Negishi's Contributions to the Development
of Economic Analysis: research programs and
outcomes
该文刊载在International Journal of Economic Theory
(special issue on
Negishi),作者Warren
Young是剑桥大学经济学博士、以色列Bar Ilan University经济系副教授。
The following persons
assisted me greatly in understanding the importance of Negishi's
path-breaking contributions to economics: Kenneth Arrow,
Jean-Pascal Benassy, Jacques Drèze, Victor Ginsburgh, Peter Howitt,
Tim Kehoe, Kazuo Nishimura, Roy Radner, Herbert Scarf, Nancy
Stokey, Steve Spear, Makoto Yano and last, but not least, Takashi
Negishi himself.
Introduction
In 1992, Negishi described himself "as a mainstream economist who
has made some contributions to the areas of general equilibrium,
international trade and neo-Keynesian economics" (1992, 227).
Indeed, few economists have written on such a wide range of topics
as Negishi. Among other things, Negishi attempted to extend the
multi-market Neo-Walrasian system in a number of directions so as
to encompass stability, imperfect competition, money, trade and
unemployment – both demarcating some of the
boundaries of mainstream economic theory and setting research agenda,
as Samuelson in Foundations of
Economic Analysis. Interestingly
enough, it was Arrow and Hahn (1971), who initially outlined some
key elements in the Negishian research program, and described the
initial impact of his early work, while Negishi himself (1972)
completed the immediate picture, as will be seen
below.
Over just a short five year period, 1958-62, Negishi made
fundamental contributions to General Equilibrium theory which
changed the course of modern economics. His 1958 paper article
reduced the number of conditions for stability of tatonnement to
gross substitution.
In his pioneering 1960 paper, Negishi provided a completely new way
of proving the existence of equilibrium, via the Second Welfare
Theorem. He established equivalence between the equilibrium problem
set out by Arrow-Debreu and what has been called "mathematical
programming", thereby developing a "method" which has been utilized
with much success by later economists working in both theoretical
and applied General Equilibrium modeling, as will be shown
below.
Negishi's 1961 paper "On the formation of prices" (1961a) was,
according to Arrow and Hahn (1971, 346) "the first study of a
process without recontract" and, according to them provided fertile
ground for extensions by Uzawa (1962a) and Hahn
(1962).
Negishi's 1961 incorporation of imperfect competition into General
Equilibrium models(1961b), while problematic to some (see, e.g.
Hart, 1985, 107) has been seen by others as his most important
contribution, as will be seen below. In this paper, he initiated
the study of imperfect competition in general equilibrium analysis.
He assumed consumers to be price takers and firms to be
monopolistically competitive. In his model, firms exhibited
subjective functions, these being consistent with the given
information regarding the current state of the market. He assumed
convexity of possible production set of firms, and clearly
indicated the problems associated with non-convexities in a
Walrasian system. Finally, he proved the existence of equilibrium
in an imperfect market setting.
His joint 1962 paper with Hahn (1962a), introduced the
"Hahn-Negishi Process" of non-tatonnement stability, while
Negishi's survey article on stability, published in 1962, is still
considered to be the most authoritative on the subject published
over the past four decades (1962b).
Any
attempt to analyze all of Negishi's "multifarious contributions",
as Drèze recently put it, would be
a Herculean effort. The object of this paper,
therefore, is to assess the impact of what can be
considered his "most significant" contributions
(Drèze, 2006, personal
communication), in terms of the research programs that
emanated from his early work (1958, 1960, 1961a, 1961b, 1962a,
1962b) and their outcomes.
Negishi on Gross
Substitutes, Welfare, and Existence of
Equilibrium
Gross Substitutes (1958)
Already in his Master's dissertation, entitled "Existence and
stability of an economic equilibrium" [in Japanese] (1957, cited in
Negishi 1972, 12, note 4), as he recalls, he had proven "the local
stability of the gross substitute case" (2000 b,
326). His first publication in English was in one
of the leading journals, Econometrica, in July
1958, and remains, along with papers by Arrow and Hurwicz (1958)
and Hahn (1958), one of the fundamental papers dealing with issues
of existence of stability of the tatonnement process. What is
interesting to also recall here is the editor's note regarding
Negishi's first published paper (1958, 445): "These papers [Hahn;
Arrow and Hurwicz; Negishi] were written independently of one
another and were submitted for publication at about the same time".
This illustrates not only the importance of Negishi's contribution
in the context of the "multiple discovery", but also highlights the
importance the editors of Econometrica placed upon
it.
Now, according to Negishi, in his 1958 paper, he "proved the local
stability of the tatonnement process under the assumptions of gross
substitutability and the homogeneity of excess demand functions"
(2000 b, 326). While Hahn's 1958 paper did not
cite Negishi, it did refer to the forthcoming work of Arrow and
Hurwicz and their proof of "a similar theorem" (Hahn, 1958,169,
note 1). Arrow and Hurwicz, for their part, referred to both Hahn's
paper and that of Negishi and wrote (1958, 546, note 44) "the
general case [regarding stability of equilibrium under the
assumption of gross substitutability] has been demonstrated
independently by Hahn... and Negishi".
And, almost 50 years later,
the legacy of Negishi's 1958 paper is still "well alive" (Hamada
and Endo, 2004, 22).
Welfare, Existence of
Equilibrium and Competitive Economy (1960) and its
impact
Theoretical extensions and
modifications
What has been called Negishi's " approach" or " method" (1960) has
been widely utilized on both theoretical and applied levels, the
former in the context of dynamic models and
infinite dimensional general equilibria; the latter in the context
of their numerical computation, as will be seen below. Similar
results to Negishi's 1960 proof of the existence of equilibria
based on what can be termed mathematical programming techniques,
were obtained by Takayama and El Hodiri (1968) and Diewert
(1970).
Mantel (1971) was the first to consider the utilization of
Negishi's1960 approach for computing equilibria. This extension, or
tatonnement algorithm, encompassed
what Mantel called "the welfare adjustment process" so as to enable
"the computation of an equilibrium solution, adjusting the weights
assigned to each individual in the social welfare function" (1971,
415).
Negishi's 1960 approach also
showed that a vector of welfare weights existed and that transfers
necessary for decentralizing the Pareto efficient outcome were
zero. In seminal papers, Bewley (1982 [1980]) and Yano (1984a, b)
applied this to dynamic models in what Kehoe later termed
characterizing "equilibria as solutions to social planning
problems" (1991, 2090). Lucas and Stokey (1984) also utilized
Negishi's approach and that of Bewley (1982 [1980]) in their
treatment of optimal dynamic growth, and while not directly citing
Negishi (1960), they took his 1960 approach to be part of the
corpus of economic theory, and utilized it as such (Stokey, 2006,
personal communication).
Kehoe and Levine (1985) modified the approaches of Negishi and
Bewley to deal with the properties of an infinite horizon
economy. More specifically, they developed an
approach by which to deal with the problem of determinacy in
settings with infinite dimensional characteristics based upon
Negishi's characterization of equilibrium as zero on the map of
excess spending (1960). Further modification
formed the basis for Kehoe, Levine and Romer
(1990). This involved conversion of the infinite
dimensional problem "into a finite dimensional Negishi problem"
(1990, 1). Following this, Kehoe, Levine and
Romer (1992), utilized the the Negishi approach to deal with
equilibria of economies with externalities and
taxes. The Kehoe and Levine (1985) approach of
utilizing the map of excess spending assuming additively separable
preferences was further extended by Belasko (1997) and Chichilnisky
and Zhou (1998).
Mas-Colell(1986) also followed Negishi's 1960 approach in his
reconsideration of the existence problem regarding price
equilibrium and exchange economy characterized by
unbounded number of commodities with a finite number of consumers,
and developed a topological version of Negishi's approach, as
manifest in Mas-Colell and Zame (1991). Dana and Le Van (1991) also
extended Negishi's approach, albeit into a "dual version", by
utilizing a Pareto optimal weighting system. This Negishi-based
"weight approach" has, in fact, come to be one of the main tools in
equilibrium asset pricing (Duffie, 1996; Becker and Boyd,
1997).
Following from the work of Dana and Le Van (1991), Duran and Le Van
(2003) applied Negishi's method to prove existence of equilibrium
in a one- sector Ramsey economy. The "Negishi-type" social planner
also provided the basis for the analysis by Jensen (2004) of
unbounded growth with consumers who are
heterogeneous.
Another extension of Negishi's 1960 approach can be found in
Ghiglino and Olszak-Duquenne (2001) and Ghiglino and Sorger (2002).
The former, by utilizing Negishi's 1960 approach, showed that the
dynamics in a two-sector neoclassical general equilibrium model
with exogenously determined labor supply-- with a single
consumption good-- is affected by the initial distribution of
capital. The latter, using the Kehoe-Levine-Romer (1991)
modification of Negishi's 1960 approach, analyzed how initial
individual values of wealth, and the wealth distribution, impacted
on the dynamics of equilibrium. And, as Ghiglino put it (2002, 5)
"the natural framework to analyze the effects of income
inequalities in a general equilibrium framework is provided by a
generalization of the Negishi [1960] approach".
Crockett, Spear and Sunder (2005) have further extended Negishi's
1960 approach to a learning rule that could ensure convergence to
competitive equilibrium. Indeed, on the theoretical level, then, it
can be said that Negishi's 1960 approach has become a "standard
tool" (Ghiglino and Sorger, 2002, 122).
Applications and Computational
Analysis
With regard to the influence of Negishi's 1960 paper upon the
development of "applied", that is "computable" general equilibrium
models, in a private communication to the present author, Ginsburgh
gave a comprehensive albeit "brief history" of the impact this
paper made. He wrote (2006, personal
communication):
Waelbroeck and I were among the first to use in an applied model
Negishi's way of proving the existence of a competitive equilibrium
in Ginsburgh and… Waelbroeck (1981)….The book came out in 1981, but
there were papers published [by me] before that, the oldest being
"Computational experience with a large general equilibrium
model"(1976) and a 1975 Cowles Foundation Discussion Paper "A
general equilibrium model of world trade. Part I: Full format
computation of economic equilibria"… Dixonplayed with the same
idea in his 1972 Harvard Ph.D. thesis which was published in 1975
as The theory of joint
maximization, but he only refers very loosely to Negishi, though it
is exactly the same model as Negishi's. He calls it "joint
maximization". Earlier than that, a paper in the spirit of
Negishi's proof... is Trzeciakowski, (1971).
More recent applications of
Negishi's 1960 approach to the computation of equilibria can be
found in Ginsburgh and Van der Heyden (1988), who apply it to the
case of the government price supports; Kehoe (1991), who dealt with
multiplicity of equilibria; Backus, Kehoe and
Kydland (1992 a, b, c), who apply
the approaches of Negishi (1960) and Mantel (1971) to calculate
equilibria in international real business cycles and dynamic
general equilibrium models of international trade; Nordhaus and
Yang (1996), who apply it to develop a computable general
equilibrium model of alternate climate-change strategies; Ginsburgh
and Keyzer (1997), who deal with the structure of
AGE models in their book; Esterban-Bravo (2004), who surveys the
computation of equilibria in GE models via interior-point methods;
Kehoe et. al (2005), who present the "frontiers" of CGE models; and
Judd (2005), who extends the approach to dynamic stochastic GE
models.
Monopolistic Competition:
1959, 1961, and 1972 vintages and their
impact
Negishi first gave this paper at the December 1959 Washington, D.C.
meeting of the Econometric Society .According to the report of the
Washington meeting, he presented his paper on Monday afternoon, 28
December 1959, at the session "Economic Theory I". The three papers
presented at the session included one by Hahn entitled "The
existence of competitive equilibrium". Koopmans also presented a
paper, entitled "Stationary Ordinal Utility and Timing
Preferences". Ando and McKenzie were the discussants for all the
papers. Negishi's paper, however, was the only
one that had an abstract published in the Washingtonmeeting Report
(1960, 677-78).
A decade later, Arrow and Hahn (1971, 151-167) extended the
existence theorem and formal model contained in what they called
Negishi's "brilliant paper" (1971, 167) via more general
assumptions such as non-convex production possibility sets (1971,
152). Negishi's monopolistic competition paper
(1961b) has been cited almost as many times as his 1960 paper, and
also originally stimulated a Negishian-based research program in
the 1970's as described by Roberts and Sonnenschein in their
Econometrica survey (1977). As they wrote (1977,
101) "Since the pioneering work of Negishi [1961b], a number of
studies have been directed towards incorporating firms which
recognize their ability to influence prices (but behave
non-cooperatively towards one another) into the Arrow-Debreu model
of general equilibrium". They listed the works of
Arrow and Hahn (1971), Fitzroy (1974), Gabszewicz and Vial (1972),
Laffont and Laroque (1976), and Marschak and Selten
(1974).
Drèze (1975), Grandmont and
Laroque (1975) and Benassy (1976) had extended, implicitly, in the
former cases, and explicitly, in the latter case, Negishi's
"brilliant paper" (1961b) in another direction, into the sphere of
disequilibrium, that is to say non-tatonnement situations, where,
as Benassy put it, "transactions can actually occur outside
equilibrium" (1976, 69).
Silvestre (1977a, 1977b) , for his part, extended Negishi (1961b)
to encompass increasing returns to scale, including Negishian-style
subjective demand functions. He also developed (1978, 397) an
alternative existence theorem to overcome what he called the
"shortcomings" in the Arrow-Hahn (1971) extension of Negishi
(1961b).
In his 1980 Econometrica
survey, Drazen noted that the "the basic work
on monopolistic competition in general equilibrium models is the
pioneering contribution of Negishi [1961b]..." (1980,290). Drazen
went on to say that besides the work of Benassy [1976] and
Drèze[1975] "a model in which
price setting is integral to agent's attempts to
"break" the constraints is that of Hahn [1978] , also based on
Negishi's work [1961b], which uses the Drèze [1975] basic framework"
(1980,291). There is, however, a problem in Drazen's linkage of
Hahn [1978] to Negishi [1961b]. This is due to the fact that Hahn
said (1978, 7) that his 1978 approach "is not the model Negishi
[1961b] considered. I have not found it in
Benassy. The kink which my formulation gives rise
to has recently been used by Negishi ... in a different context"
referring the reader to an unpublished 1974 "
Memo" by Negishi, which Hahn cited as "Unemployment Equilibrium".
In a recent communication to this author, Negishi (2006d) cleared
up the matter by saying that "Judging from the date, the paper
seems to be the one I read in a conference organized by the
Institute for Advanced Studies, Vienna, in 1974. The exact
title of the paper is "Existence of an under-employment
equilibrium." This paper was published in G. Schwoediauer, ed.,
Equilibrium and Disequilibrium in Economic Theory, D. Reidel
Publishing, 1978, pp. 497-510" [Negishi
1974,1978].
Hart (1985), in his overview of work on "imperfect competition in
general equilibrium" claimed that both Negishi's approach (1961b)
and that of Arrow and Hahn (1971) were not "very satisfactory"
(1985, 107) and "suffered from…weakness" as "the class of possible
equilibria…is very large"; the outcome of being based upon
"subjective", rather than "objective" demand (1985, 139). Hart's
points may be relevant; however, as Gabszewicz (1985, 152) noted in
his comment on Hart, the "overview" did not deal with the issue of
imperfect competition and product differentiation, as set out by
Negishi in the 1972 revision of his paper (1972, 104), an approach
that was implicitly taken up, for example, by Mas-Colell (1975) and
Drèze and Hagen (1978). In
contrast to Hart's critical view of Negishi (1961b), then, and the
fact that he did not deal with the work it stimulated, Gabszewicz
(1985, 151) wrote "The Negishi approach…received a considerable
revival of interest".
Very significant outcomes of Negishi (1961b) are found in the
non-tatonnement approach of Benassy (1976, 1978, 1982, 1991, 1995),
and in the attempt to reformulate Negishi's approach (1961b) by
Gary-Bobo (1989). It should also be recalled at
this point that Negishi's volume Microeconomic Foundations of Keynesian
Macroeconomics appeared in 1979,
but before this he had presented papers, and published articles
which formed the basis for this book (1974, 1978). Perhaps the most
influential of Negishi's articles in this field, that appeared
prior to his 1979 book, was entitled "Existence of an
under-employment equilibrium". As mentioned above, this paper was
originally presented at a conference in Viennain July 1974, and was
published in the volume Equilibrium
and Disequilibrium in Economic Theory (1978, 497-510). In this volume, Negishi's paper was
complemented by that of Benassy, "A Neo-Keynesian model of price
and quantity determination in disequilibrium" (1978,
511-544).
It is important to point out here that both papers, in addition to
Benassy (1976), preceeded the so-called
"New Keynesian" works that appeared in the 1980s (e.g. Rotemberg
1982; Mankiw, 1985). Indeed, in his 1976 paper, Benassy wrote
(1976, 69) "monopolistic price setting was incorporated for the
first time in a brilliant paper by Negishi [1961b]". The impact of
Negishi (1961b) on "New Keynesian economics" has been recounted by
Peter Howitt (2006, personal communication):
"most of modern New
Keynesian Economics owes its intellectual origins to his
[Negishi's] work in imperfect competition in General Equilibrium,
although it is, like Benassy's work which was also very
influential, hardly ever cited. I would say these works were
influential because so much subsequent work is a straightforward
extension of the concepts and techniques in them, and because
although they are not much cited, they were available in prominent
publication outlets when the work that is cited
(Blanchard-Kiyotaki, for example) was done".
More recently, Dehez, Drèze and Suzuki, in their work
on imperfect competition and fixed costs have asserted (2003, 220)
Negishi's 1961 "perceived demand approach" to be, in their opinion,
"more realistic, in many situations, than the alternative,
objective demand approach". Moreover, Negishi's approach (1961b)
has been even further extended into the area of international trade
theory by Neary (2003), in his attempt to analyze globalization and
the structure of markets.
Econometrica survey article and
"Hahn-Negishi process", 1962
Negishi's classic 1962 survey article "The stability of a
competitive economy" was originally presented, in part, at the
September 1960 Naples
meeting of the Econometric Society (Negishi
1962b, 635, note 1). The abstract of this paper was published in
the Report of the Naplesmeeting in
Econometrica (1962, 192). Among those who took part
in the discussion also published in the Report (1962, 192-194) were
Malinvaud and Wold, with a brief reply by
Negishi. In his comments, Malinvaud focused on
the implications of Negishi's analysis of "tatonnement"
and "non-tatonnement"
processes. Negishi's reply to the commentators
was "I would say that the tatonnement processes is a special case
or limiting case of non-tatonnement processes. It
must be noted that both of them lead to a point which is optimal in
the sense of Pareto" (1962, 194). Writing with
the perspective of over four decades,
Drèze has recently commented on
what Negishi said as follows (2006, personal
communication):
"I agree that limit points
of both Walrasian tatonnement and Walrasian non-tatonnement are
Pareto-efficient (under standard assumptions). The point on which
there has been occasional misunderstanding is that limit points of
Walrasian non-tatonnement are not competitive equilibria relative
to initial endowments, so the efficiency proof is a bit
different."
His 1962 survey article contained important "suggestions for future
studies" (1962b, 665-666), some of which Negishi himself took up in
his 1964 papers (1964a, b) and in Chapter 13 of his 1972
book. For example, in the 1962 survey paper, he
proposed studying the "price formation process... over Hicksian
weeks", with reference to "the cobweb process" and "the process
with interactions between expectations and inventory fluctuations"
(1962b, 666). In his 1964 paper (1964b, 649), Negishi linked
Arrow-Debreu (1954), and Enthoven and Arrow (1956), with Muth
(1961); which he repeated in Chapter 13 of his 1972 book (1972,
201). The importance of Negishi's survey article was recognized
early on. For example, Patinkin, in Money, Interest and Prices wrote (1965, 540): "The extensive literature which has
grown up in recent years on the stability question has been
usefully and critically surveyed by Takashi
Negishi".
In 1962, Negishi also published his joint paper with Hahn. The
first note in this paper (1962a, 463, note 1) said that "this is
the outcome of two papers by the authors, each written
independently. Hahn's paper [Hahn, 1960]
formulated the process of adjustment and proved some theorems which
were then generalized by Negishi..."; "Negishi's contribution" was
"a sequel" to his 1961 International Economic Review paper "On the formation of prices", written while he was
at Stanford (1961a, 26).
As Negishi recalled (2006,
personal communication) "Frank and I got acquainted …before
the Washingtonmeeting, in [the] Stanford-Berkeley regular joint
seminars in 1959-60. Frank was at Berkeleyin 1959-60 and I was
at Stanford, though, because of [the] 1958 gross-substitute paper,
we knew each other's names in 1958".
In his paper "The stability of exchange and adaptive expectations"
(1964a)--which also emanated from the research program he outlined
in his 1962 survey article--Negishi attempted to model the
relationship between prices and expectations in the non-tatonnement
process he had originally developed independently of Hahn (Negishi,
1961a), based upon the approach developed in Hahn and Negishi
(1962a) and Arrow and Nerlove
(1958).
Perhaps one of the most important outcomes of the "suggestions for
further studies" in his 1962 survey article, is Negishi's
utilization of rational expectations in his 1964 "Note" in
Econometrica entitled "Stability and rationality of
extrapolative expectations"(1964b).
Negishi did not attend the
sessions of Muth and Mills at the 1959 Washington meeting of the
Econometric Society where he gave his own paper ("Monopolistic
Competition"), but as he recalled in a letter to this author (9
Dec. 1991):
I recognized, however, the
significance of their contributions soon after they were
published, at least in my own way of interpretations. I published a
small note “Stability and Rationality of Extrapolative
Expectations” in Econometrica (1964), in which I referred
to Muth’s 1961Econometrica paper. Also, in the Chapter on
Rational Expectations of my 1965 book Kakaku to Haibun no
Riron (Theory of Price and
Allocation), I referred
to Mills’ 1962 book as well as Muth’s 1961 paper.
In fact, Negishi’s 1964 “small note” is, in my view,
quite significant, for in it he used Muth’s approach to “give
some rational basis to extrapolative expectations” (1964b, 649). In
other words, Negishi proposed rational expectations as the basis
for the endogenous
expectational assumption underlying “the
dynamic stability of multiple markets” in the system
originally proposed by Arrow and Debreu (1954) as manifest in
Enthoven and Arrow (1956). In fact, Negishi actually extended Muth’s
approach in this regard. As he put it (1964b,
649):
The rational expectation hypothesis advanced by Muth...is that
expectations are essentially the same as the predictions of the
relevant economic theory; that the economy generally does not waste
information; and that expectations depend specifically on the
structure of the entire system. However, since there is cost of
information and computation, expectations may also be called
rational when they are formed as the prediction based on a
simplified and approximated version of the economic theory, using
only limited amounts of information on a part of the system.
Extrapolative expectations will be derived below as the prediction
of the equilibrium by the use of estimated excess demand functions,
and it will be shown that the coefficients of expectations thus
derived are such that the system of multiple markets is stable when
gross substitutability and tatonnement are
assumed.
By making rational expectations the expectational basis of
the Arrow-Debreu general equilibrium model, Negishi provided
fertile ground for Radner to further develop the Arrow-Debreu
approach. For, as Roy Radner also wrote in a letter to this author
(1992, personal communication):
My own interest in the subject arose from my attempt to extend the
Arrow-Debreu model to the case of incomplete markets. The first
results of this attempt were published in 1967...This paper dealt
simultaneously with two aspects of “rational expectations”:
consistency in the expectations of future prices, and making
inferences about other agents’ information from equilibrium prices.
I like to think it had little impact because it was published in
French!" [on these and related issues, see Young and Darity, 2001
and Young, Leeson and Darity, 2004].
Negishian Research Programs:
variations on the themes of his contributions
Negishi 1960 and 1961
In order to gauge the impact of Negishi's contributions in the eyes
of his peers, this author contacted those leading economists who
worked with, or were directly influenced by Negishi, and asked them
to assess the impact of his work on the General Equilibrium and
Non-Walrasian research programs. In his reply, Kenneth Arrow wrote
(2006, personal communication):
Negishi's work...pioneered in the study of "non-tatonnement"
stability, in a paper of his own and a subsequent one jointly with
Frank Hahn... He also developed a model of general imperfectly
competitive equilibrium, based on subject[ive] demand curves, which
impressed me at the time, though it doesn't seem to have had a
permanent effect on the literature. Finally, and perhaps most
importantly, he had a proof of the existence of equilibrium based
on the idea that a competitive equilibrium maximizes a suitably
weighted sum of individual utilities. The existence proof depends
on a fixed point in the space of weights. This proposition has been
used in solving applied general equilibrium models and was also
extensively used by Lucas and Stokey in the analysis of
intertemporal equilibrium as applied to the study of economic
fluctuations.
In his reply, Drèze took the opposite
position to that of Arrow regarding the importance of Negishi's
"extension of general equilibrium to monopolistic
competition". As Drèze wrote (2006, personal
communication)
Regarding Negishi, I have all along admired his work, mostly for
the reason which he himself lists as his main motivation in his
entry for "Who's who in Economics" (3rd ed. p. 819): "I have always
tried, not so much to generalise theory mathematically, as to
enrich it with economic significance, so that it can be applied to
the problems of the real-world economy". Of course, this remark
should be applied primarily to General Equilibrium Theory, not to any brand of theory. The remarkable feature is
the combination
of respect for abstract theory as evidenced
by privileged attention to GE, and primary interest in real-world
problems [Drèze's
emphases].
Two obvious applications of the principle are: (i) the extension of
GE to monopolistic competition; and (ii) the attention to
non-Walrasian equilibria. To my own eyes, (i) stands as the most
significant among Negishi's multifarious contributions. There is
really no palatable alternative to his approach (given the
existence problems and lack of realism of the so-called "objective
demand" alternative). I am confident that it will be retained again
and again by future researchers in the area. Also, his exposition
in the 1961 article and 1972 book is very good: rigorous, concise
and understandable - what more could one ask?
In his reply, Benassy (2006, personal communication), strongly
supported Drèze's postition when he wrote
"To me the major contribution by Negishi has been his short but
incredibly influential 1961 article "Monopolistic competition and
general equilibrium". All authors writing on the subject have been
directly influenced by this highly elegant article, so I would
place it at the center of any piece on Negishi's
contributions".
Scarf, for his part, noted in his reply (2006, personal
communication) to this author:
Takashi Negishi has made many significant contributions to economic
theory, primarily, though not exclusively, in the area of general
equilibrium theory. One of his most striking innovations is his
proof of the existence of equilibrium prices based on maximizing a
weighted sum of individual utilities. Each such maximization will
produce a vector of prices and an allocation of society’s resources
in which the value of consumption will be different from income for
the typical consumer. A fixed point argument is then applied in the
space of social welfare weights to find the appropriate set of
weights for which the value of consumption is equal to income for
all consumers. Fixed point algorithms, or their equivalents, are
used to find equilibrium prices in applied general equilibrium
analysis. Computational demands depend on the dimension of the
space in which the fixed point argument is applied - typically the
number of commodities in the model. The number of consumers is
usually much smaller than the number of commodities. Applied
general equilibrium practitioners have found Negishi’s approach
extremely useful in reducing computational time and allowing much
larger problems to be solved.
Stokey, for her part, when asked by this author about the
connection made by Arrow in his reply to the present author as
cited above, that is, between her joint work with Lucas (1984), and
Negishi's 1960 "method", replied (2006, personal communication):
"Ken has a good
memory. Bob Lucas and I used Negishi's method in
our 1984 JET paper on optimal growth with
Koopmans-Diamond-Williamson preferences, which are recursive but
not additively separable over time. In our
setting, the key idea was to define a mapping on the Pareto
weights, which with those preferences evolve over time"; and
this, despite
the fact that Negishi's 1960 paper is not
cited in Stokey and Lucas (1984).
Indeed, as Spear has recently observed in a communication to this
author (2006):
…my exposure to this body of
work has been most focused on the work on existence, the work on
tatonnement stability conditions, and the non-tatonnement,
Hahn-Negishi processes….I was probably first exposed to the
existence paper in graduate school, and came to particularly
appreciate it as a way of showing existence of equilibrium in the
neo-classical capital model with finitely-many agents… I think some
results can become so well-known and so well discussed in surveys
that people stop citing them. This would
certainly explain the absence of a citation by Lucas and
Stokey.
This observation has been
confirmed by Stokey, who, with Lucas (1984)
"took Negishi's method to be
part of the corpus of modern economic theory" (2006, personal
communication).
Analytical Extension of Negishi (1960) and the "Negishi-Mantel
algorithm"
But more is involved here
than simple theoretical and computational application of Negishi
(1960), and its absorption into the "corpus" of modern theory. In
his seminal paper, Yano (1998) extended the analytics of Negishi's
1960 approach to gauge the efficacy of "temporary fiscal policy".
By extending Negishi's approach he found that, among other things
"the inefficacy of temporary fiscal policy… may be thought of as
one of the most fundamental properties of dynamic general
equilibrium" (1998, 440). The crucial implication of this result
has yet to be digested by those who deal with macroeconomic policy
and analysis.
On another level, there has been increasing utilization of what has
been called the "Negishi-Mantel algorithm" (Backus et al. 1992b,
9). For example, Cunat and Maffezzoli (2004),
apply the "Negishi-Mantel algorithm" to Heckscher-Ohlin business
cycles, while Mendoza
and Oviedo (2005), apply it to
the analysis of fiscal policy and macroeconomic uncertainty in
emerging markets. Tim Kehoe has recently provided this author with his
important account of the development of what Scarf originally
termed the "Negishi-Mantel algorithm". According to Kehoe (2006,
personal communication):
I started in the Ph.D. program at Yale in the fall of
1975. I took Herb Scarf’s general equilibrium
course (mathematical economics as it was called then) that
fall. In the spring, Herb was a visitor at
Harvard …Rolf Mantel, who was a visitor at Yale, taught the second
semester of Herb’s course. That is when I first
heard about what Rolf called the “Negishi approach” to proving the
existence of equilibrium via the second welfare theorem and a fixed
point problem in welfare weights. Rolf stressed
that Negishi’s approach relied on an underlying fixed point
problem. He explained that, in his Ph.D. thesis,
he (that is, Rolf) had tried to circumvent using fixed point
methods in developing a computational algorithm for general
equilibrium models. Of course, by the time the
principal paper taken from Rolf’s thesis, Mantel (1971), was
published, he had realized that the stability properties of a
tâtonnement process on welfare weights depended
on the properties of the underlying utility functions and
endowments of the economy. In fact, an argument
due to Uzawa (1962)[1962b] said that any proof of existence of
equilibrium in an economy whose excess demand function was
arbitrary except for the assumptions of continuity, homogeneity of
degree zero, and Walras’s law could be trivially manipulated into a
proof of Brouwer’s fixed point theorem. Rolf was
intrigued by the question of whether excess demand functions were
arbitrary except for these basic assumptions or whether they
satisfied some stronger properties that would make computation of
equilibria easier. He came up with the answer in
Mantel (1974): Aggregate excess demand functions
are, in fact, arbitrary except for these assumptions unless we
place strong restrictions on utility functions, endowments, or
numbers of consumers…
The next year, Herb Scarf was back at Yale, and he asked me to be
the grader for his course….Many of my friends and classmates, now
in their second year, including Dave Backus, took this
course. In the second semester, Herb spent a
couple of classes going over the results of Negishi, Uzawa, and
Mantel. If anyone was first to refer to a
Negishi-Mantel approach or algorithm, it was
Herb. (Or it was Dave and me talking about what
we had learned in his course.) Herb stressed that
any general algorithm for computing equilibria that would be
guaranteed to converge had to be a fixed point
algorithm. The dimensionality of the problem,
however, was determined by the minimum of the numbers of goods and
consumers. For models with lots of consumers and
few goods, we should solve a problem in price
space. For models with lots of goods and few
consumers, we should use the Negishi-Mantel approach and solve a
problem in the space of welfare weights. Herb
gave the class a homework problem with two infinitely lived
consumers and asked the students to solve it using the
Negishi-Mantel approach. Versions of this problem
still survive in the problems that I give first year graduate
students at Minnesota
in my macro course …and in exam
questions. It is also the basis of the approach
that David Levine and I took in our papers on determinacy of
equilibria…
To sum up, a number of major research programs can be identified,
therefore, as emanating from Negishi's now classicpapers, that of
1960 and 1961 (1961b) respectively. Negishi's
1960 paper forms the basis for both "theoretical" an "applied"
research programs in general equilibrium analysis, and his 1961
paper (1961b) has been almost as influential in demarcating ongoing
research up to the present in the field of imperfect competition
and non-tatonnement processes. These papers, as
has been shown above, attest to Negishi's considerable influence on
the development of modern economic theory and
analysis.
网址:http://www.biu.ac.il/soc/ec/students/teach/814/data/Negishi
IJET version.doc
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