Seminários de pesquisa econômica, 1986

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SEMINÂRIO DE PESQUISA ｅｃｏｎｾｍｉｃａ＠ 11

Ｈｬｾ＠ e Ｒｾ＠ partes) 1986

SUMÂRIO

- Análise de longo prazo com um modelo multi-setorial dinâmico da economia brasileira.

OCTÂVIO TOURINHO.

- Macroeconomia com racionamento: um modelo simplificado. RUBENS PENHA CYSNE.

- O Estado do Rio de Janeiro, e a questão do setor terciário. RALPH MIGUEL ZERKOWSKI.

- Heterogeneity, aggregation, and market wage functioBs: an empiri-cal model of self-selection in the labor market.

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-ESCOLA DE

ｐｾｓＭｇｒａｄｕａｃￃｏ＠

EM ECONOMIA

DO INSTITUTO BRASILEIRO DE ECONOMIA

DA FUNDACÃO GETOLIO VARGAS

C I R C U L A R N9 36/86

Assunto: Seminários de Pesquisa

Econômica

11

(la.parte)

Convidamos V.Sas. a participar do Scminário/EPGE

a ser realizado na oróxima 5a. feira:

Data:

07 de agosto de 1986

Horário: 15:30h

ｾｳ＠

17:30h

Local:

Auditório Eugênio Gudin - EPGE/FGV

Praia de Botafogo 190 - 109 andar

TEMA:

"ANALISE DE LONGO PRAZO COM UM MODELO MULTI-SETORIAL

DINÂMICO DA ECONOMIA BRASILEIRA"

Dr. Octávio Tourinho - IPEA

Rio de Janeiro, 31 de julho de 1986.

ＨＱ､ＧｴｾＧＭＭ

ｾ･ｹ＠ ｃｯｾ､･＠

Oliveira

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-TEXTOS PARA DISCUSSAO INTERNA

N9

86

"0 ptimal Foreign BorrO\ving in

a Multisector Dynamic

Equi1i-brium Model: A Case

Study

for Brazil

ll

•

Octãvio A. F. Tourinho

Janeiro de 1986

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-Tiragem: 100 exemplares

Trabalho elaborado em:

Agosto de 1985

Instituto de Pesquisas do IPEA

I ns tituto de Planejamento Econômico e Social

Avenida Presidente Antonio Carlos, 51

- 139/179

andar

2Ú.020

Rio de Janeiro

RJ

Este trabalho

e

da inteira e exclusiva responsabilidade de seu autor. As opl

niões nele emitidas não exprimem, n2cessariamente, o ronto de vista da

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OptiRal Foreign Borrowing in a

Xultisector ｄｹｮｾｾｩ｣＠ ｅｱｵｩｬｩ｢ｲｩｵｾ＠ r.oàel:

A

Casa Sludy for Brazil

1

by

Oclavio A. F. Tourinho2

Instituto de PlaneJamento ｅ｣ｯｮｯｾｩ｣ｯ＠ e Social - Brazil

Paper prepared for the ORSA/TIMS National Meeting

held at Los Angeles, April 14-16,1986

1 This vork was done whila the author was a Visiting Ｕ｣ｨｯｬｾｲ＠ at the Center for

Energy Policy Reseorch at the HIT Energy ｌｾ｢ｯｲｯｴｯｲｹ＠ undDr UNESCO/FINEP

fellowship BRA/82/4. FinanciaI support of UNESCO, FINEP ond I?EA is

grotefully ocknowledged. A previous version oi this 8SS0y oppeorod, as

Worxing Papar ＸｾＭＰＰＹｾ＿＠ of the MIT Energy Louorotory (June 1985).

2 ｾｨｩｬ･＠ retaining ｾｯｬ｡＠ accountability for the research ond the ｦｯｲｾ＠ in which

it is prosentad. the Quthor wishes to thonk Charlo. R. Blitzer for help in the

ｾｯ､･ｬ＠ specificotion ond suggestions on the data hondling procedures, Richard

Eckaus, Alan r.anne ond Joaquim Tolado for ｣ｯｾｾ･ｮｴｳ＠ on a previous droft, ond

Alex Meeraus and Alan Gelb for ｾｑｫｩｮｧ＠ the ｾｯ､･ｬｩｮｧ＠ aystea oí the Uorld Bank

availeble for this research.

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-ｾ＠

ABSTRACT

Th1ü paper Ｖｨｯｾｳ＠ how a ､ｹｮｾｮｩ｣＠ ｾｵｬｴｩＵ･｣ｴｯｲ＠ ･ｱｵＱＱｩ｢ｲｩｵｾ＠ ｾｯ､･ｬ＠ can be

fornuloted to be ｾ｢ｬ･＠ to ｯｮｾｬｹｺｇ＠ the ｯｰｴｩｾｾＱ＠ borrowing policy of a deve10ping

country. It olso describes how a non-linear ｰｲｯｧｲ｡ｾｾｩｮｧ＠ ｾｯ､･ｬ＠ wilh lha

prapased {e atures was constructed for Braz!1, and d1scueses the ｯｰｴｩｾ｡ｬ＠

solulion of a base cc se scenario for the ･｣ｯｮｯｾｹ＠ in the next 20 years. Tha

sensitivity ona1ysis ･ｲＮＨｰｨｾｳｩｺ｣ｳ＠ the rasponse of the ｾｯ､･ｬ＠ to different

interest rotos on foreign borrowing. alternativa export ･ｸｰｾｮｳｩｯｮ＠ and ｩｾｰｯｲｴｳ＠

requ!ienents acenarias, and different hypothesis with reapect ta future petroleun priccs and dOMestic petrolcum production. The "ain conclusion ia

that tha ｯｰｴｩｾ｡ｬ＠ 10ng run borrowing policy for Brazi1 is quite sensitive to

tha expected fulu4e interest ｲｾｴ･ｳＮ＠ and múy be different from ｳｯｾ･＠ ｾｹｯｰｩ｣＠

strategies which ora current1y being suggested to ｨｾｮ､ｬ･＠ tha developing

countries' foreign dobt ｰｲｯ｢ｬ･ｾｳＮ＠ The oLher ｩｾｰｯｲｴ｡ｮｴ＠ conclusion 1s that in

tha 18SS íavorable scenarios - protectionist foroign ･ｮｶｩｲｯｮｾ･ｮｴ＠ or higher

ｰ･ｴｲｯｬ･ｵｾ＠ pricos - it is not ｯｰｴｩｾ｡ｬ＠ to postpona the rQquired ､ｯｾ･ｳｴｩ｣＠

odJustnentú by incroasod foreign borrowing. Tha usefulness of tha model is not restricted to this Get of óimulations, sinca it con ba readily adapted to

oddress reloted issues such as foroign trode, ｩｮｶ･Ｆｴｾ･ｮｴ＠ ond indirect taxotion

policies.

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-1-1 ｾ＠ ItlTRODUCTIOX

In tha waxe of the recent internetionol financieI crisis. the need was

falt to address severa I interconnectsd questions of long-range ｮ｡｣ｲｯ･｣ｯｮｯｾｩ｣＠

planning in Brazil. They are ｾ｡ｩｮｉｹ＠ related to ｧｯｶ･ｲｮｾ･ｮｴ＠ policy with respect

to the foreign dobt. the trado balanca. cnd tha interscctoral allocation of

investnent • Tha choice between high and low foreign indebtedness wi11 ｨｾｶ･＠

to ba ｾ｡､･＠ in a context whara borrowing is costly and con ｾｮｬｹ＠ bo avoided by

generating larga trade surp1uses which constrain the growth of ､ｯｾ･ｳｴｩ｣＠

. ｣ｯｮｳｵｾｰｴｩｯｮＮ＠ Efforts deGigned to generate theso surplus9s through reduced

i.ports and increased exports will affect the size and sectoral cornposition of

output. require shifts in tha allocation of capital and labor in tha ･｣ｯｮｯｾｹＮ＠

and 1ead to ｡､ｊｵＵｴｾ･ｮｴｳ＠ in tha ｩｮｶ･ｳｴｾ･ｮｴ＠ patterns.

Thes9 iesues con be taken into account in an E:!con01\y-wide dyna .. ic

ｯｰｴｩｾｩｺ｡ｴｩｯｮ＠ ﾷｾｯ､･ｬＮ＠ which con be úpecified to be abla to ｇｶ｡ｬｾ｡ｴ･＠ tha

sovings-｣ｯｮｳｵｾｰｴｩｯｮ＠ trcdeoff. and incll1do the restrictions in tho forEign accounts and

in tha factor availcbilities. Tha activity leveIs and capital stock in each

sector. as we11 as the trade balance and net borrowing ｲ･ｱｵｩｲｾｾ･ｮｴｳ＠ can be

｣ｾｬ￧ｵｬ｡ｴ･､＠ endogenously to ｾＶｸｩｮｩｺ｡＠ ｳｯｾ｡＠ specified uti1ity function. which

insures thal lhe solution of the ｾｯ､･ｬ＠ has the desirable efficiancy

propertias.

Planning ｾｯ､･ｬｳ＠ with ｳｩｾｩｬ｡ｲ＠ obJectives ｨｾｶ･＠ bocn specifled and

ｩｾｰｬ･ｾｯｮｴ･､＠ for a nu .. bor of countria5. as 5urvayed by Taylor (1975). and ｾｯｲ｡＠

rocently by Dervis. de Melo ond Robinson (1982). Tha aodo1 described in this

pap3r i5 5ir.ilar ir. úow9 respect5 to tha one built by Blitzor and Eckaus

[1983) for Xexico. bul ｯｾｰｨ｡ｳｩＲ･ｳ＠ tho ｡ｳｰｾ｣ｴｳ＠ that se6=ed nost rolevant for

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-2-the analysis of -2-the Orazilion éituation1 • The innovotions of th8 ｾｯ､･ｬ＠

propoGsd here are a rather deta1led ｲ･ｰｲ･ｳｾｮｴ｡ｴｩｯｮ＠ oi the ío:eign debt

､ｹｮｾｾｩ｣ｳＬ＠ tha lib0ral UG8 of non-linear ｲｯｬ｡ｴｩｯｮｾｨｩｰｳ＠ in tha utility funclion

cnd in the interesl ｲｾｴｑ＠ calculations, Dnd ｾ＠ novQI ｳｾｾ｣ｩＡｩ｣ｑｴｩｯｮ＠ of the

ｴ･ｲｾｩｮ｡ｬ＠ utility tern; 011 in th8 qU8St of attoining ｾｯｲ｡＠ ｲ･｡ｬｩｇｾ＠ in the

Ｑｮｴ･ｲｴｾｾｾｯｲ｡ｬ＠ choic8 espects of the ｰｲｯ｢ｬ｣ｾＮ＠

Several ･｣ｯｮｯｾｹＭｾｩ､ｑ＠ Ｐｱｵｩｬｩ｢ｲｩｵｾ＠ nodels ｨｾｶ･＠ b2cn built far Br&zil 1n

lhe ｰｾｾｴＮ＠ but ｮ｡ｮｾ＠ ｳｴｲ･ｾＦ･､＠ the ｦｯｲ･ｩｾｮ＠ ､ｾ｢ｴ＠ ｰｲｯ｢ｬｑｾ＠ and thQ ｬｮｬ￧ｲｴｑｾｰｯｲ｡ｬ＠

chaice iCGUGS ｯｳｳ｣ｩｾｴ･､＠ uith it. LyGy ｾｮ､＠ Taylor [1930) used a ｊｯｨ｡ｮｳｯｮＭｴｹｾ･＠

podeI to analyza inco=e distribution issucs in the ＧＷＰｾＬ＠ with a ｲｾ､ｩｵｾＭｲｵｮ＠

perspectivo. Th3ir ｾｯ､ＳＱ＠ ｩｮ｣ｯｲｰｯｾｾｴＸｳ＠ ｾ＠ dotailcd ｩｮｰｾｴＭｯｵｴｰｵｴ＠ ｲｇｰｲｇｳｯｮｴｾｴｩｯｮ＠

Df thG productivQ sector, but does not includa any ￭ｯｲｾ｡ｬ＠ utility

ｾｯｸｩｾｩｺ｡ｴｩｯｮＮ＠ ｾｯ､ｩ｢ｮｯ＠ [1983J linked a procGss ｲ｣ｰｲｾｾｾｮｴｑｴｩｯｮ＠ of the onergy

systen with ｾ＠ ､･ｴｾｩＡ･､＠ ｣｣ｯｮｯｾ･ｴｲｩ｣＠ ｾｯ､･ｬ＠ of the rest of the econopy, in a

rtodel \-ihero the j-,,:a-);<:?t equilibriuM fOl- onurs-y uoods i6 found by r,õxil."lizing

｣ｯｮｳｵｾ･ｲｳＧ＠ plus ｰｲｾ､ｵｾ｣ｲｳＧ＠ 5urplua. ｔｨｾｴ＠ ｾｯ､ｑｬ＠ i9 eolv2d ｦｯｲｷｾｲ､＠ in tiPG,

without d}'II<;rnic ｯｰｴｩｄｩｺｾＧＮＺＮｩ｣ﾷｮＬ＠ und dOGo nat inc.:lude o ､ｩ｣･ｳｳｲＨｬｧｾｴ｣｣Ｎ＠

ｲｾｾｲｑｳｾｮｴｾｴｩｯｮ＠ oi tho ｩｮｴ･ｲｳ･｣ｴｯｲｾｬ＠ flows, os tha ono hore. McCarthy (1983)

II0s built a non-optirizing ｾｯｾｯｬ＠ for identity-hacDd ｾ｣､ｩｵ｡Ｍｲｵｮ＠ policy

･ｾ｡ｬｵ｡ｴｩｯｮ＠ which inc!udes the inlersectoral flows, ｾｮ､＠ also Ｘｴｴｃｾｰｴｳ＠ to

ｾ｣｣ｯｵｮｴ＠ for alI the ｦｩｮ｡ｮ｣ｩｾｬ＠ flovs ond budgGt ｲ･ｱｵｩｲ･ｾ･ｮｴｳ＠ of the several

actora oí the ･｣ｯｮｯｾｹＮ＠

1 Tho nain ､ｩｦｦ･ｲｾｮ｣ｾｳ＠ are a ;;ore ｾｇｴ｡ｩｊｾｾ＠ ｲｾｰｲｯＵ･ｮｴ｡ｴｩｮ＠ of tha borrowing

coste" i.!nd U,e ll<,.e of a •. '::H'8 õ!ltit"ioc:torl' ｦＨＮＺＺｲＮｵｬｾｴｩｯｮ＠ oi the ｴｅＭｲｲＬｩｮｾｬ＠

cünditiC'lls. In .Jdditicr" lhe r.oa!"'l prcsl=nt·,:d hQ-re ｶｾｳ＠ solved vith '"

non-ｬｩｮｄｾｲ＠ ｲｲＰＳｲｾｾｾｩｮｧ＠ ｇｬｳｯｲｩｴｨｾ＠ ｶｨｩｾｨ＠ is apt to provida ｊｾｯｲｯ＠ ｰｲｯ｣ｩｾｇ＠ r00ults ｴｨｾｮ＠

tho lir."'.:lr progranr.ing ［｝ｰｰｲｯｾＺｩＺＺｾｬｩＰｮ＠ u:;c.:d in lhe r.uxico ilodcl.

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-3-This papar also ､･ｾｯｮｳｴｲ｡ｴ･ｳ＠ that it i5 now possible to aasily solve

ｮｵｾ･ｲｩ｣｡ｬｬｹ＠ ｳｯｾ･＠ of the ｳｩｾｰｬ･ｲ＠ discreta ｴｩｾ･＠ non-linear neoclassical ｯｰｴｩｾ｡ｬ＠

control problens that arise in aodela of ･｣ｯｮｯｾｩ｣＠ growth. Thanxs to MINOS, a

program developed by Kurtagh and Saunder5 [19833, optimization packages are

now capable of handling a sizeable ｮｵｾ｢･ｲ＠ of non-linear relationships, both in

the obJective function and in the restrictions (the latter at a sOlle .... hat

highGr cost), liberating tho ･ｾｰｩｲｩ｣｡ｬ＠ nodel builder from the straight-Jacxet

of linear programming or the purely Gtatic ･ｱｵｩｬｩ｢ｲｩｵｾ＠ modcls.

The plan of the paper is 88 follo .... s. The next section presents the

model formulation, addressing ｳｯｾ･＠ of the possible extensions. Section 3

describes very briefly ｳｯｾ･＠ aspects of the ｩｾｰｬ･￣･ｮｴ｡ｴｩｯｮＬ＠ while section 4

presen.ts the "base case" solution. Section 5 contains the Gcnsitivity

analysis, with the discussion of the Rain issuea the ｾｯ､･ｬ＠ ｾ｡ｳ＠ ｾ･｡ｮｴ＠ to

address. Tha conclusion is in section 6.

2. MODEL FORMULATION

ｉｮｴ･ｲｴ･ｾｐｑｲ｡ｬ＠ choice ｰｲｯ｢ＱＸｾｳ＠ con be treated consistently in the dynanic

gen8ral equilibrium ｦｲ｡ｾｯｷｯｲｫ＠ of ｯｰｴｩｾ｡ｬ＠ growth ｾｯ､･ｬｳＮ＠ These con be extended

by including foreign debt as another ｳｴｾｴ｣＠ variabla, allowing the analysis of

the Joint ､･ｴ･ｲｾｩｮ｡ｴｩｯｮ＠ of the ｴｩｾ｡＠ poths of savings, ｣ｯｮｳｵｾｰｴｩｯｮ＠ and

borrowing that ｲＮ｡ｸｩｾｩｺ･＠ the ､ｩｳ｣ｯｵｮｴｾ､＠ value of the strean of utility iroa

futura con6umption. Two approoches can ba usad to onalyza ･｣ｯｮｯｾｩ･Ｖ＠ ｾｯ､･ｬｬ･､＠

in thi8 way. Ooe, takeo by Blanchard [1983], 1s to work in continuou5 ｴｩｾ･＠

and ･ｾｰｬｯｹ＠ ｯｰｴｩｾ｡ｬ＠ control ｾ･ｴｨｯ､ｳ＠ to derive onalyticolly the systeQ oí

differential equotions to be satisfied by the optinal poths. The other, which

ia pursued hera, i6 to solve ｮｵｾ･ｲｩ｣｡ｬｬｹ＠ a ､ｩｳ｣ｲ･ｴ｡Ｍｴｬｾ･＠ ｡ｰｰｲｯｸｬｾ｡ｴｩｯｮ＠ to the

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-<1-original ｾ｡ｸｩｾｩｺ｡ｴｩｯｮ＠ problem. Tha trod00ffs ore cloor: tha first ollows ｾ＠

ｾｯｲ･＠ ｣ｹｳｴ｣ｄｾｴｩ｣＠ explorotion of the underlying propertia$ of the ｳｹｳｴ･ｾＬ＠ while

tha s0cond ｰｯｲｾｩｴＶ＠ the use of a nora dutoilcd ｾｵｬｴｩｅｯ｣ｴｯｲｯｬ＠ ropresantation of

the ectual ･｣ｯｮｯｾｹＮ＠ ｔｨｾ＠ enalytical approach does not render ｮｵｾ･ｲｩ｣｡ｬ＠

optinizntion useless, b2COUSO it tu.ns out thot the paths of the voriobles

will in genernl ｾ･ｰ｣ｮ､＠ very ｾｵ｣ｨ＠ on the initial conditicns of the dynanic

systGn, whilo on tha othGr ｨｾｮ､Ｎ＠ tho onclytiçal Golution i6 indispensable as a

benchi'Ç.rk \Ihen ir:plc:'8nting éln ｣ｾｰｩｲｩ｣ＮＺｬｾＮ＠ l-odel. In chort, the two ｾ＿ｰｲｏＬＺＱ｣ｨ･Ｕ＠

are highly ｣ｯｾｰｬｇｾｾｮｴｾｲｹＮ＠

The ￠ｩｳ｣ｲ･ｴｾＭｴｩ￭Ｎ･＠ ｾｵｬｴｩｳｧ｣ｴｯｲｯｬ＠ nodel specifiod below chooses ｶ｡ｲｩ｡｢ｬ｣ｾ＠

in ench period such ｾＳ＠ L0ctoral production. ｳｾ｣ｴｯｲ｡ｬ＠ ｩｮｶ｣ｳｴｾ･ｮｴＮ＠ sectoral

iGports and cxports, foreign ｢ｯｲｾｯ｜ＩｩｮｧＬ＠ Gnd ｣ｯｮｳｵｾｰｴｩｯｮ＠ leveI ônd ｣ｯｾｰｯｳｩｴｩｯｮＬ＠

SUbJ8Ct to ｶｾｲｩｯｵｳ＠ ｣ｯｮｳｴｲｾｩｮｴｇＮ＠ Thcse ar8 Lh8 ｮｾｴ･ｾｩｾｬ＠ balcnçes. the foreign

exchcrlge balence, the labor supply ｣ｯｮｳｴｲｾｩｮｴＮ＠ ｾｮ､＠ the dynanic oquations for

debt and ｣ｾｰｩｴ｡ｬ＠ ｣｣｣ｵｾｵｬｯｴｩｯｮＲＮ＠

The ｦｯｲｒ｡ｬｩｾｾｴｩｯｮ＠ of the ｾｾｩｮ＠ ｣ｳｰｾ｣ｴｳ＠ of ｴｨｩｾ＠ ｰｲｯＹｲｾｒｒｩｮｧ＠ ｰｲｯ｢ｬ･ｾ＠ i5 in

the r:<:'xt !:.1Jb-sectiorl2.. h,n.:.?re thc Ｇｮｯｴｾｴｩｯｮ＠ is as follo\Js. In th0 (;quutions,

the Gire.bols i ond J c.l·e 1,.;sed as rOH und cc-lunn indices f-ar Lhe vectors and

metric8S, ｾ･ｮｯｴｩｮｧ＠ ｲ｣］ｰｾ｣ｴｩｶ｣ｬｹ＠ goods end Frcducing s8ctors. The ｰ｡ｲｯｾｯｴｾｲｳ＠

｡ｲｾ＠ ｧＲｮ･ｲＮｾＱＱｹ＠ denoted by ｬｯｾ･ｲＭ｣ｯ｣･＠ ｉ｣ｴｴｾｲｳＬ＠ ｾｮ､＠ cxogcnous v8ri3bles by

ｃｑｰｩｴｾｬ＠ Iottaro with bars undar ｴｨｾｭｾ＠ Tho ｩｮ､｣ｾ･ｳ＠ t and 9 denote ｴｩｾ･＠

pcriods, eJll of length n yeors, ｾｮ､＠ alI ｴｨｾ＠ ｶｾＬｴＢｩｇ｢ｬ｣ｳ＠ Qre r,pecified in }'e'lrly

ｴ｣ｲｾ･Ｎ＠ ｉｲｾｴｲｩｸ＠ ｾｵｾｴｩｰｬｩ｣ｯｴｩｯｮ＠ ｾｮ､＠ internol products bre dcnoted ｲ･｣ｾ･｣ｴｩｶ･ｬｹ＠

by a Etar cnd u dot ｾ｣ｴｷ｣ｾｮ＠ ｴｨｾ＠ two firrcye.

2 ｾｯｲｲｯｾｩｮ￧＠ ｩｴｾｾｬｦ＠ i6 not constrained. ｾｯｾ＠ is tho ＶｾｶｩｮＹｳ＠ rote. since the ｴＧＬｯｾＬＩｬ＠ ｴＮ［Ｑｉｪｏｾ･Ｖ＠ ｴｨ｣ｅｾ＠ laveis ｬＺ＾ｾｳ｣､＠ on ｃＧｃＧｾｾＢＺｲｩｮｧ＠ COl'jts cnd bonofits ot t!le nc.rgir ••

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-5-2.1. Ob)octlve Function

The existence of a repreúentat1ve consu"er 1s ossuned, and tha ob]ective

function of tha plonning problcm is ｣ｯｾｰｯｳ･､＠ of two ･ｬ･ｾ･ｮｴｳＺ＠ the sua over the

pIon horizon oí the total util1ty in eoch period properly discountcd Cat a

rata õ), plus tha discounted volua of post-terminal utility. Tha yoarly

ut11ity (Ut) and the,terminal utility are specified in ｰ･ｲＭ｣｡ｰｩｴｾ＠ terns, and

are ｾｵｬｴｩｰｬｩ｣､＠ by population ＨｾｴＩ＠ to obtain total ｾ･ｬｦ｡ｲ･Ｎ＠

(1)

As discussed in s8ction 2.5, the ｰｯｳｴＭｴ･ｲｾｩｮ｡ｬ＠ per-copito utiIity (V)

includes a penolty for the accuaulated foreign debt, ｾｮ､＠ a ｰｲ･ｾｩｵｮ＠ for the

leveI of capital stock3 , which exist at the end of tha ｬｾｳｴ＠ period. It

｣ｯｾｰ･ｮｳ｡ｴ･ｳ＠ for tha truncation of the ｴｩｾ･＠ horizon, assuming a stationary

stota provails in the ｰｯｳｴＭｴ･ｲｾｩｮ｡ｬ＠ period 4 •

A generalizcd ｬｯｧ｡ｲＱｴｨｾｩ｣＠ function ｷｾｳ＠ adopted to evaluate the utility

of alternative ｣ｯｮＳｵｾｰｴｩｯｮ＠ vectors in each ｰ･ｾｩｯ､＠ (Ct)5, aainly bccause it

gives riso to an extended linear expenditure syste3

(ELES).

which has often

baan used in planning ｾｯ､｡ｬｳ＠ of this typa to characteriza ｣ｯｮｳｵｾ｡ｲ＠ ､･ｾ｡ｮ､Ｖ＠ •

3 Terninal útocks are not exogenously spocified as in other nodels in this

tredlt1on •

4 The ｴｯｲｾｩｮｾｬ＠ utility term con be interproted as fulfilling the role of the

ｰｲｩｾ｡ｬ＠ oquilibrium ｡ｰｰｲｯｸｩｾ｡ｴｩｯｮ＠ in Svoronos (1985] "oqaezing" ｑＱＹＰｲｩｴｨｾ＠ for

infinite horizon convex prograns. I thank Alan Manne for pointing this out to

1118 •

5 Tha consunption vector includos non-cor.poting ipportcd ｣ｯｮｳｵｾｰｴｩｯｮＬ＠ in

edditlon to the several othar produced goods.

6 for a discussion of extended linear expenditure systegs and their

application to Geveral countries, sse Lluch, Powoll and ｗｩｬｬｩｯｾｳ＠ (197}].

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-6-The ｰ｡ｲ｡ｾ･ｴ･ｲｳ＠ of this per-capita ut11ity function are the vector of ｾ｡ｲｧｩｮ｡ｬ＠

expenditure sharea ＨｾＩ＠ and the vector of ｒｩｾｩｮｵＮ＠ leveIs of ｣ｯｮｳｵｾｰｴｬｯｮ＠ of each

good ＨｾＩＮ＠

(2)

This obJective function ｨｾｳ＠ severa 1 desirable foatures lixe, for

･ｸ｡ｾｰｬ･Ｌ＠ ｩｾｰｬｹｩｮｧ＠ a declining ｾ｡ｲｧｩｮｯｬ＠ utility of ｣ｯｮＦｵｾｰｴｩｯｮ＠ for each good,

generating a full set of own and cross price olasticities, and internalizing

the sovings decision. For thls functional for., the elssticity of

5ubstitution of expendlture betwean two consecutiva tine periods is snaller

than unit y7, ｾｮ､＠ is increasing with inconG leveI, which is consistent with

･ｾｰｩｲｩ｣｡ｬ＠ evidence rcgarding ｣ｯｮｳｵｾ･ｲ＠ ､ｾｾｾｮ､＠ in developing countries (5ee

chapter 4 in LLuch, ｐｯｾ･ｬｬ＠ and ｗｩｬｬｩ｡ｾｳ＠ (1977]). Rubinstein (1977] has 0150

offered o host of ｡ｲｧｵｾ･ｮｴｳ＠ why a function of this typa should be ｦｾｶｯｲ･､＠ in

financa ｾｯ､｡ｬｳ＠ for analyzing intertemporel choice, particularly under

uncertointy.

i.2

Constraints and Technology

Tha description of the technology, the resource ｣ｯｮｾｴｲ｡ｩｮｴｳＬ＠ and the

balancillg equations follow the slondard nultisGctoral ｯｰ･ｮＭ･｣ｯｮｯｾｹ＠ dynamic

fornulation (eee, for exempla, T6ylor (1975l). A Leontief ｳｰ･｣ｩｦｩ｣ｾｴｬｯｮ＠ ia

7 In tha linit, when tha ratio of tha ｾＱＱＱＱｮｕｮ＠ ｣ｯｮｳｵｾｰｴｩｯｮ＠ leveI to actual

consumption for ｴｨｾ＠ Goveral goods tends to zoro, the ovarall elosticity of

5ubstitution tends to that of the ｳｴｾｮ､ｯｲ､＠ logorithDic lunction, which i5

un1ty.

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-7-usad to ｾｯ､･ｬ＠ production in ･ｾ｣ｨ＠ sactor8 , ｾｩｴｨ＠ four categorias of inputs: internediate goods, non-competitive importa, ｣｡ｰｩｾ｡ｬＬ＠ and labor.

Only labor ･ｾｰｬｯｹＹ､＠ in tha ｦｯｲｾ｡ｬ＠ ｾ｡ｲｫ･ｴ＠ i6 considered Gcarce and

included in the ｦｯｲｾｵｬ｡ｴｩｯｮＬ＠ but its Gupply i6 not "odelled explicitly, baing

｡ｳｳｵｾ･､＠ to grow at an oxogonously spacifiad rata. Tha ｩｾｰｯｲｴ｡ｮｴ＠ problea of absorbing the larga nu.bera of ｾ･ｬ￭Ｍ･｡ｰｬｯｹ･､＠ and ｳｵ｢Ｍ･ｾｰｬｯｹ･､＠ that exist in the Brazilian inforMol labor ｾ｡ｲｬｾ･ｴ＠ i6 not addro6sed herege A6 o consoquenca, tha shadow prica oí labor in the infornal sector is iaplicitly belng assumed to ba zero, which i6 an ･ｸｴｲ｣ｾ｡＠ ｯｳｳｵｾｰｴｩｯｮ＠ ｾｨｩ｣ｨ＠ probably overstatos the leverage oí capital and foraal enploynent.

For the i56U96 oddrassed in thi6 ｰｾｰ･ｲＬ＠ tha foreign exchonge balance restriction ｰｬｾｹｳ＠ a crucial role, allowing tha ｾｯ､｡ｬ＠ to endogenously caleulata tha borrowing ｲ･ｱｵｩｲ･ｾＸｮｴＶ＠ in each period. ｃｯｾｰ･ｴｩｴｩｶ･＠ ｩｾｰｯｲｴｳ＠ are ｰ･ｲｾｩｴｴ･､＠

in the ｾ｡ｴ｡ｲｩ｡Ｑ＠ balances equation, ond ｮｯｮｾ｣ｯ｡ｰｾｴｩｴｩｶ･＠ ｩｾｰｯｲｴｳ＠ ara required for dor.eatic production. For ｳｩｾｰｬｩ｣ｩｴｹＬ＠ o linear function was adopted to

calculote tha export revenues ond ｩｾｰｯｲｴ＠ oxpenditures oí oach sector, but the exogenous vGctors of foreign prices can be voried to troce tha ｣｣ｯｮｯｾｹＧｳ＠

Gupply and deDond Gehedules in variou6 scenarios. ｬｉ｡ｸｩｾｵｾ＠ exports of each

｣ｯｾｾｯ､ｩｴｹ＠ in oach period were however apocified, ｩｾｰｬｹｩｮｧ＠ that the ｾ｡ｲｫ･ｴ＠

ｾｯ､ｯｬ＠ under1ying the export aector is ｣ｯｾｰ･ｴｩｴｩｶ｡＠ only up to that exogenous l!ait10 •

8 Endogonous technologico1 choiee in production eould have baen 805i1y

included in the ｾｯ､･ｬＬ＠ had tha required data been available, by edding coluMns corresponding to tho difíoront alternativa ｴｾ｣ｨｮｯｬｯｧｩ･ｳＮ＠

9 For 1983, tho opproxinote 6iza of the "infornal" ｾｯｲｫ･ｴ＠ i6 6.9 .il110n rural

and 9.6 million urben workors. This ･ｯｾｰｯｲＰＵ＠ with.7.4 ｾｩｬｬｩｯｮ＠ rural and 23.9 al1110n ｵｲ｢ｾｮ＠ ｾｯｲｬＺ･ｲ･＠ enployed in the fornal narket in that year.

10 Unfortunato1y thi6 Ｖｰ･｣ｩｦｩ｣ｾｴｩｯｮ＠ QOy lead to ＶＰｾ｡＠ degroe of "bong-bang" bohavior, in that the ｾｯ､｡ｬ＠ will in general spociolize, oxporting up to the

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-8-2.j.

Forelgn Borrowing and Oebt Servlce

By aaking the tlae path oí borrowing ｣ｮ､ｯｧ･ｮｯｵＸｾ＠ the ｾｯ､･ｬ＠ slaulates actual policy choice and allows the ･｣ｯｮｯｾｹ＠ to ｇｩｾｵｬｴｯｮ･ｯｵｇｬｹ＠ adJust tha laveI of donestic econo.ic ectivities Gnd oí ｩｾｰｯｲｴｳＮ＠ However. thera nust ba

provision for ｰ｡ｹｾ･ｮｴ＠ of intGrost and repaynent of principal either boiora or efter the ｾｯ､ｯｬＧＸ＠ tiao horizon. A certa in fraction of total debt co.es dua in each period. but it con bo rolled over by contracting for ｾ､､ｩｴｩｯｮ｡ｬ＠

borrowing, although parhaps at a higher intorest rata.

Foroign debt is ｾｯ､･ｬｬ･､＠ here using a vintoge ｾｯ､･ｬ＠ in order to properly account for tha effect of the ｳｩｴｵｾｴｩｯｮ＠ of the foreign ｾ｣｣ｯｵｮｴｳ＠ on tllQ total interest ｰ｡ｹｾ･ｮｴＸＮ＠ To indicato this. let O _g,t be the d8bt contractod in

period 9 held at ｇｴｾｲｴ＠ of period t. whera the indox 9 runs ｦｲｯｾ＠ O to t-1. The following oquation shows its dynanic5, given ｲ･ｰ｡ｹｾ･ｮｴ＠ (R) and borrowing (S) flows, ｡ｳｳｵｾｬｮｧ＠ that ｾｦｴｑｲ＠ an initlel ｡ｾｯｵｮｴ＠ ia borrowed in a period. it can only be repaid loter 11 • Since those aro both yeorly flow5, they ｾｲ･＠ entGred lnto tho debt belanc3 equation ｾｵｬｴｩｰｬｩ･､＠ by the nuubcr of years per period. Tha second oquation below defines ncxt yoar'a dobt oí one period of age as equal to tha ｳｵｾ＠ of tha yearly flows of this poriod's borrowing.

linit in the nore attractive &cctors. ond not at ali (or only residuolly) in the ｲ｡ｾ｡ｩｮｩｮｧ＠ ones. This could havo boan ｾｶｯｩ､･､＠ by incorporating into the ｾｯ､｡ｬ＠ non-lincer cxport revenue íunctions. ｾｲｯｮ＠ the ｾ｡ｴｨ｣ｾ｡ｴｩ｣｡ｬ＠ 6nd

｡ＱＹＰｲｩｴｨｾｩ｣＠ point of vicw this would hava bcen possible. but tho ｦｵｮ｣ｴｩｯｮｾｬ＠ specificationc and ･｣ｴｩｾ｡ｴ･Ｖ＠ of the relovant paranetors ｾｯｲｇ＠ not ｲ･ｾ､ｩｬｹ＠ available. &0 that lhis extonsion could not bo dona raliably at tha ｵｯｾ･ｮｴＮ＠

11 Tha ropaynont &chodule (RO.t) of initial ycar ctabt (00,1) is known. ｾｮ､＠ i5 usod In the recuraion of equatlon

(3).

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--(3)

-9-D

_g,t+l =

D

_g,t

D

t,t+l

•

- n

R

g,t for all t and Ofgft-l for alI t

The ｲ･ｰ｡ｹｾｯｮｴ＠ &chedula on any poriod's borrowing is ｡ＦＦｵｾｾ､＠ to be exogenously specifiod, and i6 independent of the period in whieh borrowing occurs. Thls ｬｾｰｬｩｇｓ＠ that the fraction of the borrowlng dane in period 9

ｾｨｩ｣ｨ＠ i5 anortizad in a later period t ｣ｾｮ＠ be calculated ｾｳ＠ a function (r) of tha dlfferGnco b8tw2en thesa ｴｾｯ＠ àates. Thls sinple ｦｯｲｾｵＱＸｴｬｯｮ＠ does not conüider changes in the ｲｯｰ｡ｹｾ･ｮｴ＠ profile of tha debt12 , which may howGvor be

a v.atter of policy choiee for sOMa eountries. In the context of tho ｾｯ､･ｬ＠

this iSSU9 i6 botter ｾ､､ｲ･ｳｳ･､＠ through &Gnsitivity ｯｮｾｬｹｳｩｳＬ＠ since changes in the naturity ｾｲ･＠ usually associated with changcs in the interest rates.

(5)

R

_g,t = r _t-g

B

₉ for all 9 and t

In ardor to ｣｡ｬ｣ｵｬｾｬ･＠ tha intúrost cost, lhis ｾｯ､ｑｬ＠ reco9nizes that a larga fraction of tha debt ｣ｯｮｴｲｾ｣ｴｇ､＠ in tha international ｦｩｮｾｮ｣ｩ｡ｬ＠ rnarxet by developingcountries oecrues intcrest on tha bosis of 8 floating rata (l.e.

LIBOR) plus a sprcad, which supposedly reflacts the ･ｯｵｮｴｲｹＭｾｰｇ｣ｩｦｩ｣＠ risk. The debt of dQvolQping eountrios olso usually has o fiy.ed rotG conponent

associatcd with loans by foraign ｧｯｶ･ｲｮｾｯｮｴｳ＠ and official institutiona,

ｳｯｭ･ｴｩｾｇｇ＠ in praferontiol terms. Since tha likelihood of largo interest Gubnidics to Brazil through fixed-rate ｬｯｾｮｳ＠ in the futura ia snall, it was

12 This is true oxcopt for tho changcs that occur as a result of tha Ｙｲ｡､ｵｾＱ＠

shift ｦｲｯｾ＠ the ｲ･ｰｾｹｾ｣ｮｴ＠ profilo of lha ｩｮｩｴｩｾｬ＠ dobt to tha ono inplied by lhe applic3tion of the ropaynent function spocifiad obova to futura borrowing. To the oxtent ｴｨｾｴ＠ the function r 15 derivod ｦｲｯｾ＠ tho forecost ｲ･ｰｯｹｾ･ｮｴ＠ stroa. on initial debt, thi8 ehange ia ｇｾ｡ｬｬＮ＠

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-10-cssuned that alI of the dabt ｩｾ＠ subJect to the floating schefte. This is

hO.9ver only a siRplification. since tha ｾｯ､ＹＱ＠ can be easily oxtsnded to allow

for this other type of debt.

As with alI othar voriablos in this Rodal. interest paynents are

calculatod in real ｴｑｲｾＶＮ＠ oxcluding tha effects of inflation of the currency

in which the dübt ia dGnonin6tod. If ｲ･ｰ｡ｹｾ･ｮｴｳ＠ for actual borrowing are

givan in ｮｯｾｩｮｾｬ＠ ｴｏｌｾＵＮ＠ higher inflation in the lending country decreases the

real valua 13 of tho dcbt at ony point in tiGa. This effoct of foreign

inflution can be sioulated in tho nodal considering o ｦｾｳｴ･ｲ＠ repaynent

8chcdule on the real dcbt.

Therefore, in any given yoar, interest payGcnta on total debt have t.o

｣ｯｾｰｯｮ･ｮｴｳＺ＠ tho first ia proportionul to tho real interest rnte, which is

･ｸｯｧ･ｮｯｵｾ＠ and con changa each period, and the sacond i5 a function of the

sprQod ｲｾｴ｣Ｕ＠ contractod for in provious borrowing, which i6 fixod for the life

of lhe 10an. As shown in oquation

ＨｾＩＬ＠

the offoctive intorest rate on debt

is tha Ｆｕｾ＠ of the renl intercst rata <h) ｾｮ､＠ lho GndogenouG spreed rate (SH):

(6)

H

_g,t =

D

ｧＬｾ＠ for alI t and 9

It vas ｡Ｕｳｵｾ｡､＠ here that these &prood rates 3ra a stationary linear

function (with slope ｾＩＮ＠ of the ratio of cnnual borrowing to on index of roal

ｩｮ｣ｯｾ･Ｎ＠ This indcx i3 approxinated by add1ng the scctoral voluo added, eõch

｣｡ｬ｣ｵｬｾｴ･､＠ os ｴｨｾ＠ product of ｧｲｯｾｳ＠ output ond ths initinl yoor Ghnres (6

vecLor vo)14.

13 i.e. doflatod by rrice ind8x of the currGncy of den03ination.

14 ｉｮ｣ｯｾ･＠ as Guch i5 not ･ｶｾｩｬｯ｢ｬ｡＠ in tha prinal of ｾｯ､｡ｬＮ＠ sinca it depends on

tho ｣ｨｾ､ｯｷ＠ pricc5 of lho 8oyoral goods. HowQver, lhe indax of grosa ､ｯｾｯｇｴｩ｣＠

product ot b08e year prices, which ia used ･ｾｯｶ･Ｌ＠ con always bo constructcd.

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The rotionale underlying oquotion (7) i& tho standard Capital Asset Pricing ｾｯ､･ｬ＠ ＨｃａｐｬｾＩ＠ for financiaI markets15 , coupled with tho ｡ｳｳｵｾｰｴｩｯｮ＠ that higher values oí ｧｲｯｾｳ＠ borrowillg (relativa to ｩｮ｣ｯｾｯＩ＠ ｾｲ･＠ perceivcd by 1enders as 6igno15 of highor volati1ity of future loturns on thoir 100n5. ｔｾｩｳ＠

6uggests that the opread rate contractcd for 10ans ta)(en out in a given year shou1d be a function of Lhe 9r055 leveI of borrowing in that SOES year.

This ｦｯｲｾｵＱＰｴｩｯｮ＠ 1s cast in a 10ng run perspectiva, and is ofíered on1y os a reesonab1e way to 100k et the cost of Eurobond funes from tbe borrower's point-of-view, ond not as an analysis oí the rationol ､･ｴ･ｲｾｩｮ｡ｴｩｯｮ＠ oí spread rates in that ｾ｡ｲｫ･ｴＮ＠ Note 01so that thi5 ｦｯｲｾｵＱ｡ｴｩｯｮ＠ ollow& tho country to 8ct ｳｯｾ･ｶｨ｡ｴ＠ like a iaonopsonist, sinca ot the optirna1 co1ution the narginal costa of foreign borrowing are equoted with its ｾ｡ｲｧｩｮ･ｬ＠ productivity.

ａＱｴｾｲｮ｡ｴｩｶ･＠ ｾｸｰＱ｡ｮ｡ｴｯｲｹ＠ ｶｾｲｩｾ｢ｬ･ｳ＠ for the sprcad rate function ｾ･ｲ･＠

considered (soa Tourinho(1985b), but tha ana tldoptcd ｾＧ｡Ｓ＠ prüferred both due to ｩｴｾ＠ properties and ｳｾｴｩｳｦ･｣ｴｯｲｹ＠ ･ｾｰｩｲｩ￧｡ｬｦｩｴＮ＠ Thc usa of net borrcwing, instead of gros5 borrowing, in tha spread rate function ｾ｡ｳ＠ Gvoided because the sGvera1 equations that were cstinated involving that varioble ｲＮｾ､＠ poor atatiitical resu1ts. This negativa result can be rationalized ii in the Eurobond horket the lending decision· ia evaluated indcpendently of the rapaynonls of proviaus borrowing, which ｾｯｵＱ､＠ bo the ｣ｾｳ･＠ if in each period tha londers wara not forced to reíinanca pGst 100n8, 05 ｾ･･ｲＮ･､＠ to happen until

a fow yoars agc.

15 It statcs that 50curitios with higher undiv0rsifiab1G risk ｾｕＦｴ＠ ｣ｯｲＮｾＸｮ､＠ a highar intorsst ｰｲｯｾｩｵｾ＠ ovor the ｲｩｾｫｬ･ｇＦ＠ rota than the ones with lcwsr risk.

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-12-Tha usa of a specification involving debl as an explanatory variabla for each pariod's spread waa avoided because, bafng stocx variabla, debt ia apt to change only slowly and not captura tha dynanics of the rate if, for exaaple, borrowing were drastically reducod. Tho dabt service to axport ratio, which ia also a naturel explenatory var1able and does not suffor from th1a

｣ｲｩｴｾ｣ｩＵａＬ＠ was ｡｢ｾｮ､ｯｮ･､＠ because of an unsatlsfactory cnpirlcal fito Howcver,

an equation using the debt to ｩｮ｣ｯｾ･＠ ratio as the independent variobla fitted

wall tha data, and ｾ｡ｳ＠ usod to calculato tha sprcad rate in the ｰｯｳｴＭｴ･ｲｾｩｮ｡ｬ＠ period, and in the sensitivity onolY81a.

2tf. Ternina! Stocks and Post-ternlnal Utility

ａｓｇｵｾｩｮｧ＠ that a stationary ato te pravails in the ｰｯｳｴＭｴ･ｲｾｩｮｯｬ＠ period, the expression for tha ｰ･ｲＭ｣ｾｰｩｴｯ＠ infinita horizon ｡ｰｰｲｯｸｩｾ｡ｴｩｯｮ＠ ter. (V) con ba derivod by calculating the indirect utility function ｾｳｳｯ｣ｩｾｴ･､＠ with the utility functlon in (1) and (2) at the tcrninal dote. Aa in equation (8), it

can be ｾｲｩｴｴ･ｮ＠ as 5-1 tiNes ü generalized logarithmic function of ｴ･ｲｾｩｮｯｬ＠

ｩｮ｣ｯｾ･ＬＧ＠ ｷｩｾｨ＠ total ninirnua Expendituro cqual to the Gum of tha ｾｩｮｩｒｵＮ＠

expenditures on tho several goods (7i in (2»16. The intuition is clear: it ia thG present velua of cn infinita ｇｴｲ･ｾｮ＠ of slngle-period stationary utility

(hence tha ｴ･ｲｾ＠ ｾＭＱＩ＠ affordcd by tha supernur.erary ｩｮ｣ｯｾ･＠ flow.

The total ｴ･ｲｾｩｮ｡ｬ＠ ｩｮ｣ｯｾ･＠ ia the SUQ aí tha lebor ｩｮ｣ｯｾ･Ｌ＠ plua the return (at a rate ｾＩ＠ on tha ｡｣｣ｵｾｵｬｯｴ･､＠ capital stock (KT). leS5 the interest cost of ｴ･ｾｭｩｮ｡ｬ＠ debt (DT). Tha tarminal ｬ｡｢ｯｲﾷｩｮ｣ｯｾ･＠ (YT) and tha yoarly

16 It i6 ｾ＠ bit tediou6 to show thia. To do it. Ｆｵｾｳｴｩｴｵｴ｡＠ tha linear ､･ｾ｡ｮ､＠

!unctions of

ELES

｢ｾ｣ｫ＠ into the ｯ｢ｪｾ｣ｴｩｶ｡Ｌ＠ and integrate by parls.

-

--

--

-

-...

•

-

-13-return on terminal capital stocK (p) are considared hera to be exogenous, but

can ba ･ｳｴｩｾ｡ｴ･､＠ on tha basia of ｳｯｾ･＠ ｰｲ･Ｑｩｾｩｮ｡ｲｹＮｲｵｮ｡Ｎ＠ This exogoneity was

r.aintoined to avoid complicating too Duch the shadow-prico structura oí the

ｾｯ､･ＱＮ＠ Letting tlT dGnote tho population at the end of the ｬｾｳｴ＠ period, and

recalling that

V

voa opecified in per-cepita ｴ･ｲｾ｡Ｌ＠ the following oquation

displays tha exprcnnion íor the per-capita ｴ｣ｲｾｩｮ｡ｬ＠ utillty.

(8)

V

=

S

-1 10g

C(YT

+ p KT - HT) / NT

The ｩｮｴｑｲ･ｾｴ＠ ｰｾｹｨ･ｮｴ＠ on the terminel debt in the equation ｾ｢ｯｶ･＠

(HT>

15

ca1culated in (9), Ilhere tha interoat rata ia ｯｳｳｵｾｯ､＠ to ba equal to tha roal

LIBOR

plus a Gpreod rata Ilhich i5 calculatad as a linoar function (with slope

ｾ＾＠ of tha sizo of total debt rolativo to the index of real ｩｮ｣ｯｾｯ＠ defined

prGviou51y17. This ｩｾｰｬｩ･ｳ＠ that tha cost of terninal ､ｾ｢ｴＮ＠ ｾｨｩ｣ｨ＠ reducos tha

post-torD1nal ｇｵｰｲｯｮｵｾｯｲ｡ｲｹ＠ incoRe, 15 a quadratic function of lho dobt.

(9)

_HT

=

_(hT

+ ｾ＠ (

DT / 1'T )] DT

3. HODEL

ｉｾｐｌｅＱｾｎｔａｔｉｏｎ＠

The nodal uas Bpp1ied to Brazil with a horizon covering twenty-íour

yeara froR 1984 to 2008, which ia divided into 6 pariods of 4 years.

ｅｮ､ｯｾｑｮｏｕＵ＠ voriables and balances ｾｲ･＠ ･ｾｴｬｮｇｴ･､＠ at the ｢ｾｧｩｮｑｩｮｧ＠ of each

pariod. The lUGt p2riod ends in 2008, the dato ftt which tho terhinal

17 Tha ｣￧ｾｾｇｮｴｳ＠ nade in connection with equation ( 6) olso apply hera, in

analogQu5 ｦｯｾｾＮ＠ ｅｱｵｾｴｩｯｮＧ＠

9>

ｑｬｾｯ＠ has a sntisfactory enpiricol fit for tha

Crazl11en dota.

-

-...

-

--...

-

-14-eondition ｾｯｲｭ＠ of tha obJactiva functlon 16 evoluoted.18 • The eonfidenea that is oeeorded to tha resulta for tha loat porioda should taka into aeeount tha faet that soma parameters of tha real ･･ｯｮｯｾｹＬ＠ whlch eorrespond to

coeffieients which are fixed in tha nodal. ｾ｡ｹ＠ changa over such o 10n9 tima span. Tho ｯ｣ｯｮｯｾｹ＠ la divldod into nina producing sectors: (1) agricultura, (2) ogro-processing, (3) construction. (4) monufacturing of capital gooda. (5) other manufacturing, (6) ｰｯｴｲｯｬ･ｵｾＬ＠ (7) utilities (oloctrlcity, water,

90S), (8) tronsport and ｣ｏｄｾｵｮｩ｣｡ｴｩｯｮＬ＠ (9) services.

Tha ｾｯ､｡ｬ＠ was ｩｾｰｬ･ｾ･ｮｴ･､＠ with tha usa of tha GAMS ｾ｡ｴｲｩｸ＠ gonerator ｾｮ､＠ solved by the non-lin6ar ｰｲｯｧｲ｡ｾｾｩｮｧ＠ ｰｾ｣ｫ｡ｧ･＠ HIHOS19. It haa 7 non-lineor equations, and its coefficients ｾ｡ｴｲｩｸ＠ has 350 rows, 484 eolunns and 1685 non-zero ･ｬ･ｾ･ｮｴｇＮ＠ At the ｯｰｴｩｾｵｾＬ＠ 48 non-linear variables are super-bosic20 •

It should be ･ｾｰｨ｡ｳｩｺｯ､＠ that MINOS 5.0, baing a non-linear progranning package, cannot in general roach exact optiffiol Golutions. Rathar, it stops at an ｡ｰｰｲｯｸｩｾｯｴ･＠ optinal solution where tha roduced gradient is zero up to ｳｯｾ･＠ vary ｳｾｯｬｬ＠ toleronca. The ｡ｬｧｯｲｩｴｨｾ＠ was ｯｬｾ｡ＩＧｳ＠ able to converge to the optinal solution, os 10ng 05 the key parar.etera (discount rate, LIBOR rate,

etc.) W8ra in the range ｾ［ｨ･ｲ･＠ the behavlor of the ､ｹｮ｡ｾｩ｣＠ system undGrlying

18 The accuracy of the infinite horizon ｡ｰｰｲｯｸｩｾｯｴｩｯｮＮ＠ evaluated by of extanding tho ｾｯ､ｯｬ＠ to a largar ｮｵｾ｢･ｲ＠ of pGriods, is ､ｩｾ｣ｵｓｓＸ､＠ in the next section

19 For an introduction to those prograr.s, E9Q respectivoly Kendrick and

ｍ･･ｲｾｵｳ＠ [1985], and ｬｬｵｾｴ｡ｧｨ＠ and SaundGrs [1983]. Tha author wishes to thank Sethu Palanieppon for providing several hints 011 ｨｯｾ＠ to ｩｲＮｰｬ･ｾｯｮｴ＠ the ｾｯ､･ｬ＠ in

the GAnS ｬＶｮｧｵ｡ｧｾＮ＠

20 Solution ｴｩｾ･＠ froR a "cold Gtart" on o CYBER Bochino ｾ｡ｳ＠ 17 seconds, but the nodol con be run in an IBM PC with G40k and ｮｕｾＸｲｩ｣＠ co-procesGor in about 4 hours. The nodal wcs developed uóing thG ｬｬ｡ｩｮｦｲｾｲＮ｡＠ vorsion of tha software becaune of lts foater turn-around tiae.

--

-

---

--

--

-

-

-15-the ｰｲｯｧｲｯｾｾｩｮｧ＠ modsl ｾｯｳ＠ stabla. On non-stobla poths it foiled in ｳｯｾ･＠

instances to find a Golution with the specified prccision.

3.1 ｄ･ｴｾ＠ base ￧ｾｳｴｲｵ｣ｴｩｯｮＲＱ＠

ｾｯｳｴ＠ of the dato for inplenenting tha nodol con be infarrcd ｦｲｯｾ＠ tha

inters8ctoral ｴｲｾｉＱｇｯ｣ｴｩｯｮｳ＠ ond final ､ｇｾ｡ｮ､ｳ＠ tablo for 1983 (Appcndix A>,

ｾｨｩ｣ｨ＠ vos constructcd by updating the set of prelininary ｴｾ｢ｬ･ｳ＠ for 1975

obtained ｦｲｯｾ＠ tho Brazilicn GtutiGtics institute (IBGE)22. lhe units for alI

the cocnoditien and factors in the ｾｯ､･ｬ＠ are consistent with this ｴｾ｢ｬ･＠ end

ore àcfined as the quantitios th3t could ba uought with one CR$ billion in

1983. ｉｾｰｬｩ｣ｩｴ＠ in this àGfinition is the hypothcsis that the oggrcgotion

within oach GQctor 1s on the basis of initial year prices. Tha other

ｩｾｰｯｾｴ｣ｮｴ＠ Gõta itcr.$ for tha "odel are ｇｨｯｾｮ＠ in Tõble 3.1 and wera obteined as

follow8.

Tha ｰｾｲｻｬ［ｲＮＧＮＳｴｬ＿ｲｳ＠ of th3 utility function (the ",cctors ｾ＠ .:llld ')) \iere

calculeted by constrúinlng the lincer ･ｹＮｰ･ｮ､ｬｴｾ･＠ ｳｙｇｴ･ｾ＠ to rcproJuce Lhe 1975

cons'.lí:ption vector, ｾｮ､＠ uGing the incor.le ｣ｬｾｳｴｩ｣ｩｴｩ･ｳ＠ ｣ｳｴｩｬ［ｾｴ･､＠ by ｜ｈｬｬｩ＼Ｑｬｾｳｯｮ＠

ond l:cCorthy [1981]. Thcse voluos ｩｾｲｬｹ＠ an ovarall elosticity of substitution

equal to 0.54 in 1933. The discount rata of Ｔｾ＠ uscd in the utiliLy iunction

iG ｣ｯｮｾｩｳｴｯｮｴＬ＠ givcn the ｬｾｮｲｧｩｮｑｬ＠ sQvings rate of .84 ｩｾｰｬｩ･､＠ by the ｾＧｳ＠ of

21 The construction of tho ､｡ｴ｡｢ｾｳ･＠ for the nodal is ､ｇＦ｣ｲｩ｢ｾ､＠ l'oro fully in

Tour jnl10 [l9<}Sb].

22 ｕｮｦｯｲｴｵｮｾｴ｣ｬｹ＠ it was not feasiblo, given th8 ｴｩｾｯ＠ ｯｹｾｩｬ｡｢ｬｾ＠ for the dota

col18ction, to ｇｩｮｵｬｴｾｮｾｑｵＵＱｹ＠ ｾｯｩｮｴｮｩｮ＠ tho ｣ｏｾｇｩｾｴ･ｮ｣ｹ＠ of tlle ＱｾＷＵ＠ ｴｾ｢ｬｯ＠ ond

ｯｴｴｾｩｮ＠ cn cxnct ￧ｯｲｲ･ｳｰｯｮ､ｾｮ｣ｯ＠ with tho ｬｬｾｴｩｯｮｾｬ＠ ｾ｣｣ｯｵｮｴｳ＠ ｢ｾＳｲ｣ｊｯｴ･ｳ＠ íor 1983.

The ｇｾｐ＠ 1n the updoted table ia ＱＰｾ＠ ｾｾｒｬｬ｣ｲ＠ thbn lhe value 1n ｬｬｬｾ＠ ｯ｣ｾｯｵｮｴ｡Ｌ＠ in

part bacG\lso a ［Ｚ［ｩｺ｣ｾ｢ｬ･＠ ､ｩｾｲＧＺｘＭｲ＿ｰ｡ｮ｣ｹ＠ alrcod)' ･ｸｩＵｴｾ､＠ in the 1975 toble ..

-...

-

-

---

-...

--

-...

-...

-

-16-Tabla 3.1, with on overaga net roal yeorly return on personol ｳｾｶｩｮｧｳ＠ of 5%.

Tóia value ia quite roasonable, given that the real coupon rate on indaxed

passboox savings in ｂｲｾｺｩｬ＠ i6 Ｖｾ＠ •

The copitol-output and ｬｾ｢ｯｲＭｯｵｴｰｵｴ＠ ccefficionts wera derived ｦｲｯｾ＠ the

respGctive ｦｾ｣ｴｯｲ＠ shores ｾｯｫｩｮｧ＠ usa oí ｳｯｾ｡＠ dopreciation and profit rotes dota

contained in Lysy ｾｮ､＠ Taylor [1980]23.

Table 3.1

Parenetera of utility and production functions

=============================================================================

Marginal l'!inimulI Capital Depre- Labor

consur.p. /total /gro5s clation /gross

shores consump. output <yearly) output

SECTOR5/GOODS ＨｾＩ＠ 1983 00 retio _{<") ra.tlo}

Synbols

Agriculture 2.41 70.8 2.600 1.6 0.1340

Agro-processing 7.63 70.8 1.520 3.7 0.0504

Constl:uction 0.572 4.2 0.1607

Man. capital.90ods 5.01 28.4 1.092 4.0 0.0845

nan. othar goods 16.46 30.2 1.278 3.6 . 0.0784

Petroleull. 3.97 42.9 2.075 3.6 0.0341

Utllities 2.72 25.4 3.556 3.4 0.1866

Transport & COk\lllun. 7.09 22.6 0.935 4.5 0.2470

Services 37.72 46.8 2.354 3.9 0.1923

Non-coJ:1pot. imports 0.79 52.0

Avorage 1.769 0.1226

］］］］］］Ｚ］］］］］］］］］］］］］］］］］］］ｾ］］］］］］ｾ］］］］］］］Ｚ］］］］］］］］］］］］ ］］］］］］］］］］］］］］］］］］］］］］］＠

23 A ｷｾｲｮｩｮＹ＠ ia in order ｾ｢ｯｵｴ＠ the re1iobility of the ､ｯｴｾＮ＠ Prinory data on

sactorol capital-output coofficients ｜ｾｑｓ＠ not ｡ｶ｡ｩｬｾ｢ｬ｡Ｌ＠ so they hod to ba

･ｳｴｩｮｾｴ｣､＠ indirectly os describod in the ｴｾｸｴＮ＠ Vory littlo ｩｮｦｯｲｲＮｾｴｩｯｮ＠ about

tha ｾ｡ｲｧｩｮｯｬ＠ ｩｮｶｯｳｴｾｯｮｴ＠ shares ｾ｡ｴｲｩｸ＠ (b) 6Kists in Brazil, 60 it hod to be

constructed piecing togcther ｩｮｦｯｲｮｾｴｩｯｮ＠ ｦｾｯｮ＠ ｾ･ｶｑｲ｡ｬ＠ sourcos, ond does not

have ｾｵ｣ｨ＠ hard data to support it. A properly ･ｳｴｩｾｌｴｑ､＠ linoar Gxponditure

ｳｹｳｴ･ｾ＠ ｜ｉｾｓ＠ 01so not ｾｶｾｩｬ｡｢ｬ･Ｌ＠ but tho elosticitios thot were ｵｳｾ､＠ ore not

expected to be vary for ｦｲｯｾ＠ tho corroct ones. Finally, tho pOSGibility thot

any of thoGO ｰｏｲｏｾｑｴＸｲ￵＠ ｾ｡ｹ＠ not bo Ｖｴｾ｢ｬｑ＠ through tino ｾｑｹ＠ cor-pound any errors

in the ･ｳｴｩｾ｡ｴｩｯｮＮ＠ Sinca no paJor doto collaction offort could be Rode for

this pro)cct, we had to do our bost with tha data on ｨｾｮ､Ｌ＠ but it ｾｵｳｴ＠ be

emphosizod that furthar work to volidota thesG coafficionts i6 nocessary.

-

-...

...

-

--

--

-

-17-Tho elopa of the function ｵｾ･､＠ to colcultlta the Gpreod rato in ooch

pariod (equotion ( 6» ｾｮ､＠ of tho ｰｯｳｴＭｴ｣ｲｾｩｮｯｬ＠ interost cost function

(oquation

(!)»

ore ｲｶｾｰＸ｣ｴｩｶＸｬｹ＠ a = 29.69 ｾｮ､＠ ｾ＠ = 5.25, with tho spread rate

iri ｰ｣ｲ｣･ｮｴｾｧ･＠ points. They were obtoined froA an analysis, using ｾｩｮｰｬ･＠

linear regression24 , of the ｲｇｾｬ＠ ｬｇｾ､ｩｮｧ＠ ratcs for Erazil in the EUrODQnd

J:'Hlrlwt b'3t .... 8I3n 1974 alld 15'84. It \.lOS ,::ceUi'.Sd thllt theG8 bahnviot-al n?l.::tions

will continue to hold in the futu4e, in üpite of thc fact that ｴｨｾｲ･＠ i3 no ｾ＠

priori rcoson .... hy thiG should be 60. If the institutional ｡ｲｾｵｮｧｾｮｾｮｴｳ＠ for

borrowing by d2\'eloping countries chllnge in the futura, [,e .... l"ules t.o d?tr:rr"line

tha ｩｮｴｾｲ･ｳｴ＠ cost of debt will hove to bo illcluded into tho ｾｑ､ＸｬＮ＠

Tha yearly roto of growth of ｰｯｰｵｬｾｴｩｯｮ＠ cnd lebor forca Ilere ｯＵｳｵｾｯ､＠ to

be 2.5% ｾｉｬ､＠ 3% respectiv8ly, con3istcntly with ｨｩｳｴｯｲｩ｣ｾｬ＠ ｢Ｘｨｾｶｩｯｲ＠ and sore

recent proJ8ctions dono in B::'.:Izil. Tha rata of ｬ｡｢ｯｲＭｬｬｵｧｬａＧＺｾｮｴｩｮｧ＠ ｴ･｣ｨｮｩ｣ｾｬ＠

progrcss U5G aGGuued to be Ｒｾ＠ ｹｾ｡ｲｬｹＮ＠

ｇｯｶ･ｲｮｾ｣ｮｴ＠ ･ｸｾ･ｮ､ｩｴｵｲ｣｡＠ ure ｾｳｳｵｾ｣､＠ to grow at thp ｓｄｾｃ＠ rale as

ｰｯｰｾｬｾｴｩｯｮ＠ growth, which ｩｾｰｬｩｑｳＮｴｨｇｹ＠ are ｩｮ･ｬｾｳｴｩ｣＠ with ｲｏｇｰｾ｣ｴ＠ to ｰ｡ｾＭ｣｡ｰｩｴｾ＠

incone. This i5 not lhe usual ･ｾｳｵｾｰｴｩｯｮ＠ in ｾｯ､｡ｬｾ＠ for Brazil, but this

ｰｾｲ｡ｾｑｴ･ｲ＠ ｣ｾｮ＠ be oasily varied to check tha 6cnsitivity of ｴｨｾ＠ Golution to

it25 •.

24 Tha

n

2 for the two ･ｬｵｯｴｩｯｾｳ＠ wara respDctivüly .47 nnd .50 and both

coefficiontü oro signific.:lnt at the ＵｾＧ＠ levol.

25 ｖｾｲｩｾｴｩｯｮｳ＠ in tha gl"owth ｲｾｴ｡＠ of governu&nt ｯｸｰ･Ｂ､ｩｴｵｲｾｾ＠ in tha ｲｯｾｾｯｮ｡｢ｬ･＠

ranSB ara not oxpoctüd to ｨｾ｜Ｇ｡＠ ony ｩｮｰｾ｣ｴ＠ 00 lllO conclusions of tho

censitivity onalYBia oí cection 5.

--

-

---

-

----

--

--

--

--

--

-

-18-for the base case ｳ｣･ｮｾｲｩｯＲＶＬ＠ the following od-hoc ossuaptions were ｾｯ､･＠

with regords to the volues of the ｲ･ｾｯｩｮｩｮＹ＠ ｰｯｲｯｾ･ｴ･ｲＶＮ＠ The real LIBOR rata

stabilizea at 5% ｹｾＸｲｬｹＬ＠ slightly lower than the current leveI, and does not

return to tha vcry low leveIs of the eorly '70s. The ｾ｡ｸｩｭｵｾ＠ ycarly growth

rate of agricultural and manuíactured exporta ia equal to 5% and 10%

respectively, envisioning an yeorly rate of increase of intarnational ｣ｯｾｭ･ｲ｣･＠

of Ｕｾ＠ and ｾｯｲｫ･ｴ＠ shore increasga for Brazilian aanufoctured gooda. It ia

" assuged that domestic patroleum production stabilizes at a laveI of 600

ｴｨｯｵ･ｾｮ､＠ bbl/day in accordance with recent forecasts, but that the gross

output of tha sBctor expands only to incorporate the value of the increased

production. This ｩｾｰｬｩＸｳ＠ a rather extrene assullIptic'n that the refining

sub-sector does not ･ｸｰｾｮ､＠ obove its basa-year capacity, and that in the ｭ･､ｩｵｾ＠

and long ter a the ､･ｾ｡ｮ､＠ increases are supplied with ｩｾｰｯｲｴｳ＠ of refined

products 27 • The torns of trade are assurned stable at the 1983 leveI.

5ensitivity anolysis with rüspect to thase parameters is shown in section 5.

Finally, due to tho difficulties with finding a dieaggregated estinate

oí capacity utilizotion appropriate to the ｦｲ｡ｾ･ｷｯｲｫ＠ oí the nodel,

full-･ｾｰｬｯｽＧｪＱ･ｮｴ＠ ...,as u"ssulled to prevail in 1'383, in spi te of the fact that i t \0,'05 a

ｲ･ｾｯｳｳｩｯｮ＠ year. In addition, since cyclical d6partures ｦｲｯｾ＠ full ･ｾｰｬｯｹｭ･ｮｴ＠

are difficult to ｨｾｮ､ｬ･＠ in models of this typa, ･ｸｰ･ｲｩｾ･ｮｴｳ＠ were not ｾ｡､｡＠ to

verify whether the inclusion of slacka in the reGource conctraints for the

26 It ￧ｾｮｮｯｴ＠ La ｇｬｬｰｨｾｳｩｺｯ､＠ enough that thesa ore only scenorio& for ｰ｡ｲ｡ｾ｣ｴ･ｲｳ＠

whoSG futuro GVOllltion we know vcry littla about. and era not pro]ections of

lhe nost ｬｩｾ･ｬｹ＠ cour3e of aventa.

27 Thi& ｾ｡ｹ＠ not have baen a veri good ｡ｳｳｵｾｰｴｩｯｮＮ＠ but it ia not ｣ｯｾｰｬｯｴ｡ｬｹ＠

unreaconeblc ･｣ｯｮｯｾｩ｣｡ｬｬｹ＠ in light of the large incrcaces in Middlc-Eastern

re!ining capacity which are schaduled to occur in lhe next few yeors •.

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-19-initiol period would leod to ｲ･ｾｇｯｮｾ｢ｬ･＠ ｲｯｳｵｬｴＲｾ＠ This ｣ｾｳｵｮｰｴｩｯｮ＠ however does

not seç.m to be overly ｰＮｯ｢ｬ｣ｭｾｴｩ｣＠ for the long-run colculotions for which this

nodol i5 Guitubla.

Tha ｲｏＦｴＭｴＸｲｾｩｮｾＱ＠ n2t return on ￧ｾｰｪｴ｡ｬ＠ (p) ｨｾ､＠ lo be Gsticated by

insuring that the ｒｮｮｾ｡ｹ＠ equation be satisfied at th8 ｢ｾｳｩｮｮｩｮｧ＠ of the ｾｯ､･ｬＧｳ＠

. n ..

post-ternin'll pC'riod. It cl!n bC! :;ho·..;n,Va ｇｩｾｰｬｩｦｩ･､＠ 'iersion of a similar

l1odel, ｴｨｾｴ＠ the ･ｱｵｩｬｩ｢ｲｩｵｾ＠ condition ｲ･､ｵ￧ｾＵ＠ to Gxpression (10)28, where the

rate oí d2cline of the per-cepita ｾＸｲｧｩｮ｡ｬ＠ utility can be approximated locally

by the rate of incroQse of ｰ･ｲＭ｣｡ｾｩｴ｡＠ ｣ｯｮｳｵｾｰｴｩｯｮ＠ divided by the overal1

Ol3Sticity of substitution.

(10)

ｉ

ｉｬｾｲｧｩｮｾｬ＠ !.";]tel

of côpital

productivity = l

utilil

Y

I ｉｲｾｴ･＠ of decline I

､ｩｾ｣ｯｵｮｴ＠ + of ｰ･ｲＭ｣ｾｰｩｴ｡＠

rate r.argin31 utility

Recall thot tha ｢ｾｓｇＭｃ｡ｾＸ＠ discount rale (S) is ond note ｴｨｾｴ＠ the

ｮ｣ｸｩｾｵｲｮ＠ ｳｵｾｴ｡ｩｮｇ｢ｬｯ＠ ｆｯｾｴＭｴｇｲｾｩｮｾｬ＠ rata of Ｙｲｯｾｴｨ＠ of p0r-capitG ｣ｯｮｳｵｾｰｴｩｯｮ＠ is

tha sum of the rote of labor-cugnenting ｴ･｣ｨｮｩ｣ｾｬ＠ progress ＨＲｾＩ＠ pllJS the rato

of increaso in tha lcbor rurket ｰｾｲｴｩ｣ｩｰ｣ｴｩｯｮ＠ ｲｾｴ･＠ ＨｏＮＵｾＩＮ＠ The ela3ticity of

st.rb::.titution in ｴｨｾ＠ e>;tendod linG\lr ｇｹＮｰｲｾｮ､ｩｴｵｬﾷ･＠ Gyst!2JlI, 5i\'on the Ｙｲｯｾｊｴｨ＠ ｮｾｴ｣ｳ＠

8ssuned õbove for population ond per-capita ｩｮ｣ｯｾ･Ｌ＠ ｾｯｵｬ､＠ averoge obout 0.66

during the planning pGriod. ｔｨｾｲｯｦｯｲ｡Ｌ＠ tho ｣ｾｰｲｯｸｩｾ｡ｴｇＮ＠ rnta of ｾｇ｣ｬｩｮ｡＠ of Lhe

ｐｑｲＭ｣Ｓｰｩｴｾ＠ Acrginal utility is ＳＮ･ｾＬ＠ and lhe ､ｩｾ｣ｲｑｴｯＭｴｩｮ｡＠ ｣ｳｴｩｾ｡ｴ｣＠ of the

roturn on capitol for the post-tGrginal period (p) is O.Ot.

28 l:otG thG ｡｢ｾ｡ｮ｣ｇ＠ of the po?ulõtion growth rotg fron (Ie), dua to the fact

thet in tt.e :::>l.J]octivo :unclicn (1) lha ｲﾷＺＺＩＺｩＮｬｾｾＢ｣ｴ＠ iú the su:. of utility across

811 individu31!3.