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Static input-output tables : an evaluation of their efficiency as a forecasting tool in the West Malaysian… Hodgins, Barbara Louise 1972

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STATIC INPUT-OUTPUT TABLES: AN EVALUATION OF THEIR EFFICIENCY AS A. FORECASTING TOOL IN THE WEST MALAYSIAN CASE by BARBARA LOUISE HODGINS B.A., University of Alberta, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1972 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e tha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Economics The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouve r 8, Canada Date O c t o b e r 2 6 , 1972 A B S T R A C T A s e r i e s of s i x consecutive input-output tables has been con-structed f o r the economy of West Malaysia for the period from 1960 to 1965. This thesis provides an evaluation of t h e i r e f f i c i e n c y when applied i n f o r e c a s t i n g intermediate output. A b r i e f review of the t h e o r e t i c a l structure of the s t a t i c input-output model developed by Leontief has been presented. P a r t i c u l a r a t t e n t i o n has been given to the economic assumptions which are necessary to make the p r e d i c t i o n procedure tenable. The b a s i c assumption of constant input co-e f f i c i e n t s was not tested d i r e c t l y , however. Instead, the empirical u s e f u l -ness of the input-output system has been evaluated i n terms of the q u a l i t y of p r e d i c t i o n s i t y i e l d s . Each of the tables from 1960 to 1964 has been used i n turn to pre-d i c t intermediate s e c t o r a l outputs for succeeding years to 1965. Input-output p r e d i c t i o n errors were calculated by reference to the observed i n t e r -mediate outputs set f o r t h i n the tables. To test the s i g n i f i c a n c e of these errors, a comparison was made with the errors that arose when corresponding pro j e c t i o n s of intermediate output were made from a naive extrapolation model. In addition the o v e r a l l e f f e c t on the input-output predictions of the length of the forecast period was analyzed and the r e l a t i v e performance of i n d i v i d u a l sectors was examined. Wherever possib l e , the e f f i c i e n c y of the West Malaysian tables was compared with that of input-output tables for the Netherlands economy. i i i i i In general the predictive power of the West Malaysian tables was not impressive. On the average the input-output forecasts proved to be superior to the naive extrapolations only when the prediction period did not exceed two years. For individual sectoral forecasts, the input-output model yielded better predictions of intermediate output in only seven of the 15 sectors considered. In every comparison with the efficiency of the Netherlands tables, the in f e r i o r i t y of the West Malaysian tables was demonstrated. Attempts have been made in the thesis to trace the reasons for the poor performance. Some improvements to the tables have been suggested. TABLE OF CONTENTS Chapter Page I. THE THEORY OF STATIC INPUT-OUTPUT MODELS 1 Introduction 1 The S t a t i c Input-Output System 3 Economic Assumptions of the Model 12 I I . THE MODEL AS A FORECASTING TOOL 21 I I I . THE INPUT-OUTPUT TABLES OF WEST MALAYSIA 34 Des c r i p t i o n of Sectors. . 44 Valuation of I n t e r s e c t o r a l Flows 46 St r u c t u r a l Change i n West Malaysia, 1960-1965 48 IV. STATISTICAL ANALYSIS OF PREDICTION ERRORS 50 Input-Output P r e d i c t i o n Errors 54 Evaluation of the Forecasts for I n d i v i d u a l Sectors 61 Comparison with Naive Extrapolation Errors 67 V. CONCLUSIONS 78 BIBLIOGRAPHY 84 APPENDIX A: ADJUSTMENT OF THE PUBLISHED 1965 INPUT-OUTPUT TABLE . . 86 APPENDIX B: INPUT-OUTPUT PREDICTION ERRORS (e. ,, ) 90 i v LIST OF TABLES Table Page 1. West Malaysia Interindustry Accounts 1960 38. 2. West Malaysia Interindustry Accounts 1961 39 3. West Malaysia Interindustry Accounts 1962 40 4. West Malaysia Interindustry Accounts 1963 41 5. West Malaysia Interindustry Accounts 1964 42 6. West Malaysia Interindustry Accounts 1965 43 7. Mean-Squared Prediction Errors of Intermediate Output Forecasts from Input-Output Tables 55 8. Sample Statistics of the Mean-Squared Prediction Errors (w^  x 10 ) from Input-Output Tables 57 9. Root-Mean-Squared Prediction Errors from Input-Output Tables v 59 10. Coefficients of the Relative Prediction Performance (5^) and the Systemmatic Nature of Prediction Errors ( e ^ f o r Individual Sectors 63 11. Mean-Squared Extrapolation Errors of Intermediate Output .69 12. Ratio of Aggregate Mean-Squared Prediction Errors to Aggregate Mean-Squared Extrapolation Errors 70 13. Median Ratios of Mean-Squared Prediction Errors (m^ ) to Mean-Squared Extrapolation Errors (rj^T«) r o r Wes? Malaysia with Corresponding Figures for the Netherlands in Parentheses 76 Al West Malaysia Interindustry Accounts 1965a . . 87 BI Input-Output Prediction Errors (e. , ) 91 Is j u r T ILLUSTRATIONS Figure 1 Schematic Representation of a Static, Open Input-Output Table 5 v CHAPTER I THE THEORY OF STATIC INPUT-OUTPUT ANALYSIS Introduction Input-output a n a l y s i s , f o r which we are indebted to Wassily Leon-t i e f , i s an adaptation of the n e o - c l a s s i c a l theory of general e q u i l i b r i u m to the e m p i r i c a l study of interdependence between economic a c t i v i t i e s . Concerned as i t i s with the i n d i v i d u a l e q u i l i b r i u m of m i l l i o n s of economic agents and the simultaneous e q u i l i b r i u m of the o v e r a l l system, the theory of general equilibrium has always been e s s e n t i a l l y mathematical i n nature. Credit f o r the f i r s t p recise t h e o r e t i c a l formulation of economic i n t e r -dependence i s generally given to Leon Walras. Contributions by Pareto, Barone, Hicks and Samuelson further enriched the theory of general e q u i l i -brium, but the f i r s t approach toward an e f f e c t i v e handling of the empiri-c a l content of such a system was made by L e o n t i e f W i t h the i n t r o d u c t i o n of h i s input-output technique, the theory of general e q u i l i b r i u m "which for 2 so long remained on the s h e l f of abstraction where Walras had placed i t , " could be studied i n q u a n t i t a t i v e terms. Leontief's basic ideas were f i r s t published i n h i s a r t i c l e , "Quantitative Input-Output Relations i n the Economic System of the United States," The Review of Economics and Statistics, 18 (August, 1936), pp. 105-25. 2 . . . Ben B. Seligman, Main Currents tn Modem Economics (New York: Free Press of Glencoe, 1962), p. 436. Seligman notes that Walras him-s e l f doubted that h i s system would ever e x h i b i t empirical usefulness for i t was u n l i k e l y that the necessary s t a t i s t i c a l data would ever become • a v a i l a b l e . 1 2 A description of the Leontief technique is f a c i l i t a t e d by follow-ing the distinction made by Dorfman: An input-output table or matrix is a set of linear formulas connecting the levels of a c t i v i t y . i n \ the various segments of the economy. Input-output analysis is the economic j u s t i f i c a t i o n and interpre-tation of these formulas and their consequences.^ If an economy could be divided at some number of sectors, say n, and i f the level of output of each sector depended exclusively on the output of some or a l l of the sectors, then the formulas relating the output of each sector to that of others would form a set of n equations in n variables. If further, these formulas were linear, "the equations could be solved by algebra, the result would be a set of sectoral outputs, mutually compatible in the sense that each sector would produce the quantity called for by the functional relationship assumed at the outset. Leontief adopted a set of economic assumptions which led to this kind of mathematical structure and invested i t with meaning. In this chapter the structure of the input-output system w i l l f i r s t be explained and following Dorfman, an interpretation of the econo-mic assumptions of the model w i l l then be given. The "conseauences" of these assumptions, particularly when the model is used as a forecasting tool, w i l l be explored in the succeeding chapters, both in theoretical terms and for empirical application, in the case of West Malaysia. Robert Dorfman, "The Nature and Significance of Input-Output," The Review of Economies and S t a t i s t i c s , 36 (May, 1954), p. 122. 3 The Static Input-Output System In essence an entire economy was visualized by Leontief as one large accounting system, with each sector having i t s own "budget" of economic activity. Each sector appeared in the system twice, as a pro-ducer of output and as a consumer of inputs. The flow of goods and services among the sectors for any specified period of time was traced within the schematic framework of a rectangular input-output table or matrix. The disposition of output was shown across a row in the table for each sector; the distribution of inputs by origin was shown v e r t i -cally in a column of the table for each sector. Either value or quantity terms could be employed: i f the former were used, totals could be computed both horizontally and verti c a l l y , yielding equations for total output and total input. (For quantities, of course, vertical totals were meaningless). Theoretically, i t was then possible to write "balance equations" which described how much of a sector's output went to others for intermediate and f i n a l use. Leontief termed the latter the " b i l l of goods," to be found in households, government purchases, foreign trade, or-:-for that matter, any sector considered to be autonomous, whose output would be determined exo-genously in the model. In his original formulation, Leontief used a "closed" input-output system wherein households were treated as a produc-tive sector, endogenous to the model. In any case at this stage, the equations are merely bookkeeping identities which require that the aggre-gate output of any sector equal the total purchases from the sector by a l l others. If i t can be assumed, however, that a technological relationship 4 exists such that the quantity of each input used in production by any sector is determined entirely by the level of output of that sector, the s t a t i s t i c a l input-output table can be used as an economic model. Combining the balance equations of the table with these assumed produc-tion functions, i t is possible to write an equation for each sector which states that i t s total output is equal to the " b i l l of goods" plus a sum each term of which depends only on the output of some productive sector. A general solution to this set of linear simultaneous equations yields a new set of equations which describe economic interdependence; specific structural characteristics of the economy are reflected in the numerical magnitude of the derived coefficients. The formal structure of input-output accounts can best be ex-pressed in symbols. Conceptual properties of the accounting system are shown in Figure 1 which introduces the symbolic notatation followed hereafter. The economy consists of n+1 sectors. Of these, one sector is autonomous; the remaining n sectors are nonautonomous and structural relationships can be established between them. Of course the autonomous sector, Leontief's " b i l l of goods," may be disaggregated to account for i t s various components, be they households, exports, government purchases, etc., and the inclusion of any activity in this sector is arbitrary. It depends largely on the purpose for which the table is to be used. As noted earlier, i t is possible to "close" the system with respect to one or more of the activities normally found in the autono-mous category by treating i t as a productive sector rather than as a part of f i n a l demand. When the household sector is incorporated this way, i t 5 PURCHASING SECTORS Intermediate Use Final Use TOTAL OUTPUT 1 • • « j • • • n 1 y. h • * • • • • PRODUCING SECTORS • • i • • Z i l • • • • • t j zn • • • • Y. « • • AT. • • • • • • • n • znl ' • • nn • Y n • n IMPORTS ml ' «7 * PRIMARY INPUTS Vl ' J * (Value Added) TOTAL INPUT Xl ' ' * J M Figure 1 Schematic Representation of a Static, Open Input-Output Table 6 establishes a direct connection between the supply of labour and consump-tion described in terms of i t s distinct sectoral components (which empiri-cally approximates the factor supply equation of general equilibrium theory). When a l l sectors are considered to be endogenous, the input-output system i s called "closed" (though a static system cannot be truly closed since endo-genous explanation of investment requires consideration of structural re-lationships between inputs and outputs which occur in different periods of time). Total production in any one of n sectors during the period selec-ted may be represented by the symbol X.t where i = l3...3n. Some of this w i l l be used to satisfy the requirements of the productive sectors, j , where j = li...in and the amount of output obtained from sector i is desig-nated as z . .. The remainder of the output, w i l l be consumed by the auto-4 nomous sector. This situation may be represented by the following balance equa-tion for each sector i: n (1.1) X.= z z .„ + ...+ z . + Y. = Z z. . + Y. Moreover total production in each sector i s equal to the value of inputs purchased from a l l sectors and from abroad, m., plus value added,v., in that sector:"* 4 In fact, any one sector disposes of i t s product in one or more of three ways: selling i t for use in further production or as a fi n a l product or adding i t to inventory. Since, for our purposes, f i n a l demand is really the difference between total supply available, and the amount used up in production, i t includes changes in stocks. "'This discussion assumes that production and use are measured in value terms. 7 n Since a l l Uses of the output of a sector are accounted f o r i n Equation (1.1) and a l l cost elements, i n c l u d i n g p r o f i t , i n Equation (1.2), i t follows that: (1.3) X. = X. (i = o = ],...,«) For each of the productive sectors, the value of t o t a l output equals the value of t o t a l input.^ The main purpose of the input-output model i s to e x p l a i n the mag-nitudes of i n t e r s e c t o r a l flows i n terms of the l e v e l s of production i n each sector. Several assumptions are necessary for such a prodedure to be theore-t i c a l l y meaningful, i . e . , to transform the s t a t i s t i c a l input-output table i n -to an economic model. F i r s t , i t must be po s s i b l e to form the n productive sectors of the table i n such a way that each sector produces a d i f f e r e n t out-put, and a s i n g l e production f u n c t i o n can be assumed f o r each one. Then i t assumed that the amount of each input used i n production by any sector i s determined e n t i r e l y by the l e v e l of output of that sector. These assumptions make i t p o s s i b l e to define the requirement, s.., of each sector j f o r the output of sector i as a unique f u n c t i o n of i t s own l e v e l of output, X.. That i s : From an accounting point of view, t h i s i s the e s s e n t i a l d i f f e r -ence between a productive and an autonomous sector; the former type, must have a balanced budget ( t o t a l input equal to t o t a l output). The values of primary inputs and f i n a l uses must only balance i n the aggregate. 8 (1.4) z.. = a. .X. 1*3 1*3 d which may be rewritten as: (1.5) a. .. = v ^t7 X. The parameters, a.., are c a l l e d input c o e f f i c i e n t s , or a l t e r n a t i v e -13 l y t e c h n i c a l c o e f f i c i e n t s , since they are generally interpreted as c o e f f i -c i e n t s of production which are t e c h n o l o g i c a l l y determined. Each shows the quantity (or value) of the output of sector i absorbed by sector 3 per unit of output i n sector j . (In the case where the system i s closed with regard to households, these c o e f f i c i e n t s show the s e c t o r a l consumption requirements of the output of labour.) S u b s t i t u t i n g Equation (1.4) in t o Equation (1.1) y i e l d s a set of n simultaneous equations i n the form: (1.6) X. = a .^X^ + a. <JC n + ... + a. X + Y. Z 2 vn n % (i = l t ..,,n) which may be solved using matrix algebra. To do so the t o t a l output l e v e l s and f i n a l demands i n the Leontief system are w r i t t e n as column vectors: X = X n and Equation (1.6) takes the form: I. n (1.7) X = AX + 7 9 where A i s the matrix of t e c h n i c a l c o e f f i c i e n t s , (1.8) A = ia.dl = [zi.] [X.r1 the superscript circumflex sig n being used to denote a diagonal matrix.^ Equation (1.7) may be rearranged as: (1.9) X - AX = Y In order to carry out the indicated subtraction, X i s m u l t i p l i e d by the 8 i d e n t i t y matrix since IX = X. This gives: (1.10) IX - AX =(I-A)X = I The matrix (I-A) i s often c a l l e d the Leontief matrix. To solve for X, the re-quired d i v i s i o n i s accomplished by f i r s t i n v e r t i n g the Leontief matrix, then premultiplying each s i d e of the equation by t h i s r e c i p r o c a l or inverse matrix: (1.11) . (I-A)'1(I-A)X = (I-A)'1! 9 The left-hand side of equation (1.11) reduces to X so that the general The matrix A i s obtained by d i v i d i n g each element, 2.., of the input-output matrix by the t o t a l output of sector j , X., as shown i n e q u a t i o n (1.5). In matrix algebra, such d i v i s i o n i s accomplished^by premultiplying the matrix of intermediate demands by the inverted diagonalized Xj vector. g The r o l e of the i d e n t i t y matrix i s s i m i l a r to the number one i n ordi-nary algebra. An i d e n t i t y matrix i s a square matrix where a l l the diagonal ele-ments are one and the non-diagonal elements are zero. ^The inverse of a matrix i s that matrix which when^multiplied by the o r i g i n a l matrix y i e l d s an i d e n t i t y matrix. Therefore (I-A) (I-A)X = IX = X i n equation (1.11). 10 s o l u t i o n of the input-output system may be stated as: (1.12) X = (I-A^Y which i s approximated by the expansion"^ (1.13) X = ( J + /. + A2 + A3 + . . . ) J This expansion serves to i l l u s t r a t e the properties of the Leontief inverse matrix, (I-A) \ which provides a general s o l u t i o n to the input-out-put system. The most t y p i c a l problem to which an open system i s applied i n -volves the p r e s c r i p t i o n of a s p e c i f i c " b i l l of goods" Y, to determine the s t r u c -t u r a l l y necessary magnitudes of a l l remaining inputs and outputs. The Leontief inverse matrix w i l l y i e l d the amount (or value) of each input d i r e c t l y and i n -d i r e c t l y required to produce the l e v e l of output prescribed by the " b i l l of goods." The t o t a l e f f e c t of a given f i n a l demand can be broken down into the 2 3 d i r e c t e f f e c t (J-h4)r and a s e r i e s of induced or i n d i r e c t e f f e c t s (A.. + A + ...)Y. Equation (1.12) may be restated as: (1.14) X = RY This s o l u t i o n i s analogous with the computation of the f i r s t few term s of the Keynesian m u l t i p l i e r s e r i e s 1 + c + a* + + ...as an approxi-mation to the value of the m u l t i p l i e r l/l-o. In the m u l t i p l i e r case t h i s w i l l work i f the marginal propensity to consume, c, i s less than unity. In the Leontief computation we have a s i m i l a r condition which states that t h i s pro-cedure w i l l work i f at l e a s t one column i n the A matrix adds up to less than unity and no column i n the matrix adds up to more than unity. This i s part of the Hawkins-Simon condition which ensures that the elements of the inverse matrix be non-negative. 11 where X i s again the vector of t o t a l output, Y i s the vector of f i n a l de-mand, and R i s the Leontief inverse matrix where (1.15) R = [r. •] = I + A + A2 + A3 + . .. The general s o l u t i o n to the input-output system may then be w r i t t e n i n n simultaneous equations of the form: (1.16) X. = v.1Y1 + r.2Y2 + ri3Y3 + ... + ^ (* - i,...n) The new set of constants, r.., derived from the o r i g i n a l parameters a.., i n -%3 I'D dicate the amount of output i n sector i that would have to be produced i f Y 3 the quantity of output of sector j absorbed by f i n a l users, were increased by one u n i t ( i n quantity or value terms). Such an increase would a f f e c t sector i d i r e c t l y (and i n d i r e c t l y ) i f i=j but when i^j the output X. i s a f f e c t e d only i n d i r e c t l y since sector i has to provide a d d i t i o n a l inputs to a l l other sectors which i n t h e i r turn must contribute d i r e c t l y or i n d i r e c t l y to the i n -crease i n the d e l i v e r y Y . made by sector j to f i n a l users. 3 Computationally the elements of the R matrix are derived, as shown i n Equation (1.15) by a sum which explains the composition of the t o t a l out-put required per u n i t of f i n a l demand. The f i r s t term J, accounts f o r the one u n i t of output to be added to f i n a l demand. The second term, A, indicates the d i r e c t input required to produce t h i s one u n i t of f i n a l demand. The next term, 2 A , shows the f i r s t - r o u n d i n d i r e c t inputs required to produce the d i r e c t input A. As A i s c a r r i e d to successively higher powers, the c o e f f i c i e n t s w i l l get close r and c l o s e r to zero. This i s another way of saying that at some point the i n d i r e c t e f f e c t s of increasing the output of each sector i n the input-output model w i l l become n e g l i g i b l e . 12 In practice the exact Leontief inverse matrix is obtained by com-puter. The reason for noting the power series approximation is that i t con-veys more clearly than the mechanical process of inversion the incremental way in which the indirect effects are propogated throughout the system.^ The inverse matrix incorporates a l l the direct and indirect re-quirements for the production of one unit f i n a l good or service, and can therefore be used to calculate equilibrium levels of output in each sector of the economy, given a set of f i n a l goods and services. When physical i n -stead of money units are used in the open system, equilibrium prices as well as equilibrium output levels may be calculated. In a closed input-output model, the level of f i n a l demand is solved simultaneously with the rest of the variables. It most closely re-sembles the Walrasian general equilibrium formulation in that both seek to solve a system of equations involving a l l prices and a l l quantities in an eco-nomy. Economic Assumptions of the Model In order to f i r s t make clear the logical structure of the input-output system, an economic interpretation of the assumptions which Leontief Iterature procedures may also be used to compute the successive rounds of production needed to satisfy a given level of f i n a l demand. Either way, of course, the incremental or iterature sequences refers only to "compu-tational time" since the input-output model used here represents a static equilibrium position, not a dynamic system. 13 made to take the s t a t i s t i c a l input-output table beyond i t s use as a purely d e s c r i p t i v e accounting device has thus far been avoided. As noted e a r l i e r , the input-output model i s based on the premise that i t i s poss i b l e to d i v i d e a l l productive a c t i v i t i e s i n an economy i n t o sectors whose i n t e r r e l a t i o n s can be meaningfully expressed i n a set of simple input functions. Chenery and Clark s t a t e that t h i s property• of the Leontief model i s derived from three basic assumptions: (1) Each commodity (or group of commodities) is supplied by a single industry or sector of produc-tion. C o r o l l a r i e s of t h i s assumption are (a) that only one method i s used i n producing each group of commodi-t i e s ; (b) that each sector has only a s i n g l e primary out-put. (2) The inputs purchased by each sector are a function*only of the level of"output of that sector. (The stronger assumption i s usu a l l y made that the input func-t i o n i s l i n e a r , but t h i s i s a matter of convenience). (3) The total effect of carrying on several types of production is the sum of the separate effects. This i s known as the a d d i t i v i t y assumption, which rules out exter-n a l economies and diseconomies.12 The f i r s t assumption gives r i s e to c l a s s i f i c a t i o n and aggrega-t i o n problems i n both t h e o r e t i c a l and empirical a p p l i c a t i o n s of the model. The p r i n c i p l e according to which the output of a sector should be as homogen-eous as poss i b l e would lead, i n the extreme, to a circumstance where each sec-tor consisted of a s i n g l e plant producing a s i n g l e product. One unfortunate > consequence of such a c l a s s i f i c a t i o n i s to greatly increase the p o s s i b i l i t i e s of t e c h n i c a l s u b s t i t u t i o n between products o r i g i n a t i n g i n d i f f e r e n t sectors. H o l l i s B. Chenery and Paul G. Clark, Interindustry Economics (New York: John Wiley & Sons, Inc., 1959), pp. 33-34. 14 In i t s f i r s t t h e o r e t i c a l formulation, the Leontief sector was assumed to be composed of plants producing a s i n g l e homogeneous commodity by s i m i l a r techniques. No such commodity would be homogeneous i n the s t r i c t e s t sense, of course, but would consist of commodities which are very close sub-s t i t u t e s f o r each other. When sectors are formed i n t h i s way, however, a fundamental d i f f i c u l t y i s encountered i n that commodities which are s u b s t i -tutes on the output side may not be s u b s t i t u t e s on the input s i d e . Complete adherence to the Leontief assumption would require both. Relaxation of t h i s requirement u s u a l l y involves a choice between aggregation according to the s i m i l a r i t i e s of output or the s i m i l a r i t i e s of the inputs of given productive 13 a c t i v i t i e s . Decisions on c l a s s i f i c a t i o n are aided by the n a t u r a l d i v i s i o n s i n productive sequences that r e s u l t from a combination of t e c h n o l o g i c a l , econo-mic and l o c a t i o n a l f a c t o r s . V e r t i c a l o r h o r i z o n t a l aggregation can, there-fore, be applied. The f i r s t stages of production w i l l be characterized by a s e r i e s of operations on some raw m a t e r i a l . Chenery and Clark suggest that "when these successive steps are performed i n r e l a t i v e l y f i x e d proportions... 14 i t i s often j u s t i f i a b l e to combine them into a s i n g l e s e c t o r . " A l t e r n a t i v e -l y , i t i s p o s s i b l e to consolidate s i m i l a r processing of a range of raw or Tibor Barna notes that these two kinds of aggregation are s i m i l a r i n s o f a r as they involve the aggregation of p a r a l l e l processes of production ( h o r i z o n t a l i n t e g r a t i o n of i n d u s t r y ) . See h i s c o n t r i b u t i o n , " C l a s s i f i c a t i o n and Aggregation on Input-Output A n a l y s i s , " to Tibor Barna (Ed.), The Structur-al Interdependence of the Economy. Proceedings of an International Conference on Input-Output Analysis (New York: John Wiley & Sons, Inc., 1954), p. 180. Chenery and Clark, op. cit.3 p. 38. 15 semi-processed materials. E m p i r i c a l l y , the most serious l i m i t a t i o n on the system of c l a s s i -f i c a t i o n i s set by the a v a i l a b i l i t y of data. Usually information about the input requirements and the d i s t r i b u t i o n of output of the productive a c t i v i -t i e s i n an economy i s gathered by i n d u s t r i a l census and i s made a v a i l a b l e according to some standard i n d u s t r i a l c l a s s i f i c a t i o n . Although c a r e f u l study of the census data may reveal p a r t i c u l a r r e c l a s s i f i c a t i o n s which im-prove the homogeneity of input-output rows or columns, " i n d u s t r i a l c l a s s i -f i c a t i o n s i n conventional use are with minor changes adequate for t h i s pur-..15 pose. When a sector of the model corresponds to an "industry" which i n -cludes some v a r i e t y of products and t e c h n i c a l conditions, i t can be asserted that output determines inputs uniquely only " i f we assume that when the out-put of one of i t s products changes, the output of a l l i t s other products change i n the same proportion ( i n the jargon we assume that the 'product mix' i s con-stant) and also that a l l t e c h n i c a l l y d i f f e r e n t segments of the industry (e.g., firms using modern techniques and those using older techniques) expand and con-t r a c t i n the same proportion. In general the larger the aggregates used i n the c l a s s i f i c a t i o n of sectors,the more tenable w i l l be the assumptions of a d d i v i t y and nonsubstitu-t a b i l i t y among outputs and less v a l i d w i l l be the assumption of a s i n g l e ( l i n e a r ) "'""'chenery and Clark, op. c i t . j p. 138. "^Dorfman, cp. cit., pp. 123-24. 16 production function for each. The second assumption of those prescribed by Chenery and Clark leads to the derivation of the crucial a. . parameters of the model. In the conventional economic theory of production, i t is asserted that many alternative input combinations are available for the production of a given amount of output and that firms choose from the many alternatives open to them, some optimal combinations of inputs which w i l l minimize the cost of production. Substitution of inputs w i l l occur in response to changes in their relative prices; the optimal combination w i l l be that where the ratios of the marginal (physical) product of each input to i t s price are equalized for a l l inputs. In the input-output model, production functions w i l l take the general form: where the sectors which contribute output to any given sector (column) are the inputs in the production function for i t . It w i l l also be recalled that the corollary to the f i r s t assumption states that only one method of production i s used by each sector. This, of course, rules out substitutabil-i t y among inputs; the production function w i l l be of the special type exhibiting fixed input proportions."^ In this case, the marginal (physical) product of (1.17) 3 3 W 23 • • • * 17, The isoquant surfaces of such a production function are L-shaped II corners. n 17 each input i s equal to zero; when the amount of one input i s expanded while a l l others are held constant no a d d i t i o n a l output can be obtained. The Leontief production f u n c t i o n may be expressed as: (1.18) 1 minimum (-^-) (i = lt....,n) where the constants, a.., represent the minimum amount of input from sector 18 i required per unit of output i n sector j . Equation (1.18) states that 19 a minimum amount (possibly zero) of each u n i t i s required f o r a given output. The output, X ., w i l l be determined by whichever of the r a t i o s z. ./a., i s 3 13 1*3 smallest. Further, when output i s to be increased by c times, a l l inputs must a l s o be increased by c times. That i s , the production function e x h i b i t s , 20 constant returns to s c a l e . The absence of s u b s t i t u t i o n p o s s i b i l i t i e s i s the most s t r i k i n g d i -vergence of the Leontief model from conventional economic assumptions. Of 18 See Robert Dorfman, Paul A. Samuelson, and Robert M. Solow, Linear Programming and Economic Analysis (New York: McGraw-Hill Book Co. Inc., 1958), pp. 208-210. 19 If any a. • i s zero (the output of that sector i s not required i n production) the corresponding term can be omitted from the right-hand side of equation (1.18) or e l s e the r a t i o zij/a^ c a n o e thought of as +°° i n which case i t would never be the l i m i t i n g smallest number. 20 Mathematically, constant returns to scale implies that the produc-t i o n function i s homogeneous of degree one. (A function i s homogeneous of de-gree n i f when each of the independent v a r i a b l e s i s m u l t i p l i e d by a constant c, the new function i s c times the o r i g i n a l function. Thus i f the function of two v a r i a b l e s , z = t/^, i s homogeneous of degree n, the following r e l a t i o n s h i p holds: f(cxtcy) = c f(z,y). When n=l the production function i s described as being " l i n e a r l y homogeneous"). In assuming such a production function, the possible e f f e c t of (dis)economies of s c a l e i s eliminated; the output per u n i t 18 course i t can e i t h e r be argued that the f i x e d proportions e x i s t because of the state of technology so that no s u b s t i t u t i o n i s p h y s i c a l l y p o s s i b l e , or that the proportions r e s u l t from optimization. Samuelson has proved, for example, that even where v a r i a t i o n i n inputs i s p h y s i c a l l y possible, i t w i l l never be eco-nomically advantageous provided that there are constant returns to s c a l e , 21 only one scarce input (labour) and no j o i n t products. K l e i n has shown that a Leontief model need not deny the p o s s i b i l i t y of f a c t o r s u b s t i t u t i o n by the use of a fixed-proportions production function for the constancy of input-output c o e f f i c i e n t s , at l e a s t i n value terms, i s consistent with a produc-22 t i o n function which permits s u b s t i t u t i o n . "In other words, the input-output proportions may be f i x e d , as i s assumed, but they w i l l be fixed by consider-of one input w i l l be a function s o l e l y of the r a t i o i n which the inputs are combined, independent of the absolute amounts of the inputs employed. A l i n -ear homogeneous production function, by i t s e l f , does not r u l e out s u b s t i t u -t i o n of inputs i n response to changes i n r e l a t i v e input prices but the Leon-t i e f case of constant input-output c o e f f i c i e n t s does. 21 See Dorfman, Samuelson and Solow, op. cit.3 pp. 224-227, 248-252. It can be shown that when a production function e x h i b i t s constant returns to scale and r e l a t i v e input prices are f i x e d , there w i l l be just one set of o p t i -mal input proportions. In Samuelson's s u b s t i t u t i o n theorem, fixed input p r i -ces are assumed by the presence of only one scarce f a c t o r , labour: the r e a l cost of any output or any other input w i l l be calculated i n terms of the amount of labour d i r e c t l y or i n d i r e c t l y required i n i t s production. The r e l a -t i v e amounts of embodied labour w i l l be determined by the state of technology so that the r e l a t i v e r e a l " p r i c e s " of a l l inputs are f i x e d . The most e f f i c i e n t input proportions w i l l be those which make the smallest ( d i r e c t and i n d i r e c t ) drains on the economy's scarce labour supply. Given the state of technology, then, any output should always be produced i n a manner which uses the same i n -put proportions, no matter what the composition or l e v e l of f i n a l demand may be, because there i s only one scarce factor to be economized. (If there were two or more scarce f a c t o r s , s u b s t i t u t i o n would occur to economize most on the one whose fi x e d supply i s most "burdened" by the consumption mix). The ob-served a . . ' s w i l l not change because r e l a t i v e input prices cannot. 22 Dorfman, op. oit.t p. 124, imputes t h i s conclusion to L. R. K l e i n on the basis of h i s a r t i c l e , "On The I n t e r p r e t a t i o n of Professor Leontief's 19 a t i o n of productive e f f i c i e n c y rather than immutable technological require-23 ments." Usually the l a t t e r premise i s made, however, and each sector of the model (except the autonomous one) i s assumed to have a s i n g l e production function i n which the quantity of each input consumed i s d i r e c t l y proportional to the quantity of output produced by that sector. The factors of proportion-a l i t y are the observed a., c o e f f i c i e n t s which are presumed to be constant i n ^3 the absence of tech n o l o g i c a l change. To complete the t h e o r e t i c a l package, the " a d d i t i v i t y " assumption noted by Chenery and Clark i s made so that a l l inputs and outputs of produc-t i v e processes are taken into account e x p l i c i t l y i n the s e c t o r a l production functions. This rules out e x t e r n a l i t i e s whereby the a c t i v i t i e s of firms a f f e c t d i r e c t l y , but without the intermediary of the market, the a c t i v i t i e s of other firms or the welfare of other people. The c l a s s i c case of the bee-keeper who locates near the apple orchard i s precluded, as are external econo-mies that a r i s e due to i n d u s t r i a l i z a t i o n or urbanization of an area. There must be no divergence between the p r i v a t e and s o c i a l cost of production nor between the pr i v a t e and s o c i a l value of output, not as an optimization p r i n -c i p l e , but as a bookkeeping p r e r e q u i s i t e . System," Review of Economic Studies, Volume 20, No. 2 (1952 -1953), pp. 131-36. K l e i n assumed a production function of the Cobb-Douglas type and found that i f producers adopt that combination of inputs which minimizes average costs, the r e s u l t w i l l be that i n each sector the r a t i o between the value of purchases from each sector and the value of output of the purchasing sector w i l l be the same whatever may be the structure of r e l a t i v e factor p r i c e s . William J . Baumol, Economic Theory and Operations Analysis (Engle-wood C l i f f s , N.J.: P r e n t i c e - H a l l Inc., 1961), p. 306. 20 Unquestionably these assumptions represent a radical departure from conventional economic thought. No explicit consideration is given in the model to the maximization of profits and consumer u t i l i t y nor to the opti-mization of resources. The static equilibrium levels of output that the model generates are not necessarily optimal, for the principal concern is with the 24 dictates of productive necessity. Yet the distinctive feature of input-output analysis is i t s devotion to empirical investigation. This is primarily what distinguishes i t from the work of Walras and later general equilibrium theorists. It employs a model which is more severely simplified and also more narrow in that i t seeks to encompass fewer phenomena than does the usual general equilibrium theory. Whether these simplifications render the model an effective tool for analyzing the empirical nature of economic interdependence is the c r i t i c a l issue. In the next chapter the use of the model as a predictive device w i l l be explored. This is but one of many applications the model can take, of course, but i t is the one central to the analysis of this paper: an investi-gation of the predictive a b i l i t y of the input-output tables of West Malaysia. This is especially true of the open model. CHAPTER II THE MODEL AS A FORECASTING TOOL Input-output models in various forms can be used for forecast-ing purposes. Only the application of a static, open model in this manner w i l l be considered here for i t provides the simplest example of the technique, has perhaps the least unpalatable assumptions, and is the form of the West Malaysian input-output tables which w i l l be the particular subject of analysis in later chapters. In the preceding chapter, the technique of input-output forecast-ing was alluded to. Briefly, once a s t a t i s t i c a l input-output table has been compiled for an economy, the structural parameters of the system can be derived and employed to project the new levels of intersectoral flows and total output that would prevail and be internally consistent with any given (planned or projected) change in the level or composition of output absorbed by the autonomous sector. Using the notation developed in Chapter I, a Leontief inverse matrix, (I-A) ^, is obtained in the gen-eral solution to the input-output relationship of the economy. A new vector of total outputs, X^, can be obtained for any prescribed vector of autonomous or fi n a l demand, Y, according to the equation: (2.1) X* = ( I - A ) ~ l l where the superscript, P, refers to the endogenously determined 21 22 p r e s c r i p t i o n . The new l e v e l s of i n t e r s e c t o r a l flows can be determined by using the elements of the inverse matrix [r. . ] , so that a new set of n 13 equations of the form (2.2) 4 ^ i l J l + Pi2 J2 + +rinYn <*-*,...,«> describe the economic interdependence of the economy at the new equilibrium. In t h i s way, the whole s t a t i s t i c a l input-output table can, i n f a c t , be projec-ted. Emphasis should be placed on the term "describe", for the input-output model i s a p o s i t i v e rather than a normative t o o l of economic analy-s i s . I t i s used to derive information about what is (e.g., the values of the t e c h n i c a l c o e f f i c i e n t s ) and what will be (e.g., the value of i n t e r s e c -t o r a l flows) given c e r t a i n assumptions, not n e c e s s a r i l y what should be. The equilibrium l e v e l s of inputs and outputs summarized i n the set of equa-t i o n s represented by Equation (2.2) are not "optimal" by any s p e c i f i c econo-2 mic standard. C l e a r l y value judgements may be made about resource a l l o -c a t i o n and income d i s t r i b u t i o n i n the formulation of a planned f i n a l demand Except i n the case of a c e n t r a l l y planned economy the "prescribed" sector of f i n a l demand does not imply a production target that must be met. See the d i s c u s s i o n i n William H. Miernyk, The Elements of Input-Output Analy-sis (New York: Random House, 1967), pp. 40-41, 80-88. 2 Input-output analysis has been linked with l i n e a r programming to incorporate maximizing behaviour. See e s p e c i a l l y Robert Dorfman, Paul A. Samuelson, and Robert M. Solow, Linear Programming and Economic Analysis (New York: McGraw-Hill Book Co. Inc., 1958), pp. 210-215, and H o l l i s B. Chenery and Paul G. Clark, Interindustry Economics (New York: John Wiley & Sons, Inc., 1959), pp. 81-136. 23 vector and the relative importance of i t s components. Even in this case though, the basic model w i l l only project what w i l l be under these circum-stances. While this feature of input-output analysis may impair i t s useful-ness in other applications, i t seems only to enhance the vali d i t y of the model when used for descriptive or predictive purposes. . A comparison of the original and projected s t a t i s t i c a l input-output tables is an exercise in comparative statics; the input-output model is concerned only with the conditions of a static equilibrium. It abstracts from the time sequence of production and exchange, and the path of adjust-ment from one equilibrium position to the next. An important dynamic aspect of production i s suppressed; attention i s focused on current inputs (the i n -puts which are used up in one productive period) and the input of capital stock (inputs which last for more than one production period) i s neglected. The static description of economic interdependence i s formulated entirely in terms of flows of commodities and services so the technical coefficients are nothing but the characteristic ratios between certain rates of output and the corresponding rates of input. Any " b i l l of goods" used in connection with the open system describes a static f i n a l demand in terms of goods and services absorbed during the time period. Of course the actual economic process involves not only flows but also stocks of commodities: inventories of raw materials, "goods in process" and finished goods, and also stocks of machinery and buildings, usually identified as fixed capital, together with residential dwellings and household stocks of durable consumer goods. A static input-output model can be modified to account for stocks as well as 24 flows of goods, but only such a dynamic model w i l l provide information about the changing pattern of outputs, inventories, investments and capacities which would attend a forecasted change in f i n a l demand. As noted earlier, a closed input-output model does not u t i l i z e an autonomous sector. It is the most ambitious version since i t attempts to explain more than any other, but i t leaves no room for autonomous investment, exogenous changes in government demand, foreign trade, or the like, and in order to determine household consumption within the model, the dubious con-cept of a household production function must be invoked. Clearly, for fore-casting purposes, the open model, wherein households, government, foreign trade and investment typically comprise the autonomous sector, is the more appropriate one. To be valid, the procedure for predicting outputs summarized in Equation (2.1) requires the assumption that the Leontief inverse matrix and hence the matrix of technical coefficients [a..], remain the same regardless ZQ of changes in the level or composition of output absorbed by the autonomous sector. As shown earlier, this assumption of constant coefficients is based on the premise that for each non-autonomous sector of the matrix, a single production function of the fixed proportions type w i l l prevail. In the dynamic model, the set of technical coefficients is supple-mented by a set of corresponding stock/output ratios, the underlying theore-t i c a l assumption being that technological conditions determine the amount of each type of stock which each sector must have as i t s disposal to produce at a certain rate of output. Dynamic input-output analysis requires more ad-vanced mathematical methods: instead of ordinary linear equations i t leads to systems of linear d i f f e r e n t i a l equations, that i s , equations which con-tain not only rates of flow for various commodities and services but also rates of changes of these rates of flow. 25 In principle, the intersectoral flows, as shown in an input-output table, are expressed in physical units although in practice, most tables are constructed in value terms. When monetary values are used, the entries in each c e l l of the table (except the column totals) can be regarded as being representative of the physical quantities of the goods and services to which they refer. This only requires that the physical unit in which one measures the entries i n each row be redefined as being equal to that amount of output of that particular sector which can be purchased for $1.00 at prices which prevailed during the interval of time for which the table i s constructed. Such a conceptual approach is necessary i f the notion of a technologically grounded production function i s to apply. The input coefficients can then be interpreted as physical constants rather than value ratios which combine the effects of both changes i n relative prices and in quantities and may be stable as a result of optimization. When value terms are used in the s t a t i s t i c a l input-output table, predictions must be made in constant prices of the base years, for i f the relative prices of the inputs change over the forecast period, the technical coefficients w i l l also change, not as a result of optimization but because the definition of "a dollar's worth" of some inputs w i l l have changed. With intersectoral flows expressed in physical terms, one way or another, a l l inputs are seen to vary proportionally with the sector's output and the a..',sare the technologically determined factors of proportionality. ^3 Presumably only when profound technological change takes place w i l l the values of the coefficients change, and the forecasting, procedure no longer 26 be tenable. There has been much controversy over the assumption of constant c o e f f i c i e n t s not only because the fixed proportions production function i s a r a d i c a l s i m p l i f i c a t i o n of conventional production theory, but be-cause i t represents perhaps an even more d r a s t i c departure from economic r e a l i t y . If held s t r i c t l y , t h i s assumption has at l e a s t four implications which appear to be contradic-ted by general observation. F i r s t i t implies that a l l inputs are uniformly affected by a change i n the scale of production, thus ignoring the time-honored d i s t i n c t i o n between f i x e d and v a r i a b l e inputs, and between short- and long-run. Second i t assumes that i n d u s t r i e s can be c l a s s i f i e d s u f f i c i e n t l y f i n e l y to eliminate multi-product i n d u s t r i e s whose input s t r u c -tures would be a f f e c t e d by changes i n the product-mix of t h e i r outputs. T h i r d , i t means that economizing s u b s t i t u t i o n s among inputs due to changes i n r e l a t i v e p r ices or a v a i l a b i l i t i e s are of n e g l i g i b l e importance. F i n a l l y , i t implies that t e c h n o l o g i c a l changes i n i n -put structures are s u f f i c i e n t l y rare and slow that they can^either be disregarded or adjusted i n simple fashion. Yet even Leontief did not expect the c o e f f i c i e n t s to be constant i n the s t r i c t sense of the word. Therefore he and l a t e r analysts addressed themselves to the r e a l issue, that i s , whether the actual range of v a r i a t i o n s i n the c o e f f i c i e n t s w i l l a f f e c t the empirical v a l i d i t y of the computations based on the assumption of f i x e d c o e f f i c i e n t s . I f the errors involved i n using the assumption are " s a t i s f a c t o r i l y small," the realism of i t need not be challenged. On the other hand, i f the v a r i a b i l i t y of the c o e f f i c i e n t s seems to warrant i t , the Chenery and Clark, op. cit., pp. 157-158. 27 concern should be with adopting t h e o r e t i c a l and empirical procedures which can take such v a r i a t i o n s into account. Technical (input) c o e f f i c i e n t s w i l l be a f f e c t e d i n general by f i v e kinds of changes i n the economy, as follows: 1. Changes in the state of technology which r e s u l t s i n the adoption of new production techniques. This p a r t i c u l a r cause for v a r i a b i l i t y i n the c o e f f i c i e n t s i s the only one e x p l i c i t l y considered i n the basic Leontief model but i t i s expected to occur slowly so as to be of l i t t l e s i g n i f i c a n c e i n short-term f o r e c a s t i n g . Various techniques have already been developed to project the new t e c h n i c a l c o e f f i c i e n t s that would p r e v a i l as a r e s u l t of long-term technological change.^ 2. Changes in the product-mix of sectoral outputs and the appearance of new industri.es 3 which frequently evolve from tech-n o l o g i c a l change, whether such changes r e s u l t i n serious v a r i a t i o n s i n the value of t e c h n i c a l c o e f f i c i e n t s i s determined l a r g e l y by the way i n which sectors are c l a s s i f i e d and aggregated i n the f i r s t place. 3. Adjustments to the input structure which may occur as a result of long-run versus short-run optimization. With i t s assump-ti o n of constant returns to s c a l e , the input-output model precludes the See the discussion i n Miernyk, op. cit., pp. 117-125, about the adaptation of a s t a t i c model i n t h i s regard, based on the notion that the input patterns of "best p r a c t i c e " firms i n an industry can be used to pro-j e c t the average input patterns of that industry at some time i n the future. 28 possibility of non-proportional changes in inputs and outputs caused by economies or diseconomies of scale adjustment. Independent st a t i s -t i c a l evidence, however, suggests that the average cost of goods is i n -6 dependent of the scale of output in a great many cases. Thus, although not totally defensible theoretically, the assumption of constant aver-age cost built into the model may not be too much out of line with the available facts. 4. Changes in the r e l a t i v e prices of inputs which w i l l lead to adjustments in optimal (minimum cost) input structure. In the short run i t is probable that price substitution phenomena are of limited importance for certain sectors of the economy, including manu-facturing, mining and u t i l i t i e s . ^ For such sectors, a fixed-proportions production function may apply very well. In the long-run though, technolo-gical change is responsible for most of the changes in relative prices that take place and i t is therefore d i f f i c u l t to distinguish between the effects of these factors. 5. The introduction of external economies or disecono-mies which w i l l give rise to changes in the observed proportionality between inputs and outputs even though the real (social) cost structure of production may remain unchanged. Externalities were assumed away in the addivity assump-tion of the model given in the f i r s t chapter, so that the total effect of See J. Johnston, S t a t i s t i c a l Cost Analysis (New York: McGraw-Hill Book Co. Inc., 1960). ^As suggested in Dorfman, op. cit., p. 125. 29 carrying on several types of production would be given by the sum of the separate e f f e c t s . To the extent that they do a r i s e during a forecast period, however, they w i l l have the e f f e c t of a l t e r i n g the values of the t e c h n i c a l c o e f f i c i e n t s that are derived from s t a t i s t i c a l data. For example, the i n s t a l l a t i o n of s o c i a l overhead c a p i t a l may reduce the p r i v a t e (observed) cost of the transportation, energy and communication requirements of c e r t a i n productive sectors. In an area where i n d u s t r i a l i z a t i o n i s taking place, the growth of a s k i l l e d labour force may a f f e c t the p r o p o r t i o n a l i t y between inputs and output. Subsidies and other forms of p r o t e c t i o n may be given i n acknowledgement of the fa c t that the s o c i a l value of c e r t a i n production exceeds the p r i v a t e value. So while the assumption of no e x t e r n a l i t i e s may be necessary i n theory, i n p r a c t i c e the e f f e c t s can be expected to a l -t e r the t e c h n i c a l c o e f f i c i e n t s of the input-output model. Apart from these frequently i n t e r r e l a t e d sources of change i n the value of the t e c h n i c a l c o e f f i c i e n t s , v a r i a t i o n s may occur simply because a t e c h n o l o g i c a l l y grounded production function i s p a r t i c u l a r l y unsuitable for c e r t a i n sectors. For example, a g r i c u l t u r a l and f i s h e r y production may be subject to large stochastic elements, and the notion of a fixed proportions production function may not be too compelling in. the case of wholesale or r e t a i l trade sectors. In t h i s connection Dorfman has posed the question: 8 "Can trade margins be regarded as s t a b l e t e c h n o l o g i c a l inputs?" Yet these Dorfman, op. cit.j p. 125. He states that an a f f i r m a t i v e answer implies an argument along the l i n e s of f u l l - c o s t p r i c i n g which, "whether or not acceptable, i s not a t e c h n o l o g i c a l argument." 30 sectors, too, must be included in the model in order to account for the f u l l output of the sectors with stable production functions. As stressed earlier though, the crucial test of the input-output system is the empirical usefulness of the assumption of constant input co-efficients. There are basically two ways in which this can be tested. One consists of direct comparison of individual coefficients at different points of time. The other involves comparing the computed results of an input-out-put projection with the actual operation of the economy. Both techniques 9 have now been widely applied, but in principle, the latter test is more sig-nificant. Any direct comparison of coefficients w i l l almost certainly reveal changes from year to year but whether these changes are "satisfactorily small" depends upon the criterion used to evaluate them. One possibility is to apply a test of s t a t i s t i c a l significance to the observed deviations from the hypothesis of no-change. But whether the hypothesis is rejected or not re-jected at the conventional level of significance, this i s not a test of the empirical usefulness of the simplifying constancy assumption. Moreover, a fundamental feature of the Leontief model is that "structural matrix errors tend to be non-cumulative and compensating as they affect input-output e s t i -mates."'"'^  Though individual coefficients may prove to be variable on direct 9 See Chenery and Clark, op. cvt., Chapter 6, for a summary of some of the results. ^V. Duane Evans, "Input-Output Computations," The Structural In-terdependence of the Economy," Proceedings of an International Conference on Input-Output Analysis (New York: John Wiley & Sons, Inc., 1954), pp. 101-102. This property comes principally from consistency within an i n -put-output table, such as that expressed in the balance equations of the f i r s t chapter. 31 examination, the overall performance of the model may be satisfactory. For these reasons, the second method is the more important one; comparisons of actual and projected outputs provide a pragmatic test of an assumption which was originally conceived to be only an approximate description of the productive structure. To conduct the test, reliable data must be available on actual f i n a l demands and total output in the forecast years, in a form consistent with the input-output table used to make the predictions. Ideally, a series of comparable statistically-derived input-output tables should be used to make a r t i f i c i a l projections and measure the resultant errors. In the case of foreward projections, this procedure would involve the application of the observed Y vectors from chronologically later tables to one or more earlier matrices, according to Equation (2.1). Prediction errors would be calculated by a comparison of the projected total output vector, , with that actually recorded in the corresponding later tables. The mere existence of errors w i l l not be sufficient to reject the no-error hypothesis, however. Nor does the absolute value of errors provide a basis for such judgement. Of course the prediction errors in themselves may serve as a basis for evaluating the relative performance of the various sectors and how the accuracy of the predictions is affected by the length of the forecast period. But even i f a conventional test of significance is applied to the errors, no indication of the empirical usefulness of the model w i l l be generated. To be meaningful, the errors resulting from the input-output projections should be compared with the errors that arise when some other means of forecasting is employed. One illuminating basis for compari-32 son is a "naive" projection which uses some completely mechanical procedure. The naive projection plays the role of the null hypothesis, and the input-output project ought to prove superior. Indeed, a large margin of super-i o r i t y would be needed to ju s t i f y the additional cost and complexity of the input-output technique.'"""'' The methodology just described w i l l be used to test the efficiency of the input-output tables of West Malaysia when used for forecasting pur-poses. A series of s t a t i s t i c a l input-output tables which describe that economy w i l l be employed to make a r t i f i c i a l projections of intermediate sectoral outputs based upon actual f i n a l demands. The prediction errors w i l l be calculated by reference to the tables themselves, then compared with the errors that result from a naive forecast of intermediate output. Hope-fully as a result of the greater time, effort and expense involved in the construction of more detailed input-output tables, the Leontief technique of forecasting w i l l prove superior to a naive projection method. Yet i t should be noted that West Malaysia is a "developing" country. The process of economic development involves a restructuring of the economy; hence, changes i n the structural characteristics of the economy are to be ex-pected. The empirical significance of such changes w i l l be revealed in part by the test already described but could be evaluated further i f the efficiency A more serious test is provided by comparison with projections based on multiple correlation of time series but because of the Increased data requirements for this type of projection, the necessary margin of super-i o r i t y would be reduced. 33 of the West Malaysian input-output tables could be compared with that of input-output tables from a "developed" country where the rate of structural change is presumably lower. Just such an evaluation w i l l be made, using for comparison the predictive efficiency of input-output tables of the 12 Netherlands, as analyzed by Guido Rey and C. B. Tilanus. In this case i t is expected that the Dutch tables w i l l prove to be more effici e n t , for forecasting purposes, than the tables of West Malaysia. \ Guido Rey and C. B. Tilanus, "Input-Output Forecasts for The Netherlands, 1949-1958," Econometvica, Volume 31, No. 3 (July, 1963), pp. 454-63. CHAPTER I I I THE INPUT-OUTPUT TABLES OF WEST MALAYSIA West Malaysia i s a r e l a t i v e l y new country, formed only i n September 1963 by a federation of Malaya, Sarawak, North Borneo (Sabah), and Singapore. Even Malaya did not become an independent nation u n t i l 1957"'" and before 1963 Sarawak and Sabah were s t i l l B r i t i s h c o l o n i e s . Before j o i n i n g the feder-a t i o n Singapore was independent i n I t s i n t e r n a l a f f a i r s , but i t s defense and f o r e i g n p o l i c y were s t i l l c o n t r o l l e d by the B r i t i s h . I t ceased to be a part of Malaysia i n August, 1965. context of rapid p o l i t i c a l change. The F i r s t Five-Year Plan of Malaya (or as i t may now be c a l l e d , "West Malaysia") was adopted i n October,1956 fo r the period ending December 31, 1960. Despite provocation by Communist g u e r i l l a s and the e f f e c t s of the world recession of 1957-58, the output of the Malayan economy grew s u b s t a n t i a l l y during the period (about four per cent per year) and more than kept pace with population which was increas-ing at an a c c e l e r a t i n g r a t e . Public investment, at a l e v e l of $1,007 m i l -l i o n , was nearly double that of the preceding f i v e years and p r i v a t e "Malaya i t s e l f was a federation of eleven states on the Malay peninsula. See R. S. Milne, Government and P o l i t i c s in Malaysia (Boston: Houghton M i f f l i n Co.., 1967). Economic development i n Malaysia has therefore taken place i n a 34 35 investment rose i n response to government i n c e n t i v e s . The establishment of an i n d u s t r i a l estate, P e t a l i n g Jaya, and tax incentives o f f e r e d under 2 the Pioneer Industry p o l i c y a t t r a c t e d i n d u s t r i a l c a p i t a l . A large part of the p u b l i c investment was d i r e c t e d to the a g r i c u l t u r a l sector to promote rub-ber replanting and new p l a n t i n g , to increase i r r i g a t i o n f a c i l i t i e s f o r r i c e production, and to launch new land development schemes designed to open up v i r g i n jungle for settlement and production. C a p i t a l expenditure programmes were also c a r r i e d out to improve transportation and communication f a c i l i t i e s and the p r o v i s i o n of u t i l i t i e s . Technological change occurred i n the t i n industry where the i n t r o d u c t i o n of the "hydrocyclonic j i g , " a device designed by government engineers to separate t i n from a l l u v i a l s o i l , r e s u l t e d i n e f f i -ciency gains of about 30 per cent, whilst permitting lower grade ore to be e x p l o i t e d and f o r e s t a l l i n g the exhaustion of reserves. Despite the advances made under the F i r s t Five-Year Plan-;-. * the economy of Malaya had serious problems. With a population i n c r e a s i n g at a r a t e of about 3.3 per cent annually there was a pressing demand f o r more food, c l o t h i n g , housing, schools, health s e r v i c e s , land and jobs. Coupled with t h i s was the need f o r economic d i v e r s i f i c a t i o n to c o r r e c t the excessive The P e t a l i n g Jaya i n d u s t r i a l estate provided developed s i t e s with access to roads, water and power. A t o t a l of 150 factory l o t s were s o l d and by 1961 more than h a l f of the f a c t o r i e s had s t a r t e d production. Inaugurated i n 1958 the Pioneer Industry p o l i c y provided for exemption from income tax fo r a period ranging from two to f i v e years for q u a l i f y i n g f i rms. By 1961 more than 50 firms had been awarded pioneer status and 35 of these had st a r t e d production. See Second Five-Year Plan 1961-1965 (Federation of Malaya: Government P r i n t e r , 1961), pp. 3-4. 36 dependence of the economy on rubber and t i n (which rendered the e n t i r e economy vulnerable to f l u c t u a t i o n s i n the export p r i c e s of these commodities) and to provide domestically more of the goods and s e r v i c e s which were being im-ported (and thereby reduce the need for f o r e i g n exchange). In 1961 the Second Five-Year Plan was i n s t i t u t e d i n an attempt to deal with these problems. I t s execution proceeded through the time of the formation of Malaysia and the withdrawal of Singapore. With the s t a b i l i -z a t i o n of the new Federation, the F i r s t Malaysia Plan of development for 1966-1970 was designed f o r Malaya, Sabah and Sarawak together. I t i s the period from 1960 to 1965, however, which i s of p a r t i c u -l a r i n t e r e s t here, for i n 1960 the government of Malaya (West Malaysia) be-gan to conduct s e c t o r a l surveys of the economy f o r the purpose of compiling annual i n t e r i n d u s t r y accounts. These data were f i r s t used by the Department 3 of S t a t i s t i c s to construct an input-output table f o r the year 1965. With the co-operation of the Government of Malaysia, the e a r l i e r accounts were obtained by Professors H. Craig Davis and Geoffrey B. Hainsworth of the U n i v e r s i t y of B r i t i s h Columbia. Under t h e i r supervision, input-output 4 tables for the years 1960 through 1964 were constructed from these data. To obtain a consistent set of tables, the one published for 1965 was modified Malaysia Interindustry Accounts 1965 (Kuala Lumpur: Department of S t a t i s t i c s , Government of Malaysia, n.d.), Table 1, p. 10. 4 Mr. C o l i n Bent and the author a s s i s t e d i n the preparation of the input-output t a b l e s . 37 slightly. (A description of the adjustments appears in Appendix A). The input-output tables constructed at UBC for the years 1960 through 1964 are shown in Tables 1 through 5 respectively, and the modified table for 1965 appears in Table 6. The series of six input-output tables spans the period from the end of the F i r s t Five-Year Plan of Malaya to the end of the Second F i v e -Year Plan. The intent and accomplishments of both Plans have been well documented in the government literature"* and these references provide an invaluable aid to anyone seeking to analyze the input-output tables of West Malaysia. Each of these input-output tables which describe the West Malaysian economy has 29 productive sectors and six categories of f i n a l demand: the Rest of the World or export demand, Fixed Assets (capital formation) and Inventories3 the two components of investment demand, Householdst Government, and Unspecified recipients of f i n a l goods produced domestically. Imports are shown in a single row as they were distributed among the productive sectors of the economy (i.e., they are not treated as inputs from the domestic sector competing with the imported goods). For each sec-tor, the tables also show the value of inputs used in production where the originating sector could not be specified, and the value of the primary factors of production u t i l i z e d (which includes entrepreneurial income, wages and salaries, indirect taxes and subsidies). A summary of the achievements made under the Second Five-Year Plan is found in the document which describes the subsequent plan, First Malaysia Flan 1966-1970 (Kuala Lumpur: Government of Malaysia, 1965). TABLE 1 W E S T M A L A Y S I A I N T E R I N D U S T R Y A C C O U N T S I 9 6 0 ( Producer Prices in Millions of Moloysion Dol lars . ) I Delivered Item: j 1 i ! i 2 | 3 5 a 7 8 10 11 12 13 14 IS 16 17 IS 19 20 21 Z2 23 24 25 26 27 28 29 TOTAL INTERMEDIATE DEMAND si H! s I i FIXED ASSETS 1 l 1 i HOUSEHOLDS II! 1 Agriculture t Livestock 1 14.7 • j let. 4 9.1 0.5 91.3 18.4 2. Rubber Pl.ntln| 1166.4 0.9 - 9.i -— 1166.4 ; 120.2 5.5 125.7 1292.1 3. Forestry 64.9 0.1 0.1 75.5 J 16.8 3.3 28.6 48. ; 124.1 *• Fishing 24.5 24.5 . 9.6 64.8 74.4 98.9 5. lining 19.2 1.4 367 .3 1.9 1.5 372.1 ; 154.2 -11.4 122.8 494.9 6. Food Indu.trle. 8.1 6.3 13.6 ! 40.0 0.7 | 15.9 270.6 327.2 160.8 Beverage. — --• 0 0.3 0.6 0.1 8.4 20.4 21.1 21.3 Tobacco — - — 0 93.9 102.6 102.6 Te.tiles 0 I 3.7 0.4 0.6 j 3.9 8.6 8.6 10. Clothing I Footwear o 1 i 4.1 4.1 4.1 11. Wood » CorV 0.3 5.1 8.6 0.3 0.2 56.1 71.0 ] 37.6 0~ I o.T" 2.2 j 0.9 ; . 16.1 56.8 127.8 17. Furniture t Fixture. 6.6 ; j 18.0 24.7 24.7 11. P.per fc Paper Product* — i ° i 0.7 ] j | 2.B 3.5 3.5 K. [Printing » Publishing 0.1 1 -e.i 1 o.6 14.6 | 1.6 | 17.3 34.1 34.^  l i . [Leather 4 Le.tn.r Product. 1 0.* 0.4 o.e : ' i i-J 1.3 : . i 16. | lubber Procciatnt ' 264. 7 11.9 | 276.6 1407.2 i9.21 1426.4 1701.0 17. | Rubber Produce* 2.2 O.L j 2.1 11.5 5.6 0.6 ! ! 22.4 40.1 42.4 IS. t Oiealcal Products 17.3 1.9 14.0 1.6 — I 36.8 98.3 10.0 ! i .o: 56.1 165.4 202.2 19. Ken-Metallic Mineral Product. 0.1 L I 27.6 ..... (-1 28.8 1.6 1.2 1.2 ! ' 1 1.3 3.) 12.5 20. Basic Metal Industrie. T 555.8 1 0.4 , 12.9 1 519.1 520.7 31. Met,] Product) 4 Machinery 0.2 T I TZJ..... i | 0.1 j 13.4 .3.1 j 26.7 1.1 ! 28.9 1 11.7 1.1 | 14.9 57.7 B4.4 22. Misc. Manufacturing Industrie. — - | 1 5.3 0.2 17.8 43.3 43.1 21. Coo.truetion j l.B~ "0.2 0.7 10.1 IS. * 4.6 5.8 18.6 39.8 20.1 I 6.5 328.4 ' j 65.B 440. 8 480.6 Electricity 4 Water 11.S 1.3 0.1 0.1 0.1 0.7 0.2 j 0.3 1.9 0.8 0,9 ! 55.6 0.5 ' 16.7 1 | M - 37.5 62.4 118-0 25. Tran.port.tion 4 Co»nlc.t Ion "lO.S 8.4 0.6 • 5.1 44.4 101.4 107.3 17.0 ! 35.6 • : i5.i 112.1 194.8 102.1 I*. Wholesale 4 Retail Tr*de 27.7 6.3 I 1.9 4.8 21.4 19.1 2.4 55.9 1.0 0.4 14.0 1.8 0.6 2.4 0.1 9.1 2.5 26.1 17.0 0.6 8.6 103.1 380.9 | 59.9 | 10.2 14.5 876. 7 1142.2 Ih45.3 27. | Sink lot i ln.ur.nc. ett. 0.8 0.8 55.4 2.9 ! 38.2 96.5 97.3 28. Dwell in... ° 1 1 265.0 265.0 265.0 29. Other Service Industries ._ .... 70.0 JO".~ 3.7 109. J "' 20.2™ ' 'i'.2~ 3.7 5.9 1 11.6 ! 615.1 355 .8 1010.6 1014.1 10. I" 5"*" T r * l e 2.1 27.6 25.9 338.2 12.5 1 4.9 15. e 9.4 5.) 0.4 I .6 o.s 0.7 1.8 2.1 0.8 32.8 3.1 1.1 2.1 7.7 0.4 57.2 4.5 19.9 140.3 22.7 6.0 12.5 " V . V 20.1 — 187.5 J^38.0 "TioTfe - | 61.1 -193.6 | -2.3 11.3 1011.5 22 78.5 1). Unspecified 11.0 1 10.5 0.6 0.4 5.1 0.3 21.6 ' 5.5 16.1 2.0 Y.'i 16.4 3579 " 28.4 " 6.4 41.3 17.6 "isi.o" 480.6 9.5 69."a 20.2 , 48. B' 216.5 *146*.6 " | D . l 11.7 | 56.8 | 41.1 -25.6 664.8 52. Frlaary Factors of Production 587.1 1261.6 j 111.8 91.4 49.0 t 11.2 j 12.3 0.4 18. 7 0.4 181.9 j 15-0 49.0 14.8 79.2 245.6 j 962.4 111.8 -r=-^-=- -3189.9 TOTAL: 766.6 1 1292.1 j 124.2 98.9 494.9 160.8 j 21.1 8.6 4.1 „ 1 1701.0 j 42.4 202.2 12.5 j520.7 84.4 118.0 102.1 j 1645.1 97.3 265.0 1014.3 1 515.7 764.2 100.0 J801.1 1774.2 LO OO TABLE 2 W E S T M A L A Y S I A INTERINDUSTRY A C C O U N T S 1961 (Producer Prices- in Millions of Moloysign Dollars). Delivered frc Clothing k Footwear v*ee 4 cori Paper & Paper Products Printing & Publishing Rubber Procusinjt Rubber Frodui Cheoical Produi in-Metallic Mineral Basic Wttil Indu; Ketal Products 4 Machinery Transportation 4 Cosnunleai '."hoteialc 4 Retail Trade 1)3.0 137.3 | i:o. 10b.: i io;.o Other Service Indus-r] Prlnary Factors of Produt 21.5 128.4 116.5 25.J I LO TABLE 3 WEST M A L A Y S I A I N T E R I N D U S T R Y ACCOUNTS 1962 (Producer Pr icel in Million* of Molgytion Oollort] Delivered (torn: I i 5 6 7 10 » 12 13 14 15 16 17 18 19 20 21 2  23 24 21 26 27 29 ill 3 I a 1 Hi 84 2.1 ]. VMcuItur* 4 Livestock 15.B IB).2 A. 1 0.4 BB.2 17.5 113.2 21.1 7.0 1.6 49 7.0 a 2. Pubicr PljntinR 940.3 940.3 1 1J . 4 '1.7 157. h 1 J' 7 , i 3. Fi>re*trv l.fl 56.1 O.l 0.4 7.8 -.5.4 14.0 1.2 10. ) 47.5 112.9 FUhfi.R 26.7 28.7 in.9 »',.! 107.2 115.9 1.1 417.5 0.3 0.1 3.1 422.1 180. J 0.2 4.1 1 4.1 . S (,. Fund Industries IB.6 9.6 1.7 0.1 6.) 36.  44. H 0. ) -11.5 312.9 164.5 ioo. s ;. 0 ! .0 0.6 0.1 20.6 22.1 72.) 8. Tobaco 0 0.4 3.2 147.4 151.0 151.0 9. Textiles 2.6 0.1 2.7 3.1 0,7 -1 . 1 •.5 9,2 ll." in. ClothinG 4 F(.tw.:ar 0.3 O.l 4.1 4.5 4,8 ii. W*.d C Turk 0.3 5.5 ll .1 0.4 0.4 60.5 78.2 29. 7 ,1 .5 0.4 17.5 10.1 1 28. 1 i:. Furnlur & Fixtures 0 7.1 19.' 21.7 ;».) 11. f-aper 4 Pap.-, fio-lurl* 0 0.7 ).0 i. J it. Print inc. 4 Publishing 0.1 0.1 0.J 1 1.1 l.fl l',.n 16.1 16. 2 u. I.tJilier 4 Icuh.T Product-. 0.4 0.4 n.H 1.1 1.1 2.1 )h. 21)6.1 12,7 219.1 1112.  19.2 1111.4 1370.7 17. Ruber Products 2.8 2.8 11.6 5.1 0.9 0.5 28.4 4h.5 49. 1 IB. Chemical P.oducts 22.fi 3.1 4.0 0.5 0.2 0.4 19.5 0.3 8.2 59.0 97.9 1 I .« 5.7 .8.1 18 1.5 24 2.5 10. Von-.l'UlUc .liner*] Product* 0.1 2.1 37.8 4fl.fl O.H i.: 0.4 I.". 1.9 11.8 :o. •.j.tr M.-I.,: In.l..-trl« 0.) 2.6 2.9 615.7 0,4 :.i :i. Mvtal Fro<l.<:ls 4 N.,rhlK-ry 0.2 0.4 0.7 20 ) 13.0 14... 0.5 4'. .2 21.6 i .i 21 . 1 91,4 128.0 Mi*.-, Iltul.tcturinir, Industrie (1.1 0.2 O.l 7.'  11.2 0.1 11.9 41.H 4...1 73. 18.5 12.0 15.9 46.4 20.6 5.5 5)7.0 102.8 M,'.9 712.\ F.lrrliritv J, W.H.-i lh. 3 1.7 0.) 11.4 0.1 a.ti 0.2 0.3 2.1 1.0 1.0 1.9 0.2 1.) 0.1 15.8 4.8 0.3 0.1 68. b 0.7 27. H 11.9 17.6 7I.0 li.*.H 21. Ti.ir.*Pnrt.nlon t fimaurtlcat lun 7.B 104.9 115.4 n.o t.l.,7 1 I." 110. 1 ill.,' )•'.'-. 1 :<•. i.'ho)*-iole ii R.-Inil Trade 31.0 7 .4 2.5 5.3 17.H If).4 2.4 S3.1 l.fl 0.) 21.7 2.1 0.7 2.3 0.2 11.5 3.5 24.0 5.4 3.4 11.0 1.2 6H.4 9.2 24.9 14.2 1.1 11.7 400., 24H.5 81.7 4.8 19.11 Mi.l 1740.1 27. B.in'.ln,; 4 Innur.in.i-. .<tc. O.H O.H M,h 2.7 4 (.•'. 11;.; 111.5 :s. [>w.l lRI 0 5.9 282.') 287.9 28 7.* 29. Ol.er Survlcf Industries 6.2 6.2 49.4 69ft . 2 in.'. 1145.1 1151.7 I<1. laport Trade 94.3 11.1 2.5 14.2 4).) 1.2 11.J 5.0 0.B 1.6 3.1 2.2 10.9 0.3 49.5 5.6 21.6 2.8 183.H 40.9 6.6 168.9 13. 3 21. H 5.7 l(i.2 17.7 201.H 778,9 289.  0.2 15.4 01 1.9 2'90.5 il. L'nspt-cl( led 17.8 15.4 ti.l n H 7).9 42.9 1.7 15.3 0.5 0.7 12.1 t .4 fl.4 4.2 0.J 28. I 6.6 27.0 B.3 2.9 17.  30.9 47 ) 14.9 19.7 56.9 6.1 18.4 43.) n. Prlaury Factors of Production 619.8 into.3 97.3 127.1 «91.4 57.0 13.0 24.6 1.9 2.0 3(1.1 7.9 0.4 18.5 0.5 132.1 16.7 60.1 22.2 13.1 55.0 7.0 240.1 85.9 252.) 1452.7 94.9 271.2 loai.a TOTAL: 842.1 \m?.i 112.9 13S.9 606,  400.8 22.3 111.0 11.9 ... 128.3 2b. 7 3.7 36.2 2.1 1370.7 49.3 242 .5 43.8 621.1 128.D 46.1 712.3 146.  349.1 1040.7 na.5 287.9 USl . 7 O TABLE 4 WEST M A L A Y S I A INTERINDUSTRY A C C O U N T S 1963 (Pioducef Pfices in Million* of Moloyt-ion Dollar*, i 2 3 5 6 7 e 10 11 » u IS 16 IB 19 20 21 22 23 24 25 26 77 28 29 J ; »3 as C 3 8 8 1 3 1 3 G =!§ 22 1. Agriculture 4 Lt.ws.iock 2S.7 115.1 U.i 13.2 16.6 Kh.O 2',. 8 10.0 7.1 51-.A '.',2.7 103.7 kubb.r F.*:uln,i 924.0 124.0 162.1 l-.'T I On*!. 1 3. F,refi;rv ! .2 63.7 0.6 0.1 0.1 6.7 7 2.4 19.1. 2.4 11 . ' 51.7 126.1 4. 26.8 26. fl 1 J . '1 ':'.>. |i',,2 1)2.0 5. Nlril.,. 445.  3.2 448. 7 191. 8 -5.2 118.r, 637. 1 e. FO«d Iddmi i-s. 26. 1 10.1 0.6 6.5 '. J.5 '.5.5 1.2 15.9 D*. 1 4.11.7 45 2.2 7. 0.1 O.l 0. i V'.'. 40.0 P. 0.2 0.1 0.3 4.6 167. 1 171.9 17 2.2 9. lexl 1l-i 1 1.2 0.1 2.0 5.3 3.7 0.4 0.5 11.5 16.1 21.4 10. Clolinn L Fjulwrar 0.1 5. . 5.4 11. Wod t c»rv. 0.1 9.1 H.2 0. 1 0.5 1.5 67.4 87 .3 18.'1 1.11 1.') IV'I MJ.* 17.9 12. Furni.ur & Flxtutcs 0.7 0. 7 0.  9.5 11.1 2*1.5 10.2 13. Paper I 1-apei Products 1 1.1 0.1 2.1 0.9 4.4 0.7 6.0 8.  J* • Frlntlns • Publishing 0 1.0 25.7 2.2 28.1 57.0 57.0 li. LealhrM 6 Luther Product* 0 2.7 2.7 16. Rubb-r Processing 248.2 II .1 7 51. J It 14.6 0.2 -23.6 1111.2 1 17H.5 .P-ubS-i Pt.4<.r". 0.4 0.4 3.0 11.2 4 .0 li.(. 6.'. 0.7 4.5 il .6 51.1 ft.-. 8 i e . CS.rtir.il rr-J-ii* 22.1 1.2 0.5 3.2 5.1 0.1 0.1 0.7 0.1 1.6 0.5 2'.. f) 0.2 n.i 0.0 12.2 1.8 4.1 1.1.8 111.2 22.-* If,. 2 811.2 2 1ft.1 31 i.fc 19. Ngn-M-t.! lie .1 Intra! Prnducls 0.1 0 1 3.2 0.2 47.  50.4 1.4 2.2 0.6 55.fi 20. e.slc Iniuac, l-r. 0.1 0.6 0.4 0.1 11.7 12.9 619.H n.4 0.4 -?i . J ',15. 1 621.2 71. -*nsl Ptduci. ii turitiu-t-/ 0. P 0.1 .1 0.2 9 29.1 12.4 '•1.9 6.2 '.0.5 1J.1 4.7 2">. 1 1 ) f 157. t -is.. liniLi-uins Imi.mnes 0.1 0.5 0.4 1 .0 1 8 D. 1 O.li •.•>. 4 M 5?.9 25. 21.2 12.4 16.0 49.6 21.7 4.4 601. K 105 7)1. S ;m.4 i . i;r<-.,:cl.y 4 'W^f 14. 9 2.4 0.6 0.4 0.1 0.8 0.2 0.1 0.4 1.9 1.5 1.5 2.1 0.5 1.9 0.1 16.6 5.8 1.2 0.1 71. J 0.  37. J 14.4 40.1 87.° 161.2 25. Transport atlun (. Coauunicat lcn B.O 1.1 107.2 118.5 11.6 74. 7 11.6 147.4 247. 1 165.S b. Vho'.fbale i Retail Trade 17.8 9.0 2.1 4.7 22.3 44.0 5.7 99.4 3.6 0.5 25.9 2.8 1.1 3.7 0.3 8.8 6.6 31.1 6.4 5.6 16.2 1.8 76.8 11.4 25.8 2) .4 1.2 11.1 489.1 264.5 82.2 12.0 27.5 124.9 1 111 . 1 :ano.4 27. BanklnR 4 lnsuiar.ee, etc. 0.8 0.8 J1.5 1.5 51.1 126.1 126.9 26. Swelings 0 6.2 294.0 100.2 JOG. 2 29. Other fervlce I nd.jst rU-« 7.3 7 . 3 59.0 7  i.lt 4 12.0 12(.5.6 1272.9 30. Iaport Ti»Je 108. ) 11.2 1.8 20.6 62.6 6.B 21.2 8.2 1.6 3.3 1.1 3.1 13.2 0.6 36.6 8.7 .'.<». 1. 6.0 158.2 51.1 8.1 166.4 8.5 19.1 5.5 17.0 17.8 148. 7 28S.8 285.4 17.4 11.9 10SS.2 2UBH.4 31. Unspecified 35.9 15.0 12.5 O.S 26.7 44.0 5.1 17.7 1.0 1.0 14.9 3.1 0.9 10.1 0.4 21.2 7.8 29.1 8.  2.4 18.4 32.1 39.6 14.7 17.3 69.6 6.  41.1 47.*7 12. Prlosrv Fsccora af Production 651.2 04 7.* 111.5 124.2 528.4 61.7 21.1 23.4 5.1 1.8 10.1 10.4 1.9 2B.4 0.7 128.1 21.3 82. B 29.1 15.7 66.0 10.4 274.2 97.8 270.2 1570.2 102.7 283.4 1193.8 TOTAL: 908.7 086.1 126.1 112.0 617.3 452.2 40.0 172.2 21.4 5.4 147.9 30.2 8.2 57.0 2. J 1370.5 62.8 31'.6 55.0 628.2 157.; 52.9 781.4 161.2 365.8 1800.4 126.9 100.2 1272.9 TABLE 5 WEST M A L A Y S I A INTERINDUSTRY ACCOUNTS 1964 (Producer Price* in Million* of Moloyiion DoHori! Delivered from: 1 2 3 S 7 8 .9 10 11 12 13 » 15 16 18 19 20 21 2  23 24 25 26 27 28 29 PP ill 1 s §1! a 1 ii 3 1 3 5 2£ ,, Acr.ei.ltlire & Llve«cr-k 32.7 199.1 11. 104.  15.8 36 1.7 24. H M6., 57 1. 7 9 35.4 2. Rubur Planting 919.6 919.6 151.9 15!. ' . 1071.5 1. For.-atrj 0.7 6B.9 0.7 0.1 0.3 6.7 77.4 24.5 2.8 29.1 56.4 133.8 4. FIthing 23.7 23. 7 20.3 92.0 112.3 116.0 5. Minig 1.5 572.0 3.7 577.2 182.1 0.4 1-2.5 759.7 A. Fod Industries 27.5 9.2 0.7 6.4 4 1.8 f:2.3 5.7 12.5 1/4.5 465.0 50d.5 7. E.vv rates n 0.9 40.9 41.8 •'. 1. *. 8. r.ib.-rco 11 0. ! 4.5 161.5 181,5 9. Tun I 1 les 0.1 0.1 4 7 0.1 5.0 4.2 0.9 19.2 24. 1 29. l 10. Clothing f. Footwear 11 0.: 0.1 5.6 5,9 5.9 11. Hand 4 Cork 0.2 7.7 7.8 0.8 82.8 99. 1 52.4 4.8 O.H 18.4 76.4 175.7 12. Furniture 4 Fixture O.H O.H. 0.1 10.5 0.1 21.2 11.9 12. 7 13. Paper 4 Paper Product* 1.0 1.1 0.1 2.2 0.9 5.6 0.7 7.2 9.4 Ii. Printing (. Publishing 0 1.9 26.7 O.H 1.6 2 7.4 60.4 60.4 15. Leather a Leather Product, « 2.8 2.1 2,8 16. Ruber Prc^-ing 202.3 12.2 214.5 1055.9 O.l 1.9 1089.  1 304,1 1 .". Ruber Products 0.4 2.6 0.1 1.2 20.5 8.9 0.8 41.5 7 1.6 70. * IS. Cheairal Products 32.2 r..i 1.5 11.3 3.9 0.4 0.7 0.' 7.R 0.7 31.0 1.4 0.3 0.7 0.1 13.9 5.4 13.6 4.0 110.4 152.8 58. f 0. 1 101.4 115.4 445. A 19. Son-Metalic Slncr.il Products 7.6 0.1 58.7 66.4 2.7 2.5 2.6 7.8 74.2 2,-r. Baifc Metal Indus,lties 0.7 22.1 22.8 721. 7 0.4 0.5 -24.8 o99.H 72  .6 Mou! PrductK 4 Machinery 1.1 0.1 0.2 0.8 33.4 11.2 48. a 9.6 43.3 35.0 1.9 31.5 121. ) 172.1 23. Misc. Manufacturing Indumr.-s 0.3 0. j 2.0 0.7 0.1 - C.I 51.1 5 5.8 5',. 1 25.1 13.2 16.2 TO— 22.1 '..I- ..V,.f) III.! 791.0 618.5 25. ElectrLui.y & Watt.r 37.4 2.7 0.5 0.4 0.4 1.0 0.2 0.1 0.7 7.1 1.6 1.5 3.1 0.4 1.9 0.2 18.8 5.9 1.4 0.2 80.5 0.7 24.1 16.2 4 1.1 94.4 17,1.9 Transportation 4 CoctunlcatIon 8.8 2.1 119.4 1 30. J 11.1 82.8 17.4 1 54 . 1 26 7.6 19 7,9 It. Wholesale i Retail Trad* 38.5 ti. 1 2.9 4.9 26.8 53.5 6.7 9.3 6.2 36.4 a.7 5.9 19.0 1.9 81.1 10.1 31.4 28.7 1. ) 16.! 546.8 264.2 65.9 15.9 2!.', 1161.7 I9:n.5 2). Ban.ig 4 J.isur.ote, etc. 0.8 O.ri )>.l 4.2 51.' i >>.; 1 16.0 2a. .veilng:; 0 8.1) » ; . o 315.0 115.0 29. Other Service industrloa 8.5 6.5 itVo K5M. ) 4M.8 1187.1 1 195.6 33. lapor. Trad« 89.7 15.3 0.8 14.5 88.8 9.0 22. 1 5.9 1.7 4.3 3.5 3.2 10.5 1.3 14.4 10.8 129.4 6.3 118.9 55.6 10.2 147.8 2.1 9.9 5.8 17.6 18.0 126.4 2)4.8 299.6 24.f 16.7 148.6 2/47.2 3!. Unspi-eif fed 41.9 I'l. I 14.6 0.9 31.7 44.2 5.0 17.0 1.3 1.0 23.0 3.3 0.8 10.2 0.5 2H.9 11.3 32.8 10.0 3.4 26.6 31.7 46.2 14.2 20.9 130.4 6.1 . 47.7 44.2 ,2. Prioa.-y Factor, of Production 671.8 1022.4 116.3 127.9 637.3 78.7 19.9 29.3 6.0 2.2 40.9 11.4 3.0 33.3 0.6 124.9 26.6 110.  35.4 21,6 66.5 12.0 299.9 112.0 292.  1615.8 111.0 298.0 1111.6 TOTAL: 9 35.4 1071.5 113.8 136.0 7S9.7 508.8 41.8 161.5 9.3 $.9 175.7 32.7 ... 60.4 2.8 1304.  76.8 445.8 74.2 722.6 172.1 848.5 174.9 397.9 1910.5 U6.0 315.0 1395.6 TABLE 6 W E S T M A L A Y S I A I N T E R I N D U S T R Y A C C O U N T S 1965 (Producer Pricei in Millions of Moloysion Dollars.) Delivered f r o * : 1 2 3 4 5 6 7 S 9 10 11 12 13 14 15 17 IB 19 20 21 22 23 24 25 26 27 28 29 TOTAL INTEBKEDUTE DEMAND KEST 07 THE UDILD g it s FIXED ASSETS a a i % 3 | a 577.5 i l l J IS 1. Agriculture 4 Livestock 48.a 110.1 11.5 137.1 14.9 424.4 30.0 11.5 2.7 621.7 1046.1 I. Rubber Planting 947.0 947.0 142.9 • 142.9 LOS9.9 3. Pore, try 0.8 69.5 0.6 0.1 0.4 7.3 76.7 27.5 1.7 26.B 56.0 134.7 *• F l f h l a t 18.8 18.B 25.7 100.2 125.9 1*4.7 5. Mining 2.0 705.1 3.4 710.6 185.4 •1.5 1B1.9 894.5 6. Food Industrie* 42.2 10.7 0.5 6.6 60.0 84.6 S.B 4.3 441.1 518.8 598.8 7. Beverages 0 1.2 1.2 40.4 42.8 42.8 8. Tobacco 0 8.1 185. B 191.9 193.9 9. Textiles 0.1 0.1 8.0 B.2 7.8 1.4 16.6 23.8 14.0 10. Clothing 4 Footwear 0 0.2 5.6 5.8 5.8 11. Wood 4 Cork 0.2 8.1 8.4 0.9 0.1 81.4 99.1 57.9 5.0 0.5 19.6 63.0 182.1 12. Furniture 6 Fixtures 0.9 0.9 0.2 11.3 0.1 22.9 34.5 35.4 13. Paper 4 Paper Products 0.9 2.5 0.1 0.1 3.6 1.7 5.3 l . S 0.5 9.3 12.9 I t . Printing 4 Publishing 0 2.9 28.6 3.5 4.1 29.0 68.1 48.1 IS. Leather 6 Lcsther Products 0 0.1 2.9 3.0 3.0 16. Rubber Processing 176.8 15.8 L92.6 1097.2 4.0 1101.2 1293.8 17. Rubber Products 0.5 3.7 4.2 23.2 10.8 1.1- 11.5 44.9 95.5 99.7 IB. Cheelcal Product* 32. J 6.9 l.S l t . l 4.1 0.2 0.3 0.7 3.« 1.1 32.0 1.1 0.3 0.7 0.2 14.7 6.6 11.0 131.2 205.2 59.7 14.8 103.6 3B3.3 514.5 19. Son-Metallic Mineral Products 0.1 8.0 72.4 80.5 6.1 2.6 0.8 9.5 90.0 20. Saslc fetal Industries 0.1 0.1 12.1 21.9 B67.7 0.4 0.6 43.1 825.6 B4S.5 21. .letel Products 4 Machinery 1.0 0.1 0.2 0.8 39.6 13.3 55.0 6.8 32.1 41.4 2.8 41.1 146-2 201.2 22. Hlsc. PUnufscturing Industries 0.3 0.3 3.4 0.6 1.0 56.0 61.0 61.3 23. Construction 26.9 13.) 16.4 37.2 29.1 4.B 672.9 136.4 841.2 900.4 24. E l e c t r i c i t y 4 Water 41.7 3.5 0.6 0.5 0.5 1.2 0.2 0.1 0.7 3.0 2.0 1.9 4.T 0.4 2.1 0.3 21.4 7.2 1.6 0.2 93.8 0.8 37.1 20.2 48.4 106.5 200.3 25. Transportstton 4 Coeaunlcation 9.6 I.J 130.1 142.0 13.3 104.3 22.7 166.1 306.6 448.6 26. Wholesale I Retail Trade 37.3 8.3 2.9 5.0 29. 8 49.6 4.5 S.B 4.2 0.5 22.1 2.8 1.0 3.9 0.3 7.8 9.0 39.3 9.5 6.2 20.1 • 2.1 79.5 10.2 26.4 1.3 14.1 405.5 296.2 B7.4 17.7 29.4 881.6 1314.3 147.1 1719.6 147.9 2B. Dwellings 0 6.8 76.4 316.0 322.8 122.8 29. Other Service Industries 9.3 9.3 966. 3 492.1 1535.0 1544.5 30. laoort Trsde 96.1 19.7 1.6 18. S 135.9 11.8 117.0 9.5 2.0 5.8 4.6 3.6 12.1 1.2 9.7 9.8 137. B 7.4 110.0 65.7 11.5 131.0 2.1 H. t 6.t 18.2 19.9 144.5 339.8 353.0 19.0 20.8 77.0 101.2 1255.2 -197.8 3213.3 872.0 32. Frlsary Factors of Production 749.9 1041.) . 114.6 135.5 755.1 104.1 6.8 18.4 31.7 2.2 7.6 1.0 2.0 i a . i 56.9 4.0 11.9 0.9 6.2 17.6 31.2 0.5 0.9 19.4 127.0 36.5 124.8 43.1 25.4 7t.l 13.a 317.9 132.1 333.4 lAOr.l 121.6 305.6 1457.0 7595.1 TOTAL: 1046.1 10B9.9 134.7 144.7 894.5 59B.B 42.8 193-9 14.0 5.8 62.1 33.4 2.9 68.1 3.0 1293.8 11.7 514.5 90.0 040.3 101.2 61.3 900.* 200.3 4*8. i 1719.6 147.9 J « . 8 1344.5 327.6 822.0 1311.3 71.* 1357.3 4740.8 24795.1 44 Desc r i p t i o n of Sectors The 29 productive sectors of the input-output tables are de-fine d by means of the i n d u s t r i a l c l a s s i f i c a t i o n used by the West Malaysian Department of S t a t i s t i c s . A b r i e f l i s t of the i n d u s t r i e s which comprise each sector follows. 1. Agriculture and Livestock: tea estates, coconut estates, palm o i l estates, l i v e s t o c k and poultry producers and other a g r i c u l t u r a l producers. 2. Rubber Planting: rubber estates and small holdings. 3. Forestry: producers of other tree crops. 4. Fishing: fishermen of both marine and f r e s h -water species of f i s h . 5. Mining: coal mines, stone quarries and metal mines ( p r i n c i p a l l y t i n and i r o n o re). 6. Food Industries: tea f a c t o r i e s , f i s h and seafood canneries, meat packing plants, d a i r i e s , f r u i t and vegetable processing plants, grain m i l l s , bakeries, sugar r e f i n e r i e s , manufacturers of cocoa, chocolate and confec-tionary items, manufacturers of other food products. 7. Beverages: breweries, manufacturers of soft drinks, and establishments engaged i n the d i s t i l l i n g , r e c-t i f y i n g and blending of s p i r i t s . 8. Tobacco: manufacturers of tobacco products. 9. Textiles: k n i t t i n g m i l l s , establishments en-gaged i n the spinning, weaving and f i n i s h i n g of t e x t i l e s , manufacturers of cordage, rope, net, etc. 10. Clothing and Footwear: manufacturers of wear-ing apparel, i n c l u d i n g footwear. 11. Wood and Cork: saw m i l l s , planing m i l l s , other manufacturers of wood and cork. 45 12. Furniture and Fixtures: manufacturers of f u r n i t u r e and f i x t u r e s . 13. Paper and Paper Products: manufacturers of paper and a l l paper products. 14. Printing and Publishing: p r i n t e r s , newspapers and other publishers of p r i n t e d matter. 15. Leather and Leather Products: tanneries and manufacturers of f i n i s h e d leather goods. 16. Rubber Processing: firms processing tapped rubber from sector 2. 17. Rubber Products: manufacturers of f i n i s h e d rubber products. 18. Chemical Products: palm o i l f a c t o r i e s , coconut small holdings, manufacturers of i n d u s t r i a l chemicals, vegetable o i l s , animal fats and o i l s , paints, varnishes, laquers, and mis-cellaneous chemical products. This sector also includes estab-lishments engaged i n the refinement, processing and manufacture of products from petroleum, natural gas and coal, which appeared i n a separate sector i n the 1965 input-output table published by the Malaysian Department of S t a t i s t i c s . 19. Non-Metallic Mineral Products: manufacturers of non-metallic mineral products. 20. Basic Metal Industries: s t e e l m i l l s , and other establishments converting ore into b a s i c metal products. 21. Metal Products and Machinery: manufacturers of metal products, machinery, e l e c t r i c a l machinery, transport equipment, etc. 22. f-riscellaneous Manufacturing Industries: estab-lishments engaged i n the manufacture of other miscellaneous products. 23. Construction: establishments which construct b u i l d i n g s , roads, bridges, port f a c i l i t i e s , e t c . 24. E l e c t r i c i t y and Water: firms generating and d i s t r i b u t i n g e l e c t r i c a l l i g h t and power and establishments providing water and s a n i t a r y s e r v i c e s . 46 25. Transportation and Communication: estab-lishments engaged i n the p r o v i s i o n of water, r a i l , road and a i r t r a n s p o r t a t i o n , services i n c i d e n t a l to transport-a t i o n , and communication s e r v i c e s i n v o l v i n g telephone, radio and microwave f a c i l i t i e s . 26. Wholesale and Retail Trade: wholesale and r e t a i l trade establishments. 27. Banking and Insurance: banks and other f i n a n -c i a l i n s t i t u t i o n s , insurance and r e a l estate firms. 28. Dwellings: purchasers of r e s i d e n t i a l dwellings. 29. Other Service Industries: firms providing edu-cation, health and medical s e r v i c e s , r e l i g i o u s organizations, i n s t i t u t i o n s providing l e g a l , t e c h n i c a l and business s e r v i c e s , hotels, restaurants, laundries, firms providing r e c r e a t i o n ser-v i c e s , domestic and personal s e r v i c e s , and the administration and defence services provided by the government. Valuation of I n t e r s e c t o r a l Flows Commodity and service flows w i t h i n the West Malaysian economy are evaluated i n terms of current producer p r i c e s . Thus the values of the i n t e r s e c t o r a l flows shown i n the input-output tables f o r 1960-1965 are de-void of marketing costs (such as transportation, insurance and warehouse charges) and are net of wholesale and r e t a i l trade mark-ups except as these costs and mark-ups accrue to productive sectors such as Sector 25, Transpor-t a t i o n and Communication, and Sector 26, Wholesale and Retail Trade. The values of i n t e r s e c t o r a l flows are also exclusive of i n d i r e c t taxes which are shown for each productive sector i n a primary input row which also includes the value of wages and s a l a r i e s , entrepreneurial i n -come and subsidies used by each productive sector. 47 Imports are valued c . i . f . so that the value of commodities re-ceived by each sector in the economy comprises three elements: the for-eign port value, the freight charges to the domestic port of entry and i n -surance charges. Import duties are not included.^ Export flows from productive sectors are recorded in producer prices with any domestic marketing costs or wholesale and r e t a i l trade mark-ups shown as inputs to the Rest of the World sector from either the Trans-portation and Communication or the Wholesale and Retail Trade sector. The total value of exports, thus, is f.o.b. the port of embarkation. In short, the treatment of intersectoral flows follows the seller's point of view throughout. This means in general that the amount of money received by the seller is registered; hence producer prices are used. From this standpoint also, indirect taxes and subsidies (which may be regarded as negative indirect taxes) are considered as a type of primary input paid for by the purchasing sector. Outputs are valued f.o.b. plant and marketing costs shown separately as inputs to the receiving sector from those sectors providing trade and transportation services. Imports are not treated as inputs from the domestically-competing sector which of course they would be from the buyer's point of view, and import duties are excluded from the valuation. Outputs destined for export are also valued f.o.b. the plant for the productive sectors but for the economy are f.o.b. the port of See Appendix A for the adjustments made to the published 1965 table to render i t exclusive of import duties. 48 embarkation with the r e s i d u a l domestic marketing costs shown as inputs to the Rest of the World sector. S t r u c t u r a l Change i n West Malaysia, 1960-1965 One of the objectives of the Second Five-Year Plan of Malaya (West Malaysia) was "to widen the v a r i e t y of Malayan production, emphasizing the development of other s u i t a b l e a g r i c u l t u r a l products i n a d d i t i o n to rubber, and g i v i n g every reasonable encouragement to i n d u s t r i a l expansion. . . Some signs of d i v e r s i f i c a t i o n were evident i n 1965 at the end of the Plan g period. Gross Domestic Product at f a c t o r cost ( i n 1960 prices) had r i s e n at an annual rate of 6.3 per cent. Several sectors had higher than average growth rates and therefore increased t h e i r r e l a t i v e c o n t r i b u t i o n to t o t a l output. These sectors included, most prominently, Construction, which grew at about 18 per cent annually, and Electricity and Water, which grew at about 12 per cent annually. The s o - c a l l e d "Manufacturing" sector of the economy which i n f a c t comprises a l l of the input-output sectors from 6 {Food Indus-tries) through 22 {Miscellaneous Manufacturing Industries)excluding Sector 16 {Rubber Processing), had an o v e r a l l growth rate of 11 per cent each year. Other sectors which grew more r a p i d l y than average included Banking and Insurance, Forestry, Fishing, and Other Service Industries, though i n these Second Five Year Plan 1961-1965, op. cit., p. 16. !See the First Malaysia Plan, op. cit., Table 2-11, p. 37. 49 cases the subsequent change in the share of G.D.P. was less than one per-centage point. Rubber production (planting and processing) increased at an average rate of only 4 . 0 per cent annually so i t s relative importance to the Malayan economy was somewhat lessened. Other sectors whose share of G.D.P. declined were Agriculture and Livestock, Mining, Transportation and Communication, and the Ownership of Dwellings. The Wholesale and Retail Trade sector maintained i t s share of G.D.P. with an annual growth rate of 6 . 1 per cent. In most cases the share of G.D.P. held by each sector did not change more than one or two percentage points from 1 9 6 0 to 1 9 6 5 . Thus while there was some structural change in the Malayan economy i t did not amount to a substantial transformation along the lines envisaged by the Plan. CHAPTER IV STATISTICAL ANALYSIS OF PREDICTION ERRORS The series of West Malaysian input-output tables w i l l now be analyzed with respect to their predictive power following the methodology bri e f l y outlined in Chapter II. Each of the tables from 1960 to 1964 w i l l be used in turn to predict intermediate sectoral outputs for each of the succeeding years to 1965. Forecast errors w i l l be measured by reference to the observed intermediate demand as set forth in the tables. To test the significance of the magnitude of these errors, a comparison w i l l be made with the errors that result from corresponding "naive" projections of intermediate output. The relative efficiency of the input-output tables as a forecasting tool w i l l be an indication of the empirical use-fulness of the Leontief model and i t s stringent assumption of constant input coefficients. It i s expected that to some extent the efficiency of the model,as applied to the West Malaysian economy, w i l l be reduced because of the pro-cess of economic development which occurred there during the period under consideration. The possible effect of development on the predictive a b i l -i t y of the model w i l l be illustrated by drawing comparisons between the efficiency of the Malaysian tables and the efficiency of tables for the Netherlands economy as analyzed by Rey and Tilanus.^" Guido Rey and C. B. Tilanus, "Input-Output Forecasts for The Netherlands, 1949-1958," Eoonometrioa, Volume 31, No. 3 (Julv, 1963), pp. 454-63. 50 51 In order to f a c i l i t a t e such comparisons, the methodology and notation adopted by Rey and Tilanus w i l l be followed throughout the a n a l y s i s . Their techniques w i l l also be used to evaluate the r e l a t i v e performance of various sectors and to show how the accuracy of the input-output p r e d i c t i o n s i s affe c t e d o v e r a l l by the length of the forecast per-i o d . The analysis centers on the a b i l i t y of the model to project i n t e r -mediate s e c t o r a l outputs, the very "heart" of a s t a t i s t i c a l input-output t a b l e . Thus i f X and Y are the vectors of gross output and f i n a l demand 2 r e s p e c t i v e l y , a s i m i l a r vector, Z, can be c a l c u l a t e d so that (4.1) Z = X - Y = AX where the ith element of Z i s the sum of the d e l i v e r i e s of the i t h sector to a l l other productive sectors or n As derived i n Chapter I, the general s o l u t i o n to the input-output system of equations was given by the matrix equation: (1.12) X = (I-A)'1! S u b s t i t u t i n g t h i s i n t o Equation (4.1) to solve f o r Z we have (4.2) Z = ACI-A^Y which i s approximated by the expansion 2 As shown i n Chapter I. 52 (4.3) Z = A(I + A + A2+ ...)Y = (/. + A2 + A3 + ...)Y By adding and subtracting the i d e n t i t y matrix within the braces {} t h i s power s e r i e s may be expressed as: (4.4) Z = {(I + A + A2 + A3 + ...) -I}Y which reduces to (4.5) Z = (cr-/.)" 1 - I}Y In the Malaysian a n a l y s i s , we have s i x matrices, A, to be denoted by At where t=l for 1960, t=2 f o r 1961, to t=6 f o r 1965. Equation (4.5) has been used to obtain p r e d i c t i o n s f o r the vector of intermediate output, Z. On the basis of the 1960 table, f o r example, forecasts were made 6f the intermediate output i n the years 1961 to 1965. The 1961 table was used to pre d i c t intermediate output i n the years 1962 to 1965, and so on. In gen-e r a l , the observed f i n a l demand i n a l a t e r year, t+r, was used to make a forecast of intermediate output on the basi s of A^, where t <_ r <_ 5 so that Equation (4.5) took the form (4.6) Z P t + x= { ( J - ^ ) " 1 -I}YUr The predicted value of the intermediate output of the i t h sector T years ahead from the base year t i s denoted as and the value of i n t e r -mediate output a c t u a l l y observed i n the input-output table of the year t+x i s given by Z., . The p r e d i c t i o n or forecast error i s defined as the dif f e r e n c e be-tween the predicted and the observed values and i s expressed as a f r a c t i o n of the value to be. predicted, For each sector i there are 15 predictions of intermediate out-put. Five of these forecasts are f o r "one year ahead" (T= 2 ), the 1961 f o r e -cast based on the 1960 ta b l e , the 1962 forecast based on the 1961 table and so on i n c l u d i n g the 1965 forecast table based on the 1964 table. In the same way there are four forecasts "two years ahead" (T=2), three forecasts "three years ahead" (T=«3) , two "four years ahead" (T=4) and only one fo r e -cast " f i v e years ahead" (T= 5 ), that i s the 1965 forecast based on the 1960 tab l e . In the corresponding analysis conducted by Rey and T i l a n u s , a se r i e s of 10 matrices were used f or the years 1948 to 1957. The vectors of f i n a l and intermediate demand were also known for 1958 so a t o t a l of 55 f o r e -casts were made for each sector. In both cases, errors have been analyzed f o r only those sectors which exhibited s i g n i f i c a n t intermediate demand. This amounted to 27 of the 35 sectors i n the Netherlands tab l e s . Of the 29 productive sectors i n the West Malaysian t a b l e s , 15 were chosen f or the purpose of the study. Nine sectors were excluded because they produced no intermediate output i n at l e a s t one year of the period 1960-1965. These sectors are: Beverages (7), Tobacco (8), Textiles (9), Clothing and Footwear (10), Furniture and Fixtures (12), Paper and Paper Products (13), Printing and Publishing (14), Leather and Leather Products (15) and Dwellings (28). Five more sectors were excluded on the basis of the fac t that the r a t i o of intermediate de-mand to f i n a l demand was p e r s i s t e n t l y l e s s than 0.1 for the period under consideration. These sectors included Rubber Products (17), Basic Metal Industries (22), Banking and Insurance, etc. (27) and Other Service In-54 dustries (29). The remaining 15 sectors accounted f o r $2,938.2 m i l l i o n , or 99.7 per cent, of the t o t a l intermediate output of $2,947.5 m i l l i o n i n I960. 3 A l l of the input-output tables i n the Dutch and West Malaysian s e r i e s are valued i n terms of current producer p r i c e s . I t i s recognized that the p r e d i c t i v e power of the model i n both applications may consequent-l y be reduced because forecasts cannot be made exclusive of p r i c e changes. The degree to which the e f f i c i e n c y of the tables i s a f f e c t e d w i l l probably vary between the two countries. Rey and Tilanus made no attempt to e v a l -uate the possible c o n t r i b u t i o n of p r i c e changes to the observed p r e d i c t i o n e r r o r s , saying only at the outset that " i t would evidently be 4 desirable to compare the r e s u l t s with those of tables i n constant p r i c e s . " When such tables are a v a i l a b l e for both the Netherlands and West Malaysia a truer t e s t of the Leontief model can be made. Input-Output P r e d i c t i o n Errors The 15 input-output forecasts made from the West Malaysian tables for each of the 15 sectors y i e l d e d a t o t a l of 225 p r e d i c t i o n errors f o r an a l y s i s . Obviously some aggregative measures must be used to evaluate In a s i m i l a r a n a l y s i s of the West Malaysian tables, 14 sectors were studied. See H. Craig Davis and Geoffrey B. Hainsworth, Input-Output Forecasts for West Malaysia, 1960-1965 (Unpublished). The 15 sectors s e l e c -ted here include those studied by Davis and Hainsworth plus Fishing, so that over 99 per cent of intermediate output i s represented (instead of "at l e a s t 95 per cent"). Rey and Tilanus, op. cit., p. 454. 55 these errors, though f or reference they are presented i n Table B l of Appendix B. One measure of the seriousness of the p r e d i c t i o n errors takes the form of the mean-squared error, defined by: 1 5 2 (4.8) m. = zr- t e.+^ XX 6-X %tt+x t=l where i s the mean-squared p r e d i c t i o n error f o r industry i for a l l forecasts T years ahead. ( A l l values f o r m. for x=5 are based on one ix observation o n l y ) . Table 7 shows the values of m. f o r the sectors under ^T consideration. TABLE 7 MEAN-SQUARED PREDICTION ERRORS OF INTERMEDIATE OUTPUT FORECASTS FROM INPUT-OUTPUT TABLES (-7T.t m u l t i p l i e d by 10,000) SECTOR (-0* PREDICTI0N 1 2 INTERVAL 3 IN YEARS •4 (x) 5 1. Agriculture and Livestock (1)-46 225 518 1075 1416 2. Rubber Planting (2) - 3 4 5 3 11 3. Forestry (3)- 232 797 1395 2793 3735 4. Fishing (4)- 691 2809 6650 11087 12716 5. Mining (5)- 70 146 164 153 275 6. Food Industries (6)- 101 69 114 224 256 7. Wood and Cork (11)- 79 243 254 334 833 8. Rubber Processing (16)- 256 523 188 28 512 56 TABLE 7 (Continued) SECTOR (£)* PREDICTION INTERVAL IN YEARS (x) 1 2 3 4 5 9. Chemioal Products .(18)- 347 950 1683 2468 2295 10. Non-Metallic Mineral Products (19)- 141 395 622 754 1076 11. Metal Products and Machinery (21)- 48 124 282 313 393 12. Construction (23)- 18 11 3 25 0 13. E l e c t r i c i t y and Water (24)- 11 16 20 3 3 14. Transportation and Communication (25)- 28 45 18 38 173 15. Wholesale and Retail Trade (26)- 477 589 496 528 628 The sector number appearing i n parentheses following the name r e f e r s to the designation used i n the input-output tables described i n Chapter I I I . The p r e d i c t i o n errors of a l l 15 sectors were then aggregated for each T to judge how the e f f i c i e n c y of the input-output forecasts v a r i e s on the whole with the length of the forecast. The mean value of m. f o r a l l sectors for each T was c a l c u l a t e d as IS -L £ m. and the r e s u l t s are shown i n Table 8, together with the values of the median and standard deviation of the mean-squared p r e d i c t i o n errors over 57 TABLE 8 SAMPLE STATISTICS OF THE MEAN-SQUARED PREDICTION ERRORS (m. x IO 4) FROM INPUT-OUTPUT TABLES IT PREDICTION INTERVAL IN YEARS (x) 1 2 3 4 5 Mean 170 463 827 1321 1621 Median 79 225 254 313 512 Standard Deviation 200 714 1687 2840 3233 As expected, the mean increases r e g u l a r l y as x increases, i . e . , when the forecast r e f e r s to a year which i s f a r t h e r into the future. The longer the length of the forecast period, the more tenuous i s the assump-t i o n of constant c o e f f i c i e n t s used i n the f o r e c a s t i n g procedure. The second l i n e of the table shows that the median value of m. also increases ^x with x, although somewhat less r e g u l a r l y . These medians are c o n s i s t e n t l y l e s s than the means because the d i s t r i b u t i o n of the values of m. i s skewed ^X i n the d i r e c t i o n of large values. The t h i r d l i n e of the table shows f o r each x, the standard deviation of . I t i s seen that d i s p e r s i o n too, i n -creases with the length of the forecast. This could also be a n t i c i p a t e d f o r as the time period increases, more of the conditions which influence the value of the c o e f f i c i e n t s can, at least p o t e n t i a l l y , occur with disparate e f f e c t s among the sectors. The a p p l i c a t i o n of least-squares to the f i v e values of the mean over i of m. ( i n the f i r s t l i n e of Table 8, without the expansion factor) 58 y i e l d s the following regression equation: (4.9) -L I m. = -0.02479 + 0.03762T R = .9926 1 5 i=l  % T (.00624) (.00188) The parenthesized numbers are the standard errors of the a constant and the b c o e f f i c i e n t . A t - t e s t reveals that both are s i g n i f i c a n t at the f i v e per cent l e v e l of s i g n i f i c a n c e . This compares with the regression equation: 1  2 ? 2 (4.10) - i - I m. = -0.00003 + 0.00598T R = .9922 2 7 i=l t T (.00116) (.00019) f o r the Netherlands tables, based upon 10 observations of the mean over i of m ^ T « ^ ^ n t h i s case only the b c o e f f i c i e n t i s s i g n i f i c a n t . Both regression equations show that the mean-squared p r e d i c t i o n errors which a r i s e from input-output forecasts of intermediate output vary l i n e a r l y with the length of the fore c a s t , and e s p e c i a l l y for the Netherlands case,, almost d i r e c t l y i n proportion with time.*' In the Rey and Tilanus a r t i c l e , op. cit., p. 458, the equation i s given simply as 7 Z m. = 0.0060T" 27 • -2-x t with no c o e f f i c i e n t of determination or standard error values shown. In order to obtain these, the Netherlands data was submitted to regression an a l y s i s and these r e s u l t s appear i n Equation (4.10) above. ^In t h e i r a nalysis c i t e d e a r l i e r , Davis and Hainsworth excluded the forecast errors of Sector 4, Fishing. As seen from Table 7, the intermediate output of t h i s p a r t i c u l a r sector was badly predicted by the input-output tab l e s . In fact for every forecast i n t e r v a l (T) Fishing had the highest mean-squared p r e d i c t i o n errors of a l l the sectors studied. This i s probably because of the s t o c h a s t i c elements which r e a l i s t i c a l l y enter into the production func-t i o n f o r that sector. (More w i l l be said of t h i s l a t e r ) . With Fishing 59 The root-mean-squared p r e d i c t i o n e r r o r (-0.02479 + 0.03762t)' for T years ahead of the West Malaysian tables i s shown i n Table 9 t o -gether with the corresponding values, (,0060T) , f o r the Netherlands t a b l e . 7 TABLE 9 ROOT-MEAN-SQUARED PREDICTION ERRORS FROM INPUT-OUTPUT TABLES PREDICTION INTERVAL (1) (2) IN YEARS (x) WEST MALAYSIA NETHERLANDS ( l ) / ( 2 ) 1 0.1132696 0.0774597 1.46230 2 0.2246108 0.1095445 2.05040 3 0.2967659 0.1341641 2.21196 4 0.3545279 0.1549191 2.28847 5 0.4041163 0.1732051 2.33316 It i s apparent that the average p r e d i c t i o n errors from the West Malaysian input-output tables are s u b s t a n t i a l l y greater than those from the Nether-excluded, Davis and Hainsworth found the regression equation [comparable to Equation (4.9)] took the value 4 e -0.0061 + 0.0172x R 2 = .986 14 • IT V The a constant has a much smaller value, i . e . , the mean-squared p r e d i c t i o n errors are more d i r e c t l y proportional to the length of the forecast than i f the Fishing sector i s included i n the a n a l y s i s . The b c o e f f i c i e n t i s also smaller i n d i c a t i n g that the p r e d i c t i v e a b i l i t y of the tables i s be t t e r . 7 I t should be noted that the p r e d i c t i o n i n t e r v a l s , 1 <_ T <_ 5 shown i n the tables do not account f o r a l l the forecasts made with the Netherlands table where predictions were made up to 10 years ahead from the base year 1948. 60 lands tables for a l l of the p r e d i c t i o n i n t e r v a l s considered. There can be several reasons f o r t h i s . One p o s s i b i l i t y i s that the Netherlands data i s simply more r e l i a b l e . C e r t a i n l y the West Malaysian tables would be improved i f commodity and service flows were traced more c l o s e l y to eliminate the large Unspecified destinations of f i n a l output and o r i g i n s of s e c t o r a l inputs. I t could also be that p r i c e f l u c t u a t i o n s during the periods considered were greater i n West Malaysia- than i n the Netherlands so that the input-output tables constructed i n current p r i c e s became a weaker for e c a s t i n g t o o l i n the former case. Or the s u p e r i o r i t y of the Netherlands tables may be due i n part to the fact that the economy i s g more s t r u c t u r a l l y interdependent than that of West Malaysia. I t could also be that economic interdependence i s bet t e r revealed i n the Nether-lands tables by the very way i n which the sectors are c l a s s i f i e d and aggregated. Yet the underlying cause f o r the differences i n the p r e d i c -t i v e power of the tables may be that s t r u c t u r a l change was occurring f a s -t e r i n West Malaysia because of the i n s t i t u t i o n of development plans and p o l i c i e s . With so many other v a r i a b l e s , however, i t i s not pos s i b l e to i s o l a t e the e f f e c t of s t r u c t u r a l change on the p r e d i c t i v e power of the Mal-aysian tables i n any general way. More information may be gleaned by r e f -erence to the performance of i n d i v i d u a l sectors i n the forecasts. One measure of the degree of s t r u c t u r a l interdependence i s the ex-tent to which the productive sectors s e l l t h e i r output for further use i n pro-duction r e l a t i v e to the amount sold f o r f i n a l use. This r a t i o (£ Z^ .: Z Y^) was 0.587:1 for the 35 sectors of the Dutch economy i n the base i. i year of the projections (1948) and 0.417:1 for the 29 productive sectors of the West Malaysian economy (1960). 61 Evaluation of the Forecasts for I n d i v i d u a l Sectors The o v e r a l l p r e d i c t i v e power of the West Malaysian input-output tables i s summarized i n Equation (4.9). From that equation i t i s observed that the mean over i of the mean-squared p r e d i c t i o n e r r o r s , m. , i s approxi-mately equal to -0.02479 + 0.03762T. By r e l a t i n g the mean-squared p r e d i c -t i o n errors of each sector to t h e i r average over it i t i s p o s s i b l e to eval-uate the p r e d i c t i v e power of the input-output tables f o r i n d i v i d u a l sectors of the West Malaysian economy. Comparable errors take the form m^l-Q.02479 + 0.03762T. I f an average over T of a l l these r e l a t i v e values i s then taken we have: 1 ^ m i x ( 4 , 1 1 ) h = :JS E , ( 6 _ T ) -0.02479 + 0.03762T where £ . i s the measure of the r e l a t i v e performance of the i n d i v i d u a l sec-g t o r s . An average performance for industry i w i l l y i e l d a value of c\.=l. Thus a higher value of 5 means a r e l a t i v e l y bad performance and a lower value means a r e l a t i v e l y good performance i n the p r e d i c t i o n of intermediate output. Rey and Tilanus discovered some r e l a t i o n s h i p between the value of £ . and the f a c t that a sector was d e c l i n i n g or expanding w i t h i n the economy. 9 To avoid m i s i n t e r p r e t a t i o n i t should be noted that the number 15 appearing i n the weight f a c t o r of Equation (4.11) r e f e r s to the number of forecast observations f o r each sector, not the number of sectors as was the case i n Equation (4.9). 62 Of course the growth or dec l i n e of a sector i s hot revealed by the mean-squared er r o r c r i t e r i o n because i t does not in d i c a t e the d i r e c t i o n of the er r o r s . To analyze t h i s we compare the alge b r a i c mean and the absolute mean of the forecast e r r o r s , e . , , for each sector and p r e d i c t i o n i n t e r -v a i , 1 5 1 5 ^ 7 / , ei,t+T a n d , \ l ^ t + r l t=l 3 t=l The r a t i o of the two means w i l l always be between -1 and 1 and the same applies to the mean over T of t h i s r a t i o obtained by the following equa-t i o n : (4.12) e . * * (6-T) t &iJt+X If the sector i s increasing i n importance i n the economy, the value of 8. w i l l be close to -1, and the converse, i f the sector i s d e c l i n i n g , the value of 6. w i l l be cl o s e r to 1. In the former case, the input-output forecasts s y s t e m a t i c a l l y underestimate the intermediate output of that sector on the assumption of f i x e d t e c h n i c a l c o e f f i c i e n t s , and i n the l a t t e r case over-estimate i t . The values of C• and 6. calculated by Equations (4.11) and (4.12) r e s p e c t i v e l y , appear i n Table 10. 63 TABLE 10 COEFFICIENTS OF THE RELATIVE PREDICTION PERFORMANCE (C.) AND THE SYSTEMATIC NATURE OF PREDICTION ERRORS (6^) FOR INDIVIDUAL SECTORS % SECTOR (£) £ . 6. 1. Agriculture and Livestock 0.421 0.899 2. Rubber Planting 0.013 -0.682 3. Forestry 1.523 1.000 4. Fishing 6.486 0.915 5. Mining 0.323 -0.690 6. Food Industries 0.359 -0.626 7. Wood and Cork 0.462 0.850 8. Rubber Processing 1-.C07 0.345 9. Chemical Products 1.905 -0.913 10. Non-Metallic Mineral Products 0.841 -0.832 11. Metal Products and Machinery 0.304 -0.927 12. Construction 0.057 0.271 13. E l e c t r i c i t y and Water 0.042 0.089 14. Transportation and Communication 0.111 -0.649 15. Wholesale and Retail Trade 1.745 0.380 An average p r e d i c t i o n performance was achieved by the Rubber Processing sector (Cg = 1.007). Ten sectors had b e t t e r f o r e c a s t i n g per-formances than t h i s . Rubber Planting had the best f o r e c a s t i n g record = 0.013) perhaps because the value of intermediate output f o r that sector f a r outstripped that of any other sector i n a l l of the years con-sidered, and i n 1960 alone, accounted for almost 40 per cent of a l l i n t e r -mediate output. On the whole, however, these sectors with large i n t e r -industry d e l i v e r i e s do not have better f o r e c a s t i n g records than those with smaller values to be predicted, an observation contrary to the r e l a t i o n s h i p 64 found by Rey and Tilanus for the Netherlands tables. It is true that Fishing, with lowest value of intermediate output, had the worst predic-tion performance (C^ = 6.486) but this result was probably due to other factors; Metal Products and Machinery had an intermediate output of only $2.2 million more than Fishing in 1960 and yet ranked f i f t h in forecast performance. Wholesale and Retail Trade, the fourth largest sector for intermediate output in 1960 had a relatively bad forecast record ( S ^ = 1.745). There also appears to be l i t t l e relationship between the predic-tion performance of the sectors and changing relative importance of the sectors in the Malaysian economy. A total of seven sectors are shown to be growing, according to the coefficient 6 in Table 10. These include Metal Products and Machinery, Chemical Products, lion-Metallic Mineral Pro-ducts, Mining, Rubber Planting, Transportation and Communication, and Food Industries. (These sectors have negative 9 coefficients in the table rang-ing in value from -0.927 to -0.626). Four sectors appear to be declining in importance having 6 coefficients equal to or very close to +1.000. These include Forestry, Fishing, A g r i c u l t u r e , and Wood and Cork. It might be ex-pected that the forecast record ( 5 ^ ) of these 11 sectors would be relative-ly bad because the tables are either systematically overestimating or under-estimating the value of intermediate output. Within the group, however, we see both the sector that achieved the best relative prediction performance (Rubber Planting) and the sector that had the worst performance (Fishing). For the 27 sectors of the Netherlands tables, the values of 65 £. were between A.65 and 0.16 with a median of 0.91 and a mean of 1.02, i n d i c a t i n g a nearly symmetrical d i s t r i b u t i o n . The West Malaysian values of £ . ranged between 6.486 and 0.013, with a median value of 0.421 and a mean of 1.040, i n d i c a t i n g an asymmetrical d i s t r i b u t i o n , skewed i n the d i r e c t i o n of high values of E . or r e l a t i v e l y bad i n d i v i d u a l performances. It might be supposed that the wider v a r i a t i o n i n Z,^ values f o r Malaysia i s a r e s u l t of the disparate e f f e c t s of development on the input structures of the Malaysian sectors and hence t h e i r r e l a t i v e forecast performances. Yet i t i s obvious that when the Fishing sector alone i s excluded from the analy-s i s , the p r e d i c t i v e a b i l i t y of the tables i s Improved, both on the whole with respect to the length of the forecast p e r i o d , ^ and i n terms of s u b s t a n t i a l l y reducing the v a r i a t i o n i n the c o e f f i c i e n t s of r e l a t i v e performance. I t was noted i n Chapter I I I that the r e l a t i v e c o n t r i b u t i o n of the Fishing sector to the Gross Domestic Product of West Malaysia increased very s l i g h t l y over the period from 1960 to 1965. This expansion has been a t t r i -buted to the mechanization of f i s h i n g boats, wider use of nets made of syn-t h e t i c f i b r e (which y i e l d better catches and are easier to operate) and to 12 increased acreage of fresh water f i s h ponds. C l e a r l y some technological change was taking place. But the bad forecast performance of t h i s sector may also be a t t r i b u t a b l e i n some degree to the sto c h a s t i c elements which enter i n t o a production function for the f i s h e r y ; even i f the t e c h n i c a l Rey and Til a n u s , op. cit., p. 455. ^The regression equation generated by Davis and Hainsworth would apply with i t s lower b c o e f f i c i e n t . 12 First Malaysian Plan, cp. cit., pp. 102-103. 66 c o e f f i c i e n t s o f t h e s e c t o r s r e m a i n c o n s t a n t , t h e c a t c h i s g r e a t l y a f f e c t e d b y t h e a b u n d a n c e o f f i s h i n t h e s e a s , t h e w e a t h e r , e t c . I n e i t h e r c a s e , i t i s c l e a r t h a t t h e W e s t M a l a y s i a n i n p u t - o u t p u t t a b l e s w o u l d b e much i m p r o v e d i f a p p r o p r i a t e a d j u s t m e n t s w e r e made t o t h e i n t e r s e c t o r a l f l o w s o f t h a t p a r t i c u l a r s e c t o r . C o n t r a r y t o t h e f a c t t h a t t h e r e a l p o r t i o n o f G.D.P. c o n t r i b u t e d b y t h e Fishing s e c t o r i n c r e a s e d d u r i n g t h e p e r i o d , t h e i n d e x 8 . s h o w s t h a t s e c t o r t o h a v e b e e n d e c l i n i n g ( 0 ^ = 0 . 9 1 5 ) . T h i s i s a l s o t h e c a s e f o r Forestry, Construction, a n d Electricity and Water. C o n v e r s e l y , t h e 9. c o e f f i c i e n t s f o r Mining a n d Transportation and Communication show t h e s e s e c t o r s t o b e e x p a n d i n g w h i l e , i n f a c t , t h e i r s h a r e s o f G.D.P. d e c l i n e d s l i g h t l y . One c o n s i s t e n t r e s u l t i s f o r t h e Agriculture and Livestock s e c -t o r w h i c h d e c l i n e d i n i m p o r t a n c e b y b o t h m e a s u r e s . T h e t h r e e s e c t o r s h a v i n g a 0 v a l u e c l o s e s t t o - 1 . 0 0 0 , Metal Prdducts and Machinery, Chemical Products, a n d Eon-Metallic Mineral Products, f o r m p a r t o f t h e l a r g e r " M a n u f a c t u r i n g " s e c t o r w h i c h g r e w a t a r a t e s u f f i c i e n t t o i n c r e a s e i t s s h a r e o f G.D.P. b e -t w e e n 1 9 6 0 a n d 1 9 6 5 . ( S o h e r e a g a i n , t h e r e s u l t s a r e c o n s i s t e n t ) . T h e 0 . c o e f f i c i e n t s w e r e d e f i n e d t o m e a s u r e t h e s y s t e m a t i c n a t u r e o f t h e i n p u t - o u t p u t p r e d i c t i o n e r r o r s f o r i n d i v i d u a l s e c t o r s . T h e r o e t i -c a l l y t h e y s h o u l d r e f l e c t t h e d i r e c t i o n , i f n o t t h e m a g n i t u d e , o f t h e a c t u a l e x p a n s i o n o r c o n t r a c t i o n o f s e c t o r s w h i c h t o o k p l a c e . I n t h i s c a s e , t h e c h a n g i n g r e l a t i v e i m p o r t a n c e o f t h e s e c t o r s h a s b e e n m e a s u r e d b y c h a n g e s i n t h e i r s h a r e o f real G r o s s D o m e s t i c P r o d u c t . T h i s means t h a t t h e tw o m e a s u r e s may sho w d i f f e r e n t r e s u l t s s i m p l y b e c a u s e t h e i n p u t - o u t p u t t a b l e s a r e n o t a v a i l a b l e i n c o n s t a n t p r i c e s . T h e f o r e c a s t e d i n t e r m e d i a t e 67 output and hence the p r e d i c t i o n errors contain an element of p r i c e change. S t a t i s t i c s on p r i c e f l u c t u a t i o n s throughout the period are sadly l a c k i n g . Data i s only a v a i l a b l e f o r selected commodities of p a r t i c u l a r 13 importance i n the export market. Two of these are t i n and i r o n ore which together account f o r most of the output of the Mining sector. While the p r i c e of i r o n ore remained f a i r l y stable from 1960 to 1965 (be-tween $25.00 and $26 . 80 per ton) the p r i c e of t i n increased by more than 75 per cent from $6,623 to $11,760 per ton. Thus while the output of the Mining sector made a d e c l i n i n g c o n t r i b u t i o n to the r e a l G.D.P. of the economy, the sector was shown to be expanding as the input-output tables i n d o l l a r terms. This example serves to emphasize the irvportance of hav-ing input-output tables i n constant p r i c e s , p a r t i c u l a r l y for f o r e c a s t i n g purposes. Comparison With Naive Extrapolation P r e d i c t i o n Errors As stressed throughout the paper the r e a l test of the Leontief model i s i t s empirical usefulness: i n t h i s case, the accuracy of the pre-d i c t i o n s i t y i e l d s . The errors that r e s u l t from input-output forecasts have now been measured and evaluated both i n terms of the o v e r a l l e f f e c t of time and the r e l a t i v e performance of i n d i v i d u a l s e c t o r s . The s i g n i f i -cance of the magnitude of these errors i s yet to be tested by a comparison 'First Malaysia Plan, cp. cit., Table 2-2, p. 23. 68 with the errors that result from "naive" forecasts. To do this, predictions of intermediate output w i l l be made by extrapolation. The method is based on the assumption that the ratio of intermediate demand to f i n a l demand prevailing in the year t is also appli-cable in the year t+x. The extrapolated value of the intermediate output of sector i in the year t+x is therefore calculated as: wh ere the values of f i n a l demand, Y. , , form the vector of f i n a l demand, t used earlier to predict intermediate output in the input-output model in Equation (4.6). It should be noted that the development of price levels over time w i l l not affect the extrapolation as long as i t is true that the rela-tive prices of intermediate and f i n a l goods do not change. The extrapolation error i s defined as: ZE - Z (4 14) e .  l*  t + T *'**T J ^,t+x corresponding to the input-output prediction error defined in Equation (4.7), In this case, the mean-squared extrapolation error is vrritten n ^ x f° r sector i, x years ahead, analogous to the m. defined in Equation (4.8), or <4-15) \x = -h tl2 %t+x The values of n. for the 15 sectors under consideration are shown in Table ix 11. 69 TABLE 11 . MEAN-SQUARED EXTRAPOLATION ERRORS OF INTERMEDIATE OUTPUT (n^ m u l t i p l i e d by 10,000) EXTRAPOLATION INTERVAL IN YEARS ( T ) SECTOR ( i ) 1 2 3 4 5 1. Agriculture and Livestock 59 152 152 108 27 2. Rubber Planting 793 821 1365 1510 1602 3. Forestry 26 87 117 120 106 4. Fishing 592 1857 3678 9954 14527 5. Mining 404 828 1061 844 466 6. Food Industries 95 32 46 114 61 7. Wood and Cork 171 354 603 710 23 8. Rubber Processing 233 470 186 6 118 9. Chemical Products 276 537 932 1424 1225 10. Non-Metallic Mineral Products 488 1020 623 41 66 11. Metal Products and Machinery 79 168 134 154 529 12. Construction 131 428 620 902 1096 13. E l e c t r i c i t y and Water 10 24 25 12 1 14. Transportation and Communication 59 128 188 356 358 15. Wholesale and Retail Trade 333 622 883 1032 719 To f a c i l i t a t e the comparison between the naive extrapolation errors and the input-output p r e d i c t i o n e r r o r s , the values of n. , and s i m i l a r l y the values of m. , are aggregated over the f i v e time i n t e r v a l s . The r a t i o of these two values f o r each sector, c £ m. /n. , XT XT T=l gives an i n d i c a t i o n of the r e l a t i v e p r e d i c t i v e power of the two methods of for e c a s t i n g . Table 12 shows the values of the r a t i o for each of the sectors t o -gether with a measure of the sector's importance as a supplier of i n t e r -70 mediate output, as expressed by the r a t i o , Zi,60 i.65 15 I (Z. e n + Z. e.\ . , t.60 %i65' .%=1 1 3 whereby the sum of the intermediate output of each sector i n 1960 and 1965 i s expressed as a proportion of the t o t a l intermediate output f o r those years. Where the r a t i o , 5 Z m . /n. T=l i s l e s s than one the input-output p r e d i c t i o n s are superior to those made by ex t r a p o l a t i o n . TABLE 12 RATIO OF AGGREGATE MEAN-SQUARED PREDICTION ERRORS TO AGGREGATE MEAN-SQUARED EXTRAPOLATION ERRORS (Relative Intermediate Output Weights i n Parentheses) SECTOR (-0 5 T. m./n. x=l 1. Agriculture and Livestock 6.575 (.116) 2. Rubber Planting 0.004 (.328) 3. Forestry 19.623 (.024) 4. Fishing 1.109 (.007) 5. Mining 0.224 (.168) 6. Food Industries 2.195 (.015) 7. Wood and Cork 0.936 (.026) 8. Rubber Processing 1.488 (.073) 9. Chemical Products 1.762 (.026) 10. Non-Metallic Mineral Products 1.334 (.017) 11. Metal Products and Machinery 1.090 (.013) 12. Construction 0.018 (.015) 13. E l e c t r i c i t y and Water 0.747 (.023) 14. Transportation and Communication 0.277 (.039) 15. Wholesale and Retail Trade 0.757 (.110) 71 The input-output tables are superior for p r e d i c t i n g intermediate output i n seven of the sectors represented, p a r t i c u l a r l y so for Rubber Planting and Construction. In another sector, lion-Metallic Mineral Pro-ducts, the two methods y i e l d nearly equivalent r e s u l t s . There are at l e a s t two sectors, however, where the input-output tables perform i n a decidedly i n f e r i o r manner: Forestry and Agriculture and Livestock. There seems to be no c l e a r r e l a t i o n s h i p between the r e l a t i v e im-portance of the intermediate output of a sector and the technique which pro-duces better forecasting r e s u l t s (although i t should be noted i n the case of Rubber Planting with the l a r g e s t portion of intermediate output, the input-output predictions were f a r superior to the extrapolation f o r e c a s t s ) . The s u p e r i o r i t y of the naive extrapolation method i n p r e d i c t i n g the intermediate output of the Forestry sector i s conspicuous. D i r e c t r e f -erence to the input-output tables reveals that the r a t i o of intermediate 14 output to f i n a l demand remained almost constant from 1960 to 1965. This occurred despite the f a c t that the pattern of d i s t r i b u t i o n f o r intermediate output changed considerably over the f i r s t three years. In 1960, Forestry sold to only four other productive sectors but i n 1961 t h i s number was doubled. From 1963 on, the sector sold r e g u l a r l y to s i x sectors. This kind of disturbance to the i n t e r s e c t o r a l flow matrix may have been respon-s i b l e for the consistent underestimation of intermediate output generated i n the input-output forecasts. (It w i l l be r e c a l l e d that Forestry was The r a t i o v a r i e d between 1.3 and 1.6. 72 shorn to have the highest 8 value, equal to 1.000 i n Table 10). C l e a r l y the assumption of constant a., c o e f f i c i e n t s was not as strong as the assump-XQ t i o n of a f i x e d r a t i o between intermediate and f i n a l demand, so the naive extrapolation y i e l d e d better r e s u l t s . S i m i l a r , though les s dramatic changes i n the i n t e r s e c t o r a l flow pattern occurred i n the Agriculture and Livestock sector. Here also the r a t i o of intermediate to f i n a l demand remained v i r t u a l l y constant through-out the period, showing even les s v a r i a t i o n than i n the case of Forestry. The net r e s u l t was the s u p e r i o r i t y of the simpler f o r e c a s t i n g device but i n t h i s case i t was not so much because the input-output forecasts were so bad as the fact that the naive extrapolations were so good. In order to e x p l a i n why some of the other sectors had r e l a t i v e l y i n f e r i o r input-output forecasts, the naive model must be s c r u t i n i z e d more c l o s e l y . The quest i s r e a l l y to f i n d what changes i n the economy would a f f e c t the extrapolations but not the input-output predictions or more probably a f f e c t the former to a greater extent. One p o s s i b l e source of change comes to mind. I t was noted i n Chapter III that one of the long-term objectives of the Malaysian govern-ment i s to reduce that country's dependence upon imports. To promote im-port s u b s t i t u t i o n the government i n s t i t u t e d programs which included the granting of tax r e l i e f to firms awarded "Pioneer" status, the development The r a t i o for Agriculture and Livestock v a r i e d only between 0.7 and 0.6. 73 of i n d u s t r i a l estates, and p u b l i c investment directed to the a g r i c u l t u r a l sector to encourage greater s e l f - s u f f i c i e n c y i n food production. The sub-s t i t u t i o n of domestically produced goods and services f o r t h e i r foreign counterparts w i l l , of course, a f f e c t the values of some t e c h n i c a l c o e f f i -cients i n the input-output m a t r i x . ^ But given the o v e r a l l property of the model to compensate for such changes i t may w e l l be that the e f f e c t upon forecast performance w i l l be n e g l i g i b l e . In t h i s exercise i t i s only necessary that the input-output model be a f f e c t e d more by import-substitution than the naive model where, ceteris paribus, the r a t i o of intermediate out-put to f i n a l demand w i l l increase. The effectiveness of the p o l i c y of import-substitution pursued by the Malaysian government has been evaluated by Hainsworth and D a v i s . ^ They have demonstrated that between 1960 and 1965 notable increases i n s e l f -s u f f i c i e n c y occurred. Of the 15 sectors being analyzed here, the r a t i o of "actual production to s e l f - s u f f i c i e n c y output" rose on the order of 22 Throughout the construction of the input-output tables, the s e l l e r ' s point of view was taken. In the treatment of imports t h i s meant that imported goods and services used i n production by sector j which are comparable with the output of sector i were not shown as inputs from that (competing) sector. Imports are wholly r e g i s t e r e d as primary inputs. Thus when import s u b s t i t u t i o n occurs, sector i may f i n d that i t s e l l s more out-put to sector j , i . e . , the a., c o e f f i c i e n t w i l l change. When imports are treated from the buyer's point: of view (imports shown as inputs from the competing s e c t o r ) , the c o e f f i c i e n t would remain unchanged. G. B. Hainsworth and H. Craig Davis, Commodity and Sectoral Import Substitution in West Malaysia, 1960-1965 (Unpublished). 74 18 per cent or more for s i x sectors. These included Rubber Processing, Min-ing, Chemical Products, Fishing, Food Industries, and Metal Products and Machinery. In another sector, Non-Metallic Mineral Products, the s e l f -s u f f i c i e n c y l e v e l f e l l by almost 36 per cent. These sectors coincide (with the exception of Mining) with the sectors shown i n Table 12 to have r a t i o s 5 ( Y. m. /ni ) T=l between 1.000 and 2.195. That i s , they form the group of sectors where the naive model did not perform i n a convincingly superior way. I t appears that i n these cases, import-substitution may have served to t i p the balance more 19 i n favour of the input-output model. The opposite approach may be taken i n the pursuit of changes which a f f e c t the r e l a t i v e performance of the models, i . e . , an e f f o r t may be made to seek those changes which a f f e c t the input-output model but not (or to a l e s s e r extent) the naive extrapolation method. As already noted, however, i t i s d i f f i c u l t to i s o l a t e and evaluate the separate sources of change i n the input-output tables of West Malaysia. From previous i n v e s t i g a t i o n s though, i t i s apparent that p r i c e changes may be an important f a c t o r . The naive model i s i n s e n s i t i v e to the kinds of p r i c e f l u c t u a t i o n which may d i s -rupt the values of the a.- c o e f f i c i e n t s . to Hainsworth and Davis, Ibid., Table 3, p. 17. 19 In the Mining sector, the increased s e l f - s u f f i c i e n c y occurred as a r e s u l t of a doubling of intermediate demand from the Basic Metal Indus-tries sector (even though imports continued to exceed domestic production over the p e r i o d ) . See Hainsworth and Davis, op. cit., pp. 19-20. In t h i s case the import-substitution had a much smaller e f f e c t on the input-output p r e d i c t i o n s than on the extrapolation forecasts. 75 Probing into the reasons for the r e s u l t s shown i n Table 12 does not l e t us escape the fundamental conclusion, however: the (implicit) n u l l hypothesis that the naive extrapolation model i s superior cannot be comfort-ably r e j e c t e d . A further comparison of the two methods of f o r e c a s t i n g involves measurement of the r a t i o of the mean-squared errors as x increases. For t h i s purpose the input-output p r e d i c t i o n s are considered superior i f the r a t i o iv. /n. . i s less than one where x' < x. As Rey and Tilanus point out: ^x %x' — J v ...Cost considerations should convince us to require that input-output forecasts ought to be much bett e r than naive extrapolation forecasts i n order that they be worth-while. Also, one should expect that data which are neces-sary f o r such extrapolations can be made a v a i l a b l e at an e a r l i e r date than a complete input-output t a b l e . This feature suggests that we should compare the mean-squared p r e d i c t i o n errors m. with more recent mean-squared e x t r a -p o l a t i o n errors n. . . .20 v ^x Table 13 shows the median over i of the r a t i o s m • /n. , f o r the ^x ^T combinations (T,T') where x >_ T' , with the corresponding r e s u l t s from the Netherlands study, where a v a i l a b l e , shown i n parentheses. The Dutch figures suggest that on the average the input-output forecasts are superior to the extrapolations as long as the d i f f e r e n c e i n p r e d i c t i o n i n t e r v a l s , x-x' i s not more than two or three years. This i s not the case f o r the Malaysian forecasts. Instead the e n t r i e s i n the table i n -dicate that input-output predictions are superior only when the p r e d i c t i o n i n t e r v a l i t s e l f does not exceed two years. Reading along the p r i n c i p a l d i a -gonal, the median r a t i o becomes equal to 1.00 where x = x' = 3, i . e when f o r e -casting three years ahead, the two methods provide equally good r e s u l t s . Rey and T i l a n u s , op. cit., p. 461. 76 TABLE 13 MEDIAN RATIOS OF MEAN-SQUARED PREDICTION ERRORS (m. ) TO MEAN-SQUARED EXTRAPOLATION ERRORS (n. ,) % X FOR WEST MALAYSIA WITH CORRESPONDING FIGURES FOR THE NETHERLANDS IN PARENTHESES EXTRA-POLATION INTERVAL INPUT-OUTPUT PREDICTION INTERVAL x x' 1 2 3 4 5 1 0.77 (0.47) 1.58 (0.95) 1.48 (1.12) 1.59 (1.39) 2.69 (1.39) 2 0.74 (0.59) 0.80 (0.71) 0.85 (0.84) 1.35 (0.81) 3 1.00 (0.52) 0.60 (0.68) 1.73 (0.84) 4 1.11 (0.62) 1.28 (0.74) 5 1.88 — When the forecast i n t e r v a l exceeds three years, the naive extrapolation tech-nique y i e l d s b e t t e r estimates* of intermediate output for the 15 sectors s t u -21 died. This i s a disappointing r e s u l t since an input-output table may eas-i l y take two or three years to be completed. As the underlying input-output tables become more outmoded r e l a t i v e to the na t i o n a l accounts data normally used to make extrapolation f o r e c a s t s , the i n f e r i o r i t y of the input-output model increases; the median r a t i o r i s e s A curious exception to t h i s general statement w i l l be noted i n Table 13. Where the extrapolation forecast i s made for a two-year i n t e r -v a l , input-output predictions are superior f o r i n t e r v a l s of up to four years. 77 as x increases r e l a t i v e to t 1 (and the e n t r i e s appear further to the r i g h t along any row or further o f f the main diagonal of Table 13). There appears to be scope, then, for improving the input-output tables by adjustment i n 22 the l i g h t of more up-to-date nation a l accounts data. The table also shows that the absolute values of the median r a t i o s are lower i n almost every case f o r the Netherlands f o r e c a s t s . Again the i n -f e r i o r i t y of the West Malaysian tables i s demonstrated, whether i t be due to the disparate e f f e c t s of p r i c e f l u c t u a t i o n s , the r e l i a b i l i t y of the data, differences i n the rate of s t r u c t u r a l change, or any of the other factors mentioned e a r l i e r when the root-mean-squared p r e d i c t i o n errors were com-pared f o r the two countries. Several methods f o r adjustment have been demonstrated i n the l i t e r -ature and at l e a s t two have been tested with promising r e s u l t s . These include the S t a t i s t i c a l Correction Method (SCM) developed by C. B. Tilanus i n h i s book, Input-Output Experiments: The Netherlands 1948-1961 (Rotterdam: U n i v e r s i t y Press, 1966) and the RAS method as stated by R. Stone and J . A. C. Brown i n t h e i r a r t i c l e , "A Long-Term Growth Model f o r the B r i t i s h Economy," i n Europe's Future in Figures, R. C. Geary, E d i t o r (Amsterdam: North Holland Publishing Co., 1962). See a comparison of these two methods applied to the Netherlands tables i n Tilanus, Ibid., pp. 119-123. CHAPTER V CONCLUSIONS Leontief would have us view the input-output model as "a bridge between theory and facts in economics."''' One may interpret this to mean that i t i s a theoretical model particularly adapted for empirical use. This feature of the model as a general equilibrium scheme was brought out in Chapter I. But the Leontief inverse matrix, i t s e l f , is a bridge in a more l i t e r a l sense when the model is used for forecasting purposes. It provides a quantitatively determined picture of the internal structure of an economic system which makes i t possible to calculate in detail the con-sequences that result from the introduction into the system of changes sug-gested by a given b i l l of goods. The easy transition between what is and what w i l l be is warranted by the assumption that the same "bridge" prevails under circumstances which change the level and composition of output ab-sorbed by the autonomous sector. Less figuratively, the assumption means that the input coefficients used to derive the matrix are constant or "change slowly over the periods 2 of time usually involved in economic forecasting and planning." The poten-t i a l sources of change have been outlined in Chapter II, though as emphasized "•"Wassily Leontief, Input-Output Economics (New York: Oxford Univer-sity Press, 1966), p. 24. 2 Ibid., p. 46. 78 79 there the r e a l t e s t of the input-output model does not l i e i n a d i r e c t t e s t of the constancy assumption, but rather i n the q u a l i t y of the pre-d i c t i o n s i t y i e l d s . In i t s t h e o r e t i c a l formulation the c o e f f i c i e n t s are expressed i n p h y s i c a l q u a n t i t i e s or i n terms of volumes i n constant p r i c e s . We have seen that the West Malaysian input-output tables are i n current p r i -ces, so the derived input c o e f f i c i e n t s are value r a t i o s . (The numerator i s the flow from sector i to sector j which i s expressed i n the prices of i, and the denominator i s the t o t a l production value of the r e c e i v i n g sec-to r Q expressed i n p r i c e s of j'). As a r e s u l t , the f o r e c a s t i n g procedure used here employs quite a d i f f e r e n t assumption from the one t r a d i t i o n a l l y used i n input-output a n a l y s i s , s p e c i f i c a l l y that the value r a t i o s between intermediate flows and t o t a l production i n current p r i c e s are constant. Yet t h i s , too, could be a workable assumption depending upon the accuracy of the p r e d i c t i o n s i t y i e l d s . To test the p r e d i c t i v e power of the West Malaysian input-output tables each was used to project intermediate output i n succeeding years given the l e v e l and composition of f i n a l demand which would p r e v a i l then. By reference to the r e a l i z e d intermediate output embodied i n the l a t e r t a b l e s , p r e d i c t i o n errors were ca l c u l a t e d . The r e s u l t s were analyzed only f o r those 15 sectors which exhibited s i g n i f i c a n t intermediate output over the period (1960 to 1965). On the average i t was found that the square p r e d i c t i o n errors increased with the time span between the predicted year and the base year approximately along a s t r a i g h t l i n e with a p o s i t i v e slope and a negative i n t e r c e p t . C l e a r l y the longer the length of the forecast period the l e s s 80 r e a l i s t i c was the assumption of constant input coefficients in value terms. The distribution of the mean-squared input-output prediction errors was asymmetrical, being skewed in the direction of large values. Dispersion increased with the length of the forecast period. For 10 individual sectors better than average results were yielded i n the prediction of intermediate output over time. Rubber Planting achieved the best performance and though i t contributes most to the total intermediate output of the West Malaysian economy, on the whole those sec-tors with large intermediate output did not have the better forecasting records. The worst prediction performance was recorded for the Fishing sector, a result which may have been due to the technological change which took place or to the fact that large stochastic elements r e a l i s t i c a l l y enter into that industry's production function. The input-output predictions systemmatically underestimated the i n -termediate output in seven of the sectors and overestimated i t in another four. Curiously there was no correspondence between the direction or mag-nitude of these errors and the observed relative prediction performance of the sectors over time. Subsequent analysis has shown that the actual growth or decline of the sectors, as measured by their contribution to real Gross Domestic Product, was not properly revealed by the nature of the input-output prediction errors. Price fluctuations may have been the malefactor here. When the average predictive power of the West Malaysian tables was compared with that of similar tables for the Netherlands, the latter proved much superior. The root-mean-squared prediction errors of the West Malaysian tables were substantially larger for every forecast interval. While this may be a result of faster structural change, i t could also be due to other d i f f e r -81 ences, e.g., in the r e l i a b i l i t y of data, the degree of structural inter-dependence, and in price fluctuations. The central test of the empirical usefulness of the input-output model was performed by a comparison of input-output prediction errors with the errors that resulted when a simpler forecasting device, requiring much less data, was used. The alternative in this case was a naive extrapola-tion model based on the premise that the (value)ratio of intermediate to f i n a l demand remains constant. Extrapolation errors were calculated in a manner precisely analogous to the input-output prediction errors. When both types of errors were aggregated with respect to the time intervals used in the forecast procedure, a ratio of the two values for each sector revealed that the input-output predictions were superior for only seven of the 15 sectors represented. No relationship was found between the rela-tive importance of the intermediate output of a sector and the technique which produced better forecasting results. For two sectors, Forestry and Agriculture and Livestock, the input-output predictions were markedly inferior. Direct examination of the tables revealed that in both cases, f a i r l y dramatic changes occurred in the sales pattern of intersectoral flows while the value of total intermediate output for each sector remained almost constant, in proportion to f i n a l demand. On the whole the input-output projections may have been more sensi-tive to certain kinds of price fluctuation so this, too, may help to account for the rather dismal forecast performance yielded by the model. For those sectors where the naive extrapolation model was not convincingly superior, 82 import-substitution may have tipped the balance more in favour of the i n -put-output model, even though i t , too, would have been affected. On the average, with respect to the time interval used in fore-casting, the input-output model is only superior as long as the period does not exceed two years. When both methods are used to forecast three years ahead, they yield equivalent results, and when the forecast period extends past that, the extrapolations yield increasingly better results. This is an unfortunate result for i t can easily take from two to three years to con-struct an input-output table, and cost considerations would require that input-output forecasts be much better than naive extrapolations in order to be worthwhile. Normally the national accounts data necessary to make extrapolations w i l l be available at an earlier date than a complete input-output table and apparently could be used to improve the predictive power df the input-output model. 1 The model did not fare so badly relative to the naive extrapolation technique in the case of the Netherlands input-output tables. Indeed, for almost every forecast period, the i n f e r i o r i t y of the West Malaysian tables was again demonstrated. In summary the predictive achievement of the input-output fore-casts for West Malaysia has not been impressive. When the relative cost of making naive extrapolation forecasts i s considered i t does not seem that the construction of input-output tables i s j u s t i f i e d for this purpose. But rather than taking this defeatist view i t can be concluded that there is room for improvement in the West Malaysian tables. 83 A f i r s t step in this direction would be the specification of the presently Unspecified recipients of f i n a l goods and sources of inputs. Clearly also the tables (or at least future ones) should be reformulated in terms of constant prices since the assumption of constant input c o e f f i -cients in value terms does not generate very satisfactory results. To do a good job of deflating input-output tables, each individual intersectoral flow should be considered and a price index constructed for i t . Admitted-ly this would be an immense task but there is a manifest need to disentangle volume and price changes. It also seems reasonable, given the government's policy of promoting local import-substitution, that for forecasting purposes, imports should be treated in the West Malaysian tables as inputs from the domestically-competing sector. Moreover, some way might be sought to im-prove the forecast performance of the Fishing sector by incorporating a more r e a l i s t i c production function. Finally i t should be possible to up-date the input-output tables using more recent national accounts data. The use here of the West Malaysian input-output tables as a fore-casting tool is but one of the many applications the model can take. It may well be that for other uses the construction of the tables is more than j u s t i f i e d . B I B L I O G R A P H Y Barna, Tibor. " C l a s s i f i c a t i o n and Aggregation i n Input-Output A n a l y s i s , " The Structural Interdependence of the Economy. Edited by Tibor Barna. New York: John Wiley & Sons, Inc., 1954. Baumol, William J. Economic Theory and Operations Analysis. Englewood C l i f f s , New Jersey: P r e n t i c e - H a l l , Inc., 1961. Chenery, H o l l i s B., and Clark, Paul G. Interindustry Economics. New York: John Wiley & Sons, Inc., 1959. Davis, H. Craig and Hainsworth, Geoffrey B. Input-Output Forecasts for West Malaysia, 1960-1965. Unpublished. Dorfman, Robert. "The Nature and S i g n i f i c a n c e of Input-Output," The Review of Economics and Statistics. V o l . 36, No. 2 (May, 1954), pp. 121-133. Dorfman, Robert; Samuelson, Paul A.; and Solow, Robert M. Linear Programming and Economic Analysis. New York: McGraw-Hill Book Co., Inc., 1958. Evans, W. Duane. "Input-Output Computations," The Structural Interdependence of the Economy. Edited by Tibor Barna. New York: John Wiley & Sons, Inc., 1954. Federation of Malaya, Second Five-Year Plan 1961-1965. Government P r i n t e r , 1961. Government of Malaysia. First Malaysia Plan 1966-1970. Kuala Lumpur, 1965. Government of Malaysia, Department of S t a t i s t i c s . Malaysia Interindustry Accounts 1965. Kuala Lumpur, n.d. Hainsworth, Geoffrey B. and Davis, H. Crai g . Commodity and Sector Import Substitution in West Malaysia,: 1960-1965. Unpublished. Johnstone, J . Statistical Cost Analysis. New York: McGraw-Hill Book Co., Inc., 1960. K l e i n , L. R. "On the In t e r p r e t a t i o n of Professor Leontief's System," The Review of Economic Studies. V o l . 20, No. 2 (1952-53), pp. 131-136. Leontief, Wassily. Input-Output Economics. New York: Oxford U n i v e r s i t y Press, 1966. 84 85 Leontief, Wassily. "Quantitative Input-Output Relations i n the Economic System of the United States," The Review of Economics and Statistics. Vol. 18 (August, 1936), pp. 105-125. Miernyk, William H. The Elements of Input-Output Analysis. New York: Random House, 1967. Milne, R. S. Government and P o l i t i c s in Malaysia. Boston: Houghton M i f f l i n Co., 1967. Rey, Guido and Tilanus, C. B. "Input-Output Forecasts f o r the Nether-lands, 1949-1958," Econometvica. V o l . 31, No. 3 (July, 1963), pp. 454-463. Seligman, Ben B. Main Currents in Modern Economics. New York: Free Press of Glencoe, A D i v i s i o n of the MacMillan Co., 1962. Stone, R., and Brown, J . A. C. "A Long-Term Growth Model f o r the B r i t i s h Economy," Europe's Future in Figures. Edited by R. C. Geary. Amsterdam: North Holland Publishing Co., 1962. Tilanus, C. B. Input-Output Experiments: The Netherlands 1948-1961. Rotter-dam: U n i v e r s i t y Press, 1966. APPENDIX A ADJUSTMENT OF THE PUBLISHED 1965 INPUT-OUTPUT TABLE The input-output table for 1965 as published by the Department of S t a t i s t i c s and shown i n Table Al1 had to be adjusted for comparability with the tables for 1960-1964 constructed at the U n i v e r s i t y of B r i t i s h Columbia under the supervision of Professors H. Craig Davis and Geoffrey B. Hainsworth. These changes are noted below: 1. The input-output tables f o r 1960-1964 were con-structed to have 29 productive sectors; the published 1965 table has 30 productive sectors. For comparability, sectors 18 and 19 of the published table were aggregated (Chemical Products and Products of Petroleum and Coal, r e s p e c t i v e l y ) . 2. The input-output tables for 1960 through 1964 were constructed exclusive of import duties and having only one row and one f i n a l demand column to represent foreign transactions, Import Trade and Rest of the World (exports), r e s p e c t i v e l y . Complete comparability could not be achieved without the accounts f o r 1965, because Row 32 of the pub-l i s h e d table shows merchandise imports " d i s t r i b u t e d to the r e c e i v i n g sectors 2 i n c l u s i v e of import d u t i e s . " To achieve the best degree of uniformity ^West Malaysia Interindustry Accounts, 1965, op. cit.,Table 1, p. 10. 2 Ibid., p. 8. 86 TABLE Al Source: Want Malaysia I^leriiduatr, WEST MALAYSIA INTERINDUSTRY ACCOUNTS l96So t^-.,:ms, «.t..t~„J of Statistics, Kuala Lunpur, Malaysia, 196). Tabic 1 , p. 10. ( P r o d u c e r P r i ces in Mil l ions of M o l o y s i o n D o l l a r s . ) Delivered froa: • 2 3 • 4 1 6 7 1 9 10 11 11 13 14 15 16 17 18 19 20 a 12 2) 24 25 26 27 28 29 30 a s IKPORT TRADE l I I S 1. Agriculture 4 Livestock 48.B 210.1 13.5 13711 14.9 30.0 11.3 2.7 577.5 1.046.1 1. Rubber Planting 947.0 142.9 1.089.9 3. for., try 0.8 69.5 0.6 0.1 0.4 7.3 27.5 1.7 26.8 134.7 Pishing IB.8 25.7 100. 2 144.7 S. Mining 1.0 703.2 3.4 185.4 -1.5 89 5 4. rood Industrie* 42.2 10.7 0.5 6.6 84.6 8.8 4.3 441.1 598.8 7. Beverages 1.2 1.2 40.4 42.8 B. Tobacco 8.1 185.8 193.9 9. Textiles 0.1 .0.1 8.0 7.8 1.4 16.6 34.0 10. Clothing a Footwear 0.2 5.6 5.8 11. Wood • Cork 0.2 8.1 1.4 0.9 0.1 SI.4 57.9 5.0 0.5 19.6 182.1 12. Furniture 6 Fixtures 0.9 0.2 11.3 0.1 22.9 35.4 11. Paper 6 Paper Producta 0.9 2.5 0.1 1.7 5.3 1.8 0 5 12.9 i t . Printing 4 Publishing 2.9 28.6 3.5 4.1 29.0 68.1 15. Leather 6 Leather Product• 0.1 2.9 3.0 16. Rubber Processing 176.8 1.097.2 4.0 I.2?3.8 17. Rubber Products 0.5 1.7 23.2 10.8 1.1 11.5 4S.9 99.7 I*. Chealcal Products 32.7 6.5 3.6 0.2 0.7 n.l 0.7 31.1 0.4 0.1 10.6 160.2 25.4 14.5 89.3 376.8 19. Products of Fctroleun 6 Coal 0.4 1.5 14.1 0.5 0.3 1.8 0.2 0.4 0.1 1.1 0.3 0.3 0.1 4.1 6.6 11.0 45.0 34.3 0.1 14.3 117.7 20. Non-Hetai11c Mineral Products 0.1 8.0 72.4 6.1 2.6 0.8 90.0 11. Balle He tai Industries 0.7 22.1 867.7 0.4 0.6 43.1 S4B.5 22. Metal Products and Machinery 1.0 0.1 0.2 0.8 39.6 13.3 8.8 52.1 41.4 2.8 41.1 201.2 21. Miscellaneous Manufacturing Industries 0.3 1.4 0.6 1.0 56.0 61.3 24. Construction 26.9 11.9 16.4 29.1 4.8 672.9 116.4 900.4 25. Electricity 4 Water 41.7 3.5 0.6 0.5 0.5 1.2 0.2 0.1 0.7 1.0 2.0 1.8 0.1 4.7 0.4 2.1 0.3 21.4 7.2 1.6 0.2 o.e 37.1 20.2 48.4 200.3 26. Transportation and Coosunlcstlon 9.6 2.3 130.1 13.5 104.3 22.7 166.1 44B.fr 27. Wholesale 4 Retail Trade 37.3 8.3 2.9 5.0 29.8 48.6 4.5 S.B 0.5 22.1 2.8 1.0 3.9 0.3 7.8 9.0 34.9 4.4 9.5 6.2 20.1 2.1 79.5 10.2 26.4 1.1 14,1 296.7 124.7 87.4 17.7 29.4 881.6 2.044.5 2B. Banking 4 Insurance, etc. 0.8 84.0 4.6 58.5 1 7. <*29. Dwellings 6.8 116.0 lai.A JO. Other Service industries 9.5 76.4 966. 1 492.1 1.544.5 31. Rest of the Uorld 0.7 0.6 IB. 2 18.5 2.630.5 30.5 43.8 145.8 2.3.18.6 32. I sport Trade 96.1 19.7 - 1.6 18.5 135.9 11.8 117.0 19.5 2.0 5.8 4.6 3.8 12.2 1.2 9.7 9.8 42.0 95.8 7.4 110.0 65.7 12.5 151.0 2.1 23.5 6.2 1.4 144.5 309.3 351.0 19.0 33.2 1.109.4 2.955.2 31. Unspecified 36.1 13.5 17.2 1.1 34.4 63.0 6.8 21.4 2.2 1.0 18.2 4.0 0.9 17.6 0.5 19.4 11.6 36-9 4.2 14.0 1.0 31.7 32.3 55.4 13.2 22.5 167.1 6.B 53.3 199.9 15.4 20.8 101.2 197.8 822.0 34. Inventories IS. Primary Factors of Production* 749.9 1.041.5 114.6 135.5 75S.2 104.1 18.4 32.7 7.6 2.0 56.9 11.9 6.2 31.2 0.9 127.0 16,5 91.7 13.1 43.1 25.4 79.1 13, fl 317.9 132.1 333-4 .733-9 121.6 305.6 1.437.0 7,919.8 TOTAL: 1,046.1 1,089.9 134.7 144.7 894.5 598.8 42.8 193.9 34.0 5.8 B2.1 35.4 12.? 68.1 ?-° 1.291.8 99.7 376.8 117.7 90.0 848.5 201.2 61.3 900.4 200.1 448.6 2,044.5 147.9 322.8 1,544.5 1.127.6 2.955.2 822.0 l . l l l . l 71.4 1.357.1 4.740.8 27.790.3 Salaries 4 Wage* 47.0 482.0 46.9 17.8 166.8 34.3 5.7 6.3 3.3 0.9 10.5 6.3 1,} IB.? 0.1 60.0 14 7 ta i 1.8 1 1 0 7.4- 41.fi 6.1 209.6 54.5 161.7 240.2 61.9 1.118.2 2.881.1 En t rep renal al Income. S7«.5 520.1 44.2 117.2 431.0 69.8 12.7 26.3 4.3 1.1 26.0 5.5 4.9 12.1 0.6 66.0 21.A 61.8 29.1 30.0 1B.0 33.2 7.7 105.9 77.4 i 87.7 857.2 47. J ,298.3 102.7 4,001.8 Indirect Taxsta 33. B M.* 31.5 0.5 157.1 0.1 0.4 6.1 0.2 1.0 fti? 11.6 0.1 0.3 2.4 6.3 "64.6 636.5 13.d I" 7.3 36.1 l .OJ i .1 Subsidies -0.4 -<».* C O 88 possible given t h i s constraint, the following changes were made: (a) Table A l , the published v e r s i o n of the 1965 table, shows a row (31) e n t i t l e d "Rest of the World" which contains, ex-cept for the entry i n Column.32, the a l l o c a t i o n of non-merchandise imports by sector. Non-merchandise imports here t o t a l $258.1 m i l l i o n . This row was deleted a f t e r the non-merchandise values had been added to Row 32, be-low i t , to show t o t a l import trade ($3,213. m i l l i o n ) . The entry i n Column 32 was l e f t out of the table e n t i r e l y , being the value of customs and im-port duties charged on non-merchandise imports. Its t o t a l , $2,630.5 m i l -l i o n , was subtracted from the t o t a l of a l l production ($27,790.3 m i l l i o n ) y i e l d i n g a revised t o t a l production f i g u r e of $24,795.1 m i l l i o n . (b) The column e n t i t l e d "Import Trade" (number 32 of the published table) contains only two e n t r i e s : $324.7 m i l l i o n i n Row 27 (Wholesale and Retail Trade) and the $2630.5 m i l l i o n i n Row 31 mentioned above. To make the table more comparable to the 1960-1964 tables, the v a l u a t i o n of customs and import duties charged to the Wholesale and Retail Trade sector was omitted. Thus $324.7 m i l l i o n was deducted from the t o t a l production f i g u r e ($2044.5 m i l l i o n ) for that sector to obtain the value of production exclusive of customs and import duties of $1719.8 m i l l i o n . I t should be noted that t h i s reduces the value of t o t a l f i n a l demand f o r that sector from $1639.0 m i l l i o n to $1314.3 m i l l i o n , and should improve the pre-d i c t i v e a b i l i t y of the e a r l i e r tables. The value of customs and import duties, $324.7 m i l l i o n , was of course, subtracted from the Wholesale and Retail Trade column, s p e c i f i c a l l y from the value of the entry i n Row 35, 89 "Primary Factors of Production," and hence the column t o t a l . The component of the entry i n Row 35 a t t r i b u t e d to i n d i r e c t taxes amounted to $636.5 m i l -l i o n . This was consequently reduced to $311.8 m i l l i o n . The Wholesale and Retail Trade column thus t o t a l s $1719.8 m i l l i o n (equal to the row). The 1965 table, a f t e r these adjustments, appears i n Table 6 i n the text as i t was used i n the f o r e c a s t s . APPENDIX B INPUT-OUTPUT PREDICTION ERRORS The input-output prediction errors calculated according to Equa-tion (4.7) appear in Table Bl for the 15 sectors considered in the analysis. For abbreviation, the sector name has been excluded; the number used to designate a sector i s that used originally in the input-output tables, which appears in parentheses in Table 7. 9 0 TABLE Bl INPUT-OUTPUT PREDICTION ERRORS (e . , ) T = 2 SECTOR 1960 1961 1962 1963 1964 1960 1961 1962 1963 1 -0.0315 0.0856 0.0488 0.1092 -0.0120 0.1769 0.1370 0.1718 0.1013 2 -0.0206 0.0259 -0.0146 -0.0119 -0.0158 0.0049 0.0107 -0.0250 -0.0270 3 0.0543 0.3211 0.0290 0.0775 0.0572 0.4021 0.3550 0.1059 0.1410 4 -0.1195 0.0801 0.2015 0.2827 0.4521 -0.0488 0.2948 0.5401 0.8617 5 -0.0532 0.1111 -0.0622 -0.1171 -0.0455 0.0519 0.0423 -0.1713 -0.1561 6 0.0564 -0.0165 -0.0552 0.0776 -0.1950 0.0386 T0.0943 0.0205 0.1300 11 0.1160 0.1407 -0.0103 -0.0403 0.0686 0.2775 0.1294 -0.0524 0.0283 16 0.1627 -0.1049 -0.1666 0.2028 0.1464 0.0406 -0.2541 0.0121 0.3780 18 -0.0706 -0.2068 -0.1621 -0.2952 0.1105 -0.2644 -0.3280 -0.4003 -0.2058 19 -0.0289 0.0950 -0.1339 -0.1687 -0.1205 0.0650 -0.0512 -0.2801 -0.2696 21 -0.0316 0.0231 -0.1435 -0.0287 -0.0436 0.0087 -0.1253 -0.1701 -0.0709 23 -0.0575 0.0625 0.0000 -0.0257 0.0367 -0.0022 0.0605 -0.0275 0.0087 24 -0.0110 0.0583 -0.0096 -0.0037 -0.0437 0.0452 0.0464 -0.0149 -0.0448 25 -0.0673 0.0087 0.0464 -0.0376 -0.0754 -0.0581 0.0549 0.0061 -0.1085 26 -0.0231 -0.0292 -0.0822 -0.0166 0.4797 -0.0484 -0.1130 -0.0973 0.4594 TABLE B l (Continued) T = 3 x = 4 T = 5 SECTOR :  1960 1961 1962 1960 1961 1960 1 0.2355 0.2686 0.1666 0.3827 0.2618 0.3763 2 -0.0094 -0.0004 -0.0384 -0.0196 -0.0147 -0.0327 3 0.4337 0.4483 0.1715 0.5271 0.5299 0.6112 4 0.1418 0.6624 1.2394 0.4641 1.4149 1.1277 5 -0.0131 -0.0792 -0.2070 -0.1282 -0.1188 -0.1659 6 -0.0437 -0.0228 -0.1783 0.0365 -0.2083 -0.1600 11 0.2635 0.0806 0.0141 0.2064 0.1554 0.2886 16 -0.1315 -0.0942 0.1739 0.0555 0.0504 0.2264 18 -0.3750 -0.5130 -0.3178 -0.0546 -0.4421 -0.4794 19 -0.0787 -0.2123 -0.3677 -0.2349 -0.3093 -0.3280 21 -0.1367 -0.1537 -0.2055 -0.1639 -0.1891 -0.1982 23 -0.0040 0.0312 0.0052 -0.0330 0.0629 -0.0070 24 -0.0300 0.0422 -0.0586 0.0261 -0.0032 -0.0171 25 -0.0160 0.0130 -0.0704 -0.0560 -0.0669 -0.1317 26 -0.1322 -0.1313 0.3379 -0.1533 0.2866 0.2506 

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