Chapter 15 Economics of defense R&D

Chapter 15

ECONOMICS OF DEFENSE R&D FRANK R. LICHTENBERG Columbia University Graduate School of Business and National Bureau of Economic Research

Contents Abstract Keywords 1. Introduction 2. Design competitions 2.1. How much private investment in defense R&D?

3. 4. 5. 6. 7.

432 432 433 434 436 437 441 444 448

Independent R&D subsidies The profitability of defense (R&D and other) contracts The impact of defense and other R&D on productivity growth The effect of defense R&D on nondefense R&D investment How do Government decision-makers respond to cost information yielded by defense R&D? 450 8. Are defense R&D programs dynamically optimal? 453 9. Conclusions 455 References 456

Handbook of Defense Economics, Volume 1, Edited by K. Hartley and T Sandler © 1995 Elsevier Science B. V All rights reserved

432

FR. Lichtenberg

Abstract This chapter examines a number of aspects of defense R&D, including: mechanisms design competitions, and independent R&D subsidies - used by the US government to encourage firms to invest their own funds in defense R&D; theory and evidence concerning both the private and social benefits of, or returns to, R&D conducted by defense contractors; the effect of defense R&D on nondefense R&D investment; the response of government decision-makers to cost information yielded by defense R&D; and the dynamic optimality of R&D projects.

Keywords research and development, procurement, design competitions, innovation, productivity, profitability, government expenditure, R&D subsidies, weapons acquisition, defense policy

Ch. 15:

433

Economics of Defense R&D Table 1 b Defense R&D expenditures in 1991 of G-7 countries

Country

Total R&D

33

123

26.8

1 2 4 3 0 0

61 30 21 16 11 6

1.6 6.7 19.0 18.8 0.0 0.0

US Japan Germany France U.K. Italy Canada a

Defense R&D as % of total R&D

Defense R&D

Defense R&D as % of GNP 0.7 0.0 0.1 0.5 0.4 0.1 0.0

Billions of 1987 dollars.

b Source: Science and Engineering Indicators [National Science Board (1993)], pp. 375-376.

1. Introduction It is the government's role to promote investment in research and development (R&D) that yields innovations in the production of public goods, such as armaments for national defense and equipment for space exploration. As Table I indicates, it is estimated that in 1991, the G-7 nations collectively spent $43 billion (in 1987 dollars) on defense R&D. (This figure may significantly understate the true amount because, as we argue below, only R&D that is directly funded by the government is officially classified as defense R&D, whereas a substantial amount of "privately-funded" R&D may also be defense-related.) About three-fourths of total estimated defense R&D was conducted by the United States; for this reason, and also because more is known about defense R&D conducted in the US, we will devote most of our discussion to US military R&D. This chapter will examine a number of aspects of defense R&D. Sections 2 and 3 describe two mechanisms - design competitions, and independent R&D subsidies used by the US government to encourage firms to invest their own funds in defense R&D. The next two sections discuss theory and evidence concerning both the private and social benefits of, or returns to, R&D conducted by defense contractors. In Section 4 we argue that the private returns, or profitability, of defense R&D may depend on contractors' ability to shift costs from commercial to government R&D. A production function/productivity growth framework for assessing the social returns to defense R&D is presented in Section 5. The effect of defense R&D on nondefense R&D investment is examined in Section 6. The question, how do government decision-makers respond to cost information yielded by defense R&D?, is pursued in Section 7. Section 8 investigates whether independent R&D projects conducted by defense contractors are dynamically optimal, in the sense defined by Grossman and Shapiro (1986). The chapter's conclusions are summarized in Section 9.

434

ER. Lichtenberg

2. Design competitions In addition to the two obvious institutional arrangements the US government 1 uses to call forth defense R&D investment - performing R&D in government laboratories, and contracting with private firms and nonprofit organizations (such as universities) to perform R&D - there is a third and quantitatively important method by which the government promotes R&D investment relevant to the provision of social goods: awarding major contracts by a method of acquisition known as "procurement by design and technical competition". In essence, this method consists in the government's simply revealing its demand for certain types of technological innovations, and encouraging private firms to sponsor the necessary R&D, the costs of which the sponsor will recover from profits on the sale of the product. Edwin Mansfield (1971) has observed that before World War II, the government tended to issue relatively few R&D contracts to industry or universities. If the government wanted private firms to perform defenserelated R&D, it would encourage them to finance it on their own. Since the beginning of World War II, the real value of government R&D contracts has increased very rapidly, and contracting has apparently become the most important of the three methods used by the government to promote R&D investment related to social goods. But the government continues to induce a considerable amount of privately financed, federal mission-oriented R&D expenditure by sponsoring design competitions. A design and technical competition (henceforth abbreviated "design competition") begins "officially" when a federal agency (such as the Department of Defense) issues a formal Request for Proposals, which is often 1100 to 2500 pages long. Three or four firms typically submit proposals (which may range from 23 000 to 38 000 pages in length) in response to requests issued by the Defense Department, which then begins an elaborate review process. The firm that submits the proposal receiving the highest "score" 2 is generally selected as the contractor, and is essentially guaranteed (unless Congress decides to cancel the project) to be awarded a sequence of contracts for R&D, production, spare parts, maintenance, training, and so forth, over a number of years. (The extent of competition beyond the design stage - e.g. prototype competition, competition for production and maintenance - appears to be quite limited.) The contracts that are initially awarded to the successful firm are officially designated as "competitive" contracts. But most of the revenue that the firm will receive by virtue of having won the competition will come from subsequent, "follow-on" contracts, which are officially designated as "noncompetitive" contracts. In fiscal year 1984, for example, the value of noncompetitive follow-on contracts after design competition

Other countries with major defense industrial bases follow a similar system, but they often lack alternative domestic suppliers; hence foreign bids (e.g. in the aerospace industry) are necessary to avoid a domestic monopoly. 2 Projected price (or life-cycle cost) is only one of many factors affecting the total score, and has a small impact on the award of the initial contract. As discussed in Section 7, however, revisions in cost estimates appear to affect significantly the government's ultimate demand.

Ch. 15: Economics of Defense R&D

435

was 2.72 times as large as the value of competitive contracts associated with these competitions. Because the winner of the design competition is virtually assured of eventually being awarded the relatively large follow-on contracts, it is often suggested that contractors are willing to incur losses (by "buying in", or submitting bids below anticipated costs) on the initial competitive contracts. I think that it is natural to pose the question of why the government does promote mission-oriented R&D by sponsoring design competitions, in addition to doing so by directly contracting with firms to perform R&D. Perhaps the most compelling possible explanations are based on imperfect information considerations. A design competition appears to be an almost perfect example of a contest, in the sense defined by Barry Nalebuff and Joseph Stiglitz (1983) and others. In a contest, or competitive compensation scheme, the individual's reward or compensation (for example, whether he is awarded a contract) is determined only by his rank vis-a-vis his competitors, rather than by his "individualistic" output (or marginal product), as is the case in the classical model of pure price competition. These authors have shown that when the principal (in our case, the government) cannot directly and costlessly observe the level of input (effort) of the agents (contractors), rewards based on relative output are superior to payments based on individualistic output. They argue that competitive compensation schemes have "... greaterflexibility and greater adaptability to change in the environment than do other forms of compensation" (p. 41), so that contest may be preferred when the risk associated with common environmental variables (for example, the difficulty of achieving technical progress in a given area) is large. Moreover, "the use of a contest as an incentive device can induce agents to abandon their natural risk aversion and adopt "riskier" and more profitable production techniques" (p. 23). Inability of the principal to monitor the (relative) ability, or productivity, of various agents, is a second type of imperfect information which may render competitive compensation schemes optimal. Suppose that both government contracts and potential contractors are heterogeneous, in the sense that one firm is more qualified to perform a given contract that other firms, but the government is uncertain about the identity of the most qualified supplier. A number of theoretical models of markets characterized by this kind of imperfect information show that it is equilibrium behavior for sellers to invest in acquiring, and for buyers to rely on, signals of quality and ability. It may be useful to interpret design competitions as signaling phenomena, in which the signal of contractor ability that the government relies on is the score on the technical proposal. Factors other than imperfect information about contractor effort and/or ability may account for the existence of design competitions. For example, judging from periodic congressional hearings and reports on the subject [see, for example, US Congress (1969)], there is strong congressional demand for competition in procurement, perhaps because Congress believes that competitive procurement promotes economic efficiency or fairness. The passage of the Competition in Contracting Act also reflects this demand.

436

FER. Lichtenberg

2.1. How much private investment in defense R&D?

There are two types of evidence (aside from case studies and anecdotal evidence concerning company proposal efforts related to specific design competitions) concerning the amount of private investment in defense R&D. The first is provided by EM. Scherer's (1984) analysis of "linked" R&D and patent data of the largest R&D performing companies. Scherer attempted to classify each of about 15 000 US patents (obtained by 443 companies between June 1976 and March 1977) by "industry of use", that is, to identify the sector(s) of the economy in which (most intensive) use of the invention was anticipated. Two of the industries of use defined by Scherer were "defense and space operations" and "government, except postal and defense". He estimated the value of company-sponsored R&D "used" by these sectors to be $1206.3 million and $378.7 million, 11.3 and 3.6 percent, respectively, of the total amount of company-funded R&D ($10.64 billion) attributed to these companies. Thus, according to Scherer's methodology, the federal government is the primary beneficiary of about 15 percent of company-sponsored industrial R&D expenditure. The second is Lichtenberg's (1988) econometric study of the private R&D investment response to government procurement in general, and design competitions in particular. The basic strategy was to estimate, using longitudinal firm-level data, regressions of private R&D expenditure on three variables: the value of the firm's competitive contracts, of its noncompetitive contracts, and of its nongovernmental sales. (The sum of these three variables is total sales.) The coefficient of the first variable was the primary concern; the other two variables were included mainly to "control" for their influence and to provide benchmarks against which to measure the effect of competitive procurement. Variants of the model were estimated on annual 1979-1984 panel data for 169 industrial firms. A major defense buildup occurred during this period: the value of federal contracts more than doubled, whereas total sales increased by only about 35 percent. The estimates implied that a $1 increase in government sales tends to induce a 9.3 cent increase in private R&D while a $1 increase in nongovernment sales induces only a 1.7cent private R&D increase. These estimates enabled calculation of the fraction ' of the total induced increase in private R&D induced by the increase in government procurement during the period. The point estimate (standard error) of v was 0.528 (0.050). The point estimate implies that slightly over half of the total induced increase in private R&D between 1979 and 1984 was induced by the increase in government sales; the limits of the 0.95 confidence interval on this share are 0.430 and 0.626. The estimates also suggested that a $1 increase in competitive procurement induces a 54 cent increase in private R&D expenditure. As noted earlier, the prospect of substantial future noncompetitive follow-on contracts awarded to the winner of the design competition makes firms willing to make R&D investments which are large, relative to the value of the initial competitive contracts. The coefficient on

Ch. 15: Economics of Defense R&D

437

noncompetitive contracts was negative but insignificant, suggesting that the entire stimulus to private R&D from government procurement comes from competitive acquisition. The remainder of the empirical analysis was devoted to extending and amplifying the major finding that a considerable quantity (and share) of private R&D investment is induced by competitive procurement. The estimates indicated that most of the longrun response of private R&D to competitive procurement is a response to future procurement. They also suggested that competitive contracts (whether or not for R&D) have a large positive effect on private R&D, noncompetitive R&D contracts have an even larger negative ("crowding-out") effect, and other noncompetitive procurement has essentially no effect. The award of noncompetitive R&D contracts signals the end of the design and technical competition. At this stage of the procurement cycle, there are incentives for firms to reduce private R&D. Losers of the competition reduce spending because the prize is no longer at stake; the winner reduces spending because the government is now willing to directly sponsor the R&D via contracting. A $1 increase in noncompetitive R&D procurement tends to reduce private R&D by more than $2. Noncompetitive non-R&D has essentially no effect on private R&D investment. In contrast to previous studies of the effect of government R&D on private R&D, which did not control for non-R&D procurement and which did not distinguish competitive from noncompetitive procurement, Lichtenberg found that the net effect of R&D procurement on private R&D is negative. But non-R&D procurement, which is about five times as large, has a stimulatory effect, so the net effect of procurement in general is positive and quantitatively important. The government therefore appears to play a larger role in determining the allocation of the nation's scientific and technical resources, hence the rate and direction of technical progress, than is perhaps generally recognized.

3. Independent R&D subsidies The Department of Defense (DoD) encourages private military R&D not only by awarding prizes in design competitions, but also by subsidizing expenditures dedicated towards winning the prizes. In other words, DoD promotes this contractor activity both by creating returns to it and by reducing the (private marginal) costs of it. The DoD policy that provides a subsidy to private military R&D is its policy regarding so-called "independent" R&D. Independent R&D (IR&D) is contractorinitiated and directed technical effort that is not sponsored by, or required in performance of a contract or grant. The contractor selects the projects that comprise its IR&D program. The DoD and its contractors consider independent, or non-contract, R&D to be "company-funded", and it is reported as such in financial statements and official government R&D statistics. But under the Defense Procurement Regulations some of the costs of IR&D are "allowable", i.e., they can be included as indirect

ER. Lichtenberg

438

costs (overhead) in contractors' DoD contracts. Each year, ceilings on the amount of allowable IR&D costs are negotiated in advance by the DoD and each of its major contractors. The existence of a subsidy to private military R&D is due to the way in which these ceilings are negotiated or determined. To develop a model of DoD's policy of allowable-cost determination, we adopt the following notation: C= ceiling on allowable costs, X= total costs incurred, R= costs recovered from DoD,

S = total sales of the contractor, D= DoD sales of the contractor. R, the amount of costs recovered from DoD, is determined by the following formula D R = min (X, C).

(1)

Cost recovered is the fraction of firm sales accounted for by sales to DoD times either costs incurred or the ceiling, whichever is lower. In practice, X > C in the case of all firms. The maximum value of the ratio CIX = 1; the mean and median values are 0.823 and 0.872, respectively. Hence min(X, C)=C. Let us define O=DIS as the DoD share of sales; we shall treat this fraction as a parameter. Then Equation (1) reduces to R = OC.

(2)

If the firm has pure cost-plus contracts with the government, then its private cost P of conducting a level of investment S is P=X-R=X- OC,

(3)

and the marginal rate of subsidy (MRS) to contractor IR&D expenditure is dR dC MRS= dX = O-, dX dX'

(4)

The marginal private cost of investment, which is generally hypothesized to determine the equilibrium rate of investment, is I - MRS. The marginal rate of subsidy, hence marginal private cost, depends on the derivative dC/dX. The value of this derivative is an empirical matter. The ceiling C is set in an agreement negotiated by the firm and DoD prior to the investment of funds. One might, therefore, regard C as predetermined, i.e. independent of the realized expenditure X. In this case, dC/dX = 0, and IR&D reimbursement has

439

Ch. 15: Economics of Defense R&D

no effect on the marginal private cost of investment; it reduces only total costs, like a lump-sum payment. But the proposition that C does not depend on X, if it is true at all, is probably true only in the short run. Winston (1985, p. 22) maintained that "the accepted ceilings are set at a fraction of the contractor's anticipated IR&D expenditures that are deemed to meet the PMR [potential military relevance] criterion and to be of value to DoD". This hypothesis can be represented as follows: Cit = aXi,A

(5)

where Cit denotes the ceiling negotiated for firm i in period t, XA denotes anticipated expenditure during the period, and 0 < a < 1. The contractor announces his anticipated expenditure in the course of his negotiations with the government, but unfortunately we do not observe the announced value. Therefore, in order to make the model operational we need to specify a relationship between the unobservable XA and actual (current and/or lagged) expenditure X. Lichtenberg (1990) pursued two alternative approaches, one based on "rational", the other on "adaptive", expectations (or anticipations); we describe here only the second approach, in which XA is assumed to be forecast by a distributed lag function of past actual expenditures, with geometrically declining lag coefficients: XA = r (Xi,t_ + HXi,t 2

H2Xi,_3 +

).

(6)

The following equation can be derived from Equations (5) and (6): Cit = /Xi,t-1 + HCi,t-1,

(7)

where - a F. In this model there is a distinction between the short-run and (long-run) steady-state derivatives of C with respect to X; these are /f and f/i(1-H), respectively. The steady state is reached when Cit = Ci,t-l. It is interesting to note that an alternative "structural" model for determining C can generate a similar (although restricted) reduced-form equation. Suppose that the change in a firm's negotiated ceiling is proportional to the degree of "excess demand" for IR&D funds, as measured by the difference between lagged costs incurred and the lagged ceiling: Cit - Ci,t_l =

(Xi,t_1 - Ci,tl) .

(8)

Such a ceiling-adjustment process would be in keeping with that old saw about the politics of the budgetary process, that the more a department (or organization) exceeds its budget the more its budget will be increased (and that a department risks having its budget cut by not spending up to the limit). Adding Ci,t,_ to both sides, Cit =

Xi, t-_1 + (1 - fi) Ci,t_

(9)

In Equation (9) the coefficients on Xi,t_1 and Ci,t_1 sum to 1, whereas, this is not the case in Equation (7). This restriction can be tested by estimating both equations.

440

FR. Lichtenberg

Lichtenberg (1990) estimated these equations using cross-sectional data for about 275 IR&D sponsoring organizations. To attenuate heteroskedasticity, and because negotiations may focus on percentage rather than absolute changes, he estimated logarithmic versions of the equations, i.e. C and X were defined as logarithms of the respective variables. In this case /i and PI(1-H) are, respectively, the short-run and (long-run) steady-state elasticities of C with respect to S. The (long-run) steady-state derivative of C with respect to X is

1 -HX

X)LR

()

and the (long-run) steady-state marginal rate of subsidy (from Equation (4)) is MRSLR

D

C

SI- HX

(11)

This expression was evaluated at the sample aggregate values of D, S, C and X to obtain an "average" estimate of the (long-run) steady-state marginal rate of subsidy. The DCAA reports data on expenditures, ceilings, and reimbursements pertaining to another type of technical effort related to IR&D: the preparation of bids and proposals (B&P). The reasoning that led to the specification of Equations (7) and (9) applies as well to B&P as it does to IR&D expenditure. The disturbances of the IR&D and B&P equations are likely to be correlated, in part because there is some fungibility of expenditures between the two categories. More efficient parameter estimates could therefore be obtained by estimating the IR&D and B&P equations jointly, using Zellner's seemingly unrelated regressions (joint generalized least-squares) technique. This procedure also enabled testing the hypothesis that the parameters of Equation (7), hence MRSLR, are the same for B&P as they are for IR&D. Joint generalized least-squares estimates of the parameter f (the coefficient on Xt-1) in both equations were positive and significantly different from zero. Thus, conditional on the lagged ceiling, the higher was lagged expenditure, the higher the current ceiling. The hypothesis that /3+H=1, which is implied by the model (8), was decisively rejected in the case of IR&D but was not rejected (at the 0.1 level) in the case of B&P. The cross-model residual correlation was -0.093, suggesting that there is some substitution between IR&D and B&P ceilings and/or expenditure. The estimates implied that the government pays 41.3% of the marginal cost of IR&D and B&P expense. This is slightly (although significantly) less than the average subsidy rate of 47.4%. The marginal rates of subsidy to IR&D and B&P appear to be quite high. The R&D Tax Credit created by the 1981 Economic Recovery Tax Act provides a benchmark against which we can compare this subsidy. The provisions of the credit allowed firms to deduct from their tax liability an amount equal to 25% of their R&D spending above a certain base-period amount. But due to certain technical features of the credit particularly the way in which the base-period amount was calculated - the effective

Ch. 15: Economics of Defense R&D

441

rate of subsidy it provided was much lower than 25%; Baily and Chakrabarti (1988, p. 119) estimate that the effective rate of subsidy was 7-8%. Moreover, the credit was only temporary - it was originally due to expire at the end of 1985 after four and a half years. In contrast, DoD's IR&D policy has remained essentially unchanged since 1970, and predecessor policies can be traced back to the 1930's. The above estimates were derived on the basis of particular assumptions about (1) the relationship between the ceiling Cit and anticipated expenditures XA, and (2) the relationship between XiA and actual expenditure, but further analysis and calculations suggested that the estimates were not very sensitive to minor changes in model specification. While these estimates revealed the magnitude of the subsidy to private military R&D, they do not reveal how much (additional) R&D is undertaken due to the existence of the subsidy. To determine this with any precision, we would need to know the price elasticity of supply of R&D, a parameter about which little is known. But the existence of the subsidy is no doubt partly responsible for the fact that the marginal private R&D intensity of government (primarily defense) sales is much higher than the R&D intensity of non-government sales - 9.3% as opposed to 1.7%. Why does the government provide a subsidy for private military R&D, in addition to establishing prizes for innovation? Presumably if the subsidy were abolished the government could continue to induce the same amount of private R&D investment by increasing the value of the prizes. The answer may be that the cost to the government of promoting a given level of investment may be lower with a combination of prizes and subsidies than it would be with prizes alone. By providing a subsidy the government in effect shares with the contractor the risk of investment; the agency theory literature suggests that such risk sharing is often optimal from the principal's (government's) point of view. Given that the government wants to provide a subsidy, why does it not do so explicitly by announcing "we'll pay 40% of your independent R&D expense, with no ceiling", rather than by imposing ceilings that are in reality influenced by past expenditures? It is not possible to offer a definitive answer to this question, but two factors may account for the institutional arrangements we have described. First, while the major objective of IR&D policy is to strengthen the defense technology base by promoting private military R&D investment, for political reasons the DoD may need at least to appear to be "controlling costs" by imposing ceilings. Secondly, the government is interested not only in encouraging private innovation but also in transferring technologies and knowledge developed in the course of independent R&D to government officials. The negotiation of ceilings provides the government with the opportunity to monitor contractor activity, thereby facilitating technology transfer. 4. The profitability of defense (R&D and other) contracts Having described some of the mechanisms by which the government induces firms to invest in defense R&D, we turn to a discussion of the private and social returns to

442

P.R. Lichtenberg

this investment. First we consider the issue of the private returns, or profitability, of defense contracts 3 . The Department of Defense (DoD) has periodically conducted comprehensive studies of defense contractor profitability. The most recent of these studies was the Defense Financial and Investment Review (DFAIR) completed in June 1985 [DoD (1985)]. With regard to profitability, the primary goal of DFAIR was to compare "profits realized on negotiated defense contracts with the profits realized on comparable commercial work" (V-26). To accomplish this, DoD asked its contractors to "isolate the profits achieved on negotiated defense contracts [by] segregat[ing] and reporting] operating results of various categories of business conducted within individual business segments" (V-26) 4. DFAIR's overall conclusion was that the "profitability of defense contracts has not been unreasonable" (IX-3). DFAIR also performed a much more cursory comparison "of profitability for DoD business to profitability for commercial business within the same business segments" during the period 1977-1983 (V-43). The estimate of this difference for all product groups combined was about 8 percentage points. It was argued, however, that this difference in average profitability was entirely attributable to a single product group aircraft - for which the differential was 14 percentage points. But research by Rogerson (1992), Thomas and Tung (1992), and Lichtenberg (1992a), imply that such comparisons of the profitability of defense contracts to the profitability of commercial work may not tell us much about the true profitability of defense contracting. This is because most (about 3/4, on average) of the sales of government contractors are to commercial (non-government) customers, and government contractors appear to be able to shift some of the overhead and pension costs of their commercial operations to the government. Rogerson (1992) argues that the methods used by defense firms for calculating the cost of products - in particular, the allocation of overhead in proportion to directly charged labor use - enables firms to shift overhead from commercial to defense business. Under this overhead allocation scheme, by incurring an additional dollar of direct government costs, the firm's government revenue will increase by more than $1 - perhaps by as much as $1.20-$1.40 - since the share of overhead reimbursed by the government increases. Rogerson argues that the overhead allocation rule provides firms with the incentive to "under-capitalize production of products with cost-sensitive revenues [e.g., defense items] and over-capitalize production of products with costinsensitive revenues [e.g., commercial items]".

3 We will discuss theory and evidence concerning the profitability of defense contracts in general, not just defense R&D contracts. We are not aware of any empirical studies of defense R&D in particular; moreover, distinguishing between the profitabilty of defense R&D and non-R&D contracts is probably even difficult in principle. 4 Since a significant fraction of costs and assets are joint between government and commercial work, the validity of these "segregations" is questionable.

Ch. 15:

Economics of Defense R&D

443

Thomas and Tung (1992) argue that government contractors are able to reduce their cost of doing nongovernment business by overfunding pension plans when employees work on defense contracts (these contributions are reimbursed by the government) and withdrawing excess pension assets when employees work on commercial business. Evidence suggests that DoD faces considerable difficulty in reclaiming its share of any overfunding. Although, in principle, regulatory authorities such as the Defense Contract Audit Agency could prevent this cost-shifting, they may focus their limited resources on more obvious abuses, such as the inclusion of nonexistent costs or costs that clearly belong to commercial activities. One could tell several (we believe reasonable) stories why the government might allow defense contractors to earn a higher rate of return on their assets than other firms earn. First, the government may wish to attract a "queue" of potential suppliers 5. Second, potential suppliers may be heterogeneous with respect to the quality of goods and services they provide, and quality is not observable ex ante by the government. A number of models [see, for example, Stiglitz and Weiss (1981)] imply that under these conditions the equilibrium price will be above the market-clearing price: the government will find it optimal to pay a price above contractors' reservation price (and allow firms to earn higher returns than they could elsewhere). When evaluating the relative profitability of government contractors we need to distinguish between three different profitability concepts: r = profitability of government business done by government contractors; :r2 = profitability of commercial business done by government contractors; and 7r3 = profitability of commercial business done by non-government contractors. By shifting costs, contractors may earn above-normal returns on commercial work, and normal returns on government business. In this case, (rl-3r 2) is clearly a downward-biased estimate of the "effect of government contracting on profitability". We need to know, not only whether arl > Jr2 (and rt > Jr3), but also whether st2 > :r 3. Unfortunately, this question was not directly examined by DFAIR or by previous DoD studies. Lichtenberg (1992a) tried to make inferences about the difference between the profitability of commercial work performed by contractors and that performed by other firms, using Compustat Industry Segment on over 9000 industry segments, 8% of which were government contractors. He was able to measure only the overall profitability of the firms in his sample, but since about 80% of contractor assets are employed in commercial operations, overall contractor profitability is predominantly determined by the profitability of their commercial business. The measure of profitability he used was return on assets: the ratio of operating profit (loss) to identifiable assets. He estimated variants of the following equation: PROFITit = ai + 6t + I3GOVPOSit + uit, 5 This situation is analagous to the classic two-sector labor market model of a developing economy

formulated by Todaro (1969). There, urban employers offer an above-market-clearing wage and attract a queue of (unemployed) rural workers.

444

R. Lichtenberg

where PROFITi, denotes the profitability of segment i in year t (t = 1984, ... , 1989); GOVPOS = 1 if the segment had positive government sales, and zero otherwise; and ai and 6 t are fixed firm- and year-effects, respectively. In this model, f3 may be interpreted as the (population) mean profitability of defense contractors minus the mean profitability of other segments, and an estimate of fi can be used to assess the magnitude and significance of the profitability differential. All of the estimates of fi were positive and extremely significant, providing strong support for the hypothesis that the profitability of government contractors is substantially higher than the profitability of other segments. The estimates indicated that the mean profitability of segments that do any business with the government is 3.0 to 3.6 percentage points higher than that of segments with no government sales, whose mean return on assets is about 4.4%. Hence the profit rate of contractors is 68 to 82% higher than that of other segments. Other estimates implied that a 50 percentage-point increase in the ratio of government sales to total sales (GOVSHR) will increase return on assets by 4.5 percentage points - from 4.4% to 8.9%. These findings presumably did not surprise most DoD contract officers: survey evidence reported in DFAIR indicates that twice as many of these officers agreed with the statement, "the profits earned by defense contractors are too high" as disagreed with it. Lichtenberg (1992a) further showed that although, in theory, asset mismeasurement could bias upward his estimates of the government/nongovernment profitability differential, a limited attempt to correct for such mismeasurement produced no evidence that this was the case. He also presented evidence that highly governmentoriented segments are significantly less capital-intensive than less government-oriented segments and noncontractors (controlling for industry). A speculative interpretation of the findings of this and the previous sections is that DoD wants to provide generous subsidies and profits to contractors, but does not wish to appear to be doing so to members of Congress and the public. 5. The impact of defense and other R&D on productivity growth This section sketches a theoretical framework for assessing the rate of return to investment in R&D in general, and defense R&D in particular, and surveys some of the empirical evidence that has been developed using this framework. The basic model that has been most widely used to assess econometrically the economic impact of R&D investment is a production function generalized to include the stock of "knowledge capital" as a factor of production: Y(t) = F (K(t), L(t), Z(t)),

(12)

where Y, real output; K, physical capital service flow (usually assumed to be proportional to the capital stock); L, real labor input (e.g. hours worked6); and Z,

6

For simplicity, we ignore issues related to "labor quality" or human capital.

445

Ch. 15: Economics of Defense R&D

knowledge capital. Just as fixed capital is a distributed lag function of investment in plant and equipment (INV), knowledge capital is a distributed lag function of R&D investment (RD). Assuming geometric depreciation, K(t) =

i (1 - 6K) i INV(t - i),

Z(t) = i (1 - 6z)' RD(t - i).

(12a)

Let us assume that the production function (12) is Cobb-Douglas, and that there are constant returns to scale with respect to the conventional inputs K and L: Y = KaLI-aZ.

(13)

Knowledge capital is assumed to be a pure public good, whereas physical capital is a "congestible" good. Therefore to double output we need double only the quantities of the conventional inputs. /3 is the elasticity of output with respect to the stock of knowledge capital, and is the key parameter for measuring the impact of R&D or knowledge capital. Taking logarithms and differentiating with respect to time, Y' = aK' + (1 - a)L' + PZ',

(14)

where a prime after a variable denotes its growth rate, e.g. Y' (dln Y)/dt. From Equation (14), the rate of labor productivity growth (Y'-L') is determined by the rate of physical capital deepening (K'-L') and by the growth rate of the knowledge capital stock (Z'): Y'- L' = a (K'- L') + Z'

(15)

Z' also influences the growth rate of total factor productivity (TFP). TFP is defined as the ratio of output to an index of conventional inputs: Y TFP= KaLl-a Hence TFP' = Y' - [aK' + (1 - a)L'] = iZ'.

(16)

Equation (16) implies that the growth rate of total factor productivity is equal to the growth rate of the knowledge capital stock times the elasticity of output with respect to knowledge capital. The objective is to estimate fl. Suppose that we have time-series data on Y, L, K, and RD. (As we will discuss below, there may be serious problems with accurately measuring some of these variables, particularly Y.) To calculate TFP', we require an estimate of a, and to calculate Z', we require an estimate of 6 z. Most analysts have been willing to assume that the conventional factors are paid the value of their marginal products, and therefore that a may be set equal to capital's share

446

FR. Lichtenberg

in total production cost (or national income), sK7. Then TFP' can be estimated by TFP' = Y' - (sKK' + (1 - SK)L'). Getting a reliable estimate of 6z is more difficult. One feasible approach is (i) to calculate the Z series using the accumulation Equation (12a) under alternative assumed values of this parameter; (ii) to estimate Equation (16) using these different series; and (iii) to select the 6 z value which provides the best fit of the TFP growth Equation (16). Griliches and Lichtenberg (1984) took this approach using industry level data for US manufacturing, and found that 6 z = 0 provided the best fit. If we are willing to assume that 6z=0, i.e., that knowledge capital does not depreciate, then Equation (16) can be re-expressed in an even simpler form. dY Z dZ dY dZ RD TFP'= - = 2(17) dZY Z dZ Y Y where -2 (dY/dZ)= the marginal product of knowledge capital. Since the rate of depreciation is zero, the net change in the knowledge capital stock (dZ) is equal to gross R&D investment (RD). Equation (17) says that the rate of TFP growth (output growth controlling for the growth in conventional inputs) equals the ratio of R&D investment to output times the marginal product of knowledge capital. Under our assumptions, Q2 may also be interpreted as the rate of return to investment in R&D. Suppose that a firm spends an extra dollar on R&D this year. Since knowledge capital does not depreciate, its stock will be $1 higher in every future year. If the marginal product of knowledge capital is Q2, its output (revenues) will be $r in every future year. Hence, 2 is the rate of return on R&D investment. Because the labor and capital engaged in R&D are usually already included in the conventional input measures L and K - that is, they are "double-counted" - Q2 represents the excess rate of return to R&D investment - the additional return received for employing these factors in R&D, rather than in ordinary production. Equation (17) embodies the implicit assumption that the rates of return to different types of R&D (e.g., defense and non-defense) are equal. To estimate the rate of return to defense R&D performed in industry, and test the null hypothesis that it is equal to the rate of return to non-defense R&D, we need to disaggregate R&D and generalize the model as follows: TFP'= 12RD, + 2RD (18) or TFP' = 21lrdl + Q2 0 rdo,

(19)

where RD 1 denotes defense R&D; RDo (-- RD-RD 1) denotes non-defense R&D; and rdi (RDi/Y), i = 0,1. Equation (19) has been estimated on data at a number of levels 7 Paul Romer (1986) has argued that the elasticity of aggregate output with respect to physical capital

substantially exceeds capital's share innational income (about 30%), and that there are increasing returns with respect to conventional inputs. However Mankiw, David Romer and Weil (1992) have argued that the apparently high capital elasticity disappears when human capital is accounted for.

Ch. 15: Economics of Defense R&D

447

of aggregation - national, industry, firm and line of business - for a large variety of sectors and samples. Due to data limitations, in many cases government-funded R&D is used as a proxy for defense R&D, and privately-funded R&D is used as a proxy for non-defense R&D. Lichtenberg and Siegel (1991) obtained the following estimates of a firm-level regression of productivity growth on federally-funded (FRD/Y) and company-funded R&D intensity (CRD/Y): TFP*' = const. + 0.03(FRD/Y) + 0.35(CRD/Y), (0.8) (13.1)

(20)

where the figures in parentheses are t-statistics. The estimated rate of return to company-funded R&D was positive and highly significant, but they were unable to reject the null hypothesis that the return to federally-funded R&D performed in industry is zero. Further analysis suggested that the impact of federally-funded R&D on productivity growth was highest among small firms, although even for them the impact was not statistically significant. Lichtenberg (1992b) estimated a somewhat different but related model using crosssectional country-level data. His estimates also implied a decisive rejection of the hypothesis that the rate of return to government-funded R&D is equal to the return to privately-funded R&D, and inability to reject the hypothesis that the return to government R&D is zero. The apparently low social rate of return to government-funded R&D should be interpreted with caution. It does not necessarily imply that government R&D does not contribute to social welfare. A substantial fraction of government-sponsored R&D is devoted to the production of intangible goods, such as national defense and health, or the reduction of "bads", such as destruction of the environment, whose value is reflected imperfectly, at best, in national accounts data. Suppose that social welfare depends on two things - national security, and everything else (or guns and butter) and that the usual static tradeoff between the two (along the production possibilities frontier) applies. Suppose further that the production of butter, but not of guns, is included in GNP. The greater the fraction of R&D and other investment a society devotes to gun rather than butter production, the lower its measured growth rate will be. Under this view, the negative coefficient on government R&D-intensity merely reflects the existence of the static tradeoff between measured output (butter) and unmeasured output (guns). Even if the negative sign of this coefficient is not surprising, however, its magnitude is of interest, since it indicates the opportunity cost (in terms of conventionally-measured output) of government-funded research. It is sometimes hypothesized that this opportunity cost is substantially reduced by pervasive spillovers from government research to the private sector. Since these

8

In contrast, the returns to company-funded R&D were statistically significantly higher for large firms.

448

FR. Lichtenberg

estimates of the coefficient on government R&D should be interpreted as the opportunity cost of government R&D net of spillovers, it appears that, even net of these spillovers, the opportunity cost to the private sector of government research is substantial. The difference between the estimated returns to company and federal R&D may be overestimated due to (more severe) problems associated with measuring, and adjusting price indexes for, quality change in military industries. However there is evidence from case studies that the return to US-government-sponsored civilian R&D programs has also been very low. According to Cohen and Noll (1991, p. 365), only one of six major federal R&D commercialization programs (evaluated using retrospective benefit-cost analysis) achieved its objectives and can be regarded as worth the effort, and that program was killed.

6. The effect of defense R&D on nondefense R&D investment The evidence surveyed in the previous section suggests that, holding nondefense R&D constant, government-funded defense R&D has essentially no effect on productivity growth. But, in principle, defense R&D could have a nonnegligible (positive or negative) indirect impact on productivity growth by affecting the quantity of nondefense R&D investment. Suppose nondefense R&D responds to the level of defense R&D according to the formula rdo = 6rdl + u.

Then the total derivative of TFP' with respect to rdl is 21 + 6t0, which depends on the returns to nondefense R&D and on the response of rdo to rdl, as well as on the returns to defense R&D. If, as the econometric evidence suggests, Q1 = 0, defense R&D could exert a negative effect on the growth rate of productivity if it tends to depress or "crowd out" nondefense R&D expenditure. There have been a number of empirical studies of the effect of government (primarily defense) R&D expenditure on private R&D. Edwin Mansfield and Lorne Switzer (1984) simply asked a sample of industrial R&D officials how company expenditures would respond to specified, hypothetical changes in federal R&D support. On the basis of their survey, these authors concluded that changes in federal support tend to induce changes in the same direction in company spending, although some of their findings seemed to suggest that crowding out may in fact occur. Most other studies have been econometric analyses of the statistical relationship between company and federal R&D expenditure in either the aggregate time-series, industry-level cross sectional, or firm-level cross sectional dimension. With the exceptions of Jeffrey Carmichael (1981) and Neil Kay (1979), most early analysts obtained estimates of 6 that were positive and significantly different from zero. In particular, using linear specifications of the relationship between company R&D

Ch. 15: Economics of Defense R&D

449

expenditure and contract R&D expenditure, David Levy and Nestor Terleckyj (1983) obtained estimates around 0.27 from aggregate times-series regressions, Richard Levin (1980) obtained a similar estimate from industry cross-sectional data, and John Scott (1984) reported estimates around 0.07 from the Federal Trade Commission Line of Business ("below" firm-level) data. These investigators seemed to interpret their results as offering at least tentative support for the hypothesis that federal support of R&D performed by industry stimulates company R&D activity. But Lichtenberg (1984) argued that errors in the specification of the company-federal R&D relationship, and/or errors in the measurement of real R&D activity by source of financing, which these studies may have committed probably resulted in estimates of 6 that were substantially upward biased. He identified two potential sources of bias - failure to allow for "fixed (industry- or firm-) effects", and erroneous "deflation" of both types of R&D expenditure - and proposed and implemented appropriate, albeit perhaps partial, remedies. Using firm-level panel data on R&D expenditure, and industry-level panel data on both R&D expenditure and employment, he was able to investigate the issues of lags, fixed effects, and deflation bias in the analysis of the government/private R&D relationship. Lichtenberg (1984) began by estimating industry-level regressions of the change in company-funded R&D expenditure on the change in federal R&D expenditure, both deflated by the GNP deflator. The expenditure regressions were estimated on annual data for twelve manufacturing industries over the period 1963-1979. The coefficient on federal R&D was positive but insignificant in equations that included industry and/or year effects. Since one might reasonably hypothesize that private R&D responds with a lag (of greater than a year) to changes in government R&D expenditures, he reestimated the models with two lagged values of the federal R&D variable included; the (sum of) the government R&D coefficient(s) was again positive but insignificant. Indeed, the hypothesis that contract R&D expenditure stimulates company-funded research appeared to be undermined rather than strengthened by allowing for lagged effects. Lichtenberg also estimated similarly specified models using data on employment of R&D scientists and engineers, rather than R&D expenditure, by source of funding; due to the difficulty of properly deflating R&D expenditures, these employment data may serve as a better index of real R&D input than inaccurately deflated cost series. These estimates implied a strong, negative contemporaneous effect of federally-funded on company-supported R&D employment. When lagged values of federal R&D were included, some estimates implied essentially no, or perhaps a weakly positive, net effect of federal R&D, but other (less restrictive) models indicated a negative long-run impact: a federally funded increase of 100 R&D scientists and engineers this year will result in a reduction of company-sponsored employment of 39 within the year, essentially no change next year, and an increase of 7 in two years. The third and last type of data Lichtenberg analyzed was longitudinal, firm-level data on R&D expenditures as a fraction of sales. He performed regressions of the ratio of company R&D to sales on the ratio of federal R&D to sales, for the years 1967, 1972, and 1977, and corresponding regressions involving changes in these variables

450

FR. Lichtenberg

during the periods spanned by these years. Estimating models in both level and firstdifference form reveals the importance of allowing for fixed effects in the analysis of R&D performance. In the 1967 and 1972 cross-sectional regressions, the coefficient on federal R&D/sales was positive and significant, indicating that firms which do more contract R&D tend to perform more own-financed R&D. It is rather surprising that the coefficient in the 1977 equation was negative, as well as larger in magnitude and more significant than the 1967 and 1972 coefficients. Only Carmichael had found negative and significant cross-sectional coefficients on contract R&D, and his estimates were smaller (of the order -0.08). But coefficient estimates in the first-difference form of the model for 1967-1972, 1972-1977, and 1967-1977 were all negative and highly significant. The point estimate of -0.26 for the ten-year interval as a whole is similar in magnitude to the coefficients in the industry-level R&D employment regressions reported above. Thus improved measurement of, and specification of the relationship between, company and federal R&D yielded evidence that was quite inconsistent with the hypothesis that defense R&D investment tends to stimulate nondefense or civilian R&D. But even these tests are not entirely conclusive, because the distinction between government and private R&D is not the same as the distinction between defense and civilian R&D, and because the defense/civilian R&D relationship may be characterized by very long lags.

7. How do Government decision-makers respond to cost information yielded by defense R&D? A "major thesis" of Peck and Scherer's (1962) seminal monograph on defense procurement was that "there is uniqueness in both the magnitude and the diverse sources of uncertainty in weapons acquisition" (p. 17). They defined two broad classes of uncertainties: internal and external. The extent of internal (and possible also of external) uncertainty about a weapon system is greatest at the beginning of its "life cycle". As resources are devoted to the system's research and development, information about the true cost of acquiring the system is generated, and the degree of technological uncertainty is reduced. How do defense decision-makers - the people in the Pentagon and Congress who make decisions about the allocation of defense resources - respond to the arrival of new information concerning the cost of weapons acquisition? Because in most economic settings, it is inefficient not to change behavior in response to new information, this question relates to the degree of efficiency of defense procurement, an issue of considerable concern to policy-makers and the public. In other words, how elastic is the government's demand for individual weapon systems? When the government's estimate of the cost of acquiring a given weapon changes as a consequence of data generated in the course of R&D, how much (if

Ch. 15: Economics of Defense R&D

451

at all) does the desired "buy" (quantity) change? An important determinant of the elasticity of demand for a specific weapon is the degree of substitutability between it and other weapons actually or potentially being acquired. Scherer (1964, pp. 54-53) suggests that even systems that have no obvious technical or operational substitutes are "threatened" by rival systems in the bureaucratic competition for budgetary support. In the early 1960's, for example, (offensive) Polaris missiles and the Nike Zeus ballistic missile defense programs were regarded by top Defense Department (DoD) officials as substitutes, in effect. Early in a program's life cycle, there is often intense competition among a few potential suppliers to develop and produce the weapon. But once the design and technical competition is over, the system is likely to be produced on a sole-source basis. The winning contractor then enjoys a monopoly with respect to the supply of the system. The extent of the contractor's market power, and his ability to earn monopoly profits, are inversely related to the elasticity of the government's demand. The higher the demand elasticity, the lower the price the contractor will seek to set and the lower his profit. It may also be the case that the higher the demand elasticity, the lower the optimal level of government expenditure to monitor and regulate the costs and profits of defense contractors. One research strategy for determining the demand elasticity is to examine empirically the relationship between revisions in cost estimates and revisions in quantity estimates across the population of major weapon systems. The revisions are from original or "baseline" estimates (made around the start of full-scale development) to "current" estimates (made at a subsequent date). Lichtenberg (1989a) formulated a simple model of revisions in weapons system quantity and cost estimates. He postulated that at any given time in the life cycle of a weapons system, the Pentagon has estimates of (the slopes and intercepts of) both the marginal cost schedule (the supply curve) and the marginal benefit schedule (the demand curve) of the system 9 . In particular, the Pentagon has such estimates at two times: the date at which full-scale development begins (time 0), and at a later date (time t). (Estimates made at time 0 are referred to as "baseline estimates".) Assume that the supply and demand schedules are log-linear. The baseline schedules may be written: InMC = 0 - aln Q,

(21)

InMB = 00o-

(22)

-1 In Q,

where MC denotes marginal cost, MB denotes marginal benefit, Q denotes quantity, and is the elasticity of demand". For simplicity, he also assumed that the baseline 9 Marginal cost consists primarily of production costs, since development costs are essentially fixed indeed "sunk" costs: they are independent of quantity purchased. '° Because the cost of developing and producing high-technology equipment is subject to considerable

uncertainty, a disturbance term should be added to equation (21); it is suppressed here for simplicity.

452

FR. Lichtenberg

quantity chosen by the government is the one satisfying the equality between InMC and InMB: InMC =lnMB4 lnQo=

-

(23)

In order for Q0 to be an equilibrium quantity, it must be the case that ,fi- > a: the demand curve must be more negatively sloped than the supply curve. Because, as we shall see below, weapons systems typically exhibit decreasing marginal costs, the condition is not a trivial one. As time passes following the start of full-scale development, decision-makers will revise their estimates of the supply and/or demand schedules. Information generated during the course of development about the cost or difficulty of acquiring the system would result in supply-curve revisions. Changes in the actual or perceived nature of the "threat" from enemy forces, and revisions in supply-curve estimates of other (complementary or substitute) systems under development would result in demandcurve revisions. We represent the Pentagon's estimates of the supply and demand curves at time t (t > 0) as follows: In MC = t - a In Q,

(24)

InMB = Ot -

(25)

-1 In Q.

Lichtenberg assumed that only the intercepts, and not the slopes, of the supply and demand curves are subject to revision; data limitations would not allow him to identify changes in the slopes. Equilibrium quantity at time t therefore satisfies: '

In Qt = _

(26)

The revision in equilibrium quantity between time 0 and time t can be calculated by subtracting Equation (23) from Equation (26): ln()Qt

Q

-5 - +

-00

' (27)

The log-change in quantity is due to both supply- and demand-curve revisions, each divided by the difference between the slopes of the curves. Equation (27), along with the baseline supply curve (21), can under certain assumptions provide a basis for estimating the parameters a and /f. Lichtenberg had data from the Selected Acquisition Reports, for 84 major weapons systems, on the quantity- and supply-shift variables ln(Qt/Qo) and (6t-60). Unfortunately, he lacked data on the demand shift (t-e 0 ). But suppose, as seems reasonable, that demand shifts are uncorrelated with supply

Ch. 15:

Economics of Defense R&D

453

shifts across weapons systems. Moreover, assume that a and fi do not vary across weapons systems. Then the regression equation, In(Qt ) = - (-l

- a)' (6t- 60)i + Ei,

(28)

where the i subscript denotes weapon system i and E is a disturbance term, will yield a consistent estimate of the nonlinear function of the parameters -(3-'-a)-l. Of course, neither a nor /f can be separately identified from this equation alone, but the available data permitted him to estimate another equation which identified a. By simultaneously estimating the system of two equations, he was able to identify both parameters. His empirical results may be summarized as follows. When the data were standardized by program base year - in effect comparing a program only with those other programs entering full-scale development at about the same time - there was a significant negative correlation between quantity and cost changes. The estimated elasticity of demand was 0.55, and was significantly different from both zero and unity. This suggests that the government's demand for specific weapons is inelastic, but not perfectly inelastic. The estimates also imply that weapons acquisition is characterized by increasing returns: the mean and median values of the elasticity of total cost with respect to quantity were 0.78 and 0.72, respectively. Further analysis revealed that the negative correlation between quantity and cost revisions - hence the nonzero demand elasticity - was entirely attributable to one component of cost revisions: those associated with changes in the acquisition schedule" . The elasticity of quantity with respect to schedule-related cost increases is about twice as great as the elasticity with respect to cost increases generally. In principle, it is possible that schedule-related cost increases are due to demand-induced stretch-outs of programs rather than supply-related, or technological, shocks. But it is not clear on theoretical grounds that unobserved demand shocks could account for the correlations he observed, and the demand-shock interpretation was also not supported by one econometric attempt to correct for it.

8. Are defense R&D programs dynamically optimal? Grossman and Shapiro (1986) studied the optimal pattern of outlays for a single firm pursuing an R&D program over time. Treating dynamic R&D investment as an optimal control problem facing a single firm, they characterized the profile of R&D expenditure as a single R&D project progresses. In this section, we briefly review the assumptions and implications of their model and report an analysis of data contained in the Defense

" As Hartley and Tisdell (1981, p. 355) have observed, system modifications are another important source of cost escalation.

454

FER. Lichtenberg

Technical Information Center's IR&D data bank to determine whether they are broadly consistent with the theory. Grossman and Shapiro assume that a firm seeks a prize of size W and that to obtain this prize it must "travel" a distance L. The instantaneous rate of advance is determined by the rate of R&D expenditure. There are decreasing returns to effort at any point in time, given that some progress is being made, but there may be a fixed start-up cost at any moment. The firm's problem is to choose expenditures at every point in time up to some terminal date to maximize the present discounted value of net profits, subject to the constraint that total progress attained at the termination date be sufficient to complete the project. The major implication of the model is that it generally is not optimal for a firm to devote a constant level of resources to its research program, even if the relationship between effort and progress is unchanging. Rather, the firm should vary its R&D expenditure directly with the current expected value of the project. In many circumstances, this value will increase as the firm achieves progress. "Circumstances" refers to whether or not there is uncertainty about the "difficulty" of the project (i.e., the distance to be traveled) or about the relationship between effort (expenditure) and progress. They show that if neither type of uncertainty is present (the deterministic case), it is optimal to increase effort over time as the project nears completion, in part because discounted R&D costs can be decreased for any given duration of the project by shifting expenditures from early to later stages. If there is only uncertainty concerning the relationship between effort and progress, a monotonously increasing effort profile remains optimal. If there is uncertainty about the difficulty of the project, the optimal pattern of investment depends on the hazard rate function. If this function is everywhere nondecreasing - i.e., if whenever success is not realized, researchers become more optimistic that a breakthrough is imminent - the optimal program again involves rising R&D outlays over time. If, alternatively, the firm learns that the project is more difficult than was originally believed, it may be optimal to reduce the scale of the R&D program, or even to abandon it entirely. Grossman and Shapiro argue that the deterministic case applies more closely to development projects than to pure research programs. Hence, their model implies that development projects should exhibit increasing effort profiles, whereas projects subject to greater uncertainty as to their difficulty (such as basic research projects) would not necessarily do so, and might be expected to exhibit flatter (or even negatively sloped) profiles. Some of the assumptions of the model are highly unrealistic, and one might therefore not expect actual data to be consistent with the theory. First, the model omits all R&D rivalry, i.e., strategic interaction among firms. Also, the assumption that the progress function is stationary over time may be more reasonable in some contexts than in others. It may be easier to make progress once some initial groundwork has been laid, though the groundwork itself cannot be rushed due to diminishing returns to more effort on this "subproject". This case would tend to reinforce the GrossmanShapiro results. But it may also be easy to make progress early on, due to a long list

Ch. 15:

Economics of Defense R&D

455

of "easy ideas to try". Then progress may slow once the difficult stage of the program is reached. Despite the possible lack of realism of the assumptions, it is of interest to assess the degree of consistency of the theory with the data. Lichtenberg (1989b) used data on over 9000 Independent R&D projects to test the hypothesis that the rate of investment in a project tends to increase as the project approaches completion. He computed, for each continuing project, the ratio (denoted R) of expected investment in the next year to average investment to date. To guard against the influence of a relatively small number of observations with very large values of R (some of which may have been outliers), he excluded from his sample observations with values of R greater than 4; his hypothesis tests are therefore likely to be conservative. The mean value of R for all projects was 1.30 and highly significantly different from 1; the median was also greater than 1 (1.14), albeit smaller than the mean. This is consistent with the general implication that the rate of investment increases as the project approaches completion. But the data were not consistent with the implication that R should be lower in the case of projects involving greater uncertainty about the difficulty of completion. Mean and median values of R were essentially the same for basic research projects as they were for applied research and development; Lichtenberg (1989b) presented evidence that the latter two categories are subject to less uncertainty than the former. He also used the IR&D data bank to develop some stylized facts about R&D investment at the project level. These are: (1) Research projects (both basic and applied) are longer and less intense than development projects; (2) the elasticity of cumulative investment with respect to project duration is greater than 1 for research projects and less than one for development projects; (3) the distributions of duration, average investment, and cumulative investment are highly skewed; (4) the shape of the duration distribution is close to lognormal, indicating that the conditional probability of project completion initially rises and then declines; (5) the degree of uncertainty about the project completion date is greater for basic research and concept formulation projects than it is for applied research and development projects.

9. Conclusions The major conclusions of this chapter may be summarized as follows: (1) Direct R&D contracting is not the only way in which the government induces private firms to invest in defense R&D; it also does so by sponsoring design competitions and providing subsidies to "independent" R&D. (2) A considerable quantity (and share) of private R&D investment is induced by competitive defense procurement. (3) The effective rate of subsidy to independent R&D exceeds 40% - much higher than the apparent (nominal) subsidy or the subsidy to other R&D. (4) The profitability of government contractors is 68 to 82% higher than the profitability of other producers; this is consistent with the hypothesis that the former are able to shift costs from their

456

FER. Lichtenberg

commercial operations to the government. (5) Both micro and aggregate estimates of the (social) "rate of return" to investment in government-funded (largely defenserelated) R&D - or its impact on productivity growth - are insignificantly different from zero, and are much smaller than estimates of the return to privately-funded R&D. (6) The best available evidence does not support the hypothesis that defense R&D tends to stimulate civilian R&D, and thereby has an indirect positive effect on productivity growth. (7) In two respects, the conduct of defense R&D and procurement appears to be "efficient" (or at least fails to be grossly inefficient). First, defense decisionmakers do seem to respond to the arrival of new information about the cost of weapons acquisition yielded by R&D: the elasticity of demand for weapons is significantly greater than zero (it is about 0.55). (8) Second, most independent R&D projects appear to be "dynamically optimal": the rate of investment increases as the project approaches completion.

References Baily, M., and A.K. Chakrabarti, 1988, Innovation and the productivity crisis (The Brookings Institution, Washington, DC). Carmichael, J., 1981, The effects of mission-oriented public R&D spending on private industry, Journal of Finance 36, 617-627. Cohen, L., and R. Noll, 1991, The technology pork barrel (The Brookings Institution, Washington, DC). DoD (US Department of Defense), 1985, Defense financial and investment review (Department of Defense, Washington, DC). Griliches, Z., and FR. Lichtenberg, 1984, R&D and productivity at the industry level: Is there still a relationship?, in: Z. Griliches, ed., R&D, patents, and productivity (University of Chicago Press, Chicago, IL) 465-496. Grossman, G.M., and C. Shapiro, 1986, Optimal dynamic R&D programs, Rand Journal of Economics 17, 581 593. Hartley, K., and C. Tisdell, 1981, Micro-economic policy (Wiley, New York). Kay, N., 1979, The innovative firm: A behavioral theory of corporate R&D (St. Martin's Press, New York). Levin, R., 1980, Toward an empirical model of Schumpeterian competition, unpublished paper (Yale University, May). Levy, D., and N. Terleckyj, 1983, Effects of government R&D on private R&D and productivity: A macroeconomic analysis, Bell Journal of Economics 14, 551 561. Lichtenberg, ER., 1984, The relationship between federal contract R&D and company R&D, American Economic Review 74, 73-78. Lichtenberg, F.R., 1988, The private R&D investment response to federal design and technical competitions, American Economic Review 78, 550-559. Lichtenberg, FR., 1989a, How elastic is the government's demand for weapons?, Journal of Public Economics 40, 57-78. Lichtenberg, ER., 1989b, IR&D project data and theories of R&D investment, Journal of Economic Dynamics and Control 13, 271-282. Lichtenberg, F.R., 1990, U.S. government subsidies to private military R&D: The Defense Department's independent R&D policy, Defense Economics 1, 149-158.

Ch. 15: Economics of Defense R&D

457

Lichtenberg, ER., 1992a, A perspective on accounting for defense contracts, The Accounting Review 67, 741-752. Lichtenberg, F.R., 1992b, R&D investment and international productivity differences, in: H. Siebert, ed., Economic growth in the world economy (J.C.B. Mohr, Tfibingen, Germany) 89-110. Lichtenberg, ER., and D. Siegel, 1991, The impact of R&D investment on productivity: New evidence using linked R&D-LRD data, Economic Inquiry 29, 203-228. Mankiw, N.G., D. Romer and D. Weil, 1992, A contribution to the empirics of economic growth, Quarterly Journal of Economics 107, 407-437. Mansfield, E., 1971, Technological change (W.W. Norton, New York). Mansfield, E., and L. Switzer, 1984, Effects of federal support on company-financed R&D: The case of energy, Management Science 30, 562-571. Nalebuff, B.J., and J. Stiglitz, 1983, Prizes and incentives: Towards a general theory of compensation and competition, Bell Journal of Economics 14, 21-43. National Science Board, 1993, Science and engineering indicators - 1993 (US Government Printing Office, Washington, DC). Peck, M.J., and F.M. Scherer, 1962, The weapons acquisition process: An economic analysis (Harvard Business School, Boston, MA). Rogerson, W.P., 1992, Overhead allocation and incentives for cost minimization in defense procurement, The Accounting Review 67, 671-690. Romer, P.M., 1986, Crazy explanations for the productivity slowdown, NBER Macroeconomics Annual 2, 163-202. Scherer, EM., 1964, The weapons acquisition process: Economic incentives (Harvard Business School, Boston, MA). Scherer, EM., 1984, Using linked patent and R&D data to measure interindustry technology flows, in: Z. Griliches, ed., R&D, patents, and productivity (University of Chicago Press, Chicago, IL) 417-461. Scott, J., 1984, Firm versus industry variability in R&D intensity, in: Z. Griliches, ed., R&D, patents, and productivity (University of Chicago Press, Chicago, IL) 233-245. Stiglitz, J., and A. Weiss, 1981, Credit rationing in markets with imperfect information, American Economic Review 71, 393-409. Thomas, J., and S. Tung, 1992, Incentives under cost-reimbursement: Pension costs for defense contractors, The Accounting Review 67, 691-711. Todaro, M., 1969, A model of labor migration and urban unemployment in the less developed countries, American Economic Review 59, 138-48. US Congress, 1969, Senate, Committee on the Judiciary: Competition in defense procurement, hearings before the subcommittee on antitrust and monopoly (US Government Printing Office, Washington, DC). Winston, J., 1985, Defense-related research and development in industry, Congressional Research Service Report No. 85-205 S, 18 October 1985.