8
ε4
7
ε5
6 5 4 3 2 1 0
−3
−2
−1 0 1 Consumption Equivalent λ (%)
2
3
return Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
Motivation
Environment
Equilibrium
Parametrization
Positive Findings
Conclusion
Preferred Tax Rates Summarize the tax choice of a typical agent as follows: 1. ψ(k, , Γ, τ ) is decreasing in ε; i.e. hh’s with lower wages choose higher taxes. 2. ψ(k, , 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
Politico Economic Consequences of Rising Wage Inequality
Dean Corbae, Pablo D’Erasmo, Burhan Kuruscu
