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Wage Risk and the Skill Premium
Ctirad Slavı́k, CERGE-EI, Prague
(with Hakki Yazici, Sabanci University, Istanbul)
January 9, 2017
Swiss Macro Workshop
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Motivation
Recent decades in the United States:
Dramatic rise in relative wages of college vs. non-college
graduates (skill premium).
Residual wage volatility has also gone up (Gottschalk and
Moffitt 1994; 2012, Heathcote et al. 2010, Hong et al. 2015).
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This Project
1
Propose a mechanism through which rise in residual wage risk
increases skill premium.
Possible interpretation: provide a novel link from within-group
inequality to between-group inequality.
2
Assess significance of mechanism by measuring how much of
skill premium increase it can account for.
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Framework and Mechanism
Key ingredients of the framework:
1
Uninsured individual labor income risk.
2
Capital-skill complementarity.
Mechanism:
↑ labor income risk → ↑ (precautionary) savings → ↑ capital
stock → ↑ skill premium, due to capital-skill complementarity.
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The Exercise
Build an incomplete markets (Aiyagari 1994) model with
capital-skill complementarity.
Focus on steady state comparisons.
Calibrate the model to 1967 U.S. economy.
Feed in changes in wage risk and other factors (technology,
skill supply, and policies) and compute skill premium in 2010.
Measure the effect of increase in wage risk on skill premium
alone by changing risk only.
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Benchmark Results
Benchmark model matches total rise in skill premium between
1967 and 2010 quite well:
1.51 → 1.9 in the data vs. 1.51 → 1.87 in the model.
Rise in wage risk alone increases skill premium by 13 pp. or
by 1/3 of the overall change observed between 1967 and 2010.
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Extensions
1
Open Economy:
Rise in savings implied by rise in risk translates into a rise in
capital in benchmark closed economy.
In an open economy, fraction of the rise in savings may be
absorbed by foreign countries.
In a calibrated open economy exercise, skill premium increases
by 8 pp. in return to the rise in risk.
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Extensions
1
Open Economy:
Rise in savings implied by rise in risk translates into a rise in
capital in benchmark closed economy.
In an open economy, fraction of the rise in savings may be
absorbed by foreign countries.
In a calibrated open economy exercise, skill premium increases
by 8 pp. in return to the rise in risk.
2
Endogenous Skill Supply:
Fraction of skilled workers exogenous in baseline analysis.
This is because in counterfactual we are interested in isolating
effect of rise in wage risk on skill premium.
Alternative exercise: Rise in risk increases skill premium by 9
pp. taking into account people’s education choice responses.
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Rest of the Talk
Environment.
Quantitative results.
Extensions.
Conclusion.
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Environment
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Environment
Aiyagari (1994) model with capital-skill complementarity.
Incomplete markets model with:
Government, measure 1 of agents and a firm.
2 types of capital: equipments and structures.
2 types of labor: skilled and unskilled.
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Production
Production Function:
F (Ks , Ke , Ls , Lu )
As in KORV (2000), equipment capital-skill complementarity:
MPLs
MPLu
increasing in Ke (independent of Ks ).
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Firm Problem
Representative firm solves:
max
Ks ,Ke ,Ls ,Lu
F (Ks , Ke , Ls , Lu ) − rs Ks − re Ke − ws Ls − wu Lu
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Skill-Biased Technological Change (SBTC)
Following KORV (2000), model SBTC as a decline in cost of
equipment capital in terms of consumption good.
Aggregate feasibility:
C +G +Ks0 +qKe0 = F (Ks , Ke , Ls , Lu )+(1−δs )Ks +(1−δe )qKe .
SBTC is a decline in q over time.
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Government
Spends G , has debt D.
Raises revenue with:
linear capital income taxes τs , τe ,
linear consumption tax τc ,
non-linear labor income taxes T (y ), implies partial insurance.
Government budget constraint:
RD + G = D + τc C + τe (re − qδe )Ke + τs (rs − δs )Ks + Tagg ,
where Tagg is aggregate labor tax revenue.
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Demographics
Each period a fraction (1 − δ) of agents born with no assets.
Agents survive from one age to another with prob δ.
No accidental bequests: assets of dead distributed among the
survivors (actuarially fair life insurance).
Agents are born skilled or unskilled (exogenous).
πi denotes the total fraction of skill type i.
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Individual Wage Risk
Each period agent of skill type i draws idiosyncratic
productivity shock zi .
Agent of skill type i and productivity zi receives a wage rate
w̄i = wi · zi per unit time, with wi = MPLi .
The process for zi is skill specific.
log (zi ) is the sum of a persistent and a transitory component.
zi is the only source of residual wage inequality.
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Preferences
Preferences over stochastic (ci,t , li,t )∞
t=0 is given by
Ei
∞
hX
i
(βδ)t u(ci,t , li,t ) .
t=0
Endogeneous labor supply allows for partial insurance.
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Agent’s Problem
vi (zi , ai ) =
max
(ci ,li ,ai0 )≥0
u(ci , li ) + βδEi [vi (zi0 , ai0 )]
s.t.
(1 + τc )ci + δai0 ≤ wi zi li − T (wi zi li ) + Rai ,
where R = 1 + (rs − δs )(1 − τs ) = 1 + (re − qδe )(1 − τe )/q is the
after-tax asset return.
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Stationary Recursive Competitive Equilibrium
Definition: SRCE are value functions vu , vs , policy functions
cu , cs , lu , ls , au0 , as0 , firm’s decision rules Ks , Ke , Lu , Ls , government policies,
distribution of types λu (z, a), λs (z, a) and prices wu , ws , rs , re , R s.t.
1
The value and policy functions solve consumers’ problem given
prices and government policies for all i ∈ {u, s}.
2
The firm maximizes profits.
3
The distribution over productivities and assets is stationary.
4
Markets clear.
5
Government BC is satisfied.
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The Mechanism
1
↑ labor income risk → ↑ (precautionary) savings, because of
incomplete insurance markets.
2
↑ savings → ↑ stock of equipment capital.
3
↑ stock of equipment capital → ↑ skill premium, due to
equipment capital-skill complementarity.
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Quantitative Analysis
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Quantitative Analysis
Overview:
Calibrate model economy to 1967 U.S. economy.
Model fit: Feed in observed changes in all factors between
1967 and 2010 and compute skill premium in 2010.
Counterfactual: Feed in the change in wage risk only and
compute skill premium.
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Production Function
Production function: KORV (2000)
1−α
η
η
Y = Ksα ν [ωKeρ + (1 − ω)Lρs ] ρ + (1 − ν)Lηu
Use α, η, ρ, δs , δe from KORV and GHK. Calibrate ω and ν.
Parameter
α
η
ρ
δs
δe
Value
0.117
0.401
-0.495
5.6%
12.4%
Source
KORV (2000)
KORV (2000)
KORV (2000)
Greenwood, Hercowitz, Krusell (1997)
Greenwood, Hercowitz, Krusell (1997)
q normalized to one in 1967.
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Agents
Cobb-Douglas utility function:
u(c, l) =
φ
1−σ
c (1 − l)(1−φ) φ − 1
1−σ
φ
.
Balanced growth path compatible.
In benchmark, use σ = 2, and calibrate β and φ.
Survival probability δ = 0.978 to match average working life
of 40 years as in Castañeda, Dı́az-Giménez, Rı́os-Rull (2003).
πs = 13.56% (CPS 1967, males aged 25-60, with earnings).
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Productivity Shocks: 1967
Hong, Seok, You (2015) estimate skill specific wage processes:
log zi,t = θi,t + εi,t ,
θi,t = ξi θi,t−1 + κi,t .
Identification: ξ and Var (θ) of entrants remains constant,
Var (ε) and Var (κ) change over time.
Variable
Variance of ε
Variance of κ
ξ
Var of θ for entrants
Skilled
0.0116
0.0037
0.9834
0.1172
Unskilled
0.0177
0.0052
0.9859
0.1488
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Government Policy: 1967
Consumption taxes τc = 5%; Mendoza, Razin, Tesar (1994).
As in HSV (AER, 2014) approximate progressive labor taxes
by T (y ) = y − χ · y 1−τl , τl = 0.185, let χ clear the budget.
Govt. expenditure G /Y = 0.16 on average.
These policy parameters (except for χ) remain constant
between 1967 and 2010 in the quantitative exercise.
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Government Policy: 1967
Capital income taxes 15% at consumer level, differential taxes
at corporate level (Auerbach, 1983): τs = 0.57, τe = 0.50.
Govt. debt D/Y = 0.36 in 1967 (St. Louis FED).
These change between 1967 and 2010 in our exercise.
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Internal Calibration
Parameter
ω
ν
φ
β·δ
χ
Value
0.8333
0.4122
0.3985
0.9908
0.8708
Target
Labor share
Skill premium in 1967
Labor supply
Capital-to-output ratio
Gvt. budget balance
Data & SRCE
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1.51
1/3
2.9
Source
NIPA
HPV
NIPA, FAT
Skill premium from CPS 1967, males aged 25-60, working at
least 260 hours a year.
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Changes in Factors
Between 1967 and 2010
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Changes in Wage Risk between 1967 and 2010
Hong et al. (2015):
Variable
Variance of εs
Variance of εu
Variance of κs
Variance of κu
1967
0.0116
0.0177
0.0037
0.0052
2010
0.0673
0.0627
0.0304
0.0157
Wage risk. Has gone up for both groups.
Risk has increased more for skilled (see also Lee et al. 2015).
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Changes in Other Factors between 1967 and 2010
Skill biased technical change:
Technology: Relative price of equipments decreases from 1 in
1967 to 0.1577 in 2010 (St. Louis FRED data base).
Change in relative skill supply:
Fraction of skilled workers increase from 13.56% in 1967 to
31.36% in 2010.
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Changes in Other Factors between 1967 and 2010
Government policy:
Capital taxes. Have decreased from τs = 0.57, τe = 0.50
(Auerbach, 1983) to τs = 0.42 and τe = 0.37 (Gravelle, 2011).
Gvt debt. Increased from 36% in 1967 to 89% in 2010.
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Main Quantitative Results
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Change in Skill Premium from 1967 to 2010
Model matches the change in skill premium quite well.
Skill premium
1967
1.51
Data
2010
1.9
Change
0.39
1967
1.51
Model
2010
1.87
Change
0.36
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Counterfactual: Change Wage Risk Only
Skill premium
Change
1967
1.51
Risk
1.64
0.13
2010 (model)
1.87
0.36
2010 (data)
1.9
0.39
Increase in residual wage risk increases skill premium by 13 pp.
That is 34% of the total increase between 1967 and 2010
Mechanism: Risk ↑ → 21% increase in equipment capital,
which ↑ skill premium due to capital-skill complementarity.
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Alternative Counterfactual
Feed in changes in other factors first, and then change in risk.
Skill premium
Change
1967
1.51
All but Risk
1.79
0.28
2010 (model)
1.87
0.36
2010 (data)
1.9
0.39
Increase in wage risk increases skill premium by 8 pp.
That is 20% of overall increase between 1967 and 2010.
Magnitude of mechanism depends on order of decomposition
due to non-linearities.
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Sensitivity to Risk Aversion
Results sensitive to degree of risk aversion, σ.
σ
1
2
4
1967
1.51
1.51
1.51
Risk
1.57
1.64
1.80
2010
1.83
1.87
1.94
Mechanism quantitatively important for range of σ.
Rise in risk creates up to 29 pp. rise in skill premium for
values of σ within plausible range.
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Extensions
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Open Economy
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Closed vs. Open Economy
Risk changes matter because they affect capital accumulation.
In a closed economy: risk → savings = investment.
In an open economy: risk → savings 6= investment.
How strong is the mechanism in an open economy?
Answer depends on the extent to which foreign countries can
absorb the rise in domestic savings.
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Open Economy
Two-country model: U.S. vs. rest of the world (ROW).
ROW modelled as a similar incomplete market economy.
International dimension:
Intertemporal trade in (single) good.
Perfect international capital mobility:
IIPUS + IIPROW = 0,
where IIP is international investment position.
No labor mobility.
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Open Economy
During this time, ”global imbalances” in world financial
markets: decline in IIPUS and global real interest rate.
Follow Bernanke (2005)’s ”savings glut” hypothesis: global
imbalances caused by rise in ROW saving.
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Open Economy
We want to:
1
Quantify role of rise in U.S. wage risk on U.S. skill premium in
open economy.
2
Investigate effect of savings glut on skill premium (secondary).
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Open Economy
Quantitative exercise:
ROW consists of top 20 trading partners of U.S.
Calibrate the parameters of the two economies together in
1967 to match in particular IIPUS and IIPROW .
Feed in changes in U.S. economy and calibrate change in
ROW saving behavior to match IIPUS and IIPROW in 2010.
Change only U.S. wage risk and measure quantitative
significance of mechanism in open economy.
Add savings glut, measure its contribution to skill premium.
Open Economy Details
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Open Economy Results
Skill premium
Contribution (pp.)
1967
1.51
2010
1.88
Risk
1.59
8
Risk + Savings glut
1.65
14
Effect of rise in wage risk on skill premium significant: 8 pp.
Mechanism weaker than in closed economy since part of the
rise in savings absorbed by ROW.
Savings glut contributed to rise of U.S. skill premium by 6 pp.
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Endogenous Skill Supply
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Exogenous vs. Endogenous Skill Supply
In baseline environment, fraction of skilled exogenous.
Reason: In counterfactual, interested in understanding effect
of rise in risk on skill premium given observed supply of skilled.
Alternative: How much does rise in risk increase skill premium
when people can alter their education decisions in response?
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Environment
Environment same as before except people choose skill level:
Newborns draw utility cost ψ ≥ 0, distributed acc. to F (ψ).
Reduced form way of capturing cross sectional variation in
psychological and pecuniary costs of acquiring a degree.
Get educated iff Es,0 [vs (z, 0)] − Eu,0 [vu (z, 0)] ≥ ψ.
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Cost of Education
Assume ψ is distributed according to exponential distribution
with parameter n > 0.
Calibrate n to match fraction of skilled in 1967: πs = 13.56%.
Note: One dimensional distribution because only one target.
Results almost identical if F is uniform instead.
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Significance of Mechanism with Endogenous Skills
Rise in wage risk increases skill premium by 9 pp.
Less than in case with exogenous skills: 9 pp. vs. 13 pp.
Fraction of skilled rises if skill premium ↑: from 13.56% to
13.92%, which prevents skill premium from further ↑.
Fraction of skilled does not rise too much because risk rises
more for skilled.
Change in risk has first order effect on skill premium.
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Conclusion
Novel mechanism through which inequality leads to inequality:
↑ wage risk → ↑ skill premium.
Mechanism is quantitatively important: 1/3 of the overall
change in skill premium in the U.S. between 1967 and 2010.
Mechanism also significant under open economy and
endogenous labor supply extensions.
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ROW Basics
An Aiyagari economy with:
Measure m̂ of agents.
Inelastic labor supply: u(c) =
c 1−σ̂ −1
1−σ .
Cobb-Douglas production function: F (K , L) = ÂK α̂ L1−α̂ .
Wage process:
log ẑt = θ̂t + ε̂t ,
θ̂t = ξˆθ̂t−1 + κ̂t ,
No government.
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ROW Savings Behavior
From being a net saver in 1960’s, U.S. has become a net
borrower in 2000’s.
Surge in the rest of the world savings, “savings glut”.
Following Kehoe et al. (2016), we use an exogenous saving
wedge ψ̂ to account for the change in ROW saving behavior:
E
∞
hX
i
(ψ̂ β̂)t u(ct ) .
t=0
We change ψ̂ exogenously to match the international
investment positions of the U.S. in 1967 and 2010.
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Calibrating the Two-Country Model to 1967
Since we know IIP’s of the 2 countries, we calibrate them
separately.
U.S. calibration as before except:
New target, US IIP / US GDP in 1967, and new parameter to
choose, R 67 (world interest rate in 1967).
Parameter
R 67
Value
1.13%
Target
US IIP / US GDP
Data & SRCE
10%
Source
NIPA
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Calibrating the Two-Country Model to 1967
ROW calibration:
Set σ̂ = 2, β̂ = βδ, α̂ = 1/3, and δ̂ = 0.08.
Set m̂67 = 9.3 (Angus Maddison dataset).
Set parameters of wage process to a weighted average of
values for Germany, U.K., France, and Italy, as estimated by
Le Blanc and Georgarakos (2013).
ξˆ
0.9335
σκ̂
0.0158
σε̂
0.0399
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Calibrating the Two-Country Model to 1967
Choose Â67 and ψ̂ 67 to match ROW IIP and GDP in 1967.
Parameter
Value
Target
Value
Source
Â67
ψ̂ 67
0.1910
0.9474
ROW GDP / US GDP
ROW IIP / US GDP
1.76
-10%
Maddison
Maddison
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Calibrating the Two-Country Model to 2010
U.S. calibration:
Choose R 10 that matches U.S. IIP in 2010.
Parameter
R 00s
Value
0.47%
Target
US IIP / US GDP
Data & SRCE
-17.5%
Source
NIPA
ROW calibration (savings glut):
Set m̂10 = 11 (Angus Maddison dataset).
Choose Â10 and ψ̂ 10 to match ROW IIP and GDP in 2010.
Parameter
Value
Target
Data & SRCE
Source
Â10
ψ̂ 10
0.3270
0.9575
ROW GDP / US GDP
ROW IIP / US GDP
2.25
17.5%
Maddison
Maddison
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