1 2 Measuring Income Mobility using Pseudo-Panel Data

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: Were poor, we cant afford to go to Disneyland with your friends.) Baby: Im 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 Yit Yit+r Y1t+r Y1t Y2t+r Y2t

Y3t+r Y3t : : : : : : Ynt+r Ynt a vector transformation from Yit to Yit+r. 14 Panel Data

Difference Income Mobility Perspectives Movement 1 ln =1 1 Origin

independence 1 ( ln ( ) ln ( 1 )) Equalizer of income ( ) 1 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 Y it Y jt+r

Y1t : ? Y1t+r : : Y2t

? ? Y2t+r Y3t ? ? Y3t+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 {, }. 24 AM APPROACH Step 3: Estimate the model . Step 4: Compute the variance of the residuals . Step 5: Compute where is a randomly drawn data point from N(0,). Step 6: Estimate the mobility measure M(, ). Step 7: Repeats Steps 5 and 6 for R times. Step 8: Take the average of M(, ) 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 , and Step 3: Retrieve the residuals , and respective variances , , . and compute their Step 4: For each cohort c, estimate the model 26 BGK APPROACH Step 5: From the model in Step 4, retrieve the residuals

Step 6: Compute where is a randomly drawn data point from N(0, ). Step 7: Estimate the mobility measure M(). Step 8: Repeat Steps 6 and 7 for R times. Step 9: Take the average of M(, ) across all iterations. DLLM APPROACH Step 1: For each time period t, estimate . Retrieve the parameter estimates , residuals , the variance of the residuals, and the coefficients of determination . Step 2: For each j {Est, LB, UB}, draw n {Est, LB, UB}, draw n2 pairs of residuals (, ) from BVN( where =

DLLM APPROACH , DLLM APPROACH Step 3: For each j {Est, LB, UB}, draw n {Est, LB, UB}, estimate . Step 4: Estimate the mobility measure Mj(). Step 5: Repeats Steps 2 to 4 for R times. Step 6: For each j {Est, LB, UB}, draw n {Est, LB, UB}, take the average of M j() across all iterations. 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: [email protected] 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-red-cla

y-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-red-cla y-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-crowded-labo r-market-symbolizing-.html http://www.123rf.com/photo_15206271_hidden-risk-and-false-advertising-concept-with-a-beautiful-tropical-island-on-the -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 ( ) = [ ( ) 1 ( 1 ) 1 ] BGK Approach c i (t )t

Y c i (t )t 2 ct c t X

c c 2 c i (t )t c i (t )t 1 ( ) V ( P(Yi (ct )t 1

c i (t )t c i (t )t e c i (t )t 1 ) 2

ect c c c c i (t )t z x t

1 i ( t ) t 1 c c c 2 z | xi (t )t , xi (t )t 1 , t 1 , ect 1 ) ( )

2 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 ~ Yi ( 2 )1 1 X i ( 2 )1 vi ( 2 )1 1 X i ( 2 ) 2 v~i ( 2 )1 =

DLLM Approach P(i(2)1 < z, Yi(2)2 < z) P(i(2)1 < z, Yi(2)2 > z) P(i(2)1 > z, Yi(2)2 < z) P(i(2)1 > z, Yi(2)2 > z) What makes AUSTRALIA an interesting case study for examining income mobility? THE WORLD AGREED ON

8 GOALS TO BE ACHIEVED BY 2015 54 OECDs 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, 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 {

{ Dang, Elbers, et al. (2011) proposed estimating income regression models of the form: 1= 1 + 1 2 = 2 + 2 where Zs are time-invariant explanatory variables of income and vs are the error terms (can be assumed to follow ~ BVN(0, )). WHAT WE KNOW: }, }

WHAT WE WANT: ^ = ^ + ^ 1 1 1 59 Quick Facts about Australias 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 OECDs average (OECD 2014). The Gini coefficient in Australia is 0.33 vs. OECDs 0.31, Undesirable? A Necessary Feature of Rapid Economic Growth? 60 DLLM APPROACH Step 1: For each time period t, estimate . Retrieve the parameter estimates , and the residuals . Step 2: Compute the mean and the variance of the residuals,

and .. Step 3: Step 3: Set the residual correlation , j {Est, LB, UB}, draw n {LB, UB}, such that and . DLLM APPROACH Step 4: Sort the residuals from lowest to highest. Step 5: For each j {Est, LB, UB}, draw n {LB, UB}, draw n2 pairs of residuals (, ) from BVN( where = Rank the residual pairs (, ) in ascending order according to the values of . DLLM APPROACH Step 6: Pair the first element of each sorted residual pair (, ) with the sorted .

Step 7: For each j {Est, LB, UB}, draw n {Est, LB, UB}, estimate . Step 8: Estimate the mobility measure Mj(). DLLM APPROACH Step 9: Repeats Steps 5 to 8 for R times. Step 10: For each j {Est, LB, UB}, draw n {LB, UB}, take the average of M j() across all iterations.

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