World Bank Reprint Series: Number 325

A. Drud, W. Grais, and G. Pyatt

lTe Transactlon Value ApproachA Systematic M\ethod of DefiningEconomywide Models Basedon Social Accounting Matrices

Reprinted with permission from T. Basar and L. F. Pau, eds. Dynamic Modelling and Control of NationallEconomies 1983, Proceedings of the 4th IFAC/IFORS/IIASA Conference and the 1983 SEDCConference on Economic Dynamics and Control, Washington, D.C., June 17-I9, 1983 (New York:Pergamon Press, 1983), pp. 241-48.

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Copyi'iglit © IrAC' Dynamnic Modelling and(i Control ofNational Econiomies. Waishington D(., USA 198.9

THE TRANSACTION VALUE APPROACH: A SYSTEMATICMETHOD OF DEFINING ECONOMYWIDE MODELS BASED

ON SOCIAL ACCOUNTING MATRICES

A. Drud, W. Grais, and G. PyattDevelopment Researrh Department, World Bank, 1818 H Street, N.W., Washington, DC 20433, UTSA

Abstract: The Social Accounting Matrix (SAM), a convenient way ofgiving a comprehensive and consistent picture of an economy, is used asthe data base for many models. The paper describes the TransactionValue (TV) Approach, a systematic way of defining, estimating, andsolving economywide multisectoral equilibrium models based on a SAM.SAM-based models define for each period a SAM with the same accountingstructure as the base SAM. The behavioral equations of a SAM-basedmodel are derived from independent descriptions of the economic agents,and the model is tied together by the accounting identities of theSAM. The TV approach has four advantages: the models are guaranteed tobe consistent, it is easy to experiment with alternative formulations,most parameters can be estimated from the base SAM, and the underlyingsolution algorithm is guaranteed to converge under very generalassumptions.

Key words: Social Accounting Matrices, Multisectoral EquilibriumModels, Developing Economies, Modeling Methodology, Consistency.

INTRODUCTION process models. This is especially truefor multisector models that are important

This paper describes the Transaction Value in modeling economic development. The(TV) approach, a method for defining, missing data must therefore be replaced byestimating, and solving a class of econo- more theoretical content. A class ofmywide general equilibrium models. It development planning models (Dervis, dealso describes SAMLIB, a corresponding Melo, and Robinson, 1982) has replaced thesoftware package. Developed at the World shortrun dynamic process description byBank, the TV-approach and SAMLIB have so assumptions of medium term (within period)far been used with more than ten models of equilibrium in most markets. That reducesvarious developing economies. the dynamics of the models to the linkages

between periods through a small number ofSince many general purpose econometric such variables as debt, capital stock, andmodeling systems are commercially avail- labor force composition.able (Drud, 1983), we feel it is appro-priate to explain why we have worked on Equilibrium models are mathematicallyyet another system. Previous systems have formulated as a set of relations thatall been designed for use with econometric equate demand and supply in differentmodels of developed economies. Most of markets; they are not normalized. Thethese systems assume, implicitly or prices that adjust to clear each marketexplicitly, that the models describe will in many models not appear directly ineconomic processes. The mathematical the market-clearing equation but onlyrequirement is that the model is nor- indirectly in expressions for supply andmalized or in fixed-point format demand of intermediates. Equilibrium

models can, like all nonsingular models,* and that the natural be normalized. But there is no natural

iterative process defined by the normal normalization, and a method that alwaysized model (the Gauss-Seidel algorithm) finds a convergent normalization is notconverges. yet known.

The time series for developing countries Because the modeling environment inseldom are long enough to allow the developing countries differs much fromsophisticated estimation of lag structures standard macroeconomic modelingand dynamic behaviour needed in economic- environments, it puts different demands on

241

242 A. Drud, W. Grais and G. Pyatt

methods and software. Our objective has SAM-BASED MODELSbeen to develop a method and a softwaresystem that can: A SAM-based model produces, for each time

period, a SAM with the same structure aso help in formulating and representing the base-period SAM. It has the following

equilibrium models, variables:

o test the models for consistency, tij The transaction value in cell(i,j), i.e. the monetary value

o estimate parameters, of the payment from account j toaccount i in current prices. We

o solve the models reliably, and assume that only nonzero cellsin the base SAM will exist in

o make it easy to change assumptions. future periods.

The paper is organized as follows. We pJ The price index associated withfirst discuss our data base -- the Social account J.Accounting Matrix (SAM) - and continuewith an example of a model based on a y. - The total monetary transactions,SAM. We then define the TV approach and receipts or expenditures, ofdescribe our assumptions and the account j.procedures for estimating paramvters andsolving the model. The overal, method is qJ - The quantity index for thesummarized in the conclusion. transactions in account j.

Only a subset of the accounts will have aTHE SOCtAL ACCOUNTING MATRIX price in-ex and an associated quantity

AS A DATA BASE index. Examples are labor (wage), capital(rent), and activities and commodities. A

The first step in building an empirical tax account will never have a pricemodel is to establish a consistent data index. A household account need not havebase. Since our equilibrium models a price index, but it could have its owndescribe the whole circular flow in the consumer price index.'economy, the most natural single-perioddescription seems to be the SAM, which is Prices, values, and quantities are relateda matrix representating the circular flow by y = pj . qj . Since we have chosen(Pyatt, Roe, and co-workers, 1977). Thematrix of rows and columns is square with all price indices to be one (1) in theone row and one column, called accounts, base period, quantity indices must befor each economic entity such as a pro- interpreted properly. One unit of laborduction sector, commodity group, househcLd or capital is defined as the amount ofgroup, or government. Each nonzero cell labor or capital that earned one unit ofrepresents a transaction and contains the income in the base period.payment in monetary units, possiblyimputed, from the column account to the The definition of a price for an accountrow account. Savings and changes in implies that the account sells a uniformstocks are included as accounts, and the product or that all transactions in theSAM must balance: the row total of row take place at the same price. Ifreceipts in an account must equal the labor in the agricultural sector differscolumn total of expenditures. from labor in the manufacturing sector,

the SAM must have separate accounts forTable 1 is a small SAM. It shows the them.payments from three factors of productionto two household groups (columns I to 3), Tables 2 and 3 give an example of a modelpayments from two composite factor inputs based on the SAM in Table 1. For each ofto the three basic factors (columns 4 and the nonzero cells in the SAM, Table 25), household expenditure (columns 6 to contains a number that defines the9), government expenditure (column 10), behavior of the cell according to thethe composition of investments by sector following list (abstracted for presentof origin (column 11), the input-output purposes from a longer list):.matrix and factor inputs to production(columns 12 and 13), and the make matrix 2 - The cell is a residual, i.e. theand the indirect taxes on commodities value adjusts such that row and(column 14 and 15). The SAM is slightly column totals become equal. Thismore disaggregate than needed, but this type of cell is used, for example inhelps in modeling. For simplicity, we the government account to indicatehave excluded foreign trade. that government savings adjust to

changes in tax and other revenuesand to changes in currentexpenditures.

The Transaction Value Approach 243

3 - The value of the cell is dete ained THE TRANSACTION VALUEexogenously. This type of cell is APPROACH TO MODELINGused, for example, to define a fixedgovernment expenditure item. The idea behind the Transaction Value (TV)

approach is that the modeler should only4 - The cell defines a tax payment as a need to specify how each cell and account

fixed proportion of the pretax behave. For cells the modeler specifiesincome in the column. the appropriate algebraic expression; for

accounts, whether the y-variable is exo-5 - The income in the column is allo- genous (such as a fixed government expen-

cated over the different rows in diture budget), or endogenous. Also to befixed proportions. It is here used specified is whether the account has ato define how the factor incomes are price and, if so, whether the price andpaid to the household groups (i.e. the quantity are exogenous or endoge-in proportion to factor endowments). nous. SAMLIB will analyze the types of

cells in each row and column and automa-6 - The cell defines a committed expen- tically generate appropriate balancing

diture in a linear expenditure equations to create a complete model.system, i.e. the payment for a fixed Redundant equations will not be generated.quantity of basic consumption. If there is a choice between alternative

forms of a balance equation, SAMLIB will11 The cells in the column are inputs try to choose the best. Combinations of

to a CES production function. In assumptions leading to economicallythe model we have assumed that labor inconsistent behavior within a singleand capital can substitute each account are caught and reported asother. modeling errors.

12 - The cells in the column are inputs The TV approach has been made operationalto a Leontief production function. by defining a menu of possible behaviorsThus, columns 12 and 13 specify that for the cells and a menu of types for thethe composite factor inputs from accounts. A restriction discussed in theaccotints 4 and 5, and the inter- next section has limited the number ofmediate inputs, enter into produc- cell types and thereby made this menution in fixed quantity ratios. approach practical. The modeler specifies

a model as a list of cell types or "TV18 The cell defines the discretionary values" and a list of account types. The

expenditure part of a linear expen- cell types include:diture system. In this illustra-tion, we have for convenience Input into a Production or Substitutionmodeled the urban household savings Function. SAMLIB can handle Leontief,as a discretionary expenditure. Cobb-Douglas, and general CES production

functions, including CES productionTable 3 defines the overall behavior of functions with infinite elasticityeach account by indicating whether corresponding to perfect substituta-

p., yj, and qj are endogenous, exogenous, bility. The system automaticallygenerates price equations that connect the

or undefined. In the illustration, prices of inputs to the prices of out-and are exogenous to reflect a fixed puts. The Cobb-Douglas specification can

also describe fixed-value shares in a nonamount of capital. Labor is assumed to be production column, in which case no priceperfectly mobile between sectors, and the equation is defined.

wage rate is used as a numeraire, i.e. p1 Expenditure Systems. There are specifi-

is exogenous and total labor income is cations for the committed and discretion-fixed relative to it. This is the same as ary expenditure components of a linear andassuming a fixed labor supply. a nonlinear expenditure system. The sys-

tem automatically generates the appropri-The following comparative statics experi- ate consumer price indices.ment has been solved. All components ofgovernment current expenditures grow 30 Tax Specifications. Tax payments arepercent financed by doubling the tax rate defined as a fixed proportion of the pre-for manufacturers and halving the agricul- tax income. The system generates pricetural tax. The elasticities of substitu- equations that adjust prices accordingly.tion between labor and capital are bothset of 0.5, and all other exogenous vari- Export Demand Functions. Exports dependables and parameters are kept at their on the price of the exportable commoditybase values. The solution is shown in (after export taxes) relative to an exoge-Tables 4 and 5. Notice that the solution nous world price. The exchange rate,comes back in the same format as the base defined as the price of the rest-of-the-SAM, making comparisons easy.

MAC-I

244 A. Drud, W. Grais and G. Pyatt

world account, can be endogenous or that aggregates capital and labor in aexogenous. composite factor input by using a CES pro-

duction function and combine the compositeImport Specifications. The system automa- factor input with the intermediates intotically generates equations that relate the final output by using Leontiefworld prices, tariff rates, and the ex- technology assumptions. This procedurechange rate to landed prices. could not be described in a single account

without rather complicated expression forOutput from a Production Possibility the cell. But with multiple accounts, oneFrontier. This specification can define of w)hich is for a comDosite factor, thefixed or price-dependent make matrices formulation is straightforward.based on Leontief or CES production possi-bility frontiers. Such disaggregations will increase the

size of the SAM and the model, making themExogenous Cells. These cells can, for look rather large. As compensation, theexample, describe transfers from abroad or output of the model will contain all thepolicy-imposed paymencs. intermediate variables. This makes it

much easier to analyze and explain resultsResidual Cells. These cells simply adjust and to trace any formulation errors.to satisfy the accounting identities andin certain cases models profits. The miniature ORANI model of Dixon and co-

workers (1982) is an example of a modelAn advantage of the TV approach and SAMLIB that grows significantly by such dis-is the ease with which different assump- aggregation. In their formulation, eachtions can be plugged in. Merely by cell in the I/O matrix and in thechanging the type of few cells and consumption system is a Cobb-Douglasaccounts, it is possible to go from a aggregate of imports and domesticallymodel with exogenous investments and an produced commodities. Since the shares inendogenous current account deficit to one the Cobb-Douglas functions all arewith fixed borrowing and endogenous different, it is necessary with ourinvestments. Assumptions about fixed or approach to create a separate accouiLt forfloating exchange rates, world market each I/O-cell and each consumptionconditions, labor supply, and the like can component. In most other models, importsalso be easily changed. and domestically produced commodities are

aggregated into a composite commodity,independent of final use, following

MODEL ASSUIPTION Armington (1969). The Armington approachis better suited to the data situation in

Conceptually, the behavior of a cell can developing countries and has the advantagedepend on any other variable in the of only creating one extra account permodel. But to systematize the description commodity group.of cells, we have restricted ourselves tobehaviors in which the value of a cell

PARAMETER ESTIMATION AND UPDATING(i,j) only depends on Pi, pj, Yi, and y;

and parameter values. Although this The cell equations all contain parametersrestriction may sound severe, almost all - such as shares, elasticities, propen-practical cases can be modeled by allowing sities to consume -- and numerical valuessome disaggregation of the SAM's accounts. for these parameters must be provided

before the model can be solved.Our model in Tables 1 to 5 contains alinear expenditure system. This is Fortunately, most base-period parametersusually written as are uniquely defined once we assume that

t,= YiPi + 0 (y~- y p) But the base-period SAM is a solution to theij i I Y . model in the base period. Shares in

we have disaggregated consumer expenditure production functions, base-year tax rates,into two accounts. The committed expendi and import and export parameters can all

be derived from the base SAM. Base-periodtus t i avalues of such parameters as elasticities

account. Whatever is left over, of substitution cannot be derived from they - p, becomes the total, yk ,of base SAM and must be estimated from inde-J O JZj pendent data sources.

the dtscretionary expenditures account viaa residual cell, and the discretionary Most parameters can in principle be time-expenditures become tk k The dependent. But, due to a lack of data, we

ik =ik k must often make simplifying assumptionscomposite factor accounts (4 and 5) have about parameter changes. Parameters inalso been included in the SAM for modeling production functions are usually keptpurposes. In effect, they allow one to constant, though our system has optionsmodel a hierarchical production function for changing base shares and defining

The Transaction Value Approach 245

efficiency parameters. Coefficients 1rn, The third step solves the model numerical-expenditure systems are usually changed ly. In this brief description of theproportional with population to reflect a procedure we will are mainly concernedconstant per capita expenditure pattern. with the spike variables and equations

since everything else can be substitutedThe parameters that can be defined from out numerically. The model can be thoughtthe base SAM are automatically initialized of asby SAMLIB. From there on, the systemallows many types of updates. The user ( (xt, Zt) 2 tWO, 1 ..., Tdefines the parameters that are time-dependent and those that not. Those that where 2t is the vector of unknown spikeare can be updated by specifying a newvalue, by specifying a growth rate, or by vcomputing new values in an interperiod exogenous and lagged variables. ;S isFORTRAN subroutine, possibly based on known from the base SAM. Starting fromprevious endogenous variables. The systemchecks that all parameter updates are , and go, we solve the model by tracingsupplied exactly once, and it checks thevalue of the new parameters. For example, b ait checks whether shares add to one and as discussed by Garcia and Zangwillwhether certain parameters are positive. (1982). t is moved along a straight

line from g to gl' and the model isTHE MODEL SOLUTION PROCEDURE solved with respect to xt for each time-

The model generation and solution step using a Newton-type algorithm. Thisprocedures are long and complicated, so we approach has several advantages over thewill limit ourselves to a rough, intuitive straightforward Newton method:description.

o Newton's method will not alwaysThe first step generates the logicalstructure of the model. Based on the cell cs fspecifications, the account types, and the from a solution. But by choosingbase SAM, SAMLIB defines the model: the the time-step properly and usingvariables and the equations, includinginformation on the variables that appear extrapolations for based onin each equation. Each variable-equation earlier steps, xt remain closepair is marked as invertible if the to a solution and Newtons methodequation can be solved analytically withrespect to that variable and if the converges fast.resulting expression is numerically o It becomes possible to handle domainstable. If the model turns out not to be constraints like nonnegativity forsquare, the solution process is stopped.Since some of the equations of the modelare defined implicitly, i.e. generated by algorithms will break down if , isthe system, it can sometimes be difficult feasible but B1 is not feasible dueto detect why a model is not square. Weare trying to develop tools to help locate to inequalities. But we tracesuch errors.

Xt with time until the firstThe second step performs a block decompo- infeasibility appears, therebysition of the model and partitions the pinpointing the exact situation insimultaneous blocks into a recursive part which the price or production leveland a spike or loop part. This partiticn becomes negative.has been discussed by Nepomiastchy andRavelli (1978) and Gilli and Rossier o The inverse Jacobian used by(1981). Going further than these authors, Newton's method is computed bywe have developed a partitioning heuris- numerical differences in the basetic, that, based on the invertibility period, and then updated with rank-linformation from the first step, selects modifications during the iterationsthe normalization of the recursive equa- as suggested by Broyden (1970), thustions as an integral part of the decompo- keeping the number of function callssition. The algorithm is based on ideas small. The rank-I modifications arein Hellerman and Rarick (1972). This similar to those used by Powell'smethod should give a smaller number of hybrid algorithm (1970a, 1970b),spike variables and therefore a model that which is very popular for generalis easier to solve - rather important equilibrium models (Dervis, de Melo,because many of our models have 1,500 to and Robinson, 1982).2,500 equations, of which 1,200 to 2,000are in one simultaneous block.

246 A. Drud, W. Grais and G. Pyatt

o The procedure can-be proven to Dixon, P. B., B. R. Parmenter, J. Sutton,converge if the model has bounded and D. P. Vincent (1982). ORANI: Amultipliers with respect to any Multisectoral Model of the Australianexternal shock, which seems to be a Economy, North-Holland Publishingfair assumption. Company, Amsterdam, Netherlands.

Drud, A. (1983). A Survey of ModelCONCLUSIONS AND DIRECTIONS Representations and Simulation

FOR FUTURE RESEARCH Algorithms in Some Existing ModelingSystems. Journal of Economic Dynamics

The TV approach has been developed to make and Control, 5, forthcoming.it easier for users without knowledge ofcomputer programming or solution algo- Garcia, C. B., and W. I. Zangwillrithms to define, solve, and experiment (1982). Pathways to Solutions, Fixedwith economywide equilibrium models based Points, and Equilibria, Prentice-Hall,on SAMs. Although we have restricted the N. J., U.S.A.class of models, it seems that most modelscan be tLandled within the system. Our Gilli, M. and E. Rossier (1981).experience from a limited number of models Understanding Complex Systems,is that our approach reduces the human Automatica, (17).input needed for building general equili-brium models. The necessary ski.Lls have Hellerman, E. and D. C. Rarick (1978).also been limited to cover modeling and The Partitioned Preassigned Pivotgeneral economic understanding. Computer Procedure (P ), in D. J. Rose and R.costs are difficult to compare: each A. Willoughby (eds.), Sparse Matricessimulation probably is slightly more and Their Applications. Plenum Press.expensive with SAMLIB, but the successrate, especially for difficult models, Nepomiastchy, P. and A. Ravelli (1978)..seems to be better than with other Adapted Methods for Solving andtechniques. Optimizing Quasi-Triangular

Econometric Models, Annals of EconomicFuture work will, apart from general and Social Measurements, 6, pp. 555-improvements in speed and reliability, 562.cover three areas. The first is to makethe system more useful for operational Powell, M. J. D. (1970a). A Hybrid Methodwork by writing a "cook-book" that for Nonlinear Equations, indescribes alternative TV formulations of P. Rabinowitz (ed.), Numerical Methodsvarious parts of the economy: e.g. for Non-linear Algebraic Equations,consumption, production, trade, and Gordon and Breach, London, UK.investment. The second area is to system-atize the formulation of interperiod Powell, M. J. D. (1970b). A Fortranlinkages, thus far a rather weak aspect of Subroutine for Solving Systems ofthe system. The third area is to expand Nonlinear Algebraic Equations, in P.the class of models. In this we envisage Rabinowitz (ed.), Numerical Methodsthe inclusion of inequality constraints for Non-Linear Algebraic Equations,and complementarity conditions to model Gordon and Breach, London, UK.changes of regime and other disconti-nuities or nondifferentiabilities in Pyatt, G. anid A. R. Roe with R. M.behavior. Lindley, J. I. Round and others

1977). Social Accounting forDevelopment Planning with Special

REFERENCES Reference to Sri Lanka, CambridgeUniversity Press, Cambridge, UK.

Armington, P. (1969). A Theory of Demandfor Products Distinguished by Ptace ofProduction, IMF Staff Papers, 16, pp.159-178.

Broyden, C.G. (1973). Quasi-Newton, orModification Methods, in G.D.Byrne andC.A. Hall (eds.), Numerical Solutionof Systems of Nonlinear AlgebraicEquations, Academic Press, N.Y.,U.S.A.

Dervis, K., J. de Melo, and S. Robinson(1982). General Equilibrium Modelsfor Development Policy, CambridgeUniversity Press, Cambridge, UK.

I I I 1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 I-------------------------------------- ----------------------------------------------------------- ---- ------------------------------ -------------- -------------------------------------------------------

I I I FACTOR FACTOR FACTOR FACTOR FACTOR HOUSEHLD HOUSEHLD HOUSEHLD HOUSEHLD GOVERNHT SAVINGS ACTIVITY ACTIVITY COHHODTY COHMODTY TOTAL II I I LABOR CAPITAL CAPITAL CGMPOSIT COMPOSIT RURAL RURAL URBAN URBAN INVESTMT AGRICULT MANUFACT AGRICULT HANUFACT II I I ACRICULT HANUFACT AGRICULT MANUFACT COM-EXP DISC-EXP COH-EXP DISC-EXP I------------------------------ ---------------------------------------------- ------- ------------- ------------.--------- ----------------- ----------------------- ------ --- ----------------------------------

I I I FACTOR LABOR I 60. 40. 100. II 2 I FACTOR CAPITAL AGRICULT I 30. 30. II 3 1 FACTOR CAPITAL HANUFACT I 50. 50. 11 4 1 FACTOR COMPOSIT ACRICULT 1 90. 90. II 5 1 FACTOR COHPOSIT HANUFACT I 90. 90. I

6 6 1 IOUSEHLD RURAL CON-EXP I 40. 10. 50. II 7 I IOUSEHLO RURAL DISC-EXP I 10. 10. I1 8 I HOUSENLO URBAN COH-EXP I 60. 20. 50. 130. II 9 I iOUSEHLD URBAN DISC-EXP 1 50. 50. 11 10 I GOVERNHT I 15. 15. 30. II 11 I SAVINGS INVESTHT I 20. 5. 25. 11 12 I ACTIVITY AGRICULT I 190. 190. I HI 13 I ACTIVITY HANUFACT 1 180. 180. 1 >

I 14 2 COMHODTY AGRICULT 2 35. 5. 45. 10. 5. 5. 70. 30. Z05. I I1 15 1 COHHODTY HANUFACT 1 5. 5. 35. 20. 20. 20. 30. 60. 195. 1 H-3I 16 1 TOTAL I 100. 30. 50. 90. 90. 50. 10. 130. 50. 30. 25. 190. 180. 205. 195. 1 i------- --------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------- p

Table 1: Example of a Social Accounting Matrix (SAM).rt

0

----------------------------------------------------------- ------------ ---------------------------------------------------------------------- ------------------------------I I I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 iS I 0----------------------------------------------------------------------------- ---- ------- --- ----- --------------------------------------------------------------------------- w----------------- p

I I I FACTOR FACTOR FACTOR FACTOR FACTOR iIOUSEHLD HOUSEHLD HOUSEHLD HOUSEHLD GOVERNHT SAVINGS ACTIVITY ACTIVITY COHHODTY COHMOOTY II I I LABOR CAPITAL CAPITAL COMPOSIT COHPOSIT RURAL RURAL URBAN URBAN INVESTHT AGRICULT HANUFACT AGRICULT MANUFACT II I I ACRICULT NANUFACT AGRICULT NANUFACT COM-EXP DISC-EXP CON-EXP DISC-EXP I------------ ------- --------- -- ------- --- ------ ---- ---- ----------------- -------------------------------- ------ -- ---- ------- ----- ---------- -- -------- ----------------------- --------------------

I II FACTOR LABOR I 11 11 II 2 1 FACTOR CAPITAL AGRICULT I 11 II 3 I FACTOR CAPITAL MANUFACT I 11 II 4 I FACTOR COHPOSIT AGRICULT I 12 1I 5 I FACTOR COHPOSIT MANUFACT 1 12 II 6 1 HOUSEHLD RURAL COM-EXP I 5 5 I1 7 I HOUSEHLD RURAL DISC-EXP I 2 1I B I HOUSEHLD URBAN CON-EXP 1 5 5 5 1I 9 I iOUSEiILD URBAN DISC-EXP I 2 II 10 IGOVERNHT 1 4 4 11 11 1 SAVINGS INVESTHT I 18 2 11 12 IACTIVITY AGRICULT I 12 11 131 ACTIVITY HANUFACT I 12 11 14 ICOMMODTY AGRICULT 1 6 18 6 18 3 5 12 12 1I 15 1 COMHOOTY NANUFACT I 6 18 6 18 3 5 12 12 1--------------------------------------------------------- ------------------------ --------------------------------------------------------------------- - ------- - - - - --

Table 2: The TV-Specification for a Model Based on the SAM in Table 1.

-,

0V

DEFINITION OF ACCOUNT TYPES: SOLUTION IN PERIOD 1;

ACCOUNT PRICE VALUE QUANTITYP Y Q

I FACTOR LABOR EXO EXO ENDO 1 FACTOR LABOR 1.00000 100.0 100.0

2 FACTOR CAPITAL ACRICULT ENiDO ENDO EXO 2 FACTOR CAPITAL AGRICULT 1.03131 30.9 30.0

3 FACTOR CAPITAL IANUFACT ENDO ENDO EXO 3 FACTOR CAPITAL MANUFACT .95393 47.7 50.0

4 FACTOR CONIPOSIT AGRICIULT ENDO ENDO ENDO 4 FACTOR COMPOSIT AGRICULT 1.01038 91.9 90.9

5 FACTOR COMPOSIT MANUFACT ENDO ENDO ENDO 5 FACTOR COMPOSIT HANUFACT .97427 86.8 89.1

6 HOUSEHLO RURAL COH-EXP UNDF ENDO UNDF 6 HOUSERLD RURAL COR-EXP 50.3

7 HIOUSEIILD RURAL DISC-EXP UNDF ENDO UNDF 7 IIOUSEHLD RURAL DISC-EXP 10.8

8 IIOUSEHLD URBAN COM-EXP UNUF ENDO UNDF 8 HOUSEULD URBAN COM-EXP 128.3

9 HOUSERLD URBAN DISC-EXP UNDF ENDO UNDF 9 HOUSERLD URBAN DISC-EXP 46.4

10 GOVERNMT UNDI ENDO UNDF 10 GOVERNMT 37.7

11 SAVINCS INVESTMT EtiDO ENDO ENDO 11 SAVINGS INVESTMT 1.06573 23.8 22.3

12 ACTIVITY ACRICULT ENDO ENDO ENDO 12 ACTIVITY AGRICULT t.00889 193.7 192.0

13 ACTIVITY MANUFACT ENDO ENDO ENDO 13 ACTIVITY HANUFACT 1.01265 180.4 178.1

14 CONMODTY AGRICULT E.1DO ENDO ENDO 14 COMMODTY AGRICULT .97198 201.3 207.1

15 COHMODTY MANUFACT ENDO ENDO ENDO 15 COMHODTY NANUFACT 1.09054 210.4 193.0

C

Table 3: Tne Definition of Endogenous and Exogenous Table 4: Solution Values for the Account Dependent

Variables for the Model in Table 2. Variables from the Model in Table 2 and 3.

03

----------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------

I I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I .

-----------------------------------------------------------------------------------------------------------------------------

r T I FACTOR FACTOR FACTOR FACTOR FACTOR HOUSEHLD HOUSEHLD NOUSEHLD HOUSEILD GOVERNHT SAVINGS ACTIVITY ACTIVITY COMMODTY COMNODTY TOTAL I P

I LABOR CAPITAL CAPITAL COMPOSIT COMiPOSIT RURAL RURAL URBAN URBANt INVESTHT ACRICULT MANiUFACT ACRICULT 4ANUFACT I

I I I AGRICULT RANUFACT ACRICULT MANUFACT COM-EXP DISC-EXP COM-EXP DISC-EXP

--------------------------------------------------------------------------------------------------------------------------------1 1 I FACTOR LABOR I 61. 39. 100. I1

1 2 1 FACTOR CAPITAL AGRICULT 1 31. 31. 1

1 3 1 FACTOR CAPITAL MANUFACT I 48. 48. I

1 4 1 FACTOR COMPOSIT AGRICULT I 92. 92. I

I 5 I FACTOR COMPOSIT HASUFACT I 87. 87. r

I 6 1 IIOUSEHLD P,URAL CON-EXP 1 40. 10. 50. I

r 7 1 IIOUSEHLD RURAL DISC-EXP I 11. 11. I

1 8 1 HOUSEHLD URBAN COH-EXP l 60. 21. 48. 128. 1

I 9 I HOUSEHLD URBAN DISC-EXP 1 46. 46. 1

I 10 I GOVEINHT I 8. 30. 38. 1

I 11 I SAVINGS INVESTMT I 19. 5. 24. I

1 12 I ACTIVITY AGRICULT I 194. 194. I

I 13 I ACTIVITY HANUFACT I 180. 180. 1

1 14 I COMHODTY AGRICULT I 34. 5. 44. 9. 7. 5. 69. 29. 201. 1

I 15 I COHNODTY NANUFACT I 5. 5. 38. 19. 26. 19. 33. 65. 210. 1

1 16 1 TOTAL I 100. 31. L8. 92, 87. 50. 11. 128. 46. 38. 24. 194. 180. 201. 210. l

------------------------------------------------------------------------------------------------------------------------------------------------------------ --------------------------------

Table 5: The Solution SAM for the Model in Tables 2 and 3.

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