This PDF is a selection from an out-of-print volume from ... · do not show either peculiarity. An Ecological Process Accordingly, it may be useful to reflect on the patterns of interaction

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

Volume Title: Information, Expectations, and Inventory Fluctuations: A Study of Materials Stockon Hand and on Order

Volume Author/Editor: Ruth P. Mack

Volume Publisher: NBER

Volume ISBN: 0-870-14478-2

Volume URL: http://www.nber.org/books/mack67-1

Publication Date: 1967

Chapter Title: Toward a Theory of Inventory Behavior

Chapter Author: Ruth P. Mack

Chapter URL: http://www.nber.org/chapters/c1415

Chapter pages in book: (p. 269 - 297)

13. Toward a Theory of Inventory Behavior

In urgent need of being written, bit by bit,is the story of how flows of information takeplace, whereof they consist, how they influ-ence expectations, how they are interpreted

in actions, and how actions affecting incomeand product are translated back into informa-tion and expectations is a story.

IMPLICATIONS CONCERNING ECONOMIC CHANGE

It is, of course, a difficult story even to embarkupon. For this there are several reasons. Oneconcerns the character of the two worlds andof their relationship to one another. In a sensethe two are one: information and action are,like mind and matter, part of the same cor-pus. Few actions do not rest on informationand are not in turn converted to a "signal."But in another sense they are part of a con-tinuum, one end of which is scraps of informa-tion and the other end of which is a concreteact. The continuum can stretch, for example,from an isolated and possibly irrelevant ob-servation of a sentence in a trade journal toa response in terms of newly rolled steel sheetspinning onto its giant spools, or from a nota-tion in a secret-service file that a cargo shipwas sighted here, not there, to young mencreeping over a beachhead. Dead center be-tween the two ends of the continuum lies thecommand.

The Role of Orders

The command is identical to action if itis always precisely converted into action. Thusif new orders, which are in essence pieces ofinformation, are never canceled and alwaysdelivered precisely as written, they are for all

intents and purposes simply predated acts—shipments. In actuality, orders are sometimescanceled, postponed, or delivered late. Never-theless the correspondence is close enough sothat new orders cannot provide an explana-tion of shipments. They are too nearly simplyan earlier version of the same thing. This isthe difficulty to which I pointed in Chapter1 when alluding to the serious deficiencies incurrent explanations of stocks in which orders,or changes in unfilled orders, play such apowerful causative part. In this book, ordershave been cast partly in the role of effectrather than cause, since one definition ofstocks includes stock on order. In a sense,then, a borderline member of the world ofinformation, outstanding purchase orders, hasbeen joined to the physical world of actionand things.

The construct belongs fully to neitherworld. To picture output and income flows,ownership must be cracked apart and stockon hand alone isolated. To study the flow ofinformation at a causal level, it is necessaryto go behind the order to see what causedit. But in spite of these deficiencies, the half-breed has talents of its own—a power to dis-play and convey information: On the onehand, ownership has a different speed of

270 SEARCH FOR EXPLANATIONS

change and process of change than has stockon hand. On the other hand, it reflects in-formation and expectations very sensitivelyand in a particular sort of way. Both char-acteristics demand recognition in the theoryof inventory cycles.

As to the speed and process of change, twodifferent manifestations are important. ForOne thing, the fact that orders swiftly embodyintentions means that, particularly for depart-ment stores, intentions, and therefore thetheory behind action, are readily visible inownership though obscure in stocks. This isa convenience rather than a new ingredient.

But the order, and its inherent fluidity, con-dition the characteristics of vertical linkagesin the economy. If only shipments or stocksare examined, the transmission of fluctuationassociated with sales-linked stock objectivesought, it would seem, to move backwardthrough the economy with sequential antici-patory leads and increasing amplitudes offluctuation. But if we concentrate on flowsof information instead, notably orders, the re-tailers' buying and producers' buying of rawmaterials can be linked with the speed oflight, or at worst the time required for threetelephone calls. The previous chapter ex-panded briefly on this point. It explains, Ibelieve, a phenomenon that has troubled stu-dents for many years—the fact that though thelogic of the acceleration principle calls forprogressive acceleration (in timing as well asvolume) as demand moves stepwise to earlierstages, empirical evidence fails to show it.'

The second attribute of ownership or out-standing materials orders, that of reflectinginformation and experience very sensitively,involves not so much the particular stock con-struct as it does a way of viewing the entireproblem of procurement. It elevates the worldof information to a place in the analysis

1 In lecture notes written thirty or forty years ago,Wesley C. Mitchell lingered over this problem. Heexplained it very tentatively in terms of inventoryobjectives conceived as fairly broad bands rather thanas precise ratios. Many subsequent students have ig-nored the problem.

where it cannot for one moment be forgotten.At the microeconomic level, emphasis on

information means that, on the one hand, thenotion of process is analyzed in terms of theinformation that the businessman uses andthe expectations that he formulates. In thecase of the procurement process, this empha-sizes the part that expectations about mar-ket conditions can play in the timing of buy-ing. It emphasizes possible changes in op-portunity costs, including qualitative changesin customers' requirements. It emphasizes andparticularizes the informational role of newsales orders.

But at a macroeconomic level, too, the em-phasis on information and expectations hasinteresting implications which I want to de-velop. One reason for trying to think throughsome of these implications is a negative one:the speed with which information in general,and orders in particular, travel undercuts thebasic assumption of "period analysis" as acomplete explanation of inventory cycles."The only indispensable assumption in thetheory of the inventory cycle is that business-men do not immediately adapt their produc-tion plan to a change in sales." 2 But insofaras orders constitute the adjustment, it can bevirtually immediate. Moreover, insofar as ex-pectations about conditions are thereason for the adjustment, it is not unlikelythat many people would want to adjust inthe same way at very nearly the same time.If so, the inventory cycle could undergo aseries of explosions or, if there were ceilingsto response, a sawtooth rattle. There must besome way to explain the fact that time seriesdo not show either peculiarity.

An Ecological Process

Accordingly, it may be useful to reflect onthe patterns of interaction between informa-tion and action and what these interactions

2 Lloyd Metzler, "Factors Governing the Length ofInventory Cycles," Review of Economics and Statis-tics, January 1947, p. 11.

TOWARD A THEORY OF INVENTORY BEHAVIOR 271

imply about the course of economic change.Biology has a word for it: "Ecology" con-cerns ". . . the relations between living or-ganisms and their environment." The focusseems directly applicable to economics whenliving organisms are restricted to man, andenvironment to the portion (largely thoughnot exclusively economic) which influenceseconomic behavior.

The way has been prepared for studies ofthe ecology of economic processes by the workof Herbert Simon. He has developed thenotion that though man is "intendedly ra-tional" in the sense attributed to EconomicMan, the best that can actually be achievedis "satisfying," not "maximizing" or even"optimizing," behavior. Divergence from op-timization is caused in part by shortcomingsof available information and man's capacityto manipulate it. This implies that satisfyingis at best slovenly optimizing fraught with un-certainty. But two characteristics are morefundamental in their implications: (1) Per-ception is necessarily selective; we appreciate,perceive, and even see not a total situationbut the part of it for which we are in somesense ready. (2) That which is deemed "satis-factory," and which serves consequently as aproximate goal, changes as events prove thegoal accessible or If these twosimple notions are taken seriously, and theyare founded on widely held psychologicalideas, the course of aggregate economic changewill typically follow a different course fromthat implied by "optimizing" behavior.

The point of view demands an analysis thatattends to the way in which a man sees, ap-preciates and thinks (on the basis of the in-formation accessible to him) and the way a

3 Webster's New World Dictonary of the AmericanLanguage, CoBege Edition, 1959.

4 Most of Herbert Simon's voluminous writings dealwith these ideas at some level. But if a single referenceis desired, I recommend Chapter 14 in Models ofMan, Social and Rational, New York, 1957, "A Be-havioral Model of Rational Choice." The article wasreprinted from Quarterly Journal of Economics,February 1955.

man acts (given his appreciations, expecta-tions, customs, and what he wishes to achieve).Moving to an aggregative level, the analysismust attend to how the thinking and the act-ing of many men influence that of one an-other. Finally, at the aggregate level, the cross-influence must be encompassed: the influenceof thinking on acting and of acting onthought, that is, on information and expecta-tions, and particularly the assurance withwhich expectations are entertained. The sim-plest way to spell out these ideas is in termsof a model in which information and expec-tations, along with actual economic condi-tions, play their appropriate parts.

Note what these objectives and conceptionsimply about the essential character of an ag-gregative model: it must be constructed outof pieces that display the behavior of individ-uals creating and responding to a Situationwhich involves the behavior of other individ-uals in an economic environment. Man is asocial animal; he is affected in his thinking,feeling, and acting by his perceptions of thethinking, feeling, and acting of other men.If an acting-reacting sequence gets under way,there is no reason at all to assume that in-dividuals will react to the situation and toone another in a fashion that can be de-scribed in terms of linear aggregate behavior.Indeed, there is every reason to expect somesort of geometry of interaction, and it may"explode" or approach ceilings. However,there is no possible way to prejudge the par-ticular aggregate function that will be foundto apply, even if it were mathematically fea-sible to use it. The point is simply that thecoefficients of response and feedback canthemselves change as time goes on. How theywill change can only be evaluated by con-structing the social process in microanalyticterms. Happily, this is a job that computersare very able and willing to take on.

Not only the logic of information systemsbut also the empirical studies of previouschapters seem to present puzzles that invitea better explanation than the aggregative ap-


proach readily affords. Chief among these isthe phenomenon of thrust. Why does owner-ship of materials, for department store re-tailers as well as for durable goods manu-facturers, appear, at an aggregate level, tobuild up abruptly as contraction ends and toexhibit the curious pattern of a uniform rateof change which abruptly ceases though otherthings continue to climb? A second minorpuzzle is the character of the timing associa-tion between changes in sensitive prices andstocks or ownership; though a relationshipseems present, ownership moves too late tobe motivated primarily by anticipation of therate of change in prices.

These empirical puzzles are joined by atheoretical one: The importance of expecta-tions in governing the timing of buying andthe speed with which information can beconveyed and responded to in terms of ordersseem capable of causing abrupt spurts inbuying followed by an equally abrupt plum-met to a hand-to-mouth position. But the timeseries show gradual build ups and declines.

Why? The models outlined in Chapter 11 leftthis question unanswered.

Clearly an explanation must focus on thoseparts of the inventory-purchase complex mostsensitive to changing expectations. Since weneed to supply a missing piece of the com-pound process of inventory fluctuation, it willbe useful to use the device of a model.

It concerns the influence of market pros-pects. But it will be useful to focus on only oneaspect of all the factors that influence positiveor negative buying associated with actual orexpected changes in market condition—de-livery conditions, assortments, quality, materi-als prices. Only the last, materials prices (otherthings the same), will be examined. This isnot by any means the most influential of thegroup; delivery conditions are doubtless themost important single factor. But expectationsabout prices have some expositional advan-tages. As a matter of fact, some of the otherelements slip in too, in spite of stern effortsto exclude them.

AN ECOLOGICAL MODEL OF PRICE-TIMED BUYING

Price-timed buying can be a positive or a nega-tive quantity. It is the increment or decrementto materials orders consequent to the fact thatmaterials prices are, or have recently been,expected to change. It concerns primarilywhen, in view of expected change in prices,materials will be purchased which are in anyevent expected to be required. If we assumeas a first approximation that the flow of goodsinto production (or, for retailers, goodsshipped to consumers) is not affected byprice-timed buying, then cumulated price-timed buying is price-timed ownership.Viewed the other way round, price-timed buy-ing effectuates desired changes in price-timedownership.

From the point of view of a purchaser, themore price-timed ownership that can be kepton order (rather than on hand), the better,

assuming that the price is fixed at the timeorders are placed and that there is no doubtwhether goods will be delivered onMaterials on hand involve financing, insur-ance, and storage costs of which materials onorder are free. However, uncertainty aboutdelivery schedules may make it desirable totake delivery on some anticipatory purchases.In any event, delivery schedules seldom giveperfect expression to the ideal separationof buying and shipments. For both reasons,

5 Prices are not always fixed at the time the orderis written. Steel producers have typically set prices atthe time of shipment. (A break in the ranks by Wheel-ing Steel was reported in The New York Times ofNovember 4, 1965.) Some products of the fats and oilsindustry have been priced in a similar way. Thesestipulations on the part of the seller force the buyerto, in effect, pay the full costs (storage, insurance, fullrisk, financing) for any price.timed buying he maywish to undertake.

13. TOWARD A THEORY OF INVENTORY BEHAVIOR 273

stocks on hand will usually reflect some price-timed buying, often of an earlier date. Shouldthe larger (or smaller) stocks no longer bedesired, a compensating adjustment of newbuying can adjust total price-timed ownershipapproximately to the level appropriate to thepresent situation. It is reasonable, therefore,to assume that the impact of price-timed buy-ing is represented by changes in ownershipwithout specifying which part of ownership—the part on hand or on order—is involved.

The model is built from three sorts of com-ponents: (1) structural characteristics of theindustry and its member firms, (2) behavioralcharacteristics that define how actions result-ing in price-timed buying are generated andgoverned, (8) market responses in terms ofprices, delivery periods, and levels of plantand resource utilization. The only lags or leadsthat are admitted are those which seem torepresent the time actually required for speci-fied processes to take place.

Structural Assumptions

Two sorts of differences are resident in thestructure of a firm and of an industry withrespect to the potential advantage of price-timed buying. First, within any firm, potentialadvantage from further buying is a functionof the level to which price-timed ownershiphas previously been extended. Second, thevarious firms in an industry differ with respectto their interest in—that is, in their proclivityto gain from—price-timed buying.

POTENTIAL COSTS AND BENEFITS OFPRICE-TIMED BUYING

That differences of both sorts are embeddedin the normal structure of business situationscan be seen by a moment's attention to thepotential costs and benefits associated withprice-timed buying. The benefit of price-timedbuying is paying less for materials; the costsare those of carrying additional goods. It isadvantageous to undertake positive price-

timed buying so long as the expected increasein prices per unit, discounted for uncertainty,during a specified period of time is greaterthan the additions to carrying costs over thesame period, other things the same. The dis-cussion early in Chapter 10 spelled out thearithmetic of this statement. It implies thatthe level of price-timed ownership is a func-tion of the expected rate of change in prices,discounted for uncertainty, other things thesame.

In Chapter 10 this discussion is part of ananalysis of other factors that bear on market-oriented buying and they imply that otherthings are not likely to remain the same. In-deed, in uncertain situations many changestend to support one another. Thus an ex-pected increase in replenishment periodmakes it advantageous to do price-timed buy-ing on the basis of an expectation of a givenprice change which is less sure than wouldotherwise be required to justify it. The sameremark applies to a change in back orders;if finished goods are sold at a price that isbased on present costs of materials, the salecan be "covered" by materials purchases with-out many of the risks that would normallyattend price-timed buying.6 These thoughtsre-emphasize the artificiality of a model thatfocuses on only one part of a process whichnecessarily moves as a whole. Since thisthought is a constant irritant, let me thenenter this blanket demurrer and cease bother-ing the reader by something that ceaselesslybothers me. Actually, as I indicate later, themodel could be changed without much diffi-culty to cover the entire phenomenon of mar-ket-oriented purchasing. However, it canbest be constructed in the first instance withthe focus on price alone.

Optimum ownership associated with expec-

6 It may be alleged that the normal procedureshould be to cover, and that the notion of price-timedbuying ought to apply to the failure to cover. Perhaps.But the critical point is that if prices were confidentlyexpected to decline (and there was no problem aboutgetting the materials later), a purchasing agent wouldnot cover.


tations of change in prices is the point atwhich the following marginal equality is at-tained:

Per cent price change perPrice-timed ownership month per unit

in terms of months =of expected sales Per cent marginal carry-

ing costs per month perunit

In actuality, the price change in the formulais of necessity the expected change and it is,in effect, discounted for uncertainty. Carryingcosts which. have previously been discussed in-clude storage, insurance, financing, physicaldepreciation, and obsolescence. The formulastates that if, for example, the price of somematerial was confidently expected to rise 3 percent per month, and carrying costs were con-fidently estimated at 18 per cent of sellingprice a year or 11/2 per cent per month, itwould be worthwhile to extend ownership bya two months' supply relative to the owner-ship appropriate to stationary buying prices.

As long as the expected rate of rise inprices (adjusted for uncertainty) remains thesame, no further price-timed ownership (andconsequently no price-timed buying) is war-ranted. If the expected rate declines price-timed buying turns negative as ownership de-clines. If the rise in prices is expected to ac-celerate further, the level of price-timed own-ership would presumably increase. However,this statement is qualified by the first assump-tion, below.

Of course expectations about prices, or any-thing else, are virtually never sure. Ac-cordingly, the right-hand side of the equationis reduced by an uncertainty discount. Thismeans that price-timed ownership is alwaysless than would be appropriate to sure ex-pectations. An increase in assurance concern-ing an expected rate of rise in prices would,then, operate in about the same way as anincrease in the expected rate of rise, as de-scribed in the previous paragraph. Conversely,increasing assurance about falls is equivalentto a faster drop, other things the same.

ASSUMPTION: INCREASING COST OF OWNERSHIP

As the number of weeks covered by advancepurchases increases, the carrying costs of stockincrease, at first gradually and eventuallyabruptly. I state this in the form of an as-sumption, though there is some empirical evi-dence to support

The possibility of physical depreciationmay sometimes increase with increasing own-ership, but the major reason for the escala-tion is the risk of obsolescence. The longerahead that requirements must be forecast, themore time there is for anticipated events toprove the forecast wrong. This is especiallyso in a seasonal business when an advanceposition crosses the months of a seasonal peak.For one thing, at the seasonal peak, advancepositions cover sales for a big month ratherthan for a normal one. For another thing,many aspects of demand may be relativelystable within a season and changeable be-tween seasons. The seasonal peaks thereforewill often mark the point of rapidly increasingrisk, which constitutes a virtual ceiling to ad-vance commitments.

A second escalation of risk involves a guessabout price itself. The longer the advancecommitment, the longer prices must continueto behave at least in the anticipated fashionif the purchase is to be justified. Thougherrors are subject to correction by secondarynegative or positive buying, it may not befeasible for the correction to be complete.

ASSUMPTION: HILL-SHAPED DISTRIBUTIONOF PROCLIVITY TO GAIN

The potential advantage in shifting owner-ship position in line with expectations aboutmaterials prices will differ for various mate-rials that an enterprise purchases and for thesame materials in different enterprises. Iwould like to refer to the degree of potentialadvantage as the "proclivity to gain from

See Franco Modigliani and F. E. Hohn, "Produc-tion Planning over Time and the Nature of the Ex-pectation and Planning Horizon," Econometrica, Janu-ary 1955, pp. 46—66.


price-timed buying." As mentioned at theclose of Chapter 2, differences in sensitivityto any factor that influences stocks is a logicalnecessity if the advantage to be derived fromstocks is a function of many costs and benefitsof specific kinds. Though businesses sharebroad characteristics, they do not share precisecost structures in the sense of identical relativeimportance of various sorts of costs and bene-fits. These things depend on the particularsof management talents, customers' needs andexpectations, financial resources, plant andproduction setup, and so on. However, it willbe useful to enlarge on the specifics of theseimplications of the earlier analysis. What thendetermines the proclivity to gain from price-timed buying?

Proclivity will be affected by the potentialgross gain from a correct guess about prices,the potential cost of carrying stocks, and theinterest of management in the guessing gameitself. In other words, it will be affected byany influence on the numerator or denomina-tor of the equation of a few pages back, andby, in effect, the subjective utility of the cal-culation. Without attempting to be compre-hensive, some of the more important charac-teristics falling in each of the three categoriesfollow.

A high proclivity is associated with the sizeof the impact on profits of likely changes inprices. This depends on several business char-acteristics, other things the same.

1. Volatile buying prices. If prices changevery little, a correct forecast can result atbest in only small advantage.

2. Low value-added relative to the cost ofmaterials. The impact on profits of guess-ing right about a given change in buyingprices is greater when materials prices re-present a large portion, and value-addeda correspondingly small portion, of thevalue of the product.

3. Cost of information. If few rather thanmany materials are used, it becomes moreworthwhile to spend time studying theprobable course of prices. Other factors

that influence the relative cost of informa-tion are also relevant.

4. A high turnover of working capital. Prof-itability is a function of the relation ofearnings to capital and is therefore re-flected in capital-earnings ratios. There-fore the significance of a given earnings-sales ratio depends on the relation of salesto capitalization. A high turnover of work-ing capital will tend to emphasize thesignificance of buying at the right price,other things the same.

5. Relation of selling prices to materialsprices. If selling prices are set for a sub-stantial period of time, the producer mayhave a period of option as to when mate-rials are bought. This is an invitation toconsider the probable changes in prices.A rather different situation, which canlikewise intensify the need for advancebuying, is that in which selling prices arehighly competitive and likely to reflect thesuccessful anticipation of changes in ma-terials prices on the part of a few impor-tant competitors.

6. Other opportunities to outdo competitors'efficiency. Sure ways of effective competi-tion are likely to be more popular thanunsure ways, and in some industries, andparticularly for some businesses, efficiencyin factory or sales management providesa strong competitive tool. When this toolis weak, recourse to the more risky oneof price-timed buying becomes more es-sential to effective competition.

A high proclivity is inversely associated withthe impact of carrying charges, and this de-pends on:

7. The possibility of stipulating when goodsare to be received independently of whenthey are ordered. When this can be donewith confidence, the cost of price-timedownership is reduced by confining itlargely to stock on order.

8. Low carrying costs. Insofar as price an-ticipation does eventuate in related


changes in stocks, low carrying costs re-duce the impact of such changes.

9. Predictable requirements which reduce therisk of obsolescence. Obsolescence can takethe form of goods that cannot be used atall, used only after a write-down, or usedinefficiently. Durable raw materials, manysimple processed materials, or standardbasic goods not subject to fickle demandare relatively resistant to these dangers.The presence of firm sales orders alsotends to eliminate this additional riskfor other sorts of materials.

A high proclivity adheres also to particularsorts of management structure and talent:

10. Personnel. Good judgment about pricechange requires that people able to makesuch judgments are available and author-ized to make them. This requires a man-agement structure that recognizes, pro-vides, and rewards this type of talent. Topmanagement talent tends to be locatedin purchasing operations where the factorspreviously mentioned contribute to a highproclivity to gain.

11. Management philosophy. The personalityand sentiment of top management can besympathetic or resistant to price-timed buy-ing to which a "speculative" onus may beattached.

The proclivity to benefit from price-timedbuying is a net result of all appropriate at-tributes in their business setting. Proclivitieswill differ by type of material and in firmscharacterized by different management prob-lems and structure. Thus a given proclivitycan be assigned to an enterprise-commodityunit.

The frequency distribution of the proclivityto benefit from price-timed buying will de-pend on the joint frequency distribution ofall of the attributes that make for a high (orlow) proclivity. What shape is the distributionlikely to have?

Consider any one of the attributes making

for a relatively high proclivity to gain fromprice-timed buying. Some commodities in somefirms in a given industry will be rich in theattribute; other commodities in the same firmor in other firms in the same industry willbe poor in it; but the very rich and the verypoor will usually be infrequent compared withthose possessing it in moderation.

For example, materials costs can be highrelative to value added (item 2 above). Thusthe cost of leather for a manufacturer ofpopular-priced men's shoes is likely to con-stitute a large proportion of value added,because manufacturing operations are highlymechanized and efficiently managed. At theother end of the frequency distribution, amanufacturer of high-priced women's shoeswill find materials costs buried under thevery large cost of many hand operations andelaborate distribution techniques. In between(consider calf leathers only) 8 lie the bulk ofcompanies, with more men's shoe manufactur-ers at the high-proclivity end and women'sshoe manufacturers at the low-proclivity end,and a substantial overlap somewhere in thecentral portion of the range where frequenciesare high.

An analogous type of distribution wouldapply to other of the characteristics listed.Thus, a low risk of obsolescence of purchasedsole and brown side leather, featured in popu-lar priced men's shoes, would imply a highproclivity (item 9 above); the multifinishedleathers characteristic of many Sorts of wom-en's shoes would place such firms at the lowend of the distribution. Again, it seems reason-able to expect some humping around thecentral area of the array.

If we think of each enterprise-commodityunit as having a rank position from one to tenfor each characteristic, then the unit's pro-clivity rating would be some sort of a weightedsum of the several ratings for each character-

S Calf and cattle hide might be considered part ofthe same commodity group, whereas kid and otherleathers are excluded as having quite different con-ditions of supply.


istic. The weights would represent relativeimportance of the characteristic in the netproclivity to gain.

Just what these distributions would looklike for a given industry cannot be determineda priori. Certainly there are fewer enterprisecommodity units with extremely high pro-clivities than with moderate ones. At somepoint, as proclivity ratings decline, it seemslikely that the number having a given ratingwould typically drop off. The distributionwould not be symmetrical, however, butskewed toward the low proclivity end. Criticalto my argument is the basic wedge shape andthe further thought that it would at leastflatten. Actually it seems likely to me thatit would usually decline at the low-proclivityend of the array. It seems safe to assume thatthese minimal requirements would be met.

In other words, for the purpose of thisanalysis we must abandon the notion of the"representative firm" and think instead of thehill-shaped firm, or industry, or group of in-dustries, or economy. The representative situ-ation is precisely not a median or some sortof average condition but the basic characterof the distribution of conditions.

STRUCTURAL ASSUMPTIONS AND PRICE-TIMEDOWNERSHIP

The essence of the two assumptions is shownin Figure 4. The top figure portrays the as-sumption of increasing costs and shows how,as increasing rates of change in materials pricesare expected, and guesses are held with in-creasing assurance, the amount of price-timedownership increases and reaches a ceiling be-yond which there tends to be no inducementto adventure further. The lower figure showsthe hill-shaped frequency distribution of enter-price-commodity units in an industry. Con.cerning the shape of the distribution, I canonly say that, pending empirical study, it seemsto me to be a reasonable one.

The implication of the two structural as-sumptions can be displayed first under thehighly artificial assumption that expectations

about prices are held with certainty and thatthere also is no uncertainty about sales oranything else capable of influencing expectedcosts or benefits from price-timed buying. Un-der these circumstances the level of ownershipassociated with expectations of higher andhigher rates of change in prices would in-crease without limit and the ceilings of Figure4 would not apply. A tabular example willillustrate the point.

Exhibit 3 assumes that the proclivities forone hundred different enterprise-commodityunits range from a maximum rating of A toa minimum rating of E: the distribution ofenterprise-commodity units among firms is,from A to E, 4, 22, 40, 28, 6, as shown inthe top line of each of the first five columns.

FIGURZ 4

Potential Gain from Price-Timed Ownership

Ceilings to P-T Ownershipfor an Enterprise—Commodity Unit

P- T

weekssupply

Rote of expected change in pricesorassurance

Hill-Shaped Frequency Distribution ofProclivity to Gain from P—T Ownership

Numberof

Prockeity index for the unit


EXHIBIT 3

Price-Timed Ownership and Buying, Assuming No Uncertainty,(tons)

Expected MonthlyRate of Rise

in Price

Ownership at Each Rate of Price Rise Buying at Sequen-tial Rates ofPrice RiseProclivity Group

AllGroups

A B C D E

1/2 4 4 4

1 8 22 30 261 1/2 12 44 40 96 662 16 66 80 28 190 942 1/2 20 88 120 56 6 290 1003 24 110 160 84 12 390 1003 1/2 28 132 200 112 18 490 100

Assume further that an expected rise of thebasic raw-material price of one-half of 1 percent per month makes it worthwhile for theA group to undertake price-timed ownershipsufficient to cover requirements for the salesof an additional month; for this an extra tonof materials per enterprise-commodity unit isneeded. A rise of 1 per cent causes the Bgroup to extend its ownership by a month'ssupply. But at that rate of price increase, theA group would extend its buying for an ad-ditional month. In each case one ton of ma-terials is involved.

As, for each group, prices reach the ratethat justifies some price-timed ownership, theamount appears in the first line of each col-umn. But at each successive rate of rise inprices, enterprise-commodity units for whichsome price-timed ownership had been justi-fied at the previous rate now should extendtheir position further. The appropriate levelsof ownership are shown in the sequentiallines for each column, that is, for each pro-clivity group. Aggregate ownership at eachrate of price change is the sum for the fivegroups shown in the next-to-last column.

Additions to price-timed ownership areachieved by means of price-timed buying. This

buying can be thought of as of two sorts:"initial price-timed buying," which lifts price-timed ownership from zero to the first positivefigure—the difference between zero and thefirst lines in each column; "secondary price-timed buying," which lifts ownership to fur-ther levels appropriate to faster rates of priceincrease—the difference between all other linesin the table. Total price-timed buying is thesum of primary and secondary buying. It isshown in the last column of the table underthe particular assumption that prices acceler-ated in the fashion represented by the se-quential lines of the table. But of course thissequence is only one of the many patterns ofchange which could take place. In generalprice-timed buying simply effectuates the dii.ference between the ownership appropriate tothe present expected rate of change in pricesand that appropriate to the previously ex-pected rate of change. Consequently, theamount of price-timed buying at a giventime depends upon the actual course of thechange in prices.

This description has made a totally Un-realistc assumption about the absence of un-certainty. Actually, uncertainty causes exten-sion of ownership to involve increasing costs


EXHIBIT 4

Structural Assumptions and Price-Timed Ownership and Buying,(tons)

Expected MonthlyRate of Rise

0wnership at Each Rate of Price RiseBuying at Sequential

Rates of. Allin Price Proclivity Group Groups Price Rise

A B C D E

1/2 4.0 4.0 4.01 7.6 22.0 29.6 25.61 1/2 10.4 41.8 40.0 92.2 62.62 12.4 57.2 76.0 28.0 173.6 81.42 1/2 13.6 68.2 104.0 53.2 6.0 245.0 71.43 13.6 74.8 124.0 72.8 11.4 296.6 51.63 1/2 13.6 74.8 136.0 86.8 15.6 326.8 30.24 13.6 74.8 136.0 96.2 18.6 339.2 12.44 1/2 13.6 74.8 136.0 96.2 20.4 341.0 1.85 13.6 74.8 136.0 96.2 20.4 341.0 0

and decreasing benefits in line with the twostructural assumptions.

To illustrate, suppose that each repetitionof secondary buying for a proclivity group isassociated with cutting the addition to price-timed ownership under certainty by first 10 percent and then 20 per cent of the units—30 percent the second time. By the third time 50per cent is lost, and 70 per cent the fourthtime. By the fifth time the ceiling has beenreached for all. In Exhibit 4 the figures ofExhibit 3 are changed in accordance withthis principle.° Now aggregate ownership itselfceases to rise after the bottom proclivity grouphas reached its ownership ceilings. If priceshad changed in accordance with successive

9 For example, in column A, price-timed ownershipunder certainty, Exhibit 3, increases by four tons asthe expected rate of price rise increases as shown insuccessive lines. Under uncertainty, Exhibit 4, weassume that four tons is cut by 10 per cent for thefirst round of secondary buying; thus price-timedownership is 4 + .90 x 4 7.6. In the second roundof secondary buying the increment of four is cut by30 per cent, thus price-timed ownership is 7.6 + .70 x4 = 10.4, etc.

lines of the table, price-timed buying wouldbe zero at that point (last column). How-ever, it would have started to decline longbefore, when the decreases in secondary buy-ing started to be larger than the increasesin primary buying.

The exhibit illustrates the implications ofrealistic structural assumptions under entirelyartificial behavioral assumptions. The lattermust now be replaced by more sensible ones.

Behavioral Assumptions

The behavior on which attention centers isprice-timed buying. By definition, it occurs inassociation with a change in price-timed owner-ship.

The amount of price-timed ownership thata firm wishes to hold depends in the firstplace on its position with respect to the twostructural assumptions: (1) the current levelof ownership—the lower the level relative tothe ceiling levels, the less strong need reasonsbe to activate a specified amount of owner-


ship; (2) the proclivity to gain from price-timed ownership—the higher the proclivity,the less strong need reasons be to activate aspecified amount of ownership.

TWO LAGS

Administrative Response Lags. The placingof an order requires that an authorized pur-chaser make a telephone call, confirmed byan airmail letter. Authorization for routinepurchases is not likely to be administrativelycumbersome. It is ordinarily delegated in ad-vance to some appropriate person. Authoriza-tion for further purchases associated with priceexpectations may be required to go throughchannels, but, in view of the presence of someleeway in most budgets, it may not actuallyneed to wait upon confirmation. In general,then, the response lag to an increase in price-timed ownership is negligible. (Contrast thiswith the lag appropriate to purchases of du-rable capital goods.) Decreases in ownership,on the other hand, may require somewhatlonger before negative price-timed buying canreduce ownership to the desired level. Themaximum rate of reduction, even if there isno new buying at all, is the current volume ofsales, item by item.

Learning Lag. Changes in price-timed own-ership occur as a response to learning, andlearning is a time consuming process. Informa-tion must be collected and inspected; it mustbe attended to in the sense of entering thefield of perception; it must be appreciatedand evaluated in terms of appropriate ac-tion.

All of these things take time and thereforegive rise to a "learning lag." However, withone exception, the lag for price-timed buyingis probably not long. The evidence bearingon the probable course of prices and onchanges in business costs or competitors' be-havior is swiftly come by. Appreciation andevaluation tend to focus on the purchasingagent's office and thus do not involve cumber-some interpersonal procedures. The excep-

tion to the potentially short learning laglies in the process whereby assurance develops.This involves what may be thought of as adepth dimension for each of the componentsof learning mentioned in the previous para-graph, with particular emphasis on the lastgroup. My point is that uncertainty must af-fect the learning process as well as being re-flected in a final evaluation such as I discussin the next two sections. Insofar as it doesaffect the learning process, it will tend todraw it out.

PRICE EXPECTATIONS AND CHANGES IN COSTS

The reason for and focus of price-timedbuying is, of course, a belief about the futurecourse of prices. The basic character of abelief about prices can be interpreted as aseries of possible rates of change with likeli-hoods associated with each hypothetical oc-currence. The complete array can be expressedin terms of an average value. Statistical de-cision theory formulates the average, the "ex-pected value," as the average of all possiblevalues weighted by their subjectively assignedprobability of occurrence. But there are a num-ber of other methods of selecting a centralvalue.10 Actually, most people probably dealwith the future without any such mental gym-nastics. Perhaps they consider, as Shacklehas claimed, only two values, "focus gain"and "focus loss."" Perhaps they make a bestguess and think also about how likely it isto turn out right. Perhaps the best guess takes

10 For a classic formulation of statistical decision,see L. J. Savage, The Foundations of Statistics, NewYork, 1954. An excellent short summary of otherdecision rules is given in Irwin D. Bross, Design forDecision, New York, 1953, pp. 102—117.

11 The notion is presented in Expectation in Eco-nomics, by G. L. S. Shackle, 2nd ed., Cambridge, 1952.An excellent short statement by Shackle appears inUncertainty and Business Decisions, edited by C. F.Carter, G. P. Meredith, and G. L. S. Shackle, 2nd ed.,Liverpool, 1957, pp. 94—104; see also G. PatrickMeredith, pp. 38—41, and the frontispiece, the three-dimensional diagram of the "model of the Shacklefunction."


the form simply of "Will prices rise, fall, ordo neither?" No doubt different people thinkin different ways and even at different times.

The advantage associated with price-timedownership also depends on carrying costs.Thus the amount that is undertaken will beinfluenced by changes which affect these costs.Previous chapters have pointed to the impactof the volume of back orders or de factofinancing costs. What competitors are doinglikewise influences the need to take a posi-tion. For one thing, it is often thought im-portant to "buy along with the trade," sinceit is more dangerous to be short if competitorsare long in supplies and less dangerous to takea long position (expecting prices to rise) ifcompetitors also are long.

ASS URANCE

We have been speaking of expectationsabout changes in prices and costs. Expecta-tions are hardly ever single-valued. An ex-pected event may happen or not happen;more usually it may happen in one of manyways. Assume, to illustrate, that "expectations"take the form of a probability distribution.Thus, a purchasing agent may believe, ex-plicitly or subconsciously, that there are 2chances out of 10 that prices will fall, 3 thatthey will stay the same, and 5 that they willrise. Accordingly he believes, with some lackof conviction, that prices will rise. His assur-ance in this expectation would increase werehis probability weights to shift to, say, 1, 2and 7. He wOuld feel more justified in buy-ing more materials ahead when the distribu-tion of weights has humped in this fashionthan when it was flatter.

Or consider an involving morespecific expectations. Suppose that a pur-chaser thinks that five values percentagechange in prices are possible—minus 1, 0,plus .5, plus 1, plus 2. Say that if he feelsrelatively sure about his evaluations, theycarry for him the probability ratios of .05, .10,.70, .10, .05, respectively. Then the "expected

value" is plus .5 per cent change.12 But if hefeels unsure, the probability ratios might bemore like .40, 0, .20, 0, .40. The "expectedvalue" is still plus .5, but the utility of price-timed buying, and therefore the amount thatwill be undertaken, is likely to have beenreduced by the consciousness that there arefour chances out of ten that the price willgo down, not up.

However, it would seem that assurance, andconsequently the action to which the opiniongives rise, can also increase as a result ofchanges of a somewhat different sort. Sincethese further processes are likely to have asignificant bearing on how assurance waxesand wanes in an interrelated market, I wantto describe them. Unfortunately, the matterhas not been much explored and is contro-versial, and therefore the argument must bedeveloped at some length. However, it is en-tirely possible to follow the model I presentby interpreting change in assurance in theconventional fashion, simply as flattening orhumping of a probability distribution—andskipping or rejecting the argument concerning"assurance" which follows. It concerns fouradditional ways in which the impact of assur-ance can be conceptualized.

First there is what William Feilner hascalled "slanting," or Donald Ellsberg "am-biguity." The notion postulates that, feeling

12 The calculation of expected value (e.v.) is:Expected price Sum

than ge,per cent —1.0 0 +.5 +1.0 +2.0

Probabilityweights .05 .10 .70 .10 .05 1.0

Prices, weighted(line I x 2) —.05 0 +.35 +.10 +.10 +.513 William Feliner, "Distortion of Subjective Proba-

bilities as a Reaction to Uncertainty," Quarterly Jour-nal of Economics) November 1961, pp. 670—690, andDonald Ellsberg in the same volume. Feilner describesthe correction factor for uncertainty in these terms,"Instead of postulating that individuals maximize themathematical expectation of utility it is, at least forsome processes, based on psychological weights thatare in the nature of distorted probabilities" (p. 676).He has developed this basic idea in a recent book,


unsure of the evidence, perhaps even of therelevance of the evidence, the decision makeris aware that his opinion is poorly foundedand unstable. This sort of feeling is not en-tirely captured in a flattening in a prob-ability distribution for it also involves a fuzzi-ness about the whole matter. Presumably, hewill put fewer chips on a fuzzy and, admit-tedly, potentially unsound judgment than ona better one.

A second way of thinking about the im-pact of assurance on action is based on thepsychology of perception. People do not sim-ply know something or not know it. Nor dothey believe things the first time they hearthem; if they did, life would be all crisis.Perception is a process which develops slowly.Ideas burrow into the "psychological field."As they burrow, they must in a sense passtests of harmony with other information. Theygain significance and the power to throwtheir weight around and influence actions.So conceived, increased assurance is a formof a more advanced degree of perception.

A third way of thinking about the capacityof price expectations to influence behavioris to let oneself slip off the polished back ofthe ceteris paribus notion. Actually, as I con-tinue to complain, it is exceedingly difficultto cling rigorously to this basic method of

Probability and Profit, Homewood, III., 1965. DonaldEllsberg discusses "ambiguity" and takes it into ac-count as a discount for uncertainty in the form of anindex. He points out that actions may frequentlyfavor "those definable" as "status quo" or "presentbehavior" since for these the degree of confidence maybe high and the range of probabilities narrow.

Price theory has long introduced the notion of adiscount for uncertainty. Oscar Lange described it as"effective expected prices." "This is the most probableprice minus the risk premium. For sellers the riskpremium is positive, for buyers it is negative" (p. 31).Oscar Lange, Price Flexibility and Employment,Bloomington, md., 1944. These notions could beinterpreted as simply resulting from the introductionof a probability distribution rather than a single-valued expectation. However, the fact that the direc-tion of discount is different for buyers than for sellerstends to bring the ideas into closer relation to theslanting or ambiguity notion discussed in the previousparagraph.

scientific thought in a context where thecausal process under examination necessarilylinks changes in independent variables in thesystem with changes in some of the elementsconfined within this ceteris pan bus com-pound. In the context of price-timed buying,it is most unusual for prices to change with-out corresponding changes in quality, deliv-ery periods, and the like. Indeed, suchchanges can readily be converted to a pricedimension. Changes in these other marketphenomena are sure to influence the subjec-tive assignment of weight to possible pricechanges. They will, in other words, affect theassurance with which the price guess is made.

Finally, "expected values" or "best guesses"are often poor summaries for a probabilitydistribution of expected values in the contextof price-timed buying. They fail to take ac-count of the differential utility of each pos-sible price. The weighting system equates theutilities to the amount of price change,whereas actually they are often asymmetrical.Failure to anticipate a price rise means thatgoods have been bought at too high a price.But price-timed buying when prices fallmeans not only that the goods are boughtat too high a price but also, in many cases,that less than optimal articles were purchased.In effect, then, the denominator of the right-hand side of the equation is, for price-timedownership, inversely correlated with the nu-merator; risk of obsolescence (in the denom-inator) ought not to be set down at its aver-age value but at values specifically relatedto specific values of the numerator, the ex-pected rate of change in price. A further asym-metry in the utility of positive and negativeerror may occur at a personal level. If pricesfall, a purchasing agent may be subject tocriticism for advance buying to which he willnot be subject for "missing the boat" if pricesrise. Virtue's veil clothes the indiscretion ofthe resistant gambler but the mistaken gam-bler is fully exposed.

I conclude that whether one thinks of the"expected value" or "best guess" about prices


as influenced by "slanting," the process ofperception, inevitably associated market phe-nomena, or asymmetry of rewards and penal-ties, conclusions about behavior are the same;a best guess about price change will be as-sociated with varying amounts of price-timedownership as assurance or confidence in it,variously defined, grows or wanes.

The Ownership SurfaceThese behavioral characteristics prescribe

that the levels of ownership implied by thestructural assumptions must be viewed inthe light of uncertainty about price expecta-tions. The levels appropriate to sure priceexpectations, as illustrated in Exhibit 4, be-come the limits which would be appropriateas assurance builds up. They are shown alongthe back wall of an ownership surface inFigure 5.

Actually, price expectations are typicallymore or less unsure. Moreover, the structuralas well as behavioral characteristics implythat many other aspects of the judgment ofnet advantage are also more or less unsure—those concerning future sales and various ele-ments of holding costs. These judgments andthose about prices are interrelated. On anyor all of these counts, then, low assurancereduces the amount of price-timed owner-ship undertaken at each expected rate ofprice change. Assurance is lowest at the frontwall of the surface.

The diagram should be thought of as rep-resenting potential ownership for a majormaterial, a commodity, in an industry. Thusthe CC'BB' rectangle represents zero price-timed ownership. Only such stocks as areneeded for servicing sales and similar mattersare held. Positive price-timed ownership is

FIGURE 5

C

-100

Demand Surface for Price-Timed Ownership Sensitivity

P-T

—2 —1 0 +1 +2Expected per ceni price change per monlh

+3


above the plane and negative ownership be-low it. If no price change is expected (centerof the plane along the lines 00'), there is, ofcourse, no P-T ownership. The rate at whichprices are expected to rise are shown to theright, and to fall, to the left of the 00' line.The higher the expected rate of increase, themore enterprise-commodity units may be in-volved in positive ownership, and the largerthe extent of their involvement. That is, thesurface rises as it moves to the right becauseof both additional units starting primarybuying and continued secondary buying.

When the expected rate of rise is very lowand also uncertain (front wall just to theright of 0), no P-T ownership is indicatedeven for firms having a very high proclivity tobenefit from price-timed buying. As we moveto the right, the diagram suggests increasingrates of rise. But actually, it is doubtful thatan expected rate has much meaning whenopinion is very unsure. There are perhapsa series of overlapping probability distribu-tions that are all so flat that their meaningis little more than "prices will probably rise";how much they are expected to rise is hardto say except that at the right it is morethan toward the center. That is why the sur-face is relatively flat at the front wall.

The backward dimension of the diagramdepicts increasing assurance. It portrays thegradual accretion of price-timed ownershipassociated with more enterprise units forwhich additions to ownership appear justi-fied, and more ownership for each partici-pant. As depicted, the backward dimensionaccounts for much of the rise in price-trendownership. This implies that decisions con-cerning desired ownership are strongly af-fected by degrees of belief. The previous dis-cussion has attributed the impact of assuranceto the changes in the shape of the probabilitydistribution of possible prices, and to the fur-ther forms that increased confidence can take.The form of a more "advanced degree of per-ception" seems to assume particular impor-.

tance as one thinks of the competition forexecutive attention among the wide variety ofthings that, minute by minute, take place ina business.

Negative price-timed ownership is a re-sponse to an expected fall in price. It is il-lustrated in the left lower section of the dia-gram. The structure is highly conjectural, butis based on the supposition that the minimumtrue hand-to-mouth position which would pre-sumably be appropriate if serious price de-cline is expected is much nearer the normalefficiency levels for ownership than is themaximum extended position. For this reasonthe surface never falls much below —150 (backleft corner), though it rises by over +300 (backright corner). Also, the difference betweenbehavior under uncertainty and under cer-tainty is less extreme.

Positive price-timed buying occurs whenan enterprise-commodity unit wishes to movefrom a lower to a higher level of price-timedownership, or from a larger to a smaller nega-tive level of ownership. It occurs, in otherwords, when there is a wish to move upwardon the ownership surface. A downward move-ment involves negative price-timed buying.Does this buying itself influence the marketsin which it takesplace?

Market Response

The analysis of market response needs tobe formulated largely in terms of price-timedbuying rather than ownership. Price-timedbuying constitutes an addition to, and nega-tive price-timed buying a subtraction from,such buying as would occur for other thanprice-oriented reasons. The greater or smallerbuying influences demand-supply relation-ships; it generates other sorts of behavior inthe contacts of buyers and sellers; it influ-ences the information that is generated inthe market place. It therefore influences ex-pectations about how prices will change inthe future. The model must make some pre-

TOWARD A THEORY OF INVENTORY BEHAVIOR 285

sumptions about the character of the severalmarket responses, and these need to be speci-fied.

Market responses are of three sorts. None ofthe responses are immediate. They all taketime, and how much time is a function ofthe things that need to occur. The severalresponses, each involving characteristic lags,concern market behavior, information andexpectations, and income generation.

MARKET BEHAVIOR AND THE MARKET-BEHAVIORLAG

Market behavior affects price, market con-ditions and levels of utilization.

Price Effect. Materials prices tend to respondto price-timed buying and the strength of theresponse is a function of the amount of buy-ing, other things the same. Diagrammatically,positive price-timed buying represents a short-term shift of a demand schedule upward andto the right. Supply schedules may also shiftupward and to the left as suppliers respondto the eagerness of buyers and perhaps alsoto some short-term rigidities in their ownproduction scheduling. Negative buyingcauses shifts in the opposite direction. Thus,in terms of the usual demand-supply-pricediagrams, a flock of small new short-termschedules for demand and supply are bornand intersect at higher levels of the verticalprice plane.

Effect on Other Market Conditions. Otherconditions in materials markets also respondto the extra demand caused by price-timedbuying. The amount of the response dependsin part on the amount of the buying and onits rate of change. Thus the speed and re-liability of deliveries may deteriorate simplybecause of short-term resistance to changingthe level of output. This means that whenonce output has achieved a new level, theresistance will subside.

The character market responses has twointeresting implications. First, it seems clearthat at this level it is not possible to isolate

the impact of price-timed buying from thatof all other market influences. Second, the lagassociated with these aspects of market be-havior could be very short indeed. Its lengthwould depend largely on the institutions ofpurchase and sale. The action-reaction pat-tern of an open market are almost immediate.For individually negotiated deals, substantialtime may be required before additional sell-ing or buying is reflected in market condi-tions, including prices. Seasonal factors canbe important. Sometimes it is conventionalfor prices to be changed only at certain timesduring the year, and a growing tendency forprices to rise or fall must wait for the ap-propriate months. If prices are going to beraised when the line is announced, some cus-tomers may be given an opportunity to stockup earlier at the old prices; this underscoresthe periodic influence. The annual trade as-sociation meetings may be the battlegroundfor a campaign to change prices.

The Level of Utilization. All these marketresponses will tend to be more severe whenthe level of utilization is high than when itis low. This observation implies a furtherinterdependency of factors affecting owner-ship. Market responses to price-timed buyingor to buying associated with other marketexpectations cannot be disentangled from re-sponses to the broader picture of supply-and-demand conditions. If so, lags may be intro-duced which can be far longer than anythus far considered. They involve cyclicalrhythms of intensification of the shorter mar-ket-oriented responses.

EXPECIATIONS MULTIPLIER AND THE EVIDENCELAG

Market responses carry information whichis used by prospective buyers and sellers asa basis of judging the future course of prices.Consequently, the responses have potentialmultiplier effects via their role as evidenceand the power of information to influenceexpectations.


Here again, the process takes time andtherefore operates with a lag. Open-marketprices are widely displayed daily if not faster.On the other hand, individual contracts be-tween producers and buyers are often secretlynegotiated, and the information may be slowto leak out, if indeed it ever does. The amountof buying being done by market leaders, thecondition of inventories and order books ofcustomers and of competitors, all constituteinformation which may take days if not weeksto become generally known.

However the point that I want to empha-size is simply that the actions listed as marketbehavior all convey information. This infor-mation, after it has had time to disseminate,influences expectations the next time around.The "feedback" thus consists not only of mar-ket actions and consequent changes in de-mand-supply relations but also of informa-tion which, along with behavior, influencesfurther expectations with multiplier effects.

INCOME MULTIPLIER AND THE INCOME LAG

When price-timed buying causes output tobe different from what it otherwise wouldbe, the resultant income flows are subject tothe usual multiplier effects. Because the situ-ation can change rapidly, payroll and otheradjustable income flows are doubtless prima-rily involved. Also, the short-term level of thepropensity to consume, which, of course, varieswidely, will affect the extent that positive ornegative price-oriented demand is amplified.Expectations may also come into play to aug-ment or mute the income multiplier effect.The lags associated with income multipliershave been widely discussed in the literature.

The Process of Change

The gadgetry of the model of price-timedbuying has now been described in terms ofa group of structural, behavioral, and marketcharacteristics which interact after severalshort delays.

Aggregate change results from the shiftingweights to be assigned to situations describedin Figure 5. The weights indicate the numberof enterprise-commodity units whose price-timed ownership is at some particular placein the ownership surface and about to shiftto some other place. The shifts take the formof positive or negative price-timed buying—movements upward or downward respec-tively in the vertical dimension. Systematicshifts in the pattern of weights will occur asa result of forces set in motion by an initialdose of price-timed buying and the businessenvironment in which it takes place. Whatis the pattern through time of the resultantbuying?

It would be satisfying to be able to answerthis question by a process table that spelledOut the action, feedback, decision, action pat-tern; but the possibility of this tidy demon-stration is barred by the basic construction.The result of the aggregate level is contingenton the character of the distribution withinthe aggregate of proclivity, impulse, feedbacksets. Moreover, it is proper to stipulate theseoccurrences only in terms of probabilities, notas things that will happen. The magnitude ofresponse will therefore depend on how se-quences unfold. If so, the aggregate of oc-currences this month has no prescribed singlerelationship to selected present conditionsand the aggregate of occurrences last monthor the month before.

Nevertheless, though statements must re-main qualitative, reasonable and realistic as-sumptions about objectives, information, pro-cedures, choices, and reactions seem to leadto the conclusion that, inherently, a spacedwave of price-timed buying will be generatedunless intercepted by elements external to themodel. Specifically: (1) cumulation is grad-ual and progressive—more buying is touchedoff per month as the situation matures thanwhen it is young; (2) cumulation takes time;(3) reversal is inherent.

I want to discuss the processes of cumula-tion and reversal without admitting factors


external to the model. Needless to say, theyare present and important, especially in con-nection with the process of expansion.

CUMULATING EXPANSION

The course of a wave in price-timed buyingof materials can be interpreted in terms ofhow and why enterprise-commodity unitsmove from one position on the diagram toanother. Start at a point where there is nolonger a general belief that prices will falland accordingly the desire for negative price-timed ownership has abated. This implies thatpositive price-timed buying has moved manyfirms from the lower left quadrant of theownership surface to somewhere in the neigh-borhood of the origin, zero in Figure 5. I seeno reason why price-timed buying in isolationcould not cease at this point at which owner-ship tends to be at efficient levels, assumingthat prices would remain stable. But I wouldlike to suppose that there have been signsof renewed demand and other healthy under-pinnings that lead to optimistic expectations.

Some firms in the industry, then, expectrises in prices, others declines. Most are un-sure. There now occurs a moderate desire forprice-timed ownership on the part of somefirms with a high proclivity to gain. Price-timed buying would be governed by the dif-ference between the previous and presentownership objective of the participating units.

Assume, now, that nothing from the out-side occurs to counteract the effects of thisinitial dose of price-timed buying. Then mar-ket responses theoretically bring about a feed-back: in minute quantities they would con-sist of behavior responses, expectation andevidence responses, and even an income mul-tiplier.

However it seems clear that in reality theremust be some threshold level below whichfeedback effects do not develop. How thethreshold should be defined and how it oper-ates need to be studied. It seems likely thatthe rate of change in final demand will beone part of the story; the sensitivity of in-

formation systems and vulnerability to com-petitive behavior will be another.

The initial dose, and the feedback effects,can influence expectations in four ways, andactions in one further way: (1) fewer enter-prise-commodity units will be subject to theexpectation of falling prices; (2) more firmsmay expect a rise in prices of more materials;(3) the expected rate of increase may rise,though this may well tend to be a later mani-festation; (4) expectations will gain in sure-ness. In terms of Figure 5, concentration ofsituations moves to the right and especiallyback. Price-timed buying is positive and thereis more of it than at the time of the originaldose.

As time goes on, there is a fifth way inwhich the situation matures. It involves theobjective facts with which firms are faced; theneed for defensive action increases. For ex-ample, competitors may be amassing low-priced inventories or suppliers working over-time. Consequently, the action based on agiven set of expectations, held with a givendegree of assurance, increases. Diagrammati-cally, the surface as a whole rises. The furtherbuying will have its own round of feedbackand multiplier effects, which in turn havefurther influences on new expectations.

All this takes time. It takes time for busi-nessmen to perceive developments and learntheir implications. The growth of assuranceis particularly deliberate, since it waits onsuccessive confirmations of expectations andevents that deepen perceptions. After deci-sions are formed, administrative response,though swift, is not instantaneous. It takestime for market conditions, including prices,to reflect the impact of new buying. It takestime for the evidence to be displayed, per-ceived, and learned to the extent necessaryto influence new expectations and the assur-ance with which they are held.

Will a snowballing process get under way,or will countervailing forces prevail? Counter-vailing forces internally generated consist of(1) reduction in initial buying because the


hump of the frequency distribution of pro-clivities has been passed; (2) reduction insecondary buying because many units ap-proach the long end of their long-short marketrange; (3) negative (or zero) price-timedbuying to correct ownership based on dis-appointed expectations about price change.Numbers 1 and 2 will not generally occur atthe early stage of movement having the basictime-consuming characteristics that I have de-scribed. Number 3, disappointed expecta-tions, is quite another matter, for its preva-lence depends on whether the stimulation toprices associated with price-timed buying islarge enough to cause prices to increase asmuch as or more than expected. Is this likelyto occur?

The answer hinges, I think, on whether ad-ditional buying is contingent primarily onthe expectation that the price rise will ac-celerate (movement to the right of the dia-gram), or on the increasing assurance thatprices will continue to rise (movement inthe backward If the former gov-erns, the situation is self-reinforcing only solong as expectation-activated buying (alongwith its ramifying effects) has a large enoughimpact on prices to validate the expecta-tion. This implies that the price rise is atleast seen to accelerate—a stringent require-ment unlikely to be met. Moreover, the timeseries showed that market-oriented ownershipdid not parallel the rate of change in prices(nor did change in ownership, hypotheticallybuying, parallel the change in the rate ofchange).

But this hypersensitivity is not likely tobe present if the growth of assurance werethe chief determinant. Assurance would in-crease as expectations are repeatedly con-firmed. If expectations attended primarily tothe direction of change in prices, confirma-tion consists of continued change in the samedirection. The time series showed the impliedassociation between market-oriented owner-ship and prices proper (or change in owner-ship and change in prices).

The process, then, compounds in the fiveways previously mentioned and desired own-ership moves backward and somewhat to theright over the surface of the diagram. Feed-back mechanisms provide a sixth mechanismwhich, along with the fifth, causes the surfaceitself to lift as the objective situation changes.This implies cumulation of a progressive sort.What brings it to a halt?

DOWNTURN AND REVERSAL

A downturn in price-timed buying occursafter the amount of positive buying reachesits peak. This definition parallels the usualidea of a peak in any economic activity. Notethat even after a downturn, so defined, manyterms might still be moving upward on theupper right segment of the ownership sur-face, but aggregate movement in the verticaldirection would have started to decrease. Ifprice-timed buying is visualized as superim-posed on an upward phase of final buying, thedownturn in price-timed buying marks thepoint at which its impact on total buyingstarts to lessen.

But for some purposes the more significantchange in price-timed buying is the point atwhich it turns from positive to negative. Atthis point the influence of the timing of buy-ing starts to depress rather than to stimulatetotal buying. Call this point reversal, admit-tedly in this special sense. It will be useful tonote how both downturn and reversal inprice-timed buying occur as a result of ele-ments internal to the model.

Structural characteristics require that price-timed buying must turn down soon after par-ticipation in it has reached its maximum. Thatit does reach a maximum is guaranteed by thehill-shaped form of the proclivity to benefitand by the ceilings to price-timed ownership.Structural characteristics do not imply thatreversal must set in; they imply that price..timed buying cease but not that it turn nega-tive.

Behavioral characteristics, on the otherhand, can account for both downturn and re-

lB. TOWARD A THEORY OF INVENTORY BEHAVIOR 289

versal. Insofar as expectations about rates ofrise in prices determine buying, a downturnwould occur when the rate of rise inrate of rise ceased accelerating; reversal wouldoccur when it started to decline. Although,as previously explained, formulations of thissort seem totally unrealistic, it is possible thatattention to rates of change becomes morecommon when a buying wave has lasted longenough for assurance about the direction ofchange to grow strong. If so, vulnerability toreversal, as well as to downturn, increasessharply at that time.

Insofar as the increasing assurance withwhich expectations are held constitutes amajor aspect of the developing situation, adownturn occurs, other things the same, whenthe rate at which assurance (more specificallythe action that it motivates) is building upstarts to slacken; reversal occurs when assur-ance begins to lessen. And it seems likely thatthis lessening can take place as a result of thelevel of activity alone. At times, for example,factors directly associated with price increasesof the past will raise doubt about their con-tinuation in the future. For one thing, ifprices reach levels that are high with respectto previous levels, this fact can raise doubtwhether they will continue to rise. For an-other thing, operating margins may narrowafter prices have risen for a while; a tend-ency of this sort is promoted by the fact thatcrude products respond more sensitively tochanges in demand than do finished products.Narrowing margins often raise doubts whetherprices will continue to rise. Structural andbehavioral characteristics, then, guarantee adownturn and virtually guarantee a reversalin price-timed buying.

But in any event market response must, itwould seem, convert downturn into reversal.The presumption rests on the suppositionthat the strength of the reaction of prices,delivery periods, or other market phenomenaare a function of the amount of price-timedbuying and perhaps also of its rate of change.Sensitivity to the latter would reflect, among

other things, the difficulties that suppliers ex-perience in changing production schedules.But within a wide range of functional rela-tionships it would necessarily be true that theamount of market response declines when theamount of price-timed buying does. If so,the information feedback signals reductionsin rates of price increase and less surenessthat some prices will continue to rise. Ifexpected rates of rise occur, or the assurancewith which the expectation of some thresh-old rate is held declines, the ownership posi-tion that is justified is reduced. In effect, en-terprise commodity units shift toward the frontand left of the ownership surface and negativeprice-timed buying effectuates the shift. Mar-ket responses to these reductions furtherreinforce the messages that convey doubtabout further rise. Aggregate price-timed buy-ing turns negative, that is, reversal occurs,when the amount of negative buying exceedsthat of positive price-timed buying, that is,when the sum of the vertical distance bywhich some enterprise commodity-units dropon the ownership surface exceeds that bywhich others rise.

DECLINE

The negative phase of a buying wave startswhile most price-timed ownership is positive,but firms are trying to reduce their positionby refraining from buying. Aggregate materi-als procurement is therefore less than theamount required to provide for final demand.However negative price-timed buying for anyfirm cannot be greater than the volume oforders that would otherwise be placed to meetfinal demand.

It seems likely that firms that had previ-ously engaged in positive buying would tryto unload in unison. Since there is a cost at-tached to positive price-timed ownership, un-certainty alone may be sufficient reason toforgo the possible benefit and engage in nega-tive buying. Uncertainty may be more con-tagious in a business community than is theexpectation of either a rise or fall. In terms


of Figure 5, when uncertainty takes hold ofindustry opinion, there is a scramble of unitsto hop from wherever they are on the right-hand segment of the surface to somewhereon the left-hand side. Thus, though the slopeof negative ownership is mild, negative buy-ing, to effectuate downward shifts in desiredownership, can be relatively extreme.

The upturn in price-timed buying occursas the number of firms, and the amount ofthe reductions desired, start to decline. Here,as for the upward peak, structural assump-tions imply that the force of negative buyingmust decline. Indeed, the minimum hand tomouth position is doubtless far closer to theefficient service level of ownership than is theceiling level; consequently declines must bot-tom off sooner.

Reversal, the start of positive buying, is

brought on by the behavioral and market re-action aspects of the model in a manner gen-erally parallel to the upper turn. However,as mentioned at the outset of this section, itseems likely that support from elements out-side of the model—elements associated withfinal demand and other marked forces—areessential to launch price-timed buying on aclimb over the positive sector of the owner-ship surface. However, if the support is pres-ent, the ground has been prepared for rapidand cumulating response. The decline of neg-ative price-timed buying has already reducedthe depressant influence on total buying ofmarket oriented elements, and firms whosebusiness has improved unexpectedly will becaught short and behave accordingly. Theirbehavior echoes in a manner previously de-scribed.

PRICE-TIMED BUYING AND THE INVENTORY CYCLE

A wave in price-timed buying has been de-scribed in terms of factors capable of produc-ing self-reversing fluctuations of endogenouslydetermined duration. It is shaped by the eco-logical process whereby opinion is formed,acted upon, diffused through the economy,and affected by it.

All Market-Oriented Buying

The model has focused on one aspect ofmarket conditions—prices. Even so, changesin other aspects which are inevitably associ-ated with changes in price—delivery period,assortments, quality—were recognized in dis-cussions of market response to price-timedbuying.

To admit these influences explicitly as partof the process embodied in a model wouldrequire, I believe, virtually no change in itsbasic structure. Indeed, the surface labeledprice-timed ownership as shown in Figure 5may well be a more realistic picture of mar-ket-oriented ownership than of expectation

focused on price alone. The rise in expectedrates of change in prices, measured along thehorizontal axis, might well not actually occurunless the increase in expected costs repre-sented by market prices were joined by costsassociated with poorer selections or longer de-livery terms. Likewise, the rising assurancediagrammed in the backward dimension couldbe caused by combinations of things that arelikely to occur. For example, if, with a givendegree of assurance, prices are expected torise and delivery periods are expected tolengthen, there is far less to be risked by in-creasing ownership than if either were ex-pected to occur without the other.

This implies that the model as de-scribed could doubtless be applied to thetotality of market prospects without funda-mental change.

Interindustry Diffusion

The ecology of a wave of market-orientedbuying in a single industry may well also


apply across industry lines. How this can anddoes occur needs study, but a few guesses maybe in order. For one thing, the industries ina single vertical sequence are linked in manyways. Changes in the prices of raw materialssuch as cotton, hides, fats and oils, and scrapmetals are known and watched by firms atlater stages of an industry as indicators ofprices and other market conditions in themore finished lines such as cloth, shoes, short-ening, autos, cooking ware, and electrical ap-paratus. From the finished end, the influ-ence of final demand has a significant bear-ing on raw materials as well as on finishedgoods markets. Between the two ends of asequence the similar expectations are pro-moted by the hourly and daily contacts ofbuyer and seller over the telephone, in theoffice, and in the market; each firm is bothbuyer of materials and seller of a product,and thus a link in a vertical chain.'4 The linkis specific in connection with unfilled orders.For a particular company, undelivered salesorders on the books can, of course, take asubstantial part of the gamble out of price-timed buying of materials.

The closer are business ties, the more surelywill diffusion occur, and the more promptly.Consequently, it is not difficult to visualizehow a buying wave can develop within asingle industry sequence. But were expecta-tions contained within these narrow channels,waves in various industries could counteractone another. If so, the quantitative impacton the economy as a whole would be smalland the multiplier effects would be virtuallynonexistent. Of great interest, therefore, arethe factors capable of diffusing a disturbanceacross industry lines.

One can only guess what these are, sincethe subject has not been studied. The hints

14 Examples of linkages of these sorts appear inThomas M. Stanbeck, Jr., "Short-Run Instability in theCotton Broad Woven Goods Industry, 1946—1951," Un-published Doctoral Dissertation, Duke University, 1954;and Ruth P. Mack, Consumption and Business Fluc-tuations; A Case Study of the Shoe, Leather, Hide Se-quence, Princeton for NBER, 1956.

of parallelism that we have observed in mar-kets so diverse as department store merchan-dising and durable goods manufacturing whetthe curiosity to know more. One obvious car-rier of diffusion is the level of final demandand its rate of change, since most commoditiesshare in some degree the fortunes of the econ-omy as a whole. Another candidate is theprice of sensitive commodities not subject tostrong independent variations in supply; forsuch commodities parallel price movementsoften occur. Here again, prices are one aspectof a more complicated set of market condi-tions, the influence of which spreads. It mayalso be that prices and market conditions insome commodities (steel is a good example)have a pervasive influence on a wide varietyof other raw metals and finished goods. Othercommon influences—credit conditions, laborconditions, special situations of broad im-portance (national and international)—arelikewise capable of some across the board in-fluence on market expectations.

The Pieces of an Inventory Model

Fluctuation in ownership associated withchanging market prospects, in which ecolog-ical interplay is of special importance, is ofcourse only one part of the total process offluctuation in stocks on hand and on order.Consequently the model of price-timed buy-ing is only one piece of a complete model offluctuation in materials inventories. Its par-ticular function is to explain why even thismost volatile set of influences does not implya sawtooth pattern of fluctuation but insteadtends to cause inventories to build up moreslowly and necessarily to retard and reverse.Other aspects of an inventory model werediscussed in Chapter 11, where differences wereindicated in the picture appropriate to de-partment stores and to durable goods man-ufacturers. The multiplier aspects associatedwith income and with expectations and theirinterrelationship were mentioned in Chapter12. By way of summary I shall put the pieces


together largely as a sequence of empty boxesfor which the previous discussions, especiallythe models of Chapter 11, serve to illustratehow they may be filled for various industriesor other sufficiently homogeneous segmentsof the economy. A model for aggregate fluctu-ation in materials inventories would probablyhave to be built up by appropriate weightingof the segments.

The major pieces that need to be describedand articulated are:

1. A forecasting procedure forming thebasis of initial buying, which recognizes theinformation typically available to manage-ment and the time periods for which fore-casts are actually required. This implies abasic distinction between firms having littleadvance knowledge of short-term changes insales other than of a seasonal sort, such asretail stores, and firms for which sales ordersor other trustworthy barometers provide abasis for reasonably good forecasts, such asmany durable goods manufacturers. It alsoimplies recognizing patterns of buying interms of the overlapping time periods that theshingled structure of procurement frequentlyimplies.'5

2. A link of desired stocks to expected saleswhich for cyclical analysis is best formulatedin incremental rather than average terms. Myemphasis is negative—a constant average re-lationship ought not to be assumed. Even aconstant incremental relation is of course arough approximation, but perhaps closeenough to realistic requirements to serve; pre-sumably coefficients for increments would typ-ically be smaller than the average ratio.

3. Changing opportunity costs of invento-ries which recognize changes in costs of carry-ing stocks, on the one hand (e.g., those associ-ated with the presence of back orders orchanges in the availability or cost of funds),

is See the discussion of department store orders andmanufacturers' orders and shipments in Chapter 11.Note in connection with the latter that orders canprovide a forecasting instrument even when goods arenot made to order.

and, on the other hand, of alternative waysof performing the functions that stocks serve(e.g., flexible employment or selling policies).

4. The influence of changes in market pros-pects and expectations concerning them onthe timing of buying. This covers influencesoriginating primarily from the supply as wellas the demand side and their ecological inter-play.

5. Methods of defining, recognizing, andcorrecting error; this is a complex element.It involves in the first place the relative im-portance of inventory goals in the frameworkof all management problems—the opportunitycosts of management attention to defining andenforcing precise inventory goals. It involvescorrection in the second instance for faultyinitial guesses about future requirements; theshingled pattern of buying mentioned in para-graph 1 has relevance here. It involves cor-rection of procurement based on expecta-tions concerning market conditions or othermatters which are found to have been in erroror which no longer apply.

6. An income and expectation multiplier.At any particular time net capital investmentin inventories is subject to some sort of in-come multiplier at an aggregate level. Butits effect can be muted or amplified depend-ing on the interpretation placed on the changein inventories on hand and on order and theexpectations thereby aroused?8

If the model is constructed in terms ofownership, all of the prescriptions can beviewed as applying roughly to the presentin the sense for which the objectives andrealistic judgments call. This makes it pos-sible to net out some of the anticipations-correction procedures, such as those impliedin the shingled orders (paragraph 1) andcorrections (paragraph 5). The income mul-tiplier in paragraph 6 operates with the lag

16 Multipliers are a central point in the analysisthat closes Chapter 12. Other specifics on this pointappear at many places in the book, but particu-larly the discussion of Exhibit 2, Cases I and II inChapter 3.


implied by successive income receipt andspending sequences. The expectation multi-plier in paragraph 6 operates with such lagsas the ecological process implies. The latterstatement applies in some degree to the cx-pectational elements in any of the paragraphs,but particularly to paragraph 4.

If the model is constructed in terms ofmaterials stock on hand, it is necessary al-ways to allow for the time required fororders to enter stock and the correctionsthat have been put into effect during thattime. Even the allowance for deliveries is dif-ficult to make in view of the long and chang-ing leads of outstandings relative to stocks.17The implications seem to be that the modelloses most of its potential analytic value if

applied to stock on hand. But it would beuseful in gauging the gross influences onstocks of previous levels of outstandings. Forexample, in 1961 and 1962, when these levelswere low, stocks would presumably tend notto be as high relative to activity as at othercomparable cyclical stages— 1950, 1954—55,1958—59.

The importance that I assign to expecta-tions and to the information conveyed byorders rules out period analysis of the Lund-berg-Metzler variety. Response in terms ofownership is visualized as potentially im-mediate, whereas the situation to whichbuying responds evolves over time periodsinherent to each particular sort of situationor process.

DIRECTIONS FOR FURTHER STUDY

I mentioned at the close of Chapter 3 thatthe strategy of scientific advance often meansthat a good question answered badly may bea necessary prelude to a good answer someyears later. The purpose of this book hasbeen primarily to test the value of a question—How do flows of information, commands, ex-pectations, contribute to the understandingof flows of goods and income? The broadquestion has sired a family of specific ques-tions discussed at the close of Chapters 11and 12. They are implicitly collected in aseries of related boxes by the model that hasjust been outlined. Fill in the answers andthe theory achieves a concrete form. At anyrate, understanding grows. Work toward thisend can, happily, utilize the great deal thathas already been done. But it may be usefulto discuss, without pretense of system, some ofthe work that needs doing.

Time Series. The most obvious need is fortime series that reveal patterns of communica-tion in the form of orders along with in-formation about actions such as shipments

17 See the discussion and illustrative example inChapter 10.

or production. Required are data for thesame firms on sales orders and purchase or-ders, shipments and receipts, and, if possible,flows at other critical points such as produc-tion starts or finished production. Informa-tion for the stock pools that these flows boundcompletes the statistical picture. By arrangingthe firms (or divisions of them) in verticallyrelated sequences, it would be possible totrace the vertical transmission of demandthrough the economy. Such sequences couldalso be related to appropriate price informa-tion. Information for stages of an industrysequence would provide the wherewithal forexamining how buying waves spread verti-cally. Information for groups of industrieswould provide insight concerning the lateraldissemination of fluctuation.

The report of the Consultant Committeeon Inventory Statistics, made to the Subcom-mittee on Economic Statistics of the JointCommittee on the Economic Report in 1955,stressed the importance of information of thissort. It recommended improvement in thedata for manufacturing stocks, shipments, andorders (Recommendation 10); it recom-


mended that information on sales, new or-ders, stocks, and outstanding orders for majordepartments of department stores be collected(Recommendation 21). There has been acareful overhauling of the manufacturingdata, but unfortunately the information isstill less than what is needed to picture theflow of orders and output on a vertical orhorizontal basis. For department stores thesituation is sad indeed. Far from providingstatistics on orders by departments, even thedata for the total stores has been discontinuedas of December 1963.

The capacity of time series to inform aboutvertical and horizontal communication offluctuation would be greatly enhanced if datafor individual firms were summarized in termsof distributions as well as in terms of theusual totals or averages. Certainly, •for ex-ample, it would be useful to know somethingof the patterns of change in the distributionof firms in an industry with respect to thenumber of weeks' supply of materials heldon hand and on order, and of rates of changein this supply.

Interviews. Statistical data of these sorts,data capable of indicating what is done withrespect to purchasing and inventory prob-lems, require the counterpoint of informa-tion bearing on why it is done. One way ofacquiring this sort of insight is to ask thebusinessmen who make the decisions. I realizethat the results of discussions are consideredunscientific and subjective. Resorting to thismethod involves a trade-off: relevance is em-phasized at the sacrifice of precision. But atthe present state of the art, it seems clear thatrelevance is often a bargain purchase. Inshort, "It is better to be vaguely right thanprecisely wrong." 18 Specifically, systematic dis-cussions with businessmen are required con-cerning the range of subjects covered in Chap-ter 2. We need to get richer and firmer knowl-

18 The remark was attributed to Wildon Carr byG. S. Shove, in "The Place of Marshall's Principles inthe Development of Economic Theory," EconomicJournal, December 1942, p. 323.

edge about the structure of costs and op-portunity costs bearing on stocks and pur-chasing. We need to understand the informa-tion systems that help to formulate and vali-date objectives. Questionnaires are, of course,entirely useless for this purpose, at least untilfar more is learned about what to ask andhow to formulate questions. Indeed, even inan open-ended interview, specific questionsabout stocks are likely at best to be only apoint of departure.

For example, if a department store execu-tive is asked whether, when sales increase 5per cent, stocks also need to increase in thesame proportion, the answer may be some-thing like this: When sales first increase 5 oreven 10 per cent, stocks need not increaseat all. But pretty soon, often in connectionwith the next periodic planning procedures,management will start to think that the highlevel is going to last. Then stocks will moveup to their customary ratio to sales. But thequestion, "Why do stocks need to rise thatmuch?" provokes answers which do not, tothe businessman, seem to hold their groundwhen probed. The investigations that needto be made consist of the discussions thatfollow, in which the man of affairs who knowsthe stuff of which good decisions are madeis provoked to explore the grammar of theprose he speaks so well.

Discussions are exceedingly flexible tech-niques of study and accordingly are sensitiveto the preoccupations of the investigator. Ifinterviews are to be fully useful, they mustprobe the subjective as well as objective fac-tors that determine how information is se-lected, appreciated, and acted upon. Of spe-cial importance in the context of the ecologi-cal aspects is the role of learning and as-surance. Is there evidence of the gradualbuildup that the ecological model assumes?If so, what information is watched, how doesaction depend on the perception of whatcompetitors, suppliers, or customers are doingor have done? How is such knowledge con-veyed among competitors, suppliers, indus-


tries? Also of particular importance to themodel are insights that can provide a basisfor estimating how proclivity distributions areshaped. Interviews and other sorts of informa-tion, then, can in effect help to redraw Figure5 and to suggest how units move from onespot on the surface to another. The answerswould doubtless be found to differ for varioussorts of industries.

Econometrics. As indicated toward the be-ginning of Chapter 9, econometrics was tabledfor the course of this investigation. One wouldhope that its talents could be enlisted to testsome of the notions that have been put for-ward and to add quantitative dimensions.As mentioned earlier, both the investigationsdescribed in this book and further informa-tion of the sorts just mentioned are prerequi-sites. But even so, formidable difficulties per-sist in incorporating the insights of this studyinto equations.

The study has shown that an understandingof the behavior of aggregate stocks must bebuilt up out of an understanding of a num-ber of parts for which causality is reasonablyhomogeneous. The analysis throws some lighton how the parts should be defined. But evenso there are major hurdles to be leaped orcircumvented.

A convincing statistical "explanation" ofthe behavior of stocks or ownership mustreconcile the observed magnitude and timingof aggregate fluctuations with a realistic viewof business operations. My findings have pre-sented the hypothesis that efficient servicingof sales, other things the same, does notrequire fluctuations as large as those whichthe statistics show and consequently "otherthings" do in fact appear to change withbusiness conditions. Econometric analysis isthus asked to identify these other things andmeasure their impact.19

19 Needless to say, the effort to identify influences onstocks other than that of sales is familiar to econ-ometric analysis. But, as I pointed out in Chapter 1,the results seem to be less than satisfactory. A majordifficulty is the too powerful influence of orders. Ifownership rather than stock is to be explained, the

At a statistical level, this underscores theusual difficulties of isolating factors whichtend to parallel one another at least most ofthe time—factors such as shipments, salesorders, labor costs, capacity utilization, marketstringency, opportunity costs of financing orexpectations about each.

At an analytic level, the potentially im-mediate response of ownership implies thatdistributed lags are a receptacle for ignorance;even for stocks, lags must have a duration thatmakes sense in terms of specific managementproblems and procedures in the context ofcyclical variation.20 Finally, the interpreta-tion of the meaning of coefficients is confusedby the possibility of multidirectional causalrelationships, including those of an ecologicalsort.21

With the help of information from inter-view studies, the ingenuity of econometricwork may contrive to circumvent the worst ofthese difficulties. If so, it seems likely that

difficulty can be described by saying that new salesorders (or backlogs) may be viewed as a cause andnew purchase orders (or outstandings) are a result.The format of the analysis must somehow accommodatethis distinction.

20 In the Context of seasonal variation, the lags wouldoften be different, and this raises questions concerningthe usefulness of analyses based on data that are notdeseasonalized when seasonal patterns are strong. Forexample, unlike cyclical variations, seasonals in salescan often be quite reliably forecast; the relative im-portance of the several explanatory variables usuallydiffers for cyclical and seasonal changes in stocks andownership; the timing of the relations among thevariables will differ. If seasonals are strong, the parain-eters of the equation system may tend to recite theseasonal rather than cyclical version of the story.

21 These qualifications of the meaningfulness ofgross correlation measures are superimposed on theworries expressed in Chapter 9, note 2, above. Indeed,perhaps the only honest test for association of thesesorts abjures the comfort of the "one period changemodel" and endeavors to reproduce history by meansof an equation system for a "process model"—one inwhich the influences presumed to be at work are fullyspecified and asked to churn out the resultant courseof the dependent variable. (For an instructive com-parison of the results of the two sorts of models, seeKalman J. Cohen, Computer Models of the Shoe,Leather, Hide Sequence, Englewood Cliffs, N.J., 1960.)Simulation may be a simpler and more flexible way toachieve a similar result.


individually fragile findings may gain collec-tive strength by a comparison of the findingsfor a number of individual industries ordepartments of department stores. The co-efficients developed for the several businesssituations ought to differ in fashions thatseem sensible in the light of other knowledgeabout each situation.

Simulation. Finally, there are serious gapsof knowledge concerning how the individual'sview of the problem, the information thathe uses, the responses that he makes, are in-fluenced by the market and how it responds toand generates new information. Processes in-volving information have been studied underthe titles of cybernetics and information the-ory. The particular sorts of processes involvedin the model of price-timed buying couldbe explored with the aid of the massive ca-pacity of the computer to manipulate andmemorize numbers. The technique of simu-lation is suitable and flexible. It has been re-peatedly put to work on the problem of trac-ing, in accordance with stochastic principle,how individual behavior builds into a timecourse of aggregate behavior.22

But my study seems to call for somethingmore than the now familiar notion of analysiswith a "feedback" from the environment. Thecharacter of the feedback is critical: it is onefor which the coefficients of reaction (at theindividual as well as at the aggregate level)themselves change. As far as I know, the

22 See especially Guy Orcutt, "A New Type ofSocioeconomic System," Review of Economics andStatistics, May 1957, pp. 116—123, and subsequent workof Orcutt and other contributors to the work of theSocial Systems Research Institute, University ofWisconsin.

Needless to say, feedbacks can be represented inmathematical models also. James Duesenberry andFranco Modigliani took this approach in their modelsof consumer buying which introduced maximum pastlevels of income as an indication of changing stand-ards of living. The advantage of simulation, as I see it,is simply, first, that a theory that proposes reactionsof people to one another is put to a sharper test ifthe process is specified at the individual level. Second,the process is likely to imply response at an aggregatelevel which is nonlinear, and therefore likely to be lostif functional forms must be predetermined.

aggregate implications of this sort of processhave not been explored. Interestingly enough,the closest thing to it that has come to myattention is in the field of epidemiology—the Reed-Frost model.23

One of the most attractive aspects of thetechnique of simulation is its capacity to testa theory constructed in terms of selected char-acteristics and behavior of individuals. Theassumptions that are made must result in aspaced and self-reversing wave; of critical in-terest is the ten- to fifteen-month thrust. Simu-lation itself can indicate what values for chiefcomponents of the model will, and what willnot, produce movements of the sort posited. Itcan indicate the support that is required fromexogenous influences. It can indicate howsensitive the picture is to reasonable rangesof variation in critical pieces of the explana.tion.24

I have suggested a number of directionsin which the effort to deepen understandingof the vertical diffusion of fluctuation associ-ated with inventory waves may be pursued.They feature the effort to understand thebehavior of individuals and how it generates

23 Work in the field of mathematical analysis ofepidemics started in the first decade of the century,when it was found that periodic recurrences of epi-demics could be deduced from and described byinformation on the number of susceptibles, contact-rates, attack-rates, and recovery ratios. Theory devel-oped over many years. However, deterministic modelsdid not seem to square with the facts, and a stochasticmodel was introduced in the middle of the 1920's.Somewhat later, the notion of a threshold was intro-duced; the proportion of susceptibles in a communitymust be above some critical value.

The approach seems to be associated with the nameof Lowell J. Reed and Wade Hampton Frost, whotaught at Johns Hopkins University. But most of thewritten expositions and much if not most of thetheoretical and empirical work appears to have beendone by others. See Norman T. Bailey, MathematicalEpidemiology, London, 1957. There are also numerousarticles in the journal, Human Biology, A Record ofResearch, September 1952, and in Jerzy Neyman, ed.,The Third Berkeley Symposium on MathematicalStatistics and Probability.

24 James Bettman intends to explore some of thesequestions through interviews and perhaps simulationin his doctoral dissertation at Yale University, GraduateSchool of Business Administration.


and feeds upon relevant information andchanging objective situations. Knowledge ofthis sort seems to me to be necessary to sci-entific exploration of the process of economicchange.

But it is perhaps not too visionary tohope that it may have some value in modify-ing the process. Most businessmen probablyprefer to buy and sell in a relatively stableand predictable market. If so, fluctuations ofthe sort that have been discussed are un-desirable. Understanding of how fluctuationis built up by the system whereby problemsare perceived and solved by businessmencould be a first step in designing better waysof solving them—ways that subdue their in-nate tendency to generate and amplify fluctu-ation. Insights would bear particularly, I sus-pect, on the problem of sustaining businessexpansion.

If it is useful to trace the move-by-movepattern whereby expectations, actions, infor-mation, and situations feed upon one anotherin connection with the buying of materialsby business enterprises, it should be usefulalso to trace analogous processes in otherfields. Certainly, for example, the "fickleness"of consumers, or the lumped equipment pur-chasing of producers, or local "construction

cycles" are not without strong elements ofinterplay among the actions of many indi-viduals as well as between individuals andthe business environment. Some elements ofthe price-timed buying model might be ex-pected to apply—the hill-shaped frequencydistributions of proclivities, the ceilings, theimportance of assurance and learning, thetime-consuming buildup of evidence, thechanging patterns of market response. Butmany other elements would differ, particularlythe length of most of the lags. Even trendgrowth, especially in developing countries,shares most of these elements.

Questions of these sorts, once raised, arehard to forget. Their hold is strengthenedby the importance that we are learning toaccord to rates of change in the economy—rates of rise during prosperity fast enoughto maintain expansion but not too fast tobe themselves maintained. Rates of change inecological processes tend to be willful at theaggregate level. Hope of adjusting them tothe requirements of stable growth seems tolie in understanding the underlying micro-process and how it cumulates. For this pur-pose the august tools of equilibrium analysismay be of limited use.

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This PDF is a selection from an out-of-print volume from ... · do not show either peculiarity. An Ecological Process Accordingly, it may be useful to reflect on the patterns of interaction