The Persistence of Learning and Acquisition Strategies

15

TUTORIAL

THE PERSISTENCEOF LEARNING AND

ACQUISITION STRATEGIESPatrick N. Watkins

The acquisition strategies implied by two theories of learning—learning curvetheory and knowledge depreciation theory—are quite different. This articlereexamines empirical data for land-based weapon systems to determine ifknowledge depreciation theory can be confirmed. Results fail to confirm knowledgedepreciation theory and support learning curve theory. The author concludesthat acquisition managers should continue to use learning curve theory to modeltheir acquisition strategies.

usefulness of learning curve theory. Weconclude that acquisition managersshould continue to use analysis based onlearning curve theory when evaluatingalternative acquisition strategies.

THE CONTEXT OF

ACQUISITION STRATEGY ANALYSIS

The twin foundations of modern ac-quisition strategy analysis are the mi-cro-economic theory of markets and thelearning curve. The premise of existinglaw and regulation is that competitivemarkets produce goods for the govern-ment at the lowest prices and best qualityavailable. Where competition exists, thegovernment routinely expects to avail it-self of its benefits. The opposite extreme

T he twin analytic foundations for ac-quisition strategy are the theory ofmarkets (from modern microeco-

nomics) and the learning curve (from in-dustrial engineering). Argot, Beckman,and Epple (1990) argue that learning doesnot persist in industrial settings. They havedeveloped a theory of knowledge de-preciation that calls into question learn-ing curve theory. In this theory learningis an attempt to keep up with changingcircumstances.

To explore the differences in and im-plications of these theories, and as anempirical test of these theories, we reex-amine data from two land-based weaponsystems, the M-113 and the M-60, andwe present new data on the Abrams Tank.The data provide little support for knowl-edge depreciation theory and confirm the

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in a market is monopoly, where one firmmaximizes profits by exploiting the mar-ginal revenue derived from demand. TheCongress and the military departmentshave addressed the problem of monopolyin military acquisition through the Truthin Negotiations Act, the Cost AccountingStandards Act, and implementingregulations.

The economic theory of the firm wasdeveloped extensively during the earlierpart of this century. The monopolistic casewas expanded to include duopoly, wheretwo firms control supply, and oligopoly,where multiple firms control supply. These

cases werealso expandedto includenonprice com-petition. Theseanalyses arenow consid-ered standardtreatments and

are covered in most micro-economics text-books. (An excellent graduate level textthat requires only college algebra isFerguson and Gould [1975].) Where clearanalogies to the classical cases exist, littleanalysis is required. For new or emergingcommercial markets, proper market re-search is usually sufficient.

Economists also have attempted to studythe case where one buyer and one sellerconstituted the market. This case becameknown as bilateral monopoly and was stud-ied as early as 1931. As Ferguson andGould note, the analysis based on classicalmodels is indeterminate. Fouraker andSiegel (1963) studied bilateral monopolyfrom the point of view of bargaining. Thisanalysis provides significant insight intothe behavior of participants in poorly

formed markets. The outcome is forparticipants to divide a total profit poolbased on their relative market power.While powerful, this analysis provides nonew tools that might help a buyer bringadditional suppliers into a market.

Acquisition strategy analysis was de-veloped to fill this gap in economic theory.For a variety of military weapon systemsthere are only a small number of potentialproducers. Some problems are rooted inthe historical practice of production ingovernment-owned facilities or withgovernment-owned production and re-search property. Some are characterized bylow production rates that discourage capi-tal investments. Some companies possesscarefully guarded trade secrets that are usedto produce weapon systems. Other barri-ers to competition exist. Historically, themilitary departments have used competi-tion strategy analysis in those cases whereacquisition managers had some reason tobelieve that competition could be intro-duced for a weapon system that either wascurrently being produced or was expectedto be produced on a sole source basis. Theanalysis usually examines the particularsof a given case to determine what barriersexist to competition and to estimate theexpected returns from competition.

The very act of inducing a competitionmay be costly. Where government-ownedproduction equipment is used by a solesource, there may be costs associated withchanging plant management from one firmto another, duplicating equipment in a sec-ond source plant, paying for investigationsand studies, paying competitors to developproposals, and leader-follower arrange-ments or educational buys. Up-front in-vestment for a program can be substan-tial, reaching into the tens of millions of

�Up-front invest-ment for a programcan be substantial,reaching into thetens of millions ofdollars.�

The Persistence of Learning and Acquisition Strategies

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dollars. Potential competitors are likelyto invest their own money in the cam-paign, and that spending can mitigate thegovernment’s investment.

The output of a competitive strategyanalysis is an assessment of alternativesto induce competitors to bid on weaponsystem production. It usually takes theform of a comparison of alternatives forcompetition with the sole source case, andmay include an assessment of one or moredual sourcing strategies. The results of theanalysis may be presented as pointestimates of expected savings, as sophis-ticated probability assessments, or inhybrid formats.

CURRENT PRACTICE

The model used to estimate the effectsof competition on weapon systems or com-ponent prices has been developing formore than 30 years. Washington (1997)provides a good historical overview. Typi-cally, the analysis begins with an existingsole source production program. Theanalysis assumes that costs will be a func-tion of quantity produced according tolearning curve theory. Effects of compe-tition are modeled as either shifts or rota-tions in the learning curve. Unique con-tracting arrangements such as multiyearcontracting with economic order quantityfunding may be modeled as well, usuallyas a shift in the curve. The models typi-cally assume that once a program revertsto a sole source status, the remaining in-cumbent will exploit its position and costwill revert to near-precompetitive levels.Analysis may proceed either by analyz-ing the functions and generating discretevalues for competitive savings, or by

probabilistic modeling, generating rangesof outcomes and sensitivity points.Watkins (1982) summarized existingknowledge of commodity learning curvesand their known probability distributions.

Traditional economic analysis does notrecognize learning curves. Rather, quan-tity produced is said to be a function ofinputs, usually labor and capital. Variousforms of the production function havebeen investigated, typically providing fordiminishing returns to inputs consistentwith the marginal productivity theory ofmicroeconomics. Perhaps the best knownis the Cobb-Douglas production functionQ = LαΚβ, where quantity produced is anexponential function of labor and capital.The modern innovation, explored by Argotet al., is the addition of a knowledge inputto the equation.

The learning curve arises from indus-trial engineering observations. As summa-rized in various places, most notably inAsher (1956), observations of plant expe-rience in a vari-ety of indus-tries, and par-ticularly in theairframe indus-try, led to theconclusion thatlabor hours and material costs decline witheach doubling of quantity produced. Costsare log-linear functions of the form, c =Axb, where labor hours or costs (c) are anexponential function of quantity produced(x) and first unit cost (A). This type ofanalysis usually assumes a given state oftooling and capital equipment. (Note thesimilarity to the Cobb-Douglas produc-tion function.) Analysts modify functionsfor changes in tooling, capital equipment,and configuration.

�Traditionaleconomic analysisdoes not recognizelearning curves.�

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The classical theory assumes that learn-ing arises from repeated physical motionand the application of both physical andconceptual learning to physical processes.The theory posits that learning persiststhrough time and is a function of quantityproduced.

The learning curve leads us to severalconclusions about competitive acquisitionstrategy:

• Incumbents with experience have acompetitive advantage. Lack of expe-rience producing a product or servicecan be a significant barrier to marketentry.

• Educational quantities can boost thecompetitive position of secondary ortertiary sources.

• Lost learning may override the effectsof competition and make it uneco-nomical to sustain multiple sources.

• Changes in production disrupt learn-ing, which is recovered with additionalquantity produced.

KNOWLEDGE DEPRECIATION

In contrast, Argot et al. argue thatknowledge depreciates rapidly. Testing theLiberty Ship data from World War II, theauthors concluded that learning depreci-ated at a rate of 25 percent per month (97percent per year) and that there was little,if any, transfer of learning between ship-yards. What little transfer did occur camefrom improvements in design. Unit laborhours were approximately constant after

design introduction. (The Liberty Shipdata is a classic public database usedextensively in learning curve studies.)

The knowledge depreciation hypothesisreflects the more recent conception oflearning as innovation. In this view thebusiness environment is ever changing andrequires firms to change (adapt), changein turn demands innovation, learning pro-duces that innovation, and innovationmakes existing knowledge obsolete. Theprocesses used to weld steel are no longerapplicable when new grades of steel andnew welding methods come into use.

The method of analysis used is similarto learning curve analysis. The basic equa-tion is log linear in labor hours, capitalinputs, and knowledge, with dummy vari-ables used to capture unique inputs.Knowledge in turn is modeled as a linearcombination of current period quantity andlast period quantity. A constant parameterapplied to prior period quantity is used tocapture depreciation of knowledge fromthe prior period.

The implications are quite different forcompetitive acquisition strategy:

• Incumbents gain no competitive advan-tage from experience.

• Competition can be effectively intro-duced at any time, provided there areno other barriers.

• Dual sourcing can be sustainedindefinitely.

• Changes in production must be ac-companied by new learning if laborefficiency is to be maintained.

The Persistence of Learning and Acquisition Strategies

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�Learning curvetheory predictsthat there is anopportunity costassociated withdual or multiplesourcing.�

COMPARISON OF RECOMMENDED

ACQUISITION STRATEGIES

As we can see from the previous dis-cussion, the contrast between the strate-gies produced by these two theories ismarked.

INCUMBENT ADVANTAGELearning curve theory predicts that in-

cumbents will have a competitive advan-tage from experience. The longer an in-cumbent has produced a product or ser-vice and the steeper the learning curve,the larger the incumbent’s advantage. Newentrants must produce substantial im-provements in first unit cost and equal orsteeper learning to be competitive. Theknowledge depreciation theory predictsthat incumbents will have no competitiveadvantage. New entrants will be on equalfooting with incumbents to the extent thatthey can produce innovations.

Stated another way, learning curvetheory posits that knowledge (particularlytacit knowledge) is a prime input to theproduction process while knowledgedepreciation theory says that, at best,knowledge is like public infrastructure, anecessary precondition to production.

TIMING OF A COMPETITION Learning curve theory leads one to in-

troduce competition as early as possiblein a production program to mitigate anypotential incumbent advantage. Similarly,educational buys or other pilot produc-tion contracts for second sources reduceincum-bent advantages in two ways: first,by increasing the quantity produced bycompetitors, thereby increasing opportu-nities for learning and improvements, and

second, by reducing the quantity avail-able to the incumbent, limiting suchopportunities.

Knowledge depreciation theory predictsthat competition will be successful at anytime, provided competitors are available.Educational buys and other pilot programsare of little value.

DUAL SOURCINGLearning curve theory predicts that

there is an opportunity cost associated withdual or multiple sourcing. Provided theincumbent hassufficient ca-pacity, anyquantity givento competingsources reducesthe quantityavailable to theincumbent andcorresponding-ly limits the opportunities for cost re-ductions through learning. If lost learningis significant, the correspondingopportunity cost can exceed the gains fromcompetition.

Knowledge depreciation theory predictsthat there are no opportunity costs associ-ated with lost-incumbent production quan-tities, and therefore any gains from com-petition are pure gains.

CHANGES IN PRODUCTIONThe weakness of learning curve theory

is that it predicts continued improvementseven after major changes in production.The Boeing “S” curve was an early at-tempt to estimate the impact of produc-tion changes on learning (Asher, 1956).Yet, for all attempts to incorporate

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�Real organiza-tional life is morecomplicated thaneither theory.�

additional techniques, learning curves donot predict the types of problems cited byArgot on the Lockheed L-1011 or morerecently, on the Boeing 757 (Boeing,1999). In these cases increasing produc-tion led to increases in both unit and totalcosts. Profitability disappeared where itshould have increased.

The theory of knowledge depreciationpredicts not only that new knowledge mustaccompany changes in production, butthat the production of new knowledge is

itself likely todisrupt the pro-cess of renew-ing existingknowledge. Inthis regard thetwo theoriesstand in stark

contrast, learning curve theory holding thatlearning is a continuous function of quan-tity produced, and knowledge deprecia-tion theory holding that learning isessentially memoryless, or Markovian.

Real organizational life is more com-plicated than either theory. Learning curvetheory was developed at a time when stan-dard industrial engineering techniquescould be applied to simplified, labor-intensive processes. Once laid out, theassembly line could be balanced and main-tained at peak efficiency using standardanalytic tools. Today, more often than not,production lines include many more op-erations than just assembly, are made upof mostly automated processes, incorpo-rate active control programs, may includeartificial intelligence, and are more com-plicated to manage. Learning curve theoryrests on a view of labor that is inherentlyself-contained. Management’s role is com-pliance and little more.

Knowledge depreciation theory is simi-larly one-dimensional, resting on theassumption that all that is needed is con-tinuous innovation to renew knowledgeof production processes. In fact, modernproduction systems are more complex bothin their management and in the interac-tions among component processes. Whilesuch complexity makes prediction moredifficult, it need not render it random. Inthis regard, knowledge depreciation theorycaptures part of the problem of implement-ing changes in production in a complexsystem, while learning curve theory doesnot.

In sum, learning curve theory calls fora careful analysis of the advantages anddisadvantages of introducing competitionfor limited production quantities and, whenthe decision is made to compete, to do soat the earliest possible moment. Lost-learn-ing opportunities may drive a decision fora competitive down-select to a singlesource. Knowledge depreciation theorypredicts competition can be successful atany time and need never be discontinued.Most important, learning curve theory pre-dicts competition will be difficult to in-duce when an incumbent has significantexperience, while knowledge depreciationtheory predicts competitors will alwaysbe available provided that there are nocapital or other market barriers.

RESULTS FROM M-113 AND M-60 DATA

Watkins (1982) presented data from sev-eral land-based weapon systems, both solesource and competitive. For this study Iselected two programs with extensive data,the M-113 armored personnel carrier andM-60 main battle tank. The M-113 is an

The Persistence of Learning and Acquisition Strategies

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ideal exemplar for learning curve theory.The competitive history yields a 91-per-cent learning curve that persists even afterthe market reverts to sole source procure-ments. The M-60 tank ought to be a fineexemplar for knowledge depreciationtheory. The M-60 had one competition fol-lowed by an entire life cycle of sole sourcecontracts. It exhibits essentially no learn-ing (99.9-percent learning curve). Bothbegan production in 1959–1960, rampedup production for the Vietnam War, rampeddown production after the war, and wentthrough successive model changes.

For each program, I followed the meth-odology described in the technical appen-dix. Model changes or significant engi-neering change proposals were treated as

shifts in the learning curve. In the case ofthe M-60, competition is modeled by aone-time shift. No attempt is made to con-trol for capital inputs as these are un-known. We know that the M-113 was pro-duced in two plants by FMC from 1966to 1971. We know that the M-60 was pro-duced in the Lenape, DE, Tank Plant in1959 and then in the newly renovatedDetroit Arsenal Tank Plant from 1960 on-ward, the shift coinciding with the oneand only competition for M-60 produc-tion. Using Argot’s model, multiple re-gression will capture changes in capitalin the dummy variable regression. In fact,the change in capital does not show up inthe M-113 data and is inseparable fromcompetition effects in the M-60 data. In

The M-113 (Armored Personnel Carrier)

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both cases, capital inputs do not influenceeither the slope of the learning curve orthe knowledge depreciation parameter andwere not pursued further.

These two systems provide an essen-tial test of the knowledge depreciationtheory. Knowledge depreciation theorypredicts rising prices with falling lot size.Learning curve theory predicts continuedimprovements with quantity produced.Both systems experienced falling produc-tion quantities in the 1970s, with the endof the Vietnam War.

The key results are as follows:

• There was no support for the predic-tion that knowledge decays. For theM-113 the best fit was with the knowl-edge depreciation factor set to “one,”that is, full retention. For the M-60 thebest fit was with the factor set to “zero”(no retention). Both results are consis-tent with the learning curve theory.

• Model changes accounted for themajority of the price variance. Theknowledge depreciation equation ac-counted for less than 5 percent of theprice variance.

• Price changes were predicted bylearning curve theory, but not by theknowledge depreciation theory. (See“Forecast Accuracy” below.)

ABRAMS MAIN BATTLE TANK EXPERIENCE

I also examined the price history on theAbrams Main Battle Tank (M-1 Series).Initial production costs trends are difficultto evaluate because of component break-out prior to 1983. The Army stabilized the

work share for the prime contractor in 1983.The Army bought 8,038 M-1 or M-1A1tanks with the last unit produced in fiscalyear 1991. The Abrams series has been solesource from initial production. Beginningin 1981 the Army applied should-cost tech-niques to reduce the cost of the primecontractor’s content.

One might expect the M-1 to be verysimilar to the M-60. The M-1 was pro-duced at two plants, along side the M-60at the Detroit Arsenal and by itself in theLima Army Tank Plant. General Dynam-ics bought Chrysler Defense in 1982 andoperated both plants for the Army, pro-ducing both the M-1 and the M-60. TheM-1 fabrication processes made signifi-cant use of robotic welding, which intheory flattens learning curves. In fact, theM-1 and the M-60 were quite different.

Key results were:

• A learning curve with a 91.4-percentslope fit the data adjusted for modelchanges.

• As with the competitive M-113 data,there is no knowledge decay. The lineof best fit was when the knowledgedepreciation factor is “one”—that is,full retention.

• Price changes were predicted well by thelearning curve while the knowledge de-preciation theory had only modest suc-cess, as discussed immediately below.

FORECAST ACCURACY

Using the equations derived from theinitial regression analysis, one can makepredictions of prices for the ensuingproduction lots. Price changes can be

The Persistence of Learning and Acquisition Strategies

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The M-1Abrams Tank

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computed directly from these predictions.The forecast price changes are then com-pared with the actual price changes usingregression analysis to measure the vari-ance explained by each equation.

This element of the analysis measuresa key difference between the two theo-ries. Learning curve theory predicts priceswill continue to decline with quantity pro-duced even when lot sizes shrink. Knowl-edge depreciation theory predicts priceswill increase with shrinking lot size anddecrease when lot size increases, regard-less of cumulative quantity produced. Allthree weapon systems had periods ofsignificant change in lot sizes. The results

confirmed learning curve theory and failedto confirm knowledge depreciation theory(Table 1).

A NOTE ABOUT LABOR EXPERIENCE

We have also gleaned extensive dataand knowledge from detailed observa-tion of operations in Army plants. Whilemuch of this data is proprietary, some ofthe conclusions we have drawn can bepresented in this public forum.

First, if we define process knowledgeas the “why” of processes, then it is ourobservation that knowledge usuallyenhances physical learning. Operator

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experience with welding, machining,grinding, or assembly operations benefitsfrom conceptual knowledge of operations,visual models, plans of operations, and avariety of experiences. The classic ex-ample is minor engineering changes.Changing the location of a hole, its size,and even the material may have little im-pact on the time it takes an experiencedoperator to drill a hole, given machine fac-tors. Similar types of changes make nodifference in assembly operations with ex-perienced assemblers. By contrast, minorchanges of any kind are likely to disruptthe pace and output of inexperiencedworkers. To the extent that learning is tak-ing place, variety actually helps workersanticipate changes and adapt to them with-out loss of productivity.

Second, changes in processes can begraded by their effects on learning. Whilesuch a system relies to a large degree onengineering judgment, observation hasborn out the general principle that changescan be grouped by the degree of impactthe changes have on learning.

Third, in forecasting labor hours, theassumption that learning is always re-tained, even under severe production dis-ruption, has been effective for us. We have

modeled changes in labor hours due todisruption by assuming the labor hourchanges decay exponentially with the pas-sage of time. This model has consistentlypredicted aggregate labor hours for a dis-ruptive event with moderate accuracy andpredicted the point of disappearance ofeffects to within one production lot.

These observations are in sharp con-trast to the knowledge depreciation theory.That theory would predict that engineer-ing changes, strikes, material shortages,or similar disruptions would result in lostlearning with no recovery. Our experienceis otherwise.

EXTENDING RESULTS TOOTHER INDUSTRIES

A journal referee noted that only twoindustries were represented in these stud-ies and asked whether the results extendedto other industries. I appreciate the ref-eree raising this important question. Wecan say several things about that issue.

First, Argot et al. did not directly testthe predictive value of their equations. Iselected automotive commodities becausethey display the least learning of all

Table 1.Correlation of Predicted Price Changes with Actual Price Changes

KnowledgeProgram Learning Depreciation

Curve Equation

M-113 .6107 .2477

M-60 .6084 –.0324

M-1 .8450 .3480

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products studied for competitive acquisi-tion strategies (Watkins, 1982). We canexpect the effects of knowledge deprecia-tion theory to be most prominent in thisindustry, especially with those programslike the M-60 that display no learning. Au-tomotive commodities should give us ourbest test of the predictive power of theknowledge depreciation theory. Given thatother industries display greater learning,one can logically expect that learning curvetheory will be more effective at predictingcosts and prices than knowledge deprecia-tion theory in such industries.

Second, learning curve theory is a ro-bust estimating tool across a variety ofindustries. During the past two decades,competitive acquisition strategies usinglearning curve theory have been success-fully developed for aircraft, munitions,electronics, and combat vehicles. Consid-ering the current lack of support forknowledge depreciation theory as an esti-mating tool and the robustness of learn-ing curve theory, it is likely that learningcurve theory will retain an advantage inpredictive power across industries.

Finally, the Liberty Ship program mayitself be unique. Thompson recently ana-lyzed new data from the National Archiveson the Liberty Ship program. He foundthat certain proxies for capital investmentthat Argot used were in fact inadequate.The new data showed that major capitalspending on capacity improvements at theshipyards continued through the first twoyears of production. Thompson attributes50 percent of the productivity gains in theLiberty Ship program to capital improve-ments, 44 percent to learning, 5 percentto relaxed quality standards, and the re-maining percent being error (Thompson,in press). Argot’s results may be due to

the rapidly changing nature of the yards’capital equipment and production pro-cesses. If so, then knowledge deprecia-tion theory may only extend to those situ-ations where process change is a signifi-cant factor. The cases examined in thispaper all used relatively stable productiontechnologies.

It is plausible that learning curve theoryis a better estimating tool for plants andproducts with relatively stable productionprocesses and that knowledge deprecia-tion theory is a better estimating tool whereproduction processes are changing rapidly.It is also plausible that learning curvetheory has an advantage as an estimatingtool regardless of the industry. Howeverplausible, these are hypotheses that remainto be tested.

A NOTE ABOUT TECHNOLOGICAL LEAPS

Common sense tells us that when radi-cal shifts in technology occur, little of ouraccumulated experience will be useful.Firms that have extensive accumulatedexperience can be vulnerable to competi-tors who lower their first unit productioncosts with new technology. Knowledge de-preciation theory seems to fit well withthis scenario.

On the other hand, firms with adaptivemanagers often learn quickly how to in-corporate new technologies into their pro-duction processes, which in turn allowsthese firms to build on their accumulatedexperience and gain even greater competi-tive advantages than new rivals. Accumu-lated managerial and production line ex-perience, or their combination, may con-tribute significantly to the introduction ofnew technologies.

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captured by product model changes andby changes in market position. Whilelearning was important, it was not as sig-nificant as either model changes or mar-ket power. Therefore, it is important toview learning curve theory as a supple-ment to market analysis—not the otherway around. Each alternative acquisitionstrategy needs to be examined in light ofthe particular details of the specific mar-ket as well as the experience of marketparticipants.

Knowledge depreciation theory failedto improve on current models of cost be-havior under varying competitive condi-tions for land-based systems. It merelyconfirmed the results from establishedanalysis. However, as knowledge depre-ciation theory is plausible under somescenarios, such as rapidly changing pro-duction processes or leaps in technology,decision makers need to consider the pos-sibility that accumulated experience mayhave less impact where these conditionsare present.

The treatment of model changes in thispaper suggests that technological leapscould be modeled using learning curves.The evidence suggests that once a tech-nological leap is made, further improve-ments will follow a learning curve. Onecan then model a technological leap aseither a new curve or as a shift in an ex-isting curve, possibly with a curve rota-tion (change in slope).

Where technological leaps are antici-pated, acquisition managers would do wellto consider using both knowledge depre-ciation theory and learning curve theoryto assess acquisition alternatives.

CONCLUSION

These results suggest that the mosteffective means we have for modeling thepotential impact of competition on acqui-sition strategies is the analysis of marketpower combined with the learning curve.It is useful to note that in the cases exam-ined here the majority of the variance is

Patrick N. Watkins currently serves as a procurement analyst working on busi-ness process reengineering and electronic commerce at the U.S. Army Tank-Automotive and Armaments Command in Warren, MI. He has 22 years experi-ence with Army acquisition, primarily in combat vehicle contracting. His work ondual sourcing and competitive strategy dates back to 1980. He recently servedas a consultant to the Abrams-Crusader Common Engine Source Selection.

(E-mail address: watkinsp@tacom.army.mil)

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REFERENCES

Argot, L., Beckman, S. L., & Epple, D.(1990, February). The persistence oflearning in industrial settings. Man-agement Science 36(2).

Asher, H. (1956). Cost-quantity relation-ships in the airframe industry. SantaMonica, CA: Rand Corporation.

Boeing Company. (1999). 1999 annualreport. Seattle, WA. Boeing Com-pany: Author.

Ferguson, C. E. & Gould, J. P. (1975).Microeconomic theory (4th ed.).Homewood, IL: Irwin.

Fouraker, L. E., & Siegel, S. (1963).Bargaining behavior. New York:McGraw-Hill.

Thompson, P. (In press). How much didthe Liberty shipbuilders learn? Newevidence for an old case study. Jour-nal of Political Economy. Availableuntil published at http://www.uh.edu/~pthompso/research/working_papers.html.

Washington, W. N. (1997, Spring). A re-view of the literature: Competitionversus sole source procurements.Acquisition Review Quarterly 10,173–187.

Watkins, P. N. (1982). Competition inautomotive commodities. Warren, MI:U.S. Army TACOM.

Williams, R. (1982). Bradley fighting ve-hicle second source assessment.Washington, DC: Army ProcurementResearch Office.

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TECHNICAL APPENDIX

SOURCES OF DATAThe data for the M-113 and M-60 are

previously published data taken fromWatkins (1982). This data was also pub-lished in Williams (1982). The contractdata are vehicle quantities and final unitprices. Final unit prices include all priceadjustments and engineering changes. Unitprices were then adjusted to 1980 dollarsusing a composite inflation index consist-ing of weighted values for industrial com-modities and average hourly earnings.Weights were assigned for each system

Fiscal DoD PriceYear Model Qty. Price ($) Infl. (1997 $)

1979 M1 110 1,475,731 0.4161 3,546,578

1980 M1 352 1,238,035 0.4641 2,667,604

1981 M1 569 926,423 0.5180 1,788,461

1982 M1 657 739,845 0.5921 1,249,527

1983 M1 686 749,676 0.6450 1,162,288

1983 IPM1 114 775,814 0.6450 1,202,812

1984 IPM1 780 753,740 0.6906 1,091,428

1984 M1A1 60 956,211 0.6906 1,384,609

1985 M1A1 840 933,966 0.7140 1,308,076

1986 M1A1 840 972,513 0.7340 1,324,950

1987 M1A1 720 1,016,036 0.7538 1,347,885

1988 M1A1 720 1,054,514 0.7756 1,359,611

1989 M1A1 720 1,080,202 0.8091 1,335,066

1990 M1A1 299 1,113,964 0.8423 1,322,526

1990 M1A1 393 1,155,121 0.8423 1,371,389

1991 M1A1 178 1,216,360 0.8785 1,384,587

Table 2. Abrams Price History

that reflected the approximate material andlabor content.

M-1 Abrams data are presented below.Unit prices are initial unit prices exceptfor fiscal year 1979 and fiscal year 1980where they are final prices. Unit pricesare then adjusted to constant 1997 dol-lars. The key difference from the M-113and M-60 data is that all Abrams pricesfrom fiscal year 1981 forward are firm-fixed prices. The only missing componentis negotiated engineering changes incor-porated after contract award. However, the

The Persistence of Learning and Acquisition Strategies

29

impact of these engineering changes is notsignificant on the analysis presented here.

Engineering changes incorporated af-ter award on one contract are included inthe new unit prices for the follow-on year.For example, changes added to fiscal year1981 would be included in the initial unitprice for fiscal year 1982. The overall ef-fect is to slightly reduce the slope of thelearning curve. The effect on regressioncoefficients is probably negligible, as theengineering change content was consis-tently around 2 percent per year for thisperiod of production. Inflation indexes areweighted in the same manner as for theM-60 and M-113.

LEARNING CURVE MODELTo estimate the learning curve I

modeled the data using the equation inFigure 3.

Model changes are often explicit in theoriginal data. Where they are missing,model changes can be estimated by as-signing the jump in prices at model change

over to the model change. All modelchanges are treated as shifts in the learn-ing curve that persist until a further changeis encountered.

KNOWLEDGE DEPRECIATION MODELTo estimate knowledge depreciation I

used the equation in Figure 4 derived fromArgot (1993).

The equation used for this article is:

Ln Ht= a0+ αααααLn qt + γγγγγLn Kt-1 + M + ut

where M is the model change matrix.

The key difference here is the lack ofterm for capital inputs. As explained inthe text, there is no discernable impactfrom changes in capital and it wasexcluded from the analysis. The form ofthe equation is derived by algebraicsubstitution and translation of parameters.

The knowledge depreciation factor isan indicator of how quickly current knowl-edge becomes obsolete. A value of “one”

ln y = ln A + b*ln x + Mt + e

where

y is the unit price in constant dollars,

x is the cumulative quantity produced,

b is the learning coefficient b = log(curve slope)/log 2,

Mt is the unique model change value at time t, and

e is an error term.

Figure 3. Equation to Estimate Learning Curve

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Ln qt = a0 + ΣΣΣΣΣaD + αααααLn Ht +βββββLn Wt + γγγγγLn Kt-1 + δδδδδZt’ + ut

where

qt is quantity of output,

aD are dummy variables with weights a, a0 being initial,

Ht are total labor hours worked,

Wt is a surrogate for capital inputs,

Kt = λλλλλKt-1 + qt, the knowledge equation,

λλλλλ is the knowledge depreciation parameter, defined on the interval [0,1],

Zt is a vector of other influences (e.g., turnover),

ut is the error vector, and

t is time period.

Figure 4. Argot�s Equation (in vector notation)

indicates knowledge is fully retained andused. It is consistent with the learning curvehypothesis. A value of “zero” indicates noretention—that is, knowledge is fully re-newed each period. An intermediate valueindicates some knowledge becomes

obsolete during each period and the fac-tor provides an estimate of the percentagethat becomes obsolete. Because the fac-tor actually measures changes in outputfor a given labor input, it is an indirectmeasure of knowledge retention.