Chapter 13 The economics of military manpower

Chapter 13

THE ECONOMICS OF MILITARY MANPOWER* JOHN T. WARNER Clemson University BETH J. ASCH RAND, Santa Monica, CA

Contents Abstract Keywords 1. Introduction 1.1. Some definitions 1.2. Summary statistics

2. The supply of military manpower 2.1. Initial enlistment supply 2.1.1. Theoretical model of the enlistment process 2.1.2. Empirical models 2.1.3. Empirical estimates 2.2. Retention 2.2.1. Theoretical models of retention 2.2.2. Empirical studies

3. Demand for military manpower 3.1. Framework 3.2. Studies of personnel productivity 3.3. Force mix issues

4. Global procurement issue: to draft or not to draft? 4.1. Economic theory of the draft 4.2. Other issues

5. The structure of pay 5.1. Stylized facts about military compensation 5.2. Theory

6. Force management issues 6.1. Women in the military

348 348 349 349 350 352 353 354 355 357 360 360 363 367 367 368 371 373 373 379 380 380 381 386 386

* We would like to thank Carl Dahlman, Judy Fernandez, Curt Gilroy, Glenn Gotz, Keith Hartley, Jim Hosek, Bernie Rostker, and especially Todd Sandler, for comments on previous drafts.

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

348

JT Warner and B.J Asch

6.2. Reserve force management issues

387

7. Civilian returns to military service 8. Summary References

390 393 394

Abstract The USA and other countries spend a significant portion of their defense budgets on personnel. Effective management of military forces requires an understanding of the economics of military manpower. Over the past three decades economists have produced a substantial body of research about the subject. This chapter distills this literature for a general audience. Topics surveyed include the supply of personnel, personnel productivity and the demand for personnel, procurement by conscription versus voluntary means, the structure of pay, the use of women and reservists, and the civilian return to military training and experience. It also points to directions for future research.

Keywords military, manpower, enlistment supply, retention, draft, conscription, volunteer force, military compensation, reserves, military women, military productivity, cost effectiveness and manpower

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1. Introduction The USA and other countries spend a significant portion of their defense budgets on military manpower and employ large numbers of personnel. In 1991, for example, the USA spent $84 billion on 1.9 million active duty military personnel and 1.1 million in ready reserve components. It is important that policymakers have an understanding of the economics of military manpower. Effective management of military personnel requires the understanding of a number of questions including the responsiveness of personnel supply to pay and other policy tools, the optimal amount of training, the optimal experience and quality mixes, and the proper mix of pay and other incentives. Because these are all questions in applied labor economics, the study of military manpower should prove interesting to a wider audience than just those responsible for policymaking. Economists have produced a substantial literature about military manpower, but as Sherwin Rosen noted in the 1986 Handbook of Labor Economics, much of their work is unavailable in the formal literature. The purpose of this chapter is to distill this literature for a general audience. The emphasis is on the USA, but studies based on other countries are selectively cited where appropriate. This survey proceeds as follows. The remainder of this introduction makes some preliminary definitions and presents some summary statistics about the size and composition of military forces in the USA and elsewhere. Section 2 examines the supply of military manpower. Section 3 examines the demand for military manpower by reviewing studies relating the characteristics of the force to measures of productivity. Implications for the optimal experience and quality mixes of the force are considered. Section 4 then reexamines the global manpower procurement issue: should military manpower be procured by a draft or by voluntary means? Section 5 addresses questions about the structure of compensation that are now only beginning to be studied. Section 6 looks at two contemporary force management issues: women in the military, and the management of the reserve forces and their relationship to the active forces. Section 7 examines the civilian return to military training and experience. Finally, Section 8 concludes the chapter. 1.1. Some definitions The military personnel systems of the USA and its major allies share many common attributes. All countries distinguish between officers and enlisted personnel. Officers are usually college graduates and have leadership and command responsibilities. Enlisted personnel usually have less education and assume the responsibilities of executing the orders of the officer corps. Within each of these designations there is a fixed rank or paygrade structure consisting of between 7 and 10 ranks. Rank structures are hierarchical, with large numbers of personnel in low ranks and declining numbers in, and lower rates of promotion to, the upper ranks. In the USA, for example, only about 10 percent of the enlisted forces occupy the top three enlisted ranks and less than 15 percent of the officer forces occupy ranks of Lieutenant Colonel and above. There

350

JT Warner and B.J Asch

is a heavy reliance on up-or-out rules to control the rank and experience distribution of the force (especially in the USA) as well as a general lack of lateral entry. Because of the lateral entry constraint, senior personnel must be "grown" from the ranks of junior personnel. In a closed military personnel system, the steady-state distribution of the force (F) and the requirement for new enlistments (E) can be derived as follows. Let ct be the continuation rate at year of service (YOS) t. Then the survival from the initial entry point to year t is st = cj. The total steady-state force is _j=

F =E + slE +

+STE=

1+

t) E.

The steady-state enlistment (or accession) requirement is therefore E=-

F

1+ T=1 St

Manyears per accession (y) are I + ETI= st. Obviously, the factors that raise continuation rates raise y and reduce E. It is important to distinguish between the total force (F) and the ready force (M). Some fraction of force is located in the training establishment and therefore not available for immediate deployment. To illustrate this idea, assume that the entire first year is spent in training and that the trainers have more than one year of experience. Let k denote the required ratio of trainers to trainees. Then the ready force is M=F-k

(-,

T

E - E =( -k)

st

t=1

)

stE. t=1

M rises with continuation rates and with the number of enlistments, but falls with the required trainer/trainee ratio. The expression for M is easily modified to account for variations in the length of training. 1.2. Summary statistics Table I shows the size of the active forces and the reserve force in the USA and its major allies. The USA, Germany, and the UK maintain the largest standing military forces, with the USA by far the largest. Germany and the UK have a somewhat greater reliance on reserve forces than does the US. All countries must enlist large numbers of personnel each year to maintain the force. In Fiscal Year (FY) 1991, the US active forces accessed 200 000 new enlisted personnel and 20 000 officers. Although with the end of the Cold War force levels are declining in the USA and elsewhere, the USA

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The Economics of Military Manpower Table 1 Force levels for USA and major allies'

Country USA Germany UK Canada Australia a

Ground forces 884 287 216 20 29

Naval force

Air force

558 31 59 12 15

Active total

502 90 7 21 19

1944 408 275 78 63

Reserve force 1806 697 349 37 29

Numbers given in thousands. Table 2 YOS distribution of US forces, FY 1990'

YOS

Army

Navy

Air Force

Marine Corps

Enlisted 0-4 5-10 11-20 21-30

50.2 26.3 21.2 2.3

49.9 27.2 20.3 2.7

35.8 31.3 27.6 5.3

59.3 23.4 15.3 1.8

Officers 0-5

35.6

45.7

30.4

37.5

6-11

29.5

26.7

34.4

26.5

12-20 21-30

25.1 9.8

19.5 7.3

25.3 9.2

28.2 7.5

a

YOS, years of service; all values given in percent.

will still have an active force of over 1.4 million when its drawdown is completed in FY 1997. Table 2 shows the year of service (YOS) distribution of US enlisted and officer forces at the end of FY 1990. The table reveals that the bulk of US personnel are found in the low YOS, with the Marine Corps having the largest percentage of inexperienced personnel and the Air Force the smallest. Less than 10 percent of US forces have more than 20 years of experience. It is evident from the table that retention and the average experience level are higher among officers than enlisted personnel. Not revealed in the data is the substantial increase in the experience of the enlisted forces since the elimination of the US draft in 1973. Army enlisted personnel with more than 4 YOS (hereafter denoted "careerists") made up 32.6 percent of the Army enlisted force in FY 1974. By 1990 the percentage had grown to 49.8 percent. The Navy careerist percentage rose from 40.4 percent in 1974 to 50.1 percent in 1990. In the Air Force the percentage increased from 51.3 percent to 74.2. The Marine Corps careerist growth has been smaller, 32.9 percent to 40.7 percent. The change

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JT: Warner and B.J Asch

in the officer experience distribution since the end of the draft has been much less dramatic. A major theme of the research cited below has been whether these increases in experience have led to a more productive force and a more efficient force.

2. The supply of military manpower Studies abound of both the decision to join the military (the enlistment decision) and the decision to remain after the expiration of the initial or subsequent terms of service (the reenlistment decision). The decision to enlist or reenlist is conveniently described using standard occupational choice theory [Rosen (1986)]. Suppose that there are two sectors of the economy - the military sector and the civilian sector. Individuals deciding whether to join the military must compare the pay and non-pecuniary benefits available in each sector. Military service is often arduous and involves exposure to risk and loss of life. But military service offers many non-pecuniary advantages over non-military employment - pride of service to one's country, the opportunity for travel, and more stable employment. Assume that individuals are able to weigh the many non-pecuniary aspects of employment in each sector and place an overall value on the non-pecuniaries associated with employment in each sector, rM and rC, respectively. Let WM denote the military wage and WC denote the civilian wage. Then the utility of joining the military is UM = WM + rM while the utility of remaining in the civilian sector is UC = WC + TC. Individuals join the military only if UM > UC, which implies that WM - WC > T - M. Simply stated, individuals join only if the pay differential (WM - WC) exceeds their net preference for civilian life, r = TC - TM The distribution of t over the relevant population determines the level of the supply curve for military service and its elasticity with respect to pay. Suppose that r M and r c follow a bivariate normal distribution over the eligible population with mean = btC i _ PM and variance 2 = a2 + 2 - 2 p7M oc. A positive value of Mindicates that, on average, the eligible population values the non-pecuniary aspects of civilian life more than the non-pecuniary aspects of military life. The shape of the supply curve is determined by the variance of the net preference factor , ( 2 ). Suppose that a 2 = 0. Such will be the case if (a) everyone has identical preferences for the two sectors or (b) p = 1 and M= c. If 2 = 0, then everyone has the net preference r equal to , in which case no-one will join if WM - WC < or WM < WC + . In this latter formulation, WC +,u is the individual's opportunity cost of serving in the military, i.e., the wage foregone plus the difference value he or she places on the non-pecuniary aspects of life in the two sectors. The military wage must exceed the civilian wage by the net preference factor before anyone will join. But if WM > WC+ then everyone will want to join, so that the supply curve is perfectly elastic at WM = WC + t. In the case of homogeneous preferences the parameter is the compensating wage differential required to make all individuals indifferent between military and civilian service. It follows that the more heterogeneous preferences are (the larger is 2 ), the less elastic the supply curve will be. Figure 1 sketches two different supply curves on

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The Economics of Military Manpower c2

0

.5N

Number of Enlistments

Figure 1. Enlistment supply curves based on small and large variations in preferences for military service.

the assumption that the net preference factor is normally distributed. N is the eligible population. When preferences are heterogeneous, only individuals for whom WM - WC > r are paid in excess of that required to induce them to join (or stay) and are said to earn economic rents (payments in excess of opportunity cost). The intercept of each supply curve is WC + r., where Tmin is the net preference of the person who is the least averse to military service. If tastes are normally distributed, then the cumulative density function of tastes, and hence the supply curve, will be S-shaped, as illustrated in Figure 1. When tastes are normal, enlistments are less responsive to pay when pay is very low or very high than when pay is in the middle range of possible values. If, instead, is uniformly distributed across the population with pdff(T) = /(m,,,ax in), then the supply curve will be linear over the range WC + Tmin to WC + max and a given pay change will have the same effect on enlistments at every point on the supply curve. 2.1. Initial enlistment supply The occupational choice framework provides a starting point for thinking about initial enlistment supply, but it needs to be expanded to understand more fully enlistment behavior. The first factor to consider is the role of human capital development in the initial enlistment decision. Individuals may join because they want to acquire skills that will be useful to them later. Individuals will be more willing to join if the skills are transferable than otherwise. Thus, the supply of potential enlistees depends upon skill transferability such that the supply curve of potential recruits to military skills that provide transferable training will lie to the right of the supply curve to the skills that provide military-specific training. The military will have to offer a higher wage in the latter skills to attract the same number of enlistments. Another human capital factor

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J5T: Warner and B.J Asch

is the availability of educational benefits. In the USA since World War II, individuals who successfully serve for some period of time qualify for post-service educational benefits. A second consideration is that individuals do not make their enlistment decision in a vacuum. The decision to enlist is shaped by environmental influences such as the advice of family and friends and societal attitudes towards military service. Orvis and Gahart (1989) analyzed the Youth Attitude Tracking Survey, a DoD-sponsored survey of US youth, and showed the importance of these "influencers" on youth's intentions to enlist and their subsequent enlistment rates. The third consideration is that the recruiting establishment also affects enlistment outcomes. The military services make a wide range of decisions regarding how to manage recruiting resources, including selecting recruiters, training them, and allocating them to recruiting stations throughout the country and selecting the level and allocation of advertising resources across media type. The services manage recruiters by assigning them quotas for the quantity of enlistments they make and for various enlistment categories (e.g., male versus female). They also generally use incentive plans that reward recruiters for various aspects of their productivity, such as certificates, badges, and improved promotion chances. The US services emphasize the recruitment of "high quality" youth, defined as highschool degree graduates who score in the upper half of the Armed Forces Qualification Test (AFQT) score distribution. During the 1980s high-quality enlistments averaged about half of total Army, Navy, and Marine Corps enlistments and 71% of Air Force enlistments. There have been significant swings in recruiting of high quality personnel since the beginning of the all-volunteer force (AVF) in 1973. Recruiting of high-quality males fell sharply in the late 1970s but rebounded during the 1980s. Factors that explain these swings are now considered. 2.1.1. Theoretical model of the enlistment process Since high-quality youth have better civilian opportunities, they are more difficult to enlist and so are thought to be supply constrained; consequently, recruiters are given more points and higher quotas for enlisting them rather than the lesser qualified. Because of these incentive and quota systems, recruiters do not passively process enlistments but may respond to enlistments by varying their level of effort and the allocation across enlistment categories. Following Dertouzos (1985), the enlistment process and the role of recruiter effort can be illustrated as in Figure 2. The recruiting production possibility curve (PPC) is given by AA'. This curve shows the feasible combinations of high- (H) and low- (L) quality enlistments that a recruiter can achieve for a given set of economic conditions, recruiting resources, and net tastes for service in the population. The mix of enlistments that the recruiter chooses depends on the shape of the PPC and the incentives he or she faces. Point Q in the diagram is the recruiter's quota for high- and low-quality recruits. If an enlistment determinant such as a recruiting resource is increased, the range of feasible enlistment outcomes increases, and if recruiters continue to supply the

Ch. 13:

355

The Economics of Military Manpower

M

0

A'

C'

B'

L

Figure 2. Recruiting production possibilities curves.

same level of effort, the PPC shifts out to BB'. The increase in potential high-quality enlistments (the desired category of enlistments from the service's perspective) holding the number of low-quality enlistments constant is given by the movement from point Q to point M. However, the movement to M assumes that recruiters maintain effort levels. As Dertouzos (1985) shows, recruiters do not have a strong incentive to overproduce because doing so can result in a higher future quota. If so, recruiters may reduce effort so that the shift in the PPC is smaller, as shown by CC'. If recruiters also have incentives to attain low-quality enlistments, their optimal outcome may therefore be a point like D, representing fewer high-quality enlistments than M. Therefore, studies that fail to account for the role of recruiter incentives will tend to underestimate the actual supply effect, the movement from Q to M. 2.1.2. Empirical models There have been two generations of research on enlistment supply during the allvolunteer force (AVF). The first-generation models were reduced-form models that ignored the potentially important role of recruiter behavior [see, e.g., Goldberg (1982), Ash, Udis and McNown (1983), Dale and Gilroy (1985), and Brown (1985) and the summary by Nelson (1986)]. The second-generation models recognized that recruiters respond to their incentive plans by varying the intensity and direction of their effort and held recruiter effort constant in their analyses. These studies include Dertouzos (1985), Daula and Smith (1985), Polich, Dertouzos and Press (1986), and Berner and Daula (1993). First-generation studies typically estimated a model of the form lnH =

lnX,

(1)

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JT Warner and B.J Asch

where H denotes high-quality enlistments and X is a vector of determinants. Since variables were entered logarithmically, parameter estimates were interpreted as supply elasticities. Following Polich, Dertouzos and Press (1986), the second-generation studies recognized that recruiters maximize their utility where their welfare is assumed to depend on the number of enlistments, quotas (Q), and recruiter effort (E). Formally, U = U(E, H, L, QH, QL),

(2)

where QH and QL are the quota for high- and low-quality recruits, respectively. We expect: UE < 0, UQ,, < O, UQL > 0, but UH > 0 and UL > O0. Recruiters are constrained in their maximization of U by the variables included in X, the factors determining the PPC in Figure 2. Accounting for recruiter utility maximization and following past literature in specifying functional form, the (structural) enlistment supply equation is specified as InH = lnL + lnX + InE,

(3)

where A is the tradeoff between H and L on the PPC. Although E is unobserved, it is posited that the level of effort depends on how well the recruiter is performing relative to quotas, or InE

=

ylln(()+

721n(

)

(4)

Substituting Equation (4) into Equation (3) gives InH = allnL + a21lnX + a3 ln QH + a4ln QL.

(5)

Since L and H are jointly determined, Equation (5) can be estimated by a two-step procedure using the following equation for low-quality recruits: InL = 0 + rllnX +

zt21n

QH + r31n QL.

(6)

Simultaneous estimation of Equations (5) and (6) gives coefficient estimates for Equation (4) which allows identification of the underlying structural parameters in Equation (3). Daula and Smith (1985) take a somewhat different approach in incorporating recruiter incentives. They estimate a switching regression model that recognizes that high-quality enlistments are demand constrained if goals are set too low (e.g., point Q is demand constrained when BB' is the PPC) and are supply constrained when Q is infeasible. When resources are increased, recruiters will move from Q to a point like D in Figure 2 in a demand-constrained environment, but to a point like M in a supply-constrained environment. Thus, the estimated effects of an increase in resources will be smaller than when enlistments are demand constrained. Daula and

Ch. 13:

The Economics of Military Manpower

357

Smith's disequilibrium model yields qualitatively similar results to other studies that incorporate recruiter behavior, as shown below. 2.1.3. Empirical estimates Table 3 presents elasticities estimated by studies of US Army enlistments that have controlled for recruiter behavior. [Warner (1990) provides Army estimates similar to those in Table 3 and makes estimates for the other services.] Some of the estimates in Table 3 come from data generated during controlled national experiments. For example, between 1980 and 1981, the Educational Assistance Test Program (EATP) was conducted whereby the USA was geographically divided into a control and three test cells for the purposes of estimating the effects of varying the structure of educational benefits on high-quality enlistments [Fernandez (1982)].1 Between 1982 and 1984, the Enlistment Bonus Test (EBT) was conducted for the Army whereby the level and the distribution of bonuses across terms of service were varied across the control and test cells [Polich, Dertouzos and Press (1986)]. Relative military pay and the civilian unemployment rate are consistently found to influence high-quality enlistments, with relative pay elasticities ranging from about 0.15 to 1.89, with a central tendency of about 0.5 to 1.0, and unemployment elasticities ranging from 0.49 to 1.36. Table 3 also presents estimated elasticities for various recruiting resources. Of these resources, high-quality enlistments are the most sensitive to the number of recruiters - elasticity estimates are on the order of 0.5. On the other hand, studies find much smaller elasticity estimates for national advertising, with a central tendency of around 0.05 to 0.10. Polich, Dertouzos and Press (1986) find that advertising has a depreciation rate of less than 100 percent, i.e., the positive effects of more advertising persist for some time even if advertising expenditures fall to their previous level. They estimate that the long-run effect of a change in advertising is about 1.4 times its initial effect. Studies also find that educational benefits have a greater effect on high-quality enlistments than do enlistment bonuses. The estimates from the EATP indicate that introducing the Army College Fund in 1982 increased high-quality enlistments by about 9 percent whereas estimates from the EBT indicate that expanding enlistment bonuses increased them by about 5 percent (which translate into elasticity estimates of 0.17 and 0.7, respectively). Both the Army College Fund and the enlistment bonus programs are targeted toward specific occupations and both programs thus have the potential to channel recruits into hard-to-fill occupations. Although educational

The GI Bill was eliminated in 1977 and replaced with a much less generous program called Veteran's Educational Assistance Plan (VEAP). Poor recruiting in the 1978-1979 period brought about the EATP experiment. The Army College Fund and the Montgomery GI Bill, an enhancement to the VEAP, were outgrowths of this experiment. Unlike the GI Bill, under these programs new recruits must participate in a contribution plan to be eligible for future benefits.

358

J.8T Warner and B.J Asch Table 3 High-quality enlistment supply elasticity estimatesa

M/C

0.49 -0. 5 5 g 1.20 0.15-0.62 0.48 1.89 0.82

UnEm

Recr

0.56 0.94 0.59 0.57-0.65 0.49 1.36 0.99

0.59 0.60 0.15 0.48-1.15 0.27 1.11 0.83

Ads

References (1) Daula and Smith (1985) (2) Polich, Dertouzos and Press (1986) (3) Goldberg (1991)

Bonus

0.09b b c 0.06 b 0.05 0.14 -0.29 0.43 0.72 0.16-0.17 0.21 -0.04 0.46 0.13b c e 0.07 k C e

Table based on Berner and Daula (1993) Abbreviations: M/C, Relative military to civilian pay; UnEm, Unemployment rate; Recr, Recruiters; Ads, National advertising; Edu, Educational benefits; Bonus, Enlistment bonus; L-Q E, Low-quality enlistments; H-Q G, High-quality goal. b Impressions, not expenditures. Study has dummy variables for the availability of various educational benefit programs, but does not estimate an elasticity of supply with respect to educational benefit levels. d Study disaggregates low-quality enlistments into two groups: AFQT category 1 3A, Non-high school graduates, and Other Enlistments (AFQT categories 3B-4). The first estimate shown is for Other Enlistments. e Pooled sample. a

Edu

L-Q E

H-Q Goal

-0.02to 11" -0.31

0.41 0.22 0.33

-0.20 to 0.38 d -0.08to 0.17

0.19

Ref.

1e,f

2h 3i 4j 5k 1m, 1n'f

f Panel data, recruiting battalion by month,

10/80-6/84. The results shown do not account for battalion effects. They do not report their results for the pooled sample. g Civilian pay only, not relative military to civilian pay. h Panel data, Military Entrance Processing Stations (MEPS) by month, 7/81-6/84. Data are expressed as difference from corresponding month in base period, 7/81-6/82. i Panel data, recruiting battalion by month, 10/80-9/88. J Panel data, recruiting battalion by quarter, 1981-1990. k Berner and Daula (1993). Panel data, recruiting battalion by month, 10/80-1/90. Results control for endogeneity of goals. e Study has dummy variables for the availability of various benefit programs, but does not estimate an elasticity of supply with respect to bonus benefit levels. m Supply constrained. m Demand constrained. (4) Kearl, Home and Gilroy (1990) (5) Berner and Daula (1993)

benefits have a larger market expansion effect, evidence suggests that enlistment bonuses are more effective at skill-channeling. 2

2 Estimates show that enlistments rose by 30-40% in the skills eligible for the enlistment bonus, holding the change in the total enlistments constant [Polich et al. (1986)]. The skill-channeling effect for educational benefits was estimated to be 17% [Fernandez (1982)].

359

Ch. 13: The Economics of Military Manpower

Table 4 Estimates of the marginal cost of recruiting resources Resource Entry basic pay Enlistment bonus National advertising Recruiters Educational benefits a

Estimated marginal cost (1990 $) 34 800 18 600 8100 7300 6900

Estimates based on Polich et al. (1986), Asch and Dertouzos (1994), and Asch et al. (1992).

The coefficient estimates for the high-quality quota and the high-quality/low-quality tradeoff parameter in the table show the importance of controlling for recruiter behavior. For example, the estimate of A from Polich, Dertouzos and Press (1986) of -0.31 implies that high-quality recruits are about 4 times as hard to recruit as lowquality ones. Daula and Smith's 1985 analysis implies a trade-off of about 8-to-1. Thus, if recruiters face insufficient rewards for achieving high-quality recruits (e.g., the point trade-off in the incentive plan is at worst less than 4-to-1), then recruiters will allocate their effort towards achieving low-quality ones. The size and significance of the high-quality quota coefficient estimates also suggest that quotas are one of the primary determinants of high-quality enlistments. Furthermore, the importance of accounting for recruiter behavior is also seen by comparing the supply elasticity estimates when enlistments are demand-constrained versus supply-constrained (the final two rows in Table 3). These estimates are smaller in the demand-constrained environment, as predicted by theory. The interaction between recruiter incentive systems and enlistment quotas is further studied in Asch (1990), Asch and Karoly (1993), and Berner and Daula (1993). Asch (1990) finds evidence that the structure of the Navy recruiters' incentive plan affected the timing and quality mix of enlistments, while Asch and Karoly (1993) show that the structure of the incentive plan for job counselors affected the number of highquality enlistments and the fill rates of various occupations. Berner and Daula (1993) indicate evidence that recruiting goals are endogenous (e.g., their size is based on past production and supply) so that recruiters who overproduce are penalized with higher quotas. The elasticity estimates in Table 3 provide the means to compute the marginal enlistment cost of various recruiting resources. Estimates from various studies are shown in Table 4. These estimates show the importance of considering both the resource effect (e.g., the elasticities in Table 3) and the policy cost in determining the optimal mix of recruiting resources. Although Table 3 indicates that (relative) military pay has a larger elasticity than advertising, Table 4 indicates that increasing pay is a relatively costly recruiting policy while increasing advertising is not. Raising pay is costly because to attract an additional high-quality recruit DoD must also raise the pay

360

JT Warner and B.J Asch

of everyone who would have enlisted anyway (i.e., pay rents). Enlistment bonuses are also a relatively costly recruiting resource. Table 4 suggests that recruiters, advertising, and educational benefits are the most cost-effective resources. However, effectiveness is measured in terms of high-quality enlistments. If other criteria for effectiveness were used, such as skill-channeling, a different ordering might result. Withers (1978) estimated enlistment supply models for the UK, Canada, Australia, and the USA for the period 1967-1973. Although the shortness of the time period and multicollinearity plagued the analysis for several of the countries studied, he obtained robust estimates for enlistments into the UK Army, with a pay elasticity estimate of 1.46 and an unemployment elasticity of 0.90. 2.2. Retention 2.2.1. Theoretical models of retention The analysis of retention poses a theoretical problem that is generalizable to any labor market setting. Consider an individual at time period t who is considering whether to stay or leave. Suppose that the individual can stay to t + 1 and then leave, t + 2 and then leave, etc. The theoretical problem is deciding the time horizon that is relevant to retention decision-making. The problem is particularly important in the US military because of the lumpiness of the military income stream - individuals are vested in a sizeable pension only upon completion of 20 years of service. The simpler solution was provided by the Annualized Cost of Leaving (ACOL) model [Enns, Nelson and Warner (1984), Warner and Goldberg (1984)]. To illustrate the ACOL approach, suppose that for an individual at year t: (1) Wj is expected military pay in each future yearj, (2) WCt is civilian earnings in future yearj if the individual leaves at t, (3) WCn is civilian earnings in future year j if the individual separates after future year n, (4) Rn is the expected present value at future year n of retired pay and other separation benefits if the individual separates after year n, (5) Rt is the present value at year t of retired pay and other separation benefits if the person leaves now, (6) Tm and r c are the preference factors previously defined, and (7) is the individual's subjective discount rate on future income. Then the present value of the future benefit from staying from period t to period n is: I (1

S,, =

j=t+l

M

R -I + (1 +p) + +

+Y

Tm

- 1 (1+ (1 +p)-

j=t+l

W

t

Y1

(lp

+ TC

(7)

j=n+

The value of leaving immediately is: wet v +

L =

c

(l +p)I + R,. ,=1+1

(8)

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The Economics of Military Manpower

The cost of leaving is Ct,n =St,n -Lt, which can be written as: E

WnY-WC

/

Rn

(1+p)t + (1 + p)n-t Rt ~~~j=t+~~

-

E

Wj -WJj

E

( + ) t-

-T(

+(9)

j=t+1

j=n+l

The first term accounts for the military-civilian wage differential over the interval from t to n, the second term measures the change in the value of retirement benefits, the third term accounts for the change in civilian opportunities brought about by service from t to n (see Section 7), and the last is the present value of the net preference for civilian life. The individual is presumed to stay if there exists at least one future time horizon over which Ct,n is positive. Of course, it could be positive over multiple periods. How to separate stayers from leavers? Saying that the individual stays if there exists at least one future horizon over which Ct,n is positive is equivalent to saying that the individual stays if the following is true over at least one future time horizon: n fint r -

m

R )WWE)n+l

w.-w.wC

M

C

Rt-R

_W~+ ( (ll~-

W

C

(l+p)J

<

(10) r-p"t+l

(l+p)j-l

The right-hand side of Equation (10) is the annualized cost of leaving, At, n. It is the annuity equivalent of the financial loss the individual experiences by separating now rather than at future period n. The retention criterion is to stay if there exists some future period n such that At, n exceeds the net preference for civilian life. Thus, an individual leaves only if c , = T - Tm > max(A,,+1, At,t+2, ...

At,T)

Let A' denote the maximum value of the annualized cost of leaving. Then the retention rate is the fraction of personnel for whom T
t

A

)

=

_

+

A-) 1

where P denotes the standard normal distribution function and ,t and a are the mean and standard deviation of the taste distribution, respectively. This model can be estimated by probit analysis with data on individual retention decisions. The reenlistment supply curve has the S-shaped property illustrated in Figure 1. This simple specification of the ACOL model does not account for dynamic selection effects. If the distribution of T is normal when individuals are making their first reenlistment decision, it will not be normal among those who in fact reenlist. Those

JT.I Warner and B.J Asch

362

who reenlist form a truncated or censored sample, depending upon whether there were other disturbances to the first-term reenlistment decision. Without unobservable influences to the reenlistment decision other than the taste factor , an implication of the model is that retention rates should be unity beyond the first decision point as long as A* is increasing, which they are not. A solution is to suppose that T is a permanent (or time-invariant) taste factor, and that other unobservable factors (random disturbances) -- such as whether or not the individual likes his commanding officer, his location of assignment, and a death in the family - affect the retention decision at each point in time. Suppose that et is a normally distributed random disturbance factor at time t with mean 0 and standard deviation a,. The probability that the individual stays at the end of any period t is P(A -T + t) = P(A -

>

- )=

(A

)

Since the 's are independent over time, the cumulative probability of retention for t periods is

Individuals with stronger preferences for civilian life have a lower probability of survival than individuals with stronger preferences for military life. The decomposition of errors into permanent and transitory components gives rise to a panel probit model. [See Black, Moffitt and Warner (1990) for more details.] When the permanent factor is not degenerate, conditional retention rates will rise with t as those with a stronger net preference for civilian life leave and those with as stronger taste for military life remain. The panel probit model thus explains the observed tendency for retention rates to rise with YOS. The model also has the feature that retention rates at different terms are not independent of one another. A higher reenlistment bonus at one reenlistment point will serve to retain more individuals on the margin of a retention decision, but these individuals will be less likely to stay at the end of the next term than others who would have stayed without the bonus. (Survival through both terms will increase unless random factors play no role in retention decisions.) Despite its frequent use in empirical studies, the ACOL model has theoretical shortcomings, as Gotz and McCall (1984) and Gotz (1990) have pointed out. Because it is based on a single dominant time horizon, the model is not consistent with fully rational decision-making. If individuals are aware that random factors might cause them to leave at each future point they will be uncertain about the exact separation date. In addition to random disturbances that might induce separation, another source of uncertainty is promotion and the likelihood of being involuntarily separated at some future date if not promoted. Because it is based on a single, dominant time horizon,

Ch. 13:

363

The Economics of Military Manpower

the model may fail to capture important elements of decision-making or adequately predict certain policy changes. Gotz and McCall (1980, 1984) developed a theoretically more appealing model of the following form. Let i denote an individual's rank and represent the probability of promotion. Assume that promotions occur at the start of a given period after last period's retention decision. Let V denote expected future utility and /3= 1/(1 +p), where p is the individual's personal discount rate. Then the model has the following structure: Si,, = ri+l,t+l (W+l,,+l + Zm + V i+l,t+l) + (1 - rTi+,t+1) (i,t+l)m

, ()

G*, = Si,, - Li,t, i,t = Pr(Gt + i,t > 0), Vi,t+l = Pit+l [i+,t+2Si+,t+ 2 + (1 - Ji+l,t+2)Si,t+2]+ (1 -

v-

i,t+l)Li,t+l.

The first equation of (11) says that the value of staying in rank i at the end of period t is a weighted average of utility if promoted and utility if not promoted, with the probability of promotion being the weight. The expected gain from staying (or expected cost of leaving) is the difference between expected utility if the individual stays and the value of leaving immediately (which is now permitted to depend upon rank). The probability of staying is the probability that G*t + Et is positive. Finally, expected utility in any rank i at the end of period t + 1 is a weighted average of the value of staying and the value of leaving, with the probability of staying supplying the weight. Individuals must begin at the maximum possible YOS (usually, 30) and solve the model recursively to obtain the values of S, V, L, and G*, and d> for each possible rank and YOS prior to the maximum YOS. If a rank has a mandatory separation point prior to YOS 30 then 1 is set to zero and V is set to L at that point. The structure in Equation (11) has an easy interpretation: in making retention decisions, individuals evaluate the payoff to all possible promotion and separation sequences that they might follow and weight those sequence by their probabilities of occurrence, which depend on tastes, the importance of random shocks to retention decisions, and the likelihood of promotion at each rank-YOS point. G*, is simply the expected value of all possible future sequences minus the value of immediate separation. Equations for the probability that an individual will remain in service from period 1 to period t (and for cohort survival) can be specified analogously to those for the ACOL model. 2.2.2. Empirical studies Since the start of the AVF, economists have conducted many studies of retention of US military personnel. Some studies have used grouped data, where the unit of observation was the reenlistment rate in a given occupation/YOS cell at a point in time; others have used maximum likelihood logit or probit techniques with data on individuals. Two have estimated trivariate logit models that distinguish between reenlistments (contracts of 3 to 6 years), extensions (contracts of less than 3 years), and separations. Some

34T Warner and B.J Asch

364 Table 5 Studies of reenlistment Study

Kleinman and Shughart (1974)' Warner and Goldberg (19 8 4 )b

Period

1966-1967 1968 1969 1971-1972 1974-1978

Goldberg and Warner (1982)C

1974-1980

Hosek and Peterson (19 8 5 )d

1976 1981

Service

Skill

Navy

Pooled

1

Ship maintenance Aviation maintenance Administration Navy Electronics Aviation maintenance Administration Air Force Pooled

1 1

Navy

Term

1,2 1,2 1,2 1 2

Cooke, Marcus and Quester (1992) e Quester and Adedeji (1991)' Smith, Sylwester and Villa (1 9 9 1)' Buddin et al. (1992) g

1979-1988

Navy

24 ratings

1

1980-1990

Marine Corps Army

Pooled

1

1974-1983 entrants 1983-1989

Army

Infantry Maintenance Administration Pooled

Infantry Comm. & Intell. Elec. & mech. maint. Air Force Pooled

Daula and Moffitt (1991, 1 9 9 2 )k Gotz and McCall (1984)1

1974-1983 entrants 1973-1977

Army

Electronics Administration Elec. & mech. maint. Infantry

Air Force Pilots Nonrated officers

1,2 1,2 1,2 1

1 1 1

1 1 1

Pay elasticity

SRBM effect

2.27 2.40 4.24 2.12 2.46

0.02 to 0.025

0.023 0.032

2.44 0.042 1.89, 2.65 0.022, 0.029 2.38, 2.98 0.034, 0.064 1.78, 2.50 0.033, 0.065 3.8 0.02 (install) 0.025 (lump-sum) 1.7 0.024 (install) 0.022 (lump-sum) 1.64 0.025 (main effect) 0.011 (sea-intensive) 2.1

0.066

1.29, 0.86 1.76, 1.12 1.90, 1.76 1 .6 0 g 1.05 h 1.80' 1.14' 1 .4 0 h 1 .3 4 h 0 .8 7 h 1.15 g 1.02 h 0.78' 0.34' 1.17" 0.50" 1.35h

1,2

large

YOS 7-8 YOS 6-7

0.8 1.4

continued on next page

Ch. 13:

365

The Economics of Military Manpower

Table 5, continued Study

Mackin, Hogan and Mairs (1993)'

Period

Service

Skill

Term

Pay elasticity

1979-1990

Army

Infantry officers

YOS 4-10 YOS 4-10

0.9 1.55

Signal Corps officers

SRBM effect

a Grouped data, logit model of reenlistment vs. separation, pay variable is log((M+B)/C). b Microdata, probit of reenlistment vs. separation, pay variable is ACOL. c Grouped data, trivariate logit model of reenlistment, extension, and separation, pay variable is ACOL. d Grouped data, trivariate logit model of reenlistment, extension, and separation, pay variables are (MIC) ratio and SRBM. e Microdata, logit model of reenlistment vs. separation, pay variables are (M/C) ratio and SRBM. ' Microdata, bivariate probit model of first- and second-term reenlistment vs. separation, pay variable is

ACOL. g Microdata, standard model of reenlistment vs. separation, pay variables are (MIC) ratio unadjusted for promotion timing and SRBM. h Microdata, two-equation model of months to E-5 and reenlistment vs. separation, pay variables are (MIC) adjusted for promotion timing and SRBM. i Microdata, standard model of reenlistment vs. separation, pay variable is ACOL unadjusted for promotion timing. J Microdata, two-equation model of months to E-5 and reenlistment vs. separation, pay variable is ACOL adjusted for promotion timing. k Microdata, panel probit of first- and second-term reenlistment decisions; pay variable is the stochastic cost of leaving. I Microdata, panel model of stay-leave decisions in three-year window around end of initial obligation; pay variable is stochastic cost of leaving. m Microdata, panel probit of stay-leave decisions in YOS 4-10, pay variable is ACOL.

studies have taken a "reduced form" approach that includes ratios of military to civilian pay (WMIWC) and Selected Reenlistment Bonus (SRB) program variables separately 3 ; others have taken a more structural approach, including bonuses in the calculation of ACOL or some other measure of relative pay. Personal attributes, environmental variables such as the civilian unemployment rate, and controls for military occupation or other in-service effects are sometimes included. Table 5 summarizes the evidence from the more comprehensive studies of reenlistment. The table records the period of observation, service/skill group that

3 The US military services use the SRB to influence reenlistments at the first term (3-6 YOS) and second

term (7-10 YOS). The Navy briefly paid third-term bonuses (11-14 YOS) in the early to mid-1980s. The services set an SRB multiplier (SRBM) for each skill and reenlistment zone that ranges from 0 to 6. Individuals may reenlist for a period of 3 to 6 years and receive a bonus equal to SRBM x monthly basic pay x years of reenlistment. Prior to April 1979, bonuses were paid in installments on the anniversary dates of the reenlistment. From that time until mid-FY 1982 they were paid in lump-sum at the time of reenlistment. Since then they have been paid partly in lump-sum and partly in installments.

366

J.T Warner and B.J Asch

is the basis of analysis, term of service, the pay elasticity calculated by the study (%Ar/%AW M ), and the estimated effect of a one-level increase in the SRBM. Pay is found to have a significant positive effect on retention. Early studies estimated retention elasticities in excess of 2.0 and SRBM effects of around 0.02-0.03, implying that a one-level increase generates 2-3 more reenlistments per 100 eligible. Lump-sum bonuses have a slightly larger impact than installment bonuses. While pay and bonuses generally have a positive impact, elasticities and bonus effects are smaller in skills with the more arduous working conditions (e.g., Army Infantry and Navy sea-going ratings). More recent studies using panel methods estimate somewhat smaller (but still statistically significant) pay elasticities [e.g., Smith, Sylwester and Villa (1991)]. Buddin et al. (1992) consider the joint endogeneity of promotion timing and retention decisions and also find smaller pay elasticities once the endogeneity of promotion is considered. Studies of officer retention estimate somewhat smaller elasticities than those estimated for enlisted personnel [Gotz and McCall (1984), Mackin et al. (1993)]. Gotz and McCall and the two studies by Daula and Moffitt offer the only empirical applications of the dynamic retention approach and each study reports tests that indicate that the model fits the data better than the ACOL model. However, the DaulaMoffitt pay elasticity estimates are so at odds with collective results from other studies that they must be considered preliminary at this point. The studies are in agreement about the effects of a number of other factors. Among those at the first decision point, married personnel, black personnel, and female personnel have a higher propensity to reenlist. The higher propensity for married personnel to reenlist is somewhat surprising given the significant negative impact that military assignment and rotation patterns have on the employment and earnings of military wives [Payne, Warner and Little (1992)], and must reflect the greater value of in-kind and non-pecuniary benefits to married personnel. Studies also agree that the propensity to reenlist is higher among those who initially enlisted for a longer term. But personnel with higher education levels and higher AFQT scores are generally found to have lower propensities to reenlist. However, the influence of demographic characteristics diminishes as YOS increases. As expected, higher civilian unemployment is usually found to cause higher reenlistment except when it induces the military to alter retention standards [Smith, Sylwester and Villa (1991)]. There is a negative relationship between the present value at enlistment of educational benefits and the probability of reenlistment [Smith, Sylwester and Villa (1991), Hogan, Smith and Sylwester (1991), Warner and Solon (1991)]. This result is to be expected: higher educational benefits attract personnel who desire to serve for an initial enlistment and then separate to use them. Similarly, higher entry pay and higher bonuses reduce retention at the next decision point because of their role in retaining individuals at the margin [Goldberg and Warner (1982), Warner and Solon (1991)].

Ch. 13: The Economics of Military Manpower

367

3. Demand for military manpower There have been significant variations in the demographic composition and experience distribution of the US armed forces during the AVF era. The question arises, do these factors matter for warfighting capability? This section briefly describes the economic approach to this question and it reviews empirical studies of the relationship between the characteristics of the force and measures of personnel productivity and the implications of these studies for the efficiency of forces with different experience and quality mixes. 3.1. Framework In their annual planning process US military planners try to determine in broad terms the forces required to fight and win various kinds of wars and regional conflicts. Desired warfighting capability is then translated into requirements for forces with a given level of readiness (R). Once the desired level of R (denoted R*) is determined, managers at the various levels in the military organization set about to determine the various combinations of ready manpower (M) and equipment (K) that will deliver the desired readiness. That is, they attempt to determine the military production function relating resources (M and K) to readiness (R): R =R(M, K). Once the combinations of M and K that can deliver R* have been determined, managers attempt to determine the most efficient or cost-effective combination and configuration of resources. Given the wide variety of equipment and its complexity, identifying the production function and determining the least-cost input combination is a daunting task for the modern military organization. The rapid pace of technological change further complicates matters. The problem of finding the most cost-effective input combination can be illustrated by supposing we are looking at an infantry company. The company delivers firepower (R) based on the quantity of rifles or other weapons at its disposal (K) and the number of ready personnel (M). Suppose that R can be delivered with different combinations of M and K and that reducing M requires an increase in K in order to maintain a fixed level of R. Then, M and K are substitutes in the delivery of R. We assume that the marginal product of K (MPK = RI/K) and the marginal product of M (MPM = ORI/M) are both positive. Define the marginal rate of substitution between K and M (MRSK,M) as MPM/MPK. We assume that the substitution of M and K becomes more difficult as the resources are traded off for one another. Thus, the marginal rate of substitution declines as M is increased and K is reduced and vice versa. The cost of a given level of readiness is minimized when the inputs are used in proportions such that MPMIMPK = PM/PK (in the case of fixed input prices) or MPM/IMPK = MCM/MCK (where MC denotes marginal cost, in the case in which input prices vary with the quantities of M and K). Input proportions change when the relative marginal cost of manpower changes. Just how much depends on the elasticity of substitution (KM). Intuitively, KM shows how easily the two inputs may be substituted for one another. Formally, oKM = (%AK/M)/(%AMPM/MPK). But if input prices are constant and costs are being

368

3.8T Warner and B.J Asch

minimized, then PM/PK = MPM/MPK, so that KM = (%AK/M)/(%APM/PK). In this latter formulation KM shows how sensitive the input mix is to a given percentage change in the input price ratio. The analysis can be extended to questions involving labor-labor substitution. Suppose that the readiness function is R=R(K,M1,M2), where Ml and M 2 are two distinct types of manpower. Then one can define the marginal rate of substitution between M 1 and M 2 as (RI/M 1)/I(ORIM 2 ) =MP1/MP 2 and the partial elasticity of substitution as (521 = (%AM 2/MI)I(%AMP IMPI2 )K=K In the analysis of labor-labor substitution, categories have been defined on the basis of rank, experience, and quality. 3.2. Studies of personnel productivity We first survey studies of personnel productivity that attempt to estimate marginal productivities of various categories of personnel and (in some cases) derive the partial elasticities of substitution between categories. Categories are variously defined on the basis of experience, rank, and indicators of quality. These studies implicitly hold the equipment stock fixed. Then we briefly consider studies of substitution between equipment and personnel. Holding equipment constant, do personnel have positive marginal productivity? Two studies performed with US Navy data [Horowitz and Sherman (1980), Beland and Quester (1991)] say yes. Both found that an increase in the manning level relative to the Navy's stated shipboard requirements for personnel improves the relevant performance measure. Better manned ships have lower maintenance downtime (Horowitz and Sherman) and are fully mission-capable a larger fraction of the time (Beland and Quester). These two studies and others cited below also found more experienced or more highly ranking personnel to be more productive than junior personnel. Using data from the 1975 Enlisted Utilization Survey, a large survey of junior Air Force personnel and their senior enlisted supervisors, Albrecht (1979) provides the most comprehensive analysis of the substitution possibilities between different experience categories of personnel. The purpose of the junior survey was to identify their supervisors and gain some other personal information. Questionnaires were then sent to senior supervisors asking them to rate the individual's net current contribution to unit production relative to the average specialist with 4 years of experience and also their estimates of the individual's net contribution to unit production one year from now and after 4 years of service. Supervisor responses were merged with personnel records for the junior member and with manning level and other data for the individual's unit. The supervisor's evaluation of each individual was interpreted to be a marginal productivity measure. Data were aggregated by unit and mean productivity was calculated for those with from 0 to y months of experience and y to 48 months; y varied from 8 to 15 months for different skills. Albrecht then estimated a two-level CES production function in which in step one ln(MPoylMPy- 48) was regressed on ln(Lo-y/Ly-48), where the term in parentheses is the ratio of personnel in the unit with O-y months of service to personnel with y- 4 8 months. The coefficient on the log-input ratio provides an estimate of the

Ch. 13: The Economics of Military Manpower

369

elasticity of substitution between personnel in the two categories. Results of the first regression were used to then calculate a weighted mean marginal product of all firstterm personnel (MPf). In step two, ln(MPf/MPc) was regressed on ln(Lf/Lc), i.e., the ratio of first-term to career (c) personnel in the unit, to estimate the relative marginal productivity and elasticity of substitution between first-term and career personnel. Since MPc is unobservable it is moved to the right-hand side and treated as an omitted variable, and expressions for the bias in the coefficient on ln(Lf/Lc) are evaluated. Albrecht analyzed 17 Air Force Specialty Codes (AFSC). Estimates of substitution elasticities within the first term ranged from 1.1 (Materials Facility Specialist) to 9.39 (Ground Radio Repairman), and the estimates were generally large. Elasticities of substitution between first-term and career personnel ranged from 1.25 (Avionics Systems Specialist) to 8.31 (Fuels Specialist), with estimates centering around 4.0. Substitution between different categories of first-termers and between first-termers and careerists is apparently relatively easy. At the margin, careerists were estimated to be from 1.41 to 2.25 times as productive as first-term personnel. The relative marginal productivity of careerists was larger, and the elasticity of substitution between firsttermers and careerists smaller, the more highly skilled the AFSC. Using a generalized Leontief production function, Marcus (1982) estimated the substitution possibilities between three rank groupings of Navy enlisted aviation maintenance personnel (El/E3, E4/E6, E7-E9). The output measures consisted of 292 observations on aviation squadron sorties and (alternatively) mission capable rates. Marcus calculated that at the sample means an additional E7-E9 has a "mission capable" marginal product 5 times larger than the marginal product of an E4/E6 and 9 times larger than the marginal product of El/E3 personnel. The estimates imply that E4/E6 personnel are about twice as productive as El/E3 personnel, an estimate consistent with Albrecht's. Hammond and Horowitz (1990, 1992) studied the relationship between pilot training time and pilot proficiency. Recent flying time and career flying time both have significant positive effects on pilot performance. The elasticity of pilot performance with respect to career hours ranges from about 0.2 to 0.6 depending on the performance measure; the elasticity with respect to recent flying hours hovers around 0.2. Although the authors argued that the results indicate a significant return to experience, especially career flying experience, the results beg the question of whether the officer selection and retention process induces the better pilots to remain in service and continue to fly and the poorer ones to separate or be reassigned early on. Is productivity related to quality measures other than experience? Indirect evidence is provided by studies of first-term enlisted survival and by studies of promotion. High-quality personnel are more likely to complete their initial enlistments [Buddin (1988), Warner and Solon (1991), Cooke and Quester (1992)]. Furthermore, highquality enlistees are promoted faster [Buddin et al. (1992), Smith, Sylwester and Villa (1991)]. To the extent that the propensity to complete an initial enlistment, or to be promoted, are correlated with contributions to military readiness, high-quality personnel are more productive than low-quality personnel.

370

J.T Warner and B.J Asch

Several studies provide more direct evidence about the quality-productivity relationship. Horowitz and Sherman (1980) found evidence that ship downtime decreases as the fraction of personnel who are high-school graduates or the mean AFQT score of shipboard personnel increases. Three studies of Army enlisted personnel found AFQT to be a significant predictor of job performance [Scribner et al. (1986), Orvis, Childress and Polich (1992), Fernandez (1992)]. The effect of mental ability on performance seems to be related to the complexity of equipment and the tasks to be performed. Orvis, Childress and Polich found Patriot Missile System operators' performance in air combat simulations to rise sharply with AFQT. This result is consistent with Fernandez (1992). Studying the performance of teams of radio operators in troubleshooting of radio faults, she estimated that a 10 point increase in the mean AFQT of the team raises the probability that the team will successfully detect at least three out of six possible faults by 25 percent. Scribner et al. (1986) found weaker, albeit still positive relationships between the AFQT levels of key tank crew members and crew performance on firing ranges. An important issue is the productivity effect of rotation policy. US military personnel move frequently. Since much military output is team-oriented, personnel "turbulence" may adversely affect unit cohesion and reduce performance. Indeed, the evidence suggests that such is the case. Horowitz and Sherman (1980) and Beland and Quester (1991) both found that Navy productivity is adversely related to crew turnover. In the latter study, the crew turnover rate averaged 12 percent per quarter (so that the annual crew turnover rate is almost 50 percent). The elasticity of the mission capable rate with respect to crew turnover is about -0.3. Furthermore, for two of three ship classes studied, Beland and Quester found that a ship's mission capable rate is related to the length of time the ship's commanding officer has been aboard ship. Kostiuk and Follmann (1989) find that the productivity of Naval Reserve recruiters doubles in their first 24 months of duty but that productivity falls as recruiters approach the date of rotation to other assignments. Scribner et al. (1986) estimated that doubling the time that a tank commander and his gunner spend in the crew from the average of 7 to 14 months would raise the crew's score by about 4 percent. These studies point out the down side of US military rotation policy. Finally, studies of capital-labor substitution are scant. Because of the longevity of much military capital equipment and the fact that the capital-labor ratio can be varied only during the initial equipment procurement stage, in the short run the substitution possibilities are limited. Over the longer run, the substitution possibilities increase as older equipment wears out and newer equipment is purchased. Clark (1978) examines capital-labor substitution in the US Navy surface fleet, estimating a substitution elasticity over the period 1956-1972 of 1.13 for all (existing plus new) capital and 1.74 for new capital. Over the period, newer ships were designed specifically to reduce increasingly relatively more expensive manpower. Ridge and Smith (1991) use UK time-series data over the period 1953-1987 to estimate the aggregate elasticity of substitution between equipment and manpower. Because the share of manpower in total costs was stable over their data period, the elasticity of substitution is estimated to be unity.

Ch. 13:

The Economics of Military Manpower

371

3.3. Force mix issues There has been a substantial increase in the average experience level of the US enlisted forces since the start of the AVF. Furthermore, various quality measures fell during the late 1970s but have increased steadily since then. Throughout the 1970s, AVF critics wondered whether a force with sufficient experience and quality to meet readiness objectives could ever be achieved. But average experience and various quality indicators improved throughout the 1980s such that today some might question whether the experience and quality mixes are in fact too rich. A force with richer experience may be more productive, but it is also more expensive, particularly when expected future retirement liabilities are considered. The question of optimal experience or quality mix is difficult because one must begin at the unit or occupational level and then aggregate. Only a handful of studies have tried to do so. Gotz and Roll (1979) attempted to derive the optimal first-term/career mix in three Army and three Air Force specialties. Each service contained a high-skill, a medium-skill, and a low-skill specialty. They began with force mixes and compensation levels in effect in FY 1977 and varied the first-term/career mix using supply/pay relationships in the mid-range of those considered in Section 2. Their calculations considered the full range of costs from initial accession to retirement costs and they allowed the total force size to vary to maintain a constant readiness level. Readiness was based on a Cobb-Douglas production function for each specialty, with productionfunction parameters set such that beginning with the observed 1977 force mix in each skill the model predicted relative careerist marginal productivity consistent with Albrecht (1979) estimates for low, medium, and high Air Force skills. They then derived the optimal aggregate career intensity for each service by weighing the intensities in the three categories by the aggregate proportions of low-, medium-, and high-skill personnel in the given service. Their results are summarized in Table 6. Calculations for the Army indicate that optimal career intensity does indeed rise with skill. (A reversal occurs in their calculations for the Air Force, apparently a result of supply-side considerations.) For comparison, the table shows the aggregate careerist percentages for the Army and Air Force in FY 1982 and FY 1990 and the percentages for the one-digit DoD occupation group that contains the skill in question. At an aggregate level, FY 1982 actual intensities are close to the Gotz-Roll calculations of the optimal force mix, but the FY 1990 forces had significantly larger careerist percentages. The growth in career content has been particularly large in the Air Force. Whether the 1990 forces were too senior is not known; much has changed since the Gotz-Roll study. 4 But the Office of the Secretary of Defense was clearly worried, for in FY 1990 it directed the services to

4 One change is an exogenous rise in desired retention, which reduces (say) the marginal bonus cost of

retaining careerists, thereby lowering MCc/MCF and increasing the optimal careerist percentage. Shifts in the occupational distribution and skill-using changes in technology could have also increased the optimal career intensity.

372

JT Warner and B.J Asch Table 6 Optimal careerist percentages as estimated by Gotz and Roll (1979)

Career

Optimal percentage

FY 1982

FY 1990

Army 50.8 a

Infantryman (L)

41

37.1 a

Auto repairman (M)

48

42.8

Field radio repairman (H) Aggregate

61 44

53.6' 44.7

47.2' 49.8

Air Force Fuel Specialist (L) Aircraft maintenance (M) Ground radio repairman (H) Aggregate

57 60 49 53

50.1 d 46.8b 50.3 52.6

755d 72.1b 62.9 64.2a

b

5 3 .2 b

a Percentage in DoD Occupation group 0 (Combat Arms).

b Percentage in DoD Occupation group 6 (Mechanical Equipment Repair). c Percentage in DoD Occupation group 1 (Electronic Equipment Repair). d Percentage in DoD Occupation group 8 (Supply/Service Handlers).

tighten retention standards for mid-career personnel. The drawdown of the active force initiated in FY 1991 necessitated the development of compensation tools for reducing the career force proportionately to the first-term force. A final comment about career content. Most of the studies have been done in a static framework. Gotz and Stanton (1986) point out that the uncertainty of warfare places a premium on personnel who can perform a variety of functions and adapt quickly to different environments. Because more experienced personnel are more likely to have been cross-trained in different skills and because of their greater variety of experiences, they are more likely to adapt to the exigencies of warfare than junior personnel. Static analyses miss this component of productivity and may therefore understate the value of more experienced personnel. Only Daula and Smith (1992) have attempted to derive the optimal quality mix of personnel. Through the Army College Fund and other mechanisms, the US Army spends a lot to attract high-quality personnel. Is it efficient to do so? Daula and Smith (1992) point out that once equipment is purchased, it is used in fixed proportions with personnel. The gain from high-quality personnel, they argue, comes not from personnel savings but from the reduced expenditures for equipment. They calculated that reducing the fraction of personnel in the Army's tank force who score 50 or above from 65 percent (base case) to 60 percent would save the Army about 5 million dollars per year in personnel costs, but with a lower-quality force the Army would need 16 more tanks to deliver the same readiness at the same cost. Improvements in the quality content of the force are more cost-effective the larger are the productivity

Ch. 13:

The Economics of Military Manpower

373

differences between different categories of personnel and the more expensive is the equipment. Once the equipment savings made possible by even tiny differences in the productivity of different quality categories of personnel are considered, the military's emphasis on recruiting and retaining high-quality personnel may be quite justified.

4. Global procurement issue: to draft or not to draft? Few public policy issues have been as divisive as how to procure military manpower. The debate was particularly vociferous in the US in late 1960s and early 1970s. In 1969 President Nixon established the President's Commission on an All-Volunteer Force, commonly known as the Gates Commission, to study the issue. The commission listed nine arguments against an AVF. 5 Specifically, an AVF would (1) be too costly; (2) be too inflexible in times of crisis; (3) undermine patriotism by lessening the belief that each citizen has a moral responsibility to serve the country; (4) become an elitist institution that might threaten democratic values; (5) be racially unrepresentative, (6) be a mercenary force; (7) encourage foreign military adventurism; (8) be less effective because only low-ability personnel would be attracted to service; and (9) crowd out other defense spending, thereby eroding the quantity and quality of defense. Advocates of a volunteer force, including most economists, countered by arguing that the first criticism was wrong on theoretical grounds, and the other criticisms were weak on empirical grounds. On the cost issue, Milton Friedman, who wrote extensively for the public press on this subject and was himself a member of the Gates Commission, flatly stated in his December 19, 1966 Newsweek column that "the real cost of manning the armed forces now ... is greater than the cost of manning a volunteer force of the same size because the volunteers would be the men who find military service the most attractive alternative." The report of the Gates Commission paved the way for the abolition of the US draft in 1973. In addition to Friedman 6, a number of economists have contributed to the draft-AVF debate [see, e.g., Oi (1967), Altman and Fechter (1967), Hansen and Weisbrod (1967), Miller (1968), and Fisher (1969)]. Lee and McKenzie (1992) recently laid out the most cogent framework to date for thinking about the cost issue. This section presents the economic theory of the draft versus AVF using the Lee and McKenzie framework and then it briefly considers some of the other points in the debate. 4.1. Economic theory of the draft The economic analysis of procurement method starts with the fact that military service imposes on a given service member the opportunity cost WC + r. The opportunity cost

5 From the Report of the President Commission on an All-Volunteer Armed Force, pp. 5 17. 6 A selection of Friedman's pieces on the draft is provided in Friedman (1972).

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J T Warner and B..! Asch

of providing a force of a given size must be distinguished from the budgetary cost, i.e., the military wage bill that is paid by taxpayers. Analysts of the 1960s, Friedman included, treated the budgetary cost as a pure transfer from taxpayers and argued that when the military wage is below a soldier's supply price, the soldier is bearing a conscription tax that is a pure transfer to taxpayers. Conversely, the higher pay in a volunteer system was treated as a pure transfer from taxpayers to service members. To develop the cost of either method, assume that the military force F is comprised of first-termers (F 1) and careerists (F2) and that the first-term and career periods are both of length 1. Let E be the number of enlistments in a given time period and cl denote the continuation rate at the end of the initial enlistment period. Therefore, in a steady state, Fl =E and F 2 = c 1E, so that F=E+c l E=(l +cl)E. Assume that the military pays a constant wage WM that is independent of period of service. The wage bill is therefore WM(1 +cl)E. Consider the supply of personnel to the military. Recall from Section 2.1 that on the assumption of a uniform distribution of r the supply curve for military service is the linear function E = a'+ b'WM, from which we may solve for WM: WM = a +bE. Each point on the supply curve represents the marginal person's opportunity cost of service. Therefore, in a volunteer system the first-period opportunity cost of E enlistees is the area under the supply curve from 0 to E: aE + 0.5bE2. If the condition WM > WC + T holds at the entry point, then in the absence of changes in military pay or civilian wages and preferences, it will hold at the end of the first term, so that cl = 1 (all volunteers stay for both periods) and the total force F = 2E. Therefore the opportunity cost of the volunteer force is 2aE+ bE2 = aF+0.25bF 2. Now consider the opportunity cost of a draft. Assume that a cohort of size N comes of age each period and is at risk of being drafted in that period. But even under a draft there will be V volunteers whose marginal opportunity costs are less than WM. The average opportunity cost of these V volunteers is a +0.5bV, and their total opportunity cost is aV+0.5bV2. Now, if E is the number of required enlistments, the military will have to draft E - V individuals. If E - V individuals are drafted at random from among those with opportunity costs in excess of a+b V, then the average opportunity cost of these individuals will be the mid-point on the supply curve between V and N, or a +0.5b(N - V). The average first-period opportunity cost of the E enlistments is therefore the weighted average V

E-V (a + 0.5EV) +

[a+ 0.5b(N + V)]

and the total first-period opportunity cost of E enlistments is aE + 0.5b(EN +EV - NV). Since V volunteers stay for the second term with opportunity cost aV+0.5bV2, the opportunity cost of the total force can be expressed as aE +0.5b(EN +EV - V)+ aV + bV 2.

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Using the facts that cl = VIE and E = F/(1 +c l), the opportunity cost of the draft force is aF+ 0.5b ((1 - cl)NF + cF 2 1 +i 1 +i It may be shown that this sum is larger than the opportunity cost of the volunteer force as long as one of the following is true: (1) cl > 0 (the draft cohort contains some volunteers) or (2) F < 2N (not everyone in the population must serve) 7. Since it is usually the case that the military does not need for everyone in the draftable cohorts to serve, and since under the draft the enlistment cohorts contain some volunteers who reenlist, the volunteer system unambiguously has the lower opportunity cost. Since the budgetary cost of a military was treated as a pure transfer from taxpayers to soldiers, the opportunity cost difference was taken to be the social cost of a draft and was almost always positive. Hence the profession's almost unanimous pronouncement that the volunteer system is preferable to a draft. Lee and McKenzie recognized that the military wage bill is not a pure transfer, but itself involves a cost. The reason is simple: when the government raises taxes (or prints money) in order to pay the military wage bill, the higher tax rates will, in general, cause distortions in economic behavior that impose deadweight losses on the economy. Browning (1987), for instance, finds the deadweight loss from income tax distortions to labor supply to be about 30-40 cents per dollar of tax revenue. Thus, a volunteer force, with its higher wage bill, will impose a larger deadweight loss from taxation than a draft force. It is therefore ambiguous whether a draft force has lower cost once the deadweight loss from taxation is considered. The deadweight loss from taxation due to each procurement method is obtained as follows. First, the military wage bill is WMF. But since the marginal supply price is a +bE, the volunteer force wage bill will be (a +bE)F = (a + bF/2)F= aF +0.5bF2 . Let /3 be the deadweight loss per dollar of tax revenue. Then the deadweight loss arising from this wage bill is (aF + 0.5bF2 ). The deadweight loss from taxation under the draft is WMF. Since WM is fixed under the draft and does not rise with E, the deadweight loss from taxation required to pay the troops does not rise as fast under the draft as under a volunteer force. Consider now training costs. Suppose that under either system training is given in the first period of service and that d is the cost of training a new recruit. Then under a volunteer force the training cost is dE = (d/2)F. Under a draft, the training cost is dE = [d/(l + cl)]F. Since cl < 1, training costs under the draft are necessarily higher than training costs in a volunteer force of equal size.

7 With their single-period model, Lee and McKenzie derived the result that either method has the same

opportunity cost if E equals N. Our more general two-period analysis says that even F = 2N (so that everyone in two successive draftable cohorts must serve), the volunteer force will have lower opportunity cost so long as the draft force contains some volunteers (i.e., c, > 0).

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JT Warner and B.J Asch Total Cost

0

2V

F'*F

F,

2N

Force Size Figure 3. Total costs of volunteer and draft forces.

The full cost of either procurement method is the sum of (1) the opportunity cost of the personnel comprising the force, (2) the deadweight loss arising from the need to raise tax dollars to pay the force, and (3) training costs. Collecting the results above, the total cost of a volunteer force is: TCA= (a(l )+ ) + ) F + 0.5b(0.5 +f)F

2

.

(12)

The marginal cost of the force under the volunteer system is: MCA F MCA = OF

(a(l + )

d) 2+ + b(O.5 + )F.

(13)

Notice that MCA is a linear function of F. The total cost of a draft force is: TCD = a+fWM± ICD 0.5b (f1 +I c, NF+ 1 + =+(olllWM+ ) F 1+

F2.)

(14)

If the draft force is less than 2V, it will be comprised only of volunteers: there is no distinction between the draft and the volunteer force. Therefore, below 2V, cl= and TCA = TCD. There is a discontinuity in TCD at F=2V because at this

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point the force begins to be composed of draftees who (1) have higher opportunity costs than volunteers and (2) impose higher training costs because of their lower retention. As F increases beyond 2V, cl = VIE= V/(F - V) decreases. Using the fact that beyond 2V, Ocll 1 F = -cllE, the marginal cost of the force under the draft may be shown to be MCD=a+ 0.5bN + WM +d+

c

1 + cl

F.

(15)

As F increases, MCD increases at a decreasing rate and approaches the constant a+ 0.5bN + WM+ d. Total force costs are plotted in Figure 3. Between 2V and F* the volunteer force has lower total cost than a draft force. Above F* the draft force has lower total cost. Intuitively, the volunteer system is cheaper below F* (but above 2V) because below F* the higher opportunity cost of the draft force outweighs the volunteer force's larger loss from taxation. Above F* the situation reverses and the draft becomes the cheaper procurement method despite its larger training costs. The crossover point F* is obtained by equating (13) and (15) and solving for F:

F* /(WM

- a)(l + cl) + 0.5(d + bN)( - cl) 0.5b[(0.25 + )(1 +cl) - cl]

(16)

F* decreases as both /5and b increase. The former condition says that the draft system dominates at a lower F* the larger is the deadweight loss from taxation. An increase in b signals a less elastic enlistment supply curve, thereby lowering the enlistment level at which the draft becomes cheaper. An increase in a, which signals a reduction in the supply of enlistees, also reduces F*. But a rise in the cost of training (d) signals an increase in F*. Which system to choose? The answer depends on the desired force level and how it is determined. If all that matters is force size, then obviously choose the volunteer force if F F*. But the military is not concerned with forces of equal size so much as forces of equal readiness. There are three reasons to believe that a volunteer force will not need to be as large as a draft force to be equally ready. First, readiness is based on the number of ready personnel (denoted M above), not the total number F. Since the draft force has more personnel in training at any given time, and since some of the training must be provided by more experienced personnel, a draft force will not be as ready as a volunteer force of equal size. Second, to the extent that productivity rises with experience, a volunteer force will not need as many personnel to provide the same readiness. (Indeed, productivity studies reviewed in Section 3.2 above indicate big returns to experience in many military occupations.) Third, volunteers are likely to be more motivated than draftees, also making the volunteer force more productive than a draft force of equal size. (A theory of effort is developed in Section 5.) Importantly, as both forces increase in size, the difference in the average experience level and in personnel turnover also widens. Thus, a proportionate increase in the size of both forces will raise the effectiveness of the

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JIT Warner and B.J. Asch

0

2V

FA

FD

2N

Force Size Figure 4. Optimal force size under draft and volunteer systems.

volunteer force relative to that of the draft force (i.e., R/OFA increases relative to dR/0FD as F increases). A second approach to the question of procurement method is to suppose that the military has an exogenous demand for a force with readiness level R*. If FA is the volunteer force and FD is the draft force that will deliver the readiness level R* (where FA
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VMCRA > VMCRD for the three reasons cited above, and the difference between them widens as F increases for the same reasons. For either procurement method, the optimal force size is the one that equates VMCR with the marginal cost of force size. Thus, in Figure 4, FA is the optimal volunteer force and FD is the optimal draft force. Once these optimal size forces are determined, then the optimal procurement method is the one that maximizes the "surplus" from defense, i.e. the difference between the total value of the readiness provided (VR) and the total cost (TC): S = VR - TC. (VR is the area under the relevant VMCR curve.) Thus, if SA is the surplus from force FA and SD is the surplus from force FD, choose the volunteer force if SA >SD. Figure 4 can be used to illustrate this approach. Suppose FA is the optimal volunteer force and FD is the optimal draft force. Then suppose that the volunteer force is expanded from FA to FD. The change in SA (ASA) is the area A, which is the excess of increase in cost over the value of readiness. Compare this to area D (ASD)which is the reduction in SD brought about from reducing the draft force from FD to FA. The volunteer system is the optimal one if SA >SD. The additional insight that follows from this approach over previous ones is that SD will rise relative to SA the more elastic are the VMCR curves. That is, the less rapidly the value that the electorate places on additional units of defense readiness declines, the more likely the draft is to be the preferred procurement method. Outward shifts in the VMCR curves brought about by the threat of war mean larger optimal force levels and a higher likelihood that the defense surplus will be maximized through conscription. 4.2. Other issues It would take us too far afield to consider all of the issues raised during the US draft debates. The Lee-McKenzie analysis and our generalization of it serve to make the general point that the volunteer force is not unambiguously superior to a draft, an argument advanced informally by draft advocates such as Kester (1986). The issue is ultimately empirical and hinges on questions about the elasticity of supply, the extent of the external threat, and the productivity differences between volunteer and conscripted forces. The concern of AVF critics was that it would be "too expensive" and that its high cost would induce an underprovision of defense. Although this argument is incorrect if the choice of procurement method and force size are based on full social costs, the argument has some basis if the military behaves as a monopsonist in its choice of force size. It is clear that the military is a monopsonist in the sense that the marginal cost of expanding the force through an increase in pay is in excess of the cost as given by the supply curve (Table 4). If the VMCR curve is not vertical and if calculations of the marginal cost of force size are based on the change in the wage bill that is required to expand force size, and not the supply curve, then under an AVF the military will enlist too few personnel (and pay them too little) 8. Despite the theoretical possibility 8 Cooper (1975) was the first to analyze the monopsony problem inherent in a volunteer force.

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J T Warner and B.J Asch

that the military will hire too few personnel under an AVF, the potential loss from monopsonistic behavior does not appear large [Quester and Nakada (1983)]. The fact that enlistments can be expanded relatively cheaply via tools other than pay (Table 4) diminishes the monopsony problem. Empirically, the stability of total US force size throughout the AVF period suggests that monopsony considerations have not played a large role in the determination of AVF force size. Other fears concerning a volunteer force do not seem to have materialized. It is doubtful that the volunteer force has become an elitist force that has threatened democratic values, that it has become a mercenary force, or that it has promoted adventurism abroad. A concern at the start of the AVF was that readiness would deteriorate because high-quality individuals would not volunteer. But the supply of high-quality recruits has proven sufficiently sensitive to pay, recruiting resources, and other inducements to enlist (and reenlist) that over the 20-year period of the AVF the quality of the entrants has been at least as good, if not better, than quality would have been under a draft. Furthermore, the AVF force has probably been more motivated than draft-era forces were. Whether quality could be maintained without conscription at much higher force levels is another (but now apparently less pressing) matter. The racial composition of the US force is still a contentious political issue; blacks currently make up 23 percent of the enlisted forces and 7 percent of the officer forces. Economists tend to see less problem with the racial composition of the armed forces than others [see, e.g., Tollison (1968)]. Finally, it is interesting to note that several US allies ended the draft earlier. The UK ended its draft in 1957. Australia ended its draft in 1945, reinstituted it for a time after 1965, but is now fully volunteer again. Except for the World War II era, Canada has had a volunteer system throughout its history. Only Germany has continued to use a mixed draft-volunteer system up to the present. Conscripts currently make up 43 percent of Germany's active duty force. Perhaps their different choices of manpower procurement method have been guided by the theory developed in Section 4.1.

5. The structure of pay 5.1. Stylizedfacts about military compensation At first blush, the US military compensation system is a complex patchwork of pays and allowances. But the various items of active duty cash compensation can be conveniently grouped into three categories: (1) basic pay, which varies with rank and YOS, (2) allowances for food and housing, which vary with rank and marital status, and (3) a large number of special pays, such as enlistment and reenlistment bonuses, flight pay, sea pay, hazardous duty pay, and so forth. Basic pay accounts for about 75 percent of US outlays for active duty personnel; allowances account for 19 percent. Although there are a large number of special pays and allowances, together they make up only about 6 percent of cash outlays for active duty personnel.

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US military personnel are vested in an immediate annuity after 20 YOS; those who separate prior to YOS 20 receive nothing unless they subsequently participate in the reserves and qualify for a reserve pension beginning at age 60. The total cost of active duty manpower is the sum of active cash pay and an accrual charge for retirement. The retired pay accrual charge is over 40 percent of annual outlays for basic pay and about a quarter of total cost, indicating that the cost of funding the retirement system is substantial. It is interesting to compare US and foreign military compensation systems. Germany, like the US, has a pay and allowance system with distinctions by marital status. But the United Kingdom (UK), Canada, and Australia all have salary systems with no preference given to married personnel. Longevity increases in the US basic pay tables are based on YOS. Longevity increases in the UK, Canadian, and Australian pay tables are based on time in grade (TIG) rather than time in service. The US has no system of explicit occupational pay differentials. Pay varies by occupation only through the application of enlistment and reenlistment bonuses and other pays that depend factors related to occupation (e.g., sea pay). However, the UK has a system of "pay bands" that vary by skill based on comparisons with civilian wages. A comparison of the pay tables of these countries shows striking similarities in the rank structure of pay. The US and its allies also have generally similar retirement systems. All countries delay retirement vesting until at least the mid-career range and provide an immediate lifetime annuity to those who serve long enough to become vested. Preliminary explanations for the commonalities in the rank structure of pay and in the retirement systems are now considered. 5.2. Theory Rosen (1992) identifies two important considerations in structuring pay. In a large, hierarchical organization it is important for the organization to assign the most able personnel to the higher-ranking positions because at the higher levels even small differences in ability can have profound effects on outcomes. Thus, while more able personnel are more productive at all levels, the relative productivity of ability increases with rank. The lack of lateral entry places a constraint on the military's capacity to fill the upper ranks with the most able personnel and suggests that it must access and "sample" a larger number of personnel before identifying those capable of performing the upper-level positions than would private-sector organizations that permit lateral entry. The other important consideration is that personnel must be induced by the structure of incentives to work hard and effectively. Individual effort is costly to monitor, so rewards must be structured to induce effort supply. In the military organization, the reward for effort is promotion. In the junior ranks, promotion is based on individual skill aquisition. But beyond the junior ranks, the promotion system resembles a contest or tournament in which only a fraction of those eligible for promotion are actually selected.

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JT Warner and B. Asch

Rosen only sketched out a model of ability sorting and effort supply in the military organization. Asch and Warner (1994a) formalize Rosen's arguments. Their model is briefly summarized here. Suppose that a is an individual ability parameter which is known to the individual but not to the military. Further, suppose that eit denotes the amount of effort that the individual would supply in rank i at time t conditional on the structure of pay, outside opportunities, and preferences. Let Z(ei,t) denote the disutility of effort such that Z'(ei,) > 0 and Z"(ei,t) > O0.Then at each point in the career an individual with ability parameter a must decide whether to remain in service and how much effort to supply. Likewise, the military must decide whether to retain the individual and whether to promote him or her. The military decides whom to promote by administering an evaluation (Ei,t) to everyone in rank i at time t, rank-ordering the evaluations, and promoting some fraction ri*,. An individual's promotion probability (ri,t) depends on his or her ability and effort and the abilities and efforts of others (a0 and e, respectively). The military may also use the evaluation to separate those whose evaluation Ei,t falls short of some minimum E'. The model is a generalization of the Gotz-McCall dynamic programming model. It has the following structure: To begin with, the expected value of future utility at the end of period t is Vi*t = cti,E(S,t G*, + Ei,, > 0) + (1 - i,t)Li,t,

(17)

where: Pi,t = pr(E' < Ei,t) pr(G Gi,t =

i+l,t+l [T'

t

+ Ei,t > 0)

+ 6 i+ + Wil, t+l +

+ (1 - ni+l it 1t+l)[Tm + i + Wm

1

= p

, )2

Vil,t+l - Z(eit+l)] +P

+l - Z(eit+l)] - Li,,

(18)

Li,t = Cit, + Ri,t + Ft,

i+l,t+ = T(a, ei,t, a, t, eitl, 7ri, t+l)

In words, expected utility Vi*t is a weighted average of the expected return to staying and the return to leaving immediately, where the weight i,t is the product of the (independent) probabilities that the military wants to retain the individual (,t) and the individual wants to stay (p,2t). The expected gain to staying Gi*t is a weighted average of the payoff to achieving next rank in period t + 1 and the return to remaining in the current rank. These returns depend on the pecuniary reward associated with the ranks (WM) and the value of rank-specific non-pecuniaries (6). The expected gain to staying G*, is the expected return to staying minus the return to leaving, which equals the present value of civilian earnings (Ci,t), vested retired or separation pay (Ri,t), and the value of non-pecuniaries in the civilian sector (Ft). Individuals desire to stay only if Gi,t + Ei,t > O, where Ei,t is the random shock to the retention decision. Individuals with higher permanent tastes for military service (Tm) are more likely to stay. If the individual is at a mandatory separation point in rank, then ]i, t = 0 and Vi t =Li,t.

Ch. 13:

The Economics of Military Manpower

383

The individual's expected future utility at the start of period t is: rm + WM +fi V t-Z(eit ).

(19)

The individual supplies effort in t to maximize Equation (19). Raising effort can raise expected future utility because (1) effort raises the probability of promotion, which conveys higher monetary and non-monetary rewards, and (2) effort reduces the probability of involuntary separation arising from a failure to meet minimum performance standards. Promotion also pushes further into the future the date at which the individual might be subject to a high-year-of-tenure rule. The first-order condition for utility maximization is: 'Pt[Ti (Wi+lt+ - Wit+l + 6 i+1 - 6i + (Vi+,t+l - Vit+l))] + p0,t [Git',t

(20)

+ (E0J2,] K - Z'(ei,t) = 0.

The first two expressions in (20) represent the discounted marginal benefit of effort. The last term, Z'(ei,t), is the marginal cost of effort. Individuals supply effort to the point at which marginal benefit equals marginal cost. The first marginal benefit term measures the direct pecuniary and non-pecuniary payoff from effort. It is apparent that the direct benefit of effort increases as the period t+ I interrank pay spread (W ,,t+ -W t+l) increases and as the difference in the value the individual places on the non-pecunaries associated with the next rank and the current rank (6i+l - 6i). Furthermore, the direct benefit of effort of all differentials beyond period t+ I are summarized in the term (V+l,t+ - Vi*t+). The direct benefit of effort is weighted by the probability of staying, such that individuals who are more likely to stay, and thus realize the reward to effort in the current period, have a higher expected reward to effort and will thus work harder. The term grt is the marginal effect of current period effort on the probability of promotion in the next period (i.e., Jr' = Ori+l,t+l/0ei,t).The direct benefit of effort is larger the more marginal effort raises the probability of promotion. Asch and Warner (1994a) show that J' is largest when the expected probability of promotion is 0.5. Marginal effort has little value when the probability of promotion is either very high or very low. They show that JT' declines the more important are the idiosyncratic determinants of promotion (i.e., "luck"). Finally, they demonstrate that y' increases with the scale of the contest. The more participants there are in the contest, the larger is the marginal value of effort. Scale matters because the more participants there are, the greater is the chance that the individual can surpass other contestants by supplying more effort. The second term of Equation (20) measures the value that effort has in avoiding separation due to failure to meet minimum performance standards 9. Since all terms 9 The term ¢0, shows the effect of marginal effort on the probability of being allowed to stay; ¢0, is

the effect of a small change in G-, on the probability of wanting to stay, and K is the effect of marginal effort on the evaluation. See Asch and Warner (1994a) for details.

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JT Warner and B.J Asch

in this expression are unambiguously positive except for G*, extra effort has value in terms of reducing the threat of involuntary separation except for those who have a very large negative expected gain to staying. For most personnel, minimum performance standards and up-or-out rules are a stimulant to effort. A main implication of the model is that, ceteris paribus, interrank pay differentials should rise as individuals progress through the ranks (i.e., the system should be skewed). Without skewness individuals will reduce effort as they reach the higher ranks because of the effect of declining promotion probabilities on the return to effort. But several factors might explain the observed lack of skewness in the US and foreign systems, including (1) the greater probability of staying as YOS and rank increase, (2) the value of rank-specific non-pecuniaries increases with rank, (3) the sheer size of the promotion contests. Additionally, an oft-cited factor that reduces the degree of skewness is that military "output" is team-oriented. Team production requires cooperation and not competition, which excessive skewness might promote [Rosen (1992)]. The lateral entry constraint also serves to reduce skewness. Since about two-thirds of enlistees remain for only one enlistment, their enlistment decisions will be based mostly on entry level pay. The lack of lateral entry means that the military must access enough personnel at the entry level to fill lower-level positions today and higherlevel positions in the future. Since ability has an increasing effect on performance as individuals progress through the ranks, there must be a sufficient number of highability personnel in the entry cohort to fill the upper-level positions in the future. But the military cannot just selectively recruit sufficient numbers of high-ability personnel because true ability is unobservable at entry. However, when entry pay is increased, the ability mix improves because higher entry pay attracts more applicants who have observable characteristics that are correlated with ability (education level and AFQT test scores) and the military can and does in fact screen on these characteristics. An implication of this discussion is that many junior personnel are overpaid due to the lack of lateral entry (i.e., they earn economic rents). The analysis highlights several potential problems with the US military compensation system. First, for the most part, intragrade pay raises are not performance based, but are provided in a lock-step fashion based on time-in-service. Some use of performance-based intragrade pay should be explored. Second, because longevity increases are based on time in service, early promotions convey only a temporary gain. In fact, slow promotees often earn more upon promotion that those who have held the rank several years. A system based on time in service blunts the advantage to working harder and achieving an early promotion and it is likely to produce a significant amount of adverse selection. A system of longevity increases based on time in grade has been recommended a number of times and the pay tables of a number of other countries, including Canada, the United Kingdom, France, and Australia, are based on time in grade. There should be further investigation in the USA of such a system. The US military retirement system has often been criticized for its high cost, its unfairness to those who separate without benefits, and its inflexibility in force

Ch. 13:

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385

management. But is it a coincidence that the US and its allies all have retirement systems that postpone retirement to a late date but provide relatively generous benefits to retirees? Asch and Warner argue not. The lateral entry constraint places the military in a much different situation from civilian employers. It must access and train large numbers of entrants before identifying for advancement those who have the talent to perform the higher-level tasks in the organization. It therefore wants to provide incentives for the most talented to stay and seek advancement and for others to leave after they discover that they are unsuitable for the upperlevel positions. That is, it must provide the proper incentives for personnel to selfsort. Delayed vesting of retired pay induces self-sorting because only those who think that they can achieve the requisite rank and longevity will stay early on while others will leave. Deferred retired pay can also motivate work effort, especially when combined with minimum performance standards for retention and up-or-out rules that prevent low-ranking personnel from staying long enough to collect retirement benefits. This discussion begs the question of when vesting should occur. But notice that there is a trade-off between the vesting date and the military's ability to pay new entrants. If the military is to meet a fixed budget constraint, earlier vesting will dissipate its capacity to raise entry pay and attract a higher-quality entry cohort. Contrary to critics of delayed vesting, it is not necessarily unfair to the bulk of entrants who never qualify for retirement benefits because they are generally overpaid as a result of the lateral entry constraint. The question now arises why retirement benefits should be part of the self-sorting mechanism. After all, why not just pay a bonus to all who reach the requisite rank and years of service? The answer has to do with retired pay's role as a separation incentive. At some point the military wants everyone, including the best personnel, to separate, even when they may still be individually very productive. The longer individuals remain in the top positions the slower will be the promotion rates for younger (and potentially equally able) personnel. Unless offset by changes in the structure of pay, reduced promotion opportunities in the junior ranks will discourage work effort in those ranks and will cause those junior personnel with the best external opportunities (i.e., the more able) to leave. Without the proper inducement, the senior personnel may not want to leave voluntarily if their military pay exceeds their best private sector alternatives. Such is especially likely to be the case for those trained in the militaryspecific skills. There is, of course, no reason why the separations required to maintain personnel flows could not be accomplished with other policy tools such as up-or-out rules. However, excessive reliance on involuntary separation to control the experience structure of the force can be bad for morale, impacting on recruiting, retention, and work effort. These adverse effects might require the payment of a "regret premium" to compensate for the prospect of involuntary separation. A relatively generous retirement system for senior personnel may be the only way to quell these problems. Asch and Warner (1994b) evaluate a number of past proposals to overhaul the US military

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retirement system. Considered in the light of the model developed in this section, most would do more harm than good. Finally, note an important implication of Equation (20). Draftees cannot be induced by compensation and personnel policies to supply effort because draftees know that their probability of staying and receiving contingent compensation () is low. This result implies that draft armies will have to devote more resources to direct monitoring and disciplining of draftees, a factor which further reduces the availability of ready personnel. Furthermore, draftees will have to be motivated by penalties for poor performance (e.g., bad conduct discharges).

6. Force management issues 6.1. Women in the military With the exception of nursing positions, the military has traditionally been a male organization. As women's role in society at large has been transformed over the last few decades, the question arises of whether the role of women in the military should more closely mirror the greater role of women in the civilian sector, and specifically whether all military positions, including combat ones, should be open to women. Binkin and Bach (1977) discuss the economics of sex integration into the armed forces. The question they pose is: what mix of military men and women can meet US national security needs at the lowest cost? Adressing this question requires information on the differential costs and effects associated with different mixes of men and women and of filling a given position with a man versus a women. Under the cost category, information is needed on the differential recruitment, training, retention, and separation (including retirement) costs. There may also be adjustment costs, such as those associated with changing facilities to accommodate women. The costs associated with military benefits, including medical costs, housing costs, and the cost of dependents may also differ depending on the mix of men and women. Are men and women equally productive? Those who oppose women serving in some military positions argue that women lack men's upper body strength and therefore could not perform equally as men in some jobs. Some also argue that because of pregnancy, women are less likely to be deployable and thus, units which have a greater mix of women are less ready. Still others argue that women would adversely affect unit cohesion, and that they are more likely to be emotionally strained by the rigors of combat. Studies of the relative costs and effectiveness of women versus men in the military generally focus on variables that are amenable to analysis, such as enlistment, attrition, and retention behavior. On these important dimensions, past studies indicate that the behaviors of women and men are often similar and respond to many of the same factors. Hosek and Peterson (1990) use a choice-based sample to estimate a logit model of the individual enlistment decisions of young men and of women and find

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that for most variables, the coefficient estimates are statistically equivalent for men and women. They use individual rather than aggregate level data since in the aggregate, women are demand constrained - more want to enlist in a given year than the services demand at the prevailing level of compensation. While they find that female and male enlisted supply generally depend on similar factors in similar ways, they do find that the intercept is smaller for women - reflecting the demand constraint - and that immediate marriage plans are a greater deterrent to women's enlistment. Overall first-term attrition rates are higher for women than for men [Buddin (1988)], but there are differences among the services. Attrition rates are higher for Navy women than Navy men during the early months of terms of service, but the rates converge over time [Fletcher et al. (1994)]. Attrition rates for men and women in the Army also converge over time, if attrition due to pregnancy is excluded [Martin (1994)]. But when attrition due to pregnancy is included, the rates do not converge. Retention behavior is similar for men and women [Quester (1988)]. When retention differs, women in fact have somewhat higher first-term retention and slightly higher long-term retention rates than men [Quester (1988), Shiells and McMahon (1993)]. The evidence on sex differences in productivity is spotty. The services presented evidence before the 1992 President's Commission on the Assignment of Women in the Armed Forces that women are less effective on two counts. First, service data suggested that women have lower deployment rates than men and that lower deployment rates detract from unit readiness. Second, evidence was presented purporting to show that women are at a disadvantage in performing military jobs requiring physical strength. Yet, the greater reliance on technical skills and the reduced reliance on physical strength over the last few decades among many military jobs, especially in the Air Force and Marine Corps, weakens the physical strength argument against the employment of women in the military. Furthermore, as noted by Fletcher et al. (1994), other physical attributes such as compact body type that are important for military jobs that are limited by space (such as in ships, submarines, and aircraft) favor women over men. For the many reasons discussed earlier, the services stress the recruitment of highquality personnel. Because of demand limitations the fraction of women who are high quality exceeds the male high-quality fraction. During the 1980s, about half of male enlistees were in the high-quality category whereas over 60 percent of female enlistees were. The relevant comparisons are not between high-quality female enlistees and highquality male enlistees, but between high-quality female and low-quality male enlistees. Along many dimensions, the women may be the more productive group. 6.2. Reserve force management issues Several characteristics of reserve service distinguish it from active service. First, only a small fraction of reservists work full-time; during peacetime most reservists are civilians. Consequently, reserve units must draw personnel from local labor markets. Second, unlike the active components where most individuals who enlist have no

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prior military experience, about half of all reserve enlistees do [Marquis and Kirby (1989a)]. Prior service personnel are generally recruited to fill the mid-career and senior positions whereas non-prior service personnel generally fill junior positions initially. Third, since reservists are primarily civilians and cannot be relocated to meet service demands in any location, skill matching is important; reserve personnel of the appropriate skill type must be recruited and retained to meet the occupation mix of the reserve units in the local area. Finally, there is no clear-cut reenlistment point in the reserves. Although reservists sign enlistment contracts, the timing of separations from the reserves bears little relation to the formal contract expiration dates. Thus, there is little practical distinction between continuation and reenlistment in the reserves. Several studies have estimated enlistment supply of non-prior service and of prior service personnel to the reserve components. Generally these studies find that the same factors affect reserve as active duty enlistment supply and in very similar ways. For non-prior service personnel, Tan (1991) finds pay elasticities between 0.43 and 0.67, unemployment rate elasticities between 0.25 and 0.45, and recruiter elasticities between 0.4 and 1.0. He also finds evidence of a negative tradeoff between nonprior service and prior service recruits; as recruiters allocate their effort towards priorservice recruits, non-prior service enlistments fall. Studying prior service enlistments into the Naval Reserve, Kostiuk and Grogan (1987) estimate a pay elasticity of 0.82 and a recruiter elasticity of 0.50. Marquis and Kirby (1989a) find a pay elasticity of 1.17 for prior service personnel affiliating with the Army Reserve and the Army National Guard. A unique set of factors that are hypothesized to affect reserve but not active duty supply are employer attitudes and policies towards reservists. Evidence from Grissmer, Kirby and Sze (1992b) suggests that reserve service imposes a cost on reservists in terms of conflicts with their primary employers, especially among those working in small firms. However, family/spousal attitudes toward reserve service had a larger effect on reservists' reenlistment decisions than did perceived civilian supervisor attitudes. It has also been argued that reserve duty differs from other secondary jobs because military service is national service and involves the risk of mobilization and the possibility of family hardships, financial loss, and injury. Mehay (1991) finds evidence indicating that several of the determinants of secondary job participation differ for reservists and civilians but that individuals do appear to choose to moonlight (regardless of whether it is in the reserves or in the civilian sector) based on relative compensation and local labor market conditions. Asch (1993) expands the moonlighting model to explicitly incorporate the risk of mobilization for reservists, and Grissmer, Kirby, Sze and Adamson (1992a) examine the options for offering insurance protection against losses incurred during mobilization. The model of the decision to stay in the reserves is fundamentally similar to the stay-leave decision in the active components. Evidence on reserve attrition indicates that the factors that are important in explaining active attrition also tend to be important in explaining reserve attrition. For both prior service and non-

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prior service personnel, higher reserve pay and higher education levels are usually associated with lower attrition, as is greater aptitude [Kostiuk and Follmann (1988), Marquis and Kirby (1989b), Grissmer and Kirby (1988)]. These studies provide mixed results on attrition of women and nonwhites compared with males and whites. One issue of concern has been high attrition among non-prior service reserve personnel. Grissmer and Kirby (1988) find attrition rates of 35 to 40 percent two years after entry. High attrition rates are costly because of the substantial training investment made by the military, and the relative short time non-prior service individuals have been in service relative to prior service who entered the reserves at the same time. But Kirby and Grissmer (1993) show that reserve attrition is not excessive because a significant fraction of those who leave the reserves later rejoin or, alternatively, join the active force. Although reserve attrition is high, only one-third to one-half of the losses are to civilian life. The rest join the active force (about 25 percent of reserve separations) or later rejoin a reserve component. When attrition is defined as separation to civilian life, Kirby and Grissmer find that reserve attrition rates are often lower than they are for comparable non-prior service personnel in the active force. Another issue of concern is the skill qualification levels of reservists. Individuals who are not skill qualified are not deployable which, in turns, adversely affects reserve unit readiness. Some evidence indicates that personnel in the reserve components are often less skill qualified than their active duty counterparts [Grissmer et al. (1994)]. Among enlisted personnel, the skill qualification level among Naval Reserve personnel is 13 percentage points lower than that of active Navy enlisted personnel. This figure is 10-13 percentage points for the two Army reserve components. One reason for the lower skill qualification level in the reserves is that most prior service accesssions require retraining; they do not enter the skills that were trained in while they were on active duty. Less than one half of prior service personnel match their active and reserve jobs when they affiliate with the reserves. The match rate is higher for the Naval Reserves (70 percent) than for the Army National Guard, where the match rate is less than one-third (Grissmer et al. 1994). These figures imply that the training cost saving associated with employing prior service over non-prior service personnel is less than is generally believed. Another reason for lower skill qualification levels in the reserves is the significant amount of personnel turnover in reserve units. The Air reserve components have the greatest stability - about 70 percent of the positions are filled by the same enlisted personnel over an 18-month period. But the Army reserve components have stability rates of only 45 to 50 percent and the Naval Reserve has the lowest rate, one-third. Eighty percent of this turnover is due to switching units within local areas rather than geographic relocation [Buddin and Grissmer (1994)]. The cause of this turbulence appears to be due to individuals' desires to change jobs or to seek promotion opportunities. The aggregate costs or benefits of this turnover remains an open question.

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The overriding issue is the structure and the appropriate mix of active and reserve forces 10. The US Congress has generally favored a greater reliance on the reserves than the services have. At issue is the substitutability of reserve and active forces and their relative cost. The ease of substitution depends on the speed with which reserve forces can be mobilized and on the relative unit readiness of the reserve and active forces. Some reserve force components are virtually perfect substitutes for their active force counterparts and have the advantage of lower peacetime costs. Examples are Air National Guard and medical units. But anecdotal evidence indicates that in direct combat units the reserve forces require a long lead time for mobilization and are not as combat-ready as the active forces II . One of the key force mix questions is whether a given active/reserve mix that meets national security goals is sustainable. Analyses of alternative mixes assume that reserve readiness can be maintained regardless of the mix. However, a constraint on the degree to which the active force can be reduced and the reserves increased is the supply of active veterans to the reserves. As the active force gets smaller, the flow of veterans to the reserve forces falls. This constraint is important because of the contribution of prior service personnel to reserve readiness. While direct evidence on the relative contributions of prior service versus non-prior service personnel is scarce, there is an important difference between them that affects readiness, and that is cumulative military experience. Grissmer et al. (1994) shows that among personnel in similar paygrades, non-prior service personnel have about half the military experience of prior service personnel. Debate over the constitution of the active and reserve forces will no doubt continue. More research is needed to understand better the productivity differences between prior service and non-prior service personnel in each of the reserve components.

7. Civilian returns to military service The military has long been viewed as a good training ground for the nation's youth, and the military can have a significant impact on the general society given the thousands of individuals who enter and leave service each year. From an academic perspective, it is interesting to know whether the training and experience acquired in service have a payoff once individuals separate. It is also important from a policy perspective, since the design of an effective compensation system depends on how military service impacts future civilian alternatives.

'o A recent Congressionally mandated study addresses this issue in great detail. The discussion in the text draws heavily from the study's final report [National Defense Research Institute (1992)] as well as from Grissmer et al. (1994). " Some Army Reserve armor units activated early in the Gulf crisis were not ready for overseas deployment even after months of training at the National Training Center in California.

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Underlying the returns-to-service literature are the human capital hypothesis and the screening hypothesis. According to the human capital hypothesis, once individuals leave military service their earnings relative to nonveterans will depend on the amount of military training and experience received and their transferability to the civilian sector. For the same amount of training and experience, veterans' civilian earnings will be less than the earnings of comparable non-veterans if all or part of that training and experience is not transferable, because those who directly entered the civilian labor market accumulated civilian human capital while those who entered the military did not. Some types of military training and experience are more transferable than others. According to the screening hypothesis, even if military training does not provide skills that can be used in the civilian sector, military service may still give a positive (negative) return if civilian employers view military service as evidence of desirable (undesirable) work qualities that are inherent to those who serve. Thus, military experience may serve as a signal of the innate characteristics of those who enter the military [DeTray (1982)]. Evidence of a positive or negative return to service is thus consistent with both the human capital hypothesis and the screening hypothesis. However, from the standpoint of addressing the question of what roles the military might play in, say, developing youth, knowing which hypothesis is the correct one is crucial because they yield different policy prescriptions. The general approach to estimating whether there is a veteran's premium in the civilian labor market is to estimate an equation of the form In W = 6V+Xfi + ,

(21)

where W is the individual's civilian wage, V represents veteran's status, X is a vector of other individual characteristics, E is a random error term, and 6 and i are parameters to be estimated. The parameter represents the veteran's premium (if it is positive) or penalty (if it is negative). Studies that apply ordinary least squares (OLS) to Equation (21) generally find that World War II veterans earn a premium [Fredland and Little (1980), Rosen and Taubman (1982)] but that Vietnam-era veterans suffer a penalty [Rosen and Taubman (1982), Berger and Hirsch (1983)]. Furthermore, there is some evidence that the veteran premium is larger for non-whites and for the less educated 12 A problem for all of these studies is the failure to control for sample selection bias. Sample selection bias occurs when the unobservable factors that determine earnings () are correlated with veteran's status (V). Such will be the case if individuals are not randomly assigned to the veteran and non-veteran groups. Non-random assignment can occur two ways: (1) those who enter military service are not a random sample of Xie (1992), for example, tracks earnings of synthetic cohorts of veterans in the March Current Population Survey of each year from 1964-1984. Among white veterans, he finds negligible earnings differences between veterans and non-veterans once a host of other factors are controlled for. But black veterans earn 6% more than non-veterans. 12

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all qualified youth and (2) those who leave military service are not a random sample of all enlistees. In fact, considerable evidence indicates that the decision to enter or separate from service is not random. The correlation between E and V can be positive or negative, depending on the circumstances. Given that the military screens potential entrants and tends to reject those with lower aptitude and physical exam scores, it could be that V and E are positively correlated since those who score low are likely to be low earners as well. In this case, OLS estimates of 6 will be biased upward. But the correlation could be negative if the more able find enlistment unattractive (as during the early AVF period) or if they are successful in avoiding the draft (as may have been the case during the Vietnam era). Sample selection bias can also arise if the decision to leave the military is not random. The bias could be negative if up-or-out rules force the separation of less able personnel (while the more able stay), but it could also be positive if those with the best civilian alternatives are the ones who actually separate. Only five studies have attempted to correct for selectivity bias: Angrist and Krueger (1994), Angrist (1989, 1990), Gilroy et al. (1992), and Bryant et al. (1993). The latter two employ Heckman's two step method of correcting for sample selection bias [Heckman (1979)]. Angrist's various studies use a simpler instrumental variables technique: find a variable correlated with veteran's status (V) but not the unobservable determinants of earnings (E) and use it as an instrument for V. He takes advantage of the lottery nature of the draft, which randomly assigned youth into draft status based on birth date to form an instrument for V. Analysis of results based on simple OLS with those based on instrumental variables techniques find that estimates -based on OLS are inconsistent whereas those based on the instrumental variables method are not. Angrist (1989) finds a penalty of 28 to 35 percent for white Vietnam-era veterans and a premium (that is only marginally significant) of between 20 to 40 percent for black veterans. Using alternative data sources, Angrist (1990) arrives at qualitatively similar results. Angrist and Krueger (1994) restudy the earnings of World War II veterans. Using an instrument for veteran status based on birth year and month, they estimate a wage penalty of 6.4 percent using the instrumental variable method but a 7.8 percent premium using OLS. Specification tests indicate that the negative estimates based on the instrumental variable technique are consistent while the OLS estimates are not. The two studies of AVF veterans find mixed results. Gilroy et al. (1992) find that white veterans initially earn less upon leaving service but then earn more relative to a comparable group of nonveterans who entered the civilian market upon leaving high school. Over an 8-year time horizon, the premium for non-Hispanic whites is estimated to be about 5 percent. But they find a zero returns for blacks and for Hispanics. Bryant et al. (1993) also focus on AVF veterans. Contrary to Gilroy et al. and more consistent with the various Angrist studies, they estimate a veteran wage penalty of between 1 and 8 percent. The wage penalty is estimated to be greater for whites than for nonwhites. The bulk of the veterans in these studies served for relatively short periods. Thus studies that contrast veteran and non-veteran earnings tell little about how longer periods of service affect future civilian earnings capacity compared with civilian

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experience. And since none of these studies controlled for military occupation, they tell nothing about whether post-service earnings depend upon the type of training. One such study that addresses these questions is Borjas and Welch (1986), who studied the earnings of military retirees who were surveyed in the 1977 Defense Retiree Survey along with a matched sample of veterans from the March 1977 Current Population Survey (and who presumably served for relatively short periods) 13. Over the span of the second-career, officer retirees who work year-round earn 14 percent less than their veteran counterparts and enlisted retirees earn 20 percent less. Enlisted personnel in the Combat Arms skills lost an additional 13 percent. Goldberg and Warner (1987) found similar patterns studying the Social Security earnings over the period 1972-1977 of a large sample of enlisted personnel that separated in FY 1971. For three occupation categories that appear a priori to provide transferable training (e.g., Electronics Equipment Repair), the authors could not reject the hypothesis that additional military experience adds as much as civilian experience to future civilian earnings. In these skills, military and civilian experience appear to be perfect substitutes. But other skills do not appear a priori to provide as much transferable training (e.g., Combat Arms), as a year of military experience was found to add less to subsequent civilian earnings than a year of civilian experience. Over a 20-year career, the earnings loss is about 20 percent in the non-transferable skills. To summarize, the bulk of evidence fails to support a finding that military service conveys a post-service return that is in excess of the return from civilian experience. Collectively, the studies suggest that for short periods of service the return to military service is roughly comparable to the return to civilian experience. In fact, that those who enter for one term of military service do not suffer a large loss should be considered a positive result, for it suggests that military service is a legitimate avenue for the acquisition of human capital. But those individuals who serve for longer periods in non-transferable skills do suffer a loss of earning power, a fact that must be considered in the design of the military compensation system.

8. Summary It is evident from this survey that over the past two decades economists have contributed a substantial body of literature on the economics of military manpower. For the USA at least, supply relationships and the relationships between experience and productivity are now reasonably well understood. Future research should focus on the relationship between productivity and incentives and how effectively military personnel systems sort personnel into their most suitable positions. The bulk of research has focused on the USA. But pay and personnel practices do vary across

13 Comparing retirees with (short-service) veterans should eliminate some of the entry-level selection bias since all entrants met initial screens.

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countries. Whether differences in practices generate differences in outcomes would be a particularly fruitful avenue of future work. As militaries in the US and elsewhere accumulate more data about the effectiveness of women and reservists, economists will no doubt play a role in the analysis and interpretation of those data. Finally, this survey has said little about the military downsizings now underway in the USA and elsewhere. It is too early to tell what effects they will have on various measures of effectiveness and how military organizational structures might be modified to minimize their impact. But the downsizings, which generate exogenous changes in force size and force structure, will create numerous opportunities to better understand the economics of military manpower.

References Albrecht, M., 1979, Labor substitution in the military environment: implications for enlisted force management, R-2330-MRAL (RAND, Santa Monica, CA). Altman, S., and A. Fechter, 1967, The supply of military personnel in the absence of a draft, American Economic Review 57, 19-31. Angrist, J., 1989, Using the draft lottery to measure the effects of military service on civilian labor market outcomes, in: R. Ehrenberg, ed., Research in labor economics (JAI Press, Greenwich, CT) 265-310. Angrist, J., 1990, Lifetime earnings and the Vietnam era draft lottery: evidence from social security administration records, American Economic Review 80, 313-336. Angrist, J., and A. Krueger, 1994, Why do World War II veterans earn more than nonveterans?, Journal of Labor Economics 12, 74-97. Asch, B., 1990, Navy recruiter productivity and the Freeman plan, R-3713-FMP (RAND, Santa Monica, CA). Asch, B., 1993, Reserve supply in the post-Desert Storm recruiting environment, MR-224-FMP (RAND, Santa Monica, CA). Asch, B., and J. Dertouzos, 1994, Educational benefits versus enlistment bonuses: a comparison of recruiting options, MR-302-OSD (RAND, Santa Monica, CA). Asch, B., and L. Karoly, 1993, The role of the job counselor in the military enlistment process, MR-314-P&R (RAND, Santa Monica, CA). Asch, B., and J. Warner, 1994a, A theory of military compensation and personnel policy, MR-439-OSD (RAND, Santa Monica, CA). Asch, B., and J. Warner, 1994b, A policy analysis of alternative military retirement systems, MR-465-OSD (RAND, Santa Monica, CA). Asch, B., J. Dertouzos, J. Hosek and B. Rostker, 1992, Restructuring DoD's accession plans in the coming decade, White paper (RAND, Santa Monica, CA). Ash, C., B. Udis and RF. McNown, 1983, Enlistments in the all-volunteer force: A military personnel supply model and its forecasts, American Economic Review 73, 144 155. Beland, R., and A. Quester, 1991, The effects of manning and crew stability on the material condition of ships, Interfaces 21, 111 120. Berger, M., and B. Hirsch, 1983, The civilian earnings experience of Vietnam-era veterans, Journal of Human Resources 18, 455-79. Berner, K., and T. Daula, 1993, Recruiting goals, regime shifts, and the supply of labor to the army, Defence Economics 4(4), 315-328. Binkin, M., and S. Bach, 1977, Women and the military (The Brookings Institution, Washington, DC).

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Black, M., R. Moffitt and J. Warner, 1990, The dynamics of job separation: the case of federal employees, Journal of Applied Econometrics 5, 245-262. Borjas, G., and F. Welch, 1986, The post-service earnings of military retirees, in: C. Gilroy, ed., Army manpower economics (Westview Press, Boulder, CO) 295 313. Brown, C., 1985, Military enlistments: what can we learn from demographic variation?, American Economic Review 75, 228-234. Browning, E., 1987, On the marginal welfare cost of taxation, American Economic Review 77, 11-23. Bryant, R., V. Samaranayake and A. Wilhite, 1993, The effect of military service on the subsequent civilian wage of the post-Vietnam veteran, Quarterly Review of Economics and Finance 33, 15-31. Buddin, R., 1988, Trends in attrition of high quality military recruits, R-3539-FMP (RAND, Santa Monica, CA). Buddin, R., and D. Grissmer, 1994, Skill qualification and turbulence in the army national guard and army reserve, MR-289-RA (RAND, Santa Monica, CA). Buddin, R., D. Levy, J. Hanley and D. Waldman, 1992, Promotion tempo and enlisted retention, R-4135FMP, The (RAND, Santa Monica, CA). Clark, R., 1978, Capital-labor ratios in a military service: a putty-clay application, in: R. Cooper, ed., Defense manpower policy (RAND, Santa Monica, CA) 11-23. Cooke, T., and A. Quester, 1992, What characterizes successful enlistees in the all-volunteer force: a study of male recruits in the U.S. Navy, Social Science Quarterly 73, 238 252. Cooke, T., A. Marcus and A. Quester, 1992, Personnel tempo of operations and navy enlisted retention, CRM 91-150 (Center for Naval Analyses). Cooper, R., 1975, The social cost of maintaining a military labor force, R-1758-ARPA (RAND, Santa Monica, CA). Dale, C., and C. Gilroy, 1985, Estimates in the volunteer force, American Economic Review 75, 547-441. Daula, T., and R. Moffitt, 1991, Estimating a dynamic programming model of army reenlistment behavior, in: C. Gilroy, D. Home and D. Smith, eds., Military compensation and personnel retention (US Army Research Institute, Alexandria) 181-201. Daula, T., and R. Moffitt, 1992, Estimating dynamic models of quit behavior: the case of military reenlistment (US Military Academy). Daula, T., and D. Smith, 1985, Estimating enlistment supply models for the U.S. army, in: R. Ehrenberg, ed., Research in labor economics (JAI Press, Greenwich, CT) 7, 261-309. Daula, T., and D. Smith, 1992, Are high quality personnel cost-effective? the role of equipment costs, Social Science Quarterly 73, 266-275. Dertouzos, J., 1985, Recruiter incentives and enlistment supply, R-3065-MIL (RAND, Santa Monica, CA). DeTray, D., 1982, Veteran status as a screening device, American Economic Review 72, 133-142. Enns, J., G. Nelson and J. Warner, 1984, Retention and retirement: the case of the U.S. military, Policy Sciences 17, 101-121. Fernandez, J., 1992, Soldier quality and job performance in team tasks, Social Science Quarterly 73, 253-265. Fernandez, R., 1982, Enlistment effects and policy implications of the educational assistance test program, R-2935-MRAL (RAND, Santa Monica, CA). Fisher, A., 1969, The cost of the draft and the cost of ending the draft, American Economic Review, 59, 239-254. Fletcher, J., J. McMahon and A. Quester, 1994, Women in the navy: the past, the present, and the future, Occasional paper (Center for Naval Analyses). Fredland, J., and R. Little, 1980, Long-term returns to vocational training: evidence from military sources, Journal of Human Resources 15, 49-66. Friedman, M., 1972, An economist's protest (Thom, New Jersey).

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Gilroy, C., T. Daymont, P. Andrisani and R. Phillips, 1992, The economic returns to military service: race-ethnic differences, Social Science Quarterly 73, 340-359. Goldberg, L., 1982, Enlistment supply: past, present, future, CNS 1168 (Center for Naval Analyses). Goldberg, L., 1991, Recent estimates of enlistment supply models (Economic Research Laboratory, Reston, VA). Goldberg, M., and J. Warner, 1982, Determinants of navy reenlistment and extension rates, CRC 476 (Center for Naval Analyses). Goldberg, M., and J. Warner, 1987, Military experience, civilian experience, and the earnings of veterans, Journal of Human Resources 22, 62-81. Gotz, G., 1990, Comment on the dynamics of job separation: the case of federal employees, Journal of Applied Econometrics 5, 263-268. Gotz, G., and J. McCall, 1980, Estimation in sequential decisionmaking models: a methodological note, Economics Letters 6, 131-136. Gotz, G., and J. McCall, 1984, A dynamic retention model for air force officers: theory and estimates, R-3028-AF (RAND, Santa Monica, CA). Gotz, G., and R. Roll, 1979, Defense resource management study supporting papers: first-term career mix of enlisted military personnel (RAND, Santa Monica, CA). Gotz, G., and R. Stanton, 1986, Modeling the contribution of maintenance manpower to readiness and sustainability, R-3200-FMP (RAND, Santa Monica, CA). Grissmer, D., and S. Kirby, 1988, Changing patterns of nonprior service attrition in the army national guard and army reserve, R-3626-RA (RAND, Santa Monica, CA). Grissmer, D., S. Kirby, M. Sze and D. Adamson, 1992a, Insuring mobilized reservists against economic losses, unpublished manuscript (RAND, Santa Monica, CA). Grissmer, D., S. Kirby and M. Sze, 1992b, Factors affecting reenlistment of reservists: spousal and employer attitudes and perceived unit environment, R-401 I-RA (RAND, Santa Monica, CA). Grissmer, D., S. Kirby, R. Buddin, J. Kawata, J. Sollinger and S. Williamson, 1994, Prior service personnel: a potential constraint on reserve forces, MR-362-OSD (RAND, Santa Monica, CA). Hammond, C., and S. Horowitz, 1990, Flying hours and crew performance, P-2379 (Institute for Defense Analyses). Hammond, C., and S. Horowitz, 1992, Relating flying hours to aircrew performance: evidence for attack and transport missions, P-2609 (Institute for Defense Analyses). Hansen, L., and B. Weisbrod, 1967, Economics of the military draft, Quarterly Journal of Economics 82, 395-421. Heckman, J., 1979, Sample selection bias as a specification error, Econometrica 47, 153 162. Hogan, P., D. Smith and S. Sylwester, 1991, The army college fund: effects on attrition, reenlistment, and cost, in: C. Gilroy, D. Horne and D. Smith, eds., Military compensation and personnel retention (US Army Research Institute, Alexandria) 317-354. Horowitz, S., and A. Sherman, 1980, A direct measure of the relationship between human capital and productivity, Journal of Human Resources 15, 67-76. Hosek, J., and C. Peterson, 1985, Reenlistment bonuses and retention behavior, R-3199-MIL (RAND, Santa Monica, CA). Hosek, J., and C. Peterson, 1990, Serving her country: an analysis of women's enlistments, R-3853-FMP (RAND, Santa Monica, CA). Kearl, E., D. Horne and C. Gilroy, 1990, Army recruiting in a changing environment, Contemporary Policy Issues 8, 68-78. Kester, J., 1986, The Reasons to Draft, in: W. Bowman, R. Little and T. Sicilia, eds., The all-volunteer force after a decade (Pergamon-Brassey's, New York) 286 315. Kirby, S., and D. Grissmer, 1993, Reassessing enlisted reserve attrition: a total force perspective, N3521-RA (RAND, Santa Monica, CA). Kleinman, S., and W. Shughart, 1974, The effects of reenlistment bonuses (Center for Naval Analyses).

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