Cross-sectional Facts for
Macroeconomists: UK
Richard Blundell and Ben Etheridge
(University College London and Institute for Fiscal Studies)
Preliminary Draft
Fifth PIER IGIER International Conference
Inequality in Macroeconomics: Facts and Theories
November 2007
Layout for talk
•
•
•
•
Basic UK data sources and issues
Overall characterisation of the trends since 1978
Specific features of the dispersion and covariation
How much can we learn about the decomposition
of income risk from repeated cross-sections?
– Key variance-covariance decompositions
– Results from a simulated stochastic economy
• Some conclusions
– All underlying spreadsheets, figures and tables for the
UK project are at www.ifs.org.uk/
1
Data Series
• Basic UK data for the period 1978 – 2005
–
–
–
–
–
–
Consumption
Income
Earnings
Participation
Hours
Covariances for all these series over this period.
• Income dynamics
– All measures from 1991
• Wealth
– Recent cross-sections only
Data Sources and Issues
• 1978 – 2005 is from consistent repeated crosssection household surveys
–
–
–
–
Family Expenditure Survey (1969 onwards)
Family Resources Survey (1993 onwards)
Labour Force Survey (1978 onwards)
Survey of Personal Incomes (tax records: 1994 onwards)
• Household Panel Data (BHPS) from 1991 onwards
– Low quality interval consumption questions
– Use this mainly for income dynamics
– Wealth data only in 1995 and 2000 surveys
2
Summary Facts #1
• Consumption and Income:
– Income dispersion, for all measures, rose strongly in
the 1980s, with some further rise in the late 1990s.
– Consumption dispersion, for all measures, rose quite
strongly in the early 1980s and then again, although at
a slower rate, in the late 1990s.
– The covariance between the two series rose
monotonically until the late 1990s.
– Strong growth in top percentiles in late 1990s
– Cohort patterns show important life-cycle growth in
dispersion
Summary Facts #2
• Employment and Hours:
– Secular decline in male participation until mid 90s
• accentuated at later ages
• accentuated for low education groups
– Systematic cohort growth in female participation,
strongest in mid and late 1980s.
– Different employment and hours profiles between
women in couples with children and single mothers
• Strong growth in proportion of single mothers
– Little change in variance of hours worked for men
– Increase in the covariance of participation in couples
3
Summary Facts #3
• Earnings and wages:
– Dispersion of male earnings rises, dispersion of male
hourly wages rises at a slower rate.
– Dispersion of female earnings is flat and then declines
recently, dispersion of female hourly wages rises but at
a slower rate than male hourly wages.
– Covariance of earnings rises and then declines.
– Covariance of hourly wages rises and then flattens.
Some Figures and Tables
4
Figure 1a: Income and Consumption Dispersion
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
1978
1981
1984
1987
1990
1993
Var of log Equiv Consumption
1996
1999
2002
2005
Var of log Equiv Income
Source: FES.
Figure 1b: Income and Consumption: Variance-Covariance
0.6
0.75
0.7
0.5
0.65
0.6
0.4
0.55
0.3
0.5
0.45
0.2
0.4
0.1
0.35
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Variance log Equiv Consumption
Variance log Equiv Income
Covariance
Correlation, Right Axis
Source: FES.
5
Figure 1c: Income Measures: Dispersion by time
0.9
0.8
0.7
0.6
0.5
0.4
Wages of Male Heads
Gross Earnings
20
04
02
00
20
20
98
96
19
19
19
94
92
90
19
19
19
88
86
84
19
19
19
82
80
19
19
78
0.3
After-Tax Non-Financial Income
Source: FES.
Figure 1d: Income (after tax) Decomposition: Dispersion by time
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
SD of Log After-Tax Income
Houshold Composition
Age
04
20
00
02
20
98
20
19
96
19
94
19
92
19
90
19
88
19
86
19
82
80
84
19
19
19
19
78
0
Residual
Education
Region
Source: FES.
6
Figure 1e: Income Inequality, by Cohort
0.6
0.5
0.4
0.3
0.2
0.1
0
25
27
29
31
33
35
37
39
41
1930s
43
1940s
45
47
49
51
53
55
57
59
1950s
Source: FES.
Figure 1f: Consumption Inequality, by Cohort
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
25
27
29
31
33
35
37
39
1930s
41
43
1940s
45
47
49
51
53
55
57
59
1950s
Source: FES.
7
theoretical percentiles
5
8
6
7
9
Figure 1g: The distribution of log consumption: UK FES
95
75
25
3
4
0
.2 .4 .6 .8
observed density
1
5
3
4
5
6
7
observed percentiles
8
9
Standard Deviation of Logs: 0.4941 Skewness: 0.0192 Kurtosis: 0.0474
P-values: Kolmogorov-Smirnov: 0.1684 Skewness: 0.4113 Kurtosis: 0.0645
COHORT 1940-49, AGE 41-45
Source: Battistin, Blundell and Lewbel
theoretical percentiles
5
7
9
6
8
Figure 1h: The distribution of log income: UK FES
95
75
25
3
0 .2 .4 .6
observed density
4
.8
1
5
3
4
5
6
7
observed percentiles
8
9
Standard Deviation of Logs: 0.4774 Skewness: -0.0130 Kurtosis: 0.1610
P-values: Kolmogorov-Smirnov: 0.0000 Skewness: 0.5705 Kurtosis: 0.0000
COHORT 1940-49, AGE 41-45
Source: Battistin, Blundell and Lewbel
8
theoretical percentiles
6
5
7
8
9
Figure 1i: The distribution of log consumption: UK FES
95
75
25
3
4
0 .2 .4 .6 .8
observed density
1
5
3
4
5
6
7
observed percentiles
8
9
Standard Deviation of Logs: 0.5348 Skewness: 0.0132 Kurtosis: -0.0030
P-values: Kolmogorov-Smirnov: 0.6692 Skewness: 0.6280 Kurtosis: 0.9192
COHORT 1940-49, AGE 51-55
Source: Battistin, Blundell and Lewbel
Figure 2a: Overall Employment and Growth Rates
6%
90
5%
3%
70
2%
1%
60
0%
Major
Thatcher
50
Real GDP growth
4%
-1%
Blair
-2%
2004
1999
1994
1989
-3%
1984
40
1979
Employment rates (%)
80
Year
All
Male
Female
Low skilled
GDP growth
9
Figure 2b: Employment by education and gender, by year
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
0.5
Female - College
Male - Leave at 18
Male - College
Female - Compulsory
Female - Leave at 18
Male - Compulsory
Source: FES.
Figure 2c: Employment by cohort and gender, by age
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
59
57
55
53
51
49
47
45
43
41
39
37
35
33
31
29
27
25
0.2
1925-29, Male
1935-39, Male
1945-49, Male
1955-59, Male
1965-70, Male
1925-29, Female
1935-39, Female
1945-49, Female
1955-59, Female
1965-70, Female
Source: FES.
10
Figure 2d: Hours by education and gender, by year
50
45
40
35
30
25
Leave at 18, Male
Leave at 18, Female
04
20
02
00
20
20
19
98
96
94
19
19
92
90
19
88
86
College, Male
College, Female
19
19
84
19
19
82
80
19
19
19
78
20
Compulsory, Male
Compulsory, Female
Source: FES.
Figure 2e: Variance-Covariance Structure of Participation
0.35
0.3
0.25
0.2
0.15
0.1
0.05
Var of Participation of Head
Covariance
04
02
20
20
00
20
98
19
96
19
94
19
92
19
88
90
19
19
86
19
84
19
82
19
80
19
19
78
0
Var of Participation of Spouse
Correlation
Source: FES.
11
Figure 2f: Variance-Covariance Structure of Hours of Work
0.5
0.4
0.3
0.2
0.1
0
1978
1984
1981
1990
1987
1993
1996
2002
1999
2005
-0.1
Var of log Hours of Male Heads
Var of log Hours of Female Spouses
Covariance
Source: FES.
Figure 2g: Cross-section Employment over the Life-Cycle: Men
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
16
18
20
22
24
26
28
30
32
34
36
38
40
1975
42
44
1985
46
48
1995
50
52
54
56
58
60
62
64
66
68
70
72
74
2005
Source: LFS.
12
Figure 2h: Cross-section Employment over the Life-Cycle: Women
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
16
18
20
22
24
26
28
30
32
34
36
38
40
42
1975
44
1985
46
48
1995
50
52
54
56
58
60
62
64
66
68
70
72
74
2005
Source: LFS.
Figure 2i: Employment Rates for Women by Demographic Group
0.9
0.8
0.7
0.6
0.5
0.4
0.3
1978
1983
singlenokids
1988
singlekids
1993
1998
couplenokids
couplekids
2003
13
Figure 3a: Variance-Covariance Structure of Earnings
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1978
1981
1984
1987
1990
1993
1996
1999
2002
2005
Variance of log Earnings of Head
Variance of log Earnings of Spouse
Covariance
Correlation
Source: FES.
Figure 3b: Variance-Covariance Structure of Wages
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1978
1981
1984
1987
Var of log Wages of Male Head
1990
1993
1996
1999
2002
Var of log Wages of Female Spouse
2005
Covariance
Source: FES.
14
Figure 3c: Normalised Log wage inequality by cohort over age
1.2
1.1
1
1921-1925
1931-1935
1941-1945
0.9
1951-1955
1961-1965
1971-1975
0.8
0.7
64
60
62
56
58
52
54
48
50
44
46
40
42
36
38
32
34
28
30
24
26
20
22
0.6
Income dynamics
• Consider the simple decomposition:
ln Yi , a ,t = Z i', a ,t λ + f i + yiP, a ,t + yiT, a ,t
where
yiP, a ,t = yiP, a −1,t −1 + ζ i , a ,t
• permanent component following a martingale process
• and a transitory or mean-reverting component yT = v
w ith v it =
q
∑θ
j=0
j
ε i , a − j ,t − j and θ 0 ≡ 1.
• implies a simple structure for the autocovariance of
Δy ≡ lnY - Z' λ
• variance-covariance results from BHPS in Tables I a-c.
15
Table Ia: The Covariance Structure of Wage of Male Head
Year
var(∆yt)
cov(∆yt,∆yt+1)
cov(∆yt,∆yt+2)
cov(∆yt,∆yt+3)
1994
0.0536
(.0041)
0.0609
(.0058)
0.0459
(.0026)
0.0435
(.0020)
0.0466
(.0020)
0.0423
(.0024)
0.0477
(.0026)
0.0502
(.0026)
0.0459
(.0022)
0.0480
(.0031)
0.0460
(.0026)
-0.0106
(.0017)
-0.0102
(.0019)
-0.0104
(.0014)
-0.0094
(.0014)
-0.0100
(.0015)
-0.0098
(.0018)
-0.0169
(.0018)
-0.0150
(.0015)
-0.0137
(.0015)
-0.0151
(.0016)
-
-0.0020
(.0015)
-0.0003
(.0016)
-0.0006
(.0013)
0.0000
(.0012)
-0.0001
(.0015)
-0.0005
(.0015)
0.0008
(.0014)
-0.0015
(.0016)
0.0009
(.0017)
-
-0.0007
(.0015)
0.0019
(.0016)
-0.0009
(.0013)
0.0000
(.0013)
0.0029
(.0016)
-0.0001
(.0015)
0.0001
(.0016)
0.0004
(.0016)
-
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Variance of log residuals, BHPS
Table Ib: The Covariance Structure of HH Earnings - BHPS
Year
var(∆yt)
cov(∆yt,∆yt+1)
cov(∆yt,∆yt+2)
cov(∆yt,∆yt+3)
1994
0.1458
(.0080)
0.1319
(.0068)
0.1022
(.0052)
0.1301
(.0066)
0.1265
(.0064)
0.1183
(.0059)
0.1078
(.0051)
0.1121
(.0057)
0.1061
(.0053)
0.1171
(.0063)
0.1280
(.0069)
-0.0437
(.0051)
-0.0315
(.0044)
-0.0291
(.0041)
-0.0319
(.0044)
-0.0305
(.0041)
-0.0275
(.0036)
-0.0235
(.0034)
-0.0239
(.0036)
-0.0180
(.0037)
-0.0314
(.0045)
-
0.0063
(.0044)
-0.0004
(.0045)
-0.0051
(.0036)
-0.0042
(.0044)
-0.0010
(.0036)
-0.0020
(.0034)
-0.0022
(.0033)
-0.0144
(.0042)
-0.0037
(.0039)
-
-0.0050
(.0045)
-0.0048
(.0038)
-0.0019
(.0034)
-0.0077
(.0036)
0.0006
(.0038)
0.0046
(.0031)
0.0117
(.0041)
-0.0044
(.0041)
-
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Variance of log residuals, BHPS
16
Table Ic: The Covariance Structure of HH Income - BHPS
Year
var(∆yt)
cov(∆yt,∆yt+1)
cov(∆yt,∆yt+2)
cov(∆yt,∆yt+3)
1994
0.0990
(.0043)
0.1013
(.0044)
0.0842
(.0034)
0.0906
(.0037)
0.0890
(.0037)
0.0852
(.0035)
0.0899
(.0039)
0.0864
(.0039)
0.0861
(.0037)
0.0936
(.0044)
0.0965
(.0048)
-0.0276
(.0030)
-0.0261
(.0027)
-0.0227
(.0025)
-0.0243
(.0026)
-0.0269
(.0026)
-0.0222
(.0026)
-0.0260
(.0026)
-0.0256
(.0028)
-0.0219
(.0029)
-0.0293
(.0033)
-
0.0037
(.0026)
-0.0015
(.0028)
0.0000
(.0024)
-0.0032
(.0025)
-0.0042
(.0025)
-0.0024
(.0024)
0.0007
(.0026)
-0.0090
(.0029)
-0.0030
(.0028)
-
-0.0072
(.0030)
-0.0027
(.0025)
-0.0007
(.0024)
0.0005
(.0023)
0.0000
(.0026)
0.0025
(.0025)
0.0050
(.0027)
-0.0010
(.0030)
-
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Variance of log residuals, BHPS
How much can we learn from repeated
cross-sections about income risk?
• With CRRA preferences, the Euler equation is:
Citβ −1 =
1 + rt
Et e ΔZ it +1ϑ Citβ+−11
1+ δ
• We show that this can be approximated by:
Δ ln Cit ≈ Γit + ΔZ it 'ϑ + π itζ it + γ tLπ it ε it + ξit
• Implies a set of over-identifying cross-section
(and panel) moments
17
Identifying the Decomposition of Shocks
• To judge the ability of the model to identify the underlying
parameters and processes, simulate a stochastic economy.
• In the base case the discount rate δ=0.02, also allow δ to
take values 0.04 and 0.01. Also a mixed population with
half at 0.02 and a quarter each at 0.04 and 0.01.
• In such cases the permanent variance follows a two-state,
first-order Markov process with the transition probability
between alternative variances.
• For each experiment, simulate consumption, earnings and
asset paths for 50,000 individuals.
• Obtain estimates of the variance for each period from
random cross sectional samples of 2000 individuals for each
of 20 periods: Figure 4a.
Figure 4a: A Simulated Economy, permanent shock variance estimates
0.016
0.012
0.008
0.004
0
1
2
3
4
5
truth
6
7
8
9
approximation
10
11
12
impatient
13
14
15
16
17
18
19
heterogeneous
Source: Blundell, Low and Preston (2005)
18