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Estimating equivalence scales from satisfaction data with endogenous income and household size data

Authors:
Susanne Elsas at University of Bamberg
Susanne Elsas
Melanie Borah
Melanie Borah
Melanie Borah
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Abstract and Figures

Analyses of income inequality across households crucially depend on equivalence scales. They define income increments necessary to keep a household's living standard constant as it is joined by additional adults or children. Such scales have frequently been estimated using income satisfaction data, yet under the assumption that household income, size and structure are exoge-nous. The present paper is the first to relax this assumption and consider the possible endogeneity of income and family size in income satisfaction. This involves an empirical analysis of SOEP data using fixed-effects regressions with heteroscedasticity-based instruments. Our results confirm that endogeneity is relevant in the regression; equivalence weights, however, appear to be not generally biased from endogeneity.
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PROBLEM SET
• Equivalence scales are used to assess welfare and
financial needs. • Scales are obtained from, e.g.,
satisfaction data (Schwarze 2003). • Endogeneity of
income and household size → biased estimates of
welfare / financial needs.
Accounting for endogeneity when estimating
equivalence scale elasticity from satisfaction data.
INSTRUMENTAL VARIABLE ESTIMATION
GMM estimation with heteroscedasticity-based instruments (Lewbel 2012), fixed
effects and clusterd standard errors.
Instrument construction is based on two steps
(implemented in Baum and Schaffer (2012)):
1. Auxiliary regression of endogenous regressors,
e.g.  on exogenous variables  of the model,
where  :
2. Instruments are product of sample-centered
model variable and residuals from step 1:
 is one of the
j
instruments for .
RESULTS
DATA AND MEASURES
Data: SOEP v37, 1985 to 2020, sample restrictions:
•Households w/o adults other than partner or adult children.
•No households w/ more than 7 children or children aged
30+ or individuals w/ special needs (care recipients).
•Respondents aged 18 to 100.
•W/o outer 2% of each year‘s per capita income distribution.
•W/o refugee and high income subsamples.
Measures:
•Income satisfaction = 0 to 10 Likert Scale.
•Monthly net household income.
•Household composition (number of household members
and of children < 14 y.).
•Exogenous controls (z): age, age2, interviewer experience.
•Additional controls: survey wave2, survey wave3, education,
hospital overnight stays, marital status, region (East/West),
labor market participation status, home ownership.
PAPER
Susanne Elsas1 & Melanie Borah2
1 State Institute for Family Research at the University of Bamberg, Germany 2 Otto von Guericke University Magdeburg, Germany
REFERENCES
1. Schwarze, J. (2003): Using Panel Data on Income Satisfaction to Estimate Equivalence Scale
Elasticity. Review of Income and Wealth, 49(3), 359-372.
2. Lewbel, A. (2012): Using Heteroscedasticity to Identify and Estimate Mismeasured and
Endogenous Regressor Models. Journal of Business & Economic Statistics, 30(1), 67-80.
3. Baum, C.F. & Schaffer, M.E. (2012): IVREG2H: Stata module to perform instrumental variables
estimation using heteroskedasticity-based instruments. Statistical Software Components,
S457555, Boston College Department of Economics, revised 11 Jul 2021.
CONTACT
susanne.elsas@ifb.uni-bamberg.de
orcid.org/0000-0001-5255-1080
CONCLUSION
Endogeneity of income and household size attenuates estimates in income satisfaction regressions.
In sum, the welfare effect of income is incorrectly estimated
Equivalence scale estimates are moderately affected: children’s needs are actually slightly lower.
Estimating equivalence scales from satisfaction data
with endogenous household size and income
MODEL
Where:
 = income satisfaction
 = household income
 = n of children <14 in the household
 = n of individuals in the household
i
= individual
t
= survey year
 =log 

+++
 =log  + log    log  +++
 =
()
 =+
 = (
) + 
Fig. 1: Heteroscedasticity in log(h)
SOEP v37. Own calculations. 356,317 observations
of 46,291 individuals.
OLS IV
a0.454 0.443
b0.045 0.058
Fig. 2: Binned scatterplots of predicted values of
income satisfaction
Lower equiv. weights for
children.
Families with children
enjoy higher welfare
than expected from OLS.
Tab 1: Estimated equivalence scale parameters
Fig. 3: Distribution of differently equivalized
incomes
SOEP v37. Own calculations. 356,317 observations of 46,291 individuals.
Endogeneity in the income measure and
in household size and composition atten-
uates estimates in income satisfaction
regression w/o IV. Incorrectly
estimated welfare effect of income.
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