so-called Computable General Equilibrium (CGE) models which were introduced
into the ... equilibrium, macro models that are antecedent to the contemporary.
March, 1986
Bulletin Number 86-1
ECONOMIC DEVELOPMENT CENTER
I -k•• \•z,,-
I
-
I
7•. .."-.
A COMPUTABLE GENERAL EQUILIBRIUM MODEL FOR DEVELOPMENT POLICY ANALYSIS A. Erinc Yeldan
ECONOMIC DEVELOPMENT CENTER Department of Economics, Minneapolis Department of Agricultural and Applied Economics, St. Paul UNIVERSITY OF MINNESOTA
A COMPUTABILE GENERAL EQUILIBRIUM
MODEL
FOR DEVELOPMENT POLICY ANALYSIS
A.
Erinc Yeldan
February,
1986
Graduate student and Research Assistant, Department of Agricultural and Applied Economics, University of Minnesota. paper has been supported in part by a grant Research for this from The Cargill Foundation and the International Economics version of the paper was presented An earlier Division of ERS. as a seminar at the Agricultural Development workshop, University of Minnesota. I am grateful to Professors Edward Schuh, Terry Roe, of the Agricultural %JamesHouck, and the participants Development Workshop for valuable comments and suggestions. however, are solely mine. All the remaining errors,
A COMPUTABLE GENERAL EQUILIBRIUM MODEL FOR DEVELOPMENT POLICY ANALYSIS
The purpose of so-called introduced
this paper is
Computable General
to present an example of the
into the Applied Economics
more than a decade ago and proved medium/long-term planning exercises. ari sen
in
a little for both
policy analysis
for such modelling has
r-esp-onse to the well.-known short-comings and
world economies,
equilibrium constructs. the interwoven structure
of the
applied policy analysts have always
about the anaLlytical
models. Thus, the growing has led
just
to be very useful
The underlying motivation
Due to the complexities and
skeptical
literature
and development
limitations of the partial
real
(CGE) models which were
Equilibrium
to the explicit
powers of
need for
aim of
was formalized by Kenneth Arrow,
equilibrium
increasingly
converting
equi librium system from an abstract
195)0s) into a realistic
partial
been
general
models
the Walrasian
mathematical
general
apparatus
Gerard Debreu and others
and applicable
model
(as in
the
of actual
economi es. The CGE Mode:l.s have, until many countries,
some examples,
the existing
to:
Taylor & Black
(1974,
Dervis & Robinson
Malaysia) ; Lanka).
(1978,
(1980,
questions.- :L
models include,
Chile) ; Adelman
Cardoso & Taylor
Feltenstein
policy
different
addressing
cite
Korea);
now, been successfully applied to
Turkey);
& Robinson Ahluwalia
(1979, Brazil); Argentina).
but not
To limited
(1978,
& Lysy
S. (1979,
de Melo (1980, Sri
de Melo & Robinson
Colombia),
Lewis & Urata
(1983,
Turkey) ; Lundborg
Malaysia);
Gupta & Togan
(1984,
India,
(1984,
Kenya and Turkey).
(1980,
The paper
first introduces the broad
class
of
general
equilibrium, macro models that are antecedent to the contemporary CGE formulations.
There,
I try
to provide an interpretative
essay on such early multi-sector constructs and follow the path to the evolution of the idea of building price-endogenous, nonlinear macro models that can capture both the market-optimization behavior of
individual
agents and the commanding nature of the
exogenously specified government The second and third segments of the CGE model.
policies.
sections in
turn, build the different
The paper concludes with a compact
presentation of the core CGE equations and two Appendices, one on the Linear Expenditure derivation
and another on the endogenous
System:
of the price elasticity
of
demand,
both of which
will
be used in the modelling process.
1.
INTRODUCTION:
A PRELUDE TO THE CGE MODELS
The earliest multisector planning models were based on the simple input-output linkages among economy.
various sectors of the
With these models, assuming a fixed-cofficients --
Leontieff --
Technology for each
sector, and given
the estimates of
input-output coefficients across sectors, the planner was in a position to calculate the necessary output
level at each sector
in order to satisfy a targeted final consumption bundle. To be more concise, letting A be the matrix input-output coefficients as.ij,
with a±j
being the amount of
input i necessary to produce 1 unit of opuput j; gross output vector by X, and the final
of fixed
and denoting
consumption vector by C,
the material-balance
X
AX
Now, bundle,
can be written
as:
+ C
(I-1)
suppose- the planner
has some targeted
indicated by the vector
problem can for
equation
C
be found by solving
'Then the
consumption
"solution" to the
the material-balance
equation
X:
X =
Equation satisfy
(I
-
A) .
C
(1-2)
(1-2) gives gross production requirements the targeted
Leaving the static,
consumption
aside the rather fixed
of such models
criteria
for setting
the absence
simplistic
has been
of the gross output
and cumbersome ng,
an optimization
consumpti-on
bundle,
the determination
vector
X,
nature of
thIe most. i mportan t
the lack of
the targeted
of such criteria,
to
demand.
i n put-"out p ut model.i
drawback
i.n order
becomes an ad
of C,
C.
Yet,
in
and hence
hoc exercise in
matrix algebra. Later,
another
class
of
F'rogr-ammin ig Models succeeded shortcomings of
the early
multisector in
models,
overcoming
input-output
exercises.
explicit
objective function was introduced
involved
optimizing this Again,
constraints. static
linear Max
RX s.t.
X
and cr
retaining
:i:B 0 U::
model
many other Here an
and the problem
function subject to certain
programming Ax
th i s,
known as Linear
(linear)
the same notation for can be formulated
X and A,
as follows:
the
a vector of objective function weights and B is
where R is
Given data on R,
vector of resource constraints. feasible set F =
{XIAX :i B;
a solution vector X* Linear
problem
interesting implications for
particular,
Min WB s.t.
WA W
R C)
problem;
and only if
X*,
the Duality Theorem
for the primal problem
is
the dual
a feasible vector W exists for
such that,
-
R) X*
Equations
(I-3)
= 0
W* AX*--B) (WA
Now,
a vector of constants.
if
economic
given the above linear programming
states that a feasible vector, optimal
then
the dual problem could be written as:
(primal),
where W is
bounded and non-empty,
the
Models coupled with the so-called Duality
Programming
In
is
: 0
if
can be found to the above problem. 0
Bj
> 0
La)jX"j j
-
X" > 0
implies
EW"ia,..a i
-
Thus,
in
R
> 0
general
Ea.i j
-
X'*
implies
W*
-
EW'*aAj i
at optimum,
4
= O
(1-5)
= 0
(I-6)
Rj == 0 X~*
implies
if,
BE
0C=
(I-7)
(I-8)
any one of the constraints
in
either
problems
is
not binding
negative or strictly variable
positive)
carries
(i.e.
function weights, of
and
positive
(I-5)
and
levels,
(1-8)
allows us to interpret "input prices".
(1-6)
state
that
the associated
state
In
the dual
this
only fully
context,
used inputs have
that
price
must be zero.
only those activities
supply Further,
which
be carried
(1-
do not incur out at
levels. Thus,
insights
the linear
programming
for the general
modelled economies.
However,
the fact
the heuristic physical
First
assumption
a wellI-defined
of all,
that
mixed economies
constraints,
the multipliers
at
the opt:i.mum,
properties
of
models are based planner,
on
in
command
of
yet
subject
to
seeks to maximize
for the whole society.
designed
where individual
the dual
of the economy,
and natural
nor
such
a fictitious
welfare function
Cit. .. well-suited,
that
interesting of
they share other
productive activities
technological
provides
of market prices
should not be taken to imply that market prices as well.
approach
equi librium relationships
share the marginality conditions
thus,
the
as objective
prices and for those inputs where the fi:xed
positive
certain
we interpret
the complementary
any losses at the optimum must actually
all
if
the R vector
W, as
and
ex.ceeds demand, 7)
dual
the elements of matrix. A as input
per unit output
vector
further,
inputs,
slackness conditions naturally
equations
strictly
a zero value,
B vector as fixed supplies of
multipliers,
either
then the corresponding
To carry the analysis a little
requirements
is
They are,
f or the state-capital
agents independently
i st try
to
max:imize their an
own well-being
environment regulated
degrees.
In
determine
certain
this
to a budget constraint
by the government
environment,
The planner
the productive activities
can be affected
at varying
only indirectly
does not have real
independent
in
agents taken together
of the economy,
many other
bureaucracy
individual
outcomes that
by the planner.
decisions of
subject
command on all
but relies
"optimizers",
on the each exerting
an influence on the specific development path of the economy. The remedy to this
observation
is,
of course,
to construct
a
model where endogenous prices and quantities are allowed to transmit market
information
through different sectors of the
economy, thereby simulating the workings of and
intervened,
by a
social
yet absolutely
planner)
endogeneity
cannot
programming
models.
difficulty
lies
in
markets.
Yet,
this
To cite the fact
that
economic
in
result
program cannot
as a by-product
allocation
and production program is
result
from its
impact
on the structure
dual
in
general structure
consistent solution. of
"shadow"
expect
and saving factor
constraint
that
the resource by the solution of
factor
the quantities
solution
6
if
will
in
that
to put it
with the incomes and Indeed,
and
equations
prices
Or,
determined
demand,
are the outcome of the primal
and relations
functions,
of the maximization.
one cannot
linear
behavior
primal
include th'e
the linear
"the crucial
current endogenous
But the standard
differently,
a
-level of price
the main problem,
functions must be expressed
a linear
not commanded
be designed within the realm of
consumption
of
(i.e.
decentralized
such as budget constraints,
commodity prices.
a perhaps regulated
budgets that
prices have any supplied
general
that
not equal
the sol
demanded
quant.tites
general,
the one hand,
implied
those models which
and
linkages between the resulting General model
incorporate
by
the
dual
Equilibrium
prices,
models.
finds the market become te
solves for clearing
so:urces o)f
groups and determine
investment patterns
income generation
is
and sectoral
sectors. model
updates the initial
until
tatonnement
convergence It
paper
only
solve of
variables feed
exogenous
a
as the
set
of
in
and
turn
OQuantities imported
domestic production elasticities. through
of differential
The the saving which,
profit
demands in
algorithm and
iterates
in
rates
this
turn
across
manner,
the
prices through
a
the whole process
achieved.
for the
however, the
The rule
that
relative
economy.
normalization
practice.
demand.
function of
excess
su.ch
across sectors These
guess of do.mestic
should be noted,
can
has to
is
about one
investment share parameters,
After calculating
Walrasian
is
for various household
also endogenized
as a function
brium
groups and
economy as well
rates.
rule
the model prices
to
Yet into most
and
model,
commonly
designed
resorted
in
this
the
this,
achieve the
on
are termed Computable
levels
prices and relevant
behavior
are determined
the output
the pattern of
international
equii
Given an arbitrary
wage/rental
exported are solved as a
costs,
This paper
into the analysis.
the model
general
on the other,
inc:orp'orates the :international
that
price endogeneity
various worker--consumer
of demand (CGE)
enable this
the fundiamental
the incomes of
patterns
domestic markets
real..L
are
i on 1". •
ut
In
and
that
a
the
planner
completely to
and
which
will also be used here is to employ a no-inflation benchmark by level
defining a constant
of the price index,
which
prices and real
only relative
concern devoted
without much
phenomena as well very short-run,
to monetary problems.
stabilization
economic theory; superstructure
is still
a
interwoven with the microeconomic simple behavioral
general
for focusing on a vast array
These arguments should not be taken,
general
equations
Further,
tool.
will
of development however,
have
such
and cumbersome
may turn out to be too general
model
in
ad hoc macro-monetary
own drawbacks as an analytical
useful
of monetary
a very difficult branch of
and building an
equilibrium system through
an exercise
using
analyses.
monetary spheres of the economy
and
Thus,
incorporation of the interactions between
equilibrium framework
its
variables would matter,
as the possibility of using such models for
On the one hand, the real
set
Equilibrium Models,
rule precludes the treatment
such a normalization
is
quite consistent
Walrasian General
with the early treatment of in
is
This choice
by the modeller.
exogenously
which
to be a issues.
to imply that
planning monetary phenomena is not possible or ill-advised all together. Depending on the question in hand and the time horizon to be analyzed, the monetary sphere of the economy can be incorporated into the CGE framework in various ways. elegant model
that
tackled
by Adelman and Robinson income distribution strategies Thus,
in
in
this
For example, a very
task quite effectively 1978 work,
their
of different
consequences
which
is
provided
focuses on the
development
South Korea.
to recapilulate,
the reader has to appreciate
8
the fact
that
in
applied
policy analyses much depends
on the specific
purpose of the model-building effort and the access to realistic data supplies, which
is
a major restraint on students of
still
Development Economi cs. constructed in
The Model
Dervis et.
from the works of
(1978); Lewis and Urata Lundborg
(1984).
this paper is al.
(1982);
Its distinguishing features are:
(2)
recognition of
product markets;
(3) recognition of
the sectoral
incentive-pack:ages The Model stages.
granted
is
construction which is static
(1) expliicit
and
(4)
wage
endogenous
subsidies arising from export-
by the government.
is constructed
The first stage
and designed to be run in
a within-period general in
parameters, the Stage 1 Model,
equilibrium
as will
and other
be called hereafter, finds
the relative prices and solves for all real/structural
the overall
In
two
its equations and variables.
Given certain exogenous government policy variables
of the economy.
and
in certain
inter-sectoral
labor;
expor't
(1978)
as distinct from private
monopoly power
differences for the same type of calculation of
Dervis and Robinson
(1983); Adelman and Robinson
specification of the public enterprises enterprises;
adapted and updated
other words, it
variables
comprises the core system of
Model.
The second stage, on the other hand, is designed to up-date the
exogenous variables of
system and
the
basically used for the
Armed with this background model.
I
first stage.
first
purpose of
we can begin
introduce the system of
9
It
is a dynamic
"aging" the
Model.
constructing
ncotation that
will
our be
used throughout
the entire
Model.
adhered to the following (1)
Endogenous any bar
are denoted
on them.
lower case letters
All
which
(2)
All
Greek
(3)
Letters
(4)
involved.
i
The subscripts
(e.g.
a:j,
of d. in
and rm)
and are
the Stage 1 stage.
variables.
are policy variables to be set
are omitted for all
all
range from
(..)
with a bar,
the second
not
without
by the government.
Time subscripts
explicitly,
in
are parameters
letters
letters
fixed parameters
with a circumflex
are time lags
(5)
capital
needs to be updated
letters
exogenously
by capital
(with the exception
exogenous variables or Model
I
legend of principles:
variables
(-)
Unless otherwise specified,
Thus,
unless otherwise specified
variables refer
to the current period.
and j
1 to n. or bj.),
sector of origin
variables unless there
are used for
sectors.
They always
When these two are used together the first
subscript
and the second
always refers
to the
to the sector of
destination. (6)
The subscript ranges from
(7)
Subscript
s
refers
to different
skill
types of
labor and
1 to m.
f is
the public firm
used to distinguish (p:
private;
10
g:
between the private and
public).
II - THE OPEN CGE MODEL:
STAGE 1
The core equations of
in
forms are constructed
functional with
the Stage
of
the presentation
in
1 Model this
their
expilicit We first
section.
begin
the price system.
PR ICES
model
To begin
invokiing
restrictions, tradables modelled
the absence of
the neo-classical
too small
to affect
is
these should be fed in
in
especially
practice,
the perfect
exaggerates
fixed
The applied macro models,
aggregation
the
quite
misleading Another
sectoral perfect
and
activities,
of
the domestic
involve a at
such
levels
assumption
substitubility
fair
may
the
price
due to the understable etc.,
data limitations,
greatly
price system and
system.
of
of the productive
assumption
substitubility
trade policy over determination
aggregation
variables.
when we are trying to build
the role of the international
computation,
and
markets
as given,
domestic
of
price
The prices for the open
models with limited degrees of disaggregation sectors,
price
or endogenous,
the international
into the model
the
implies that
by the given world
to solve at all.
are determined
that
the country being
there remains no independent,
system for the model economy model
assumptions,
the world prices,
prices are set
relative
any trade
and that
substitutes
Thus,
However,
in
are perfect
the domestic ratios.
with,
to the applied model
problems
presents some interesting
builder.
an open economy
of the price system in
The specification
reasons
amount
of
of lead
to
results. difficulty,
as
illustrated
11
by
Dervis et.
al.
( 1982,
Chapter 3)
is
that
assuming
hypotheses
along with
the above mentioned neo-classical
the specification of the productive
technology as one of constant
returns to scale,
result
in
extreme specialization in the sectors that the domestic economy has comparative advantage, with no home production ever sectors that it doesn't have.
not supported by empirical
trade is
is a very crude
of the way economies engage into international trad.e
portrayal and is
Obviously, this
on the
abound,
Two-way sectoral
evidence.
especially at high
levels of
aggregation.
A formulation to handle these problems has been proposed in a 1969 paper
by Armington which distinguishes
only by their kind place of
machinery,chemical -
e.g.
production.
In
commodities not but
also by their
Armington's commodity system, not
only
is each good different from any other good, but also each good is assumed to be differentiated by the country of origin of
supply. Following Armington's hypothesis, domestically produced
goods and
imports are assumed to be imperfect substitutes.
To
reflect this, we define a tradable composite commodity CCI,
which
is a CES aggregation of the domestic commodity DC:t, and the imported
foreign good,
CES function, ai,
M±.
The elasticity
of
the difference between
substitute them with agriculture, food
of the
reflects the differences between the domestic
and imported good from the buyer's viewpoint the greater
substitution
each other).
processing
whereas for 'the capital
DC±
and M1
and
Plausibly in
or textiles,
goods sectors it
12
(the smaller the as ,
aC
the harder
to
sectors such as
is fairly large,
is quite low.
The ex.plicit .formulation of i-th
= B I.
where BS ,
":i.
M,.
S.
the
( -8,.)
o•
DC
(II-
. are parameters;
good in
substitution,
(
-I/P/
-P
+
and p
the imported
CCI
and p:.i
is
by the expression
The consumers are then
with
just like
related to the elasticity ao
=
Accordingly
the aggregate output CC±..
of
1 /+pi.
hypothesized as mi.nimizing a co(st "technoology"
a firm trying to produce a specified level
mini mum cost.
)
giving the share of
G S
function subject to the CES composite commodity
PC-.,
in
sector is: ---
CC:
the composite commodity
M 1
and DC,. are like
of output at
"inputs"
producing
"Therefore, the composite good price,
can be exipressed u.sing the cost function of the CES
I: gy < > te hnol. ff± .
PC . = 1 / B
where PM.i is wh:i ch will tariff
( i-C :k) PM .
(1 - 6
rate tm±.,
= PFWM
(1+tm,.)
"- EPCj
is
1 I-( I:-2)
ER
usually dollar).
(I I-3)
the specification of
ac1
the ad valorem
(defined as units of
unit of foreign currency,
their- product ti on pl an s.
where tni
1
price F'WM:.,
and the ex-change rate ER
also introduce the net price,
= PD.
( l-cr,.) F D,.
be determined by the world
To complete
P N.:i
)
the domestic c.urrency price of the imported good,
domestic currency per
FPM :
Cy±. +
PN-=.,
the price system I will
upon which the producers make
Thus;
-
tn.
PD,. + sn-c
the indirect tax
PDF).
rate and sn.i:
(11 -4)
is
the net production
versus public
the granted
enterprises,
of one unit
input
of intermediate
stands for the amount
production
subsidy rate
j
Further,
used for the
gives the value of
Hence EPCjaj.
i.
of
is
as across sectors.
among firms as well
differentiated aji
towards private
Depending on the government's attitude
subsidy.
J-t
inputs used in
intermediate i-th
of
the production
one unit of
the
good. The two other prices used in
PWEI
and the export price,
PKý
capital,
at a later point of the Stage 1 Model. however,
will
be introduced
below,
At this juncture, of
I will turn to the specification
technology of
the price of
the Model,
the production
the economy.
PRODUCTION TECHNOLOGY AND FACTOR MARKETS
The crucial
assumption
CGE Model
of the Open
a single commodity the Hicksian
sense).
is
in
that
models, as entries
envisaged
to produce
(may be thought as an aggregate-commodity Conversely,
very much
in
sector
the tradition
input-output
in
each such commodity is
enables us to continue to define of an
is
each sector
associated with a single production specification,
the productive sphere
constructing
of the economy. of
This
early economy-wide
the productive
sectors
table.
As hinted in the net-price equation
(II-4),
the intermediate
input demands has been assumed to constitute a linear system with fixed-coefficient production technology for such input-usage.. The retention of this specification is not necessary for the nonlinear CGE Model
and extensions of this technology have been
14
in
t ried
Lewis and Urata
(1983)
and also in
Ahluwalia and
For purposes of realism we may need to separate
(1979).
the technol]ogy of
intermediate
technol.ogy for primary specification is
inputs from the production
inp.uts -
capital and labor,
the production technology available to a
firm can be thought to be given by either a oneCobb-.Dougl as funrction of f:
r
(-^" :I.
= A.r
Our
perhaps the simplest way to achieve this.
particular,
In
X.f±i
Lysy
l)
capital
and labor
in
or
a two-]evel
each sector
L+ : -a
Tr LI.U±
K.i
i,
(11-5)
or
X f'-.
i Kf
= A
where L.:
I.... L.
is
.~.
( II-6)
further formulated
di ff:erent skill
levels
as a CES aggregation of
below).
(11-7
The modeller can choo)se either
of
the spec if icat ion for
produc.tion technology for a particular firm or sector, the two,-level Cobb-Douglas because it between all
is
labor
is
labor types on the one hand, assumed in Then, for
the
the
I will
Model.
f i. xed-coeff is
formulation
i ci ents, amount
be used to
of
of substitution
the same and equal and to capital
to that between
on the other,
as was
(II-5).
retain For
However,
technology seems to be more realistiic
very unlikely that the elasticity
types of
the
the two-level
such technology, composite
c api tal
make up one unit
good of
good
Cobb-Douglas technology
capital
with
originating real
15
is
thought
elements
b.j•
,
from sector capital
in
sector
as a
where i j.
that
b.i j will
Further, capital
stock is assumed to be fixed
period modelling
of the first
combine machines
This assumption tries
stage.
capture the fact that capital
in the within-
i.e. that
is not "malleable", cannot
once installed
to
be converted
into trucks
easily. Li±,
The labor parameter,
of the Cobb-Douglas production
technology is
given by a further
skill
Thus;
types.
CES aggregation of m different
( II-7)
,... , L. i m)
I,,. = L- .i (L»'n
where L.F:R.o- " R-, is
m skill
distinguish between More detailed
levels
However,
reportedly
world applications
Cobb-Douglas functional
degree
of parameter
yielded quite realistic
II
N
technology
of our model,
N
X .
estimation
results
properties
in
real
-- X:.
Eaj a-
X €.:.}
4
16
of the
we should first
the gross production possibility set Xf
",CX . :i. I
forms
(see References).
from the nDt. production possibility set,
X÷.
that need to be
and parameter
to turn to the mathematical
production between
"moderate"
of
specifications
always faces the trade off
specification
The CES and two-level
used here require a
Now,
the production technology
functions mean more parameters
between vigorous functional estimation.
the Model.
more detailed
and the applied modeller
estimated,
and have,
in
specifications of
are of course possible. the production
So we
a CES function of skill categories.
distinguish
= {Xf
which is:
,..
,X, n
N
The desirab.le property. of course strictly convex. convex
is that the set X.- be
this is ac hieved if thnd
A
t he set
X+ is stri c•tl y
and the Hawk ns--Si mon cond i t ions are sat i s i ed.
basically
achieve convexity by assuming capital
fix ed.
)
We
stocks to be
conve:xity is to be increased with
Further, the degree of
the number of fix.ed factors of production in
each firm,
this implies the well-celebrated hypothesis of:
since
diminishing
returns to scale to the variable factors. In contrast to retaining
the neo-classical
properties in its
productio.n technology, the Model recognizes two ki:nds of imperfections for the portrayal one is the ex.plicit
allowance
of market behavior.
The first
of monopoly power in certain is the recognition of
productiv e sectors; the other
intersectoral
wage differences for the same category of labor. Incorporation of
mono(poly power into CGE type policy models
has not been a common practice Robinson
1978 study).
Yet,
(with the e.xception of Adelman &. in a recent p)aper
Per Lundb(:rg
provides evidence from the Malaysian tin market showing that the frequent procedur-e of m:isleading results
assuming comp1etitive markets may lead to
(see Lundborg,
Especial.ly, when
effects of different policy
analyzing the distributional packages,
1984).
existance of monopoly power may have important
consequences which the competitive markets cannot generate.
The
income flows arising from the monopoly profits may be substantial
,
and may further result
in biased
innovations
(of the
Binswanger -..Hayami - Ruttan type) affecting the i ntertemporal grow':.t h I:)ath ( of the ec on omy. p 1 a
-3 . .' ) N .
) >~:,
on the other hand, its
3
/ Wp
suffers from
decisions,
labor-hire
associated with the
1 / Lp, AL 3
and from
"politicization"
of
incentives. In
particular,
distorted by an is
interference factor,
INT±
(0
,j. c i nsc E
r=
Sectoral
"umJ
1 / 1 NT]
1
i'
[I
'WI,.,)
>s , .-M,,) Ri,
Xr
/ ( I NT'. 'W: : ,.) ]3
1/ (,..k
tun
Total
XS,.
= XS,.
sector i
output in
(I
+ XS,
Given labor demands in
= E
each sector,
category s can be calculated.
each skill
DL,
then becomes:
(Lp
,
total
-17)
labor demand
for
Thus,
(11-18)
+ L.i,.)
i
In fixed
at
natural
Stage SLi,,:. growth
I,
l.abor
These, rate
for
supplies by skill however, l.abor
wi:ll. be and
21
type are endogenized
assumed to
be
by assuming
recoglnizing the possibi.lity
a o.f
migratiU.on from agricultural
to urban
sectors in the second,
dynamic stage of the CGE Model. Given *fixed labor supplies for each market clearing nominal
wage rate,
W.,
skill
category, the
can be found via iteration
on
DL
- SSL
= O
(11-19)
Note that,
for certain
skill categories
the nominal
wage
rate can be taken as given or having a lower bound, reflecting,
for instance,
becomes a fixed variable and the level determined by the level The model factor
The'n W.fi,
government's policies on minimum wages. of employment is
of demand.
can further be enriched by specifying monopolistic
markets reflecting
flow of the core model, Having derived
labor unions' power and so on.
however, will
the wage bill,
The
remain the same.
the profits of the enterprises
can easily be calculated as residuals in the sectoral
value added,
Thus, the private enterprise profits become:
RPF'
=
PF'Nr,
XSp:,i
-
E
WpA ,,,:,L LF) ,,J
and the public enterprise profits
R C3.
PNg±
'
XSj.
Ez
(II
-2"0)
(losses if negative) are:
(II-21) (11-21
FOREIGN
TRADE
Now we can construc:t the trade equations of the import side, problem
recall
domestic: In
good,
that the marginal to their
function
with imported
good,
M:,.
a
and the
the buyer's problem
demand
ratio
is
which satisfies
simply to find the condition
rate of substitution between Mi
and DC.
be
respective price ratios.
convenience,
I
repeat here the composite commodity
(II -1)
-
CCI,. :=
CC.,
Economics jargon,
For
"cost
IDC. , taken as "inputs".
the import-domestic
equal
where the relevant
was one of a CES formulation used to "p3roduce"
composite commodity,
On
that we have specifi ed the buyer's
as one of cost minimization,
function"
our model.
B.:L .I:
M..
I.
-
+
::.
-"1/p
(II - 1)
( - E. ) DC
The Lagrangean of the buyer's problem is:
S = PMi.
MI. + PD.
* DCi
+ > LCC
- BBi ( 8M-.
-'.:.
+
where CCi is order
(l-&:L)
a pre-specified
conditions of this
mi
Recall
M/./DCt
that
DC±
=
1/
:'
]
level
(11-22)
of
"output"
of CC:.
The first
problem yield:
( 1/ 1-
(PD.i/PM.t )
.'i = 1/l+p:.'.,
-
)
is
the elasticity
Import demand for commodity i
.. )
(II-23)
of
substitution.
can be found easily from
(II-23):
Mi.
calculated and be fed into
(II-24)
DC,.
point DC, is
at this
However,
.)
(C/l-
(PD.i/PMi.)
=
Yet,
(II-24).
without
import-quantities domestic production/consumption cannot be realized and there is and M±
A simple trick
simultaneously.
market,
DS.,
decisions
solving for
both DC±
solves the problem,
domestic supply minus exports.
given by total
is
knowing the
that domestic supply for domestic
by using the identity
however,
no way of
needs to be
It
not yet known.
We
get, DS. = XSi
Further,
in
DCs
Hence,
=
(11-26)
DSi
using
Mi
(II-25)
E,
product market equilibrium we must have
=
commodity
-
i
(11-26)
we can derive the import demand
for
as:
(
(PD' /PMi )
/l-i)
DS,.
(11-27)
which is a workable relation for the Model. On the export side, price for each commodity. prices as in
equation
we first
need to formulate the export
Similar
(11-3),
to the treatment
of import
the export price relations can be
formulated as follows:
PEj. = PWE±
where PEI.
is
from sector
*
(II--28)
(1 + SE±.)ER
the domestic currency receipts per unit exported i;
SE.
is
the rate of export subsidy for the product
24
of
sector i.;
CU.r rr e n i
and PWE:,. is the -fixed world price in foreign
,,
Further, there are certain have to impose on
constraints that
(11-28) to guarantee meaningful
price of
, the domestic
commodity i,
then
the Model
instruct the productive enterprises to export all output
leaving
nothing for domestic consumption.
situation should, of
commodity i d omest i cal
than
will
of the domestic Such a
course exert upward pressure on PD.. until
both prices are equalized. possibility that
we
results in the
Note that if PE.,. happens to be greater
rest of our model. FPD
behavioral
Thus, although there is
PE:. > PDi. and that
all
the logical
domestic demand for
mgight b:e satisified through imports, whhil.e all
that is
y produced be i n g sol d abroad, we will rule out. t hi s
extreme behavior by recognizing the following constraints on the ex:port side. PD.
!:PE.i. such that
if
PD., - PE. , E
if
PD> Yet,
!:0
PEi , Ei
= 0
another problem is the very hypothesis we have invoked
about the treatment of tradeables in general. distinguish products by country of origin
Accordingly, we
and hence, there is the
possibility that the export demand functions .for the home country's products may be less than infinitely elastic. The export then
be in
E.
demand functions for
the form:
E. (AWPF
, PWEI)
our country's products must
is an
where AWPi
world price for products in the
"aggregated"
all
aver.age of
trade policies
costs and
production
reflects a wei..ghted.
as well
s ector i 's out!:put category which,
of all
countries. In
special
sense that PWE:L
However,
the small
retain
we will
),
E.(
the specific form of the export
designing
AWP
PWE,
costs will
(II-29)
as we present them
increase in
the export
leads to a fall
to remain constant export demand market
there will
for product
i
the price of
and raise
In
be an
and
our our
Also an
or a devaluation
(an increase
the latter
if
case,
increase for our
hence,
an
increase
AWF'.
were
country's
in
our
world
share.
Following (1982)
FWE .
in
increase
into the world market.
subsidy rate in
an
deduce that
increase PDI
exportables
of ER)
sectoral
rate:
we can easily
(II-29)
production
Dervis and Robinson
one can make the assumption
whole behave according generalized composite in
in
= PD./[ (l+SE.)ER3
From
by the
determined
as reflected
export policy
the exchange
and
in the
as fixed and given.
endogenous price,
now becomes an
domestic production costs, subsidy rates
country assumption
be treated
will
demand function
to the rules
CES function specifying
good.
(1978) that
and
also Dervis et.
the world consumers
of cost
minimization
form:
26
as a
with a
the world commodities as a
We can then specify the export
the single elasticity
al.
demand
functions
E . = E.,
(AW ./ PF'WE
(I -30)
)
where ':(.is the elasticity of export demand and EJ.i.is the normal trend level
PWE,.
of the home country exports when AWP:I.
Having thus constructed the export demand equations, what
is
left for us is to find an endogenous expression for the export subsidy rate, SE,..
Many governments, instead of
granting a
single ad valorem subsidy rate to ex porters, provide a comp:lex set
of incentives for producers to encourage the ex.portation of
their products.
These incentives may range
neighbor mercantilist policies, to a tradables.
In this paper,
from beggar-thy-
laissez--faire treatment on•
a policy pacl.kage consisting of four
different ex.port incentive schemes is recognized modelled
These are:
son tn.:, (1) rebates on pr.).oduction taxes,
the products destined for exports; income tax
and explicitly
(2)
allowance on the corporate
at a certain percentage rate of export
earnings;
permission of
.dutyfree intermediate 'imports used for the
production of
exports;. and
valorem export subsidy paid out of
(tax
(4) if
(3)
a sectorally di.fferentiated ad negative)
rate which is directly
the government budget.
It w:i.ll further be assumed sets sectorally differentiated
in the Model
that the government
"eligibility criteria"
that may benefit from the above schemes,
on ex.ports
such as exports destined
for designated world markets, or export earnings exceeding some minimum value in foreign currency, etc.
Depending on the
st.r i ctness of these cond i t i ons it will b e assumed that the eli gi bility rate for exports in the pr'od.ucti on tax
r'ebate and
allowance on corporate income tax schemes is historically around
27
is
For the remaining
exports.
of total
ee. percent
two schemes ee
taken to be 100.O under
Therefore, sector
TSR±
i
will
= tn:.
be:
* ee:L
* FPWE
which corresponds
* ER
allowance
granted
TKA = kta
* Eee
* EE
income tax
TSA:.
* PFWEi
* eel
which corresponds
percent.. income tax
total
(II-32)
, E,
* ER
the granted corporate
kta
* ee± scheme,
allowance
income tax allowance rate.
(corporate)
PWE.
* ER
income tax rate,
scheme is:
subsidy on exports due to this
= tk
of tn.
is:
Letting tk denote the capitalist total
(II-31)
to subsidy equivalent
Under the corporate
where kta is
subsidy granted to
scheme total
the first
* E.
(II-33)
to an ad valorem subsidy of
tk ,
ee.
kta
percent. As for value of
the third
imported
scheme,
observe
intermediate
that
the domestic
inputs used for export
currency
production
is:
EMI.
= EPWMj
* ER * dj
, mj
* a.:
(II-34)
E±
J
where d. is the domestic use ratio of the j-th composite good (see equation
11-57 below);
and mnj
ratio introduced in equation gives the amount of
imported
is the import-domestic good
II-23 above.
Thus d
intermediate good
good i produced and exported.
28
* mj
* 'a
j, per unit of
tax to be paid on such imports then becomes:
import
Total
=T Etmj. , PWM.. 1
T"EMI'
dj ,
ER R
,
m.J
a...j
)
(II--3
Ei
which gives rise to an ad valorem subsidy rate of *dj mj
Etm.j* FWM
) per unit of exports.
* (1/PWE.
aji
-i
Combining
=- (tn . + tk
SE:i.
export subsidy rate becomes:
the realized overall
on exports,
+ Etm.j
(II-36)
ee,.
* kta)
d..
* PWMI.
PWEi in
equation
above expression further entails solved by numerical Balance
* M:. -
EPWM ±
) + te,.
(I/PWE:
a.j. 2
m..
J
which appears in
subsidy/tax rate of te.
sectoral
with an explicit
Note that since the
(11-29). PWE. ,
it
needs to be
methods.
of Payments EquIilibrium is
E.
EF'WE:,.
FF -
then achieved when,
C 0
WR
(I1-37)
.
where F and WR starnd for resource
the ex:ogenous value remittances,
inflow and workers'
of the net
foreign
respectively. (which
is
the
If
as well a
exchange rate is
allowed to adjust freely
policy decision,
hence we continue to use a circumflex. on ER),
will if
(I1-37)
need to be iterated until the government chooses to fix
is
satisfied.
at some value,
ER
guarantee that Balance of Payments Equilibrium would (a to
surprise to no one!); imports
ration
resources. abound
and
works cited
or
try
hence, to
Such commercial the :i.n
interested
reader
the References
there is
no
be satisfied
or get
more
foreign
analyses using CGE Models may wish
to this
29
Per contra,
the government would need either
increase exports, policy
ER
to
paper.
consult
with
the
are
INCOMES GENERATION,
CONSUMER DEMANDS
The functional Model
AND SAVINGS
incomes of different consumer
are generated using the results derived in
groups of the the factor
markets and the derivations are quite straight forward. For labor- skill-type total
YL.
s,
assuming that the tax
rate is
ts
disposable income can be written as:
=
where w group
E
(1-ts)
is
',Lp,.
(WI
+
S..Lg.±.)
the share of workers'
)
4
*WR'ER
remittances
(II-38)
captured by labor
s.
Capitalists'
disposable income becomes:
ERP,
YK =: (l-tk)
(I 1-39)
Fublic enterprises'
YK3 =
+ W
(1-tk)
aggregate after-tax
income is:
ERG.
(II-40)
Government's total
income
is: (II-41)
YG = Ets E(WpisLpi,
+ tk E(RF'.
+ RG± -
+ ECtm ,*PWM.t
-
kta'eei*PWE. sEREi±)
ER,'M-EtmAjPWM.,
+ Etni :F'PDXSI-ee: .
+ W,.iL,,,)
'*PWE± 'EREi]
ERd-j *mj
-
Yte
a.1 ,E±3
*PFWEi *ER E,
sn
1 [sn±
,PD'D.
,XSp,.
+ sn.,
(
,-.O,
(B-4)
C.K:
CL..
where of
I
and
.,
type-s,
are
income
and of
of
elasticities
the capital
ists,
consumption
respectively.
clemand Note that
the system of
is
consumption demands
function of PC~'s
specified as a
originally
(the composite good prices); of
need to have an expression for the elasticity price. demand with respect to the dom.estic ...
( CL.
t.i . =
) * (FPC./F'PD.
) * (PCi../CL.B
/F'PC
which explains the presence of tFOD,±
)
i
(B-5)
(F'PD./PC,. )
(the elasticity
of composite
(B-3) and
(8-4).
Thus:
F:'C
(-I)
(B-6)
F-DI
In order to find the elasticity of first begin by writing the components of
Z.
we use
government consumption demands are given by the
fixed share-coefficients. 0 Mt-
we
consumption
Thus,
price with respect to the domestic price) in The sectoral
and yet,
investment demand we Z±
more clearly:
E (HjTFPS + HGj ,( IF)/PKj]3
= Ebij -i
(Hj*TPS + HGj*'GIF)/( Eb
SEb,. j
..,*PCJ
(-7)
*I.,
j
Thus: 9Z./aPC,
= -Eb... -
CH..jTPS + HG.j, GIF3/(Eb,: , FPC .)
j
I*:
which yields z
s..ZC == (Za./PCFC
=
-E Cbi. .j = -E
) * (PC./Za)
(Hj'*TPS+HGj *,GIF)(PCF:',/Z.)/(bUi
The latter
component
/ d W ....,. * d W .. ,,,/ld D ) :i
(dL...j,,/dW..i,,; dW.js,/dPD:s.)
is
embedded
in
solution algorithm for clearing the labor markets and yet observable
in
a functional
formm.
able to make use of the functional
(1)
I am indebted to Prof• point.
T".
In
what
follows,
relationship
the is
we are
(B-11 ).
Roe f:or his comments on this
67
1)
not
not
intermediate demand
of
The assumption that the elasticity
is XT)
zero,
Yet,
clearly puts a downward
as we argued,
bias on the aggregate value of
.
due to the fixed-coefficients technology, of
overall price sensitivity
the
intermediate demands have to be very
low and the incurred bias shouldnot be substantial. P'C;
Our final
task is
to derive an expression for
to,-
.
Since, aT
FPC
(l-a.-
= 1/B.tE6:.
i.A
)
+
PMi
( -a•
1/I
)
-a.,
J
PD,.
(1-$.)
(B-12)
we have a 9aPCC /sPD
=
(PC:. /PD
a i.t
)
(l/B.)
(PD
/PCF . )