THE ECONOMIC WEEKLY ANNUAL NUMBER FEBRUARY 1962

Multisector Models for Planning A R u d r a

It is paradoxical that the development of refined econometric techniques applicable to planning has gone farther in countries which have not accepted the philosophy of planning while there have been few theoretical contributions to the techniques of planning from countries which have adopted planning.

As a result, the development of theory in one part of the world has suffered from being detached from practical application while the tremendous wealth of experience of practical planning acquired in the other part of the world has not enriched theoretical knowledge.

Linear programming used in multisectoral growth models can have practical application to planning only in an economy which is totally planned; yet the development of the techniques of programming as well as of growth models have taken place in countries which either do not have any planning at all or have, at most, some applications of partial planning. This is true even though it is to a Soviet academician that the credit goes for first stating the programming problem in its purely mathematical form.

Indian planning has not benefited much till now from any application of econometric techniques. This raises the question : To what extent do we really have econometric techniques and methods that can usefully be applied to planning but which have been neglected?

[The views expressed here are those of the author and do not in any way, involve the Indian Statis­tical Institute of which he is an employee. This requires to be emphasised as the two books under review' are publications of the Institute.]

I T i s a w e l l k n o w n fact that our P lanning Commission has, d u r i n g

the last five or six years, received technical advice f r o m a large num­ber of experts in the f ie lds of eco' nometrics and model b u i l d i n g ha i l ­i n g f rom many of the notable un i ­versities of the West. I n d i a n uni­versities and ins t i tu t ions have had the pr ivi lege of p lay ing host to pract ical ly all the leading names of this par t icu lar w o r l d . M a n y of them have come here not on br ie f lecture tours, bu t have spent several months and worked hard . Despite a l l this , i t cannot be said that the T h i r d F ive Year Plan has been prepared in a way fundamental ly different f r o m the F i r s t Five Year Plan. A r e we to lay the blame for this state of affairs on ly on the i n ­sular i ty of our planners or are there also lacunae in the models and methods tha t render them i n a p p l i ­cable in actual p lanning? Rather than at tempt a s t ra ight f o r w a r d review of the two publicat ions, it may be more useful to look at

"Planning for India : Selected Explorations in Methodology '' by Ragnar Frisch; issued under the auspices of the Indian Statistical Institute; published by Asia Pub­lishing House, 1960. Pp i i i + 86: price Rs 11.25.

"A Demonstration Planning Mo­del for I n d i a " by Jan Sandee; issued under the auspices of the Indian Statistical Institute; publish­ed by Asia Publishing House, 1960. Pp iv + 60

them f r o m this par t icular angle. ( I n any case, at least insofar as Professor Frisch's work is concern­ed, it would be somewhat point­less as wel l as imprope r to review it as late as this considering that the publ ica t ion presents on ly an early fragment of a l ine of t h i n k i n g that he has been developing almost continuously d u r i n g the last six or seven years.)

Utility of Multisector Models

I t should, however, be clearly understood at the very outset that i t is not the o p i n i o n of the reviewer that mult isector p r o g r a m m i n g models cannot be of service in the prepara t ion of a p l a n ; he is f i rmly convinced that they can be. It is, however, his content ion that i f mul t isector models have not as yet been used in p l ann ing in Ind i a , i t is to a large extent due to the com­plexities of the task. A model by its very nature and purpose makes an abstraction of the r e a l i t y and sim­plifies the p rob lem. The loss of details is more than compensated by the greater c l a r i t y and a more effective t ack l ing of the p rob lem which it permits. But there is a cer ta in po in t in s impl i f ica t ion be­yond which a p rob l em ceases al­together to be the same, so tha t a course of act ion based on such an over-simplif ied model w i l l y i e ld a result that is not merely less satis­fac tory bu t one t h a t is altogether unsatisfactory. No mult isector mode l

has as yet been formula ted in Ind ia that does not base itself on a deg­ree of s impl i f ica t ion l y i n g on the wrong side of this crucia l poin t .

Fr isch considers a 22 sector model where the sectors are d iv ided in to four broad groups: p r i m a r y products, large scale manufactures, small scale manufactures, and 'con­struct ion, trade t ranspor t and ser­vices'. He considers two problems d i f fer ing by the t ime horizons en­compassed, a Coming Year problem relevant to annual p lann ing and an Asymptot ic Problem relevant to perspective p lann ing . Sandee deals w i t h only 13 mater ial p roduc t ion sectors and considers a single t ime horizon, namely ten years.

Assumption of Constant Coefficient

Frisch makes the usual Leon t ie f assumption about the ou tpu t of a sector being related to an i n p u t i n ­to the' sector by a constant coeffi­cient for a l l the sectors. Th i s as­sumpt ion presumes ( i ) constant technology, ( i i ) constant industry composi t ion and ( i i i ) constant work organisat ion and the usual objec­t ion raised against i t is that such constancies are incompat ib le w i t h the very idea of development. This object ion is generally va l i d about any sector in any economy, but when i t concerns some of the more unorganised sectors of an under­developed economy, the asumption amounts to one of those cases of

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over-simplif icat ion w h i c h render an ent i re analysis qu i t e useless. Of course, on a pure ly f o r m a l plane there is not and cannot be any dif­ference between one sector and another. But for the more organised sectors and especially for of manu­fac tu r ing industries, i t may not be too unrealist ic to assume that changes in technology, composi t ion, w o r k i n g method and organisat ion take place o n l y slowly so tha t one can expect the use of coefficients estimated on the basis of present data to give results that wou ld be approximat ions of the t rue results In the case of the unorganised i n ­dustries, however, any assumption of s tabi l i ty of the coefficients is hazardous in an add i t iona l way. They are subject, even w i t h i n a relatively short per iod of t ime, to very unsystematic and large fluctua­tions reflecting the sh i f t ing charac­ter of technology (understood in the nar row and special sense of the sector of inpu t coefficients fo r a par t icu la r indus t ry ) composit ion and organisat ion in such a sector.

The point may be i l lustrated by the agr icul ture sector. The Leontief assumption of constant coefficient here would i m p l y c o n s t a n t propor­tions between the i n p u t items in agr icul ture , e g seed, chemical fer­t i l i s e r s organic manures i r r i g a t i o n water, etc. These p ropor t ions ob­served d u r i n g any per iod are purely functions of that par t icu lar period and arc l iable to qu ick and errat ic changes. Th i s gives rise to difficul­ties of est imation. Estimates based on the input-output table of any one year w i l l be merely fo r tu i tous ; which pa r t i cu la r propor t ions are to be adopted as representing present technology?

Additivity Assumption

The modif ica t ion introduced by Sandee in his model is a definite improvement . He removes the as­sumption of constant coefficients as far as agr icul ture is concerned, treats the inputs in to agr icul ture as inde­pendent variables, introduces fresh coefficients that measure increase in p roduc t ion in agr icu l ture due to un i t quan t i ty of each type of i n p u t and treats these effects of the d i f ­ferent inputs in an addi t ive fashion One w i l l recognise tha t th is i s noth­i n g but the " y a r d s t i c k " technique used by the P l ann ing Commission.

The a d d i t i v i t y assumption i s i n i t ­self a h igh ly questionable one, bu t Sandee is r i g h t in dec id ing that i t is preferable to the assumption of constant coefficients.

Frisch extends his table consist­ing of 22 rows and columns by 4 rows and 4 columns to achieve a symmetry in the sense of each row total equal l ing each co lumn to t a l . I t is not quite clear w h y he insists on this fo rmal symmetry, for he in t ro­duces one row for factor income and another for gross savings and corres­pond ing ly one column for household current out lays inc lud ing savings and another for investment; he them introduces special symbols to denote add i t ion over rows and columns leaving out the savings row and investment co lumn. Fr isch applies the p r inc ip l e of constant coefficients to all the columns and fo r a l l the cells, excepting the column f o r i n ­vestment. That is to say the break­downs of household out lay, expor t , and Government outlay are each conceived in terms of r i g i d propor­t ions; import , tax incidence, savings and factor income for each sector are also r i g i d l y related to the out­pu t of each sector. Sandee's model is free of such r ig id i t i e s ; he only subjects the i nd iv idua l cell entries in the household outlay, expor t and stock b u i l d i n g column to upper am) lower bounds.

On the other hand. Sandee's model does violence to rea l i ty by complete ly leaving out of account al l the non-material p roduct ion sector ' and the Government sector. Th i s introduces serious errors in a l l the balance equations ( f o r the non-mater ia l product ion sectors are con­nected w i t h the mater ial p roduc t ion sectors by input -output relat ions) and neglects ent irely the problem of re la t ing i n d i v i d u a l targets w i t h overal l macro-economic measures and balances. Thus the problem of achieving balance between income, eonsumption and savings, between Government outlay and tax receipts, and b r i n g i n g these balances to bear upon the i n d i v i d u a l targets is com­pletely by-passed.

Breakdown of Capital Formation The treatment of the breakdown

of capi ta l fo rmat ion in the plan per iod presents a serious log ica l difficulty in the use of any m u l t i -sector model for overal l p l ann ing purposes; it is a difficulty that can­

not be qui te surmounted and can at best be evaded w i t h v a r y i n g degrees of success. The cur ren t period's ou tpu t in the different sectors does not have any logical re la t ion either w i t h capital forma­t ion tak ing place in the sector dur­i n g the same per iod, or w i t h the p a r t of o u t p u t of the sector going to capi tal fo rmat ion (on account of the t ime lag of m a t u r i t y of invest­m e n t ) . A logical re la t ion exists between the flow of ou tput of a pe r iod w i t h the average stock of capital d u r i n g the same p e r i o d ; that is to say, between the output of the current per iod and the investments of the preceding periods. The capi­ta l f o rma t ion of the current per iod therefore is log ica l ly related only w i t h the outputs of future years. No extension of the t ime hor izon can qui te el iminate the problem, fo r there w i l l always be a fu ture .

Fr isch in h i s Coming Year pro­blem connects the entries in the i n ­vestment co lumn (representing flow of goods from the different sectors to capi ta l fo rma t ion ) to investment in the different sectors w i t h the help of a ma t r i x of coefficients represen­t i n g the component breakdown of investment in each sector. There is an unwarranted r i g i d i t y in the assumption of constant coefficients here, for it implies investment in a sector to have a given component breakdown ho ld ing separately for every i n d i v i d u a l t ime per iod . The investments in the different sectors are, however, not l inked to the out­put through the in termediary of any capital ou tpu t ratios. As a matter of fact investments in the different sectors are the base variables in his model.

In the Asymptot ic Problem. Frisch introduces var iable t ime lags of i n ­vestment fo r the different sectors but eliminates a l l complications and doesawav w i t h ( ra ther than solves!) all difficulties presented by the co­lumn for capi ta l fo rmat ion . He gives the problem a t ime setting where the economy has reached what he calls an "asymptot ic condi­t i o n " of s t r ic t p ropor t iona l i ty bet­ween al l the measures of the econo­my, where the passage of t ime changes each quant i ta t ive aspect of the economy in the same d i rec t ion and by the same propor t ion . W i t h this extremely s impl i fy ing assump­t i on , Fr isch can collapse a mul t ip le

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per iod problem into a single per iod one The results cannot but be of doubtful pract ical value. Probably no economy in the wor ld is any ' where near reaching the "asympto­tic cond i t ion ' ' ; but insofar as an underdeveloped economy l i ke ours is concerned, the real i ty is so far f r o m the assumption that once again, results derived f r o m i t can­not but be bereft of a l l u t i l i t y . Sandee also avoids the problem but does so in a way that is more ac­ceptable. He first works out an equ­a t ion connecting the expansion of product ion in each sector to capi ta l format ion in the sector ( w i t h three breakdowns) and then relates to i t the final year's investment in the sector by assuming that investment in each sector increases during; the ten year pe r iod along; a straight l ine pa th .

Consumption and Investment Sandee uses aggregate mater ia l

consumption as the preference func­t i o n . He claims that "due to the peculiar structure of the model, th is simple target is wider than i t seems. As investment and welfare ( i n the sense of consumption) go together maximis ing one means max imis ing the other ' ' . I t i s not clear in what sense the statement is to be taken. It is one th ing to say that the results obtained by maxi­mis ing consumption and maximis ing income wou ld approach each other asymptot ical ly as the t ime horizon is extended indef ini te ly . B u t that is not what Sandee says and his state­ment as it stands is incorrect and somewhat misleading. Max imisa t ion of consumption would also maximise investment only if the two are func­t ionally related. an assumption wh ich Sandee does not make. Maximisa t ion of consumption would, of course, maximise investment in the consumer goods industries (g iven constant technology') in the in te rven ing years, and therefore in the final year (thanks to his assump­t i o n of l inear growth of invest ' m e n t ) . I t would not maximise in ­vestment in the investment goods industries, and therefore not over' al l investment.

However, it is better to use a simple macro-economic measure l ike aggregate consumption as the pre­ference func t ion , than construct functions of more than one var i ­able w i t h subjective assignment of neights as Fr i sch does. This has

always appeared to the reviewer as the weakest po in t in Frisch's me­thod. Fr isch considers a l inear funct ion of three variables, u, m i l ­lions of new jobs created annually, v , annual rate of investment; and we net annual increase in India 's net fore ign assets. The fo l lowing quotations f r o m Frisch's text i l lus t ­rate the type of arguments used to decide upon the numerical values of the weights he attaches to t h e m :

"Since 2,5 m i l l i o n annual ly would be a satisfactory achieve­ment in u and 10 per cent a satis­factory achievement in v, one may say that a given increase u

2.5

w o u l d be considered roughly equivalent to an equally large in­crease in v ''

1 0 " M y guess is that the co-effi-cient of equivalence is somewhere in the neighbourhood of 1.3. That is to say, one would be equally satisfied w i t h a progress report te l l ing of a m i l l i o n ton steel plant bu i l t en t i re ly by I n d i a n means and a progress report tell­i n g of a 1.3 m i l l i o n ton steel p lant bu i l t ent i rely by means of fore ign loans, everything else be-i n g the same."

Subjective Judgment W i t h due respect to P r o f Frisch,

the reviewer cannot but express his doubt whether the in t roduc t ion of this type of pure ly personal and subjective judgment does not knock the very bot tom out of the objecti­v i t y and ra t iona l i ty which is sup-posed to be the s trong points of the p rogramming approach. Af t e r a l l , every point w i t h i n the solution space would give a satisfactory plan in the sense of meeting al l the balance and boundary cond i t i on ' . The next step of searching for the "op t ima l p l an" can be of interest on ly i f the c r i t e r ion o f o p t i m a l l y is objective in the sense of being something that could generally be accepted as one ( though not the only one) measure of satisfaction of the performance of the economy. Opinions may differ as to whether the greatest importance should be given to employment , or standard of l i v i n g or the rate of g rowth of the economy or the acquis i t ion of fore­ign exchange reserves, bu t each of them could f o r m the basis of an op t ima l i t y . I f however sen a t tempt

i s made to combine al l of them in a single func t ion w i t h the help of weights, the " o p t i m u m " wou ld be­come a func t ion of pu re ly personal judgment and preferences and cease to be meaningful . A p a r t f r o m that, i f personal judgments have to be entertained it is not clear why and on what basis they should be l imi t ed to only a few of the mea­sures. There is scope fo r personal subjective judgment in relat ion to most of the more impor tan t p l an targets and such judgment does i n ­deed play an impor tan t role in a plan as i t is now prepared by the Planning Commission. One wou ld have thought that the p rog ramming approach is adopted to avoid such personal subjective judgments.

The shortcomings pointed ou t in Frisco's model are such that by themselves they make i t qui te un­suitable for direct appl ica t ion in Ind i a . Sandee's model must be admit ted to be more amenable to adaptat ion. I t fails not by having too many untenable asumptions and unacceptable r igidi t ies but by being rather incomplete. A planning model to be accepted for pract ical appl ica t ion cannot afford to have as many gaps as it contains. Sandee is remarkably fresh and imaginat ive in the way he treats inputs in to agr icul ture and in the way he avoids capital-output ratios in agr icul ture and introduces a var iable standing for Extension works.

This, however, is not enough: much more care has to be taken of the agriculture, sector before any model can be accepted fo r applica­t i on to I nd i an p lanning . I t seems that a satisfactory solut ion w i l l only be had if agricul ture is related to investment and the various inputs th rough empir ica l curves drawn on the basis of actual projects of va r i -ous types for extending i r r i ga t i on , fert i l iser i npu t and other Extension services.

O n l y a concluding remark need be made about the difficulties that would be fared by the planners in mak ing use of such models. Tin-state of our economic statistics is such that most of the coefficients needed in the use of such models cannot be calculated w i t h any accu­racy; but that need not be stressed at a t ime when we are discussing the inadequacies of the models; for that at least the model builders cannot be held responsible.

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