Table Of ContentSTUDIES IN
MACROECONOMIC
THEORY
Volume 2
REDISTRIBUTION AND GROWTH
Edmund S. Phelps
Department of Economics
Columbia University
New York, New York
ACADEMIC PRESS
A Subsidiary of Harcourt Brace Jovanovieh, Publishers
New York London Toronto Sydney San Francisco
COPYRIGHT © 1980, BY ACADEMIC PRESS, INC.
ALL RIGHTS RESERVED.
NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR
TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC
OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY
INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT
PERMISSION IN WRITING FROM THE PUBLISHER.
ACADEMIC PRESS, INC.
Ill Fifth Avenue, New York, New York 10003
United Kingdom Edition published by
ACADEMIC PRESS, INC. (LONDON) LTD.
24/28 Oval Road, London NW1 7DX
Library of Congress Cataloging in Publication Data
Phelps, Edmund S
Studies in macroeconomic theory.
Includes bibliographies.
CONTENTS: v. 1. Employment and inflation,
v. 2. Redistribution and growth.
1. Macroeconomics—Addresses, essays, lectures.
I. Title.
HB171.P468 339.3 78-68344
ISBN 0-12-554002-7 (v. 2)
PRINTED IN THE UNITED STATES OF AMERICA
80 81 82 83 9 8 7 6 5 4 3 2 1
To my parents
PREFACE
This volume collects most of my scholarly papers on the behavior and
public control of distribution and growth in the market economy. Its princi
pal subject is public finance; more broadly, the theory of economic policy.
Stabilization questions, and hence the Keynesian side of fiscal policy, are the
focus of my previous collection in this series.
It has been a rule in these volumes not to republish material from my
previous books, so this volume does not contain my essay Fiscal Neutrality
toward Economic Growth nor the papers in my Golden Rules of Economic
Growth. By drawing on other expositions, though, including my first treat
ment of the Golden Rule, the collection manages to be substantially com
plete. The commentaries with which each group of papers is prefaced record
my present position where it has moved away from my earlier opinions. The
introductory essay previews and reworks some principal themes.
A basic view shared by these two collections is that every issue in public
policy raises a problem of intergenerational social choice, yet such prob
lems are not safely left as programming exercises in intergenerational
utilitarianism; other criteria have to be sought and tested. This volume con
tains all the main chapters in a wide search for some better principle of social
choice: the notion of fiscal neutrality toward national saving, the game-
equilibrium approach to intergeneration inconsistency, and finally an argu
ably Rawlsian (though not Rawls's own) conception of intergeneration eco
nomic justice.
In beginning this project I worried that an audience incessantly excited
by inflation and recession (and now energy shock) might find this second
volume too tame compared to its monetary predecessor. When the neoclas
sical authors laid capital and value theory in a placid setting, ushering into
XI
economics a century of wald und wiesen, they were not writing for the mod
ern sensibility. Nor has the economics of distribution and growth seen a
paradigm shift like the rise of micro-macro theory in monetary economics.
In reviewing the papers in this volume, however, I found myself caught
up again by their concerns. Below the still surface of fiscal and capital theory
lie deep questions: the justice of balanced budgets, the efficiency of contem
porary tax practice, the rationality of the market economy. And the recent
rebellion against fiscal analysis lacking substitution effects—the miracle of
the lump-sum tax—seems certain to be judged a major development, one
which some papers here have helped along.
Much of this collection is the product of joint work. The collaborations
more than a decade ago, with Manos Drandakis, Richard Nelson, and Karl
Shell, arose accidentally out of associations with friends whose ideas I saw
as rounding out my own additions to the positive theory of economic growth.
Later, Janusz Ordover and John Riley played crucial roles in the difficult
analysis of ' maximin' intergenerational justice, taking generous time away
from their primary research interests to do it.
In studying economics these past three decades my debts of gratitude
have piled too high to acknowledge more than a few of them, let alone to
repay them. There is first my debt to James Nelson, dating from college days
at Amherst. His demonstration that in economics one could be serious with
out being solemn encouraged me to pursue the subject.
I owe some of my early fascination with the theory of interest and
growth to a graduate school where Irving Fisher was patron saint, and par
ticularly to the brilliant instruction there by Tjalling Koopmans and James
Tobin. A little later Paul Samuelson and Robert Solow were equally influen
tial. To have found myself racing with them and the others for the next result
in growth theory was the thrill of my youthful career.
Last there has been John Rawls, whose illuminating vision of a serious
welfare economics drew me back to public finance and growth. This Rawls-
ian road is less traveled than the one I took earlier, but in the end that may
have proved an advantage.
Let me acknowledge, in conclusion, the substantial material aid without
which these collections would probably not have come into being. For several
years I hardly put pencil to paper without assistance from the National
Science Foundation, so most of my papers received its support, and its latest
grants contributed to the preparation of these two volumes. A fellowship
from the Guggenheim Foundation helped as well. There was a sabbatical
from Columbia University during which I completed the first volume, and an
invitation to the University of Mannheim where, in the peace of the nearby
Odenwald, I finished the present volume.
xii PREFACE
INTRODUCTION: TAXATION,
REDISTRIBUTION, AND GROWTH
It is only a quarter century ago that the theory of public finance was
recaptured from Keynesian extremists. If ironing out business fluctua
tions is charged to the central bank instead of the Fisc, then fiscal
policy—the choice of the tax structure and the algebraic budgetary
surplus—can again be governed by neoclassical principles. Tax cuts that
expand demands for current consumption and leisure divert non-idle re
sources from capital formation of sure use in the future.
The first halting steps in the rehabilitation of public finance theory
were taken with the crutch of the fictitious lump-sum tax. In a series of
papers, Paul Samuelson examined the economic behavior of a society
taxing and transferring among its members in such a way as to maximize
any social welfare function with the ordinal Bergson-Samuelson proper
ties that every person's consumption of every good "counts" for social
welfare but with diminishing marginal social-welfare weight. Such a
well-ordered society, one not hung up in social conflict, would expunge
Pareto-type inefficiencies, end unequal material endowments among like
persons, provide collective goods without user charges, and possess social
indifference curves—much as well-functioning families are said to do.
The optimum (social-welfare maximizing) distribution of taxes,
though, and the consequent distribution of well-being somehow escaped
attention.1 The role of transfers and taxes in optimum redistribution was
neglected as well in the rudimentary theory of optimal distortionary taxa
tion begun by a few French and English economists in the 1950s. In those
models the population of income earners is taken to be homogeneous, so
no redistribution would contribute to social welfare; tax revenue is wanted
for some other reason. In such a world, distortionary taxes really are
"second best"—other than as devices to correct certain externalities (un-
1 Years later James Mirrlees saw that if the social-welfare function being maximized is
symmetrical, as when reflecting an even-handed ethical criterion plus identical tastes and
capacities for enjoyment, then the strong will be taxed to a point at which they are worse off
than the weak. (Such poetic-justice reversals cannot be engineered by non-lump-sum taxes
on income, sales, etc.)
1
internalized by the market)—and the absence of the first best lump-sum
tax is unexplained.
The engaging question for public finance theory in the era to which I
am referring, roughly from Korea to Vietnam, was the total size of tax
revenue to be collected in excess of the government's transfers, subsidies,
and expenditure—the budgetary surplus (or deficit) to be chosen. The
neoclassical or full-employment growth model built by Robert Solow and
Trevor Swan was read as a message about budgetary policy: Stiffer taxa
tion to reduce the fraction of national product spent for private consump
tion would, by allowing more investment, gradually raise the capital stock
to a higher track and thus also the national income.
The discovery of the Golden Rule of Accumulation showed that each
tax-induced constriction of the propensity to consume (expressed as a
ratio to national income) will ultimately boost the level of national con
sumption, following its initial contraction, onto a higher track as well, if
and only if the social rate of return to investment—the profit rate purified
of imperfectly competitive elements—would otherwise remain indefin
itely above the growth rate of the capital stock. On that golden condition,
then, heavier taxation unaccompanied by greater public spending would
eventually produce a higher standard of living for future generations. Of
course, in that "long run" we are all dead. Yet the intergenerational
utilitarianism of Frank Ramsey, which had become the prevailing philos
ophy of the time, mandated such a sacrifice on our part for the sake of our
successors.
The fiscal requirements of an ascent to the Golden Rule state were
made explicit in the growth model with overlapping generations of life-
cycle worker-savers developed by Peter Diamond. Raising the capital-
output ratio to its Golden Rule level, if we assume its steady-state ten
dency corresponding to the original fiscal policy was short of that level,
would entail a sustained reduction of the public debt as a ratio to national
output; this is so at least in the vicinity of the Golden Rule state where, in
fact, debt "crowds out" capital dollar for dollar. The public debt was thus
a "burden" if and insofar as its maintenance (as a ratio to output) by a
tolerant fiscal policy left the capital-output ratio short of its Golden Rule
level.2
It is impressive to see how much the theory of fiscal policy has
2 If there was any contrary doctrine voiced in opposition to the prevailing wisdom it was
the notion that taxation should seek merely to "neutralize" the false wealth represented by
existing holdings of public debt plus the false wealth that would be added if the intertemporal
plan for public expenditure were financed by further public debt creation. The claim was that
if that fiscal stance of "neutrality" toward economic growth were adopted, the resulting
volume of private saving and investment "determined in the market" would accurately and
2
changed complexion in one decade. The fiction of the lump-sum tax has
been abandoned. While not an "impossible" levy, it is an inoptimal one
because its imposition, by risking unfairness, would lower the expected
value of social welfare; maybe the object of the levy will not be the
breadwinner he seems to be. If people's respective wage rates in each
activity, properly netted of equalizing differentials reflecting non-
pecuniary differences among jobs, cannot be observed by the fiscal au
thorities, then collecting tax revenue requires taxing the observable and
measurable things that people do—their earning, spending, saving, etc.
What drove the lump-sum tax from economics, however, was the demon
stration by James Mirrlees that modeling the heterogeneity of the work
force, without which the lump-sum tax would be unobjectionable, and
optimizing the structure of necessarily "distortionary" taxes in such a
model presented no insuperable analytical difficulties.
The recognition of distortionary taxes has implications of obvious
importance. Even the structure of taxes that raises revenue "to capacity"
does not indicate 100% tax rates since at such confiscatory rates the
activities being taxed, and with them the tax base, would disappear. A
stiffer tax rate intended to raise more revenue, to reduce the public debt,
and to boost the capital stock might be counterproductive through a chill
ing effect on the activity being taxed or some other taxed activity.
The other change in public finance theory is more attitudinal than
analytical. Among the general public the goal of material progress from
generation to generation suffers dwindling support. Among economists,
too, the long trudge to the Golden Rule state, where profit rate and growth
rate have converged to a common constant that is presumably zero, no
longer seems widely compelling—its utilitarian underpinning no longer
axiomatic. The diminished enthusiasm for "growth" is another reason
why interest has shifted from the welfare benefits of heavier taxation (for
the sake of future people) to the welfare benefits that will accrue to all
generations from selectively lighter taxation. It is nonetheless true, of
course, that if we are to go beyond the mild objective of finding Pareto
improvements we shall need some detailed conception of intergenera-
properly express the intertemporal-intergenerational preferences of the present society as
they actually exist.
Some valid arguments can be made on behalf of that position when applied purely to a
Barro and Bailey world of dynastic families whose generations are consecutively interlinked
by bequests. But those arguments all fall to the ground once we admit, in the spirit of the
life-cycle model of saving, families that are constitutionally opposed to bequests or that
would make negative bequests if legally enforceable. Then a policy of fiscal neutrality at best
possesses strategic value in the intergeneration pension game.
3
tional as well as intragenerational justice in order to identify social-welfare
gains from tax reforms.
This essay is a brief and informal introduction to the welfare econom
ics of fiscal policy in its recently transformed state. It focuses on some
classic questions that happen to have interested me and to which I have
sometimes contributed. The first section addresses the effects of tax fi
nance on the potential social welfare of future generations. The next sec
tion, on the just structure of taxation, takes up the taxation of capital and
the question of progressivity. The last section discusses the determination
of the shadow rate of interest and the shadow budget constraint in a
setting of intergenerational justice.
I
Cicero said that man plants trees for future generations. Had he
rather remarked that man levies taxes for future generations he would
have founded fiscal theory (instead of capital theory). Realpolitik aside—
after all, the next generation might repudiate the public debt if the present
generation were to abuse its power to finance through debt issue—the
present generation gains nothing from tax financing in whole or in part its
government spending instead of borrowing. If there is a gain from tax
financing it must accrue to the next generation.
The overlapping-generations model without bequests, extended to
encompass heterogeneous workers able to vary continuously their
supplies of effort and of private saving, leads to two propositions in this
regard. If a tax measure taken by the government notionally belonging to
the present generation of worker-savers over their two-period lifetime
raises the potential social welfare of the next generation, all the spending
activities of the government being held constant, the fiscal measure must
also raise the present discounted value of the total tax revenues collected
from the present generation over its two-period lifetime, thus reducing the
final budgetary deficit and public debt, when the discounting is done at the
original social rate of return to investment (as distinct from the ex post rate
of return).3 The converse is not true, however, and the second proposition
differs from it: If a tax measure produces a rise of the final budgetary
surplus and hence a decline of the public debt, when these changes are
calculated on the basis of the original social rate of return, and if any
resulting increase of the public debt or decrease of the capital stock with
which the next generation is confronted in sufficiently small (small enough
to save the next generation from the workings of diminishing returns),
3 The implicit or notional final public debt here is equal at par to the negative of the
following: the new capital stock plus its social rent, the latter figured at the original social
rate of return, minus the new claim to retirement consumption.
4
then there results an unambiguous increase in the potential social welfare
of the next generation. This point can be illustrated with the aid of Figure
1, where it can be seen that a rightward and parallel movement of the
straight line passing through the initial point does not guarantee that the
new point will lie on a better social-welfare contour for the next genera
tion.
The key to this result is to see that the next generation is the recipient
of a certain producer's surplus: In the illustrative one-product case, it is
the excess of the final output, F{K, . . . ), that the next generation opti
mally chooses to produce with the capital bestowed on it by the present
generation, K, minus the consumption claim against that output which
must (injustice) be paid to the present generation in its retirement,X. (Of
course the next generation's own bestowal of capital to its successor is
another minus, just as its own consumption claim in retirement is a plus;
however we are free to treat these further terms as preoptimized constants
Figure 1. This diagram indicates the contours of constant potential social welfare and
associated concepts.
5
