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A study of aggregation bias in estimating the market for home heating and cooling equipment

01 May 1989-Lawrence Berkeley National Laboratory (Lawrence Berkeley Lab., CA (USA))-
TL;DR: The degree of bias that would be introduced in a study if only average data across SMSAs or states were used at several points in the investigation is examined, and proper treatment allows market shares and elasticities to be found with little error relative to the disaggregate models.
Abstract: Econometricians frequently propose parametric models which are contingent on an underlying assumption of rational economic agents maximizing their utility. Accurate estimation of the parameters of these models depends on using data disaggregated to the level of the actual agents, usually individual consumers or firms. Using data at some other level of aggregation introduces bias into the inferences made from the data. Unfortunately, properly disaggregated data is often unavailable, or at least, much more costly to obtain than aggregate data. Research on consumer choice of home heating equipment has long depended on state-level cross-sectional data. Only recently have investigators been able to build up and successfully use data on consumer attributes and choices at the household level. A study estimated for the Electric Power Research Institute REEPS model is currently one of the best of these. This paper examines the degree of bias that would be introduced in that study if only average data across SMSAs or states were used at several points in the investigation. We examine the market shares and elasticities estimated from that model using only the mean values of the exogenous variables, and find severe errors to be possible. However, if the models were calibrated on only aggregate data originally, we find that proper treatment allows market shares and elasticities to be found with little error relative to the disaggregate models. 22 refs., 4 figs., 10 tabs.

Summary (1 min read)

2. Introduction to Aggregation Bias Theory

  • That paper dealt with the estimation of probit models for dichotomous choice problems (i.e., choice between only two alternatives).
  • The authors developed their analysis in the context of choice of transportation mode.
  • The authors will briefly review issues in their work that are relcvant to the current paper.

I

  • Almost all discrete choice estimation models start from an assumption that the utility a consumer derives from his choice is some linear combination of his own and the choices' attributes, plus a random term with some assumed distribution.
  • Thus, the probability that the consumer will choose alternative 1 depends on the probabilistic nature of the diITcrence bctwecn the two random terms.
  • In very simplified form, these techniques work by dividing the population into groups for which the set 01' exogenous variables is more or less homogeneous.
  • The authors can exploit this relationship to express a whole range of arc elasticities using only the three parameters of a quadratic curve.
  • A new market share (under a change in some exogenous variable) can be calculated as a function of the old market share, the elasticity, and the relative perturbation size necessary to reach the new value of the exogenous variable: (4.3).

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RECE:IVED
U,WRENCE
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LA80RA.TOR
LBL-20333
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Berkeley
Laboratory
.
Ii;I
UNIVERSITY OF
CALIFORNIA
APPLI
ED
SCI
ENCE
DIVISION
OF.
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1989
A Study ofAggregation Bias in
Estimating the
Market
for Home
Heating
and
Cooling Equipment
D.J. Wood, H. Ruderman, and J.E. McMahon
May 1989
liBRARY
AND
DOCUMENTS SECTION
TWO-WEEK
LOAN
COpy
This
is
a Library
Circulating
Copy
which
may
be
borrowed
for
two
weeks.
APPLIED
SCIENCE
DIVISION
Prepared for the U.S. Department ofEnergy under Contract Number DE-AC03-76SF00098
..

DISCLAIMER
This document
was
prepared as an account
of
work
sponsored
by
the United States Government. Neither the United States
Government nor any agency thereof. nor The Regents of the
University
of
California. nor any
of
their employees. makes any
warranty. express or implied, or assumes any
legal
liability or
responsibility
for
the accuracy. completeness. or usefulness
of
_
.......
~
~--
'-'--,
-
Lawrence
Berkeley
Laboratory
Library
University
of
California,
Berkeley

""
.
LBL-20333
A
STUDY
OF
AGGREGATION
BIAS
IN
ESTIMATING
THE
MARKET
FOR
HOME
HEATING
AND
COOLING
EQUIPMENT*
David
J.
\Vood, Henry
Ruderman
and
James E. 11cMahon
Energy Analysis
Program
Applied Science Division
Lawrence Berkeley
Laboratory
University
of
California
Berkeley, California
94720
May
1989
ABSTRACT
Econometricians frequently propose
parametric
models which are contingent on
an
underly-
ing assumption
of
rational
economic agents maximizing their utility. Accurate estimation
of
the
parameters
of
these models depends on using
data
disaggregated
to
the level
of
the
actual
agents,
usually individual consumers
or
firms. Using
data
at
some
other
level of aggregation introduces
bias
into
the
inferences made from
the
data.
Unfortunately, properly disaggregated
data
is often
unavailable,
or
at
least, much more costly
to
obtain
than
aggregate
data.
Research on consumer choice of home heating equipment has long depended on state-level
cross-sectional
data.
Only recently have investigators been able
to
build up
and
successfully use
data
on consumer
attributes
and
choices
at
the household level. A
study
estimated for
the
Electric
Power Research
Institute
REEPS
model is
currently
one
of
the
best of these.
This
paper
examines
the
degree of bias
that
would be introduced in
that
'study if only aver-
age
data
across SMSAs
or
states
were used
at
several points in
the
investigation. \Ve examine
the
market
shares
and
elasticities estimated from
that
model using only the mean values
of
the exo-
genous variables,
and
find severe errors
to
be possible. However, if the models were calibrated on
only aggregate
data
originally, we find
that
proper
treatment
allows
market
shares
and
elasticities
to
be found
with
little
error
relative
to
the disaggregate models.
* This work was supported by the Assistant Secretary for Conservation
and
Renewable Energy, Office
of
Building
and
Community Systems, Building Equipment Division
of
the U.S.
Department
of Energy, under Con-
tract
No. DE-AC03-76SF0009S.


-.
LBL-20333
A
STUDY
OF
AGGREGATION
BIAS
IN
ESTIMATING
THE
MARKET
FOR
HOME
HEATING
AND
COOLING
EQUIPMENT
David
J. Wood,
Henry
Ruderman
and
James
E. McMahon
1.
Introduction
The
uncertain
status
of
future
energy supplies
relative
to
demand
has
been a
point
of
con-
cern
in
this
country
for more
than
a decade. A
number
of
empirical studies
have
been conducted
to
estimate
the
factors
that
influence
demand
in one fashion
or
another
[2,3,4,5,5,9,12]. Some
of
these
have
been
in
support
of
computer
models
that
simulate
long-run
national
energy
demand
[6,12].
These econometric
studies
take
a common view
that
energy-related decisions
are
made
by
rational
economic
agents
seeking
to
maximize
their
own
utility,
For
the
studies
listed above,
that
decision is
the
choice
of
a specific fuel
or
technology for residential space heating.
The
statistical
techniques used
to
estimate
the
determinants
of
that
decision fall
into
a general category called
discrete choice modeling. In this context,
the
issue
of
aggregation
bias can be critical.
l
Aggregat£on
b£as
is a geneml terlll for enol'S induced
by
a
mismatch
of
the
economic
theory
(of
individual
consumers)
and
the
level
of
aggregation
of
data
(e.g.,
mean
values
at
the
state
or
national
level).
It
has
two
distinct
forms:
1)
bias
in
the
prediction
of
market
shares
and
elasticities for aggregate groups, using pal'ame-
tel'S from a household choice model
and
representative
values
of
independent
variables (fre-
quently
the
means) for
the
gl'OUp;
and
2)
bias
in
the
parameters
of
a houscllold
utility
maximization
choice model
estimated
on
data
aggregated
at
some regional Icvcl.
This
paper
offers examples
of
the
potent,ial severity
of
both
types of bias.
The
former is found
to
be
potentially
dangerous, leading to predictions of
market
share
which
are
severely in error;
the
latter
is found
to
be much less
of
a problem if handled correctly.
The
present
paper
is organi:wd as follows: Section 2 contains a
brief
introduction
to
the
theory
of
aggregation bias.
That
section is
strongly
influenced by
McFadden
and
Reid [16],
but
has
been
cast
in
the
context
of
consumer choice
of
space
heating
systcms.
The
first form
of
aggregation
bias (prcdict.ion
of
aggregate
market
shares
or
elasticities using
only
mean
values) is
taken
up
in Section 3.
This
bias
has
been extensively analyzed in
the
litera-
ture
on
transportation
modal choice [1O,1l,16,L7,18,19,20].
That
literature
has
largely focused
on
bias-reduction
methods
generally called c1assljicalz'on techniques; they depend
on
the
relationship
between
the
bias
and
the
covariance
matrix
of
the
independent
variables. These techniques were
generally proposed as being
computational
short-cuts
to
the
goal
of
bias-free
market
share
esti-
mates.
That
goal can also be achieved
through
sample enumeralz'on, the calculation
of
predicted
choice
probabilities
for every
member
of
a
random
sample
from
the
population.
1 Readers interested
in
a brief review of the literature on home heating appliance choice are referred to Wood,
Ruderman, and McMahon
1221.
I\lore extensive reviews may
be
found
in
Dohrmann
[41
or Hartman
171.
A
com-
plete review of issues and techniques
in
discrete choice modeling
is
in
Amemiya
[11·
-1-

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