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Policy Analysis of Shadow Pricing, Foreign Borrowing, and Resource Extraction in Egypt Kemal Dervis Ricardo Martin SWP622 Sweder van Wijnbergen WORLD BANK STAFF WORKING PAPERS Number 622 Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized
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Policy Analysis of Shadow Pricing,Foreign Borrowing, and
Resource Extraction in Egypt
Kemal DervisRicardo Martin SWP622
Sweder van Wijnbergen
WORLD BANK STAFF WORKING PAPERSNumber 622
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WORLD BANK STAFF WORKING PAPERSNumber 622
Policy Analysis of Shadow Pricing,Foreign Borrowing, and
Resource Extraction in Egypt
Kemal DervisRicardo Martin
Sweder van Wijnbergen
£ThRNATIOPiAL MONETARY FUNDJOINT II3RARY
MIAR ') 1984
INT IMNATIONAL BANiK FORMYIZZOl.TRUC.I10N J?D D£'XELOPMEllT
The World BankWashington, D.C., U.S.A.
Copyright O 1984The International Bank for Reconstructionand Development / THE WORLD BANK1818 H Street, N.W.Washington, D.C. 20433, U.S.A.
First printing January 1984All rights reservedManufactured in the United States of America
This is a working document published informally by the World Bank. Topresent the results of research with the least possible delay, the typescript hasnot been prepared in accordance with the procedures appropriate to formalprinted texts, and the World Bank accepts no responsibility for errors. Thepublication is supplied at a token charge to defray part of the cost ofmanufacture and distribution.
The views and interpretations in this document are those of the author(s) andshould not be attributed to the World Bank, to its affiliated organizations, or toany individual acting on their behalf. Any maps used have been preparedsolely for the convenience of the readers; the denominations used and theboundaries shown do not imply, on the part of the World Bank and its affiliates,any judgment on the legal status of any territory or any endorsement oracceptance of such boundaries.
The full range of World Bank publications is described in the Catalog of WorldBank Publications; the continuing research program of the Bank is outlined inWorld Bank Research Program: Abstracts of Current Studies. Both booklets areupdated annually; the most recent edition of each is available without chargefrom the Publications Sales Unit of the Bank in Washington or from theEuropean Office of the Bank, 66, avenue d'Iena, 75116 Paris, France.
Kemal Dervis is chief of the Industrial Strategy and Policy Division in theIndustry Department of the World Bank; Ricardo Martin and Sweder vanWijnbergen are economists in the Bank's Development Research Department.
Library of Congress Cataloging in Publication Data
Dervis, Kemal.Policy analysis of shadow pricing, foreign borrowing,
and resource extraction policies in Egypt.
(World Bank staff working papers ; no. 622)1. Egypt--Economic conditions--1952- --Mathematical
models. 2. Egypt--Economic policy--Mathematical models.3. Shadow prices--Egypt--Mathematical models. I. Martin,Ricardo, 1947- . II. Wijnbergen, Sweder van,1951- . III. Title. IV. Series.HC830.D47 1983 338.962 83-21882ISBN 0-8213-0277-9
Abstract
This paper describes a long-term optimal growth model for Egypt
focussing on issues of investment allocation, optimal saving and foreign
borrowing, extraction of natural resources (oil and gas) and shadow pricing.
All sectors of the economy other than oil and gas are aggregated into
nontraded or traded goods; only the latter can substitute (imperfectly) for
imported goods. Oil and tradable goods can be exported, although the latter
faces a downward slopping demand curve.
The model is run first with exogenous total investment and foreign
borrowing; then investment is left free, subject only to an absorption
capacity constraint limiting the speed with which it can increase from period
to period. Finally, foreign borrowing is allowed to vary, with the interest
rate charged to loans being an increasing function of the amount borrowed. In
all variants of the model we test the sensitivity of the results to changes in
some of the basic parameters (future oil prices, discoveries of new oil/gas
reserves, pure rate of time preference).
Besides characterizing the optimal growth paths in terms of the level
and allocation of investment, the rate of oil and gas extraction, and the mix
of domestic savings andi foreign borrowing, the model generates paths for the
shadow prices of foreign exchange, natural gas and the social rate of
discount, with application for project evaluation.
Extracto
En este documento se describe un modelo de crecimiento 6ptimo a largo
plazo para Egipto, centrado en materias relativas a la asignacion de fondos para
inversiones, el ahorro y los empr6stitos externos 6ptimos, la extracci6n de
recursos naturales (petr6leo y gas) y los precios de cuenta. Todos los sectores
de la economia distintos del petr6leo y el gas se agrupan como bienes no comer-
ciados o comerciados; s6lo estos ultimos pueden sustituir (imperfectamente) a
los bienes importados. El petr6leo y los bienes comerciables pueden exportarse,
aunque estos ultimos se enfrentan a una curva de demanda descendente.
El modelo se pone a prueba primero con inversiones totales y empresti-
tos externos ex6genos; luego, se deja libre a las inversiones, con sujeci6n
solamente a una limitaci6n de la capacidad de absorci6n que restringe la veloci-
dad a la cual pueden aumentar de un periodo a otro. Finalmente, se permite que
varien los empr6stitos externos, constituyendo el tipo de interes cobrado sobre
los prestamos una funci6n creciente de la cantidad tomada en prestamo. En todas
las variantes del modelo probamos la sensibilidad de los resultados a los cam-
bios en algunos de los parAmetros basicos (precios futuros del petr6leo, descu-
brimiento de nuevas reservas de petr6leo o gas, tasa pura de preferencia
temporal).
Ademas de caracterizar las trayectorias 6ptimas de crecimiento desde
el punto de vista del nivel y la asignaci6n de fondos para inversiones, de la
tasa de extraci6n de petr6leo y gas y de la combinaci6n de ahorro interno y
empr6stitos externos, el modelo genera trayectorias para los precios de cuenta
del tipo de cambio, del gas natural y de la tasa social de actualizaci6n, con
aplicaci6n en la evaluaci6n de proyectos.
Ce document decrit un modele de croissance optimale A long terme pour
l'Egypte qui fait intervenir les decisions d'investissement, l'epargne optimale
et l'emprunt exterieur, 1textraction des ressources naturelles (petrole et gaz)
et l'utilisation des prix virtuels. Tous les secteurs de l'6conomie autres que
celui du petrole et du gaz sont agr6ges en biens non echanges ou echanges avec
l'ext6rieur; seuls les biens echang6s avec l'ext6rieur peuvent se substituer
(imparfaitement) aux biens importes. Le petrole et les biens echangeables
peuvent etre export6s bien que, pour ces derniers, la courbe de la demande soit
descendante.
On utilise d'abord le modele pour obtenir l'investissement total
exogene et l'emprunt exterieur; puis on laisse l'investissement fluctuer, 6tant
entendu qu'une capacite d'absorption limitee freine le rythme auquel il peut
s'accroitre d'une periode A l'autre. Enfin, on laisse varier l'emprunt
exterieur, l'int6ret percu sur les prets 6tant une fonction croissante du
montant emprunte. Dans toutes les variantes du modele, nous avons teste la
sensibilit6 des resultats aux variations de certains des parametres de base
(prix du p6trole a terine, d6couvertes de nouveaux gisements de petrole/gaz, taux
de preference pure pour le present).
Non seulement le modele permet de caract6riser les sentiers de
croissance optimale du point de vue du volume et du choix des investissements,
du rythme d'extraction du petrole et du gaz, et du dosage epargne interieure-
emprunt exterieur, mais il permet de determiner des trajectoires pour les prix
de reference des devises, le gaz naturel et le taux d'actualisation social, qui
pourront servir pour l1'valuation des projets.
Table of Contents
Chapter Description Page
1. Introduction: The Basic Questions 1
2. The Initial. Conditions: Egypt at the Beginning 6of the 1980's
3. The Model 19
3.1 Production Functions 223.2 Material Balances 233.3 The Balance of Payments and foreign debt 253.4 Capital Accumulation 273.5 Resource Exhaustion Constraints 283.6 The Objective Function 29
4. Valuation on the Optimal Path 32
4.1 Conditions for Static Efficiency 324.2 The Social Discount Rate 394.3 Dynamic Optimality Conditions 424.4 Changes in Relative Prices 45
5. The Nature of Optimal Growth Paths: StructuralAdjustment in a Long-Run Perspective 47
5.1 Experiments with fixed total investment 475.1.1 A Base Case Scenario 485.1.2 The Base Case 505.1.3 Shadow Prices in the Base Case 615.1.4 Sensitivity to Oil and Gas Reserves 685.1.5 Sensitivity to the Real Price of Oil 755.1.6 Sensitivity to the Growth of Domestic Demand
for Energy 885.2 Experiments with Endogenous Investment 92
5.2.1 A Fundamental Optimality Condition 925.2.2 The Base Run 995.2.3 Variants on the Base Run 112
5.3 Experiments with Endogenous Investmentand Optimal Foreign Borrowing 124
5.3.1 The Base Case with Foreign Borrowing and EndogenousCapital Accumulation 125
5.3.2 An Alternative Oil Price Scenario 129
6. Conclusions 1356.1 Some Robust Policy Conclusions 1356.2 Shadow Prices and Project Evaluation 137
Table of Contents (continued)
7. Footnotes 1428. References 1449. Appendices 145
9.1 Appendix A: A Summary of the Egyptian Model 1459.2 Appendix B: Calibration of the Model 1559.3 Appendix C: Absorptive Capacity Constraints 1589.4 Appendix D: The Steady State Capital Stocks 160
Figures
Figure 1: Share of Exogenous Resources in TotalResources 9
Figure 2: The Impact of an Exogenous Foreign 11Resource Transfer
Figure 3: Share of each Sector in Gross Output, Value 15Added and Employment
Figure 4a: Pricing of Natural Gas When Use is 35Demand Constrained
Figure 4b: Pricing of Natural Gas When Supply Constraints 38are Operative
Figure 5: The Ratio of Exogenous Resources to Non Oil 52domestic Value Added
Figure 6: Oil Production and Exports 54
Figure 7: Measures of Export Expansion and Import 56Substitution
Figure 8a: Share of Tradable in Domestic Non-oil Economy 58
Figure 8b: Ratio of Consumption of Tradable to Non 59Tradable Goods
Figure 9: The Composition of Exports 62
Figure 10: Real Exchange Rates: Price of Nontrade 63 & 65Goods in Terms of Various Traded Goods
Figure 11: Decomposition of the Price of Oil 67
Figure 12: Decomposition of the Price of Gas 69
Figure 13: Production of Oil under Alternative Reserve 72Scenarios for the Oil and Gas Sector
Figure 14: Capital in the Traded Sector under AlternativeReserve Scenarios 73
Figure 15: Price of Gas under Alternative Reserve Scenarios 74
Figure 16: Alternative Oil Price Scenarios After Year 2000 79
Figure 17: Tilted and Permanently Lower Price Scenarios 80
Figure 18: Oil Output under Different Price Scenarios 81After Year 2000
Figure 19: Oil Output under Different Price Scenarios 82
Figure 20: Real Consumption under Different Price Scenarios 83
Figure 21: Capital Stock in the Traded Sector under 85Different Price Scenarios
Figure 22: Price of Gas under Different Price Scenarios 86After Year 2000
Figure 23: Price of Gas Under Different Price Scenarios 87
Figure 24: Real Consumption under Different Scenarios for 93the Efficiency in the Domestic Use of Energy
Figure 25: Stock of Capital in the Traded Sector under 94Different Scenarios for Energy Efficiency
Figure 26: Composition of Wealth, Base Run 100
Figure 27: Oil Revenues and Exogenous Transfers 101as a Share of Total Income
Figure 28: Fraction of the Labor Force Employed in the 104T-Sector
Figure 29: Cost and Benefits of Two Hypothetical 108Projects
Figure 30: ARI, *ARI and CRI in the Base Run .111
Figure 31: Composition of Wealth, Low Reserve Case 114
Figure 32: Share of Oil, Oil Revenues and Exogenous 115Transfers in Total Income, Low Reserve Case
Figure 33: Oil Extraction Path in the Base Run and inthe Favorable Price Scenario 119
Figure 34: Oil Extraction in the Base Run and Low TimePreference Case 120
Figure 35: ARI and *RI in Base Run and Low Time PreferenceScenario 123
Figure 36: Various Discount Rates in the Base Run withOptimal Foreign Borrowing 128
Figure 37: Different Oil Price Scenarios 130
Figure 38: The Real Exchange Rate (NT/FT) under DifferentOil Price Scenarios 133
Figure 39: Optimal Borrowing Levels (Commmercial Debt)Under Different Oil Price Scenarios 134
Tables
Table 1: Tradables, Non-tradables and "ExogenousResources 14
Table 2: Exogenous Variable Estimates for the BaseCase Scenario 50
Table 3: Average Annual Sectoral Growth Rates: 57The Base-Case
Table 4: Growth of Macroeconomic Aggregates: The Base Case 60
Table 5: Alternative Scenarios for Oil and Gas Reserves 70
Table 6: The Impact of Alternative Oil Price Scenarioson the Growth Macroeconomic Aggregates 76
Table 7: Alternative Scenarios for the Real Price of Oil 78
Table 8: The Impact of Alternative Reserve Scenarios onthe Growth of Macroeconomic Aggregates 89
Table 9: Alternative Scenarios for Domestic-EnergyEfficiency 91
Table 10: The Impact of Different Energy EfficiencyScenarios on production structure, energyand use and GDP growth rates 91
Table 11: GDP Growth in the base run with optimal capitalaccumulation 105
Table 12: Growth Rate of GDP and Consumption in BaseRun and in runs with alternative utility 122function parameters
Table 13: Consumption Growth Rate with and withoutForeign Borrowing 126
Table 14: Optimal Current Account Deficits underDifferent Oil Price Scenarios 132
1. Introduction: The Blasic Questions
This study presents a model of the Egyptian economy that focuses on
some of the most import-ant aspects of the trade strategy and investment
planning related choices that Egypt faces over the next two decades. The
approach is that of optimal growth theory applied to the specific challenge of
long-term planning in Egypt. But the issues addressed are of more general
interest and the approach taken should be useful in the context of other
efforts of long-term development planning. The questions raised in this study
reappear in different contexts and are of importance whenever the need for
substantive "structural change" is anticipated.
To focus on the essentials one has to discard many details,
aggregate and oversimplify. We hope that the optimizing model presented in
this study can provide the economic policy maker with a framework which makes
reality more transparent by bringing out the most essential features of the
complex choices that must be made. Once the most basic choices are brought
into focus, the aggregate model should be useful as a unifying framework for
more complete and detailed studies of selected economy-wide and sectoral
issues. In particular, the resolutely long run and optimizing nature of the
model should yield results that can be incorporated into more disaggregated
medium-term consistency models. Similarly, the aggregate shadow prices
derived from the dual solution of an optimizing model can become a useful
input into more detailed sectoral estimates of shadow prices, by providing the
crucial link between long-run optimal growth considerations and the detailed,
but by necessity more partial, procedures of sector studies and project
appraisal.
- 2 -
The most fundamental dynamic choices faced by an economy can be
summarized in the form of two basic questions: (i) how much to invest, and
(ii) where to invest. These are the two basic issues addressed in this
study. The answers are by no means obvious. Much depends on the returns that
society can get on additional investment, on the consumption requirements that
must be satisfied, on society's long-term willingness to save and on the terms
on which domestic resources can be complemented by foreign capital.
Conditions vary from country to country. However, the question of
how far to push the investment effort remains as an important challenge to
the policy maker. There will never be an ideal answer to this question. To a
considerable extent it depends on value judgements relating to intertemporal
income distribution on which reasonable people can simply disagree.
Nevertheless, every society does make choices relating to aggregate
investments and it is imporant to analyze the key determinants of these
choices. Trying to determine an optimal composition of investment leads to an
even more complex set of issues. Should the emphasis be on housing, schools,
social infrastructure, or do the export producing and import competing
commodity producing sectors deserve top priority? In Egypt, these optimal
saving and investment questions are further complicated by two important
characteristics of the Egyptian economy: (i) a substantial part of Egypt's
wealth lies under the ground in the form of oil and gas reserves. These oil
and gas reserves are currently generating a substantial flow of income (close
to one fourth of GDP), but they represent a stock of finite, non-reproducible
wealth that cannot be renewed and expanded like physical plant and
infrastructure. Moreover, there is a substantial amount of uncertainty
attached to the quantity of reserves and to the price at which oil can be sold
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on the world market; (ii) in recent years, Egypt has benefitted from an
unusually large flow of foreign savings in the form of workers remittances
and concessional foreign aid. Sustained growth in these flows is doubtful.
These are two key features of the resource base in the early 1980's, and it is
against this background that an attempt must be made to evaluate the choices
open for the future.
The economic model that will support the analysis throughout this
study is an aggregative, optimizing, long-term growth model that distinguishes
three sectors: (i) a sector producing tradeable goods (exportable commodities
and import substitutes); (ii) a sector producing non-tradeable goods; and
(iii) the oil and gas sector. The basic objective of the policy-makers is
assumed to be the maximization of a discounted stream of domestic consumption
over time. There is the usual trade-off: restraining consumption in the
short-run allows more saving and, provided there are positive real returns on
saving, more consumption in the long-run. There is a balance of payments
constraint: in any given period the value of imports cannot exceed the sum of
tradable commodity exports, oil exports, foreign transfers and net borrowings
from abroad. There are also physical and technological constraints: increases
in domestic production are limited by the amount of physical capital that can
be installed, the size of the productive labor force and the technological
improvements that can be achieved. Finally, there is an exhaustible resource
constraint: the cumulative production of oil and gas cannot exceed available
reserves. Within this framework the key strategic policy choices facing the
country over the next 20 to 30 years can be summarized as follows:
(a) How much should Egypt save? Should the savings effort increase
over time, decrease or remain constant?
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(b) In what form should Egypt save and invest? The country's total
wealth can be decomposed into: (i) real capital assets (factories,
infrastructure, etc. 1'); (ii) wealth in the form of oil and gas
underground; and (iii) financial claims on the outside world
(reserves in the Central Bank, net claims on foreigners). The
process of saving and investing can add or substract to these three
types of wealth. In view of the alternatives, what constitutes an
optimal distribution of saving? Note in this context that oil
extraction "decumulates" the second and foreign borrowing the third
type of wealth.
(c) Given a certain overall rate of "physical" investment (alternative
(i) in (b) above), how should capital accumulation be allocated
between the tradable, the non-tradable and the oil and gas
producing sectors? What factors determine an optimal allocation?
While we shall discuss specific "optimal" growth paths, the primary
objective is to analyze the interdependence between the various decisions that
must be made and the sensitivity of optimal policy rules to key parameters,
such as the degree to which Egypt is willing to take a "long-run view", the
estimated magnitude of oil and gas reserves, and the return Egypt can hope to
get on physical investment.
A second important objective of the modelling work is to provide
insights into the price and incentive structure that should accompany an
optimal savings and investment strategy. With a three sector model not much
can be said, of course, on the microeconomic structure of shadow prices. But
some of the aggregate parameters that are usually given exogenously to project
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planners can be analyzed in a dynamic general equilibrium framework with the
kind of optimizing model presented below. In particular, the following
questions arise:
(d) What is a reasonable time path for the social rate of discount?
The degree of time preference and risk aversion remain fundamental
value judgements that cannot be avoided, but the sensitivity of the
social discount rate to long-run macroeconomic trends can be
explored systematically with an applied optimal growth model.
(e) How should the real exchange rate behave to support an optimal
growth path? This "relative price" is important for investment
planning and project appraisal procedures for it determines,
loosely speaking, how costs and benefits that can easily be
expressed in terms of foreign exchange should be valued in
comparison to costs and benefits that are essentially of a domestic
nature.
(f) The third important macroeconomic price is the real wage. It too
may vary over time, and its time path is of course intimately
linked to the time paths of the social discount rate and the real
exchange rate.
These are fundamental, strategic questions that can be analyzed
quite naturally with a numerical optimal growth model. While finding correct
answers is difficult and will always contain a large dose of "arbitrary"
judgement, it is perhaps worth stressing that in one way or another decisions
have to be, and are being, made on all these issues. When a project is
rejected on the grounds that it does not yield an internal rate of return of,
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say, 10 percent, this decision reflects a judgement on the appropriate
discount rate. When any particular exchange rate is used to convert, say,
projected domestic construction costs to a dollar numeraire, there is implicit
in the calculation a judgement on the future path of the real exchange rate.
What this study attempts to do is to analyze these issues in an explicit
dynamic and optimizing framework to bring out the interdependence of the key
variables that affect the process of investment planning and to clarify the
strategic choices that we made in any economy.
2. The Initial Conditions: Egypt at the Beginning of the 1980's
The 1970's witnessed a radical transformation of the structure of
Egypt's resource base. In terms of overall growth in resources available to
the economy, the last decade has been a period of rapid expansion. Defining
total resources as the sum of gross domestic product and net imports (domestic
resources plus net resources from abroad), one gets an average annual growth
rate of about 12 percent over the 1974-1981 period. This means that real
resources available to the economy more than doubled in seven years.
While total resources increased at a remarkable rate, the
composition of these resources underwent a radical change. Four major
developments led both to the rapid growth in Egypt's resources and to the
change in their composition:
(1) The petroleum (and gas) sector emerged as the financially dominant
sector of the economy with production rising from less than 8
million tons in 1974 (worth about $800 million at world prices) to
more than 32 million tons (worth almost $8 billion) in 1981. In
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constant dollars, this represents an average annual growth rate of
about 27 percent.
(ii) Remittances from workers abroad increased from $190 million to
$2,800 million in 1981, a dramatic increase averaging to about 32
percent a year in constant dollars.
(iii) The Suez Canal was re-opened and enlarged and Canal earnings
reached about $900 million in 1981.
(iv) Finally, direct foreign investment and net MLT lending increased
significantly, particularly if one distinguishes between the pure
balance of payments supporting grants and loans of the mid 1970s
and the more autonomous development project directed capital
inflows of the 1978-1981 period.
Let us define "exogenous resources", RE, as the sum of Egypt's share
of petroleum output valued at world prices (deducting the foreign companies
share), workers- remittances, Suez Canal earnings and net foreign capital
inflows:
Egypt's Share Workers' Suez Net ForeignRE = of Petroleum + Remittances + Canal + Capital
& Gas Output Earnings Inflows
By calling these resources "exogenous" we do not mean to imply that
their magnitude is totally unresponsive to domestic economic policy. They are
"exogenous" more in the sense of having very little to do with the product-
ivity of Egypt's domestic labor force that is overwhelmingly employed in agri-
culture, industry and services. It is also true that their magnitude is very
much dependent on factors beyond the policy makers control (world oil prices,
the political situation in the countries hosting Egyptian workers, etc.).
- 8 -
Figure 1 plots the ratio of RE to total resources available to the
Egyptian economy for the 1974-1982 period.The picture tells a striking
story. The ratio of exogenous to total resources went from about 6 percent to
45 percent in the early 1980's. The most dramatic part of the increase
occurred between 1976 and 1980. After 1980 the ratio starts showing a
decline. Crucial questions facing Egyptian policy makers and planners relate
to the impact RE has on the domestic economy and its most likely behavior in
the future. Will RE continue to grow. in absolute terms? Will it grow or
decline as a percentage of total resources? What implications does an
alternative growth path of RE have for overall economic growth? For
investment allocation? For exchange rate policy? For project selection?
These are some of the difficult questions that lie behind the policy debate in
Egypt and that will be discuss below. An important challenge for the
economist is to try to derive from the macroeconomic analysis operational
implications for investment planning and project appraisal.
Tradables, Non-Tradables and the Real Exchange Rate:
While there are some significant differences between oil revenues,
remittances, Suez Canal earnings and foreign aid flows, they all basically
represent a transfer the magnitude of which bears very little relationship to
productivity, wages and resource growth in the non-oil domestic economy.
Moreover, the transfer accrues in the form of foreign exchange and, therefore,
implies immediate command over resources that are tradable on the world
market. An increase in exogenous foreign exchange resources implies an
immediate increase in the capacity of a country to consume easily traded
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- 10 -
commodities and services. There are some commodities and services, however,
that are not easily traded. For such commodities, availability of foreign
exchange does not signify an immediate increase in potential consumption.
Housing is one example of such relatively non-tradable commodities. In
contrast to tradables such as clothing or food, it is not possible to increase
domestic consumption of housing by increasing imports or reducing exports:
housing is non-tradable in the sense that transport costs are simply too high
to make significant trade a viable alternative. Substantial portions of an
economy s output have this characteristic of non-tradability (many services,
construction, electricity, transport and communication networks are all
relatively non-tradable). A rapid increase in exogenous foreign exchange
flows does not allow an equally rapid increase in the consumption of such
items, since their supply can only be increased by raising domestic
production. In contrast, the supply of a tradable commodity can be increased
quickly by importing more or exporting less.
The impact of a sudden increase of exogenous foreign exchange flows
on the structure of an economy has traditionally been described with the help
of a simple two sector model (see Buiter and Purvis (1982), Corden and Neary
(1982) and van Wijnbergen (1980, 1981)). Figure 2 below reproduces the by
now well established stylized representation of the impact effect of a foreign
transfer. The economy has two sectors (tradables and non-tradables). In the
absence of any other resources, the production possiblity frontier AB is also
the consumption possibility frontier and the economy will produce and consume
at P=C. The slope of the produ lion possibility frontier at P=C defines the
equilibrium relative price of non-tradables in terms of tradables, a price
that is defined as the real exchange rate.
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Figure 2
The Impact Effect of an Exogenous Foreign Resource Transfer
sooa5 e ,
A a-<I V'
I \I__ _ I \; ,C
O B noKtoFW~~~~~I~ ~ ~ ~~~od
- 12 -
Now assume that this economy all of a sudden receives an exogenous
resource transfer that is equal in value to, say, 30 percent of its tradable
output. The production possibility frontier does not change since the -
capacity to produce tradables or non-tradables is not (immediately) affected
by this transfer. But given any point on AB, the economy can now consume AA
more of tradables by simply importing them from abroad. On the other hand,
the economy's ability to consume non-tradables remains constrained by domestic
productive capacity.
It is easy to see, therefore, that the consumption possibility
frontier shifts vertically to A B B and that consumption and production after
the transfer will be at C and P respectively. As income has risen, the
economy consumes more of both tradables and non-tradables (real income goes
from U to U ). To achieve this, more non-tradables must be produced. This
implies shifting resources out of tradables into the non-tradable sector.
This shift, in turn, requires a rise in the relative price of non-tradables,
in other words a real appreciation of the exchange rate, so that the initial
imbalance is corrected by an increase in the supply of non-tradables and a
reduction in demand for them, both brought about by an increase in their
relative price.
The magnitude of the real appreciation depends on how easy it is to
substitute in consumption nontraded and traded goods, and on the curvature of
the consumption possibility set A'B'B 2/ This possibility set equals the
vertical sum of the transfer and the production possibility frontier, so its
curvature is determined by the curvature of the latter. This curvature is
probably larger in the short run, as existent sector specific equipment,
machines, trained labor, etc. are not easily shifted from one type of
- 13 -
production to another. In the medium run, though, the stock of capital and
labor in each sector can be adapted via depreciation, new investment,
training, etc., so that the long-run transformation curve is likely to be
flatter than the short-run frontier.
While the model is usually discussed with reference to a positive
transfer of resources, the same analysis, in reverse, applies when a country
loses foreign resources.' The shift would be from P' and C' to P=C, reflecting
a loss in real income, a shift of resources into tradables and a rise in their
relative price.
In the longer run population growth and accummulation of physical
capital shifts the frontier AB over time. In a forward looking model the
change in relative prices due to the transfer, as well as future changes will
affect the magnitude and allocation of investment, as we will discuss below.
It is this simple theoretical model of an economy that provides the
starting point for our analysis and the basis for a disaggregation of the
Egyptian economy into three sectors: (i) tradables, (ii) non-tradables, and
(iii) oil and gas. The base period is fiscal year 1981/1982 and the
disaggregation is based on the grouping of sectors presented in Tab-le 1.
The value of gross output is, of course, only one way of measuring
the relative importance of the various sectors. Figure 3 may give the reader
a better overview of tlhe 1981 Egyptian economy by comparing the share of the
three "kinds" of sectors in gross value-added output and employment. A
striking fact is the contrast between the importance of RE in total resources
(output or value-added) and the insignificant share of employment in the
"exogenous resource" sector.
- 14 -
Table 1
Tradables, Non-Tradables and "Exogenous Resources"
1. Tradables
(a) Tradable Agriculture(b) Industry(c) Tradable Services
2. Non-Tradables
(a) Construction(b) Housing(c) Electricity(d) Other Infrastructure(e) Non-Tradable Services
3. Exogenous Resources
(a) Oil and Gas(b) Workers' remittances(c) Suez Canal(d) Net Foreign Capital Inflows
The big challenge that faces Egypt at the beginning of the 1980's
arises from the need to gradually shift the structure of growth, from "natural
resource" and "foreign resource" based growth to growth based on the rapid
expansion of the domestic economy accompanied by growth of productive domestic
employment. To underline the importance of the challenge, let us look a
little more closely at the four basic components of what we have defined as
exogenous resources.
Figure 3
Share of each Sector in Gross Output, Value Added
and Employment
a. Shares in Value-Added b. Shares in Gross Output c. Shares in Employment
R
T : Traded Sector NT : Non-Traded Sector RE : Exogenous Resources
- 16 -
Workers' remittances have grown at spectacular rates during the last
decade characterized by rapidly rising outmigration. Looking into the future,
it is very difficult to project continuous substantial outmigration of the
type that occurred in the 1970's. The host countries, mainly in the Gulf,
have reached their absorptive capacity limits. Of course, real incomes in the
Gulf will probably continue to rise, although at a slower pace, and as long as
migrants send home a constant fraction of their incomes, one should expect
remittances to continue to grow in real terms. Unfortunately, there is a good
chance that both the savings rate and the proportion of savings sent home in
the form of remittances will decline over time. As migrants get used to their
income levels and as they get more established in their new environments,
their consumption standards are likely to go up. Moreover, while for Egyptian
workers in particular, the attachment to the Nile Valley will remain strong,
the passage of time is bound to have some effects and an increasing portion of
their savings may be directed to purchasing assets (houses, cars, etc.) in the
host countries. This has been the pattern elsewhere and something similar is
likely to happen with Egyptian migrants. Much, of course, will depend on
political conditions, and investment opportunities in Egypt compared to
investment opportunities abroad. The most likely scenario is one of
continuous but moderate and gradually slower growth, going in real terms from
about 3 to 4 percent per annum in the 1980's, to maybe 1 or 2 percent after
1990. If overall economic growth in the Egyptian economy can proceed at 6 or
7 percent per annum, one should expect the share of remittances in total
resources to gradually decrease over the next decades.
Net foreign assistance flows have been important for Egypt through-
out the 1970's. The existing pipeline and the commitments already made by
- 17 -
Egypt's friends and international lending institutions are sufficient to allow
some real growth of foreign aid over the next few years. But the level of new
commitments is showing only a slow increase, so that eventually the growth in
disbursements may slow down and the level of gross resource 'transfers may
stabilize. Debt service payments, on the other hand, are due to increase
substantially after 1982. This could lead to a situation where the level of
net foreign assistance flows remains essentially constant. There is of
course, direct foreign investment, but profit repatriations are likely to
limit any net balance of payments contribution to very i\odest levels.
Turning to the Suez Canal, further rapid growth in the volume of
traffic is unlikely. Tariffs have already been raised and the possibility of
traffic diversion puts an upper limit on the level of tariffs. The most
likely scenario is one of moderate growth, more or less in line with world
trade, at 4 or 5 percent: per annum, but the experience of spectacular
expansion that has characterized the 1970's cannot be repeated.
Finally, and most importantly, there is oil and gas. Recoverable
reserves from established fields are currently estimated around 500 million
tonnes (3.4 billion barrels). Given vigorous exploration activity and the
fact that proven reserve estimates do not take into account future new
discoveries in as yet unexplored areas, a reserve estimate of 900 million
tonnes (about 6.5 billicin barrels) would seem to constitute a reasonable, base
case scenario. At 1981 output rates, this constitutes 29 years worth of
production. On the other hand, if oil production were to grow at the same
- 18 -
rate as the economy, say 6 or 7 percent every year, these reserves would be
completely exhausted in less than 20 years.
Fortunately gas can, to some extent at least, come to the rescue.
Proven reserves did not exceed 10 Tcf in 1980 (equivalent to 240 million
tonnes of oil) but given the rapid increase in reserve estimates and using a
proven +1/2 possible formula, total reserves may be close to 25 T/f or about
600 million tonnes of oil equivalent. Adding oil and gas one can arrive at a
base case estimate of total recoverable oil and gas reserves of about 1500
million tonnes. At present production levels and assuming, for the moment,
perfect substitutibility in use, this represents 47 years of production. On
the other hand, with 6.5 percent growth in annual production, reserves would
be exhausted in about 30 years. Of course, the exportable surplus of hydro-
carbons would dissappear well before reserves reach this total exhaustion
limit.
The combination of these factors constitutes an important challenge
to the Egyptian economy. It seems that before the end of this century, Egypt
will have to effectuate the transition from an economy where natural and
foreign based resources account for almost half of total resources to an
economy where the role of these resources is much more modest, where growth is
based on the expansion of domestic tradables and non-tradable production and
where foreign exchange must come primarily from industrial exports.
The next century may seem far away but development is a long-term
process and what distinguishes good development planning from a succession of
crisis management policies is precisely the presence of a long-term
perspective. Policies cannot be elaborated overnight, time is required for
projects to be carried out, for resources to shift and for economic structure
- 19 -
to change. A long-run perspective, even if it is filled with uncertainties
and involves only-rough estimates of the future environment, seems essential
if development policy is to be formulated with a sense of direction and long-
term purpose.
3. The Model
This section provides a description of the specific optimizing
growth model that was built to analyse the kind of fundamental policy problems
referred to above. While our starting point is the three sector framework
discussed in Section 2 (tradables, non-tradables and exogenous resources) the
model has some extensions and special features reflecting important aspects of
reality that we wanted to introduce into the analysis. The features are the
following:
(i) There is an explicit input-output structure and commodities are
required as inputs in production as well as for final use.
(ii) Domestically produced tradables and tradables produced in the
rest of the world are imperfect substitutes. While the world
price of imports is exogenously given to the Egyptian economy,
the proportion of imports in total domestic deman,d for tradable
intermediate and consumer goods is responsive to the relative
price of imports in terms of domestically produced tradables.
(iii) There is no such substitution possibility for investment goods,
imported capital goods remain a fixed proportion of total
investmenat
- 20 -
(iv) Domestically produced tradables can be used in the domestic
economy or they can be exported. The world price of Egyptian
exports (excluding oil, Suez, remittances) does depend, however,
on their volume. The relative price of exports (terms of trade)
will fall with increases in volume, although we assume a high
demand elasticity so that large increases in exports can occur
with relatively minor declines in price.
(v) We distinguish oil from natural gas. Gas can substitute for oil
as a source of energy only up to a certain point. Also gas is
treated as non-tradable. For Egypt, LNG exports are not
considered a viable alternative even with optimistic reserve
estimates.
(vi) The production of oil in any period is endogenous. However,
production costs depend on the ratio of the flow of extraction
to the stock of proven reserves. Since production costs are to a
very large extent borne by foreign oil companies who "recover"
their costs by getting a share of total production, rising
production costs in the oil sector are reflected by a rising
share of the foreign oil companies. Moreover, proven reserves
are updated every time period by adding new discoveries and
subtracting current production levels. New discoveries are
exogenously projected so that total reserves are also
exogenously given to the model.
(vii) The production of gas is treated somewhat differently in that
investment costs are borne by Egypt, rather than foreign
companies and per unit production costs are assumed constant.
- 21 -
There is therefore a standard capital output ratio reflecting
the need for domestic investment in the gas sector.
(viii) The marginal efficiency of total economy-wide investment
declines if investment grows too rapidly. While there is no
"absolute" absorptive capacity constraint that constitutes a
rigid upper bound for investmient in any period, the productivity
of investment falls if it exceeds a certain critical level
determined for every period by the rate of technical progress,
the rate of growth of the labor force and the level of
investment in previous periods.
In the equations below, all endogenous variables are denoted by
upper case Roman letters. Parameters and/or exogenous variables are denoted
by lower case Roman letters, letters with bars or Greek letters. The
subscript refers to sectors or "resources" defined in the following way:
i = 1, for traded goods (exported and used domestically)
i = 2, for non-traded goods
i = 3, for petroleum
i = 4,ifor natural gas
i = 5, for "foreign exchange"
i = 6, for the composite commodity made up of imports and
domestically produced tradables.
Using this notation, we have the following set of primal
constraints, with the corresponding shadow prices indicated on the left:
- 22 -
3.1 Production Functions
-P1 t -Pi1-/pI(Vlt >0) X < yi(a 1KIt + (1 - a1 )(Ltg1 ) ) (1)
-P2 -p2 1/2 (V >0) 2t < Y2(2 2K + (1 - a2)(L g) )(2)2t2t t 2 2t 2 2tg2
(V 3t > ) X3 f3(K 3t, R3t' t) 3
(V4t >0) X4 f4(K4t, t) (4)
Here, Xit, Kit and Lit refer to output, capital stock and
employment levels in the four sectors, while R3t is the stock of oil
reserves at the beginning of the period. In the tradable and non-tradable
sectors, output is constrained by neo-classical production functions that
allow some substitution between capital and labor, with the substitution
elasticity given by a KL = 1/(1 + P There is labor augmenting technicaloi
progress reflected in the growth factors gi.
Production constraints in the oil and gas sectors, f3 and f4, are
of a different nature. For oil, the cost of production depends critically on
the relationship between the stock of reserves and the flow of extraction.
Given a certain number of fields and certain levels of reserves, there is an
upper limit on how much oil or gas can be produced without endangering the
long-term productiveness of the fields. Nevertheless, with the aid of
secondary and tertiary recovery techniques, oil production can be maintained
at high levels even in old fields with small reserve to production ratios.
The model captures this relationship by linking cost recovery share of the
- 23 -
foreign oil companies to the production-reserve constellation. Capital
expenditures in the oil sector are overwhelmingly financed by the oil
companies. The companies then recover their costs "in kind" by getting a
certain amount of cost recovery oil in addition to their contractual share in
profit oil. Attempts to push production beyond "normal" levels will run into
diminishing returns to the Egyptian economy reflected in a steeply increasing
cost recovery share. 3/
In the gas sector, the same kind of relationship does in fact exist
between reserve levels and production flows but there is somewhat greater
flexibility. There are also important institutional differences. The foreign
companies role is minor and domestic investment is required to expand
productive capacity. These considerations as well as computational
constraints have led us to drop the variable production costs specification
for gas and use a specification based on a simple capital output ratio plus
quantity constraints on annual output 4/
3.2 Material Balances
The second group of constraints reflect the intermediate input
requirements of production and are arranged in the form of material balance
equations setting total use of a commodity equal or below total available
supply from production and trade. We have:
(P lt > ) Dit + Eit + sI Yt <^X lt (5)
(P6t 0) C + E a < Y6 (a 6 D1t + (1 - a )M (6)6t 6t i 6~~jXj t6i
- 24 -
(P 0) c + Ea X + s Y <X (7)(P2t > °) C2t + ; 2jXjt 2+ t < X2t
(P 3t 0 ) E3t+ a3jXjt + E;a 4Xjt -x4t) <-3t (8)
(P4t ' ) x4t ' E a4JXjt 9
j~~~~~
The first three constraints refer to the domestic non-oil and gas
economy. The supply of domestically produced tradables, Xit must be greater
than what is required for domestic consumption or intermediate use, Dit, for
investment, sjYt (when s, is a fixed ratio) and what is exported, Elt. The
amount Dit then combines with imports Mit to supply the composite tradable
commodity that is either consumed, C6t, or used as an intermediate input
E a6t Xjt, in equation (6). The material balance for non-tradables is
simpler: total supply, X2t, must suffice to meet consumption demand, C2t'
intermediate demand, E a2jXjtp and investment demand, s2Yt.
Turning to the oil and gas sector, we distinguish between two kinds
of (intermediate) demands: (i) a demand that can only be met by petroleum,
reflected in the input coefficients a3 j, and (ii) a demand that can be met by
petroleum or gas, reflected in the input coefficients a4J. For example,
electricity can be generated by gas or oil; on the other hand, we assume that
cars and trucks will continue to require petroleum products. Material
balance equation (8) states that the total supply of petroleum, X3t, must be
greater than total demand composed of exports, E3t and domestic demand, where
the latter decomposes into a portion that is petroleum specific, E a3jXjtp
and a portion that could be met partially or entirely by gas, E a4JXjt' To
- 25 -
the extent that the latter demand is in fact covered by gas output, X4t,
domestic demand for petroleum declines. For example, if gas has totally
replaced oil wherever it can, we would have E a 4jXjt = X4t and the demand for
oil would consist only of exports and non-substitutable uses. Of course E3t
could turn negative if domestic use outruns domestic production, in which case
Egypt would become a net importer of oil. In addition to the material balance
constraint there is also, however, a special constraint on the supply of
gas. The output of gas is constrained by domestic demand through
equation (9): given the probable range of Egypt's reserves and the market
conditions in the region we do not consider exports of LNG to be a viable
alternative, so that domestic demand in the sense described above (all
possible uses where gas can replace oil), acts as a constraint on the total
production of gas.
3.3. The Balance of Payments
The balance of payments reflects society's budget constraint: the
value of imports cannot exceed the sum of export earnings, factor receipts,
and net foreign capital inflows.
(P5t > °) PW14 M + PW M <P (E - X + PWElt + Ft . (10)5t > itltlt Ot Ot= <W3t 3t Ut3t tt t
where
Mit = Imports of initermediate and final goods.
Mot = S5Yt, investment good imports.
Fpet the endogenous price of exports determined by the ratio of a growingt
world demand lbase export level, ge Elo, and actual exports Elt. The
elasticity is variable. For export levels below gtE , the price ise10I
- 26 -
independent of the quantity exported (the elasticity is infinite).
As exports increase beyond that level, the elasticity declines, with
an asymptotic limit of n -
0 = the share of foreign companies in total oil production so that
Elt - 0tX3t is Egypt's physical share in oil exports. We
have Ut = fs(X3t, R3t), with fs reflecting the dependence of
production costs on extraction rates and reserve levels.
PW3t = the exogenous world price of oil.
PWlt = the exogenous world price of intermediate and consumption good
imports.
PWot = The exogenous world price of imported capital goods.
Ft = non-oil exogenous resources (worker's remittances, Suez earnings and
net foreign capital inflows).
By choice of units all prices except the oil price equal unity in
the base period. Oil is expressed in million tonnes so that the base year
price is the 1982 price of a ton of Egyptian oil ($216 or $30 per barrel).
Import prices are exogenous and remain at unity throughout the planning
horizon. This simply reflects the fact that we are dealing with a real model
(everything is expressed in terms of constant 1981 prices), and that relative
price changes will be measured with respect to the exogenous import prices.
For example, if the price of oil is assumed to grow at one percent per annum,
this means that Egypt can buy one percent more imports per annum with a given
physical quantity of oil exports.
Ft consists of three components: worker remittances, which are
assumed to remain constant in per capita terms; Suez Canal revenues, which are
assumed to grow in line with world trade at a rate g, and a mixture of aid
- 27 -
and concessional debt flows which is assumed to be constant in 1980 real
dollar terms. The miKture of concessional debt and aid is constructed in such
a way that per capita concessional debt is constant over time.
Commercial debt is kept at its initial level (making the current
account exogenous) in two of the three sets of experiments performed. Set one
is conducted with exogenous capital accumulation and commercial debt (Section
5.1) and set two introduces optimal capital accumulation but keeps the Current
Account exogenous (Section 5.2). Section 5.3 contains the most general set of
experiments where optLmal physical capital accumulation is combined with
optimal foreign borrowing.
3.4 Capital Accumulation
Capital is accumulated through investment, and there is a one period
lag between the time iLnvestment takes place and the time new capital becomes
fully productive. We have:
(PKit > °) Kit < (1 - di)K it_ + Yi)t-1 (11)
where di is the depreciation rate. In practice, we shall use two-year
periods when running the model, so that we in effect assume that once physical
investment has started, the average gestation lag is two years.
Total resources devoted to capital accumulation are denoted by Yt so
that E Yit 4 Yt. We experiment with both exogenous and endogenous totali
investment. Moreover, we also impose an absorptive capacity constraint that
introduces diminishing returns to aggregate investment beyond what is already
implicit in the production functions. There is a critical investment
- 28 -
level, Yt , itself a function of time and previous levels of investment,
beyond which an increasing part of the "excess" investment is wasted and does
not yield effective new capital. Formally:
*4
Yt if yt - Yti it-l4 J~~~~~~~~~=l
(PIt 2 ) i=1 Y it 4 (12)i=l g(Ytp Y) if t > ii it-
t t j.=l t-
The specific functional form of the functions Yt and g is given
in Appendix A. This specification is designed to capture the difficulties
inherent in trying to raise investment very rapidly beyond customary levels.
These difficulties have been observed in many countries and are due to a
multitude of causes ranging from limited port and transport capacity to lack
of specific complementary factors such as sufficient management or specially
skilled labor. To try and capture all this with a single absorptive capacity
constraint is, of course, an imperfect solution. But the formulation adopted
reflects an important aspect of reality that is central to the problems of
investment planning and that should not be neglected.
3.5 Resource Exhaustion Constraints
The last two constraints reflect the fact that petroleum and gas
production over the years is ultimately limited by total recoverable
reserves. It is this limit on cumulative production that distinguishes oil
and gas from other industrial and agricultural commodities. Oil and gas are
exhaustible resources that cannot be reproduced ad infinitum. In this context
it is important to distinguish between "proven" or "discovered" reserves and
- 29 -
reserves that will be discovered in the future. The distinction is important
because production costs and therefore, indirectly, production flows, are
determined not by total reserves that will eventually be discovered, but by
reserves in existing, known oil and gas fields. We have:
(S3,t >-°) R3,t 3,t-1 ^ 3,t X3,t (13)
(S4,t 2°) R4,t 4,t-1 ^ 4,t X4,t (14)
where R and D refer to reserves stocks and discovery flows. Initial reserves
and discovery flows ares exogenous. The magnitude of future discoveries, is of
course subject to great uncertainty. But it is precisely by exploring the
impact of different reserve scenarios that we can hope to gain a better
understanding of the role of exhaustible resources in the determination of
optimal levels and allocations of investment, and in the determination of
shadow prices that wou:Ld support optimal strategies.
3.6 The Objective Function
Subject to the constraints described above, the model tries to
maximize a social welfare function which is taken to reflect the long-term
development objectives of Egyptian society. In defining the social welfare
function, several factors are taken into account. First, when society is
faced with the choice between an additional unit of consumption today or the
same additional unit tomorrow, the first option is preferable: in technical
terms the pure rate of time preference is positive. This is taken into
account by discounting the utility of future consumption by a factor 6 for
- 30 -
each period in the future. Second, society cares about the level of consump-
tion of the representative family of each generation, and as society gets
richer the value of an additional unit of consumption declines. Utility U is
therefore a declining function of per capita consumption. On the other hand,
it does matter how many families are consuming at that level,5/ so that the
index of per capita consumption is multiplied by total population. Third, the
model specifies a constant rate of substitution between tradables and non-
tradables, where tradables are in fact a .composite" of domestically produced
and imported goods. Thus we have in effect a nested two-level CES utility
function. At the first level imports and domestic tradables aggregate into
the composite tradable consumption good. At the second level, this composite
commodity and the non-tradable commodity yield a CES index of utility. Thus
we have:
T -W = z L t U (15)
t=O twhere
ut= y (a C*_Pu + (1 - a )C* P)/Puu u 6t u 2t
6= the discount or pure time preference factor, which equals the inverse
of (1 + the social discount rate).
I= the consumption elasticity of social welfare (1 + elasticity of the
marginal utility of real income).
C*it = Cit/Lt = consumption per capita of good i, i = 2,6.
- 31 -
Finally, while our model stops at t=T , time does of course
continue and the income of future generations is also valuable. In fact it
could be argued that we should consider an infinite horizon, since by taking a
positive rate of time preference we are already given enough of an advantage
to present and near future generations. But to obtain numerical results we
must, inevitably, work with a finite number of periods T . That is not
really a problem with exogenous investment if T is not too small, since in
that case the only instrument for intertemporal arbitrage is the oil/gas
extraction policy, and all reserves would be exhausted by the end of that
period anyway. But with endogenous investment, if no constraint or valuation
is attached to the terminal stocks, a substantial part, or maybe even all, of
the capital stock will be "eaten up" in the final periods, which is clearly
not a reasonable solut:Lon.
The way this problem is handled in the endogenous investment case is
by exploiting the Turnpike property of optimal growth models: when the
planning horizon is long enough the economy will spend most of its time
growing at a constant rate, with the capital stocks in each sector equal to
its steady state values.6/ That suggests as a good approximation to the
infinite horizon problem, to constraint the terminal capital stocks to be not
smaller than those steady state values. That is,
*Ki,T KiT i = 1,2 (16)
with K = steady state capital stock in the i sector.iT
Notice that the "steady state" capital stock is a function of time
because of technological progress; if capital is redefined in "efficiency
units" that problem goes away.
- 32 -
Of course this method only works if the planning horizon is long
enough to allow the economy to get close to the turnpike values. We therefore
work with a longer horizon (30 periods or 60 years) in the endogenous
investment case than in the fixed investment case, where the horizon is 20
periods or 40 years. This extension of T was chosen after some
experimentation with different values; when extending T further ceases to
influence the solution in the first 30 years significantly, T is considered
long enough.
A final point one should notice is that changes in oil price
scenarios, energy I/O coefficients, utility function parameters, etc. will
change those steady state values Ki . Whenever such experiments were
performed, the steady state values were adjusted accordingly.
4. Valuation on the Optimal Path
One of the attractions of working with an optimizing model is that
it generates as part of the optimal solution a set of dual variables that
measure the contribution to the objective function of relaxing the constraints
of the model. Most of these variables can readily be interpreted as shadow
prices for the different goods or factors.
4.1 Conditions for Static Efficiency
Associated with each of the "material balance" equations in the
primal problem, there is a dual variable (Pit) which is the shadow price of
the corresponding good. There are shadow prices for domestically produced
traded goods (Plt), nontraded goods (P2t)' oil (P3t), foreign exchange or
imported goods (P5t), and the "composite" good defined from produced and
- 33 -
imported traded goods (P6td* We normalize the price of imports to one, so
that P5t measures the value of foreign exchange in the model.
The first two optimality conditions set the domestic shadow price of
oil and of traded goods equal to the marginal revenue at border (international
prices) multiplied by the value of foreign exchange:
P3t P p5t W3 t ( 1)
Plt = p5t(1-1/ n pTe (2)
where n is the elasticiLty of demand for exports. 7/
If Natural Gas were an internationally traded commodity, its shadow
price should be its international price (adjusted for all extra costs incurred
to make it tradeable). When international trade is not a relevant alternative
(like in Egypt, where the size of gas reserves do not justify a liquefaction
plant) gas should be priced at its fuel price equivalent if on the margin it
substitutes perfectly for fuel oil. If, however, gas use is restricted by
substitution possibilities and the level of demand at fuel oil parity price, a
wedge may open up between the price of gas and its fuel oil equivalent. In
this exercise we made the admittedly extreme assumption that gas is a perfect
substitute up to 50%. of total energy use, and cannot substitute at all above
that cut-off rate. The cut-off rate increases to 60% over the first 10
years. The variable P4t (the shadow price associated with the equation
defining maximum demand for gas in any period) measures the gap between both
prices:
- 34 -
PGt = p3t p4t (3a)
so that when the use of gas is demand constrained, P4t will be positive and
the shadow price of gas will be below its fuel oil equivalent.
Consider first the case where P4t is larger than zero but where
there are no supply constraints on production and distribution of natural gas
(Figure 4a).
If there is a finite amount of gas that will be exhausted, say, at
time T , the price has only two components, extraction costs MCt and rent
4t~~~~~~~~~~~~~~~~~to reserves, 4
PGt =MCt + S4t (3b)
= X Pjt aj4 + Q4t b4 + 5 4t
Efficient exploitation of the natural gas resource will lead to a rental
component rising at the relevant rate of discount with the price of gas
reaching its fuel oil equivalent at the moment of exhaustion (cf. Section 4.3
below). Which discount rate is relevant will depend on the numeraire in which
the price of gas is expressed if there are gradual relative price changes in
the rest of the economy.
This price path will provide a floor for the price of gas when
supply constraints are operative. In that case the shadow price of gas picks
_ 35 _
Figure 4a:
Pricing of naturaL gas when use is demand constrained
Price fuel oil equivalent
P eprice
rent toIgas reserves
v Unit extraction costs
T time
- 36 -
up a third component, rent to the factors constraining supply. The fuel oil
price equivalent will provide a ceiling. Figure 4b is an attempt to clarify
matters.
At QA the "supply price" of fuel oil intersects with the inverse
demand curve for energy (exclusive of the "non-substitutable" part of gas).
If supply or distribution constraints limit gas output below QA '
substitution possibilities on the demand side are not yet exhausted and the
shadow price of gas equals its fuel price equivalent, P oil (P3t in our
model).
If supply constraints limit output to any value above QB where the
inverse demand curve intersects with the price floor set by rent to reserves
and unit extraction costs, these supply constraints are not operative.
Accordingly, they earn zero rent in that case and we are back in the case of
Figure 4a where the shadow price of gas equals unit extraction costs plus rent
to reserves.
If constraints on production and distribution of natural gas limit
output to an intermediate value, say Qc 9 the price of gas will be in between
its ceiling P3t and its floor MCt + S4t and the supply constraint
accordingly picks up a rent equal to
Q - MC - S44t =P gt t 4t (4)
where Pgt = pE C) . PE( ) is the inverse demand curve for energy
exclusive of the part for which gas is no substitute.
- 37 -
Notice that QC is an interesting number that could be used inQ4t
shadow-pricing projects expanding say distribution facilities (like
pipelines).
As time goes on, both the demand for gas and the supply constraints
will increase; accordirngly the ratio P gt/Poil may go through several phases
before it eventually reaches unity (for an example see Figure 12).
In the case of oil, instead of using domestic capital, the cost of
extraction additional to intermediate inputs is borne by foreign companies,
which are compensated through a share in the value of output (a . The
corresponding equation is:
3t= jPia3 + Q3t+ Z3t + P5t 3t ( + X3taQ /3X3t) * (5)
The production functions have associated dual variables (Vit) which
give unit value added per sector. That is:
Vit = Pit - E Pjtaj, i = 1,2 (6)
These variables also measure the contribution of primary factors to output:
it' Fi/Kit - Qit = rental value of Ki (7)
Vit' aFi/31 it Wt =shadow wage rate
where Fi(Kit, Lit) are the production functions defined in (1) - (2).
- 38 -
Figure 4b
Pricing of natural gas when supply constraints are operative
Inverse Demand Curve for Energy, P (Qt)Price E t
oil
! c ~~~~~rent to supply .B
rent to gas reserves. ~~ ~~I I I
eunit extraction costs
- 39 -
The last equation already incorporates a further optimality
condition, namely that labor is allocated in such a way that its marginal
product is equal in all sectors. The rent on capital goods may differ between
sectors, as capital once installed cannot be shifted to other uses.
There are two more static efficiency conditions: one defines the
optimal way of produciag the composite X6 from imports and domestically
produced traded goods:
Dlt P6 a6 P5t (8)
mit 1-6 lit
The other shows the opitimal consumption of nontraded goods (C2t) and the
traded composite (C6t), defined by the equalization of the marginal rate of
substitution in consumption and production:
1+ Pt(C 2tI/C ) = (1-Y2)P 6t/y2p2t (9)
In both equations Pi reflect the substitution possibilities (as Pi approach
its lower bound, -1, substitution becomes easier), and a6 and 2 are "share"
parameters that are obtained from base year data.
4.2 The Social Discount Rate
The price variables discussed above are useful for project
evaluation as they give the social value of the corresponding goods and/or
factors. At any point in time only relative prices matter, so that any
numeraire can be used to define prices. It is important to remember, however,
that when evaluating projects with costs
- 40 -
and benefits spread over several periods, the numeraire chosen determines the
appropriate discount factor.
Our model provides a natural generalization of the one-consumption
good model (where that consumption good is the obvious numeraire): total
utility is a homothetic index of consumption of both goods, so that we can
define an exact price index for real consumption to use as numeraire.
Let us consider briefly how the appropriate discount rate is
obtained in models with only one consumption good-8. Suppose a project uses
one unit of that good today and produces b units tomorrow. By definition,
social objectives are defined by the function:
W = EL C ^- (10)t t
to be maximized among all feasible paths of per capita consumption (C t)
The change in W when the project is undertaken is (when the project is small)
AW E6-tC*c lbt t
t
By definition bo = -1 and b1 - b. The project should be approved, if and only
if it results in an increased value for the objective function, i.e. when:
_ C*~l + c6 lC"_ 1 b > 0 (11)
That is, future benefits must be discounted at the Consumption Rate of
Interest (CRI) defined by:
- 41 -
CRI -g I (12)C
where g = C /C is the growth factor of real consumption. The social
discount rate is larger the larger is 6 , as the future is considered
relatively less valuable. Also, with declining marginal value of per capita
consumption (i.e. f < 1), the more consumption per capita is expected to grow
the more the future should be discounted: if consumption is expected to grow,
the marginal utility of consumption decreases and consumption in the future
will be less valuable for that reason.
The rate of growth of the population drops out of the expression for
the consumption rate of interest due to the specification of social objectives
in (10). An alternative specification used in the literature does not weight
per capita consumption by the size of the population. Practically this has an
impact identical to having a smaller time preference factor, so that a specif-
ication that maximizes the sum of unweighted per capita consumption with a
high pure time preference factor, is equivalent to a specification maximizing
the sum of population weighted per capita consumption with a low pure time
preference factor. Whichever specification one choses, it is necessary to
test the sensitivity of the growth path to variations in the time preference
factor.
As noted above, the assumption of homothetic preferences allows us
to interpret the model as having only one consumption good. The CRI can be
obtained as in (12), diefining C* as total real consumption (i.e. utility, Ut,
which is equal to the value of consumption divided by the exact price index
defined by the function U(C2 t, C6t)). In Chapter 5 we will also compare the
- 42 -
CRS with discount factors in terms of other numeraires.
4.3 Dynamic Optimality Conditions
The optimal solution also generates values of all stocks in the
model: capital in each sector and reserve of oil and gas.
The prices associated with the capital updating equations, PKit,
must satisfy two optimality conditions:
(i) they must equal the discounted value of the future contribution
of Kit to real consumption over the planning period, plus their terminal
values.
(ii) they must also equal the cost of reproduction of capital, with
allowances for lags in the maturation of investment and constraints on the
quantity of investment that can be usefully undertaken during a given period
(i.e. absorptive capacity).
If we define all variables in terms of real consumption and assume,
to simplify notation, a constant social discount factor, CRI, we must have:
PK = T-Et Qist+sCRI -s +dQi t T (13)it ,t+s +-i$TCR
where Qi,T is the terminal value of Ki, and Qi,t is the marginal productivity
of capital in the ith sector, defined in (5) and (7).
Capital goods are assumed to be composed of nontraded goods,
domestically produced traded goods and imports, in fixed proportions. The
cost of new capital goods is therefore:
PKt =sPit + s2P2t + s5P5t (14)
- 43 -
There are two factors mediating the connection between the value and the cost
of reproduction of capLtal. First, investment takes time in becoming fully
productive. In our case the maturation lag is just one period, so that:
PIt = PKit/CRIt i = 1, 2, 3 (15)
The fact that (15) has to hold for all three capital goods reflects
our assumption that alL capital goods are homogeneous before being committed
to any particular sector.
A second reason why PIt is not necessarily equal to the cost of
reproduction of capita:L goods is the presence of absorptive capacity
constraints: resources devoted to investment are less efficient in generating
production capacity beyond a certain level (due to lack of qualified workers,
bottlenecks in infrastructure, etc.). In general we must have
PIt > PKt (16)
with strict inequality when absorption capacity is a binding constraint. The
actual connection between PIt and PKt in the model is also affected by the
impact of current investment on relaxation of future capacity constraints (see
Appendix A).
The value of the remaining two stocks in our model, oil and gas
reserves, are more easLly described, as they can not can be reproduced nor
have any use besides aLlowing future extraction.
An efficient allocation of social wealth between all available
assets will lead to equal rates of return on all of them. For natural gas the
- 44 -
only component of the rate of return is capital gains on reserves, so the
rental value of gas follows (13a).
s4t s4t+l / CRIt+l (13a)
The value of gas reserves increases at the social discount rate:
when they equal the fuel oil equivalent minus marginal extraction costs,
reserves will be exhausted.
For oil the marginal return on keeping one more unit in the ground
has two components because of the assumption that extraction costs depends on
the level of reserves. If Q3t+l is the reduction in marginal extraction
costs during period t+l (incurred at the beginning of the period) by having
one more unit in the ground at the beginning of period t+l 9/, the rental
value of oil must follow (13b):
s3t= Q3,t+l + S3t+1/CRIt+1 (13b)
The rental value of oil reserves may decline, contrary to the case
of gas, as their increasing scarcity pushes up marginal extraction costs. It
is possible that the rent becomes zero at a positive reserve level, indicating
that extraction costs have become too high to make extraction worthwhile:
economic exhaustion may come before physical exhaustion if extraction costs
depend on remaining reserves.
- 45 -
4.4 Changes in relative prices
In section 1 we discussed how changes in the level of Exogenous
Resources were expected to affect relative prices in a simple traded-nontraded
model: increasing Exogenous Resources results in an appreciating real
exchange rate (i.e. an increase in the relative price of nontraded goods), and
a real depreciation should be associated with declining inflows, to facilitate
substitution, away from traded goods in consumption and toward them in
production. As we noted there, the magnitude of the adjustment required
depends on "how different" domestic tradeables are from domestic non-
tradeables, in the way they combine factors of production if production
characteristics were identical between the two sectors, the output of
tradeables could expand without the need for a rise in their relative price
(this of course assumes; perfect mobility, we in fact postulate that capital
goods are mobile ex ante, but sector specific export, but given the high rates
of investment and forward looking nature of optimizing models, the constraints
on mobility is almost never binding). However, our description of the
Egyptian economy is considerably more complicated than the simple two goods
model, making the dynamic behaviour and indeed even the definition of "the"
real exchange rate also more complex.
In the first place, we specify the need for changes in the terms of
trade as exports expandL. That makes the real exchange rate relevant for
consumption decisions dLifferent from the one determining the relative
productivity of domestic factors in the traded and home goods sectors (since
importables and exportaLbles enter in different proportions in the consumption
and production baskets; in fact we assume that only imperfect substitutes of
imported goods are produced domestically). As the economy adjusts to lower
- 46 -
exogenous inflows by producing more exports, the price of imports (the foreign
good) rises relative to the prices of both domestic goods (tradeables and non-
tradeables). This terms of trade effect forces a "devaluation" not in the
sense of a rise in the price of domestically produced tradeables relative to
the non-tradeables, but in the sense of a rise on the price of foreign goods
compared to domestic goods.
A second factor that complicates the dynamics of relative prices is
that, in addition to a reduction of exogenous inflows, which other things
equal, leads to a rise in the relative price of tradeables compared to non-
tradeables, there is a sustained increase over the planning period in the
overall capital/labor ratio of the economy and in the price of energy. That
tends to reduce, for a given composition of output, the price of the sector
which is relatively more capital intensive and less energy intensive,
respectively. Stylized facts about the Egyptian economy suggest that the
nontraded sector is more energy intensive (since it includes such energy users
as transportation, electricity) and less capital intensive (because of the
inclusion of services), than the sector producing tradable goods. As a
result, both capital accumulation and the increasing cost of energy tend to
counteract the tendency toward an increase in the relative price of
tradeables, associated with the reallocation of resources required to reduce
the dependence on Exogenous Resources.
- 47 -
5. The Nature of OptimaL Growth Paths:Structural Adjustment in a Long-Run Perspective
5.1 Experiments with fixed total investment
Once an economic model has been constructed and can be operated, it
becomes a kind of laboratory with the help of which alternative scenarios can
be explored, different views of the future can be contrasted and different
strategies can be evaluated. The experiments reported below illustrate some
of the analytical features described in the preceeding sections. They were
designed to contribute ito a better understanding of some of the basic
characteristics of Egypt-s future growth and are designed to help evaluate the
most important policy options.
For the first set of experiments the growth of physical investment
is kept approximately constant and the trade balance is fixed exogenously.
This assumes that total investment escapes the control of the policy maker,
that Egypt cannot or will not use net foreign borrowing as a significant
policy variable and that: workers remittances and Suez Canal earnings grow at
some exogenous predetermined rate. Given these constraints, there are two
major issues that the optimizing model can explore: the allocation of
investment between tradables and non-tradables and the optimal pace of oil and
gas extraction. Note that in so far as oil and gas extraction require
investment in the oil and gas sector, investment allocation also determines
the pace of extraction, so that experiment set A can be defined as focusing on
resource allocation given exogenously fixed total streams of investment and
foreign capital and an exogenously given profile of oil and gas reserves.
- 48 -
5.1.1 A Base-Case Scenario
To give us a basis against which to test the sensitivity of the
model to variations in exogenous variables and parameter estimates, it is
useful to start by exploring a base case scenario which can then be used as a
kind of reference path.
A key factor determining the characteristics of any optimal growth
path derived from the model is, of course, the view one takes about oil and
gas reserves. Clearly, there is a tremendous amount of uncertainty relating
to the magnitude of hydrocarbon reserves. Proven reserves in Egypt are low
compared to annual production levels and projected growth of domestic use.
For oil, a comprehensive recent study estimates proven reserves to be between
2.6 and 3.6 billion barrels in 1980 (360 and 500 million tons). This amounts
to no more than 10-14 years worth of production at current rates. Prospects
for new discoveries are good, however, and there is a great deal of investment
in exploration. Over the past few years this search for oil has produced a
steady stream of small but significant discoveries, adding between 20 and 40
million tons on average to proven reserves every year. For natural gas, the
situation is similar. The point estimate in 1980 for total proven reserves
from established fields and new well finds was 8.3 trillion cubic feet,
equivalent to about 200 million tons of oil equivalent. On the other hand,
most analysts are quite optimistic about reassessments of existing fields and
new discoveries. The same puts probable and possible "guesstimated"
undiscovered gas at 23 Tcf or 550 million tons of oil equivalent. Note that
this is a kind of upper bound for the next twenty years. The study in fact
works with a "proven reserves + half probable + one quarter possible" formula
that yields 15.5 Tcf as the most likely reserve scenario for natural gas.
- 49 -
There are, however, more optimistic estimates, ranging up to 35 Tcf or 840
million tons of oil equLvalent and it is also worth stressing that the study
is not concerned with the post-2000 period so that small discoveries that
might still be made in the outer years are discounted.
In light of the above, we start by focusing on a base-case scenario
with the characteristics presented in Table 2.
As described in Section 2 above, oil extraction costs are endogenous
and depend on the relationship between the rate of extraction and the stock of
"already discovered" reserves. While a similar relationship exists for gas,
it is weaker and given the relatively more plentiful supply, we are ignoring
it in the range of variation explored with these experiments. Production
costs in the gas sector are assumed constant and do not depend on the reserve
to extraction ratio.
Based on these assumptions about hydrocarbon reserves and other
parameter values described more fully in Appendix A, the model has been solved
numerically to generate a base case optimal growth path and associated shadow
prices.
We shall first describe in some detail the characteristics of the
base case optimal growth path and then test the sensitivity of the most
important variables to variations in reserve scenarios, oil prices and foreign
exchange inflows.
- 50 -
Table 2Exogenous Variable Estimates for the Base Case Scenario
Proven Reserves Projected New Total1981-/1982 Discoveries 1981-2011 Reserves
Petroleum Reserves 500 m.t 400 m.t. 900 m.t.
Gas Reserves 250 m.toe. 300 m.toe. 550 m.toe.
World Price of Crude Oil 2.7 percent real annual growth 1983/84-1989-90
1.8 " " 1989/9 0-2000/ 01
0.5 " " 2001/ 04-20! 0/11
Suez Canal, Remittances 3.5 " " " 1981/82-2010/11and Net Foreign Capital
Economy-wide Investment 5.5
Economy-wide Labor Force 2.7
5.1.2 The Base Case
The most important underlying factor explaining the characteristics
of the optimal growth path is the behavior of what we have called "exogenous
resources", RE, composed of Egypt's share of petroleum output, workers'
remittances, Suez Canal earnings and net foreign capital inflows. Figure 5
below describes the ratio of exogenous resources to total resources for the
base case scenario.
It is clear from Figure 5 that under base case assumptions Egypt
will have to adjust to a very substantial transformation in its resource
- 51 -
base. This R ratio t:o domestic value added goes up to 82% while oil and gas
production is expanding and declines gradually there after to about 40% around
2010.
Developments in the oil and gas sector are the most important
determinant of the behavior of the RE ratio. Figure 6 summarizes output and
export paths for oil and gas, given the base case discovery and reserve
assumptions.
In the base case scenario total oil production continues to grow
throughout the 1980's, peaks at the end of the decade at about 52 million tons
a year (a little more than one million barrels a day) and then declines quite
rapidly. By the year 2010, oil reserves are nearly exhausted. Egypt's share
of oil production also broadly follows this pattern with the decline accentu-
ated by the decrease of the ratio of Egypt's share to total production,
reflecting higher production costs and therefore higher cost recovery
transfers to foreign oiL companies as the ratio of output to reserves falls
over time. While oil production follows this pattern, natural gas production
increases steadily between 1981/1982 and the year 2000. It then levels off at
a rate of 20 million tonis of oil equivalent.
The dotted line in Figure 6 describes the behavior of Egypt's oil
exports derived as the difference between oil and gas production (net of the
foreign companies' share) and domestic consumption. Egyptian energy exports,
caught between a levelling off in production of oil and gas, increased
extraction costs and steady growth in domestic demand, start declining after
1988/89 and, by 2003/2004, the base case projects net energy imports, growing
rapidly thereafter. Two points are worth stressing in this context:
- 52 -
Figure 5
Ratio of Exogenous Resources to Domestic Value Added
0.9- - 0.9
0.8o- - 0.8
0.7 - 0.7
0.6- 0.6
0.5- .- 5.S
0.4- \ 0.4
0.3- -1 , 0.31980.0 1990.0 2000.0 2010.0 2020.0
- 53 -
(1) The behavior of net exports (or imports) of energy often appears to be
the crucial variable. In fact, what matters is the magnitude and rate of
change of total oil and gas production. For example, consider the adjustment
problems faced by two hypothetical countries. Country A initially produces 80
million tons of oil and gas, exports 40 million and consumes 40 million
domestically. Country B produces 40 million, consumes the same 40 million and
has no net crude. Five years later, Country A still produces 80 million tons,
consumes 60 million and exports 20 million tons. On the other hand, Country B
produces 50 million, consumes 60 million tons and has, therefore, become a net
importer. Nevertheless, other things equal it is Country A that will have
suffered from a greater adjustment problem.
(ii) The model projects net oil imports after 2004. These imports can also be
interpreted as imports of "alternative energy" in the form, for example, of
foreign exchange expenditures on nuclear power plants, nuclear fuels and
nuclear technology. Egypt is, in fact, planning to generate nuclear power
starting around 1990 and this interpretation of the projected "oil" imports is
not inconsistent with the view of the future of Egyptian energy planners,
although the base case scenario seems to suggest that these expenditures
should not occur before the end of the century. Of course nuclear power
requires bulky investmenits so that the path of foreign exchange expenditures
would be much more irregular than that depicted in Figure 6.
- 54 -
Figure 6
Oil Production and Exports
,_________ OIL AND GAS OUTPUT…____ SHARE OIL COMPANIES
. C : OIL EXPORTS O
c) __.___ _
0:
Zc,
DO. _ __ __ __ ___
E-ec.,,
O '., _°~~~~~~~~~~~~~~~~~~9,
C) . 0
a) I
192 0
1980.0 1990.0 2000.0 2010.0 2020.0
- 55 -
Given exogenous overall investment and an exogenous trade balance,
there are only two possible adjustments to the decline in exogenous foreign
exchange receipts described above: export expansion or import substitution.
Figure 7 below depicts both processes at work on the base case optimal growth
path.
Export expansion occurs in the form of a greater share of tradables
having to be exported. From Figure 7 it is apparent that the late 1980's and
early 1990's would be a period of dramatic export expansion under base case
assumptions. Non-oil merchandize real annual export growth would average 5.3
percent from 1981/82-1986, 12.7 percent from 1987 to 1991, 13.7 percent from
1992 to 1995 and then decline gradually to 10.2 percent from 1996 to 2001
before stabilizing around 8.3 percent thereafter. The share of exports in
domestic production of tradable commodities would rise from about 13 percent
in the first half of tlhe 1980's, to 32 percent at the end of the planning
horizon. While this is a very large increase over a relatively short period
of time, it would bring Egypt's share of exports in tradable output to a level
only a little bit above the average 25-30 percent characterizing most semi-
industrial economies. Nonetheless, given the severe land limitations
constraining agriculture, such an increase requires sustained and very rapid
growth in manufactured exports over a period of 10 to 15 years.
Parallel to the process of export expansion, the share of imports in
domestic intermediate and final consumption would have to decline from 37
percent in the early 1980's to 27 percent at the end of the planning horizon.
- 56 -
Figure 7
Export Expansion and Import Substitution
SHARE OF EXPORTS IN PRODUCTION OF TRADABLES
......... SHARE OF IMPORTS IN DOMESTIC USE OF TRADABLE GOODS .
0.40- ...... - 0.40
....... ............ ......
0.35/ 0.35
0.30 0 - 0.30
0.25 - - 0.25
0.20 - IP. 20
0.l5 - 0.15
0
0.10 I I I 0.101980.0 1990.0 2000.0 2010.0 2020.0
- 57 -
All this amounts to a substantial increase in the share of the
tradables producing sector in the economy. Figure 8a describes the base case
results in terms of the share the tradable sector has in the capital stock,
employment and output in the domestic non-oil and gas economy. All these
shares increase nearly 15 points during the planning period.
The structural adjustment depicted in Figure 8a is necessary to
allow the required degree of export expansion and import substitution. But
that only describes the supply side of the economy. The demand side also
adjusts, although given the limited substitutability that is possible between
the broad groups of tradable and non-tradable commodities, the adjustment is
not that dramatic, as shown in Figure 8b.
The structural adjustment characterizing the optimal growth path can
also be described in terms of growth rates. Table 3 below summarizes the
growth pattern for the four sectors distinguished by the model.
Table 3
Average Annual Sectoral Growth Rates : The Base-Case
(Percentages)
Tradables Non-Tradables Oil Gas
1982-1985 7.0 6.4 6.0 30.01986-1991 6.7 5.6 2.2 8.91992-1995 7.2 4.4 4.31996-2001 6.6 4.6 -9.4 4.02002-2011 6.2 4.8 -16.5 0.0
- 58 -
Figure 8a
Share of Tradable in Domestic Non-oil Economy
|___________CAPITAL., EMPLOYMENT
--------- VALUE ADDED
0.75- 0.75
0.70- 0.70
0.65-
0.60 - 0.60
0,55 ./ ,,w' . - 0.55
0.50 , 0.50
0.45 .. ....-. 0.45
0.40- - 0.40I980.0 1990.0 2000.0 2010.0 2020.0
- 59 -
Figure 8b
Ratio of Consumption of Tradable over Non tradable Goods
1.27- - 1.27
1.26 - 41.26
1.25 - 1.25
1.24- - 1.24
1.23- 1.23
1.22- - 1.22
1.21- - 1.2119.013 1990.0 2000.0 2010.0 2020.0
- 60 -
Over the entire planning horizon, domestic production of tradables
has to grow more rapidly than domestic production of non-tradables. The
deviation from balanced growth is most pronounced in the 1992-1995 period
during which the structural adjustment process is particularly dramatic.
After the end of the century, the difference between the growth rates again
narrows as the economy gradually adjusts to the near-exhaustion of oil
reserves and the levelling off in the gas sector.
At this stage, it may be useful to remember that throughout, by
assumption, investment grows at an annual rate of 5.5 percent. Table 4 below
summarizes the behavior of the main macroeconomic aggregates.
Table 4
Growth of Macroeconomic Aggregates: The Base Case
(Percentages)
GDP Imports Consumption Investment Exports
1982-1985 8.7 6.6 7.6 5.5 10.21986-1991 5.1 5.2 4.7 5.5 6.31992-1995 2.7 3.8 2.7 5.5 2.81996-2001 2.7 3.9 2.6 5.5 2.92002-2011 3.0 7.3 2.8 5.5 8.2
GDP plus imports always equals the sum of consumption, investment
and exports. With investment growth fixed and constant and imports-exports
also fixed and growing at an approximately constant rate (between 3.2 and 4.1
percent) it is clear that the growth path of consumption must closely follow
the growth path of GDP. As GDP growth declines to less than 2 percent in the
- 61 -
mid-1990's due to declining production in the oil sector (see Table above),
consumption growth also must decline, since neither a reduction in investment,
nor an increase in the resource gap can take place.
The behavior of total exports (and therefore imports) constitutes an
interesting feature of the growth path. Total exports first grow very rapidly
(10.5 percent), then the growth rate becomes very small during the period of
peak oil exports, before rising again. Figure 9 below separates the growth
path of exports into its two components: oil exports and non-oil, tradable
goods exports.
The combination of very slow GDP growth and slow export growth
during the 1992-1995 period, leads to low import, and even lower consumption,
growth rates. Given that population growth is likely to remain above 2.9
percent per annum in tlhe early 1990's, 1.9 percent growth in total consumption
implies a small decline in per capita consumption during that period, when the
structural adjustment process reaches its most difficult stage.
5.1.3. Shadow Prices Ln the Base Case
(a) Price of traded and nontraded goods
The same process of transition to a post-oil economy can be seen
from the valuation side of the model. The initial period of rapid expansion
in oil revenues is reflected in an increase in the price of nontraded goods
measured either in terms of imports, exports, or the domestic price of traded
goods produced at home (Figures 10).
Soon enough, however, the relative decline in Exogenous Resources as
proportion of the domestic economy begins to make tradable goods scarcer and
- 62 -
Figure 9
The Composition of Exports
0TOTAL EXPORTS........... ......NET OIL EXPORTS----------- EXPORTS OF TRADABLE GOODS
BO.O 80.0
60.0 2 -0.0
40.0 - 40.0
20.0 - 20.0
0.-"',.,,,- 0.0
-20.0 . -.20.0
-40.0- -- 40.01980.0 1990.0 2000.0 2010.0 2020.0
- 63 -
Figure 10a
Real Exchange Rates: Price of Nontraded Goods in
Terms of Various Traded Goods
PRICE IN TERMS OF IMPORTS.......... PRICE IN TERMS OF THE COMPOSITE TRADED GOOD
0.95- _ - 0.95
0.9go - ' .' ... . 0.90
0.85- - 0.85
0.80- - 0.80
0.75 - -0.751980.0 1990.0 2000.0 2010.0 2020.0
- 64 -
therefore, more expensive to consumers and more valuable to producers. As
Figure IOA shows, there is a substained fall of the price of nontraded goods
in terms of imports and the composite traded good consumed domestically. This
drop in the consumption real exchange rate is just the price counterpart of
the declining share of nontraded goods in consumption seen in Figure 8.
In the production side the story is slightly more complicated. On
the first place, there is a widening gap between the domestic price of
exportables and the price of exports, reflecting the fact that when the volume
of exports cannot be expanded without reducing the unit value obtained from
them, it is optimal to divide the output of tradable goods between the
domestic and foreign markets in such a way that a wedge (an "optimal tariff")
exists between international and domestic prices: the latter should be equal
to the marginal revenue from exports, which is lower than the price paid by
foreign consumers. Figure 10B shows that the average values of traded goods
(i.e. the average of domestic and foreign prices, with weights proportional to
the share of output going to each market) does in fact increase with respect
to the price of nontraded goods (dashed line).
There is a second reasons why the ratio between domestic prices of
nontraded and traded goods is not a perfect indicator of the incentives for
allocating domestic resources among sectors: part of the increase in PN/PT is
needed just to compensate for increasing cost of energy, without really
implying that domestic factors could earn more there. As Figure 10b shows, in
fact the ratio of value added in both sectors hardly changes from the late
80-s on: most of the increase in PN/PT is due to increasing price of oil. The
domestic cost of energy is also the reason for the fall in real exchange rates
in the late 1980's and its rise in the late 1990's: these two periods mark the
- 65 -
Figure lOb
Real Exchange Rates: Price of Nontraded Goods in
Terms of Various Traded Goods
Price of Nontraded Over Price of Traded Goods.............. Ratio of Unit Value Added
-------------- Price of Nontraded Over Average Value of Traded GoodsPrice of Nontraded Over Price of Exports
1.00 - 1.00
0.95- - 0.95
090 - 0 #t ~~~~--- ,------0.985- . ~ . -0.90
0.85 - 0.85
0. 80- 0.80
0.75 -0.751980.0 1990.0 2000.0 2010.0 2020.0
- 66 -
beginning and end, respectively, of the decade of cheap natural gas (see b),
below), as its production/distribution capacity expands (temporarily) beyond
domestic demand. Nontraded goods are more energy intensive, so they benefit
more from low cost energy.
(b) Price of Gas; Shadow Price of reserves of oil and gas
The price of oil is exogenous to the model. In the base case
scenario it is assumed to be constant in real terms until 1984 and grow from
then on at an annual rate that declines from 3% to around 2% in 2010. We
discuss alternative price scenarios in section 5.1.5.
The model divides the price of oil in three components: rent to the
stock of reserves, cost of extraction and rent to capacity limits. As Figure
11 shows, the latter component is significant at the begining of the planing
period, while production capacity is being built up. The rent component rises
up to about 60% of the price of oil, but later declines as lower reserves lead
to higher extraction costs.
The price of gas and its decomposition in rent to reserves,
extraction cost and rent to capacity limits, is presented in Figure 12. As
discussed in section 3.2, (see also section 4.1) we approximate the
substitution possibilities between oil and gas by differentiating sharply
between uses in which they are perfect substitutes (55% of total demand for
energy), and uses in which gas cannot replace oil products at all. In
addition, there are output constraints (including limitations in the capacity
to transport the gas to users). The value (shadow price) of gas is therefore
eqbal to its fuel oil equivalent (i) whenever the production constraints do
not allow us to exhaust domestic substitution possibilities, or (ii) when
- 67 -
Figure 11
Decomposition of the Price of Oil
(US$/barrel)
VALUE OF OIL RESERVES
.......-- PLUS RENT TO CAPACITY CONSTRAINTS
- - EGYPTIAN SHARE
! -.-.--.- PRICE OF OIL
70.0- - 70.0
60.0 7 60.0
so. 0 - // -50.0
40.0 ./," ' 40.0
30.0 -~. - - -
30.0 - 30.0
20.0 / 20.0
10.0- I- 1980.O 1990.0 2000.0 2010.0 2020.0
- 68 -
reserves are so scarce that it is optimal not to produce so much as to
substitute fuel oil wherever it is possible, in order to allow some production
in future periods.42' As shown in the figure, the result of these factors is
that only during about 10 years from the late 1980's the price of gas is below
(by 25-30%) to its fuel-oil equivalent.
At exhaustion time, production capacity constraints are not binding,
so the price of gas equals extraction costs plus rent to reserves. As the
cost of extraction is independent from the stock of reserves, the value of
reserves is constant in discounted value (i.e. it grows at the social rate of
discount). The difference between the price of gas, net of extraction costs,
and the value of reserves is the imputed rent to the production (and
transportation) capacity constraints of gas. They show the considerable
payoff that would accrue to projects increasing the quantity of gas that can
be produced and delivered to users (Figure 12).
5.1.4. Sensitivity to Oil and Gas Reserves
It is clear that oil and gas reserve estimates have an influence on
the nature on the optimal growth path. In a first set of experiments we have
tested the sensitivity of the projected "structural adjustment path" to
variations in oil and gas reserves, keeping all other exogenous variables
constant. Table 5 describes three of the alternative reserve scenarios that
have been explored.
These various reserve scenarios are based on a fairly non-
controversial estimate of initial proven reserves (500 m.t. for oil and 250
m.t.e for gas) and projected new discoveries the magnitude of which is, of
course, much more uncertain. It would be a fundamental mistake, however, to
- 69 -
Figure 12
Decomposition of the Price of Gas
-_____ VALUE OF GAS RESERVES.......... PLUS RENT TO PRODUCTION/DISTRIBUTION
- - … PRICE OF GASPRICE OF OIL
70.0- - - 70.0
60.a- //- 60.0
so. a 7/ 50.0
1 0.0- , ,' /- 40.0
30.0 - 30.0
20.0 / 7 - 20.0
10.0 10.01980.0 1990.0 2000.0 2010.0 2020.0
- 70 -
attach zero probability to new discoveries given: (i) the large investment
effort in exploration that is underway, and (ii) past performance which has
produced a steady stream of small discoveries of both oil and gas. There is
little doubt that new oil and gas will be discovered in Egypt. The question
only relates to the magnitude and time pattern of these discoveries.
Table 5
Alternative Scenarios for Oil and Gas Reserves
(Million tonnes Oil equivalent)
Base High Oil Low OilCase and Gas & Gas
Reserves Reserves
Proven Oil Reserves 500 500 500
New Oil Discoveriesover the Planninghorizon 400 655 100
Proven Gas Reserves 250 250 250
New Gas Discoveriesover the Planning 300 590 150horizon
Regarding oil, the base case assumes annual discovery flows starting
at 25 million tons in the mid-1980's and then declining gradually to 10
million tons in the mid-1990's before ending in the year 2000. The optimistic
scenario assumes higher initial discovery rates, again declining but with
- 71 -
discoveries continuing throughout the planning horizon. The pessimistic
scenario, on the contrary, projects only very small discoveries ending after
the early 1990's.
For gas, the situation is somewhat different. Exploration in the
very promising Nile Delta region has only recently got underway and the next
10 to 15 years are likely to be characterized by steady rather than declining
discovery rates.
Figure 13 below describes the production schedules for the three
scenarios explored: the Base Case compared to the high reserves (oil and gas)
and low reserves (oil and gas) scenarios. Larger reserves postpone the period
of self sufficiency in oil by about 5 years, while with low reserves imports
are necessary about 8 years earlier than in the base run. The production of
oil/gas and traded goods are (non perfect) substitutes, so that the stock of
capital in the traded sector becomes large with low reserves and smaller with
large reserves (cf. Figure 14). The most dramatic effect of changing the
reserve estimates is on the pricing of gas. As we discussed above (Section
4.1) it is only when all domestic opportunities for substituting fuel oil by
gas have been exhausted that the price of gas can fall below that of its oil-
equivalent. In the base reserve scenario that happens only for a 10-years-
period in the late 1980's and 1990's. As Figure 15 shows, with low reserves
the period of cheap gas entirely disappears, while large gas reserves extend
it to most of the plannlng horizong (after the initial period of capacity
constrained gas output).
- 72 - -
Figure 13
Production of Oil Under Alternative Reserve Scenarios
[o- - - -- LRWC OIL ND CflS RESERVES
CA Q
C;_ _ci0 {D
LF)
C) C)
I~~~~~~~
2zC>_ * \ci
ci - ~~~~~~~~~~~~~~~C3
*~~~~~~
t 980. .1990. 0 2000.0 2010. 0 2020 .0
- 73 -
Figure 14
Capital in the Traded Sector Under Alternative Reserve Scenarios
[71 BRaSE mcn[L - LRRE OIL AND GAS RESERVESG) o LOW OIL FN GAS RESERVES
a:o~~~~~~~~~~~~~~~~~t
O :^-*-.O~ .I--. 'Cr)
G: .. 4 c
H Cy *
0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-
G ~ ~~~~~~~~ . . *.
G O v--' ~~~~~* 4
C) 's
CD c \ t___ oaS) , _%.
Lc'R .v~~~~~~ v
Cr) 9BS* 93.0 2000 21.0 2:' 0
C3CC CD~~~~~
'I 02~~~~~~~~~~~~~~~~~~~r
LLJO vci
C 9B. 199.I2000 2100 22.
- 74 -
Figure 15
Price of Gas Under Alternative Reserve Scenarios
§ R~~~WSE CRISE- - - - - LNRrE OIL RND CS R£SERES
O .............. LOW OIL RND PRS RESERVES C
.~o _ :
o , _ ~~~~~~~~~~~~~~~~C)
-f 2
C) M~~~~~~~ I~~
C~L) cmII
Q cm~~~~~~~~ 0-~~~~~~~~~
0~to L/ 0
cr-~~~~~~~~~~~~~~~~~~~
LU') /
CD ~ ~ ~ ~ ~ ~ 10(90 I~~~~~~~~~~~~~~~~~C
CS ci~~~~~~~~~~~~~
19800 190. 200.0 0100 220.
- 75 -
Table 6 describes the sensitivity of GDP, consumption and export
growth to the alternative reserve and production scenarios.
High reserves allow a larger rate of growth of GDP and consumption
through the planning period, although the difference in average annual rates
is no more than 1%. The early 1990's is still the most difficult period,
while there is an improving trend after the year 2000, as the economy
successfully completes the transition toward a much reduced role of the oil
and gas sector. As the last part of the table shows, with pessimistic
scenarios for new oil discoveries, non oil exports must grow at very large
rates during the late L980's and early 1990's (near 15% per year) just to keep
total export revenue from falling behind import requirements. The bright side
of low reserves is that the economy reaches its non-oil based steady growth
path sooner. And indeed, toward the end of the planning period the three
scenarios hardly differ from each other.
5.1.5 Sensitivity to the Real Price of Oil
So far the growth path of the real price of oil was kept constant
throughout the experiments. The price scenario adopted is the World Bank's
"official" scenario of 3 percent real growth until the early 1990's and a
gradually declining price growth thereafter. According to this scenario, the
price of a barrel of crude in constant 1981 prices would be $38 in 1990, $49
in the year 2000 and $59 in the year 2010.
Any public or private economic decision maker must project the real
price of oil: unfortunaLtely there is no escape from this, despite the obvious-
ly massive uncertainty attached to future oil prices. The path of world oil
prices will depend on a multitude of factors such as worldwide discovery
- 76 -
Table 6
The Impact of Alternative Reserve Scenarios on theGrowth of Macroeconomic Aggregates
(Percentages)
Base High LowCase Reserves Reserves
GDP1982-1985 8.7 8.9 8.71986-1991 5.1 5.8 3.01992-1995 2.7 2.9 1.81996-2001 2.7 3.0 2.62002-2011 3.0 4.1 3.9
Consumption
1982-1985 7.6 7.8 7.61986-1991 4.7 5.2 3.01992-1995 2.7 2.8 1.81996-2001 2.6 3.0 2.42002-2011 2.8 3.9 3.6
Exports1982-1985 10.3 10.4 10.41986-1991 6.3 7.2 3.31992-1995 2.8 3.1 2.11996-2001 2.9 3.2 8.62002-2011 8.2 5.4 7.5
Non Oil Exports
1982-1985 7.7 6.6 8.11986-1991 11.6 11.0 14.91992-1995 11.8 11.9 12.41996-2001 10.5 10.1 9.72002-2011 8.6 7.8 7.5
- 77 -
rates, worldwide economic growth, technological developments affecting other
forms of energy (solar, nuclear, biomass, etc.), conservation and domestic
price policies and, last but not least, political developments of various
sorts affecting the production and worldwide trade of hydrocarbons. All these
factors could combine Ito drive the barrel of oil steadily up in value. On the
other hand, the combination of a series of technological breakthroughs, major
new discoveries and slow economic growth in the major consuming nations could
lead to constant or even declining oil price.
To explore the sensitivity of the optimal growth path to variations
in the assumptions about future oil prices, we conducted two sets of
experiments with alternative oil price scenarios. In the first group we only
change prices in the far future (after the year 2000). In the second group
oil prices are higher (lower) when the economy is a net importer and lower
(higher) when it is a net exporter,i.e. the price schedules are tilted. For
comparison we also include a scenario with oil prices uniformy below the base
run values. We discuss; a scenario with even lower prices throughout (falling
initially to $25 per barrel) in Section 5.3, where optimal foreign borrowing
is allowed. Table 7 and figures 16 and 17 describe the scenarios discussed
here.
If the expected price of oil in the latest part of the planning
period is larger than in the Base Case, there is an incentive to save oil
initially, to be able to extract it later, when it will be more valuable.
That is exactly what Figure 18 shows. There are changes in the allocation of
capital, which are just the mirror image of the changes in oil output.
- 78 -
Table 7
Alternative Scenarios for Real Price of OilPrice per barrel of Oil (constant 1981/87 US$)
(1981/2 US$ per barrel)
High LowPrices Prices Low Low First High First
Year Base After After Price High Later Low Later2000 2000
1985 31.8 31.8 31.8 26.7 26.7 32.4
1990 37.9 37.7 37.7 27.3 27.3 40.3
2000 48.7 43.8 51.1 35.0 35.0 50.8
2010 58.9 44.2 68.6 42.4 42.4 54.4
Figure 19 describes the oil output path under the tilted price
scenarios. When the oil price is "Low First, High Later," we have just a
magnification of the incentive toward future extraction found on the "High
Price After 2000" scenario. In the other cases there is only a small bias
toward earlier extraction, as initial prices increase relatively more (or fall
relatively less) than future prices.
The different price scenarios have however a significant impact on
real consumption, which is of course our welfare indicator (see Figure 20).
If prices are Low First - High Later, that is bad on both counts: oil can be
sold abroad only at a low price, and it becomes expensive when it must be
imported. That shows up in the figure, where real consumption is seen to be
more than 12% below its Base values, in the midle of the "temporary-cheap oil"
- 79 -
Figure 16
Alternative Oil Price Scenarios After Year 2000
BASE PRICE
-HIGH PRICE AFTER 2000...... ... LOW PRICE AFTER 2000
00-
m~~~~~~~~~~~~~~~~
LI~~~~~~~~~~~~~~
0 .
tJ' #~~~~~~~~~~~/
CD,
19m).O l9m.( 2000.0 2010.0 2020.0
- 80 -
Figure 17
Tilted and Permanently Lower Price Scenarios
BASE PRICE-- …- LOW PRICE
........... LOW FIRST, HIGH LATERHIGH FIRST, LOW LATER
o 0.............
o / 0
'9~~~~~~~~
19g0.o 1990.O 0D.0 20X0.0 2020.0
- 81 -
Figure 18
Oil Output Under Different Price Scenarios After Year 2000
BASE PRICE----------- HIGH PRICE AFTER 2000
........... LOW PRICE AFTER 2000C ....................... o0
0-
I .0 .4
O ~~~~~~~~.
Pa'~~~~~~.44 ... a
J°_ / CD 10
-J~~~~~~~~~~~~~~~~c00 0lgo. 2 .4 2000 a
- 82 -
Figure 19
Oil Output Under Different Price Scenarios
BASE… - - - - LDOW PRICE
.......... LOU F fRsr, HJAH LflTER-Q -. * *HIGH6 FIRST,LOW LATER 1
C1) 1'L(O O
U)
Dc) M~~~~~~~~~~~~~~~~~~~~~~~~~~
0W
II~~~~~~~~~~~~~~~~~~C
q X
6 ~ ~ ***. \C.C
C 9
0) M
2980.0 1990. 0 2e00. 0 2010.0 2020.0
- 83 -
Figure 20
Real Consumption Under Different Price Scenarios
BASE
…---------- LOW PRICE........... .LOW FIRST, HIGH LATER
HIGH FIRST, LOW LATER
G -- - U, _
cnu,~~~~~~~~~~~~~~~L
Log
C-,
0 e~~~~~~~~~~~~~~0
_) o o
G- 63_ _
Cl ~ ~ ~ ~ ...
a:.-- /.
C.3 ~ '
o3 CD.zr Ea 9.0 20. 000 2 .
- 84 -
period. The reallocation of oil output is substantial, actually allowing
continued exports within the period of high prices: Peak consumption is
actually higher than in the Base Case during that period of additional exports
(2000-2010). Things are much brighter when cheap oil is permanent ("Low
Price" scenario), as better future perspectives makes it advisable to
compensate lower prices with larger output, generating only a small fall in
real consumption.
The last price scenario (High-Low) is good for the same reasons that
the Low-High case in bad; the magnitude however is modest given the size of
the price differential with the Base Run.
Figures 21 and 22 describe the allocation of the capital stock and
the price of gas, in reference to the Base Price scenario. The stock of
capital in the traded sector is seen to follow the same pattern as real
consumption, and for the same reasons. With permanently low prices, more
production of tradeable goods is required initially (1980-2000), to compensate
for lower oil revenues, but later more of the capital stock can be allocated
to the production of nontraded goods, since energy imports are cheaper. This
second period of relaxation is absent in the Low-High prices scenario, so that
oil/gas reserves are exhausted at a lower rate, requiring a larger proportion
of the capital stock in import substitution/export production (which in our
model are the same thing). An interesting result is how the strong temporal
bias from combining low initial prices with high prices after year 2000
completely eliminates the period of "cheap" gas. The reason is that, from the
perspective of the later 1980's, higher future prices and lower current ones
increase the value attached to keeping gas in the ground: its rental value
increases, and production is shifted towards the high price future to such an
- 85 -
Figure 21
Capital Stock in the Traded Sector Under Different Price Scenarios
| . W~ESE
.-- -....... Low FrRST, HIGH LR1flRC,o) -C-* HICH FIRST,LOW LMEER
e) -_ q-4
V)
¢~~~~~. *j*:. ic
0* 99~~~~~~~~~~~~~~~~~~~*
cr: . .
C:; 'C
-(0
C) N
w-4, a
,_0.1. -%. ~ -* O. \ 202
Cc c
C) Cs ' * ~ 6~~
19BO.0 1990.0 2000.0% 2000 22.
PRICE OF GAS OVER PRICE OF OIL0.5. D.6 D.7 .8 0.9 1.0
co 0
.o X ~~...................... =.;,,,. .,io o
c)4 D.5 D.6 0.7 0.8 0.9 00
:1~~~~~~~.
ro I
0.6~~~~~~~~~~~~~I 0002.8
- 87 -
Figure 23
Price of Gas Under Different Price Scenarios
D.SE---- LOW fRIC
............ LOw FRST, HICH LRTERO -*-* HIrHFrRS7,LDW LRO
C: Co ,0
9o-0~~~~~~~~~~~~~~~~~~0
EcJ
00
tLi
0~~~~~~~~
Cs
Ln In~~~~~~Cs1!(90LJ99W0 2000 200. 02.
- 88 -
extent that the demand constraint is not binding anymore and the wedge between
the fuel price equivalent and the shadow price of gas disappears.
Substantially higher initial effort in the production of non-oil
tradables is required with pessimistic price projections. Still, that effort
is not enough to compensate for lower oil export earnings, so that total
exports, imports and GNP grow at a slower rate than in the base case (see
Table 8). The optimistic view on the backstop (Low Price after 2000) reduces
the need for rapid growth in the next century, as the imported energy bill
does not grow so fast.
5.1.6. Sensitivity to the Growth of Domestic Demand for Energy
While varying projected reserves and oil prices, we have so far kept
the behavior of domestic energy input coefficients constant across experi-
ments. Specifically, we assumed that starting in 1986/87, energy input
coefficients would slowly decline, reflecting more energy efficient
investments and a gradual increase in domestic energy prices.
Domestic energy prices in Egypt in the base period are extremely
low, less than 20 percent on average of the corresponding world price
levels. These low prices, combined with rapid economic growth in the 1970's
and rapid urbanization, have led to extraordinarily high growth rates of
domestic demand in the late 1970's and early 1980's. In the recent past total
demand for energy increased at rates averaging more than 10 percent per annum.
It is extremely unlikely that such rapid growth will be sustained
beyond the mid-1980's. Economy wide growth was exceptionally high (averaging
almost 10 percent) during the 1977-1980/81 period. No matter which scenario
we choose, the future will be characterized by more moderate overall growth,
- 89 -
Table 8
The ITapact of Alternative Oil Price Scenarioson the Growth of Macroeconomics Aggregates
(Percentages)
High Low High LowPrices Prices First First
Base After After Low Low HighCase 2000 2000 Price Later Later
GDP
1982-1985 8.7 8.7 8.7 7.5 7.5 8.81986-1991 5.1 4.7 5.7 4.5 1.7 5.41992-1995 2.7 3.0 2.2 3.2 5.5 2.81996-2001 2.7 3.0 2.3 3.4 5.0 2.42002-2011 3.0 2.7 3.6 3.7 3.4 3.0
Consumption
1982-1985 7.6 7.6 7.6 6.8 6.8 7.71986-1991 4.7 4.3 5.1 4.2 1.8 4.91992-1995 2.7 2.9 2.2 3.1 5.0 2.71996-2001 2.8 2.8 2.4 3.2 4.6 2.32002-2011 2.0 2.3 3.5 3.5 2.9 3.0
Total Exports
1982-1985 10.2 10.2 10.2 8.8 8.8 10.41986-1991 15.3 5.6 7.3 5.5 1.7 6.81992-1995 2.8 3.1 2.2 3.4 6.5 3.01996-2001 83.2 8.8 7.7 7.9 8.2 7.9
Non Oil Exports
1982-1985 7.7 7.7 7.7 11.9 11.9 7.21986-1991 11.6 12.4 10.6 10.4 15.0 11.31992-1995 1]L.8 11.1 12.8 10.6 7.1 11.91996-2001 10.5 10.2 10.9 9.5 7.3 11.12002-2011 8.6 9.1 7.9 8.0 8.6 8.4
- 90 -
translating into more moderate domestic demand growth. More important in this
context however, is the fact that Egypt is gradually moving towards higher
domestic prices and is also contemplating major efforts to improve the energy
efficiency of the domestic economy. There are some very large and very
inefficient energy users in domestic industry. There is therefore the
potential for considerably reducing energy coefficients as higher prices and
efficiency-improving investments show their effect.
To explore the impact of different assumptions about domestic energy
efficiency on the nature of the optimal growth path, we have compared the base
case to two different scenarios derived from the assumptions presented in
Table 9. It shows how the unit energy requirement in each sector is assumed
to change through time in the different scenarios. The Base Case postulates a
decrease of 13% in the quantity of energy used per unit of output between the
present and the year 2000, as a result of domestic pricing policy, changes in
technology and the composition of output, during a period of increasing energy
prices. The High Energy Efficiency case, assumes that these savings can be
taken further, so as to reduce the energy/output coefficient by the end of the
century to 78% its initial value (and to 63% by 2010). In the Low Energy
Efficiency scenario no conservation effort is made, domestic users of energy
are subsidized, etc. so that energy use per unit of output increases (by 10%
near the year 2000) over its initial levels. In addition to the behavior of
the energy coefficient, a major determinant of the domestic demand for energy
is the composition of output. In particular, the nontraded sector is
significantly more intensive in the use of energy, as it includes some of the
big users, e.g. transportation, electricity. That somewhat moderates the
effect of reduced energy efficiency when the economy's net oil importer, since
- 91 -
more demand for energy requires more production of tradable goods to pay for
them, what reduces the average energy/output coefficient. But as Table 10
makes clear, continuing low energy efficiency nevertheless puts the economy
under considerable stress, reducing by almost one half the annual rates of
growth in GDP at the end of the planning period. The large energy imports
requirements also calls for even more rapid growth in the production of
tradable goods.
Table 9
Alternative Scenarios for Domestic- Energy EfficiencyIndex of Energy Requirements per Unit of Output
High energy Low EnergyYear Base Case Efficiency Efficiency
1985 1.0 1.0 1.01990 96.3 93.8 103.12000 86.9 78.7 110.92010 77.5 62.5 118.8
Table 10The Impact of Different Energy Efficiency Scenarios
on production structure, energy use and GDP growth rates
Ratio of ProductionGDP Real Domestic Use of Tradable to
of Energy Nontradable GoodsHigh. Low High Low High Low
Base Eff. Eff. Base Eff. Eff. Base Eff. Eff.
1982-85 8.7 8.7 8.7 6.5 6.5 6.5 .8 .8 .81986-91 5.1 5.3 4.6 4.9 4.3 6.6 1.3 1.2 1.71992-95 2.7 2.8 2.6 4.5 3.8 6.2 2.3 2.2 2.61996-2001 2.7 3.0 1.9 4.3 3.5 6.1 2.3 2.0 2.92002-2011 3.0 3.5 1.7 4.2 3.2 5.9 1.8 1.5 2.7
- 92 -
Figures 24 and 25 present the same story, in comparison with the
Base run. The cumulative impact of higher energy intensity on real consump-
tion is substantial, particularly in the period of net energy imports. On the
other hand increases in energy efficiency could increase real consumption by
near 10% toward the later parts of the planning horizon. The magnitude of the
reallocation of capital between sectors with changing energy efficiency
(Figure 25) appears as modest: the total capital stock in the traded sector is
only about 6% higher (toward the end of the planning period) with Low Energy
Efficiency than in the Base Case. But two things should be pointed out. One
is that this reallocation comes on top of a substantial reorientation of
tradable goods, so it may not be so easy to accomplish. The second is that
the lower increase in KT is partly due to the significantly lower energy
intensity of traded goods with respect to nontraded goods, and that may
represent a further challenge, when the mean of tradable goods expands beyond
those currently produced.
5.2 Experiments with Endogenous Investment
5.2.1 A Fundamental Optimality Condition
Throughout the analysis in the preceding sections, the rate of
growth of investment, and therefore the pace of capital accummulation was
fixed at 5.5 percent per annum. This specific growth rate was chosen because
it appears reasonable as a long-run average, in light of Egypt's development
objectives as well as the experience of other developing or semi-industrial
economies. The growth of investment was kept constant, however, only as a
first step in the analysis of the growtlh and structural adjustment process.
- 93 -
Figure 24
Real Consumption Under Different Scenarios for theEfficiency in the Domestic Use of Energy
BASE,-s _ _ - - - ~HIGH ENERGY EFFICIENCYLiG ...... .... LOW ENERGY EFFICIENCY
ta: - -
{ -I - _
CO
o -_. .,- -
a: '@@ *.
0~~~~~~~~~
0
aZ'
G 9O0 90.ao1.0 2 .ci
0
U) .z0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
c;Q C:)
a: 1980.0 1990.0 2000.0 2010.0 2020.0(Ii
- 94 -
Figure 25
Stock of Capital in the Traded Sector Under Different Scenarios
for Efficiency in the Domestic Use of Energy
fL-i . BASE
HIGH ENERGY EFFICIENCYaGm o ............- LOW ENERGY EFFICIENCY o
E,L_ O-.,,,-_
G .'
O ,:
(C)
b
(10~~~~~~~~~~~~~~~~~(
0
CD {
J s al~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
E 19B0.0 1990.0 2000.0 2010.0 2020.0
- 95 -
In fact, one of the key questions facing the investment planner is precisely
how to determine the optimal investment rate. This section attempts to
contribute to a better understanding of the issues involved. How should
investment behave on an optimal growth path? Should it be a rising, constant
or declining fraction of total resources? If more oil and gas is discovered,
should the economy-wide investment rate rise or decline? What is the
sensitivity of the optimal investment rate to different oil price scenarios?
To alternative assumptions about social time preference or the pace of
technical progress?
These questions are, of course, linked to the issue of optimal
foreign borrowing. In this section we analyze optimal investment behavior
keeping the current account fixed exogenously before, in a later section,
allowing capital flows to become endogenous. Full endogeneity of capital
flows is not a very realistic assumption in Egypt's case since both domestic
and international political factors are very important in determining their
possible range of varialtion.
Before turning to the numerical results derived from experiments
with the model, it is worth discussing in a qualitative way the important
factors that will influence the behavior of the optimal savings and investment
rate:
(i) Traditional national accounting treats income derived from the
extraction of a natural resource just like any other kind of
income generated in the economy. This similarity is quite
misleading. The income derived from a textile plant or from a
cotton fielcd is different from the income derived by operating an
oil well. I]n the former case, the generation of net income (after
taking account of capital depreciation) does in no way subtract
- 96 -
from the stock of wealth available to the economy. But in the
case of an exhaustible resource the generation of current income
is accomplished by running down the country-s wealth. It is
intuitively clear, therefore, that the optimal proportion of
savings in national "income depends on the nature of that
"income". To the extent that income generation implies natural
resource decumulation, it would appear that this decrease in
national wealth should be compensated by a higher investment rate
that builds up alternate forms of wealth. Another way of looking
at it is by noticing that the only way the exhaustible stock of
oil can be shared with generations to come after the exhaustion
date is to transform it into a form of reproductible wealth.
(ii) With investment able to vary endogenously, the economic return of
investment will always be equated to the consumption rate of
interest on an optimal growth path. The economic return on
investment is measured by the increased consumption stream made
possible by the additional investment and/or any increase in the
value of capital goods. As long as that economic return exceeds
the CRI, it is worth increasing the investment effort until the
marginal return on investment inclusive of capital gains equals
the marginal cost of postponing consumption.
(iii) In a country with exhaustible resources, the required equality
between the consumption rate of interest and the marginal
productivity of investment extends to the return on "investment'
achieved by keeping the natural resource in the ground. The net
economic return on the natural resource must also equal the
consumption rate of interest. The time path projected for the
- 97 -
world price of oil is, of course, an important determinant of the
economic raite of return on holding reserves in the ground. With
higher expected future real prices, it is worth keeping more oil
and gas in the ground. First, oil production costs depend on the
extraction to reserve ratio. The rate of return or limiting
extraction reflects therefore both the expected price appreciation
and the decrease in production costs achieved by reducing the
future output to reserve ratio. Second, while the income derived
from extraction could be consumed, a large fraction of it will or
should in faLct be invested in acquiring alternative forms of
wealth in thle form of capital goods, either through imports or
domestic production. This brings us back to the factors discussed
in (i) and (ii) above. In fact, on an optimal path, investment
and saving must be such that at every point in time, the following
equality is satisfied.
The Economic Rate of The Social The Economic Return onReturn of Investment = Rate of 5 Holding Natural
in Capital Goods Interest Resource Reserves
This equality reflects the essential efficiency condition character-
izing an optimal growth path. While the basic concepts are quite clear, in
practice one has to be very careful when interpreting this optimality
condition. It strictly holds only if each of the three "rates of return" is
expressed in terms of a common unit of account and is defined to include any
"capital gains" or "capiltal losses" that may arise because of relative price
changes.
The model used for the endogenous investment experiments is similar
to the one used in the previous section, with two differences: first, we do
not distinguish between oil and gas, as that distinction does not seem
- 98 -
particularly relevant for the issues discussed in this section; second, we
incorporate the real world fact of absorptive capacity constraints on capital
accumulation in the form of a diminishing marginal efficiency of investment.
We assume that capacity constraints apply only to aggregate
investment, on an economy wide level, reflecting shortages in such crucial
factors as management capability, special skills, port capacity and the
transportation network. As explicit and detailed modelling of these factors
is outside the scope of the aggregated model, we have adopted a shortcut to
incorporate them. Up to a cut-off level XLIM no absorptive capacity
constraints are operative; XLIM is set at 10 percent above the actual increase
in capital generated by last year-s investment. After that, the extent to
which resources devoted to investment actually generate usable capital goods
declines exponentially on the margin.
The existence of such a constraint does not affect the basic
optimality condition equating economic rates of return but care should be
taken in defining the marginal productivity of devoting one unit of income to
capital formation when such constraints are binding: resources devoted to
investment will not generate capital on a one for one basis when the
constraint is binding, so their marginal productivity should be adjusted
downwards.
For example, the costs of a steel mill or a land reclamation project
are of two kinds. First, there are the energy, labor, capital and raw
material costs that are traditionally taken into account in project
evaluation. Second, there are the more subtle and indirect costs imposed on
the economy by projects that use the particular scarce factors that are
responsible for the overall absorptive capacity limits on the economy.
- 99 -
The declining marginal efficiency of investment schedule is anl
attempt to capture in the model these very real yet often neglected costs of
rapid capital accumulation. On the other hand, this treatment also implies
that projects that lead to a relaxation of such constraints should carry a
premium over the value of capital if only future outputs of the project itself
are considered.
5.2.2 The Base Run
The Base Run values once again vividly demonstrate the major trans-
formation Egypt will have to go through in the next decade or so. Consider
for example Fig. 26 which gives the composition of wealth as a function of
time.
The value of oil in the ground (including anticipated future
discoveries) currently accounts for 65% of total wealth while the value of the
capital stock in the traded goods sector is about 19% of total wealth. Twenty
five years from now however, oil wealth will have fallen to 18% of the total,
while capital in the T-sector then makes up 56% of total wealth, if at least
optimal extraction, saviLngs and allocation policies are followed. This major
shift towards capital in the T-sector is needed to replace oil revenues as a
source of foreign exchange. The share of oil in total wealth in the fixed
investment case is much higher 20 years from now (26%), reflecting the fact
that extraction of oil and capital accumulation are considerably higher over
the next 25 years if capital accumulation is left free to vary over time.
Around that time (2005) rent income and "exogenous" resource transfers will
only make up 33% of total income, as opposed to 48% in the base year (Figure
27).
- 100 -
Figure 26
Composition of Wealth, Base Run
SHARE OF OIL RESERVES IN TOTAL WEALTH...... CAPITAL STOCK IN TRADABLES OVER TOTAL
WEALTH
1.0- - 1.0
0.8"O.8a - 0.8
0.6- 0.6
0.4- 0.4
0.2 - 0.2
0.0- 0.01980.0 1995.0 2010.0 2025.0 2040.0
TIME
- 101 -
Figure 27
Oil Revenues and "Exogenous Transfers" as a Share of Total Income
0.50 - 0.50
0.45 -0. 45
0.40- - 0.40
0.35- - 0.35
0.30 - - 0.30
0.25 0.25
0.2 4 0.201980.0 1995.0 20;0.0 20Z5.0 2040.0
TIME
- 102 -
One of the more important indications to come out of this run is
that the rapid depletion of oil wealth necessitates a faster rate of capital
accumulation than is currently undertaken. In our base run first period gross
investment takes 29% out of GDP as opposed to the 27% currently devoted to it
because absorptive capacity constraints are binding (more on that in the
discussion of the ARI) but that share quickly rises to 33% in 1983-84 and
continues to go up to reach a peak of 43 in the middle of the next decade. If
we look at net investment this translates into a savings rate out of Net
National Income (inclusive of exogenous transfers) of only 22% because
absorptive capacity constraints cause a shortage of profitable investment
projects and accumulation of Foreign Assets is ruled out by assumption. But
the optimal savings rate is clearly higher during the period of high oil
revenues, reaching a peak of 37% out of National Income in 1990 before it
settles down to about 30% in the post-oil period around the turn of the
century. This comes down to a marginal savings rate out of oil income of not
less than 51.4% during the peak year in 1990!
All this implies that over the immediate future (1981-86) capital
accumulation should accelerate at more than 15% as absorptive capacity
constraints losen up rather than the 6% currently envisaged. Also an
increasingly large share of that investment program, starting out at 57% but
increasing to 71%, will have to be channeled into capital formation in the
traded goods sector.
The net effect of the decline of oil revenues and build up of
capital in the T-sector is of course a rapid increase in both exports of non-
oil traded goods and import substitution. The volume of exports should grow
considerably faster than GNP over the planning horizon (for 1981-86 the
numbers are 14.7% and 9.0% respectively.)
- 103 -
Due to the anticipated deterioration in the terms of trade these
numbers look less dramatic in value terms (exports grow 13% in value terms
over that period). Also the share of domestically produced traded goods in
the consumption of traded goods in general will rise considerably from around
63% now to 74% in 2005.
To make all this possible a major shift of non-oil production
towards traded goods, away from NT goods, is called for when oil revenues
start declining. Figure 28 gives the proportion of the labour force to be
employed in the T-sector as a function of time.
A gradua:L appreciation of the real exchange rate (price of NT goods
in terms of domestically produced T-goods, the relevant definition for
domestic resource allocation) of 7% during the period with oil (the next 20
years) is called for, to be partially reversed later on (the real exchange
rate eventually drops nearly 3% from that peak level), to sustain this
reallocation.
The rapid increase in exports can only be achieved if Egypt's
external competitiveness; improves, the "warranted growth rate" of exports is
higher than that of world trade. Accordingly, a considerable deterioration in
the terms of trade is necessary over the next 25 years (10%).
The net effect of all this on GNP is a heady 9% real growth
projection for 1981-86 and 8% for 1986-1992. These percentages are somewhat
lower if oil revenues are not included, non-oil GDP will grow at 8% and 6.6%
respectively during 1981-1986 and 1986-92. After that, the decline in oil
revenues slows down GDP growth to a rate below population growth until about
30 years from now. Non-oil GDP of course grows much faster after 1992 at 5.2%
but it takes several decades before that component starts dominating the
declining oil component, it is not until 2010 that the model predicts real
- 104 -
Figure 28
Fraction of the Labor Force Employed in the T-Sector
0.6 0.6
0.4- . 1 , , - 0.419O.0 1995.0 2010.0 2025.0 2040.0
TIME
- 105 -
growth rates of 3.5% and higher for total GDP. Part of that reflects the
decline in the terms of trade (the growth measures mentioned refer to GNP with
world traded final goods as numeraire). In constant prices the post-oil
decline is less dramatic (Table 11).
Table 11: GDP Growth
(Percentage)
A. Numeraire Imports
Years Oil Non-oil Total
1986-1992 9.7 6.6 7.81992-1996 - 2.5 5.2 2.61996-2002 - 2.8 4.3 2.22002-2012 - 9.0 4.1 2.12012-2020 -13.8 4.3 3.5
B. Constant Prices
Years Oil Non-Oil Total
1981-1986 9.1 7.4 8.01986-1992 6.5 8.7 8.01992-1996 -5.1 7.7 4.21996-2002 -5.1 5.6 3.82002-2012 -10.8 4.8 3.72012-2020 -15.0 4.3 4.0
Finally the energy side. Oil output under this scenario will peak
10 years from now at around 70 m ton but will decline gradually thereafter (in
volume terms). Energy use is however predicted to rise rapidly at slightly
less than 10% over the next decade (in value terms), although the growth rate
- 106 -
gradually declines from there on to settle down at approximately 5% in the
next century. In volume terms domestic energy use will grow at 7.2% over the
next decade, as our oil price scenario implies an average growth rate somewhat
below 2.5% over the next 10 years. The 7.5% growth rate for energy use in
volume terms is more than a full percentage point below the corresponding rate
for GDP, mainly because traded goods production grows several percentage
points faster than non-traded goods production and has a much lower energy
input coefficient (the difference is due mainly to the inclusion of electric
power generation in NT production). Under this scenario Egypt will become a
net importer of energy at the end of the century.
Finally what may be the most important part of this analysis, the
analysis of the intertemporal project analysis parameters the ARI and the CRI.
Two major factors dominate the behaviour of the Period to period
ARI. -1. The first one is that absorptive capacity constraints rule out an
immediate jump of the level of investment from the current level to the one
indicated by a proper intertemporal optimizing analysis. This constraint will
be relaxed over time which in turn leads to a value of capital (in terms of
"real consumption") that falls over time and accordingly a higher ARI now than
later on, after the Absorptive Capacity constraint ceases to be binding. The
existence of Absorptive Capacity constraints (and their anticipated relaxation
over time) indicates that less investment should be undertaken than without
those constraints; it is very important however that this does not simply
imply the use of a higher ARI for all projects. This would not only lead to
less investment but would also unduly bias its composition towards quick-
yielding projects. What such a situation will lead to is a high period-to-
period ARI initially but a lower one later on. It can not be stressed enough
- 107 -
that the use of simple Internal Rate of Return criteria in such circumstances
is extremely misleading.
Consider an extremely simplified example. Let us assume two
projects, both of which occur outlays up front of $1 million. Project one
yields all its benefits two years from now. Those benefits are $1.15 million,
giving an internal rate of return of 15% (Fig. 29). The second project has
the same cost structure but yields no benefits until 5 years from now, to the
amount of $2.01 million. This project also has an internal rate of return of
15%, so according to IRR methodology they would both be accepted or rejected
depending on whether the "Cut-off rate" is below or above 15%. At the current
IBRD rule of thumb (10% cut off rate) both would be accepted.
Now consider what happens when the time path of the discount rate
changes over time in a manner similar to what we described before:
Year: 1 2 3 4 5
ARI1 10 10 10 10 10
ARI2 17 15 10 10 10
Of course at the flat ARI1 pattern both projects have a positive
Net Present Value (NPV). At the second ARI pattern however project one has a
NPV of - $17,000 and should therefore not be undertaken, while the second
project has a NPV of $120,000 and should therefore still go through. Under
the second scenario project one should be rejected and project 2 accepted;
nevertheless, they have the same internal rate of return of 15%. Clearly IRR
calculations give misletading information when comparing projects with
different time-phasing of net benefit streams.
- 108 -
Figure 29
Costs and Benefits of Two Hypothetical Projects
6 US*
I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2~~~~~ ~~ _____ i n
-11 --
- 109 -
The value of capital goods in this model has two components: the
first major component is simply the discounted value of all future output to
be produced by the "marginal" machine. The second is related to our
assumption that the Absorptive Capacity constraint is related to past capital
accumulation. More investment now will accordingly relax the AC constraint in
the future. Accordingly, if the AC constraint is anticipated to be binding
tomorrow, capital formation will be more useful than when it is not because of
this externality. In our model all capital formation has this property; in
the real world this is of course not the case. Accordingly, we separated
these two components of the value of capital and also derived an ARI that does
not incorporate this e.xternality (*RI in Fig. 30). Clearly, ARI > *RI
because the value of this externality declines over time. This does NOT mean
that when two projects with identical cost-benefit structure but the first one
with this externality (road building project) and the second without (candy
factory) are compared, the first one has to be rejected because of the higher
ARI. One should also iLncorporate the higher value of its output: during the
period of binding capacity constraints capital goods (roads) are more valuable
than consumption goods (candy). It is easy to show with the numbers coming
out of this exercise that when two of these projects have exactly the same net
benefits over time the road project will nevertheless have a higher Net
Present Value the higher ARI and similar net benefit streams not-
withstanding. The valuation difference dominates the ARI difference. In our
case the value of capital including this externality (roads) in terms of
capital excluding this externality falls from 1.5 to 1 between now and 1990.
- 110 -
The second factor determining the ARI is the existence of a major
temporary component in current income (oil revenues). As we discussed before
in the discussion of the optimal savings rate, this leads to temporarily high
savings and investment programs. The implication of that is, once again, not
a lower ARI for all projects, but a period-to-period ARI that is low during
the period of high but declining oil revenues and high after revenues have
stopped flowing in.A "flat" ARI pattern would again produce a biased
composition of aggregate investment, in this case against quick-yielding
projects.
The combined result of the gradually relaxed AC constraints and the
decline of oil revenues gives a U-shaped ARI pattern (Fig. 30).
The CRI pattern does not follow the ARI pattern exactly because the
relative value of capital in terms of the price of a "representative" bundle
of consumption goods changes over time. Initially the value of capital falls
faster than the value of an additional unit of consumption because of the
gradual relaxation of the absorptive capacity constraints and the rapid
accumulation there after so that the CRI is lower than the ARI during that
period (see Fig. 30). After about 12 years however there are no significant
changes in the relative value of capital goods in terms of consumption goods
so that the CRI equals the ARI.
After the effect of the binding absorptive capacity constraint has
died out the CRI also follows a U-shaped pattern because of the currently high
but declining pattern of oil revenues. The story is really the same as the
one told for the ARI but seen from a different angle. Remember that the only
endogenous component in the CRI is the growth rate of per capital consumption.
This growth rate is falling initially, in line with the gradual decline in oil
- ill -
Figure 30
ARI, *RI and CRI in the Base Run
ACCOUNTING RATE OF INTEREST (ARI)...... .ACC. RATE OF INT. IGNORING ABSORPTION CAPACITY (*RI)
…- CONS0UMPTION RATE OF INTEREST (CRI)
0.20- 0.20
0.1 0.15
0.12 -0.12
0.08- ~~~~~~~~~~0.08
0.04 - T-0.04
I gs0. a 1995.0 2010.0 2025.0 2040.0TIME
- 112 -
revenues, making for a gradually declining CRI. After the oil has run out the
decline stops and the growth rate gradually climbs back up towards it steady
state value, which is reflected in a gradual increase in the CRI in the second
half of the planning period.
5.2.3 Variants on the base run
(a) No Absorptive Capacity Constraints
The impact of the absorptive capacity constraint on the ARI is most
clearly seen by comparing the base run time pattern of the ARI with that
obtained in the first variant presented: this is a run made under the
assumption that there is no absorptive capacity constraint at all, resources
devoted to capital formation lead one for one to increases in the capital
stock. The ARI is more than 8% lower in the first period, a difference that
takes about 10 years to fade away. From there on the ARI is the same. Of
course Tobin's q, the value of capital over its reproduction costs, is always
equal to one in this run. There are some relative price changes between
capital and consumption, but not enough to drive a significant wedge between
the CRI and the ARI. Initial investment is unbelievably high, the
optimization exercise indicates that in the absence of absorptive capacity
constraints a full 54% of GDP should be devoted to capital formation in the
first period. Absorptive capacity constraints bring that down to a more
realistic 29%. The value of capital is naturally much lower initially, in
fact only half of the value in period 1 in the base run. One third of that
difference is caused by the lower future marginal productivity in period 2 and
later (the capital stock is bigger in those periods because of the high
initial investment). The remaining two thirds of the difference is due to the
- 113 -
fact that new capital has beneficial effects in the base run because it
loosens up future AC constraints, benefits that are absent in this variant.
GNP growth in the first 6 years is more than 2% higher each year because of
the very high initial level of investment but later differences are minor.
Consumption grows nearly three times (2.8 to be precise) faster but from a
much lower base, first period consumption is 28% below the base run value. Of
course a substantially higher level of exports is needed to cover the import
requirement of the accelerated investment program, non-oil exports are 44%
higher than in the base run case. In the short run oil output cannot be
increased much, because of capacity limits; accordingly, the extraction
pattern is very similar. In the absence of binding capacity limits on oil
output in the first coupLe of periods extraction would of course have
accelerated.
(b) Different oil reserve scenarios
Consider now some variants where the AC constraints are reimposed,
but where the reserve level is varied. The reserve level used in the base run
is the best current estimtate, but considerable uncertainty is attached to it.
Explicit incorporation of that uncertainty in the optimization will not be
attempted here. Instead we present some runs under alternative scenarios.
Consider for example the case where discoveries will fall off much
faster, say that total discovered and un-discovered reserves are only 1
billion ton. Oil output will then peak earlier and at a lower level and the
share of oil in wealth and of oil revenues in income will decline considerably
faster (see Fig. 31 and FLg. 32).
- 114 -
Figure 31
Composition of Wealth, Low Reserve Case
SHARE OF OIL RESERVES IN TOTAL WEALTH...... .CAPITAL STOCK IN TRADABLES OVER TOTAL WEALTH
1.0- 1.0
0.5 0.8.. .
0.6 - * 0.6
0.4- - 0.4
0.2- - 0.2
0.0- -- 0.01980.0 I95.0 2010.0 2025.0 2040.0
TIME
- 115 -
Figure 32
Share of Oil, Oil Revenues and Exogenous Transfersin Total Income, Low Reserve Case
BASE CASE
..... .LOW RESERVES
D. 50 - 0.50
0.45- 0.45
0.40 -* 0.40
0.35 - 0.35
0.30 ~~~~~~~~~~0.1300.30-\ OD
0.25 - ..* 0.25
0.20- - - 0.2019B0.0 1995. 0 2010.0 2025.0 2040.0
TIME
- 116 -
Twelve periods from now oil will represent only 7.6% of total wealth
as opposed to 18% in the same period in the base run. The capital stock in
the T-sector will now constitute 65% of the total in period 12 instead of 56%,
the base run value in that period. Oil revenues and "exogenous resources"
will then make up only 28% instead of 33% of total income. Egypt will turn
into a net importer 4 years earlier than in the base run case.
GDP will grow much slower over the 1986-1992 period (4.8% instead of
7.8%; between now and 1986 the rate of growth is the same), but non-oil
exports will have to grow considerably faster (nearly 4% points a year) during
that crucial transition period (the second half of the next decade). The
savings rate must be nearly 3 percentage points higher during the peak period
of oil revenues 8-10 years from now because the decline will be much
steeper. The real appreciation is somewhat smaller in the beginning, but the
differences are small because of the flatness of the transformation curve.
Of course more or less the opposite occurs when discoveries turn out
better than expected. Under the high reserve scenario (total level 2.1
billion tons). Investment, after the AC constraint ceases to be binding, will
take a percentage point less out of GDP initially (about 4 percentage points
less when compared with the Low Reserve case). Egypt would remain a net oil
exporter 10 years longer than in the Low Reserve case and 6 years longer than
in the Base Run case. GDP would continue to grow at 8.3% during 1986-1992
before slowing down gradually. Oil would still make up more than 30% of total
wealth (30.8%) two and a half decade from now, while oil revenues and
exogenous reserves would make up 37% of total income at that time. Of course
non-oil exports do not have to grow as fast as in the base case (2 percentage
- 117 -
points less in volume terms over the next 6 years). Accordingly, the terms of
trade deteriorate slighltly less (2%) over the next 25 years.
(c) Alternative oil price scenarios
All this is based on the assumption that oil prices, after a flat
period between 1981 and 1984, will grow at a rate that gradually declines from
2% to zero 60 years hence. Two alternative growth rate scenarios were
considered. Under the Unfavourable scenario oil prices are lower during the
time that Egypt is a net exporter, and higher thereafter (see Figure 17).
The impact on extraction of oil is fairly predictable: there is a
shift away from current towards future extraction. The initial value of oil
reserves is considerably lower (11%). Total wealth falls a little bit less,
with about 3%. GNP growth is substantially slower under this scenario, 7%
p.a. instead of 9% over the 1981-86 period and 5.9% instead of 7.8% over the
1986-1992 period). Non--oil exports of course have to be higher and grow
faster (3 percentage points over the first six years in volume terms) because
of the shift in the extraction pattern. Initial consumption falls nearly 1%,
a difference that increaLses over time commensurate with the 3% drop in total
wealth. The real exchange rate (price of non-traded over traded goods)
depreciates gradually under the combined impact of lower oil revenues and a
supply response to lower oil prices based on the higher energy intensity of
Non-Traded goods, but the differences never reaches more than 2%.
The second alternative scenario is one favourable for Egypt: prices
are high during its period as a net exporters and low (compared with the Base
Run) during the periods in which they are a net importers (see again Figure
17).
- 118 -
The shift in extraction pattern now goes the other way of course,
you want to be left with less oil when the growth in oil prices stops (Figure
33). Note by the way that we may have a zero growth rate in the real price of
oil and at the same time a finite extraction rate with some oil kept in the
ground because of the dependence of extraction costs on reserve levels: more
oil left in the ground lowers future extraction costs. It is this link that
leads to finite extraction rates even during the periods of zero growth in oil
prices without capacity constraints. The new scenario leads to a small
increase in wealth of nearly 2% and a comparable upward shift of the
consumption pattern over time, but somewhat tilted towards the future. GNP
growth is substantially higher than in the unfavourable case, and a little bit
higher than the Base Run values (9.2% for 1981-86 and 8% for 1982-92).
(d) Alternative utility function parameters
The final two runs vary parameters of the utility function. First
we made a run equal to the Base Run in all respects except for a significantly
lower rate of pure time preference (2% a year instead of 4.5%). The most
striking effect is on oil extraction (Fig. 34).
Capacity limits on output are never binding, and, as theory would
predict, a major part of oil extraction is shifted towards the future. In
2005 oil wealth still makes up 25% of total wealth, seven percentage points
more than in the base run. Non-oil exports accordingly grow at a much faster
pace initially (a stunning 21% in volume terms over the next 6 years, a Korea
like performance) if oil production is slowed down that dramatically. To make
room in world markets, several percentage points of further increases in
competitiveness are called for over the next two decades.
- 119 -
Figure 33
Oil Extraction Path in the Base Run and in theFavourable Price Scenario
BASE CASE...... .FAVOURABLE OIL PRICE
80.0- -_______________________________ - B0.0
70.0 - -7,
60.0 60.0
50 0 6~~~~~~~~~~0.0
50.0 50.0
40.0- / \ _ 40.0
30.0- 30.0
20.0- @1 ~20.0
10.0 10.0
0.0- ;'s-i-~ ,_,5.0 2010.0 - 0.01 980.0 1995.0 2010.0 2025.0 2040.0
TIME
- 120 -
Figure 34
Oil Extraction in the Base Run and Low Time Preference Case
BASE CASE......... .LOW RATE OF TIME PREFERENCE
80.0- - G0.0
70.0- 70.0
60.0- 60.0
50.0 \.. 50.0
40.0 / 400
30.0 - 30.0
20.0- 20.0
10.0 - 0O.0
0.0- 0.019B0.0 1995.0 2010.0 2025.0 2040.0
TIME
- 121 -
The lower rate of time preference of course also translates into a
faster pace of capital accumulation in the first part of the planning horizon
(also cumulatively, the steady state capital stocks in period 30 are about 10%
higher than in the Base Run). First period investment is 12% higher than in
the base run, a difference that rapidly increases as AC constraints are
relaxed; at the end of the planning horizon this is reversed. The savings
rate out of net income starts off at 25.5%, 3% above the base run level, and
reaches a peak of 46.5%, a full 10 percentage points above the corresponding
base run values. The ALC constraint is binding for two more years and the
higher pace of first period investment results in a further 6% of efficiency
loss on top of the 6% lost in the first period in the base run (6% of total
resources devoted to capital accumulation). The ARI starts out higher, the
initial value of capital is very high because the AC constraint is tighter,
and declines more rapidly because of the faster pace of capital accumulation
(which pushes out future AC constraints), so that the ARI is higher initially.
It falls quickly to a rate considerably below Base Run values, as one would
expect given a rate of time preference difference of one and a half percentage
point (Fig. 35).
Of course the *RI (which is based on a value of capital that does
not take into account the effect of current capital accumulation on future AC
constraints) is uniformly lower than in the base run case. The net effect on
GDP is a considerable smoothing of the growth rate. Total consumption growth
is lower initially (first 12 years) but consistently higher from there on.
In a final run we kept the low rate of time preference, but
increased the curvature of the utility function substantially. The precise
value of the elasticity of marginal utility with respect to per capita
- 122 -
consumption was chosen to insure the same steady state capital stock in the
base run. This results in an elasticity of 1.017 instead of 0.5.
Table 12:
Growth Rate of GDP and Consumption in Base Run and runs
with alternative utility function parameters
GDP Total Consumptionp=1.0404 p=1 .0404
Year Base Run(*) p=1.0404 1-nr1.017 Base Run p =1.0404 1-rj=1.017
1981-85 9.0 5.3 8.9 4.5 0.2 3.9
1986-91 7.8 8.6 7.0 4.9 4.7 3.8
1992-95 2.3 4.8 3.2 4.9 6.3 4.7
1996-01 2.2 3.8 2.9 3.2 4.8 4.0
2001-11 2.1 3.2 2.9 3.0 3.9 3.8
2012-20 3.5 3.4 3.3 3.7 4.0 4.1
(*) Base run: 1-n = .50, p = 1.093 (4.5% on annual basis)
The growth rates of GDP and consumption are even smoother now than
in the low time preference case (Table 12). Oil extraction is slower than in
the Base Run, but not as dramatically as in the previous run. In 2005 oil
still makes up 21% of total wealth, closer to the equivalent Base Run value of
8% than the p=1.0404 value of 25%. The savings pattern is also intermediate
between these two: higher than the base run (the savings rate out of net
income starts out at 24% and reaches a peak of 41% before tapering off slowly
to around 30%) but not as high as in the low time preference run.
*RI, BASE CASEARI, BASE CASE ...... *RI, LOW TIME PREFERENCE
.... ARI, LOW TIME PREFERENCE
1.25 [ 1 0.25 D IU v0.20 \ P
.00-. . -5 0.15 0.07 -
0.06 1 2
TIME T1Mw
0.01 'Dli
I
0
'.00- -~~~~~~ ~~~0.00 0_ __ __02_ _ __ __-__ _ __ _
190.001.0 205. 2400 980. 0 995. 0 2030.0 202U5. 0 2040.
T IME TI MI1
- 124 -
5.3 Foreign Borrowing
In the experiments described above the current account has been kept
exogenous; it follows such a time path that per capita debt is constant
throughout. Accordingly optimal foreign lending or borrowing was not
considered.
Of course both capital and oil are assets that can be used to
smooth consumption expenditure, but both these assets have obvious limitations
if used for that purpose. In this section a foreign capital market is
introduced, with a constraint on terminal debt that insures a final period
debt - GNP ratio equal to the one Egypt has now. The base run incorporates
the real world feature of a substantial wedge between borrowing and lending
rates; for technical reasons that transition was made a continuous function of
per capita commercial debt rather than a discontinuous jump at zero. The
model is in all aspects identical to the one used in 5.2 except for the CA
constraints, the period by period constraint of 5.2 are now replaced by an
intertemporal budget constraint.
Equation 10 of page 25 is replaced by the following set of
equations:
PW M + PW Mot < PW3t (E3t °t X3t) -tEt t
- rt CD t1/Gt_l + CADt (1Oa)
where rt CDt l/Gt_l reflects interest payments on beginning of period debt
and CADt is the current account deficit during period t
Current account deficits lead to higher debt:
- 125 -
CDt = CADt+ CDt_1 /Gtl (1Ob)
Final period debt CDt has to be below a value CDt chosen in such a way that
the period T Debt-GDP ratio equals the one at the beginning of the planning
period.
The cost of borrowing, rt, depends on beginning of period debt
CDt_l and, in some runs, on the debt service ratio. Introducing the debt
service ratio as an argument in the cost of borrowing function did not lead to
qualitatively different results, so these runs are not reported here. So for
the runs analysed here, lOc holds:
rt = h(CD t) , lim h = r, .lim h = r (10c)
CD+- CD+=
r was taken to be 6% per year (keep in mind we are talking about the real
rate of interest), and r as 3%. This spread between borrowing and lending
rates is substantially larger than those observed in practice, but is meant to
capture other, non-interest costs of borrowing such as commissions, front-end
fees, etc. The precise functional form of h( ) is given in Appendix A (page
IV, V).
5.3.1 The Base Run with Foreign Borrowing and Endogenous Capital Accumulation
Capital accumulation is predominantly constrained by absorptive
capacity constraints in the first few periods, not by availability of savings;
accordingly the introduction of foreign borrowing does not lead to significant
changes in the investment path and the ARI. The average cost of borrowing is
- 126 -
between 6 and 3 percent a year (real rate) where the high number applies to
positive commercial debt positions and the low number to negative commercial
debt positions (the real rate of return of net lending is assumed to be 3%).
The difference for most variables is minor compared with the no
borrowing base run, except for the time path of consumption and therefore,
given production, such variables as non oil exports, etcetera. Consumption
now is smoothed considerably, although not completely (Table 13).
Table 13
Consumption Growth Rate with and without Foreign Borrowing
Periods 1-3 4-6 7-8 9-11 12-16 17-20
No borrowing 3.5 5.7 6.1 3.8 3.3 3.7
Borrowing 3.2 4.6 4.7 3.3 3.1 3.7
The uniformly higher or equal growth rate in the no-borrowing case reflects
the fact that initial consumption is substantially higher in the borrowing
case (7% in the first period): no borrowing implies a higher growth rate from
a lower level. An interesting feature is that the consumption growth rate is
about 1.3% higher during the period of gradual real appreciation than during
the periods with a real depreciation. This is related to the fact that
foreign loans are denominated in foreign traded goods while consumers also
consume non-traded goods. A gradual real appreciation then implies that the
- 127 -
economy is borrowing in terms of goods that are becoming cheaper over time and
accordingly should speed up consumption now and slow it down in the future
(see Martin and Selowsky (1981) and Dornbusch (1982), for an elaboration of
this point). The reverse holds during a gradual depreciation. The increase
in initial consumption is larger in traded goods than in non-traded goods, so
not surprisingly the volume of non-oil exports is substantially below the no
borrowing base run case (31%) although it grows substantially faster in the
first six years (25% instead of 14.7%). The lower volume of non oil exports
should not come as a surprise, there is now an alternative form of foreign
exchange (borrowing). A more macro-view would be that borrowing allows higher
consumption now (which of course will result in lower consumption in the
future) given that oil revenues are increasing initially and borrowing against
future income is now possible.
The time path of per capita debt is straightforward, an increase
initially before oil income reaches its peak (borrowing against future income)
with nearly 30% betweea now and 1900-1990, a decline thereafter when oil
revenues peak (per capita debt falls off 10% from its 1900-1990 peak level),
after which an increasingly fast accumulation of debt takes place as oil
revenues dwindle to finally hit its exogenously imposed terminal constraint.
That constraint is set such that the terminal debt/GNP ratio is the same as
the initial one.
Finally, the smoothing effect of borrowing can be seen by comparing
the CRI in the case with and without borrowing: the "dip" around the period
where the absorptive capacity constraint ceases to be binding has disappeared
(Figure 36).
- 128 -
Figure 36
Various Discount Rates, Base Run with Optimal Borrowing
CONSUMPTION RATE OF INTEREST (CRI)
- ACCOUNTING RATE OF INTEREST (ARI)
..... ACCTG. RATE OF INT. IGNORING ABS. CAP (*RI)
0.20o-1
Il
0.15- 1.15
9
.. I
.O- ... v 1.30
1960.0 1995.0 =1W.o 202s.a 2040.0
- 129 -
5.3.2. An Alternative Oil Pice Scenario
The "Base Run" oil price scenario used in most of the analysis up
until now was rapidly made obsolete by the events of late 1982-early-1983.We
therefore present an alternative run, with the most general version of the
model, under the assumption of a substantial downward shift in the entire
schedule of oil prices (Figure 37).
The welfare effects of such a relative price change (oil is cheaper
in terms of everything else) depend on your net export position in oil; the
situation is complicated in the case of Egypt because it is exporter for the
next decade at least, but will turn into a net importer after that. The
question then comes down to whether the benefits of lower oil prices during
the future net importer phase outweigh the losses during the current net
exporter phase. An alternative but equivalent way of looking at it is by
looking at the gross flows (oil output and oil use) and see what changes in
the value of those flows do to the value of the assets making up Egypt's
wealth: oil in the ground, physical capital and labour stock. The value of
oil in the ground, according to the model, falls with nearly 25%, the rent on
a barrel of oil kept in the ground falls from $14.60 to $11.16. On the other
hand lower oil prices lead, ceteris paribus, to more value added left over to
pay capital and labour. The value of capital (discounted value of all its
future marginal products) indeed increases with slightly above 5% as derived
from the dual of the opt:Lmal solution under the new price scenario. The
entire path of the marginal product of labour ("shadow wage") also shifts up
around 5%. The net effect can not be signed on a priori grounds; the
numerical outcome indicates that future benefits in fact dominate current
- 130 -
Figure 37
Different Oil Price Scenarios
- BASE CASE
---- ALTERNATIVE OIL PRICE SCENARIO (US$/61)
ao.0 5~~~~~~~~~~0.0
7.0- 70.0
60.0- 60.0
50.0 , - 50.0
n 40.3- / ,' ~/ 40.0
30.0- o 30.0
20.0- a I - 20.01§O. 0 199S.O 2010.0 2025.0 204e.0
- 131 -
losses: the discounted utility of current and future consumption in fact
increases under the low price scenario, although not much, with 1.5 percentage
point.
The higher marginal productivity of capital at lower oil prices
calls for more investment although that increase is kept in check during the
initial few periods by ithe absorptive capacity constraints. Over the first
six years investment should, at lower oil prices, be about 2% higher than in
the base run, a difference that will increase as absorptive capacity
constraints cease to be binding further in the future.
Current GNP faLlls by one percentage point (in fact the growth rate
will also be lower by an average 1.5% over the first six years), and
investment should go up; should one conclude that since wealth has in fact
increased a little bit, aggregate consumption should also rise, necessitating
an increase in the optimal CA deficit and an increase in foreign debt? Higher
or equal wealth coupled with lower current income would argue yes; however,
the gradually increasing loss in oil revenues leads to a gradually increasing
real depreciation in comparison with the base run, indicating that loans taken
out now will have to be paid back in traded goods that are becoming more and
more expensive (see our discussion of the real cost of borrowing and gradual
relative price changes in the previous paragraph). This argues for less
borrowing rather than more and a "tilt" of the consumption pattern towards
less consumption now and more in the future, and accordingly less foreign
borrowing and a lower CA deficit.
The numerical solution indicates that the second ("cost of
borrowing") effect dominaLtes, the increasing real depreciation over the first
couple of years calls for a slowdown in consumption and initial decrease in
- 132 -
the CA deficit that is gradually reversed over time. From the period where
the real exchange rate starts catching up again, (the level remains
permanently below the Base run path, but the difference starts to decrease
again from 1990 onwards), foreign borrowing increases above the base run
level, as the real cost of borrowing and wealth effects now work in the same
directions. See Figures 38 and 39.
The accompanying optimal current account deficits are presented in
Table 14.
Table 14:
Optimal Per Annum Current Account Deficits Under the Base Runand an Alternative Scenario Oil Price Scenario
(Billion US$)
Case 1981-82 1983-84 1985-86 1991-92
Base Run 3.46 2.22 1.88 1.81
Alternative 2.05 1.60 2.48 3.27Oil Price Scen.
In looking at those numbers one should take the indicative nature of such
results into account, the patterns produced by these runs will come out under
a wide variety of assumptions, but specific numbers are rather sensitive to
things we do not know much about.
Finally, maybe it is worthwhile to point out that the lower oil
prices call for a significant shift towards non-oil exports, which should be
substantially higher in the low oil price scenario (nearly 30%), necessitating
both a decline in consumption and a shift away from traded goods (hence a real
depreciation). Clearly the composition of investment also has to change in
favour of capital in the traded goods sector.
,-133 -
Figure 38
The Real Exchange Rate (NT/FT) UnderDifferent Oil Price Scenarios
------- REAL EXCHANGE RATE IN THE ALTERNATIVEPRICE SCENARIO AS RATIO OF BASE CASEVALUES
1.O3JS- _____.___-____________
1.000 -_1. O
0.99- 0.995
0.990 0.990
D. 9S - 0. 9go.s«,-- - a.3
0.9?5- - 0.975
.9 - 0.970
1953.13 290.0 2200.0 2010.0
- 134 -
Figure 39
Optimal Borrowing Levels (Comm. Debt) UnderDifferent Oil Price Scenarios
| - - - -DEBT INT ALTERNATIVE PRICE SCENARIO
| ~~~AS RATIO OF BASE CASE VALUES
3.5 3.5
. ~~~~~~~~I .1t
3.0- 3.0
2.5- 2.5
2.0 - 2.0
l.5 / ~~~~~~~~~ 1~~.5
.0DI / -1.0
0.51 0.5
C.0- I I - 0.0
0SSO.0 2CO0.0 20l0.0
- 135 -
6. Conclusions
We have constructed and used a highly aggregated intertemporal
optimizing model to explore the sensitivity of optimal policies with respect
to such exogenous variables as world oil prices, level of reserves, energy
efficiency, rate of time preference, etc. under a variety of assumptions about
capital accumulation and foreign borrowing. Those assumptions range from both
being completely exogenous to both being endogenous and incorporated in the
optimization process.
Rather than presenting a summary of the many experiments performed,
it may be more useful to devote this section to discussing two general classes
of results. The first refers to a set of Egypt-specific policy conclusions,
in the form of the time patterns obtained for such aggregate variables as oil
revenues, savings, investment and foreign debt, which are robust across all
scenarios for exogenous parameters and prices. These patterns could serve as
inputs in medium term, dissaggregated consistency models. The second class of
results relates to the practice of shadow pricing and project evaluation: we
obtain implications for the realtive price of traded and non-traded goods, the
relation between relative price changes and foreign borrowing, the path of the
accounting rate of interest, and the pricing of natural gas which are of
substantial practical significance but very hard to derive without a model
like the one used here.
6.1. Some Robust Policy Conclusion
The long-run optimal growth model developed in this paper was used
to analyse some of the fundamental macroeconomic challenges implicit in
Egypt's economic structure. While there is a great deal of uncertainty
- 136 -
relating to oil and gas discoveries, world prices and other exogenous
variables, such as long term growth of remittances, it is nonetheless possible
to derive some robust conclusions that can serve as guidelines to development
strategy in Egypt:
(i) Revenues from oil and gas are a very special kind of income.
They imply decumulation of wealth unless they are converted
into other productive assets. It is misleading not to
differentiate GDP in the non-oil economy from this "income"
derived from resource depletion. Workers' Remittances, Suez
Canal earnings and foreign aid are also "exogenous" resources
that should be viewed as a "transfer" to the economy not based
on domestic production. In an economy where a large function
of current expenditure is financed by decumulation of an
exhaustible resource or out of transfers that may not be
available in the future, there is a very serious need for
structural adjustment necessitating a high rate of investment
directed towards the traded goods sectors.
(ii) An optimal growth strategy will therefore require very high
investment rates during the 1980s. The analysis suggests that
investment rates between 30 and 35 percent of total resources
are desirable targets for economic policy. A high proportion
of this investment should be directed into export expanding and
import-substituting activities. Over the next two decades the
growth of non-oil merchandise exports will have to be in the 9
to 13 percent range and imports will have to grow more slowly
than domestic production. These are difficult targets to
- 137 -
achieve and sustain over an extended period. They reflect a
very substantial structural transformation of the economy that
must begin very soon and will reach its most difficult stage
some time during the 1990s.
(iii) While Egypt may experience short term macroeconomic
difficulties of a "cyclical" nature in the mid-1980s, the
contribiution of the oil and gas sector to total resources will
continue to be large for the next 5 to 8 years. The big
challenge lies further in the future, when some time during the
1990s the share of "exogenous resources" will start showing a
rapid and sustained decline as Egypt adjusts to a new type of
economy where growth comes mainly not from increases in oil and
gas production but from productivity growth and factor
accumulation in the domestic non-oil economy.
(iv) Egypt's foreign debt is not particularly high in view of the
cost of borrowing on the one hand and the marginal productivity
of capital, if well deployed, on the other. Current Account
deficits in the range of 3% of GDP are indicated as reasonable
in the light of our experiments, although they should decline
and may be even reversed during the peak period of oil revenues
in the early nineties.
6.2 Shadow Prices and Project Evaluation
While the results discussed in 6.1 are very Egypt-specific, there
are other aspects of our results which seem of much wider relevance.
(i) When analysing relative price adjustments required by the long-
- 138 -
run structural adjustment process, it is important to
distinguish between the relative price of domestic tradables
vis-a-vis domestic non-tradables, and the relative price of
domestic goods in general (tradables and non-tradables) vis-a-
vis goods produced by the rest of the world. The former
relative price, which we could call the internal real exchange
rate, will have to change to bring about the required expansion
in production of tradable goods only to the extent that this
sector uses a mix of factors of production very different from
that used to produce non-traded goods.
The external terms-of-trade issue should be
distinguished from the tradables/non-tradables relative price
issue. Even if there were no change at all in domestic
relative prices, there would still be a need for a depreciation
in the external terms of trade, or a decline in the relative
price of domestic goods in terms of foreign goods, because
exports cannot expand without an accompanying increase in
external competitiveness. While the first kind of real
exchange rate adjustment depends on the "degree of difference"
between domestic tradables and non-tradables, the extent to
which an external terms of trade adjustment is needed depends
on the extent to which a country must accept lower net export
prices (net of transportation costs) when it wants to expand
its world market share.
ii) One of the interesting results of the foreign borrowing
analysis is the interaction between changes in the real
- 139 -
exchange rate and optimal Current Account deficits. A gradual
depreciation (traded goods becoming more expensive in terms of
non-traded goods) makes foreign borrowing, for any given rate
of interest, more expensive in terms of consumption foregone to
repay the loan.
In one particular case, the current account response
to a downward shift of the entire schedule of current and
future oil prices (in effect the shift from the "median"
predictions mid-1982 to the median prediction mid-1983) was
reversed because of this effect. Lower oil prices are bad for
Egypt now (they are net exporters) and good in the future (when
they are net importers). On balance this shift made them
better off. Also current income went down, so any one-good
borrowing model would have implied a larger CA deficit early
on. However the decline in oil prices also necessitates a
steep depreciLation over the next few years which was shown to
reverse that conclusion: the optimal response involved a
smaller, not a bigger CA deficit.
(iii) Another important conclusion relating to the shadow price
covering from the optimizing model, relates to the structure of
interest ratEts and particularly the time path of the accounting
rate of interest (ARI). The common practice of using a
constant period to period ARI was shown to be seriously
misleading in these circumstances. If absorptive capacity
constraints are tight now but are gradually relaxed over time
the value of capital declines more rapidly than it will when
- 140 -
they cease to be binding, indicating that the period to period
ARI should be high now but low later. Use of a high ARI
throughout would produce an undue bias in favor of quick-
yielding projects. It cannot be stressed enough that Internal
Rate of Return criteria (current bank practice!) are extremely
misleading in such circumstances.
A similar effect is caused by high but temporary oil
revenues. This calls for a low ARI now, but a higher one in
the future, when revenues tighten up. Use of a uniformly low
ARI would now unduely bias against quick yielding projects.
All this has its counterparts in the valuation of capital
goods, another useful output one obtains from a model like
this.
(iv) The final price of interest is the shadow price of natural
gas. When exports would not be viable (the net back value
assuming perfect substitution with oil in the user countries
would be far too low) and domestic substitution possibilities
are exhausted, a wedge may open up between the shadow price of
gas and its fuel-oil equivalent. The way that wedge moves
depends on the intertemporal pattern of energy demand and gas
supply and the accounting rate of interest. (The ARI
influences the extraction pattern and therefore the supply at
any given moment). Without binding supply constraints, the
opportunity cost of producing gas, and hence its price, is just
the cost of extraction/distribution plus the rent to gas
reserves. Low gas reserves reduce the size of the wedge and
- 141 -
can eliminate it completely. Rapid increase in domestic demand
for energy also tends to close the wedge, by pushing gas demand
and extraction to its physical limits.
- 142 -
Footnotes
_/ It is best, in this context, to think of human resources as real
capital assets. Human capital can be increased by real investment, in
a manner similar to physical capital formation.
2/ If nN and N are the compensated price elasticity and income
elasticity for nontraded good, and eN the supply elasticity, the
change in the real exchange rate, PT - PN' when there is a transfer
of F as proportion of GNP is given by - NF/(rN + eN) * It can be
shown that when both factors are mobile, eN is directly proportional
to the average of the elasticities of substitution and inversely
proportional to the square of the difference in labor intensity in
both sectors.
3/ For the exact specification see Appendix A.
4/ That is f4(K4t) = min lb4K4t, H4tI*
5/ The reason is that we do not want future generations to be penalized
for living in a more populated society: this formulation gives equal
weights (before discounting) to future and present representative
families.
6/ The steady state is reached after oil and gas reserves have been
exhausted, of course. It also requires a constant real price for oil
after T, which we assumed in the base case to be $73. The steady
states values were recalculated as needed for different scenarios.
Their precise definition is spelled out in Appendix D.
7/ As we mentioned before, n is a function of the volume of exports and
is very large for exports below a "normal" level. That normal level
- 143 -
itself grows over time. See Appendix B for the exact functional
form.
8/ See Squire and Van der Tak, (1975).
9/ That is Q3,t = P3,tx3,t at/R 3,t-1
10/ Note that with constant costs of extraction it would seems that case
(ii) above could not hold for more than one period. On the one hand
we know from Hotelling's rule (equation 13a in section 4.3) that the
rental value of gas grows at the rate of interest, so the price of
gas net of extraction costs should do that too as supply constraints
earn zero rent in this scenario; on the other hand the price of gas
should also equal its fuel oil price equivalent in case (ii). At
constant discount rates either one of these conditions cannot hold
for more than one period unless oil prices net of gas extraction
costs grow at that constant rate, an implausible scenario.
In our model however the rate of growth of the unit value of
reserves is an endogenous variable through the dependence of the
discount rate on relative price changes (see also section 5.3 for a
discussion in the context of foreign borrowing). That allows for
more flexibility than in traditional one (final) good optimal
extraction models.
11/ It is misleading to use a single ARI in an economy facing major
future changes in income streams (exhaustion of oil). We will
discuss the pattern of the period-to-period ARI(t). To discount back
from t1to 0 one forms a discount factor
((1+AR(1) (1+-AR(2))..(1+AR(t1)).
- 144 -
References
Buiter, W. and D. Purvis (1983), "Oil, disinflation and exportcompetitiveness: a model of the Dutch disease," in J. Bhandariand B. Putnam (ed.), The International Transmission of EconomicDisturbances under Flexible Exchange Rates (MIT Press, forthcoming).
Corden, M. and J.P. Neary (1982), "Booming sectors and De-industrializatinin a Small Open Economy," Economic Journal, 92 (December).
Dixit, A. H. (1976), The Theory of Equilibrium Growth, (Oxford U. Press, 1976)
Dornbusch, R. (1983), Real interest rates, home goods and optimal externalborrowing, Journal of Political Economy, 91 (February).
Martin, R. and M. Selowsky (1981), "Energy prices, Substitution and OptimalBorrowing in the Short Run," World Bank Staff Paper #460,forthcoming, Journal of Development Economics, 1983.
Squire, L. and H.G. van der Tak (1975), Economic Analysis of Projects,The Johns Hopkins University Press.
van Wijnbergen, S. (1980), "Inflation, Employment and the Dutch Diseasein oil exporting countries: A Short Run Disequilibrium Analysis,"World Bank mimeo, forthcoming, Quarterly Journal of Economics, 1984.
(1981), "Optimal Capital Accumulation and the Allocation ofInvestment between Traded and Nontraded Sectors in Oil ProducingCountries," World Bank mimeo.
World Bank (1983), Arab Republic of Egypt: Issues of Trade Strategy andInvestment Planning.
- 145 -
Appendix A: Summary of the Egyptian Model
1. Variables
(i) Primal (Activity Level)
Cit = Final consumptions good i
Xit = Gross domestic output of good i
Kit = Capital stock used to produce good i
Lit = Employment in sector i
Eit = Exports of good i
Mit = Imports of good i
Ft = Net exogenous inflows of foreign exchange (aid, remittance, etc.)
Zit = Intermediate use of good i
Yit = Effective investment in sector i
H3t = Maximum procluction of oil per period
H4t = Maximum production of gas per period
It = Total investment
*= Level of investment at which absortion capacity becomes a binding
constraint
HEt = Level of exports at which price starts to decline
ut = Utility level (i.e. real consumption) in period t
R3t = Reserves of oil at the end of period t
R4t = Reserves of gas at the end of period t
CDt = End of Period Commercial debt
CADt = Current Account Deficit
- 146 -
DSRt = Debt Service Ratio in period t
rt = Cost of Borrowing
All the above variables are measured in per capita terms.
Lt = Labor force in period t
(ii) Coefficients
aij = Unit requirement of good i to produce good j
PWit = International price of good i
Pi = Substitution parameters
6 = Discount rate
= 1 + Elasticity of the marginal utility of income
g = 1 + rate of growth of the labor force
gi = 1 + rate of labor augmenting technical change, i = 1,2
ai = Share parameters in the production functions
bi = Capital-Output ratio in sector i
Si = Share of sector i in the production of new capital
di = I - depreciation rate
n = price elasticity of exports
(iii) Dual (Shadow prices)
xt = Marginal utility of real consumption
Pit = Unit value of final good i
vit = Unit value added in sector i
- 147 -
rit = Marginal Productivity of Capital in sector i
qit = Unit value of Capital Goods in sector i
S3t = Unit value of reserves of oil
S4t = Unit value of reserves of gas
PIt = Unit value of Investment goods
Wt = Marginal Productivity of labor
The sectors are:
1 - Traded Goods (exported and used domestically)
2 - Non-traded Goods
3 - Oil and gas sector
4 - Gas sector (measured in tons of crude equivalent)
5 - Non Competitive Imports
Sector 6 is used as an aggregation index for sectors 1 and 5, defining a
composite importable good, which is used in consumption and production.
2. Objective Function
T cv = E 6 tUt
t=1
(At) Ut= (y C - +Cu (l-y )C u u (1)t 2 2t 2 6t
3. Constraints
(i) Production functions
(V t) > ) lt-p I l -pi -,/p2(vi)>0 it < A1(a~Klt + (1-oti~)(Lltg) I) (2)
- 148 -
-P2 ~ ~ )t )P2 )2(3
(v 2 t °O) x2t < A2(a2K2t + (1-a2)((l-Llt )g2)
(v 3 t a 0) X3t < Min {K3 3 t/b 3 H3 t (4)
(v4 t >O) X4t < min {K34t /b 3 , H4t} (5)
K33t 34t 3t
(ii) Material balances
(pit 0) Zt + Eit + SIIt xit (7)
(p2t ) c2t + s2It + a21xIt + a22x2t + a23 3t 2t (8)
(p3t °) E3t +a31xIt + a32x2t 4 x3t + x4t (9)
(PGt 0) X4t - a41Xlt a 4 2X 2 t 0 (10)
-P6 -6 -'P
(p6t °) 6t 61 it a62x2t + a63x 3t < A6a6Zit + (l-a6)Z5t 6 (11)
(pt 5t 5 tt S t Iit+ 3tE3t + Ft 6(R3,t-l)3tX3t 12)
- 149 -
In the version with endogenous foreign borrowing, (12) is replaced by
(P5t °) m t tElt + L3t(E3t -e(R 3 t-. 1 )x 3 t) + Ft - rtCDt_ /g + CADt (12a)
rt+l = ELIBOR(t)/(l+A ( -A1CDt))+ A2 DSRt /Min(.00l,DSUB-DSRt) (12b)
is the cost of borrowing; ELIBOR(t) is the LIBOR rate (6% p.a. in section
5.3); p ) is the Cumulative Normal Distribution and AO, A1, A2 are
parameters (equal to .0:3, .7 and 0. in the runs reported here).
The Debt Service Ratio (DSRt) is defined as real amortization
(considering a 5% rate of world inflation and an average maturing of loans of
20 years) plus interest, divided by total export revenues.
The change in the stock of Debt from period to period is given by:
(q7t °0) CDt = CDt-1/g + CADt (12c)
since, CDt' as all other variables in our model is defined in per capita
terms.
(iii) Investment
(qt ° 0) Kit diKi,t_1 /g + Yi t-1 /g i = 1,2,3 (13)
3 It if I ( Y(PIt ° 0) X Yi = I t t (14)
i=1 g(It, Yt t >t
*The funtions Ytand g are defined in Appendix C.
- 150 -
Rt0 R R X (15)(qRt) 3,t-1 3,t/g 3t
qG R =R /g (16)(Rt) R4 1 t = R3/g
(iv) Terminal Conditions
(qiT )iKiT iT i = 1,2 (17)iT > O) KiT ~KT
The steady state capital stocks KiT are defined in Appendix D. With
endogenous borrowing, there is also a condition on terminal debt:
(q 7T 0) CDT 4 CDT (17a)
where CDT is a value which produces approximately the same Debt/GNP ratio that
Egypt had at the beginning of the planning period.
4. First Oder Condition for Maximization
The Lagrangian function for this problem is:
T -Pu -PU 1/
t=l t t[Ut - (Y2C2t + (1-y2)C6 u
2 -Pi -Pi -1/p 1 l vt t- 3tK3 b 3-v 2H3tI- v, vit[Xit-Ai(ai Kit + (1-ai)Lit ) ] - [v3tX3t - v3itK33t 3 32 3t]
- [v 4 tX 4 t - v4 ltK 3 t/b 3 -v42tH4t]
- 151 -
Plt[Zlt+Elt+Slt Xlt: P2t] C2t+S2 t+a2xit +a22x 2t +a23x 3t+a24x4t-X2t]
33t [E 3 t+a 3 1Xt+a 3 2X2t-X 3tjX4 t - PGtI[X4t-a 4 1 Xlt-a 4 2 X2 ]
p6t[C6t +61 Xit 62x2t 63 3t 64X4t
-p 6 p l6 -e(E-R
-A6(a6Zit +(l-a 6)Z5t ) ] p5t[Zst+ssIt-1 tE - 3t(E3t (E3t e(R3,t-l )X3t Ft]
3 0itK it[ diKit-/g Yi,t-1/g]
3 *
(pitX Yit PIl,t It PI2,tg(,t1Yd)]
s 3 t(R 3 ,tR 3 ,tl /g -FX ) - s 4 t(R 4 t - R4 ,t-1/g+ 4t )i + qi i=I 3
The dual equations (first order conditions for maximization) are:
(i) Allocation of consumption
1+pu
(C 2 t ° 0) XtY2 (UIt/C 2 t) P 2t (18)
1- p(C 6 t > 0) At(1-Y2)(Ut/C 6 t) 4 P6t (19)
(ii) Value added
(Xit) vlt = - p2 ta2 1 - p3ta3 1 - p6ta6 1 (20)
- 152 -
(X2t) v2t P2t - p2ta22 - p3ta32 - p6ta62 (21)
(X3t) v3t P3t - p2ta23 - p6ta63 - q3t P5t n3t t (22)
(X4t) v4t P4t - p2ta24 - PGta64 - q4t (23)
where P4t ' p3t - PGt (24)
(iii) Optimal production conditions
(Ll) wt = v (1ai)(Aigi) iLitx i - 1,2 (25)it
(Kit) r A (-X)l Pi i -1,2 (26)it ~ ~~t itiAi' Kit
v 3 ~~~~ =v 3 1 ~~~~~~~ ~(27)3t ' 31,t +v32,t (7
-V +V ~~~~~~~~~~~(28)v 4t w 41,t 42,t
(K3t) r3t - 31tb - V41 l/b4 (29)
(iv) Value of the stock of capital and Value of Reserves
(Kit) qit rit + diqi,t+l/g i - 1,2,3 (30)
(R3t) 53t 83 t + p56l 3tE36 t (31a)
- 153 -
where 0wt 3 a t,X3t 3t is the increase in the share of foreign oil
companies as extraction costs increase due to depletion of reserves
(R4t) 4t 84,t+l/g i = O,G (31b)
(v) Value of new capital
(Y it °O) qit/g+ PI2,t+1 pIt i 1,2,3 (32)
with PIt PIIt + pI2,t (33)
and gt+l ' 9(It+i' Y- the absortion constraint function defined in
Appendix B.
(it > 0) PIJL,t + PI2,t agt/Iat < Slpit + S2P2t + S5 p5 t (34)
(vi) Exports
P5t if Elt < HEt
(Elt) Pit (35)
pst(Elt/HEt) 1 otherwise.
(E3t) P5t 3t P3t (36)
(vii) Aggregation of imports and traded goods
(Zit ° 0) ' 6 p6 tA6 (X 6 t/Zit) i 4 pit
- 154 -
p6 ~l+p 6(Z5t 0) (1-a )p A6 (X /Z ) 6 < 5t (38)(Z 6 6t 6 6t 5t 5
5. National Aggregates
Per capita gross national product is given by any of the following
expressions:
t it lt 2t 2t (v3t + S3t )X3t + (V4t + s4t)X4t + (p5t1 IIt - pit)Elt
Y = (r tKltr 2tK 2t+r 3tK3t)+wt+v32,t 3t+S3tX3t+V42,t H4t 4tX4t+(p5tt-pit )Eit
Yt= (P 2 tC 2 t+P 4 tC 4 t) + (slPlt+S2 P2t + 5P5t)It + (p,tE,t + P 3 tE 3 t - PstM5t)
The first expression is the usual definition as sum of value added in all
sectors plus rents (plus the implicit optimal tariff to exports). The second
expression defines income as factor payments to capital, labor and rents in
the oil and export sector. Finally we show the decomposition in consumption,
investment and current account surplus.
- 155 -
Akppendix B: Calibration of the Model
Table 1 presents the basic data about the Egyptian economy in
1981/82 which was used to calibrate the parameters of the model
1. The input-output coefficients are obtained as the ratio of inter-
mediate use to gross output (e.g., aNT = 2.617/16.056 = .163, etc.), and they
are:
Y .163 .205 10013
(aid) = .324 .601 0.
.382 .245 .0017
2. The share and scale coefficients for the production functions were
obtained from estimates of the (constant) elasticity of substitution and initial
_P _P ~-1/ pfactor shares as follows. Given the production X = A(aK P+(1-a)L )
if S = WL/VX is the share of labor in value added (V is the value added
coefficient W the wage rate), we have cV(l-a) = (K/L)PS/(1-S). The results
are:
Table 1: Base Year EconomyTMillion of Egyptian Pounds
Oil E Total Net Gross Unit
Sector Traded Nontraded gas Composite Interaediate Export Consumption Investment Output Price
Traded 0 0 0 13.225 13.225 2.219 0 .612 16.056 1.
Montraded 2.617 3.218 0.47 0. 5.882 0. 7.773 2.041 15.696 1.
Oil 10.656 0. 0. 32.5 .1728/ton
(tons) 5.205 9.438 0. 0. 14.643
Gas 0. 0. 0. 2.8 .1728/ton
Traded Composite 6.133 3.846 .060 0. 10.039 0. 10.872 0. 20.911 1.
Inports 0. 0. 0. 7.686 7.686 -10.136 18.645 2.45 0. 1.
Value Added 6.407 7.001 5.993 0. 39.3623 -4.3475 18.645 5.103 58.7628 Un
Gross Output 16.056 15.696 6.07 20.911
Capital 20.002 17.779 .198 0. 37.979 1.
Labor 5.828 5.233 0. 0. 11.061
Investment 1.755 3.258 .09 5.103
Notes: (1) Foreign exchange is converted at the rate of 1.25 US$/LE
(2) Base price of oil is 30$/b, which translates to (30$/b) x (7.2b/ton) x (.8LE/$) - 172.8 LE/ton.
(3) The external accounts were balanced as follows: Exports minus imports (-4.3475) + Remittances (2.4) + Suez, Non Factor
Income, Direct Foreign Investment (2.1432) - Share of foreign oil companies (1.20976) + Grants and others (1.014) - 0.
(4) Capital goods are estimated to be a fixed proportion mix of nontraded goods (40%), domestically produced traded goods
(12x) and imports (48x).
- 157 -
Table 2
Substitution Share ScaleSector parameters Share parameter parameter
(p/l) (S) (a) (A)
Nontraded 1. / .5 0.55 .2625 1.4384
Traded 0. /1. .40 .4 1.3146
Composite -0.5/2. .36758 .4331/ 1.9647
Notes: 1/ Corresponds to share of imported goods in production of thecomposite.
Note that although the share and scale parameters in Table 2 are
estimated under the assumption of coefficient use of factors within each
sector, there is nothing to guarantee an efficient allocation between
sectors. In fact, the first period of optimizing model shows a significant
reallocaiton of labor toward the nontraded sector.
3. Extraction cost of oil. The average cost of extraction of oil is
assumed to increase as the ratio of output to existent reserves increases.
These costs reduce the egyptian share of the avlue of oil output, since the
foreign companies receive more as cost recovery. The function used to
determine the share of foreign companies (Dt) is:
Dt = .17232 + .69591.RO(O)XO(t)/(RO(t-1) + .001)
where RO(t), XO(t) are reserves and output of oil in period t. Initial
reserves are introduced to calibrate the initial share to the base data
(.2154).
- 158 -
Appendix C: Absorptive Capacity Constraints
B.1 Define effective capital accumulation as Y and resources devoted to
capital accumulation as I. Then
4)-it = y<~it
i-lYi Yt< It
Absorptive capacity constraints are assumed to affect aggregate investment and
to apply to large increases with respect to previous periods. We assume that
investment below a certain cut-off limit Y goes through without efficiency
losses:
yt =It if It < Y
Y is a mark up on last periods effective capital accumulation. In that way
the ACC will not be binding in steady state at replacement (in efficiency
units) investment rates:
4y ( X y )* 1.2i-l it-i
i.e., an annual increase of 10% gives no problems.
The marginal efficiency of the excess of Y over Y* declines
exponentially:
I > Y => dY = exp[- a(I - Y )]dI
- 159 -
Simple integration then leads to the following formula:
It if It < Yt
Yt
Y + a (1 - exp(- a(I-Y*))) if I > Y
a is set equal to 2.3. This value implies that the marginal efficiency
declines to 10% when I = 2 Y
A natural measure of efficiency losses equals (I - Y)
- 160 -
Appendix D: The Steady State Capital Stocks
The structure of the model is such that if all variables are defined
in terms of efficiency units of labor (remember technical change is labor
augumenting), it has a steady state solution - provided the real oil price is
constant and the exogenous inflows of foreign exchange are also constant in
terms of efficiency labor.
With an infinite horizon, the economy would tend to that steady
state, and even with a finite, but large, horizon most of the growth path will
be "close" to it (for rigorous discussion of this and related propositions see
any text on growth theory, e.g. (Dixit) 1976)).
The equation defining the steady state capital stocks Ki in
efficiency units equals
3
I = [GL * GLT - DEP] * I Ki (1)i-l
(1) incorporates our assumption of equal depreciation rates across sectors.
DEP is one minus the depreciation rate, GL and GLT are one plus the rate of
labour growth and technological progress respectively.
The rate of return in each sector is defined as
R* 3* RVi aFi
i ii * * (
where Vi equals per unit value added in sector i and ) Si Pi represents
the reproduction costs of capital, all calculated at steady state prices.
- 161 -
In steady sta,te the following holds for each ri :
ri = (DELTA x(GLT) n_ -DEP) (3)
where DELTA is 1 plus the rate of time preference and 1-n equals the
elasticity of marginal utility of consumption with respect to consumption.****
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Deals speciflcally with the principles World Bank Staff Working Paper No. above.of revenue sharing in India. 540.1982. 118 pages. Supplements to World Debt Tables are
ISBN 0-8213-0098-9. $5.00. issued periodically as informationVoL 11: India-Studies in becomes available; the currentState ,ltances updates are included with orders forChristine Wallich NEW World Debt Tables.Examines In detail the Implications ofrevenue sharing for project flnance. Thailand: An Analysis of
Structural and Mon- The Impact of Contractual Savings onResource Mobilization and Alloation:VoL 11k: The Measurement of Structural Adjustments The Experience of MalayslaTax Effort of State Govern- Ame Drud, Waflk Grais, and Socil sccuflty Funds in Slngaporemcnts, 1973-1976 Dusan Vujovic and the Phippines: Ramifications ofRaja J. Chelliah and This study was prepared as a Inetent PoUcdesNarain Sinha background paper for the preparation ivestments of Social Security Funds
of a tructral-ajustmnt lon to In india and Sri Lanka: LoegislationAttempts to evaluate the tax perfor- of a structural-adJustment loan to and Experincemance of particular states in terms of Thailand and is a follow-up to a pre- Parthasarathi Shome andthe average tax effort of all states. vious paper entitled 'Aggregate Katrine Anderson Saito
Demand and Macroeconomic World Bank Reprint Series: Nlumber 144.World Bank Working Paper No. 523. Imbalances in Thailand:' Comparative Reprinted fi,m The Malayan Economic Review. uol.September1982. vol. 1, 85 pages, vol. II, statistics are used, within the frame- 23. no. 1 (April 19781.54-72: Labour and Society,186 pages, vol. III, 85 pages. work of a four-sector macroeconomic wL. 5. no. I (January 1980J.19-30: and The Indlian
ISBN 081003Xuo 00wl model to assess alternative ways of Journal of Economics, vol. 60, part 3, no. 238ISBIY 0-8213-0013-X vol. 1, $5.00, vol. II f macroeconomic adjustment in the (January 1980).349-60.
$5.00, vol. III, $3.00. Thai economy. Discusses speciflcally Stock nO. RP-0144. tree of charge.flscal policy interventions, manipula-tions of the exchange rate, and pro-ductivity Improvements and their
Policy Responses to External Shocks inSelected Latin American CountriesBela Balassa
World Bank Reprint Series: Number 221.Reprintedfrom Quarterly Review of Economics andBusiness. vol. 21, no. 2 (Summer 1981).131-64.Stock 11o. RP-0221. free of charge.
Restructuring the World Econonsy:Round 11ilollis Chenery
World Bank Reprint Series: Number 204.Reprinted from Foreign Affairs(Summer 1981).:102-7120.Stock No. RP-0204. free of charge.
Risk Assessments and Risk Premiumsin the Eurodollar MarketGershon Feder and Knud Ross
World Bank Reprint Series: Number 220.Reprinted from The Journal of Finance, uol'. 37.no. 3 (June 1982):679-91.Stock No. RP-0220. Free of charge.
Italian: "Analisi economica dei progetti The Effects of Populationdi inuestimento"in Analisi dei progetti Growth, of the Pattern ofdi investimento: il metodo della Banca Demand, and of TechnologyMondiale. Marsilio Editori, s.p.a., on the Process of Urbaniza-S. Croce 518/A, 30125 Venice, tion: An Application to IndiaItaly. 1978. Rakesh MohanISBN 10-4108-8, L8,800. This paper uses a non-linear, three-
Portuguese: Analise econ6mica de pro- sector, two-region wage-and-pricejetos. LTC-Livros Tecnicos e Cientlficos, endogenous dynamic generalS. A., Au. Venezuela, 163, 20.220-Rio de equilibrium model to study the effect
Approaches to Purchasing Janeiro, R J, Brazil. 1979. of population growth, the pattem ofdemand, and of technological change
Power Parity and Real ISBIY 85-216-0017-8, $8.00 equivalent, on urbanization in the context of aProduct Comparisons paperback. low-income developing country start-Using Shortcuts and Spanish: Analisis econ6mico de proyec- ing at a low level of urbanization.Reduced Information tos. Editorial Tecnos, 1977. World Bank Staff Working PaperSultan Ahmad ISBN 84-309-0719-X, 435 pesetas. No. 520.1982. 47 pages.
World Bank Staff Working Paper No. ISBN 0-8213-0008-3. $3.00.418. September 1980. ii + 60 pages(including 14 tables, bibliography). Economic and SocialStock No. WP-0418. S3.00. Analysis of Projects and of N_L_ W
Price Policy: The Morocco
Comparative Study of the Credit Proiect u India, 1975-1985: AManagement and Organiza- Kevin M. Cleaver Sources and Uses of Fundstion of Irrigation Projects ApproachAnthony E Bottrall World Bank Staff Working Paper No. Armando Pinell-Siles and
World Bank Staff Working Paper No. 369. January 1980. 59 pages (includ- V.J. Ravishankar458. May 1981. 274 pages (includi i n g This paper presents sources and uses3 appendixes). Stock No. WP-0369. $3.00. of funds accounts integrated in a
Stock No. WP-0458. $10.00. macroeconomic framework forEconomy-Wide Models and analyzing financing patterns andDevelopment Planning economic interdependence among,DevrelopmBitent Plnigsectors in India, contrasting the
Economic Analysis Charles R Blitzer, period 1975-80 with the Sixth Plainof Projects Peter B. Clark and period. 1980-85.
Lyn Squire and Lance Taylor, editors World Bank Staff Working Paper Mo.Herman G. van der Tak Surveys the specification and uses of 543.1982. 92 pages.
Reconsiders project appraisal and medium-term and perspective ISBN 0-8213-0205-5. S3.00.recommends a more systematic and economywide planning models.consistent estimation and application Oxford University Press, 1975; 4th General Equilibrium Modelsof shadow prices and a calculation of pr,inting, 1982. 382 pages (including for Development Policyrates of return that take explicit selected additional readings, bibliogra- Kemal Dervis, Jaime de Melo,account of the project's impact on the phy, subject and author index). and Sherran Robinsondistribution of income. adSemnRbnoThe Johns Hob pkins university LC 74-29171. ISBN 0-19-920074-2, Provides a comprehensive study of1975 4thn Hprinti ng ve1981. 14Pagess $9.95 paperback. multisector, economywide planning19 75; 4th printing, 1981. 164 pages pmodels with particular emphasis on(including appendix, glossary, issues of trade, distribution, growth,bibliography). and structural change. Theoretical
LC 75-40228. ISBN 0-8018-1818-4, discussion of the properties of$6.50 ({2.75) paperback. multisector, applied general
equilibrium models is combined withFrench: Analyse economique numerical applications to particulardes projets. Economica, 1977; 2nd countries and problems. The modelsprinting, 1981. considered range from input-output
ISBIY 2-7178-0014-X, 29 francs. and linear programming to the morerecent nonlinear computable generalequilibrium (CGE) models. Theauthors consider how these models
can be used to analyze questions of liuman Resource Develop- Phase : A System of Inter-growth and structural change, the ment and Economic Growth national Comparisons ofselection of foreign exchange regime, In Developing Countries: A Gross Product andand the impact of alternative develop- ~ ment strategies on the distribution of Simultaneous Model Purchasing Powerincome. The empirical applications David Wheeler Irving B. Kravis,are based both on cross-country World Bank Staff Working Paper No. Zoltan Kenessey, Alan Hieston,analysis and on the experience of par- 407. July 1980.130 pages (including and Robert Summersticular countries and demonstratehow such models provide a useful 8 appendixes, bibliography). * Establishes the methodology and pre-framework for policy analysis. Parthcu- Stock No. WP-0407. $5.00. sents comparisons of gross domesticlar attention is focused on the product per capita and currencyproblems of planning and policy for- purchasing power for ten countries inmulation in mixed-market economies 1970 and six of the same countriesand on the nature of models required few in 1967.to capture the important mechanisrns' The Johns Hopkins University Press,that constrain policy markets. Incorporating Uncertainty 1975. 306 pages (including
Cambridge University Press, 32 East into Planning of Industrial- glossary, index).57th Street, [lew York, N.Y. 10022. ization Strategies for LC 7J-19352. ISBNI 0-8018-1606-8,1982. xviii + 526 pages. Developing Countries $27.50 (f16.50) hardcover;LC 81-12307. ISBtl 0-521-24490-0, Alexander i. Sarris and ISBIl 0-8018-1669 -6, $8.95 (25.50)$42.50 hardcover, ISBN 0-521-27030-8, Irma Adelman paperback.$17.95 paperback. This survey of existing literature on
planning under uncertainty focuseson issues of intemational trade and Phase 11: International Com-
NYEW investment allocation. Various ways of parlsons of Real Productincorporating uncertainty into target- and Purchasing Power
The Global Framework: planning models are discussed and living B. Kravis, Alan n eston,The GlobalFramework:proposals for possible empirical and Robert Summers
An Update applications are outlined.Brian Nolan WrdUpdates Phase I and adds six newWorld Bank Staff Working Paper No. countries, comparing the flgures forThis paper presents the methodologi- 503. January 1982. 58 pages (including the sixteen countries for the yearscal background to the Global Model- appendix, references). 1970 and 1973.ling Framework used in the WorldDevelopment Report exercises of the Stock No. WP-0503. $3.00. The Johns Hopkins University Press,World Bank. It gives an overall view of 1978. 274 pages (includingthis framework and discusses in l inde)some detail the data base supporting Interdependence in glossary, index).the global analysis and the methods Planning: Multilevel LC 77-17251. ISBI 0-8018-2019-7,of reconciling data from various Programming Studies of the $25.00 (f15.00) hardcover; ISBNsources. Ivory Coast 0-8018-2020-0. $8.50 (£5.00)World Bank Staff Working Paper Louis M. Goreux paperback.No. 533. 1982. 58 pages. Provides a system for analyzing eachISBN 0-8213-0047-4. $3.00. component of a country's economy Phase 111: World Product and
independently and relates the interde- Income: International Com-pendencies between the components. parsons of Real GDP
Human Factors The Johns Hopkins University Press, Irving B. Kravis, Alan Heston,Pojec rork 1977. 448 pages (including bibliogra- and Robert Summers
and Francis J. Lethemphy, index). This report restates and extends theLC 77-4793. ISBN 0-8018-2001-4, methodology set out in the first twoWorld Bank Staff Working Paper No. $27.00 (f16.20) hardcouer; volumes. Particular attention is given397. June 1980. 85 pages (including ISBN 0-8018-2006-5, $9.95 to the problem of comparing services3 annexes, 5 charts, bibliography). (26.00) paperback. and to the conflicting demands of
regional and global estimates. Com-Stock No. WP-0397. $3.00. parisons are given of prices, real per
The International capita quantities, and final expendi-Comparison Project ture components of GDP for thirty-Chreevompaiso that establish a four countries for 1975. By relatingThree volumes that establish aworldwide system of intemationalcomparisons of real product and ofthe purchasing power of currencies.
the results to certain widely available A Model of an Agricultural used to estimate the project's effectsnational income accounting data and lHousehold: Theory and on key national variables, thus per-related variables, the authors develop Evidence mitting a full social cost-benefitextrapolating equations to estimate analysis of the project.per capita GDP' for the thirty-four Howard N. Barnum ahealysis Hofkthe projest. jP-scountries for 1950 to 1978. In addi- and LynThe Johns Hopkins Uniersity Press.tion, the 1975 distribution of world Innovative model of short-run 1982. 336 pages (including maps andproduct by region and per capita behavior that combines production index).income class is estimated. The and consumption decisions in a LC 81-48173. ISBN 0-8018-.2802-3,1975 results confirm relations theoretically consistent fashion for an $30.00 hardcouer.between both quantities and prices agricultural household.and per capita income found in theearlier volumes. The Johns Hopkins Uniuersity Press, Redistribution with GrowthThe Johns Hopkins Uniuersity Prss 1980. xi + 107 pages (including Holins Chenery,1982. 398 pages. appendix, references). Montek S. AheuwaiarLC 81-15569. ISBN 0-8018-2359-5, LC 78-21397. ISBN 0-8018-2225-4, Clive Bell John H. Duloy,$35.00 hardcouer: ISBN 0-8018-2360-9, $6.95 (i.475) paperback. and Richard Jolly$15.00 paperback. Describes existing inequality in
The Political Economy of incomes in developing countries andLandsat index Atlas of the Specialized Farm Credit proposes a reorientation of develop-
Institutions in Low-income meit policy to achieve more equitableDeveloping Countries distribution.of the World CountriesFourteen four-color maps, applica- J. D. Von Pischke, Oxford University Pess, 1974; 4thtions of Landsat imagery, reading and Peter J. Heffernan, and printing, 1981. 324 pages (includinguses of the index maps, and pro- Dale W. Adams annex, biblography).cedure for securing imagery. World Bank Staff Working Paper No. ISBN 0-19-920070-X, $9.95 (i5.00)ihe Johns Hopkins University Press, 446. April 1981. iii + 99 pages. paperback.1976.17 pages,131/2" x 21", spiral Stock No. WP-0446. $5.00. French: Redistribution et croissance.bound. Presses Universitaires de France, 108,LC 76-46190. ISBN 0-8018-1923-7, boulevard Saint-Germain, 75006 Paris,$12.00 (S7.25) paperback. NEW France, 1977.
ISBN 22403102, 58.20 francs.
Methodologies for Measur- Project Evaluation In Spanish: Redistribuci6n con creci-ing Agricultural Price Regional Perspective: A miento. Editorial Tecnos, 1976.Intervention Effects Study of an Irrigation ISBN 84-309-0624-X, 880 pesetas.Pasquale L. Scandizzo Project In Northwestand Colin Bruce Malaysia
Clive Bell, Peter Hazell, andWorld Bank Staff Working Paper No. Roger Slade394. June 1980. x + 96 pages This innovative study develops quan-(including 4 appendixes, references). titative methods for measuring theStock No. WP-0394. $5.00. direct and indirect effects of
agricultural projects on their sur-rounding regional and nationaleconomies. These methods are thenapplied to a study of the Muda irriga-tion project in northwest Malaysia. Alinear programming model is used toanalyze how a project changes thefarm economy, and a social account-ing matrix of the regional economy isthen estimated. This provides thebasis for a semi-input-output model,which is used to estimate the indirecteffects of the project on its region.Thereafter, a similar methodology is
Risk Analyis in Techniques for Project WRINTSProject Appraisal Appraisal under Uncertainty The Meaning of Technologlcal MastezrLouis Y. Pouliquen Shlomo Reutlinger h RKeatlion to Transfer of Technokogy
Discusses methodological problemis Presents a method of evaluating risk World Bank Reprint Saries: Lrumyer 217.and the usefulness of simulation; in Investment projects and means for Reprinted from Annals of the American AcadmyIllustrated by three case studies. using quantitative measures of risk in of Political and Social Science, ol. 458 (tNouem-
decisionmaking. ber 1981).12-26.The Johns HYopkins University Press,1970; 4th printing, 1979. 90 pages. The Johns Hopkins University Press, Stock No. RP-0217. free of charge.
LC 79-12739. ISBN 0-8018-1155-4, 19 70; 4th printing, 1979. 108 pages$5.50 (~.025) paperback. ' (including annex, bibliography). The model of an Agricultural
LC 74 -9482 7. ISBN 0-8018-1154-6, Household in a Multi-Crop Econofmy:French: Lappreciation du risque dansp The Case of KoreaI'evaluation des projets. Dunod Editeur, $5 95 (0-50) papeback. Choong Yong Ahn, Inderjit Singh. and24-26, bouleuard de l'tl6pital, 75005 Lyn SquireParis, France, 1972. World Bank Reprint Series: lumber 222.
What Is a SAM? A Layman's Reprinted from The Review of Economics and21 francs. Guide to Social Accounting Statistics. vol. 63. no. 4 (fNovember 191):20-25.
Matrices Stock NIo. RP-0222. free of charge.
Shadow Pces for Project Benjamin B. King The Reklvance of the Dual Economy
Appraisal In Turkey World Bank Staff Working Paper No. Model: A Case Study of Thailand
Afsaneh Mashayekhi 463. June 1981. 59 pages (including Trent Bertrand and Lyn Squire
World Bank Staff Working Paper No. references). World Bank Reprint Series: Nlumber 219.
392. May 1980. 57 pages. Stock No. WP-0463. $3.00. (1980):480-rr. c
Stock No. WP-0392. $3.00. Stock No. RP-0219. free of charge.
Social Cost-Beneflt Analysis:A Guide for Country andProject Economists to theDerivation and Applicationof Economic and SocialAccounting PricesColin Bruce
World Bank Staff Working Paper No.239. August 1976. ii, iII + 143 pages(including 6 annexes).Stock No. WP-0239. $5.00.
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