C ONSUMPTION I NEQUALITY AND FAMILY L ABOR
S UPPLY
C HAIR L ECTURE "P ROFESSOR C ARLOS L LOYD B RAGA "
Richard Blundell
University College London & IFS
University of Minho, 2013
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
1 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
I
Focus on labor market shocks as the primitive source of uncertainty.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
I
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various measures of inequality is mediated by
multiple ‘insurance’ mechanisms
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
I
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various measures of inequality is mediated by
multiple ‘insurance’ mechanisms, including:
1 Labor supply: family labor supply (wages! earnings! joint
2
3
4
earnings)
Taxes and welfare: (earnings! income)
Assets: Saving and borrowing (income! consumption)
Informal contracts, gifts, etc.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
I
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various measures of inequality is mediated by
multiple ‘insurance’ mechanisms, including:
1 Labor supply: family labor supply (wages! earnings! joint
2
3
4
earnings)
Taxes and welfare: (earnings! income)
Assets: Saving and borrowing (income! consumption)
Informal contracts, gifts, etc.
But how important are each of these mechanisms?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
I
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various measures of inequality is mediated by
multiple ‘insurance’ mechanisms, including:
1 Labor supply: family labor supply (wages! earnings! joint
2
3
4
earnings)
Taxes and welfare: (earnings! income)
Assets: Saving and borrowing (income! consumption)
Informal contracts, gifts, etc.
But how important are each of these mechanisms?
How do they change over the life-cycle and the business cycle?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
I NTRODUCTION
This lecture is mostly based on recent research with Luigi Pistaferri
and Itay Eksten at Stanford - NBER Working Paper, circulated.
In this work we begin by noting that inequality has many
dimensions:
I Wages! earnings! joint earnings! income! consumption
I
Focus on labor market shocks as the primitive source of uncertainty.
The link between the various measures of inequality is mediated by
multiple ‘insurance’ mechanisms, including:
1 Labor supply: family labor supply (wages! earnings! joint
2
3
4
earnings)
Taxes and welfare: (earnings! income)
Assets: Saving and borrowing (income! consumption)
Informal contracts, gifts, etc.
But how important are each of these mechanisms?
How do they change over the life-cycle and the business cycle?
How should we design policies to best insure these shocks?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
2 / 60
O VERVIEW
Seek to answer the question: How do individuals and families deal
with labour market shocks over their working life?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
3 / 60
O VERVIEW
Seek to answer the question: How do individuals and families deal
with labour market shocks over their working life?
Investigate how assets and labor market shocks combine to impact
on household consumption.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
3 / 60
O VERVIEW
Seek to answer the question: How do individuals and families deal
with labour market shocks over their working life?
Investigate how assets and labor market shocks combine to impact
on household consumption.
Draw on panel and administrative data from the US, UK and
Norway.... and make use of new information on consumption,
earnings and assets.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
3 / 60
O VERVIEW
Seek to answer the question: How do individuals and families deal
with labour market shocks over their working life?
Investigate how assets and labor market shocks combine to impact
on household consumption.
Draw on panel and administrative data from the US, UK and
Norway.... and make use of new information on consumption,
earnings and assets.
I
I
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
3 / 60
O VERVIEW
Seek to answer the question: How do individuals and families deal
with labour market shocks over their working life?
Investigate how assets and labor market shocks combine to impact
on household consumption.
Draw on panel and administrative data from the US, UK and
Norway.... and make use of new information on consumption,
earnings and assets.
I
I
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
3 / 60
O VERVIEW
Seek to answer the question: How do individuals and families deal
with labour market shocks over their working life?
Investigate how assets and labor market shocks combine to impact
on household consumption.
Draw on panel and administrative data from the US, UK and
Norway.... and make use of new information on consumption,
earnings and assets.
I
I
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
3 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
4 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
5 / 60
C ONSUMPTION I NEQUALITY IN THE US
By age and birth cohort
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
6 / 60
L ABOUR M ARKET S HOCKS AND C ONSUMPTION
We focus on income, consumption and wage dynamics. Why?
I
It is a key way of thinking about the transmission of shocks over the
life-cycle and the mechanisms used by families to ‘insure’ against
shocks.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
7 / 60
L ABOUR M ARKET S HOCKS AND C ONSUMPTION
We focus on income, consumption and wage dynamics. Why?
I
It is a key way of thinking about the transmission of shocks over the
life-cycle and the mechanisms used by families to ‘insure’ against
shocks.
I
In turn it provides a coherent framework for studying the evolution
of inequality over the life-cycle and the business cycle too.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
7 / 60
L ABOUR M ARKET S HOCKS AND C ONSUMPTION
We focus on income, consumption and wage dynamics. Why?
I
It is a key way of thinking about the transmission of shocks over the
life-cycle and the mechanisms used by families to ‘insure’ against
shocks.
I
In turn it provides a coherent framework for studying the evolution
of inequality over the life-cycle and the business cycle too.
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
7 / 60
L ABOUR M ARKET S HOCKS AND C ONSUMPTION
We focus on income, consumption and wage dynamics. Why?
I
It is a key way of thinking about the transmission of shocks over the
life-cycle and the mechanisms used by families to ‘insure’ against
shocks.
I
In turn it provides a coherent framework for studying the evolution
of inequality over the life-cycle and the business cycle too.
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
7 / 60
I NCOME D YNAMICS
To set the scene, consider consumer i (of age a) in time period t, has log
income yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + yPit + yTit
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
8 / 60
I NCOME D YNAMICS
To set the scene, consider consumer i (of age a) in time period t, has log
income yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = yPit
B LUNDELL , UCL & IFS ()
1
+ vit
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
8 / 60
I NCOME D YNAMICS
To set the scene, consider consumer i (of age a) in time period t, has log
income yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = yPit
1
+ vit
and where yTit is a transitory shock represented by some low order MA
process, say
yTit = εit + θ 1 εi,t 1
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
8 / 60
I NCOME D YNAMICS
To set the scene, consider consumer i (of age a) in time period t, has log
income yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = yPit
1
+ vit
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
8 / 60
I NCOME D YNAMICS
To set the scene, consider consumer i (of age a) in time period t, has log
income yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = yPit
1
+ vit
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.
My new research splits income into individual earnings within a
family.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
8 / 60
I NCOME D YNAMICS
To set the scene, consider consumer i (of age a) in time period t, has log
income yit ( ln Yi,a,t ) written
yit = Zit0 ϕ + f0i + yPit + yTit
where yPit is a persistent process of income shocks, say
yPit = yPit
1
+ vit
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.
My new research splits income into individual earnings within a
family.
Detailed work on Norwegian population register panel data....
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
8 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
9 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
10 / 60
C ONSUMPTION G ROWTH AND I NCOME "S HOCKS "
To account for the impact of income shocks on consumption 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
(1)
providing the link between income shocks and consumption.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
11 / 60
C ONSUMPTION G ROWTH AND I NCOME "S HOCKS "
To account for the impact of income shocks on consumption 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
(1)
providing the link between income shocks and consumption.
For example, Blundell, Low and Preston (QE, 2013) show in the
permament-transitory model, for any birth-cohort
∆ ln Cit = Γit + ∆Zit0 ϕc + (1
π it )vit + (1
π it )γLt εit + ξ it
where
Assetsit
Assetsit + Human Wealthit
and γLt is the annuity value of a transitory shock for an individual
aged t retiring at age L.
π it
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
11 / 60
C ONSUMPTION G ROWTH AND I NCOME "S HOCKS "
To account for the impact of income shocks on consumption 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
(1)
providing the link between income shocks and consumption.
For example, Blundell, Low and Preston (QE, 2013) show in the
permament-transitory model, for any birth-cohort
∆ ln Cit = Γit + ∆Zit0 ϕc + (1
π it )vit + (1
π it )γLt εit + ξ it
where
Assetsit
Assetsit + Human Wealthit
and γLt is the annuity value of a transitory shock for an individual
aged t retiring at age L.
I With (1 π it ) measured through asset data we can examine
mechanisms in addition to self-insurance.
I But typically use (1), as asset data is poorly measured and estimate
the κ t0 s as a catch-all for all forms of insurance - until recently!
π it
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
11 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
For families with low net wealth estimates of κ cvt are typically close
to unity and the transmission of transitory shocks κ cεt is significant.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
For families with low net wealth estimates of κ cvt are typically close
to unity and the transmission of transitory shocks κ cεt is significant.
Allows us to track the relationship between the distribution of income
shocks and consumption across the life-cycle and business cycle.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
For families with low net wealth estimates of κ cvt are typically close
to unity and the transmission of transitory shocks κ cεt is significant.
Allows us to track the relationship between the distribution of income
shocks and consumption across the life-cycle and business cycle.
I Spike in the variance of permanent shocks during the 80s and 90s
recessions.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
For families with low net wealth estimates of κ cvt are typically close
to unity and the transmission of transitory shocks κ cεt is significant.
Allows us to track the relationship between the distribution of income
shocks and consumption across the life-cycle and business cycle.
I Spike in the variance of permanent shocks during the 80s and 90s
recessions.
But can we do a better job by incorporating asset data?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
For families with low net wealth estimates of κ cvt are typically close
to unity and the transmission of transitory shocks κ cεt is significant.
Allows us to track the relationship between the distribution of income
shocks and consumption across the life-cycle and business cycle.
I Spike in the variance of permanent shocks during the 80s and 90s
recessions.
But can we do a better job by incorporating asset data?
And what of family labour supply as an ‘insurance’ mechanism?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
Estimates of transmission of permanent shocks to consumption κ cvt
average around .64 (Blundell, Pistaferri and Preston, AER, 2008).
Higher values of κ cvt for younger families and lower as families
approach retirement.
For families with low net wealth estimates of κ cvt are typically close
to unity and the transmission of transitory shocks κ cεt is significant.
Allows us to track the relationship between the distribution of income
shocks and consumption across the life-cycle and business cycle.
I Spike in the variance of permanent shocks during the 80s and 90s
recessions.
But can we do a better job by incorporating asset data?
And what of family labour supply as an ‘insurance’ mechanism?
And "non-separabilities" between consumption and work?
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
12 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
3
Non-linear taxes and welfare
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms ‘β’,
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms ‘β’, - and check for advance
information.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms ‘β’, - and check for advance
information.
Empirical results allow for non-separability, heterogeneous assets,
correlated shocks to individual wages in families
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms ‘β’, - and check for advance
information.
Empirical results allow for non-separability, heterogeneous assets,
correlated shocks to individual wages in families
Here I’ll briefly present results with new data from the PSID
1999-2009.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
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13 / 60
I N OUR RECENT WORK LOOK AT FOUR KEY
MECHANISMS :
1
Self-insurance (i.e., savings) through a direct measure of π it
2
Joint labour supply of each earner, through a measure of the
employment and hours of family members.
3
Non-linear taxes and welfare
4
Other (un-modeled) mechanisms ‘β’, - and check for advance
information.
Empirical results allow for non-separability, heterogeneous assets,
correlated shocks to individual wages in families
Here I’ll briefly present results with new data from the PSID
1999-2009.
I
I
More comprehensive consumption measure - over 70% of the budget.
Asset data collected in every wave - housing, financial, mortgage and
other debt.
B LUNDELL , UCL & IFS ()
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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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14 / 60
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 ()
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15 / 60
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 ()
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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
1
ui,1,t
B ui,2,t C
C
B
@ vi,1,t A
vi,2,t
0
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 ()
00
σu1 ,u2
σ2u,2
0
0
I NEQUALITY AND FAMILY L ABOR S UPPLY
0
0
σ2v,1
σv1 ,v2
0
0
σv1 ,v2
σ2v,2
11
CC
CC
AA
U NIVERSITY OF M INHO , 2013
16 / 60
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
1
ui,1,t
B ui,2,t C
C
B
@ vi,1,t A
vi,2,t
0
1 0 2
σu,1
0
BB 0 C B σu1 ,u2
B C B
i.i.d. B
@@ 0 A , @ 0
0
0
00
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 across the life-cycle and across the
business cycle.
B LUNDELL , UCL & IFS ()
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16 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
(0.007)
0.032
(0.005)
0.012
(0.006)
0.043
(0.005)
(0.22)
(0.07)
U NIVERSITY OF M INHO , 2013
17 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, 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
I NEQUALITY AND FAMILY L ABOR S UPPLY
β ) (1
π i,t ) η h,w
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, becomes:
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)
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, becomes:
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)
declines with β (outside insurance allows more smoothing)
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, becomes:
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)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earning share)
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, becomes:
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)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earning share)
increases wtih tolerance of intertemporal fluctuations.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, becomes:
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)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earning share)
increases wtih tolerance of intertemporal fluctuations.
declines with "added worker" effect - Marshallian labour supply
elasticity.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
E XTENDED T RANSMISSION PARAMETERS :
Consumption growth:
∆ ln Cit = κ cv1 t vi,1t + κ cv2 t vi,2t + κ cu1 t ∆ui,1t + κ cu2 t ∆ui,2t + ξ it
Key transmission parameter: consumption response to a permanent
wage shock, becomes:
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)
declines with β (outside insurance allows more smoothing)
increases with si,j,t (j’s earning share)
increases wtih tolerance of intertemporal fluctuations.
declines with "added worker" effect - Marshallian labour supply
elasticity.
similar transmission equations for family labour supply.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
18 / 60
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 ()
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19 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
55-59
60-65
U NIVERSITY OF M INHO , 2013
20 / 60
D ISTRIBUTION OF s BY A GE
si,t
Human Wealthmale,i,t
Human Wealthi,t :
B LUNDELL , UCL & IFS ()
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21 / 60
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)
I NEQUALITY AND FAMILY L ABOR S UPPLY
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D ISTRIBUTION OF π BY A GE
π i,t
Assetsi,t
Assetsi,t +Human Wealthi,t :
B LUNDELL , UCL & IFS ()
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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)
I NEQUALITY 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)
U NIVERSITY OF M INHO , 2013
24 / 60
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 ()
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M ARSHALLIAN E LASTICITIES : B Y A GE
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
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M ARSHALLIAN E LASTICITIES : B Y A GE
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
27 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
28 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-10%
U NIVERSITY OF M INHO , 2013
28 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-10%
-6.9%
U NIVERSITY OF M INHO , 2013
28 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-10%
-6.9%
-6.8%
U NIVERSITY OF M INHO , 2013
28 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-10%
-6.9%
-6.8%
-4.4%
U NIVERSITY OF M INHO , 2013
28 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-10%
-6.9%
-6.8%
-4.4%
-3.8%
U NIVERSITY OF M INHO , 2013
28 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
29 / 60
I NSURANCE VIA L ABOR S UPPLY (S HOCK TO M ALE
WAGES ): B Y A GE
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
30 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-3.1%
U NIVERSITY OF M INHO , 2013
31 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-3.1%
-2.5%
U NIVERSITY OF M INHO , 2013
31 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
-3.1%
-2.5%
-2.1%
U NIVERSITY OF M INHO , 2013
31 / 60
P UTTING THE PIECES TOGETHER ...
Focus on understanding the transmission of inequality over the
working life.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
32 / 60
P UTTING THE PIECES TOGETHER ...
Focus on understanding the transmission of inequality over the
working life.
From wages! earnings! joint earnings! income! consumption.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
32 / 60
P UTTING THE PIECES TOGETHER ...
Focus on understanding the transmission of inequality over the
working life.
From wages! earnings! joint earnings! income! consumption.
Addressing some of the key ‘puzzles’ in the literature.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
32 / 60
P UTTING THE PIECES TOGETHER ...
Focus on understanding the transmission of inequality over the
working life.
From wages! earnings! joint earnings! income! consumption.
Addressing some of the key ‘puzzles’ in the literature.
Documenting the importance of four different ‘insurance’
mechanisms
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
32 / 60
P UTTING THE PIECES TOGETHER ...
Focus on understanding the transmission of inequality over the
working life.
From wages! earnings! joint earnings! income! consumption.
Addressing some of the key ‘puzzles’ in the literature.
Documenting the importance of four different ‘insurance’
mechanisms:
I
Saving and credit markets
I
Taxes and welfare
I
Family labour supply
I
Informal contracts, gifts, etc.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
32 / 60
P UTTING THE PIECES TOGETHER ...
Focus on understanding the transmission of inequality over the
working life.
From wages! earnings! joint earnings! income! consumption.
Addressing some of the key ‘puzzles’ in the literature.
Documenting the importance of four different ‘insurance’
mechanisms:
I
Saving and credit markets
I
Taxes and welfare
I
Family labour supply
I
Informal contracts, gifts, etc.
Showing the value, and possibilities for collecting, good panel data
on consumption, earnings and assets.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
32 / 60
A ND GATHERING UP THE RESULTS ...
Need to allow for non-stationarity over the life-cycle and over time
I
I
variances (of persistent shocks) display an U-shape over the
(working) life-cycle,
note the spike in the variance of permanent shocks during the 80s
and 90s recessions.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
33 / 60
A ND GATHERING UP THE RESULTS ...
Need to allow for non-stationarity over the life-cycle and over time
I
I
variances (of persistent shocks) display an U-shape over the
(working) life-cycle,
note the spike in the variance of permanent shocks during the 80s
and 90s recessions.
Found that family labor supply is a key mechanism for smoothing
consumption
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
33 / 60
A ND GATHERING UP THE RESULTS ...
Need to allow for non-stationarity over the life-cycle and over time
I
I
variances (of persistent shocks) display an U-shape over the
(working) life-cycle,
note the spike in the variance of permanent shocks during the 80s
and 90s recessions.
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
33 / 60
A ND GATHERING UP THE RESULTS ...
Need to allow for non-stationarity over the life-cycle and over time
I
I
variances (of persistent shocks) display an U-shape over the
(working) life-cycle,
note the spike in the variance of permanent shocks during the 80s
and 90s recessions.
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 little evidence for additional
insurance
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
33 / 60
A ND GATHERING UP THE RESULTS ...
Need to allow for non-stationarity over the life-cycle and over time
I
I
variances (of persistent shocks) display an U-shape over the
(working) life-cycle,
note the spike in the variance of permanent shocks during the 80s
and 90s recessions.
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 little evidence for additional
insurance
I
lots to be done to dig deeper into these, and other, mechanisms.
I
consider detailed consumption components....
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
33 / 60
Consumption Inequality and Family Labor Supply
Chair Lecture "Professor Carlos Lloyd Braga"
Richard Blundell
University College London & Institute for Fiscal Studies
University of Minho, 2013
Many thanks!
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
34 / 60
E XTRA S LIDES
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
35 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
36 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
37 / 60
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 cw2 wc2
1
0
B
η h1 w2 wh12 C
A = λB
@
η h2 w2 wh22
η h1 w1 wh11
η h2 w1 wh21
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
37 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
38 / 60
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 )]
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
38 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
39 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
π i,t ) η h,w
U NIVERSITY OF M INHO , 2013
40 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
40 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
40 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
40 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
40 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
40 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
40 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
41 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
41 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
41 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
42 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
42 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
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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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44 / 60
I NCOME DYNAMICS - MORE DETAILS
Our focus here is on non-stationarity, heterogenous profiles, and
shocks of varying persistence.
B LUNDELL , UCL & IFS ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
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45 / 60
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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45 / 60
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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45 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
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46 / 60
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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46 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
46 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
46 / 60
I DIOSYNCRATIC T RENDS
For each cohort we consider several alternative models for the
heterogenous profile βi pa :
B LUNDELL , UCL & IFS ()
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U NIVERSITY OF M INHO , 2013
47 / 60
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)] .
I NEQUALITY 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
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
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47 / 60
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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 2013
47 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
+ vi + ∆ρ εi .
U NIVERSITY OF M INHO , 2013
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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
I NEQUALITY AND FAMILY L ABOR S UPPLY
1
T 1
1
σ2T + ω 2T + ρ2 ω 2T
U NIVERSITY OF M INHO , 2013
1
C
C
C
A
48 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
[(1
ρ) ι, ξ 0 ]T .
U NIVERSITY OF M INHO , 2013
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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
I NEQUALITY AND FAMILY L ABOR S UPPLY
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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 ()
I NEQUALITY AND FAMILY L ABOR S UPPLY
j
U NIVERSITY OF M INHO , 2013
49 / 60
N ON - LINEAR TAXES
e it = (1
Y
B LUNDELL , UCL & IFS ()
χt ) (H1,t W1,t + H2,t W2,t )1
I NEQUALITY AND FAMILY L ABOR S UPPLY
µt
U NIVERSITY OF M INHO , 2013
50 / 60
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
µ
1)
U NIVERSITY OF M INHO , 2013
50 / 60
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)
I NEQUALITY 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)
(0.045)
1.039
0.858
(0.01)
(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
B LUNDELL , UCL & IFS ()
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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
I NEQUALITY AND FAMILY L ABOR S UPPLY
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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 )
I NEQUALITY AND FAMILY L ABOR S UPPLY
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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)
B LUNDELL , UCL & IFS ()
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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
I NEQUALITY AND FAMILY L ABOR S UPPLY
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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 ()
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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
I NEQUALITY AND FAMILY L ABOR S UPPLY
1
C
C
A
U NIVERSITY OF M INHO , 2013
57 / 60
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]
I NEQUALITY AND FAMILY L ABOR S UPPLY
U NIVERSITY OF M INHO , 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
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]
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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
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
β ) (1
π i,t ) η h,w
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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
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
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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
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
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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
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
π i,t ) η h,w
j
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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
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
I NEQUALITY AND FAMILY L ABOR S UPPLY
β ) (1
π i,t ) η h,w
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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 ()
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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 ()
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