labor supply, endogenous wage dynamics and tax...
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Labor Supply, Endogenous Wage Dynamics andTax policy
Árpád Ábrahám Jay H. Hong Ricardo Santos
EUI Rochester Trinity
Preliminary
15th February 2011
Introduction Data Model Numerical Exercise Conclusion
Motivation
20 30 40 50 60 70 805
10
15
20
25Dynamic Effect
hours (h)
w′
10th pctl : w = 5.42
25th pctl : w = 8.07
50th pctl : w = 11.49
75th pctl : w = 16.02
90th pctl : w = 28.56
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
MotivationI Current hours do not only affect current earnings but also
affect future earnings potential.I In particular, current hours will affect the probability of wage
growth (or drop).I The work of Santos (2009) shows that this effect of current
hours on future wages is significant and varies considerablyacross income quintiles.
I labor supply decision takes into consideration threecomponents
I static componentI dynamic componentI level of wealth
I Possible interpretations: on-the-job human capitalaccumulation, learning-by-doing, tournament-type laborcontract.
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Introduction
I ’Static’ labor supply elasticity can be misleading when thedynamic effect is present.
I Implication on aggregate response to changes in tax system.
I To this end, we develop a GE model where both componentsof labor supply are included
I Heterogeneous agents (productivity, and asset position)
I The presence of incomplete markets.
I Two self-insurance mechanisms: precautionary savings andthe labor supply decision
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Related Papers
I Labor Supply in Dynamic Setting
I Santos (2009), Gicheva (2010), Bell & Freeman (2001)I Imai & Keane (2004), Elsby & Shapiro (2009), Hansen &
Imrohoroglu (2009)I Pijoan-Mas (2006), Michelacci & Pijoan-Mas (2009)
I Tax Reform and Labor Supply
I PrescottI Conesa, Kitao, Krueger (2009), Heathcote, Storesletten,
Violante (2010)I Keane (2009)
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Outline
1. Data• Isolating the dynamic component in the data• Empirical Results
2. Model• Environment• Definition of the competitive equilibrium• Mechanism
3. Numerical Exercise• Calibration/Estimation• Results• Tax Changes
4. Conclusions
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Data
I Current Population Survey (CPS) - March
I Demographic criteria: white men, age ∈ [25,65]
I (Weekly) Hours: 8 ≤ h ≤ 98
I Employed: positive earnings, not in armed forces,w ≥ 0.5 × minimum wage
I Matched 1 year panel
I 2004-2006 (28,714 obs)
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
DataKey Statistics
• (h,w)
2004-2006quintile hi wi corr
1 41.29 4.61 0.02
2 43.01 7.73 0.00
3 42.92 10.57 -0.02
4 43.09 14.39 0.02
5 42.96 31.64 -0.04
q5/q1 1.04 6.87
all 42.67 13.88 0.01
(std) (10.43) (14.95)
cv 0.24 1.08
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
DataIntermediate regressions
I Step 1: obtain ”clean” measure of wages
logwt = β0 + βX , for t and t + 1
w∗t = wt/wt
I Step 2: obtain ”clean” measure of hours
ht = β0 + βX , for t and t + 1
h∗t = ht/ht
where X ≡ (age, age2,Dedu,Docc)
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
DataFirst Stage: Wage Regression
logw = β0 + βX
β S.E. t-statcons (Managerial,<HS) .995 .06697 14.86age .050 .00303 16.50age2 −.0005 .00003 −14.32edu2 (HS) .245 .01502 16.33edu3 (Some College) .354 .01629 21.73edu4 (College) .504 .01584 31.81edu5 (Post College) .761 .01875 40.57occ2 (Professional) −.124 .01179 −10.56occ3 (Sales) −.219 .01356 −16.11occ4 (Administrative) −.392 .01746 −22.45occ5 (Services) −.490 .01519 −32.24occ6 (Transportation) −.384 .01533 −25.04occ7 (Operatives, Farming, etc) −.296 .01159 −25.51
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
DataFirst Stage: Hours Regression
h = β0 + βX
β S.E. t-statcons (Managerial,<HS) 29.870 1.1974 24.95age 0.672 0.0541 12.51age2 −0.008 0.0006 −12.97edu2 (HS) 1.394 0.2685 5.20edu3 (Some College) 1.378 0.2912 4.76edu4 (College) 1.646 0.2832 5.82edu5 (Post College) 3.763 0.3353 11.21occ2 (Professional) −3.293 0.2108 −15.58occ3 (Sales) −1.428 0.2425 −5.91occ4 (Administrative) −4.939 0.3122 −15.84occ5 (Services) −4.687 0.2716 −17.24occ6 (Transportation) −1.798 0.2742 −6.53occ7 (Operatives, Farming, etc) −4.217 0.2072 −20.39
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Life Cycle Wage Profile by Education Group
20 25 30 35 40 45 50 55 60 65
6
8
10
12
14
16
18
20
22
age
wage
(w)
Life-Cycle (by Education)
edu1edu2edu3edu4edu5
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
DataKey Statistics
• (h∗,w∗)
2004-2006quintile h∗i w∗i corr
1 1.01 0.48 0.01
2 1.01 0.77 0.04
3 1.02 1.01 0.01
4 1.01 1.31 0.00
5 0.99 2.51 -0.10
q5/q1 0.98 5.27
all 1.01 1.22 -0.05
(std) (0.24) (1.22)
cv 0.24 1.00
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
DataDistribution (Raw data vs. Cleaned data)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Share of people (%)
Sha
re o
f wag
e (%
)
Lorenz Curve (wage)
w: gini= 0.39w∗: gini= 0.33
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Share of people (%)
Sha
re o
f hou
rs (
%)
Lorenz Curve (hours)
h: gini= 0.12h∗: gini= 0.12
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Second Stage: Wage growth regression(I) Dynamic Effect
log(w∗t+1/w
∗t ) =
2∑i=0
2∑j=0
θij(logw∗t )ih∗t
j + ε, ε ∼ N(0, σ2ε)
Coefficient S.E. t-statθ00 -.422 .0492 -8.59θ10 -.752 .0536 -14.04θ20 .082 .0330 2.50θ01 .591 .0921 6.41θ11 .179 .1050 1.71θ21 -.153 .0706 -2.17θ02 -.163 .0437 -3.73θ12 .015 .0517 0.29θ22 .064 .0381 1.69
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Wage Growth(I) Dynamic Effect
20 30 40 50 60 70 80
−60
−40
−20
0
20
40
Dynamic Effect
hours (h)
wag
egrow
thrate(%
)
10th pctl
25th pctl
50th pctl
75th pctl
90th pctl
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Wage Level(I) Dynamic Effect
20 30 40 50 60 70 805
10
15
20
25Dynamic Effect
hours (h)
w′
10th pctl : w = 5.42
25th pctl : w = 8.07
50th pctl : w = 11.49
75th pctl : w = 16.02
90th pctl : w = 28.56
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Dynamic Effect
5 10 15 20 25 305
10
15
20
25
30
w
w′
Dynamic Effect
: h= 29.68: h= 38.38: h= 41.41: h= 46.95: h= 56.90
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Interpretation: Wage growth regression
• Working additional 5 hours/week (one hour a day)current wage (w) ∆w ′ additional Annual
hourly wage Earnings
10th percentile ($5.5) 0.94% 7.73 cents $17025th percentile ($8.8) 2.23% 22.75 cents $50050th percentile ($11.5) 2.90% 33.48 cents $73575th percentile ($14.9) 3.59% 46.46 cents $102190th percentile ($28.6) 5.18% 88.16 cents $1937
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Dynamic EffectPredicted Wage over age
20 25 30 35 40 45 50 55 60 65
6
8
10
12
14
16
18
20
22
age
wage
(w)
90th pctl : h = 56.90
50th pctl : h = 41.41
10th pctl : h = 29.68
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The Model - Consumer/Worker
I Standard Intertemporal preferences
∞∑t=0
(βs)tu(ct , ht)
I Productivity in terms of efficiency unit (xt)
xt ∈ [x , x ] ≡ X
I Budget Constraint
ct + at+1 = (1 + rt)at + wtxtht − T (rtat + wtxtht)
ct ≥ 0
at+1 ≥ 0
ht ∈ [h, h] ≡ H
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The Model - Transition Process of Productivity
I Benchmark Model (Dynamic Effect)
log x ′ = Ω (log x , h) + ε
I For comparison (No Dynamics) - Aiyagari with labor choice
log x ′ = Ω(log x) + ε
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The Model - Production
• Production: Yt = AKαt N
1−αt
where
Nt =
∫xthtdµt
Kt =
∫atdµt
• Government
G = Tt ≡∫
T (rtat + wtxtht)dµt
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The Model - Recursive Problem
V (x , a) = maxc,a′,h∈H
u(c , h) + βs
∫x ′V (x ′, a′)dF (x ′|x , h)
subject to
c + a′ = (1 + r)a + wxh − T (ra + wxh)
c ≥ 0, a′ ≥ 0
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Equilibrium
I Workers maximize their lifetime utility
I The firm maximizes its profit
I Markets clear
I Gov’t Budget Balance
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Self-Insurance Mechanism
I Standard precautionary savings.
I Static and Dynamic effect of working.
I Progressivity of taxes affecst labor supply:• usual static substitution and income effect• allocative efficiency: the timing of labor supply• changing incentives via dynamic effect• the role of labor supply as an insurance mechanism• general equilibrium effects
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Calibration
• Parameters
I Model period: 1 year
I Depreciation: δ = .08
I Capital Share: α = .36
I Survival Prob: s = .975 (Average Life span = 40 years)
I Weekly Hours: H = [h, h] = [8, 98]
I Productivity: X = [x , x ] = [1, 60]
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Calibration
• Preference
u(c , h) =c1−σ
1− σ+ B
(1− h)1−γ
1− γ
• Tax Function (Gouveia and Strauss (1994))
T (y) = τ0
(y − (y−τ1 + τ2)
− 1τ1
)I τ0=.258
I τ1=.768
I τ2=2.097 to match G/Y=15%
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Tax function
0 0.5 1 1.5 2 2.5 30
0.05
0.1
0.15
0.2
0.25
income
mar
gina
l tax
rat
e
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Calibration• Productivity
I Model with Dynamic Effect
log(x ′/x) =2∑
i=0
2∑j=0
θij(log x)ihj + ε, ε ∼ N(0, σ2ε)
I Model without Dynamic Effect
log(x ′/x) =2∑
i=0
θi (log x)i + ε, ε ∼ N(0, σ2ε)
I Newborn (or someone who has chosen not to work in a givenperiod)
log(x) = η, η ∼ N(0, σ2η)
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Calibration
• Measurement Error (From French (2004) and HSV (2008))
I W = exp(εw )wx , εw ∼ N(0, .207)
I h = exp(εh)h, εh ∼ N(0, .167)
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
CalibrationIndirect Inference
I Given (δ, s, α,H,X , τ0, τ1)
I we iterate on (σ, γ,B, β, τ2,G ) and the true θ’s, σ2ε , µη, ση.
I Match µh∗ , σh∗ , µw∗ , σw∗ , ρ(w∗, h∗), K/Y and G/Y themeans and standard deviation of wages of people who werenot employed last period and the θ’s and σ2ε from the dataestimation.
I For the latter we run a simulation
I Contaminate the simulated data with (σ2εw , σ2εh
)
I Run the same dynamic regression as the one we did on realdata with using simulated data.
I Minimize ||θdata − θmodel||.I This way we ’control’ for both measurement error and
selection.
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Model Fit
Moments Target Benchmark No Dynamics
K/Y 3.2 3.20 3.17G/Y 0.15 0.14 0.15mean(h) 0.33 0.31 0.39sd(h) 0.078 0.065 0.097mean(x∗) 1.22 1.22 1.22sd(x∗) 1.22 1.10 1.31σε 0.524 0.530 0.517
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Model Fit
Moments Benchmark No Dynamics
Gini (Wealth) 0.316 0.394Gini (Consumption) 0.044 0.052Gini (Hours) 0.087 0.113Gini (Wage) 0.338 0.312Gini (Earnings) 0.405 0.407
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Parameters
Moments Benchmark No Dynamics
β 0.9806 0.9805σ 7.1957 6.4297γ 8.5652 4.5948B 1.1345 0.7378σε 0.7520 1.068τ2 1.913 1.894
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The Fit of the Dynamic Effect
20 30 40 50 60 70 805
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15
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25Dynamic Effect (Data vs. Model)
hours (h)
w′
10th pctl : w = 5.42
50th pctl : w = 11.49
90th pctl : w = 28.56
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The True vs. Estimated Dynamic Effect
20 30 40 50 60 70 805
10
15
20
25Dynamic Effect (Data vs. True)
hours (h)
w′
10th pctl : w = 5.42
50th pctl : w = 11.49
90th pctl : w = 28.56
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
The Effect of Selection
20 30 40 50 60 70 805
10
15
20
25Dynamic Effect (Clean vs. True)
hours (h)
w′
10th pctl : w = 5.42
50th pctl : w = 11.49
90th pctl : w = 28.56
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Hours and Asset Wealth
I Borrowing constrained agents (low productivity in particular)use hours to smooth consumption subject to the usual staticincome and substitution effect. ⇒They may work less whenthey have a higher shock. ⇒ More progressivity may reducethe need of such insurance, so low income agents may workless although their tax rate is reduced.
I Agents with high level of assets get good insurance throughasset levels. ⇒ So, similarly to first-best, they work morewhen they have high income. ⇒ More progressivity reducesdifferences between pay-offs hence high income agents workless and low income agents work more.
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Tax PolicyTo be completed
0 0.5 1 1.5 2 2.5 30
0.05
0.1
0.15
0.2
0.25
0.3
0.35
income
mar
gina
l tax
rat
e
(1) Benchmark(2) Flat rate(3) Progressive
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Aggregate Effects of the Change in Tax systemMoments Benchmark
(1) (2) (3)
Output 1.234 1.265 1.114Consumption 0.719 0.724 0.699Hours 0.319 0.315 0.307Human Capital 0.619 0.623 0.578Capital 4.206 4.458 3.582G/Y 0.142 0.144 0.116
Moments No Dynamics
Output 1.266 1.307 1.205Consumption 0.756 0.764 0.761Hours 0.391 0.393 0.395Human Capital 0.662 0.664 0.651Capital 4.017 4.356 3.598G/Y 0.147 0.147 0.130
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos
Introduction Data Model Numerical Exercise Conclusion
Conclusion
I We show that current hours do affect future earningspotential.
I Dynamic effect varies considerably across income group.
I Dynamic effect should be taken into account to correctlymeasure the labor supply elasticity.
I The aggregate response of hours and human capital to taxcode changes (to be confirmed).
Labor Supply, Endogenous Wage Dynamics and Tax policy Abraham, Hong, Santos