,~ . Technical Report 634/

A New Approach to

Managing the Army

01 Selective Reenlistment

Bonus

Sheldon E. Haber, Enrique Lamas,

and Judith H. Eargle

The George Washington Univesit

Manpower and Personnel Policy Research Group

* Manpower and Personnel Research Laboratory

O-TIC

19-LECTE

_ _ _ A

8 U. S. Army

Research Institute for the Behavioral and Social Sciences

June 1984

*Aoprovecl fos oubitc release; dittnbution uni rnited.

96 2 1 90
U. S. ARMY RESEARCH INSTITUTE

FOR THE BEHAVIORAL AND SOCIAL SCIENCES

A Field Operating Agency under the Jurisdiction of the

Deputy Chief of Staff for Personnel

L. NEALE COSBY

EDGAR M. JOHNSON Colonel, IN

Technical Director Commander

Research accomplished under contract .

for the Department of the Army

The George Washington University

-- -.- , . . ..-

Technical review by -

Hyder Lakhani

Curtis Gilroy

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1. EPRT UMBnE Repr 634 : GOP ACCESSI No ECI IENT*S CATALOG NUMBER

4. TITLE (and Subtitle) S YEO EOT&PRO ~EE

A NEW APPROACH TO MANAGING THE ARMY SELECTIVE October 1982-December 1983

RENISMN BNS6. PERFORMING ORG. REPORT NUMER. §p

7. AUTNOR(s) S. CONTRACT OR GRANT NUMBER(@)

t Sheldon E. Haber, Enrique Lamas, and

Judith H. Eargie (GWU) MDA 903-82-C-0383

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I0. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reveres se ft noco.einv and ideuntify by block numer)

Reenlistment <-bMilitary pay,- (Civilian pay,-'

Economics, Recruitment cost,*, Economic analysis,*

Selective Reenlistment Bonus Human capital; Military essentiality code.

.Retention Training cost; /

24L ASIrNAc? (cemam e reverve ohl Knsoeiy an #ewUily by block nmbe)

>The authors develop a theoretical model of profit maximization in which

the Selective Reenlistment Bonus (SRB) is treated as a wage premium payable to

servicemen who are more productive, more costly to recruit and train, and less S

likely to continue in the Army in the absence of the SRB. Empirical estima- ~ 0I

S tion of the model is based on measuring a serviceman's productivity (in terms A

of his civilian counterpart's occupational wage), recruitment and training /r~w

costs, and separation rates. Multiple regression equations are used to estimate civilian wages (a proxy for productivity) as a function of (CniudV.'~

DO, LIToWO 17 INO65I @LEEUNCLASSIFIED%

i SECURITY CLASSIFICATION OF THIS PAGE (Whekn Does Entered)
UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE(Wh, Det En.tered)

ARI Technical Report 634

20. (Continued)

civilian occupation, education, and age of the worker. The empirical model

groups Military Occupational Specialties (MOS) into three categories--Combat

Arms, Technical, and Support Services.

.a

The results for servicemen in grade E-4 reveal that the average SRB

calculated by the model ($5,247) should be about the same as the actual

payments ($5,297) for servicemen in Combat Arms, but should be higher

($7,308) compared to the actual ($5,312) for Technical occupations, and

lower ($1,942) compared to the actual ($3,757) payments in the Support

Services. J,.

The research shows that retention rates in Technical MOS can be raised

by increasing the SRB. The required increase in SRB expenditures can be

funded by reducing SRB payments in the Support Services. "

2.) L "%

r

% J

*".." .-

..- 7z

-6*%* %*h

UNCLASSIFIED ii SECURITY CLASSIICATION OF THIS PAGC(Won Dem Enfered)

:i-% 
Technical Report 634

A ANew Approach to

Managing the Army

Selective Reenlistment

Bonus

Sheldon E. Haber, Enrique Lamas,

and Judith H. Eargie *...

The George Washington University,

Submitted by

Curtis L. Gilroy, Chief

Manpower and Personnel Policy Research Group

Approved as technically adequate

and submitted for publication by gI

Joyce L. Shields, Director ..

Manpower and Personnel Research

Laboratory

U.S. ARMY RESEARCH INSTITUTE FOR THE BEHAVIORAL AND SOCIAL SCIENCES

5001 Eisenhower Avenue, Alexandria Virginia 22333

Office, Deputy Chief of Staff for Personnel

Department of the Army

June 1984

I' Army Project Number Manpower and Personnel

20M6731AM5

AWpred for pubic 1 =iIs dMrbutl- N elst
-11 V IRM V 7- 517). .6'wT 7.K717M. -- - - . .

ARI Research Reports and TechnicalI Reports are intended for sponsors of

olR&D tasks and for other research and military agencies. Any findings ready

for implementation at the time of publication are presented in the last part

of the Brief. Upon completion of a major phase of the task. formal recoinmendations for official action normally are conveyed to appropriate military

agencies by briefing or Disposition Form.%

i
ACKNOWLEDGMENTS

Sheldon Haber and Judith Eargle are Professor of Economics and Research

Associate, respectively, at the George Washington University. Enrique Lamas,

now at the Bureau of the Census, was an Economist at the U.S. Army Research

Institute. This research was conducted under Contract No. MDA 903-82-C-0383

with The Consortium of Universities of the Greater Washington area. The authors are grateful to Dr. Arvil V. Adams, Consortium Research Director, and

Dr. Curtis Gilroy and Dr. Hyder Lakhani, Manpower and Personnel Policy Research

Group, U.S. Army Research Institute, for helpful comments. The views expressed

are solely those of the authors and do not necessarily represent those of any

of the aforementioned individuals, the U.S. Army, or the Department of Defense.

:-

.i

m%

VB o.

S. °o.

:.---::

vi " '

,I .....
A NEW APPROACH TO MANAGING THE ARMY SELECTIVE REENLISTMENT BONUS

EXECUTIVE SUMMARY

Requirement:

The U.S. Army Research Institute conducts research on manpower, personnel,

and training issues of particular significance and interest to the U.S. Army.

The objective of this research was to develop a basis for the reenlistment

bonus that would improve its effectiveness and efficiency.

Procedure:

The authors develop a theoretical model of profit maximization in which

the selective reenlistment bonus (SRB) is treated as a wage premium payable to

servicemen who are more productive, more costly to recruit and train, and less

L likely to continue in the Army in the absence of the SRB. Empirical estimation

of the model is based on measuring a serviceman's productivity (in terms of his

civilian counterpart's occupational wage), recruitment and training costs, and

separation rates. Multiple regression equations are used to estimate civilian

wages (a proxy for productivity) as a function of civilian occupation, education, and age of the worker. The empirical model groups Military Occupational

Specialties (MOS) into three categories-Combat Arms, Technical, and Support

Services.

S:.'.

Findings:

The results for servicemen in grade E-4 reveal that the average SRB calculated by the model ($5,247) should be about the same as the actual payments

($5,297) for servicemen in Combat Arms, but should be higher ($7,308) compared .'.

to the actual ($5,312) for Technical occupations, and lower ($1,942) compared

to the actual ($3,757) payments in the Support Services.

Utilization of Findings:

The research shows that retention rates in Technical MOS can be raised by

increasing the SRB. The required increase in the SRB expenditures can be

funded by reducing SRB payments in the Support Services.

vii

. . . . . ...- , - . %o .5.* . . .°
A NEW APPROACH TO MANAGING THE ARMY SELECTIVE REENLISTMENT BONUS

CONTENTS

Page

INTRODUCTION. .. ........ .......... ......... ... 1

hREENLISTMENT MODELS AND THE SELECTIVE REENLISTMENT BONUS... .. .. .... 6

SELECTIVE REENLISTMENT BONUS MANAGEMENT .. ......... ........ 13

Current SRB Guidelines .. .... ..... ..... .... . . . . 14

A Digression on Classification of Career Management Fields

and Military Occupational Specialties into Major Army

Occupation Groups .. ......... .......... ...... 17

LEmpirical Data Relating to the Current SRB Program. ...... ..... 22

A HUMAN CAPITAL APPROACH TO COMPUTING SELECTIVE REENLISTMENT

BONUS LEVELS .. ..... .. .. .. .. .. .. .. .. .. .. .. .... 27

Te BasiC Model. .. ......... ......... ......... 28

The Extended Model .. ................ . . . . . . 30

* Extending the Model to the Military Sector .. . . . . . .31

SEPARATION RATES . .. .. .. .. .. .. .. .. .. .. .. . . . . . . 38

The Separation Rate and Measures of Retention .. . ... . . . . . . . 38

A Digression on Army Strength as of September 30, 1980 .. ........ 40

Continuation Rates in the Same MOS ........ .. .. . ........ 42

TRAINING COSTS .. ..... ......... .......... ...... 47

Recruitment Cost . . . . . . . . . . . .. .. .. .. .. .. .. . .48

pTraining Cot . .. .. ........ .................. 51

*CIVILIAN EARNINGS IN OCCUPATIONS ANALOGOUS TO MILITARY SPECIALTIES . . . . 56

MODIFICATIONS TO THE INITIAL SRB CALCULATION . . . . . . . . . . . . . . . 64

Military Essentiality .. .. ...... . .. .. .. .. .... 64

Shortfall113 ... . . . .. . . . . . . .66

High Performance Soliers.......... . . . . . 69

%! ~Additional Overrides. ..... ..... .. .. .. . . .. . ... 69

The Interest Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Regular Military Compensation. .. ...... . . . . . . . . . . . . . 71

ix
CONTENTS (Continued)

Page

SRB LEVELS CALCULATED FROM THE MODEL ...... ................... ... 75

CONCLUSION AND SUGGESTIONS FOR FURTHER RESEARCH ... ............. 85

LIST OF TABLES

Table 3-1. Percent distribution of enlistees within major Army

occupational group by career management field .. ....... .. 20

3-2. New SRB payments by zone, fiscal year 1981 -

fiscal year 1983 ...... .... ... ...... ..... . 23

3-3. New SRB payments by major occupational groups and zone,

fiscal year 1981..... ... . . . ............. 25

5-1. Percentage distribution of enlistees by zone and major

Army occupational group, September 30, 1980 ......... 41

5-2. Percentage distribution of enlistees by zone,

September 30, 1980. . .. . ...... . zne. . . . . . . . 43

5-3. Continuation rates in the same MOS by major Army

occupational group, fiscal year 1981 ............. . ...-. 45

6-1. Per capita active Army recruitment costs, fiscal year 1981 . 4""

6-2. Recruitment costs, excluding enlistment bonuses, by

major Army occupational group, January 1982 .. ......... ... 52

6-3. Cumulative training costs by major Army occupational

group, October 1981 . . . . . . . . . ............ 54

7-1. Major civilian occupational groups corresponding to

major Army occupational groups ................ 57

7-2. Estimated regression coefficients from earnings equations

for civilian occupations corresponding to IDOS subgroups . . . 59

7-3. Estimated value of output (earnings) of enlistees by

major Army occupational group, fiscal year 1981 ....... 61

8-1. Number and percentage of MOS with a shortfall by

major Army occupational group . . . . . . . . . . . . . . .. 70

8-2. Regular military compensation by major Army

occupational group ........... . 73

.., . .,

X %'--
CONTENTS (Continued) .

Page ~

Table 9-1. Model SRB values, s*, by major Army occupational group . . . . 77

9-2. Model SRB values, modified by filters and overrides,-

by major Army occupational group. .... ......... ... 79

9-3. Percentage distribution of MOS with a positive SRB

by major Army occupational group, zone A .. ....... .... 83 C

xi
1 hI

.Zia

Chapter 1: Introduction

In recent years the military services have offered bonuses to induce

* reenlistment in military occupational specialties (MOSs) where supply

has fallen short of requirements. The need for reenlistment bonuses

1

stems from the way in which military pay is structured. The most important element of military pay, i.e., basic pay, is based on skill

attainment and level of responsibility which vary by pay grade but not

by MOS, holding pay grade constant. However, at a given pay grade not

all military occupations are equally attractive, either to those who

view military service as a potential career or to those who view it as a

temporary job in which training can be obtained and skills transferred

*::" to the civilian sector. Hence, workers with a given skill proficiency ,-.

"- can often earn more in the civilian sector where supply and demand

conditions determine wage rates than they can in the military. Since

* basic pay in a given pay grade is invariant among MOSs, reenlistment

bonuses provide a means of aligning military and civilian compensation,

thereby making military service more attractive.

In managing a reenlistment bonus program, a number of questions '77

must be addressed. For example, how many dollars should be spent on

reenlistment bonuses? What criteria should be used in determining the

occupational specialties in which a bonus will be offered? Given that a

bonus is offered in an occupational specialty, what amount should be

offered? Should the bonus be offered to all takers in an MOS in which

77p
2

it is offered, or should preference be given to some groups? Additionally,

attention must be given to effectiveness and efficiency. The effectiveness

of the SRB program means how well additional income is distributed

to those groups whose labor services are most Important in meting the

Army's manpower objectives. For a bonus program to be efficient, .

bonuses should be offered only to those who would not reenlist in the

absence of such a program. To the extent that bonuses are given to

individuals who would reenlist even without a bonus, the cost of the

bonus program will be greater than necessary. But in formulating policies

to insure that a bonus program is effective and efficient, consideration

needs also to be given to other aspects of bonus management. For example,

bonuses which are offered for a short time and then withdrawn may not

provide an adequate signal Indicating career opportunities in a given

occupational specialty. Also, bonuses should be tied to an Individual's

* ~performance in addition to serving as a monetary inducement to reenlist. ~ ~

The first objective of this research is to develop a reenlistment

bonus methodology which improves on the effectiveness and efficiency of

current SRB procedures. The main building block of this methodology is

a model which relates pay to output, training costs, and turnover In

competitive labor markets. In the pages that follow, this model is

applied to the reenlistment bonus problem whose setting is the military

labor market where pay is administratively determined by Congress and

taken as given by military manpower managers.

The output of the model is a set of values that yield an effective

reenlistment bonus schedule defined in terms of MOS, pay grade, and "

. .-.-.-..-......... _.................. ....... ,,'L':',. - ''. ,-',. / '.-. ".' " ""'°-'. ." -".--"-"' .: .' " - - " -"- - '- .* -*"-"" - " - " ' -', -- '-""'"
SRB zone. Efficiency is Indirectly built into the model by providing larger

bonuses to individuals who are ls likely to reenlist. It should be noted,

however, that the model does, by and of Itself, enable one to determine the

optimal reenlistment bonus budget necessary to meet the Army't manpower goals.

The second objective of the research Is to explore policy Issues

relating to the way in which reenlistment bonuses are ourrently determined. "-..1*

This analysis will provide insights into some desirable properties which

should be exhibited by an SRB program. In the course of the discussion , %

It will be seen that the proposed SRB methodology incorporates a number

of these desirable properties.

In the chapters that follow, a number of related topics are discussed.

Chapter 2 describes briefly the use of regression models to determine

the supply elasticity of the SRB and how such models fit into the more

general framework of managIng an 3RB program.

In Chapter 3, past and current reenlistment policies which have shaped

the structure of the Army's 333 program are examined. These policies

are analyzed within the broad context of SRB program management. .z

The basic model utilized for computing proposed SP3 levels is discussed

in Chapter 4. The model is then expanded to accommodate management --

criteria to fit the military context in which it is being applied.

The inputs to the model are described and summarized in Chapters 5,

6, and 7. These inputs are the separation rate, training cost, and output

associated with each pay grade and bonus tone for specified kinds of

2

labor.

The full model for calculating SRB bonus levels utilizes several

*'****'*S*'*~ 5* , 
filters which modify the initial SRB calculation. The first of these

filters masures the military essentiality of a MOS. The second Identifies

those instances where a MOS Is in short supply. A third utilizes Information

about an individual's performance in the Army to improve the efficiency

Sof the SRB. The last filter adjusts the computed SRB levels so that

their range is consistent with that of the FY 1981 SRB schedule. Each

of these filters is discussed in Chapter 8.

The SRB levels computed using the model developed in this study are

summarized in Chapter 9. The conclusion and suggestions for further

research in the management of the Army's SRB program are provided in

-. Chapter 10.

"W°

, ... :.-. :?
5

Chapter 1 Footnotes

I This need is apparent in an all-volunteer military environment but

was reoognized as early as 1965 when the draft was still in force.

In 1965 Congress established the variable reenlistment bonus program

as a means of increasing retention in short-supply technical specialties.

See U.S. Department of Defense, Office of the Secretary of Defense,

Military Compensation Background Papers: Compensation Elements and

Related Manpower Cost Items, Their Purpose and Legislative Background,

Third Quadrennial Review of Military Compensation, August 1979.

(Referred to below as Third Quadrennial Review of Military Compensation).

2 Unless otherwise stated all data in this report were obtained from

the Defense Manpower Data Center (DMDC) in Monterey, California.

Their generous assistance is gratefully acknowledged.

. %.

: .. .. .
6"

Chapter 2: Reenlistment Models and the

Selective Reenlistment Bonus

In this chapter we describe one way in which the SRB problem can be

addressed, namely, by using a regression model designed to estimate the

elasticity of reenlistment with respect to bonuses. The advantages of

and problems in using such an approach for setting SRB levels are discussed .

below within the larger context of the problem of SRB program management. ... .

In order to put the 3RB problem in its proper perspective, we begin

with a discussion of how the demand for and supply of personnel in an

MOS are determined. Put most simply, the demand for personnel in an

MOS, D, can be considered as given by strategic and technological

considerations. hile this approximation holds for the short run, it Is

clear that in the long run demand cannot be divorced from supply, since

shortfalls in personnel may lead to changes in the design of field equipment

and ultimately to changes in personnel requirements. For purposes of

determining SRBs, personnel requirements are treated as a fixed parameter.

In the absence of a SRB, the reenlistment rate, designated by a, .

depends on a number of variables expressed as:

(1) =a +bw di xi

where w is the military wage, the x i are variables such as level of

'. ...

:::::::

'.* •
education, marital status, race, the opportunity cost of remaining in

the military, and the coefficients b and di measure the change in a for

unit ohanges in w and the zi, respectively.

When a SRB, denoted by a, is offered

(2) a b w s di i z- x L_' :

The coefficient o measures the change In the reenlistment rate a for a

unit change in a, holding everything else constant. The elasticity of

reenlistment with respect to the bonus is defined as the percentage

change in the reenlistment rate when the bonus level changes by one

percent.

The supply of career personnel in an MOS can be written as

3 S mR +F

where F represents reenlistees who have passed a length of service threshold

* sufficiently long so that they will remain in the Army until retirement,

. R represents the personnel who are potential candidates for reenlistment,

i.e. potential careerists, and as before a Is the proportion of R who .

reenlist.

°, ... ' °

. . . . . . . . .". . - 4 4 4.
8

Assuming that equation (3) is correctly estimated, it is useful

to inquire as to how It can be utilized in establishing SRB levels.

Presumably the bonus "payoffm Is higher in MOSs with a high reenlistment

elasticity, and hence it can be argued that larger SRBs should be offered

In these MOSs. One problem with this approach is that the reenlistment

elasticity, by and of itself, does not provide sufficient information to

determine whether a bonus should be offered, since the MOSs with a high

reenlistment elasticity may already be adequately staffed with career I'-. '

personnel, i.e. in these MOSs it may be that D > S. Put another way, it

is not clear why MOSs with a high reenlistment elasticity would also .

necessarily be those MOSs in which there is a shortfall in career personnel.

One solution to this problem is to offer an SRB only in those MOSs where

there is a shortfall. While this is an acceptable way of resolving this

particular problem, it should be recognized that if the unconstrained

outcomes differ markedly from the constrained ones, the solution Is

achieved through a rule which overrides the model rather than by the

model itself.

If an SUB is given only in those MOSS where there is a shortfall,

the reenlistment regression model can provide a simple, but not necessarily

preferred way of insuring that D u Sin each occupational specialty.

Given the percentage Increase In reenlistments that would equate demand

and supply in an MOS and knowing the reenlistment elasticity with respect

to the bonus, one can compute the SRB level which sets D x S. Of course,

it may be that the SRBs determined In this manner are greater than the

budgeted amount. In this event, which Is not unlikely, one Is confronted

S- . ..... .. ,--- .. ."
9

with the problem of how to reduce RB levels to fit the specified budget.

When estimated 3RB expenditures exceed the budget, the natural

inclination is to reduce the SRB levels in those MOSs with the lowest SK

reenlistment elasticities. This, however, can lead to unanticipated and

unwanted consequences. The reason for this 18 that the MOSs in which it

Is most important that Incumbents continue in their specialty may be the %

ones with the lowest reenlistment elasticity with respect to the bonus.

Those MOSS are likely to be the ones which are unattractive, either because

they do not engender skills that can be transferred to the civilian sector

or the skills can be easily transferred to the civilian sector at pay rates

that are substantially higher than In the military sector. In these circumstances individuals may be reluctant to reenlist unless a very high

bonus is offered. Thus rather than reducing SRB levels in these MOSS,

it may be desirable to raise them in order to meet readiness requirements.

,

In addition to the difficulty of framing appropriate S3B policy **.A

based only on reenlistment elasticity information, there are several issues

which must be addressed in estimating reenlistment elasticities. Among

the more Important issues is how the data used in the estimation process

are to be aggregated. In the early literature, grouped data were examined

using a simple linear or log linear model. More recently as data sets

with information for individuals have become available, more complex

models, e.g., logit and probit models, have been employed. When similar

explanatory variables are utilized, these different models yield different

reenlistment elasticities with respect to pay.

There is also some question as to bow to define the pay variable.

A ~. :-:-..-.--.-.
10

Some investigators use a relative pay measure, i.e., military pay/olvilian

pay; others use an absolute measure, i.e., they treat military and civilian

pay as separate variables. The latter procedure results in higher pay

elasticity estimates than the former. Moreover, military and civilian

pay can be defined in different ways. In defining military pay threeor four-year time horizons are generally used, but longer ones are also

possible. In estimating civilian pay, civilian workers with similar

characteristics as potential reenlistees are typically looked at; however, -

it Is what non-reenlistees actually earn In the civilian sector which is

the more relevant proxy of the opportunity cost of remaining in the

military. Reenlistment elasticities are higher for longer time horizons

and when vet'erans' earnings are used instead of the earnings of their

5

civilian counterparts.

The reenlistment elasticity also depends on the type of data used

and how it is aggregated. Longitudinal data on individuals yield lower -:

elasticity estimates than cross-sectional data. Coll agregation, e.g.,

using career management fields (CMs) instead of MOSs reduces the variance

of the occupational variable and also leads to lower elasticity estimates.

Still another problem in estimating reenlistment elasticities is

model specification. Whereas all models take into account such variables

as age and educational attainment, most omit other variables which may

be equally important, e.g.j, the variety of training an individual receives

may Influence his perception of multiple career opportunities in the

military. Other non-economic factors which may bear on the reenlistment %

9 . decision come readily to mind. #7

• %' " *,

. % , . - . P. . . , .,. * . , . * . . . . -. ,-. - . . . . . .. . .. , %-. . % ° .
1 1 [ ,

ro. PIS

Besides these problems which affect the accuracy of reenlistment

elasticities, there are data problems which must be dealt with. First,

data specific to each service is required. Second, bonus elasticities N.

10

are needed by occupational specialty and zone. Third, it Is generally

assumed that the impact on reenlistment of a SRB is the same as that of

a change in the military wage, i.e., the SRB is subsumed into the wage

variable. Not only is the SRB variable omitted from most models, but the .-

dependent variable typically includes all reenlistaents whether or not

they meet the SRB extension of service requirement, i.e., extension of :

one's current contract for a minimum of three adiinal years of service. 1.

Despite the difficulties in estimating reenlistment elasticity .

models with respect to a SHB, they are useful for achieving consistency

between expected SRB expenditures and the actual bonus budget. SRBs can

be established in a rational manner without recourse to such models,

however. The approach developed in this study is designed to achieve ...-. *

this objective.

,--x.

-, --

£ 0 '
12

Chapter 2 Footnotes

1 For the SRB problem the demand for personnel is for career personnel,

which conventionally refers to personnel with 4 or more years of

service. In practice, however, the Army offers SRBs to individuals

with 21 or more months of service.

2 In a number of models w is expressed as the ratio of the military

wage to the civilian wage. Additionally, the bonus is often included

in the military wage. In this case the elasticity of reenlistment

with respect to the bonus and to the military wage are assumed to be

the same.

3 See William R. Bowman and George Thomas, Forecasting Reenlistment

Rates in the AVF Era: Methodological Issues and Preliminary Results,

United States Naval Academy, 1982, p. 8.

4 I=., p. 10.

5 2=-9.., p. 8 .

6 I=9., p. 15. ~I%

7 I=±., p. 8. For additional discussion of methodological issues

involved in estimating reenlistment elasticities, see Thomas V. Daula

and Thomas W. Fagan, Modelling the Retention Behavior of First-Term

Military Personnel: Methodological Issues and a Proposed Specification,

United States Military Academy, 1982.

8 See Sheldon E. Haber, Terence Ireland, and Herbert Solomon, Manpower

Policy and the Reenlistment Rate, The George Washington University,

Serial T-1201, June 1974.

9 See, for example, Bowman and Thomas, oR-eit- and Donald Atwater and

Murray Rowe, A Method for Estimating the Effects of Military Compensation

on Retention, Navy Personnel Research and Development Center, October

25, 1982. '.'.

10 Currently, the Department of Defense (DoD) provides serx.. vi-,

reenlistment rates for zone A. No estimates disaggregated by

occupational specialty are available. See U.S. Department of Defense,

Office of the Assistant Secretary of Defense, Manpower, Reserve Affairs,

and Logistics, Administration of Enlisted Personnel Bonus and Proficiency

Pay Programs, DoD Instruction 1304.22, October 1, 1978.
* 13

Chapter 3: Selective Reenlistment Bonus Management

The necessity for offering reenlistment bonuses has been recognized

ever since the nation's military service was organized. In 1949 the --.

rules for conferring reenlistment bonuses, at that time wch were given

to AUl reenlistee3 Irrespective of which MOS they reenlisted in, were

considerably improved by basing the amount of the bonus on reenlistment

length rather than on length of service in the military. In 1954 the

reenlistment bonus level was reduced for individuals reenlisting more

than once, since retention rates rise with length of service even in the

absence of a bonus. A further improvement was made in 1965 when, in

addition to the regular reenlistment bonus (RRB), a variable reenlistment

bonus (VRB) was authorized for individuals reenlisting in critical skill

occupations. Recognizing that the RRB was being paid to individuals

serving in MOSs where retention was high as well as in MOSs where it was

low, the RRB was replaced by the SRB in 1974. At the same time the VRB

2

was phased out since its objective and that of the S3R were similar.

This brief outline of the antecedents of the SRB program illustrates

major fundamental changes in bonus management as it pertains to Improving

retention in the military. The proposals made in this study have a more

limited objective, i.e., to improve the effectiveness and efficiency of

the SRB within the current framework. While the model developed to met .7

this objective utilizes Army data, it is believed that the general approach

is also applicable to the other military services. ,*- .

";; I':
141

A. Current SRB Guidelines

Selective reenlistment bonuses are now offered in three zones.

Reenlistments falling between 21 months and 6 years, 6 and 10 years, and

10 and 14 years of active service are defined as occuring In zones A, B,

and C, respectively. One of six levels of skill criticality, indicated

by bonus multiples 1 through 6, may be designated in each zone. The

bonus level is given by the product of the bonus multiple, an individual's

monthly basic pay, and the aditional years of active service, not to

exceed 6 years, which are obligated. No bonus is offered where the *bonus

multiple* is Q.

Several management rules must be met for a candidate to qualify for

an SRB. The individual must be in pay grade E-3 or higher, must be

eligible for reenlistment, must be qualified in an NOS where an SRB is

3

offered, and must reenlist or extend service in that HOS. Moreover, the

individual must reenlist or extend for at least 3 years of additional

service, and the reenlistment or extension period plus existing prior

active service must add to at least 6 years, 10 years, or 14 years of

4

service in zones A, B, and C, respectively. Only one SRB can be awarded

in each zone, and beginning in FY 1981 the maximum bonus in a zone was

5

set at $16,000. Since January 1982 one-half of the SRB is paid upon

reenlistment, the remainder being paid in equal annual installments over

the reenlistment or extension contract; prior to this date the SRB was

paid in one lump sum.

In assessing these guidelines, it Is useful to determine the outcomes

which are implicit in the way they are framed. For example, by offering

,- .. .. . .. . . .. . . -. -..- - . .. .. .. *. . .. . . .. . . . . . . . .-. *. ., -. -.,..- -. .,- . -, . . , .' --
15

a SRB only when the additional years of active obligated service exceed

3 years, a minimum number of extra years of service is guaranteed during

which the bonus can be recouped. Tying the bonus level to the number

of extra years of service also serves as an inducement to reenlist or

extend for more than the minimum required to become a candidate for the ,...,

SRB. This inducement is further strengthened by limiting to one the

number of bonuses that can be offered in each zone.

The designation of three zones presumably is to take account of varia- -

tions in the reenlistment rate and shortfalls during the first and subsequent

reenlistment periods. Indeed, the generally high reenlistment rates among

individuals with extensive service is consistent with the zone C upper

bound of 14 years of service. All else being the same, the positive

relationship between the reenlistment rate and length of service suggests

that, on average, the bonus multiple should decline in moving from one

zone to the next. Likewise, the number of MOSs in which an SRB is offered

should diminsh.

Another outcome of the current guidelines, resulting from the use

of a constant bonus multiple in a zone, is that within each zone a bigger

bonus is offered to individuals in the higher pay grades because of

their higher basic pay. But since pay grade and the reenlistment rate

are positively related to length of service, a larger proportion of

individuals may be expected to reenlist in the higher pay grades than in

the lower ones in the absence of the bonus. Hence, everything else

being the same, the efficiency of the SRB may be improved if the bonus

multiple declined with pay grade within a zone.

* . . , . * . ,
16

The basic philosophy of the SRB program is to offer a 3RB only win 6

skills with chronic retention problems and/or service manning shortages.*

While there is no doubt that this is the primary intention of the program,

the major goal has been elsewhere described as providing 'a monetary

incentive to encourage personnel to reenlist in military skills which

have high training costs and which are in critical supply."

The DoD also considers two additional criteria in their review

which deserve separate mention because they pull in different directions.

One pertains to 'improvements to be expected at various bonus levels,'

i.e., the incremental gain in the reenlistment rate or bonus yield

consequent upon a change in the bonus multiple. The other states "the --

appropriate level for a bonus...is determined by the amount of increased -.1

retention needed to overcome or alleviate the shortage...in zones within

a skill.* As indicated earlier, for some MOSs both the bonus yield and

retention rate may be low; in these cases it is not clear which criterion

should be given the greater weight. Again it is important to recognize

that consideration of the bonus yield by and of itself may result in an

undesired outcome.

Similarly, the maningfulness of a shortfall depends on factors other

than the fill rate. For example, the implications of a given shortfall

in an NO with a high training cost will be different from the same

shortfall in an NOS with a low training cost. Thus it is conceivable

that one may want to stockpile personnel in the former NOS (resulting in

a fill rate exceeding one) and to do so by offering a SRB. Bere again

it is useful to look at SRB levels absent overrides such as shortfalls.

..-
.F-X -M '.) Ar.-vu i~'U~j . -*~. 'W 7 T. P- - "W

17

The problem of giving overriding weight to any single criterion, such

as shortfalls, is that it ignores other variables which also need to be

considered. The difficulty of incorporating several variables In a decision

model, however, Is how to combine them. One approach to this problem in to

une a multiplicative model. For example, Griffin, in addressing the problem

of first-term attrition, develops an attrition severity index which is the

product of five variables, the product being scaled between the values of 0

10

and 1. In another study including similar variables, the variables were

themselves scaled between 0 and 1 and then weighted by an *importance factor*

11

(also scaled betwen 0 and 1) from questionnaire information. The weighted

values are then used in a linear programing model to obtain SRB multiples.

In this paper a human capital theory model, relating separation rates,

training costs and output in the military, Is utilized to compute a SRB. The

bonus levels are computed from an analytical model and represent wage differentials meaured In dollars per year. Discussion of this model is deferred

to the next chapter.

B. A Digression on Classification of Career Management Fields and Military

Occupational Specialties into Major Army Occupation Groups

Before examining empirical data relating to the current SRB program

we first digress to look at the problem of how to summarize such information. One way of summarizing the data Is by career management field

*-. (ClH). Using ClI categories there are still 31 groupings, hence a simpler

method of aggregation mst be resorted to. The mapping used in this , ,-
18 w

study leaves the traditional MOS to CWF classification undisturbed.

In this report each CMF is assigned to one of three occupational

groups denoted as Infantry (I), Technical (T), or Support (S) (referred

to below as major Army occupational groups or more simply as major IDOS

groups). The procedure for doing this was as follows:

(1) Each MOS was classified into a tio-digit subgroup defined by ".-L

the Integrated Defense Occupational Stratification (IDOS) system developed

12

by DoD as a means of cross-referencing civilian and military workers.

(2) The enlistees in each HQS within a CMF were then aggregated on

the first digit of the IDOS subgroup code into the three major groupings

Infantry, Technical, and Support (see Table 3-1).

The IDOS subgroup codes comprising the Infantry, Technical, Support

specialties are

IDOS subgroup codes T and R - Infantry:

Military-Unique Personnel (T) - Personnel

in occupations with no civilian equivalent,

e.g., infantrymen and artillerymen

Laborers, Operators, and Routine Maintainers (R)

Personnel who operate equipment and provide

labor and routine maintenance in transportation, -

supply, and installation areas

IDOS subgroup codes 0 and P - Technical:

Technical Personnel (G) - Personnel in areas

that require extensive special training, e.g.,

scientific and engineering technical personnel

and Intelligence technical personnel

Craftsmen, Mechanics, and Production Workers (P)

- Personnel able to install, maintain, repair,

or fabricate material and equipment

' First digit of IDOS subgroup in parenthesis.

,-.:. . . . ., ,.. . -. . ,, .,,: . ;,,, , . .'..,.-,..-. . ..... ,-,.... . . .,.. .. ..... -,.,.....,..-:--. ......:..............-...
-- ~~~~k - ~ ~-- UVILP. 

19

IDOS subgroup codes J and M - Support: U

Clerical Personnel (M) - Personnel who perform

typing and filing and operate office equipment

Service Personnel (H) - Personnel who provide

security, medical, and domestic and personal

services

(3) Each 27 was then assigned to the major Army occupational

group with the largest proportion of the CW Is personnel. As a result

of this last step, all MOSs in a CMF are in the malor_ I0s group of the

parn . °H 

To illustrate the procedure it is seen from Table 3-1 that 53.3

percent of the personnel In CWF 51, General Engineering, are in the

Technical specialties; the remaining personnel are In the Infantry (44.1

percent) and Support (2.5 percent) specialties. This CW was

assigned to the major occupational group *Teohnical* personnel since it

contains a plurality of the personnel. The same plurality rule was used

to categorize each CMI.

While this mapping of CMs (and MOs) to major Army occupational group

can be viewed simply as an accounting detail, it is some interest to

note that most CM~s are homogeneous with respect to the IDeS classification

system, but some are not. No attempt 1s made in this study to reduce

the heterogeneity inherent In the IDOS classification system since this

would mean departing from the way the Army groups MOSs by CE'.

p. °.

--- ~ * * ;; :.' .- .- :-.-

. * _:* 
20

Table 3-1

Percent Distribution of Enlistees within Major Army Occupational

Group by Career Management Fielda

ator Army Occupational Group

Military

Essentialt

Career Manaement Field I S Toa al 

Infantry (11)0 100.0 • 100.0 1

Combat Engineering (12) 6.30 93.7 100.0 1

Field Artillery (13) 65.8 e 34.2 100.0 1

Air Defense Artillery (16) 92.00 8.0 100.0 1

Armor (19) 100.0 100.0 1

Air Defense Missile

Maintenance (23) 100.0 100.0 2

Ballistic/Land Combat

Missile and Light Air

Defense Weapons Systems

Maintenance (27) 100.0 100.0 2

Aviation CommunicationsElectronics Maintenance

(28) 100.0 100.0 2

Communications-Electronics

Maintenance (29) 100.0 100.0 2

Communications-Electronios

Operations (31) 40.9 59.1 100.0 2

EW/Intercept Systems

Maintenance (33) 100.00 100.0 2

* General Engineering (51) 144.1, 53.3 2.5 100.0 3

Chemical (51) 97.3 2.7e 100.0 2

Ammunition (55) 100.0, 100.0 2

Mechanical Maintenance (63) 100.0 100.0 2

Transportation (614) 81.7. 18.14 100.0 2

Aviation Maintenance (67) 71.0 29.0 0 100.0 2

Administration (71) 22.6 77.5 100.0 3

Automatic Data

Processing (741) 0 50.14 49.6 100.0 3

Supply and Service (76) 55.5 3.9 40.6 100.0 3

Recruitment and

Reenlistment (79) 100.00 100.0 3

Telegraphic Engineering (81) 100.0 100.0 3

Public Affairs and Audio

Visual (814)o 70.6, 29.14 100.0 3

Medical (91) 96.5 3.6 100.0 1

2..

. :.1 :.: :.
21

Table 3-1 Continued

Percent Distribution of Enlistees within Major Army Occupational

Group by Career Management Field *.*.'

Majocr Army Occupational Group

Military

Essentib alit~

* Carter Management Field 14 b~1 ....... .... ~ a

Petroleum (92) 95.8 41.2 0 100.0 2

Food Service (941) 100.00 100.0 3

Law Enforcement (95) 0 100.0 100.0 3

Military 

Band (97) 

Intelligence (96) 100.0 

100.0 

9 100.0 

100.0 

2 

3

*

EW Cryptologic *Operations (98) 100.0 100.0 1

a As of September 30, 1980.

b I =Infantry, T zTechnical, S =Support.

c Rounded to 100.0 percent.

d Code 1 z High, 2 zMedium, 3 zLow.

e Career Management Field code in parenthesis.

CMajor Army occupational group (major IDOS group) In which each MOS is

classified in this study.

Source: Derived from data provided by the Defense Manpower Data Center - and U.S. Army Concepts Analysis Agency.
22

C. Empirical Data Relating to the Current SRB Program

Empirical data on SRB payments matching the detail needed in this study,

i.e., by MOS, zone, and pay grade, could not be retrieved by DMDC as of

the study date. Despite this shortcoming, salient aspects of the current

SRB program can be inferred from data provided by the U.S. Army Personnel .

Center (MILPERCEN) to see how they conform to the guidelines discussed

earlier (see Tables 3-2 and 3-3).

As can be seen from Table 3-2, the total dollar value of new SRB payments

made by the Army was $65.6 million in FY 1980. In F! 1982 $98.2 million was

expended for new SRBs with an additional increase in the SRB budget planned

for FY 1983. If planned expenditures for FY 1983 are realized, the number

of new SRBB offered will increase while the average new SRB payment will

fall. Thus, it appears that the Army may be opting to offer more but -

smaller reenlistment bonuses.

It is also noted from Table 3-2 that between FY 1980 and FY 1982 the

average new SRB payment was higher in zone C than zone B and higher in zone

B than in zone A. Given the positive relationship between retention rates

and zone, it is not clear why bonus levels should be positively related to

13 zone. However, the proportion of the SRB budget in this zone and in

zone C has consistently been smaller than that allocated to zone A where

retention is lowest. Indeed, it is this allocation of the SRB budget %'".

within zones which is indicative of the emphasis given to the retention

rate in management of the 3RD program. >;' "

"..-*-. _s7 . . . ... . . . . . . . . . . . . . . . . . .... 

" '.''..#.'"'' -"' ''.. .. :'' "'"' ..' "/"..' '"' *.' -. * * -*.-'-' * *.,.- . * -'<'..-- n . .p./' > -tp ' . *. ..- '.. . -S....

I"-=P- -" -' '" @ -"?-i ' .- - y ' -" i":- 'J "'- =

"_. _,• 17," ". " -,". .j"_ J!_ "a?.- a L "_ J = % . , %J _= ". _ _JP~ i '= "J _-S. 
wm 91M MWW

23

Table 3-2

NOv SRB Payments by Zone, FY 1981 -FY 1983

Zone

F! 1980 b~a

Total Nov Paymentsb 57.1 6.41 2.1 65.6 a Number of Nov Paymeats 141.1 1.2 0.41 15.8

Average Nov Payment 41,04o0 5,207 5,930 11,155

F! 1981

Total New Payments 77.3 111.0 2.0 120.3

Number of Nov Payments 141.9 6.7 0.3 21.9

Average Nev Payment 5,183 6,1241 7,068 5,4196

FY 1982

Total Nov Payments 58.9 37.41 1.9 98.2

Number of Nov Payments 13.6 7.5 0.3 21.41

Average Nev Payment 41,3411 4,973 6,325 41,591

pF! 1983e

Total Nev Payments 87.3 18.9 2.2 108.11

Number of Nov Payments 23.11 3.8 0. 27.8

Average Nov Payment 3,737 41,912 3,4182 3,8941

Sa Zone A a21 to 72 months, B a73 to 120 months, C z 121 months to 141 years.

b In millions of dollars.

a In thousands.

d Total dollar value of new payments/number of nov payments. The values

In the table are calculated from the original data prior to rounding

of the numerator and denominator.:. .

e Budgeted for FY 1983. Actual payments FY 1980 - FY 1982.

Source: Unpublished data from the U.S. Army Personnel Center (I4ILPERCEN).
214

A more detailed view of the distribution of the 3RB is obtained

from Table 3-3. On average, in zone A bonus levels were higher in the

Infantry and Technical specialties than in the Support specialties. In

zone B, however, the average SRB level in the Support MOSs vas not such

different than in the other two major occupational areas.* Nonetheless,

even in this zone the smallest fraction of the 3RD budget was allocated t

to the Support specialties; over all zones only $5.6 million of $120.3

million was spent In bonuses for the Support specialties.

61
25

Table 3-3

New SRB Payments by Major Occupational Groups and Zone,

F! 1981

Zone

Major Army b

OCCuDational GOQUD BL L C Total

Infantry b

Total New Payments 45.4 26.2 0 71.8

Number of New Payments 8.6 4.1 - 12.7

Average New Payment 5,297 6,392 8,000 5,657

Technical

Total New Payments 27.6 13.8 1.5 42.9

Number of New Payments 5.2 2.4 0.2 7.8

Average New Payment 5,312 5,691 7,265 5,482

Support

Total New Payments 4.3 1.0 0.2 5.6

Number of New Payments 1.2 0.2 - 1.4

Average New Payment 3,757 5,892 5,184 4,072

Total

Total New Payments 77.3 41.0 2.0 120.3

Number of New Payments 14.9 6.7 0.3 21.9

Average Neow Payment 5,183 6,124 7,068 5,4196

a Zone A = 21 to 72 months, B = 72 to 120 months, C = 121 months to 11 years.

b In millions of dollars.

o In thousands.

d Less than 500 new SRB payments.

e Total dollar value of now payments/number of new payments. The values

in the table are calculated from the original data prior to rounding of

the numerator and denominator.

Source: Unpublished data from the U.S. Army Personnel Center (KILPERCEN).

. . . . ... . . . .. . . . . . .
p"-.~S~ ~JW ~ Z-rWJ~Jri'2 L7Jr '. W -I -A A -

26

Chapter 3 Footnotes

I Authority for the first reenlistment bonus was established in 1971.

See U.S. Department of Defense, Manpower Personnel and Financial

Management, Report on the Selective Reenlistment Bonus Program, May

1, 1982, p. 4. (Referred to below as Report on the Selective

Reenlistment Bonus Program).

2 =b., pp. 6-8.

3 In special circumstances individuals can receive an SRB by reenlisting

in a critical skill even though they are not qualified in that skill.

4 After FY 1983 enlistees who extend their military contract will be

ineligible for an SRB.

5 Except for Navy nuclear personnel where the maximum is $20,000.

Zib., pp. 10-12. J..,

6 b p. 12.

7 Third Quadrennial Review of Military Compensation, a2,=., p. 12..

8 Report on the Selective Reenlistment Bonus Program, g2,=., p. 12.

9 Lo~ct

10 The variables included relate to retention, replacement cost, shortfalls,

military essentiality, and size (i.e., the number of Individuals in

an occupation). See Patricia Griffin, A First-Term Attrition Severity

Index for U.S. Navy Ratings, Naval Postgraduate School, June 1981,

M.A. Thesis, pp. 91 and 109.

11 See U.S. Army Concepts Analysis Agency, Selective Reenlistment Bonus

(SRB) Study, Bethesda, Md., August 1982, pp. 5-2 to 5-6. (Referred

to below an Selective Reenlistment Bonus (SRB) Study).

12 See U.S. Department of Defense, Office of the Assistant Secretary of

Defense, Manpower, Reserve Affairs, and Logistics, Occupational

Conversion Manual: Enllsted/Officer/Civillan, September 1980.

13 The FY 1983 projection Indicates SRB levels in zone C (but not zone B)

are being reduced below that of zone A.

-N..-

. * . --.. . . .- . -- . .. -~-. *- - . .. -. . - - -. --.. - . .. -.-" .
27

Chapter 4: A Human Capital Approach to Computing

Selective Reenlistment Bonus Levels

The variables consistently referenced in discussions of the SRB are

occupational shortfalls, retention rates, and training costs. An approach

to handling these diverse aspects of the SEB decision process can be

found in the literature on human capital theory.

Economists have been interested in the relationship between pay, Z

training costs, and turnover since, at least, the 1960s. More recently

Goldfarb and Hosek have examined the question of which of two groups of

workers, each having the same training costs and productivity but different

2

turnover rates, a firm should hire. Haber and Lauas have extended their

model by relaxing the assumption of equal training costs and equal

productivity so that one can now address the question of how much more a ._

firm can pay a group of workers without raising labor costs, if as a

result of paying a higher wage, the group's separation rate were to

decline by a specified amount.

In this chapter the extended model Is applied to the SRB problem.

The model assumes that firms maximize profits and labor markets are open

and competitive. The military, of course, Is a nonprofit organization,

Its labor market is a closed one, and there is only indirect competition

with civilian sector labor markets. For this reason alone the model

provides only a heuristic solution to a preferred SRB structure. Nonetheless the model has the important advantage of providing a rational and

4 . 4 . 4 A . ,

. ... " " " " '"" " " * " " " " "" 4 " " " *' . .. ' . ....... ".". ." '* -'. 2 '- .-.- 4 ' : ' " -. " - '. . , 21 , " " " ' ' '"__ _ _ _J__ -_ _ _ _r__ _ _ _ _-__ _ _ _ _ _ __ _ .. _ ... - 4.4 .4 - -,'-'.'. "'_,'',-''.-'-_-% i
W-.- D. - 7 - W. W -w - d I

28

consistent way of setting SRB levels which explicitly takes into account

differences in turnover, training costs, and outputs among groups of

workers. Hence it represents a distinct advance over the current procedure.

A. The Basic Model

The basic model is set within the framework of the profit maximizing

firm. It assumes that firms incur training costs for each employee

hired and they must recover these costs over an employee's term of

employment. The profit maximizing firm recoups its costs by paying

employees less than the value of their output, i.e., less than their

marginal value product. The difference between marginal value product

and the wage rate, discounted to the present, and summd over all periods

during which an employee remains in the firm's employ is the return to

the firm on its investment in training. Since an employee may separate

from a firm at any time, employers use an expected value calculation in

which the discounted return in any period is multiplied by the probability

that the worker will be in the firm's employ during the period. Profit

Is maximized when the number of employees hired is such that the expected

present value of the return from offering training equals the cost of

training. This equilibrium condition for maximizing profit is more

formally expressed by

r1) [ ,HVt 11wt] )t - C 0"

S %,4" J ,.fL1"1
L -29

where T is the employer's time horizon, KVPt and wt are the marginal

value product of labor and the wage rate in time period t, respectively,

r is the discount rate, S is an employee's separation probability, and C V.._

is training costs. The term In brackets is the discounted return

t

during period t; (1-S) is the likelihood that the discounted return

will be realized during the period. The product of these two terms is

*the expected present value of the return. The firm maximizes profits by

hiring workers until the expected present value of the stream of returns

falls into equality with the costs of training additional workers.

Assuming an employee's marginal value product, wage rate, and

separation rate are constant through time and that the firm's time horizon

is sufficiently long, the steady-state equilibrium condition Is given by

(2) (MIVP-w) .L c:o.0. 

r+3

From equation (2), the wage differential between two groups of

workers which leaves a firm indifferent between hiring one or the other

when each group has the same marginal value product and the same training

cost is found to be LC(3) 1 w2 "1+r 1$ - S1 ).

As can be seen from equation (3), if group 2's separation rate exceeds

' . ... .....-. . . -.. -. i :. '2
30

that of group I workers, group I can be paid a higher wage.

B. The Extended Model

In the basic model it is assumed that the marginal value product

and training costs of two groups of workers are equal. In this section *-.

the model is extended by removing these restrictions. As before, It is

assumed that an employee's marginal value product, wage rate, and separation

rate are constant through time and that the time horizon is long. Instead-_

of assuming two groups of workers with the same marginal value product

and the same training costs, we now assume these can differ, i.e.,

MVP1 MVP2 and C1 C2 . Thus equation (2) can be rewritten as

,- ~(MVP 1 -w 11 .

1 I 1S 1 - C C 0 .',,

(MVP - w1) lt

2 2 1+2 - C = 0

Under these conditions the wage differential leaving a firm indifferent

between the two groups can be shown to be 7-

(w Wl - w2 (MVPI - MVP2) (11+-2)"L (1+31 •"- { r1+r -

In estimating equation (Ii), the marginal value product is measured

by annual earnings; the time interval for measuring 3 is a year; and the

total cost of training Is assumed to be expended at the moment of hire.

ILI%* .

---..--
31 ~

The wage rate is measured in dollars per year. In contrast to the models

oited in the previous chapter, the variables in this model do not enter

as a product scaled between 0 and 1.

From equation (4) one notes that for MVP 1 u MVP 2 and C2 a C1 the

first term on the right equals 0 and the last two terms reduce to -9-(32 S O,

1+r

i.e., (4) reduces to (3) when the assumptions of the previous section

are satisfied. Again it is seen that the group with the lower turnover

(assumed to be group 1) Is paid a higher wage, all other things being equal.

Moreover, even when C1 a C2 the premium that can be paid group I increases

proportionately with training costs. If group 1ts training costs are -

also lower than group 2's (as well as its separation rate), the premium

paid to the former group would be still higher.

C. Extending the Model to the Military Sector

As just indicated, in the civilian sector employers pay a premium

to workers with a low separation rate, and the lower their training

costs, the higher the premium they can pay. On the other hand, in the

military sector It is desirable to pay bonuses to workers with a high

separation rate, and the higher their training costs, the larger the

bonus they should receive. Because of the arduous nature of military

employment in some specialties, and because in some specialties enlistees

can earn more In the civilian sector, turnover may be excessive. Indeed,

the greater the training costs, the more likely are there to be opportunities

for employment in the civilian sector. It is for these reasons that a SRB

................................ •, , ..... o .... , .... ,
32

is provided to enlistees in selected MOSs so the investment made in such

individuals is not lost to the military.

In establishing a wage and bonus structure for the military, attention

should be given to the relationship between that structure and turnover.

Consider the case of the Infantry specialties. One way of reducing turnover ,. .

in these specialties is to offer a bonus, but how such should be offered?

To answer this question, information is required about the functional

relationship for infantrymen between changes in the separation rate and

',.:....

the bonus, and the reduction in the cost of acquiring and training infantrymn, given the decline in the separation rate when a bonus is offered.

It should be clear from Chapter 2 that this information is not readily

obtained given the state of the art in estimating the elasticity of

reenlistement.

A much simpler approach and the one adopted in this study is to

determine the bonus which would leave one indifferent between accessing . -

and training infantrymen and, say, support specialists, presupposing

that payment of the bonus would equalize the separation rate of both

groups. It should be noted that what is important here is not whether

the actual decline in the separation rate equals the presumed decline

for any group , but rather the benefit that would accrue to the military,

as measured by the wage premium it could offer, if the separation rate

were to decline by a specified amount.

The benefit that would accrue to the military if the separation rate

of, say, infantryment (group 1) were to decline to that of support

,*%." %'

' . 4

......................... *. * *o *~~* 
U

33

specialists (group 2), can be written as

(5) w - 2 (MVP I KVP 2) c L(1S) - C2 2 • 

L14r 1+r'

As in equation (4), a premium is given to the group with the higher

value of output, in this case, in the military. The terms in the bracket,

however, are reversed to take account of the difference noted above

between the role of a wage premium in the military and civilian sectors.

As can be seen from equation (5), a bigger bonus will be given to those

OS3s with high separation rates, high training costs, and large outputs.

Since equation (5) yields a bonus structure that is oonsistent with the

objectives of the SRB program, it tends to be effective. Also, since

the larger bonuses are offered in those HOSs where retention is low, all

other things being the same, equation (5) tends to be efficient. The

benefit derived in using equation (5) in the manner suggested is that it

provides an algorithm by which a bonus can be computed for each OS 4 1.

vis-a-vis a base or standard group, e.g., a Support OS..

While the model provides a basis for computing the bonus, s, for

the problem at hand several modifications are needed. First, we define

an adjusted bonus

(6) sI = s-(ImC I-RHC2)

where

a = wI - w2 as defined in equation (5) and

and RNC 1 - RMC 2 z the difference in regular military compensation

between group I and group 2 workers.

The need to adjust s by the difference in regular military compensation

Lb.

* ~ ~ ~ ~ ~ -~. ~ .. '. ~ ~ ~i ~ 2.A*. ~ .~ .. S'6%'~' ~ ~ .% -~ ~ ~ 1 
34

*. (RHC) between a given group I and the base or standard group 2 in due to our

computing the SRB by pay grade and zone. In the present context, the bonus

a measures the wage premium In the absence of differences In compensation

between groups of workers. If the differential in compensation between the

two groups equals s, it is clear that no bonus would be necessary to realign

the pay structure. It is only when a exceeds the actual differential in

pay that a realignment is needed; as indicated in (6), the realignment,

*'. all other things being the same, is given by s - (ENC 1 - ZC 2 ).

A second iteration yields the algorithm used in our study to determine

SRB levels, which we denote by se*:

(7) 9. = Kin (s' x E z P x G, $16,000), R < 0

0, H

where

E = a filter measuring the military essentiality of a NOS,

P z a filter to identify high performance soldiers, .

H z a filter measuring shortfalls,

and G = a filter for adjusting SRB levels. -1-

In addition to accounting for IiNC, in calculating SRB levels one

should also consider the Importance of a MOS for accomplishment of the

Army's mission objectives. In part, a KOS's Importance is given by the

marginal value product variable in equation (5), since this variable

measures output at the margin of production. For example, radar repairmen

are more likely than general office clerks to contribute to output

independent of the sector, military or civilian, in which they are employed.

°

-. * K:.:..< .. :Z:KC.~ .....
35

Hene one can use output as measured by earnings in the civilian sector

as a proxy for output in the military. But the uniqueness of many military

specialties suggests the need for another variable, In addition to output

in the civilian sector, which more directly gets at the contribution of

an MOS to Army mission capability. We denote this variable by E and use

it to measure the military essentiality of a MOS. Needless to say, the

development of military essentiality values is a research task in itself.

It suffices at this point in the discussion to note that military

essentiality codes (MECs) are best derived indirectly through a

questionnaire approach rather than directly measuring It by selecting a

value, say, between 0 and 100. Additionally, anchoring the military

essentiality scale at 0 when the maximum essentiality value is large

should be avoided.

The filter E aim at improving SRB effectiveness by giving bonus

preference to MOSs that are highly essential to Army readiness. But III

not all persons in these MOSs make effective soldiers. Likewise, effective

soldiers can be found In other MOSs which are not of the highest

essentiality. The filter P is designed to identify such individuals.

This can be done by forming the ratio

Lenath of service to achieve a given nay grade

Average length of service to achieve the given pay grade

"5'- ".'*.

'*- ...

..- =._-_. .
a -'.- - - .

36

Individuals who attain a given pay grade more rapidly than the tim

taken by the average individual can be presumed to be high performanes

6

soldiers. All else being equal, the reenlistment of these individuals

should contribute most to the Army's readiness. An alternative approach

to evaluating a soldier's performance, say, by the assignment of a numerical

or letter grade similar to those given students would yield a sore accurate

measure of an individual's military performance, but this may be impractical

from the point of view of SRB management.

It is noticed that shortfalls enter into the computation of sit as

an override. In the model, H measures the fill rate, I.e., the percentage

that operating strength comprises of authorized strength. A 1S with

7e.

H > 100.0 indicates a surplus of personnel; MOSs with H values between 90.0

and 100.0 are considered to be in balance; MOSs with an H value of less

than 90.0 are defined as being in short supply; in practice, SRDs are

- only given when H < 90.0.

The last filter, 0, is used to adjust the bonus levels so that they

are consistent with that of the FT 1981 SRB schedule. Consistency is

defined here by constraining the model SRB. so that the computed SRB in

pay grade E-4, zone A of the Infantry specialties approximately equals

the average SRB actually paid to bonus recipients in zone A of the Infantry

specialties in FY 1981, i.e., $5,297 (see Table 3-3). Additionally, in

. consonance with current SRB policy, in the calculation of s a maximam

of $16,000 in used. Not indicated in the above formulation, since small

values of sf are possible, and It Is costly to administer a program -'-

when many small SR are offered, a MLnaa SRB value i% also used.

SRBs below $1,000 are set equal to 0.

!H Aa I:A -!L-
5%%

Chapter 4 Footnotes

1 See Gary S. Booker, Human Canital? A Theoretical and Empirical Analvsis

with Special Reference to Education, Columbia University Press, 19641

and Walter W. 01, *Labor as a Quasi-Fixed Factor,w Journal of Political

gonomy, December 1962, pp. 538-555.

2 See Robert S. Goldfarb and James R. Hosek, "Explaining Male-Female

Wage Differentials for the Same Job." The Journal of Human Resources,

Winter 1976, pp. 98-108.

3 See Sheldon E. Haber and Enrique Lamas, *Pay, Training, Turnover, and

Hiring and Retention Decisions,' Journal of Behavioral Economics,

Summer 1983, pp. 1-21.

4 Unless otherwise indicated, the references to MOS in this section

should be understood to mean a HOS, zone, pay grade combination since

the SRB computation is at this level of detail.

5 The outcome of anchoring a variable to a 0 base is that the bonus

gradient with respect to military essentiality, or any other variable

scaled in this manner, becomes very steep. The effect is to preclude

the offering of an SRB even though other variables might indicate

that it should be awarded.

6 It is of interest to note that the characteristics of individuals who are

most likely to complete their first term of service are the same as the

characteristics of persons who attain a given pay grade early, given that

they complete their initial service contract. See Sheldon E. Haber,

Factors Influencing Attrition in the Marine Corps, The George Washington

University, Program in Logistics, Serial T-306, March 1975 and Sheldon

E. Haber, Factors Influencing Trainability in the Marine Corps, The George

Washington University, Program in Logistics, Serial T-314, April 1975.

Sq

•-. . -°
38

Chapter 5: Separation Rates

The variables entering the model described in the previous chapter

are the separation rate, training Cost, and the value of output in the

military sector. In this chapter we discuss the first of these variables,

i.e. the separation rate. While the summary data presented here are by

major Army occupational group, more detailed estimates by NOS were used

in the actual model computations.

A. The Separation Rate and Measures of Retention

Although the model is couched in terms of the separation rate, it is

initially more convenient to discuss measures of retention. The standard

measure of retention is the unadjusted reenlistment rate which is defined as

(1) Reenlistees / (Reenlistees + Eligible separators).

Included in this measure are all individuals who reenlisted or separated

(given they were eligible to reenlist) during a given year.

Another useful way of computing the reenlistment rate is

(2) Reenlistees / (Reenlistees + Separators, Including

ineligible separators).

This rate is of some interest as it gives a more accurate representation

of personnel losses. Although ineligible separators are not as qualified

as eligible separators, the former like the latter embody human capital

investments made by the Army.

Manpower losses to the Army my be inferred from still another

measure called the continuation rate. A continuation occurs when an

individual remains in the Army between two points of time, typically one

........ . * . *~-,**.-.***-. : : : : 
39

year apart. The continuation rate is computed as

(3) Continuations / (Continuations + Nonoontinuations)

where the denominator includes all persons in the Army at the initial time

point and the numerator contains all continuators including non-reenlistees.

Still another measure of retention which is particularly important

for the SRB problem relates to continuations in the same OS. This

measure which we denote as the *same HOS continuation rate" (SOSCR), is

defined as

(4) Continuations in the same OS / (Continuations + Nonoontinuations)

where the denominator is the same as in measure (3).

In this study, the separation rate, S, is one minus measure (4). The

separation rate defined in this manner is analagous to the definition .- -

of turnover in the civilian sector. Conforming to standard practice,

the time interval over which measure (4) is computed is one year.

It is to be emphasized that the more familiar measure of retention

used by the military services, namely, the reenlistment rate, is not

utilized in the SRB computation. Instead, the model requires that a

continuation rate measure of retention be utilized. The reason for this

is that in the model the SRB is based on the retention behavior of al -.

individuals, rather than those classified as eligible for reenlistment

after their performance on the job is observed over an extended period

2

of time. Moreover, of the two continuation rate measures defined above,

measure (4) is the more appropriate one in the SRB context, since the

skills specific to a MOS are, to an important extent, lost to the Army

when enlistees transfer out of MOSs in which an SRB should be offered. .

... .................. ** *....". -...... .. -,' .- a.a -. %. . -. %ka--' ,.a' 'D.....%
-Z -417 VT--.,; .; T .- 7 .. . . .,. .. ... . . . . .. ... -. :.

40 L~. - . o

B. A Digression on Army Strength as of September 30, 1980

By way of Illustrating the data pertaining to retention, It is

useful to look first at the composition of the enlistee population. As

of September 30, 1980, Army enlistee strength was 668,336 of wich 43.8,

31.2, and 25.0 percent were in the Infantry, Technical, and Support

"-S. '.-.

specialties (see Table 5-1). '.

One question which arises with respect to the distribution of enlistees

among the major Army occupational groups is how it changes by length of

service, or in the SRB context, by zone. Migration between the occupational

groups can be viewed in two ways. It may be deemed undesirable because

it results in multiple and, therefore, higher training costs; on the .% * %

other hand, it may be advantageous to have personnel trained in diverse

skill areas. Bowever, if the area where initial training is one in

which an SRB should be offered, it can be presumed that the disadvantages

of migration outweigh the advantages.

As indicated in Chapter 3, the major portion of the Army's SRB

budget is allocated to the Infantry specialties. It is of some interest,

therefore, to determine the extent to which there is migration out of ..-

the Infantry specialties and the specialties which out-migrants enter.

Information pertinent to this aspect of manpower management is found in - "

the top portion of Table 5-1. As can be seen from the figures shown,

there is some migration out of the Infantry specialties as length of

service increases, but it is Dot overwhelming. The percent of enlistees

in the Infantry specialties declines from 47.7 to 39.5 between zones 1 3 "..

and 5. but this represents only a 17.2 percentage point decline.

-1k.'.

5,. - ' - . . . J -. - .- ' + - " -- " - % " + ' - " ,,. " - "," - " " . " . "-. ° - " " " .. . " . " % . ".] .,'..'.'+, = ', .
41

Table 5-1

Percentage Distribution of Enlistees by Zone and Major

Army Occupation Group, September 30, 1980

Major Army -. *

Occunational Group

* . -., 

Zong 4.7 2.

1 47.7 28.9 23.14 100.0

A 44.0 31.0 25.0 100.0 ", "."*

B 38.9 3'4.3 26.9 100.0

C 37.4 36.1 26.5 100.0 -.

5 39.5 33.2 27.3 100.0

Pay Grade

E-1 50.7 26.9 22.1 100.0

E-2 49.1 29.7 20.9 100.0

E-3 145.3 29.5 25.2 100.0

E-4 44.7 29.9 25.1 100.0

E-5 37.8 314.8 27.4 100.0

E-6 11.0 314.1 24.9 100.0

E-7 37.0 36.1 26.9 100.0

E-8 43.6 31.9 21.6 100.0

E-9 43.6 25.2 31.2 100.0

Total 43.8 31.2 25.0 100.0

a IzInfantry, TfTechnical, S=Support.

b Rounded to 100.0 percent.

c Zone 1 = length of service under 21 months, A = 21 to 72 months,

B =73 to 120 months, C = 121 months to 114 years, 5: over 114 years.

S..

- ' .p .

* . - .* .-.--. ,-
42

Considering the Army's expressed preference for younger people in the

Infantry specialties, this decline is at most a modest one. Additionally,

migrants appear to shift into the Technical specialties, more so than

the Support specialties. This is particularly true in zones A through C

where the SRB Is offered.

A second aspect of Table 5-1 worth noting is that the percentage of

enlistees by major IDOS group is not very different among the various

pay grades. There does appear to be a greater concentration of enlistees 4

in the Technical specialties at the higher pay grades, but the increase,

again, is at best modest. It is this fact coupled with the equal pay of

individuals in the same pay grade, irrespective of military specialty,

that is the stimulus for the SRB program.

Another very strong relationship, namely, between length of service and

pay grade, is seen in Table 5-2. As can be seen from this table, zone A is

comprised almost exclusively of E-4s and E-5s - 87.1 percent of the enlistees

in this zone fall into these two pay grades. In zone B, 90.1 percent of the

enlistees are in pay grades E-5 and E-6. And enlistees in pay grades E-6 -

and E-7 comprise 87.7 percent of all enlistees in zone C. Given the absence

of 2-1s through E-3as and 3-Ga and 1-9s in zones A to C, the present analysis

is limited to pay grades E-4 through E-7.

C. Continuation Rates In the Same 1403

As noted, the measure of retention used in this study Is the

continuation rate in the same MOS (denoted as the CR3403). The empirical

data for this measure is summarized in Table 5-3. In construoting this

• ~~~~~~~~~~~........ .. .... . . .. % .° o. °° - . .-. . .- - . .o .- .°. .-. °.° - . .*. - . - . . . . ,. - .* *>,* - .* . - -. .*
*7 77- 77 - 117- 

143

Table 5-2

Percentage Distribution of Enlistees

by Zone, September 30, 1980

Zone

B-I 34.2 1.1 0.2c

E-2 26.0 1.8 0.1-

E-3 32.3 9.1 0.6 0.1

E-4I 7.14 58.5 7.5 0.7 0.1

E-5 0.1 28.6 419.8 11.2 1.5

E-6 0.1 0.8 40.3 60.1 20.1

E-7 - - 1.14 27.6 52.9

E-8 ---- 21.2

E-9 - 4.2

Totald 100.0 100.0 100.0 100.0 100.0

a Zone 1 = length of service under 21 months, A = 21 to 72 months,

B =:73 to 120 months, C = 121 months to 114 years, 5 =over 114 years.

b IlInfantry, T=Technical, S=Support.

c Blank indicates that less than 0.5 percent of the enlistees

in a specified zone are in the given pay grade.

d Rounded to 100.0 percent.
e table, all gains during FY 1981, including new reenlistees and reenlistees

with prior service who separated for more than 30 days, were added to L

the strength figures underlying Tables 5-1 and 5-2 to obtain a more N.

accurate estimate of continuation rates, since some people who enter the

Army during the fiscal year also leave during the year. Additionally,

the count of oontinuators includes people who were accessed during the

year. The need to take account of gains is particularly important in

computing continuation rates for the E-1 pay grade. For the SRB problem,

the inclusion of accessions during the fiscal year is less important but

still desirable. One further point about Table 5-3: the figures in the

table are weighted averages over the MOSs contained in each major Army

occupational group.

Examination of Table 5-3 reveals some familiar patterns. In every case,

the CRSMOS increases with pay grade, holding zone constant. (As noted, this

is why it is inefficient to give the same bonus, all else being the same,

to enlistees in the higher pay grades In a zone). Likewisev the CRSOS

tends to be higher in the zones with longer length of service, holding

pay grade constant. One also notices that for the pay grades characterizing

zone A, the CRSMOS is lowest in the Infantry specialties and highest in the

Support specialties, which suggests, but does not confirm, that in this zone

the largest SRBs should be given to enlistees in the former group and

the lowest SRBs to enlistees in the latter group. In the higher pay

grades, however, a different pattern emerges; the lowest continuation

rates are found In the Technical specialties, suggesting that SRB levels

should be highest for this group of occupations in zones B and C. -'
415

Table 5-3

Continuation Rates in the Same HOS by Major 9

Army Occupational Group, FY 1981

Major Army

Occupational Group Pay Grade

Infantryb

A 61.7 71.3 -

B - 741.4 83.9 -

C -- 86.2 89.5

Technical

A 63.41 73.41 -

B -741.1 80.9 -zC -- 83.11 85.2

Support

A 66.5 73.11 -

B - 77.0 83.3 -

C -- 87.0 89.7

a Zone A 21 to 72 months, B z 73 to 120 months, C :121 months to

111 years. '

b Excluded from the analysis because of the small percentage of

enlistees In the cell (see Table 5-2).

* V.
-. - T . - - -' -

b% 46

116W

Chapter 5 Footnotes

1 The a reenlistment rate is similar to measure (1) except that

it includes only individuals whose service contract terminates in a

given time period, e.g., FY 1981.

The continuation rate is a more accurate measure of supply than the reenlistment rate because the former indicates what percentage of

Individuals In an employer's entire work force will remain from one

year to the next. This is not to say that the effect of the SRB on ,"

reenlistment rates is not of Interest, e.g., knowledge of the reenlistment

elasticity with respect to the SRB is necessary for the problem of

matching projected SRB expenditures and the SRB budget.

3 Table 5-1 includes two zones besides the SRB zones A to C. These are

zone 1, defined as less than 21 months of service, and zone 5, defined

as more than 14 years of service.

4 As will be indicated later, when training costs and value of output

in the military are taken into account, the model indicates that in

zone A the SRB levels in the Technical specialties should be higher

than those in the Infantry specialties.

*q' *i .

% ° . .% % , . . % .% • -. % % %- . ,- .. . . - . . - .. --. .. . - . . ., . - -% -
47

Chapter 6: Training Costs .___

16

A major element in the replacement cost of a soldier is the investment

which the Army makes in his training. While this particular cost is the

only element of replacement cost included in the model as formulated in

Chapter 4, other elements which should be included are recruitment and

separation costs, e.g., unemployment insurance. In the SRB context these

costs, like training costs, also represent savings that are realized when

an incumbent in a position is retained. However, there is one separation

cost which must be treated differently, namely, retirement cost. Since

this cost may be expected to rise pursuant to the offering of a bonus,

it should be netted out in the calculation of replacement cost.

Thus, instead of training costs alone, the replacement cost relevant

to the SRB calculation is:

Replacement Cost Recruitment cost q Training cost +

Separation cost, not including retirement

cost - Expected incremental increase in

retirement cost

Because the estimation of the large number of separation costs and of

retirement cost entails an effort beyond the scope of this study, they

are nol considered here.
7,] ~I'->..

- A. Recruitment Cost

The total cost incurred by the Army in recruiting active personnel 1

during the second quarter of FY 1981 was $15 million. This figure

includes direct costs, such as identifying individuals interested in

serving in the Army, testing potential enlistees, and enlistment bonuses;

indirect costs, e.g., advertising and nonproduction personnel coats at

recruiting stations; and overhead costs, e.g., costs of operating regional

and headquarters recruiting commands and Armed Forces Examining and

2

Entrance Recruiting Stations. A breakdown of these cost categories on a

per capita basis by level of education is provided in Table 6-1.

It should be noticed that the figures for high school graduates in

Table 6-1 refer to individuals with a diploma. In contrast, the DDC

data, to which the recruitment cost estimates are applied, include

recipients of a Graduate Equivalency Diploma (GED) among the count of

high school graduates. It would have been desirable to distinguish

between individuals with a GE)D and a *true* high school diploma in the

DMDC data, but this was not possible. Hence our estimates attribute the

higher recruitment cost of diploma graduates to a larger number of enlistees

than, in fact, were actual diploma graduates.

The higher recruitment Gost for high school graduates than for

non-high school graduates, $4,048 versus $2,327, is attributable to the

high school graduate being sought out by recruiters while the high

school dropout is often a Owalk-in" at recruiter stations. Additionally,

only the former receive enlistment bonuses. .i* .-.

The direct costs in Table 6-1 are variable costs because they change

* "-" ' °. o . ,' o* -*mo -"*-•"I . . .

.E'm * _.-'L ...,,_.:.'.2. ._ _'._._, . ... _...... ,'.'.'...'. ... .. ... m ,.m%. .,,, .. . .m.. ... > , .
4I9

Table 6-1 a

Per Capita Active Army Recruitment Costs, FY 198 1a

Non-Righ School High School

Graduate Graduate

Direct Costs 541 1,889 - .

Enlistment Bonus 0 644'1

Other Direct Costs 51 1,245

Indirect Costs 1,342 1,715

Overhead Costs 4 444

Total, Including 2,327 4,048

Enlistment Bonus

Total, Excluding 2,327 3,4104.

Enlsitment Bonus

a Second quarter.

Source: Derived from U.S. Army, Office of the Auditor General, Audit of

Cost of Recruiting, Report No. 4W 82-701, 28 January, 1982,

pp. 13 and 15.

.. .. . . .-... 

................ .. . .-

•~,L~ b K'.*..§*...-.. * . ,
_ .~~ 1 . ' ' 71 rsoj & -o; ,

50

. , *o°

with the number of enlistees. For example, the coat of enlistment bonuses

only increases when additional enlistees are accessed into MOSs where

such bonuses are given. 'The indirect and overhead costs, however; are

sunk costs which are fixed in the short run and independent of the

11

number of persons accessed Into the Army during any given year.

Because high school graduates require numerous contacts before

signing a contract whereas high school dropouts tend to be walk-ins,

- variable costs should comprise a higher proportion of recruitment cost

for the former group than for the latter. This Is indeed the case as

can be inferred from Table 6-1 where variable, i.e., direct, costs

(excluding enlistment bonuses) are 36.6 and 23.3 percent of recruitment

costs (excluding enlistment bonuses) for high school and non-high school

graduates, respectively. It should be noted our estimates differ from

those in the Recruiting Cost Audit study where variable costs as percentage

*of recruitment costs (excluding enlistment bonuses from each category of

cost) are lower for high school graduates, 31.8 percent, than for high

5

school dropouts, 6.7 percent.

In calculating the SRB, recruiting costs (excluding enlistment

bonuses) were utilized. From Table 6-1, it Is seen that these costs

*averaged $3,404 for high school graduates and $2,32T for non-high school

graduates. Since our unit of observation is HOS, 7dy grade, and SRB

zone, where a the recruitment cost figures are by level of education, we -.

weighted the two coat figures by the percentage of enlistees who were

high school and non-high school graduates to arrive at a single value

for each cell. Thus for 1O 11B, Infantryman, pay grade E-4, zone A

I:

:. .. .-..-...... </ . -... .-.,,-. -....-.. o , -.. ... ... ... . .. ... , -..-. .. .. ..-... .. '. ', ... :.-;, ....-...... . .- . ..: -: . ..,° . ..,
in which 82.9 percent of the recruits were high school graduates In FY

1981, our estimate of recruitment costs vas $3,220 (m .829 z $3,404 .

.171 x $2,327). Similar figures by major Army occupational group are

shown in Table 6-2.

B. Training Cost

The training cost figures used in this study, expressed in FY 1981

dollars, are taken from the Military Occupational Specialty Traiing

6

Cost Handbook (MOSB). They include only those costs incurred In formal

training programs, i.e., on-the-job training costs (OJT) are not included.

The formal training costs accounted for are (1) military pay and allowances

for students, faculty, and training and support activity personnel, (2)

operating expenses, e.g., for utilities and for training and support -

activities, (3) ammunition expended in training, and (4) the annual

replacement cost of equipment. However, such costs as medical and

retirement costs associated with the upkeep of personnel involved In the

training process are not considered. Major construction and other

7

identifiable one-time special expenses are excluded, since these

represent capital expenditures rather than outlays for operations.

The NOSB training costs are classified into variable and fixed

costs. Variable costs, e.g., military pay and allowances for students,

vary with student enrollment. On the other hand, fixed costs, e.g.,

equipment replacement cost, are constant In the short run and Independent

of student enrollment. For small changes in student enrollment levels

only the variable component of training cost should be considered in

•. . ..

,,,. .... I-(: ,,

.° -° ' - - q -. . ° . ,. • . .,. / -- ./ :'% , .o- - .: .-.°o.- °o- -.. : .-.. >.. , .-. i .K- ..- .. . . - - . ,,-
52

Table 6-2

Recruitment Costs Excluding Enlistment Bonuses,

by Major Army Occupational Group, January 1982

Major Army

Oocupati 2 nal Group Arade Pay 

and Zon li

Infantry b

A 3,258 3,349 - -

B - 3,375 3,1400 -

C - - 3,401 3,404

Technical

A 3,314 3,371 - -

B - 3,390 3,402 -

C - - 3,404- 3, 404

Support

A 3,326 3,380 - -

B - 3,393 3,402 -

C - - 3,403 3,401

a Zone A - 21 to 72 months, B = 73 to 120 months, C = 121 months to

14 years.

b Excluded from the analysis because of the small percentage of

enlistees in the cell (see Table 5-2).

Source: U.S. Army, Office of the Auditor General, Audit of Cost of

Recruiting, Report No. 82-701, 28 January, 1982.

". ..-.-... .- ¢- : p.-.. . ,- -.. o.': . , .- -.......-..- -... ..- *.. -. '. . - - -. -.. .. ...-.. ; .
53

estimating replacement cost. For purposes of this study it is assumed

that school enrollments do change only marginally in the presence of the

SRB program; hence the training cost figures in the SRB calculation %-%

include only the variable cost component of total training cost.

The HOSB formal training cost data fall into two categories. The

first is reception and basic training coats which are the same for each

MO3; the second is course costs which vary by 4OS. In the HOSE, these .7

costs are shown as cummulated training costs for skill levels 1 through

5 where the former corresponds to pay grade E-4 and the latter to pay

grade E-8. As noted in the previous chapter, the relevant pay grades

for the SRB problem are pay grades E-4 through E-T.

The cumulative variable training costs used in this study are

summarized in Table 6-3 by major Army occupational group. The need for

cumulative training costs is generated by the model in that the relevant

cost is that which would be incurred if a given worker were replaced by

another one of equivalent skill. The figures shown are simple averages

over the MOSs in each major Army occupational group.

As can be seen from Table 6-3, by far the highest training costs

* are found in the Technical specialties. Tramning costs in these specialties

are 58.2 percent higher than in the Infantry specialties In pay grade

E-4; the differential declines among the higher pay grades but is still

34.1 percent higher In the former than in the latter specialties in pay

grade 2-7. Training costs in the Infantry and Support specialties are

found to be about the same. Thus on the basis of training costs alone,

one would want to give a bigger SRB In the Technical specialties.

7.-

.. ~p ~ p ~p .. .- . . --.-.-

~ ~.. p ~ -. - * -- ~ . -..<.:.
K514

Table 6-3

Cumulative Training Costs

by Major Army Occupational Group, October 1981

Occupatitional GroupPaGre

Infantry 8,591 11,1114 16,511 21,589

Technical 13,593 16,871 23,1141 28,9148

Support 8,763 13,125 16,568 17,577

Source: U.S. Army Finance and Accounting Center, Cost Analysis Division,

Military Occupational Specialty Training Cost Handbook (NOSE)

Volume 1, Enlisted, October 1981.
55

S% %.

Chapter 6 Footnotes

1 See U.S. Army, Office of the Auditor General, Audit of Cost o

Recruiting, Report No. MW 82-701, 28 January, 1982, p. 1. (Referred ..-.

to below as Recruiting Cost Audit).

I 2 1=±~., p. 13.

3 In the second quarter of FY 1981 the average cost of the enlistment bonus

per enlistee was $64. The average cost of the bonus, given that an

individual received a bonus, was $1,327 (derived from =k±d., p. 8).

While not part of this study, it is clear that the model in Chapter 14

is also applicable to the problem of allocating enlistment.bonuses.

4 Although enlistments are positively related to advertising costs,

once an advertising budget is determined this cost element becomes

fixed. In the long run, however, which in this case exceeds a year

since advertising budgets are revised annually, advertising costs are

- variable. Advertising Costs, which were allocated entirely to high

school graduates (see 1=., p. 10), comprised 22.2 percent of the

indirect costs of $1,715 for this group.

5 See IM=d., pp. 13 and 15. The difference between our figures and

those derived from the Recruiting Cost Audit study is due to differences

in the allocation of general indirect costs by level of education.

Since indirect costs are fixed, we allocated the total of such costs,

exclusive of advertising costs, $52,781,859, equally among all 40,090

contracts written in the second quarter of FY 1981. The advertising

costs (see Lb=d., pp. 7, 8, 10, and 12) of $11,845,T71 were also

allocated equally but only among the 31,722 high school enlistees on

the assumption that non-high school enlistees would have entered the

Army in the absence of such outlays.

6 U.S. Army Finance and Accounting Center, Cost Analysis Division,

Military Occupational Specialty Training Cost Handbook (MOSB), Volume

1, Enlisted, October 1981. (Referred to below as MOSB data).

T bLk=., pp. I-A-1, 2, and 4.

--. . ..

-. b . . *' . - . . - . . . . ..-. . . . . . . . . *"-"*.i ... 

.*.. . . . .. . . . . .. . .. . . .. . . *...* . . . . . . . . . . .
56

Chapter 7: Civilian Earnings in Occupations Analogous

to Military Specialties

In the civilian sector the value of a worker's output is assumed to

be measured by earnings. The mechanism which permits valuation of physical

output in money terms is the pricing system. Since there is no market

for national security, the same evaluation of a soldier's output is not

possible. Yet it seems reasonable to assume that, for the most part,

there is a rough correspondence between the value of output in military

specialties and in civilian occupations which require similar labor

inputs. This is the approach used to measure marginal Value product in

the military, i.e., MVP in our model.

In approximating the value of output in the military sector , military

and civilian occupations were aligned as shown in Table 7-1. It will be

noticed that the infantry specialties for which there are no equivalent

civilian occupations are assumed to correspond to the operative occupations.

These specialties are assumed to have higher skill requirements than the I

laborer occupations but lower skill requirements than the craftsman

occupations. Koerover, a significant fraction of personnel in the infantry

are involved in transport; this latter job group would be classified

among operatives in the civilian sector.

In determining the earnings of the civilian counterparts of military

personnel, a regression model was formulated. Given the context of the

. .. . . . . - a..,. c~ dt. .. t..2..t - a.a~t..A....- - - . --- . . .,
57

Table 7-1

Major Civilian Occupational Groups Corresponding 4

to Major Army Occupational Groups

Major Army DOS One-Digit Major

Occupational Group Subaroun Civilian Occupations

Infantry:

Military-Unique Personnel T Operatives, Including

transportation equipment operatives

(601 -715)a

Laborers, Operators, and R Operatives, including

Routine Maintainers transportation equipment operatives

(601-715)

Technical:

Technical Personnel G Technicians (080-085

and 150-173)

Craftsmen, Mechanics, and P Craftsmen and kindred

Production Workers workers (401-580)

Support:

Clerical Personnel .7 Clerical and kindred

personnel (301-395)

Service Personnel M iervice workers, excluding

private household (901-965)

*a Census occupation codes shown In parenthesis. See U.S. Department of

Commerce, Bureau of the Census, 197Q Census of Population. Classified Index of

- Industries and Occupations, 1971, PP. 10-14.

Z7.
58

study and the available data, the model was specified as follows:

in E = a + b1 +c1 2

where In E is the natural log of the earning of full-year, full-time

civilian workers; X, represents experience, defined as age - years of

education - 6 years; X2 denotes years of education; and £ is the error

term. The data are restricted to males age 18-32, excluding individuals

with only an elementary school education or who graduated from college.

Age and education were entered into the regression equation as continuous

variables. The data utilized were from the March 1982 Current Population

Survey conducted by the Bureau of the Census in which earnings information

2

can be obtained for individuals who worked full-year, full-time in 1981.

The regression model was run separately for the six occupational

groupings in Table 7-1. It should be noticed that the same regression

equation is used to estimate the output of both IDOS subgroups T and R,

i.e., the subgroups defining the Infantry specialties. Thus, whereas

there are 6 IDOS subgroups, there are only 5 different estimating equations.

The model results are shown in Table 7-2. From this table, It is seen

that, as expected, earnings are positively related to both experience

and education. All the coefficients have the correct sign and all but

one are significant at the 0.01 level of significance; the remaining

coefficient is significant at the 0.05 level of significance. In all

but one instance, the return to education is greater than the return

.

",p . . 4 p 4 . , . ° . .

. - . ° - . - . .- . - . - - , - . ,- • . . . . . . ° -
,.7 ,TO

59

Table 7-2

Estimated Regression Coefficients from Earnings Equations _

for Civilian Occupations Corresponding to DOS Subgroups

Constan X1 (Experience) X2 (Edugiaton)

*Military-Unique 8.4184 0.029 0.06~4 .09

Personnel, T (0.116) (0.001) (0.008)

Laborers, Operators, 8.3181 0.029 O.0631 .09

and Routine (0.116) (0.0041) (0.008)

Maintainers, R .

Technical Personnel, G 8.833 0.051 0.033 .23 -.

(0.312) (0.013) (0.020)

Craftsmen, Mechanics, 8.507 0.037 0.063 .09

and Production (0.1411) (0.005) (0.010)

Workers, P I-F

Clerical Personnel, J 8.112 0.0370.058 .11003

(0.22 ,) (0.008) (0.015)

Service Personnel, N 7.734 0.0141 0.090 .13

(0.215) (0.008) (0.015)

a Standard errors of the regression coefficients are in parentheses.

S'..:.-

* S Ii

-: S ,

• '- ..

1% iiP.

, '[ . ' .

. ,' *.%.4
60

to experience. The percentage of the variation in earnings explained by

the experience and education variables, however, is not large; for the

technician occupations it is 23 percent, but less is explained in the

case of the other occupational subgroups. The primary reason for the

2

low R values is the homogeneity of the population. Not only are women

excluded, but the high paying professional and managerial occupations,

as well as the low paying laborer occupations, are also excluded. Moreover,

the experience and education variables are constrained to younger persons

who attended high school but did not complete college. .

Notwithstanding the relatively low predictive value of the model,

there are noticeable differences in earnings in the sample population,

as reflected by the figures in Table T-3. The earnings figures in this

table were derived as follows: For non-high school (high school) graduates,

it was assumed that years of experience was equal to two (one) year plus

length of military service. Length of military service was then computed

for each HOS, pay grade, SRB zone, and education (high school or non-high

school graduate) combination; all the enlistees in a cell were assumed

to have the same length of service and, hence, experience. Given the

3

experience and associated educational level for a cell, the antilog of

the dependent variable in the appropriate regression equation was then

computed. The earnings figures derived in this manner were then weighted

by the fraction of high school and non-high school graduates having the same

NOS, pay grade, and SRB zone characteristics, thereby taking account of

education in estimating earnings, but simplifying further calculations

by reducing the matrix of observations from four to three dimensions.

"2-" :"2""'";"'"2,' ." ."°: ."°".' " *. '-". -" . ... "-... ,' ."* , . " "- ' -. ,. , . . ." " " , - . . . - - - , - - ,, ;
61 "I

N:'N'

Table 7-3

Estimated Value of Output (Earnings) of Enlistees by

Major Army Occupational Group, 1981

Major Army OouainlPal Grade

Group and Zone A. 5. 6 1

Infantry ..- .

A 11,860 17,575 b

B - 13,993 11,598

*c- - 16,755 16,939

Technical

A 12,24l7 12,986 -

B - 14,690 15,378

C 17,866 17,993

Support

A 9,276 9,986 "

B - 11,363 11,658

C - - 13,512 11,2211

a Zone A z 21 to 72 months, B 3 73 to 120 months, C a 121 months to 11 years.

b Excluded from the analysis because of the small percentage of enlistees

in the cell (see Table 5-2).

. . . .. .. .. .,

-4%°

I

I'°

• .-.-',: '--.:".'--.-.:" '.? .:" : ''-'? :"--'.-'.-'. ".:'.:'-: '..-..' ..--. " .':, :."'. ' - " -

"'. : ,': . - :-':..'2 .':.': ":'':.. -.'-.'-.' -.'..'-.'..'.. :" 4
62

Finally, It should be noted that the figures in the table are simple Eli,

averages of the earnings in each OS aggregated over the three major

Army occupational groupings.

As can be seen from Table 7-3, the estimates of the value of military

output are positively related to SRB zone, holdi. pay grade constant.

Of greater interest, the value of military output rises with pay grade,

holding SRB zone constant. Holding SRB zone constant on average, the

value of output among pay grades rises by 3.8, 3.8, and 5.1 percent In

the Infantry, Technical, and Support specialties, respectively. Comparing

the value of output In pay grades 9- and E-7, one noteq that it is

higher in the latter pay grades by 42.8, 46.9, and 53.3 percent in the *:; -

Infantry, Technical, and Support specialties, respectively.

Of particular relevance to the SRB calculation, the value of output

is highest in the Technical occupations. Comparing the Technical and

Infantry specialties, it is found that the marginal revenue product is

3.3 percent higher in the former than in the latter specialties in pay

grade E-4; the relative differential increases progressively to 5.9

percent in pay grade E-7. Substantially larger relative differentials,

ranging from 26.5 to 32.0 percent, are observed when the Technical and

5

Support specialties are compared. Considering only the information

pertaining to the value of military output, the largest SRBs should be

given to the Technical specialties.

::'.::
63

Chapter 7 Footnotes

1 Data for males are used because the bulk of the Army is comprised of

males, and there is no reason to believe that the military output of

women differs from that of men. Only 1.3 percent of Army enlisted

personnel graduated from college in FY 1981, hence the educational

restriction. See U.S. Department of Defense, Directorate for Information

Operations and Reports, Selected Manpower Statistics, FY 1981, p. 62.

2 Full-year workers are those who work 50-52 weeks; full-time workers I

are those who usually work 35 hours or more per week.

3 Enlistees in a cell containing high school (non-high school) graduates .

were assumed to have completed 12 (11) years of school.

J4 Thus, while enlistees were classified by MOS, pay grade, SRB zone,

and education to estimate earnings, the education vai-iable was eliminated

from the SRB model by weighting for the educational composition in

each MOS, pay grade, and zone combination.

5 For a comparison of how regular military compensation, RMC varies by

major Army occupational group, pay grade, and zone, see Chapter 8.

s.....-.

* . ..

*,. ....

...................... .'.. ... .. ,.... '-'-•....-.-.- •-..-, - -.-. ". ,,-'
Chapter 8: Modifications to the Initial SRB Calculation .-

In addition to the three variables - the separation rate, training cost,

and the value of output - underlying the basic extended model - other Informa- -

tion, designated as filters, Is needed for the SR calculation described in

Chapter 4. These filters are discussed In greater detail In this chapter.

Also discussed Is the calculation of regular military compensation.

A. Military Essentiality

As noted, the value of output of full-year, full-tibe workers in the

civilian sector provides only an Imperfect measure of the contribution of

enlistees to national security. This is Illustrated by NOS 11B, Infantryman,

for which there is no civilian counterpart occupation. As a means of reducing

the distortion that may be Introduced by use of civilian occupational data as

a proxy for the value of output in military specialties, we include a filter

which measures the military essentiality of a NOS In the SRB calculation.

Military essentiality can be derived indirectly through a questionnaire

. approach or estimated directly by asking Individuals to rate MOSs in terms

of their relative importance to mission readiness. Although we believe the

Indirect questionnaire approach is preferred, the impleentation of this

approach Is beyond the scope of the study. As an alternative we used the

military essentiality codes (MECs) developed by the U.S. Army Concepts

Analysis Agency (CAA). The agency asked up to 10 managers and decision

makers in the U.S. Army Military Personnel Center and In the Office of

I ** * -*..:.- ~ * *.. *.'..-'.: .;**. 
I65 - .

the Deputy Chief of Staff for Personnel to rate the military essentiality of

each CHF, where military essentiality was defined as *the relative importance I

of an NOS that makes it indespensable in the conduct of the combat mission of

I

the Army.' In the CAA procedure, the mission essentiality of a C was coded

1, 2, or 3 by each participant with I corresponding to most essential and 3

to least essential. Each participant's military essentiality rating (NEC)

was then weighted to obtain an gvral NEC for a CMI. The MOSs belonging

2

to each CMI were then assigned the overall NEC of their parent CHF. ..

The CAA data indicate the number of participants ohoosing a NEC of 1, 2,

or 3 to describe the military essentiality of a CMI. Instead of the CAA's ,-

weighting formula, we Used a plurality rule in assigning an overall NEC to

each CMF. For example, in CMI 54, there were 3 'votes' for rank 1, 4 for

rank 2, and 3 for rank 3. This CMI was assigned an NEC of 2. As in the CAA

procedure, we assigned the CMI s military essentiality code to each NOS comprising the CMF. The MECs used In this study are shown in Table 3-1. A

review of Table 3-1 indicates the following distribution of CMFs classified

by NEC and major Army occupational group:

Ma lo- Army OccuDational Group

* fI _~ ,L. J. ."". "

0 7

2 4 8 1 13 --

*3 ._1_ ..5_ .L 1..._ !.:

Total 9 16 5 30

- - - - - - -;.-,- ,

*-**.* -
66

As can be seen from this distribution, the Infantry specialties have the

highest NEC codes; the lowest NEC codes are found in the Support

speoialties.

Having determined the military essentiality code of a CHF, we next

converted the ordinal NEC to the cardial value of in the model (see

Chapter 4). The functional relationship used was one developed in stocking

Polaris submarines. In particular, we derived the cardinal E values

from the ordinal MEC codes us g the relationship

-A(MEC-1) . .".

E Ze where MC c 1, 2, or 3.

For the value of A used in this study, i.e., A z 0.70, the values of E

corresponding to the NEC codes are -'2-

1 1.00

2 0.50

3 0.25

Thus, everything else the same, the SRB In NOSs with a military essentiality *

code of 2 and 3 will be one-half and one-quarter, respectively, of the

SRB in MOSs with an NEC of 1. It should be recognized that our choice

of A, while judged to be reasonable, Is arbitrary, and that the preferred

value is best determined by the Army.

B. Shortfalls

One important way In which the effectiveness of the SRB Is maintained is

to offer It only in MOSs where there is a shortfall. The measure of shortfalls

aa

I,'-:-

* . .~~~~~~~~~~~~~~~~~~ ...............................................
- ,- ..-.. ,

67.-,T

employed in this study is the percentage that operating strength comprises

5

of authorized strength. As a first approximation, it is tempting to use the :e

overall fill rate for an HOS in determining whether a SRB should be offered

in a specialty. A problem with this procedure is that while the overall

fill rate may indicate that a MOS is in balance, the fill rate for some pay

grades may indicate a shortage. This possibility, which is not atypical,

can be Illustrated by reference to MOS 16E, Hawk Fire Control Member.

The fill rate for MOS 16E, Hawk FC Crew Member, was 108.1, suggesting

6

a surplus of personnel.

E-1/E-3 186.5

E-4 75.6

E-5 108.7

E-6 76.9

E-I and E-5 83.3

E-5 and 9-6 89.4

E-4 to E-6 81.5

E-1 to E-6 108.1

A more accurate representation of supply-demand conditions in this MOS,

however, can be obtained by considering the career fill rate, i.e., the

fill rate for pay grades E-4 and higher, which is seen to be 81.5. The

fill rates for pay grades E-4 to 1-6 indicate a shortage of personnel.

Even in this case, an apparent surplus is found for pay grade 9-5.

The problem of determining whether a shortfall exists and should be

reduced by offering a SRB is complicated by the fact that the supply-demand

........ . -.... .... . . . .. . . .. ,.. ,. .. • . .. ,',,-'.-.,',-. . . -.- ,,-, ,.....
I 68

relationship in one pay grade cannot be determined independently from that

in another pay grade. One way of getting at this problem is to estimate the

expected fill rate for a pay grade which takes into account the likelihood

of an individual continuing in an HOS and the likelihood of promotion.

The expected fill rate, E (Fill Rate), oould be calculated as follows:

E (Fill Rate) = [(Strength in pay grade I at the beginning

of the year

X Continuation rate (in the same 408 and pay grade))

+ (Strength in pay grade i-1 at the beginning

of the year

X Promotion rate from pay grade i-I into pay grade i

in the same HOS))

+ Transfers into pay grade i from other KOSs]

/ Authorized strength in pay grade i.

Since this approach requires extensive programming, it was judged to be beyond

the scope of the study. Instead, the fill rate was oomputed for pay grades E-4-.

and E-5, pay grades E-5 and E-6, and pay grades E-6 and E-7, for zones A, B,

and C, respectively. For M05 16E, these fill rates are found to be 83.3, 89.4,

7

and 76.9 (for pay grade 6 only). Assuming a shortage of personnel exists

when the fill rate falls below 90.0, it is seen from the figures shown above

that a shortage of personnel is indicated in MOS 16E in every zone.

The results of applying the aforementioned procedure are shown in

Table 8-1. The figures in this table show the number and percentage of

--. 5 .

* . .5 .S .. . . . . . . . * .5.5 *-*. °.o

. . . . . . . .. S 5 * * . . .. 

.. . . . . . . .. . . . 5*~.5 .... .-...... . • --. ' -. . - ,- , -* . - .. . -'- - .... '5..5 " i.-

". ,'".""- "" ."- "'2.-",".?..-''-"- ,."."".i" .''.?." .. . -"-."" '-- .. .. ..... - "'.. '" , . - .
W, ~ ~ ~ o; - 71

69

MOSs with a shortfall, defined as H < 90.0, by major Army occupational

group and SRB zone. As can be seen from the table, In FY 1981 shortfalls

were most prevalent In zone A and in zone C for the Infantry specialties.

C. High Performance Soldiers

As indicated in Chapter 4, it Is desirable to give bigger bonuses

to the more effective soldiers. One way of identifying a high performance

soldier is by the time taken to attain a given pay grade relative to

other soldiers. Since this information pertains to each individual

soldier, it cannot be included In the SRB calculation before the fact.

Hence we assume that

p= Length of service to achieve a given Day grade

Average length of service to achieve the given pay grade

equals 1.0 for every enlistee. This means that the filter P is, --

effectively, neutral with respect to the S3B calculation. S.4. , -

D). Additional Overrides

In order to insure that the proposed SRB schedule is conformable

with the current one, several adjustments are necessary. First, It is

necessary to impose an upper bound on the SRB; in consonance with current

SRB policy, this upper bound is set at $16,000. Second, to avoid

uneconomically small SRBs, a lower bound of $1,000 was established;

computed SRBs smaller than this amount were set equal to zero. Third,

WS

* .-. .

o ..

,- Io

L' -''- ..' .,' -,-"."-", ,.'.'.'.' ,' . *- " '. ,- . V . ..':'.'.- *..'-.'- ' '- '-- ' .--- ...- . -"-< .- ,~. . --:------.•.
70

Table B-1

a _

Number and Percentage of MOSs with a Shortfall by

Major Army Occupational Group

Major Army b Ml

Occupational SEE Zone

GPOIAD

Infantry

Number of 1405s 27 23 28

Percent of MOSs 412.2 35.9 413.1

with a shortfall

Technical

Number of MOSs 62 58 50

Percent of MOSs 412.8 38.11 37.6

with a shortfall

* Support

Number of MOSs 20 16 16

Percent of MOSs 115.5 341.0 37.2

with a shortfall

* a Defined as operti~g to authorized strength less than 90 percent.

b Zone A =21 to 72 months, B :72 to 120 months, C 121 months

to 111 years.
- . 1 ' 7: d .W , - 7 7 W 7 9 N7

the model provides for a filter G which can be used to modify the SRB

levels so that the proposed and current SRB schedules are pegged to a

common point. The common point is chosen as the average bonus level in

zone A for the Infantry specialties in FY 1981.

I-,'

E. The Interest Rate

In calculating the SRB levels, it is necessary to determine a discount

rate r. While there is much debate concerning the appropriate discount

rate for problems in which there are tradeoffs in resource use, we use a

discount rate of 10 percent. For the SRB problem, the choice of r is

not as important as in other studies, since there is typically a constraint

which must be met. In this study, the constraint is the matching of the

model and current SRB levels for the Infantryman specialties in zone A.

;4.

F. Regular Military Compensation

Because the model yields SRB values which vary by pay grade and

zone, it is necessary to take account of regular military compensation

(RMC) in the SRB calculation. Our computation of RMC is based on the FY

1981 pay schedule. For each MOS, pay grade, and zone, average length of

service was determined and then RMC was computed for the pay grades

relevant to each zone. The RMC values calculated in this manner are

provided in Table 8-2. '

As is to be expected, there Is little variation in RMC between major

Army occupational groups, holding pay grade and SRB zone constant. In

contrast, the value of military output, i.e., MVP in the model, was

e •I

o,,

. - ,%*-
72

found to be higher in the Technical specialties than in the Infantry and

Support specialties (see Chapter 7).

The largest variations in RMC, of course, are among pay grades.

Holding SRB zone constant, on average, 34C among pay grades increases by

12.6, 12.1, and 12.5 percent In the Infantry, Technical, and Support y

specialties. Comparing RHC In pay grades E-4 and E-7, it in found that

it ins higher by 55.2, 54.4, and 54.5 percent, respectively, in the Infantry,

Technical, and Support specialties. These figures are larger than the

oorresponding MVP figures, suggesting that RHC may rise at a faster

rate than earnings In the civilian sector. This is seen more clearly by * - -

comparing the B14C and MVP figures for pay grades E-4 and E-7. For pay

grade E-4, RMC exceeds HVP by 2.5, 0.6, and 31.1 percent In the Infantry,

Technical, and Support specialties. The corresponding figures for pay

grade E-7 are 11.3, 4.7, and 32.6 percent.

- .. .... '-"*w'*'I . .
- 73

Table 8-2

Regular Military Compensation by ..

Major Army Occupational Group

Major Army

Occupational Pay Grade

Group and Zonea h.1

* Infantryb

A 12,153 13,919 - b

B 14,526 16,278-

C - 16,949 18,863

Technical

A 12,1714 13,896 --

B -141,534 16,212 -

C - 16,883 18,831

Support

A 12,167 13,858 --

B -14,521 16,189 -

C - 16,785 18,798

a Zone A =21 to 72 months, B =73 to 120 months, C =121 months to 141 years.

*b Excluded from the analysis because of the small percentage of enlistees

in the cell (see Table 5-2).

-'7
Chapter 8 Footnotes ,___

1 See Selective Reenlistment Bonus (SRB) Study, 2k,=., p. 5-2.

2 1±_.

3 For only two CMFs was there no plurality. In one case, 9 participants

split their vote evenly between ranks 1, 2, and 3; the intermediate

rank 2 was chosen for this CHF. In another case, 10 participants

split their vote evenly between ranks 2 and 3. To be conservative

the CiF was assigned a rank of 2.

4 For additional discussion, see U.S. Department of the Navy, Repair

Parts Support Requirements for Special Projects Office Fleet Ballistic

Missile Subsystem Equipment, SPINST P4423.27, 27 August 1963 and H.

Denlooff, J. Fennell, S.E. Haber, V.H. Marlow, F.W. Segel, and Henry

Solomon, *The Polaris Military Essentiality System,' Naval Research

Logistics Quarterly, December 1964, pp. 235-57.

5 The fill rate figures used in this study are from unpublished data,

as of September 1980, provided by the U.S. Army.

6 The data for MOS 16E are for pay grades E-1 to E-6. Pay grades E-7

to E-9 are not defined for this MOS.

7 In each case, the fill rate is oomputed by combining the two pay

grades. Thus, for zone A, the fill rate is for pay grades E-4 and

E-5 taken together. Likewise for zones B (and C) pay grades E-5 and

E-6 (E-6 and E-7) were combined. In some cases only one pay grade

was represented In a zone, e.g., in MOS 16E, the highest pay grade is

E-6. In this instance, the fill rate for pay grade E-6 by itself was

used to determine if the MOS was In short supply In zone C. The

rationale for this prooedure is that the bulk of enlistees in zone A,

B, and C are In pay grades E-I and E-5, 3-5 and 3-6, and E-6 and E-7,

respectively (see Chapter 5, particularly Table 5-2).

8 It should be noticed that SRBs can be given to E-3s although there

are relatively few enlistees in this pay grade in zone A. For this

study, It is assumed that E-3s would be given the same SRB as 3-4s.

Likewise, If a SRB is given to an E-I (E-5) in zone B (C), the SRB is

the sam as that for an E-5 (E-6).

.

....

. . . . * 
75

I;, b%**,.. .

Chapter 9: SRB Levels Calculated from the Model

In the preceding chapters, the discussion has focused on the variables . .,

for which empirical data must be obtained to implement the proposed SRB

model. These variables include the continuation rate, S; recruitment

and training Costs, together denoted as C; the value of military output

as measured by earnings in the civilian sector, MVP; and regular military

compensation, RMC. Additionally, values for military essentiality, E,

the fill rate, H, and the budget filter, 0, must also be determined.

As indicated in the model, not all variables pull in the same

direction. For example, continuation rates are lowest in the lower pay

grades, suggesting that the SRB should be concentrated in zone A.

Cumulative training Costs are higher in the higher pay grades, however, - .

thereby suggesting a contrary conclusion. Likewise, the value of military

output rises with pay grade, but the rise in this variable with respect

to pay grade is not as rapid as the rise in regular military compensation

with respect to pay grade, negating the need for an SRB in zones B and

C. Shortfalls are also somewhat less prevalent in these zones. Similarly,

except for the Support specialties, the preferred ordering of major Army

occupational groups is not readily apparent.

In examining how the model operates, the value of s was computed

first since it is free of filters and overrides. The s values are

summarized In Table 9-1 by major Army occupational group. It will be

recalled that the of values for a OS are derived in terms of a base MOS,

and SRB zone. The base group in the oomputation is MOS 71L, Administrative

.. . . . . . ..... . . *,*" . .. ..-.- ~ . . .

. . . . . . . . . . . . . . . . . . . .
T6

Specialist, which is a Support specialty; the base pay grade and zone

I

are E-4 and zone A, respectively. Because there is a base group, some

of the SRBs as initially computed were negative. In Table 9-1, the

negative SRBs are treated as if their value were zero. In this table

and the subsequent ones in this chapter, the SRB values are simple averages

,. aggregated over the MOSs in a major Army occupational group.

In assessing Table 9-1, it is noticed that the model SRBs for the ___-

Technical specialties are substantially larger than for the Infantry and

Support specialties. Moreover, while in most instances the SRB levels

for the Infantry specialties are higher than for the Support specialties, .'-'

the differences are relatively small when compared to those between

these specialties and the Technical specialties. The figures that stand

out most strongly, however, are the high SRBs in zone C. The reason for

2_

this is the importance of training costs in the SRB calculation.

The sensitivity of the model to training costs explains the high %

SEs for the Technical specialties. For many MOSs in the Infantry and

Support specialties, training costs are similar so that the SEB levels

in these specialties do not diverge by mach; for these two occupational

groups the value of output variable is a primary determinant of the SRB

level, particularly for pay grade 3-I- in zone A. At higher pay grades,

particularly In zone C, training costs are the most important determinant,

so that even though separation rates are much smaller in zone C vis-a-vis ,- %:-;

zone A, the calculated SRB values are approximately twice as high in the

latter zone as in the former. Likewise, within SRB zone the larger

training costs at the higher pay grades have a greater effect on the SRB

p..4..%:.'.-.

J% %- . %- .-

AA . , . _t& Z. 
-j --..-- -Z T7- -, -.

.1.7

Table 9-1

Model SUB Values, as, by Major Army Occupational Group

SBZDa db Percentage of MOSs

SR oeadAvage RB with SUB > 0

Pay Grade T

A: E-4l 5,650 11,773 3,592 89.9 93.8 76.7

E-5 6,373 13,182 6,959 89.9 90.7 811.8

B: E-5 7,1041 14,092 8,233 92.41 91.4i 83.0

E-6 10,4413 18,782 8,699 941.0 91.6 83.7

C: E-6 11,361 19,2413 9,4165 94.0 93.6 87.5 w

E-7 114,4124 23,856 10,002 83.6 841.8 73.2

a Zone A 21 to 72 months, B T 2 to 120 months, C =121 months to 14 years.

b Negative SUB3 treated as if their value were zero.

*c I :Infantry, T =Technical, S =Support.

s'
78

level than the sm ler separation rate (at the higher pay grades).

At the same time that the model points up how important training

.. necsta are for making preferred SRB decisions, It raises the question of \

how to explain the very high SRB values in zone C, given that the current

SRB schedule provides only minimal emphasis to this ZOne. The reason

for this anomaly is that while training cost considered by itself argues .-

for a high SRB in zone C, another important factor, namely, retirement

cost, is not considered In the model. Providing a reenlistment bonus in

zone C where enlistees have 10 to 14 years of service could Induce them

to continue in service until retirement. The additional cost incurred by

such a policy may easily outweigh the savings in training cost which

might be realized were individuals in zone C to reenlist for another

tour of duty. Hence, the model results are most relevant to zone A

where the likelihood is small that acceptance of a SRB will result in an

individual continuing in military service till retirement (given that

the person would not have done so in the absence of a SRB).

The large percentage of MOSs with a positive SRB in Table 9-1 is due

to the selection of MO 71L, Administrative Specialist, as the base group;

for this group, training costs are relatively low so that the bulk of the

MOSs are candidates for a SRB. As can be seen from comparing Panel A,

Table 9-2 with Table 9-1, there is a substantial decline in the percentage

of MOSs which would receive a SRB when the fill rate is considered. In

zone A, for example, the percentage of MOSs with a positive SRB is reduced

to between 31.9 and 40.4 percent. In general, when the fill rate is

taken into account in the SRB calculation, the SRB levels rise; this is -:
79

Table 9-2

Model SRB Values, Modified by Pilters and Overrides, A

by Major Army Occupational Group

St *a an vreSBPercentage of MOSs

SRB Zone and _ Average RB with SRB > 0

Pa Grad

Panel A0

A: E-4 5,604 12,260 3,452 39.1 39.1 37.2

B-5 6,705 13,833 7,909 31.9 40.4 39.1

B: E-5 7,949 17,300 8,933 36.4 36.4 29.8

E-6 12,013 23,6148 9,536 32.8 33.8 30.2

C: E-6 12,093 23,247 13,110 41.8 37.9 32.5

E-7 16,399 31,018 11,850 41.8 28.6 16.7

Panel Bd

A: E-l 4,736 7,251 1,162 39.1 39.1 37.2

E-5 5,576 7,502 2,242 31.9 40.4 39.1

B: E-5 6,727 9,638 2,411 36.4 36.1 29.8

E-6 10,039 13,768 2,621 32.8 33.8 30.2

C: E-6 9,955 13,465 3,865 41.8 37.9 32.5

E-7 13,285 18,541 3,705 41.8 28.6 16.7 .'

* . o ii * .~°.' -- A.
80

Table 9-2 continued

SIB one Avea~eSiBPercentage an of MOSs

andAverage ____ withSR N-0

Pal Grade 2

PanelCe

A: E-41 5,2417 7,308 1,9412 341.8 28.1 141.0

E-5 5,7241 6,896 2,702 37.7 36.0 30.41

B: E-5 6,636 8,3041 2,922 36.41 341.6 23.41

E-6 9,731 10,9241 3,033 32.8 33.1 25.6

C: E-6 9,4187 10,526 41,14T7 41.8 27.9 30.0

E-T 11,518 12,803 3,706 111.8 28.6 16.7

a Zone A a21 to T2 months, B T 2 to 120 months, C =121 months to 141 years.

b I = Infantry, T z Technical, S =Support.

a Panel A: No SIB given in MOS-SRB zones with a shortfall, I.e., H 90.0.

d Panel B: Figures In Panel A adjusted for military essentiality weight E.

D e Panel C: Figures In Panel B adjusted for SiB maximum (minimum) -- $16,000

($1,000).

r7'-
- 81 _

particularly so in the Technical specialties where training costs are

high to begin with, and Indicates that training costs are substantially

higher in MOSs where there is a shortfall. This Is not at all surprising .i

since it is the MOSs with the highest training costs for which civilian

sector employment opportunities are most likely to be greatest.

When the military essentiality values, E, are applied, the SRB

structure changes in still another way. As shown in Panel B, Table 9-2,

SNB levels are reduced in all major Army occupational groups with the

greatest reductions being registered in the Technical and Support I

specialties, particularly the latter where the average SRB for pay grade

E-4, zone A is $1,162; moreover, even in zone C, the SRB average for the

Support specialties increases to a maximum of only $3,685.

Another finding from Panel B is that even after adjusting for military

essentiality, the differential between the SRB levels for the Technical

and other specialties is significantly larger than the similar differentials

under the current SRB procedure. This is the most important empirical

finding of our study, and suggests that the SRBs for the Technical 7.

specialties should be raised vis-a-vis those In the Infantry specialties;

it also suggests that a larger proportion of MOSs in which a SRB is

offered should be in the Technical MOSs.

The last Iteration in implementing the model involves (1) adjusting

the SRB levels so the average SRB in pay grade E-4, zone A for the Infantry :-":'

specialties approximates the corresponding SRB figure ($5,297) for the

same zone and specialties In FY 1981; (2) setting a ceiling of $16,000 . .. Sfor each SRB; and (3) setting a floor of $1,000 by treating SRBs of less

:-7- -

. *.,. - -.-

- * - *~'h*~.'*.*.-*- S *.S -**. S..-."*'*~
-Lx r-xv".- -z. -]r

82

" than this value as if they were zero. The results of this iteration are

- shown in Panel C, Table 9-2. It should be noted that, fortuitously, the

value of 0 which satisfies the first of these three steps was 1.00;

application of the second and third steps yields the figures in Panel C

where it is seen that the average SRB in zone A for the Infantry specialties

is $5,247. As expected, the result of this iteration is that the percentage

of Support MOSs in which a bonus would be given is reduced, since it is

these specialties where the SRB levels are lowest.

In concluding this chapter, we compare In Table 9-3 the distribution 711

of MOSs by major Army occupational group based on the model and the

current procedure as evidenced by the data underlying Table 3-3. For

* the reason cited above, the figures are restricted to zone A. As indicated

by Table 9-3, the two distributions are quite similar.

It should be noted, however, that training cost figures are understated

since they were not adjusted for attrition. Had adjusted training cost -

figures been used, it is likely that the representation of the Technical

MOSs, among the MOSs in which a SRB is given by the model, would be

substantially higher than shown in Table 9-3. Ti .

;:! -., *. .
83

Table 9-3

Percentage Distribution of MOSs with a

Positive SEB by Major Army Occupational Group, Zone A

Major Army

Occupational Model urnt--

*Infantry 32.0 28.1

Technical 60.0 641.8 ~

Support .0,

Total 100.0 100.0

a Pay grade E-4I.

b FY 1981.
84

Chapter 9 Footnotes

1 It should be noticed that SRBs can be given to E-3s although there

are relatively few enlistees in this pay grade in zone A. For this

study, it is assumed that E-3s would be given the same SRB as E-4s.

Likewise, if a SRB is given to an E-4 (E-5) in zone B (C), the SRB is

the same as that for an E-5 (E-6).

2 Another reason, but one which is less important, is that the arithmetic

mean is sensitive to outlyers, in this case, very large SRBs for

particular MOSs.

3 The same question can be raised about the high SRB values in zone B,

particularly for pay grade E-6. To a lesser extent, the answer here

is the same as the one given in the text.

i A detailed listing of MOSs and computed SRBs are available from the

authors upon request.

V1?

(S 1~J

_____ ____ ____ ___ ___ ____ ____ ____ ___ ___ ____ ____ ___ ____ ___ .v.::-.°:
. ... ..

85

Chapter 10: Conclusion and Suggestions for Further Research

'a

2 The virtue of the model discussed in this study is that it provides

a means for integrating a large set of variables in calculating an effective

and efficient SRB schedule. In particular, the model takes account of

retention rates, training costs, and the value of military output by

MOS, pay grade, and SRB zone. The major conclusion of this research

is that training costs are inadequately reflected in the FY 1981 SiB

schedule. Were this factor given additional weight In the current SRB

procedure, SRB levels would be increased in the Technical MOSs, and a

larger proportion of MOSs in which a SRB is offered would be in these

specialties.

It should be noted that the model as specified can be improved in

several ways. The most important way in which this can be done is to

include in the model the effect of the SRB on retirement costs. When an

individual is induced to reenlist who might otherwise have not done so

in the absence of a SRB, the likelihood of that individual remaiing in

service until retirement increases. Since retirement benefits are

substantial, this raises the cost of offering a SRB; if retirement costs

are not considered, this could lead to larger than optimal SRBs being

offered. Indeed, this Is clearly the case when the model is applied to

I zone C, and less so, but still the case, for zone B. A way of incorporating

retirement costs in the model was developed but because of time limitations

this part of the model could not be tested and is not discussed in this study.

L

L
86

Another area where the methodology can be improved pertains to

-training costs. The training oost estimates used in this study are not

ajusted for attrition. The costs of replacing an enlistee in a given

pay grade include the expenditures on individuals who are unable to rise

through the ranks to fill the given individual's position as well as the

expenditures on the individual who is ultimately successful in filling

that position. A procedure for estimating training costs adjusted for

attrition was devploped, but again time limitations prevented its

incorporation into the model calculations.

Still another aspect which deserves attention is how to tie the

model to the budget process. Were information on reenlistment elasticities

with respect to the SRB available, it would be possible to determine the

expected outlays associated with a given SRB schedule and to compare

these outlays with the available SRB budget. Adjustments to the SRB

schedule or SRB budget could then be made before the schedule is implemented

rather than after implementation.

As noted, we have used military essentiality codes derived from an

earlier Army study in which a panel of experts was asked to assign a code

of 1, 2, or 3 to measure the military essentiality of career management

fields. Ideally, it would have been preferred if military essentiality

codes had been available by MOS. It is believed that the preferred way

of obtaining such information at this level of detail is through a

questionnaire approach rather than directly asking individuals to rank

each specialty.

Finally, information on enlistment bonuses was not used in estimating
4m

67

rrutment costs. One reason for this omission was the difficulty

encountered in estillting the inmer of individuals by NOB who were potential

candidates for the enlistment bouas in 71 1981. It is clear that theI

model of this study could also be applied to caoulatinK enlistment

bonus levels.

II

,-.,.,'