C ONSUMPTION S MOOTHING , A SSETS AND FAMILY
L ABOR S UPPLY
Richard Blundell
University College London & IFS
ECB October 2013
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
1 / 56
M OTIVATION
Based on recent work with Luigi Pistaferri and Itay Eksten at
Stanford: "Consumption Inequality and Family Labor Supply".
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
2 / 56
M OTIVATION
Based on recent work with Luigi Pistaferri and Itay Eksten at
Stanford: "Consumption Inequality and Family Labor Supply".
In this work we note that inequality has many dimensions:
I
Wages! earnings! joint earnings! income! consumption
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
2 / 56
M OTIVATION
Based on recent work with Luigi Pistaferri and Itay Eksten at
Stanford: "Consumption Inequality and Family Labor Supply".
In this work we note that inequality has many dimensions:
I
I
Wages! earnings! joint earnings! income! consumption
Focus on labor market shocks as the primitive source of uncertainty.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
2 / 56
M OTIVATION
Based on recent work with Luigi Pistaferri and Itay Eksten at
Stanford: "Consumption Inequality and Family Labor Supply".
In this work we note that inequality has many dimensions:
I
I
Wages! earnings! joint earnings! income! consumption
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various types of inequality is mediated by
multiple ‘insurance’ mechanisms
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
2 / 56
M OTIVATION
Based on recent work with Luigi Pistaferri and Itay Eksten at
Stanford: "Consumption Inequality and Family Labor Supply".
In this work we note that inequality has many dimensions:
I
I
Wages! earnings! joint earnings! income! consumption
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various types of inequality is mediated by
multiple ‘insurance’ mechanisms, including:
I
Labor supply: family labor supply (wages! earnings! joint
earnings)
I
Taxes and welfare: (earnings! income)
I
I
Assets: Saving and borrowing (income! consumption)
Informal contracts, gifts, etc.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
2 / 56
M OTIVATION
Based on recent work with Luigi Pistaferri and Itay Eksten at
Stanford: "Consumption Inequality and Family Labor Supply".
In this work we note that inequality has many dimensions:
I
I
Wages! earnings! joint earnings! income! consumption
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various types of inequality is mediated by
multiple ‘insurance’ mechanisms, including:
I
Labor supply: family labor supply (wages! earnings! joint
earnings)
I
Taxes and welfare: (earnings! income)
I
I
Assets: Saving and borrowing (income! consumption)
Informal contracts, gifts, etc.
But how important are each of these mechanisms?
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
2 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
Investigate how assets and labor market shocks combine to impact
on consumption.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
Investigate how assets and labor market shocks combine to impact
on consumption.
Point to the importance of constructing panel/administrative
linked data that allow all three measures.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
Investigate how assets and labor market shocks combine to impact
on consumption.
Point to the importance of constructing panel/administrative
linked data that allow all three measures.
With Luigi and Itay we make use of the new PSID data on
consumption, earnings and assets.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
Investigate how assets and labor market shocks combine to impact
on consumption.
Point to the importance of constructing panel/administrative
linked data that allow all three measures.
With Luigi and Itay we make use of the new PSID data on
consumption, earnings and assets.
We show that family labor supply, credit market and the
tax/welfare system all have key roles to play in the ’insurance’ of
shocks. Credit and family labor supply act together to insure
shocks.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
Investigate how assets and labor market shocks combine to impact
on consumption.
Point to the importance of constructing panel/administrative
linked data that allow all three measures.
With Luigi and Itay we make use of the new PSID data on
consumption, earnings and assets.
We show that family labor supply, credit market and the
tax/welfare system all have key roles to play in the ’insurance’ of
shocks. Credit and family labor supply act together to insure
shocks.
Finding: Once assets, family labor supply and taxes (and welfare)
are properly accounted for, we can explain the link between these
series and there is less evidence for additional insurance.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
O VERVIEW
Focus on how families deal with labor market shocks.
Investigate how assets and labor market shocks combine to impact
on consumption.
Point to the importance of constructing panel/administrative
linked data that allow all three measures.
With Luigi and Itay we make use of the new PSID data on
consumption, earnings and assets.
We show that family labor supply, credit market and the
tax/welfare system all have key roles to play in the ’insurance’ of
shocks. Credit and family labor supply act together to insure
shocks.
Finding: Once assets, family labor supply and taxes (and welfare)
are properly accounted for, we can explain the link between these
series and there is less evidence for additional insurance.
Some consumption inequality descriptives....
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
3 / 56
C ONSUMPTION I NEQUALITY IN THE UK
By age and birth cohort
.1 .15
Variance
.2 .25 .3 .35
.4 .45
.5
Variance of log nondurable consumption
20
30
40
50
60
70
Age
1940
1960
B LUNDELL , UCL & IFS ()
1950
1970
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ECB O CTOBER 2013
4 / 56
I NCOME I NEQUALITY IN THE UK
By age and birth cohort
.1 .15
Variance
.2 .25 .3 .35
.4
.45
.5
Variance of log net income
20
30
40
50
60
70
Age
1940
1960
B LUNDELL , UCL & IFS ()
1950
1970
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ECB O CTOBER 2013
5 / 56
C ONSUMPTION I NEQUALITY IN THE US
By age and birth cohort
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
6 / 56
The existing literature (references in paper) usually relates
movements in consumption to predictable and unpredictable
income changes as well as persistent and non-persistent shocks to
economic resources.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
7 / 56
The existing literature (references in paper) usually relates
movements in consumption to predictable and unpredictable
income changes as well as persistent and non-persistent shocks to
economic resources.
A little background on the empirical strategy for income and
consumption dynamics behind these results...
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
7 / 56
I NCOME D YNAMICS
Consider consumer i (of age a) in time period t, has log income
yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + pt f1i + yPit + yTit
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
8 / 56
I NCOME D YNAMICS
Consider consumer i (of age a) in time period t, has log income
yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + pt f1i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = ρyPit
B LUNDELL , UCL & IFS ()
1
+ vit
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
8 / 56
I NCOME D YNAMICS
Consider consumer i (of age a) in time period t, has log income
yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + pt f1i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = ρyPit
1
+ vit
which adds to the individual-specific trend pt fi and where yTit is a
transitory shock represented by some low order MA process, say
yTit = εit + θ 1 εi,t
B LUNDELL , UCL & IFS ()
1
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
8 / 56
I NCOME D YNAMICS
Consider consumer i (of age a) in time period t, has log income
yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + pt f1i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = ρyPit
1
+ vit
which adds to the individual-specific trend pt fi and where yTit is a
transitory shock represented by some low order MA process, say
yTit = εit + θ 1 εi,t
1
A key consideration is to allow variances (or factor loadings) of yP
and yT to vary with age/time for each birth cohort.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
8 / 56
I NCOME D YNAMICS
Consider consumer i (of age a) in time period t, has log income
yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + pt f1i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = ρyPit
1
+ vit
which adds to the individual-specific trend pt fi and where yTit is a
transitory shock represented by some low order MA process, say
yTit = εit + θ 1 εi,t
1
A key consideration is to allow variances (or factor loadings) of yP
and yT to vary with age/time for each birth cohort.
Find pt f1i to be less important and ρ closer to unity, especially in the
30-59 age selection.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
8 / 56
I NCOME D YNAMICS
Consider consumer i (of age a) in time period t, has log income
yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + pt f1i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = ρyPit
1
+ vit
which adds to the individual-specific trend pt fi and where yTit is a
transitory shock represented by some low order MA process, say
yTit = εit + θ 1 εi,t
1
A key consideration is to allow variances (or factor loadings) of yP
and yT to vary with age/time for each birth cohort.
Find pt f1i to be less important and ρ closer to unity, especially in the
30-59 age selection.
Detailed work on Norwegian population register panel data....
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
8 / 56
L IFE - CYCLE I NCOME D YNAMICS
Variance of permanent shocks over the life-cycle
Variance of Permanent Shocks : Average Cohort Effects all
e
du
Individual Market Income
Individual Disposable Income
0.1
0.05
0
30
35
40
45
50
55
Source: Blundell, Graber and Mogstad (2013), Norwegian Population Panel.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
9 / 56
L IFE - CYCLE I NCOME D YNAMICS
Norwegian population panel (low skilled)
Variance of Permanent Shocks : Average Cohort Effects LowSkilled
Individual Market Income
Individual Disposable Income
0.1
0.05
0
30
35
40
45
50
55
Source: Blundell, Graber and Mogstad (2013).
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
10 / 56
C ONSUMPTION G ROWTH AND I NCOME "S HOCKS "
To account for the impact of income shocks on consumption we
introduce transmission parameters: κ cvt and κ cεt , writing consumption
growth as:
∆ ln Cit = Γit + ∆Zit0 ϕc + κ cvt vit + κ cεt εit + ξ it
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
11 / 56
C ONSUMPTION G ROWTH AND I NCOME "S HOCKS "
To account for the impact of income shocks on consumption we
introduce transmission parameters: κ cvt and κ cεt , writing consumption
growth as:
∆ ln Cit = Γit + ∆Zit0 ϕc + κ cvt vit + κ cεt εit + ξ it
which provides the link between the consumption and income
distributions.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
11 / 56
C ONSUMPTION G ROWTH AND I NCOME "S HOCKS "
To account for the impact of income shocks on consumption we
introduce transmission parameters: κ cvt and κ cεt , writing consumption
growth as:
∆ ln Cit = Γit + ∆Zit0 ϕc + κ cvt vit + κ cεt εit + ξ it
which provides the link between the consumption and income
distributions.
For example, in Blundell, Low and Preston (QE, 2013) show, for any
birth-cohort,
∆ ln Cit = Γit + ∆Zit0 ϕc + (1
where
π it
π it )vit + (1
π it )γLt εit + ξ it
Assetsit
Assetsit + Human Wealthit
and γLt is the annuity value of a transitory shock for an individual
aged t retiring at age L.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
11 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms.
information".
B LUNDELL , UCL & IFS ()
I And test for "superior
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms.
information".
I And test for "superior
I Distinctive features of this paper:
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms.
information".
I And test for "superior
I Distinctive features of this paper:
- Allow for
I
I
I
non-separability,
heterogeneous assets,
correlated shocks to individual wages.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms.
information".
I And test for "superior
I Distinctive features of this paper:
- Allow for
I
I
I
non-separability,
heterogeneous assets,
correlated shocks to individual wages.
- Use new data from the PSID 1999-2009
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
12 / 56
I N THIS PAPER WE LOOK CLOSER AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labor supply of each earner
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms.
information".
I And test for "superior
I Distinctive features of this paper:
- Allow for
I
I
I
non-separability,
heterogeneous assets,
correlated shocks to individual wages.
- Use new data from the PSID 1999-2009
I
I
More comprehensive consumption measure.
Asset data collected in every wave.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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NIPA-PSID C OMPARISON
1998
2000
2002
2004
2006
2008
PSID Total
NIPA Total
ratio
3,276
5,139
0.64
3,769
5,915
0.64
4,285
6,447
0.66
5,058
7,224
0.7
5,926
8,190
0.72
5,736
9,021
0.64
PSID Nondurables
NIPA Nondurables
ratio
746
1,330
0.56
855
1,543
0.55
887
1,618
0.55
1,015
1,831
0.55
1,188
2,089
0.57
1,146
2,296
0.5
PSID Services
NIPA Services
ratio
2,530
3,809
0.66
2,914
4,371
0.67
3,398
4,829
0.7
4,043
5,393
0.75
4,738
6,101
0.78
4,590
6,725
0.68
Note: PSID weights are applied for the non-sampled PSID data (47,206 observations for these
years). Total consumption is defined as Nondurables + Services. PSID consumption categories
include food, gasoline, utilities, health, rent (or rent equivalent), transportation, child care,
education and other insurance. NIPA numbers are from NIPA table 2.3.5. All numbers are
nonminal
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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D ESCRIPTIVE S TATISTICS FOR C ONSUMPTION
Consumption
Nondurable Consumption
Food (at home)
Gasoline
Services
Food (out)
Health Insurance
Health Services
Utilities
Transportation
Education
Child Care
Home Insurance
Rent (or rent equivalent)
Observarions
PSID Consumption
1998
2000
27,290
31,973
6,859
7,827
5,471
5,785
1,387
2,041
21,319
25,150
2,029
2,279
1,056
1,268
902
1,134
2,282
2,651
3,122
3,758
1,946
2,283
601
653
430
480
8,950
10,645
1,872
1,951
2002
35,277
7,827
5,911
1,916
28,419
2,382
1,461
1,334
2,702
4,474
2,390
660
552
12,464
2004
41,555
8,873
6,272
2,601
33,755
2,582
1,750
1,447
4,655
3,797
2,557
689
629
15,650
2006
45,863
9,889
6,588
3,301
36,949
2,693
1,916
1,615
5,038
3,970
2,728
648
717
17,623
2008
44,006
9,246
6,635
2,611
35,575
2,492
2,188
1,844
5,600
3,759
2,584
783
729
15,595
1,984
2,011
2,115
2,221
Notes: PSID data from 1999-2009 PSID waves. PSID means are given for the main sample of estimation: married
couples with working males aged 30 to 65. SEO sample excluded. PSID rent is imputed as 6% of reported house value
for homeowners. Missing values in consumption and assets sub-categories were treated as zeros.
B LUNDELL , UCL & IFS ()
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ECB O CTOBER 2013
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D ESCRIPTIVE S TATISTICS FOR A SSETS AND E ARNINGS
Total assets
Housing and RE assets
Financial assets
Total debt
Mortgage
Other debt
PSID Assets, Hours and Earnings
1998
2000
2002
332,625 352,247 382,600
159,856 187,969 227,224
173,026 164,567 155,605
72,718
82,806
98,580
65,876
74,288
89,583
7,021
8,687
9,217
2004
476,626
283,913
192,995
115,873
106,423
9,744
2006
555,951
327,719
228,805
131,316
120,333
11,584
2008
506,823
292,910
214,441
137,348
123,324
14,561
First earner (head)
Earnings
Hours worked
54,220
2,357
61,251
2,317
63,674
2,309
68,500
2,309
72,794
2,284
75,588
2,140
Second earner (wife)
Participation rate
Earnings (conditional on participation)
Hours worked (conditional on participation)
0.81
26,035
1,666
0.8
28,611
1,691
0.81
31,693
1,697
0.81
33,987
1,707
0.81
36,185
1,659
0.8
39,973
1,648
Observarions
1,872
1,951
1,984
2,011
2,115
2,221
Notes: PSID data from 1999-2009 PSID waves. PSID means are given for the main sample of estimation: married couples
with working males aged 30 to 65. SEO sample excluded. PSID rent is imputed as 6% of reported house value for
homeowners. Missing values in consumption and assets sub-categories were treated as zeros.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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H OUSEHOLD D ECISIONS IN A U NITARY F RAMEWORK
Household chooses Ci,t+j , Hi,1,t+j , Hi,2,t+j
Et
T t
j=0
to maximize
T t
∑ (1 + δ )
τ
v (Ci,t+τ , Hi,1,t+τ , Hi,2,t+τ ; Zi,t+τ )
τ =0
subject to
Ci,t +
B LUNDELL , UCL & IFS ()
Ai,t+1
= Ai,t + Hi,1,t Wi,1,t + Hi,1,t Wi,2,t
1+r
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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H OUSEHOLD D ECISIONS IN A U NITARY F RAMEWORK
Household chooses Ci,t+j , Hi,1,t+j , Hi,2,t+j
Et
T t
j=0
to maximize
T t
∑ (1 + δ )
τ
v (Ci,t+τ , Hi,1,t+τ , Hi,2,t+τ ; Zi,t+τ )
τ =0
subject to
Ci,t +
Ai,t+1
= Ai,t + Hi,1,t Wi,1,t + Hi,1,t Wi,2,t
1+r
Our approach
Extend previous work and express the distributional dynamics of
consumption and earnings growth as functions of Frisch elasticities,
‘insurance parameters’ and wage shocks
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
16 / 56
WAGE P ROCESS
For earner j = f1, 2g in household i, period t, wage growth is:
0
∆ log Wi,j,t = ∆Xi,j,t
βj + ∆ui,j,t + vi,j,t
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
17 / 56
WAGE P ROCESS
For earner j = f1, 2g in household i, period t, wage growth is:
0
∆ log Wi,j,t = ∆Xi,j,t
βj + ∆ui,j,t + vi,j,t
0
1
ui,1,t
B ui,2,t C
B
C
@ vi,1,t A
vi,2,t
00
1 0 2
σu,1
0
BB 0 C B σu1 ,u2
B C B
i.i.d. B
@@ 0 A , @ 0
0
0
B LUNDELL , UCL & IFS ()
σu1 ,u2
σ2u,2
0
0
C ONSUMPTION AND FAMILY L ABOR S UPPLY
0
0
σ2v,1
σv1 ,v2
0
0
σv1 ,v2
σ2v,2
11
CC
CC
AA
ECB O CTOBER 2013
17 / 56
WAGE P ROCESS
For earner j = f1, 2g in household i, period t, wage growth is:
0
∆ log Wi,j,t = ∆Xi,j,t
βj + ∆ui,j,t + vi,j,t
0
1
ui,1,t
B ui,2,t C
B
C
@ vi,1,t A
vi,2,t
00
1 0 2
σu,1
0
BB 0 C B σu1 ,u2
B C B
i.i.d. B
@@ 0 A , @ 0
0
0
σu1 ,u2
σ2u,2
0
0
0
0
σ2v,1
σv1 ,v2
0
0
σv1 ,v2
σ2v,2
11
CC
CC
AA
Allow the variances to differ by gender and across the life-cycle.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
17 / 56
WAGE PARAMETERS E STIMATES
Baseline
Sample
Males
Females
Correlation of shocks
B LUNDELL , UCL & IFS ()
All
0.033
Trans.
σ2u1
Perm.
σ2v1
Trans.
σ2u2
Perm.
σ2v2
Trans.
ρu1 ,u2
0.244
Perm
ρv1 ,v2
0.113
C ONSUMPTION AND FAMILY L ABOR S UPPLY
(0.007)
0.032
(0.005)
0.012
(0.006)
0.043
(0.005)
(0.22)
(0.07)
ECB O CTOBER 2013
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C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1 0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
B LUNDELL , UCL & IFS ()
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
0
1
∆u1,t
κ c,v2
B ∆u2,t
κ y1 ,v2 A B
@ v1,t
κ y2 ,v2
v2,t
C ONSUMPTION AND FAMILY L ABOR S UPPLY
1
C
C
A
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1 0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
where the key transmission parameters
κ yj ,uj
=
B LUNDELL , UCL & IFS ()
1 + η hj ,wj
0
1
∆u1,t
κ c,v2
B ∆u2,t
κ y1 ,v2 A B
@ v1,t
κ y2 ,v2
v2,t
1
C
C
A
! [Frisch]
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1 0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
where the key transmission parameters
κ yj ,uj
=
B LUNDELL , UCL & IFS ()
1 + η hj ,wj
! [Frisch]
0
1
∆u1,t
κ c,v2
B ∆u2,t
κ y1 ,v2 A B
@ v1,t
κ y2 ,v2
v2,t
1
C
C
A
κ yj ,vj ! [Marshall]
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1
0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
κ c,v2
κ y1 ,v2
κ y2 ,v2
where the key transmission parameters
κ yj ,uj
κ c,vj
=
1 + η hj ,wj
= (1
B LUNDELL , UCL & IFS ()
β ) (1
! [Frisch]
π i,t ) si,j,t
1
∆u1,t
C
B
A B ∆u2,t C
@ v1,t A
v2,t
1
0
κ yj ,vj ! [Marshall]
η c,p 1 + η hj ,wj
η c,p + (1
C ONSUMPTION AND FAMILY L ABOR S UPPLY
β ) (1
π i,t ) η h,w
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1
0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
κ c,v2
κ y1 ,v2
κ y2 ,v2
where the key transmission parameters
κ yj ,uj
κ c,vj
=
1 + η hj ,wj
= (1
π i,t
B LUNDELL , UCL & IFS ()
β ) (1
! [Frisch]
π i,t ) si,j,t
1
∆u1,t
C
B
A B ∆u2,t C
@ v1,t A
v2,t
1
0
κ yj ,vj ! [Marshall]
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
Assetsi,t
Assetsi,t + Human Wealthi,t
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1
0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
κ c,v2
κ y1 ,v2
κ y2 ,v2
where the key transmission parameters
κ yj ,uj
κ c,vj
=
1 + η hj ,wj
= (1
β ) (1
si,j,t
B LUNDELL , UCL & IFS ()
! [Frisch]
π i,t ) si,j,t
1
∆u1,t
C
B
A B ∆u2,t C
@ v1,t A
v2,t
1
0
κ yj ,vj ! [Marshall]
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
Human Wealthi,j,t
Human Wealthi,t
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1
0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
κ c,v2
κ y1 ,v2
κ y2 ,v2
where the key transmission parameters
κ yj ,uj
κ c,vj
=
1 + η hj ,wj
= (1
β ) (1
! [Frisch]
π i,t ) si,j,t
0
κ yj ,vj ! [Marshall]
η c,p 1 + η hj ,wj
η c,p + (1
η h,w = si,j,t η hj ,wj + si,
B LUNDELL , UCL & IFS ()
1
∆u1,t
C
B
A B ∆u2,t C
@ v1,t A
v2,t
1
β ) (1
j,t η h j ,w
C ONSUMPTION AND FAMILY L ABOR S UPPLY
π i,t ) η h,w
j
ECB O CTOBER 2013
19 / 56
C ONSUMPTION AND E ARNINGS G ROWTH
The ’Simple’ Separable Case
0
1
0
∆ct
0
@ ∆y1,t A ' @ κ y1 ,u1
∆y2,t
0
0
0
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
κ c,v2
κ y1 ,v2
κ y2 ,v2
1
∆u1,t
C
B
A B ∆u2,t C
@ v1,t A
v2,t
1
0
Introduce now β, representing insurance over and above savings,
taxes and labour supply ! networks, etc.
Key transmission parameter becomes:
κ c,vj = (1
B LUNDELL , UCL & IFS ()
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
C ONSUMPTION AND FAMILY L ABOR S UPPLY
β ) (1
π i,t ) η h,w
ECB O CTOBER 2013
20 / 56
I DENTIFICATION WITH ASSET DATA
Note that β is not identified separately from π
Back out π from the data and estimate β
Observed in PSID
π i,t
z }| {
Assetsi,t
Human Wealthi,t + Assetsi,t
|
{z
}
Projected lifetime earnings
Human wealth is projected using observables that evolve
deterministically (e.g. age).
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
21 / 56
I DENTIFICATION WITH NON - SEPARABILITY
When preferences are non-separable, we have:
1 0
κ c,u1
∆ct
@ ∆y1,t A ' @ κ y1 ,u1
κ y2 ,u1
∆y2,t
0
κ c,u2
κ y1 ,u2
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
0
1
∆u1,t
κ c,v2
B ∆u2,t
κ y1 ,v2 A B
@ v1,t
κ y2 ,v2
v2,t
1
C
C
A
κ c,uj ! non-separability between consumption and leisure j
κ yj ,uk ! non-separability between spouses’ leisures
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
22 / 56
D ISTRIBUTION OF s BY A GE
.62
.64
s
.66
.68
.7
Human Wealthmale,i,t
Human Wealthi,t :
.6
si,t
30-34
B LUNDELL , UCL & IFS ()
35-39
40-44
45-49
Age of household head
50-54
C ONSUMPTION AND FAMILY L ABOR S UPPLY
55-59
60-65
ECB O CTOBER 2013
23 / 56
D ISTRIBUTION OF s BY A GE
si,t
Human Wealthmale,i,t
Human Wealthi,t :
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
24 / 56
D ISTRIBUTION OF π BY A GE
800
Assetsi,t
Assetsi,t +Human Wealthi,t :
0
.1
.2
Pi
.3
0
200
400
600
Total Assets (Thousands of Dollars)
.4
.5
π i,t
30-34
35-39
40-44
45-49
50-54
Age of household head
Pi
B LUNDELL , UCL & IFS ()
55-59
60-65
Total Assets (Thousands of Dollars)
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
25 / 56
D ISTRIBUTION OF π BY A GE
π i,t
Assetsi,t
Assetsi,t +Human Wealthi,t :
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
26 / 56
R ESULTS : W ITH AND W ITHOUT S EPARABILITY
E (π )
β
η c,p
η h1 ,w1
η h2 ,w2
(1)
Additive separ.
0.181
(0.008)
0.741
(0.085)
0.201
(0.077)
0.431
(0.097)
0.831
(0.133)
η c,w1
-.-
η h1 ,p
-.-
η c,w2
-.-
η h2 ,p
-.-
η h1 ,w2
-.-
η h2 ,w1
-.-
B LUNDELL , UCL & IFS ()
(2)
Non-separab.
0.181
(0.008)
0.120
(3)
Non-separab.
0.181
(0.008)
0
(0.098)
0.437
(0.124)
0.514
(0.150)
1.032
(0.265)
0.141
(0.051)
0.082
(0.030)
0.138
(0.139)
0.162
(0.166)
0.128
(0.052)
0.258
(0.103)
C ONSUMPTION AND FAMILY L ABOR S UPPLY
0.448
(0.126)
0.497
(0.150)
1.041
(0.275)
0.141
(0.053)
0.082
(0.031)
0.158
(0.121)
0.185
(0.145)
0.120
(0.064)
0.242
(0.119)
ECB O CTOBER 2013
27 / 56
M ARSHALLIAN E LASTICITIES : B Y A GE
-.1
0
.1
.2
.3
.4
Marshallian Elasticities
30-34
35-39
40-44
45-49
50-54
Age of household head
55-59
60-65
Wife's Marshallian Elasticity
Head's Marshallian Elasticity
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
28 / 56
M ARSHALLIAN E LASTICITIES : B Y A GE
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
29 / 56
M ARSHALLIAN E LASTICITIES : B Y A GE
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
30 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO M ALE WAGES )
The average response of total earnings (y = y1 + y2 ) to a permanent
shock to the male’s wages:
∂∆y
= |{z}
s
∂v1
bs=0.69
B LUNDELL , UCL & IFS ()
∂∆y1
+ (1 s)
| {z }
∂v
| {z1 }
1 bs=0.31
b
κ y1 ,v1 =0.98
∂∆y2
∂v
| {z1 }
= 0.44
b
κ y2 ,v1 = 0.81
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
31 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO M ALE WAGES )
The average response of total earnings (y = y1 + y2 ) to a permanent
shock to the male’s wages:
∂∆y
= |{z}
s
∂v1
bs=0.69
∂∆y1
+ (1 s)
| {z }
∂v
| {z1 }
1 bs=0.31
b
κ y1 ,v1 =0.98
∂∆y2
∂v
| {z1 }
= 0.44
b
κ y2 ,v1 = 0.81
Response of consumption to a 10% permanent decrease in the male’s
wage rate (v1 = 0.1):
one earner, fixed labor supply and no insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-10%
ECB O CTOBER 2013
31 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO M ALE WAGES )
The average response of total earnings (y = y1 + y2 ) to a permanent
shock to the male’s wages:
∂∆y
= |{z}
s
∂v1
bs=0.69
∂∆y1
+ (1 s)
| {z }
∂v
| {z1 }
1 bs=0.31
b
κ y1 ,v1 =0.98
∂∆y2
∂v
| {z1 }
= 0.44
b
κ y2 ,v1 = 0.81
Response of consumption to a 10% permanent decrease in the male’s
wage rate (v1 = 0.1):
one earner, fixed labor supply and no insurance
two earners, fixed labor supply and no insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-10%
-6.9%
ECB O CTOBER 2013
31 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO M ALE WAGES )
The average response of total earnings (y = y1 + y2 ) to a permanent
shock to the male’s wages:
∂∆y
= |{z}
s
∂v1
bs=0.69
∂∆y1
+ (1 s)
| {z }
∂v
| {z1 }
1 bs=0.31
b
κ y1 ,v1 =0.98
∂∆y2
∂v
| {z1 }
= 0.44
b
κ y2 ,v1 = 0.81
Response of consumption to a 10% permanent decrease in the male’s
wage rate (v1 = 0.1):
one earner, fixed labor supply and no insurance
two earners, fixed labor supply and no insurance
with husband labor supply adjustment
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-10%
-6.9%
-6.8%
ECB O CTOBER 2013
31 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO M ALE WAGES )
The average response of total earnings (y = y1 + y2 ) to a permanent
shock to the male’s wages:
∂∆y
= |{z}
s
∂v1
bs=0.69
∂∆y1
+ (1 s)
| {z }
∂v
| {z1 }
1 bs=0.31
b
κ y1 ,v1 =0.98
∂∆y2
∂v
| {z1 }
= 0.44
b
κ y2 ,v1 = 0.81
Response of consumption to a 10% permanent decrease in the male’s
wage rate (v1 = 0.1):
one earner, fixed labor supply and no insurance
two earners, fixed labor supply and no insurance
with husband labor supply adjustment
with family labor supply adjustment
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-10%
-6.9%
-6.8%
-4.4%
ECB O CTOBER 2013
31 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO M ALE WAGES )
The average response of total earnings (y = y1 + y2 ) to a permanent
shock to the male’s wages:
∂∆y
= |{z}
s
∂v1
bs=0.69
∂∆y1
+ (1 s)
| {z }
∂v
| {z1 }
1 bs=0.31
b
κ y1 ,v1 =0.98
∂∆y2
∂v
| {z1 }
= 0.44
b
κ y2 ,v1 = 0.81
Response of consumption to a 10% permanent decrease in the male’s
wage rate (v1 = 0.1):
one earner, fixed labor supply and no insurance
two earners, fixed labor supply and no insurance
with husband labor supply adjustment
with family labor supply adjustment
with family labor supply adjustment and other insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-10%
-6.9%
-6.8%
-4.4%
-3.8%
ECB O CTOBER 2013
31 / 56
I NSURANCE VIA L ABOR S UPPLY (S HOCK TO M ALE
WAGES ): B Y A GE
-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
60-65
fixed labor supply and no insurance
with family labor supply adjustment
with family labor supply adjustment and other insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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I NSURANCE VIA L ABOR S UPPLY (S HOCK TO M ALE
WAGES ): B Y A GE
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
33 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO F EMALE WAGES )
The average response of total earnings to a permanent shock to the
female’s wages:
∂∆y
= |{z}
s
∂v2
0.69
∂∆y1
∂v
| {z2 }
κ y1 ,v2 = 0.23
+ (1 s)
| {z }
0.31
∂∆y2
= 0.25
∂v2
| {z }
κ y2 ,v2 =1.32
Response of consumption to a 10% permanent decrease in the female’s
wage rate (v2 = 0.1):
two earners, fixed labor supply and no insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-3.1%
ECB O CTOBER 2013
34 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO F EMALE WAGES )
The average response of total earnings to a permanent shock to the
female’s wages:
∂∆y
= |{z}
s
∂v2
0.69
∂∆y1
∂v
| {z2 }
κ y1 ,v2 = 0.23
+ (1 s)
| {z }
0.31
∂∆y2
= 0.25
∂v2
| {z }
κ y2 ,v2 =1.32
Response of consumption to a 10% permanent decrease in the female’s
wage rate (v2 = 0.1):
two earners, fixed labor supply and no insurance
with family labor supply adjustment
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-3.1%
-2.5%
ECB O CTOBER 2013
34 / 56
I NTERPRETATION : I NSURANCE V IA L ABOR S UPPLY
(S HOCK TO F EMALE WAGES )
The average response of total earnings to a permanent shock to the
female’s wages:
∂∆y
= |{z}
s
∂v2
0.69
∂∆y1
∂v
| {z2 }
κ y1 ,v2 = 0.23
+ (1 s)
| {z }
0.31
∂∆y2
= 0.25
∂v2
| {z }
κ y2 ,v2 =1.32
Response of consumption to a 10% permanent decrease in the female’s
wage rate (v2 = 0.1):
two earners, fixed labor supply and no insurance
with family labor supply adjustment
with family labor supply adjustment and other insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
-3.1%
-2.5%
-2.1%
ECB O CTOBER 2013
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S UMMARY AND CONCLUSIONS ...
Focus on understanding the transmission of inequality over the
working life.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
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S UMMARY AND CONCLUSIONS ...
Focus on understanding the transmission of inequality over the
working life.
Found that family labor supply is a key mechanism for smoothing
consumption
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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S UMMARY AND CONCLUSIONS ...
Focus on understanding the transmission of inequality over the
working life.
Found that family labor supply is a key mechanism for smoothing
consumption
I
I
especially for those with limited access to assets,
and non-separability between consumption and labour supply is
essential.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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S UMMARY AND CONCLUSIONS ...
Focus on understanding the transmission of inequality over the
working life.
Found that family labor supply is a key mechanism for smoothing
consumption
I
I
especially for those with limited access to assets,
and non-separability between consumption and labour supply is
essential.
Once family labor supply, assets and taxes (and benefits) are
properly accounted for, there is less evidence for additional
insurance
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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S UMMARY AND CONCLUSIONS ...
Focus on understanding the transmission of inequality over the
working life.
Found that family labor supply is a key mechanism for smoothing
consumption
I
I
especially for those with limited access to assets,
and non-separability between consumption and labour supply is
essential.
Once family labor supply, assets and taxes (and benefits) are
properly accounted for, there is less evidence for additional
insurance
I
lots to be done to dig deeper into these, and other, mechanisms.
I
consider detailed consumption components and form of
non-separability.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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E XTRA S LIDES
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
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R ESULTS BY AGE , EDUCATION AND ASSET SELECTIONS
E (π )
β
η c,p
η h1 ,w1
η h2 ,w2
η c,w1
η h1 ,p
η c,w2
η h2 ,p
η h1 ,w2
η h2 ,w1
Baseline
0.181
0.120
Age 30-55
0.142
0.177
Some college+
0.202
0.117
(0.098)
(0.089)
(0.072)
0.437
(0.124)
0.465
(0.044)
0.368
0.343
0.514
0.467
0.542
0.388
(0.05)
(0.150)
(0.036)
(0.045)
1.032
1.039
0.858
(0.265)
0.141
(0.099)
0.113
(0.051)
(0.018)
0.082
0.065
(0.030)
0.138
(0.139)
0.162
(0.166)
0.128
(0.01)
0.083
(0.029)
0.097
(0.034)
0.162
(0.022)
0.087
(0.012)
0.142
(0.032)
0.169
(0.084)
(0.04)
(0.037)
0.986
(0.105)
0.127
(0.016)
0.07
(0.009)
0.129
(0.154)
0.154
(0.038)
(0.038)
(0.052)
(0.011)
(0.012)
0.115
0.079
0.258
0.205
0.255
0.172
(0.103)
0.101
(0.097)
Top 2 asset terc.
0.245
0.046
(0.022)
(0.027)
(0.01)
(0.021)
Note: Specifications (2) to (4) - Non-bootstrap s.e.’s
B LUNDELL , UCL & IFS ()
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C ONCAVITY AND A DVANCE I NFORMATION
Concavity of preferences. Use the fact that:
0
η cp pc
B
@
η h1 p hp1
η h2 p hp2
I
η cw1 wc1
η h1 w1 wh11
η h2 w1 wh21
η cw2 wc2
1
0
B
η h1 w2 wh12 C
A = λB
@
η h2 w2 wh22
d2 u
dc2
d2 u
dl1 dc
d2 u
dl2 dc
d2 u
dcdl1
d2 u
dl21
d2 u
dl2 dl1
d2 u
dcdl2
d2 u
dl1 dl2
d2 u
dl22
1
1
C
C
A
Appendix shows concavity cannot rejected, and is numerically
satisfied at average values of wages, hours, consumption.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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C ONCAVITY AND A DVANCE I NFORMATION
Concavity of preferences. Use the fact that:
0
η cp pc
B
@
η h1 p hp1
η h2 p hp2
I
η cw1 wc1
η h1 w1 wh11
η h2 w1 wh21
η cw2 wc2
1
0
B
η h1 w2 wh12 C
A = λB
@
η h2 w2 wh22
d2 u
dc2
d2 u
dl1 dc
d2 u
dl2 dc
d2 u
dcdl1
d2 u
dl21
d2 u
dl2 dl1
d2 u
dcdl2
d2 u
dl1 dl2
d2 u
dl22
1
1
C
C
A
Appendix shows concavity cannot rejected, and is numerically
satisfied at average values of wages, hours, consumption.
Advance Information. Consumption growth should be correlated
with future wage growth (Cunha et al., 2008, and BPP 2008).
I
Test has p-value 13%
B LUNDELL , UCL & IFS ()
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R ESULTS : E XTENSIVE M ARGIN
Estimate a "conditional" Euler equation, controlling for changes in
hours (intensive margin) and changes in participation (extensive
margin)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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R ESULTS : E XTENSIVE M ARGIN
Estimate a "conditional" Euler equation, controlling for changes in
hours (intensive margin) and changes in participation (extensive
margin)
∆EMPt (Male)
∆ht (Male)
∆EMPt (Female)
∆ht (Female)
Sample
Instruments
Regression results
(1)
(2)
0.144
(0.269)
0.073
(0.075)
B LUNDELL , UCL & IFS ()
26.3
135.5
98.4
91.2
86.5
77.7
(0.021)
0.356
0.362
(0.169)
(0.176)
0.220
(0.100)
0.171
(0.094)
All
lags
2nd ,4th
Note: ∆xt is defined as (xt
0.013
First stage F-stats
(1)
(2)
23.4
xt
EMPt (Male)=1
2nd ,4th lags
1 ) / [0.5 (xt
+ xt 1 )]
C ONSUMPTION AND FAMILY L ABOR S UPPLY
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WAGE PARAMETERS BY A SSETS AND A GE
(1)
All
Sample
Males
Females
Correlations of
Shocks
(2)
(3)
1st asset
tercile
2nd, 3rd
asset
terciles
(4)
age<40
(5)
age>=40
Trans.
σ2u1
0.033
(0.007)
0.03
(0.009)
0.042
(0.009)
0.042
(0.013)
0.028
(0.008)
Perm.
σ2v1
0.035
(0.005)
0.027
(0.006)
0.039
(0.007)
0.025
(0.009)
0.039
(0.007)
Trans.
σ2u2
0.012
(0.005)
0.023
(0.009)
0.011
(0.007)
0.02
(0.015)
0.01
(0.005)
Perm.
σ2v2
0.046
(0.004)
0.036
(0.007)
0.05
(0.006)
0.053
(0.013)
0.042
(0.005)
Trans.
σu1,u2
0.202
(0.159)
-0.264
(0.181)
0.39
(0.197)
0.459
(0.28)
0.115
(0.201)
Perm.
σv1,v2
0.153
(0.06)
8,191
0.366
(0.142)
2,626
0.096
(0.066)
5,565
0.041
(0.174)
2,172
0.162
(0.063)
6,019
Observations
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
B LUNDELL , UCL & IFS ()
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
C ONSUMPTION AND FAMILY L ABOR S UPPLY
π i,t ) η h,w
ECB O CTOBER 2013
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T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
declines with π i,t (accumulated assets allow better insurance of
shocks)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
declines with π i,t (accumulated assets allow better insurance of
shocks)
declines with β (outside insurance allows more smoothing)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
declines with π i,t (accumulated assets allow better insurance of
shocks)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earnings play heavier weight)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
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T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
declines with π i,t (accumulated assets allow better insurance of
shocks)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earnings play heavier weight)
increases with η c,p (consumers more tolerant of intertemporal
fluctuations in consumption)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
41 / 56
T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
declines with π i,t (accumulated assets allow better insurance of
shocks)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earnings play heavier weight)
increases with η c,p (consumers more tolerant of intertemporal
fluctuations in consumption)
declines with η h j ,w j ("added worker" effect)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
41 / 56
T RANSMISSION PARAMETERS :
Consumption response to j’s permanent wage shock:
κ c,vj = (1
β ) (1
π i,t ) si,j,t
η c,p 1 + η hj ,wj
η c,p + (1
β ) (1
π i,t ) η h,w
declines with π i,t (accumulated assets allow better insurance of
shocks)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earnings play heavier weight)
increases with η c,p (consumers more tolerant of intertemporal
fluctuations in consumption)
declines with η h j ,w j ("added worker" effect)
declines with η hj ,wj only if j’s labor supply responds negatively to
own permanent shock. In one-earner case, true if
(1
B LUNDELL , UCL & IFS ()
β ) (1
π i,t )
η c,p > 0
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D ATA AND S AMPLE S ELECTION
PSID biennial 1999-2009:
I
PSID consumption went through a major revision in 1999
F
F
F
I
I
~70% of consumption expenditures. Good match with NIPA
The sum of food at home, food away from home, gasoline, health,
transportation, utilities, etc.
Main items that are missing: clothing (now included), recreation,
alcohol and tobacco
Earning and hours for each earner
Assets data available for each wave
B LUNDELL , UCL & IFS ()
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D ATA AND S AMPLE S ELECTION
PSID biennial 1999-2009:
I
PSID consumption went through a major revision in 1999
F
F
F
I
I
~70% of consumption expenditures. Good match with NIPA
The sum of food at home, food away from home, gasoline, health,
transportation, utilities, etc.
Main items that are missing: clothing (now included), recreation,
alcohol and tobacco
Earning and hours for each earner
Assets data available for each wave
To begin with focus on:
I
I
I
Married couples, male aged 30-60 (with robustness on 30-55 group)
Working males (93% in this age group)
Stable household composition
B LUNDELL , UCL & IFS ()
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D ATA AND S AMPLE S ELECTION
PSID biennial 1999-2009:
I
PSID consumption went through a major revision in 1999
F
F
F
I
I
~70% of consumption expenditures. Good match with NIPA
The sum of food at home, food away from home, gasoline, health,
transportation, utilities, etc.
Main items that are missing: clothing (now included), recreation,
alcohol and tobacco
Earning and hours for each earner
Assets data available for each wave
To begin with focus on:
I
I
I
Married couples, male aged 30-60 (with robustness on 30-55 group)
Working males (93% in this age group)
Stable household composition
Methodology: Use structural restrictions that ‘theory’ imposes on
the variance covariance structure of ∆ci,t , ∆yi,1,t and ∆yi,2,t
B LUNDELL , UCL & IFS ()
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S OME E CONOMETRICS I SSUES
Measurement error
I
I
For consumption, use martingale assumption and mean-reversion
For wages, use external estimates from Bound et al. (1994)
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
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S OME E CONOMETRICS I SSUES
Measurement error
I
I
For consumption, use martingale assumption and mean-reversion
For wages, use external estimates from Bound et al. (1994)
Non-Participation
I
I
~20% of women in our sample work 0 hours in a given year
Selection adjusted second moments
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
ECB O CTOBER 2013
43 / 56
S OME E CONOMETRICS I SSUES
Measurement error
I
I
For consumption, use martingale assumption and mean-reversion
For wages, use external estimates from Bound et al. (1994)
Non-Participation
I
I
~20% of women in our sample work 0 hours in a given year
Selection adjusted second moments
Inference
I
I
Multi-step procedure
Block bootstrap standard errors
B LUNDELL , UCL & IFS ()
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I NFERENCE
Multi-step estimation procedure:
I
I
I
I
Regress ci,t , yi,j,t , wi,j,t on observable characteristics, and construct the
residuals ∆ci,t , ∆yi,j,t and ∆wi,j,t
Estimate the wage parameters using the conditional second order
moments for ∆wi,1,t and ∆wi,2,t
Estimate π i,t and si,t using asset and (current and projected) earnings
data
Estimate preference parameters using restrictions on the joint
behavior of ∆ci,t , ∆yi,j,t and ∆wi,j,t
GMM with standard errors corrected by the block bootstrap.
B LUNDELL , UCL & IFS ()
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N ON -S EPARABILITY AND M EASUREMENT E RRORS
0
B
B
B
B
@
∆wi,1,t
∆wi,2,t
∆ci,t
∆yi,1,t
∆yi,2,t
1
0
1
0
C B
C B
C ' B κ c,u
1
C B
A @ κ y ,u
1 1
κ y2 ,u1
0
1
1
0
0
1
κ c,u2
κ y1 ,u2
κ y2 ,u2
κ c,v1
κ y1 ,v1
κ y2 ,v1
κ c,v2
κ y1 ,v2
κ y2 ,v2
1
0
∆ui,1,t
C
C B ∆ui,2,t
CB
C @ vi,1,t
A
vi,2,t
∆ξ w
i,1,t
∆ξ w
i,2,t
C
C + ∆ξ ci,t
A
y
∆ξ i,1,t
y
∆ξ i,2,t
1
y
c
where ξ w
i,j,t , ξ i,t and ξ i,j,t are measurement errors in log wages of
earner j, log consumption, and log earnings of earner j.
B LUNDELL , UCL & IFS ()
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I NCOME DYNAMICS - MORE DETAILS
Our focus here is on non-stationarity, heterogenous profiles, and
shocks of varying persistence.
B LUNDELL , UCL & IFS ()
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I NCOME DYNAMICS - MORE DETAILS
Our focus here is on non-stationarity, heterogenous profiles, and
shocks of varying persistence.
Individual i of age a in time period t, has log income yi,a (
ln Yi,a,t )
yi,a = ZTi,a ϕa + f0i + f1i pa + yPi,a + εi,a
where βi pa is an individual-specific trend, allow non-zero
covariance between f0 and f1 .
B LUNDELL , UCL & IFS ()
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I NCOME DYNAMICS - MORE DETAILS
Our focus here is on non-stationarity, heterogenous profiles, and
shocks of varying persistence.
Individual i of age a in time period t, has log income yi,a (
ln Yi,a,t )
yi,a = ZTi,a ϕa + f0i + f1i pa + yPi,a + εi,a
where βi pa is an individual-specific trend, allow non-zero
covariance between f0 and f1 .
yTi,a is the persistent process with variance σ2a
yTi,a = ρyTi,a
1
+ vi,a
and εi,a is a transitory process (can be low order MA) with variance
ω 2a (can be low order MA).
B LUNDELL , UCL & IFS ()
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I NCOME DYNAMICS - MORE DETAILS
Our focus here is on non-stationarity, heterogenous profiles, and
shocks of varying persistence.
Individual i of age a in time period t, has log income yi,a (
ln Yi,a,t )
yi,a = ZTi,a ϕa + f0i + f1i pa + yPi,a + εi,a
where βi pa is an individual-specific trend, allow non-zero
covariance between f0 and f1 .
yTi,a is the persistent process with variance σ2a
yTi,a = ρyTi,a
1
+ vi,a
and εi,a is a transitory process (can be low order MA) with variance
ω 2a (can be low order MA).
Allow variances (or factor loadings) of vi,a and εi,a to vary with
age/time for each birth cohort and education group.
B LUNDELL , UCL & IFS ()
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I DIOSYNCRATIC T RENDS
The idiosyncratic trend term pt f1i could take a number of forms.
Two alternatives are worth highlighting:
I
(a) deterministic idiosyncratic trend:
pt f1i = r(t)f1i
where r is a known function of t, e.g. r(t) = t,
B LUNDELL , UCL & IFS ()
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I DIOSYNCRATIC T RENDS
The idiosyncratic trend term pt f1i could take a number of forms.
Two alternatives are worth highlighting:
I
(a) deterministic idiosyncratic trend:
pt f1i = r(t)f1i
I
where r is a known function of t, e.g. r(t) = t, and
(b) stochastic trend in ‘ability prices’:
pt = pt
with Et
1ξt
B LUNDELL , UCL & IFS ()
1
+ ξt
= 0.
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I DIOSYNCRATIC T RENDS
The idiosyncratic trend term pt f1i could take a number of forms.
Two alternatives are worth highlighting:
I
(a) deterministic idiosyncratic trend:
pt f1i = r(t)f1i
I
where r is a known function of t, e.g. r(t) = t, and
(b) stochastic trend in ‘ability prices’:
pt = pt
with Et
1ξt
1
+ ξt
= 0.
Evidence points to some periods of time where each of these is of
key importance. Deterministic trends as in (a), appear most
prominently early in the working life. Formally, this is a life-cycle
effect.
B LUNDELL , UCL & IFS ()
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I DIOSYNCRATIC T RENDS
The idiosyncratic trend term pt f1i could take a number of forms.
Two alternatives are worth highlighting:
I
(a) deterministic idiosyncratic trend:
pt f1i = r(t)f1i
I
where r is a known function of t, e.g. r(t) = t, and
(b) stochastic trend in ‘ability prices’:
pt = pt
with Et
1ξt
1
+ ξt
= 0.
Evidence points to some periods of time where each of these is of
key importance. Deterministic trends as in (a), appear most
prominently early in the working life. Formally, this is a life-cycle
effect.
Alternatively, stochastic trends (b) are most likely to occur during
periods of technical change when skill prices are changing across
the unobserved ability distribution. Formally, this is a calender time
effect.
B LUNDELL , UCL & IFS ()
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I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
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I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
1
Baseline Specification: f1i = 0
B LUNDELL , UCL & IFS ()
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I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
1
2
Baseline Specification: f1i = 0
Linear Specification: pa = γ1 a + γ0 , so that
∆ρ pa = (1
where ξ 0
[a
B LUNDELL , UCL & IFS ()
ρ (a
ρ ) γ0 ι + γ1 ξ 0
1)] .
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I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
1
2
Baseline Specification: f1i = 0
Linear Specification: pa = γ1 a + γ0 , so that
∆ρ pa = (1
3
ρ ) γ0 ι + γ1 ξ 0
where ξ 0 [a ρ (a 1)] .
Quadratic Specification: pa = γ0 + γ1 a + γ2 a2
B LUNDELL , UCL & IFS ()
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I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
1
2
Baseline Specification: f1i = 0
Linear Specification: pa = γ1 a + γ0 , so that
∆ρ pa = (1
3
4
ρ ) γ0 ι + γ1 ξ 0
where ξ 0 [a ρ (a 1)] .
Quadratic Specification: pa = γ0 + γ1 a + γ2 a2
Piecewise-Linear Specification:
8
>
if a 35
< κ 1 a + 35 (1 κ 1 )
pa =
a
otherwise
>
:
κ 2 a + 52 (1 κ 2 )
if a 52
with knots at age 35 and age 52.
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
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I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
1
2
Baseline Specification: f1i = 0
Linear Specification: pa = γ1 a + γ0 , so that
∆ρ pa = (1
3
4
5
ρ ) γ0 ι + γ1 ξ 0
where ξ 0 [a ρ (a 1)] .
Quadratic Specification: pa = γ0 + γ1 a + γ2 a2
Piecewise-Linear Specification:
8
>
if a 35
< κ 1 a + 35 (1 κ 1 )
pa =
a
otherwise
>
:
κ 2 a + 52 (1 κ 2 )
if a 52
with knots at age 35 and age 52.
Polynomials up to degree 4.
B LUNDELL , UCL & IFS ()
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C OVARIANCE STRUCTURE
Suppose we observe individual i at age a = 1, ..., T, we then have
T 1 equations ∆ρ yia ( yi,a ρyi,a 1 ). In vector form
∆ρ yi = ((1
B LUNDELL , UCL & IFS ()
ρ) ι, ∆ρ pa )
f0i
f1i
+ vi + ∆ρ εi .
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C OVARIANCE STRUCTURE
Suppose we observe individual i at age a = 1, ..., T, we then have
T 1 equations ∆ρ yia ( yi,a ρyi,a 1 ). In vector form
∆ρ yi = ((1
ρ) ι, ∆ρ pa )
f0i
f1i
+ vi + ∆ρ εi .
The Variance-Covariance matrix in general has the form:
Var(∆ρ yi ) = Ω + W where W =
0 2
σ2 + ω 22 + ρ2 ω 21
ρω 22
0
0
2
2
2 + ρ2 ω 2
2
B
ρω
σ
+
ω
ρω
0
2
3
3
2
3
B
B
..
2
@
.
0
ρω
ρω 2
3
0
B LUNDELL , UCL & IFS ()
0
ρω 2T
C ONSUMPTION AND FAMILY L ABOR S UPPLY
1
T 1
1
σ2T + ω 2T + ρ2 ω 2T
ECB O CTOBER 2013
1
C
C
C
A
49 / 56
C OVARIANCE STRUCTURE
Suppose we observe individual i at age a = 1, ..., T, we then have
T 1 equations ∆ρ yia ( yi,a ρyi,a 1 ). In vector form
∆ρ yi = ((1
ρ) ι, ∆ρ pa )
f0i
f1i
+ vi + ∆ρ εi .
The Variance-Covariance matrix in general has the form:
Var(∆ρ yi ) = Ω + W where W =
0 2
σ2 + ω 22 + ρ2 ω 21
ρω 22
0
0
2
2
2 + ρ2 ω 2
2
B
ρω
σ
+
ω
ρω
0
2
3
3
2
3
B
B
..
2
@
.
0
ρω
ρω 2
3
0
0
ρω 2T
1
T 1
1
σ2T + ω 2T + ρ2 ω 2T
1
C
C
C
A
For the linear heterogeneous profiles case:
Ω = [(1
B LUNDELL , UCL & IFS ()
ρ) ι, ξ 0 ]
σ20
ρ01 σ0 σ1
ρ01 σ0 σ1
σ21
C ONSUMPTION AND FAMILY L ABOR S UPPLY
[(1
ρ) ι, ξ 0 ]T .
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R EMOVING A DDITIVE S EPARABILITY: T HEORY
Approximating the first order conditions (intensive margin):
∆ci,t '
B LUNDELL , UCL & IFS ()
η c,w1 + η c,w2
η c,p ∆ ln λi,t
+η c,w1 ∆wi,1t+1 + η c,w2 ∆wi,2t+1
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R EMOVING A DDITIVE S EPARABILITY: T HEORY
Approximating the first order conditions (intensive margin):
∆ci,t '
η c,w1 + η c,w2
η c,p ∆ ln λi,t
+η c,w1 ∆wi,1t+1 + η c,w2 ∆wi,2t+1
Interpretation:
I
I
C and H substitutes (η c,wj < 0) ) Excess smoothing
C and H complements (η c,wj > 0) ) Excess sensitivity
B LUNDELL , UCL & IFS ()
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R EMOVING A DDITIVE S EPARABILITY: T HEORY
Approximating the first order conditions (intensive margin):
∆ci,t '
η c,w1 + η c,w2
η c,p ∆ ln λi,t
+η c,w1 ∆wi,1t+1 + η c,w2 ∆wi,2t+1
Interpretation:
I
I
C and H substitutes (η c,wj < 0) ) Excess smoothing
C and H complements (η c,wj > 0) ) Excess sensitivity
Moments
1 0
0
κ i,c,u1
∆ci,t
@ ∆yi,1,t A ' @ κ i,y ,u
1 1
κ i,y2 ,u1
∆yi,2,t
κ i,c,u2
κ i,y1 ,u2
κ i,y2 ,u2
κ i,c,v1
κ i,y1 ,v1
κ i,y2 ,v1
0
1
∆ui,1,t
κ i,c,v2
B ∆ui,2,t
κ i,y1 ,v2 A B
@ vi,1,t
κ i,y2 ,v2
vi,2,t
1
C
C
A
where (for j = 1, 2)
κ i,c,uj = η c,wj ; κ i,yj ,uj = 1 + η hj ,wj ; κ i,yj ,u j = η hj ,w
B LUNDELL , UCL & IFS ()
C ONSUMPTION AND FAMILY L ABOR S UPPLY
j
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N ON - LINEAR TAXES
e it = (1
Y
B LUNDELL , UCL & IFS ()
χt ) (H1,t W1,t + H2,t W2,t )1
C ONSUMPTION AND FAMILY L ABOR S UPPLY
µt
ECB O CTOBER 2013
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N ON - LINEAR TAXES
e it = (1
Y
χt ) (H1,t W1,t + H2,t W2,t )1
µt
Implications for underlying structural preference parameters, e.g.
e
η hj ,wj =
B LUNDELL , UCL & IFS ()
η hj ,wj (1
µ)
1 + µη hj ,wj
(with e
η hj ,wj
η hj ,wj for 0
C ONSUMPTION AND FAMILY L ABOR S UPPLY
µ
1)
ECB O CTOBER 2013
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N ON - LINEAR TAXES
e it = (1
Y
χt ) (H1,t W1,t + H2,t W2,t )1
µt
Implications for underlying structural preference parameters, e.g.
e
η hj ,wj =
η hj ,wj (1
µ)
1 + µη hj ,wj
(with e
η hj ,wj
η hj ,wj for 0
µ
1)
Labor supply elasticities (w.r.t. W) are dampened: Return to work
decreases as people cross tax brackets
B LUNDELL , UCL & IFS ()
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L OADING FACTOR M ATRIX : E STIMATES
Response
to
Consump.
v1
v2
(1)
0.13
(0.060)
0.07
Separable case
Husband’s
earnings
(2)
1.15
(0.067)
0.16
Wife’s
earnings
(3)
0.54
(0.206)
1.53
(0.040)
∆u1
(0.057)
(0.101)
0
1.43
0
∆u2
0
0
1.83
B LUNDELL , UCL & IFS ()
(0.097)
Non-separable case
Consump.
Husband’s
Wife’s
earnings
earnings
(4)
(5)
(6)
0.38
0.98
0.81
(0.057)
0.21
(0.037)
0.14
(0.051)
(0.133)
0.14
(0.139)
C ONSUMPTION AND FAMILY L ABOR S UPPLY
(0.131)
0.23
(0.048)
1.51
(0.150)
0.13
(0.051)
(0.180)
1.32
(0.087)
0.26
(0.103)
2.03
(0.265)
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Heterogeneity:
(1)
Baseline
E (π )
β
0.181
0.120
0.142
0.177
(0.198)
(0.089)
0.437
η c,p
(2)
Age 30-55
(3)
Some college+
0.202
0.117
(0.072)
(4)
Top 2 asset terc.
(5)
Age variance
(6)
Sel.correct.
0.245
0.046
0.181
0.109
0.176
0.129
(0.084)
(0.077)
(0.076)
(0.124)
(0.044)
0.465
0.368
0.343
(0.04)
(0.037)
(0.041)
0.514
0.467
0.542
0.388
0.575
0.509
(0.05)
0.42
0.473
η h ,w
1 1
(0.150)
η h ,w
2 2
(0.265)
(0.099)
(0.097)
(0.105)
(0.086)
1
0.141
0.113
0.162
0.127
0.15
0.150
(0.051)
(0.018)
(0.022)
(0.016)
(0.018)
(0.017)
η h ,p
1
0.082
0.065
0.087
0.07
0.087
0.088
η c,w
1.032
(0.030)
(0.036)
1.039
(0.01)
(0.045)
0.858
(0.012)
(0.037)
0.986
(0.009)
(0.04)
1.005
(0.01)
(0.038)
1.095
(0.092)
(0.01)
2
0.138
0.083
0.142
0.129
0.11
0.122
(0.139)
(0.029)
(0.032)
(0.154)
(0.026)
(0.028)
η h ,p
2
0.162
(0.166)
0.097
0.169
0.154
0.129
0.143
η h ,w
1 2
(0.052)
(0.011)
(0.012)
0.258
0.205
η c,w
η h ,w
2 1
0.128
(0.103)
(0.034)
0.101
(0.022)
(0.038)
(0.038)
0.115
0.079
(0.01)
(0.011)
0.141
0.125
0.255
0.172
0.285
0.253
(0.027)
(0.021)
(0.038)
(0.022)
(0.033)
(0.01)
(0.021)
Note: Specifications (2) to (6) - Non-bootstrap s.e.’s
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A PPROXIMATION OF THE E ULER EQUATION (1)
δ
From λi,t = 11+
+r Et λi,t+1 , use a second order Taylor approximation
(with r = δ) to yield:
∆ ln λi,t+1
ω t + εi,t+1
where
1
Et (∆ ln λi,t+1 )2
2
= ∆ ln λi,t+1 Et (∆ ln λi,t+1 )
ωt =
εi,t+1
Then use the fact that
∆ ln UCi,t+1
∆ ln UHi,j,t+1
B LUNDELL , UCL & IFS ()
= ∆ ln λi,t+1
=
∆ ln λi,t+1
∆ ln Wi,j,t+1
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A PPROXIMATION OF THE E ULER EQUATION (2)
Consider now Taylor expansion of UCi,t+1 (= λi,t+1 ):
UCi,t+1
UCi,t
UCi,t+1
UCi,t
∆ ln UCi,t+1
UCi,t + (Ci,t+1
Ci,t+1 Ci,t
Ci,t
1
∆ ln Ci,t+1
η c,p
Ci,t ) UCi,t Ci,t
UCi,t Ci,t Ci,t
UCi,t
and therefore, from
∆ ln λi,t+1
ω t+1 + εi,t+1
get
∆ ln Ci,t+1 =
B LUNDELL , UCL & IFS ()
η c,p (ω t+1 + εi,t+1 )
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A PPROXIMATION OF THE LIFE TIME BUDGET
CONSTRAINT
Use the fact that
#
"
T t
EI ln ∑ Xt+i
i=0
T t
= ln ∑ exp Et
1 ln Xt+i
i=0
exp Et 1 ln Xt+i
T t
i=0 ∑j=0 exp Et 1 ln Xt+j
T t
+∑
+O EI ξ Tt
( EI
Et
1 ) ln Xt+i
2
for X = C, WH and appropriate choice of EI .
Goal: obtain a mapping from wage innovations to innovations in
consumption (marginal utility of wealth)
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