BACK OF THE ENVELOPE (BOTE) MODEL FOR ONE COUNTRY
TWO FACTORS AND FOUR COMMODITIES (124) WITH MATHS
APPENDIX SHOWING HOS ORIGIN AND 123 ALTERNATIVE
Paper originally presented at
16th
Annual GTAP Conference
June 12-14, 2013
Shanghai, China
Penultimate draft
David Evans
Sussex European Institute
University of Sussex
Niyati Ghelani
Independent Researcher
Calcutta
September 2013
Table of Contents
LIST OF ACRONYMS 4
1. POVERTY IMPACT OF MACROECONOMIC SHOCKS AND POLICIES 6
1.1 A LITTLE HISTORY 6
1.2 BUILDING BLOCKS REQUIRED 6
1.3 THE AVAILABLE BUILDING BLOCKS 7
(i) Household Surveys 7
2
(ii) CGE Models 7
(iii) Macroeconomic Models 7
(iv) Article IV Macroeconomic Projections 8
(v) Our Work to Date 8
(vi) New Applications of the DSGE Model 9
1.4 USING CGE MODELS TO ASSIST IN POLICY MAKING 9
1.5 OVERVIEW OF THE PAPER 9
2. THE 124 BOTE, 123 HOS AND 123 PRSP MODELS IN A COMPARATIVE CONTEXT 11
2.1 PRODUCTION TREE FOR THE 124 BOTE MODEL 11
DIAGRAM 1: PRODUCTION TREE FOR THE 124 BOTE MODEL WITH COMPLETE SPECIALISATION 13
2.2 PRODUCTION TREE FOR THE 123 HOS MODEL 14
DIAGRAM 2: PRODUCTION TREE FOR THE 123 HOS MODEL WITH INCOMPLETE SPECIALISATION 15
2.3 PRODUCTION TREE FOR THE 123 PRSP MODEL 15
DIAGRAM 3: PRODUCTION TREE FOR THE 123 PRSP MODEL 17
3. THE 124 BOTE, 123 HOS AND 123 PRSP MODELS IN DIAGRAMS 18
3.1 THE INITIAL EQUILIBRIUM OF THE 124 BOTE MODEL 18
DIAGRAM 4A: INITIAL EQUILIBRIUM OF THE 124 BOTE MODEL 19
PRODUCTION POSSIBILITY FRONTIER IN 3 DIMENSIONS 19
DIAGRAM 4B: INITIAL EQUILIBRIUM OF THE 124 BOTE MODEL 22
CONSUMPTION POSSIBILITY FRONTIER IN 3 DIMENSIONS 22
DIAGRAM 4C: INITIAL EQUILIBRIUM OF THE 124 BOTE MODEL 24
CONSUMPTION POSSIBILITY FRONTIER WITH MORE DETAIL 24
DIAGRAM 4D: INITIAL EQUILIBRIUM OF THE 124 BOTE MODEL 25
CONSUMPTION POSSIBILITY FRONTIER IN 2 DIMENSIONS 25
DIAGRAM 4E: THE INITIAL EQUILIBRIUM OF THE 123 HOS MODEL 27
PRODUCTION POSSIBILITY AND CONSUMPTION POSSIBILITY FRONTIERS 27
DIAGRAM 4F: THE INITIAL EQUILIBRIUM OF THE 123 PSRP MODEL: CONSUMPTION POSSIBILITY
FRONTIERS 28
3
4. IMPACT EFFECTS OF IN THE 124 BOTE MODEL 29
4.1 IMPACT EFFECTS OF INCREASING FSAV IN 123 BOTE MODEL 29
DIAGRAM 5A: CONSUMPTION POSSIBILITY FRONTIER WITH FSAV AND NO NON-TRADABLE GOODS 30
DIAGRAM 5B: CONSUMPTION POSSIBILITY FRONTIER WITH FSAV AND NON-TRADABLE GOODS 31
DIAGRAM 5C: CONSUMPTION POSSIBILITIES FRONTIER IN 2 DIMENSIONS WITH FSAV 32
DIAGRAM 5D: EQUILIBRIUM PROPORTIONS OF COMPOSITE GOOD ON IMPORT SIDE WITH FSAV 33
4.2 IMPACT EFFECTS OF TERMS OF TRADE (TOFT) IMPROVEMENT IN 124 BOTE MODEL 34
DIAGRAM 6A: CONSUMPTION POSSIBILITY FRONTIER WITH TOFT CHANGE AND NO NON-TRADABLE GOODS 35
DIAGRAM 6B: CONSUMPTION POSSIBILITY FRONTIER WITH TOFT CHANGE AND NON-TRADED GOOD 36
DIAGRAM 6C: CONSUMPTION POSSIBILITIES FRONTIER IN 2 DIMENSIONS WITH TOFT IMPROVEMENT 37
DIAGRAM 6D: EQUILIBRIUM FOR IMPORTS AND DOMESTICALLY TRADABLE GOODS WITH TOFT CHANGE 37
4.3 OTHER IMPACT EFFECTS – TECHNICAL CHANGE AND CHANGE IN UNEMPLOYMENT IMPROVEMENT38
4.4 MEASURING THE REAL EXCHANGE RATE 38
5. RESULTS FROM THE 124 BOTE MODEL SUMMARISED 39
(i) Increased Foreign Savings 39
(ii) Favourable Terms of Trade Effects 39
6. CONCLUSIONS 40
REFERENCES 41
APPENDIX 44
A.1 THE MATHEMATICAL STRUCTURE OF THE 124 BOTE MODEL 44
A.1.1 WELFARE FUNCTION 44
A.1.2 EXPORTS AND THE DOMESTIC TRADABLE GOOD 45
A.1.3 IMPORTS AND THE DOMESTIC TRADABLE GOOD 46
A.1.4 PRODUCTION SIDE 47
TABLE A1: ALL VARABLES AND PARAMETERS 49
4
List of Acronyms
124 BOTE
One country, 2 factors, 4 commodities BOTE model
123 HOS
One country, 2 factors, 3 commodities HOS model
123 PRSP One country, 2 factors, 3 commodities PRSP model
BOTE
BOTE
BOTE
Back of the Envelope
CARIS Centre for the Analysis of Regional Integration at Sussex
CES Constant Elasticity of Substitution
CET Constant Elasticity of Transformation
CFA Comprehensive Framework of Action
CGE Computable General Equilibrium
CPI Consumer Price Index
DfID Department for International Development
DSGE Dynamic Stochastic General Equilibrium
ECF Extended credit Facility
EDRI Ethiopian Development Research Institute
ERCA Ethiopian Revenues and Customs Authority
ESF Exogenous Shocks Facility
FAO Food and Agriculture Organisation
FSAV Foreign Savings
GDP Gross Domestic Product
HOS Heckscher-Ohlin-Samuelson
IDS
Institute of Development Studies
IFPRI International Food Policy Research Institute
5
IFS International Financial Statistics
IMF International Monetary Fund
IMMPA Integrated Macroeconomic Models for Poverty Analysis
LHS Left Hand Side
LIC Low Income Country
LTO Large Tax Payers Office
MPS Marginal Propensity to Save
PPF Production Possibility Frontier
PRGF Poverty Reduction and Growth Facility
PRSP Poverty Reduction Strategy Papers
RHS Right Hand Side
SAM Social Accounting Matrix
TofT Terms of Trade
UN United Nations
UNDP United Nations Development Programme
UNICEF United Nations International Children's Emergency Fund
WEO World Economic Outlook
WFP World Food Program
6
1. Poverty Impact of Macroeconomic Shocks and Policies
1.1 A Little History
Since the Bretton Woods Agreement in 1944, the IMF has predominantly focussed on the
short and medium term financial stability of its member countries and of the global economy
whereas the World Bank has focussed on long term economic development and poverty
alleviation. Since 1999, the two institutions have come together to promote poverty reduction
through the Poverty Reduction and Growth Facility (PRGF), which is framed around
comprehensive, country-ownedPoverty Reduction Strategy Papers (PRSPs). The PRGF was
succeeded by the Extended Credit Facility (ECF) as the Fund‟s main tool for providing
medium-term support to Low Income Countries (LICs). Historically, there has been
widespread criticism of the IMF for the poverty impact of its structural adjustment policies
and more recently of its poverty alleviation strategies under the PRSP/ECF facility. Typically,
such poverty alleviation strategies take place in the context of macroeconomic shocks and
policies. Yet, no agreed methodology has been developed tosystematise the measurement of
poverty impacts of macroeconomic shocks and policies, or to improve the choice of
macroeconomic policies with a view of poverty alleviation. Recently, the IMF has focussed
its attention on new macroeconomic research on growth rather than poverty reduction (see
IMF-DfID, 2012).The two objectives are not necessarily complementary so that it makes
sense for poverty reduction to remain the primary objective against which macroeconomic
policies should be assessed. Some of the policy issues for which new research is needed
arediscussed below.
1.2 Building Blocks Required
There are three modules required for developing the capacity of measuring the poverty
impacts of macroeconomic shocks and policies. These include:
(i) A macroeconomic model that has the capacity to translate macroeconomic shocks
and policies into projected impacts on the macro economy, starting from the effect
on the macroeconomic aggregates such as private household income and
expenditure, government income and expenditure, savings and investment, foreign
savings, to imports and exports.
(ii) An economy-wide model that solves over time with the capacity to translate
macroeconomic shocks and policy impacts on macroeconomic aggregates into
disaggregated impacts on- inputs and outputs, household income and expenditure,
government income and expenditure, savings and investment and foreign savings.
(iii) A good database for constructing the macroeconomic and economy-wide models
for measuring poverty impacts.
Some of the capacities and datasets required for building a macro economy-wide module of
poverty impact analysis of macroeconomic shocks and policies are available in the World
Bank and/or the IMF, but not all of them are integratedinto a macro economy-wide database
to support modelling for poverty impact analysis.
7
1.3 The Available Building Blocks
(i) Household Surveys
Central to poverty analysis is the ready availability of disaggregated household
surveys for developing and low income countries, provided by the World Bank.
However, most World Bank poverty analysis is built around household surveys
usingsectoral or partial equilibrium methods. A sectoral approach is perfectly
justifiable for some purposes but not suitable for our purpose without integration
into a Social Accounting Matrix (SAM)suitablefor modelling economy-wide
analysis.
(ii) CGE Models
A substantial amount of economy-wide Computable General Equilibrium
(CGE)modelling in both comparative static and recursive dynamic mode has been
carried out at the World Bank but usually with no short-run macroeconomic
component. For example, the studies by Bourguignonet al (2003, 2008) are
important for long-run economy-wide analysis of inequality.
The recursive-dynamic version of CGE models have a standard static CGE model
base year from which forward projections are made for the next period. Next
period projections are for variables such as investment and for key exogenous
variables such as world prices so that a new solution to the model can be found. In
this way, each period is the platform from which projections are made for the next
period until the desired number of years is reached.
There are also country specific macroeconomic models for low-income countries
with a poverty impact facility such as Agénor et al eds (2007, Ch5) that have
developed independently but with World Bank assistance. These models have
useful components which could be adapted for use in other models, such as labour
market and public investment specifications. However, the modelling of the
financial system for archetypal low income countries within one model is
expensive. Also, itis not connected to the operational work of the IMF as in
Article IV reports, therefore missing the immediacy of links with IMF
macroeconomic policies.
(iii) Macroeconomic Models
At the IMF, there is a large body of regularly published macroeconomic
projections in the country Article IV reports, prepared using a Financial
Programming Framework. These projections are consistent and are made by IMF
staff in conjunction with the relevant representatives from each country but have
no behavioural determination.More recently, the research department at the IMF
has prepared a series of background studies on low income African countries
using Dynamic Stochastic General Equilibrium (DSGE) models(see Berg et al.,
2006). The background DSGE models have been followed up by an on-going
research project (IMF-DfID, 2012). The application of DSGE models to LICs is
new. The CGE models discussed under (ii) above largely rely on cross-section
econometric analysis for the estimate of parameters. The DSGE models use pre-
base year data for time series econometric estimates of model parameters,
includingforward-looking expectations. The DSGE models generate equilibrium
8
projections form and measure policy impacts as a deviation from the projected
equilibrium results. In the early background DSGE studies, the economy-wide
component of poverty impact analysis was rudimentary.
(iv) Article IV Macroeconomic Projections
Perhaps the most interesting project from our point of view is the work of
Devarajan and Go (1998, 2003) at the World Bank which links the IMF Article IV
macroeconomicprojections to a miniature CGE model called the 123 PRSP
model.The 123 model refers to one country, two factors and three goods- a
domestic tradable good, an export good and an import good. Devarajan and Go
emphasise the capacity of the 123 PRSP model to estimate changes in the real
exchange rate in response to macroeconomic shocks and policies, a key variable
for transmitting macroeconomic shocks and policies into a poverty response.
Unfortunately, the absence of a non-traded good means that real exchange rates
cannot be estimated by the 123 PRSP model as normally conceived in
international trade theory. See Evans (1989) for a summary of a standard
Heckscher-Ohlin-Samuelson (HOS) trade model with a non-traded good. See
also,Salter (1959) and Swan (1960).
(v) Our Work to Date
In our work to date, we have found it useful to draw on the rich Article IV
macroeconomic projections for the short and medium run. An Ethiopian example
combining Article IV macroeconomic projections with a large SAM-based CGE
model has been carried out (Evans and Ghelani, 2012) for estimating poverty
impacts of macroeconomic shocks and policies. We have also found it useful to
develop a 124 BOTE miniature model (Back of the Envelope, one country, two
factors and four goods), which captures the essence of our larger Ethiopian
example by making a correct specification of non-traded goods in the
measurement of the real exchange rate in a single country CGE model.
The124 BOTE model lays bare the HOS and 123 PRSP model roots for a single
country model. The miniature 124 BOTE model can also be thought of as the
fundamental building block which assists in the choice of the CGE model size and
the associated SAM for developing further applied examples in this area and
which helps interpret the results of a larger single country CGE model. For
example, the dramatic growth of minerals exports in low income African countries
leads to an appreciation of the real exchange rate and possibly strong Dutch
Disease effects. The extent to which the 124 BOTE model can be disaggregated
for particular country applications is an empirical matter. Labour force and
household disaggregation govern the extent to which the particular country models
can capture inequality and the poverty impact of macroeconomic shocks and
policy changes.
There is much more to building the 124 BOTE model than to compare it with
models long consigned to the history of economic thought. A clear and accurate
miniature 124 BOTE model provides insights into the role of non-tradable goods
in single country CGE models. Think of the new mineral finds in Africa or the
dramatic expansion of shale oil production in the US and the consequent Dutch
9
Disease effects that follow. The analytical strength of the 124 BOTE model means
that it can be used to help at many levels in new research in this area.
(vi) New Applications of the DSGE Model
The proposed new applications of the DSGE model in (IMF-DfID, 2012) will
generateprojections of key macroeconomic aggregates for the African LICs
covered in the new research. These projections could be linked to our CGE models
to obtain poverty impacts of macroeconomic shocks and policies along side
poverty impacts estimated using Article IV projections. Such comparative poverty
impact results should enrich the findings of the DSGE class of models.
1.4 Using CGE Models to Assist in Policy Making
All of the models discussed above provide the policy maker with the empirical basis for
“what if” policy experiments. Just how good the policy making process will be depends on
the quality of the data, the appropriateness of the model, the skills of the modeller and the
quality of the interaction between modeller and the policy making process. There are several
advantages from using a recursive dynamic CGE model linked to Article IV type projections.
(i) The recursive dynamic model is a structural model which through the data used
(household surveys, input/output tables and much else) keeps the modeller and
those in the policy process closely in touch with the real economy in the base year
and in projections.
(ii) Recursive dynamic models use the actual base year as the primary basis from
which forward projections of the model economy are made. The real economy
projections are the benchmark against which macroeconomic shocks and policy
experiments are assessed. This contrasts with the DSGE model, which generates
equilibrium projections from which macroeconomic shocks and policies are
assessed.Given the increasing frequency of crises in the global economy over the
last forty or so years, it is more and more difficult to argue that the quantities and
prices observed in the real economy are in equilibrium. Also, the estimated
equilibrium in the DSGE models of LICs built has a weak representation of the
economic structure of an economy.
(iii) DSGE models use forward looking expectations which are notoriously difficult to
reliably measure and estimate.
(iv) An important advantage of relying on the Article IV macroeconomic projections
at this stage of development of research in this area is the accessibility and
simplicity of the methodology for generating and testing alternative
macroeconomic policies within LIC countries and by other stakeholders.
1.5 Overview of the Paper
In section 2, the 124 BOTE model is presented and compared with its HOS and 123 PRSP
model roots using productiontree diagrams. In section 3, the 124 BOTE model is presented in
3-dimensional and 2-dimensional diagrams for an initial equilibrium and compared with an
initial equilibrium in the 123 HOS and 123 PRSP models. In section 4, the initial equilibrium
in the 124 BOTE model is displaced by an increase in foreign savings, FSAV and terms of
trade, TofT. The 3-dimesnional diagrams in sections 3 and 4 will be familiar to those readers
with a trade-theory background. Where possible, the mathematical derivation of the slopes of
10
functions based on the mathematical appendix will be given and motivated with words. The
impact effects of the increased FSAV and TofT on economic welfare, the real exchange rate
and poverty are shown diagrammatically. Section 4 ends with a discussion of the impact
effects of technical change, changes in unemployment, measuring the real exchange rate and
on empirical application of the 124 BOTE-type models. The full 124 BOTE model is
presented in the Appendix using a general mathematical formulation.
11
2. The 124BOTE, 123 HOS and 123 PRSPModels in a
Comparative Context
2.1Production Tree for the 124 BOTE Model
The 124 BOTE model is completely specialised except that each tradable sector has two-way
trade. It reduces a large open single country CGE model to a series of 3 and 2-dimensional
diagrams which have a strong affinity with the typical HOS trade theory diagrams. Similarly,
Dixon and Rimmer (1999) reduce the results of indirect tax changes obtained from a large
dynamic recursive CGE model to 2-dimensional BOTE supply and demand diagrams. The
Dixon and Rimmer calculations derive their usefulness from the fact that their BOTE results
closely approximate the empirical results of their larger model which can be readily
understood by policy makers. The usefulness of the diagrammatic form of the 124 BOTE
model arises from its capacity to explain the strategic results of a large single country CGE
model analytically using 3 and 2-dimensional diagrams. At some later date it should be
possible to construct an empirical version of the 124 BOTE model to use in conjunction with
a larger single country CGE model.
Another feature of the124 BOTE models is that the key 3-dimensional diagrams can be
reduced to more familiar 2-dimensions. In addition, the HOS model can be illustrated as a
special case of the 124 BOTE model. As is well known, empirical trade models tended
towards complete specialisation, for example, the Ricardian model by Evans (1972). The
same tendency arises with HOS models where the number of goods is very much larger than
the number of factors; see for example Evans (1972). Dixon et al (1977, 1982) was the first to
use Armington functions to eliminate the drive towards complete specialisation in a large
open single country CGE model. Similarly, the 123 PRSPmodel can be shown as a 2-
dimensional reduction of the 124 BOTE model without a non-traded good.
Diagram 1 below shows the production tree of the 124 BOTE model. First, at the lowest
level, capital and labour are used in the tradable and non-tradable sectors to produce the
tradable and non-tradable sector goods using constant returns to scale production functions.
The RHS of the bottom level shows the supply and demand conditions for labour and capital.
On the next tier, the LHS shows the output of the tradable sector, the composite good,
madeup of exports, and the domestic tradable good, via the composite good disaggregation function referred to as the composite good on the export side. Within the
tradable sector, , the export good, subtitutes imperfectly with the domestic tradable
good, .The penultimate tier shows the aggregation of the domestic tradable good and
imports, and , into the domestic demand composite, , referred to as the
composite good on the import side. The import good, substitutes imperfectly with the
domestic tradable good, . The balance of payments is shown on the RHS of the export and
import entries. At the final level of the production tree, the composite good on the import
side, and the non-tradable good, combine to produce country welfare. The upper RHS entry shows the real exchange rate as used in the theory of international trade where there are
non-tradable goods, the price of non-tradable goods relative to the price of the tradable sector
output. The number of tradable sectors in the 124 BOTE model can be increased without
12
increasing the tendency of complete specialisation, since, with the composite goods specified
on the export and import side, each additional sector will have two-way trade.
13
Diagram 1: Production Tree for the 124 BOTE Model with Complete
Specialisation
14
2.2 Production Tree for the 123HOS Model
Diagram 2 shows the standard HOS model with two tradable and one non-tradable good and
two factors of production. The key difference between the 123 HOS model and the 124
BOTE model is the degree of substitutability between (i) export goods and domestic tradable
goods, and between (ii) imports and domestic tradable goods. In the 124 BOTE model, within
the same sector, export goods and domestic tradable goods are imperfect substitutes.
Similarly, imported goods and domestic tradables are imperfect substitutes. In contrast, in the
standard HOS trade model, within the same sector, export, domestic tradable and import
goods are identical and are therefore perfect substitutes. When both tradable goods are
producedin the 123 HOS model there is incomplete specialisation and the real exchange rate
varies as resources shift between the tradable goods production and non-tradable goods
production. The final pattern of trade depends upon the pattern of demand. With complete
specialisation in the 123 HOS model, non-tradable goods are produced together with one or
other of the traded goods. Thus, for any sector, the 124 BOTE-type models will generate two-
way trade, whereas the 123 HOS type models have a tendency towards complete
specialisation. Second, for any sector, exports, domestic tradable goods and imports are
imperfect substitutes in the 124 BOTE model, while these are perfect substitutes in the 123
HOS model. The structure of Diagram 2 is similar to Diagram 1. With two traded goods, it is
assumed that good 1 is always the exported good and good 2, the imported good.The first
level shows the allocation of the two factors to each good and the second level shows the
demand for each good. The balance of payments is shown on the RHS together with the real
exchange rate. Note that, is a trade-weighted average world price of the traded goods that enters the expression for the real exchange rate. Finally, the top level shows the welfare
function where each of the three goods contribute to economic welfare. The real exchange
rate varies as the resources shift between the tradable and non-tradable goods. With many
more tradable goods than factors, a high degree of specialisation is likely in the
multidimensional HOS model.
The production tree for the 123 HOS model shown in Diagram 2 is for the case of incomplete
specialisation. The 124 BOTE and the 123 HOS models look very similar in the production
tree forms, however, the difference arises from the composite good functions on the export
and import side of the 124 BOTE model. In the 124 BOTE model, the domestic tradable good
and the export good are substitutes on the production side. Similarly, the domestic tradable
good and the imported good are substitutes on the consumption side. Thus, the composite
good functions allow the 124 BOTE model to include 4 goods including 1 non-tradable good,
and 2 factors with 2-way trade in each tradable sector, whereas the HOS model with 3 goods
including 1 non-tradable good has a tendency towards complete specialisation so that the
importable good will not normally be produced, reducing the 123 HOS model shown in
Diagram 2 to a 122 HOS model.
15
Diagram 2: Production Tree for the 123 HOS Model with Incomplete
Specialisation
2.3 Production Tree for the 123PRSP Model
The production tree for the 123 PRSP model, which is from Devarajan and Go (2003), is
shown in Diagram 3 below. It is clear from the comparison of the 124 BOTE and the 123
PRSP models in Diagrams 1 and 3 that models are identical except the latter has no non-
traded good and therefore no real exchange rate as used in trade models. Further, the 123
PRSP model does not reflect what is actually done in the large single country CGE models. In
the absence of a real exchange rate as defined in trade theory, Devarajan and Go suggest the
ratio of the price of composite good on the import side over the price of exports/imports,
⁄ or ⁄ as measures of the real exchange rate. Neither price ratio has
anything to do with the real exchange rate as normally defined in trade theory, the 124 BOTE
model or standard single CGE models. The multi-sector extensions of the 123 PRSP model
treats sectors with low Armington elasticities as being “semi-tradables”. The sizes of the
composite good elasticities on the import side or Armington elasticities have nothing to do
16
with the tradability but indicate the extent to which imports are substitutable with domestic
tradable goods. When defining non-tradable goods it is better to define them as those goods
or sectors for which there are no imports at all. For modelling, it is better to let the data speak
when distinguishing between tradables and non-tradables. The share of production that is
tradable varies greatly between economies where small economies tend to have small shares
of non-tradable goods and large economies tend to have much larger shares of non-tradables.
For example, in our Ethiopian example (Evans and Ghelani, 2012), the share of non-traded
production is about 30%. Dixon and Rimmer report a non-traded share of output of over 60%
for their US CGE model.
17
Diagram 3: Production Treefor the 123 PRSP Model
18
3. The 124 BOTE, 123 HOS and 123 PRSP Modelsin
Diagrams
3.1 The Initial Equilibrium of the 124 BOTE Model
When constructing the production possibilities frontiers (PPFs) and consumption possibilities
frontiers (CPFs) it was assumed that the domestic tradable sector was capital intensive and
the non-tradable sector was labour intensive. It was also assumed that all the production
functions, the composite goods function on the export side and the composite goods function
on the import side were constant returns to scale. The combined effect of the latter
assumption allowed for useful simplification of the diagrammatic argument. It was also
assumed that the welfare function was homothetic. As before, the export good and the
domestic tradable good are imperfect substitutes. Finally, notice in Diagram 4a below, the
prices and quantities of the traded sector and are made up of the exports and domestic
tradable goods and , and , respectively. It will quickly become apparent that the
tradable sector output, will be an aggregation of the outputs, and of the tradables
sector. In CGE applications, base year quantities are measured in base year accounting prices.
Thus, as shown in the Appendix in equations (A.17a) and (A.17c), and .
The PPF shown in Diagram 4a below is defined for three goods, and . The
composite good on the export side, is made up from the domestic tradable good,
and the export good, . In Diagram 4a, the locus of extreme points (A0, C, B0) are
defined by the composite goods function on the export side when non-tradable goods
production is zero or = 0 for a given amount of the composite good, . At A0, and
are zero. Revenue maximisation subject to the composite goods function on the export side yields the relationship between relative prices and the proportions of the domestic
tradable and export good when all capital and labour is used in production. Thus, when
and fora given amount of the composite good , the ratio of the quantities of the
exported good and the domestic tradable good / will be a function of the relative
prices of the export good and the domestic tradable good ⁄ , drawn as an inverse
relationship with a negative sign in the north-east quadrant of Diagram 4a. When the set of
relative prices ⁄ is given, the final equilibrium for = 0 will be at C.
The final step in building the PPF is to add in the production of the non-tradable good .
Consider the case at , when and are zero, thenas production of will increase and
will fall as capital and labour shift from production; the frontier is the normal production possibilities frontier for two goods and two factors. Note that it is the composite
good on the export side, that enters into the production function and a normal
production function for the non-tradable good . By assumption, the domestic tradable
goods sector is capital intensive relative to non-tradable goods production. In this case, as
expands relative to , wages will rise relative to the returns on capital. By similar
argument, at , the output of the non-tradablegood, and that of the domestically tradable
good, will be zero. As the production point shifts around the locus , the production
possibilities frontier is mapped out in space and for a given set of relative prices
⁄ , the final equilibrium for = 0 will be at H. When the export good and the domestic tradable good are both non-zero and given by the
proportions, / corresponding to the rays OC and DE, the PPF will be on the locus
19
and relative prices ⁄ . The final production possibilities frontier will be the
three-dimensional surface ) in (Qdt ,Qe , Qn) space as shown in Diagram 4a below.
Diagram 4a: Initial Equilibrium of the 124 BOTE Model:
Production Possibility Frontier in 3 Dimensions
There are a number of properties of the PPF shown in Diagram 4a that can be developed. The
optimal proportions of ( ⁄ ) given by the ray OC in ( , ) space can apply for any
feasible value of the non-tradable good such as shown in Diagram 4a. The
transformation curve GEH shows the trade-off between the domestic tradable good and
the export good when . The point E was chosen such that ⁄ is the same as
at C and the optimal proportions of ⁄ are the same at E as at C. Holding ⁄
constant the locus of points on the PPF surface can be traced out as on CEF0, and the optimal
proportions ⁄ will be constant for every point on the locus CEF0. Moreover, the
transformation curve GEH for can be projected onto the ( , ) space, given by
as shown by the dashed lines in Diagram 4a. Since all the functions used in
constructing the PPF are constant returns to scale, the frontiers A0CB0, GEH and
have exactly the same shape, a property which is exploited below when reducing the results
in 3-dimensions to 2-dimensions in Diagram 4d.
20
The slopes of the functions shown in Diagram 4a can be made more precise using the
mathematical appendix. Thus the slope of the composite good transformation curve on the
export side at C and E in ( , ) space is defined in equation A.16 in the Appendix:
⁄ ⁄ ⁄ ⁄ from equation (A.16)
In words, equation (A.16) says that the negative of the inverse of the price of domestic
tradable good relative to the price of the exported good is equal to the marginal contribution
of each good, respectively, to thecomposite good on the export side.
Similarly, the loci , and show the transformation of the composite good,
into the non-traded good, as capital and labour shift from the traded sector to the
non-traded sector.The slope of the transformation curve at G, E and H in ( , ) space is determined by the equilibrium requirement that the return to capital and the return to labour is
the same in each sector and the marginal revenue products of capital and labour are the same
in each sector. This is equivalent to shifting the relative price terms to the LHS and the ratio
of the marginal products to the RHS in equations(A.46) or (A.47)from the Appendix, yielding
the desired relationship between the relative price of the composite good on the export side
and the non-traded good shown in equations (A.46) and (A.47) below:
⁄ ⁄ ⁄ (A.46)
Or, alternatively,
⁄ ⁄ ⁄ (A.47)
The relative price of the composite good on the export side compared with the non-traded
good is inversely proportional to the ratio of the marginal productivity of capital and labour,
respectively, in each sector.
More generally, the loci showing the trade-off between and production as the price
of the domestic traded good relative to the price of exports, ⁄ changes can be shown
using the shares of and in the total output of the composite good on the export side.
Thus, from the breakdown of the price of the composite good on the export side, using
quantity share in equation (A.17b) in the Appendix, equations (A.46) and (A.47) can be re-
written as equations (A.46a) and (A.47a) below:
⁄ ⁄ (A.46a)
Or, alternatively,
⁄ ⁄ (A.47a)
In (A.46a), when the share is equal to zero, we have ⁄ at G in Diagram 4a.
Similarly, when the share of is equal to zero, we have ⁄ at H in Diagram 4a.
As the shares and move between zero and 1, the relative price of the composite
good on the export side, ⁄ moves from G to E to H in Diagram 4a.
The CPF is shown in Diagram 4b below. The key difference between the PPF and the CPF is
that exports are used to obtain imports which enter into consumption. For , and with
all capital and labour employed in production for the composite good on the
21
export side, the frontier A0B0 in the upper quadrant of Diagram 4b gives the maximum
possible levels of and with all capital and labour allocated to the traded goods sector,
for given relative prices − ⁄ at C. Exports can be transformed into imports at given
world prices ⁄ inthe upper left hand quadrant and imports are transferred by the 45-
degree line in the lower left-hand quadrant of Diagram 4b to the lower vertical axis.
Exports, are used to purchase imports, which enter final consumption when combined
with the domestic tradable good to form the composite good on the importside,
.The composition of the composite good on the import side ( is determined by
the relative prices − ⁄ at C in the lower RHS quadrant in Diagram 4b.
Thus, in the lower part of Diagram 4b, the frontier A0B0 in space replaces the
frontier A0B0 in ( space in Diagram 4a. When non-traded goods production ,
the point C on A0B0 in the lower RHS quadrant of Diagram 4b is an equilibrium point on the
consumption side and the relative price of the domestic tradable good to the price of exports
equates to the relative price of the domestic tradable good to the price of the imports or
− ⁄ ⁄ . The remainder of the CPF follows the shape of PPF with
obtained through exports at given world prices and . Thus the slope of the CPF for
any locus of points such as GEH is given by the equations (A.46a) and (A.46b) with
replacing and replacing when there are no capital imports or FSAV=0.
When there is non-traded goods production, for a given production and consumption of the
non-tradable good , the locus HG on the CPF surface gives the possible equilibrium
combinations of and . For a given production and consumption of the non-tradable
good , the locus GEH on the CPF surface gives the possible equilibrium
combinations of and . A possible final equilibrium is at point E which for given constant returns to scale production and composite goods functions and a homothetic welfare
function, can be chosen such that the slope of HG at E is given by the price ⁄
which are the same as at C on A0B0 and as at on , the projection of HEG onto
the ( , ) plane. The proportions of and are also the same at C, E and , given
by the rays OC and DE. Similarly, moving around the locus CEF0 keeps the relative price
⁄ constant but the relative price of the composite good on the import side
⁄ increases as increases and declines. This is none other than the inverse of the real exchange rate with a negative sign first encountered in Diagram 1. Here
and in subsequent discussion, the algebraic values of relative prices are shown in the
diagrams and in ⁄ is the inverse of the trade theory value of the real exchange
rate with a negative sign. However, the direction of change in ⁄ in Diagram 4b
and other diagrams is the same as the trade theory version shown in Diagram 1. Thus, for a
shift in equilibrium from C to E in Diagram 4b, ⁄ increases, an appreciation of
the real exchange rate ⁄ as measured in trade theory.
22
Diagram 4b: Initial Equilibrium of the 124 BOTE Model
Consumption Possibility Frontier in 3 Dimensions
These properties can be developed by reference to the mathematical appendix. The
determinants of the slope of GEH at E can be made more precise from eq (A.24).
⁄ ⁄ ⁄ ⁄ (A.24)
Substituting equation (A.25) into (A.24) yields equation (A.25a)
23
⁄ ⁄ (A.25a)
In equation (A.25a), when the share is equal to zero, we have ⁄ at G in
Diagram 4b. Similarly, when the share of is equal to zero, we have ⁄ at H in
Diagram 4b. As the shares and move between zero and 1, the relative price of
the composite good on the import side ⁄ moves from G to E to H in Diagram 4b.In words, for a given share of the import and domestic tradable good, the relative price of
imports, and the domestic tradable good, are proportional to the marginal contribution
of each good, respectively to the composite good on the import side.
Similarly, the transformation of the composite good on the import side, , into the non-
traded good at constant prices ⁄ on a locus such as CEF0 whose slope governed by
the underlying production functions as in (A.46a) and (A.46b) above except that is
replaced by and by for the case where . As varies from 0 to 1, the possible equilibrium point E varies from G to H. The final equilibrium at a point such as
E is determined when the social welfare function touches the locus CEF0 at E. That is, when
equation (A.8) from the Appendix is re-written as equation (A.8a):
⁄ ⁄ (A.8a)
In words, the equilibrium price ratio at E that satisfies the welfare function is equal to the
negative of the ratio of the marginal contribution of the composite good on the import side to
economic welfare divided by the marginal contribution of the non-traded good to welfare.
To summarise, the final equilibrium at E must satisfy the economic welfare function shown in
equation (A.8a) above, the underlying production functions shown in equations (A.46a) and
(A.46b), the composition of the composite goods function on the import side as in equation
(A.25a), and the composition of the composite good function on the export side as in equation
(A.16). Only when all of these conditions are satisfied simultaneously will a point such as E
be an equilibrium point.
24
Diagram 4c: Initial Equilibrium of the 124 BOTE Model
Consumption Possibility Frontier with More Detail
Diagram 4c is identical to Diagram 4b in all respects except an additional cone is D1G1H1is
added with the output of the non-tradable good equal to . As in Diagram 4b,
the relative price ⁄ is constant on the locus CEE1F0 but the relative price
⁄ is falling and the real exchange rate, the relative price of non-tradable to
tradable goods is increasing. The amount of the domestic tradable composite good
falls as rises but the proportion of the export good and the domestic tradable good,
⁄ is constant as indicated by the rays OC, DE and D1E1. The fall in is also
tracked by the projections and since is inside .
25
As can be seen from equation (A.1) in the Appendix, the welfare function is in two
dimensions and it is difficult to plot in 3-dimensional space in Diagram 4c. However, given
the assumptions of constant returns to scale functions and a homothetic welfare functions,
Diagram 4c can be reduced to 2-dimensions and the final equilibrium illustrated in Diagram
4d below.
Diagram 4d: Initial Equilibrium of the 124 BOTE Model
Consumption Possibility Frontier in 2 Dimensions
Diagram 4d is constructed from Diagram 4c and from the welfare function as given by
equation (A.1) above. For example, at given initial relative prices ⁄ and
, the length of the ray OC in Diagram 4c gives an extreme point C0 in Diagram 4d for the
production of , the quantity of the composite good on the import side. As C on the ray
OC moves along the locus CEE1F0, the amount of the composite good on the import side
available, falls until it reaches zero as increases until it reaches a maximum at F0
inDiagram 4d. The locus of possible equilibrium points CEE1F0corresponds to the frontier
C0CC’F0 in Diagram 4d above. The final equilibrium at C in Diagram 4d is where the welfare
function in the initial position Idmn0 is tangent to C0CC’F0 at C. The point C in Diagram 4d
corresponds to E in Diagram 4c where DE gives the amount of in Diagram 4c and OE in Diagram 4d above. A shift in the welfare function at constant initial prices of the domestic
tradable and imported goods ⁄ to could shift the final equilibrium point
from C to C’ in Diagram 4d, increasing the output of the non-tradable good from OD to OD1
in Diagram 4d, and from OD to OD1 in Diagram 4c. Thus a shift in the welfare function towards more non-tradable goods will decrease the relative price of the composite good on
the import side relative to non-tradable goods, ⁄ or an increase the price of non-tradable relative to tradable goods, an appreciation to the real exchange rate.
The initial equilibrium of the 123HOS model is shown in Diagram 4e below. The Diagram
looks similar to a normal HOS trade diagram with the two goods, and with the
addition of a non-traded goods production so that all capital and labour are used to produce
the traded goods and A0CB0 is the PPF. In the same way that the PPF for the 123 model was
mapped out, the locus of extreme points in production space will be given by A0CF0. When
26
and for given world prices ⁄ , production will be at C and consumption
anywhere along the CPF frontier A1CB1. When , say for OD, the locus of extreme
production points will be given by GEH. Given the same world price ratio as before,
⁄ , production will be at E and the CPF frontier will be G1EH1. As for the 124 BOTE model as the production point shifts C to E to F0 for constant terms of trade, the locus
of production points CEF0is mapped out. At constant terms of trade, as Qn increases and
and decrease in proportion, the real exchange rate, ⁄ will increase.
Why then should the empirical trade models abandon 123 HOS models for the 124 BOTE
models? The answer is that production along a locus such as CEF0with incomplete
specialisation only happens by chance when the number of traded goods increases
dramatically relative to the number of factors, in which case there will be incomplete
specialisation. Keeping as the exported good, complete specialisation will take place in
Diagram 4e when the terms of trade improve for and the locus of production points shift
from CEF0 to A0GF0 and there will be no production of . As before, as the production
point shifts from A0 towards G and F0, the output of increases, declines and the real exchange rate appreciates.
As already foreshown, the 123 PRSP model shown in Diagram 4f is a truncated version of the
CPF for the 124 BOTE model as set out in Diagram 4b, with non-traded goods production
. Without non-traded goods, the 123 PRSP model has no real exchange rate as normally specified in international trade theory. As such, the 123 PRSP model does not
provide a miniature version of standard open single country CGE models.
27
Diagram 4e: The Initial Equilibrium of the 123 HOS Model
Production Possibility and Consumption Possibility Frontiers
28
Diagram 4f: The Initial Equilibrium of the 123 PSRP Model: Consumption
Possibility Frontiers
In section 2.2, the structure of the standard HOS trade model with a non-traded good was
discussed in terms of a production tree diagram. The standard finding is that the HOS model
with many goods has a tendency towards complete specialisation. This tendency can be made
vivid within the context of the CPF for the 124 BOTE model shown in Diagram 4b. In the
HOS case, the export good, and the domestic tradable good, are perfectly substitutable
so that A0B0 in the upper quadrant of Diagram 4b will be a straight line. Thus, the CPF in the
lower part of Diagram 4b has a curved surface in ( space following the
production functions and a flat or linear surface in ( space for each amount of the
non-traded good, . There is complete specialisation in the 124 BOTE model with only one
traded good produced, which is used to export and obtain imports , combining with
the non-traded good in consumption on the B0F0 frontier. Exports do not enter into
consumption. The 124 BOTE model in HOS mode has lost intra-industry trade and shows complete specialisation.
In section 2.3, the 123 PRSP model was discussed in terms of the production tree diagram.
The fact that the 123 PRSP model does not have a non-traded good is made vivid by the
initial equilibrium in Diagram 4b, where the 124 BOTE model collapses to the 123 PRSP
29
model in the lower quadrant when the non-traded good, (see Devarajan and Go, 2003, Ch.13).
As argued in the discussion of Diagram 4b, the correct measure of the real exchange rate is
⁄ , not ⁄ or ⁄ as stated in Devarajan and Go (2003). It is clear
from the lower LHS quadrant of Diagram 4b that the elasticity of substitution between the
imported good, and the domestic tradable good, the Armington elasticity in the
applied CGE country models has nothing to do with non-tradable goods, when properly specified.
4. Impact Effects ofin the 124 BOTE Model
4.1Impact Effects of Increasing Foreign Savingsin the 124 BOTE
Model
This section shows how the initial equilibrium changes when foreign savings, FSAV is
changed from the initial value of zero, first in 3-dimensions and then in 2-dimensions.
Diagram 5a shows how the CPF changes when FSAV increases when the non-tradable good
production is zero, . In Diagrams 5b-5d, non-tradable goods production is non-zero or
in the initial equilibrium before FSAV increases and the initial equilibrium shifts.
In Diagram 5a below, exports are generated in the upper part of the diagram and transformed
into imports for consumption in the lower part of the diagram. The initial CPF is shown by
the frontier A0B0F0 and the initial equilibrium is at C0 with , for the initial prices,
⁄ . The ray OC0 gives the proportions of and in the composite good on the
import side, . Since = , the proportions in the composite good on the export side at
C0 in the upper part of Diagram 5a and in the composite good on the import side at C0 in the
lower part of the diagram are the same. The increase in foreign savings shifts both, the world
price line = to the left and shifts upwards the original frontier A0B0F0 linearly by the
amount FSAV1 such that the new frontier is A0S1B1F1F0. The new CPF is made up of the
original surface A0B0F0 and a new vertical component A0S1F1F0.
When , as relative prices adjust to FSAV1, the new equilibrium is at C1 in the lower
part of Diagram 5a with relative prices equal to ⁄ . The share of and in the
composite good on the import side shifts from the ray OC0 to OC1; as the price falls
relative to , the share of imports rises when FSAV1 is introduced. Imports, increase to
OB1 and the production of increases to OA1. From the upper part of Diagram 5a it can be
seen that the increased production of is also equal to OA1 but there is a fall in exports
to OB1 as the relative price of exports fall. Because = , the relative prices at C0 and C1,
respectively, in the upper and lower parts of the Diagram 5a are the same. That is,
⁄ ⁄ and ⁄ ⁄ . The breakdown of the price changes can also be seen from the lower part of Diagram 5a. At the initial output of the
domestic tradable good at increased foreign savings, FSAV1 increases imports by C0C1
at the initial relative price ⁄ ⁄ at the consumption point . The
final adjustment takes place when consumption shifts to C1 and the final relative prices fall to
⁄ . Finally, the breakdown of imports with FSAV1 can be seen from the upper left
30
hand quadrant in Diagram 5a. Total imports are given by B1JI, with the export component
equal to , and the foreign savings component FSAV1 measured by
.
Diagram 5a: Consumption Possibility Frontierwith FSAV and no Non-Tradable
Goods
Diagram 5b below shows what happens when FSAV1 is introduced and when non-tradable
goods, , are produced. Diagram 5b is the same as 5a except for the initial and new
equilibrium points added for non-tradable goods, being produced. For a possible
31
initial equilibrium point E0 on the interior frontier G0H0 is shown, where E0 is on the locus
C0F0 at constant initial prices – ⁄ . By construction, the proportions of and in
the composite good on the import side, at C0 and E0, are the same since the rays OC0
and DE0 are parallel. With FSAV1 and for a possible equilibrium point E1 on the
interior frontier is shown, where E1 is on the locus C1F1 at constant final prices
⁄ . By construction, the proportions of and in at C1 and E1 are the
same since the rays OC1 and DE1 are parallel.
Diagram 5b: Consumption Possibility Frontier with FSAV and Non-Tradable
Goods
32
The catch with Diagram 5b is that it is difficult to locate the new equilibrium point
diagrammatically because it is in 3-dimensions. The 2-dimensional Diagram 5c shows how
this can be done.The final equilibrium point, which is derived from Diagram 5b, is illustrated
in Diagram 5c below:
Diagram 5c: Consumption Possibilities Frontier in 2 Dimensions with FSAV
In Diagram 5b the amount of the composite good on the import side, , is given by the
length of the ray OC0. As increases and falls, the trade-off between the composite
good on the import side and the non-tradable good at the initial relative prices ⁄
can be derived by plotting the changes in the amount of and as the point C0 moves
to the left on C0E0F0. As increases the locus of possible equilibrium points is mapped out.
A possible equilibrium point is given by E0 when . In 2-dimensions, this trade-off
is shown in Diagram 5c as A0E0F0. Given the welfare function Idtmn0, and the initial
equilibrium is given by E0. When the maximum amount of the composite good on
the import side is given by OA0 in Diagram 5b in Diagram 5c. The final equilibrium for the
composite good on the import side and the non-tradable good with an increase in welfare is at
E1 compared with the initial equilibrium, E0 and a new level of welfare . The real
exchange rate at E1 appreciated compared with E0 in Diagram 5c, or
⁄ > ⁄
.The final equilibrium composition of and in the
composite good on the import side, is shown in Diagram 5d below:
33
Diagram 5d: Equilibrium Proportions of Composite Good on Import Side with
FSAV
By construction, ⁄ < ⁄
i.e. ⁄ rises from E0 to E1, i.e. falls
relative to .
In Diagram 5d, the equilibrium points E0 and E1 correspond to the same equilibrium points E0
and E1 in Diagram 5b. The frontiers G0E0H0 and G1E1H1in Diagram 5d are projections into
2-dimensional space ( from the same frontiers in 3-dimensional space in Diagram
5b. Since the price of imports falls as FSAV increases, the proportion of in the composite
good on the import side, , increases in proportion to the shift from OE0 to OE1.
In summary, the effects of an increase in foreign savings to FSAV1 will:
- increase economic welfare , as shown in Diagram 5c
- lead to an appreciation of the real exchange rate, as shown in Diagram 5c
- increase the output of the non-tradable good, as shown in Diagram 5c
- increase imports and the share of imports in tradable goods final consumption shown
in Diagram 5d
- decrease exports, which can be shown from Diagram 5d, where H0H1 is equal to the
increase in FSAV1 and M0M1 is the increase in imports; by inspection, the increase in
imports is less than the increase in foreign savings, so exports must have decreased.
34
4.2 Impact Effects of Terms of Trade (TofT) Improvement in 124
BOTE Model
The analysis of terms of trade effects runs along similar lines to the analysis of FSAV
changes. The impact of terms of trade changes with is shown in 3-dimensions in
Diagram 6a below and for in Diagrams 6b, 6c and 6d. The key difference between a
foreign capital inflow and a terms of trade improvement is that the terms of trade
improvement has a multiplicative effect on foreign exchange receipts, whereas increased
foreign savings has a linear effect on foreign exchange receipts. Thus, the CPF in Diagrams
5a and 5brises by a constant amount equal to the increased foreign savings, whereas in
Diagram 6a and 6b, the CPF rises by a proportion equal to the terms of trade improvement.
This difference is best seen by comparing Diagrams 5b and 6b. Diagram 5b shows a
relatively modest fall in exports of in the upper quadrant and by contrast, a large
increase in imports, in the lower quadrant and also showsa substantial increase in
production of . In the case of a terms of trade improvement shown in Diagram 6b, the
upper quadrant shows a relatively large decrease in exports , and a smaller increase in
domestic production, whereas the lower quadrant shows a large increase in imports .
The difference between the two cases arises because, with increased FSAV but no terms of
trade change, the substantially increased imports from increased FSAV must combine with
increased production of in the composite good on the import side . When there is
no change in FSAV but a terms of trade improvement, the increased production in is small, the fall in exports is much less and the benefits of the terms of trade improvement are
focussed on increased imports.
35
Diagram 6a: Consumption Possibility Frontier with TofT Change and no Non-
tradable Goods
36
Diagram 6b: Consumption Possibility Frontier with TofT Change and Non-traded
Good
The terms of trade effects shown in 3-dimensions in Diagram 6a and 6b are shown in 2-dimensions
in Diagrams 6c and 6d. In Diagram 6c, the initial extreme points A0E0F0 correspond to the points on
the locus C0E0F0 in Diagram 6b where the ray OC0 measures the initial amount of the composite
good on the import side OA0. As production increases, decreases and the points on the
locus C0E0F0 in Diagram 6b are potential equilibrium points as are the points A0E0F0 in Diagram 6c.
For the initial level of welfare shown by Idtm0, the final equilibrium point will be E0 in Diagram 6c
below. The initial equilibrium real exchange rate will be ⁄ .
37
Diagram 6c: Consumption Possibilities Frontier in 2 Dimensions with TofT
Improvement
Similarly, Diagram 6d below maps in 2-dimesions the trade-off between the output of the domestic
tradable good production, and imports, . Thus from the 3-dimensional CPF shown in Diagram
6b for , the locus GE0H maps out the possible combinations of and . These are shown in Diagram 6d below by the locus GE0H.
Diagram 6d: Equilibrium for Imports and Domestically Tradable Goods with TofT
Change
38
The final step in the analysis of the impact effects of terms of trade improvement can be shown from
Diagram 6b in 3-dimensions. As already noted, the improvement in the terms of trade shifts the
terms of trade line in the upper LHS upper quadrant of Diagram 6b. This translates into a
proportional upward shift in the CPF, pivoting around the initial lower RHS frontier AGG1F0 and the
final CPF after the terms of trade improvement is A0B1H‟F0G1G. When the improvement in the
terms of trade increases from the initial level from OD0 to say OD1, the locus of possible equilibrium points on the CPF, G1E1H‟ lift over the initial locus of possible equilibrium GE0H as
shown in Diagram 6b. Translated from the 3-dimensional to the 2-dimensional Diagram 6c, the
effects of the terms of trade improvement shift the initial equilibrium from E0 to E1 increasing
welfare, appreciating the real exchange rate, increasing non-traded goods output , and increasing
the output of the composite good on the import side. From the upper part of Diagram 6b it can be
seen that exports fall. The effects of the terms of trade improvement on the shares of and in the composite good on the import side can be seen from the points E0 and E1 in Diagram 6d. The fall
in the relative price of the imported good leads to a large increase in imports and only a relatively
small expansion in the output of .
4.3 OtherImpact Effects –Technical Change and Change in
UnemploymentImprovement
Without an empirical context, consideration of possible technical change adds little to the 124 BOTE
model. When all technical change is disembodied Hicks-neutral and the same for all factors, the PPF
shown in Diagram 4a by A0B0F0 simply shifts outwards by the amount of technical change. The
same happens for the CPFs in Diagrams 4b and 4c, and the CPF in the 2-dimensional Diagram 4d.
Not much can be added without an empirical application of a single country CGE model.
In many single country CGE models, labour is disaggregated at least into skilled and unskilled
labour. Often, skilled labour is modelled with a market clearing wage and unskilled labour with a
fixed real wage generating unemployment in model solutions. Here, we explore briefly the behaviour
of the 124 BOTE model with unemployed labour at a fixed real wage. In this case, a fall in the fixed
real wage will shift the CPF shown in Diagram 4b in a similar matter to Hicks-neutral technical
change described above except the effect on relative commodity prices will be greater in the non-
traded labour intensive sector compared with the traded goods sector.
Thus, in Diagrams 4b, 4c and 4d, lowering the fixed real wage will shift the CPF outwards with a
bias towards non-traded goods. The impact of changing the real wage through changes in
unemployment will be biased towards labour intensive goods.
4.4 Measuring the Real Exchange Rate
One strong conclusion that arises from our discussion of the 124 BOTE model is that the selection of
non-tradable vs. tradable sectors is an empirical matter. For very large economies such as the US
with relatively low trade to GDP ratio, the prior expectation is that the share of non-tradables in
domestic production will be large. For low-income countries such as Ethiopia, we have found that
non-tradables comprise about 25-30% of the total production.
In applied CGE modelling once the non-traded goods are identified empirically, it makes sense to
measure the real exchange rate on the import side by the ratio ⁄ as measured in the 124 BOTE model when there is a large structural current account deficit. This can be calledthe trade
theory measure of the real exchange rate.
39
Somewhat to our surprise, we have learnt in writing this paper that the direct measure of the trade-
theory real exchange rate is seldom used. Rather, it is measured from the model money exchange
rate, ER deflated by some domestic price index such as the consumer or the wholesale price index
for tradables and non-tradables, respectively. This approach works when the difference between
world price of tradables and the domestic price of tradables is fully accounted by the model money
exchange rate, ER and other modelled trade barriers such as tariffs. There is an unaccounted
discrepancy between world prices marked up by the money exchange rate, other identified trade
barriers and the domestic price of tradables. Our argument is that there is no need to grapple with
such gaps or discrepancies when the real exchange rate can be measured directly by the ratio
⁄ .
5. Results from the 124 BOTE Model Summarised
The 124 BOTE model set out above could be empirically specified with an appropriately aggregated
country SAM with CES functions incorporated in the CET and Armington composite goods and the
production functions and some sort of LES treatment of consumption, rather than the general
mathematical formulation in the Appendix. Such an empirical 124 BOTE model run in parallel with
a much larger country CGE model could help provide clearer insights into the results from the large
CGE model, for example, a variety of macroeconomic policy shocks on the real exchange rate as in
the 2-dimesnsional CPF diagrams. The smallest size 124 BOTE-type model that could begin to give
useful stand-alone empirical results would require up to 8-10 productive sectors, disaggregation of
labour to include at least skilled and unskilled labour with an urban and rural breakdown, and a
disaggregation of households at least by rich and poor, urban and rural. Such a minimum sized 124
BOTE-type model would be much smaller than the typical single country CGE model and would
need to be able to specify: unemployment functions; alternative closures; tax, tariff and other
revenue instruments; and possibly the specification of rent seeking behaviour affecting both
inequality and poverty.
For the moment, it is useful to draw together the main qualitative findings from the 124 BOTE
model in two key areas of policy concern, increased foreign savings and improved terms of trade.
(i) Increased Foreign Savings
In summary, the qualitative effects of increased foreign savings are:
increase economic welfare , not including any welfare costs of future repayment of foreign savings,
lead to an appreciation of the real exchange rate,
increase the output of the non-tradable good,
increased imports and an increased share of imports in the composite good on the import side,
sharply decreased exports
povertyreduction as a result of the expansion of the labour intensive non-traded good output relative to the capital intensive domestic tradable good and the associated increase in real
wages.
(ii) Favourable Terms of Trade Effects
In many respects, the effects of improved terms of trade are similar to the increase in foreign
savingscase described above. The key differences lie in the particular sector compositionof the
40
TofTchanges on exports and imports. For example, in a larger Ethiopian example (Evans and
Ghelani (2012), terms of trade improvement for coffee and horticulture has a particular rather than
general effect on household income and poverty reduction impacts. Similarly, home produced cereal
and food production is an important non-traded good with specific household effects when the real
exchange rate appreciates.
6. Conclusions
Some of the ways in which building the 124 BOTE miniature model has shed light on this area of
research are summarised below.
1. The comparison between the 124 BOTE and 123 PRSP models has shed light on the
treatment of non-traded goods and the measurement of the real exchange rate in this class of
models. As a core miniature model, it was found that the treatment of non-traded goods and
the measurement of the real exchange rate in the 123 PRSP class of model deviates from the
standard international trade theory and is deeply misleading.
2. The exploration of key qualitative results from the 124 BOTE model when shocked by an
increased inflow of foreign capital or an improved TofT throws light on the likely results
from an empirical application of the 124 BOTE class of models.
3. Full empirical specification of the 124 BOTE model alongside an empirical application of a
larger single country CGE model further increases the insights obtained, especially for
explaining key results to policy makers, exploiting the reduction of aggregate results to a 2-
dimensional diagram. This is likely to be import for policy purposes in African LICs where
rapidly expanding mineral exports can yield Dutch Disease effects, and where TofT effects
can be important as well, affecting both exports and imports.
4. The 124 BOTE model could help to open up an area of research that links projections of
macroeconomic shocks and policies to a small CGE model that captures the poverty and
other macroeconomic impact effects, whether from Article IV projections or from DSGE
models.
5. With further research it should also be possible for the miniature 124 BOTE model to be
integrated into single country DSGE models to provide the poverty and other real economy
impact analysis.
Thus, the 124 BOTE-type miniature model is useful for checking out the fundamentals of CGE
modelling in a new area, by making sure that it stays true to its roots and also delivers on key
variables such as real exchange rate. It also helps elucidate the essence of the results of larger CGE
model, for example in the 2-dimensional presentation of the results of larger CGE models. The
correct specification of non-traded goods in model formulation is important in empirical practice,
especially when there are strong real exchange rate effects which driveDutch Disease and TofT
effects.
41
References
Agénor, P-E, A. Izquierdo and H.T. Jensen, 2007, Adjustment Policies, Poverty, and
Unemployment: The IMMPA Framework, London, and Blackwell.
Ahmed, H., A. Amogne, T. Tebekew, B. Teferra, E. Tsehaye (Ethiopian Development Research
Institute), P. Dorosh (International Food Policy Research Institute), S. Robinson, D.Willenbockel
(Institute of Development Studies at the University of Sussex, Brighton), 2010, “A Regionalized
Social Accounting Matrix for Ethiopia 2005/6”. Technical Report for the UN World Food
Programme, Addis Ababa. This report is based on collaborative EDRI-IDS-IFPRI research
funded by the World Food Programme project Impact of Drought and Food and Fuel Price
Increases on Economic Performance and Poverty in Ethiopia.
Bailey, R., June 2011, „Growing a Better Future: Food justice in a resource-constrained world‟,
OXFAM International.
Berg, A, Philippe Karam, and Douglas Laxton1, 2006, “A Practical Model-Based Approach to
Monetary Policy Analysis—Overview”, 2006, International Monetary Fund WP/06/80.
Blejer, M., Cheasty, A., 1988, „High Inflation, Heterodox Stabilization, and Fiscal Policy, World
Development, Vol. no. 16, No. 8
Bourguignon, F., L. da Silva, P., 2003, “The Impact of Economic Policies on Poverty and Income
Distribution: Evaluation Techniques and Tools”, World Bank, Oxford University Press.
Bourguignon, F., L. da Silva, M. Bussolo, 2008, “The Impact of Macroeconomic Policies on Poverty
and Income Distribution: Macro-micro Evaluation Techniques and Tools” (Equity and
Development Series), London: Palgrave MacMillan.
CARIS (Centre for the Analysis of Regional Integration at Sussex), 2007, Briefing Paper, No.1,
February.
Cirera, X., N. McCulloch and L.A. Winters, 2001, Handbook of Trade and Poverty, DfID and CEPR,
London.
Bourguignon, F., Robilliard, A, Sophie., Robinson, S., 2005, “Representative Versus Real
Households in The Macro-Economic Modeling of Inequality”, Representative versus Real
Households in the Macroeconomic Modeling of Inequality, Ch.10, Cambridge University Press
Dagher, J., Gottschalk J., and Portillo, R., 2010, “Oil Windfalls in Ghana: A DSGE Approach”, IMF
Working Paper No. 10/116.
Devarajan, S., and D.S. Go, 2003, “The 123 PRSP model”, Tool Kit for Evaluating the Poverty and
Distributional Impact of Economic Policies, Ch. 13, World Bank
Devarajan, S., D. S. Go, J. D. Lewis, S. Robinson and P. Sinko, 1997, “Simple General Equilibrium
Modeling”, Ch 6 in Applied Methods for Trade Policy Analysis: A Handbook, Cambridge
University Press
42
Devarajan, S. and D.S. Go, 1998, “The Simplest Dynamic General-Equilibrium Model of an Open
Economy”, Journal of Policy Modelling.The World Bank, Washington, DC USA
Dixon, P.B., B.R. Parmenter, G.J. Ryland and J. Sutton, 1977,“ORANI, A General Equilibrium
Model of the Australian Economy: Current Specification and Illustrations of Use for Policy
Analysis”, Vol. 2 of the First Progress Report of the IMPACT Project, Australian Government
Publishing Service, Canberra, pp. xii + 297.
Dixon, P.B., Parmenter, B.R., Sutton, J., Vincent, D.P., 1982, “ORANI: A Multisectoral Model of
the Australian Economy”, Contributions to Economic Analysis 142, North-Holland Publishing
Company, pp. xviii + 372.
Dixon, P.B., M.T. Rimmer, 1999, “Change in Indirect Taxes: A Dynamic General Equilibrium
Analysis”, Australian Economic review, 32, issue no. 4, pp. 327-348
Dixon, P.B. and M.T. Rimmer, 2002, “Dynamic General Equilibrium Modelling for Forecasting and
Policy: A Practical Guide and Documentation of MONASH”, North-Holland, Elsevier,
Contributions to Economic Analysis 256
Dixon, P.B., and M.T. Rimmer, 2009, “Economy-wide effects of reducing illegal immigrants in U.S.
Employment”, Contemporary Economic Policy, COEP-Jan-2009-00006.R.
Dixon, P.B., M.T. Rimmer, Honkatukia, J., 2010, “The marginal costs of funds in the VATTAGE
model of Finland: a back of the envelope justification of the welfare effects of additional
government revenue”, Paper presented at the Annual GTAP Conference 2011, GTAP Resource
#358
Evans, H.D., 1889, Comparative Advantage and Growth, Harvester Press, Hemmel Hempstead.
Evans, H.D., 2010, “Macroeconomic Impacts and Development Outcomes for Low Income
Countries: First Exploration of Macroeconomic Links to Ethiopia and Ghana Distribution and
Poverty Models”, Background paper prepared for Thirteenth Annual GTAP Conference, June
2010, Penang, Malaysia. GTAP resource #3381.
Evans, D., Ghelani, H., 2011, “Macroeconomic Policies and Poverty Impacts: Case studies of
Ethiopia and Ghana”, Paper prepared for 14th Annual GTAP Conference, June 2011, Venice,
Italy.
Geda, A., Degefe, B., 2005, “Explaining African Growth Performance: The Case of Ethiopia”,
African Economic Research Consortium Working Paper.
IMF, 2008, “Staff Medium-Term Projections (Ethiopia)”, IMF Country Report, No. 08/264 July.
IMF, 2010a, “The Federal Democratic Republic of Ethiopia—Staff Report for the 2010
Article IV Consultation and First Review under the Exogenous Shocks Facility”, IMF EBS/10/97
May 27.
IMF, 2010b, “The Federal Democratic Republic of Ethiopia—Second Review of theArrangement
under the Exogenous Shocks Facility”, IMF EBS/10/197 October 26.
43
Klugman, J., ed., 2002, A Sourcebook for Poverty Reduction Strategies, World Bank, ISBN: 978-0-
8213-4978-6.
Rayner, B., P. Mathieu, J. Honda and N. Kinoshita, 2011, “The Macroeconomics of scaling-up Aid:
The Case of Ethiopia”, draft working paper, IMF Research Department.
Robinson, S., Willenbockel, D., Ahmad, H., Dorosh, P., 2010, “Implications of Food Production and
Price Shocks for Household Welfare in Ethiopia: A General Equilibrium Analysis”, Draft Report,
Addis Ababa, January.
Salter, Wilfred (1959). “Internal and External Balance: The Role of Price andExpenditure Effects.”
Economic Record, Vol. 35, pp. 226-38.
Swan, T. (1960). “Economic Control in a Dependent Economy.” Economic Record, Vol. 36, pp. 51-
66.
Expenditure Effects.” Economic Record, Vol. 35, pp. 226-38.
Uzawa, H., 1961,”On a Two-Sector Model of Economic Growth”, Review of Economics and
Studies, Vol. 29, No 1 (October), pp.40-47.
Willenbockel, D., 2011, „Exploring Food Price Scenarios Towards 2030 with a Global Multi-Region
Model‟, OXFAM Research Report
World Bank, 1999, Building Poverty Reduction Strategies in Developing Countries, the
Development Committee, September, Washington DC.
World Bank, 2003, A User‟s Guide to Poverty and Social Impact Analysis. Washington, D.C.
World Bank, 2003, The Impact of Economic Policies on Poverty and Income Distribution:
Evaluation Techniques and Tools, Washington DC
44
APPENDIX
A.1 The Mathematical Structure of the 124 BOTE Model
The mathematical functions used to describe the 124 BOTE model are similar to those used in neo-
classical growth theory, for example Uzawa (1961). The 124 BOTE model is driven by a simple
welfare function, the maximisation of household consumption. There are four goods and two sectors.
There is an export good and a domestically tradable composite good, both produced by the domestic
tradable sector, an import good and a non-tradable good produced by the non-tradable sector. The
output of the domestic tradable sector is a composite good made up of the imperfectly substitutable
export and domestically tradable good, and The import and domestic tradable composite good enters into household consumption along with the non-traded good.
The mathematical model is set out in modular form. The equations follow closely the schematic
version of the Johansen model set out in Dixon et al (1992, 1999) except that a more general
mathematical formulation is used. In the 124 BOTE model, the diagrams themselves were drawn
using computer aided drawings rather than using an exact numerical example.
A.1.1 Welfare Function
The welfare function in the simplest 124 BOTE model is household consumption. The household
sector chooses its consumption levels from a composite good and the non-traded good subject to the
budget constraint.
Max (A.1)
(A.2)
Introducing the Lagrangean multiplier , equations (A.1) and (A.2) are reduced to:
(A.3)
The first-order conditions for welfare maximisation are:
(A.4)
(A.5)
(A.6)
45
Solving equations (A.4) and (A.5) to eliminate yields:
⁄ (A.7)
Equation (A.7) can be re-written as:
⁄
⁄ (A.8)
Finally the household sector budget , is given by factor income:
(A.9)
The variables and parameters are defined in Table 1 below.
A.1.2 Exports and the Domestic Tradable Good
Exports are treated as imperfectly substitutable with domestic tradable goods production. The choice
between exports and the domestic tradable goods is a function of relative prices determined by the
revenue-maximising problem shown in equations (A.10) and (A.11) for a given level of the
composite good on the export side, .
Maximise revenue (A.10)
st (A.11)
Introducing the Lagrangean multiplier , eqs (A.10) and (A.11) are reduced to
Maximise ( ) (A.12)
The first order maximising conditions are:
⁄ (A.13)
⁄ (A.14)
(A.15)
Using eq (A.13) and (A.14) to solve for , we obtain:
⁄ ⁄ ⁄ ⁄ (A.16)
Finally, the model accounts for all costs so that the price of the tradable sector output is given by the
costof the composite good and by the cost of the components as in eq (A.17) below:
(A.17)
46
However, noting that, at the initial base period accounting prices it will always be the case that
(A.17a)
Defining share terms in an obvious way:
(A.17b)
Equations (A.17) can be re-written as:
(A.17c)
It turns out that the share formulation is useful in decomposing the price of the composite good on
the export side as is done in the discussion of Diagram 4a in the text.
A.1.3 Imports and the Domestic Tradable Good
Imports are treated as an imperfect substitute with the domestic tradable good forming a composite
good, . The choice between imports and domestic tradable production is a function of relative prices determined by the cost minimising problem shown by equations (A.18) and (A.19) below for a
given level of the composite good on the import side, .
Minimise Cost (A.18)
st (A.19)
Introducing the Lagrangean multiplier , eq (A.1) & (A.2) are reduced to:
Minimise ( ) (A.20)
The first order minimising conditions are:
⁄ (A.21)
⁄ (A.22)
(A.23)
Using eq (A.21) and (A.22) to solve for in eq (A.24), we obtain:
⁄ ⁄ ⁄ ⁄ (A.24)
Finally, the model accounts for all costs so that the price of the composite good is given by the cost
of the components as in eq (A.25) below:
(A.25)
47
A.1.4 Production Side
There are two sectors, the domestic tradable sector and the non-traded sector. There are constant
returns to scale production functions employing two fully mobile factors, capital and labour. The
domestic tradable sector is assumed to be capital intensive and the non-traded sector labour
intensive.
The cost-minimisation problems for each sector for a given level of output is shown in equations
(A.26) and (A.27), (A.28) and (A.29) below:
Minimise cost (A.26)
st (A.27)
And,
Minimise Cost (A.28)
St (A.29)
Introducing the Lagrangean multipliers and , the cost minimizing conditions for each sector can
be re-written:
Minimise ( ) (A.30)
Minimise (A.31)
The first order minimizing conditions from eq (A.30) and (A.31):
⁄ (A.32)
⁄ (A.33)
⁄ (A.34)
⁄ (A.35)
The conditions that the model accounts for the value of inputs is:
(A.36)
(A.37)
Finally, the conditions that the demand for factor equals supply are:
(A.38)
(A.39)
The four cost minimizing conditions (A.35)-(A.38) can be used to eliminate the Lagrangean
multipliers and yielding eq (A.40) and (A.41) below:
48
⁄ ⁄ ( ⁄ (A.40)
⁄ ⁄ ⁄ (A.41)
Equations (A.40) and (A.41) express the idea that the ratio of the rate of profit to the wage rate in the
tradable sector producing is equal to the ratio of the marginal products of capital and labour;
similarly in the sector.
Following Uzawa (1961), the equilibrium conditions (A.32)-(A.35) can also be re-written using the
relationship between the value of the marginal product and factor returns or:
⁄ (A.42)
⁄ (A.43)
⁄ (A.44)
⁄ (A.45)
Using eq (A.42) and (A.44) to eliminate r and eq (A.43) and (A.45) to eliminate w, we find:
⁄ ⁄ ⁄ (A.46)
⁄ ⁄ ⁄ (A.47)
From the breakdown of the price of tradables, and the composite good on the export side
price, into and the quantity shares from (A.17b), equations (A.46) and (A.47) can be re-written as equations (A.46a) and (A.47a) below:
⁄ ⁄ (A.46a)
Or, alternatively,
⁄ ⁄ (A.47a)
49
Table A1: All Varables and Parameters
is the measure of welfare; is the welfare function.
is the price of the non-traded good (equal to )
is the quantity of the non-traded good (equal to )
is the price of output from the tradable sector
is the output from the tradable sector
is the price of the output from the non-tradable sector
is the output of the non-tradable sector
is the price of imported good
is the quantity of the imported good
is the price of the export good
is the quantity of the export good
is the price of domestic tradable good
is the quantity of the domestic traded good
is the price of the composite good on the export side
is the given quantity of the composite good on the export side made up of
is the price of the composite good on the import side
is the given quantity of the composite good on the import side made up of
is the factor income as received by the households
are the stocks of capital and labour
r, w is the rate of profit and the wage rate
is the amount of capital used in the production of the composite domestic
tradable sector
is the amount of capital used in the production of the non-tradable sector
is the amount of labour used in the production of the tradable sector
50
is the amount of labour used in the production of the non-tradable sector
FSAV foreign capital inflow