WI's 1375
POLICY RESEARCH WORKING PAPER 1 1375
Policy Lessons from a Simple -'MispaW desmithowt
specify, solve, and draw
Open-Economy Model policylessons from small, wo-
sector, general equilibrium
models of open economies.
Sl7antayanan Devaraian--
Delfin S. Go
Jeffrey D. Lewis
Sherman Robinson
Pekka Sinko
Tfhe World Bank
Polic-y Reseach Departmen
November 1994
Public~~~~~~~~~~~- E:n--c Division::
I POLICY RESEARCH WORKING PAPER 1375
Summary findings
Devarajan, Go, Lewis, Robinson, and Sinko show how policy results may run counter to received wisdom. For
two-sector models can be used to derive po'icy lessons example, when the substitution efftct of an adverse
about adjustment in developing econoTnies. external shock dominates, real depreciation is
In the past two decades, changes in the external inappropriate. An infusion of foreign capital does not
environment and in economic policies have been the key necessarily benefit the nontradable sector, as the results
factors in the Derformance of developing economies. By of -Dutch disease" models suggest (for example, in the
and large the shocks have involved the external sector: extreme case of nearly infinite substitution elasticity
terms-of-trade shocks or ctutbacks in foreign capital. The between imports and domestic goods). When import
policy responses most commonly proposed have targeted tariffs are significant sources of public revenue, potential
the external secror: depreciating the real exchange rate revenue losses from tariff cuts must be offset by other
or reducing discortionary taxes to make the economy revenue sources to maintain the external current account
more competitive. The authors provide a starting point balance. The paper shows a simple way to calculate the
for analyzing the relation between extemal shocks and necessary tax adjustment.
policy responses. A major advantage of small models is their simplicity.
Starting from a small, one-country, two-sector, three- The example in this paper can be solved analytically -
good (1-2-3) model, tle authors outline how the effects either graphically or algebraically. It also can be solved
of a foreign capital inflow and terms-of-trade shock can numerically, using such widely available PC-based
be analyzed. They derive the assumptions underlying the spreadsheet programs as Excel.' The numerical
conventional policy recommendaion of real exchange implementation involves only modest data requirements.
rate depreciation in response to adverse shocks. The The data that governments normally release on national
implications of such trade and fiscal policy instruments income, fiscal, and balance of payments accounts are
as export subsidies, import tariffs, and domestic indirect sufficient
taxes can also be studied in this framework.
The authors show that the standard advice to 'A companion Excel-bascd model is available. Bank staff can copy
depreciate the real exchange rate in the wake of an the spreadsheet file "123.xls" from the Policy Research
adverse terms-of-trade shock rests on the condition that Department's nctwork drive, prd@prdsvrfllworldbank, under
the income effect of the extemal shock dominates its the directory 'models.' The file can also be requested from the
substitution effect. But, depending on the characteristics interner electronic mail address prdpe@)'worldbank.org. The file will
of the economy (for example, the trade elasticities), be available on the Banks Gopher in the future.
This paper - a product of the Public Economics Division, Policy Research Department - is part of a larger effort in the
department to develop tools for analyzing tax policyq Copies of the paper are available free from the World Bank, 1818
H Srreet NW, Washington, DC 20433. Please contact Carlina Jones, room N10-063, extension 37699 (38 pages).
November 1994.
The Policy Research Workung Paper Serws disseminates the findings of work in progrss to encourag the exchange of ideas about
develpment isswute An objective ofthe series is toget the findings outuicly, even ifthe presentations am less tha fily polished The
papers carry the names of tbe authors and sbould be used and cited accordingly. 7he fndings, interpretations, and condusions are the
authors' own and should not be attribured to the World Bank, its Exeutive Board of Directors, or any of its member counties.
Produced by the Policy Research Dissemination Center
Policy Lessons from a Simple
Open-Economy Model
Shantayanan DevaTrajan, World Bank
Delfin S. Go, World Bank
Jeffrey D. Lewis, World Bank
Sbernan Robinson, IFPRI and University of California at Berkeley
Pekka Sinko, Government Institute for Economic Research, Finland
Policy Lessons from A Simple, Open-Economy Model'
1. INTRODUCTION
This paper describes how to specify, solve, and draw policy lessons from small two-sector, general
equilibrium models of open, developing economies. In the last two decades, changes in the external
environment and economic policies have been instrumental in determining the performance of these
economies. The relationship between external shocks and policy responses is complex; this paper provides
a strting point for its analysis.
Two-sector models provide a good starting point because of the nature of the external shocks faced
by these countries and the policy responses they elicit These models capture the essential mechanisms by
which external shocks and economic policies ripple through the economy. By and large, the shocks have
involved the external sector tenns of trade shocks, such as the fourfold increase in the price of oil in 1973-
74 or the decline in primary commodity prices in the mid-1980s; or cutbacks in foreign capital inflows. The
policy responses most commonly proposed (usually by international agencies) have also been targeted at the
'Forthcoming as achapter in Franqois and Rein(1994). Thlis paper is derived extively from rwo previous ones: Devarajan. Lawis. and
Robinson (1990) and Go and Sinko (1993).
external sector. (I) depreciating the real exchange rate to adjust to an adverse terms of trade shock or to a
cutback in foreign borrowing and (2) reducing distortionary taxes (some of which are trade taxes) to enhance
economic efficiency and make the economy more competitive in world markets.
A "minimaliste model that captures the shocks and policies mentioned above should therefore
emphasize the external sector of the economy. Moreover, many of the problems -- and solutions - have to
do with the relationship between the external sector and the rest of the economy. The model thus should
have at least two productive sectors: one producing tradable goods and the otier producing nontradables.
If an economy produces only twaded goods, concepts like a real devaluation are meaningless. Such a country
will not be able to affect its international competitiveness since all of its domestic prices are determined by
world prices. If a country produced only nontraded goods, it would have been immune to most of the shocks
reverberating around the world economy since 1973. Within the category of tradable goods, it is also useful
to distinguish importables and exports. Such a characterization enables us to look at terms-of-trade shocks
as well as the impact of policy instruments such as import tariffs and export subsidies.
The minimalist model that incorporates these features, while small, captures a rich array of issues. We
can examine the impact of an increase in the price of oil (or other import and/or export prices). In addition,
this model enables us to look at the use of trade and fiscal policy instruments: export subsidies, import tariffs,
and domestic indirect taxes. The implications of increases or decreases in foreign capital inflows can also
be studied with this framework.
While the minimalist model captures, in a stylized manner, features characteristic of developing
countries, it also yields policy results that cut against the grain of received wisdom. For example, it is not
always appropriate to depreciate the real exchange rate in response to an adverse international terms-of-trade
shock; reducing imporL tariffs may not always stimulate exports: unifying tariff rates need not increase
efficiency; and an infusion of foreign capital does not necessarily benefit the nontradable sector (in contrast
to the results from "Dutch disease" models).
Deapn-Go-Lwis-Roobison-Sinka 2
A major advantage of small models is their simplicity. They make transparent the mechanisms by
which an external shock or policy change affects the economy. In addition, the example presented in this
paper can be solved analytically - either gmphically or algebraicAlly. It also can be solved numerically by
using the most widely-available, PC-based spreadsheet progmms hence, it is not necessary to learn a new,
difficult programming language in order to get started. The presentation will introduce the approach used
to solve larger, multisector models. Finally, these minimalist two-sector models behave in a similar fashion
to more complex multisector models, so we can anticipate some of the results obtained from multisector
models.
The plan of the paper is as follows. In Section 2. we present the simplest two-sector models. We
specify the equations and discuss some modelling issues. We then analyze the imlpact of terms-of-trade
shocks and changes in foreign capital inflows. In Section 3, we describe an easy way of implementing the
framework and use it to discuss some policy issues. The conclusion, Section 4, draws together the main
points of the paper.
Dearajn-aLcwss-SbimnsoSinka 3
Table 1: The Basic 1-2-3 CGE Model
Flows
(1) X = G(E, Ds; 0) (10) pq = f,(pa, p)
(2) S= F(M, DD;c) (11) RN 1
(3) QD = Y Equilbrium Conditions
(4) E = g_(p, p) (12) D D' =
(5) M = z(P F P ) (13) QD QS = o
D,D
(6) Y = P-X + R.B (14) pw nM - pwE-E= B
Prices Identities
(7) P= R-pwm (i) Pz.X a P'-E + 'D
(8) Pe R pw (ii) Pr*_Q pmSM + pi.DD
(9) px= g1(p, pd) (iii) y, a s .QD
Endogenoaus Variables
E: Export good Pt: Price of aggregate output
M: Import good Pq: Price of composite good
D5: Supply of domestic good R. Exchange rate
D0: Demand for domestic good
QS: Supply of composite good Exogenous Variables
QD: Demand for composite good pw': World price of export good
Y: Total income pw'0: World price of import good
Pr: Domestic price of export good 2: Balance of trade
Pm Domestic price of import good a: Import substitution elasticity
Pd: Domestic price of domestic good Q: Export transformation elasticity
Deaaan-GaLewis-Robinson-Sinko 4
2. TWO-SECTOR, THREE-GOOD MODEL
The basic model refers to one country with two producing sectors and three goods; hence, we call
it the "1-2-3 model." For the time being, we ignore factor markets. The two commodities that the country
produces are: (I) an export good, E, which is sold to foreigners and is not demanded domestically, and (2)
a domestic good, D, which is only sold domestically. The third good is an import M, which is not produced
domestically. There is one consumer who receives all income. The country is small in world markes, facing
fixed world prices for exports and imports.
The equation system is presented in Table 1. ne model has three actors: a producer, a household,
and the rest of the world. Equation I defines the domestic production possibility frontier, which gives the
maximum achievable combinations of E and D that the economy can supply. The function is assumed to
be concave and will be specified as a constant elasticity of tansfornation (CEI) function with
fnsformation elasticity 1. The constant, X, defies aggregate production and is fixed. Since there are no
intermediate inputs, X also corresponds to real GDP. The assumption that X is fixed is equivalent to
assuming full employment of all primary factor inputs. Equation 4 gives the efficient ratio of exporis to
domestic output (E/D) as a function of relative prices- Equation 9 defines the price of the composite
commodity and is the cost-function dual to the frst-o3tvr condition, equation 4. The composite good price
P2 corresponds to the GDP deflator.
Equation 2 defines a composite commodity made up of D and M which is consumed by the single
consumer. In multisector models, we extend this tratment to many sectors, assuming that imports and
domestic goods in the same sector are imperfect substitutes, an approach which has come to be called the
Armington assumption.? Following this treatment, we assume the composite commodity is given by a
2I See Amign (1969).
Dtqa.oLii-Vbt ik 5
constant elasticity of substitution (CES) aggregation function of M and D, with substitution elasticity o.
Consumers maximize utility, which is equivalent to maximizing Q in this model, and equation 5 gives the
desired ratio of M to D as a function of relative prices.3 Equation 10 defines the price of the composite
commodity. It is the cost-function dual to the first-order conditions underlying equation 5. The price, P.q
corresponds to an aggregate consumer price or cost-of-living index.
Equation 6 determines household income. Equation 3 defines household demand for the composite
good. Note that all income is spent on the single composite good. Equation 3 stands in for the more
complex system of expenditure equations found in multisector models and reflects an important property
of all complete expenditure systems: the value of the goods demanded must equal aggregate expenditure.
In Table 1, the price equations define relationships among seven prices. There are fixed world prices for E
and M; domestic prices for E and M; the price of the domestic good D; and prices for the two composite
commodities, X and Q. Equations I and 2 are linearly homogeneous, as are the corresponding dual price
equations, 9 and 10. Equations 3 to 5 are homogeneous of degree zero in prices - doubling all prices, for
example, leaves real demand and the desired export and import ratios unchanged.4 Since only relative prices
matter, it is necessary to defne a numeraire price; in equation I1, this is specified to be the exchange rate,
R.
Equations 12, 13, and 14 define the market-clearing equilibrium conditions. Supply must equal
demand for D and Q, and the balance of trade constraint must be satisfied. The complete model has 14
equations and 13 endogenous variables. The three equilibrium conditions, however, are not all independent.
Any one of them can be dropped and the resulting model is fully determined. models. Finally, these
minimalist two-secter models behave in a similar fashion to more complex multisector models, so we can
In the multisecor models. we add expenditue ficions with many goods based on utility maidmizzaion at two levels. First alkloc
expcnditur among goods. Second, decde on sactoral impor ratios. In the 1-2-3 modeL the CES function defining Q can be reatcd as a utility
hnction dircdtly.
' For the demand equation, one must show that nominal income doubles when all prices double. including the echdan rate. Tracing the
element in equation 6. it is asy to denostrate that nominal incorn goes up proportionatly with prices
Dewrcjaa-Go.Lewis-Robhnsn.Sinko 6
anticipate some of the results obtained from multisector models.
To prove that the three equilibrium conditions are not independent, it suffices to show that the model
satisfies Walras' Law. Such a model is "closed" in that there are no leakages of funds into or out of the
economy. First note the three identities (i, il, and iii) that the model satisfies. The first two arise from the
homogeneity assumptions and the third from the fact that, in any system of expenditure equations, the value
of purchases must equal total expenditure.' Multiplying equations 12 and 13 by their respective prices, the
sum of equations 12, 13, and 14 equals zero as an identi-y (moving B in equation 14 to the left side). Given
these identities, simple substitution wi ll show that if equations 12 and 13 hold, then so wust 14.
The 1-2-3 model is different from the standard neoclassical trade model with all goods tradable and
all tradables perfect substitutes with domestic goods. The standard model, long a staple of trade theory,
yields wildly implausible results in empirical applications.' Empirical models that reflect these assumptions
embody "the law of one price," which states that domestic relative prices of tradables are set by world prices.
Such models tend to yield extreme specialization in production and unrealistic swings in domestic relative
prices in response to changes in trade policy or world prices. Empirical evidence indicates that changes in
the prices of imports and exports are only partially transmitted to the prices of domestic goods. In addition,
such models cannot exhibit two-way trade in any sector ("cross hauling'), which is often observed at fine
levels of disaggregation.
Recognizing these problems, Salter (1959) and Swan (1960), specified a two-sector model
distinguishing "tradables" (including both imports and exports) and "nontradables." Their approach
represented an advance and the papers started an active theoretical literatue. However, they had little impact
on ernpirical work. Even in an input-output table with over five hundred sectors, there are very few sectors
' In dis model equation 3 and idenLiry iii ae the same In a multisecor modcl. as noted above. idcntity iii is a necessary property of any systcm
of expenditure equations.
' Enpirical problems wih tdis specificaion have been a thorn in the side of modelers sincc the carly days of linear programming modcls. For
a survey, see Taylor (I 975).
De.arwnGo-Lewis-Robinson-Sio 7
which are purely non-traded; i.e., with no exports or imports. So defined, non-traded goods are a very small
share of GDP; and, in models with 10-30 sectors, there would be at most only one or two non-traded sectors.
Furthennore. the link between domestic and world prices in the Salter-Swan model does not depend on the
trade share, only on whether or not the sector is tradable. If a good is tradable, regardless of how small is
the trade share, the domestic price will be set by the world price.
The picture is quite different in the 1-2-3 model with imperfect substitutability and transformability.
All domestically produced goods that are not exported (D in Table 1) are effectively treated as non-tradables
(or, better, as "semi-tradables'). The share of non-tradables in GDP now equals one minus the export share,
which is a very large number, and all sectors are treated symmetrically. In effect, the specification in the
1-2-3 model extends and generalizes the Salter-Swan model, making it empirically relevant.
De Melo and Robinson (1985) show, in a partial equilibrium framework, that the link between
domestic and world prices assuming imperfect substitutability at the sectoral level depends critically on the
trade shares. both for exports and imports, as well as on elasticity values. For given substitution and
transformation elasticities, the domestic price is more closely linked to the world price in a given sector the
greater are export and import shares. In multisector models, the effect of this specification is a realistic
insulation of the domestic price system from changes in world prices. The links are there, but they are not
nearly as strong as in the standard neoclassical trade model. Also, the model naturally accommodates two-
way trade, since exports, imports, and domestic goods in the same sector are all distinct.
Given that each sector has seven associated prices, the model provides for a lot of product
differentiation. The assumption of imperfect substitutability on the import side has been widely used in
empirical models.' Note that it is equally important to specify imperfect transformability on the export side.
'TTh CES forTnulation for the impon-aggregation function has been criticized on econometric grounds (see Alston et aL (1990) for an examplc).
It is certainly a restrictive fonn. For example. it constrains the income elasticity of demand for impons to be one in every sector. Rather than
compicte rcjection of approachcs rclying on imperfect substitutability, this criticism would seem to suggest that it is time to explore the many
altemative functional forms that are available. For example, Hanson. Robinson. and Tokarick (1989) estimate sectoWl import demand functions
based on the almost ideal demand system (AIDS) formulation. They find that scctoral cxpenditure elasticities of inport demand mc generally much
greater than one in the U.S. results consistent with cstimates from macroeconomnciric models. Factors oiler than relativc prices appear to affect
Devarjan-Go-Lenuss-Robhhson-Sinko 8
Without imperfect transformability, the law of one price would still hold for all sectors with exports. In the
1-2-3 model, both import demand and export supply depend on relative prices.'
Do Melo and Robinson (1989) analyze the properties of this model in some detail and argue liat it
is a good stylization of most recent singlc-country, trade-focused, computablc general equilibrium (CGE)
models. Product differentiation on both the import and expon sides is ver appealing for applied models,
esp,ecially at the levels of aggregation typically used. The specification is a faithful extension of the Salter-
Swan model and gives rise to normally shaped offer curves. 'fhe exchange rate is a well-dcfined relative
price. If the domestic good is chosen as the numeraire commodity, setting Pd cqual to one, then the exchange
rate variable, R. corresponds to the rcal exchange rate of neoclassical trade theory: the relative price of
tradables (E and M) to non-tradables (D). Trade theory models (and our characterization in Table 1) often
set R to one, with Pd then defining the real exchange rate. For other choices of numeraire, R is a monotonic
function of the real exchange rate.9
The 1-2-3 model can also be seen as a simple programming model. This fornulation is given in
Table 2, and is shown graphically in Figure 1. The presentation emphasizes the fact that a single-consumer
general equilibrium model can be represented by a programming model that maximizes consumer utility,
which is equivalent to social welfare.'0 [n this model, the shadow prices of the constraint equations
correspond to market prices in the CGE model." We will use the graphical apparatus to analyze the impact
trade shares, and it is importanl to study what they might be and how they operate. Alston and Green (1990) also estimatcd the AIDS import
formulation. A related paper is Shiells. Roland-Holst. and Reinert (1993).
' Dervis. de Mclo, and Robinson (19S2) specify a logistic export supply function in place of equation 4 in Tabic 1. Their logistic function is
locally cquivalent to the function that is derived from the CET specification.
Dervis, de Melo. and Robinson (1982), Chapter 6. discuss this relationship in detail.
"' Ginsburgh and Wacibmeck (1981) discuss, in detail, the general casc wherc a multi-consumer CGE model can be represented by a
programming model maximizing a Negishi social welfare function. See also Ginsburgh and Robinson (1984) for a brief survey of the technique
applied to CGE models.
" In the pwgramming model, we implicitly choosc Q as the numeraire good, with P. a 1. In the graphical analysis, we sd R a 1.
DevcrajanGo-Gewis-Robinsn-Sinbo 9
of two shocks: an increase in foreign capital inflow and a change in the intemational tenns of trade.'2 We
will also use this programming-model formulation, including endogenous prices and tax instruments, to
derive optimal policy rules under second-best conditions.
Table 2: The 1-2-3 Model as a Programming Problem
Maximize Q = F(M, DD; a) (absorption)
with respect to: M, E, DD, D)S
subject to:
Shadow Price
(I) G(E, Ds; 0) 5 (technology) Ax = px/Pi
(2) pw8- M s pwe- E + B (balance of trade) Ab= Rjpq
(3) D) s D)S (domestic supply and demand) d Pd/pq
The transfornation function (equation I in Table I and constraint I in Table 2) can be depicted in
the fourth (south-east) quadrant of the four-quadrant diagram in Figure I. For any given price ratio pd/P.,
the point of tangency with the transformation frontier determines the amounts of the domestic and exported
good that are produced. Assume, for the moment, that foreign capital inflow E is zero. Then, constraint 2,
the balance-of-trade constraint, is a straight line through the origin, as depicted in the first quadrant of Figure
1. If we assume for convenience that all world prices are equal to one, then the slope of the line is one. For
a given level of E ptoduced, the balance-of-trade constraint determines how much of the imported good the
county can buy. [ntuitively, with no capital inflows (1] = 0), the only source of foreign exchange is exports.
The second quadrant shows the 'consumption possibility frontier," which represents the combinations of the
domestic and imported good that the consumer can buy, given the production technology as reflected in the
"rhe discussion follows de Mdo and Robirnon (I 98).
De=Praan-Go-Lewis-Robinson-Sinko 10
M
Bado" of Tra*
C
Q-Fg'AD ) - (
DD~ 7 ' .
pd/pu~, I dP
, - - I
' I
- -n d
I I~~~~~~~~~~~~~I
Figere 1: The 1-2-3 Programming Model
transformation frontier and the balance of trade constraint. When world prices are equal and trade is
balanced,thfe consumption possibility frontier .s the mirror image ofthe transformation frontier. Equatien
2 in Table I dcfines 'absorption," which is maximized in the prograrnming problem. The hngency between
the "iso-absorption" (or indifference) curves and thie consumption possibility frontier will determine the
amount of Dand Mthe consumer wil11demands at price ratio pd/pm. The economyproduces at point Pand
consumes at pOillt C.
Now consider what would happen if foreisgn capital inflow increased from its initial level of zero to
some value iN > O). For cxample. the country gains additional access to world capital markcets or receives
some foreign aid. Alteratively, there is a prinary resource hoom in a country where the asource is
DevbalaneGotLecsuRopinsonpSiii e I
effectively an enclave, so that the only direct effect is the repatriation of export earnings." In all of these
cases, we would expect domestic prices to rise relative to world prices and the tradable sector to contract
relative to the nontradable sector. In short, the country would contract "Dutch disease."
eLL
-.. B~~~~~~~~u~af 2)wI
..8~~~~... .....
1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~3
Q-F(MJP)9 / /AI
* I I / * I
B J 'jB I/f
* I / I I /
la~~~~~~~~~~~~ 3
Figure 2: Increasc in Foreign Capital Inflow
That this is indeed the case can be seen by examining Figure 2. 'Me direct effect is to shif;c the
balance of trade line up by 13. This shift, in tum, will shift the consurption possibility frontier up vertically
by the same Ei. Thec new e.quilibrium point will depend on the nature of the imnport aggregation function (the
consumee,s utility fiunction). In Figure 2, the consumption point moves from C to C*7 widi increased demand
for both D and M and an increase in the price of the domestic good. Pl. On the production side, the relative
price has shifted in favor of the domestic good and against the export -an appreciation of the real exchange
" Se Benjaumi and Devarajan (1985) e-r Baliamin. Devarajan. anld Weiner 11939).
Devartan-C;Lwis-Robinson Sinlro 12
rate.
Will the real exchange rate always appreciate? Consider two polar extremes, which bracket the
range of possible equilibria. Suppose the elasticity of substitution between imports and domestic goods is
nearly infinite, so that the indifference curves are almost flat. In this case, the new equilibrium will lie
directly above the initial one (point C), since the two consumption possibility curves are vertically parallel.
The amount of D consumed will not change and all the extra foreign exchange will go towards purchasing
imports. By contrast, suppose the elasticity of substitution between M and D is zero, so the indifference
curves are L-shaped. In this case (assuming homotheticity of the utility function), the new equiiibrium will
lie on a ray radiating from the origin and going through the initial equilibriumr In this new equilibrium, there
is more of both D and M consumed, and the price ratio has risen. Since PI" is fixed by hypothesis, pd must
have increased - a real appreciation. The two cases bound the range of possible outcomes. The real
exchange rate wil1 appreciate or, in the extreme case, stay unchanged. Production of D will either remain
constant or rise and production of E, the tradable good in this economy, will either stay constant or decline.
The range of intermediate possibilities describes the standard view of the Dutch disease.
Consider now an adverse terms of trade shock represented by an increase in the world price of the
imported good. The results are shown in Figure 3. The direct effect is to move the balance of trade line,
although this time it is a clockwise rotation rather than a translation (we assume that initially fl = 0). For
the same amount of exports, the country can now buy fewer imports. The consumption possibility frontier
is also rotated inward. The new consumption point is shown at C*, with less consumption of both imports
and domestic goods. On the production side, the new equilibrium is P*. Exports have increased in order
to generate foreign exchange to pay for more expensive imports, and Pc/Pd has also increased to attract
resources away for D and into E. There has been a real depreciation of the exchange rate. q
Will there always be a real depreciation when there is an adverse shock in the international tenns
of trade? Not necessarily. The characteristics of the new equilibrium depend crucially on the value of a,
Dcwujan-Go.Lews- RohinSoninko 31
I,B AtI
Bdime, VfTrnd,
. . ... ... ...
I . ,I
7' ':1
* IIV
Figure 3: Change in World Prices
t[he elasticity of substitution beween imports and domestic goods in the import aggregation function.
Consider thie extremes of a = O and a = . In the first case, as in Figure 3, there will be a reduction
in the amount of domestic good produced (and consumed) and a depreciation of the real exchange rate. In
the second case, however, flat indifference curves will have to be tangent to te new consumption poss:.bility
frontier to the left of the old consumption point (C), since the rotation flattened the curve. At the new point,
output of D rises and the rcal exchange rate appreciates. When a = 1, thiere is no change in either the real
cxchange rate or the production stnuctur of the economy. The inituition behind this somewhat unusual result
is as follows."4 When thle price of imports rises in an economy, there are two effects: an income efrect (as
the consuuner's real income is now lower) and a substitution effect (as domestic goods now become more
'' We derie the reult analytically below-
DemrqaenGLLnwisRobisorn-Sinko 14
attractive). The resulting equilibrium will depend on which effect dominates. When a c 1, the income
effect dominates. The economy contracts output of the domestic good and expands that of the export
commodity. In order to pay for the needed, non-substitutah'e import, the real exchange rate depreciates.
However, when a > 1, the substitution effect dominates. The response of the economy is to contract exports
(and hence also imports) and produce more of the domestic substitute.
For most developing countries, it is likely that a c 1, so that the standard policy advice to depreciate
the real exchange rate in the wake of an adverse terms of trade shock is correct. For developed economies,
one might well expect substitution elasticities to be high. In this case, the response to a terms-of-trade shock
is a real revaluation, substitution of domestic goods for the more expensive (and non-critical) import, and
a contraction in the aggregate volume of trade. In all countries, one would expect substitution elasticities
to be higher in the long run. The long-run effect of the real exchange rate will thus differ, and may be of
opposite sign, from the short-run effect
The relationship between the response of the economy to the tenns-of-trade shock and the elasticity
of substitution can also be seen by solving the model algebraically. By considering only small changes to
the initial equilibrium, we can linearize the model and obtain approximate analytical solutions. We follow
this procedure to analyze the impact of a terms-of-trade shock.'
Let a 'A" above a variable denote its log-differential- That is, . = d(Inz) = dnz . Log-
differentiate equations 4. 5, and 14 in Table 1. assuming an exogenous change in the world price of the
import The results are:
E -5D =Q-
"'Dc Mclo and Robinson (19S9) derive thecioscd-ronn solution for the counuy's ofcr curve in the 1-2-3 model. A more complete discussion
and mathematical derivation is given in Devarajan. Lewis. and Robinson (1993).
Devarujan-Go-Lews-Robinson.Sinko t5
M D = a (pfd _ wm)
Mf + p6w M = E
Eliminating AM, D and E and solving for P gives
;di a -I .
Cy + a
Thus, whether pd increases or decreases in response to a terms of trade shock depends on the sign of (a - 1),
confirming the graphical analysis discussed above. Figure 4 illustrates the impact of a 10 percent import
price shock on P' under varying trade elasticities, 0 < a < 2 and 0 < a < 2. Note that the direction of change
in P1will deternnine how the rest of the economy will adjust in this counterfactual experiment. If P1falUs (the
real exchange rate depreciates), exports will rise and production of the domestic good will fall.
Our analysis with the 1-2-3 model has yielded several lessons. rirst, the bare bones of multisector
g2Pneral equilibrium models are contained in this small model. Second, and perhaps more surprisingly, this
two-sector model is able to shed light on some issues of direct concem to developing countries. For
example, the appreciation of the real exchange rate from a foreign capital inflow, widely-understood
intuitively and derived from more complex models, can be portrayed in this simple model. In addition,
results from this small model challenge a standard policy dictum: always depreciate the real exchange rate
when there is an adverse terms-of-trade shock. The model shows the conditions under which this policy
advice should and should not be followed.
Denqjan-Go-Lzwis-Robinhon-i&nko 16
5
Figure 4: Import Price Shock, Trade Elasticities, and Domestic Prices
Of course, many aspects of the economy are left out of the small model. In particular, there is no
government, factor markets, and intermediate goods; the framework is also static. Devarajan, Lewis, and
Robinson (1990) discuss several extensions and modeling issues in a one-period setting; Devarajan and Go
(1993) present a dynamic version ofthe 1-2-3 framework in which producer and consumer decisions are both
intra- and intertemporally consistent. All these extensions require that the model be solved numerically. We
turn therefore to the numerical implementation of the 1-2-3 model, extending the basic 1-2-3 model to
include the government sector in order to look at policy intruments such as taxes
Devajean-Go-Lewis-RobinsnoSinlko 17
Table 3: The 1-2-3 Model with Govemment and Investment
Real Flows Prices
(1) X =G(E,Ds;o) (I0)Pm=(I I + t").R.pw"'
(2) QS = F(M,DD;a) (I ) PD = (l + t)-R.pW
(3) Q0=C+Z+G (12) P'=(I +t')-Pq
(4) E/D = g2(pc,pd) (13) PI, g(pC,Pd)
(5) WD0 = f,(P',Pt) (14) Pq = f1(P",P')
Nominal Flows (15) R= I
(6) T = t'-RRpwm-M Equilibrium Conditions
+ V_pq4QD (16) Do - Ds = 0
+p.y-Y (17) QD _ QS =0
- t4R.pwc.E (18) pw"-M - pw'-E - ft - re=
(7) Y= P-X + tr-Pq + re-R (19) P'Z - S = O
(8) S i-Y + R-B + ss (20) T - Pqi - tr-Pq - ft*R- Sr=0
( 9) C -P' = (I - si - ty) Y
Accounting Identities
(i) P._X Pc.E + pd.DS
(ii) Pq.Qs P.'M + PlOD'
Eadogenous Variables: Exogenous Variables:
E: Export good pw": World price of import good
M: Import good pw': World price of export good
D)S: Supply of domestic good tr: Tariff rate
DD: Demand for domestic good tt: Export subsidy rate
Qs: Supply of composite good t: sales/excise/value-added tax rate
QD: Demand for composite good ty: direct tax rate
P': Domestic price of export good tr: government transfers
P: Domestic price of import good ft: foreign transfers to government
Pd: Producer price of domestic good re: foreign remittances to private sector
P': Sales price of composite good s: Average savings rate
PI: Price of aggregate output R: Aggregate output
Pq: Price of composite good G: Real government demand
R. Exchange rate B: Balance of trade
T: Tax revenue rQ: Export transformation elasticity
S5: Government savings a: Import substitution elasticity
Y: Total income
C: Aggregate consumption
S: Aggregate savings
Z: Aggregate real investment
Dearajw-obwisRbson-SinAo 18
Table 4: List of Parameters and Variables in the Excel-Based 1-2-3 Model
A B C D E F a H I
4 Parameters Exogenous Variables Base Year Current Endogenous Variables Base Year Current CuriBase
6 Elasticity for CET 1st) 0.60 World Price of Imports (wm) 0.89 0.89 Export Good (El 0.33 0.33 1.00
7 Elasticity for CESIQ Isq) 0.60 World Price of Exports (we) 1.01 1.01 Import Good IM) 0.60 0.60 1.00
8 _ Supply of Domestic Good (Dsl 0.67 0.67 1.00
9 Scale for CET (at) 2.22 Import Tariffs (tm) 0.13 0.13 Demand of Domestic Good (Odl 0.67 0.67 1.00
10 Share for CET (bi) 0.77 Export Duties (teo 0.01 0.01 Supply of Composite Good (Gs) 1.18 1.18 1.00
11 Rho for CET (rt) 2.67 Indirect Taxes (tol 0.08 0.08 Demand of Composite Good (0d) 1.18 1.18 1.00
12 - Direct Taxes tty) 0.03 0.03
13 Scale for CESIQ (sql 1.97 Tax Revenue ITAX) 0.20 0.40 2.00
14 Share for CES/Q Ibql 0.38 Savings rate (syl 0 17 0.17 Total Income (YI 1.13 2.26 2.00
1E Rho for CES/Q (rql 0.67 Govt. Consumption (GI 0.10 0.10 Aggregate Savings (SI 0.27 0.53 2.00
18 _ Govt. Transfers (trl 0.12 0.12 Consumption (Cn) 0.83 0.83 1.00
17 Foreign Grants (ft) 0.02 0.02 _ _ _
la Net Priv Remittances (reI 0.01 0.01 Import Price (Pm) 1.00 2.00 2.00
19 _ Foreign Saving 18) 0.08 0.08 Export PrIce (Pe) 1.00 2.00 2.00
20 Output (XI 1.00 1.00 Sales Price (PI) 1.08 2.17 2.00
%11 Price of Supply IPqI 1.00 2.00 2.00
22 Price of Output IPx) 1.00 2.00 2.00
23 _ _ __ Price of Dom. Good (Pd) 1.00 2.00 1.00
24 Exchange Rate (Er) 1.00 2.00 2.00
26 Investment (ZI 0.25 0.25 1.00
27 Government Savings ISgi *0.01 -0.02 1.00
28 _ Walras Law IZ-SI 0.00 0.00
29 _
Devara.fan-Oo-lewlis-Robleson-Slako ]9
Table 5: List of Equations in the Excel-Based 1-2-3 Model
J K L
3 = . ____ _ __ _ _ __ _ __ _ ___ _
4 Eq.# Equations
5 _ Real Flows
6 1 CET Transformation (CETEQ) =at*(bt*EA(rt)+(1 -bt)*DsA(rt))A(lrt)
7 2 Supply of Goods (ARMG) =aq*(bq'MA(_rq)+(1-bq)*DdA(-rq))A(-1/rq)
8 3 DomesUc Demand (DEM) =Cn+Z+G
9 4 E10 Ratio (EDRAT) =( (PelPd)/(bVl(1-bt)) )A( 1(rt-1))
1a 6 MID Ratio (MDRAT) =( (Pd/Pm)*(bql(1-bq)) )(11(1+rq))
11 Nominal Flows
12 6 Revenue Equation (TAXEQ) = tm*wm*Er_M + te'PeE + ts'Pq'Qd + tyY
13 7 Total Income Equation (INC) = Px*X+ tr*Pq + re*Er
14 8 Savings Equation (SAV) =sy*Y+Er*B+Sg
15 9 Consumption Function (CONS) =Y*(1-ty-sy)lPt
16 Prices
17 10 Import Price Equation (PMEQ) =Er'wm*(1+tm)
18 11 Export Price Equation (PEEQ) =Er*wel(1+te)
19 12 Sales Price Equation (PTEQ) =Pq*(1+ts)
20 13 Output Price Equation (PXEQ) =(PEIE+Pd*Ds)/X
21 14 Supply Price Equation (PQEQ) =(PmrM+Pd*Dd)tQs
22 15 Numeraire (REQ) -1
23 Equilibrium Conditions
24 16 Domestic Good Market (DEQ) =Dd - Ds
25 17 Composite Good Market (QEQ) =Qd -Os
26 18 Current Account Balance (CABAL) =wm*M - we*E -ft - re
27 19 Government Budget (GBUD) = Tax - G*Pt - tr*Pq + ft*Er
28
DevaraJan-Go-Lewi.r-Robinson-Sinko 20
3. NUMERICAL IMPLEMENTATION
As a means of evaluating economic policy or extemal shocks, general equilibrium analysis has
several known advantages over the partial approach and its numerical implementation has become
increasingly the preferred tool of investigation.", So far however, CGE models are cumbersome to build,
requiring extensive data, model calibration, and the leaming of a new and often difficult programming
language. For that reason, tl:e- partial approach still dominates practical applications because of its
simplicity. In the field of public finance, for example, it is a relatively simple affair for non-specialists to
deal with tax ratios, the projections of collection rates of taxes and their corresponding bases, and, if
necessary, to augment the analysis with estimations of tax elasticities. '7 Moreover, since only ratios of taxes
to GDP are used, the partial approach has the further advantage of requiring the least information and
offering a quick way of looking at the revenue significance of taxes. Nevertheless, using fixed ratios and
assuming zero-elasticities ignores the feedback into other markets and the division ofthe tax burden; it limits
the investigation and leads to an incomplete picture. General equilibrium analysis avoids these limitations
but the problem has been to find an easy and convenient way of doing it.
Fortunately, the simplicity of the 1-2-3 model and the availability of more powerful Windows-based
spreadshect tools for the desktop PC, like Microsoft Excelfor Windows (Excel hereafter),'8 provide appealing
and tempting alternatives for CGE modeling. These tools have built-in graphics, easy integration with other
Windows applications, and convenient access to interesting add-in programs. Being much easier to learn and
use, they make CGE analysis more accessible to economists who are otherwise discouraged by unwieldy
programming. A model based on a popular spreadsheet program can also become an effective vehicle for
"h Robinson (1989) contains a survey of CGE applications to developing countries.
X See A Prmst(1962) and R. Chclliah and S. Chand (1974) fora discussion of such an approach.
'" Mkrosoft Excel and Windows are tradcmarks of Microsoft Corporation.
Denarajan-.GaLewis-Robinson-Sinko 21
illustrative and educational purposes. While Excel is one example and hardly the only software suitable for
economic modeling, the robustness and flexibility of its solver function, which is quite capable of finding
numerical solutions of systems of linear and non-linear equations and inequalities, as well as its
userfriendliness and wide distribution make it a particularly attractive tool for potential CGE modelers.
In what follows, we describe a stepwise procedure to implement the 1-2-3 model using Excel."' We
also run a few policy simulations by applying the model to one small open economy, Sri Lanka.
3.1 The 1-2 3 Model with Government and Investment
In the previous section, the discussion of the 1-2-3 model focused on the relative price of traded
goods relative to the price of domestic goods and how this real exchange rate adjusts in response to
exogenous shocks. In order to apply the framework to a particular country however, it has to be modified
to fit real data and to handle policy issues. For example, the real exchange rate is not an instrument which
the government directly controls. Rather, most govermments use taxes and subsidies as well as expenditure
policy to adjust their economies. Nor did the previous section touch on the equality of savings and
investment which is important in bringing about macroeconomic balance or equilibrium. Table 3 presents
an extended version of the 1-2-3 model to include govemment revenue and expenditure and also savings and
investment. We make sure that the modifications introduced will conform to data that are commonly
ivailable (see calibration below.) In the new set-up, four tax instruments are included: an import tariff C,
an export subsidy f, ar indirect tax on domestic :ales t', and a direct tax rate P. In addition, savings and
investment are included. The single household saves a fixed fraction of its income. Public savings
(budgetary deficit or surplus) is the balance of tax revenue plus foreign grants and government expenditures
(all exogenous) such as government consumption and tmnsfers to households. The current account balance,
1The discussion of Excel procedurs is compatible with latest release. versmn 5. We also include in the footnotes where applicable. how to
implement the samc procedures in the previous version of Excel
Devwwa,-Go-Leww-Robinson-Sink. 22
taken to represent foreign savings, is the residual of imports less exports at world prices, adjusted for grants
and remittances from abroad. Output is fixed for reasons cited in section 2. Foreign savings is also
presently fixed, so that the model is savings-driveni; aggregate investment adjusts to aggrcgate savings.20
In sum, we have 20 equations and 19 endogenous variables. By Walrs' law however, one of the equations,
say the savings-investmcnt identity, is implied by the others and may be dropped.
3.2 Defining Model Components
Building the i-2-3 framework in Excel requircs the usual modeling steps: (1) declaration of
parameters and variables: (2) data entry; (3) assignment of initial values to variables and parameters; and
(4) specification of equations. In addition, the model has to be precisely defined as a collection of
equations; in some cases, it may require an objective function to be optimized. Finally, the solver is called
to conduct numerical simulations.
A suitable way to arrange the 1-2-3 Model in an Excel worksheet is to assign separate columns or
blocks for paramneters, variables and equations. Separate columns are assigned for the base year and
simulation values of variables. Labels and explanations for parameters, variables, and equations are easily
provided in the adjacent left column to improve readability. We also assign a block for the data set with both
initial and calibrated values displayed. Thus, we are able to arrange all necessary ingredients conveniently
on a single worksheet.
323 Variables and Pammeters
Table 4 is an example of how to organize the parameters and variables in an Excel-based model.
We separate out from the rest of the exogenous variables the parameters related to the trade elasticities; the
' In the albmative investmcn:-driven closue. aggrcgatc investment is fixed and savings adjust through foreign savings (endogenous). For a
discussion of alternative macro-closures. see the original work of Sen (1963) or the surves by Ratso (1982) and Robinson (1989).
Devarjan-Go-Lewis-Robinn-Slnko 23
trade elasticities are generally defined at the outset of an experiment and parameters such as the share and
scale values of the CES and CET functions are calibrated just once for both the base case and the current
simulation (see the calibration section below). Colurmn A provides a brief description of each parameter and
Column B lists the corresponding numerical value. The exogenous variables (described in Column C)
specify the external or policy shocks introduced in a particular experiment - their magnitudes are defined
in Column E while their base-year values are presented in Column D. Likewise, the endogenous variable3
are listed in Column F to 1. New values are computed for the endogenous variables during a simulation and
entered in Column H as Current. Column 1, Cur/Base, provides simple indices of change of the endogenous
variables.
A useful feature in Excel is the capability to define names for various model parts. This is done by
using the Name command and Defile option under the Insert menu?' The cell in B6 of Table 4, for example,
can be called by its parameter namne, st; hence, we can refer to parameters, variables, or equations by using
their defined or algebraic names instead of cell locations. By doing this, we make the model specifications
easier to read and mistakes easier to detect. To keep track of these names, it is advisable to write them out
in explanation cells adjacent to the corresponding parameters, variables, and equations. In the example
shown in Table 4, we write a short description and put in parenihesis the Excel label or name. Base year and
current values of variables are distinguished using the normal convention -in the case of export good E. for
example, the base year level is labelled as EO while E is retained for the simulated level.
3.4 Equations
The organization of the equations of our model is illustrated in Table 5. The equations are numbered
and listed (in Column J of Table 5) in the same order as Table 3. Column K of Table 5 lists the equation
descriptions and the Excel names in parentheses. The corresponding mathematical expressions are entered
1 Prior to version 5 of Excel. this is donc by using dhe Define Name comnd in te FomdJa menu.
DevarnTaj-Go-Lewis-Rohisan-Sinko 24
in Column L. In the normal mode the fornulas are hidden in the background and only the current numerical
values are evident. The formulas are easily displayed by using the Options command on the Tools menu,
selecting (or clicking) the View tab, and choosing Formulas in the Window Options box.'
In a spreadsheet like Excel, a formula is typically entered into a cell by writing out just the right-
hand side of an equation as shown in Table 5. To complete the equation, each of these mathematical
expressions has to be matched and set equal to a variable defined as above (see Solver section below).
The complicated expressions in Column L of Table 5 require some explanations. Equation I and
2, called CETEQ and ARMG in Excel, are the right-hand expressions of the CET and Armington (CES)
functions in the 1-2-3 model, which usually take the following algebraic form:
Y = A[6-X,P + (1 - 6))Z2]J
where the CES substitution elasticity a and CET transformation elasticity n are given by a = 1/(1 - p);- < p
<+1 in the CES case and 0 = 1/(p - 1); I < p < + in the CET case. In the Excel implementation, the share
parameter a are labeled as bi or bq. the exponent p as ri or rq, and the elasticities as st or sq. Equation 4,
EDRAT. is the rght-hand side of the export supply function or the first order condition of the CET function:
E (1 - [ 1)-P Q
D 8.pd
n In earlier versions of Excel. the equalions are easily unveiled by pulling down the Opt.onr menu and sclccting Formula among the
Display opoons.
Dewrrajtzn-Go-Lawia-Robinon-Sinko 25
while equation 5 (MDRA2 in Table 5 is the corresponding case (import demand function):
- = - 1
D (1 - 6d- Pa.
the dual price equations, equation 13 (PXEQ) and 14 (PQEQ), can take the following the form:
p =4' [aI(I-P) pP(P-) Oi. (1 - 65)'1-([ p) (t-p
However, in practice, it is often convenient to replace the dual price equations with the expenditure identities,
invoking Euler's theorem for linearly homogeneous functions:
x
pq = pM + pd.D
In the 1-2-3 model, the dual price equations embody the same infornation as the CET export transformation
and CES import aggregation functions. In some applications, it is convenient to include the dual price
Dearajan-Go-Lewis-Robinson-Siko 26
equations, but drop the CET and CES functions.
3.5 Calibration
Another convenient feature of the 1-2-3 framework is its modest data requirements. Data froni
national income, fiscal, and balance-of-payments accounts, those normally released by national govemments,
are sufficient To carry out the model, we used the 1991 data for Sri Lanka (Table 6). The original data were
measured in billions of rupees. In the calibration, all data were scaled and indexed with respect to output,
which is set to 1.00 in the base year (note Columns P and T). I
Table 7 and 8 show the calibration of parameters and variables. The values of the parameters and
variables are linked to the data in Table 6 so that model calibration is automatically done whenever the
elasticities or base year data are changed. In Table 7, the calibration of the exponents, r and rq, of the CET
and CES fimctions (in Cells Bl land BI5} follows the discussion of the equations above. Given the base-
year values of the exports EO, imports MO, and domestic good DsO or DdO, the share parameters bt and bq
are calculated using the formulas in Cells BiD and B14; these are derived from the input demand functions
of CET and CES functions (see equation section above), respectively. The scale parameters at and aq are
computed from the CET and CES functions directly in Cells B9 and B13, respectively. An alternative
procedure for calibration is to fix the variables and ask Excel to solve for parameter values that satisfy the
base year equilibrium. Thus, one need not derive explicit formulas for the parameters, which is a useful
property when dealing with more complicated functional forms.
1RHowevcr. calibration needs t be mepeated very timc dwt dasticitics or base-year data arm alLcred.
Deyaraan.GoLewis-Robiason-SJn 27
Table 6: Data in the Excel-Based 1-2-3 Model
M N 0 P Q R S T
3 - _ __ _ __ ___ -__ _ _ _ =__ _ _ _ -__ _ _ _ _ _ __ _ _ _ _ _ _ _ ---- . -
4 Data - Sri Lanka, 1991 . _ ---- _
a6 I Rs Billion Output=1 R_s Billion Output=1
6 National Accounts 3 Fiscal Account
7 1 Output (Value Added) 324.69 1.00 Revenue 76.18 0.23
8 _ Wages 163.32 0.50 NonTax 8.02 0.02
9 _ _ Current Expenditure 83.76 0.26
10 GDP at market prices 375.34 1.16 Goods & Services 35.58 0.11
11 _ Private Consumption 291.69 0.90 Interest Payments 22.07 0.07
12 PubIUc Consumptlon 35.58 0.11 Transfers & Subsidies 26.10 0.08
13 Investment 86.38 0.27 _ Capital Expenditure 3517 0.11
14 Exports 106.39 0.33 Fiscal Balance -43.35 -0.13
15 Imports 144.7 0.45
16 _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ _ _ ___ _ _ _ _ _
17 Tax Revenue 4 Balance of Payments
18 2 Sales & Excise Tax 32.03 0.10 = Exports - Imports -38.32 -0.12
19 _ Import Tariffs 18.62 0.06 = Net Profits & Dividends -0.78 0.00
20 _ Export Duties 1.14 0.00 _ Interest Payments -8.82 -0.03
21 _ Payroll Tax 0.00 0.00 Net Private Transfers 11.60 0.04
22 Personal Income Tax 3.54 0.01 Net Official Transfers 7.90 0.02
23 _ Capital Income Tax 12.84 0.04 Current Account Balance -28.42 -0.09
24 _ Total 68.16 0.21 .
25 _ _ External Debt 260.50 0.80
26 _ Debt Service Payments 20.21 0.06
27 _ _ _
Devarajan-Go-Lew#z-Robin.on-Sinko 28
Table 7: Calibration of Parameters In the Excel-Based 1-2-3 Model
A B
4 Parameters
6 Elasticity for CET (st) 0.6
7 Elasticity for CES/Q (sq) 0.6
8 _
9 Scale for CET (at) Xbt)Ds
10 Share for CET (bt) =11( 1+(PdO/PeO)*(EO/DsO)A(rt-1))
11 Rho for GET (rt) =1/st + 1
12
13 Scale for CESIQ (aq) =QsO/( bq*MOA(-rq)+(1-bq)*DdOA(-rq) )A(-1Jrq)
14 Share for CES/Q (bq) ( (PmO/PdO)*(MO/DdO)A(1+rq) )I( 1+ (PmO/PdO)*(MO/DdO)A(1+rq))
15 Rho for CES/Q (rq) = 1/sq -1
16 29
Deawraapn.Co.LeifIs.Robftuon.Sfnko 2D
Table 8: Calibration of Variables in the Excel-Based 1-2-3 Model
a D E F
. 3 ._ _ _ _ _ _ _ _ _ _ _ __ ___ _ _ _ _ _ _
4 Exagenous Variables Base Year Current Endogenous Variables Base Year
6 ___ _ _ __ _ _ _-__ _ _
6 World Price of Imports (wm) =PmO/ErO/(1 +tmO) =wmO Export Good IE) =P14
7 World Price of Expons (we) -PeO (1 +teOl)ErO =weO Import Good (MI =P15 + P19
8 _______________________ _______ Supply of Domestic Good IDs) - 1 -EO
9 Import Tariffs itm) =0191015 =tmO Demand of Domestic Good (Idl -OsO
10 Export Duties (te) =0201014 =teO Supply of Composite Good 10s) =MO + DdO
11 Indirect Taxes its) =Pl8/QsO -tsO lemand of Composite Good (0d) =aSo
12 Direct Taxes (tyl -SUM(P21IP23U1YO =tyc I
13 _Tax Revenue (TAX) -tmO'wmO MOErO+teOgPeO'EO+tsO'PqO QdO+tyOYO
14 Savings rate (sy) =IYO - CnOIPqO II +tsO) - ty YO)tYO -syO Total Income IY1 - PxO XO + trO@PqO + reO'ErO
16 Govt. Consumption IG) =P12111 + tsO)lPqO =GO Aggregate Savings (SI =SY0VO + ErOBO + SgO
16 Govt. Transfers (trl =(T1 1 + T12-T8)lPqO -trO Consumption (Cn) lPi IPiD
17 Foreign Grants (ftl -T22tErO -ftO
IB Net Priv Remittances Ire) =SUM(Tl9.T21JIErO =reO Import Price IPm) 1
19 Foreign Saving IB) -wmOMO - woO EO - ItO - reO]JErO =80 Export Price (Pel 1
20 Output (Xt f =XO Sales Price (Pt) -PqO 11 +tsO)
21 _ Price of Supply (Pqg )
22 _ Prlce of Output IPx) l
23 _ Price of Dom. Good (Pd) 1
24 Exchange Rate (Er) 1
26 __ _ _ _ _ _ _ _ ____
26 _ Investment (Z) =Pl3lPtO
27 Government Savings ISgi - TaxO - GOPtO - trO*PqO + ftO-ErO
28 ___________________ ___________________________ W alras Law tZ-Sl -ZO'PtO- SO
29 - _
Devarajan-Go-Levfs.RobEwson-Sinko 30
3.6 Solving the Model
llsrto 1:EclsSle
E-M,Ds.Dd.Qs.0d.Tox-Y.SSC.Cm P,PlPPe.
CNS_11 = Cn
DEM - Od 3 _
llustrationl1: Excel's Solver
Excel's solver is capable of solving a system of non-linear equations. The first step is to delineate
parts of the worksheet that make up the model and specify the problem for Excel solver. This is done by
selecting the Solver command from the Tools menu in Excel.24 A Solver Parameters dialog box will appear
on the screen (Illustration 1). Like in GAMS,Z another numerical modeling software, Excel solves the model
as an optimization or programming problem. In the Set Target Cell space, at the top ofthe dialog box, the
name of the variable that is being maximized (max option) or minimized (min option) in the objective
function may be entered. We select the consumption variable CN in this case but this has no effect in a CGE
application since there will be as many variables and equations. The space may also be left empty. The
optimal' solution is found By Changing Cells, where all the endogenous variables in the model are entered
using their namnes or cell locations, and Subject to the Constraints, where all equations and non-negativity
24 Prior o version 5. this is done by selecting die Solver command from the Formula menu in Excel
2' GAMS sads for the General Algebraic Modding System. See Brooke, Kenduick. and Mecraus (1988).
D1evrarjar-Go-Lewis-Robinxn-Sinko 31
constraints of the model are listed. The Add option in the dialog box allows us to specify the equations and
constraints one at a time. For example, the line highlighted in Illustration I matches the mathematical
expression of the Armington function to total supply (ARMG=Q), which corresponds to the first equation
of our model when arranged alphabetically.
The Options command in the Solver Parameters menu controls the solution process. The Options
command lets one adjust the maximum iteration time and tolerance level as well as choose the appropriate
search method. In the model, we used the Newton solution algorithm that proved out to be robust and fast.
Average time for solving simulations with a 486/33 PC was around 10 seconds.
The model is run by choosing the Solve command. The solver starts iterating and the number of trial
solutions appear in the lower left part of the worksheet. Once a solution that satisfies all the constraints has
been found, the solver stops and displays a dialog box for showing the results. A variety of ways for
reporting the outputs is possible. One can now choose between displaying the solutiorn values on the
worksheet or restoring the original values (initial guesses) of variables. Also, one may choose the option
that produces both the original values and solution values. If there is no shock and the model is correctly
calibrated, one should find a solution where all the variables equal their base year values within the fined
tolerance3' For example, 033, the base-year value of EO (export good) in Cell G6 in Table 4, is entered
as the initial guess orcurrentvalue forthe variable E in CellH6. It is important to entersome feasible initial
guesses for current values of variables before starting the solver. An empty cell is interpreted as zero, which
is frequently an infeasible value for a variable.
^ A good away of stsing the mokdl is to maximize and minimize the objective variable, which should produce identical soludons in a gncrid
equilibrium framework.
Devaanan.Go-Lrwis-Robirson-Sinka 32
3.7 Simulations
To test the model, we conduct two experiments. The first is a trivial case -- we double the nominal
exchange rate, which is our numeraire. This is done by changing the right-hand side of equation 15 from
1.0 to 2.0 as shown in the cell L22 in Table 5. After the experiment is run, the results are shown as the
current values of the variables in Column H of Table 4. As expected, all prices and incomes double while
all quantities remain the same.
Next, we look at one important tax policy issue in developing countries - the fiscal/revenue
implications of a tariff reform. Tariffs are a significant source of public revenue in many developing
countries. In Sri Lanka, about 28 percent of tax revenue came from import duties in 1991. Therefore, the
potential revenue losses of a tariff reduction in any attempt toward trade liberalization has to be offset by
other revenue sources so as to prevent the balance of extemal payments from deteriorating.?7 In the
experiment, we set the tariff collection rate to 0.05 (down from 0.13 in the base year) and ask by how much
the domestic indirect taxes need to be raised to maintain the current account deficit fiom deteriorating, while
keeping the same level of productive investment in the economy. To do this, we simply replace investment,
Z, with the sales tax, ts, in the variable list and run the 1-2-3e model again. To attain the policy objective
above, we find that sales and excise taxes need to be raised by about 33 percent (from the current rate of 0.08
to 0.11 in cells G25 and h25, respectively, in Table 9). This figure of course depends, among others, on the
degree of substitution possibilities between imports and domestic goods. Due to the 'automatic' calibration
embedded in the worksheet, it would be straightforward to test the sensitivity of the results on alternate value
of critical parameters by just entering newv estimates to the corresponding cells.
" Greenaway and Milncr(1991) and Mitm (1992) discuss the substitution ofthe domestic and btade taxes in gracr dctails
Devarajan-Go-Lewis-Robinson-Sinka 33
Table 9: Coordinated Tariff and Tax Reform
F G H I
3 _ _
4 Endogenous Variables Base Year Current CurlBase
5ll
6 Export Good (E) 0.33 0.33 1.02
7 Import Good (M) 0.50 0.51 1.01
8 Supply of Domestic Good (Ds) 0.87 0.67 0.99
9 Demand of Domestic Good (Dd) 0.67 0.67 0.99
10 Supply of Composite Good (Qs) 1.18 1.18 1.00
11 Demand of Composite Good (Qd) 1.18 1.18 1.00
12 X _
13 Tax Revenue (TAX) 0.20 0.19 0.95
14 Total Income (Y) 1.13 0.10 0.97
15 Aggregate Savings (S) 0.27 0.26 0.98
16 Consumption (Cn) 0.83 0.83 1.00
17
18 Import Price (Pm) 1.00 0.93 0.93
19 Export Price (Pe) 1.00 1.00 1.00
20 Sales Price (Pt) 1.08 1.05 0.97
21 Price of Supply (Pq) 1.00 0.95 0.95
22 Price of Output (Px) 1.00 0.97 0.97
23 Price of Dom. Good (Pd) 1.00 0.96 0.96
24 Exchange Rate (Er) 1.00 1.00 1.00
25 Indirect Taxes (ts) 0.08 0.11 1.33
26 Investment (Z) 0.25 0.25 1.00
27 Government Savings (Sg) -0.01 -0.01 1.10
DevaraJan-Go.-Lewl-Robinson-Sinko 34
4. CONCLUSION
This paper shows how two-sector models can be used to derive policy lessons about adjustment in
developing countries. Starting from a small, one-country, two-sector, three-good (1-2-3) model, we show
how the effects of a foreign capital inflow and terms-of-trade shock may be analyzed. In particular, we
derive the assumptions underlying tde conventional policy recommendation of exchange rate depreciation
in response to adverse shocks.
We also implemented die model using a popular spreadsheet software, Excel, and by using widely
available data. While Excel is not suitable for all type of tax or CGE models and certainly other programs.
like GAMS, offer greater capability and indexing ease (e.g. over sectors or time), it is simple to use and a
great way to get started. Add-in programs also extends its potential in new directions; for example, it is
possible to add the element of uncertainty over critical parameters (e.g., trade elasticities) or exogenous
shocks (e.g. the collapse of an export market like the CMEA trade) by performing risk analysis and Monte-
Carlo simulations."
The models in this paper present a stylized picture of how developing economics function. They
are useful for qualitative analysis. However, policymakers are also concerned with the magnitude of the
response to their initiatives. Furthermore, they require models that incorporate the more distinctive structural
and institutional features of their economies. The lessons drawn from this paper will facilitate the
interpretation of results from more complex models, since these are essentially multisectoral analogues of
the small models developed here.
zSec, for example. Go (1994).
Devarajan-Go-Lewis-Reobinson-Sinko 35
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