Consumer Behavior, Cost of Living Measures, and the Income Tax

125 Pages·1986·4.34 MB·English

by  Prof. Michael R. Baye, Prof. Dan A. Black (auth.)

Lectu re Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and W. Krelle
276
Michael R. Baye
Dan A. Black
Consumer Behavior,
Cost of Living Measures,
and the Income Tax
Springer-Verlag
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Editorial Board
H.Albach M. Beckmann (Managing Editor)
P. Dhrymes G. Fandel J. Green W. Hildenbrand W. Krelle (Managing Editor)
H.P.Kunzi K.Ritter RSato U.Schittko P.Schonfeld RSelten
Managing Editors
Prof. Dr. M. Beckmann
Brown University
Providence, RI 02912, USA
Prof. Dr. W. Krelle
Institut fOr Gesellschafts- und Wirtschaftswissenschaften
der Universitat Bonn
Adenauerallee 24-42, 0-5300 Bonn, FRG
Authors
Prof. Michael R Baye
Department of Economics
Texas A&M University
College Station, TX 77843, USA
Prof. Dan A. Black
Department of Economics
University of Kentucky
Lexington, KY 40506, USA
ISBN-13: 978-3-540-16797-6 e-ISBN-13: 978-3-642-46587-1
001: 10.1007/978-3-642-46587-1
Library of Congress Cataloging-in-Publication Data. Baye, Michael R., 1958- Consumer behavior,
cost of living measures, and the income tax. (Lecture notes in economics and mathematical systems;
276) Bibliography: p. 1. Income tax. 2. Consumers. 3. Cost and standard of living. I. Black, DanA.
II. Title. III. Series.
HJ4629.B39 1986339.4'186-20315
ISBN-13: 978-3-540-16797-6
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© Springer-Verlag Berlin Heidelberg 1986
2142/3140-543210
TO M'LISSA AND SUSAN
PREFACE
This material is based upon work supported by the National
Science Foundation under grant #SES-8410190. Any opinions, findings,
and conclusions or recommendations expressed in this publication are
those of the authors and do not necessari~y reflect the views of the
National Science Foundation. This support was crucial to the
completion of this project, and we are grateful for it.
As is usually the case when doing academic research, we are
also indebted to a number of individuals. Robert Gillingham, John
Greenlees, Jack Triplett, and Paul Harte-Chen freely gave of their
time to share their ideas concerning income-based cost of living
indices. Seminar participants at the BLS, the University of Karlsruhe,
and Tilburg University provided insightful comments on preliminary
portions of the manuscript. Bill Stober provided encouragement, and
Desmond Lo and Albert Tsui read parts of the manuscript. We owe a
special thanks to Bert Balk for providing detailed handwritten comments
on a preliminary draft. Evelyn Buchanan and Audrey Abel did an
excellent job of typing and retyping numerous drafts of the manuscript.
Finally, a very warm thanks to our wives, for enduring.
CONTENTS
Page
PREFACE
PART I. PRELIMINARIES ••••••••.••••••••••••• It • • • • • • • • • • • • • • • • • 1
Chapter One: Introduction ••••••••••••••••••••••••••• 2
Chapter Two: Mathematical Preliminaries ••••••••••••• 20
PART II. CONSUMER BEHAVIOR ••••••••••••••.••••••••••••••••••••• 28
Chapter Three: Consumer Behavior in tne Absence
of an Income Tax ••.•••.........•..•.......... ; ....... 29
Chapter Four: Consumer Behavior in the Presence
of an Income Tax................ ... . . . . . . . . . . . . . . . . .. 43
PART III. ECONOMIC INDICES IN THE ABSENCE OF TAXATION •••••••••• 57
Chapter Five: The Konus and Frisch Expenditure-
Based Cost of Living Indices •••••••••••••••••••••••.•• 58
Chapter Six: Wage and Nonwage Income-Based
Measures of the Cost of Living in the Absence
of an Income Tax ...............................- ...... 69
PART IV. ECONOMIC INDICES IN THE PRESENCE OF TAXATION ••••••••• 76
Chapter Seven: A Simple Taxable Income-Based
Cost of Living Index .•............ " ................ It. 77
Chapter Eight: The Full Income and Nonwage
Income-Based Cost of Living Indices •••••••••.••••••••• 84
PART V. THE THEORY IN PRACTICE............................... 91
Chapter Nine: Topics in Applied Analysis •••••••••••• 92
Chapter Ten: Changes in Government Goods and
the Tax Code ••••••..•...•••.•.•.••••.•••••••••••••••• 108
BIBLIOGRAPHY ••••••••••••••••••••••••••••••••••••••••••••••••••••• 11 2
PART I
PRELIMINARIES
CHAPTER ONE: INTRODUCTION
Income based measures of the cost of living have become increas-
ingly important in recent years (cf. Cagan and Moore (1981), Gilling-
ham and Greenlees (1983), Kay and Morris (1984), and Triplett
(1983». The basic idea behind the concept of an income-based cost
of living index is to compa're the levels of pretax income necessary
to maintain some base standard of living under alternative price and
tax regimes. This is in contrast to an expenditure-based index of
the cost of living, which is designed to compare the expenditures
(exclusive of taxes) necessary to maintain the base standard of liv-
ing under 'alternative price regimes.
In order to illustrate the important distinction between these
two concepts, consider a ceteris paribus doubling of all prices. In
this case the expenditures net of taxes necessary to maintain the
base standard of living doubles, and hence an expenditure based mea-
sure of the cost of living will also double. But if pretax income
doubled and taxes are unindexed and progressive, one could not afford
the base standard of living because the doubling of pretax income
would lead to a higher marginal tax rate and a higher real tax bill.
Consequently, a doubling of all prices will, ceteris paribus, more
than double the income-based cost of living index.
Income-based measures of the cost of living are important for
two primary reasons. First, as noted by Cagan and Moore (1981), they
are the relevant index concept to be used in income escalation mea-
sures because such cost of living adjustments are usually a percent-
age of existing pretax income. Escalation measures based on an ex-
penditure-based cost of living index will lead to an underadjustment
of income. The importance of an income-based cost of living index
for purposes of escalating income has been mitigated somewhat in the
United States, due to the ~ecent indexation of the tax codes. None-
theless, many countries and indeed many states within the United
States presently have un indexed tax codes, and the construction of an
income-based cost of living index for purposes of income escalation
remains important.
Secondly, the income-based concept of the cost of living is im-
portant because it is the correct means of deflating a time series of
data on pretax income. Because of the absence of such a measure of
the cost of living, economists typically deflate pretax income (or
3
GNP) by using an expenditure-based measure of the cost of living, or
more frequently the CPI approximation to an expenditure-based index.
Recently, Kay and Morris (1984) and Gillingham and Greenlees
(1983) have done pioneering empirical research on incorporating taxes
into a price index for Britain and the United States, respectively.
While neither of these studies constructed an income-based cost of
living index, which requires the estimation of consumer preferences,
they do suggest that the distinction between income and expenditure-
based cost of living indices is empirically significant. For ex-
ample, Gillingham and Greenlees found that between 1967 and 1981 the
average annual rate of change in their TPI (an approximation to an
income-based index) was 7.6%, whereas the average annual rate of
change in the CPI (an approximation to an expenditure-based index)
was 6.8%.
In this monograph, we develop the theory of income-based cost of
living indices. Our methodology differs in three respects from the
studies mentioned above. First, the existing studies are empirical
in nature, while our focus is on theoretical issues. Second, the ex-
isting studies incorporating taxes into a price index are not based
on consumer preferences, and hence do not allow for substitutions
among commodities as prices and tax codes change. As such, they are
approximations to an income-based cost of living index. We develop
the theory of income-based cost of living indices from a model of
maximizing behavior, and thus our analysis allows for substitutions
among goods as the incentives to consume the goods change over time.
Third, and perhaps more importantly, existing approximations to
an income-based cost of living index do not account for the labor-
leisure decisions of consumers. Our analysis of consumer behavior
explicitly models the labor-leisure decision, and as such, our income-
based cost of living indices allow consumers to substitute between
goods and leisure as the ~ftertax wage changes. Because leisure
is, in effect, a tax deductible good, one might expect such substitu-
tions to be amplified as marginal tax rates increase.
In order to accomplish our purpose, it is necessary for us to
develop the theory of consumer behavior in the presence of an income
tax, and to provide an examination of traditional cost of living in-
dex theory. Because of the technical nature of our results, it is
useful to provide a descriptive survey in this introduction of works
on (1) consumer behavior in the presence of nonlinear budget sets,
4
and (2) cost of living indices. Our introduction concludes with an
overview of our monograph.
1. Consumer Behavior with Nonlinear Budget Sets
In order to construct cost of living indices that allow for sub-
stitutions among goods and leisure, it is necessary to specify the
behavior of the consumer. Unless the income tax system is propor-
tional, the budget constraint is nonlinear. In Figure 1.1, we depict
a simplified budget set of a consumer that faces a proportional in-
come tax, and in Figure 1.2, we depict the budget set of a consumer
that faces a progres~ive income tax that is piecewise linear. In
Figure 1.1, 6 represents the total endowment of time, P is the price
of consumption, and T represents the marginal tax rate. The solid
line represents the budget set with the proportional income tax and
the broken line represents the budget set of the consumer without
taxes. Note that the presence of a proportional income tax has two
effects. First, it reduces the income of the consumer. Second, the
tax on income reduces the price of leisure. Holding utility con-
stant, the presence of the proportional income tax will in-
crease the quantity of leisure consumed. The negative income effect,
however, (assuming that leisure is a normal good) reduces the quant-
ity of leisure consumed. Thus, the total effect of the proportional
income tax on labor supply is ambiguous.
As far as traditional theory is concerned, the presence of a
proportional income tax presents no major problems: If the price of
leisure and nonlabor income is weighted by one minus the marginal tax
rate to obtain the "effective price" of leisure, then the resulting
demand system satisfies all the classical properties. Mark Killings-
worth (1983), in his excellent review of the labor supply literature,
notes that several empirical studies assumed that the tax system was
proportional. Killingsworth calls these works "first generation
studies." Perhaps the most important of the first generation studies
is Abbott and Ashenfelter (1976). This study estimated consumer pre-
ferences over eight broad commodity groups, including leisure.
Abbott and Ashenfelter's preferences parameters have been used fre-
quently in other studies. For instance, Pencavel (1977, 1979) used
these estimates to construct his real wage estimates. Similarly,
Cole and Harte-Chen (1985) used the data and methodology in their
study.
5
Consumption
Good
,
" ...... w
Slope =
"- P
' ........ /
"-,
" . ,
SI ope = (I-T)w', ,
P ,
')
I
I
I y/ P
(I-r)y/P {
8 Leisure
FIGURE 1.1
BUDGET SET WITH A PROPORTIONAL TAX