Labour Income Dynamics and the Insurance
from Taxes, Transfers, and the Family
Richard Blundell1
1
Michael Graber1,2
Magne Mogstad1,2
University College London and Institute for Fiscal Studies
2
Statistics Norway
June 2013
INTRODUCTION
I
Inequality has many dimensions
• individual earnings → joint earnings → income → consumption
I
Here we explore the links between individual earnings, and
individual and family disposable income over the life cycle
I
Examining the role of taxes and transfers, and spouse’s labour
income to smooth/attenuate shocks
I
Make use of detailed population register (panel) data from
Norway
I
Provide a detailed picture of life-cycle inequality dynamics by
following many birth cohorts across their working life-time
KEY QUESTIONS
I
An extensive literature has concentrated on assessing the types
and levels of income risk (for a review see Meghir and Pistaferri,
2011).
I
This literature has pointed out three key ingredients of potential
significance:
• persistence of shocks
• age and time dependence in the variance of shocks
• heterogeneous age profiles
1
How do these factors vary over the life-cycle and differ across
education groups and birth cohorts in Norway?
2
To what extend does the tax and transfer system attenuate these
various factors in the evolution of life-cycle inequality in Norway?
3
What happens when we add in income sources of other family
members?
WHAT WE FIND
I
The nature of labour income dynamics in Norway
• quite different by skill groups
• quite different at different points in the life-cycle
• quite different at different points in time
I
The impact of taxes and transfers in Norway
• remarkable flattening of life-cycle inequality
• reduces persistence of shocks
• reduces the variance of transitory and permanent shocks
I
The comparison with family income dynamics:
• spouse’s income seem to matter less for the dynamics of inequality
• balance between assortative matching and insurance
INCOME DYNAMICS
I
For each birth cohort we write log-income of individual i of age a as
log Yi,a = X0i,a ϕ + αi + βi a + vi,a + τi,a
• X includes a polynomial in age and its interaction with education,
dummies for region, maritial status and family size and the
interaction of the latter.
• βi a is an individual-specific linear trend in age, allow for correlation
between α and β.
• vi,a is the persistent process,
vi,a = ρvi,a−1 + ui,a
where ui,a is a mean-zero shock with variance σa2 .
• τi,a is the transitory component assumed to follow an MA(1)
process,
τi,a = εi,a + θεi,a−1
where εi,a is a mean-zero shock with variance ωa2
I
We allow variances to vary in an unrestricted way with age and across
birth cohorts and education groups. By averaging across cohorts at a
given age we account for calendar time effects.
Details
DATA
I
Panel data covering the entire Norwegian population, 1967-2006
• several registry databases linked through unique identifiers for
each individual
• include individual demographic information (including gender, date
of birth, and marital status) and socioeconomic data (including
years of education, market income, cash transfers)
• unique family identifiers allow us to match spouses and parents to
their children
I
Income variables
• individual market income: annual pre-tax earnings
• individual disposable income: annual earnings and cash transfers
net of taxes
• family disposable income: pooled disposable income of the
spouses adjusted by the square root equivalence scale
Household Income by Source
TAXES AND TRANSFERS
I
Transfer system (including DI benefits, child benefits, etc.)
• Since 1967, key program parameters are fairly stable over time
I
Tax system (2006): Progressive through deductions and surtaxes
• 7.8% social security contribution on labour income
• (taxable income - deductions) is taxed at a flat rate of 28%
I
I
single persons/dual earner couples: 50% of standard deductions
two surtax brackets adding an additional 9 and 12 percent to the
marginal tax rates
Marginal Tax Rates 2006
• over time, the the Norwegian tax system has become less
progressive through a series of policy changes
Average Tax Rates over Time
SAMPLE SELECTION
In each year we select
I
males born between 1925 and 1964
• between the ages of 25 and 60
• non-immigrants and non-self-employed
• with non-zero earnings
Non-participation
I
Applying these restrictions gives us an unbalanced panel with
• 40 time periods
• 1,004,294 individuals ( 25,107 individuals on average per cohort)
I
This sample is then partitioned into three mutually exclusive
groups according to educational levels
• low-skilled (33%): not having completed high school
• medium-skilled (48%): high school degree
• high - skilled (19%): attended college
Participation of the Spouse
Marriage Rates
12.5
12.2
E(y)
11.9
11.6
11.3
11.3
11.6
E(y)
11.9
12.2
12.5
AGE PROFILES IN INDIVIDUAL EARNINGS
25
35
45
55
25
35
age
45
55
age
Market Income
Disposable Income
Disposable Income
Medium-Skilled
12.5
Low-Skilled
Market Income
E(y)
11.9
12.2
I concave profile over the life-cycle
I very flat for the low-skilled, very steep
for the high-skilled early in life
11.6
I progressive nature of the tax and
11.3
transfer system dampens the the
25
35
45
55
age
Market Income
High-Skilled
Disposable Income
income differentials between high
skilled and low skilled after age 35
1
Var(y)
.5
0
0
.5
Var(y)
1
1.5
- VARIANCES OF INDIVIDUAL EARNINGS
1.5
AGE PROFILES
25
35
45
55
25
35
age
45
55
age
Market Income
Disposable Income
Disposable Income
Medium-Skilled
1.5
Low-Skilled
Market Income
1
I U-shaped profile over the life-cycle
Var(y)
I remarkable flattening of the increase in the
.5
variance of individual log-income due to
the tax and transfer system especially for
0
the low-skilled at the end of the life-cycle
25
35
45
55
age
Market Income
High-Skilled
Disposable Income
12.5
12.2
E(y)
11.9
11.6
11.3
11.3
11.6
E(y)
11.9
12.2
12.5
AGE PROFILES IN FAMILY EARNINGS
25
35
45
55
25
35
age
Disposable Income
12.2
E(y)
11.9
11.6
11.3
35
45
55
age
Market Income
High-Skilled
Market Income
55
Disposable Income
Medium-Skilled
12.5
Low-Skilled
25
45
age
Market Income
Disposable Income
.9
Var(y)
.6
.3
0
0
.3
Var(y)
.6
.9
1.2
- VARIANCES OF FAMILY EARNINGS
1.2
AGE PROFILES
25
35
45
55
25
35
age
Disposable Income
.9
Var(y)
.6
.3
0
35
45
55
age
Market Income
High-Skilled
Market Income
55
Disposable Income
Medium-Skilled
1.2
Low-Skilled
25
45
age
Market Income
Disposable Income
ESTIMATION RESULTS
Individual Market Income
Individual Disposable Income
Family Disposable Income
Low
Medium
High
Low
Medium
High
Low
Medium
High
ρ
1.000
(0.000688)
1.000
(0.000571)
1.000
(0.027814)
0.822
(0.008926)
0.928
(0.014485)
0.881
(0.023016)
0.819
(0.006960)
0.861
(0.006742)
0.788
(0.018279)
σα2
-
-
-
0.068661
(0.010491)
0.000616
(0.004425)
0.025430
(0.028066)
0.052308
(0.008960)
0.045921
(0.014064)
0.028585
(0.022444)
σβ2
0.000000
(0.768047)
0.000000
(0.491246)
0.000000
(0.032024)
0.000030
(0.000005)
0.000008
(0.000003)
0.000046
(0.000018)
0.000026
(0.000004)
0.000026
(0.000005)
0.000024
(0.000009)
θ
0.254247
(0.007009)
0.256168
(0.006322)
0.316701
(0.010004)
0.218405
(0.007418)
0.233300
(0.006241)
0.292595
(0.010581)
0.224079
(0.008485)
0.250136
(0.005868)
0.294728
(0.011812)
I Taxes and transfers reduce the persistence of shocks; e.g. when ρ = 0.82 the
effect of an income shock is reduced to 14 percent of its initial value in ten years
I Persistence only changes little when we go from individual disposable income to
family disposable income
I Some evidence for heterogenous profiles, but not in market income
Profiles
VARIANCE OF PERMANENT SHOCKS
.2
.15
2
σa
.1
.05
0
0
.05
σa
.1
2
.15
.2
Robustness
25
30
35
40
age
45
Individual Market Income
50
55
Individual Disposable Income
30
35
40
age
Individual Market Income
45
50
55
Individual Disposable Income
Medium-Skilled
0
.05
σa
.1
2
.15
.2
Low-Skilled
25
25
30
35
40
age
45
Individual Market Income
High-Skilled
50
55
Individual Disposable Income
I U-shaped profile over the life-cycle: importance of
non-stationarity in age
I quite different across skill groups: large shocks for
high-skilled early in life and for low-skilled at the
end of the life-cycle
I taxes and transfers: flattening of the age profiles;
e.g., a permanent shock of one standard deviation
implies a 16 (10) percent change in market
income (disposable income) for a low-skilled aged
55.
I adding spouse’s income: closely mirroring, slightly
larger
VARIANCE OF TRANSITORY SHOCKS
.125
2
ωa
0
0
.025
.025
.05
.05
ωa
2
.075
.075
.1
.1
.125
Robustness
25
30
35
40
age
45
Individual Market Income
50
55
Individual Disposable Income
30
35
40
age
Individual Market Income
45
50
55
Individual Disposable Income
Medium-Skilled
.125
Low-Skilled
25
0
.025
.05
ωa
2
.075
.1
I a decreasing and convex profile over
the lifetime: importance of
non-stationarity in age
I early in life transitory shocks are much
larger for the high-skilled than for the
low-skilled + a larger MA(1) parameter
I adding spouse’s income: closely
mirroring, slightly larger
25
30
35
40
age
45
Individual Market Income
High-Skilled
50
55
Individual Disposable Income
0
.05
2
σa
.1
.15
NON - STATIONARITY IN TIME
30
35
40
age
45
50
55
Gap in log GDP
−.1 −.05 0 .05 .1
25
20
30
40
age
1950
Example
50
1962
60
SUMMARY
I
The nature of labour income dynamics in Norway
• quite different by skill groups
• quite different at different points in the life-cycle
• quite different at different points in time
I
The impact of taxes and transfers in Norway
• remarkable flattening of life-cycle inequality
• reduces persistence of shocks
• reduces the variance of transitory and permanent shocks
I
The comparison with family income dynamics:
• spouse’s income matters less for the dynamics of inequality
• balance between assortative matching and insurance
ESTIMATION
Back
I
I
Let yi,a,t ≡ log Yi,a,t − X0i,a,t ϕ̂t be the residual income of individual
i at age a and time t.
For a given cohort, the theoretical moments we use is the
Covariance matrix of the quasi-difference
(∆ρ yi,a ≡ yi,a − ρyi,a−1 ),
2
σα
ραβ σα σβ
ραβ σα σβ
((1 − ρ) ι, ∆ρ a)0
2
σβ
h
i +Var ui + 1 + (θ − ρ) L1 − ρθL2 εi
Var (∆ρ yi ) = ((1 − ρ) ι, ∆ρ a)
I
Calendar time effects are accounted for by averaging these
moments across cohorts (equal weights) for a given age
I
For a given ρ, we then minimize the distance between the
theoretical and empirical moments and pick the estimates
associated with ρ that yields the minimum norm.
EXCLUDING LOW INCOMES
.2
.15
2
σa
.1
.05
0
0
.05
σa
.1
2
.15
.2
Back
25
30
35
40
age
Individual Market Income
45
50
55
Individual Disposable Income
.15
2
σa
.1
.05
0
25
30
35
40
age
Individual Market Income
30
35
40
age
Individual Market Income
45
45
50
55
Individual Disposable Income
50
55
Individual Disposable Income
Medium-Skilled
.2
Low-Skilled
25
EXCLUDING LOW INCOMES
.1
.075
2
ωa
.05
.025
0
0
.025
2
ωa
.05
.075
.1
Back
25
30
35
40
age
Individual Market Income
45
50
55
Individual Disposable Income
.075
2
ωa
.05
.025
0
25
30
35
40
age
Individual Market Income
30
35
40
age
Individual Market Income
45
45
50
55
Individual Disposable Income
50
55
Individual Disposable Income
Medium-Skilled
.1
Low-Skilled
25
NON - PARTICIPATION
0
.1
.2
LFP−rate
.3
.4
.5
.6
Back
20
30
40
50
60
age
Total
Medium−Skilled
Low−Skilled
High−Skilled
70
NON - PARTICIPATION
12.5
Individual market income
10.5
11
11.5
12
10
9.5
9.5
10
Individual market income
10.5
11
11.5
12
12.5
Back
45
50
55
60
45
50
age
E(y|staying next year)
E(y|exiting next year)
E(y|staying next year)
E(y|exiting next year)
Individual market income
10.5
11
11.5
12
10
9.5
50
55
age
E(y|staying next year)
E(y|exiting next year)
MA(2) in y|staying next year
MA(2) in y|exiting next year
Medium-Skilled
12.5
Low-Skilled
45
55
age
MA(2) in y|staying next year
MA(2) in y|exiting next year
MA(2) in y|staying next year
MA(2) in y|exiting next year
60
60
PARTICIPATION R ATES S POUSE
1
.8
LFP−rate
.4
.6
.2
0
0
.2
LFP−rate
.4
.6
.8
1
Back
25
35
45
55
age
1
.8
LFP−rate
.4
.6
.2
45
age
45
Medium-Skilled
0
35
35
age
Low-Skilled
25
25
55
55
M ARRIAGE R ATES
.9
.7
marriage−rate
.5
.3
.3
.5
marriage−rate
.7
.9
Back
25
35
45
55
age
.9
.7
marriage−rate
.5
45
age
45
Medium-Skilled
.3
35
35
age
Low-Skilled
25
25
55
55
AVERAGE TAX R ATES
0
10
Average tax rate (%)
20 30 40 50 60
70
80
Back
0
500000
Income (2001 NOK)
Single person, 2006
Single person, 2001
Single person, 1979
1000000
Single person, 2004
Single person, 1994
M ARGINAL TAX R ATES
0
10
Marginal tax rate (%)
20
30
40
50
Back
0
500000
Income (2001 NOK)
Single person, 2006
1000000
Single earner couple, 2006
THE ROLE OF CAPITAL INCOME
Back
Total household income by income source for each decile:
Decile
Labour income
Self-employment
Capital income
Cash Transfers
1
42%
4%
-5%
59%
2
45%
5%
1%
49%
3
58%
5%
1%
36%
4
68%
4%
1%
26%
5
74%
4%
1%
21%
6
77%
4%
2%
17%
7
79%
5%
2%
14%
8
81%
5%
2%
12%
9
82%
6%
3%
9%
10
69%
11%
15%
5%
- IND DISPOSABLE INCOME
HETEROGENOUS PROFILES
13
12.5
12
log(y)
11.5
11
10.5
10.5
11
11.5
log(y)
12
12.5
13
Back
25
30
35
40
45
50
55
age
25
30
35
40
45
50
55
age
Medium-Skilled
13
Low-Skilled
10.5
11
11.5
log(y)
12
12.5
I non-negligible fanning out
I Note however, negative correlation
between initial conditions and growth
rate. Thus some of the fanning out will
be offset.
25
30
35
40
45
age
50
55
Time Effects
0
.025
.05
ωa
2
.075
.1
.125
Back
25
30
35
40
45
50
age
1944
1954
1964
1949
1959
55