Direct Estimation of Equivalence Scales and More Evidence on Independence of Base

Publication Date01 October 2017
AuthorMartin Biewen,Andos Juhasz
Date01 October 2017
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12166
Direct Estimation of Equivalence Scales and More
Evidence on Independence of Base*
Martin Biewen† and Andos Juhasz
Department of Economics, University of T¨ubingen, Mohlstr. 36, 72074 ubingen,
Germany (e-mail:
University of T ¨ubingen
We explore a direct approach to estimating household equivalence scales from income
satisfaction data. Our method differs from previousapproaches to using satisf action data for
this purpose in that it can be used to directly fit and evaluateclosed-for m and non-parametric
equivalence scales of any desired form. Its flexibility makes it easy to consider specific
aspects such as income dependence or more specific information on household composition
(such as whether household members live in a partner relationship). We estimate and
evaluate a number of scales used in the literature. If the equivalence scale is assumed to be
independent of income and to depend only on household size, we do not reject the validity
of the widely used square-root scale at conventional significance levels. Wealso test GESE
and GAESE restrictions (Donaldson and Pendakur, 2003, 2006) and investigate in detail
to what extent household economies of scale depend on income. Our results suggest that
the income dependence differs fundamentally across household types (rising economies
of scale for ‘family’ households, falling economies of scale for multi-adult households
without children and no income dependence for other households).
I. Introduction
Equivalence scales are used to make the utility of income comparable across heteroge-
neous households. They thus play a crucial role in various fields of welfare and public
economics such as the measurement of inequality and poverty, or the design of tax- and
welfare systems. In principle, three main approaches have been used to construct or
estimate equivalence scales.1The first approach is based on the estimation of consumer
demand systems (see, e.g. Muellbauer, 1980, Pashardes, 1995, Pendakur, 1999). As shown
JEL Classification numbers: J31, J71, C02, D31.
*Weare g rateful to twoanonymous referees, Stephen Jenkins, Andrew Oswald,Carsten Schr ¨oder, Viktor Steiner,
Andreas Peichl, Phillipe van Kerm, Dean Hyslop, Regina Riphahn,Andrea Weber and seminar participants at EEA
2014, ESPE 2015, ZEW Mannheim, LISER Luxembourg, Erlangen/N¨urnberg, Osnabr ¨uck, TU Berlin and theAuss-
chuss f¨ur Sozialpolitik for many helpful comments. The data used in this paper (SOEP v27, 1998–2010) were made
availableby the German Socio-Economic Panel Study (SOEP) at the German Institute for Economic Research (DIW),
1See Coulter, Cowell and Jenkins (1992), Lewbel and Pendakur(2008a) and Schr ¨oder (2009) for overviews.
876 Bulletin
by Blundell and Lewbel (1991), this approach is challenged by identification problems
unless additional assumptions are made. One such assumption is that the equivalence scale
is independent of reference income (‘Independence of Base Assumption’, Lewbel, 1989,
Blackorby and Donaldson, 1993). More general restrictions have been suggested by Don-
aldson and Pendakur (2003, 2006). A second approach is based on subjective data on
income or life satisfaction. In one variant, this approach uses survey data that directly lets
respondents describe which income levels they associate with different levels of welfare
(e.g. van Praag, 1968, 1991, Kapteyn and van Praag, 1976, Koulovatianos, Schmidt and
Schr¨oder, 2005). A drawback of this approach is that respondents are askedto make assess-
ments of situations that may be very hypothetical to them. This drawback is not present in
the second variant of the subjective approach whichonly uses information on how satisfied
respondents are with their own factual income (e.g. Melenberg and van Soest, 1996, Belle-
mare, Melenberg and van Soest, 2002, Schwarze, 2003, Bollinger, Nicoletti and Pudney,
2012). The third approach to constructing equivalence scales is an ad hoc one. It uses
‘expert’ assessments or more or less arbitrary rules-of-thumb in order to define the weights
different household members receive in the equivalence scale. Examples are the so-called
OECD equivalence scale or the square-root equivalence scale (see Buhmann et al., 1988,
Atkinson, Rainwater and Smeeding, 1995, or OECD, 2005). Although this latter approach
is less evidence-based than the first two approaches, the equivalence scales resulting from
it are by far the most widely used ones in practice.
In this paper, we contribute to the second line of research, that is, we use income
satisfaction data in order to estimate equivalence scales. Our paper aims to make three
contributions. First, we present a unified and flexible way to estimate equivalence scales
from satisfaction data. Our approach differs from previous approaches in that it can be used
to directly estimate and evaluate equivalence scales of any prespecified functional or non-
parametric form. Previous contributions were usually confined to specific functional forms
which were often restrictive or just chosen for convenience (see literature review below).
Our estimates are based on the simple idea that the equivalence scale should be fitted such
that the utility assigned to income is equalized across household types. In our approach,
the particular form of the scale may be freely chosen by the user. Given the parametric
nature of our procedure, we can carry out full statistical inference about functional forms,
equivalence scale parameters and related hypotheses such as whether equivalence scales
depend on specific household features. For example, we can test whether the exact ages of
household members matter, or to what extent the equivalence scale depends on whether
some of the household members are in a partner relationship. The latter was suggested
by Bollinger et al. (2012), who argue that household economies of scale should be much
higher in this case because partners share more goods than non-partners.
A second contribution of this paper is that we present a detailed analysis of the income
dependence of equivalence scales based on satisfaction data, whereas most of the literature
on this topic is based on consumer demand systems.2Our results on income dependence
are directly based on the satisfaction statements of household members without reference
to consumption choices, consumption theory or assumptions such as utility maximization.
2One of the few exceptions is Koulovatianos et al. (2005) who present evidence based on hypothetical income
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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