1
2
Measuring Income Mobility
using Pseudo-Panel Data
Arturo Martinez Jr.,
and Mark Western, Michele Haynes, Wojtek Tomaszewski
(Institute for Social Science Research, The University of Queensland)
Australian Statistics Conference
Official Statistics Methodology Session
9th July, 2014
3
Mom: Listen to me, I have to tell you something...
Baby: I am listening…
(Uh oh, looks like she found out
what I did to my nappies) 4
(Mom: We’re poor, we can’t afford to go to
Disneyland with your friends.)
Baby: I’m sorry, what
did you just say?!?
5
20%
20%
20%
20%
20%
7
> 90%
Inequality is increasing.
8
Inequality and Income Mobility
Q. What does increasing inequality represent?
A. It depends on income mobility regime.
9
Baby: Someday, I will see
Mickey Mouse too.
10
What makes the
PHILIPPINES
an interesting
case study?
The Philippines is a rapidly growing economy.
.
In 2012, its economy grew by approx. 6%.
ECONOMIC GROWTH:
approx. 5 %
AVE. HHLD INCOME
GROWTH:
0.4 %
(US$2) POVERTY RATE:
45% to 44%
INCOME INEQUALITY:
0.44 to 0.43
Household income
distribution stagnant?
13
How do we measure income mobility?
Income mobility can be regarded as
Y1t
Y2t
Y3t
:
:
:
Ynt
Y1t+r
Y2t+r
Y3t+r
:
:
:
Ynt+r
a vector transformation from Yit to Yit+r.
14
Panel Data
Difference Income Mobility Perspectives
Movement
Origin
independence
Equalizer
of income
1
𝑁
𝑁
𝑖=1
𝑌𝑖𝑡
| ln
|
𝑌𝑖𝑡−1
1 − 𝐶𝑜𝑟𝑟𝑒𝑙(ln 𝑌𝑖𝑡 − ln 𝑌𝑖𝑡−1 )
𝑇
𝑡=1 𝑌𝑖𝑡 )
𝐼𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦(
1 − 𝑇
𝑡=1 𝐼𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦(𝑌𝑖𝑡 )
16
Relationship between various mobility measures
0
.2
.4
0
.5
1
-.2
0
.2
.4
0
.5
1
.6
.4
Field-Ok
.2
.4
King
.2
0
40
ARJ
20
0
1
Hart
.5
0
.6
.4
Shorrocks
.2
0
.4
.2
Fields
0
-.2
.1
.05
CDW
0
1
Poverty
Persistence
.5
0
.1
Poverty
Inflow
.2
.4
.6
0
20
40
0
.2
.4
.6
0
.05
.1
0
.05
.05
17
0
.1
Repeated Cross-Sectional Data
Y1t
?
:
Y1t+r
:
:
Y2t
?
?
Y3t
?
:
:
?
Ynt
Y2t+r
?
Y3t+r
:
:
Ynt+r
?
No one-to-one mapping of individual income.
18
Is there a way out of this problem?
19
Cross-Sectional Data
Time t
Time t+r
Measuring Income Mobility using Pseudo-Panel Data
Time t+r
Measuring Income Mobility using Pseudo-Panel Data
Time t
Time t+r
Suppose we have two time periods, t-1 and t, and we denote
our income mobility measure of interest as M(Yit-1, Yit).
Antman-McKenzie (AM) (2005, 2007)
Bourguignon, Goh and Kim (BGK) (2004)
Dang, Lanjouw, Luoto and McKenzie (DLLM) (2014)
23
AM APPROACH
Step 1: For each time period t = 1, 2, group all sampled units
into different cohort groups.
Step 2: Compute the average income of each cohort
{𝑦𝑐𝑡−1 , 𝑦𝑐𝑡 }.
24
AM APPROACH
Step 3: Estimate the model 𝑦𝑐𝑡 = 𝛼𝑦𝑐𝑡−1 + 𝜀𝑐𝑡 .
Step 4: Compute the variance of the residuals 𝑉(𝜀𝑐𝑡 ).
Step 5: Compute 𝑌𝑖(1)2 = 𝛼𝑌𝑖(1)1 + 𝜀𝑖(1)2 where 𝜀𝑖(1)2 is a
randomly drawn data point from N(0,𝑉(𝜀𝑐𝑡 )).
Step 6: Estimate the mobility measure M(𝑌𝑖(1)1 , 𝑌𝑖(1)2 ).
Step 7: Repeats Steps 5 and 6 for R times.
Step 8: Take the average of M(𝑌𝑖11 , 𝑌𝑖(1)2 ) across
all iterations.
25
BGK APPROACH
Step 1: For each time period t = 1, 2, group all sampled units
into different cohort groups.
Step 2: For each cohort c, estimate
𝑌𝑖𝑐2 2 = 𝛽𝑡𝑐 𝑋𝑖𝑐 2 2 + 𝜀𝑖𝑐 2 2 and 𝑌𝑖𝑐3 3 =
Step 3:
compute
𝑐
𝑌𝑖 1 1 =
𝛽𝑡𝑐 𝑋𝑖𝑐 3 3
𝑐
Retrieve the residuals 𝜀𝑖 1 1 ,
their respective variances 𝜎𝜀2𝑐1 ,
𝑐 𝑐
𝛽𝑡 𝑋𝑖 1 1
+ 𝜀𝑖𝑐 3 3
𝑐
𝜀𝑖 2 2 and
𝜎𝜀2𝑐2 , 𝜎𝜀2𝑐3 .
+
𝑐
𝜀𝑖 1 1 ,
𝑐
𝜀𝑖 3 3
and
Step 4: For each cohort c, estimate the model 𝜎 2𝜀𝑐𝑡 =
𝑐
2
𝑐 2
𝜌 𝑉 𝜀𝑖𝑡−1 + 𝜎𝑒𝑐𝑡
26
BGK APPROACH
Step 5: From the model in Step 4, retrieve the residuals 𝜎𝜀2𝑐𝑡 .
Step 6: Compute 𝑌𝑖𝑐1 2 = 𝛽2𝑐 𝑋𝑖𝑐 1 1 + 𝜌𝑐 𝜀𝑖𝑐 1 1 + 𝑒𝑖𝑡𝑐 where 𝑒𝑖𝑡𝑐 is
2
a randomly drawn data point from N(0, 𝜎𝑒𝑐𝑡
).
Step 7: Estimate the mobility measure M(𝑌𝑖
1 1 , 𝑌𝑖 1 2 ).
Step 8: Repeat Steps 6 and 7 for R times.
Step 9: Take the average of M(𝑌𝑖11 , 𝑌𝑖(1)2 ) across all iterations.
DLLM APPROACH
Step 1: For each time period t, estimate 𝑌𝑖(𝑡)𝑡 = 𝛽𝑡 𝑋𝑖(𝑡)𝑡 +
𝜗𝑖(𝑡)𝑡 . Retrieve the parameter estimates 𝛽𝑡 , residuals 𝜀𝑖(𝑡)𝑡 ,
the variance of the residuals, 𝜎𝜗2𝑡 and the coefficients of
determination 𝑅𝑡2 .
Step 2: For each j ∈ {Est, LB, UB}, draw n2 pairs of residuals
(𝜀𝑖(2)1 , 𝜀𝑖(2)2 ) from BVN(0, 𝜗 ) where
2
𝜎𝜗1
𝜌𝑗 𝜎𝜗1 𝜎𝜗2
𝜗=
2
𝜌𝑗 𝜎𝜗1 𝜎𝜗2
𝜎𝜗2
DLLM APPROACH
𝜌𝑒𝑠𝑡
ρyc1yc2 V Yi1 V Yi2 − β1′ V(Xi )β2
=
σϑ1 σϑ2
𝜌𝐿𝐵 = ρyc1yc2 , 𝜌𝑈𝐵 =
β′1 V(Xi )β2
V Yi1 V Yi2
DLLM APPROACH
Step 3: For each j ∈ {Est, LB, UB}, estimate
𝑗
𝑌𝑖 2 1
= 𝛽1 𝑋𝑖
𝑗
𝜀𝑖 2 1 .
Step 4: Estimate the mobility measure
𝑗
Mj(𝑌𝑖 2 1 , 𝑌𝑖 2 2 ).
Step 5: Repeats Steps 2 to 4 for R times.
Step 6: For each j ∈ {Est, LB, UB}, take the average of
𝑗
Mj(𝑌𝑖 2 1 , 𝑌𝑖 2 2 ) across all iterations.
2 2
+
MAIN DATA SOURCE
FAMILY INCOME AND EXPENDITURE SURVEY (FIES)
Three survey waves: 2003, 2006, 2009
Sub-sample of the data (2003, 2006 and 2009 waves)
comprises panel data
From the panel sub-sample, I drew independently drew
Smaller sub-sample to create cross-sectional data
EMPIRICAL APPLICATION
• Use pseudo-panel estimation on the cross-sectional data
to estimate income mobility.
• Compare income mobility estimates derived from actual
panel data and pseudo-panel data.
32
EMPIRICAL APPLICATION
Table 1. Poverty Dynamics, 2003-2006
33
EMPIRICAL APPLICATION
Table 2. Poverty Dynamics, 2006-2009
34
EMPIRICAL APPLICATION
Table 3. Poverty Dynamics, 2003-2009
35
EMPIRICAL APPLICATION
Table 4. Other Measures of Income Mobility, 2003-2006
36
EMPIRICAL APPLICATION
Table 5. Other Measures of Income Mobility, 2006-2009
37
EMPIRICAL APPLICATION
Table 6. Other Measures of Income Mobility, 2003-2009
38
SUMMARY
Examining income mobility provides a more
comprehensive analytical tool for studying income
distribution.
Pseudo-panel estimation provides a good alternative
approach to genuine panel data-based procedures.
Pseudo-panel techniques perform satisfactorily in
estimating different mobility indicators that are based
on the movement and equalizer of income
perspectives.
RESULTS
Poverty outflow
Poverty inflow
15
10
8
10
6
4
5
2
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 4009-10
RESULTS
Poverty persistence
Nonpoor
80
10
8
60
6
40
4
20
2
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 41
09-10
RESULTS
ARJ
King
80
25
20
60
15
40
10
20
5
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
42
RESULTS
Fields-Ok
150
Hart
80
60
100
40
50
20
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
43
RESULTS
CDW
Fields
10
20
0
0
-10
-20
-20
-40
-30
-60
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
44
RESULTS
Shorrocks
60
40
20
0
01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10
45
THANK YOU!
email correspondence:
a.martinez2@uq.edu.au
Sources of Images
http://www.pinoygenius.com/
http://aspanational.wordpress.com/2011/11/22/is-the-american-dream-over-the-disappearing-middle-class/
http://blog.sekiur.com
http://blog.shiftspeakertraining.com/lifestyle/is-your-money-mindset-making-you-poor//tag/worm/
http://www.easyvectors.com/gallery/Notes/2
http://www.lovelyphilippines.com/tag/poverty-poverty/
http://www.backtobasicslearning.com/schoolblog/2013/06/want-to-help-set-a-world-record-join-lego-build-days-at-redclay-schools-all-are-welcome/
http://www.businessinsider.com.au/clos-ette-closet-design-wealthy-photos-2011-9
http://archbishop-cranmer.blogspot.com.au/2008/03/poverty-in-uk-blights-1m-rural-homes.html
http://www.onyamagazine.com/australian-affairs/the-indigenous-australian-poverty-trap/
http://isiria.wordpress.com/2008/07/18/world-poverty-on-the-increase/
http://www.webdesigncore.com/2010/10/21/faces-of-poverty-33-arresting-photogaphy/
http://noahpinionblog.blogspot.com.au/2014/01/how-will-conservatives-save-poor.html
http://nypost.com/2013/10/10/rich-versus-the-filthy-stinking-rich/
http://thepoisedlife.com/967/rich-people-problem-poise/
http://j-walkblog.com/index.php?/weblog/posts/picture_of_the_day/
http://www.backtobasicslearning.com/schoolblog/2013/06/want-to-help-set-a-world-record-join-lego-build-days-at-redclay-schools-all-are-welcome/
http://2politicaljunkies.blogspot.com.au/2009_11_01_archive.html
http://jasonshofner.wordpress.com/
Sources of Images
http://2politicaljunkies.blogspot.com.au/2009_11_01_archive.html
http://jasonshofner.wordpress.com/
http://www.indonesia.hu/news.php?id=169&news=achieving_indonesia%E2%80%B2s_golden_moment_of_economic_gro
wth&l=en
http://scriptshadow.blogspot.com.au/2009/08/malcom-mccree-and-money-tree.html
http://www.123rf.com/photo_10566708_several-people-out-of-work-compete-for-a-single-available-job-in-a-crowdedlabor-market-symbolizing-.html
http://www.123rf.com/photo_15206271_hidden-risk-and-false-advertising-concept-with-a-beautiful-tropical-island-onthe-sea-as-a-natural-g.html
http://www.accountancyage.com/aa/opinion/2180874/accountancys-taking-steps-social-mobility
http://www.genome.duke.edu/genomelife/2011/03/take-pause/
http://www.prx.org/pieces/27431-what-if-counterfactuals-examine-what-might-h
http://www.adelaidenow.com.au/news/gap-between-rich-and-poor-widening/story-e6frea6u-1226063787085
http://www.bbc.com/news/magazine-20255904
http://www.theepochtimes.com/n2/australia/gap-between-rich-and-poor-growing-welfare-group-5528.html
http://www.macrobusiness.com.au/2013/01/australian-income-inequality-worsens/
AM Approach
yc(t )t  yc(t 1)t 1  xc(t )t  f c(t )t  c(t )t
λ𝑐
𝑡 𝑡
= 𝛼[𝑌𝑐
𝑡 𝑡−1
− 𝑌𝑐
𝑡−1 𝑡−1 ]
BGK Approach
c
i (t )t
 X

 
Y
c
i (t )t
c
t
c c
i (t )t 1
  ( ) V (
2
ct
c 2

c
i (t )t
c
i (t )t
e
c
i (t )t 1
c
i (t )t
) 
2
ect
c c
c c
ˆ
ˆi (t )t
z


x




t

1
i
(
t
)
t

1
c
c
c
c
2
P(Yi (t )t 1  z | xi (t )t , xˆi (t )t 1 , ˆt 1 ,  ect 1 )  (
)
2
ˆ ect 1
DLLM Approach
Yi (1)1  1 X i (1)1   i (1)1
Yi ( 2 ) 2   2 X i ( 2 ) 2   i ( 2 ) 2

~
ˆ
Yi ( 2)1  1 X i ( 2)1  vi ( 2)1
 ˆ1 X i ( 2) 2  v~i ( 2)1
2
𝜎𝜗1
∑ϑ =
𝜌𝜎𝜗1 𝜎𝜗2
𝜌𝜎𝜗1 𝜎𝜗2
2
𝜎𝜗2
DLLM Approach
∅(
∅(
𝑧−𝛽1 𝑋𝑖(2)2
𝜎𝜗1
𝑧−𝛽1 𝑋𝑖(2)2
𝜎𝜗1
∅( −
∅( −
,
𝑧−𝛽1 𝑋𝑖(2)2
𝜎𝜗1
𝜎𝜗2
,−
𝑧−𝛽1 𝑋𝑖(2)2
𝜎𝜗1
𝑧−𝛽2 𝑋𝑖(2)2
,
,−
| 𝜌 = 0) ≤ P(𝑌i(2)1 < z, Yi(2)2 < z) ≤ ∅(
𝑧−𝛽2 𝑋𝑖(2)2
𝜎𝜗2
𝑧−𝛽2 𝑋𝑖(2)2
𝜎𝜗2
𝑧−𝛽2 𝑋𝑖(2)2
𝜎𝜗2
𝑧−𝛽1 𝑋𝑖(2)2
| 𝜌 = 1) ≤ P(𝑌i(2)1 < z, Yi(2)2 > z) ≤ ∅(
𝜎𝜗1
,
𝑧−𝛽1 𝑋𝑖(2)2
𝜎𝜗1
| 𝜌 = 1) ≤ P(𝑌i(2)1 > z, Yi(2)2 < z) ≤ ∅( −
| 𝜌 = 0) ≤ P(𝑌i(2)1 > z, Yi(2)2 > z) ≤ ∅( −
𝑧−𝛽2 𝑋𝑖(2)2
𝜎𝜗2
𝜎𝜗1
𝑧−𝛽1 𝑋𝑖(2)2
𝜎𝜗1
𝑧−𝛽2 𝑋𝑖(2)2
,−
𝑧−𝛽1 𝑋𝑖(2)2
| 𝜌 = 1)
𝜎𝜗2
,
𝑧−𝛽2 𝑋𝑖(2)2
,−
𝜎𝜗2
| 𝜌 = 0)
| 𝜌 = 0)
𝑧−𝛽2 𝑋𝑖(2)2
𝜎𝜗2
|𝜌 =1
What makes
AUSTRALIA
an interesting
case study for
examining
income mobility?
THE WORLD AGREED ON
8 GOALS
TO BE ACHIEVED BY
2015
54
OECD’s Better Life Index
Housing
Governance
Income
Health
Jobs
Life Satisfaction
Community Safety
Education
55
Classical Pseudo-Panel Estimation
• Pioneered by Deaton (1985)
• Creates synthetic panels by aggregating analytical units into cohorts which
are repeatedly observed in RCS
• Applications in sociology, economics, finance, biology, etc.
• Useful for estimating origin independence based concept of income
mobility, e.g., income elasticity in a regression framework,
𝑌𝑖𝑡 = 𝛼𝑌𝑖𝑡−1 + 𝜀𝑖𝑡
𝑌𝑐𝑡 = 𝛼𝑌𝑐𝑡−1 + 𝜖𝑖𝑡
56
Classical Pseudo-Panel Approach: General Idea
Cross-sectional surveyt
Age-cohort
averaget
Cross-sectional surveyt+r
Age-cohort
averaget+r
1950s
1950s
1960s
1960s
1970s
1970s
1980s
1980s
1990s
1990s
Creates one-to-one mapping of cohort average income.
57
Classical Pseudo-Panel Approach
Cons
Pros
• Not prone to bias caused by attrition
in panel surveys
• Useful in measuring income mobility
at the macro-level even in the
presence of measurement error
• Facilitates analysis of trends for
longer periods
• Arbitrary choice of cohorts
• Induces bias in the presence of timevarying cohort-level measurement error
Loss of information  not useful in
examining income mobility at the microlevel ; only useful for originindependence perspective
58
Addressing Loss of Information
{𝑌𝑖1 , 𝑌𝑗2 }
{𝑌𝑗1 , 𝑌𝑗2 }
• Dang, Elbers, et al. (2011) proposed estimating income regression models
of the form:
𝑌𝑖1 = 𝛽1 𝑍𝑖 + 𝑣𝑖1
𝑌𝑗2 = 𝛽2 𝑍𝑗 + 𝑣𝑗2
where Z’s are time-invariant explanatory variables of income and v’s are
the error terms (can be assumed to follow ~ BVN(0, ∑ϑ )).
WHAT WE KNOW:
𝛽1 , 𝛽2 , 𝑍𝑖 , 𝑍𝑗 , {𝑣ℎ1 }, {𝑣𝑗2 }
WHAT WE WANT:
𝑌𝑗1 = 𝛽1 𝑍𝑗 + 𝑣𝑗1
59
Quick Facts about Australia’s Income Distribution
The wealthiest quintile account for 61% of total household
net worth while the poorest quintile account for 1%.
Ave net worth (richest 20%): $2.2 million per hhld
Ave net worth (poorest 20%): $31,205 per hhld
Income inequality is slightly higher in Australia than
OECD’s average (OECD 2014).
The Gini coefficient in Australia is 0.33 vs. OECD’s 0.31,
Undesirable? A Necessary Feature of
Rapid Economic Growth?
60
DLLM APPROACH
Step 1: For each time period t, estimate 𝑌𝑖(𝑡)𝑡 = 𝛽𝑡 𝑋𝑖(𝑡)𝑡 +
𝜗𝑖(𝑡)𝑡 . Retrieve the parameter estimates 𝛽𝑡 , and the residuals
𝜀𝑖(𝑡)𝑡 .
Step 2: Compute the mean and the variance of the residuals,
𝜇𝜗𝑡 and 𝜎𝜗2𝑡 ..
Step 3: Step 3: Set the residual correlation 𝜌𝑗 , j ∈ {LB, UB},
such that 𝜌𝐿𝐵 = 0 and 𝜌𝑈𝐵 = 1.
DLLM APPROACH
Step 4: Sort the residuals 𝜀𝑖(2)2 from lowest to highest.
Step 5: For each j ∈ {LB, UB}, draw n2 pairs of residuals
(𝜀𝑖(2)1 , 𝜀𝑖(2)2 ) from BVN(0, 𝜗 ) where
2
𝜎𝜗1
𝜌𝑗 𝜎𝜗1 𝜎𝜗2
𝜗=
2
𝜌𝑗 𝜎𝜗1 𝜎𝜗2
𝜎𝜗2
Rank the residual pairs (𝜀𝑖(2)1 , 𝜀𝑖(2)2 ) in ascending order
according to the values of 𝜀𝑖(2)2 .
DLLM APPROACH
Step 6: Pair the first element 𝜀𝑖(2)1 of each sorted residual pair
(𝜀𝑖(2)1 , 𝜀𝑖(2)2 ) with the sorted
𝑗
𝜀𝑖 2 1 .
Step 7: For each j ∈ {Est, LB, UB}, estimate
𝛽1 𝑋𝑖
2 2
+
𝑗
𝑌𝑖 2 1
=
𝑗
𝜀𝑖 2 1 .
Step 8: Estimate the mobility measure
𝑗
Mj(𝑌𝑖 2 1 , 𝑌𝑖 2 2 ).
DLLM APPROACH
Step 9: Repeats Steps 5 to 8 for R times.
Step 10: For each j ∈ {LB, UB}, take the average of
across all iterations.
𝑗
Mj(𝑌𝑖 2 1 , 𝑌𝑖 2 2 )