Applied General-Equilibrium Analysis: Birth, Growth, and Maturity

Charles L. Ballard Michigan State University

and

Marianne Johnson

University of Wisconsin Oshkosh

September 13, 2016 Key Words: Applied General-Equilibrium Models, Computational General-Equilibrium Models, Computable General-Equilibrium Models, History of Applied Economics, Computers in Economics JEL Codes: B21, B23, B4, C53, D58

Charles L. Ballard, Professor of Economics, Michigan State University. ballard@msu.edu. Marianne Johnson, Professor of Economics, University of Wisconsin Oshkosh. johnsonm@uwosh.edu. We are grateful for helpful comments from Roger Backhouse, Spencer Banzhaf, Jeff Biddle, Béatrice Cherrier, Don Fullerton, Verena Halsmayer, Steven Medema, John Singleton, Roy Weintraub, John Shoven, and two anonymous referees. Any errors are our responsibility.

1

Applied General-Equilibrium Analysis: Birth, Growth, and Maturity

Walrasian general-equilibrium theory provided the central framework of 20th century

economics, “the ultimate model of the market” (John Shoven and John Whalley 2015, 2). Joseph

Schumpeter considered it the “Magna Carta” of economics, providing both a constitutional

document and a map for the field (1954, 242 and 827).

In the 1950s and 1960s, Harry Johnson (1951-52, 1956), Arnold Harberger (1962), and

others used general-equilibrium methods to study a variety of applied policy issues, such as the

welfare effects of tariffs and the incidence of the corporate income tax. The models used by

these researchers were small enough that they could be solved analytically. By the 1970s,

economists were developing general-equilibrium models of sufficient size and complexity that it

was necessary to use computers to find numerical solutions. In this paper, we will discuss both

analytical and computational models, but our main focus is on the computational models. The

computational models have come to be known as applied general-equilibrium (AGE) or

computational GE or computable GE (CGE) models. We will refer to the computational models

as AGE models, even though the analytical models also fall under the rubric of applied work.

AGE models involve mathematical specifications of the behaviors of agents, who interact

through supply and demand for different goods in a Walrasian general-equilibrium system.

Government policies are typically modeled as constraints to be manipulated. The models

produce computer simulations of the effects of policy changes on economic variables, such as

prices, quantities, growth rates, employment, income, and economic efficiency. AGE models are

most widely employed in international trade, public finance, economic development, and

2

environmental economics, in situations where policy changes have many competing direct and

indirect effects.

AGE is an umbrella term for a diverse family of related approaches, which we outline

below.1 We devote much of our attention to the intellectual tradition of Herbert Scarf, which is

“the most direct link between [general-equilibrium] theoretical work and CGE modeling” (Peter

Dixon and B.R. Parmenter 1996, 6). Building on advances in applied mathematics and

computing capabilities, Scarf’s (1967, 1973) algorithm allowed researchers to find an explicit

numerical solution for a Walrasian general-equilibrium system, “a revolutionary advance that has

helped shape policies affecting every American” (Glenn Hubbard, quoted in Sam Roberts 2015).

Economists have long distinguished between theoretical work and ‘applied economics’

(Beatrice Cherrier 2015; Til Düppe and E. Roy Weintraub 2014). However, there is variation in

the exact sense in which different research traditions are ‘applied’. For example, there is a

significant difference in the meaning of ‘applied’ between the large-scale macroeconomic

models of the 1960s, which are discussed in this volume by Verena Halsmayer (2016), and many

of those in the Scarf tradition. Certainly both approaches address problems of practical

importance and rely on actual data. However, Scarf and his students pushed the boundary of

applied economics to include numerical simulations of fairly stylized theoretical models. For

example, when Charles Ballard, Shoven, and Whalley (1985) investigate the marginal excess

burden of taxes in the United States, they simulate the effects of an increase in public

expenditure, financed by a one-percent increase in every one of the dozens of effective tax rates

in their model. Although the marginal excess burden is an important issue, the simulations in

this paper are clearly not tied to the analysis of any specific policy proposal. More generally,

much of the work in the Scarf tradition focuses on welfare calculations, which are probably of

3

much more interest to academic economists than to policy makers. It could be said that some of

the research in the Scarf tradition blurred the distinction between theoretical and applied work.

We concentrate on the history of AGE analysis between 1970 and 2000, although we

briefly touch on more recent developments. The history of AGE analysis reveals how a number

of developments, including computerization, have profoundly shaped applied economics. The

field experienced an explosion of research activity in the 1970s and 1980s, with substantial

numbers of publications in leading journals. After that, although AGE researchers continued to

produce a considerable volume of output, there was a pronounced drop in the number of articles

appearing in top journals. We examine the forces that came together to produce the early growth

of AGE analysis, and we review a variety of possible explanations for the subsequent

marginalization.

Origins of AGE Analysis

Looming behind all of the research discussed here is the pioneering work of Léon Walras

(1899 [1954]). Walras developed the idea of representing an economy as a system of

simultaneous equations, and he suggested that a tâtonnement process might be capable of finding

a general equilibrium. However, Walras was unable to prove the existence of an equilibrium.

Thus, while Walras’s work was ground-breaking, “one could never confidently employ general

equilibrium analysis unless one had first made sure that a general equilibrium model possessed a

solution” (Mark Blaug 1992, 577).

During the mid-20th century, three distinct strands of research evolved to provide the

foundations for the development of AGE analysis. These strands came together in the 1970s, at

a time of rapid growth in computing power. The first strand originated with the pioneering work

4

on input-output analysis by Wassily Leontief, who is sometimes known as the grandfather of

AGE analysis (Olav Bjerkholt 2009; Dixon and Maureen Rimmer 2010). Leontief (1936, 116)

sought to supply “an empirical background for the study of the interdependence between

different parts [of the economy] on the basis of the theory of general economic equilibrium.”

However, the simplest Leontief input-output models are quite mechanical. In Scarf’s judgment,

the Leontief model was indeed “a disaggregated version of a general equilibrium model,”

although it was “deficient in its treatment of consumer demand” and in the modeling of

production (1994, vi). Decades later, Leontief’s students Dale Jorgenson and Peter Dixon would

expand on his work, employing advances in computational mathematics, general-equilibrium

theory, and computers to build large-scale AGE models. (Figure 1 depicts some important

branches of the AGE family tree.)

Leontief specified an economic system in terms of linear relationships among sectors. In

a similar vein, Leonid Kantorovich, Tjalling Koopmans, George Dantzig, Nicholas Georgescu-

Roegen, and others developed the techniques of linear programming in the 1930s and 1940s.

Applications presented at the Cowles Commission’s Conference on Activity Analysis and Linear

Programming, in Chicago in 1949, provided a significant boost to general-equilibrium analysis

(Düppe and Weintraub 2014). Linear programming quickly became “the main object of many

research groups,” including those centered at RAND and Cowles (Georgescu-Roegen 1950,

214).

The second strand of research that provided the foundation for AGE analysis consists of

the existence proofs of Lionel McKenzie (1954) and Kenneth Arrow and Gérard Debreu (1954).

5

Figure 1. Lineage of AGE Models

The third strand of research that contributed to the development of AGE analysis was the

rise of general-equilibrium analytical techniques, often using models with no more than two

sectors, two factors, and two countries. Much of this work was carried out by economists

working on issues involving international trade (Eli Heckscher 1949; Johnson 1951-52 and 1956;

James Meade 1955; Paul Samuelson 1948).

Harberger (1962) brought these analytical techniques into the field of public finance, to

investigate the incidence of the corporation income tax. Harberger’s contribution is important to

6

the development of AGE models, since we can see Harberger’s influence very clearly in the

models of the Scarf tradition, particularly Shoven and Whalley (1972) and Shoven (1976).

Harberger (1962, 215) argued that it was “clear that a tax as important as the corporate

income tax…should be analyzed in general-equilibrium terms,” and constructed a two-sector,

two-factor model to analyze the issue. Dividing production into corporate and non-corporate

sectors, Harberger calibrated his model to U.S. data from the 1950s. He developed a system of

linear equations that could be solved for the change in the net rental price of capital resulting

from a small change in the corporate tax.

Harberger’s model provided powerful insights, but it suffered from important limitations.

Since Harberger used analytical methods to solve the model (rather than numerical ones), the

model was only tractable with a limited number of goods, factors, and sectors. The desire to

expand the number of sectors and agents was a major motivation for the researchers who would

develop AGE models (Shoven and Whalley 1992, 2). A related problem was that Harberger’s

model was based on differential calculus, so the results were only strictly meaningful for small

policy changes.

Harberger’s work sparked a flurry of research on the corporate income tax (John Cragg,

Harberger, and Peter Mieszkowski 1967; Marian Krzyzaniak and Richard Musgrave 1968;

Mieszkowski 1967). However, economists still yearned for models that could provide greater

detail and sophistication.

We now briefly describe the AGE traditions associated with Leif Johansen and Dale

Jorgenson, before returning to the Scarf tradition.

7

Johansen’s Model and Descendants

Johansen (1960) is widely credited with developing the first AGE model, a multi-sector,

computer-based model, designed to study the long-run growth of the Norwegian economy

(Bjerkholt 2009). Halsmayer (2016) identifies Johansen’s intellectual heritage in macro-growth

models and Leontief input-output analysis, rather than the Walrasian general-equilibrium

tradition. By incorporating utility-maximizing households and cost-minimizing industries in his

model, Johansen broke from earlier input-output models, which had lacked clearly specified

descriptions of behavior. However, Johansen (1960, 1 - 2) understood that his model was

severely constrained by data availability and computing power.

Today, the influence of Johansen is identifiable in the Australian ORANI and MONASH

models, developed by Dixon, Brian Parmenter, Kenneth Pearson, Alan Powell, and others

(Dixon and Parmenter 1996; Dixon and Rimmer 2010). These models arose out of a

collaboration between Dixon, et al., and the Australian government, establishing the IMPACT

Project in 1975. The goal was to build an AGE model to analyze the economy-wide implications

of changes in government policies toward industry, trade, and development in Australia.

Particular attention was paid to employment changes in various sectors of the economy, and to

the implications of reducing tariffs. The resulting ORANI model was unique, having more than

100 sectors. MONASH is the dynamic version.

Johansen’s influence can also be seen in the Global Trade Analysis Project (GTAP).

GTAP was founded in 1992 by Purdue University’s Thomas Hertel, who took advantage of a

Fulbright Scholarship in 1990 to study with the Australian group. Under Hertel’s leadership,

GTAP has become the world’s largest AGE enterprise, with members in more than 160

8

countries. The latest GTAP data base covers 57 commodities for 140 regions. See Hertel (1997)

and https://www.gtap.agecon.purdue.edu/about/history.asp.

The AGE models of Lance Taylor (1983) and Irma Adelman and Sherman Robinson

(1978), developed for the World Bank, were also influenced by Johansen’s work (Bjerkholt

2009; Benjamin Mitra-Kahn 2008). The Adelman-Robinson approach was used to examine the

welfare effects and income-distribution implications of macroeconomic policy changes in

developing and transitional countries. Their models have been used extensively in policy work,

and the World Bank remains an important center for AGE analysis.

These various descendants of the Johansen model are related through the modeling

strategies they employ, through their close connections with governments and global economic

institutions, and through a focus on very detailed policy analysis. These highly disaggregated

AGE models can be used to measure changes in employment by sector, as well as changes in

prices and the incomes of consumers. This level of practical detail is a defining feature of the

Johansen legacy (Halsmayer 2016).

Jorgenson-Style Models

The influence of Leontief is clearly apparent in the models developed by Jorgensen and

his collaborators, although Jorgenson-style models came to include so many other features that

they can be seen as a distinct approach to AGE modeling. Jorgenson and Edward Hudson (1974)

built a nine-sector production model to examine the long-run effects of energy policies in the

United States. The approach has since been applied to a wide variety of questions, including the

efficacy of carbon taxes and other pollution-control mechanisms, and economic growth under

different tax regimes. The models used by Jorgenson and his collaborators have grown

9

tremendously in scale over the years. A recent version has 35 production sectors and 35

categories of consumption expenditure in every period, and the model is cast forward 120 years

into the future. A distinguishing feature of Jorgenson models is that they use econometric

estimation to generate a relatively large proportion of the parameter values for the system.

The Scarf Tradition

Scarf’s tradition of AGE analysis emerged separately from the Johansen, Dixon, and

Jorgenson models, at the nexus of his own work on computational algorithms (Scarf 1967, 1973)

and of McKenzie-Arrow-Debreu general-equilibrium theory. Scarf’s early work at RAND with

Dantzig and Arrow proved pivotal for developing his interest in neoclassical general-equilibrium

theory (Scarf 1973, ix–x). Challenged by Arrow, Scarf built on advances in linear programming

to develop an algorithm to compute solutions for numerically specified general-equilibrium

models. Scarf’s algorithm was important because it was the first to provide a constructive proof

of existence, even if subsequent advances meant that it was not employed very frequently, as

modelers adopted faster computational methods.2

Awarding Scarf a distinguished fellowship, the American Economic Association stated

that his

…path-breaking technique for the computation of equilibrium prices has resulted in a

new subdiscipline of economics: the study of applied general equilibrium models…Scarf

was the catalyst behind the creation of this subfield of the profession and in the

transformation of the general equilibrium model from a purely theoretical construct to a

useful tool for policy analysis” (1992, online).

10

Arrow (1983, 10) similarly draws a line straight from the Cowles Conference of 1949, through

his theoretical work with Debreu, to Scarf and the “new field of applied general equilibrium

theory.”

The binding constraint for AGE work had long been the lack of sufficient computing

capability (Scarf 1973, 2–3). However, by 1970, expanded computer storage, faster processing,

and programming languages such as FORTRAN greatly reduced the cost of AGE analysis.

Shoven and Whalley (2015, 1) recount that their work in AGE analysis was a matter of

“being in the right place at the right time…Peter [Mieszkowski] had just taught us the

Harberger two-sector model used in public finance and we were quite aware of other

small-scale general equilibrium models…used in international trade. These models had

to be kept incredibly simple and small in order to be analytically tractable. At the same

time, Scarf had taught us his just-developed method of computing economic equilibria

for arbitrarily large Walrasian general equilibrium models.” (Shoven and Whalley 2015,

3) 3

Shoven (1976) demonstrated that, with the aid of computers, the effects of capital taxes could be

studied in a style reminiscent of Harberger.

Interestingly, neither Scarf (1967, 1973) nor Shoven and Whalley (1972, 1973, 1992) cite

Leontief or Johansen. Rather, they define their lineage as starting with Arrow and Debreu and

following Johnson and Harberger.4 None of their early applications use the terms “applied” or

“computable” in describing the general-equilibrium models. Rather, the authors talk of

“empirical estimates of the consequence of distortions” (Shoven and Whalley 1972, 281) and

“empirical evaluation of…tax proposals” (Shoven and Whalley 1973, 475). However, by the

11

1980s, “applied” and “computable” were routinely appended to “general equilibrium” to refer to

this approach.

AGE models of this type require the explicit mathematical specification of functional

forms for consumer utility functions and firm production functions, for all agents and sectors.

Once the functional forms are chosen, modelers must assign numerical values to the parameters

of the functions. Some of these values may be chosen from the econometric literatures that have

produced elasticity estimates. However, to close the model, it is necessary to assign numerical

values to many additional parameters. Researchers in the Scarf tradition accomplish this through

a process of calibration, choosing the parameter values so that the base-case equilibrium

replicates the benchmark data exactly.

Most of Scarf’s students worked on applications of general equilibrium (Arrow and

Timothy Kehoe 1994, 174).5 While less actively involved in policy making than the Australian

modelers or those at the World Bank, a few researchers in the Scarf tradition have built applied

policy models, including those for the U.S. Treasury to simulate tax-policy changes, and country

models of Mexico and the Soviet Union. However, much of the work in the Scarf tradition

focused on numerical explorations of theoretical claims.

AGE Analysis Reaches Maturity

AGE modeling surged in the late 1970s, along with the growth in computing power. The

Conference on Applied General Equilibrium Analysis in Coronado, California, in 1981, marked

the coming of age of AGE analysis. The conference brought together the traditions of Johansen,

Jorgenson, and Scarf-Shoven-Whalley. Attendees included a large number of those who would

make major contributions to AGE analysis, including Ballard, Dixon, Don Fullerton, Lawrence

12

Goulder, Jorgenson, Robinson, Scarf, Shoven, and Whalley. The resulting conference volume

(Scarf and Shoven 1984) demonstrated the wide range of problems that modelers could tackle.

As interest in AGE analysis grew, so did the publication of model-description books and

conference volumes, including Dixon, Parmenter, John Sutton, and D.P. Vincent 1982; Scarf and

Shoven 1984; Ballard, Fullerton, Shoven, and Whalley 1985; Alan Manne 1985; John Piggott

and Whalley 1985; Lars Bergman, Jorgenson, and Ernö Zalai 1990; and Shoven and Whalley

1992. Numerous papers based on AGE models were published in top-tier journals during this

period, including Shoven and Whalley 1972 and 1973; Hudson and Jorgenson 1974; Shoven

1976; Fullerton, A. Thomas King, Shoven, and Whalley 1981; Mansur and Whalley 1982;

Fullerton 1983; Richard Harris 1984; David Cox and Harris 1985; and Ballard, Shoven, and

Whalley 1985. “By the mid-1980s, the applied general equilibrium models were workhorse

tools for economic policy evaluation” (Shoven and Whalley 2015, 5). Some went even further,

arguing that AGE analysis was superior to empirical econometrics because of its grounding in

mainstream neoclassical models (Dixon 2006; O’Rourke 1995; Shoven and Whalley 1984).

The rapid growth of AGE research led inevitably to growing pains. Well into the 1980s,

a large fraction of AGE models continued to use special-purpose computer programs, most

frequently written in FORTRAN. Coding choices, personal peculiarities, miscommunication

with coders, and differences among software versions and computer operating systems meant

that simulations could not always easily be verified and shared across different groups of

researchers (Mark Horridge, Alex Meeraus, Ken Pearson, and Thomas Rutherford 2013). This

led to accusations that AGE models were “black boxes” which were “a bit dubious. They are

huge, they are complex, and they…produce results that cannot be traced to an accessibly small

set of simple assumptions.” (Michael Rauscher 1999, F799)

13

In response, the AGE community moved to achieve greater consensus regarding

methods, tools, and data (Dixon 2006). While this included standardization of data sources and

general agreement on the specification of some model equations, perhaps the largest

improvement came from the development of two general-purpose computing packages that could

perform AGE calculations: GAMS (General Algebraic Modeling System) and GEMPACK

(General Equilibrium Modeling Package). These computer programs are now used by more than

80 percent of modelers, and while “it is still possible to implement and solve CGE models using

other software…if you want your model to be understood by other policy modelers, it pays to

use software familiar to them” (Horridge, et al. 2013, 1331).

GAMS was modified for economic applications at the World Bank beginning in the mid-

1970s. GEMPACK was developed specifically for AGE analysis by Dixon’s team at the Center

of Policy Studies (CoPS). CoPS unveiled the program in 1984, simultaneously launching

training courses on GEMPACK, the ORANI model, and general-equilibrium modeling.

However, it was not until 1991 that the program could accurately simulate large nonlinear

models (Horridge, et al. 2013). “GAMS and GEMPACK dramatically reduced the required level

of knowledge of numerical methods and computing, and also reduced the time required in

writing and checking computer programs. Both software systems facilitated communication by

allowing models to be transferred conveniently between users and between sites” (Dixon and

Rimmer 2010, 12).

Simultaneously, AGE analysis became increasingly associated with policy work, as the

World Bank and CoPS emerged as global centers. Their roles were solidified in part by the

development of the software packages. The models developed by CoPS “have probably had

14

more influence on policy than has any other AGE model”, largely because of “the interaction of

academic economists with government officials” (Ballard 1992, 1501).

However, for the most part, AGE analysis remained confined to a limited number of

fields of economics. According to O’Rourke (1995, 1), “the only courses in which you actually

get to use GE models tend to be international trade and public finance,” as well as economic

development. (In the following years, the field of environmental economics would also see a

surge of AGE analysis.) This may be attributed partly to the evolution of the Scarf tradition,

which built on the two-sector models in trade and public finance, as well as the types of

questions that AGE models are best equipped to tackle.

The Shift in Publishing Patterns

A Google Ngram of “applied general equilibrium” and “computable general equilibrium”

shows a sharp upward trajectory from 1980 to 1994, after which the use of the terms in books

declines noticeably. An examination of journal publishing patterns reveals that, since the late

1980s and early 1990s, articles employing AGE methods have been found almost exclusively in

field journals. Since 1987, of 609 articles using AGE analysis published in journals indexed by

Web of Science, only 6.4 percent are in economics journals ranked in the top fifty.6 By way of

comparison, “regression” yields 5535 results over the same period, with 18 percent appearing in

top-fifty journals. “Monte Carlo” appears in the titles of 963 papers, 13.5 percent of which were

published in top-fifty journals. Other papers in this volume demonstrate the concurrent rise of

experimental economics, game theory, and quasi-experimental methods (Andrej Svorenčík 2016;

Matthew Panhans and John Singleton 2016) and the decline of ‘pure’ theory (Jeff Biddle and

15

Daniel Hamermesh 2016; see also Backhouse and Cherrier 2014). These papers suggest that

significant shifts occurred in what is perceived as top-tier research.

Since 1987, only nine articles using AGE analysis have been published in the top five

journals, none more recently than 2002. In contrast, 51 articles using AGE methods were

published in the top five from 1970 to 1986. 7 Currently, the most frequent publishing outlets are

Journal of Policy Modeling (63 papers since 1987) and Economic Modelling (51).8

The decline of AGE analysis in top journals raised questions about the health of the field,

a concern that has been voiced since the mid-1990s. Dixon and Parmenter (1996) asked “Is the

field past its peak? Is it in danger of going stale?” Mitra-Kahn attributed the concern to “an

institutional shift” as early as the late 1980s, that took applied general-equilibrium modeling

“partly out of academia, and completely into the policy arena” where “theory started to yield to

empirical necessity” (2008, 22). Dixon’s and Jorgenson’s (2012) collection gives evidence of

this shift, as practical policy work vastly outweighs the more ‘academic’ contributions that were

common in earlier AGE collections.

What Happened?

In this section, we consider several explanations for the apparent marginalization of AGE

work since the 1990s. Before continuing, however, we need to emphasize that high-quality work

continues to be carried out by AGE researchers, even though little of that work is ending up in

the top journals. Much of this story is interrelated with the evolution of what ‘applied’

economics entailed, and a growing distinction between economic research with immediate policy

relevance – increasingly associated with economists working in government, think tanks, and

international institutions – and an applied economics that is primarily conducted by economists

16

in academic institutions. Dixon (2006, 19) warns that, if a research team is located at a

university, “… researchers may then respond to the imperatives of academic publishing. These

are technical novelty, adherence to current academic fashions and succinctness” (italics added).

Dixon asserts that these imperatives are at odds with building AGE models, which “requires

application of relevant economic theory (rather than novel or fashionable theory)” (ibid).

Natural Ebb and Flow

At least part of the trend can possibly be attributed to mere changes in fashion. In many

disciplines, it is common for lines of inquiry to experience an ebb and flow over time.

More substantively, it is possible that the most important problems that could logically be

addressed by AGE models had been resolved, leaving ‘only’ policy analysis. O’Rourke (1995,

1) argued that while “CGE models are useful in their place…the range of questions which they

can satisfactorily answer is rather narrow.” After two decades of work, economists had

developed a good sense of the answers that could be provided by AGE models to central

economic questions. According to this view, it is only natural that AGE analysis should

experience a relative decline.9

Barriers to Entry

Another possibility is that high barriers to entry into the field of AGE analysis

discouraged the development of alternative competing models, leaving a few dominant

centers, but an absence of new ground-breaking work. The development of GAMS and

GEMPACK “played a key role” in establishing the World Bank and CoPS as centers for

AGE work (Dixon and Rimmer 2010, 11). However, despite claims that standardized

17

software has made AGE analysis accessible to more people, today’s AGE centers are

highly institutionalized policy-analysis centers, with large teams of supporting graduate

students, faculty, staff, and policy experts.

Mitra-Kahn (2008) documented the rise of a team of AGE researchers at the World Bank

in the 1980s and 1990s. Similarly, CoPS has relied on large teams of researchers with financial

support from the government. This institutional structure was pivotal for CoPS becoming a

global AGE center (Dixon 2006).

Lack of Empirical Verification

It is possible for AGE modelers to assess the sensitivity of their results with respect to

changes in key parameters, and hundreds of research papers written by AGE modelers do include

sensitivity analysis.10 However, AGE models are not usually empirically testable in the sense in

which many economists understand testability. These models are typically used to simulate the

effects of proposed policy changes, rather than to track the effects of actual policies. Thus many

AGE studies consider policies that are never actually implemented. When a policy that has been

studied using an AGE model is implemented, the actual policy usually comes in a form that is

not fully consistent with the model. As a result, it is usually not possible to collect data that

would provide a truly convincing test of whether the predicted effects occur. Consequently,

some empirically minded economists have been skeptical of the results that emerge from AGE

studies.

18

Sensitivity to Model Specification

Expanded computing power allowed researchers to build increasingly sophisticated

models with more sectors, more types of agents, and multiple governmental policies, but it was

not clear that the additional detail improved the quality of the insights. Tyler Fox and Fullerton

(1991) compare the full model of Ballard, Fullerton, Shoven, and Whalley (1985) with a greatly

simplified model that eliminates many of the details of the larger model. They show that

changes in the assumed elasticity of substitution between labor and capital have affect the results

more than all of the modeling complications combined.

Lans Bovenberg and Goulder (1996) build on an earlier analytical model by Bovenberg

and Ruud de Mooij (1994) to assess the effects of Pigouvian environmental taxes in the presence

of pre-existing tax distortions. They find that, as a result of interactions with the rest of the tax

system, the optimal Pigouvian tax is always less than the first-best Pigouvian tax that would

obtain in the absence of other distortions. However, this result depends critically on their

assumption that the demand for goods is homothetic, so that all expenditure elasticities are equal

to one. Ballard, John Goddeeris, and Sang-Kyum Kim (2005) show that, if some goods have

expenditure elasticities less than one, the optimal Pigouvian tax can exceed the first-best tax.

A similar result from the environmental-economics literature is found in Kathy Baylis,

Fullerton, and Daniel Karney (2013). Many AGE models have found that a pollution restriction

in one region or sector will be offset by an increase in pollution elsewhere, which is known as

“leakage”. However, Baylis, Fullerton, and Karney show that this result can be reversed, leading

to “negative leakage”, if the model is changed to allow for interregional factor mobility. The

result turns on the assumption about factor mobility, and not on the number of sectors, the

number of regions, the energy types, or other details of the model.

19

It is difficult to know what effect these results have had on the overall reputation of AGE

analysis. However, it is possible that these and other examples of sensitivity to model

specification may have led to skepticism regarding AGE analysis, at least in some circles.

Disagreements among Different Schools of AGE Analysis

Another possible explanation for the marginalization of AGE work can be found in the

debates over the inner workings of the models from different AGE traditions.

The calibration approach used to close the model in the Scarf tradition has been

criticized because the methods are seen by some as relying too heavily on exogenous estimates

of key elasticities. An alternative to “quick and dirty calibration procedures” (Wiegard 1986,

84) is econometric estimation of a larger fraction of the relevant parameters and elasticity

values. Jorgenson-type models typically use long time series to estimate the parameters of

translog production and consumption functions. However, as Mansur and Whalley (1984)

pointed out, it is simply impossible to rely exclusively on econometric estimation, except in

extremely restrictive settings. Mansur and Whalley (1984, 125) acknowledged the problems

with the calibration approach, but also demonstrated the weaknesses of the econometric

approach: “Statistically well-grounded estimation procedures may indeed only be

implementable for models so simplified that they remove much (or even most) of the detail that

interests policy makers.”

The econometric approach has some very attractive features, but Jorgenson et al. have

overstated the advantages while obscuring the fact that they employ calibration themselves.

For example, Jorgenson, Richard Goettle, Mun Ho, and Wilcoxen (2013) calibrated their base

case to a set of energy-use projections, calibrated the path of emissions to an exogenously

20

specified series, and calibrated government fiscal policies to the assumption that the budget

deficit and current-account deficit will be zero by 2060. They also assumed that, beyond 2020,

the domestic interest rate will remain at 5.47 percent indefinitely.

The ‘estimation versus calibration’ debate between the Jorgenson and Scarf approaches

appears to have generated more heat than light, and it is possible that this has damaged the

reputation of AGE modelers in the wider economics profession.

Questionable Results

In some circumstances, the differences between calibration and estimation are not very

substantial; researchers have exaggerated the differences for rhetorical effect. This is

especially true in static, one-period models, or in the static sub-models of dynamic models. In

a static context, the Scarf ‘calibration’ approach and the Jorgenson ‘estimation’ approach are

merely somewhat different techniques for attempting to anchor the model to empirical reality.

However, one problem, which is potentially of critical importance, arises exclusively in

dynamic models. Many researchers who have used dynamic simulation models have made

little or no attempt to ground the intertemporal behavioral responses in their models to

empirical reality.

In both the Scarf tradition11 and the static parts of the Jorgenson tradition, there is an

attempt to impose behavioral elasticities on the simulation model. Lawrence Summers (1981)

turned this methodology on its head by using a simulation model to generate behavioral

elasticities. Summers’s simulation model abstracted from a large number of forces that could

influence savings behavior. Nevertheless, Summers claimed that the savings elasticities

21

generated by his model (which were an order of magnitude larger than many of the savings

elasticities found in the econometric literature) were “realistic”.

Many other researchers have employed intertemporal simulation models that share

broad structural similarities with the model of Summers. The result is that in a popular class of

AGE models, the savings responses of consumers can be astonishingly large. For example,

Alan Auerbach and Laurence Kotlikoff (1983) simulated the switch from an income tax to a

consumption tax, using a model similar to that of Summers. They found that the policy change

led to an instantaneous increase in the national savings rate, from ten to 42 percent.

Summers (1981) and Auerbach and Kotlikoff (1983) both assumed that labor supply is

fixed. Typically, when researchers extend this type of model to include a labor-leisure choice,

they specify within-period utility as a function of consumption and leisure. As a result, the

same forces that lead to large increases in saving (as consumers reduce current consumption

and augment future consumption) can also lead to large increases in labor supply (as

consumers reduce current leisure). For example, when Jorgenson and Wilcoxen (2002)

simulated the effects of adopting a national retail sales tax, they found an instantaneous

increase of 30 percent in the number of hours worked.

It is possible to construct intertemporal simulation models that do not yield such

unrealistically large intertemporal responses. David Starrett (1982) was the first to analyze the

problem of excessive sensitivity in intertemporal simulation models, and he shows that the

responses can be reduced by incorporating a minimum required level of consumption into the

utility function. Over the years, Auerbach, Kotlikoff, and their collaborators developed

models that were not nearly as sensitive as the model in the original paper. A decades-long

series of refinements to the model culminated in Altig, et al. (2001). One of these refinements

22

is a set of adjustment costs in the investment process. Altig, et al. also use a smaller value for

the intertemporal substitution elasticity than was used by Auerbach and Kotlikoff (1983).

Altig, et al. also assume a smaller rate of technological change. This mutes the intertemporal

responses, because it reduces the present value of the resources that can be reallocated across

time periods in response to a change in the rate of return.

In the preceding paragraph, we have mentioned four of the many ways in which the

excessive sensitivity seen in early intertemporal AGE models can be controlled. It is clearly

possible to eliminate the more extreme behavioral responses that these models can produce, if

the researcher is willing to go to the trouble of refining the model. However, there is great

variation in the extent to which different researchers have paid attention to this problem.

The Black-Box Critique

Extreme results such as the ones mentioned above have almost certainly damaged the

credibility of AGE modelers. As Ballard (2002, 3) puts it, “to the rest of the economics

profession and to the rest of the world, it may appear that our results come from a mysterious

‘black box.’ Some may take the outcome of the black box on faith, but others may not. Faith,

once lost, is not easily restored.”

The extreme results that can arise in intertemporal AGE models are not the only source of

the ‘black-box critique.’ The opaqueness of the computer coding also probably contributed to

the perception. Amedeo Fossati and Wolfgang Wiegard (2002) argue that AGE models are

“black boxes” because the causal links between assumptions and outputs are often obscure for

anyone other than the builder of the model. Judd (1997) asserts that the black-box critique

undermined the status of AGE analysis with journal publishers.12

23

One response to the black-box criticism was for AGE practitioners to publish papers and

books designed to make the workings of AGE models more transparent. These include the

books listed in an earlier section, as well as Fox and Fullerton 1991, and Dixon and Parmenter

1996. Expositions such as these are highly ‘applied’ but are not typically published in top

journals.

The black-box critique is most readily leveled at large-scale models, with large numbers

of economic agents and/or large numbers of goods and sectors. Another response has been to

develop AGE models on a smaller scale. For example, Ballard (1990) and Ballard, Goddeeris,

and Kim (2005) use models with one consumer who must choose from among labor, leisure, and

two goods. Bovenberg and Goulder (1996) deal with the black-box critique in a very appealing

way, by using a small-scale analytical model alongside a larger AGE model, and then comparing

the results.

Of course, many of the questions that have inspired AGE researchers can only be

investigated using large-scale models.13 To the extent that AGE modelers are interested in

questions that can only be addressed with complicated, large-scale models, some degree of

exposure to the black-box critique is probably inevitable. Anyone who uses the full version of

the GTAP model could potentially encounter the black-box criticism. However, the GTAP team

are to be commended for their extraordinary efforts to minimize the black-box criticism by

providing extensive documentation, and by sponsoring training sessions around the world.

Conclusions

Applied general-equilibrium models have been characterized in disparate ways. Tim

Hazledine (1992, 1) suggests that “the idea behind CGE is possibly important enough to be of

24

Nobel quality.” Others see the models as “powerful policy-relevant tool(s)” (Shoven and

Whalley 2015, 5). However, the “actual models are often uneasy compromises compared to

their theoretically pure parents” (Kehoe, T.N. Srinivasan, and Whalley 2005, 9). Critics see

AGE models as little more than black boxes.

In this paper, we document the growth and development of AGE analysis in the 1970s

and 1980s, spurred by advances in general-equilibrium theory and computerization. We consider

several distinct strands of AGE analysis, but focus on the Scarf tradition. We also discuss the

subsequent reduction in the amount of AGE-based research that was published in the top

professional journals. We attribute the relative decline of AGE analysis to a variety of credibility

issues, and to high barriers to entry into the field, as well as to changes in fashion. Additionally,

AGE analysis has increasingly had to share room over the past three decades with a wide variety

of other tools, including experimental and quasi-experimental methods, advanced econometric

methods, and game theory.

Much of the prestige of applied general-equilibrium analysis derived from the “explicit

aim…to convert the Walrasian general equilibrium structure…from an abstract representation of

an economy into realistic models of actual economies…The idea is to use these models to

evaluate policy options” and to be “practical” (Shoven and Whalley 1984, 1008). Additional

benefits were the “detail and complexity” of the models and the ability to “provide substantial

detail for policy makers” through the use of multi-sector, multi-consumer/producer models that

could only be solved by computerized numerical simulation (ibid). As we have seen, however,

‘practical’ and ‘applied’ had different meanings across the different strands of AGE analysis.

Nevertheless, all of this work pushed the boundaries of applied economics.

25

Despite the decrease in AGE-based publications in top journals, it is too early to write the

obituary for AGE analysis. A substantial amount of high-quality AGE work is being done to this

day.

26

References

Adelman, Irma, and Sherman Robinson. 1978. Income Distribution Policy in Developing Countries: A Case Study of Korea. Stanford, CA: Stanford University Press for the World Bank. Altig, David, Alan J. Auerbach, Laurence J. Kotlikoff, Kent A. Smetters, and Jan Walliser. 2001. “Simulating Fundamental Tax Reform in the United States,” American Economic Review 91 (3): 574-595. American Economic Association. 1992. “Herbert E. Scarf – Distinguished Fellow,” American Economic Review 82 (4): 711-712. Arrow, Kenneth J. 1983. “Cowles in the History of Economic Thought,” Presented at The Cowles Fiftieth Anniversary Celebration, June 4, New Haven, CT. http://cowles.yale.edu/sites/default/files/files/conf/50th/50th-arrow.pdf Arrow, Kenneth J., and Gérard Debreu. 1954. “Existence of an Equilibrium for a Competitive Economy,” Econometrica 22 (3): 265 – 290. Arrow, Kenneth J., and Timothy J. Kehoe. 1994. “Distinguished Fellow: Herbert Scarf’s Contributions to Economics,” Journal of Economic Perspectives 8 (4): 161 – 181. Auerbach, Alan J., and Laurence J. Kotlikoff. 1983. “National Savings, Economic Welfare, and the Structure of Taxation,” in Martin Feldstein (ed.), Behavioral Simulation Methods in Tax Policy Analysis. Chicago: University of Chicago Press for the National Bureau of Economic Research: 459-493. Backhouse, Roger, and Béatrice Cherrier. 2014. “Becoming Applied: The Transformation of Economics After 1970,” The Center for the History of Political Economy Working Paper Series No. 2014-15. https://hope.econ.duke.edu/node/1057 Ballard, Charles L. 1988. “The Marginal Efficiency Cost of Redistribution.” American Economic Review 78 (5): 1019-1033. Ballard, Charles L. 1990. “Marginal Welfare Cost Calculations: Differential Analysis vs. Balanced-Budget Analysis,” Journal of Public Economics 41 (2): 263-276. Ballard, Charles L. 1992. “Review of General Equilibrium Modeling and Economic Policy Analysis, edited by Lars Bergman, Dale W. Jorgenson and Ernö Zalai,” Journal of Economic Literature 30 (3): 1500 – 1502. Ballard, Charles L. 2000. “How Many Hours are in a Simulated Day?” Unpublished manuscript, Michigan State University.

27

Ballard, Charles L. 2002. “Studying the Past and Future with Infinite-Horizon Simulation Models,” in Amedeo Fossati and Wolfgang Wiegard (eds.), Policy Evaluation with Computable General Equilibrium Models. New York: Routledge: 3 – 19. Ballard, Charles L. 2015. “Review of Double Dividend: Environmental Taxes and Fiscal Reform in the United States, by Dale W. Jorgenson, Richard J. Goettle, Mun S. Ho, and Peter J. Wilcoxen,” National Tax Journal 68 (2): 459-466. Ballard, Charles L., Don Fullerton, John B. Shoven, and John Whalley. 1985. A General Equilibrium Model for Tax Policy Evaluation. Chicago: University of Chicago Press for the National Bureau of Economic Research. Ballard, Charles L., John H. Goddeeris, and Sang-Kyum Kim. 2005. “Non-Homothetic Preferences and the Non-Environmental Effects of Environmental Taxes.” International Tax and Public Finance 12 (2): 115-130. Ballard, Charles L., John B. Shoven, and John Whalley. 1985. “General Equilibrium Computations of the Marginal Welfare Costs of Taxes in the United States,” American Economic Review 75 (1): 128-138. Baylis, Kathy, Don Fullerton, and Daniel H. Karney. 2014. “Negative Leakage.” Journal of the Association of Environmental and Resource Economists 1 (1): 51-73. Bergman, Lars. 1990. “The Development of Computable General Equilibrium Modeling,” in Lars Bergman, Dale W. Jorgenson, and Ernö Zalai (eds.), General Equilibrium Modeling and Economic Policy Analysis. Cambridge, MA: Basil Blackwell: 3 – 32. Bergman, Lars, Dale W. Jorgenson, and Ernö Zalai (eds.), General Equilibrium Modeling and Economic Policy Analysis. Cambridge, MA: Basil Blackwell. Biddle, Jeff E., and Daniel S. Hamermesh. 2016. “Theory and Measurement: Emergence, Consolidation, and Erosion of a Consensus,” 2016 HOPE Conference: Becoming Applied: The Transformation of Economics After 1970, April 1 – 2. Duke University, Durham, NC. Bjerkholt, Olav. 2009. “The Making of the Leif Johansen Multi-Sectoral Model,” History of Economic Ideas 17 (3): 103 – 126. Blaug, Mark. 1992. Economic Theory in Retrospect, 4th Edition. New York, NY: Cambridge University Press. Bovenberg, A. Lans, and Lawrence H. Goulder. 1996. “Optimal Environmental Taxation in the Presence of Other Taxes: General-Equilibrium Analyses,” American Economic Review 86 (4): 985-1000. Bovenberg, A. Lans, and Ruud de Mooij. 1994. “Environmental Levies and Distortionary Taxation,” American Economic Review 84 (4): 1085-1089.

28

Cherrier, Béatrice. 2015. “Classifying Economics: A History of the JEL Codes,” SSRN Working Paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2537382 Combes, Pierre-Philippe, and Laurent Linnemer. 2010. “Inferring Missing Citations: A Quantitative Multi-Criteria Ranking of All Journals in Economics.” Working Paper. https://server1.tepper.cmu.edu/barnett/journal_ranking_2010.pdf Cox, David, and Richard Harris. 1985, “Trade Liberalization and Industrial Organization: Some Estimates for Canada,” Journal of Political Economy 93 (1): 115 – 145. Cragg, John G., Arnold C. Harberger, and Peter Mieszkowski. 1967. “Empirical Evidence on the Incidence of the Corporate Income Tax,” Journal of Political Economy 75 (6): 811 – 821. Dixon, Peter B. 2006. “Evidence-based Trade Policy Decision Making in Australia and the Development of Computable General Equilibrium Modelling,” Center of Policy Studies Working Paper. Monash University. Dixon, Peter B., and Dale W. Jorgenson (eds.). 2012. Handbook of Computable General Equilibrium Modeling. Amsterdam: North-Holland. Dixon, Peter B., and Maureen T. Rimmer. 2010. “Johansen’s Contribution to CGE Modeling: Originator and Guiding Light for 50 Years,” Working Paper, Center of Policy Studies, Monash University, General Paper No. G-203. Dixon, Peter B., and B.R. Parmenter. 1996. “Computable General Equilibrium Modeling for Policy Analysis and Forecasting,” in Hans M. Amman, David A. Kendrick and John Rust (eds.), Handbook of Computational Economics, Volume 1. Amsterdam: North Holland: 3 – 85. Dixon, Peter B., B.R. Parmenter, John Sutton, and D.P. Vincent. 1982. ORANI: A Multisectoral Model of the Australian Economy. Amsterdam: North-Holland. Düppe, Till, and E. Roy Weintraub. 2014. Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit. Princeton, NJ: Princeton University Press. Foley, Duncan. 1999. “The Ins and Outs of Late Twentieth-Century Economics,” in Arnold Heertje (ed.), The Makers of Modern Economics. Northampton, MA: Edward Elgar: 70 – 118. Fossati, Amedeo, and Wolfgang Wiegard. 2002. “Introduction,” in Amedeo Fossati and Wolfgang Wiegard (eds.), Policy Evaluation with Computable General Equilibrium Models. New York: Routledge: xvii - xxiii. Fox, Tyler, and Don Fullerton. 1991. “The Irrelevance of Detail in a Computable General Equilibrium Model,” Economics Letters 36 (1): 67 – 70.

29

Fullerton, Don. 1983. “Transition Losses of Partially Mobile Industry-Specific Capital,” Quarterly Journal of Economics 98 (1): 107-126. Fullerton, Don, A. Thomas King, John B. Shoven, and John Whalley. 1981. “Corporate Tax Integration in the United States: A General Equilibrium Approach,” American Economic Review 71 (4): 677-691. Georgescu-Roegen, Nicholas. 1950. “Leontief’s System in Light of Recent Results,” The Review of Economics and Statistics 32 (3): 214- 222. Halsmayer, Verena. 2016. “‘Applying Theory’ to Data and Policy-Making?” 2016 HOPE Conference: Becoming Applied: The Transformation of Economics After 1970, April 1 – 2. Duke University, Durham, NC. Harberger, Arnold C. 1962. “The Incidence of the Corporate Income Tax,” Journal of Political Economy 70 (3): 215 – 240. Harris, Richard. 1984. “Applied General Equilibrium Analysis of Small Open Economies with Scale Economies and Imperfect Competition,” American Economic Review 74 (5): 1016 – 1032. Hazledine, Tim. 1992. “A Critique of Computable General Equilibrium Models for Trade Policy Analysis,” Conference Paper, International Agricultural Trade Research Consortium, Dec. 12 – 14, 1991. Heckscher, Eli. 1949. “The Effect of Foreign Trade on the Distribution of Income,” in Howard S. Ellis and Lloyd A. Metzler (eds.), Readings in the Theory of International Trade. Philadelphia: The Blakiston Co. for the American Economic Association: 272-300. Hertel, Thomas W. (ed.) 1997. Global Trade Analysis: Modeling and Applications. Cambridge, UK, New York, and Melbourne: Cambridge University Press. Horridge, Mark, Alex Meeraus, Ken Pearson, and Thomas F. Rutherford. 2013. “Solution Software for Computable General Equilibrium Modeling,” in Peter B. Dixon and Dale W. Jorgenson, (eds.), Handbook of Computable General Equilibrium Modeling. Amsterdam: North Holland: 1331 - 1381. Hudson, Edward A., and Dale W. Jorgenson. 1974. “U.S. Energy Policy and Economic Growth, 1975 – 2000,” Bell Journal of Economics and Management Science 5 (2): 461 – 514. Johansen, Leif. 1960 [1974]. A Multisectoral Study of Economic Growth. Amsterdam: North-Holland. Johnson, Harry G. 1951-1952. “Optimum Welfare and Maximum Revenue Tariffs,” Review of Economic Studies 19 (1): 28-35.

30

Johnson, Harry G. 1956. “General Equilibrium Analysis of Excise Taxes: Comment,” American Economic Review 46 (1): 151-156. Jorgenson, Dale W., Richard J. Goettle, Mun S. Ho, and Peter J. Wilcoxen. 2013. Double Dividend: Environmental Taxes and Fiscal Reform in the United States. Cambridge, MA: MIT Press. Jorgenson, Dale W., and Peter J. Wilcoxen. 2002. “The Economic Impact of Fundamental Tax Reform,” in George R. Zodrow and Peter Mieszkowski (eds.), United States Tax Reform in the 21st Century. Cambridge, UK: Cambridge University Press: 55-88. Judd, Kenneth L. 1997. “Computational Economics and Economic Theory: Substitutes or Complements?” Journal of Economic Dynamics and Control 21 (6): 907 – 942. Kalaitzidakis, Pantelis, Theofanis P. Mamuneas, and Thanasis Stengos. 2011. “An Updated Ranking of Academic Journals in Economics,” The Canadian Journal of Economics 44 (4): 1525-1538. Kehoe, Timothy J. 1987. “Review of Introduction to the Use of General Equilibrium Analysis, by Richard R. Cornwall,” Economica 54 (214): 266 – 267. Kehoe, Timothy J., and Edward C. Prescott. 1995. “Introduction to the Symposium: The Discipline of Applied General Equilibrium,” Economic Theory 6 (1): 1- 11. Kehoe, Timothy J., T.N. Srinivasan, and John Whalley. 2005. “Introduction,” in Timothy J. Kehoe, T.N. Srinivasan, and John Whalley (eds.), Frontiers in Applied General Equilibrium Modeling. Cambridge, UK: Cambridge University Press: 1-12. Koopmans, Tjalling C. (ed.). 1951. Activity Analysis of Production and Allocation. New York: Wiley. Krzyzaniak, Marian, and Richard A. Musgrave. 1968. “Incidence of the Corporation Income Tax in U.S. Manufacturing: Comment,” American Economic Review 58 (5): 1358 – 1360. Leontief, Wassily W. 1936. “Quantitative Input and Output Relations in the Economic Systems of the United States,” Review of Economics and Statistics 18 (3): 105 – 125. Manne, Alan S. 1985. Economic Equilibrium: Model Formulation and Solution. Berlin: Springer. Mansur, Ahsan, and John Whalley. 1982. “A Decomposition Algorithm for General Equilibrium Computation with Application to International Trade Models,” Econometrica 50 (6): 1547 – 1557.

31

Mansur Ahsan, and John Whalley. 1984. “Numerical Specification of Applied General Equilibrium Models: Estimation, Calibration and Data,” in Herbert E. Scarf and John B. Shoven (eds.), Applied General Equilibrium Analysis. New York: Cambridge University Press: 69-127. Mathiesen, Lars. 1985. “Computation of Economic Equilibria by a Sequence of Linear Complementarity Problems,” Mathematical Programming Study 23: 144-162. McKenzie, Lionel W. 1954. “On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems,” Econometrica 22 (2): 147-161. Meade, James E. 1955. The Theory of International Economic Policy, vol. 2: Trade and Welfare. Oxford, UK: Oxford University Press. Merrill, O.H. 1972. “Applications and Extensions of an Algorithm that Computes Fixed Points to Certain Upper Semi-Continuous Point-to-Set Mappings,” Unpublished Ph.D. dissertation, University of Michigan. Mieszkowski, Peter M. 1967. “On the Theory of Tax Incidence,” Journal of Political Economy 75 (3): 250 – 262. Mitra-Kahn, Benjamin. 2008. “Debunking the Myths of Computable General Equilibrium Models,” Schwartz Center for Economic Policy Analysis and Department of Economics, The New School for Social Research, Working Paper Series. O’Rourke, Kevin. 1995. “Computable General Equilibrium Models and Economic History,” presented at the 20th Annual Meeting, Social Science History Association, November 16 – 19, 1995, in Chicago, IL. Panhans, Matthew T., and John D. Singleton. 2016. “The Empirical Economist’s Toolkit: From Models to Methods,” 2016 HOPE Conference: Becoming Applied: The Transformation of Economics After 1970, April 1 – 2. Duke University, Durham, NC. Piggott, John, and John Whalley (eds.). 1985. New Developments in Applied General Equilibrium Analysis. Cambridge, UK: Cambridge University Press. Rauscher, Michael. 1999. “Review of Global Trade Analysis: Modeling and Applications, edited by Thomas W. Hertel,” Economic Journal 109 (459): F799 – F800. Roberts, Sam. 2015. “Herbert Scarf, An Economist’s Mathematician, Dies at 85,” New York Times (November 21). Samuelson, Paul A. 1948. “International Trade and the Equalisation of Factor Prices,” Economic Journal 58 (230): 163-184. Scarf, Herbert. 1967. “The Approximation of Fixed Points of a Continuous Mapping,” SIAM Journal of Applied Mathematics 15 (5): 1328-1343.

32

Scarf, Herbert (with the collaboration of Terje Hansen). 1973. The Computation of Economic Equilibria. New Haven, CT: Yale University Press. Scarf, Herbert E. 1994. “Foreword,” in Jean Mercenier and T.N. Srinivasan (eds.), Applied General Equilibrium and Economic Development: Present Achievements and Future Trends, v – vii. Ann Arbor, MI: University of Michigan Press. Scarf, Herbert E., and John B. Shoven (eds.). 1984 [2008]. Applied General Equilibrium Analysis. New York: Cambridge University Press.

Schumpeter, Joseph A. 1954. History of Economic Analysis. New York, NY: Oxford University Press.

Shoven, John B. 1976. “The Incidence and Efficiency Effects of Taxes on Income from Capital,” Journal of Political Economy 84 (6): 1261-1284. Shoven, John B., and John Whalley. 1972. “A General Equilibrium Calculation of the Effects of Differential Taxation of Income from Capital in the U.S.,” Journal of Public Economics 1 (3): 281 – 321. Shoven, John B., and John Whalley. 1973. “General Equilibrium with Taxes: A Computational Procedure and an Existence Proof,” Review of Economic Studies 40 (4): 475 – 489. Shoven, John B., and John Whalley. 1984. “Applied General-Equilibrium Models of Taxation and International Trade: An Introduction and Survey,” Journal of Economic Literature 22 (3): 1007 – 1051. Shoven, John B., and John Whalley. 1992 [1995]. Applying General Equilibrium. New York: Cambridge University Press. Shoven, John B., and John Whalley. 2015. “Herbert Scarf (1930 – 2015),” for the Econometric Society. http://www.econometricsociety.org/sites/default/files/inmemoriam/scarf_shoven_whalley.pdf Starrett, David A. 1982. “Long Run Savings Elasticities in the Life Cycle Model.” Research Paper No. 24, Stanford Workshop in the Microeconomics of Factor Markets. Department of Economics, Stanford University. Summers, Lawrence H. 1981. “Capital Taxation and Accumulation in a Life Cycle Growth Model,” American Economic Review 74 (4): 533-544. Svorenčík, Andrej. 2016. “Allocating Airport Slots – The History of Early Applied Experimental Research,” 2016 HOPE Conference: Becoming Applied: The Transformation of Economics After 1970, April 1 – 2. Duke University, Durham, NC.

33

Taylor, Lance. 1983. Structuralist Macroeconomics: Applicable Models for the Third World. New York: Basic Books. Walras, Léon. 1899 [1954]. Éléments d'économie politique pure. Translated into English as Elements of Pure Economics, translated by William Jaffé. London: Allen and Unwin. Wiegard, Wolfgang. 1986. “Review of Applied General Equilibrium Analysis, edited by Herbert E. Scarf and John B. Shoven,” Journal of Economics 46 (1): 82-86.

34

End Notes

1 We exclude the macroeconomic simulation models known as Dynamic Stochastic General

Equilibrium (DSGE), which deserve a separate and detailed consideration.

2 Scarf’s algorithm begins the search for equilibrium at a corner of the simplex, which is

typically far from the actual equilibrium, and it searches over a fixed grid. Thus if Scarf’s

algorithm is to find a close approximation to the equilibrium, it must take a large number of

small steps, which is computationally expensive. This problem was overcome by O.H. Merrill

(1972), whose “restart algorithm” could begin with a rough grid, and quickly move to

successively finer grids. (The Merrill algorithm was used in some of the work of Shoven,

Whalley, and their co-authors.) Lars Mathiesen (1985) and others developed techniques to

calculate equilibria efficiently through a sequence of linear complementarity problems.

Adherents of Johansen models developed very efficient techniques for inverting large matrices.

Others found that quasi-Newton methods and simple tâtonnement algorithms could often

calculate equilibria very quickly. By 1990, researchers could choose from among a large number

of efficient computational algorithms.

3 After moving to Yale in 1963, Scarf regularly taught a two-semester graduate course in

mathematical economics. Scarf’s students were exposed to optimization via linear programming,

Kuhn-Tucker methods, dynamic programming, and “a systematic review of general equilibrium

theory… and including Gérard Debreu’s proof (1959) of existence” (Duncan Foley 1999, 72).

4 Ahsan Mansur and Whalley (1984) were among the first from the Scarf tradition to cite

Johansen.

5 In addition to Shoven and Whalley, Scarf’s students included Rolf Mantel (PhD 1965) on an

alternative algorithm for computing equilibria, Ana María Martirena-Mantel (1966) with a model

35

of economic fluctuations, Terje Hansen (1968) on computing equilibria, Frank Levy (1969) on

demographic issues, Michael Todd (1972) on pivot theory, Andrew Feltenstein (1976) on the

Soviet economy, Marcos Fonseca (1978) on the general-equilibrium effects of international trade

policy, Kehoe (1979) and Ludo van der Heyden (1979) on technical aspects of general-

equilibrium modeling, and Jaime Serra-Puche (1979) on the Mexican economy.

6 Web of Science indexes articles from 1987 through 2015. Terms searched include CGE,

computational general equilibrium, computable general equilibrium, applied general equilibrium,

and numerical equilibrium, and variations that appeared in the title of articles. The data were

accessed on July 16, 2015. For a list of journal rankings, see Kalaitzidakis, Mamuneas, and

Stengos (2011). In the top fifty journals, papers using AGE models were most commonly

published in World Development (nine papers), Journal of Public Economics (six), and Journal

of Development Economics (five).

7 Using JSTOR, we employed the same search terms as in the previous footnote, but also added

“general equilibrium,” limiting our search to American Economic Review, Quarterly Journal of

Economics, Journal of Political Economy, Econometrica, and Review of Economic Studies.

Search returns were then evaluated individually to see whether the article qualified as “applied”

general equilibrium or “theoretical” general equilibrium. A search for “applied general

equilibrium” finds 18 articles before 1987, and one after.

8 These journals are ranked 204 and 191 (Combes and Linnemer 2010). Papers using AGE

methods are frequently published in Energy Policy (ranked 24), American Journal of

Agricultural Economics (22), and Energy Economics (19).

9 By the 1990s, Scarf had shifted his focus to problems of integer programming, and supervised

very few PhDs working on AGE.

36

10 The amount of sensitivity analysis varies widely. Judd (1997) argues that additional sensitivity

testing would give readers a better sense of what was driving the results. It is possible that the

absence of systematic sensitivity analysis in some cases has contributed to a lack of confidence

among members of the economics profession, regarding the results of AGE analyses.

11 The earliest models in the Scarf tradition, developed by Shoven and Whalley, were static, one-

period models. In the late 1970s, they and Fullerton developed a dynamic model in which the

consumption/saving decision in every period is governed by a utility function with two

arguments, defined over present consumption and an annuity that can be purchased with today’s

saving. This model, which is described in detail in Ballard, Fullerton, Shoven, and Whalley

(1985), can be calibrated to any desired elasticity of saving with respect to the rate of return.

Similarly, the labor-supply decision is governed by a utility function defined over current

consumption and current leisure, and can be calibrated to any desired value for the

uncompensated labor-supply elasticity. In turn, the compensated labor-supply elasticity can be

controlled by adjusting the time endowment. (See Ballard 2000.) These model structures

completely avoid the problems of excessive intertemporal responses that are discussed in this

section. The problems arise in models in which consumer behavior is described by a lifetime

utility functional, defined over consumption and leisure in every period. A model with a lifetime

utility functional has some very attractive features, but it does lead to the possibility of excessive

intertemporal responses.

12 Judd (1997, 935) also apportions some of the blame to journal editorial policies, for limiting

important discussion of computational procedures in articles.

13 Even if one sets out to use a small-scale model, it is not always possible to do so. An early

version of the model described in Ballard (1988) had two consumers. In response to requests

37

from editors and referees, the number of consumers was increased to five, and then to ten. The

published version has 384 consumers.