this pdf is a selection from an out-of-print volume from ... · pdf filein inferring...

This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research

Volume Title: Problems of Capital Formation: Concepts, Measurement,and Controlling Factors

Volume Author/Editor: Conference on Research in Income and Wealth

Volume Publisher: NBER

Volume ISBN: 0-870-14175-9

Volume URL: http://www.nber.org/books/unkn57-1

Publication Date: 1957

Chapter Title: Capital Coefficients as Economic Parameters: the Problemof Instability

Chapter Author: Anne P. Carter

Chapter URL: http://www.nber.org/chapters/c5585

Chapter pages in book: (p. 287 - 310)

CAPITAL COEFFICIENTS AS ECONOMIC PARAMETERS:THE PROBLEM OF INSTABILITY

Anne P. CarterHarvard Economic Research Project

The issue of fixed versus variable coefficients is generallysettled by faith rather than fact. This is easy to understand Fewcan doubt the possibility of producing most products in a variety ofways, but it will be some time before there is sufficient informationfor a comprehensive quantitative appraisal of the importance ofvariability. Furthermore the importance of substitution and themethods appropriate for dealing with it can be judged only in rela-tion to a specific model in a given temporal context. theevidence is fragmentary, the search for empirical capital coefficientsfor the dynamic input-output model has yielded some insight intothe problem of variability in technique of production in disaggregatedschema. The purpose of this paper is to outline and discuss someproblems posed by the variability of productive methods in the im-plementation of a dynamic input-output model.

The search for empirical capital coefficients has focused atten-tion on the problems of variability to a far greater extent thanstudies of input flows on current account. There are reasons, bothin the types of data used and in the theoretical structure of themodel, which explain the greater apparent variability of capital re.quirements. Input coefficients were derived primarily from censusinformation. Thus interplant differences in input-output ratios wereautomatically obscured in the aggregation of inputs and outputs forall plants in an industry. In the absence of analogous over-allcoverage of stocks of capital goods, capital coefficients were de-

Note: This paper draws upon a number of studies of capital requirementsconducted at the Harvard Economic Research Project. The author wishesto acknowledge the contributions of the various members of the Projectwho participated in these studies, particularly Mrs. Carol Cameron andMrs. Helen Kistin. Both of them played major roles in the analysis ofcapital requirements in the chemical industries. Mrs. Cameron alsoshouldered major research responsibility in the follow-up studies of un-balanced expansions and of capital requirements in carbon black produc-tion. However, the conclusions based on these studies which are pre-sented in this paper are those of the author.

287

CAPITAL COEFFICIENTS AS PARAMETERS

rived from descriptions of small samples of individual plants. Wheremore than one plant was covered, interplant differences in fixedasset-output ratios and by inference in technique became apparent.Were the input-output flow ratios studied on the same basis, similarvariation might well be observed.

In inferring industrywide coefficient matrices from individualplant input structures, the various plant coefficients are viewed asa distribution of which the industrywide coefficients constitute anoutput-weighted mean0 When dealing with the substitution question,it is important to remember that dispersion among plants does not initself imply instability of the industrywide coefficients over time.To understand the stabilities of flow and capital coefficients overtime, it is necessary to examine the pattern in which the distribu-tion of component techniques changes.

It is at this point that the basic theoretical characteristics offlow and capital coefficients must be examined. In the dynamicinput-output model, two aspects of input structure are distinguished:ratios of time rates of input to time rates of output, or flow coeffi-cients, and ratios of stocks of goods to time rates of output, orcapital coefficients. A thorough description of a productive processshould include stock-flow and flow-flow relationships both for so-called current account inputs and for capital inputs. Thus it shouldinclude inventory as well as input flow coefficients and capital re-placement flow as well as fixed capital coefficients Every inputhas both a stock and a flow characteristic. The usual stress on thestock aspect of fixed capital and the flow aspect of current accountinputs rests on the relatively high ratio of stock to flow in theformer, and the low ratio in the latter.

Since stock and flow relationships describe different aspects of agiven technique, in general, both are affected by technical change.Except in special cases, a new technique means both new capitalcoefficients and new flow coefficients. But a change in techniqueand hence a change in the flow coefficients requires investment innew capital goods. The capital cost of changeover coupled withthe durability of old capital provides an important stabilizing ele-ment for flow coefficients. By and large, flow coefficients canonly change in step with the rate of investment in new capital goodsand hence their revision is hampered by the inertia of old capitalstocks. The new technique is introduced only gradually as capacityis expanded or old capital goods are replaced with new capitalgoods. Only when a new technique entails drastic savings in flows

288


that are sufficient to offset the cost of replacing old capital willthis inertia be overcome quickly. The larger the capital stock re-quirements per unit of capacity, the greater the inertia to beovercome.

Capital coefficients themselves are not stabilized by the inertiaof old capital. It may seem paradoxical that capital requirementstend to stabilize input coefficients while capital coefficients them-selves do not partake of the stabilizing influence. This is relatedto the orientation of the model. In each industry, total input flowsare generated by current account requirements of all the producingunits and by additions to stock required for the expansion of ca-pacity. Hence input coefficients should reflect .all technologies inuse, and capital coefficients only the techniques employed in thenewest sector of the industry. Essentially, input coefficients areaverage; capital coefficients are incremental.

To recapitulate: While, at any given time, input coefficients arerepresentative of a wider range of techniques than capital coeffi-cients, they tend to be relatively stable because of their "moving

property. Capital coefficients are more sensitive, de-scribing technical characteristics of the incremental portion of theindustrial capacity picture only. Furthermore capital coefficientsin dynamic input-output models describe prospective rather than"sunk" investment. Hence they are not subject to the technologi-cal inertia which characterizes the great bulk of industrial capacityat any given time. Since previous technological commitments im-pose little restriction on the choice of techniques in the incrementalsector of capacity, technical investment parameters must reflectmany known technical possibilities including newly discoveredtechniques. Thus it is reasonable to expect that variability of tech-niques will be a much more pressing problem in the prediction ofnew capital requirements than it was in dealing with flow coeffi-cients; and it may prove wise to use a technical model of capitalrequirements which differs radically from the fixed coefficientmatrix used for flows.

In an immediate sense, the variety of alternative productivemethods makes it difficult to derive unique capital coefficientswhich correctly predict actual requirements per unit of capacity ina given expansion. The problem of variability appears most com-monly in one of the following four forms: problems of choice amongalternative processes, among variants within major processes,among varieties and grades of a given commodity produced, and

289

CAJ'ITAL COEFFICIENTS AS PARAMETERS

choice among expansions in the form of new plants, balanced addi-tions, and the various kinds of unbalanced additions. At least thefirst three forms of variation are closely interrelated. The dis-tinction between interprocess and intraprocess variability is basedon engineering definitions of process. Economically the distinctioncan be reduced to a matter of industrial classification. The samecan be said of the distinction between product and product grade.Frequently differences among or within processes are correlatedwith differences in product grade, and the choice among processalternatives is conditioned by grade requirements rather than bycost economies in a particular industry. For example the choice be-tween woolen and worsted yarn systems makes a marked differencein the types and costs of equipment required per pound or per dollarvalue of output. Value of cotton spinning and weaving equipmentper pound will vary by five or more times, depending on the qualityof output. Variation per dollar of output is smaller but still ap-preciable since machinery, raw material, and labor costs constitutedifferent proportions of total product value for different grades. Thechoice between electric furnace and open hearth steelmaking isconditioned primarily by grade rather than immediate cost con-siderations. Investment in electric generating capacity per unitconsumed depends on the time distribution of loads over the day0

Variability of Capital Requirements in the Chemical Industries

These are just a few random instances of the relation betweencapital requirements and product grade. The interrelationshipsamong different types of variability are illustrated somewhat moresystematically by the results of, the Harvard Economic ResearchProject studies of capital requirements in the chemical industries.Of roughly seventy chemical products for which records of WorldWar II expansion of capacity in the form of new plants or balancedadditions were available, ten were represented by more than oneprocess, separately identifiable in engineering terms. This doesnot imply, of course, that there were technological alternatives foronly ten products, but rather that the choice among alternativeswas not unique for these ten products. In the case of at least fourof these ten, synthetic rubber, carbon black, ethyl alcohol, andoxygen, the choice of process is known to be determined primarilyby the qualitative characteristics desired for the product.

In a few cases, material was available for comparing total equip.ment costs per unit of capacity within groups oi plants producing

290


similar products by nominally identical processes,1 The range ofvariation within three processes is shown in Tables 1, 2, and 3.

1 shows total equipment costs per unit of capacity for fournew plants producing synthetic rubber, "Buna S."

TABLE 1

Equipment Costs per Unit of Capacity, Synthetic Rubber, Buna S'

Plant Approximate Size IndexEquipment Cost per Ton

per Year

A,

100 $60B •. 100 93C 200 65D 250 55

Equipment cost per ton per year in these plants varied from $55to $93. One might expect part of this variation to be accounted forby differences in the sizes of the plants in question. For thisreason an index of plant size (capacity) was constructed with eachplant's capacity expressed as a percentage of that of the smallestplant. for plants B, C, and D unit cost varied inversely withplant size, the cost per unit of A, the smallest plant, was almostas low as that of D, the largest.

Total costs (equipment plus construction) per unit of capacity forten new gas furnace process carbon black plants are presented inTable 2, together with their respective size indexes.2 Obviouslythe range in unit equipment costs of roughly 400 per cent cannot beexplained entirely in terms of differences in plant size. Even amongplants of identical capacity, equipment costs vary by more than 100per cent. Some increase in homogeneity was attained by singling

'These are all World War II expansions covered by applications forcertificates of necessity, which are requests for accelerated amortizationprivileges on new facilities for federal tax purposes. They usually con-tain detailed descriptions of the costs of the facilities in question.

black is a fine bulky carbon obtained as soot by the directimpingement of a burning flame on a metal surface. Nowadays it is usedprimarily, in the manufacture of natural and synthetic rubber. Differentgrades of black, varying in size and surface area of carbon particles,produce different properties in rubber.

There are two major processes for producing carbon black: the channeland the furnace process. Channel and furnace blacks differ in theirproperties. Only the furnace process is discussed in the present paper.In this process, differences in grade are achieved by varying the time rateat which fuel is fed to the furnace and by the degree of fuel combustion.

A more elaborate analysis of investment in carbon black during thepostwar period is discussed below.

291


TABLE 2

Equipment Costs per Unit of Capacity, Carbon Black Plants,Gas Furnace Process

Plant Approximate Size IndexEquipment Cost per

Pound per Year

E 100 80.032F 100 0.084C 200 0.053H 250 0.030aI 325 0.028J 325 0033aK 550 0.053aL 550 0.020aM 600 o.022aN 650 0052a

producing SRF (semi-reinforcing furnace) grade black—one ofthe standard grades.

TABLE 3

Equipment Costs per Unit of Capacity, Sulfuric Acid andOleum, Contact Process

Plant Approximate Size IndexEquipment Cost per Ton

per Year

0 100 812P 100 6Q 175 9R 200 9S 300 7T 400 8

out a group of plants producing a particular grade, although thegrade information furnished on World War II certificates of necessitywas not very reliable. There was also reason to believe that thespecial influences of wartime conditions affected the ratios.

Equipment cost per unit of capacity for plants making sulfuricacid and oleuni from sulfur by the contact process behaved some-what more systematically, although even in this case not all thevariability is easily explained.

In Table 3, two plants, Q and R, are balanced additions3 ratherthan new plants. Althohgh 0 and P are approximately equal in size,the unit equipment cost of P was only half that of 0, and was lowerthan that of any of the larger plants.

3Balanced additions are defined as comprising substantially identicalequipment but possibly different construction items than new plants.

292


Variability of Capital Requirements with Grade ofProduct and Scale of Plant

To appraise the relative importance of the various factors con-tributing to inhraprocess variability in capital requirements, a moredetailed study of capital requirements per unit of capacity in carbonblack production was undertaken. For this study, a group of oilfurnace plants built during the period 1950—1951 was chosen sincethese were described in greater detail on certificates of necessitythan most of the World War II expansions. By this time most of thecarbon black expansions were oil furnace process. The gas furnaceprocess, most common among World War II expansions, was onlyscantily represented, and there was only one expansion in channelblack.

The procedure adopted was as follows: First, the array of capital-to-capacity ratios for all plants in the sample was examined (Table4). The coefficients are presented in terms of total cost broken

TABLE 4

Capital Coefficients for Carbon Black, Based on New Plant CurrentCertificates, Oil Furnace Process

Plant FirmaGrade ofProductb

Capacityper Year

(miii. lbs.)

Investment RequiredPound per Year

per

Construction EquipmentcTotalCost

1 A FEF HAF 44 S0.006 $0.029 $O.0352 A FEF HAF 50 0.005 0.038 0.0433 B HAF 24 0.022 0.057 0.0794 C5d D

HAFIIAF

3235

0.015 0.0740.021 0.050

0.0880.071

6 E HAF 36 0.014 0.037 0.0517 C HAF 40 0.009 0.048 0.0578 B HAF (or SAF) 50 0.014 0.041 0.0559 F HAF 72 0.010 0.036 0.046

be G . SAF 15 0.036 0.124 0.160

aActual company names have been concealed, but plants of the samefirm are designated by the same letters.

There are different grades of oil furnace black: FEF—fast extrudingfurnace black—has large particle size. HAF—high abrasion furnaceblack—has medium particle size. SAF.—.super abrasion furnace black—

small particle size.equipment cost includes engineering service cost.

Coefficients for this plant are based on actual costs.eThIS plant was actually a completely new entire producing unit for a

new grade of product at an already existing plant.Note: Capital coefficients are based on estimated costs found in current

certificates of necessity granted for carbon black expansion, 1950—1952.Component parts may not equal totals because of errors of rounding.

293


down into equipment and construction costs. The standard devi-ation of each set (total, equipment, and construction) of coefficientswas computed as a measure of variability.4

An attempt was then made to reduce variability by eliminatingthe effect of differences in grade. This was done in each of twoways: first by limiting the sample to plants producing a singlegrade (HAF blacks), and second by converting coefficients for FEFand SAF blacks to an HAF basis using typical ratios of capital re-quirements for these grades supplied by engineers.5 The effect ofincreasing the homogeneity of the sample can be observed inTable 5.

TABLE 5

Average Total Coefficients for New Oil Furnace Carbon Black Plants,Showing Effect of Grade on Variability

Mean Standard CoefficientCoefficient Deviation of Variation(dollars per

(1)pound per year)

(2)(2) ÷ (1)

(3)

All plants, unadjustedfor grade:a

Total cost 30.069 30.034 0.49Construction 0.015 0.009 0.60Equipment 0.053 0.027 0.51

HAF plants only:bTotal cost 0.064 0.015 0.23

Construction 0.015 0.005 0.33Equipment 0.049 0.012 0.24

All plants, adjusted toHAF grade:C

Total cost 0.063 0.015 0.24Construction 0.014 0.006 0.43Equipment 0.049 0.013 0.27

aBased on 10 plants: 2 combined FEF and HAF plants, 7 HAF plants,1 SbAF plant.

Based on 7 HAF plants.CBased on 10 plants, all adjusted to HAF grade.

Both adjustments for grade differences reduced interplant varia-tion in the ratio of total capital to capacity by 51 per cent, vari-ability in equipment cost to capacity by a little more than that

'See Table 5.5The author wishes to thank Alan F. Beede and C. A. Stokes of Godfrey

L. Cabot, Inc. for their cooperation in this matter.

294


amount, and variability in construction cost to capacity by some-what less—about 45 and 28 per cent for the elimination of non-HAFplants and the adjustment to HAF grade respectively.

These observed results are consistent with theoretical expecta-tions. That grade accounts for a lower proportion of variability inconstruction than in equipment costs is to be expected since spe-cific site conditions explain a relatively large proportion of vari-ability in this category.6 The findings confirm the general thesisthat differences in product grade are important in explaining vari-ability of capital requirements.

The next stage in the carbon black study was the investigationof the contribution of scale to coefficient variation. For this pur-pose least squares lines of regression of the ratio of total capitalto capacity on plant size were computed for HAF plants, and alsofor all plants, adjusted to an IJAF basis. In each case the standarderror of estimate about the line was computed and compared to therespective standard deviation. The difference between the standarderror of estimate and the standard deviation, divided by the standarddeviation, measures the proportion of variability (after the elimina-tion of grade differences) which is explained by the scale factor.In both cases the proportion of remaining variability explained byscale was (0.015 — 0.O10)/0.015 or 33 per cent.

Summary

In summary then it was possible by means of adjustment for inter-plant differences in product quality and scale to reduce the standarddeviation of the ratios of total capital to capacity from 0.034 toabout 0.010, or from about 49 per cent to about 16 per cent.

The evidence just presented is fragmentary in relation to thetotal economic picture. It would be premature to crystallize theimpressions of interplant variability of capital requirements basedon experience with this single product. Provided that this is bornein mind, it is useful to consider what more general findings of thissort would imply for the prediction of expenditures on capital goodsin the dynamic input-output model.

First of all the wide range of interplant variation suggests that itis not safe to infer capital coefficients from expenditure informationon one or two expansions without considerable supplementary tech-nical information and an over-all knowledge of the industry's pecul-

'See "Capital Coefficients for the Chemical Industries," Harvard Eco-nomic Research Project, hectoçaphed, 1952.

295


iar characteristics.7 Second, the fact that a sizable proportion ofvariability can be traced to identifiable factors, such as grade andplant size, suggests that the problem may be brought under controlthrough elaboration of the model to take explicit account of theseitems. Thus it would seem feasible to express capital requirementsin each industry as functions of the sizes of units to be built andsome index of product grade. Many other studies of capital-to-capacity relationships have shown that it is feasible to derive pro-duction functions in terms of more than one product dimension.6

The problem for prediction is not so much the difficulty in elabo-rating the capital-to-capacity relationship itself. The more elabo-rate relationship is generally a by-product of the derivation of thecoefficients in any case. The more difficult problem is that ofpredicting what the actual sizes of plants to be built and the dis-tribution of product grades will be.

Perhaps surprisingly, the former, i.e. the prediction of plant size,is apt to be considerably more difficult than the latter. Economictheory of the firm tells us that, given the demand for the productand the production function, the optimum plant size is determined,provided of course that production costs vary systematically withplant size. In fact, however, plants of different sizes continue tobe built simultaneously in a given industry despite strong apparenteconomies (or disecononiies) of scale. This is because, within abroad range dictated by over-all economic considerations, size ofplant is influenced strongly by specific site conditions and otherlocal factors. Information about these factors is generally very de-tailed and too cumbersome to encompass in a general interindustrymodel.

The best that can be done with the scale problem at this stageis to base capital coefficients on an estimate of average size ofplant to be constructed in any given expansion. This may involvesome bias where capital coefficients are nonlinear functions ofscale. However, it will guard against the more serious danger ofinferring coefficients from the observation of abnormally large or

'With respect to variability, the use of accounting data in the derivationof capital coefficients may have some advantage provided that the firmsare large and technological change is not great. At least they providebroader coverage than a single expansion; but of course there are otherdrawbacks.

for example, Wassily W. Leontief, et al. Studies in the Structureof the American Economy, Oxford, 1953, Chaps. 7, 8, 10, and 11, and"Preliminary Approximation of Output Capacity of U.S. Petroleum Re-fineries," hectographed, Rice Institute, Dept. of Economics, 1952.

296


small plants. A further contribution to the solution of this problemmay be forthcoming as an outcome of research on the problem ofresources in the interindustry context currently under way.

The grade problem is somewhat more hopeful since the distribu-tion of grades to be produced is often closely related to the dis-tribution of industries consuming the product. In carbon black, thegrade requirements depend primarily on the amounts of natural andsynthetic rubber produced and on the proportions of the variouskinds of tires to be made.9 Exploratory work indicated the feasi-bility of relating load factors in electric public utilities to the in-dustrial distribution oi demand for power.1° Similarly it should bepossible to estimate grade requirements for such industries assteel, petroleum, and nonferrous metals from a knowledge of theircustomer industries.

The method suggested is essentially one of introducing addi-tional product dimensions jn the first round, i.e. in the relationshipof an industry's capital requirements to the distribution of demandby its immediate customers. In some cases where the grades ofconsuming industries' outputs have important effects on capital re-quirements in the producing industry, it should be possible to ex-tend the grade interrelationships to the second round or further.This is equivalent to the suggestion that greater stability be soughtthrough a finer industrial classification, a classification in which,for example, FEF carbon black comes from a different industry thanHAF black, and "Buna S" from, a different than "Thio-kol."1 Use of grade parameters as an alternative to disaggregationis a device like the process service industry.ia The choice of onemethod of elaboration instead of another is a matter of expediency.Use of grade parameters may be helpful in maintaining processidentity for the study of technological change.

The estimation of grade or quality requirements, or disaggrega-tion, in industries selling directly to consumers is likely to be mostdifficult. To include final demand industries in such a schemewould require a more detailed description of the bill of goods.

9Satisfactory estimates of requirements by grade were made on thisbasis during World War II. These are described in the unpublished rec-ords of the War Production Board.

'°See Judith Balderston, "Notes on Alternative Methods of PredictingCapacities of Electric Public Utilities," Harvard Economic ResearchProject, hectographed, 1952.

11These are two different types of synthetic rubber.'2For a discussion of wocess service industries, see Mathilda Holzman,

"Problems of Classification and Aggregation," Studies in the Structure ofthe American Economy.

297


There is no reason why the introduction of grade parameters, or thedisaggregation process, should not be approached piecemeal as thenecessary relationships are developed industry by industry. Thisis an area in which it will be possible to integrate special insightsin particular industries into the general economic picture.

The moral implicit in the foregoing discussion is that estimatesof such complex dynamic elements as fixed capital accumulationare not cheap. Furthermore it is interesting to note that the intro-duction of price substitution or, on a general equilibrium level,optimum programming does not solve the sort of operational problemwhich has been stressed thus far. Not all variability can be re-duced to price substitution within a given industry. To the extentthat choices among processes, as well as among variants of thesame process, are conditioned by special characteristics of re-source or product specifications, the improvement of estimates canbest be accomplished through refinement of classification. Intro-duction of grade parameters would require not only the elaborationof process descriptions but also the description of the speciallimiting relationships between process and output characteristics.Thus, without prejudging the importance of price substitution, sup-plementary technical relationships or equivalent disaggregationshould be introduced within the fixed coefficient framework.

Capital Requirements for Balanced and Unbalanced Expansions

Before speculating further on methods for dealing with variabilityin capital-to-capacity relationships, it might be well to discuss theother forms of variability noted, namely the balance problem and,finally, process substitution. Three major types of expansion canbe distinguished: new plants, balanced additions, and unbalancedadditions. Balanced additions are defined as expansions at thesite of existing capacity which require essentially the same amount(and kinds) of equipment expenditures as new plants but not neces-sarily a full complement of construction expenditures. Unbalancedexpansions add less than a full complement of both equipment andconstruction. Hence one would expect unbalanced expansions to becheaper than balanced and balanced cheaper than new plants, perunit of capacity. Operationally it is sometimes difficult to dis-tinguish between unbalanced expansions of capacity and conversionsto new products or grades because of the necessarily rudimentarydescriptions of product at this stage in the development of primarydata. full information, it would be. reasonable to deal withconversions as a special form of unbalanced expansion.

298

CAPITAL COEFFICLENTS AS PARAMETERS

If there were a clear ranking of new plants and balanced and un-balanced additions according to cost per unit of expansion, onewould expect that the opportunities for expansions of each typewould be filled successively in ascending order of unit cost ofproduct for each type. As in Ricardian rent theory, all the possi-bilities of unbalanced expansions would be absorbed first, thenthose of balanced expansions, and finally, if necessary, those ofnew plants. If the options for each type were marketable, one wouldexpect them to be valued at differential cost of expansion. How-ever, study of the problem reveals that decisions as to type of ex-pansion are complicated by dynamic expectational considerationswhich seem to belie conclusions based purely on short-run costconsiderations.

Despite this last complication, it is essential to the understand-ing of this form of capital cost variability to consider the niecha-nisms whereby opportunities for unbalanced expansions are created.The possibility of expanding capacity with less than a full com-plement of capital items implies a situation of initial imbalance inexisting plants. Such imbalance is created in three ways: (1) pur-posive creation of initial imbalance with an eye toward futuregrowth, (2) partial changeover for cost reduction, and (3) processconversions.

Imbalance Because of Expectations of Future Growth

The rationale for the creation of initial imbalance is to be foundin definite or indefinite expectations of future expansion. In thelight of such anticipations it pays to build in extra capacity inthose items where there are striking economies of scale or whereinitial installation of excess capacity is cheap relative to the costof adding to these facilities in the future. If future expansion iscontemplated, it is cheaper to build in extra plumbing and wiringduring initial construction than to add to them at a later date. Whenthere are large economies of scale in process or storage units, it iswise to install larger units in anticipation of future expansionrather than to install additional small ones at some future date.

The possibility of taking advantage of such economies of scalein equipment is limited, however, by efficiency losses in operatingcertain types of equipment units at rates substantially below ca-pacity. For this reason most of the initially designed imbalance islimited to excess construction items, such as land improvementsand utilities rather than to equipment, while excess equipment is

299


TABLE 6

Percentage Distribution of Equipment Expenditure for Balancedand Unbalanced Additions, by Major Industries of Origin

Plants Handling Liquidsand Solids Plants Handling Liquids

Mean forBalanced

Mean forUnbalanced

Mean for Mean forBalanced Unbalanced

Additions Additions Additions Additions. (30 plants) (31 plants) (14 plants) (13 plants)

I'rocesa equipment:SIC 3443 9 12 12 12SIC 3559 27 37 26 39S1C3567 3 3 2S1C3569 3 3 5 8SIC 3585 5 5 5

Total processequipment 49 60 51 61

Piping:SIC 3591 and 3592 14 8 21 8

Electrical:S1C361 7 4 6 9

equipment:S1C3561 5 9 9 12S1C3563 2 7 1 1

SIC 3564 2 2 ••.S1C3821 3 1 4 1

Total auxiliaryequipment 12 19 14 14

Other 19 9 10 7

indicates less than 0.5.Note: Percentages may not total 100 because of rounding.Source: Averages for balanced additions were oltained from Capital Co-

efficients for the Chemical Industries, Harvard University Economic Re-search Project, Appendix VI, Table IV.

generally confined to storage and process piping capacity.'3 Thisis borne out by a study of the distribution of capital expendituresfor expansions of various degrees of balance in the chemical in-dustries. The cost patterns of the expansions reflect, indirectly,

'Process piping is an engineering term which refers to valves, pipes,and fittings for the network of piping which serves the various chemicalprocessing equipment units directly. Process piping is to be distinguishedfrom plumbing and sewerage lines, which connect the plant as a whole tooutside supply and disposal facilities. The latter are generally classedwith construction rather than equipment. In practice the distinctionbetween process piping and other piping is often difficult to make.

300


the initial state of balance of the plants' capacities. However, theinitial condition of a plant relative to given expansion may bethe cumulative result of many successive additions to a new plant,and provisions for still further anticipated growth may be built intoan addition to capacity as well as into a new plant.

Table 6 compares the percentage distribution, by SIC industry oforigin and by broad functional groupings, of equipment expendituresfor balanced and unbalanced expansions. Since balanced expan-sions are defined in terms of the similarity of their equipment dis-tributions to those of new plants, new plants and balanced additionsare lumped together in this comparison.14 Expansions were groupedby type of process, but it was not possible to maintain identicalproduct mixes for the averages being compared.

Table 6 reveals that expenditure on process equipment is asmaller proportion of total equipment expenditure in balanced thanin unbalanced expansions, while relative expenditures on piping arehigher in the former. This is in accord with theoretical expecta-tions outlined above. Expectations of higher expenditures on elec-trical installations in balanced additions are not borne out un-equivocally. This may be due in part to difficulties in classifica-tion of expenditures by industry of origin It is almost impossibleto distinguish operationally between expenditures for electricalwork which belong with equipment and those which are classifiedunder construction. The above discussion of the advantage of over-building in electrical categories would of course cover the total ofequipment and construction expenditures of these items.

Table 7 gives a comparison of various types of construction costsfor new plants, balanced additions, and unbalanced additions. Thisshows that new plants involve relatively more construction expensethan balanced additions,15 and balanced additions relatively morethan unbalanced additions. Within the construction cost category,new plants tend to cost more than balanced additions, and balancedadditions more than unbalanced additions, in nonbuilding as com-pared with building construction items. The subdivision of non-building construction into utilities and land improvement yields

'4A detailed description of this study of balanced and unbalanced addi-tions is on file at theHarvard Economic Research Project.

"There is danger of circularity in comparing construction expendituresin new plants and balanced additions since they are defined as identicalwith respect to equipment but not to construction expenditures. Hence onemay be tempted to place a plant in one category rather than another on thebasis of its construction outlays. This pitfall was avoided by supple-mentary checks on initial capacity at the site.

301

TA

BL

E 7

Med

ian

and

Mea

n R

atio

s of

Con

stru

ctio

n an

d E

quip

men

t Exp

endi

ture

s to

Tot

al C

ost

in N

ew P

lant

s, B

alan

ced

and

Unb

alan

ced

Add

ition

s

Med

ian

Exp

end

it ur

e R

atio

saM

ean

Exp

endi

ture

Rat

iosa

New

Bal

ance

d(I

nbal

.N

ewB

alan

ced

Unb

al.

Plan

tsA

dditi

ons

Add

ition

sPl

ants

Add

ition

sA

dditi

ons

Rat

io to

tota

l pla

nt c

ost o

f ex

pend

iture

for

:E

quip

men

t0.

720.

790.

970.

690.

770.

84C

onst

ruct

ion

0.28

0.21

0.03

0.31

0.23

0.16

Bui

ldin

g co

nstr

uctio

nN

onbu

ildin

g co

nstr

uctio

n0.

170.

1!0.

150.

060 0

0.20

0.11

0.16

0.07

0.13

0.03

Rat

io to

tota

l con

stru

ctio

n co

st o

f ex

pend

iture

for

:B

uild

ing

cons

truc

tion

Non

huild

ing

cons

truc

tion

Rat

io to

tota

l non

build

ing

cons

truc

tion

cost

of

expe

nditu

re f

or:

Lan

d im

prov

emen

tU

tiliti

esM

isce

llane

ous

0.61

0.39

0.19

0.71

0.10

0.73

0.32

0.01

0.99 0

b1.

00 0

0.19

c

0

0.62

0.38

0.03

0.67

0.33

0.lO

e

0.89

:0.

01

0.22

O.4

1c0.

59c

aAJl

rat

ios

excl

ude

"Ser

vice

."bB

ased

on tw

enty

.sev

en p

lant

s.B

ased

on

elev

en p

lant

s.B

ased

an

fort

y-fi

ve p

lant

s.eB

ased

on

twen

ty-n

ine

plan

ts.

Not

e: G

roup

s of

med

ian

ratio

s m

ay n

ot to

tal 1

.00

due

to th

e sm

all n

umbe

r of

ent

ries

.So

urce

: Med

ian

ratio

s fo

r ne

w p

lant

s an

d ba

lanc

ed a

dditi

ons

wer

e ob

tain

ed f

rom

Cap

ital C

oeff

icie

nts

for

the

Che

mic

alIn

-du

stry

, Har

vard

Eco

nom

ic R

esea

rch

Proj

ect,

1952

, App

endi

x V

I, T

able

XI.


ratios contrary to expectation; expenditures on land improvement inunbalanced expansions and those on utilities in balanced additionsare inexplicably high. This may possibly be a result of poor dataand classification difficulties in this particular cost area, whichnotably lacked descriptive detail.

There may be some objection to the use of the terms balancedand unbalanced expansions in this context. If the general hy..pothesis concerning initial imbalance is correct, then all expan-sions, properly speaking, will be unbalanced, some in one andothers in another direction. A new term is needed to describe thesedifferent kinds of expansion. The evidence just presented was, byand large, consistent with the thesis concerning initial imbalance,but explicit standards by which to judge the balance of particularplants are extremely difficult to find. If truly balanced plants arerarely built, absence of blueprints for them is quite understandable.

Unbalanced Expansion Induced by Technological Changeand Process Conversion

Technological change is a second reason for unbalanced expan-sions. Two aspects of the relationship between technologicalchange and unbalanced expansions should be distinguished. First,technological changes are often introduced through unbalanced ad-ditions to existing plant, additions of particular items which changeproductive methods, or replacements of parts of the existing capitalstock. Second, the innovation process creates imbalance by in-creasing productivity in certain areas of the productive process butnot in others. Thus a particular plant may find itself with bottle-necks which must be eliminated before full advantage can be takenof the innovation, or which can be eliminated, should additionalcapacity be desired.

The importance of innovation in generating unbalanced expan-sions is illustrated by a detailed tabulation of unbalanced expan-sions in the carbon black industry during the Korean emergency(1950—1951) and during World War II. The sample covered was notchosen selectively, but included all unbalanced expansions in gasand oil furnace black for which certificates of necessity wereavailable (see Table 8).

The itemization of equipment purchases and changeovers gives aclue to the characters of the individual expansions. Of the elevenexpansions described, all but three include direct innovational ex-penditure: four plants introduced secondary collection facilities, afeature that has become workable only quite recently. Two of the

303

1A

Cur

rent

1950

2A

Cur

rent

1950

3D

Cur

rent

1951

Con

vers

ion

of f

urna

ce, a

dditi

onof

col

lect

ion

and

pelle

tizin

geq

uipm

ent

Add

ition

of

colle

ctio

n an

d pe

l-le

tizin

g eq

uipm

ent s

ubse

quen

tto

con

vers

ion

of f

urna

ceA

dditi

on o

f dr

um m

agne

ts, f

uel

lines

, con

veyo

rs, s

cree

ns, m

ikro

-pu

lver

izer

s, c

onve

rsio

n of

rea

ctor

s,oi

l sto

rage

. fac

ilitie

s, c

ar s

potte

rs.

load

ing

syst

em

B. R

ecov

ery

Syst

ems

4B

Cur

rent

1951

5C

Cur

rent

1952

6D

Cur

rent

1952

7C

Wor

ld W

ar11

—19

46

Add

ition

of

bag

filte

rs a

ndpe

lletiz

ers

Add

ition

of

bag

filte

rs a

ndbe

ad m

achi

nes

Smok

e ab

atem

ent f

acili

ties

and

pelle

tizer

sA

dditi

on o

f m

ultic

yclo

nes,

scr

ewco

nvey

ors,

and

insu

latio

n

FEF

1.50

BA

F-FE

F2.

50

HA

F-FE

F13

.00

BM

F1.

80

100.

158

0.15

8

20.

004

0.18

80.

192

70.

002

0.07

00.

072

100.

073

0.07

3

(con

tinue

d on

nex

t pag

e)

CT

AB

LE

8

Cha

ract

eris

tics

and

Cos

ts o

f U

nbal

ance

d E

xpan

sion

s fo

r C

arbo

n B

lack

, Oil

and

Gas

Fur

nace

Proc

esse

s

Plan

tN

umbe

rFi

rma

Peri

od a

ndY

ear

ofC

onst

ruct

ion

Incr

ease

in C

apac

ityC

osts

Mill

ions

Per

Cen

tG

rade

of

of P

ound

s of

Ini

tial

Nat

ure

of E

xpan

sion

Bla

ck1'

Per

Yea

rC

apac

ity

Con

-E

quip

-T

otal

stru

ctio

nm

ent

Cos

t(p

er p

ound

of

capa

city

)

•A

. Con

vers

ion

from

Gas

to O

il Fu

rnac

e B

lack

C,

'O C,

"1 C, z cn

HA

F-FE

F32

.00

*0.0

01*0

.004

*0.0

05

HA

F-FE

F57

.00

...0.

013

0.01

3t,j z U

,H

AY

10.2

05

0.02

70.

027

.

Pla

ntN

umbe

r Fi

rma

Peri

od a

ndY

ear

ofC

onst

ruct

ion

Gra

de o

fN

atur

e of

Exp

ansi

onB

lack

b

Incr

ease

in

Cap

acity

Cos

ts

Mill

ions

of P

ound

sPe

r Y

ear

Per

Cen

tof

Ini

tial

Cap

acity

Con

-E

quip

-T

otal

stru

ctio

nm

eat

Cos

t(p

er p

ound

of

capa

city

)

C. R

emov

al o

f B

ottle

neck

8D

Cur

rent

1952

Add

ition

of

com

plet

e fu

rnac

e an

dpe

lletiz

ing

units

with

aux

iliar

ies

FEF

23.6

025

0.00

30.

024

0.02

7

D. M

isce

llane

ous

Equ

ipm

ent

8B

Cur

rent

1951

Add

ition

of

15 h

oppe

r ca

rs

10 11

A C

Wor

ld W

ar11

—19

45W

orld

War

11—

1945

Add

ition

of

pelle

t mill

s w

ithdr

yers

, scr

eens

, and

aux

iliar

ies

SRF

Add

ition

of

pelle

tizer

s, w

ithco

nvey

ors,

agi

tato

rs, m

otor

s,an

d fo

unda

tions

13.1

6C

33•

...0.

012

0.01

2

apla

nts

of th

e sa

me

firm

are

des

igna

ted

by th

e sa

me

lette

r.bD

iffe

rent

grad

es o

f fu

rnac

e bl

ack

are

prod

uced

fro

m d

iffe

rent

raw

mat

eria

ls. T

he f

urna

ce ix

oces

s us

ing

ftat

ural

gas

as

a ra

wm

ater

ial p

rodu

ces

grad

es H

MF

(hig

h m

odul

us f

urna

ce)

and

SRF

(sem

irei

nfor

cing

fur

nace

bla

ck).

The

se g

rade

s w

ere

prod

uced

inW

orld

War

II

expa

nsio

ns. T

he f

urna

ce p

roce

ss u

sing

oil

as a

raw

mat

eria

l pro

duce

s H

AF

(hig

h ab

rasi

on f

urna

ce)

and

FEF

(fas

tex

trud

ing

furn

ace)

.cN

o ca

paci

ty in

crea

se w

as g

iven

for

this

pla

nt. T

he a

dditi

on o

f th

e pe

lletiz

ers,

con

veyo

rs, e

tc. d

id n

ot in

crea

se c

apac

itybu

t mer

ely

mad

e th

e pr

oduc

t in

a m

ore

usef

ul f

orm

.in

dica

tes

less

than

0.0

005.

TA

BL

E 8

(co

ntin

ued)

Co 0 Cn

'O r 0 t-j

'TI

[TI

'-I I


World War II expansions introduced pelletizing equipment, pel-letizing being a type of product finishing which was new at thetime. Three were conversions from one type of fuel to another.16The remaining two expansions, 8 and 9, constitute some form ofbottleneck removal. The bottlenecks may have been created eitherby earlier innovational activity or by some other source of initialimbalance. One cannot fail to be impressed by the degree to whichtechnological change colors the unbalanced expansion picture inthis industry.

A comparison of the capital Cost per unit of capacity for theseunbalanced expansions with the capital-to-capacity ratios for newplants in carbon black'7 yields one conclusion which may be sur-prising: the coefficients for secondary recovery systems showgreater cost per unit of capacity than the new plant coefficients.Despite their initial expense, secondary recovery systems are eco-nomic because they increase product with no additional raw ma-terial or labor cost.

Like the types of innovation already described, conversions in-crease capacity without requiring a full complement of new capitalgoods and hence constitute unbalanced expansions. Conversionsdo not necessarily imply change to a newly discovered process,however. The chief feature distinguishing conversions from othertypes of unbalanced expansion is that other potentially effectivecapacity is eliminated by them. The introduction of interindustryor intraindustry conversions into the dynamic input-output modelwould modify the pattern of irreversibility in investment presentlyenvisaged. Conversions constitute another special form of sub-stitution. To estimate the economic advantage of conversion, onemust know not only the tec1inical properties of the processes sepa-rately but also the cost of interchanging them. When conversionopportunities are taken into account, capital coefficients of indi-vidual industries become dependent on the amount of excess Ca-pacity in other industries.

Problems in Predicting the Volumes of Balancedand Unbalanced Expansions

There is as yet no over-all estimate of the relative importance ofunbalanced expansions as compared with new plants in the capitalpicture. There is every indication, however, that unbalanced ex-pansions account for a sizable proportion of capital formation. Of a

"This is a form of change.17See Tables 2 and 4.

306


list of some nine hundred 'World II expansions in the chemicalindustries, at least half the number of expansions were unbalanced.Since the capital cost of unbalanced expansions is generally quitedifferent from that of new plants, this problem contributes an im-portant element to variability in capital requirements.

It has been suggested18 that this particular type of variabilitycan be overlooked safely in predicting Costs of expansion for anindustry as a whole since imbalances of individual expansions indifferent directions tend to dovetail, and such dovetailing tends toyield a balanced picture in the aggregate. Reliance on this tendencyinvolves three pitfalls: (1) there is no guarantee that the varioustypes of imbalance will dovetail over any given time span, (2) aswas explained above, there is a bias involved in using new plantcoefficients to represent truly balanced expansions, and (3) insofaras unbalanced expansions are generated in the technological changeprocess, there will be no tendency for them to balance out, evenover the long run.

As in the case of the grade problem, the problem of unbalancedexpansion might alternatively be handled through a revision of in-dustrial classification. In dealing with the balance problem, how-ever, a form of vertical rather than horizontal di3aggregation iswarranted. Instead of dealing with carbon black production—or theproduction of a particular grade of carbon black—as a single in-dustry, one might subdivide it into a combustion industry, a collec-tion industry, a pelletizing iiidustr?-.—or even into a "piping serv-ices to carbon black production" industry, "building services tocarbon black" industry, etc. Such a procedure converts the un-balanced expansion problem from a problem of variability of capitalrequirements per unit addition to capacity to a problem of explain-ing excess capacity in certain industries.

This device is useful in emphasizing the over-all economic paral-lel between interindustrial and intraindustrial imbalance and therelation between imbalance and excess capacity. However, thereare additional substantive problems in explaining intraindustrialexcess capacity which cannot be eliminated solely by reclassifica-tion. Interindustrial excess capacity can be explained partly interms of changes in the bill of goods which alter the relative de-mands for the products of various industries. On the other hand

leSee "The Economic. Impact of the Planned Capacity Expansion i;Primary Aluminum, Alumina, and Copper Milling," Bureau of Mines, hecto-.graphed, 1952.

'9These are all stages in carbon black production.

- 307


changes in the bill of goods will effect the same change in capacityrequirements for all capital goods required in the production of aparticular product. A fall in carbon black requirements cuts equallythe need for combustion, precipitation collection, and, all otherservices contributing to carbon black output. Whether the problemof plant imbalance is treated directly as variability of capital 'co-efficients or through vertical disaggregation, the same kinds ofmodifications in the theory of capital purchase, i.e. gearing pur-chases to future expansion plans rather than a simple accelerator,are required. The treatment of conversions also remains substanti-ally the same in either case. However, provided that vertical dis-aggregation is effected along engineering process lines, the ap.proach through disaggregation will facilitate the study of techno-logical change in relation to industrial balance. This considerationis important in the choice of industrial classification schema ingeneral as well as in relation to the imbalance picture.

The interdependence of problems of variability and industrialclassification cannot be overstressed, both in relation to the qualityproblem and to proceés balance. In each case disaggregation wasproposed as a device for narrowing a range of indeterminacy ininput-output relationships. In disaggre gating, however, one shouldnot overlook the possibility that a higher level of accuracy in onedirection can be achieved at the expense of greater indeterminacyin another. With a finer industrial classification, one can expectgreater precision in the prediction of some factor requirements, but,in other directions, more possibilities of substitution among similarproducts formerly lumped together. This does not imply that aneconomic interdependence system is neutral with respect to alternativeclassifications—that any given change adds a problem here andsubtracts one there. On the contrary this discussion is intended tostress the importance as well as the delicacy of the choice of anindustrial classification.

Variability of Capital Requirements and Process SubstitutionThis brings us to the fourth major aspect of the variability prob-

lem, process substitution in the orthodox sense. The discussionthus far has pointed up special problems of variability of capitalrequirements which will not be solved simply by describing a setof alternative processes in place of a single process. These havebeen problems which do not arise from the specific limitations of afixed coefficient model. By and large they are problems on anoperational level and would remain a plague in almost any generaldynamic interdependence scheme.

308


However, as was noted early in this paper, the choice amongternative processes is more serious in predicting capital require-nients than in predicting inputs on current account. The bulk ofinterprocess switching requires new investment associated with ex-pansion or changeover, and capital coefficients or some counterpartof capital coefficients must describe this element of change incapital stocks. Even with respect to capital coefficients, however,there are Some elements in the general equilibrium context whichtend to stabilize the relative advantages of alternative processesin the short run. One can expect a certain amount of stability inthe structure of relative factor prices conditioned by the inertia ofcapital structure and thus of input-output relationships in other in-dustries.2° While the inertia of a given capital structure does notin itself stabilize capital coefficients in its own industry, it in-directly stabilizes capital requirements in other industries by im-parting a steadying influence to input structures and hence toprices. Relative price stability, in turn, steadies the relative ad-vantages of a given set of alternative processes, decreasing vari-ability in capital coefficients. Such considerations, however, willnot forestall shifts in process advantage in response to sizablechanges in the hill of goods or the basic resource position of theeconomy.

Nor do these stabilizing influences apply to substitutions arisingin connection with technological change. Even within a frameworkof stable factor supply conditions, new processes are always beingdiscovered which can compete successfully with old ones. In orderto predict capital expenditures, one must know whether there is anew technology which will govern expansions, and also whether thesavings entailed in utilizing the new technique are sufficientlygreat to warrant replacement of old capacity with new.

There is evidence that the rate at which new methods are de-veloped is sufficiently great in some sectors to render total capitalcoefficients in error by 50 per cent or more within a few years. Thechemical industries are full of examples, particularly in some ofthe newer products such as nylon and plastics. In such industries,incremental capital coefficients are rendered obsolete at an ap-pallingly rapid rate and the Cost advantage of newer processes isoften great enough to warrant substantial scrappage of old equip-ment for changeover purposes as well. Where such radical technicalchanges occur, the explicit introduction of process substitution

•into the dynamic input-output model is essential. It is equally im-

20For a discussion of the "inertia of capital structure" see above.

309


portant that the model absorb a changing roster of process alter-natives. These considerations are important not only for improvingestimates of capital requirements per unit increase in capacity butalso for predicting the volume of capacity which will be replaced.To take realistic account of the process of technological change, itis necessary to relax not only the fixed coefficient assumption butalso the simple accelerator theory of capital formation. Researchon modification of the dynamic input-output model to take techno-logical change into account is currently under way.

Conclusion

The foregoing account of variability problems in the prediction ofcapital requirements is by no means comprehensive. The discus-sion was limited to problems of estimating over-all capital expendi-ture. The classification and/or substitution problems inherent inestablishing breakdowns of capital requirements by industry oforigin warrant full treatthent on their own. Furthermore the prob-lems of quality and of balance cannot be dealt with independentlyof the more general problems of classification and product mix, ofwhich they constitute but a single aspect.

A partial review of the problems of estimating capital require-ments in a disaggregated scheme is disheartening, but it would be amistake to evaluate the returns of dynamic input-outputmodels independently of these difficulties. Regardless of the fateof interindustry models, however, someone must deal with theseproblems in the long-run development of economic knowledge. Judg-ment as to "where we go from here" is still largely a matter offaith.

310

this pdf is a selection from an out-of-print volume from ... · pdf filein inferring...

Documents