OISCUSSION PAPER

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Development Research Department< Economics and Research Staff

World Bank

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The views presented here are those o f the author, acd they should nJt b e interpreted a s r e f l e c t i n g those of the World Bank

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Abstract

Mul t i sec tor economy-wide models have long been used t o analyze - pol icy problems and the c h a r a c t e r i s t i c s of growth I n developing c o u n t r f e s ,

Many of these models have attempted t o incorpora te ' ' s t r u c t u r a l i s t " -

fee tu res such a s r i g i d i t i e s , l imi ted s u b s t i t u t i o n p o s s i b i l i t i e s , i m p e r f e c t

markets, and d i sequ i l ib r i cm adjustment mechanisrr.~. Two d i f f e r e n t mode l l ing

methodo lo~ ies have been widely used: . ( l ) l i n e a r and non l inea r p r o g r a m i n g

models, which involve optimization a t t h e economy-wide l e v e l , and (2) ooopnta3le

general equi l ibr ium (CCE) nodels which s imula te the workings of a sps tzm

of interdependent markets. It has long been recognized t h a t , under strong

assu iq t ions , the re a r e formal s i n i l a r i t i e s between t h e market p r i c e s

determined i n a CGE node1 and the shadow p r i c e s generated i n c e r t a i n

programmicg models: Howsver, incorpora t ing s t r u c t u r a l i s t f e a t u r e s r a i s e s

a nr~nber of t h e o r e t i c a l d i f f i c u l t i e s i n i n t e r p r e t i n g the shadow p r i c e s

generated by programing models, and i n reconc i l ing the two d i f f e r e n t

modelling apprazches. I n t h i s paper, w e d i s c a s s the r e l a t i o n s h i p s between

the two modelling approaches under a v a r i e t y of assumptions a5out t h e way

I n w1,ich an economy opera tes and, second, consider approaches t o e x t e n d i n g

the fralocvcrk t o represent more r e a l i s t i c but t h c o r e t i c a l l y more d i f f i c u l r

a systems. We c ~ n s i d e r , i n p a r t i c u l a r , i s s u e s of ma.:roecor.omic el;.clflitrium, I

Table of Contents -

1. Introduction

. 2. Optimization and Market Equilibrium

3. Competitive Equilibrium Models

4. Model Specification and Empirical Solution

5. Prices in Planning Models

6. Macroeconomic Equilibrium

7. Conclusion

References

* I Equilibrium and Prices in Multisector Models -

1. Introduction

Advances in economics-indeed, in any science--occur through an . interplay among different strands or styles of analysis. First, a complex

? reality must be simplified and "stylized" in order to isolate the most

important features relevant for a particular problem. Second, theories must ' -

be developed that explain the relationships among the various important ,

factors. Finally, empirical models are needed to quantify the effects under

study and to test the validity of both the stylization and the theory as

representations of the real world. There is a natural tension among the three

strands of analysis, but any real understanding of how economic systems

function and evolve must be based on a successful integration.Ll In

development economics, both the need for integration and the tension are

widely perceived, and the difficulties in achieving a satisfactory integration

are also especially great.

In his career, Hollis Chenery is rare in that he has made major

contributions in all three strands of analysis. His work on "patterns of

development" has been very important in determining the stylized facts of long 4

run growth and structural ;hange. He has had a majo; impact on the

theoretical development and application of multisector models, and he has also -

- * I We are il;debted to Irma Adelman, Mathias Dewatripont, Peter Dixon, Jeffrey -

Lewis, ~ $ n Manne, T.N. Srinivasan, Lance Taylor, Jean Waelbroeck, and - Larry Westphal for comments Gn earlier drafts.

11 The current shambles in macroeconomics is a good example of what happens - when theory, empirical models, and stylized facts diverge.

been a p e r s i s t e n t c r i t i c of t h e n a i v e a p p l i c a t i o n of " s t a n d a r d " t h e o r y t o

a n a l y z e problems of d e v e l o p i n g c o u n t r i e s . H e h a s a rgued f o r a " s t r u c t u r a l i s t "

a p p r o a c h t o t h e o r i z i n g and model b u i l d i n g t h a t emphas izss r i g i d i t i e s , l i m i t e d

s u b s t i t u t i o n p o s s i b i l i t i e s , i m p e r f e c t m a r k e t s , and d i s e q u i l i b r i u m a d j u s t m e n t

mechanisms .A/ M u l t i s e c t o r models i n t h i s "Chener ian" t r a d i t i o n , which i n c l u d e

most models a p p l i e d t o d e v e l o p i n g c o u n t r i e s , a r e c h a r a c t e r i z e d by a t t e m p t s t o

c a p t u r e such s t r u c t u r a l i s t f e a t u r e s , o f t e n by imposing v a r i o u s s p e c i a l

I n e q u a l i t y c o n s t r a i n t s i n t h e c o n t e x t of l i n e a r o r n o n l i n e a r programming

3 / models .- More r e c e n t l y , economywide s i m u l a t i o n models have been deve loped

which s e e k t o c a p t u r e t h e r o l e of p r i c e s and t h e workings of t h e market .

system. These e q i r i c a l g e n e r a l e q u i l i b r i u m models o p e r a t e by s p e c i f y i n g t h e

b e h a v i o r a l r u l e s f o r t h e v a r i o u s economic a c t o r s (e.g. , p r o d u c e r s and

consumers) and e x p l i c i t l y s o l v i n g t h e r e s u l t i n g h i g h l y n o n l i n e a r model t o

y i e l d m a r k e t - c l e a r i n g p r i c e s and e q u i l i b r i u m v a l u e s f o r a l l v a r i a b l e s . W h i l e

t h e y have been wide ly used t o s i m u l a t e p e r f e c t l y c o m p e t i t i v e m a r k e t s , . t h e r e

a r e a l s o many evamples of m u l t i s e c t o r g e n e r a l e q u i l i b r i u m models which embody

" s t r u c t u r a l i s t " e l e m e n t s such a s b e h a v i o r a l r i g i d i t i e s o r c o n s t r a i n t s on t h e

o p e r a t i o n of i m p o r t a n t marke t s ( e s p e c i a l l y t h e f a c t o r and f o r e i g n exchange

4 / marke t s X.- , I

I n c o r p o r a t i n g s t r u c t u r a l i s t f e a t u r e s i n t o m u l t i s e c t o r models h a s l e d -

,.u 6. L L r I . ~ ~ . l ~ l ~ ~ i i l u ~ i ~ . V L I . ~ L I S A U L ~ oecdubtf ~ p 1 r ~ c a l pracclce has o f c e n g o t t e n b L

21 See , f o r example, Chenery (1975) and Chenery ( 1 9 7 9 ) , C h a p t e r 2 . - 3 / For some examples , s e e Chenery (1971, 1 9 7 9 ) ; B l i t z e r , C l a r k and -

T a y l o r ( 1 9 7 5 ) ; and Adelman and Thorbecke (1966) .

4 / For a s u r v e y of development models, see D e r v i s , de Melo, and Robinsor? - (1982) .

ahead of t F e a v a i l a b l e t h e o r y . T h e r e a r e e s s e n t i a l l y two s o u r c e s of

problems. F i r s t , many cf t i e c o n s t r a i n t s imposed i n b o t h programoing a n d

s i m u l a t i o n models a r e based on nacroeconomic theory-- for example , p r o b l e m s of

s a v i n g s - i n v e s t m e n t e q u i l i b r i u m o r f o r e i g n exchange c o n s t r a i n t s . However,

m u l t i s e c t o r models a r e f u n d a m e n t a l l y based on n e o c l a s s i c a l , multi-market.,

g e n e r a l e q u i l i b r i u m t h e o r y t h a t is e s s e n t i a l l y W a l r a s i a n , w i t h l i t t l e room f o r

problems of macroeconomic " imbalance . "l! Any i n c o r p o r a t i o n of such

macroeconomic f e a t u r e s i n t o e m 2 i r i c a l models h a s a n -- ad hoc f l a v o r t h a t ar ises

from t h e f a c t t h a t t h e r e i s a s y e t no a c c e p t a b l e t h e o r e t i c a l r e c o n c i l i a t i o n

61 between t h e two b r a n c h e s of theory.-

F o r example , t h e r e a r e many macro mc.'rls i n which nominal wages -

a n d / o r t h e exchange r a t e a r e assumed t o be f i x e d , o r t o v a r y t o a c h i e v e some

n o t i o n of macro "ba lance . " C a p t u r i n g t h e i m p l i c a t i o n s of such a s p e c i f i c a t i o n

may r e q u i r e t h e i n c l u s i o n of v a r i o u s k i n d s of a s s e t s ( i n c l u d i n g money) and

a s s e t m a r k e t s i n t o t h e model, which r a i s e s s e r l o u s t h e o r e t i c a l problems i n

i n t e g r a t i n g r e a l and monetary v a r i a b l e s i n a g e n e r a l e q u i l i b r i u m model.

However, it. is o f t e n p o s s i b l e t o c a p t u r e macro " s t o r i e s " i n mul t i rna rke t

g e n e r a l e q u i l i b r i u m models i n which o n l y r e l a t i v e p r i c e s m a t t e r . While t h e

r e s u l t i n g models a r e no l o n g e r s t r i c t l y W a l r a s i a n , t h e y n o n e t h e l e s s do n o t

7 / r e q u i r e t h e e x p l i c i t c o n s i d e r a t i o n ofimoney o r o t h e r a s s e t s . - . t

A second s o u r c e of t e n s i o n a r i s e s f rom t h e fac t . t h a t , e v e n w i t h i n t h e -

- - *

5 / A s D e r v i s , de He18 and Robinson (1982) p u t i t (p . 6 ) : "Walras racer t h a n - Keynes is t h e p a t r o n s a i n t of m u l t i s e c t o r a n a l y s i s . " -

. . 6 / S e e , f o r example , Wein t raub (1979) and Hahn (1977) . - 7/ Below, we r e s t r i c t o u r a t t e n t i o n t o s u c h models. However, we w i l l o f t e n -

r e f e r t o "nominal" v a r i a b l e s and magni tudes . C l e a r l y , a l l "nominal" f l o w s i n t h e s e models must be i n t e r p r e t e d i n t e r m s of some n u n e r a i r e , b u t n e e d n o t i n v o l v e money e x p l i c i t - l y .

Walras ian framework, t h e r e a r e d i f f i c u l t i e s i n i n t e r p r e t i n g programming models

a s r e p r e s e n t i n g t h e func t ion ing of marke t systems. It has long been

recognized t h a t t h e r e a r e formal s i m i l a r i t i e s between t h e market p r i c e s

determined i n a g e n e r a l e q u i l i b r i u m system and t h e shadow p r i c e s t h a t a r e

gene ra t ed from c e r t a i n planning models. Y.ie equ iva l ence of "market" and

"shadow" p r i c e s g e n e r a l l y depends on very s t r o n g t h e o r e t i c a l assumptions a b o u t

t h e way agen t s behave and markets work. S ince a c t u a l economies never s a t i s f y

such assumptions, b u i l d e r s of programming models have developed ingen ious ways

of r e l a x i n g t h e s t r i n g e n t assumpt ions , whi le t r y i n g t o p re se rve t h e l i n k s .

between t h e v a r i o u s p r i c e systems. Chenery was deeply involved i n seminal

work i n t h i s a r e a which sought t o ex tend t h e l i n e a r programming frafiework. t o

i nc lude non-l inear s p e c i f i c a t i o n s and more c a r e f u l t r ea tmen t of shadow

p r i c e s . / While such op t imiz ing models came c l o s e t o a n e x p l i c i t

c o n s i d e r a t i o n of marke t -c lear ing p r i c e s , unresolved t h e o r e t i c a l p r o b l e m a r e

e v i d e n t i n most a c t u a l a p p l i c a t i o n s .

T h i s paper has two main o b j e c t i v e s . F i r s t , we seek t o c l a r i f y t h e

r e l a t i o n s h i p between programming models, which invo lve o p t i m i z a t i o n a t t h e

s y s tern-wide l e v e l , and e m p i r i c a l gene ra l e q u i l i b r i u m models which involve

s i m u l a t i n g a system of i n t e rdependen t markets. Second, w e c o n s i d e r approaches I I a

t o ex tending e m p i r i c a l gene ra l e q u i l i b r i u m models t o provide a framework f o r

modeling more r e a l i s t i c b u t t h e o r e t i c a l l y more complex sys tems , e s p e c i a l l y

i nvo lv ing problems of macroeconanic equ i l i b r ium. We cons ide r two sbch macro - i s s u e s : f o r e i g n exchange c o n s t r a i n t s and sav ings - inws tmen t equ i l i b r iu in .

I

Chenery's " two-gap" model i s perhaps t he most famous example which

81 See Chenery and Kretschmer (1956) , Chenery and Uzawa (1956) , and Chenery - and Raduc.he1 (1971). See a l s o Tay lo r (1975).

i n c o r p o r a t e s problems of both f o r e i g n exchange c o n s t r a i n t s and savings-

inves tment e q u i l i b r i u m , and h a s long provided a major focus of d i s c u s s i o n o f

t h e s e problems i n developing countries.?! We a l s o cons ide r more r e c e n t models

of savings- investment e q u i l i b r i u m i n t h e " s t r u c t u r a l i s t " s choo l . . The paper is organized a s fol lows: I n S e c t i o n 2 , we d e f i n e t h e b a s i c

I i n g r e d i e n t s of economywide models, de sc r ibed i n terms of "op t imiza t ion" o r

"market s imu la t i on . " I n S e c t i o n 3, we show how t h e s e two approaches r e f l e c t

t h e same economic framework i f w e restrict our a t t e n t i o n t o pu re ly c o m p e t i t i v e

market systems. S e c t i o n 4 ex t ends t he t h e o r e t i c a l d i s c u s s i o n t o cons ide r

d i f f e r e n t approaches t o s p e c i f y i n g and s o l v i n g e m p i r i c a l models. S e c t i o n 5

goes beyond t h e Walrasian compe t i t i ve framework and c o n s i d e r s how m u l t i s e c t o r

market e q u i l i b r i u m models have been extended t o i n c o r p o r a t e d i f f e r e n t c o n c e p t s

of macroeconomic equi l ib r ium.

2. Op t imiza t ion and Market Equ i l i b r ium

It is convenient t o d e s c r i b e a g e n e r a l e q u i l i b r i u m model i n terms of

i ts: (1 ) a c t o r s , (2 ) behav io ra l r u l e s , (3 ) s i g n a l s , (4) i n s t i t u t i o n a l

s t r u c t u r e , (5 ) system c o n s t r a i n t s and (6) maximand ( i n an op t imiz ing model).

The economic "ac to r s " i n t h e economy a r e t he a g e n t s whose behavior w e

s e e k t o ana lyze and/or whose w e l f a r e m a t t e r s t o p o l i c y makers ( f o r example, 4

f i r m s , consumers, the' gbvernment, and t h e r e s t ok t he world) . I n terms of

1 0 1 d a t a , we must provide t h e economic accoun t s of each of t h e s e agents - -

These ag+ t s o p e r a t e acco rd ing t o behav io ra l r u l e s r e f l e c t i n g t h e i r b a s i c

91 See Chenery and S t r o u t (1966). - 101 For t he e n t i r e model, t h e s e accoun t s can be summarized i n a s o c i a l -

account ing ma t r ix (SAM) whose rows and columns g ive t h e r e c e i p t and expend i tu re flows f o r a l l agen t s . One advantage of t he SAM framework is t h a t i t d e p i c t s i n one t a b l e a l l t h e nominal f lows among t h e a g e n t s i n t h e economy.

mot iva t ion . For example, f i rms a r e t y p i c a l l y assumed t o maximize p r o f i t s and

consumers t o maximize u t i l i t y , s u b j e c t t o v a r i o u s c o n s t r a i n t s . Agents make

t h e i r d e c i s i o n s based on s i g n a l s which a r e v a r i a b l e s genera ted i n t h e

economy. For example, i n a w m p e t i t i v e economy, t h e only impor t an t s i g n a l s

a r e p r i c e s . I n o t h e r s e t t i n g s , s i g n a l s such a s q u a n t i t i e s might be r e l e v a n t .

The i n s t i t u t i o n a l s t r u c t u r e of t h e model economy d e l i n e a t e s t h e

" r u l e s of t h e game" acco rd ing t o which t h e v a r i o u s agen t s i n t e r a c t . I f one

assumes p e r f e c t compe t i t i on , t h e n each agent i s a p r i c e t a k e r , marke ts a r e

assumed t o work p e r f e c t l y , and a l l 6 r i c e s a r e f l e x i b l e . One can s p e c i f y

v a r i o u s imper f ec t ions o r c o n s t r a i n t s i n t h e i n s t i t u t i o n a l s t r u c t u r e t h a t w i l l

a f f e c t t h e o p e r a t i o n of t h e model; f o r example, a f i x e d wage. One might t h e n

assume t h a t f i r m s w i l l s e t t h e i r l a b o r demands given t h e f i x e d wage and t h a t

any excess supply of l abo r i s s imply i n v o l u n t a r i l y unemployed. I n t h i s

example, t h e l a b o r market " c l e a r s " wi th demanders s a t i s f i e d and s u p p l i e r s o f f

t h e i r supply curves .

Embodied i n t h e i n s t i t u t i o n a l s p e c i f i c a t i o n a r e assumptions about t h e

s i g n a l s which t h e a c t o r s c o n s i d e r i n making d e c i s i o n s . For example, under

p e r f e c t compet i t ion a c t o r s need on ly know p r i c e s . A l t e r n a t i v e l y , i f some

market i s monopo l i s t i c , then one must s p e c i f y t h a t t he monopolis t makes supp ly

d e c i s k n s based on in fo rma t ion abou t t h e demand f u n c t i o n s of t h e demanders,

no t j u s t t h e market p r i c e . I n a model wi th some f i x e d p r i c e s , a g e n t s w i l l -

also be suo jec t co rat-ionlng. i'he nar+re or che required s i g n a i s and ttle .L

a b i l i t y ( o r i n a b i l i t y ) t o decompose t b . o p e r a t i o n of the economy i n t o

Jlr d e c e n t r a l i z e d a c t i v i t i e s by s e p a r a t e agen t s a r e c r u c i a l f e a t u r e s of t h e model.

With t h e s p e c i f i c a t i o n of t h e agen t s , t h e i r mo t iva t ion , and t h e

i n s t i t u t i o n a 1 c o n s t r a i n t s under which they i n t e r a c t , a gene ra l e q u i l i b r i u m

model i s s t i l l no t comple te ly determined. There a r e s t i l l v a r i o u s c ~ n s t r a i n t s

t h a t must be s a t i s f i e d , bu t t h a t a r e n o t t a k e n i n t o a c c o u n t by any i n d i v i d u a l

a g e n t i n making h i s d e c i s i o n s . These a r e " sys tem c o n s t r a i n t s " which

e s s e n t i : l l y d e t e r m i n e t h e c h a r a c t e r i s t i c s of a n " e q u i l i b r i u m " i n t h e

economy. I n d e e d , a n e q u i l i b r i u m c a n be d e f i n e d f o r m a l l y as a set of s i g n a l s

s u c h t h a t t h e d e c i s i o n s of a l l a g e n t s j o i n t l y s a t i s f y t h e sys tem

c o n s t r a i n t s . For example, i n a c o m p e t i t i v e e q u i l i b r i u m model, t h e a s s u m p t i o m

t h a t a l l m a r k e t s c l e a r w i t h e x c e s s demands of z e r o is a sys tem c o n s t r a i n t that

d e f i n e s t h e n a t u r e of a a a r k e t e q u i l i b r i u m .

The n o t i o n o f sys tem c o n s t r a i n t s i s fundamenta l t o a n u n d e r s t a n d i n g

of how a model o p e r a t e s and c a n i n c l u d e much more t h a n s t a n d a r d models of

marke t e q u i l i b r i u m . For example , i n t h e l i t e r a t u r e on a p p l i e d g e n e r a l

e q u i l i b r i u m models , t h e term "model c l o s u r e " h a s been used t o r e f e r t o how an

economywide model a c h i e v e s b a l a n c e between s a v i n g s and i n v e s t r e n t 9 The

t e rm is c o n f u s i n g i n t h a t any f u l l y s p e c i f i e d g e n e r a l e q u i l i b r i u m model

s a t i s f y i n g Walras' Law is c l o s e d i n t h e s e n s e t h a t t h e r e a r e no v a r i a b l e s left

i n d e t e r m i n a t e . Macro " c l o s u r e " is r e a l l y b e t t e r s e e n as a sys tem c o n s t r a i n t

d e f i n i n g macroeconomic equ i l ib r ium--an approach t h a t w i l l be deve loped f u r t h e r

below. C a. ---- . .

The u s e of sys tem c o n s t r a i n t s t o d e f i n e a n " e q u i l i b r i u m " can b e seen

. . as a u s e f u l s i m p l i f i c a t i o n and a s u b s t i t u t e f o r w r i t i n g o u t a c o m p l e t e

d e s c r i p t i o n of dynamic a d j u s t m e n t processes. F o r example, i n s t e a d of

s p e c i f y i n g t h a t market e x c e s s . demands must e q u a l z e r o d u r i n g 'a p e r i o d , one

c o u l d w r i t e dLwn, a s p a r t of t h e model, dynamic " d i s e q u i l i b r i & " p r i c e * . - a d j u s t m e n t r u l e s which d e s c r i b e how p r i c e s a r e d e t e r m i n e 6 p e r i c d by p e r i o d .

Such a s p e c i f i c a t i o n i s t h e o r e t i c a l l y q u i t e d i f f i c u l t t o i m p l r s e n t and

111 S e e , f o r example , T a y l o r (1979) and D e r v i s , de Melo, and Robinson - ( 1 9 8 2 ) , C h a p t e r s 5 and 12.

c o m p l e t e l y c n n e c e s s a r y i f one i s w i l l i n g t o a c c e p t t h e m a r k e t - c l e a r i n g s y s t e n

c o n s t r a i n t s a s a r e a s o n a b l e d e s c r i p t i o n of t h e f i n a l r e s u l t of s u c h a p r o c e s s

w i t h i n t h e t i m e p e r i o d d e s c r i b e d by t h e model. There a r e , h ~ w e v e r , times when

I s u c h m a r k e t - c l e a r i n g assumpkions a r e n o t r e a s o n a b l e . I n a p p l i e d g e n e r a l

e q u i l i b r i u m models of deve loped c o u n t r i e s , i t i s u s u a l l y assumed t h a t c a p i t a l -

i s mobi le a c r o s s s e c t o r s and i s a l l o c a t e d s o a s t o e q u a t e s e c t o t . s l r e n t a l

. ra tes - -an e q u i l i b r i u m c o n d i t i o n t h a t i s c o n s i s t e n t w i t h a n a s s u m p t i o n of

p e r f e c t c a p i t a l marke t s . l l ! I n models r ! d e v e l o p i n g c o u n t r i e s , such a n

a s s u m p t i o n i s r a r e l y i f e v e r r e a s o n a b l e , and s o mode le r s have hzd r o s p e c i f y

I e x p l i c i t l y how t h e s e c t . o r a 1 a l l o c a t i o n of i n v e s t m e n t i s d e t e r m i n e d from p e r i o d

t o p e r i o d .

F i n a l l y , f o r a programming model, one must s p e c i f y t h e form of t h e

maximand. I n p l a n n i n g models , t h i s i s t y p i c a l l y some measure of u t i l i t y o r ,

a l t e r n a t i v e l y , a g g r e g a t e consumption. It is a l s o p o s s i b l e t o s p e c i f y some

s o r t of "p lanner ' s p r e f e r e n c e f u n c t i o n " which need n o t be based on w e l f a r e

t h e o r y . The maximand i s , of c o u r s e , c r u c i s l i n d e t e r m i n i n g and i n t e r p r e t i n g

t h e shadow p r i c e sys tem. We w i l l , i n t h i s p a p e r , r e s t r i c t o u r s e l v e s t o

programming problems whose maximands r e f l e c t u t i l i t y f u n c t i o n s of consumers .

I n t e rms of t h e f e a t u r e s d e s c r i b e d above , we w i l l now p r o v i d e f o r n a l

d e f i n i t i o n s . o f "market e q u i l i b r i u m " and "programming" m d e l s , and t h e n e x a m i n e

t h e z;sumptions under which t h e y have t h e same s o l u t i o n . We assume t h a t t h e r e

a g e n t s a r e consumers and p r o d u c e r s . Thare a r e m conc.lmers ( w i t h s u b s c r i p t i)

e a c h of whom h a s a n i n i t i a l endowment 06 ~ o m m o d ~ t i e s , w i ' F o l l o w i n g s t a n d a r d

p r a c t i c e i n t h e g e n e r z l e q u i l i b r i u m l i t e r a t u r e , "commodit-ies" i n c l u d e f a c t - o r s

1 2 1 For some examples , s e e S c a r f and Shoven (1983). -

of production such as labor and capital as wel? 3s consumcr goods and

intermediate goods. The consumption bundle of each consumer is given by the

vector x o Xi, where X is the set of possible consu.mption bundles available i i

to consumer i s t There are I- producers (with subscript j) each of wton

chooses a production point y & Y where Y is the set of feasible production 1 1' 1

points for prcducer j determined by the available :ethnology. The production

point y is a vector with positive elements denoting outputs 'and negative 1 elements denoting inputs. We also assume that agents respond to prices (in a

way to be defined later) in making decisions, and so we can write xi(pl and

y (p) to represent the vectors of demand curves for consumer i and supply 1 curves of producer j14/ Aggregate demand, supply, and endowments are given

by the vectors:

Definition 2.1: Market Equilibrium. The allocation xi(p) (1-1, ..., m) and yj(p) (=l,...,n, supported by the market price vector p, constitutes a

market equilibrium if:

(a) no commodity is in excess demand,

(b) consumers satisfy their budget constraints,

Poxi 6, L O T aii i, A

where income, R,,, is defined in Assumptiorl 3.2 belc;~,

8 . 131 Note that the condition xi E X does not include the budget constraint - i

facing consumers which must be considered separately.

141 T;~ese "curves" may be functions or correspondences, de~ending on the - assumptions of the model.

( c ) a d d i t i o n a l system c o n s t r a i n t s a r e s a t i s f i e d ,

( d ) i n d i v i d u a l corsumption and p roduc t ion p l a n s a r e f e a s i b l e ,

x i (p) F Xi and y . (p) E Yj f o r a l l i and j. J

Assuining t h a t each consumer i s on h i s budget cons:.raint ( f o r p r o p e r l y

de f ined Ri), then t h e system a s a whole must s a t i s f y Walras' Law: p.e<p), = 0-

The a d d i t i o n a l system c o n s t r a i n t s a(-) C 0 w i l l be used t o r e p r e s e n t

d e v i a t i o n s f ion , o r e::t.ensions t o , t h e s t and? rd r r eoc i a s s i ca l a s s u m p t i o n s of a

compe t i t i ve market. equilibrium. The p r i c e ; rector p i s inc luded i n t h e list of

argunients because such f u n c t i o n s a r e o f t e n concep tua l ly d e f i n e d i n n o m i n a l

terms. For example, macro i s s u e s can be t r e a t e d by impgsing a s c o n s r r a i a t s on

t h e model f u n c t i o n s t h a t determine v a r i a b l e s such a s agg rega t e s a v i n g s ,

i n v e s t v e n t , p u b l i c income, and/or expend i tu re . The a(-) can a l s o be u s e d , f o r

exzslple, t o r e p r e s e n t t h e ba lance of t r a d e and/or "second 5es t" c o n s t r a i n t s

such a s p r i c e d i s t o r t i o n s .

The second approach d e f i n e s a programming model used by a p l a n n e r t o

determine an optimum a l l o c a t i o n o r p lan . Assume t h a t t h e p l anne r h a s a

w e l f a r e f u n c t i o n V(xl, ..., x ,, Y y * a * , Yn) ~ h i c h he s eeks Zo maxlmize.

D e f i n i t i o n 2.2: A Plan. The al- cation xi ( i - 1 , ..., m) andayj ( j=l , . . . ,n) ,

c 0 n s t i t u t . e ~ a p l an i f i t i s a solut:.on of t h e fo l lowing mathemat ica l program: -

L L . ~ . < v , . , .Cm, , . . . , &

I n ' wi th r e s p e c t t c ~ x and y , - s u b j e c t t o I)

x E X and y E Y f o r a l l i and j. i i j j

nenote by n the shadow prices associated with the excess deaaed or

material hsiance conetraints, x - y - w < 0, which "support" the p r W +

solution. Then, the planning authority can use the shadow prices n generated

by the plan to decentralize decisions. With the n's as signals, agents e l l

respond with demands xi(n) and supplies yi(n) which will satisfy the p l a n and

also individual budget constraints. In general, there is no reason to e _%ct

the solution of a plan to be a market equilibrium with prices equal to r and

there is no guarantee in the plan that individuals will satisfy their -get

constraints (evaluated at shadow prices n).

Ve will consider below the conditions under which the s o l u t i o ~ of a

plan including the shadow prices n constitutes a narket equilibrium vitb

h.

p = n = p. The a(;, . . .) G 0 system constraints have been discussed above.

Note thatthere is a vector of prices that are either exogenously giver or

endogenous. For example, they might represent fixed world prices in a lode1

where a(-) is the balance of trade. However, it is often desirable to specify

such constraints defined with "solution" prices. For example, an aggregate

savings constraint should conceptually be defined in nominal terms. S~lch a

specification causes computational problems since we then require that = n,

and shadow prices then appear as part of the constraints in the p r i m 8

problem.. Although various modelers have been quite ingenious in their

attempts to specify theoretically justifiable additional system constraints -

w l c n r i x e u prices, S U C I ~ at1 ~ P P C C ~ C I I is: L. ~ d i ~ j~ti is: ia;~c;i- , . . i.1 -:;c .r&-: 4 . L - section, we will restrict Gur attention ~o competitive market equilibrfa in 8 . t which the additional a(-) < 0 constraints do not appear, and then later move

on to models that incorporate such constraints.

3. Competitive Equilibrium Models - We first specify how prodgcers and consumers behave and then discuss

two approaches to specifying a competitive equilibrium model.

Assumption 3.1: Producer Behavior. Producer j takes prices p as given and

chose9 his production point so as to max.imize his profits p-y subject to his 1 ' technological constraints 8 Yj Yjo Y represents the production technolw 1 available to firm j.

Assumption 3.2: Consumer Behavior. Consumer 1's preferences can be

represented by a utiiity function Ui(xi). He takes prices p as given and

chooses his consumption bundle so as to maximize Ui(xi) subject to x c XE and i

to his budget constraint p.xi < Ri. Ri is his incime which consists of the

value of his endowment p.wi and the profits distributed by firms to h?.m

according to the share parameters 0 (where eij ij .

1) Thus, Ri p-ui +

Definition 3.1 : Competitive Equilibrium. The allocation xi(:) and y (3. j

supported by the price vector p, is a competitive equilibrium if Assumptions

3.1 and 3.2 are satisfied and no commodity is in excess demand:

Clearly, a competitive equilibrum is a special case of a market

equilibrium (and will satisfy Walras' Law). Wc now define a spacial case of a I

plan which yields solutions which are "Pareto Optima."

nefinf?ion 3.2: Pareto Ootimal Plan. The allocation x L k ) and y,(n), - -- --- -- . --

I-i_. ' i supported by the shadow price vector a associated with the constraints~x - y - - - . f -

151 Note that in models with constant returns to scale production functioas, - profits - are zero at a competitive equilibrium. Then p.y (p) = 0 a d Ri - p w . The distribution of income is determined by dndowmencs and prices, independently of the 0 parameters.

w < 0 , i s a P 2 r e t o Optimal P l an i f i t is a s o l u t i o n of t h e fo l l owing

161 mathemat ica l program:-

max la iui(xi)

w i t h r e s p e c t t o x and y,

s u b j e c t t o

The a 's a r e c a l l e d "wel fa re weights" and a r e s t r i c t l y p o s i t i v e . i

We a r e now ready t o s t a t e two major e x i s t e n c e theorems which b r f d g e

D e f i n i t i o n s 3.1 and 3.2. The f i r s t is t h e Arrow-Debreu theorem t h a t u n d e r

s u i t a b l e assumptions t h e r e e x i s t s a v e c t o r of p r i c e s suppor t i ng a c o m p e t i t i v e

equ i l i b r ium. The second, due t o Negishi (1960), is t h a t t h e r e e x i s t c e r t a i n

p l a n s t h a t y i e l d compe t i t i ve e q u i l i b r i a .

1 7 1 Theorem 3.1: Ex i s t ence of Equi l ib r ium P r i c e s . Under s u i t a b l e assumptions,-

t h e r e e x i s t s a v e c t o r of market p r i c e s ;; such t h a t t h e c o n d i t i o n s d e f i n i n g a

competi t i v e equ i l i b r ium ( D e f i n i t i o n 3.1) a r e s a t i s f i e d . Assumptions 3 . 1 and

3.2 s p e c i f y i n g producer and consumer behavior a r e s a t i s f i e d and no commodity

i s i n exces s demand: e (7 ) = x(7) - y(7) - w < 0.

T h i s is t h e c l a s s i c Arrow-Debreu e q u i l i b r i u m r e s u l t : t h e r e e x i s t s a

. ', set of p r i c e s such t h a t p r o f i t maximizing producers and u t i l i t . y ~ m a x i m i z i n g

consumers, s u b j e c t t o t h e i r budget c o n s t r a i n t s , w i l l g e n e r a t e p r o d u c t i o n and

consumption d e c i s i o n s such thac exces s demands a r e non-pos i t ive .

161 Given t h e maximand, t h e s o l u t i o n i s c l e a r l f a P a r e t o Optimum s i n c e it - would always i n c r e a s e t h e maximand t o make one person b e t t e r o f f w i t h o u t making someone e l s e worse o f f .

171 The assumptiono a r e t e c h n i c a l and somewhat more g e n e r a l f o r Theorem 3.1. -. See Arrow ani Hahn (1971) and Negish i (1960). I n most e m p i r i c a l mode l s , t hey a r e s t r eng thened s o a s t o a s s u r e s t r i c t l y p o s i t i v e p r i c e s and z e r o exces s d e ~ a n d s .

Theorem 3.2: Existence of Equilibrium Welfare Weights. Under suitable

assumptions, there exists a vector of non-negative welfare weights such i

that the solutions of the Pareto Optimal Plan (Definition 3.2), with

- - associated shadow prices 7, are competitive equilibria with p = n.

The essence of the Negishi Theorem is that there exists at least m e

set of welfare weights such that the allocations xi and y and the shadow 1

prices from the solution of the programming problem will satSsfy the

individual budget constraints (evaluated at p = r). Thus, if consumers a d

producers behave as stated in Assumptions 3.1 and 3.2, there exists a p l a m i n g

model the solutions of which are competitive equilibria.

In the definition of a competitive equilibrium, the budget

constraincs are an explicit part of the model, while in the programming

problem in the Negishi Theorem the budget constraints do not appear

explicitly. Ginsburgh and Waelbroeck (1981) present a program which adds the

budget constraints explicitly and show that this Msster Program includes the

models in Theorems 3.1 and 3.2 as special cases.

Definition 3.3: A Master Program

1 ai Ui(Xi) with respect to x and y

subject to I t

I: E xi; Y1 Yj

- d 8 Zf one drops the material balance constraints (x - y - w < O), the

remaining program embodies the behavioral specification u~3:z;-lying Theorem 3.1

(for a given set of fixed prices). This can be seen intuitively as follows

(and can be proved without difficulty). Given p, the various budget

constraints can be loosened by increasing profits of any producer (p.y.). 3

Hence, at the solution, profits must be maximized. Given ai > 0, the -era11

maximand is a weighted sum of individual utilities. Given p and profit

maximizl~g production plau y the overall problem car1 be decomposed in- m 1 ' subproblems. Thus the overall maximum is .achieved when each consumer

naximizes his utility subject to his budget constraint. Note that this

solution is independent of the choice of welfare weights (no 'lump sum

transfers are allowed). The program for the Negishi theoren is obiained from

the master program by dropping the individual budget constraints. In tbe

Negishi thecrem, of course, the welfareweights are important because tke

shadow prices of the material balance constraints depend on them. At

equilibrium, in fact, the welfare weights are equal to the inverses of the

marginal utility of income for the consumers.

Ginsburgh and Waelbroeck (981) prove an existence theorem which

essentially links Theorems 3.1 and 3.2 and emphasizes the symmetry between the

competitive model and certain plannlng models.

Theorem 3.3: Competitive Equilibrium in a Master Program.

Let n be the vector of shadow prices associated with the

x - y - w < o constraints of the Master Program. Any solution in which f';

fl p is a competitive equilibrium (where k i's positive scalar).

In any Walrasian general equilibrium model, it is well known that I -

only relative prices "matter" andqthat one is free to choose a numeraire to 6

set the absolute price level. ISTheorem 3.1 (Arrow-Debreu) , the implfcation

- is that sonie normalization rule czn be imposed on the solution price vector

- p, for example p = 1 (assuming pl is ?.on-zero) In Theorem 3 . 2 (Negishi), a

1 4

normalization can be imposed on the welfare weights, say a = 1. In Theorem 1

3.3 (Ginsburgh-Waelbroeck), the vector of shadow prices (n) at equilibrium

does not depend on t h e choice of we l fa re w e i g h t s s l One 1s f r e e t o normalize

p r i ces a s i n t h e Arrow-Debreu model, f o r example by dropping t h e f i r s t

m a t e r i a l balance c o n s t r a i n t and s e t t i n g pl = 1.

4. Model S p e c i f i c a t i o n and Empirical So lu t ion

A v a r i e t y of empi r i ca l genera l equ i l ib r ium models have been b u i l t

based on t h e d i f f e r e n t underlying approaches i m p l i c i t i n t h e s e e x i s t e n c e

theorems. We w i l l distingu:.ah two broad f a m i l i e s of models: ' (1 ) Computable

General Equil ibrium (CGE) models ( t h e term introduced by Adelman and Robinson)

and (2 ) A c t i v i t y Analysis General Equil ibrium (AGE)' models introduced by

Ginsburgh a ~ d Waelbroeck (1981f11 CGE models a r e based o n the model

underlying Theorem 3.1, and s imula te the behavior of producers and consumers

t o genera te numerical ly t h e set of excess demand equat ions . For example, i f

u t i l i t y func t ions and p r o d u c ~ i o n func t ions a r e "well-behaved" n e o c l a s s i c a l

func t ions , then i t i s poeeible t o write o u t the var ious f i r s t - o r d e r c o n d i t i o n s

e x p l i c i t l y and genera te a s e t of consumer demand func t ions and producer supply

funct ions . Assuming a l l p r i c e s a r e s t r i c t l y p o s i t i v e , t h e s o l u t i o n problem

then reduces t o f ind ing a s e t of p r i ces which makes a l l excess demands equa l

zero. The model involves a l o t of non-linear mathematics, but no i n e q u a l i t y

c o n s t r a i n t s . AGE models, on the o the r hand, a r e cha rac te r i zed by i n e q u a l i t y

181 For a proof, see Gineburgh and Waelbroeck (1981)L pp. 69-70. To see t h i s - i n t u i t i v e l y , suppose you s t a r t from equ i l ib r ium p p r i c e s , and s o l v e t h e Z I ~ T S ~ C T 7 t 3 q r a n - ~ q ~ t h o t l t th?? -1,-lteri3!. 5.71 l?,ci. f c c n ; t r . ~ ints .: The ? ~ L : T I : ~ ? s o l u t i o n is independent of the choice of a's, and s a t i s f j e s , by d e f i n i t i o n t h e budget and the balance c o n s t r a i n t s . C lea r ly the a d d i t i o n of t h e mater ia l -ba lance c o n s t r a i n t s . w i l l not change t h e primal go lu t ion . ~ o w e v e r , ? v a r ~ i n ~ the a's w i l l change the m u l t i p l i e r s a s s g i a t e d with t h e budget c o n s t r a i n t s .

19/ See Adelman and P-obinson (1978); Dervis , de Melo and Robinson (1982); and - Scarf and Shoven (1983) f o r examples of CGE models. For AGE models, i n a d d i t i o n t o Ginsburgh and Waelbroeck (1981), s e e Manne e t a l . (1980), who independently developed a s i m i l a r approach, and Dixon (1975) who empi r i ca l ly implemented the Negishi approach.

constraints and are always cast in the format of a programming problem of the

type specified in Theo~ema 3.2 or 3.3.

We will discuss the differences between the two approaches in terms

of the different strategies required to solve the models. Such an algorithmic

focus has two advantages. First, ease of solution is a major criterion for

choosing between different model formulations and, second, the different

solution strategies highlight the major differences in structure between the

two families, and among different models within the AGE family.

Any method of solving a general equilibrium model empirically can be

seen as a general algorithmic procedure consisting of two steps. The first

step is a "function evaluation" which consists of solving a mathematical

program or a set of equatiots in which a certain number of parameters are

fixed. The second step is that of "parameter revision." The solution of the

function evaluation step is examined to test whether certain equilibrium

conditions are satisfied. If they are, stop the procedure. If not, change

some parameters and go to a new function evaluation step. In terms of this

general two-step procedure, there are at least three strategies for solving

CGE and AGE models based on Theorem 3.1, 3.2 and 3.3.

Strategy 1: based on Theorem 3.1. The function evaluation step

involves evaluating, for giver prices p, the consumer depland and producer -*

supply equations, x(p) and y(:,)g The solutions determine the aggregate

1 , 1 . > C e x ~ e b a - d e ~ l d r l d d q U d C ~ u I 1 5 . A a . <.cLt laa J i32?.da L, r _ -,, , ' . . ;

equilibrium price vector. If not, the price vector has to be modified and a

8 new function evaluation step is started*

201 Some technical issucs concerning the nature of these relationships are - being finessed here. In fact, for empirical models, these equations are virtually always well-behaved functions.

S t r a t e g y 2: based on Theorem 3 . 2 . For a g iven v e c t o r of welfare

weights a , s o l v e t h e m t h e m a t i c a l program. Using t h e s o l u t i o n , check w h e t h e r

every consumer i s on h i s budget c o n s t r a i n t . I f so , a i s an e q u i l i b r i u m v e c t o r

of we l f a re weights and t h e s o l u t i o n , i n c l u d i n g the shadow p r i c e s , r e p r e s e n t s a

compe t i t i ve equ i l i b r ium. I f n o t , r e v i s e t h e a's and s t a r t a new f u n c t i o n

evaluation.

S t r a t e g y 3: based on Theorem 3.3. For a g iven v e c t o r of p r i c e s p, -

s o l v e t h e Master Program and check whether t h e d u a l p r i c e s H a s s o c i a t e d w i t h

t h e excess-demand c o n s t r a i n t s a r e e q u a l t o p- I f so , s t o p ; t h e s o l u t i o n is an

equi l ibr ium. I f n o t , chhnge t h e p r i c e v e c t o r p and start a new f u n c t i o n

To summarize, i n S t r a t e g y 1, p r i c e s a r e r ev i sed u n t i l e x n e s s demands

a r e a l l non-posi t ive, e ( F ) < 0. For S t r a t e g y 2, we l f a re weights a r e r e v i s e d

u n t i l "excess-budget" equa t ions a l l equa l ze ro , b i (z ) = H(:)').X~(;) - Ri(a) - 0. -

For S t r a t e g y 3, p r i c e s a r e r ev i sed u n t i l n (7 ) - p = 0. 22/ Parameter r e v i s i o n

invo lves some kind of a lgo r i thm f o r s o l v i n g systems of non-l inear equa t ions .

I A v a r i e t y of such a lgo r i thms a r e now a v a i l a b l e , and t h e cho ice amoRg them is

231 l a r g e l y a t e c h n i c a l i s s u e of c o s t and convenience-

I I n c o n t r a s t , t h e f u n c t i o n e v a l a a t i o n phase i n v o l v e s a c h o i c e s o l u t i o n

s t r a t e g j dased on a l t e r n a t i v e ex i s tLnce theorems and on d i f f e r e n t ways of

formula t fng e e model. For example, i f i t i s p o s s i b l e t o s p e c i f y t h e model as - .wr"

I '9 a CGE model by w r i t i n g ou t t h e excess-demand equa t ions e x p l i c i t l y , i t is

- w *

21/ Since, a s noted above, t h e shadow p r i c e s z a r e independent of t h e c h o i c e - of a's, t h e a's can be s e t a r b i t r a r i l y t o any s t r i c t l y p o s i t i v e numbers-

I

I -

22/ More g e n e r a l l y , kn(;) - p = 0 where k i s a p o s i t i v e s c a l a r . - 23/ Both Ginsburgh and Waelbroeck (1981) and Dervis , d e Melo arid Robinson -

(1982) survey s o l u t i o n a lgo r i thms .

p r o b a b l y e f f i c i e n t t o do s o s i n c e i t g r e a t l y s i m p l i f i e s t h e f u n c t i o n

e v a l u a t i o n I n g e n e r a l , however, one c a n n o t a l w a y s s o l v e t h e

i n d i v i d u a l consumer and p r o d u c e r problems t o y i e l d e x p l i c i t e x p r e s s i o n s for

svlpply and demand. T h e r e are a numher of r e a s o n s why s u c h a f o r m u l a t i o n m i g h t

n o t be p o s s i b l e o r d e s i r a b l e . r .

F i r s t , even when a l l t h e c o n s t r a i n t s t a k e t h e for11 of e q u a l i t i e s , i t

may be i m p o s s i b l e t o g e t e x p l i c i t f u n c t i o n s from t h e f i r s t - o r d e r c o n d i t i o n s

f o r a maximum. One is t h e n f o r c e d n u m e r i c a l l y t o s o l v e a s y s t e m of n o n - l i n e a r

e q u a t i o n s ( f i r s t - o r d e r c o n d i t i o n s ) e i t h e r f o r e v e r y a g e n t o r f o r t h e economy

a s a whole ( u s i n g Theorem 3.1). I n such a c a s e , i t might w e l l be e a s i e r t o

d e a l w i t h t h e m a t h e m a t i c a l program d i r e c t l y i n t h e AGE f o r m a t and r h u s a v o i d

h a v i n g t o w r i t e o u t t h e f i r s t - o r d e r c o n d i t i o n s e x p l i c i t l y .

Second, one may w e l l w i sh t o s p e c i f y i n e q u a l i t y c o n s t r a i n t s , wh5ch

t h e n r e q u i r e s a n AGE approach . I n c h o o s i n g t h e CCE f o r m u l a t i o n , a m o d e l e r

must have f a i t h i n t h e smoothness and c o n t i n u i t y p r o p e r t i e s of n e o c l a s s i c a l

u t i l i t y and p r o d u c t i o n f u n c t i o n s . While s u c h a s s u m p t i o n s may be r e a s o n a b l e

f o r t h e demand s i d e -- a t l e a s t a t t h e l e v e l of a g g r e g a t i o n of most m o d e l s -- t h e y a r e o f t e n f e l t . t o be u n r e a s o n a b l e f o r p roducers . One i n t e r e s t i n g

p o s s i b i l i t y would be t o c o n s t r u c t 7 mixed AGE-CGE model i n which t h e demand * r

s i d e is t k p r e s e n t e d by e x p l i c i t demand f u n c t i o n s w h i l e t h e p r o d u c t i o n side i s

r e p r e s e n t e d by oqe o r s e v e r a l l i n e a r o r n o n - l i n e a r a c t i v i t y a n a l y s i s models. - 5 . P r i c e s i n P l a n n i n g ~ d d e l s -

The e a r l y p r o g r a k i n g models were r a r e l y s p e c i f i e d as t r u e AGE I,

models , a l t h o u g h some of t h e p l a n n i n g models came c l o s e . E 1 E m p i r i c a l m d e l

2 4 / I n d e e d , t h e same p r o c e d u r e c o u l d be u s e d w i t h t h e N e g i s h i theorem, l e a d i n g - t o a CGE model w i t h e x p l i c i t excess -budge t e q u a t i o n s .

2 5 / B l i t z e r e t a l . (1975) p r o v i d e s a good s u r v e y . See a l s o Dixon (197.5). -

b u i l d e r s have r u n i n t o problems w i t h p r o g r a m i n g models f o r a nunber of

reasons . F i r s t , l i m i t a t i o n s on t h e a b i l i t y t o s o l \ ? e programming models h a v e

l e d t o s i m p l i f i c a t i o n s t h a t y i e l d u n r e a l i s t i c behav ior . For example, a l l t h e

e a r l y models used l i n e a r programming, which i s prone t o c o r n e r solutions a n d e

ex t reme s p e c i a l i z a t i o n . Modelers t hen imposed v a r i o u s ad hoc bounds on

product- ion, consumption, i nves tmen t , e x p o r t , and import a c t i v i t i e s i n o r & e r t o

a c h i e v e " r e a l i s t i c " behav io r , t u t which r e s u l t e d i n d i s t o r t i o n s i n t h e shadow

p r i c e system.

Second, even when n o t c o n s t r a i n e d by s o l u t i o n technology , mode l e r s

have o f t e n s p e c i f i e d e m p i r i c a l models whose u n d e r l y i n g t h e o r e t i c a l s t r u c t u r e

h a s l e d t o u n r e a l i s t i c r e s u l t s . Perhaps t h e b e s t example is t h e s p e c i f i c a t i o n

of t r a d e which h a s long prov ided a major f o c u s f o r a p p l i e d programming

Problems a r i s e because most modelers have i n t r o d u c e d i n t e r n a t i o n a l

t r a d e u s i n g t h e smal l -count ry assumpt ion and a l s o assuming t h a t domes t - i c a l l y

produced and impor ted goods a r e p e r f e c t s u b s t i t u t e s . The excess-demand

c o n s t r a i n t s x C y + w a r e r e p l a c e d by x + e C y + m + w (where e and m a re

e x p o r t and impor t v e c t o r s ) , and a ba l ance of payments c o n s t r a i n t is added,

e pm.m - p .e C 0. The p r i c e s pm and pe a r e assumed f i x e d ( d e f i n i n g t h e "small-

coun t ry" a s sumpt ion ) , which i m p l i e s i n f i n i t e l y e l a s t i c e x p o r t demand and

i a p o r t supp ly e q u a t i o n s . T h i s s p e c i f i c a t i o n l e a d s t o extreme s p e c i a l i z a t i o n cL . t

even i n t h e non- l inear c a se and modelers have r e a c t e d by imposing a n h r of

ac!;'.tticn-i!. !lot ~~zr;;r3L:,t:; t.0 ;-:;~!cP t!i:: i l ? l ~ t i o r , 1nTr.2 i -c : ; i l i : i t i l : . S!~!C': :

3 c o n s t r a i n t s p i ck up shadow p r i c e s and d i s t o r t t h e p r i c e system. - * -

26/ For examples , s e e some of t h e c a s e s t u d i e s i n Chenery (1971) and Adelman - and Thorbecke (1966) . Evans (1972) p robab ly ha s t h e most s o p h i s t i c a t e d t r e a t m e n t of t r a d e i n a l i n e a r programming model. See a l s o t h e corrlrnents on Evan's model by Dixon and B u t l i n (1977) w h ~ c r i t i c i z e i t w i t h i n t h e framework of g e n e r a l e q - ~ i l i b r i u m theo ry .

The i n t r o d u c t i o n of p r i c e d i s t o r t i n g -- ad hoc c o n s t r a i n t s has been much

d i scus sed i n t he p l ann ing l i t e r a t u r ; ( s e e , f o r example, Tay lo r :1975)). I f

such c o n s t r a i n t s can be j u s t i f i e d a s a d d i t i o n a l system c o n s t r a i n t s t h a t d e f i n e

a r ea sonab le n o t i o n of economic equ i l i b r ium, then t h e r e is no t h e o r e t i c a l

problem-27/ For example, i n c l u d i n g a balance-of- t rade c o n s t r a i n t i s p e r f e c t l y

l e g i t i m a t e t o d e f i n e t h e n o t i o n of e q u i l i b r i u m i n t h e market f o r " f o r e i g n

exchange." I f t h e added c o n s t r a i n t s can be seen a s a l e g i t i m a t e p a r t of t he

c o n s t r a i n t s f a c i n g an i n d i v i d u a l agen t , then a g a i n t h e r e i s no t h e o r e t i c a l

problem. For example, i f an upper bound on ou tpu t i n a s e c t o r can be defended

a s p a r t of t h e t e c h n i c a l c o n s t r a i n t s f a c i n g a producer (and hence p a r t of t h e

d e f i n i t i o n of h i s p roduc t ion p o s s i b i l i t y s e t Yj), then i t s i n c l u s i o n r a i s e s no

problems of i n t e r p r e t a t i o n of t h e shador. p r i c e s . When added c o n s t r a i n t s canno t

be defended e i t h e r a s p a r t of t h e d e f i n i t i o n of o v e r a l l e q u i l i b r i u m o r a s p a r t

of t h e c o n s t r a i n t s f a c i n g i n d i v i d u a l a g e n t s , then i t becomes imposs ib l e t o

i n t e r p r e t t he s o l u t i o n a s r e f l e c t i n g t h e o p e r a t i o n of a market system. Any

survey of e x i s t i n g models r e v e a l s tha t . such problems v e r e very common.

Empi r i ca l p l ann ing models have o f t e n been used i? s i t u a t i o ~ \ s where

"macroeconomic" i s s u e s such 2s balance-of- t rade and lo r savings-investment.

"imbalances" a r e impor tan t . Some l i n e a r programming m d e l s were ex tended t o

i n c l u d e such "macroeconcmic" c o n s t r a i n t s , buk o f t e n exp re s sed i n r e a l t e rms

( i . e . , w i thou t referr.!ce t o s o l u t i o n p r i c e s ) and s o hard t o j u s t i f y a s

(1966) incorporar -es "Keynesian" agg rega t e sav ings f u n c t i o n s t h a t do no t - . -

8 r r e f l e c t t h e behavior of i n d i v i d u a l agen t s . They a r e i n s t e a d j u s t i f i e d a s - r e f l e c t i n g rnactoeco~iornic e q u i l i b r i u m co r .d i t i ons , bu t w i t h no e x p l i c i t

271 These a i e t h e c o n s t r a i n t s @(-) < 0 d e f i n e d i n s e c t i o n 2. -

c o n s i d e r a t i o n of t h e nominal flow of s a v i n g s and investment i n t he system.

The more r e c e n t l i t e r a t u t e on model "closure"--how a model de te rmines

agg rega te s av ings and investmenr--has a l s o r a i s e d the i s s u e of macroeconomic

e q u i l i b r i u m i n t h e context of CGE m o d e l s l 8 / We t u r n t o t h e s e i s s u e s i n the

nex t s e c t i o n .

6. Macroeconomic Equ i l i b r ium

I I n t h e compe t i t i ve model, t h e nomitial f lows among agen t s a r e v e r y

s t r a i g h t f o r w a r d . Producers pay out t h e i r r e c e i p t s t o households who, i n turn,

spend a l l t h e i r income on goods. The focus i s on t h e " r e a l " system, which is

I e q u i l i b r a t e d by f l e x i b l e p r i c e s , and no a d d i t i o n a l assumptions a r e needed to

I ensu re t h a t t h e v a r i o u s nominal incorce ac.d expendi ture f lows a r e c o n s i s t e n t or

i n equ i l i b r ium. I n Table 1, t h e compe t i t i ve e q u i l i b r i u m model is extended

I somewhat and presented i n a form t.hat w i l l f a c i l i t a t e a d i s c u s s i o n of i t s

I macroeconomic f e a t u r e s . The p r e s e n t a t i o n is i n t h e framework of a CGE model,

I b u t could e a s i l y be done i n t h a t of an [GE m o d e l 1 The equat ions d e s c r i b i n g

I t he product and f a c t o r markets a r e p re sen ted s e p a r a t e l y ( s e p a r a t i n g t h e

nega t ive f a c t o r i npu t e lements i n t h e y j v e c t o r s from t h e p o s i t i v e o u t p u t

e lements) . The p r i c e v e c t o r i s a l s o s p l i t i n t o two v e c t o r s , w i th p now

denot ing only product p r i c e s and w denot ing f a c t o r p r i c e s . The consumer

,itfcome v a r i a b l e s Ri i n t h e tnodels a r e nG.1 r ep laced by " i n s t i t u t i o n a l " i ? ~ m i n a l - income and expend i tu re s , \ and E k = These i n s t i t u t i o n s (inta.rxed by k) would

~ n c i u u s riot o n l y householas , but. a l s o ocher a c t o r s such a s the gove~nmen t , an e.:-r-

aggrega te "bank" which c o l l e c t s s av ings and buys investilnent goods, and t h e

r e s t of t h e world. Each i n s t i t u t i o n has a nominal expe%diture and an k

281 See Fruno (1979) who i n t r o d u c e s a symposium d e a l i n g wi th such i s s u e s , - l a r g e l y i n t h e con tex t of models of income d i s t r i b u t i o n .

291 See, f o r example, Ginsburgh and Vaelbroeck (1981), Chapter 4. -

Table 1

Product Markets, Factor Markets and Flow of Funds

Product and Factor Harkets -- I Nominal Income and Expenditure

Real Flows:

(1) Product supply xS(p,W) I ( 7 ) Institutional income W+Vs, 4)

No~inal Flows:

(2) Product demand xD(P,t) 1 (8) Institutional expenditure s(R ,̂ 4) I

I

(3) Factor supply. F'(W,~) I (4) Factor demand ~ ~ ( w , ~ )

System Constraiqts - I Sys tea Constraints

Ncminal Flow Identities

S (5) Product markets xD - X = 0

I I (6) Factor markets F~ - F' = 0

D (11) w.F I p . ~ S Factor income equals

total sales.

(9) Macro balances

(10) Price normalirition

(12) lk zk : W.F' Institutional income equals factor income.

(13) PoxD lk Bk Total demand equals institutional expenditure

I I

r Eauilibratinn variables -

I ... ;,,%&-P = vecwr of p r d c c t prices, L

I

w = vecCbr of factor prices, and e

= vect8r of additional equilibrating variables.

a s s o c i a t e d commodity e x p z n d i t u r e f u n c t i o n . The system c o n s t r a i n t s , e q u a t i o n s .

(5) and ( 6 ) , d e f i n e e q u i l i b r i u m i n t h e f a c t o r and p roduc t m a r k e t s , e x a c t l y a s

i n t h e models above.

The nominal f l o w s i n t h e sys tem a r e give,. by e q u a t i o n s ( 7 ) , (a) , and

( 9 ) . E q u a t i o n ( 7 ) maps f a c t c r incomes i n t o i n z ; i t u t i o n a l incomes, w i t h a l l

f a c t o r s u p p l i e s b e i n g p a i d w ( c o r r e s p o n d i n g t o p.w i n t h e e a r l i e r models) .

E q u a t i o n (8) i s new and a l l o w s f o r t h e p o s s i b i l i t y t h a t ex a n t e e x p e n e i t u r e

p l a n s of i n s t i t u t i o n s need n o t match t h e i r income--a p o s s i b i l i t y n o t a l l o w e d

i n t h e e a r l i e r models. New sys tem c o n s t r a i n t s - - e q u a t i o n (9)- -def ine flow-of-

f u n d s e q u i l i b r i u m and new e q u i l i b r a t i n g v a r i a b l e s ($I d i s c u s s e d below) a r e

i n t r o d u c e d . E q u a t i o n (10) i s t h e p r i c e n o r m a l i z a t i o n e q u a t i o n t h a t d e f i n e s

t h e n u m e r a i r e p r i c e and sets i t t o t h e exogenous c o n s t a n t F. T h i s e q u a t i o n i s

l i s t e d a s a n o n i n a l sys tem c o n s t r a j n t s i n c e i t s e t s t h e a b s o l u t e p r i c e l e v e l

30/ and hence a f f e c t s a l l nominal magnitudes.-

E q u a t i o n s (11) - (13) p r e s e n t v a r i o u s nominal f low i d e n t i t i e s

i m p l i c i t i n tt,e e q u a t i o n s . They r e f l e c t fundamenta i a t t r i b u t e s of t h e

" c i r c u l a r f low" i n t h e economy. I n t e rms of a model, t h e r e q u i r e m e n t i s t h a t

a l l f u n d s must be a c c o u n t e d f o r and t h a t e v e r y r e a l t r a n s a c t i o n must g e n e r a t e

a c o r r e s p o n d i n g nominal f low. Adding (11) - (13) i n d i c a ' e s t h a t t h e t h r e e

sys tem c i n s t r a i n t s (5), ( 6 ) and ( 9 ) t a k e n t o g e t h z r s a t i k f y Walras' Law:

; o w ejcdiupies w l l i c l a r i f y che + l a t i o n s h i p s between macroeconomic 1

and market e q u i l i b r i a . Cons ider a m o c i e l s h a t i n c l u d e s amon: i t s i n s t i t u t i o n s

30/ I n models which a r e n o t homogeneous, t h e a b s o l u t e p r i c e l e v e l " m a t t e r s " - and i s s u e s of n e u t r a l i t y become i m p o r t a o t . Thc a g g r e g a t e p r i c e e q u a t i o n t h e n no l o n g e r s i m p l y se r l res t o d e f i n e t h e numera i re . Hansen (1970) p r o v i d e s a c l e a r e x p o s i t i o n a f such i s s u e s i n t h e c o n t e x t of W a l r a s i a n models.

t h e " r e s t of t h e world," which buys e x p o r t s and s e l l s impor t s , and a "bank' o r

agg rega t e c a p i t a l account which c o l l e c t s s a v i n g s and buys inves tment goods.

The a s s o c i a t e d system c o n s t r a i n t s a r e t h e equa t ions s p e c i f y i n g balance-of-

payments e q u i l i b r i u m and savings- investment e q u i l i b r i u m , which we d i s c u s s i n

3 1 1 more d e t a i l b e l o u

A s a benchmark, one should s t a r t w i th t h e c l a s s i c a l model which tries

t o c a p t u r e such macroeconomic phenomena by s imply adding some new marke t s -

The ba lance of payments is modeled by a&iPng a market f o r for t i ign exchange i n

which stipply i s gene ra t ed by s e l l i n g e x p o r t s and demand by buying i m p o r t s - A

new p r i c e , t h e exchange r a t e , is in t roduced a s ' the e q u i l i b r a t i n g v a r i a b l e -

Sav in~s - inves tmen t is modeled by adding a market f o r " loanab le funds" i n w h i c h

supply i s g iven by s a v i n g s and demand by investment . Both supply and denand

a r e assumed t o be s e n s i t i v e t o t h e i n t e r e s t r a t e , which i s t h e new

e q u i l i b r a t i n g v a r i a b l e . I n terms of t h e framework i n Table 1, t h i s classical

approach is r e a l l y an a t t empt t o keep macroeconomics i n t h e Walras ian

framework. No s p e c i a l t r ea tmen t of nominal f lows i s r e q u i r e d . One s i m p l y

d e f i n e s new commodities, markets , and p r i c e s which a r e added t o t h o s e on the

l e f t s i d e of Table 1. While appea l ing , few economists would accep t t h i s

approach wi thout e x t e n s i v e q u a l i f i c a t i o n s . These new "markets" a r e c l e a r l y - t

s p e c i a l and t h e "commodities" a r e q u i t e d i f f e r e n t from f a c t o r s and produced

~ o o d s . They r e a l l v do n o t f i t t h e s i m n l e W a l r a s i a n pa rad igm o f a b a r t e r

econony i n which only r e l a t i v e p r i c e s ma t t e r . 3 - 0 -

The i n t e r m c t i o n s between t h e r e a l and nominal s i d e s of T a w e 1 h a v e . * provided much f u e l f o r economic cont roversy . A t one ex t reme, i n a world of

311 I n our d i s c u s s i o n , w e w i l l focus on t h e system c o n s t r a i n t s and t h e c h o i c e - of e q u i l i b r a k i n g v a r i a b l e s , and n e g l e c t any d e t a i l e d d i s c u s s i o n of t h e b e h a v i o r a l r u l e s of t h e i n s t i t u t i o n a l a c t o r s .

c o m p e t i t i v e marke t s and n e u t r a l money, t h e r e a l economy is i n s u l a t e d i r o ~

" d i s t u r b a n c e s " emanat ing from t h e nominal s i E e . M u l t i s e c t o r p l a n n i n g m o d e l s

have u s u a l l y focused e x c l u s i v e l y on t h e r e a l s p h e r e , w i t h a medium t o long

te rm h o r i z o n , and have i g n o r e d l i n k s between :he r e a l and nominal s i d e s , Irm a

c o m p e t i t i v e economy, Ln which t h e r e is f u l l employment of a l l f a c t o r s , such a

f o c u s is c l e a r l y w a r r a n t e d . Both t h e o r y and e x p e r i e n c e wit-h e m p i r i c a l d e l s

i n d i c a t e t h a t w h i l e d i s t u r b a n c e s i n t h e nominal s i d e of t h e model may affect

t k 2 c o m p o s i t i o n of p r o d u c t i o n and demand, t h e y have l i t t l e e f f e c t on a g g r e g a t e

o u t p u t and growth i n a c o m p e t i t i v e n e o c l a s s i c a l wcrLd. U n f o r t u n a t e l y , the

r e a l world d o e s n o t a p p e a r t o be s o f l n x i b l e and e x h i b i t s phenomena s u c h as

pro longed p e r i o d s of unemployment, wide v a r i a t i o n s i n growth r a t e s , and s t rong

l i n k s from macroeconomic a d j u s t m e n t mechanisms t o t h e r e a l economy. M o d e l e r s

have l o n g s o u g h t t o c a p t u r e s u c h phenomena i n models a p p l i e d t o b o t h d e v e l o p e d

and less developed economies. We w i l l d i s c u s s two examples from t h e d e v e l -

opment. l i t e r a t u r e t h a t f o c u s on sav ings - inves tment e q u i l i b r i u m . t h e C h e n e r y

two-gap model and t h e L a t i n American d i s t r i b u t i o n a l o r s t r u c t u r a l i s t m o d e l s .

The two-gap model s t a r t s from t h e b a s i c p r e m i s e that . , i n a d e v e l o p i n g

c o u n t r y , r e a l i n v e s t m e n t and p r o d u c t i o n r e q u i r e i m p o r t s of c a p i t a l g o o d s a n d

i ~ : t . e r m e d i a t e i n p u t s . The e x i s t e n c e of such "non-cornpet< t ive . " i m p o r t s of

c r u c i a l i n p u t s is a c h a r a c t e r i s t i c f e a t u r e of many development p l a n n i n g models

w i t h w h i c h Chenery i s a s s o c i a r ~ c ! T,t. i s o5e of :\le ZL-I jor :S-I!:,I~.>; :,f .;,!,;I-

he h a s c a l l e d t h e " s t r u c t u r a l i s t " approach t o development p o l i c y and p r o w i d e s a - 3 3 / s t r o n g p o t e n t i a l l i n k between t h e b a l a n c e ~ l ? ~ a ~ m e n t s and t h e r e a l econopy-

We can j u s t i f i a b l y d e s c r i b e t h e r e s u l t i n g p o t e n t i a l i m ~ a c t of f o r e i g n exchange

3 2 / See Chenery (1980) , C h a p t e r s 4 , 8, 9 , and 1 0 , and Adelman and C h e n e r y - (1966) .

3 3 / See Chenery (1975) and Chenery ( 1 9 7 9 ) , Chap te r 2. -

s h o r t a g e s on p roduc t ion and growth i n a model a s t h e "Chenery e f f e c t ." The two-gap model, wi th i t s r i g i d i t i e s and assumpt ion of non-

c a n p e t i t i v e , complementary impor t s , h i g h l i g h t s t h e impact of t h e b a l a n c e of

payments on t h e r e a l economy. However, t h e Chenery e f f e c t remains i m p o r t a n t t

even i n a model i n which more s u b s i t u t a b i l i t y is assumed.34/ - One can t h u s

i c a p t u r e t h e impact of f o r e i g n exchange c o n s t r a i n t s on growth i n CGE model,

which assume s u b s t i t u t a b i l i t y , p r i c e f l e x i b i l i - t y , and market c l e a r i n g .=/ The

essence of t h e Chenery e f f e c t and of t h e two-gap model r ema ins , even i n d e l s

which a r e f a r more n e o c l a s s i c a l t han any of t h e e a r l y programming models i n

which t h e i d e a s were f i r s t embodied.

I n t h e two-gap model, f o r e i g n exchange and s a v i n g s provide t h e focus

of macroeconomic equ i l i b r ium. Another s t r a n d of vork i n t h e de-~e lopment

l i t e r a t u r e focuses on t h e l i n k s between t h e d i s t r i b u t i o n of income, a g g r e g a t e

s a v i n g s , and hence macroeconomic equ i l i b r ium. The n a t u r e of t h e l i n k s d e p e n d s

on the way i n which savings- investment e q u i l i b r i u m i s achieved . According to

what h a s been c a l l e d t h e L a t i n American " s t r u c t u r a l i s t " s c h o o l , r e l a t i v e p r i c e

mechanisms--including a f l e x i b l e exchange rate--cannot ach i eve macro

e q ~ i l i b r i : ~ ~ because of s t r u c t u r a l r i g i d i t i e s i n c e r t a i n markets.=/ A

d i f f e r e n t mechanism t h a t works through changes i n t h e d i s t r i b u t i o n of i n c a n e I I

'* i s s p e c i f i e d . The fundamental assumption is' t h a t c e c i p i e n t s of c a p i t a l and

.* 3 4 1 d i c h a l o p o u l o s (1975) d i s c u s s e s a two-gap model i n which imported and - comes t i c c a p i t a l goods a r e subs t i t u t a b l e acco-ding t o a CES f unct io;,

l&rvls , de Melo, and Robinson (1982) deve lop t h e i m p l i c a t i o n s :f i m f i r f e c t S t b s t i t u t a b i l i t y i n some d e t a i l i n t h e con tex t of CGE models.

35/ See, f o r example, Derv is and Robinson (1982) who u s e a CGE model t o - ana lyze t h e causes and ir .gact of a foreig.1 exchange c r i s i s i n Turkey, F ind lay (1973) , Chapter 1 0 , makes t h e same t h e o r e t i c a l po in t and a r g u e s t h a t t h e two-gap model can be s een a s a s p e c i a l c a s e of a n e o c l a s s i c a l model.

361 See, f o r example, Diamand (1978). -

wage income have d i f f e r e n t s a v i n g s r a t e s and hence changes i n t he d i s t r i b u t i o n

of income .*.ill a f f e c t o v e r a l l s av ings . T h i s "Kaldor e f f e c t " p rovides a m a j o r

37 1 l i n k between t h e r e a l economy and t h e nominal side,,

Tay lo r (1979) d i s c u s s e s a number of models t h a t not only i n c o r p o r a t e

t h e Kaldor e f f e c t , but a l s o make two assumptions about t h e i n s t i t u t i o n a l

s t r u c t u r e of t h e economy. F i r s t , agg rega t e inves tment i s f i x s d exogenously

and, second, t h e wage is assumed not t o c l e a r t h e l abo r market. The f i r s t - c a n

be s een a s a c a d d i t i o n a l system c o n s t r a i n t d e f i n i n g macroeconomic e q u i l i b r i u m

i n t h e nominal s i d e . g l The second p r e s e n t s a more d i f f i c u l t problem of

i n t e r p r e t a t i o n .

I n terms of t h e framework i n Table 1, the assumption t h a t t h e l a b o r

market does no t c l e a r i m p l i e s t h a t one should drop t h e cor responding sys t em

c o n s t r a i n t i n equa t ion (6). Some assumption must a l s o be made about how t h e

exces s supply i s r a t i o n e d i n t h e system--what happens t o t h e unemployed? The

s i m p l e s t t r ea tmen t is t o assume t h a t f i r m s a r e always on t h e i r demand c u r v e s

S f o r l abo r . I n equa t ion (7) , F is r ep l aced by $, and t h e unemployed a r e

e s s e n t i a l l y assumed t o drop o u t of t h e econcmy. They r e c e l v e no income and

g e n e r a t e no e f f e c t i v e demand.- 391 The l a b o r supply f u n c t i o n i n equa t ion ( 3 )

becomes a s i d e equa t ion to compute t h e amount of unemployment, but has no real

& f f e c t on t h e model economy. Note t h a t t h i s ' t rkatment e n s u r e s t h a t t h e '

remaining system c o n s t r a i n t equa t ions s t i l l s a t i s f y Walras' Law. -

Given t h a t t h e s y s t m c ~ s t r a i r ~ t f o r t h e l a b o r market is dropped, L

371 See Kaldor (1955). - 381 The assumption of f i x e d agg rega t e inves tment is u s u a l l y s p e c i f i e d i n real -

terms, bu t can be j u s t as e a s i l y handled i n nominal t-erms.

391 The unemployed could a l t e r n a t i v e l y be assumed t o r e c e i v e income th rough - t r a n s f e r s wi th* ~t changing t h e e s s e n t i a l n a t u r e of t h e model.

what t hen is t h e r o l e of t h e tor-responding wage i n t h e new model? I n t h e s e

models, t h e r e a l wage becomes t h e e q u i l i b r a t i n g v a r i a b l e t o ach i eve s av ings -

inves tment e q u i l i b r i u m on t h e nominal s i d e . The wage a d j u s t s t o a c h i e v e &

d i s t r i b u t i o n (and l e v e l ) of income t h a t g e n e r a t e s t h e neces sa ry s a v i n g s t o 4

v a l i d a t e t h e exogenous l e v e l of inves tment , and t h e r e is an "equ i l i b r ium" real

c wage t h a t a c h i e v e s macro ba lance . A s w i t h t h e two-gap approach, t h e e x t r e m e

v e r s i o n of t h e model s e r v e s t o focus a t t e n t i o n on an impor tan t mechanism.

Both foreign-exchange-product ion l i n k s and d i s t r i bu t ion -mac ro l i n k s a p p e a r t o

be very impor t an t i n s t i t u t i o n a l c h a r a c t e r i s t i c s t h a t should be i n c o r p o r a t e d

i n t o models of deve loping econoiaies, even a t t h e p r i c e of compromising t h e

p u r i t y of t h e Arrow--Debreu model.

6. Conclusion

M u l t i s e c t o r models have come a long way from t h e e a r l y s t a t i c input -

ou tpu t model. Throughout t h e i r development, t h e r e h a s a lways been a t e n s i o a

between e m p i r i c a l p r a c t i c e and a v a i l a b l e theory . Recen t ly , wi th t h e r a p i d

advances i n s o l u t i o n a l g o r i t h m s , t h e gap between t h e development of new

t h e o r e t i c a l models and t h e a b i l i t y t o implement them e m p i r i c a l l y has nar rowed

cons ide rab ly . Indeed, r e c e n t models a r e o p e r a t i n g on t h e border between macro

and micro t heo ry , where t h e r e a r e many t h e o r e t i c a l i n c o n s i s t e n c i e s and no 0 *

widely accep ted r e c o n c i l i a t i o n . The f i e l d is very a c t i v e , wi th a number o f

d f f f e r e n t a p p r o a c h e s b e i n q p u r s u e d ~ i m u l t a n e o u s l v . Our p u r p o s e has been t o

s -or t o u t some of t h e l i n k s among t h e d i f f e r e n t approaches and t o i n d i c a t e the -

l i n e a g e t h a t n r e l a t e s t he c u r r e n t models t o p a s t e m p i r i c a l p l e n i n g models, as 0

well a s t o t h e o r e t i c a l l y founded g e n e r a l e q u i l i b r i u m models.

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