Discussion of
\Wage Volatility and Changing Patterns of Labor Supply"
by Hye Mi You, Jay Hong and Byoung Hoon Seok
Dirk Krueger
University of Pennsylvania, CEPR, and NBER
11th New York/Philadelphia Quantitative Macroeconomics Workshop
May 10, 2013
Objective of this Paper
ws " in last 30 years in the US.
Explain why hhus " despite w
u
Note: if substitution e ect dominates income e ect, there is no puzzle.
Proposed explanation: (ws) " and (wu) " but (ws)= (wu) " :
Higher (relative) wage risk leads to increase in \precautionary labor
supply".
Rest of paper: construct life cycle consumption-savings model with
endogenous labor supply to quantify the importance of this channel.
The Facts
hs "
hu
[Figure 4]
ws "
wu
[Figure 1]
(ws) " and (wu) " but (ws)= (wu) " [Figure 2]
Figure 4: Trends in the Male Hours Worked in the U.S.
37
Figure 1: Trends in Skill Premium for U.S. Men between 1967 and 2006
Figure 2: Estimated Variances of Persistent and Transitory Wage Shocks
Figure 3: Variance Decomposition of Log Wage Residuals
36
Figure 1: Trends in Skill Premium for U.S. Men between 1967 and 2006
Figure 2: Estimated Variances of Persistent and Transitory Wage Shocks
Figure 3: Variance Decomposition of Log Wage Residuals
36
The Model
Perpetual youth model: constant probability of dying : Fixed education type e 2 fu; sg: Standard incomplete markets. Choices ct; at+1; ht:
Stochastic wage process:
wte exp( t + t)
e
=
t
t 1 + !t
N (0; e t) and ! t
t
Question: how does
hst
hu
t
evolve over time as
N (0; e!t)
wts
wtu
and
s
t
u
t
and
s
!t
u
!t
change?
Remark: Not clear production side and GE needed to answer question.
Results
Transition Dynamics [Figure 10(b)]
Figure 10: Transition Dynamics: Hours Di¤erences between Skilled and Unskilled Men
Transition (1967−2000+)
4.5
4
4
3.5
3.5
3
3
Hours Diff
Hours Diff
Transition (1967−2000+)
4.5
2.5
2.5
2
2
1.5
1.5
Model
data
1
1950
2000
2050
Model
data
1
2100
1960
1965
1970
1975
year
1980 1985
year
1990
1995
2000
2005
2010
Figure 11: Counterfactual 1: Same Increase in Wage Uncertainty as the Unskilled
Transition (1967−2000+)
Transition (1967−2000+)
46
5
S (Bench)
U (Bench)
S (CF)
U (CF)
45
Bench
CF
4.5
4
44
Hours Diff
wk. Hours
3.5
43
3
2.5
42
2
41
1.5
40
1950
2000
2050
1
1950
2100
2000
year
2050
2100
year
Figure 12: Counterfactual 2: Same Change in Shock Composition as the Unskilled
Transition (1967−2000+)
Transition (1967−2000+)
45.5
4.5
S (Bench)
U (Bench)
S (CF)
U (CF)
45
Bench
CF
4
44.5
3.5
44
3
Hours Diff
wk. Hours
43.5
43
2.5
2
42.5
1.5
42
1
41.5
0.5
41
40.5
1950
2000
2050
2100
year
0
1950
2000
2050
year
42
2100
Is There a Puzzle? Income vs. Substitution E ect
Abstracting from wage risk
uh(c; h)
=w
uc(c; h)
Thus
uh(cst; hst)=uc(cst; hst)
wts
= u
u
u
u
u
uh(ct ; ht )=uc(ct ; ht )
wt
Is There a Puzzle? Income vs. Substitution E ect
Example
1: Greenwood-Hercowitz-Hu
man preferences: u(c; h) =
0
1
log @c
1+ 1
h
A:
1
1+
Then
hst
hu
t
=
wts
wtu
!
and we are done!? What's wrong with this? Implausibly low (zero)
income e ect?
Is There a Puzzle? Income vs. Substitution E ect
Example 2: Separable preferences with constant Frisch labor supply
1+ 1
c1
h
:
1+ 1
elasticity: u(c; h) = 1
hst
hu
t
=
Then
wts= (cst)
wtu= cu
t
!
:
Attanasio-Davis (1996): In data over longer time horizon %
%
wts
wtu
: Then
hst
hu
t
=
wts (1
wtu
)
. Puzzle starts to open up if
1: For parameters from paper (1
by about 7%:
cst
cu
t
)
=
0:2; and thus
hst
#
hu
t
Is There a Puzzle? Income vs. Substitution E ect
This paper u(c; h) =
Then
1
1
c1
1
c
c
hst
hu
t
(1 h)1 h
e 1 h
+
=
"
with
s
s c
u wt = (ct )
u
u c
s wt = ct
#
c
= 1:5; h = 4:24:
1
h
Again presuming Attanasio-Davis are right on consumption, then
1
1
and thus
hst
hu
t
hst
hu
t
wts
wtu
=
should go down as
wts
wtu
!
c 1
h
goes up (but not by that much
since c > 1; but only moderately so). Now we have a puzzle. What
if c = 4:
Is There a Puzzle? Income vs. Substitution E ect
What does data say about size of income vs. substitution e ects?
Large literature in empirical public nance (see Keane 2010, Saez,
Slemrod and Giertz 2012) on Marshallian (uncompsensated), Hicksian
(compensated) labor supply elasticity.
Results vary (a lot!): depend on whether static or dynamic (w/o or
with human capital) model is estimated. Paper needs to engage with
that literature, since even qualitative results depend on it.
Noe: model has predictions about
cst ast+1
; au
cu
t
t+1
: Evaluate them.
Right Mechanism?
s-households face stronger increase in wage risk, increase level of labor
supply for precautionary reasons.
Do households in fact respond to wage shocks by adjusting labor supply
(as their model envisions) in order to insure consumption?
Yes, absolutely (Blundell, Pistaferri and Saporta-Eksten, 2013). But....
It's all about labor supply adjustment of the wife! Why the obsession (in model, data) with boring prime-age males? Look inside the
household!
-7
-6
-5
-4
-3
-2
Response of Consumption to a 10% Permanent
Decrease in the Male’s Wage Rate
30-34
35-39
40-44
45-49
50-54
Age of household head
55-59
fixed labor supply and no insurance
with family labor supply adjustment
with family labor supply adjustment and other insurance
       

60-65
Remarks about Model Elements I: Life Cycle
No explicit life cycle.
Precautionary savings motive important for young households, not so
much for older households (see e.g. Gourinchas and Parker, 2002).
Same likely true for precautionary labor supply mechanism.
Strong prediction: change in relative hours ought to be more important
for young than for old households? Is that true in the data?
Remarks about Model Elements II: Expectations
Timing in changes of hours depends strongly on when households learn
about the changes in wage structure.
Not entirely clear in paper...But I believe households are initially (1967)
surprised about these changes, but then have perfect foresight about
fwte; e t; e!tgt=2000
t=1967 :
What if they gradually learn about future changes in wage risk?
In general this is a hard problem since one has to make assumptions
and they matter (I presume a lot) for the timing of the transition path.
Concluding Remarks
Paper addresses an important empirical observation with state of the
art quantitative analysis.
Mechanism is plausible and wage data suggests it is quantitatively
promising.
Solidify argument that income e ect is large relative to substitution
e ect. Otherwise there is no puzzle (and thus no paper).
Broaden the focus to family labor supply.