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

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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