Parallel Session IARIW 2014

1. Background
Methods
Additional Thoughts
Summary
Cross Sectional and Longitudinal Equivalence
Scales for West Germany Based on Subjective Life
Satisfaction
Session 2B: Equivalence Scales over Time and Space
J. Faik
University of Vechta and FaSo, Germany
33rd IARIW General Conference, Rotterdam, 2014
J. Faik Equivalence Scales

2. Background
Methods
Additional Thoughts
Summary
Outline
1 Background
Using life satisfaction to measure equivalent income
2 Methods
Model specification and data
Empirical Work
3 Additional Thoughts
Possible extensions
J. Faik Equivalence Scales

3. Background
Methods
Additional Thoughts
Summary
Using life satisfaction to measure equivalent income
Outline
1 Background
Using life satisfaction to measure equivalent income
2 Methods
Model specification and data
Empirical Work
3 Additional Thoughts
Possible extensions
J. Faik Equivalence Scales

4. Background
Methods
Additional Thoughts
Summary
Using life satisfaction to measure equivalent income
Equivalence Scales
Fundamental objective is to allow comparisons in terms of
equivalent incomes.
Require a measure of wellbeing. E.g. expenditure on
necessities (Daley et al, 2014).
Differentials in wellbeing can be measured over households of
different sizes.
The quantity of income required to offset differentials in
welfare is the equivalence scale.
J. Faik Equivalence Scales

5. Background
Methods
Additional Thoughts
Summary
Using life satisfaction to measure equivalent income
Equivalence Scales
What is the appropriate measure of wellbeing?
Life satisfaction is a broad and appealing welfare concept.
Captures all factors subjectively regarded as important to the
individual.
Includes non-economic factors.
Cardinal interpretation. Interpersonal comparability and
Easterlin paradox.
J. Faik Equivalence Scales

6. Background
Methods
Additional Thoughts
Summary
Using life satisfaction to measure equivalent income
Dynamic Scales
This paper is concerned with comparison over time as well as
over cross sections.
Longitudinal scales refer to intertemporal utility (i.e. over the
life cycle).
Cross-sectional scales refer to intratemporal utility.
Variable scales - the degree of adjustment depends upon
income.
J. Faik Equivalence Scales

7. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Outline
1 Background
Using life satisfaction to measure equivalent income
2 Methods
Model specification and data
Empirical Work
3 Additional Thoughts
Possible extensions
J. Faik Equivalence Scales

8. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Data
SOEP Data is used.
Income is household-post government from 1983-2009.
Focus on West Germany as East German data doesn’t appear
until 1992.
Define cohorts based on 10 year intervals in first wave of
panel.
Born 1920-1929, 1930-1939, 1940-1949, 1950-1959,
1960-1969.
Life satisfaction 0-10 where 10 is complete satisfaction.
J. Faik Equivalence Scales

9. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Conceptual Framework
Estimate income utility curve (utility is life satisfaction) for
different household sizes.
Determine the income level required to compensate for this
change.
Look at compensating variations across cohorts.
J. Faik Equivalence Scales

10. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Model Specification
LS = α + β
√
y +
l
i=1
γl cl + φs + e
Estimate model for a reference household (r) and a
comparison household (h).
Set LSr = LSh.
α + β
√
yr + φsr
= α + β yh +
l
i=1
γl ch
l + φsh
yh
yr
=

1 +
φ sr − sh − γl cl
β
√
yr


2
J. Faik Equivalence Scales

11. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Example
A worked example is given
Set LSr = LSh = 5, α = .4, φ = 0.1, γ = 0.1
Solving gives
yh
yr
= 0.956
Type h requires 95.6% of the income level of type r.
J. Faik Equivalence Scales

12. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Sensitivity of EQ Scale
∂E
∂yr
= −z
√
yr − z
y2
z =
φ 1 − sh − γch
β
∂E
∂sh
= −
2φβ
√
yr
β2yr
+
φ 1 − sh
β2yr
−
γch
β2yr
∂E
∂ch
= −
2β
√
yr
β2yr
−
2φch 1 − sh
β2yr
+
2γ2ch
β2yr
J. Faik Equivalence Scales

13. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Outline
1 Background
Using life satisfaction to measure equivalent income
2 Methods
Model specification and data
Empirical Work
3 Additional Thoughts
Possible extensions
J. Faik Equivalence Scales

14. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Cohort Specific Trends
Figure : Life Satisfaction
J. Faik Equivalence Scales

15. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Cohort Specific Trends
Figure : Income
J. Faik Equivalence Scales

16. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Cohort Specific Trends
Figure : Household Size
J. Faik Equivalence Scales

17. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Results
Cross-sectional scales are estimated first.
Estimates from1984 cross-section approximately in line with
square root scale.
Seem to become flatter over time, implying large economies of
scale.
Could increasing fixed costs (e.g. housing) be responsible?
Germany didn’t seem to experience property bubble.
Higher values when the sample is restricted to adults.
J. Faik Equivalence Scales

18. Background
Methods
Additional Thoughts
Summary
Model specification and data
Empirical Work
Results
Longitudinal estimates require a reference group.
All estimates are calculated relative to persons aged 35-44.
Equations for LS are estimated for both cohorts and solved
simultaneously
Repeated for “all persons” and “only adults”.
Scale weights appear to be either U shaped, or decreasing
over time.
Lower economies of scale for young individuals.
Scales are again pretty flat. We don’t require much income to
offset an additional family member.
J. Faik Equivalence Scales

19. Background
Methods
Additional Thoughts
Summary
Possible extensions
Outline
1 Background
Using life satisfaction to measure equivalent income
2 Methods
Model specification and data
Empirical Work
3 Additional Thoughts
Possible extensions
J. Faik Equivalence Scales

20. Background
Methods
Additional Thoughts
Summary
Possible extensions
Points to consider
Results appear to rest on causality flowing from income to life
satisfaction.
Regressions appear not to control for other factors besides
income and HH size.
Life satisfaction probably affects income. Is endogeneity
important here? Are there logical instruments?
Increasing household size may bring social rewards - should
these be compensated or not?
Could fixed effects regressions handle some of these problems?
Author points out household compositional changes are a
barrier - is there some way around?
How would results look for other welfare concepts?
J. Faik Equivalence Scales

21. Background
Methods
Additional Thoughts
Summary
Possible extensions
Points to consider
What are the implications of lowering scales as people age?
Are the longitudinal scales sensitive to the choice of reference
group?
Square-root specification provides neat analytical solutions to
EQ scales.
However this may be highly restrictive. Could some other
concave specification work better?
E.g. allow the exponent to be an estimatable parameter,
consider log-functional form, or use semi-parametric
specification.
J. Faik Equivalence Scales

22. Background
Methods
Additional Thoughts
Summary
Summary
Innovative approach for estimation.
The fact that they appear similar to square root scale (when
estimated in mid1980s) is appealing.
Estimates agree with other papers (e.g. Chalier, 2002).
J. Faik Equivalence Scales