Plenary session 5

1. POLARIZATION OF TIME AND INCOME –
A MULTIDIMENSIONAL APPROACH WITH
WELL-BEING GAP AND MINIMUM
2DGAP: GERMAN EVIDENCE
JOACHIM MERZ & BETTINA SCHERG
33rd General IARIW conference – Rotterdam,
Session 5: Time and Well-Being
August 28, 2014
Presentation by: Lars Osberg
Dalhousie University

2. Methodology Challenge: merge 2 Literatures
Polarization + Multi-Dimensional Well-Being
• “Polarization”? – but rich & poor have different problems
• “Erosion of Middle Class” is the real issue
• Why worry? Unknown implications of declining % society inhabiting a
common social space, dealing with shared social reality
• “Multi-Dimensional”? – but can’t market work convert time
into Gary Becker’s “Full Income”?
• “Full income” values all time @ marginal hour – misstates utility
implications of (Income, Leisure) combinations
• M&S: suggest & estimate CES indifference curves
• Trends in Germany 1991/92 to 2001/02 ?
• German Socio-Economic Panel (GSOEP) + German Time Use
Survey (GTUS)

3. “Both” Criteria or “Either” or “Enough of”
Intersection Approach Compensation Approach
(Weak Focus)
Union Approach
(Strong Focus)
2 x 2 x 2 x
2 z
1z
2 z
1z
2 z
1 x 1 x 1 x
1z
Multidimensional Poverty
zj unidimensional poverty lines (j=1,2)
Source: own figure
Multidimensional POVERTY - Identification

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

5. Multidimensional POLARIZATION - Identification
Multidimensional Isopolarization Contours (a.k.a. “Indifference Curves”)
- Compensation Approach (Weak Focus) in the Two-Dimensional Case
Source: own illustration, CES indifference curves of our application
Affluence
Poverty

6. Aggregated CES multidimensional poverty line
      
Aggregated CES multidimensional affluence line
      
ij x quantity of person in dimension





dimension parameter for dimension
substitution parameter
returns to scale
constant
j
i j
w j



z 1  1  2  2  V w z w z

   
 
    r 1 1 2 2 V w r w r

   
 

7. Multidimensional Polarization: Minimum 2DGAP
r
2
r
2
x
v2
p2
r
1 x
Minimum 2DGAP:
c = Min. Distance Source: own (x, 1figure
x) to IMD-Line, a = 2D xcontribution, b = 2D xcontribution
21 2 slope of c = orthogonal slope of IMD-Line
•
•
•
a
b
x1 p1
x2
v1
•
•
•
•
•
•
c
•
p
r
1
p
a
c
b
b
Multidimensional
Polarization
Compensation
Approach (Weak Focus)
•
Affluence
•
Poverty
•
•

8. Minimum 2DGAP
Aggregation and Mean Minimum Polarization 2DGAP
Mean minimum polarization 2DGAP:
1 1 n n
   
C c c
i i
n n  
poor i poor rich i rich

9. Which time matters for well-being?
“Genuine personal leisure time”
final personal time available after all commitments
(market work + home production + commuting + personal care)
German Time Use Survey 1991/92 and 2001/02
- codes: Social life, conversation and entertainment,
participation at sport activities, hobbies and games, mass
media
• Persons twelve years (1991/92) / ten years (2001/02)
and older, German population in private households
surveyed four times the year
Analysis restricted to “Economically Active”
LO: life-cycle ? students, “housewives” & retired ??

10. Time & Income: CES Subjective Well-Being Function
CES estimation by a log Taylor expansion following Kmenta 1967
    1 2
V    w I   w L   w  w I  L 
ln ln ln 1 ln 1 ln ln
2
OLS estimation: LHS = Self-reported life satisfaction (11 point Likert Scale);
 
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
CES Econometrics (GSOEP 2002) :
Substitution elasticity (curvature):  1/(1) 1.422
(  0, complementary Leontief ,  1, Cobb Douglas,   , 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.

11. Empirical Analyses – Poverty & Affluence 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)

12. Headcount Ratios in Different Poverty Regimes -
Germany 1991/92 and 2001/02
600
500
400
300
200
100
0
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%
0 200 400 600 800 1000 1200 1400 1600
Net Equivalence Income (in Euro per month and prices 2002)
Genuine Leisure Time (in minutes per day)
P1 + P2 + P3 = Multi-dimensionally Poor
1991/92 = 12.6%
2001/02 = 12.2%
600
500
400
300
200
100
0
2001/02
IMDP Line
P4: 1.3%
P2: 1.0%
P1: 2.5%
Income Poverty Line
P6: 50.3%
Time Poverty Line
P5: 36.2%
P3: 8.7%
0 200 400 600 800 1000 1200 1400 1600
Net Equivalence Income (in Euro per month and prices 2002)
Genuine Leisure Time (in minutes per day)
Nil Change in multi-dimensional Poverty= 0.4%
But big change in P5 [% time poor but income compensates] (54.7%→ 36.2%)

13. Affluence Headcount Ratios: Germany 1991/92 & 2001/02
700
600
500
400
300
200
IMDA: 8.11% IMDA: 5.47%
700
600
500
400
300
200
Very Few “Time Rich” = R1 + R2 + R5 = 2.2% → 1.6%
(unsurprising – economically active AND more than 6.6→7.5 hours daily personal time ??)
R1 + R2 + R3 = Multi-dimensional RICH
1991/92; IMDA = 8.1%
2001/02: IMDA = 5.5 %
Change at TOP = - 2.6 %
100
800 1000 1200 1400 1600 1800 2000 2200 2400
Net Equivalence Income (in Euro per month and prices 2002)
Genuine Leisure Time (in minutes per day)
100
1000 1200 1400 1600 1800 2000 2200 2400 2600
Net Equivalence Income (in Euro per month and prices 2002)
Genuine Leisure Time (in minutes per day)
IMDA Line
R5: 1.63%
Income Affluence Line
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
Income Affluence Line
R1: 0.37%
Time Affluence Line
R3: 5.06%
R4: 20.22%
R2: 0.12% R2: 0.04%

14. Declining Polarization?
Multidimensional
Headcount Ratios
1991/92 2001/02
Index Index Ratio Diff. Test1
• “Middle Class” Head-Count Ratio
• “Middle Class” = 1- [Multi-Dimensional “Poor” + Multi-Dimensional “Rich” ]
• 1991/92 = 1 – [0.126 + 0.081] = 0.793
• 2001/02 = 1 – [0.122 + 0. 055] = 0.823
1991/92
=100
p-values
Multidimensional
IMD2 poor 12.55 12.16 97 0.425
Headcount
Ratio
rich 8.11
5.47 67 0.000
***
poor &
rich
20.66
17.63 85 0.000 ***

15. Increasing 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
Diff.
test
2DGAP c increases
significantly
2DGAP income component
increases significantly
2DGAP time component
increases significantly
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 ***
Strongest polarization
intensity: in the intersection
of time as well as income.
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
P3: not compensated time
deficit even by above
poverty income: significant
increase
Source: own calculations with GTUS 1991/92 and 2001/02, active population

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

17. Multidimensional Polarization in Socio-Economic Groups
Selected Results:
• different growth for gender, age, education, the family structure and West
vs. East Germany.
• Self-employed - more often affected by income, time and multidimensional
IMD polarization
• 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.
• …

18. LO: Remaining Questions
• “Time Poverty” and “Time Affluence”
• Are relative criteria (60% median & 150% median) taken from
income poverty literature necessarily appropriate?
• Restriction to “economically active” of all ages implies non-random
sample selection (especially if <25 or >65)
• How to interpret Student/Retired or “Child Care Years” Life Cycle
Phases & well-being implications ?
• The “declining middle class” is the reason we care about
“polarization” – so why not measure it directly ?
• Does % population in common shared [income, time] social space
predict political participation, voluntary activity, civil society?