Plenary session 5 5.1 misschien merz scherg lars osberg polarization of time and income iariw august 24 30 2014-merz and scherg

Polarization of Time and Income – A Multidimensional Approach
Polarization of Time and Income –
A Multidimensional Approach with
Well-Being Gap and Minimum 2DGAP:
German Evidence
Joachim Merz and Bettina Scherg*
International Association for Reseach in Income and Wealth IARIW 2014
Conference, Rotterdam, The Netherlands, August 24 - 30, 2014
* Univ.-Prof. Dr. Joachim Merz, Dipl.-Volkswirtin Bettina Scherg, Leuphana University Lüneburg, Faculty of Economics,
Behaviour and Law Sciences, Research Institute on Professions (Forschungsinstitut Freie Berufe (FFB), Chair „Statistics and
Professions“, CREPS (Center for Research in Entrepreneurship, Professions and Small Business Economics), IZA (Institute
for the Study of Labour (Merz)), Scharnhorststr. 1, 21332 Lüneburg, Tel.: +49 4131 / 677- 2051, Fax: +49 4131 / 677- 2059,
merz@uni.leuphana.de, scherg@uni.leuphana.de, www.leuphana.de/ffb
1 Univ.-Prof. Dr. Joachim Merz, Dipl.-Vw. Bettina Scherg, Research Institute on Professions (FFB), Leuphana University Lüneburg

Polarization - Introduction and Background
• A growing polarization in society accompanied with an erosion of the middle
class experiences more and more attention, at least in Germany, on recent
economic and social policy discussion.
• Drifting apart: far reaching and multitude consequences for the economy and in
general for quality of life.
• Main question so far: Is there a growing disperse of the “income scissors”
which describes that “the poor are going to be poorer and the rich to be
richer?” (Grabka and Frick 2008)?
• Large literature about inequality and in particular with focus on the poor, but only
a few theoretical and empirical studies which explicitly encompass both poles of
the income distribution.
• Lack of research on multidimensional polarization, in particular if time is
considered as one dimension

Research Concern
Multidimensional Polarization of Time and Income in Germany
Methodology
• Multidimensional Polarization index with substitution/compensation between
multiple polarization dimensions by a CES-type well-being function .
• New Multidimensional Polarization Gap approach: Minimum 2DGAP intensity
measure for transparent singular attributes – important for targeted policies
– in an interdependent compensation approach.
Application
• Time and Income as multidimensional polarization attributes. Respecting social
inclusion/social participation (Sen) by “genuine personal leisure time”.
• CES well-being function for measuring time and income compensation is
estimated by the German population and not arbitrarily chosen.
• German Evidence: Polarization analyses of the active population – working
poor, working rich - using the German Socio-Economic Panel 2002 as well as
the German Time Use Surveys 1991/92 and 2001/02.

Unidimensional Polarization Indices
Foster and Wolfson 2010: focus on the middle class, polarization is characterized by
an increase in bipolarity and spread from the median
Esteban and Ray 1994: group building, polarization increases the more
homogeneous the groups and the greater the differences between the groups
Wang und Tsui 2000: average relative gap to median
Scheicher 2010: average relative gap to the poverty and affluence thresholds, focus
on the poor and the rich
Multidimensional Polarization Indices
Gigliarano and Mosler 2009: decomposition of inequaltiy measures in “between
group inequality” and “within group inequality”, same intention as Esteban and
Ray; matrix of attributes, allows interdependence between attributes by
substitution elasticity (but arbitrarily based in application)
Scheicher 2010: 1. individual gaps (difference of x to x threshold), 2. for each
individual build sum of gaps over attributes 3. average of individual sum of gaps
Problem: Adding up of different dimensions (like minutes for time and $ for
income); no interdependence between attributes

Our Further Agenda
- Multidimensional Polarization – Identification and Aggregation, CES
- Multidimensional Polarization – New Compensation Based Indices (CES)
- New Minimum Multidimensional Polarization Gap (2DGAP)
- Application:
Time and Income Multidimensional Polarization – Germany

Multidimensional Polarization – Identification

Identification
Multidimensional POVERTY Axiomatic (Bourguignon and Chakravarty 2003):
Poverty: The majority of unidimensional poverty axioms could be conveyed to
the multidimensional level (e.g. symmetry, monotonicity, continuity, principle of
population, scale invariance and subgroup decomposability).
Focus axiom different: two possibilities for the multidimensional context:
1. “A poverty index should be independent of quantities lying above
dimension thresholds.” (Strong Focus Axiom)
2. “A poverty index should be independent of non-multidimensional-poor
persons` quantities.” (Weak Focus Axiom)

Measuring Multidimensional POVERTY - Identification
Intersection Approach Compensation Approach
(Weak Focus)
Union Approach
(Strong Focus)
2 x 2 x 2 x
1 x 1 x 1 x
2 z
1 z
2 z
1 z
2 z
1 z
Multidimensional Poverty
zj unidimensional poverty lines (j=1,2)
Source: own figure

Measuring Multidimensional AFFLUENCE Identification
Intersection Approach Compensation Approach
(Weak Focus)
Union Approach
(Strong Focus)
r1 r1 r1
1
r2 r2 r2
(d) (e) (f)
Multidimensional Affluence
Multidimensional Multidimensional Poverty Affluence
rj unidimensional affluence lines (j=1,2)
Source: own figure

Extension: Multidimensional POLARIZATION - Identification
Multidimensional Isopolarization Contours - Compensation Approach (Weak Focus) in
the Two-Dimensional Case
Source: own illustration, CES indifference curves of our application
Affluence
Poverty

Multidimensional Polarization - Aggregation
How to achieve multidimensional isopolarization contours –
compensation approach (weak focus axiom)?
Multidimensional poverty
Interdependence of the (two) single poverty attributes by a
Constant Elasticity of Substitution (CES) type well-being function
(already expressed e.g. Lugo and Maasoumi 2009, pp. 12, 16, Bourguignon
and Chakravarty 2003, p. 38, Merz and Rathjen 2014a, 2011 and others).
Multidimensional polarization
A slightly more flexible CES-type well-being function for an individual well-being
indicator (extension of Merz and Rathjen 2014a,b for poverty)
evaluates the interdependence of both polarization dimensions by:

CES well-being indicator (weak focus axiom) (Merz/Rathjen 2011; poverty)
i 1 ( i1 ) 2 ( i2 ) V w x w x
r r r g = é - + - ù- êë úû
CES Indifference curve
n
= éé êëë ( g ) ( - r /
n ) - ( - r
)
ù ù û úû
2 1 1 2 / / i i x V w x w
Aggregated CES multidimensional poverty line
( -
1/ )
( ) ( ) z 1 1 2 2 V w z w z
u
r r r g = é - + - ù - êë úû
Aggregated CES multidimensional affluence line
r
i j
=
=
=
=
=
ij x quantity of person in dimension
w j
r
n
g
dimension parameter for dimension
substitution parameter
returns to scale
constant
j
( ) ( ) r 1 1 2 2 V w r w r
u
r r r g = é - + - ù - êë úû

Multidimensional Polarization –
A New Compensation Based Approach
(Multidimensional CES Well-Being Function)

Compensation: Multidimensional Polarization
by a CES Well-Being Function
1 2 V (x , x )
Median Line: Multidimensional Well-Being Polarization, Extension of Wang and
Tsui 2000
é - ù = ê ú
P V x x V m m
1 ( , ) ( , )
i i
1 2 1 2
mult ,
m
å
n V m m
( , )
n
=
ë û
1 1 2
i
a
Poverty and Affluence Line: Multidimensional Well-being Polarization, Extension
of Scheicher 2010
a b
poor rich n n
é - ù é - ù = ê ú + ê ú
P V z z V x x V x x V r r
1 ( , ) ( , ) 1 ( , ) ( , )
å å
i i i
1 2 1 12 1 2 1 2
mult ,
rel
n V z z n V x x
( , ) ( , )
ë û ë û
poor i Î poor rich i Î
rich i i
1 2 1 2
poor rich n n
1 ( , ) ( , ) 1 ( , ) ( , )
[ ] [ ] , 1 2 1 12 1 2 1 2
= å - + å -
a b
mult abs i i i
n n
rich

Compensation: Multidimensional Polarization
by a CES Well-Being Function
Asymmetry: Multidimensional Well-Being Polarization
1 2 V (x , x )
ìï n a poor é - ù ïü ïì n
b
rich é ù ïü = - í ê ú ý í ê ú ý
îï ë û ïþ ïî ë û ïþ
1 ( , ) ( , ) / 1 ( , ) ( , )
å å
i i i
1 2 1 12 1 2 1 2
mult , rel ,
ratio
n V z z n V x x
( , ) ( , )
rich i i
1 2 1 2
ìï 1 n poor ïü ì 1 n
rich ü = í ( , ) - ( , ) ý / í ( , ) - ( , )
ý
îï ïþ î þ
[ ] [ ] , , 1 2 1 12 1 2 1 2
å å
a b
mult abs ratio i i i
n n
rich

Minimum Multidimensional Polarization Gap (2DGAP)

Multidimensional Polarization: Well-Being Gap
Affluence Line
Poverty Line
xr
2
pr
2
p2
x1 x2
p1 pr
1
xr
1
Well-Being Gap (Vz – Vi) , (Vr – Vr
i)
Vi
Vr
Vz
Vi
r

Multidimensional Polarization: Minimum 2DGAP
Minimum 2DGAP:
c = Min. Distance (x1, x2) to IMD-Line, a = 2D x1 contribution, b = 2D x2 contribution
slope of c = orthogonal slope of IMD-Line

Minimum 2DGAP definition and property
Minimum multidimensional poverty/affluence 2DGAP c =
shortest length (Euclidean norm) to the respective isothreshold line.
Shortest length = linear path orthogonal to the slope at the respective point of the CES-type
isothreshold line:
with
2 2 0,5
P P
= = éë - + - ùû
c c p x p x
( ) ( )
1 1 2 2
( ) 2 ( ( ) ) 2 0,5
min!
= éë p - x + f p - x
=
1 1 1 2
ùû 1
-
ææ ö ö = ççæ ö - ¸ ¸ ççç ¸ ¸ ¸ ççèè ø ø¸ ¸ è ø
r r
u
-
f p V V w p -
r
w
1 1 1 2 ( ) z /
z
g
1 p c
The iterative solution of the non-linear equation for then allows to calculate and in the
sequel the attribute lengths of and for a respective .
1 2 x = (x , x )
b
Note, because of the quadratic distances the procedure for the poverty as well as for the
affluence situation is the same.

Minimum 2DGAP
Appealing characteristics of Minimum 2DGAP Intensity
(compensation approach, weak focus)
• Well-being approach: manifold of paths from (x1,x2) individual well-being Vi to the
poverty Vz respective affluence well-being line Vr; : blurred situation.
• Minimum 2DGAP: unique path to escape poverty as an optimized compensation.
• Provides the specific compensation relation (marginal rate of substitution)
c ' = - 1/ c ' = - a / b, c '
= ¶ c = tan( ) =
b / a
a ^
x
1
¶
• Singular contributions (a: first dimension; b: second dimension) are directly
interpretable (like in € or time use units) and transparent, ensuring
compensation.
• Minimum 2DGAP allows targeted multidimensional polarization policies
according to singular attributes respecting its interdependence.

Minimum 2DGAP
Aggregation and Mean Minimum Polarization 2DGAP
Mean minimum polarization 2DGAP:
1 n 1 n
= å + å
C c c
i i
n Î n Î
poor i poor rich i rich
with its singular aggregated components

Relative Minimum 2DGAP
crel = c / cmax
2 2 0,5
max max 1 1 ( ) ( ( , )) min! z c =Pc P= éë p + f p V ùû =
where
Relative singular attribute gap intensities
1 max 1 max / / ( , ) rel rel z a = éëa p a ùû and b = éëb f p V b ùû
(only applicable for poverty gaps since affluence gaps are unbounded)

Application
Multidimensional Polarization – Germany

Time and Income - Multidimensional Polarization Attributes
Why Income?
Income is the traditional and most-widely accepted poverty attribute and typically the
focus of policy.
The affluent are commonly defined by a large amount of material resources with
focus on income and wealth.
Why Time?
Time is a general requirement for daily living activity and is important for
individual well-being simply by allowing or prohibiting desired activities for poor and
rich alike.
Increasing time squeeze and time stress underlines the importance of time (Sullivan
2007, Rosa 2003, Linder 1970).
The importance of the time dimension for poverty analyses – not yet for the rich -
with different specific definitions is emphasized meanwhile by other studies (Merz
and Rathjen 2014a,b, 2011, Zacharias 2011, Goodin et al. 2008, Burchardt 2008,
Calvo 2008, Harvey and Mukhopadhyay 2007, Bittman 1999 or Vickery 1977).

…
Time is a necessary resource for any activity, in particular for social participation.
Our focus: Genuine personal leisure time:
final personal resort which remains after all commitments and – in particular - allowing
social participation (Sen’s 1999 capability approach, social exclusion/inclusion).
Why Interdependence/Substitution/Compensation?
Economic perspective:
Fundamental trade-off between time for consumption (earnings) or time for leisure
Microeconomic allocation problem:
max U(C,L) s.t. time and income constraints
max U(z) with household production function z = f(x,t)
s.t. time and income constraints

Databases
• German Socio-Economic Panel (GSOEP) 2002
CES estimates by satisfaction data
• German Time Use Surveys (GTUS) 1991/92 and 2001/02
no satisfaction data,
but detailed time use diary data

Database – German Time Use Surveys
German Time Use Survey 1991/92 and 2001/02
• Persons twelve years (1991/92) / ten years (2001/02) and older,
German population in private households
• Quoted sample, four times the year
• Genuine Personal Leisure Time: Activities that are allocated to
one of the categories „Social life, conversation and
entertainment“, „participation at sport activities“, „hobbies and
games“ as well as „mass media“
1991/92 2001/02
No. of households 6,774 5,144
No. of persons 15,366 11,908
No. of diaries 30,732 35,685
See Ehling (1999), Ehling, Holz and Kahle (2001) and Ehling
(2003) for further information.

Source: Time use diary example, German Time Use Survey 2001/02

Time and Income - CES Well-Being Function Estimation
CES Econometrics (GSOEP 2002) :
CES estimation by a log Taylor expansion following Kmenta 1967
( ) ( ) [ ]ln ln ln 1 ln 1 1 ln ln 2
V = g +n w I +n - w L - rn w - w I - L +e
2
OLS with life satisfaction lhs Vi, (details in Merz and Rathjen 2014a)
( ) 0,108
3,550 0,519 0,297 0, 481 0,297 0,297 i i i V = ´ ´I + ´L
=
=
I Net Equivalence Income in Euro per month
L Genunie Leisure Time in Minutes per day
Substitution elasticity (curvature): s =1/(1+r) =1.422
(s = 0, complementary Leontief , s =1, Cobb - Douglas, s = ¥, perfect substitution)
Hicks’ elasticity of substitution: relative change in the proportion of the two attributes with respect to the relative change
of the corresponding marginal rate of substitution, measuring the “easyness” of substitution.

Estimated CES Well-Being Function
( ) 0,108
3,550 0,519 0,297 0, 481 0,297 0,297 i i i V = ´ ´I + ´L
600
500
400
300
200
100
0
=
=
0 200 400 600 800 1000 1200 1400 1600
Net Equivalence income (in Euro per month)
Genuine Leisure Time (in minutes per day)
8
7,5
7
6,5
6
5,5
5
4 1000
5,5
5,6
5,7
5,8
5,9
6
6,1
6,2
6,3
6,4
6,5
6,6
6,7
6,8
6,9
7
7,1
7,2
7,3
7,4
7,5
Source: own calculations with GSOEP 2002, active population
I Net Equivalence Income in Euro per month
L Genunie Leisure Time in Minutes per day
0
100
200
300
400
500
600
0
4,5
Nutzen
Pers. Freizeit (in Minuten pro Tag)
Nettoäquivalenzein
kommen (in Euro
pro Monat)
7,5-8
7-7,5
6,5-7
6-6,5
5,5-6
5-5,5
4,5-5
4-4,5
Well-Being Surface
Genuine Leisure Time
Net Equivalence Income
Isopolarization Contours

Empirical Analyses – Poverty Lines
1991/92 2001/02
Income Poverty Line
(= 60% Median Net Equivalence Household Income)
665.78 793.55 €
Time Poverty Line
(= 60% Median Individual Genuine Personal Leisure Time)
159 186 min
Well-Being Poor Vpoor = f(Ipoor, Lpoor) 6.704 6.827
Income Affluence Line
(= 150% Median Net Equivalence Household Income)
1,664.46 1,983.97 €
Time Affluence Line
(= 150% Median Individual Genuine Personal Leisure Time)
397.50 465 min
Well-Being Rich Vrich = f(Irich, Lrich) 7.402 7.538
Source: own calculations with GTUS 1991/92 and 2001/02 using statistical software Stata, all individuals included
for the calculation of median Net Equivalence Income (1991/92: n_hh=6774; 2001/02: n_hh=5144), persons older
eleven years included for the calculation of median Personal Leisure Time (1991/92: n=30732; 2001/02: n=34060)

Headcount Ratios in Different Poverty Regimes -
Germany 1991/92 and 2001/02
IMDP Line
P4: 1.2%
P2: 1.0%
P1: 2.3%
1991/92
Income Poverty Line
P6: 31.5%
Time Poverty Line
P5: 54.7%
P3: 9.3%
IMDP Line
P4: 1.3%
P2: 1.0%
P1: 2.5%
IMDP: 12.6% IMDP: 12.2%
2001/02
Income Poverty Line
P6: 50.3%
Time Poverty Line
P5: 36.2%
P3: 8.7%
Remarkably: P3: Working poor, where even above poverty income is assigned not to
compensate the time deficit
IMDP Line is the multidimensional time and income isopoverty threshold based on the CES estimates.
Source: own calculations with GTUS 1991/92 and 2001/02, active population

Headcount Ratios in Different Affluence Regimes -
Germany 1991/92 and 2001/02
IMDA Line
R2: 0.12% R2: 0.04%
R5: 1.63%
R1: 0.49%
Time Affluence Line
R6: 72%
1991/92
R3: 7.50%
R4: 18.26%
IMDA Line
R5: 1.14%
R6: 73.17%
2001/02
IMDA: 8.11% IMDA: 5.47%
R1: 0.37%
Time Affluence Line
R3: 5.06%
R4: 20.22%
Remarkably (2001/02):
R4: 20.22% are assigned not to be IMD affluent though income rich but time poor; their time deficit
is assigned not to be compensated even by high income.
R3: Only 5.06% IMD affluent are assigned to compensate their time deficit by high income.
IMDA Line is the multidimensional time and income isoaffluence threshold based on the CES estimates.

Empirical Analyses – Multidimensional Headcount Ratios
Multidimensional
IMD2 poor 12.55 12.16 97 0.425
Headcount
Ratio
rich 8.11
5.47 67 0.000
poor &
rich
1 p-values of two sample difference in means tests with
variance inhomogeneity assuming unequal variances;
*** = 0.1% significance
** = 1% significance;
* = 5% significance
Source: own calculations
GTUS 1991/92 and 2001/02, active population
1991/92 2001/02
Index Index Ratio Diff. Test1
1991/92
=100 p-values
***
20.66 17.63 85 0.000 ***
2 IMD: Interdependent Multidimensional (IMD) compensation
approach ; Poverty: CES well-being at 60% of income
respective time median (CES well-being (1991/92) = 6.704,
CES well-being (2001/02 = 6.827)
IMD: Interdependent Multidimensional (IMD) compensation
approach; Affluence: CES well-being at 150% of income
CES well-being (2001/02 = 7.538

Empirical Analyses – New Compensation Approach:
Multidimensional Polarization, CES Well-Being Gap
Overall multidimensional
polarization gap: slight decrease
Pmedian= gap, rel. to median m
Ppoles = gap, rel. to the poverty/affluence thresholds
1 p-values of two sample difference in means tests with variance
inhomogeneity assuming unequal variances;
*** = 0.1% significance ;** = 1% significance;
* = 5% significance
CES well-being (2001/02 = 6.827)
CES well-being (2001/02 = 7.538

Mean Minimum Multidimensional Polarization Gaps (2DGAP C) 1991/92
and 2001/02, Germany – Polarization Centres
Source: own calculations, GSOEP 2002 and GTUS 1991/92 (black) and 2001/02 (blue), weighted data
1. the mean 2DGAPs are relative small, thus the poverty and affluence positions are relative near the
respective interdependent multidimensional polarization thresholds.
2. there is a particular move of the mean affluent 2DGAP to higher income over the decade.
3. relative steep ascending mean 2DGAPS pinpoints the importance of the time component.

Kernel Densities of Minimum Multidimensional Polarization Gaps
(2DGAP c) 1991/92 and 2001/02, Germany
Source: own calculations, GTUS 1991/92 and 2001/02

Multidimensional Polarization – Mean Minimum
Multidimensional Polarization Gap (2DGAP)
2DGAP: Mean Minimum 2DGAP c 2DGAP: Mean Minimum Income
2DGAP a
(in €)
2DGAP: Mean Minimum
Time 2DGAP b
(in minutes per day)
1991 2001 Index
1991
=100
Diff
test
1991 2001 Index
1991
=100
Diff
test
1991 2001 Index
1991
=100
2DGAP c increases
significantly
2DGAP income component
increases significantly
2DGAP time component
Strongest polarization
intensity: in the intersection
of time as well as income.
P3: not compensated
time deficit even by
above poverty income:
significant increase
Polarization intensities:
poor dominance: A
rich dominance: B
poor: increase, significant
rich: no significant change
Diff.
test
Total 141.30 167.23 118 *** 29.27 38.56 132 *** 135.98 159.89 118 ***
Poor P1 106.48 152.21 143 *** 50.52 72.09 143 *** 92.85 133.11 144 ***
P2 56.32 74.75 133 * 35.51 46.67 131 43.19 57.82 134 *
P3 34.54 44.10 128 *** 7.64 10.71 140 *** 33.58 42.66 127 ***
IMD 49.38 68.50 139 *** 17.72 26.11 147 *** 45.11 62.20 138 ***
Rich R1 188.66 204.65 108 36.26 40.30 111 183.98 199.59 108
R2 39.79 95.74 241 * 16.30 46.04 282 * 36.27 83.92 231 *
R3 86.42 90.96 105 9.85 9.76 99 85.63 90.30 105
IMD 91.92 98.73 107 11.55 12.09 107 90.87 97.69 108

Multidimensional Polarization in Socio-Economic Groups
Selected Results:
• Various socio-demographic groups show different uni- and multidimensional
polarization and different growth for gender, age, education, the family
structure and West vs. East Germany.
• Self-employed are remarkable more often affected by income, time and
multidimensional IMD polarization than any other occupational group.
• IMD polarization headcount ratios for couples with two and more kids and
for single parents with kids (2DGAP c) are high and increasing with more
kids.
• Policy concern and attribute transparency (2DGAP): Group specific findings
are important for group specific policies.
• …

Concluding Remarks
New:
Time and Income Interdependent Multidimensional Polarization Approach:
– Extended CES Well-Being Measures and
– Minimum Multidimensional 2DGAP
Substitution/compensation (weak focus axiom) by a CES well-being
function evaluated by the German population (SOEP)
2DGAP approach disentangles the singular polarization attributes while
ensuring the compensation between the polarization attributes; important for
targeted economic and social policies.
Data:
Germany: SOEP, GTUS 1991/92 and 2001/02

Main empirical findings for working poor and rich:
Remarkable and significant impact of compensation (weak focus axiom)
between genuine personal leisure time and income in general and in
polarization regimes also outside the intersection one.
In particular of empirical importance:
IMD poor (P3): time poverty not compensated even by above threshold
poverty income (2001/02: 9.3%);
IMD rich (R3): affluent time deficit compensated by above affluence
income (2001/02: 5.1%).
Not IMD rich (R4): affluent time deficit not compensated by above
affluence income (2001/02: 20.2%).
Different importance and development of poverty and affluence poles.
Importance of time: All empirical results stress the relevance of genuine
personal leisure time with its social participation aspect as an important
polarization dimension.

Overall ten years 1991/92 to 2001/02 development:
• Multidimensional polarization headcount ratios:
significant decrease
• Multidimensional polarization well-being gap:
slight decrease
• Minimum multidimensional polarization 2DGAP intensity:

Multidimensional Polarization Policy Implications
Beyond all such measuring: Poverty is different to Affluence
Societal Evaluation, Justice and Social Norms …
Antipoverty policies:
• income: minimum wages, working hour arrangements, …
• time: for a better coordination and support of the daily life – with respect to the
labour market, the child care situation, public goods, commuting etc.
“Antiaffluence” policies
• income: top income tax rate, “Reichensteuer”, ceiling of manager income
• time: ?
Further thinking about polarization attributes: income, wealth, health, education …
How many inequality, how many polarization is desired/necessary/fair …?

Thank you for your attention
Polarization of Time and Income –
A Multidimensional Approach with Well-Being Gap
and Minimum 2DGAP: German Evidence
Joachim Merz (merz@uni.leuphana.de) and Bettina Scherg (scherg@uni.leuphana.de)
www.leuphana.de/ffb

Polarization? Why not just regard Inequality?
If inequality decreases polarization might increases
Pigou-Dalton Transfer Axiom (valid for all inequality measures):
Progressive Transfer: Transfer from the rich person to the poor person, after
transfer the rich person should not be worse positioned than the poor.
Each progressive transfer reduces inequality (for each inequality measure) but
increases polarization .
Thus, inequality measures are improper to measure polarization.

Compensation at the polarization centres 2001/02:
via slope 2DGAP C crossing the polarization threshold (marginal rate of substitution):
Poverty:
c' = - A/ B = -
0.42 ^ Assigned amount of time to exchange one EURO income locally is about 0.42
minutes; i.e. it is less than a one to one compensation, 0.42 minutes are enough to
compensate €1 which highlights the particular importance of time.
Affluence:
The comparable slope is 0.12; i.e. 0.12 minutes are enough to
compensate €1 which highlights the even stronger time importance for the affluent.

Applied Poverty Concepts – Isopoverty contures
600
500
400
300
200
100
Personal Leisure Time
Income Poverty Line Income Poverty Line
Multidimensional Poverty
0 200 400 600 800 1000 1200 1400 1600
Source: own figure
600
500
400
300
200
100
0
5,5
5,6
5,7
5,8
5,9
6
6,1
6,2
6,3
6,4
6,5
6,6
6,7
6,8
6,9
7
7,1
7,2
7,3
7,4
7,5
0
0 200 400 600 800 1000 1200 1400 1600
5,5
5,6
5,7
5,8
5,9
6
6,1
6,2
6,3
6,4
6,5
6,6
6,7
6,8
6,9
7
7,1
7,2
7,3
7,4
7,5
Time Poverty Line Time Poverty Line
IMDP Line
Net Net Equivalence Income Equivalence Income
Personal Leisure Time
Compensation Approach
(Weak Focus)
Union Approach
(Strong Focus)

Input Distance Function Approach and Minimum 2DGAP
K observed input/poverty attribute vector
Y technical efficient input vector
Y* economic (cost) efficient input/poverty attribute vector
U preferred output/well-being level
Technical efficiency:
TE=0Y/0K
Allocative Efficiency:
AE=0R/0Y
Total Economic Efficiency:
EE=AExTE=0R/0Yx0Y/0K=0R/0K
Input Distance Function: Production Input Distance Function: Production
K
Y*
Y
X1
X2
R
U
0
Y*=Y=K
X1
X2
U
0
Assumptions/Requirement:
constant price ratio (slope of the cost line).
Total economic efficiency
TE=AE=EE=1
0Y/0K=0R/0Y=0R/0K=1

Poverty
Input Distance Function: Well-being Minimum 2DGAP
Y*
X1
K
X2
U
0
. Y*
X1
K
X2
U
0
c
individuals optimize their well-being level given their
attributes and a constant individual price ratio (slope
of the budget line).
IDF=0K/0Y*
gap/discrepance between individual poverty status
and non-poverty status
individuals optimize their well-being level given their
attributes. This approach allows a changing individual
price ratio to reach the optimal compensation.
Minimum 2DGAP c= shortest gap to escape poverty
status

Affluence
Input Distance Function: Well-being Minimum 2DGAP
K
X1
Y* .
X1
X2
U
0
Y*
K
X2
U
0
c
individuals optimize their well-being level
given their attributes and a constant
individual price ratio (slope of the budget
line).
IDF=0K/0Y*
gap/discrepance between individual
affluence status and non-affluence status
individuals optimize their well-being level given
their attributes. This approach allows a changing
individual price ratio to reach the optimal
compensation.
Minimum 2DGAP c= shortest gap to loose
affluence status

Why are we interested in the top of the income distribution?
Atkinson 2003:
 Different parts of the distribution are interdependent; the outcome of
one group is affected by the outcome for others
 Top Income as Command over Resources: “is the game is worth the
candle?” Germany 2002: the top 10% (1%) taxpayers pay 51,4% (20,9%)
of the income taxes!
 Top Income as Command over People: capacity to opt out; exit
strategy as voluntary isolation (private provision of educati0on, health
care, gated communities) is a source of power
 Top Income in a Global Perspective: Global players; the proportion of
globally rich has risen since 1970 (Bourguignon and Morrison 2002,
Atkinson 2003); US the number of globally riched doubled between 1972
and 1992
 …

Richness limit by Plato (427-347 B.C.)
(744b) … there should be four different classes appointed according to
the amount of property. The limit of richness for the highest class,
which should not be passed over, should be the fourfold value of the
share in land (lot) of a citizen; the poverty limit is the value itself which
should not be diminished.
… if a person have yet greater riches, he has to give back the surplus to the
state.
…the share in land (lot) of each citizen should be large enough to satisfy
a modest household, and the total number of shares should be large
enough to enable its possessors to build an army great enough to protect
against offences and to successfully help neighbours who are unfairly
attacked.
Platos laws, 5th book, pp.11-14, 39, 43
(Translation according to Constantin Ritter, Platos Gesetze, Neudruck der Ausgabe Leipzig 1896, Scientia Verlag Aalen, p. 43)

Measuring the Rich – Some Further Approaches
The rich
…by participation in a social group regarded to be rich:
e.g. executives of major companies, famous artists, celebrities, family
dynasties
… by subjective definitions:
A combination of survey answers defines the subjective affluent line
(analogous to subjective poverty lines.
… by absolute levels:
Like being a (multi-)millionaire either by income level (like the Fortune list
of the richest 100 millionaires) or via savings (as in Auerbach and Siegel
2000 or Deutsche Bank 2000).
… by the deviation from some average income:
Analogous to a poverty line as a percentage (e.g. 50%) of the mean or
median income: a multiple of such a mean or median like 150%, 200% or
300% or by a multiple of the standard-deviation.

Literature
Bittman, M. (1999), Social Participation and Family Welfare: The Money and Time Cost of Leisure,
SPRC Dis-cussion Paper No. 95, Sydney.
Bourguignon, F. and S.R. Chakravarty (2003), The Measurement of Multidimensional Poverty, in:
Journal of Economic Inequality 1, 1, 25-49.
Burchardt, Tania (2008), Time and Income Poverty, Centre for Analysis of Social Exclusion, London
School of Economics, London (UK).
Esteban, J.-M. and D. Ray (1994), On the Measurement of Polarization, in: Econometrica, 62 (4),
819–851.
Esteban, J.-M., Gradín, C. and D. Ray (2007), An Extension of a Measure of Polarization, with an
Application to the Income Distribution of Five OECD Countries, in: Journal of Economic Inequality
5 (1), 1–19.
Foster, J. and M.C. Wolfson (2010), Polarization and the Decline of the Middle Class. Canada and the
U.S, in: Journal of Economic Inequality 8 (2), 247–273.
Foster, J., Greer, J. and E. Thorbecke (1984), A Class of Decomposable Poverty Measures, in:
Econometrica, Vol. 52, No. 3, 761-766.
Gigliarano, C. and K. Mosler (2009), Constructing Indices of Multivariate Polarization, in: Journal of
Economic Inequality, 7 (4), 435–460.

Goodin, R., Rice, J., Parpo, A. and Eriksson, L. (2008), Discretionary Time: A New Measure of
Freedom, Cambridge University Press, Cambridge (UK).
Grabka, M. und J.R Frick (2008), Schrumpfende Mittelschicht – Anzeichen einer dauerhaften
Polarisierung der verfügbaren Einkommen, Wochenbericht des DIW Berlin, Nr. 10/2008,
Berlin.
Harvey, A.S. and A.K. Mukhopadhyay (2007), When Twenty-four Hours is Not Enough: Time
Poverty of Working Parents, in: Social Indicators Research, 82, 1, 57-77.
Kakwani, N. and J. Silber (2008): Quantitative Approaches to Multidimensional Poverty
Measurement, Houndmills, Basingstoke, Hampshire: Palgrave Macmillan.
Kmenta, J. (1967), On Estimation of the CES Production Function, in: International Economic
Review, Vol. 8, No. 2.
Lugo, Maria Ana and Esfandiar Maasoumi (2008), Multidimensional poverty measures from an
information theory perspective, Paper prepared for the 30th General Conference of The
International Association for Research in Income and Wealth, Portoroz, Slovenia, August 24-
30.
Lugo, Maria Ana and Esfandiar Maasoumi (2009), Multidimensional poverty measures from an
information theory perspective, OPHI Working paper No. 10, Oxford Poverty & Human
Development Initiative,10).
Merz, J. and T. Rathjen (2009), Time and income poverty - An interdependent multidimensional
poverty ap-proach with German time use diary data, Forschungsinstitut Freie Berufe (FFB),
Leuphana Universität Lüneburg, FFB-Discussion Paper No.79, Lüneburg.

Merz, J. and T. Rathjen (2011a), Intensity of Time and Income Interdependent Multidimensional
Poverty: Well-Being and Minimum 2DGAP – German Evidence, Forschungsinstitut Freie Berufe
(FFB), Leuphana Universität Lüneburg, FFB-Discussion Paper No.92, Lüneburg.
Merz, J. and T. Rathjen (2011b), Sind Selbständige zeit- und einkommensarm? – Zur Dynamik
interdependenter multidimensionaler Armut mit den deutschen Zeitbudgeterhebungen, in:
Bekmeier-Feuerhahn, S., Mar-tin, A., Merz, J. and U. Weisenfeld (Eds.), Die Dynamik
tiefgreifenden Wandels in Gesellschaft, Wirt-schaft und Unternehmen, LIT-Verlag, 219-239.
Scheicher, C. (2010), Measuring Polarization via Poverty and Affluence, Köln Discussion Papers in
Statistics and Econometrics, Köln.
Schmidt, A. (2004), Statistische Messung von Einkommenspolarisierung, Eul Verlag, Erste Auflage,
Lohmar.
Sen, A.K. (1985), Commodities and Capabilities, North-Holland, Amsterdam.
Sen, A.K. (1999), Development as Freedom, Knopf Publishers, New York.
Sen, A.K. (2008), The Economics of Happiness and Capability, in: Bruni, L., Comim, F. and M.
Pugno, Capa-bilities & Happiness, Oxford University Press, Oxford (UK), 16-27.
Peichl, A. Schaefer, T. and C. Scheicher (2010), Measuring Richness and Poverty – A Micro Data
Application to Europe and Germany, in: The Review of Income and Wealth, 56 (3), 597–619.
Vickery, C. (1977), The Time-Poor: A New Look at Poverty, in: Journal of Human Resources, 12, 1,
27-48.
Wang, Y.-Q. and K.-Y. Tsui (2000), Polarization Orderings and New Classes of Polarization Indices,
in: Journal of Public Economic Theory, 2 (3), 349–363.

Appendix

Measuring Polarization - Unidimensional

Inequality vs. Polarization
1000 1000
Before:
6 persons with unequal
incomes
After:
3 and 3 persons with
equal incomes
-> inequality reduced
polarization increased
Pigou-Dalton-Transfer Axiom:
Progressive Transfer: Transfer from the rich person to the poor person, after
transfer the rich person should not be worse positioned than the poor.
Each progressive transfer reduces inequality (for each inequality measure) but
increases polarization .

Measuring Polarization
First pioneering efforts of measuring polarization: Foster and Wolfson 2010
and Esteban and Ray 1994.
They characterized polarization in two different ways:
Foster and Wolfson 2010:
• middle class focus
• measure the change of income poles by comparing income distributions.
Esteban and Ray 1994:
• Group building with homogeneous income (e.g. via occupation
assuming similar income in a certain occcupation)
• More polarization: more homogeneity of groups, greater differences
between group income means, greater groupsizes

Unidimensional Polarization Measures
Foster and Wolfson 2010 characterized income polarization as
• a decrease of the middle class
• and an increase in the poles of the income distribution.
Both characteristics are modelled by two different polarization curves.
Income spread:
Bipolarity:
1 ( )
S q
( )
- -
F q m
m
=
0.5 1 ( )
- -
= ò
B ( p )
dp
q
F p m
m
m = Median
q = population
fraction
The polarization index is given by twice the area under the second polarization
curve B(q)
0.5 1 ( )
= ´ ò
FW 2
- -
P dp
q
F p m
m

Extensions
Wang and Tsui 2000
present a class of polarization indices which are based on the Foster and Wolfson
index with relation to the median by:
P y m
n
= 1 å -
WT i
n m
=
1
i
a
m = Median
yi = income of
individual i
n = number of
observation
Scheicher 2010
defines polarization by aggregating measures of poverty (Foster, Greer and
Thorbecke 1984) and affluence (Peichl et al. 2010).
The focus thereby is on incomes outside the middle class interval.
a b
P z y y r
= å - + å -
S 1 i 1 i
univ
n z n y
rich i
z = poverty line
r = affluence line
yi = income of individual i
npoor/rich = number of poor/rich
individuals

Polarization with separate groups by Esteban and Ray 1994
• the population is divided into g groups.
= åå -
P K p 1
+
a p m m g g
i j
= =
1 1
ER
i j i j
πi = population fraction
of group i
μi = mean income of
group i
g = number of groups
• the members of the same group, who are homogenous, strongly identify with
each other, but members of different group feel alienated from each other.
• each group should be as similar as possible in terms of the members’
attributes.
• The degree of accordance is described by the population fraction of the
group, the degree of alienation results from the absolute income distances
• Polarization of the population then is expressed as the sum of the accordance
and alienation the individuals have relative to each other

Extensions
Esteban, Gradín and Ray 2007
• Problems of the former Esteban and Ray index is the loss of the information
about the dispersion of income within the group so the true polarization is
overestimated by an underestimated inequality.
• Esteban, Gradín and Ray 2007 expanded the index by an approximation error
ε which corrects this overestimation by an optimization process.
• This process classifies the given number of groups, so that the variance of the
income within the groups is minimal.
=åå - - -
EGR grouped
P p 1
+ap m m be G G
g g
i j
= =
1 1
( )
i j i j
πi = population fraction
of group i
μi = mean income of
group i
g = number of groups

Duclos, Esteban and Ray 2004
• Duclos, Esteban and Ray 2004 extend Esteban and Ray 1994 for continuous
distributions.
• The measure does not require anymore the division into groups, which now
are based on a non-parametric kernel density estimation.
• The polarization index is obtained by describing the empirical distribution
function by an estimated kernel density function.
with
P F f y a a y dF y
a = ò
DER ( ) ( ) ( ) ( )
y
y
= + - - ò
a y m y F y xdF x
( ) (2 ( ) 1) 2 ( )
-¥

Measuring Polarization - Multidimensional

Multidimensional Polarization Measures
Gigliarano and Mosler 2009
• They argue: the splitting of the population into groups should not be
based only on income, but rather on other attributes like education, wealth or
health.
• Idea: construction of a class of multidimensional polarization measures by
decomposing different inequality measures with measuring the relative
group size.
• Then: polarization consists of …
• Inequality within groups
• Inequality between the groups
• a sufficient group size
• This measure is a multidimensional extension of the group approach of
Esteban and Ray 1994.

Gigliarano and Mosler 2009 (cont.)
• Polarization increases if between group inequality rises
• Polarization decreases if within group inequality rises
• The more equal the different group sizes, the greater is the polarization of
the population. Based on this idea they construct three kinds of indices:
æ ö
P B X S X
( ) ( )
( )
( ) ( ) ( )
= ç è W X + c
¸´ ø
= - ´
( )
GM
1
GM
f
y
t
P B X W X S X
2
P GM
B X S X
3
æ ö
( ) ( )
= ç è B ( X ) + W ( X )
+ c
¸´ ø
X = matrix including N
individuals with K
attributes
B(X) = inequality
between groups
W(X) = inequality
within groups
S(X) = group size
c= positive constant

Scheicher 2010
• the multidimensional index is a combination of poverty and affluence
measures (analoge to the unidimensional case)
• it is based on a set of attributes of the individuals modeled in a vector y
• it measures the distance of the poor or affluent (concerning each attribute)
to the poverty / affluence threshold and sums the distances over each
attribute and each individual
( ) min{ , } ,
ìï - - Ïëé ûù éë ùû = í îï Îéë ùû
( ,[ , ] ) ( , , ) i ij j j
d y , z ,
r
y z y r if y z r
ij j ij j ij j j
if y z r
0 ,
ij j j
ij j j
d y z r =åd y éëz r ùû
j
S 1 ( ,[ , ])
= å
P d y z r
mult i
i
n
yij = value oft the jth
attribute (dimension)
of individual i
zj = poverty threshold of
dimension j
rj = affluence threshold of
dimension j
n = number of observation

• Persons twelve years (1991/92) / ten years (2001/02) and older,
German population in private households
• Quoted sample, four times the year
• Genuine Personal Leisure Time: Activities that are allocated to
one of the categories „Social life, conversation and
entertainment“, „participation at sport activities“, „hobbies and
games“ as well as „mass media“
1991/92 2001/02
No. of households 6,774 5,144
No. of persons 15,366 11,908
No. of diaries 30,732 35,685
See Ehling (1999), Ehling, Holz and Kahle (2001) and Ehling
(2003) for further information.

Empirical Analyses – Polarization Literature Measures
1991/92 2001/02
1991/92
=100 p-values
FW (mid range) und EGR(groups):
sign. decrease in income,
not sign. decrease in time
Unidimensional
Income
Polarization
Foster & Wolfson 0.0996 0.0908 91 0.000 ***
Esteban, Gradin &
0.0506 0.0458 91 0.000 ***
Ray
Gap Wang & Tsui 0.4356 0.3894 89 0.000 ***
Gap Scheicher 0.4104 0.4034 98 0.286
poor 0.1905 0.2215 116 0.005 **
rich 0.2199 0.1820 83 0.000 ***
Gaps:decrease in income
Time
Foster & Wolfson 0.1239 0.1214 98 0.379
Esteban, Gradin &
0.0608 0.0600 99 0.357
Ray
increase in time
Gap Wang & Tsui 0.4074 0.4205 103 0.000 ***
Gap Scheicher 0.5115 0.5073 99 0.484
poor 0.4037 0.3899 97 0.018 *
rich 0.1078
0.1174 109 0.388
Multidimensional
Scheicher (Gap) 223.64 224.02 100 0.953
1 p-values of two sample difference in
means tests with variance
inhomogeneity assuming unequal
variances;
* = 5% significance
2 IMD: Interdependent
Multidimensional (IMD)
compensation approach ; Poverty:
CES well-being at 60% of income
respective time median (CES well-being
(1991/92) = 6.704, CES well-being
(2001/02 = 6.827)
IMD: Interdependent
Multidimensional (IMD)
compensation approach; Affluence:
(1991/92) = 7.402, CES well-being
(2001/02 = 7.538
GTUS 1991/92 and 2001/02,
active population

New Mean Minimum Multidimensional Polarization Gaps (2DGAP c)
1991/92 (black) and 2001/02 (blue), Germany
1991
1991
2001
2001
Source: own calculations, GSOEP 2002 and GTUS 1991/92 and 2001/02, weighted data
income
time

2DGAP a
(in €)
2DGAP time component
2DGAP: Mean Minimum
Time 2DGAP b
2DGAP income component
1991 2001 Index
1991
=100
Diff
test
1991 2001 Index
1991
=100
Diff
test
1991 2001 Index
1991
=100
2DGAP c increases
significantly
intensity: in the intersection
P3: not compensated
time deficit even by
above poverty income:
Diff
.
test
Total 141.30 167.23 118 *** 29.27 38.56 132 *** 135.98 159.89 118 ***
P1 106.48 152.21 143 *** 50.52 72.09 143 *** 92.85 133.11 144 ***
P2 56.32 74.75 133 * 35.51 46.67 131 43.19 57.82 134 *
Poor
P3 34.54 44.10 128 *** 7.64 10.71 140 *** 33.58 42.66 127 ***
IMD 49.38 68.50 139 *** 17.72 26.11 147 *** 45.11 62.20 138 ***
Poor
R1 188.66 204.65 108 36.26 40.30 111 183.98 199.59 108
R2 39.79 95.74 241 * 16.30 46.04 282 * 36.27 83.92 231 *
Rich
R3 86.42 90.96 105 9.85 9.76 99 85.63 90.30 105
IMD 91.92 98.73 107 11.55 12.09 107 90.87 97.69 108
Rich
P1+R1 295.14 356.86 121 *** 86.78 112.39 130 *** 276.56 332.7 120 ***
P2+R2 96.11 170.49 177 *** 51.81 92.71 179 *** 79.46 141.74 178 ***
Rich
&
Poor
P3+R3 120.96 135.06 117 *** 17.49 20.47 117 *** 119.21 132.96 112 ***

Empirical Analyses – Headcount Ratios
Unidimensional
Income poor 4.19 4.82 115 0.043
Headcount
Ratio
rich 26.25
25.65 98 0.361
Unidimensional
Headcount Ratios poor:
Time poor 43.06 47.34 110 0.000 ***
rich 2.24 1.55 69 0.000 ***
Multidimensional
IMD2 poor 12.55 12.16 97 0.425
rich 8.11 5.47 67 0.000 ***
poor &
rich
1 p-values of two sample difference in means tests with
variance inhomogeneity assuming unequal variances;
* = 5% significance
GTUS 1991/92 and 2001/02, active population
1991/92 2001/02
1991/92
=100 p-values
*
20.66
17.63 85 0.000 ***
Unidimensional
Headcount Ratios:
affluent decrease,
significant for time
Multidimensional
affluent decrease
significantly
CES well-being (2001/02 = 6.827)
CES well-being (2001/02 = 7.538

2DGAP a
(in €)
2DGAP: Mean Minimum
Time 2DGAP b
1991 2001 Index
1991
=100
Diff
test
1991 2001 Index
1991
=100
Diff
test
1991 2001 Index
The time asymmetry
between the 1991
poor and the
rich is remarkable.
=100
It reduce over the
considered decade
2DGAP c increases
significantly 2DGAP income component
intensity:in the intersection
increases significantly 2DGAP time component
Diff
.
test
Total 141.30 167.23 118 *** 29.27 38.56 132 *** 135.98 159.89 118 ***
P1 106.48 152.21 143 *** 50.52 72.09 143 *** 92.85 133.11 144 ***
P2 56.32 74.75 133 * 35.51 46.67 131 43.19 57.82 134 *
Poor
P3 34.54 44.10 128 *** 7.64 10.71 140 *** 33.58 42.66 127 ***
IMD 49.38 68.50 139 *** 17.72 26.11 147 *** 45.11 62.20 138 ***
Poor
R1 188.66 204.65 108 36.26 40.30 111 183.98 199.59 108
R2 39.79 95.74 241 * 16.30 46.04 282 * 36.27 83.92 231 *
Rich
R3 86.42 90.96 105 9.85 9.76 99 85.63 90.30 105
IMD 91.92 98.73 107 11.55 12.09 107 90.87 97.69 108
Rich
P1+R1 295.14 356.86 121 *** 86.78 112.39 130 *** 276.56 332.7 120 ***
P2+R2 96.11 170.49 177 *** 51.81 92.71 179 *** 79.46 141.74 178 ***
Rich
&
Poor
P3+R3 120.96 135.06 117 *** 17.49 20.47 117 *** 119.21 132.96 112 ***
141.30 167.23 118 *** 29.27 38.56 132 *** 135.98 159.89 118 ***

Working arrangement poor vs. not poor 2001/02
cat=1 core/not fragmented, cat=2 core/fragmented, cat=3 non-core/fragmented,
cat=4, non-core/fragmented
80
60
40
% poor not poor
20
0
1 2 3 4
poor 56,38 30,5 8,28 4,85
not poor 66,12 26,73 4,33 2,82
category

Multidimensional Polarization in Socio-Economic Groups of Interdependent Multidimensional Time and Income
Polarization 2001/02, Germany
Polarization Headcount Ratio Well-Being Gap Multidimensional Polarization Minimum 2DGAP
Income
Index
1991
=100
Time
Index
1991
=100
IMD*
Index
1991
=100
Mean
Index
1991
=100
Mean c
Index
1991
=100
Mean a
Income
(€)
Index
1991
=100
Mean b
Time
(min.)
Index
1991
=100
Gender
Male 29.84 99 47.29 115 17.76 92 0.3525 103 182.97 134 40.51 152 175.34 133
Female 31.55 99 51.65 98 17.40 76 0.2845 80 135.34 92 33.88 105 128.46 91
Age
12-17 17.05 76 40.57 103 17.90 135 0.2846 114 158.86 89 69.38 105 140.47 86
18-24 20.32 79 38.45 95 14.65 81 0.2776 84 158.23 111 45.83 126 148.90 111
25-44 28.79 101 50.92 109 17.97 84 0.3171 95 157.61 117 37.47 136 150.20 116
45-65 36.16 97 49.75 109 18.16 86 0.3520 95 174.20 120 36.08 130 167.79 120
>65 54.33 139 59.91 161 20.65 84 0.2662 45 189.54 110 55.76 283 175.89 103
Education
A-Level 45.86 107 52.52 114 19.07 76 0.3579 97 172.75 113 36.81 113 166.35 115
Vocational Dipl. 33.50 71 48.46 104 18.46 70 0.2919 74 163.61 115 37.92 134 156.19 114
Second. School II 24.92 93 49.54 107 18.33 85 0.3212 96 167.12 117 42.47 130 158.45 116
Second. School I 22.90 87 45.16 103 15.08 91 0.3217 100 155.57 127 32.79 135 149.65 126
No certificate 28.69 219 48.84 158 17.64 145 0.2595 54 131.82 63 32.41 95 126.62 63
Occupation
Self-employed 52.88 100 59.44 114 33.95 96 0.4563 95 240.22 129 59.59 168 227.72 128
Liberal. Prof. 59.84 - 49.64 - 28.29 - 0.4278 - 230.50 - 50.67 - 220.54 -
Entrepreneur 48.16 - 66.11 - 37.79 - 0.4510 - 231.47 - 62.20 - 218.11 -
Civil Servant 53.22 97 47.83 124 18.97 82 0.3220 80 135.19 104 16.37 84 133.84 104
White-Collar 33.88 102 50.14 103 14.34 69 0.2886 88 130.23 103 24.43 72 126.69 104
Blue-Collar 15.41 78 46.35 110 14.95 85 0.2561 88 155.62 127 37.06 124 149.97 128
Working Hours
<20 21.70 75 47.74 116 22.24 105 0.2597 88 170.52 112 44.65 94 162.31 116
21-38 24.74 71 44.03 107 13.62 78 0.2745 82 151.23 112 31.58 115 145.84 112
39-40 27.98 115 47.70 103 14.23 71 0.3001 102 151.38 130 31.14 118 146.37 131
41-44 32.57 149 50.91 113 16.84 90 0.3508 78 187.05 100 36.04 106 182.01 100
…>45 46.75 106 60.99 115 27.9 92 0.4024 91 187.40 115 45.74 163 177.82 113
HH-Size
Single-HH 30.13 132 50.40 122 15.88 81 0.3067 88 178.73 109 36.52 77 172.49 123
Couple 0 Kids 56.07 110 46.82 108 18.17 69 0.3294 90 150.37 106 26.76 112 145.84 106
Couple 1 Kid 23.95 136 47.47 102 14.04 95 0.2780 94 127.73 98 31.69 106 122.67 98
Couple 2 Kids 14.61 97 49.36 97 16.34 78 0.2833 85 146.62 97 42.85 148 138.69 94
Couple >2 Kids 20.94 114 57.65 100 31.68 118 0.2973 96 191.76 147 84.28 294 170.43 135
Single par. 1 Kid 31.18 121 40.46 78 22.23 105 0.3337 90 232.64 133 65.03 145 218.50 132
Single par. >1Kid 22.96 81 51.77 82 17.43 40 0.2491 119 146.09 151 47.44 114 135.88 158
Other structure 25.96 73 50.99 120 17.46 96 0.3693 102 160.14 129 52.63 212 148.68 124
Region
West Germany 32.98 90 46.43 110 16.26 87 0.3193 85 161.59 121 36.16 141 154.57 120
East-Germany 19.38 114 59.77 114 23.65 93 0.3536 113 191.00 126 46.06 128 182.51 126
* IMD: Interdependent Multidimensional polarization compensation approach Source: own calculations with GTUS 1991/92 and 2001/02, active population

Multidimensional Polarization- Mean Minimum
1 P1/R1: regime of income and time
poor/rich individuals 2 P2: regime of
income poor but time not poor
individuals 3 P3: regime time poor but
not income poor individuals; R2 regime
of time rich but not income rich
individuals; R3 income rich but time not
rich individuals
4 Two sample difference in means test
with variance inhomogeneity and
unequal variances; *** = significant on
the 1% level; ** = significant on the 5%
level; * = significant on the 10% level.
5 IMD: Interdependent Multidimensional
(IMD) compensation approach ; Poverty:
(1991/92) = 6.704, CES well-being
(2001/02 = 6.827)
IMD: Interdependent Multidimensional
(IMD) compensation approach;
Affluence: CES well-being at 150% of
income respective time median (CES
well-being (1991/92) = 7.402, CES well-being
(2001/02 = 7.538)
Source: own calculations with GTUS
1991/92 and 2001/02, active population

It is to be expected that different individual resources and limitations will result in a
different polarization picture for different socio-economic and socio-demographic
groups.
Gender:
•Females are more often than males affected by poverty or affluence referring to
unidimensional income and time polarization.
•In contrast males face a deeper multidimensional polarization gap (2DGAP c)
allover and with respect to income and time.
•The 2DGAP polarization increased the most (2DGAP a, b, c) between 1991/92 to
2001/02 for males.

Age:
•Individuals who are over 65 years old and who are still working more than 5 daily
hours a day are the group with the highest unidimensional polarization headcount
ratios in the poles as well as under the multidimensional IMD polarization regimes.
•The older the individuals are the deeper are the polarization gaps (2DGAP c), too.
•The importance of age for both distributional poles is remarkable and underlines a
particular erosion of the middle class for the elderly.
Education:
•Individuals with an A level (“Abitur”) show the most intense polarization.
•The higher the education level, the higher is the headcount ratio of the affluent.
•Secondary schooling is connected with the fastest polarization growth.

Occupation:
•Self-employed are remarkable more often affected by income (52.88%), time
(59.44%) and multidimensional IMD polarization (33.95%) than any other
occupational group.
•Dividing the Self-employed into the Liberal Professions (“Freie Berufe”) and
Entrepreneurs, reveals that the high percentages should be traced back to the high
percentages of the Entrepreneurs with regard to time and IMD polarization,
however not for income polarization.
•Furthermore, polarization intensity measured by multidimensional gaps show the
highest spread for the self-employed (2DGAPc) and in particular for genuine
personal leisure time (2DGAP b).
•Multidimensional polarization for the self-employed grew the most followed by
blue-collar workers.

This is a remarkable result:
•common sense tells that (liberal) professions (Freie Berufe) and entrepreneurs
(tradesmen) as self-employed are rich by money and, because of their
independence and time sovereignty, are rich by time, too.
•Since two thirds of the individuals in the two poles under IMD polarization are
found in the poverty pole the deprived situation is of particular importance for the
self-employed beyond the relatively dominant affluent gap contribution
•This underlines self-employed results multi-dimensional time and income poverty
results for the self-employed by Merz and Rathjen 2011b.

Working Hours:
•The highest polarization headcount ratios and the largest multidimensional
polarization intensity (2DGAP) c are found for those with the most working hours,
which, as to be expected, strengthen the affluent individuals.
Region:
•Though unidimensional income and time poverty headcount ratios are higher in
West Germany the multidimensional picture is different.
•The relative number of individuals in the distributional poles are higher in East
Germany (23.65% vs. 16.26% in West Germany) and the polarization intensity
overall and with regard to income and time is greater in East Germany than in West
Germany showing the influences of opposite economies.

Household/Family Structure:
•Whereas the IMD polarization headcount ratio for couples with two and more kids
is the highest among the family groups the polarization is strongest for single
parents with kids (2DGAP c).
•Single parents with kids also show the relative highest time gap. According to
further results, this is mainly due to the poverty pole. They face a strong polarization
increase by 33% (2DGAP c) over the decade.
•The increase is even stronger for single parents with more children (51%) and
pinpoints growing tension for single parents.

To summarize:
•As expected various socio-demographic groups show different uni- and multi-dimensional
polarization and different growth for gender, age, education, the family
structure and West vs. East German.
•Remarkably multidimensional polarization of time and income of self-employed as
well single parents attract specific attention.
•Our quantification of multidimensional time and income polarization for various
socio-demographic groups Germany is important to detected groups of specific
concern.
•Many further factors are expected to be included to explain and to formulate
targeted policies. This discussion has to be postponed to further research.

Plenary session 5 5.1 misschien merz scherg lars osberg polarization of time and income iariw august 24 30 2014-merz and scherg

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (15)

Similar to Plenary session 5 5.1 misschien merz scherg lars osberg polarization of time and income iariw august 24 30 2014-merz and scherg

Similar to Plenary session 5 5.1 misschien merz scherg lars osberg polarization of time and income iariw august 24 30 2014-merz and scherg (20)

More from IARIW 2014

More from IARIW 2014 (20)

Recently uploaded

Recently uploaded (20)

Plenary session 5 5.1 misschien merz scherg lars osberg polarization of time and income iariw august 24 30 2014-merz and scherg

Editor's Notes