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A systems simulation model of the Kenyan economy
OMEGA, The Int. Jl of Mgmt Sci., Vol. 3, No. 5, 1975
A Systems Simulation Model of the Kenyan Economy CHARLES C SLATER University of Colorado
GEOFFREY WALSHAM University of Nairobi (Received November 1974; in revised form February 1975)
This paper describes a systems simulation model of the national economy of Kenya. The model contains an input/output production component linked to a consumption component, disaggregated into nine income classes. Capital formation and government are integrated into the model as interactive elements. The model is demand driven and thus growth rates in the productive sectors are generated endogenously as a function of demand. The model has been used by the Kenyan Ministry of Finance and Economic Planning for forecasting and policy evaluation problems. A contributory factor in the successful implementation of the model is its ability to supply detailed quantitative forecasts which, in a developing country, are not readily available from routine sources. In addition, the model deals explicitly with income distribution and inflation consequences which are issues of current concern to local development planners.
INTRODUCTION THE WORK described in this p a p e r concerns a general systems s i m u l a t i o n m o d e l o f the n a t i o n a l e c o n o m y o f K e n y a . T h e m o d e l was d e v e l o p e d by the a u t h o r s d u r i n g a one year p e r i o d f r o m A u g u s t 1973. A b r i e f d e s c r i p t i o n o f some aspects o f the w o r k has a l r e a d y been p u b l i s h e d in K e n y a [12]. T h e p u r p o s e o f the present p a p e r is to r e a c h a wider a u d i e n c e o f m a n a g e m e n t scientists w h o a r e interested in the use o f s i m u l a t i o n for m a c r o - e c o n o m i c modelling. The m o d e l has been a p p l i e d in a d e v e l o p i n g c o u n t r y , where detailed w o r k on policy p r o b l e m s is often c o n s t r a i n e d by the scarcity o f skilled m a n p o w e r . T h e use o f a s i m u l a t i o n m o d e l provides d e v e l o p m e n t p l a n n e r s with i n f o r m a t i o n for decision m a k i n g which c a n n o t easily be o b t a i n e d by alternative m a n u a l m e t h o d s . This was a m a j o r factor in helping to interest decision m a k e r s in the m o d e l a p p r o a c h . A n o t h e r factor in successful i m p l e m e n t a t i o n was the conscious effort m a d e at the design stage to ensure t h a t the m o d e l was c a p a b l e o f dealing with issues o f current concern to local policy makers. I n p a r t i c u l a r , inflation effects 557
Slater, Walsham--Model of the Kenyan Economy and income distribution consequences were given considerable emphasis in model construction. In this paper some b a c k g o u n d is given on other work of relevance to economic systems modelling. This is followed by a detailed description of the general structure and the individual components of the Kenyan model. Two applications are included to illustrate the scope of the model and finally, some conclusions are suggested.
BACKGROUND Much of the early work on general systems theory originated in the physical sciences, but in the past few years it has been applied to a far broader set of problems. These include planning and control studies in such diverse areas as industrial processes, urban and regional planning, traffic and transportation management, water resources management and economic development [5]. Two recent survey articles of general interest in the area of economic modelling are Young et al [14, pp. 145-165] and Peston [9]. Applications of economic systems modelling to developing countries include Abkin and Manetsch [1, 97-107], De Haen and Lee [2], Holland [4] and the BACHUE models of the World Employment Programme [3]. The conceptual framework of the general systems model of the Kenyan economy described in this paper was influenced by the work of Koenig [6, 7, 8], which led to the development of two simulation models by Slater, Riley et al [10, 11] to describe elements of the Puerto Rican food marketing system and the market economy of the northeast of Brazil. The Kenyan model is a direct descendant of the Brazilian model. The motivation for the modelling effort in Brazil was to provide an orderly means of assessing trade-offs resulting when modern institutions, such as supermarkets, displaced traditional distribution workers in developing economies. On the one hand, consumers would enjoy lower prices as a result of modern institutions; on the other hand, employment in the traditional marketing system is reduced. Starting from this interest in marketing processes, a general descriptive model of the economy of a developing country has evolved. The Brazilian model was concerned with the distribution problems of a region, and had only three productive sectors and five consumer groups. The Kenyan model deals with the total economy, has nine productive sectors and nine consumer classes, and in addition, capital formation as well as government are integrated into the model as interactive components.
G E N E R A L STRUCTURE OF THE MODEL Fig. 1 shows a condensed d i a ~ a m of the overall system in any given year. The direction of the arrows in the diagram indicate money flows, whereas the 558
Omega, Vol. 3, No. 5 flows of goods and services are in the reverse direction. The model consists of a nine sector input/output production component linked to a consumption component by four sales sectors from which consumers make direct purchases. The productive and sales sectors are listed in Fig. 1. Some further clarification may be necessary for the sales sectors. The throughput of traditional produce is consumed directly by subsistence farmers and does not pass through a commercial sector. The throughput of the commercial sector is split into goods and services, the latter including such activities as hotels and transport services. Lastly, the utilities sales sector includes electricity and water for which consumers pay directly. The consumption component is disag~egated into nine income classes, four rural classes A to D and five urban classes E to I. Consumer income is generated by wages and rents from productive sectors, including income in kind from subsistence agriculture. There is also an internal money transfer activity from richer to poorer income classes. Each class is characterized by fixed parameters representing real income, average consumption and savings propensities, average taxation and income transfer behaviour to other classes. Thus, the income and expenditure pattern within a given class remains constant over time, but the numbers of households within each class varies with time depending on total income changes, inflation, population increases and rural-urban migration rates. IMPORTS Infermed,ale Consumolto~
t
Investment Wages
1,
tt
Rents
NINESECTORINPUT/OUTPUT PROOUCTIONCOMPONENT
SALES SECTORS
CONSUMPTIONCOMPONENT
l-Z'l 171 [ ]
a~lrlculture
low
[]
Ruril
N~gh
[]
FZl IZ]
Manufactur=ng
], construction o,to,ng.o. []
[]
LOw
!
.....
FIG. 1. Overall model structure.
3/~--D
High
Savings
GOVERNMENT G~ernment [ ?MPONENT [ ' ~ . . . . . t
OMEC^
Urban
559
-':-
~ I~U.MA,,Ur~ I
Investment--==II,=--
Slater, Walsham--Model of the Kenyan Economy The government component receives income in the form of taxes and loans which it uses to operate government services, to create investment, to service loans and thus to generate a surplus or deficit. A capital formation component draws resources from consumers, productive sectors, government and foreign loans. Capital is then invested in the productive sectors and this creates demand due to construction expenditures, increases productive capacity, and alters input/output coefficients. The remaining flows shown in Fig. 1 concern imports to and exports from the nine productive sectors. Exports are a simple aggregate by sector, whereas imports are split into three types. Capital imports are related to the investment in each sector, whereas intermediate imports are a function of gross output. Consumption imports occur in the case where demand exceeds the capacity of the sector.
The technical coefficients and propensities of the overall system were estimated using a complete set of actual data, mainly from government records for the year 1971. The model then advances in time units of one year. To generate later years, anticipated changes in price levels of imports, wages, rents and interest rates, as well as policies affecting government and private investment strategies, bring about changes in the capacity of the economy, income distribution and effective demand. It is important to note that demand then determines production rather than the reverse. Thus the model generates predicted sectoral growth rates endogenously as a function of demand. The actual method used to go from one year to the next is programmed as a series of sequential operations. This computational sequence is described in the flow diagram of Fig. 2. The solid line gives the actual sequence of the computer simulation program; the dotted line shows other information transferred between parts of the process. In the next section, we describe the flow diagram in some detail.
DETAILED MODEL DESCRIPTION The order of topics discussed below follows the actual sequence of the computer simulation as shown in the flow diagram of Fig. 2.
Consumer demand Given the number of households within each income class, the first component of the model calculates the total consumer demand for the output of the four sales sectors from which consumers make direct purchases. For example, Consumer direct Number of households Average consumption propensity demand for = ~' in class k x in class k for commercial goods commercial goods all income classes k
560
Omega, Vol. 3, No. 5
~ST~RTOFYEAR> I CONSUMER DEMAN~ Gvi enconsume,nr¢omediStrlbulionand
onsumptlon propenl~t~es,total consumer de,an( on t~e productive sectors ~scalculated: a~so total consumer ta~es, savings and direct impo~s.
GOVERNMENT
|
Government income is calculated as the sum Of taxes, and loans. Government expenditure ;stead in exogenously and defiot is ~he residua¢ e xoend~ture-income.
duty
I I I |
I% IJ |
.
.
.
.
Given export and stock chang(t figu res " l i b read in exogenously hnal demand is Calculalad as the sum of COnsumer demand, government consumption. cor~struction effect demand, exports and s~ock changes.
.
[
CAP;TALFORMATIC]N
I
/
PRODUCTION
Given the flnel output of the produc~;ve l sectors and the 4evelsof inflation, a calculation 1~ is m~ldeof wages and tents to consumerS, tola~ business taxes and intermedrate imports.
|
I l I I
G;ven final demand data. standard input/output anaWsr~is used to generate the gross output of the pfociuctlve ~,ectars. (f this exceeds the capacity consIraint forthat Sector. remalnlng demand is met by consumption imports.
calcutat~:1
t
/
O~
IMPACT CAPITAL INVESTM ENT~ Capital inves:ment has lhe fo~:ow,ng effects: 1, Demand Is generated by the const ruchon =~fte~tof cap*:al | ~nvestment. 2. Capacity ;s increased, 3. Input, out put technical coefficlen
I .... ,*ered.
Given exogenous change~ ~nthe price o~ imports, w ~KJes.Tents.depreciation, interest and tales. ~he new price at the output (ram the productiv~ sector s ~s
[
Caoita~ formation is calculated ~ the sum of consumer savings, b~s=ness savings government cao*tal e~ponditure and private caohal
.moor,s. FINAL DEMAN0
.
I
I I
! I I I I l ~ ~ ~ ~
| |
D INCOME ISTRIBUTION
| L
~ ~
J G;~en exogenous population growth and migration ~ates. toget her whtl endogenous data on consumer income and inflation levels, the total population is red~smbuted amongst ",he income classes. A calculation is also made of number= in wage employment in each income Class.
t TO START OF NEXT YEAR >
FIG. 2. Model computational sequence. Direct consumer demand on the four sales sectors is converted to demand on the nine productive sectors using a matrix giving the proportion o f the throughput of the sales sectors originating in each productive sector.
Government Government income is calculated as the sum o f indirect taxes, consumer taxes, duty on imports, and loans to government. These items are calculated endogenously within the model depending on the performance of the economy during the previous year; with the exception of loans to government which are read in exogenously. Government policy on consumption expenditure, capital 561
Slater, Walsham--Model of the Kenyan Economy formation expenditure and subsidies are also read in exogenously and their sum results in total government expenditure. The source for government policy data was originally the 1974-1978 Development Plan, but later modified values were supplied by the Ministry of Finance and Economic Planning. It is worth noting that the model can be used to assist planners in the Ministry in determining these values. Policy simulation exercises can be carried out by varying total government expenditure and also by varying the pattern of expenditure, both in terms of different amounts to the various sectors and also in type of expenditure within each sector.
Capital formation and the impact of the capital investment Capital formation within each sector is calculated as the sum of consumer savings allocated to that sector, business savings, government capital expenditure and private capital imports. The impact of capital investment is then considered as a three stage process. This is a novel feature of the model which needs more detailed explanation. First, capital investment is assumed to have a construction effect. Total investment in any given sector is used partly for capital imports, but the remainder pays for such items as buildings, roads, land improvement and other internal productive outputs. Thus the construction effect of capital investment results in the creation of direct demand on the nine productive sectors of the economy, a considerable proportion being demand on the Building and Construction sector and the Services sector. The second impact of capital investment is to alter the capacity of the sector. Since this model is demand driven, it is assumed that capital investment does not directly result in increased output, but only increased capacity. The extra capacity is utilized if demand rises sufficiently to require it. The third effect of capital investment is to alter the input/output technical coefficients within the model. For example, Tobin [13] demonstrated in Kenya that the long term impact of capital investment within the economy is to gradually reduce the number of jobs per unit of output. This reduction can be estimated as a function of total capital investment within any given productive sector. Similarly, capital investment affects other technical coefficients, such as the degree of dependence on intermediate imports for production, and the pattern of rental income changes.
Final demand and production Having determined final demand, the provisional gross output of each sector can be calculated using standard input/output analysis. If the provisional gross output exceeds the capacity of the sector, the balance of demand is met by consumption imports at world prices. This is particularly relevant in the agricultural sector where shortfalls in local production must be met by the importation of foodstuffs. The model includes a weather factor which has the effect of 562
Omega, Vol. 3, ,Vo. 5 reducing the capacity of the agricultural sector in a bad weather year, thus simulating the impact of unfavourable climatic conditions.
Price inflation and payments Exogenous data are read in to the model on price changes in imports, wages, rents, depreciation, interest and taxes; a number of these are policy variables which can be regulated by government. Corresponding output price increases can be calculated using standardinput/output analysis. When the final output of each of the productive sectors is known, together with levels of price inflation in each sector, a calculation is made of wages paid and rental incomes to each of the consumer classes. Income distribution This is the final stage in the computational sequence of the model which redistributes the total population amongst the nine income classes. It draws together the generated data on income increases and inflation changes, together with exogenous data on population increase and rural-urban migration rates. This component of the program is concerned with setting new values for nk (k = 1, 9), being the numbers in each of the nine income classes. Using the population change data we can calculate the new total rural and total urban populations which gives the equations: 4 X n~ = total rural population k=l 9
2 n~ = total urban population k=5 Using the generated values for income increase we can calculate the change in total urban and rural income. Suppose that )'k (k = 1, 9) is the income per household for each class, we obtain two more equations: 4
Z k=l
n~yk = total rural income
9 Z n~yt, = total urban income k=5 Thus we have four equations in the nine unknowns n~ (k = 1, 9) and no unique solution exists. However, additional information was generated, in the section on price inflation and payments, giving income and inflation changes by income class. This data can be used to arrive at the values of n~ as follows. For each income class k, a measure of real income increase to that class can be calculated as 563
Slater, Walsham--Model of the Kenyan Economy being the difference between the change in total income to that class, F A C I N C (k), less the price inflation experienced by that class, F A C I N F (k). The factor [FACINC (k) -- F A C I N F (k)] is a measure of the increase in real income to class k which enables members within that group to transfer to the next highest class (k + 1). However, the number able to transfer to class (k ÷ 1) is also a function of the difference in average income between the two classes. So additional limiting factors are imposed, dependent on the difference between the average income in consecutive classes. For example, the number of households transferring from income class A to income class B = Old number of households in class A × 0.5 × [FACINC (1) -- F A C I N F (1)]. This transfer procedure results in new estimated values for nk (k = 1, 9). Finally it is necessary to ensure that the four earlier equations in the nine unknowns are exactly satisfied. This is accomplished by an adjustment to the number of households within the highest and lowest income classes in the urban and rural areas. At the completion of the redistribution of the population amongst income classes, a calculation is made of those in wage employment in each class dependent on the employment spectrum within each productive sector. This enables numbers not in wage employment to be calculated, which is an important political variable in urban areas where high unemployment rates threaten stability.
Summary and computing aspects The component of income distribution completes the computational sequence of the model. The model is recursive and the sequence for the succeeding year starts with the component of consumer demand. The actual computer program of the model is written in F O R T R A N IV and has been run mainly on an ICL 1902A computer. It occupies 18K of core store on this machine and takes 8 mffautes of elapsed time to run for a simulated period of 7 years.
APPLICATIONS The model has been applied, in conjunction with personnel from the Kenyan Ministry of Finance and Economic Planning, to a number of development planning problems. The set of applications can be loosely grouped into the two categories of pure forecasting and the simulation of alternative policy options. We will give a description of one application in each of the areas.
Forecasting The base year of the model was chosen to be 1971, since the dynamic nature of a developing economy requires the use of a recent year for parameter estimates. The model generates forecasts from 1972 onwards and validation checks were carried out for the period 1972-1973, for which Kenyan government data 564
Omega, Vol. 3, iVo. 5 had been published. The results were satisfactory and further validation will be carried out for later years as actual data become available. A future period for which reasonably reliable exogenous data were available was the duration of the current Kenyan Development Plan, 1974-1978. The Plan was formulated mainly during 1973 and includes predictions of growth rate by sector and other measures of economic performance. Thus a useful exercise with the model was to predict the performance of the economy for 1974-1978 using later information than that used by the Plan. The results from this model exercise included a wide range of measures of economic performance, and some of the important ones showed considerable differences from the Plan. First, the Plan forecasted an overall growth rate of 7-4~ per year whereas the model forecast was only 5"8~o per year overall growth. Later work with the model suggested that even this latter rate is unlikely to be achieved, as worsening terms of trade continue to have adverse effects on the economy. Secondly, model predictions on employment growth and Government deficit were considerably less optimistic than those shown in the Plan. A final area of difference in model and Plan forecasts concerned income distribution. Table 1 summarises the model forecasts, which showed a further concentration of income over the period 1973-1978. The Plan suggested that Government policies should lead to a more equal distribution of income by 1978, but this was not quantified. The model suggested in quantitative terms that this objective was unlikely to be achieved with current policies. TABLE 1. MODEL FORECASTSOF CHANGING INCOME DISTRIBUTION
% of total income held by lower 50% of the income strata % of total income held by upper 2 ~ of the income strata
1973
1978
17~0
15%
30%
39~o
Simulation of alternative policy options The above application of the model is an example of the pure forecasting role in which problem areas are uncovered and quantified, but no attempt is made to suggest remedies. From the policy planners' viewpoint, a rather more useful type of model application concerns the evaluation of alternative policy options, with a view to suggesting which of a number of strategies is preferable. It is not possible, in policy planning at the macro.economic level, to formulate an objective function which matches the political and economic beliefs of all the interested parties to the decision problem. The approach taken with this model is 565
Slater, Walsham--Modelof the Kenyan Economy to extract a number of different measures of economic performance forecasted under alternative strategies. These are presented to decision makers, who then exercise the necessary judgement of trade-offs. The application described here concerns the problem of government policy to alleviate the worst effects of imported inflation in the agricultural sector. The prices of imported farm inputs, in particular fertilizers, experienced an extremely rapid inflation in price during 1973-1974. The Kenya Government could intervene and limit the price rises to farmers by means of subsidies on the imported price. Also, by means of the price control mechanism, Government could raise the prices to consumers in order to maintain existing margins for the farmer, or could limit consumer price rises and force farmers to absorb some of the extra costs. The simulation model was used to examine the consequences of some of these alternative strategies. The results from this exercise gave considerable evidence against forcing farmers to absorb some of the extra costs of imported farm inputs. Growth, income distribution and government deficits were all favourable when passing price rises through to consumers. The only significant cost shown for this strategy was a slight increase in general inflation levels. The case for and against the use of government subsidies on the imported price of fertilizer was less clear. Growth and income distribution consequences were marginally favourable when allowing a subsidy, but at the cost of a considerable increase in government expenditure and thus gross deficit. Clearly the model is not able to quantify some of the political consequences of suggested strategies. For example, a rapid rise in consumer food prices antagonises the politically powerful urban work force in Kenya and puts pressure on the Government to allow wage rates to rise more rapidly.
CONCLUSIONS One conclusion which can be drawn from this work is that it is possible to interest and involve top level planners in a developing country in the use of this type of model. The simulation model can provide the decision maker with more information than would be obtainable through routine sources, and this was a major factor in successful implementation. Another factor which helped to interest local decision makers was the income distribution feature of the model. Economic planners have tended to deal indirectly with the redistributive consequences of various policy options, since traditional economic models and analysis, for the most part, do not have mechanisms linking fiscal actions to income distribution. The Kenyan model enables these interactions to be dealt with explicitly. 566
Omega, Vol. 3, No. 5
ACKNOWLEDGEMENTS The authors would like to thank the staff of the Ministry of Finance and Economic Planning of the Government of Kenya who have co-operated on this work. In addition, Dr Mahendra Shah of the University of Nairobi has contributed many helpful suggestions, both on the work and on the preparation of this paper.
REFERENCES 1. ABKIN MH and MANETSCHTJ (1973) A generalised system simulation approach to agricultural development planning and policy making. IFA C/IFORS Symposium on Systems Approaches to Developing Countries, Algiers, Conference Proceedings. 2. DE HAEN H and LEE JH (1972) Dynamic models of farm resources allocation for agricultural planning in Korea: application of recursive programming within a general systems simulation approach. Agricultural Sector Formulation Project Working Paper, Michigan State University, October. 3. Economic-Demographic l~4odelling Activities of the World Employment Programme (1973) International Labour Office, Geneva. 4. HOLLAND EP et al (1966) Dynamic Models for Simulating the Venezuelan Economy. Simulmatics Corporation, New York. 5. IFAC--Proceedings of the 5th World Congress (1972) Paris. 6. KEENEY HG, KOENIG HE and ZAMACH R (1967) State Space Models of Educational Institutions. 2rid International Conference of the Organization for Economic Cooperation and Development, Paris. 7. KOENIGHE and BLACKWELLWA (1961) Electro-Mechanical System Theory. McGraw-Hill, New York. 8. KOE,'mG HE, HILMERSONA and JUAN L (1968) Alodern Systems Theory in Agricultural Industry--An Example. American Society of Agricultural Engineering. 9. PESTON MH (1974) Economics and quantitative economics: a defence. Omega, 2(2), 147-156. 10. RtLEY H, SLATERCC et al (1970) Food Marketing in the Economic Development of Puerto Rico. Latin American Studies Centre, Michigan State University. 11. SLATER CC, RILEY H et al (1969) Market Processes in the Recife Area of Northeast Brazil. Latin American Studies Center, Michigan State University. 12. SLATERCC and WALSHAMG (1974) A General Systems Simulation of the Kenyan Economy. Working Paper No. 174, Institute for Development Studies, University of Nairobi, Kenya. 13. TOBIN J (1972) Estimates of Sectoral Capital[Output Ratios for Kenya. Discussion Paper No. 171, Institute for Development Studies, University of Nairobi, Kenya. 14. YOUNG P, NAUGHTONJ, NEETHLINGC and SHELLSWELLS (1973) Macro-economic modelling--a case study. In 3rd IFAC Symposium on Identification and System Parameter Estimation Proceedings. North Holland.
567
A Systems Simulation Model of the Kenyan Economy CHARLES C SLATER University of Colorado
GEOFFREY WALSHAM University of Nairobi (Received November 1974; in revised form February 1975)
This paper describes a systems simulation model of the national economy of Kenya. The model contains an input/output production component linked to a consumption component, disaggregated into nine income classes. Capital formation and government are integrated into the model as interactive elements. The model is demand driven and thus growth rates in the productive sectors are generated endogenously as a function of demand. The model has been used by the Kenyan Ministry of Finance and Economic Planning for forecasting and policy evaluation problems. A contributory factor in the successful implementation of the model is its ability to supply detailed quantitative forecasts which, in a developing country, are not readily available from routine sources. In addition, the model deals explicitly with income distribution and inflation consequences which are issues of current concern to local development planners.
INTRODUCTION THE WORK described in this p a p e r concerns a general systems s i m u l a t i o n m o d e l o f the n a t i o n a l e c o n o m y o f K e n y a . T h e m o d e l was d e v e l o p e d by the a u t h o r s d u r i n g a one year p e r i o d f r o m A u g u s t 1973. A b r i e f d e s c r i p t i o n o f some aspects o f the w o r k has a l r e a d y been p u b l i s h e d in K e n y a [12]. T h e p u r p o s e o f the present p a p e r is to r e a c h a wider a u d i e n c e o f m a n a g e m e n t scientists w h o a r e interested in the use o f s i m u l a t i o n for m a c r o - e c o n o m i c modelling. The m o d e l has been a p p l i e d in a d e v e l o p i n g c o u n t r y , where detailed w o r k on policy p r o b l e m s is often c o n s t r a i n e d by the scarcity o f skilled m a n p o w e r . T h e use o f a s i m u l a t i o n m o d e l provides d e v e l o p m e n t p l a n n e r s with i n f o r m a t i o n for decision m a k i n g which c a n n o t easily be o b t a i n e d by alternative m a n u a l m e t h o d s . This was a m a j o r factor in helping to interest decision m a k e r s in the m o d e l a p p r o a c h . A n o t h e r factor in successful i m p l e m e n t a t i o n was the conscious effort m a d e at the design stage to ensure t h a t the m o d e l was c a p a b l e o f dealing with issues o f current concern to local policy makers. I n p a r t i c u l a r , inflation effects 557
Slater, Walsham--Model of the Kenyan Economy and income distribution consequences were given considerable emphasis in model construction. In this paper some b a c k g o u n d is given on other work of relevance to economic systems modelling. This is followed by a detailed description of the general structure and the individual components of the Kenyan model. Two applications are included to illustrate the scope of the model and finally, some conclusions are suggested.
BACKGROUND Much of the early work on general systems theory originated in the physical sciences, but in the past few years it has been applied to a far broader set of problems. These include planning and control studies in such diverse areas as industrial processes, urban and regional planning, traffic and transportation management, water resources management and economic development [5]. Two recent survey articles of general interest in the area of economic modelling are Young et al [14, pp. 145-165] and Peston [9]. Applications of economic systems modelling to developing countries include Abkin and Manetsch [1, 97-107], De Haen and Lee [2], Holland [4] and the BACHUE models of the World Employment Programme [3]. The conceptual framework of the general systems model of the Kenyan economy described in this paper was influenced by the work of Koenig [6, 7, 8], which led to the development of two simulation models by Slater, Riley et al [10, 11] to describe elements of the Puerto Rican food marketing system and the market economy of the northeast of Brazil. The Kenyan model is a direct descendant of the Brazilian model. The motivation for the modelling effort in Brazil was to provide an orderly means of assessing trade-offs resulting when modern institutions, such as supermarkets, displaced traditional distribution workers in developing economies. On the one hand, consumers would enjoy lower prices as a result of modern institutions; on the other hand, employment in the traditional marketing system is reduced. Starting from this interest in marketing processes, a general descriptive model of the economy of a developing country has evolved. The Brazilian model was concerned with the distribution problems of a region, and had only three productive sectors and five consumer groups. The Kenyan model deals with the total economy, has nine productive sectors and nine consumer classes, and in addition, capital formation as well as government are integrated into the model as interactive components.
G E N E R A L STRUCTURE OF THE MODEL Fig. 1 shows a condensed d i a ~ a m of the overall system in any given year. The direction of the arrows in the diagram indicate money flows, whereas the 558
Omega, Vol. 3, No. 5 flows of goods and services are in the reverse direction. The model consists of a nine sector input/output production component linked to a consumption component by four sales sectors from which consumers make direct purchases. The productive and sales sectors are listed in Fig. 1. Some further clarification may be necessary for the sales sectors. The throughput of traditional produce is consumed directly by subsistence farmers and does not pass through a commercial sector. The throughput of the commercial sector is split into goods and services, the latter including such activities as hotels and transport services. Lastly, the utilities sales sector includes electricity and water for which consumers pay directly. The consumption component is disag~egated into nine income classes, four rural classes A to D and five urban classes E to I. Consumer income is generated by wages and rents from productive sectors, including income in kind from subsistence agriculture. There is also an internal money transfer activity from richer to poorer income classes. Each class is characterized by fixed parameters representing real income, average consumption and savings propensities, average taxation and income transfer behaviour to other classes. Thus, the income and expenditure pattern within a given class remains constant over time, but the numbers of households within each class varies with time depending on total income changes, inflation, population increases and rural-urban migration rates. IMPORTS Infermed,ale Consumolto~
t
Investment Wages
1,
tt
Rents
NINESECTORINPUT/OUTPUT PROOUCTIONCOMPONENT
SALES SECTORS
CONSUMPTIONCOMPONENT
l-Z'l 171 [ ]
a~lrlculture
low
[]
Ruril
N~gh
[]
FZl IZ]
Manufactur=ng
], construction o,to,ng.o. []
[]
LOw
!
.....
FIG. 1. Overall model structure.
3/~--D
High
Savings
GOVERNMENT G~ernment [ ?MPONENT [ ' ~ . . . . . t
OMEC^
Urban
559
-':-
~ I~U.MA,,Ur~ I
Investment--==II,=--
Slater, Walsham--Model of the Kenyan Economy The government component receives income in the form of taxes and loans which it uses to operate government services, to create investment, to service loans and thus to generate a surplus or deficit. A capital formation component draws resources from consumers, productive sectors, government and foreign loans. Capital is then invested in the productive sectors and this creates demand due to construction expenditures, increases productive capacity, and alters input/output coefficients. The remaining flows shown in Fig. 1 concern imports to and exports from the nine productive sectors. Exports are a simple aggregate by sector, whereas imports are split into three types. Capital imports are related to the investment in each sector, whereas intermediate imports are a function of gross output. Consumption imports occur in the case where demand exceeds the capacity of the sector.
The technical coefficients and propensities of the overall system were estimated using a complete set of actual data, mainly from government records for the year 1971. The model then advances in time units of one year. To generate later years, anticipated changes in price levels of imports, wages, rents and interest rates, as well as policies affecting government and private investment strategies, bring about changes in the capacity of the economy, income distribution and effective demand. It is important to note that demand then determines production rather than the reverse. Thus the model generates predicted sectoral growth rates endogenously as a function of demand. The actual method used to go from one year to the next is programmed as a series of sequential operations. This computational sequence is described in the flow diagram of Fig. 2. The solid line gives the actual sequence of the computer simulation program; the dotted line shows other information transferred between parts of the process. In the next section, we describe the flow diagram in some detail.
DETAILED MODEL DESCRIPTION The order of topics discussed below follows the actual sequence of the computer simulation as shown in the flow diagram of Fig. 2.
Consumer demand Given the number of households within each income class, the first component of the model calculates the total consumer demand for the output of the four sales sectors from which consumers make direct purchases. For example, Consumer direct Number of households Average consumption propensity demand for = ~' in class k x in class k for commercial goods commercial goods all income classes k
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~ST~RTOFYEAR> I CONSUMER DEMAN~ Gvi enconsume,nr¢omediStrlbulionand
onsumptlon propenl~t~es,total consumer de,an( on t~e productive sectors ~scalculated: a~so total consumer ta~es, savings and direct impo~s.
GOVERNMENT
|
Government income is calculated as the sum Of taxes, and loans. Government expenditure ;stead in exogenously and defiot is ~he residua¢ e xoend~ture-income.
duty
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.
.
.
.
Given export and stock chang(t figu res " l i b read in exogenously hnal demand is Calculalad as the sum of COnsumer demand, government consumption. cor~struction effect demand, exports and s~ock changes.
.
[
CAP;TALFORMATIC]N
I
/
PRODUCTION
Given the flnel output of the produc~;ve l sectors and the 4evelsof inflation, a calculation 1~ is m~ldeof wages and tents to consumerS, tola~ business taxes and intermedrate imports.
|
I l I I
G;ven final demand data. standard input/output anaWsr~is used to generate the gross output of the pfociuctlve ~,ectars. (f this exceeds the capacity consIraint forthat Sector. remalnlng demand is met by consumption imports.
calcutat~:1
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IMPACT CAPITAL INVESTM ENT~ Capital inves:ment has lhe fo~:ow,ng effects: 1, Demand Is generated by the const ruchon =~fte~tof cap*:al | ~nvestment. 2. Capacity ;s increased, 3. Input, out put technical coefficlen
I .... ,*ered.
Given exogenous change~ ~nthe price o~ imports, w ~KJes.Tents.depreciation, interest and tales. ~he new price at the output (ram the productiv~ sector s ~s
[
Caoita~ formation is calculated ~ the sum of consumer savings, b~s=ness savings government cao*tal e~ponditure and private caohal
.moor,s. FINAL DEMAN0
.
I
I I
! I I I I l ~ ~ ~ ~
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D INCOME ISTRIBUTION
| L
~ ~
J G;~en exogenous population growth and migration ~ates. toget her whtl endogenous data on consumer income and inflation levels, the total population is red~smbuted amongst ",he income classes. A calculation is also made of number= in wage employment in each income Class.
t TO START OF NEXT YEAR >
FIG. 2. Model computational sequence. Direct consumer demand on the four sales sectors is converted to demand on the nine productive sectors using a matrix giving the proportion o f the throughput of the sales sectors originating in each productive sector.
Government Government income is calculated as the sum o f indirect taxes, consumer taxes, duty on imports, and loans to government. These items are calculated endogenously within the model depending on the performance of the economy during the previous year; with the exception of loans to government which are read in exogenously. Government policy on consumption expenditure, capital 561
Slater, Walsham--Model of the Kenyan Economy formation expenditure and subsidies are also read in exogenously and their sum results in total government expenditure. The source for government policy data was originally the 1974-1978 Development Plan, but later modified values were supplied by the Ministry of Finance and Economic Planning. It is worth noting that the model can be used to assist planners in the Ministry in determining these values. Policy simulation exercises can be carried out by varying total government expenditure and also by varying the pattern of expenditure, both in terms of different amounts to the various sectors and also in type of expenditure within each sector.
Capital formation and the impact of the capital investment Capital formation within each sector is calculated as the sum of consumer savings allocated to that sector, business savings, government capital expenditure and private capital imports. The impact of capital investment is then considered as a three stage process. This is a novel feature of the model which needs more detailed explanation. First, capital investment is assumed to have a construction effect. Total investment in any given sector is used partly for capital imports, but the remainder pays for such items as buildings, roads, land improvement and other internal productive outputs. Thus the construction effect of capital investment results in the creation of direct demand on the nine productive sectors of the economy, a considerable proportion being demand on the Building and Construction sector and the Services sector. The second impact of capital investment is to alter the capacity of the sector. Since this model is demand driven, it is assumed that capital investment does not directly result in increased output, but only increased capacity. The extra capacity is utilized if demand rises sufficiently to require it. The third effect of capital investment is to alter the input/output technical coefficients within the model. For example, Tobin [13] demonstrated in Kenya that the long term impact of capital investment within the economy is to gradually reduce the number of jobs per unit of output. This reduction can be estimated as a function of total capital investment within any given productive sector. Similarly, capital investment affects other technical coefficients, such as the degree of dependence on intermediate imports for production, and the pattern of rental income changes.
Final demand and production Having determined final demand, the provisional gross output of each sector can be calculated using standard input/output analysis. If the provisional gross output exceeds the capacity of the sector, the balance of demand is met by consumption imports at world prices. This is particularly relevant in the agricultural sector where shortfalls in local production must be met by the importation of foodstuffs. The model includes a weather factor which has the effect of 562
Omega, Vol. 3, ,Vo. 5 reducing the capacity of the agricultural sector in a bad weather year, thus simulating the impact of unfavourable climatic conditions.
Price inflation and payments Exogenous data are read in to the model on price changes in imports, wages, rents, depreciation, interest and taxes; a number of these are policy variables which can be regulated by government. Corresponding output price increases can be calculated using standardinput/output analysis. When the final output of each of the productive sectors is known, together with levels of price inflation in each sector, a calculation is made of wages paid and rental incomes to each of the consumer classes. Income distribution This is the final stage in the computational sequence of the model which redistributes the total population amongst the nine income classes. It draws together the generated data on income increases and inflation changes, together with exogenous data on population increase and rural-urban migration rates. This component of the program is concerned with setting new values for nk (k = 1, 9), being the numbers in each of the nine income classes. Using the population change data we can calculate the new total rural and total urban populations which gives the equations: 4 X n~ = total rural population k=l 9
2 n~ = total urban population k=5 Using the generated values for income increase we can calculate the change in total urban and rural income. Suppose that )'k (k = 1, 9) is the income per household for each class, we obtain two more equations: 4
Z k=l
n~yk = total rural income
9 Z n~yt, = total urban income k=5 Thus we have four equations in the nine unknowns n~ (k = 1, 9) and no unique solution exists. However, additional information was generated, in the section on price inflation and payments, giving income and inflation changes by income class. This data can be used to arrive at the values of n~ as follows. For each income class k, a measure of real income increase to that class can be calculated as 563
Slater, Walsham--Model of the Kenyan Economy being the difference between the change in total income to that class, F A C I N C (k), less the price inflation experienced by that class, F A C I N F (k). The factor [FACINC (k) -- F A C I N F (k)] is a measure of the increase in real income to class k which enables members within that group to transfer to the next highest class (k + 1). However, the number able to transfer to class (k ÷ 1) is also a function of the difference in average income between the two classes. So additional limiting factors are imposed, dependent on the difference between the average income in consecutive classes. For example, the number of households transferring from income class A to income class B = Old number of households in class A × 0.5 × [FACINC (1) -- F A C I N F (1)]. This transfer procedure results in new estimated values for nk (k = 1, 9). Finally it is necessary to ensure that the four earlier equations in the nine unknowns are exactly satisfied. This is accomplished by an adjustment to the number of households within the highest and lowest income classes in the urban and rural areas. At the completion of the redistribution of the population amongst income classes, a calculation is made of those in wage employment in each class dependent on the employment spectrum within each productive sector. This enables numbers not in wage employment to be calculated, which is an important political variable in urban areas where high unemployment rates threaten stability.
Summary and computing aspects The component of income distribution completes the computational sequence of the model. The model is recursive and the sequence for the succeeding year starts with the component of consumer demand. The actual computer program of the model is written in F O R T R A N IV and has been run mainly on an ICL 1902A computer. It occupies 18K of core store on this machine and takes 8 mffautes of elapsed time to run for a simulated period of 7 years.
APPLICATIONS The model has been applied, in conjunction with personnel from the Kenyan Ministry of Finance and Economic Planning, to a number of development planning problems. The set of applications can be loosely grouped into the two categories of pure forecasting and the simulation of alternative policy options. We will give a description of one application in each of the areas.
Forecasting The base year of the model was chosen to be 1971, since the dynamic nature of a developing economy requires the use of a recent year for parameter estimates. The model generates forecasts from 1972 onwards and validation checks were carried out for the period 1972-1973, for which Kenyan government data 564
Omega, Vol. 3, iVo. 5 had been published. The results were satisfactory and further validation will be carried out for later years as actual data become available. A future period for which reasonably reliable exogenous data were available was the duration of the current Kenyan Development Plan, 1974-1978. The Plan was formulated mainly during 1973 and includes predictions of growth rate by sector and other measures of economic performance. Thus a useful exercise with the model was to predict the performance of the economy for 1974-1978 using later information than that used by the Plan. The results from this model exercise included a wide range of measures of economic performance, and some of the important ones showed considerable differences from the Plan. First, the Plan forecasted an overall growth rate of 7-4~ per year whereas the model forecast was only 5"8~o per year overall growth. Later work with the model suggested that even this latter rate is unlikely to be achieved, as worsening terms of trade continue to have adverse effects on the economy. Secondly, model predictions on employment growth and Government deficit were considerably less optimistic than those shown in the Plan. A final area of difference in model and Plan forecasts concerned income distribution. Table 1 summarises the model forecasts, which showed a further concentration of income over the period 1973-1978. The Plan suggested that Government policies should lead to a more equal distribution of income by 1978, but this was not quantified. The model suggested in quantitative terms that this objective was unlikely to be achieved with current policies. TABLE 1. MODEL FORECASTSOF CHANGING INCOME DISTRIBUTION
% of total income held by lower 50% of the income strata % of total income held by upper 2 ~ of the income strata
1973
1978
17~0
15%
30%
39~o
Simulation of alternative policy options The above application of the model is an example of the pure forecasting role in which problem areas are uncovered and quantified, but no attempt is made to suggest remedies. From the policy planners' viewpoint, a rather more useful type of model application concerns the evaluation of alternative policy options, with a view to suggesting which of a number of strategies is preferable. It is not possible, in policy planning at the macro.economic level, to formulate an objective function which matches the political and economic beliefs of all the interested parties to the decision problem. The approach taken with this model is 565
Slater, Walsham--Modelof the Kenyan Economy to extract a number of different measures of economic performance forecasted under alternative strategies. These are presented to decision makers, who then exercise the necessary judgement of trade-offs. The application described here concerns the problem of government policy to alleviate the worst effects of imported inflation in the agricultural sector. The prices of imported farm inputs, in particular fertilizers, experienced an extremely rapid inflation in price during 1973-1974. The Kenya Government could intervene and limit the price rises to farmers by means of subsidies on the imported price. Also, by means of the price control mechanism, Government could raise the prices to consumers in order to maintain existing margins for the farmer, or could limit consumer price rises and force farmers to absorb some of the extra costs. The simulation model was used to examine the consequences of some of these alternative strategies. The results from this exercise gave considerable evidence against forcing farmers to absorb some of the extra costs of imported farm inputs. Growth, income distribution and government deficits were all favourable when passing price rises through to consumers. The only significant cost shown for this strategy was a slight increase in general inflation levels. The case for and against the use of government subsidies on the imported price of fertilizer was less clear. Growth and income distribution consequences were marginally favourable when allowing a subsidy, but at the cost of a considerable increase in government expenditure and thus gross deficit. Clearly the model is not able to quantify some of the political consequences of suggested strategies. For example, a rapid rise in consumer food prices antagonises the politically powerful urban work force in Kenya and puts pressure on the Government to allow wage rates to rise more rapidly.
CONCLUSIONS One conclusion which can be drawn from this work is that it is possible to interest and involve top level planners in a developing country in the use of this type of model. The simulation model can provide the decision maker with more information than would be obtainable through routine sources, and this was a major factor in successful implementation. Another factor which helped to interest local decision makers was the income distribution feature of the model. Economic planners have tended to deal indirectly with the redistributive consequences of various policy options, since traditional economic models and analysis, for the most part, do not have mechanisms linking fiscal actions to income distribution. The Kenyan model enables these interactions to be dealt with explicitly. 566
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ACKNOWLEDGEMENTS The authors would like to thank the staff of the Ministry of Finance and Economic Planning of the Government of Kenya who have co-operated on this work. In addition, Dr Mahendra Shah of the University of Nairobi has contributed many helpful suggestions, both on the work and on the preparation of this paper.
REFERENCES 1. ABKIN MH and MANETSCHTJ (1973) A generalised system simulation approach to agricultural development planning and policy making. IFA C/IFORS Symposium on Systems Approaches to Developing Countries, Algiers, Conference Proceedings. 2. DE HAEN H and LEE JH (1972) Dynamic models of farm resources allocation for agricultural planning in Korea: application of recursive programming within a general systems simulation approach. Agricultural Sector Formulation Project Working Paper, Michigan State University, October. 3. Economic-Demographic l~4odelling Activities of the World Employment Programme (1973) International Labour Office, Geneva. 4. HOLLAND EP et al (1966) Dynamic Models for Simulating the Venezuelan Economy. Simulmatics Corporation, New York. 5. IFAC--Proceedings of the 5th World Congress (1972) Paris. 6. KEENEY HG, KOENIG HE and ZAMACH R (1967) State Space Models of Educational Institutions. 2rid International Conference of the Organization for Economic Cooperation and Development, Paris. 7. KOENIGHE and BLACKWELLWA (1961) Electro-Mechanical System Theory. McGraw-Hill, New York. 8. KOE,'mG HE, HILMERSONA and JUAN L (1968) Alodern Systems Theory in Agricultural Industry--An Example. American Society of Agricultural Engineering. 9. PESTON MH (1974) Economics and quantitative economics: a defence. Omega, 2(2), 147-156. 10. RtLEY H, SLATERCC et al (1970) Food Marketing in the Economic Development of Puerto Rico. Latin American Studies Centre, Michigan State University. 11. SLATER CC, RILEY H et al (1969) Market Processes in the Recife Area of Northeast Brazil. Latin American Studies Center, Michigan State University. 12. SLATERCC and WALSHAMG (1974) A General Systems Simulation of the Kenyan Economy. Working Paper No. 174, Institute for Development Studies, University of Nairobi, Kenya. 13. TOBIN J (1972) Estimates of Sectoral Capital[Output Ratios for Kenya. Discussion Paper No. 171, Institute for Development Studies, University of Nairobi, Kenya. 14. YOUNG P, NAUGHTONJ, NEETHLINGC and SHELLSWELLS (1973) Macro-economic modelling--a case study. In 3rd IFAC Symposium on Identification and System Parameter Estimation Proceedings. North Holland.
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