Transcript THE CONCEPT OF THE STOCHASTIC EQUIVALENCE SCALES. …

THE CONCEPT OF THE
STOCHASTIC EQUIVALENCE
SCALES. THEORY AND
APPLICATIONS
By
Stanislaw Maciej Kot
Discussant: Michael Ward
Context and Issues
• Rich data in a raw or derived state are not
necessarily representative data.
• The World Development Report, World
Development Indicators and UNDP Human
Development Report all contain a variety of per
capita measures based on total population
counts. But these are dominantly ‘mean’
population indicators that tend to confound
rather than illuminate proper international
comparative analysis relating to input, output
and impact because of significant differences in
national demographic characteristics.
• They do not serve the role of proxy indicators
Representative Equivalence
Scales
• While politicians are keen on talking about
‘every man, woman and child’ as the appropriate
public reference base, the subject matter of the
aggregate variable – be it consumption,
production, income, wealth, energy use, calorie
intake, health expenditure, education outlays,
teachers, etc demands a different ‘base’ or
denominator for the measure to be truly
meaningful for policy purposes and analysis
• Even in the case of consumption or household
expenditure, the non-homogeneity of household
groups creates problems both of inter-HH
comparisons and of marginal versus average
Theory versus Practice
• All current equivalence scales – of which there
are many with each type specifically depending
on the characteristic under investigation – are
arbitrary
• Only in the case of expenditures is there a
genuine possibility of applying economic
[consumption] theory to define equivalent virtual
per capita values
• Such a set of scales needs to mimic, for each
household size, the total utility values reflected
in individual welfare functions, personal
consumer preference and behaviour
• The author sets out to determine, theoretically,
Author’s Objectives
• to define a concept of stochastic equivalence
scales (SES) constituted by an holistic paradigm
of welfare
• illustrate with empirical examples from
household surveys [using Poland 2000 as a
case study]
• use non-parametric and parametric applications
to demonstrate relevance of approach by
reference to the one person household
distribution function
Methodology
• Starting point is individual welfare reflected in a
given person’s income utility function
• This is assumed to be a convenient and valid
representation of consumer preference. This
implies adpting a disposable income concept to
reflect consumption, acceptable at lower levels
of income but not so for higher overall levels
associated with larger families
• Familiar PROBLEM: To aggregate individual
welfare to derive a total social welfare function
• As Arrow convincingly demonstarted, this is not
possible in rigorous practical terms [although
this has not stopped many economists from
The Impossibility of aggregating
individual welfare functions
• The problem of inter-personal comparability is found to
be unacceptable to most economic theorists
• In practice, analysts cannot assume individual
preferences are independent and isolated from the
preferences, and revealed spending, of others.
• This problem spills over into the related issue of deriving,
conceptually, relevant equivalence scales for converting
consolidated data of one form or another into an
hypothetical individual function
• This has to be in conformity with the conventionally
recognised theory of consumer behaviour.
• consumer theory may be even less appropriate than
other premisses about individual spending drawn from
market research and observed personal behaviour
Author’s solution
• Determine an holistic concept of welfare or
social preference relations based on a benefit
function for the population (the welfare of
society) as a whole
• Find a benefit function [BF] consisting of an
income distribution, f(x) that can be transformed
into a welfare distribution f(w) via the
transformation of a random variable x into a new
random variable w. The BF takes the form of
b.R*->R where b is estimated from the
distribution data
• [See author’s paper for the applied algebra!]
Logic of Equivalence
• Need to compare the welfare of households with
various needs
• Differentiation of needs is usually associated
with the differences in household demographic
structure – size of HH, age and sex profile.
• Compare populations of various decomposable
homogeneous groups with standard reference
group, in this case, single-person household
• Main aim to obtain equivalent welfare level of
comparable households of different sizes and
composition.
EXAMPLES
(Using 2000 HBS for Poland)
1] Abbreviated Social Welfare Function, nonparametric form
u= u´(1-G) where G is Gini coefficient and u is an
approximation for u´ and the deflator value is
defined accordingly from estimates of the mean
income of the sub-group concerned and its
specific gini coefficient:
Example: Nine groups, ranked by hh size
With a mean and gini for each size group
Note: closeness of fit of each derived distribution
for different HH size with the single household
reference group across every income level
2] Example of 25 groups
• Non-parametric application with adults and
children less than 18 years old (more complex
divisions)
• Also parametric forms represented by a power
equivalence scale with constant elasticity in
relation to hh size (a condition that can be
relaxed)
• Compare methods of Buhmann et al (Rainwater
and Smeeding), OECD, Coutler and Katz
Continuous Power Functions
• Parametric approaches also demonstrate
a trajectory for power functions that flatten
off very quickly, revealing very little
difference in the adjustment factors to be
applied for 4, 5, 6 [and above] household
sizes; can this be real [especially as some
equivalent scales for larger families have
lower values] and be attributable to
household economies of scale? Or is this
a statistical artefact akin to curve fitting?
Outcomes, problems and questions
• The practical application of the SES
methodology appears simple, seems to work but
is it conceptually valid? In particular, is the
transformation factor/scalar used clearly related
to economies of scale?
• Is Poland 2000 with an even income distribution
a special case? Can we really assume that the
gini is so similar in each income sub-group as
HH size and incomes rise?
• Is the income distribution ’neutral’ in the sense
that the single group may be based in an urban
location and larger families live on the land?