f

Study

Report

94403

Model Description and Proposed Application

MO n for the Enlisted Personnel Inventory, Cost,

-1; and Compensation Model

N• D. Alton Smith, Danny Eichers, Donald E. Rose, Jr., ((U and David Rostker

Systems Research and Applications Corporation 0

S DTIC 'ELECTE

AUG 1 7 1994D]

F

United States Army Research Institute

for the Behavioral and Social Sciences

SJuly 1994

94253 Approved for pubi resas; dlftuilo Is unimhd. 94-2593194,8 IIIIIIHIIKNIY.•- 94 8 16 1 05
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4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Model Description and Proposed Application for the Enlisted MDA903-92-D-0021

Personnel Inventory, Cost, and Compensation Model 2Q465803D

730

6 AUTHOR(S) 1331

Smith, D. Alton; Eichers, Danny; Rose, Donald E., Jr.; C09

and Rostker, David

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Systems Research and Applications Corporation REPORT NUMBER

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U.S. Army Research Institute for the Behavioral AGENCY REPORT NUMBER

and Social Sciences

ATTN: PERI-RS ARI Study Report

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Contracting Officer's Representative, Peter M. Greenston.

12a. DISTRIBUTION/ AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release;

distribution is unlimited.

13. ABSTRACT (Maximum 200 words)

The Enlisted Personnel Inventory, Cost, and Compensation (EPICC) Model is a

PC-based analysis tool that aids Army personnel planners in assessing the inventory

and cost implications of changes in compensation and other personnel policies. The

EPICC prototype was developed by SRA Corporation under a research and development

effort sponsored by the U.S. Army Research Institute for the Behavioral and Social

Sciences (ARI). EPICC assists Army personnel planners in assessment of the cost

and inventory implications of alternative Army-wide policies that may be under consideration. It is the ideal tool for this purpose because it is composed of three

modules that touch on all aspects of personnel policy analysis: an inventory projection module, a compensation module, and a cost module. The inventory projection

module is the core of EPICC. Using an analyst-defined scenario, which includes

specifications of both compensation and personnel management policies, the module

"#wages" a baseline enlisted force for up to 9 fiscal years. Along with the projected

inventories, the module estimates losses (normal, involuntary, and forced), reenlistments and extensions, promotions, and non-prior-service accession requirements.

(Continued)

14. SUBJECT TERMS 15. NUMBER OF PAGES

Personnel inventory projection Manpower 128

Cost estimation Personnel policy evaluation i6. PRICE CODE

Compensation --

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

OF REPORT OF THIS PAGE OF ABSTRACT

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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

EDGAR M. JOHNSON

Director

Research accomplished under contract

for the Department of the Army

Systems Research and Applications Corporation Accesion For

Technical review by NTIS CRA&M DTIC 7AB [

LTC Thomas Daula UfI3ain1ourced o

Peter M. Gteenston Justification ..............

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DISTRIDUFION: diMsthis report hasfeen made by ease * distribution of to: U.S. Army h Institute for the

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NOTE: he findings in this report are not to be construed as an offici Department of the Army positim unless o dpgated by oter authorized documents.
ARI Study Report 94-03

13. ABSTRACT (Continued)

The compensation-reenlistment module uses the analyst's assumptions about military

compensation and macroeconomic conditions over the projection period to adjust

base-year reenlistment rates for changes in these factors. The adjusted rates are

then used in the inventory projection module to age the force. The cost estimation

module calculates the budget costs of the enlisted inventories projected in the

inventory projection module. Because the cost estimation process is fully integrated

with the inventory projections, little additional user effort is required to obtain

cost information along with personnel counts. This adds an important dimension to

the personnel policy analysis model, as different strategies for achieving a desired

force structure can be easily evaluated on the basis of expected costs. The cost

estimation methodology in the EPICC model is derived from the budget model in the

Army Manpower Cost System (AMCOS).

EPICC provides the Army, for the first time, a single model in which inventory,

cost estimation, and compensation-reenlistment modules are linked. The integration

of these three personnel analysis tools in EPICC facilitates the complete evaluation

of policy alternatives by eliminating the often difficult task of working with three

different, and sometimes inconsistent, models and improves decision-making ability.

Lii
Study Report 94-03

Model Description and Proposed Application

for the Enlisted Personnel Inventory, Cost,

and Compensation Model

D. Alton Smith, Danny Elchers, Donald E. Rose, Jr.,

and David Rostker

Systems Research and Applications Corporation

Selection and Assignment Research Unit

Michael G. Rumsey, Chief

Manpower and Personnel Research Division

Zita M. Simutis, Director

U.S. Army Research Institute for the Behavioral and Social Sciences

5001 Eisenhower Avenue, Alexandria, Virginia 22333-5600

Office, Deputy Chief of Staff for Personnel

Department of the Army

July 1994

P.y Proud Number PeronW a Trodn

2046563073 Amtlysl Activils

Appovd for pubLi reiN; dulbudon b unllrnd.

lii
FOREWORD

This report describes the development and application of a

PC-based manpower and personnel policy analysis model--the

Enlisted Personnel Inventory, Cost, and Compensation (EPICC)

model. This model serves as an easy-to-use, well-documented tool

for use by Army manpower analysts and decision-makers to project

the long-run effects of manpower policies and resource decisions

on the enlisted force. It does this by integrating the results

of existing research on the links between manpower compensation,

retention, and costs with an inventory projection capability. In

so doing it enhances the analyst's ability to capture the complex

interactions among a variety of policies and factors: compensation, promotion and separation, quality management, and external

factors (e.g., labor market conditions). As a PC-software tool,

EPICC can also serve as an effective device to orient and train

officers newly assigned to manpower and personnel analysis functions. We are currently developing a set of training lessons for

those purposes.

EDGAR M. JOHNSON

Director

v
MODEL DESCRIPTION AND PROPOSED APPLICATION FOR THE ENLISTED

PERSONNEL INVENTORY, COST, AND COMPENSATION MODEL

MXECUTIVE SUMMARY

Requirement:

The Enlisted Personnel Inventory, Cost, and Compensation

(EPICC) model is a result of the need for an operational model

available to policy makers that would evaluate the costs and

benefits of the various manpower policy options, such as offering

separation incentives, changes in tour length, and changes in

promotion opportunity.

Evaluating numerous Army personnel policies has long been

problematic because of second-order effects on the rest of the

force. For example, increases in compensation or retirement

benefits may increase retention, but if end-strength is held

constant the higher retention reduces enlistment requirements and

partially offsets the cost of higher benefits. If policy evaluations exclude such second-order effects, the results could

be seriously flawed and lead to inefficient personnel policy

decisions.

Procedures:

The work was divided into two phases. The first phase was

composed of three parts: (1) the development of a conceptual

design for EPICC, (2) the development of a cost data interface,

and (3) the development of a prototype model to calibrate alternative policy scenarios at the all-Army level. The second phase

modified the EPICC prototype to allow personnel policy analysts

to model and evaluate separation incentives.

To drive the EPICC model, we collected baseline data from

the Army's Enlisted Master File (EMF) for the period of May 1989

to May 1990, the most recent stable period prior to Desert

Shield/Desert Storm and the force drawdown. The baseline rates

consist of reenlistment,' extension, and non-ETS continuation

rates that reflect the actual transactions occurring during that

period. These rates were applied to a starting inventory of

enlisted personnel that reflect the FY92 year end inventory. We

also included those personnel policy parameters that were in

effect in September 1992.

'Reenlistment rates in EPICC define the behavior of soldiers

facing a reenlistment decision, whether eligible or not. EPICC

is unable to model reenlistment eligibility as defined by

AR 601-280.

vii
Findings:

The Enlisted Personnel Inventory, Cost, and Compensation

(EPICC) nodel is a PC-based analysis tool that aids Army personnel planners in assessing the inventory and cost implications of

changes in compensation and other personnel policies.

The inventory projection module is the core of EPICC.

Using an analyst-defined scenario, which includes specifications

of both compensation and personnel management policies, the

module wages" a baseline enlisted force for up to 9 fiscal years.

Along with the projected inventories, the module estimates losses

(normal, involuntary, and forced), reenlisatments and extensions,

promotions, and non-prior-service accession requirements.

The compensation-reenlistment module uses the analyst's

assumptions about military compensation and macroeconomic conditions over the projection period to adjust base-year reenlistment

rates for changes in these factors. The adjusted rates are then

used in the inventory projection module to age the force.

The cost estimation module calculates the budget costs of

the enlisted inventories projected in the inventory projection module. Because the cost estimation process is fully integrated with the inventory projections, little additional user effort is

required to obtain cost information along with personnel counts.

This adds an important dimension to the personnel policy analysis model, as different strategies for achieving a desired force

structure can be easily evaluated on the basis of expected costs.

The cost estimation methodology in the EPICC model is derived

from the budget model in the Army Manpower Cost System (AMCOS).

Utilization of Findings:

EPICC assists Army personnel planners in their assessment

of the cost and inventory implications of alternative Army-wide policies that may be under consideration. It is the ideal tool

for this purpose because it is composed of three modules that

touch on all aspects of personnel policy analysis.

1. Inventory Rrojection. A personnel inventory is the

stock of soldiers at a particular point in time, arrayed by key characteristics, such as grade or years of service. The inventory projection module predicts how that stock will change over

time as individuals enter and leave the force under different

Army-wide personnel policy scenarios. The inventory projection module can also be used to predict losses, determine accession

requirements, and identify changes in the composition of the

enlisted force.

2. Comnensation-reenlistment link. Changes in military

compensation affect reenlistment rates, which are the key input

in assessing the year-to-year losses from an inventory. The

compensation-reenlistment module provides the quantitative link

viii
between compensation policy changes and reenlistment rates and

controls for differences among demographic groups.

3. Cost estimation. Any change in personnel policies has

cost as well as inventory implications. The cost estimation

module determines the budget cost of a particular inventory by

applying appropriate cost factors to the stocks and flows associated with the inventory.

EPICC provides the Army for the first time, a single model

in which inventory, cost estimation, and compensationreenlistment modules are linked. This advantage significantly

improves decision-naking because the analysis of multidimensional

issues often requires the interaction of the three activities

just described. Therefore, the integration of these three

personnel analysis tools in EPICC facilitates the complete

evaluation of policy alternatives by eliminating the often

difficult task of working with three different, and sometimes

inconsistent, models.

ix
MODEL DESCRIPTION AND PROPOSED APPLICATION FOR THE ENLISTED

PERSONNEL INVENTORY, COST, AND COMPENSATION MODEL

CONTENTS

Page

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

Application of EPICC . . . . . . .............. 1

Features of the EPICC Model ......... ........... . . . 2

Report Organization . . . . . . . . . ......... 6

Additional Documentation . . . . . . . . .. . . . . . . 7

INVENTORY PROJECTION MODULE . ............ ... 9

Inventory Dimensions . . .................. 9

Projection Methodology•. . * * * * . * * * * * * * * *. 10

Inventory Module Inputs and Outputs ............. 22

COMPENSATION-REENLISTMENT MODULE ............. 27

Adjustment Equations Modify the Reenlistment Rates . . . 28

Variables in the Adjustment Equations . . . . . . . . . 29

Parameters of the Adjustment Equations . . . . . . . . . 32

Separation Incentives in EPICC . . . . . . . . . . . . . 34

Summary . . . . . . . . . . . . . . . . . . . . . . . . 35

COST ESTIMATION MODULE . . . . . . . . . . . . . . . . . . 37

EPICC Cost Estimation Methodology . . . . . . . . . . . 37

Estimating Budget Costs ................ . . 38

Cost Module Output . . . . . . . . . . . . . . . . . . . 50

Summary . . . . . . . . . . . . . ............. 51

TECHNICAL REQUIREMENTS . . . . . . . . . . . . . . . . . . 53

Data Processing Requirements . . . . . ........... 53

Hardware Requirements . . . . . . . . . . . . . . . . . 53

User Interface . . . . . . . . . . . ............ 53

MODEL VALIDATION . . . . . . . . . . . . . . . . . . . . . 57

Assumptions . . . . . . . . . . . . . . . . . . . . . . 57

Validation Results . . . . . . . . . . . . . . . . . . . 59

xi
CONTENTS

Page

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . 63

Single Integrated Tool for Personnel Policy Analysis . . 63

A Valuable Training Tool . . . . . . . . . . . . . . . . 63

REFERENCES . . . . . . . . * . . . . . . . . . . . . . . . 65

APPENDIX A. DISCUSSION OF COST POLICY MODULES . . . . . . A-1

B. DISCUSSION OF THE INVENTORY PROJECTION MODULE

DATA REQUIREMENTS . . . . . . . . . . . . . . B-i

C. LINKING ACCESSION SUPPLY TO EPICC: DESIGN

CONCEPT PAPER . . . . . . . . . o . . . . . . C-i

D. USER'S GUIDE TO MODIFYING PAY ELASTICITIES IN EPICC . . . .. o .. . . . . . . . . . . . D-1

LIST OF TABLES

Table 1. Inventory Projection Scenario . . . . . . . . . . 23

2. Inventory Module Output ........ ..... 25

3. Separation Incentive Effects in EPICC . . . . . . 35

4. User Accessible EPICC Cost Module Variables . . . 50

5. ELIM-COMPLIP FY93 Actual Losses and EPICC FY93

Projected Losses . . .. ...... .. .... 60

6. ELIM-COMPLIP FY93 Actual Gains and EPICC FY93

Predicted Gains ........... ...... 61

7. Comparison of the FY94 President's Budget (FY93

Costs $000) with EPICC Predicted Costs . . . . . 62

8. Comparison of FY93 Actual Costs for Recruiting

with EPICC Predicted Costs ($M) . . . . . . .. 62

LIST OF FIGURES

Figure 1. EPICC Model Schematic ............. 2

2. Inventory Projection Steps . . . . . . . . . . . 11

3. Compensation-Retention Module Schematic . . . . 28

xii
CONTENTS

Page

Figure 4. Diagram of the Cost Module Interface ...... .. 38

5. EPICCMain Menu . . . . . .............. 54

6. Define Scenario Main Menu ... ........... .. 54

7. Default Reenlistment Rates . . . . . . . . . .. 55

xiii
MODEL DESCRIPTION AND PROPOSED APPLICATION FOR THE ENLISTED

PERSONNEL INVENTORY, COST, AND COMPENSATION MODEL

INTRODUCTION

The Enlisted Personnel Inventory, Cost, and Compensation

(EPICC) Model is a PC-based analysis tool that aids Army

personnel planners in assessing the inventory and cost

implications of changes in compensation and other personnel policies. The EPICC prototype was developed by SRA Corporation

under a research and development effort sponsored by the U.S.

Army Research Institute for the Behavioral and Social Sciences

(ARI). This report documents the construction of the initial

prototype model. It addresses the conceptual framework,

methodology, data requirements, and uses of the EPICC model.

In this introduction we describe the application for which

EPICC could be used as a personnel policy analysis tool in the

first section. The second section provides an overview of the

model, describing the features of the model used in evaluating policy isaues. The last section outlines the organization of the

remainder of the report.

Application of EPICC

EPICC is a deterministic model by design. It assists Army

personnel planners in their assessment of the cost and inventory implications of alternative policies that may be under

consideration. It is the ideal tool for this purpose because it

is composed of three modules that do the following:

1. Inventory projection module. As the name suggests, a

personnel inventory is the stock of soldiers at a particular

point in time, arrayed by key characteristics, such as grade or

years of service. The inventory projection module is a Markov

model that predicts how that stock will change over time as

individuals enter and leave the force under different personnel policy scenarios. The inventory projection module can also be

used to predict losses, determine accession requiiements, and

identify changes in the composition of the enlisted force.

2. Cost estimation module. Any change in personnel

policies has cost as well as inventory implications. The cost

estimation module determines the budget cost of a particular inventory by applying appropriate cost factors to the stocks and

flows associated with the inventory.

3. Com2ensation-reenlistment module, Changes in military

compensation affect reenlistment rates,2 which are the key input

2 fecnlistment rates in EPICC define the behavior of soldiers

facing a reenlistment decision, whether eligible or not. Since

EPICC is unable to model reenlistment eligibility as defined by

AR 601-280, we used the total population facing a reenlistment

1
in assessing the year-to-year losses from an inventory. The

compensation-reenlistment module provides the quantitative link

between compensation policy changes and reenlistment rates.

EPICC provides the Army for the first time, a single model

in which inventory, cost estimation, and compensationreenlistment modules are linked. This advantage significantly

improves decision-making since the analysis of multi-dimensional

issues often requires the interaction of the three activities

described above. For example, in allocating the dollars

available for Selective Reenlistment Bonuses (SRBs), the

inventory module identifies projected mismatches between

personnel and requirements for the next year. The compensationreenlistment module shows the bonus increase needed to close

personnel gaps in particular occupations, and the cost estimation

module calculates whether a given allocation of bonuses will be

within the total SRB budget. The integration of these three

personnel analysis tools in EPICC facilitates the complete

evaluation of policy alternatives by eliminating the often

difficult task of working with three different, and sometimes

inconsistent, models.

gre 1. EPICC Model Schematic

Features of the EPICC Model

Figure 1 shows the key components of the prototype EPICC

decision as the denominator in calculating rates.

2OO
model. In addition to the inventory, compensation-reenlistment,

and cost estimation modules which contain the policy tools just

discussed, the model includes a user interface which accepts the

analyst's scenario assumptions and provides results in a variety

of formats. A key feature of the user interface is the extensive

use of menus and function keys along with a series of help

screens to guide the user through the operation of the model. We

outline the features of each of the modules in turn, starting

with the core of EPICC, the inventory projection module.

Inventory Projection Module

Using a projection scenario defined by the analyst, this

module "ages" the baseline enlisted force, determines accessions

and promotions, and calculates summary measures describing the

projected force. The inventory projection module includes the

following features:

1. Inventories are dimensioned by both YOS and grade,

providing views of the experience distribution of the force by

both rank and time in service.

2. EPICC includes separate subinventories defined by

gender, ethnic category (white and other), and quality. Quality

is divided into six groups (AFQT category I-IIIA, IIIB, and IV,

for high school diploma graduates and others). As noted above,

disaggregating inventories allows force composition issues to be

addressed by the model.

3. The inventory module produces annual projections over a

nine-year horizon (current year, two budget years, and the sixyear planning cycle).

4. Inventories are projected according to an endstrength

constraint that is set by grade3 ; however, it determines NPS

accessions utilizing user-specified distributions. For example,

the model reflects the differences in how accessions are

determined for high quality and other soldiers.

5. A time-to-ETS (Expiration of Term of Service)

distribution which ages according to enlistment and reenlistment

term assumptions is used to calculate the composite continuation

rates in the model. As compared with using a static ETS

distribution, this approach captures the inventory effects of

policy changes affecting term lengths.

6. The rate used to convert accessions into first-year

endstrength is calculated from attrition rates during the first

year of service and assumptions about the quarterly timing of

3

Although currently disconnected, the model also has the

capability to project inventories with the user specifying

accession constraints. To activate this feature would require

minor modifications.

3
accessions.

7. Soldiers are initially promoted to fill vacancies, which

are determined as the difference between projected strengths and

requirements in a grade. This provides a link between the

manpower and personnel worlds as changes in requirements will

affect promotion rates. In addition the model accepts user

specified promotion rate floors and calculates the losses needed

to achieve the minimum promotion rates.

8. EPICC accepts assumptions about involuntary losses and

models the implications of changing these policies, including

changes to retention control points, and increases or decreases

in the numbers of QMP losses that are expected to be boarded

out.4

9. The inventory implications of early decision policies in

which soldiers are allowed to make reenlistment decisions before

the ETS points can be modeled in EPICC.

10. The analyst can directly modify the baseline

reenlistment, extension, and non ETS continuation rates. This

allows for the evaluation of policies not already programmed into

the model.

These features provide the personnel policy analyst with

greater projection accuracy and analysis flexibility. Projection

accuracy is improved through the use of procedures such as that

used to convert accession flows to a first year inventory stock.

Analysis flexibility is enhanced by allowing the user to change

as many of the assumptions that define a projection scenario as

possible. We believe that the EPICC inventory module, as

constructed, gives the analyst the ability to address a wider

variety of personnel issues than has previously been the case for

the Army enlisted force.

Com•ensation-Reenlistment Module

The compensation-reenlistment module uses the analyst's

assumptions about military compensation and macroeconomic

conditions over the projection period to predict how baseline

reenlistment rates will change in the future. These predicted

rates are then used in the inventory projection module to age the

enlisted force. The elements of military compensation that can

be specified by the EPICC user include:

1. Annual increases in basic military pay, both force-wide

4QMP losses might be expected to increase, say, if the Army

decides to raise the standards of quality for promotion to the

senior grades.

5This feature is currently disconnected, but can be

reactivated with minor modifications.

4
and targeted to YOS/grade groups;

2. Annual changes in allowances by pay grade, including

BAQ, BAS, and VHA;

3. Annual SRB levels and the payment pattern by MOS; and

4. Several options for computing retirement benefits and

other separation incentives.

In addition the analyst can specify annual changes for the two

macroeconomic factors that affect enlisted retention, the level

of civilian earnings and unemployment.

Reenlistment rates are adjusted for compensation assumptions

using reenlistment models developed in the Army Compensation

Models Project. The prototype for the compensation-reenlistment

module is the Army Reenlistment Model (ARM), which predicts

reenlistment rates for seven CMFs using assumptions similar to

those defined above.

Cost Estimation Module

The cost estimation module in EPICC is based on AMCOS.

Using the AMCOS data base and policy modules, the analyst

specifies assumptions that determine how cost factors for the

major cost elements are calculated. For example, assumptions

about pay and allowance changes, in addition to affecting

reenlistment rates and the inventories, automatically adjust the

cost factors associated with annual compensation. Thus, as in

AMCOS, the analyst can tailor the cost factors to suit a

particular analysis rather than use historical data that is

inappropriate. Features of the cost estimation module include:

1. Accuracy and Completeness. EPICC uses the Army's most

up-to-date and comprehensive cost data, grounded in economic

theory and institutional detail.

2. User Flexibility. The EPICC cost module permits userdefined scenarios, special case modification of cost factors, and

tailored output.

The cost factors are applied against the appropriate flows

and stocks derived from the inventory projection module. For

example, using analyst-supplied assumptions about the quarterly

distribution of accessions, promotions, and losses, the module

calculates the manyears implied by the starting and ending

inventories and multiplies these manyears by the compensation

cost factors to determine the budget costs associated with

military compensation.

Operation of EPIC

As required in the development contract, the prototype of

the EPICC model operates on an AT-style microcomputer with a

5
standard 640K of random access memory and a hard disk storage

device. The current EPICC prototype requires approximately 5

megabytes of disk storage space and, with a math coprocessor, will be able to generate both inventory and cost projections for

a particular scenario in minutes. Run times will, of course, be

faster on more advanced microcomputers.

EPICC incorporates a number of features to make the model

straightforward to use, including:

1. Menu-based operation. The user will operate the model

through a system of menus, including those for defining

scenarios, choosing calculation options, and selecting output

formats.

2. Default scenario assumDtions. As a result of the

flexibility of the model, there are many assumptions in a

projection scenario. EPICC comes complete with a full set of

default assumptions based on historical data. In most

applications the analyst will only have to change those

assumptions relevant to the issue being evaluated.

3. Scenario editing. To reduce obvious input errors, the

user interface checks assumptions on entry and, if necessary,

prompt the analyst for a new entry. Function keys are also used

to allow for speedy editing. For example, the user can apply a

single multiplier to groups of numbers, copy numbers from one

projection year to a range of projection years, and set a range of rates to a single factor using function keys.

4. Automatic file management, Storage and retrieval of

scenario definition, baseline data, and results files are

invisible to the user.

5. On-line helD. Help files accessible during program

operation provide on-line assistance to the user of EPICC. This

complements the written documentation that is provided with the

model.

Results from EPICC are provided to the analyst in a spreadsheet- compatible form. This gives the analyst the flexibility to

perform additional calculations on the results using a

spreadsheet and graphics package of his or her choice.

Report Organization

The remainder of this report describes the EPICC model.

Chapters 2, 3, and 4 present the key components of the model, the

inventory projection module, the compensation-reenlistment link,

and the cost estimation module. For each module, we describe the

conceptual framework, the methodology used by the model, the list

of input variables required by the module, including both

baseline data and user assumptions, and the output variables

generated by the module. We describe, at the level of specific

equations, the calculations which convert the inputs to outputs.

6
Chapter 5 discusses the technical aspects of the EPICC

prototype, including hardware requirements, the user interface,

and installation procedures. Chapter 6 presents the results of

our model validation using an out of sample prediction for FY93.

Chapter 7 is our conclusions. Appendix A discusses, in greater

detail, the cost equations to include underlying variable

definitions and data sources. Appendix B discusses the input data

requirements for the inventory module to include data sources and

extraction programs. Appendix C describes the design concept

paper linking accession supply to the EPICC model.

Additional Documentation

In addition to on-line help screens, two companion reports

provide additional information for the user / policy analyst:

Eichers, D., Sola, M., McLernan, G., EPICC User's Manual, Systems

Research and Applications Corporation, January 1994; and Eichers,

D., EPICC Technical Documentation, Systems Research and

Applications Corporation, January 1994.

7
INVENTORY PROJECTION MODULE

The inventory projection module in the core of the Enlisted

Personnel Inventory Cost and Compensation Model. Using an

analyst-defined scenario, which includes specifications of both

compensation and personnel management policies, the module "ages"

a baseline enlisted force for up to 9 fiscal years. Along with

the projected inventories, the module estimates losses (normal, involuntary, and forced), reenlistments and extensions,

promotions, and nonprior service accession requirements. This

chapter describes the analytical design of the inventory projection module.

It is organized in three major sections. The first section

describes the basic structure of the inventories in the module,

the inventory *dimensions". The next section details the

projection methodology by following the steps used to generate the results for each fiscal year. The final section summarizes

the inputs to and outputs from the inventory projection module.

Inventory Dimensions

Each inventory in EPICC is an Army-wide inventory dimensioned by grade (8 columns -- E1-3, E4, ES, E6, E7, ES, E9,

and a total) and years of service (31 rows -- YOS 0-1 through YOS

29-30+ and a total). Year of service and grade are the central

characteristics of military personnel inventories, related to

both the productivity and costs of a particular force.

For each fiscal year, the total enlisted inventory in EPICC

is divided into "subinventories", which are defined by the

interaction of the following characteristics:

1. Ethnic Category. Because of the significant differences

in continuation rates between white and other soldiers, we

distinguish subinventories by theme groupings, using the REDCAT

designation on the EMF.

2. G Given the limitations on occupations open to

women, it is important to include gender in the definition of the

subinventories so that these restrictions can be reflected in

inventory projections.

3. Aacession Dualitv. The quality composition of the

enlisted force is of continu-Lng policy interest. The EPICC

subinventories have six quality categories defined by the

interaction of APQT (Category I-IIA, IIB, IV) and high school

graduation status (diploma graduates, others).

An additional subinventory, including all soldiers for whom data

on one or more of the above characteristics is missing, provides the correct roll-up to the total force. In total, then, there

are 25 subinventories (2 ethnic groups x 2 gender groups x 6

9
quality groups + 1 missing) in EPICC.6

EPICC projects the enlisted force by summing the projections

for this mutually exclusive and exhaustive set of subinventories.

There are two reasons for accumulating the total inventory within

an occupation from subinventories rather than directly projecting

the total force. First, Army decision makers are often as

interested in the composition of the force across these

characteristics as in the total numbers. Second, starting with

disaggregated projections will generally provide a more accurate

projection of the total force. Retention research has

demonstrated that both ETS and nonETS continuation rates vary

significantly with soldier characteristics. To the extent that

the composition of the enlisted force changes over the •rorection

period, using continuation rates averaged across the baseline

force composition will generate less accurate predictions than

the disaggregated approach.

EPICC generates year-end inventories and associated

statistics for a maximum of 9 projection years -- the current

year, two budget years and a six-year planning (POM) cycle. The

model accepts separate scenarios for each of the projection years

so that the effects of a series of basic pay raises, for example,

can be evaluated. 7 In the next section we describe the

projection methodology.

Projection Methodology

Figure 2. provides an overview of the inventory projection

methodology. Six major steps are required to estimate the

inventory for each projection year.

1. The inventories from the previous year are decremented

by involuntary losses from the Quality Management Program (QMP)

and the application of retention control points (RCPs).

2. The continuing force is determined. Reenlistments,

extensions, and normal losses are calculated in this step.

3. Prior service accessions are added to the inventory.

5 Disaggregation by military occupation would also be useful

in some policy applications. Defining subinventories by both

soldier characteristics and occupation, however, significantly

increases the complexity of an inventory projection model, both

from a computational and an analytical standpoint. See Smith et

al., 1990, for a discussion of the design implications. The

projection methodology implemented in EPICC, however, provides

the foundation for this more general model.

7Some scenario assumptions are restricted to be the same in

all projection years. These are noted in the description of the

prediction methodology.

10
SCLENARIO ASSUIMPTIONS DALTA•]•]

* Sr•n•ism Can.I NPew

SU.8.W U QWM Lu.. by Gi.e

*AM. M Ase. Dm e91burn

4~.i Thrne.ivnoyi rmtdt ilvcnisadme

.2...i- dw Fwf

*Vsaus 1 p foors F e o , h

R dedutose inob Force a fRIM) Seletiv RetreentBad Mal 

SEs), r whn. 4 0eo 

endstengt tarets scault edho4 anb thes acesiosarted ade

Figure 2. Inventory Projection Steps

4. The inventory is promoted to fill vacancies and meet

user-supplied promotion floors. Forced losses, such as

Reductions in Force (RIFs) and Selective Early Retirement Boards

(SERBe), are determined along with promotions.

S. The number of nonprior service accessions needed to meet

endstrength targets is calculated, and these accessions are added

to the inventories.

6. Finally, with the flows of personnel into and out of the

inventory determined, the time-to-ETS distribution, which is used

in the calculation of the continuing force, is updated.

These steps are repeated for each projection year.. Our

discussion of the projection methodology is organized around

these major steps.

Remove Involuntary Losses

The approach used to model involuntary losses implies an

assumption about what these soldiers would have done if not

involuntarily separated. For example, applying a continuation

rate to an inventory, and then subtracting a user-supplied amount

of involuntary losses to determine actual continuations,

11
implicitly assumes that these losses reduce continuations onefor-one. This is unrealistic as some soldiers who are

involuntarily separated might have otherwise been normal losses.

By removing involuntary losses before applying continuation

rates, we assume that involuntary losses come both from

continuations and normal losses, with the proportion determined

by the continuation rate. This is a conservative approach in

that we are less likely to overstate the net effect of changes in

policies affecting involuntary losses.

In symbols, the adjusted inventory for YOS i, grade j,

subinventory k, and projection year t-l, E*.L,, is

t-,•, = £IjokoC-1 E, , I-RL- jt (1)

where Ej.. 1 is the previous year's inventory, RLW represents the

RCP losses in the projection year, and QLI represents QMP

losses. The previous year's inventory is baseline data for the

first projection year and projected inventories for the remaining

years. The equations for estimating RCP and QMP losses are

described below.

We use the following conventions for the subscripts to the

variables in this section: (1) the index for YOS, i, refers to

the upper end of the yearly YOS intervals and, therefore, ranges

from 1 to 30; (2) the index for grade, j, ranges from 3 (El-3) to

9; (3) the index for subinventory, k, ranges from 1 to 25; (4)

the index for projection year, t, ranges from 1 to 9.

Superscripts on the inventory variable, such as the asterisk,

indicate intermediate inventories used in the projection process.

The year-end inventories -- the output for each projection year -

- have no superscript.

RCP Loosen. To determine RCP losses, the analyst sets the

maximum year of service by grade. Soldiers who have years of

service greater than that maximum in the projection year and are

at the expiration of their term of service (ETS) are classified

as RCP losses. Formally, the number of RCP losses in YOS i,

grade J, subinventory k, and projection year t is given by

PaL ak o o > R k~e li id ' for i> 1(2)

RL• a 0 for i g i7

where iJ1 is the maximum year of service in grade j.

The term d&.1 is the proportion of soldiers in YOS i and

subinventory k who are at ETS in the projection year. This is

taken from time-to-ETS (TTE) distributions which describe, for

each subinventory, the proportion of soldiers at each YOS with an

ETS date in the current projection year, the next year, and so

12
on. In our notation, time-to-ETS is indexed by a superscript,

ranging from 0 (at ETS) to 5 (five years to ETS). We describe

the role of the TTE distributions in more detail in the next

section.

QOMPLosses. QP losses are specified by the analyst in two

steps. First, the estimated number of losses by grade and

projection year is entered. Then, the distribution of these

losses across YOS is specified for each grade. within a

YOS/grade cell, losses are distributed across the subinventories

in the same proportions as the previous year's inventory.

Therefore, QMP losses in YOS i, grade j, and subinventory k is

given by

( E ,J ,t1)

where 015 is the number of losses by grade and projection year

and the p's specify the YOS distribution for each grade. The

final term in equation 3 distributes the losses by subinventory.

A given YOS distribution may lead to situations in which the

number of losses allocated to a particular YOS/grade/subinventory

cell is greater than the population in that cell. EPICC checks

for this problem while subtracting QMP losses from the inventory.

Infeasible allocations are listed in a report to the user, the

maximum possible number of losses is taken, and the projection

proceeds.3

Continue the Force

In EPICC the continuing force is determined as the sum of

three personnel "flows" -- reenlistments at ETS, extensions at

ETS, and nonETS continuations. Each flow is estimated by

applying cell-specific rates to the number of soldiers in

subinventory cells of the adjusted previous year inventories.

The rates are based on historical data, adjusted for usersupplied assumptions about changes in compensation and personnel

management policies.

There are two reasons for estimating continuations by

summing personnel flows rather than applying a single

continuation (or loss) rate. First, because of the nature of

enlistment contracts, continuation rates at ETS are generally

much lower than nonETS continuation rates. Thus, an overall

'Alternatively, if no YOS distribution is specified, the

module distributes losses across both years of service and

subinventories in the same proportions as the previous year's

inventory. This procedure will produce feasible allocations in

all inventory cells.

13
continuation rate is a weighted average of two very different

values, where the weights are defined by the proportion of

soldiers at ETS. Even if the underlying ETS and nonETS

continuation rates are stable, it is unlikely that the proportion

of soldiers at ETS in a given cell would be constant through

time.' More accurate overall continuation rates can be obtained

by starting with separate ETS and nonETS continuation rates and

projecting the proportion of soldiers at ETS along with the

inventories. This is the approach used in EPICC.

Second, compensation and personnel management policy changes

have different effects on the various personnel flows. An

increase in the average Selective Reenlistment Bonus (SRB) will

increase reenlistment rates but have little, if any, effect on

nonETS continuation rates. To correctly evaluate the impact of

these policy changes, then, it is necessary to be able to adjust

rates that represent specific types of personnel flows.

In the remainder of this section we describe how each of

these three personnel flows is calculated in the inventory

projection module.

ETS Reenlistments. In EPICC ETS reenlistments are defined

as reenlistments occurring among soldiers who have an ETS date

during the projection year. The equation for ETS reenlistments

in YOS i, grade J, subinventory k, and projection year t, R4, is

R11jke !-- (d•'ke-1) (.rk8Jkezk)(

where the ri's are baseline reenlistment rates defined by YOS and

subinventory; 6at is a reenlistment rate adjustment factor

determined by compensation and macroeconomic assumptions; and

is a reenlistment rate adjustment factor used by the analyst to

model changes in personnel management policies.

Equation 4 specifies that reenlistments are the product of

the population "at risk" -- calculated by multiplying the

adjusted previous year inventory times the proportion at ETS - -

and a predicted reenlistment rate. The predicted reenlistment

rate is, in turn, the product of three factors -- a baseline ETS

reenlistment rate, an adjustment factor derived from analyst

assumptions about military and civilian compensation, and a userspecified adjustment factor for changes in personnel management

policies. We describe the methodology for calculating the

baseline reenlistment rates in Appendix B. The compensation

adjustment factors, which vary by projection year, are the output

from the compensation-retention module described in Chapter 3.

The A's add flexibility to the inventory projection module.

'For this to be true, the base and projection year

inventories would have to be in a steady-state with constant

endstrength and accessions.

14
Policy changes that are not explicitly modeled in EPICC can be

evaluated using off-line estimates of expected changes in

reenlistment (and other) rates. The analyst can define one set

of adjustment factors which is applied to all projection years.

Note that the ETS reenlistment rate and the proportion at

ETS in each projection year are dimensioned by YOS and

subinventory only. Effectively, we assume that the ratio of ETS

reenlistments to inventory size is constant across grades within

a subinventory/YOS cell. This assumption greatly reduces the

storage requirements of the model, as baseline reenlistment rates

and TTE distributions do not-have a grade dimension, without

significantly affecting the accuracy of the projections.

Compared with the variation in reenlistment rates captured by the

YOS and subinventory dimensions of the rates, the variation

across grade within a subinventory/YOS cell is relatively small.

ETS Extensions. ETS extensions in the inventory module are

given by

t1(dok, •-3) (exijA• 5

where EX4 is the number of extensions in YOS i, grade j,

subinventory k, and projection year t; ex& is the baseline

extension rate; and A: is the personnel management adjustment

factor for extensions.' 0 Using the same at-risk population,

extensions are determined from historical extension rates, as

adjusted by the analyst. Like reenlistments, extension rates do

not have a grade dimension. Unlike reenlistments, we assume that

the number of extensions is not affected by changes in relative

military compensation.

User adjustments to ETS reenlistment and extension rates

could result in an ETS continuation rate that is greater than 1.

EPICC audits the adjusted rates and warns the user if this

problem exists.

NonETS Continuations. This flow constitutes the remainder

of the continuing force. NonETS continuations are calculated as

lift EAJkt. (I-d10 (-(6,kte-3) (nc,-A 

where NCp is the number of nonETS continuations in YOS i, grade

l0In an inventory model, the definition of a reenlistment and

an extension depends on the definition used in constructing the

underlying rates. For EPICC we define reenlistments as

continuations which increase the ETS date by 36 or more months.

An extension increases the ETS date by less than 36 months.

15
j, subinventory k, and projection year t; nc& is the baseline

nonETS continuation rate; and A is the analyst-supplied

adjustment factor for this rate. The number of nonETS

continuations is calculated as the product of the inventory at

risk for a nonETS decision and adjusted continuation rates. As

with reenlistments and extensions, nonETS continuation rates are

dimensioned only by YOS and subinventory.

NonETS continuations include a substantial proportion of the

total reenlistments and extensions that occur in a given fiscal

year. It is important to keep track of nonETS reenlistments and

extensions for two reasons. First, the distribution of nonETS

continuations among reenlistments, extensions, and year-to-year

continuations affects the TTE distribution. A shift toward more

early reenlistments will affect the at-ETS proportions in future

years, raising the average continuation rate in those years.

Second, accurate budget estimates require a realistic estimate of

reenlistments because of SRB costs.

We use baseline data to allocate nonETS continuations to

reenlistments and extensions. Let rp' be the proportion of

continuations that are reenlistments among soldiers with YOS i in

time-to-ETS n. Let epP be the same proportion for extensions.

Then nonETS reenlistments, extensions, and year-to-year

ccntinuations, which we denote by C, are given by

Rljkt NCIukerIp

EXTJkt - NCijkt epM (7)

CIOkt - NCijkt(1 - rpP - epj1)

where these equations are defined for n>O. The reenlistment and

extension proportions can not be modified by the analyst,

however, we anticipate that in future modifications to the model

the user will be able to modify these proportions."

With these personnel flows defined, the module calculates

total reenlistments, extensions, and normal losses using the

following equations:

"

11

Note that equations 6 and 7 imply that non-ETS

reenlistments are not adjusted for changes in relative military

compensation. We assume that these reenlistments are primarily

driven by administrative factors, such as adapting enlistment

terms to overseas tour requirements.

16
RX1jkt - E, R,~f 8

ZJlojt -E';Jkt - (Rilke + E~~C+ r. Cfft,)

where NL represents normal losses. ETS and nonETS reenlistments

are summed to provide total reenlistments during the projection

year; total extensions are calculated analogously. Normal losses

are simply the difference between the previous year's inventory,

adjusted for involuntary losses, and the continuing force.

Add Prior Service Accessions

Prior service accessions are specified by the analyst in two

steps. First, the total number of accessions by projection year,

AP, is entered. Then, a subinventory distribution, nk, and a

grade distribution, iL, are specified; both distributions are

used for all projection years. Prior service accessions are

distributed across the remaining inventory dimension, YOS, in

proportion to the adjusted previous year inventory. The equation

for prior service accessions by inventory cell is

A -js A PS1 k- LJE-i, " ), (9)

With the third step complete, the continuing force plus

prior service accessions can be calculated as

EIC z RiO +jX0 -14, ~~+NC,...lJ~k~t+AI" (10)

where the superscript C on the inventory variable denotes the

continuing force, as adjusted for both involuntary losses and

prior service accessions. Note that at this point, we "age" the

force by increasing the year of service index. This implies that

all continuation flows are indexed by a soldier's YOS at the end

of the previous year. We use this convention, rather than

reporting continuation flows by YOS at the end of the projection

year, so that the flows can be easily matched to inventories from

which they are generated.

Calculate Promotions

The third step of the projection methodology calculates

promotions. The model promotes to fill vacancies, subject to

user-supplied promotion floors. If these floors exceed the

available vacancies, forced losses in the form of RIFs and SERBs

are generated to provide sufficient additional vacancies to meet

17
the specified promotion minimums.

This approach implies that promotions1 2 for a particular

grade are the maximum of (1) vacancies in that grade and (2) the

minimum number of promotions for that grade. Starting with E9,

the number of promotions in projection year t, P.,, is given by

Pt-ma~x(V,,~ , ___

where (11)

"V9 9 Ef,9, k, t

V,4 is the number of E9 vacancies in projection year t. It

equals the E9 requirement in year t, Sq.,, minus the continuing

force of E9's, which is calculated by summing over YOS and

subinventory. Requirements are specified by the analyst as part

of the projection scenario. P0' is the minimum number of

promotions, which is calculated as the product of the E9

continuing force; baseline promotion rates, p,, and user-supplied

adjustment factors, 4.t, which can be defined by projection

year.13

If the minimum number of E9 promotions exceeds E9 vacancies,

forced losses equal to the excess are removed from the continuing

inventory. Thus, forced losses are defined as

I- ( Ef9 , (12)

___t 9r tkIDk 1 

where FL9,, is the number of E9 forced losses in projection year

t. In the current version of the model, these losses are

allocated across YOS and subinventory cells in proportion to the

continuing force. A rule-based allocation procedure is under

development as a modification to the model.

The distribution of total E9 promotions by year of service

is determined by the analyst, who selects "primary" and

"secondary" promotion zones and a ratio of secondary to primary

"1Promotions in EPICC are defined as the actual advancement

to the next grade, i.e., the "pin-on" points.

"Note that we are using the DCSPER definition of "promotion

rate", which is the number of promotions into grade E9 divided by

the E9 endstrength. Although this is different from the

traditional method of calculating promotion rates, it was the

definition being used by DCSPER at the time of model development.

18
promotions. The distribution then is defined as

I.k* .,k for i in the secondary zone

r1 ,E9,k,)

P,9,, - (-1 e --E- 9 "k for i in the primary zone

Et i9,k, t

I,9, , t = 0 otherwise

where 0 is the proportion of promotions occurring in the

secondary zone. This same sequence of steps is then repeated to

determine ES promotions, and so on.

Finally, the year-end :iventory for projection year t is

calculated by combining the continuing force, forced losses, and

promotions in and out as

- EIj=t-FLjkt÷(Pijkt-ci,j.,,,) (14)

This equation is defined for YOS 1-2 through YOS 29-30+; the

final inventory in YOS 0-1 is determined in the next step.

Calculate NonDrior Service Accessions

Having estimated all the losses from the inventory, we

calculate the number of nonprior service (NPS) accessions

required to meet a user-supplied endstrength goal for the

projection year. Analytically, it is convenient to divide the

computations into two parts.

First, we determine the number of soldiers needed in the YOS

0-1 cells to meet the endstrength goal. This is given by

k =kE,3 i - Ek(130EihZikt) (5

The left-hand side of equation 15 is the inventory in YOS 0-1 and

grade E1-3, summed across the subinventories. This must equal

the endstrength constraint in projection year t, displayed as the

sum of the requirements by grade, less the continuing force.

Because of attrition between the accession point and the end

of a fiscal year, the number of accessions required to meet the

endstrength goal will be greater than the required YOS 0-1

inventory. The equation for the total number of nonprior service

accession required in projection year t is

19
- rk Et,3,,t (16

The numerator is the required YOS 0-1 endstrength, taken from the

previous equation.

The denominator is the rate at which the accession flow is

"converted" to the YOS 0-1 stock. Because the required number of

accessions is sensitive to the value of this conversion rate, we

pay special attention to the factors that affect it. The overall

conversion rate is calculated as a weighted average of the rates

by subinventory -- the expression in brackets -- with the weights

being user-defined proportions of accessions for each

subinventory, the X's. Thus, when the analyst modifies the

accession mix by quality or demographic characteristics, the

number of accessions needed to achieve a particular endstrength

will change.

The subinventory conversion rates are, in turn, a weighted

average of subinventory-specific 3-month attrition rates, the

a's, where the weights are the proportion of total accessions

entering in each quarter of the fiscal year, *,.14 Therefore, the

conversion rate is also sensitive to the timing of accessions.

The distribution of accessions across subinventories, the

attrition rates by subinventory, and the quarterly distribution

factors can all be modified by the user of EPICC. Nonprior

service accessions by subinventory, A:', are simply the product

of total accessions and the subinventory distribution factors.

Update Time-to-ETS Distribution

This is the final step in the projection algorithm for each

year. The TTE distribution is projected using the continuation

flows determined in steps 2 and 3 and user-supplied distributions

for initial term, reenlistment, and extension lengths. With

access to the initial term distribution, for example, the analyst

can project the future inventory effects of changing the mix of

accession terms.

Let yI through 'y be the proportions of nonprior service

accessions enlisting for terms of 2 through 6 years. Then, the

new TTE distribution for soldiers in the YOS 0-1 cell is simply given by

"4These attrition rates are defined as the proportion of

soldiers starting a 3-month service interval who have left by the

end of the interval.

20
3' 0

(17)

dz',,k, tfor n> o

That is, the proportion of soldiers who will be one year away from ETS in the next projection year is the proportion of twoyear nonprior service accessions, and so on.

Let 71 and 72 be the proportions of extensions for 1 and 2

years. Then, the values of d0 and dI for soldiers in YOS

categories 1-2 through 29-30+ are given by

dot (CL + - ) / u (18)

-ik (c!,,I + 2Xk + '4C) / Efkt

That is, next year's at-ETS population includes soldiers one year

away from ETS in the current projection year who continue, C',

and soldiers at ETS in the current projection year who extend for

one year, EXO. The proportion at ETS is the number in these

categories divided by the continuing force inventory.A Both 2-

year extensions for those at ETS in the current projection year

and 1-year extensions for those one year away from ETS currently will result in being one year away from ETS in the next

projection year.

Reenlistments and prior service accessions enter the

calculations for those two years away from ETS in the next

projection year. Let v3 through 76 be the proportions of

reenlistments for 3 through 6 years. Dropping the subscripts, the formula for d2 for soldiers in YOS categories 1-2 through 29-

30+ is

d2 -[C3 + ÷2EX + ?X 2 + Z3(R0

o4AP)] / Rc (19)

Note that we assume that prior service accessions have a time-toETS distribution similar to reenlistments, not initial

enlistments.

The equations for the remaining TTE categories are

"Forced losses are not explicitly used in calculating the

new TTE distribution. This is equivalent to assuming that these

losses are drawn proportionately from the TTE distribution.

21
d3 -1C 4 + 49E2+ TX + : 4 (RO.Aps) + 'C3 R1 ] / SC

d4 -[C5 + * V2*X3 + * ' + XS(R÷OA") + X * + ÷XR 2] / EC

(20)

d s - [-EV +4 + 2T+,2)Ms X,(R° +A ) +( X..)R- + (L J)R (2))

+ R3 + R +R 5 1] /C

Note that we constrain the maximum WE to be 5 years. Because

there are very few soldiers who, more than 2 years away from

their ETS, extend their ETS date by more than 3 years, this

simplification will not introduce significant errors into the TWE

projections.

Inventory Module Inputs and Outputs

Inputs to the inventory module fall into two categories:

scenario assumptions and baseline data.

22
Table 1

Inventory Projection Scenario

I Ipecified y

Cowgetion/macroeco=omic scenario (Sec 3) Projection year

Strength Constraints

0 Uaseline inventory" Grade, subinventory, YOS

* Initial time-to-3TB distribution"G YOS

* Requirements/Endstrength Projection year, grade

e Accession distribution Projection year, subinv

* Quarterly timing of NPS accessions/losses Projection year

Promotion Parameters

"* Minimum promotion rates Projection year, grade "* Promotion rate adjustment factors Projection year, grade

"* Primary/secondary zones Grade

* Ratio of secondary to primary zone promotions Grade

PS Accessions

"* Number Projection year "* Grade distribution

" Subinventory distribution ,,

Retention Rates/Adjustment Factors

"* Reenlistment rates Year, YOS, subinventory "• Extension rates Year, YOS, subinventory "* Non-ETS continuation rates Year, YOS, subinventory

Involuntary Losses

"* Retention control points (RCPs) Projection year, grade "* QhP losses Projection year, grade

"* Distribution of QMP losses Grade, YOS

Distribution of Term Lengths

"* Initial term lengths Projection year, subinv

"* Reenlistment term lengths Projection year

Sxtension term lengths Projection year

Table 1, above, summarizes the scenario assumptions we have

discussed in this section. When the inventory module is

activated, these assumptions are set at default values calculated

from baseline data. However, all of these assumptions can be

modified by the analyst using a series of menu-driven screens,

and the modifications stored as a new scenario. The baseline

data requirements for the inventory projection module are

described in Appendix B.

Output from the inventory module is available at two levels

of detail. The summary level output provides the user with key

l6User does not have access to starting inventories.

23
categories of output dimensioned by projection year or projection

year and grade. The next level of detail provides the user with

a complete set of output for all categories of data by

subinventory, grade, and YOS. The breakout of data that is

available is summarized in Table 2.

In addition to the output files described in Table 2, the

model will generate files that can be imported to a standard

spreadsheet program. The "Report Generator" function will parse

the output data with delimiters and, for the mid- and detailed

level, will break the single output files into separate files for

each category.

24
Table 2

Inventory Module Output

Category Level of Detail

mlIImSwummary Suammiary by Subinv

md strength rade x PY YOS and grade totals

Total LoSS" YOS and grade totals

Normal Losses -grade x VY YOS and grade totals

RC Losses Y, YOS and grade totals

Forced Looses grade x PY YOS and grade totals

OW Losses o grade x Y i YO and grade totals

YPS Attrition Losses grade x PY ,_Total

Total Accessions PY

NPS Accessions PY Total

PS Accessicns ,Y YOS and grade totals

Total Reenlistments grade x PY YOS totals

Total Initial Reenlistuents _y

Total Mid-term Reenlistments VY

Total Career Reenlistments _Y

ITS Reenlistments grade x PY YOS totals

XTS Initial Reenlistments _y

XTS Kid-term Reenlistments Py

T8 Career Reenlistments _y

Non-ITS Reenlistments grade x Vy YOS totals

Ncn-ITS Initial Reenlistuents _y

Non-ITS Mid-term Reenlistments _y

MomU-IT Career Reenlistuentm _Y

Extensions YOi totals

Promotions grade xPr

Percent of Mistorical Promotion Rate' grade x _Y

Percent minority" grade x VY

Percent Cat I-IIA'7 grade x VY

17

Percentages can be easily tailored to user's needs

25
COMPENSATION-REENLISTMENT MODULE

The compensation-reenlistment module uses the analyst's

assumptions about military compensation and macroeconomic

conditions over the projection period to adjust base year

reenlistment rates for changes in these factors. The adjusted

rates are then used in the inventory projection to age the force.

By establishing a link between military compensation and

reenlistment rates, this module allows the analyst to address the

following types of issues:

1. What are the inventory and manpower cost implications of

proposed pay raise and allowance changes? If military pay is

projected to decline relative to the civilian sector, for

example, how much will voluntary losses increase? What are the

added costs of maintaining a given endstrength in this

environment, including increased accessions and training?

2. What are the likely effects of changes in unemployment

and civilian wage inflation on the inventory? How will losses

change and what costs must be incurred to achieve endstrength

targets? How will the composition of the inventory change across

demographic and quality dimensions?

3. What are the likely effects of a proposed temporary

separation incentive? What additional losses will be realized

and how will this effect the composition of the enlisted force?

4. What is the appropriate mix of compensation elements in

the military pay and benefits package? How would increasing

basic pay but reducing retirement benefits, for example, affect

the career content of the enlisted force?

Issues like these arise annually in the budget planning process

and sporadically as particular portions of the military

compensation package are reassessed in study groups like the

Quadrennial Review of Military Compensation (QRMC). Without the

compensation-reenlistment module, they can only be evaluated

using ad hoc adjustments to the baseline reenlistment rates.

Figure 3 provides an overview of the compensationreenlistment module. User-defined assumptions about compensation

policies and macroeconomic factors are the primary inputs to the

module. The outputs are reenlistment rate adjustment factors by projection year, YOS, and sub-inventory.

As in any modeling effort, the accuracy of the projections

under different compensation scenarios is only as good as the

quality of the compensation-reenlistment link. Our methodology,

derived from the Annualized Cost of Leaving (ACOL) model of

reenlistment behavior, has a sound theoretical foundation and a

successful track record in similar policy applications. The

specific implementation of the methodology is guided by the

findings from the Army Compensation Models Project (ACOMP). In

27
* INNAIOR

Figure 3. Compensation-Retention Module Schematic

this project compensation-reenlistment models were estimated and

tested for selected cM8.

This chapter describes the compensation-reenlistment link.

The first part of this chapter describes the adjustment equations used to modify the reenlistment rates. The next section

describes the variables used in the adjustment equations and

outlines how they are obtained. In the final part of this

chapter we detail how to estimate the key parameters of the

adjustment equations.

Adjustment Equations Modify the Reenlistment Rates

Let rLk be the base-year reenlistment rate in year of

service (YOS) i and subinventory k. The adjusted reenlistment

rate for projection year t is given by

r1k - 1

where 4• = Z•+aNACOL•-AcOL4)+(UNe -UN°) (21)

z4k = ind PThe superscript t indicates projection year (0 is the base year), the ACOL's are annualized cost of leaving variables calculated

from user assumptions about military/civilian compensation and

projected promotion patterns, the UN's are user-supplied projections of unemployment, and the cr's are parameters.

28

0 am pow
To reduce computation time, we calculate ACOLs only by year

of service and fiscal year. That is, the same ACOL changes are

used to adjust reenlistment rates for all subinventories. Even

with the same ACOL changes, the difference between adjusted and

base year reenlistment rates will vary across subinventories for

two reasons. First, different a's are used for high quality and

other subinventories. Second, the adjustment produced by

equation (21) depends on the level of the base year rate, which

varies across subinventories.

Variables in the Adjustment Equations

For the base year and each projection year, the adjustment

equation requires a vector of ACOLs by YOS and an unemployment

rate. The base-year values can be calculated once and stored;

the projection-year values depend on user-supplied assumptions

and the results of the inventory projection.

Consider the ACOLs first. They are defined as

1+8

(Wnt- ~n +on d-i+ (d RP., -RI) - Sl2

ACOLZ = max, 8 + (22)

where

" a is career length. Career length runs from 1 to 30-

i, in increments of one year. For each year of

service, ACOLs must be calculated for all potential

career lengths and the maximum ACOL value chosen.

"* WM. is expected annual military compensation. It is

calculated for each year of service as

t 1 9

WKI 3.d [BPn(1 +0. 25SRBIneETSfle)+ALjJPnj (23)

where BP is basic pay in year t for grade j and YOS n,

SRB, is die average SRB multiplier for YOS n, ETSn is the

proportion of soldiers at ETS in YOS n, ALI is the sum of

allowances for grade j in year t, pt is an inflation index

for projection year t (base year index equals 1), and p, the proportion of soldiers with YOS n who are in grade j.

Basic pay and allowances are derived from the base-year

pay and allowance tables, adjusted by the appropriate

pay and allowance increases assumed by the user. SRB

payments are estimated using the average multiplier (including zero for MOSs without a bonus), the

proportion of soldiers at ETS, and an assumed three-year

29
reenlistment term. The p's are generated from usersupplied assumptions about inflation rates in the

projection years. The p's are calculated from the total

enlisted inventory projected for the end of the previous

year.

Basing expected military compensation on projected grade

distributions goes part of the way to closing the

promotion-pay loop discussed in the design paper. If

promotions slow down, for example, the cost of leaving,

and reenlistment rates, will fall because expected

military pay is lower. This interaction between the

inventory and compensation-reenlistment models is an

improvement over the initial approach, but it does mean

that the compensation-reenlistment module must be

exercised at the beginning of each projection year.

* WC, is expected annual civilian compensation. It is

calculated from an earnings function with the form

WCe = exp(P0+ 1i+P2i (24)

where wt is an index of civilian wage inflation in

projection year t relative to the base year."' The

parameters will be supplied from ACOMP research results.

* 0, is other compensation. This vector of inputs

allows the user to model the reenlistment rate

effects of new military pays (positive values) or

monetary incentives to leave (negative values).

* d is a real discount factor. This should be a

variable in the code, although it does not need to be

accessible to the user. Initially assume a 10%

discount rate, which means that d should equal

1/(1.1).

* Rj., is the annual value of retirement pay for a

soldier retiring with i+s years of service. There

are three formulas for retirement pay depending on

"

1 8

Equations (23) and (24) use wage and price inflation factors

to express both WM and WC in base-year dollars.

30
the soldier's accession year

I. = BPI.S""

I. Rt .025(i+s) E dj-I

BP+, .92PT+ 1 d97P 1

where BP43 = B3s+ "952B•'-I+"907BPits'2 3

III. R1+, [.025(i+s• dB4-i -. O(30-i-I F dn-i

SP= /Jn-Tel 1 P /n-i÷s÷l

(25)

Under all three formulas, retirement pay is positive only

if years of service at retirement, i+s, is greater than or

equal to 20. This means that the two values of R in

equation (22) only need to be calculated for decisions at

YOS 20 and greater. 19

Formula I applies to soldiers who entered before FY81.

They receive 2.5% of their highest-year basic pay -- we

assume that is the last year -- from the year following separation until death, which we assume occurs at age

75.20 Formula II, which bases retirement pay on the

high-three average of basic pay, applies to soldiers

enlisting between FY81 and FY86. 21 Formula III, which

cuts retirement pay rates from retirement through age 62

(or YOS 44), is for soldiers entering after FY86. In

all cases, basic pay is deflated by the price index to

measure retirement in the same year dollars as the other

"The discounting factors in equation (25) can be more easily

calculated by combining present value and annuity formulas, as

follows:

dn'- 1 d- _1 I

where N is either 44 or 57.

20

Assuming accession at age 18, the imputed YOS at age 75 is

57.

21It is nominal, rather than real, pay which counts in this

calculation. The real values of BP for the preceding two years

must, therefore, be deflated. We assume a 5% pay raise in equation

(25).

31
compensation elements.

Note that because these formulas are tied to accession

cohorts, the appropriate formula to use in calculating retirement pay for decisions at a given year of service

depends on the projection year. As the projection

proceeds, more years of service will fall under the

newer, and less generous, retirement systems, causing

reenlistment rates to fall ceteris paribus. This is an

important application of the compensation-reenlistment link.

o SIi is the annual value of a separation incentive

offered in YOS i. It is multiplied by a factor

that represents the proportion of soldiers eligible for the incentive in YOS i and MOS k. SI• is

calculated with the equation

S = multli)(o t (r) I Ed

where mult(i) is the product of a user supplied

multiplier times the number of years served at the

time of separation, i. The next term calculates

the value of the soldiers average base pay over the

last m years of service. The last term discounts

the value of annuities that will be paid to the

separated soldier over x(i) years to a present

value, where x is a user supplied multiplier.

Note that these calculations only apply to a single

separation program for a single year. In addition,

this algorithm takes into account the "lagged

effect" caused by soldiers being forced to make a

reenlistment decision early. With the increased

losses from nonETS cells, there will be a smaller

than normal inventory aging into the ETS cells and

thereby will effectively reduce reenlistments in

subsequent projection years.

The other variable in the adjustment equation, the

unemployment rate series, consists simply of a base-year value --

the national unemployment rate for 18-64 year olds -- and

assumptions about projection year values that are supplied by the

user.

Parameters of the Adjustment Equation

The a's in equation (21) are derived in the model from user32 -
supplied pay and unemployment elasticities. 2 This gives the

model an advantage in that the ACOL calculations no longer have

to mirror the ACOL calculations used in the econometric

estimation. The elasticities serve as a common metric for

translating ACOL coefficients based on one definition of the

annualized cost of leaving into ACOL coefficients consistent with

equation (22).

This solves two problems usually encountered in implementing

an ACOL-based compensation-retention link. First, making the

ACOL calculations in the projection model and the econometrics

match usually means ignoring some of the individual detail that

can be used in the econometric modeling. 23 When the ACOL

calculations don't have to be identical, the best econometric

results can be pursued. Second, the model is more flexible

because new research results on the reenlistment effects of

relative pay and unemployment changes can be incorporated into

EPICC without reprogramming the model.

Our method is to solve for the °L parameters that, using

equation (21), produce the percentage change in reenlistment

rates expected, given the assumed pay elasticities, with a 101

increase in basic pay and allowances. -This yields

a -e-ACOL II 4+ 1

(27)

where ACOL= (ACOL' -ACOL•)

41 = 0qPAY 0.lila

ACOL÷0 is the ACOL value that results when basic pay and

allowances are increased by 10%, and nPAY is the reenlistment pay

(28)

where UN; = (UN'0 UN0 )

51=0.lljnF

22For a more detailed discussion of how to apply these

elasticities, see Appendix D.

23Two examples where econometric estimation can be more

precise than is feasible in aggregate models are predicting

promotion points using individual-based promotion time models and

adjusting for time censoring through methods such as the ACOL-2

model.

33
elasticity. The formula for the &ý parameters is analogous.

In each of these equations the a's need only be recalculated

if (1) the elasticity assumptions are changed or (2) the base

year is updated. We have made initial estimates for both the pay

and unemployment elasticities using ACOMP and other research

results and provided them as default values in the model.

Separation Incentives in EPICC

In those situations when a separation incentive is in

effect, the adjusted retention rate is actually a blended rate

resulting from a weighted average of the "old" and "new" rate.

The "old" rate is the adjusted rate without the affect of the

separation incentive. The "new" rate is the adjusted retention

rate with the affect of the separation incentive. The blended

rates are calculated in the following way.

rnew = (1-e)rold + (e)r,, (29)

crew ` (1 -e) crO.d + (e)ri

where rold is the reenlistment rate with no incentive, r3i is the

reenlistment rate given a separation incentive, crOld is the

continuation rate with no incentive for soldiers not at ETS, and

e is the percentage of soldiers eligible for the separation

incentive.

Note we estimate continuation rates in the presence of a

separation incentive by blending existing continuation rates with

adjusted reenlistment rates. A separation incentive affects the

retention of nonETS soldiers in two ways. They receive

additional compensation for leaving, and they have the

opportunity to make a "reenlistment" decision prior to their ETS

(the same effect as an early out program).

Lifting the term commitment through a separation incentive

will also cause lagged effects on the reenlistments observed for

the affected cohorts in years after the program. NonETS soldiers

who are offered an incentive, but choose to stay, will likely

reenlist at higher rates when their ETS arrives. To model these

effects, we assume those who were eligible for the separation

incentive and stayed, will reenlist at the higher continuation

rate rather than the normal reenlistment rate.

Given this assumption, the reenlistment rate for ETS

soldiers in the year following their eligibility for a separation

incentive is calculated as

row= (e) Croid+ (l-e*) Rold

(30) = (e) r51 where e (e=.,(0

e (e) rzi + (l-e) croild

34
The term e* is the proportion of the remaining members of the

affected cohort that were eligible for the incentive. It will be

less than e because of the higher separation rate among the

eligibles. Because crold>rold, equation 30 increases the

reenlistment rate, as desired. We recalculate the reenlistment

rates of cohorts affected by a separation incentive program for 3

years after the program year.

Table 3 summarizes the various effects of a separation

incentive on soldier retention and shows which are incorporated

by the approach used in EPICC.

Table 3

Separation Incentive Effects in EPICC

Effects of Separation Incentive Modeled in EPICC

Program year effects on retention rates - Additional civilian pay yes - Term of service commitment lifted yes - Change in pay elasticity yes

Lagged effect on reenlistments - Lifting term commitment yes - Change in taste distribution no (small effect)

Reenlistment rate changes in anticipation of no (DRM and expectations

incentives model required)

Summary

Our design for this module has the following features:

1. A wide variety of military pay policies can be easily

modeled.

2. The methodology for linking compensation to reenlistment

is based on the ACOL model, the most widely used approach in

assessing the retention effects of alternative compensation

policies.

3. The research design for estimating the critical

compensation-retention parameters is based on findings from the

Army Compensation Models Project.

This completes the discussion of the compensation-reenlistment

module. The next chapter discusses the estimation of costs.

35
COST ESTIMATION MODULE

This module calculates the budget costs of the enlisted

inventories projected in the inventory module. Because the cost

estimation process is fully integrated with the inventory

projections, little additional user effort is required to obtain

cost information along with personnel counts. This adds an

important dimension to a personnel policy analysis model, as

different strategies for achieving a desired force structure can

be easily evaluated on the basis of their expected costs.

The cost estimation methodology in the EPICC model is

derived from the budget model in the Army Manpower Cost System (AMCOS). The chapter is divided into three parts. The first

part provides an overview of the cost estimation methodology used

in EPICC. Next, the chapter describes how each of the various

elements that are included in personnel costs, such as military

pay, recruiting costs, and PCS expenditures, are estimated.

Finally we summarize the cost information that is generated by

this module. Appendix B. provides a detailed discussion of the

cost methodologies, variable definitions, and data requirements.

EPICC Cost Estimation Methodology

The EPICC cost module estimates costs in a two-step process

as shown in Figure 4. First, cost factors representing all the

major personnel cost elements are calculated using baseline cost

data, cost equations, and user assumptions. These factors

measure the budget or flow costs associated with a particular

event, such as an accession or reenlistment, or associated with

maintaining a stock of soldiers over a period of time, such as

annual basic pay. The cost factors are stored in a structured

cost data base (SCDB).

In the second step of the EPICC cost module methodology, the

cost factors are applied against a personnel inventory. The

results are summed to provide a total cost estimate, as well as

costs disaggregated by major appropriation, grade, and cost

element.

One of the strengths of this approach is that the

assumptions underlying the calculation of many of the cost

factors can be changed to tailor cost estimates to the needs of a

particular analysis. For example, Permanent Change of Station

(PCS) costs depend, among other factors, on the number of

rotational moves and the number of such moves depends on policy variables such as the proportion of soldiers stationed OCONUS and

the average OCONUS tour length. Cost estimates based on simple

averages of historical PCS costs cannot reflect the cost effects

of changes in these variables. The cost factors are specified,

through the cost equations, as functions of important policy variables. When the user changes these policy variables, the

cost factors are modified appropriately.

37
•DINVENTORY

OREPROJECTION FORCE

DTMOULE OTU

COMPIENSATION MODULE..

AND

DETAILED

COST COST

DATA ESTIMATION SD

Figure 4. Diagram of the Cost Module Interface

In keeping with our goal of providing a flexible analysis

tool the design of the cost estimation module for the EPICC model

allows almost all of the underlying assumptions used in the cost

estimation equations to be modified by the user. Analysts can

always use the default assumptions to provide an easily-defined

common basis for force costing.

In the next section we describe the details of the cost

estimation process.

Estimating Budget Costs

This section is organized by the major cost elements. First

we describe the costing methodology for the six elements which

the user can modify. In each of these the user may adjust the

assumptions underlying the estimation of the cost factors. These

cost elements are basic pay and allowances, recruiting costs,

reenlistment costs, permanent change of station costs, training

costs, and separation costs. In the discussion for each of these

cost elements, we review the cost equations, noting the data

sources and the assumptions that can be changed by the analyst.

We also describe how the cost factors resulting from those

equations are applied against output from the inventory

projection module. The remaining cost factors, which cannot be

changed by the user, are discussed next. Finally, we describe

some additional cost estimation options available to the EPICC

user.

38
Basic Pay and Allowances

This cost element includes basic pay, quarters (BAQ) and

subsistence (BAS) allowances, and variable housing allowances

(VHA).

1. The cost factors for basic pay are defined by grade and

year of service. They are calculated simply by updating the

baseline annual pay table according to the growth rates in

military pay assumed by the analyst.

2. The cost factors for BAQ, BAS, and VRA are defined by

grade. First, the baseline annual allowance tables are increased

to reflect the growth in allowances assumed by the user. Then,

the table amounts are weighted by the proportion of soldiers with

and without dependents (BAQ) and the proportion of soldiers

receivinq housing allowances (BAQ, VHA).•

k ise these cost factors are defined on an annual basis,

they wi± be applied against the man years in a grade or gradeYOS cell for a projection year. Man years will be estimated in

the cost module using the beginning and ending inventories for a

projection year and the assumptions made by the analyst about the

quarterly timing of accessions, losses, and promotions.

Let El* be the inventory in year of service i, grade j, and

projection year t at the end of the ne quarter. It is given by

an

( .2)[ .25), (l C . q) L )

a J10

p (31)i A )~j

CO are the continuations (reenlistments + extensions + nonETS

continuations) in an inventory cell defined by year of service i,

grade J, and projection year t. L* are the losses (separations +

lateral losses) from the same cell. P* are the promotions out of

the cell. A* are the accessions (nonprior service + lateral

accessions) into the cell. Finally, q-, q;, and qf are the userspecified proportions of losses, promotions, and accessions

occurring in the e1 quarter.

Starting with last year's inventory in a particular cell, we

2 The default values for the dependents status and allowance

recipients proportions are defined by grade using baseline data.

The user, however, can change these values.

39
age one-fourth of the continuing force out of the cell (first

brackets) each quarter; take qL of the losses each quarter

(second brackets), age in one-fourth of the continuations from

the preceding year of service, adjusted for qp promotions into

and out of the cell (third brackets); and add qA accessions.

To obtain average man years, the quarterly inventories are

averaged as follows

4

+'J't-• + (32)

Nlit 5

where MY is man years. Although these calculations seem somewhat

complex, we believe the importance of pay and allowances in

personnel costs makes the effort to get a better estimate of man

years worthwhile.

Accession Costs

The recruiting cost function developed under the original

EPICC contract, and described in Appendix C, replaces the AMCOS

methodology for calculating accession costs in EPICC.

Implementation is discussed in two parts: the inputs to the cost

function and the cost/resource outputs.

n The analyst enters inputs organized into six

categories as follows:

1. Enlistment supply elasticities. The input screen

displays a default set of elasticities which, with the exception

of the constant, can be changed by the user. If any of the

elasticities are changed, EPICC will recalculate the constant to

assure that the enlistment supply function is still accurate for

FY92.

2. Quality tradeoff parameters. The recruiting cost screen

also allows the analyst to change the assumed tradeoff between

high quality and other recruits. EPICC will automatically

recalculate the underlying enlistment supply function parameters.

3. Resource prices and fixed recruiting costs. Base year

values for these prices can be changed in the recruiting cost

screen. To estimate projection year costs in then-year dollars,

EPICC inflates the recruiter price using the MPA inflation rate,

advertising using the OMA rate, and fixed recruiting costs using

an average of the MPA and OA rates.

4. Market factors. The unemployment and relative military

pay assumptions by projection year are the same as those used to

adjust reenlistment rates.

40
5. Contracts. The projected number of high, medium and low

quality contracts to be used in estimating recruiting costs are

generated by the inventory module.

To facilitate the evaluation of alternative supply elasticities, quality tradeoffs, and resource prices, a pop-up

screen accessed from the primary recruiting cost screen

duplicates the information in Table 2, showing the optimal

resource mix and costs associated with new parameters for FY92

for comparison with the actual results.

Oput, The cost function generates the following items for

each projection year in an EPICC run:

1. Total recruiting costs, by appropriation. Total costs

are given by the following equation.

CT = + AN4jII + C, (33)

These total costs are allocated by appropriation as follows:

- Advertising: OMA - Recruiter costs: MPA and OMA in proportion

to base year appropriation shares - Enlistment bonus: MPA

- Army College Fund: MPA - Fixed recruiting costs: Base year MPA/OMA

shares

2. Minimum-cost resource/incentive mix, including the

number of production recruiters, the amount of advertising, the

average enlistment bonus, and the average value for the ACF.

Reenlistments

The primary cost associated with reenlistments is the

Selective Reenlistment Bonus (SRB). The value of an SRB is

determined by the formula in equation 34. As the SRB award level

SRB - award level .monthly base pay .years of obligated service

(34)

is set by MOS and by years-of-service zones (corresponding to the

first through third reenlistment decisions), the average cost of

an SRB per reenlistment will vary by skill and YOS.

To calculate the average SRB payment for soldiers in a

particular YOS, we use the award levels specified by the analyst

in defining the compensation scenario, average monthly base pay (calculated from the pay tables and the grade distribution

projected from the inventory module), and the average reenlistment term assumed by the analyst in defining the

inventory projection scenario. The average SRB payment is

41
divided between current and future year costs using the lump sum/installment distribution specified for the compensation scenario. If the lump sum percentage is 50%, for example, half

of the SRB payment is applied against the number of reenlistments

projected by the inventory module for the current year in the

particular occupation and YOS. The remaining SRB payment divided

by the number of years in the reenlistment term (minus one) is

applied against projected reenlistments in the future years.

For any projection year and occupation, total SRB costs are

the sum of the lump sum and installment payments (from pervious

years) for all years of service.

Permanent Chanae of Station

To estimate PCS costs, we define cost factors by type of

move -- accession, separation, training, rotational, and

operational -- and grade. We outline the calculation of these

factors by type of move, noting how each is applied to the

inventory projection results.

Acces n. The cost factor for accession moves is the

average cost per accession move.Y We apply this factor against the number of accessions in a projection year.

S The cost factors for separation moves equal the

estimated average costs per separation move by grade. We use

weight allowances by grade to expand the all-Army average cost of

a separation move into a per-grade cost,

ACj A(WA4

where ACSEm is the Army average cost of a separation move, WAý is

the average weight allowance in grade j, and Sj and S are the

grade j and total baseline strengths, respectively.2

' The

expression in braces is an index formed by dividing the average weight allowance in grade j by the average weight allowance for

5 Per-move average costs, by type of move, are available

from ODCSPER.

26For equations 33, 34, and 35, we recognized that a better

estimate can be calculated based on the distribution of the

population appropriate for each equation; however, we did not

have access to this data by MOS.

42
the entire enlisted force." The cost factors for separation

moves are applied against the by-grade separations projected by

the inventory module.

ZriniL. The training move cost factors are defined as the

average cost of a training move by grade. They are calculated in

an analogous fashion to the separation move factors, so that

22M ACr" WAI

AC a -I (35)

WAI

where ACd" is the Army average cost for a training move.

Training cost factors will be applied to training events which,

as described below, will be estimated in the cost module by

summing the number of promotions in a projection year to grades

requiring additional training.

Rotational and Operational. These cost factors, unlike the

previous ones, are defined as the average cost of rotational and

operational moves per soldier in a particular grade. In

calculating CONUS and OCONUS moves the key assumption is that

operational moves are generated as a residual, after moves out of

CONUS fill the empty OCONUS positions and separations are

accounted for. This means that the average cost of a rotational

move can be expressed as

A =- AC'~' WA 0C [OC~l - cj)] - OC(Acc)) (6

where ACa°• is the Army average cost of a rotational move. As

before, the term in brackets adjusts theArmy average for

different weight allowances by grade. The final term in

parenthesis is the expected number of rotational moves per

soldier. The per capita moves required to move members from

overseas and to replace those departing overseas is given by two

times the proportion of members stationed overseas, 20C, divided

by the expected OCONUS tour length, TL¶, less the per capita

moves required to rotate members who will be separating from the

Army, the second term in brackets, less a percentage that

represents accession moves to OCONUS positions, OC(Acc), where

I The average weight allowance by grade is calculated using

the current weight allowances and the proportions of soldiers in

each grade who do and do not have dependents. Weight allowances

can be altered by the EPICC user. As described in the pay and

allowances section, the dependents status information will come

from the baseline year, unless it is modified by the user.

43
Acc is the percentage of the total force that are accessions.

The per capita moves value for those members whose OCONUS tour

has ended is achieved by multiplying the proportion of members

stationed oversees by the average continuation rate, c1, to avoid

double counting moves associated with separations.

The average cost of an operational move per member is then

calculated as

onf" .ACI o4....1! -OCk) [Ok-OAl-r.1 (I -OCk) (Acc))

WA S kk 3J

(37)

Where AC'I is the Army average cost of an operational move. The

second term, in brackets, is the expected value of making an

operational move, which equals the per capita moves required to

fill CONUS positions (the proportion of CONUS members divided by the average CONUS tour length, TV), less the number of positions that will be filled by members rotating back from OCONUS, the

second term in brackets, and less the proportion of those

accession moves made to CONUS positions . Both the rotational

and operational move cost factors will be applied against the

projected number of soldiers by grade.

Default values for the proportion of soldiers stationed

overseas and the average CONUS and OCONUS tour lengths derived

from baseline year data will be supplied with the model, but the

analyst can change these assumptions and thereby alter the

rotational and operational cost factors.

Training costs consist of all the variable costs of

individual training included in the following categories:

1. Recruit Training. An eight week introductory and combat

survival skill training course given to enlisted personnel upon their initial entry into military service. This category also

includes training to prior service personnel in need of refresher

training.

2. Initial Skill Training. Includes all formal training normally given immediately following recruit training and leading

to the award of a military occupational specialty (MOS) at the

lowest level.

3. One Station Unit Training (OSUT). Combines recruit

training and initial skill training for enlisted personnel in the

combat arms and certain combat skills into a single course.

Training is conducted at a single station under a single cadre.

4. Skill Progression Training, Specialized skill training

44
provided to enlisted members subsequent to initial skill

training. Through it the student gains the knowledge to perform

at a higher skill level or in a superior position.

5. Professional Training. Noncommissioned Officer

Education System training which is provided on an increasingly

selective basis to noncommissioned officers to prepare them to

perform increasingly complex tasks (e.g., PLDC, ANCOC, BNCOC,

USASMA).

Training cost factors are calculated using the average costs

per graduate for the various courses reported in ATRM-159 (TRADOC

courses) and in a similar cost report produced by the Army Health

Services Command for medical courses. These reports display

calculated course costs based on Instructor Contact hours,

student load, costs of supplies, ammo and the flying hour program

and indirect costs based on medical support, base support and

family housing.

Training costs are applied to the inventory in two ways.

The average initial training cost -- the sum of recruit training,

initial skill training, and OSUT -- will be applied to the total

number of accessions. The costs of advanced training will be

applied to the number of promotions into the grade for which the

training is required. The model uses the following relationship

to calculate training costs.

SAcjjc'SLjk

A;: SLik AC]~ SL~(38)

where A"Cr4 is the baseline average variable cost of training per

graduate from courses in MOS k and grade j. The variable SLA is

the student load for courses given in MOS k and grade j.

SeDaration Costs

Separation payments are made to a soldier upon separation

from the Aainy. There are three types of separation benefits that

service members may receive, depending upon their qualification.

These benefits are:

(1) Accrued Leave. Each service member that is separated

from the Army is entitled to receive payment for the amount of

unused leave she or he has accumulated.

(2) Involuntary Separatlon. Any member forced out,

regardless of when he or she entered the service, who has been on

active duty at least six years receives a one-time, lump-sum

payment. If a member is not qualified for retention -- e.g.,

QMP, overweight, past a RCP -- she or he may receive only a

partial payment. Those members separated for misconduct are not

45
eligible for separation pays.

(3) Voluntary Separation. The services are offering bonuses

to selected members with between 6 and 18 years of service as an

incentive to leave active duty voluntarily. The bonuses may be

offered to members who have more than six years active service as

of December 5, 1991. Members may choose between an annuity (VSI)

or a lump sum (SSB). This program is effective through FY95.

EPICC makes calculations for two types of costs applied to

these categories of separation - separation incentive costs and

other separation costs.

Separation Incentive Costs. To calculate the cost of

provieing separation benefits to members, we first calculate the

cost of each of the three types of payments. Either the payment

is a lump sum or it is an annuity. To calculate the cost of the

lump sum payment, regardless of the reason for separation, we use

the calculation

Pmt1 = i (zatelu"') (foss 1 .) (12BP1 j) (39)

where i equals a member's YOS, index c indicates the category of

separation (i.e., c - 1 indicates voluntary separation, c - 2

indicates involuntary separation with eligibility for full

benefits, and c - 3 indicates involuntary separation with only

partial payment authorized), rate, is the percentage of basic pay

used depending on the category of separation (ratelk" .15,

ratePW - .10, rate3hIv - .05, and rate,' - .025 for each YOS),

lossa is the number of losses experienced in category c by

members in YOS i. 12BPU is the annual basic pay for a member in

YOS i and grade j.

To estimate the net present value of providing an annuity to

eligible members voluntarily separating, we use the following

calculation:

"" ] i (rateha) ( 1 °ss) (12BP1 ,) (40) U +Z

where n is the year that the annuity is paid, minus the current

year, and r is the annual discount rate (.10).

The user has the choice of specifying an incentive program

with either a lump sum or an annuity. EPICC will only model one

program at a time. Depending on which type of payment is in

effect, EPICC calculates the total cost of separation incentives

by multiplying either the value for Pmt1 or Pmtlw by the

calculated number of Incentive Program "takers".

Other Senaration Pay. (Lump sum leave payments plus

46
severance/disability pay plus separation move). To determine the

cost of separation for all other service members, the following

calculations apply.

a. When a service member leaves the service, the member is

authorized to cash in any unused leave at the rate of basic pay

to which he or she is entitled at the time of separation. The

average cost of the lump sum leave payment is calculated by

multiplying average number of months leave accrued for each grade

by base pay by the probability of separation.

AC- =ACF.AM p. (41)

b. Some service members are also authorized severance pay

for disability retirement. The average cost of disability

severance is calculated by dividing the total severance pay by

the total number of all separatees by grade.

ACe Sev. (42)

A7-.tot J

c. Average cost for other separation pay is the sum of the

above costs.

S= -A + * AC&*W (43)

To calculate the total cost of other separation, the model

multiplies the above per capita cost by the total number of

losses by YOS as calculated by the model for each projection

year.

Other Costs

In addition to the cost elements described above the cost

data base will include the following cost elements:

1. Retired Pay Accrual provides the funds for DoD's

contribution to its military retirement fund under the provisions

of 10 USC 1466 of the FY 1984 Defense Authorization Act, P.L.

98-94. Under the accrual concept (effective in FY85) each

Service budgets for retired pay in the Military Personnel account

and transfers funds on a monthly basis to the Military Retirement

Trust fund from which payments are made to retirees. Per capita

retired pay accrual cost is determined by multiplying basic pay

by a fixed normal cost percentage rate obtained from the DoD

47
actuary. 2 s

2. Medical Benefits consists of all fixed and variable

nonpay costs that provide health care to the soldier and his

family. It includes the Civilian Health and Medical Program for

the Uniformed Services (CHAMPUS) and the care provided by the

military hospital system. Health care support costs are broken

into two pieces, the cost of CHAMPUS and the cost of care in the

military hospitals. CHAMPUS costs will vary as a function of

family size and age of dependents. Family size tends to vary

directly with grade. Average cost, then, is estimated by using

the total government cost for CHAMPUS (inpatient and outpatient

care) divided by total number of user beneficiaries (dependents

of active duty sponsor). This gives us average cost per

beneficiary and can be multiplied by the average family size per

grade to determine average CHAMPUS cost per grade. Military

health care support costs are a function of the size and number

of military hospitals and the medical force structure. These are

costs the Army would incur regardless. The model determines the

average cost per eligible person by dividing the total hospital

operating costs by the number of eligible persons. This is

multiplied by the average family size by grade to obtain a per

capita cost by grade.

3. Special Pays include hazardous duty, sea/foreign duty,

diving duty, overseas allowances, language proficiency pay,

family separation allowance, and special duty assignment pay. Special duty assignment pay is authorized only for a selected

population of enlisted members assigned to demanding and/or

duties with higher degree of responsibilities such as special

forces or recruiting assignments and overseas extensions. The

model will include the per capita average cost of special pays by grade and occupation.

4. Other Benefits consist of all fixed and variable costs

that provide miscellaneous benefits. It includes death

gratuities paid to beneficiaries of military personnel who die on

active duty, apprehension of deserters, unemployment compensation

paid to eligible ex-servicemen, survivor benefits paid to

spouses and children of deceased service members, family

separation allowance, clothing allowances, benefits provided

under the MWR program, and government contribution to social

security tax. Average cost of other benefits are determined by

23 This cost factor will be recalculated based on user input

for each of the variables listed in paragraph 3.2, Appendix A,

under retirement benefits; benefits accrual rate by YOS, type of

COLA, and number of years is included in the salary base.

"

2 In a downsizing environment, applying unemployment

compensation factors to manyears as opposed to losses will

ultimately underestimate unemployment costs; however, the effect

will not be seen for several projection periods.

48
dividing their total cost in the baseline year by the total

number of soldiers in the inventory in the same year.

All of the cost factors associated with the Other Costs

category are percapita costs that will vary only according to

changes in manyears and adjustments for any inflation. All of

the cost factors described above will be applied to the projected

inventories calculated by the inventory projection module.

Other Features of the Cost Estimation Process

The EPICC model provides the user with two additional

features for limited modification of the cost factor data base.

The user may select/deselect each of the cost elements so that an

analysis may focus on a specific cost element or group of cost

elements. Second, the user has the option of specifying

inflation rates that vary by budget appropriation and projection

year. Positive inflation rate assumptions will provide budget

costs in then-year dollars for each of the projection years.

Table 4 summarizes all the cost factor assumptions the user

may modify by dimension.

49
Table 4.

User Accessible EPICC Cost Module Variables

Cost Element Variables Dimensions

Military - Base Pay gradexYOSxproject yr(PY) Compensation - BAQ/VWA gradexPY - BAS gradexPY - % w/dependents gradexPY - % getting BAQ-4n-cash gradexPY

Retirement - Multiplier for 20 YOS - Multiplier for 30 YOS - Multiplier for age 62 - No. years in base - Non-pecuniary benefit - Portion of COLA used -Entry year_____________

PCS - Weight Allowance gradexdepndt status - Avg cost PCS move move category - OCONUS tour length - % OCONUS - CONUS tour length

SRB - Bonus multiplier zonexMOSxPY

Recruiting - Resource prices for: -- Recruiters -- Advertising

-- Avg MEPS cost - Fixed Cost - Elasticities for: -- Recruiters -- Advertising -- Enlistment Bonus

-- Education Benefits -- Unemployment -- Rel Military Pay - Recruiter tradeoffs

Separation Incentive - Designation as lump sum

or annuity - No. years of annuity - Non-pecuniary benefit - Projection year - Separation eligibility MOSxYOS - Separation elasticities YOSxPY

Cost Module Output

The cost estimation module will store the cost factors in a

structured cost data base. The user will be able to view the

detailed cost factors in the data base before applying the

factors to the inventory projections. If the user wishes to

change the assumptions underlying the cost factors, he or she

will rerun the appropriate cost equations, generating a new

structured cost data base.

50
Summary costs are obtained by applying the cost factors to

the projection results. These costs will include a total

enlisted force cost by projection year, plus total costs

disaggregated by grade, cost element, and budget appropriation.

Summary

The EPICC cost estimation module gives the personnel analyst

the significant added capability of understanding the budget as

well as inventory implications of alternative personnel policies.

This module is based on the budget model in the Army Manpower Cost System, with modifications that capitalize on the detailed

inventory data available in EPICC to provide better budget

estimates. The cost estimation methodology we have specified

has the following features:

1. Cost factors for most of the significant cost elements

are determined by modeling the Army's personnel system, rather

than simply averaging last year's costs. This allows the user to

adjust the cost factors for policy changes.

2. In addition to a bottom line, the cost estimation module

will provide costs disaggregated by major cost element and

appropriation, aiding the analyst in understanding why a given

policy has its particular cost implications.

3. Because of the similarity between the EPICC cost

estimation module and AMCOS, updates of cost data and

improvements to the AMCOS policy modules can be incorporated into

EPICC with little modification. The similarity also means that

the extensive AMCOS user community will be able to easily understand and utilize the cost estimation functions in the EPICC

model.

The next chapter describes the technical requirements for

the model.

51
TECHNICAL REQUIREMENTS

EPICC is a user-friendly, high speed computer model

requiring moderately sized hardware with no special modifications. The model will run on the equipment currently available to the Army DCSPER Staff. This chapter discusses the

model's processing requirements, hardware requirements, and the

user's interface.

Data Processing Requirements

We have built EPICC around a set of data structures that

allocate the computer's memory for storage of data elements.

These data elements include user inputs, other inputs, intermediate results, and outputs. The dimensions of these data

elements vary, but most are dimensioned by SUBINVENTORY(25),

YOS(31), and GRADE(S), for a total of 6200 cells per element.

Overall, EPICC uses about 40,000 cells or 160 kilobytes (k)

of computer memory to store data. EPICC's programming code and

executive "shell" (windows and menus) consume an additional 250k.

The entire EPICC system then, requires about 410k. The DOS

operating system allows access to a maximum of 640k of memory, of

which about 100k is usually used by DOS itself and other

programs. This leaves about 540k available for running applications like EPICC. Because EPICC currently requires 410k, it fits well within the memory normally available through DOS on

an IBM PC. However, the use of any memory resident software

could degrade the performance of the model.

Hardware Requirements

The EPICC model requires the following minimum configuration

to run efficiently:

1. An IBM compatible PC with at least 640k bytes of RAM;

2. A math co-processor; 3. A large hard disk (at least 20mb of unused, available

space).

In addition, we recommend that for each office using the

EPICC model, a single machine be dedicated to the EPICC project. This configuration allows each office to make multiple runs of

the model and still retain the output on the PC. A large hard

disk is required to store the model's large amount of output which is written to ASCII files as opposed to binary files. The

ASCII format allows the user to easily import the output files to

a spreadsheet or graphic's package for further analysis.

User Interface

We have incorporated a number of features in the EPICC model

to make it very user-friendly. The model gives the user a

completely self-contained analytical tool. It features a menubased operation, a default set of scenario assumptions, a

53
scenario editing capability, automatic file maintenance, and a

set of on-line help screens. Each are further discussed below

and a full discussion is included in the EPICC User's Manual.

Menu Based Operation

The user is able to

operate the EPICC model through

a system of menus combined with

the extensive use of function

keys. For example, through

these menus the user is able to

specify scenarios, choose a am

calculation options, and select

output formats. By making use R ", b

of function keys the user will

be able to initiate common

functions with the stroke of a

single key.

The menus are set up so

that the user can define a run Figure 5. EPICC Main Menu

scenario for the whole model

and then operate either the

inventory projection module,

the cost module, or both (see

Figure 5). When the user

selects the option to define

the run scenario, he/she will

be guided through data entry.

The user will be able to input

data for inventory projection,

the compensation-retention link, or cost estimation (see

Figure 6). Each of these menu no* *b Ib.

items leads the user to

additional screens that contain

the full set of data files.

Default Scenario Assumotions .. Figure 6. Define Scenario Main

EPICC is a complex Menu

personnel projection,

compensation and cost model with the flexibility to vary just

about any underlying variable. As a result of this flexibility,

there are a large number of screens that contain the scenario

assumptions for a given run. To simplify the initial data input

to these screens, the model comes with a complete set of default

assumptions based on historical data. In most cases the analyst

will only have to change the small number of assumptions that

apply to the issue being evaluated. To make those changes the

user simply has to call up the appropriate screen and edit the

default data. An example of the default reenlistment rates is

shown in Figure 7.

54
Scenario Editing

As we have already

pointed out, the flexibility

of the EPICC model requires a

large volume of underlying M &M V.Ma UMnO 9M---

data that the user might want U, awmI _madooffe

to edit for any given aim SMo..

scenario. In some cases the A LIMam o.l.m. Id. 6A1

user may need to replace ma. i,

large pieces of the default - m ,am .

data. To reduce obvious -HM. MU-M-SM Sin

input errors normally MUM ,L= a.s'I.

associated with inputting U•,UVS •M• m

large volumes of data, the ,., nb M .mOf .

user interface will check

assumptions on entry and, if

necessary, will prompt the Figure 7. Default Reenlistment

user for a correction. Rates

If the user changes any assumptions that require a change

elsewhere in the data, the user interface will prompt the user

for the additional entry. We have also structured the scenario

screens according to which module they are predominately tied to.

For example, pay and allowances assumptions feed both the

compensation-reenlistment module and the cost estimation module,

but they are primarily tied to the compensation-reenlistment

module and are accessed through the "Compensation Data" menu

item.

Automatic File Manacement

In many cases a change to data in one part of the model will

trigger a recalculation in another part of the model. To ensure

that these recalculations are done, the storage and retrieval of

all data and results files will be automatic and invisible to the

user. For example, when the user inputs changes to the baseline

pay tables, the model will automatically update the costs ad the

retention rates.

On-line HeIm Screens

To provide the user with easily accessible help, EPICC will

contain imbedded documentation to help the user during operation

of the model. The help screens are designed to provide the user

with a discussion of the part of the model being used at the

time. For example, if the user is modifying reenlistment rates,

the F1 key will provide a pop-up screen with a complete

discussion on reenlistment rates, how they are applied in the

model, and what impact a change might have. If this discussion

does not answer the problem, an SRA phone number will also be

provided. This set of on-line helps compliment the written

documentation (user's manual) that will be provided with the

model.

55
The next chapter discusses the validation of the inventory

projection and cost estimation capabilities of EPICC.

56
MODEL VALIDATION

We validated both the inventory projection and cost

estimation capabilities of the EPICC model by performing an out

of sample prediction for FY93. Inventory and cost estimations

were made using ex post information for the input variables so

that validation was able to focus on the estimation methodology.

We did not want to confound the estimation problems with

difficulties in estimating values of what are essentially

covariates.

Our approach to validating EPICC inventory and cost

estimating methodologies entailed comparing EPICC inventory

predictions for FY93 with the FY93 actual values obtained from

the September 1993 Final Update run of ELIM-COMPLIP (Alternative

Number E930950P). The predicted costs from EPICC were compared

to the FY93 column of the FY94 President's Budget.

Assumptions

The following paragraphs present the assumptions we used to

validate EPICC. They are grouped into assumptions about

inventory projection, the economy, recruiting, and separations.

Inventory Projection Assumptions

The following assumptions were made regarding personnel

policies and selected gains and losses.

QMP Losses for FY93 equal 1,440 and the Army expects no

forced losses

EPICC has no category for soldiers who are returned to

military control (RTMC) and reserve component (RC)

accessions; therefore, the model adds 1,437 (RTMC) and

159 (RC) to the 7,732 PS accessions and treats the

total as PS accessions

Retention Control Points (RCPs) are as stated in

Chapter 4, AR 600-200; however, EPICC does not model

retention of soldiers in a promotable status

Promotion rates are not constrained to a minimum

PCS tour lengths for CONUS are assummed to be 3.2 years

and OCONUS is assummed to be 1.9 years with 1/3 of the

force in OCONUS

Economic Assumptions

The following table reflects the economic environment for

FY93.

Civilian pay will increase by 2.4t in FY93

57
* Unemployment is assummed to be 6.7%

* Inflation applied to all appropriations is 2.4%

* The average personal discount rate is 10%

0 Consumer price index growth is 2.4%

Recruiting Assumptions

The recruiting module in EPPIC is separate from the other

AMCOS output and estimates recruiting costs based on the

following assumptions.

• The recruiting cost function describes the minimum

costs associated with achieving a given recruiting

mission specified by quality level. It is based on the

actual recruiting experience of FY90 which is described

by the following parameters:

- High Quality Accessions were 63,000; Medium Quality

Accessions were 1,100; and Low Quality Accessions were

25,200. (These were number of contracts)

- "Foxhole" recruiters used were 5,700

- Cost of advertising was $55.6M

- The average enlisted bonus was $935

- The average value of educational benefits was $272

- The fraction of contracts that were DEP losses (i.e.,

they were not accessions) is 0.15

We also assummed the following supply elasticities

- Recruiters is 0.25

- Advertising is .05

- EB is 0.07

- Ed Benefits (vis-a-vis the accrual value) is 0.03

- Low Quality tradeoff is 1 to 6

- Med Quality tradeoff is 1 to 2

- Relative military pay is .80

- Unemployment is .70

58
SeDaration Assumptions

We assummed that a separation incentive policy would be in

effect in FY93. The program is assummed to be a single VSI/SSB

program and is modeled in EPICC as an SSB policy (most takers of

the separation incentive have chosen the SSB). The following

assumptions apply:

The eligible populations are in YOS 6-17 for the

following MOS: 12C, 14D, 16D, 16E, 23R, 24H, 24K, 24N,

24R, 25L, 27B, 27F, 27G, 27H, 27J, 27K, 29J, 29N, 31C,

31M, 31N, 31Y, 39D, 42C, 55G, 63B, 67N, 74C, 74D, 74F,

91M, 97E, 98G

To account for eligibles by grade we further refined

the YOS dimension by using the following grade

surrogates

30

- E-5s are assumed to match up with YOS 6-12

- E-6s are assumed to match up with YOS 10-20

- E-7s are assumed to match up with YOS 14-20 (after

20 YOS, losses are counted as retirements)

The lump sum payment is calculated as 0.15*YOS*Base Pay

We assumed a value of $1500 for non-monetary benefits

(e.g., three months worth of medical, PX, commissary)

Validation Results

The model was run using the above stated assumptions and the

output was then aligned with the FY93 actuals. As can be seen in

Table 5, the EPICC reenlistment rates are accurately predicting

reenlistments.

30The software has since been modified to accept a grade

dimension from the user.

59
Table 5

ELIM-COMPLIP FY93 Actual Losses and EPICC FY93 Projected Losses

ELIM-COMPLIP (FY93 actuals) EPICC (FY93 projected)

Immed Reenl 73,906 Reenlistments 71,935

Retirements 12,608 Normal Losses 6,876

Early >20 YOS Retire 256 SERBs 0 ETS Losses 43,312 Normal Losses 73,249

<20 YOS

Adverse Losses 20,981 RCPs 1,092

Other Losses 33,077 RIFs 0

(VSI/SSB Takers) 4,755 QMPs 1,440

NPS Attrition 8,194

(SSB Takers) 4,807

Since the ETS losses are a complement of the reenlistment rate,

we can safely assume that the ETS losses are being accurately

predicted as well (EPICC includes ETS Losses in the total for

Normal Losses). The separation incentive module is also

accurately predicting the number of VSI/SSB takers.

NonETS losses are predicted with less accuracy. The model

is predicting about 50% of the actual numbers of retirements,

which we believe is due to the overall impact of the downsizing

on losses in general. It is also underestimating adverse losses

due to the same thing. Because of the turbulence being

experienced by the Army during these past few years, more than

the expected number of personnel are retiring. If soldiers are

not eligible for retirement, they are using other means to be

honorably released from the Service. Note the large number of

losses in the "other" category from ELIM-COMPLIP. This category

of losses includes all the administrative losses such as

compassionate discharges, failure to meet Army weight standards,

and separation for convenience of the government. With the model

underestimating losses in general, it follows that the estimated

value for NPS attrition will be low as well. However, that

number will increase if the number of retirements and nonETS

losses were to be increased.

Predicted gains are compared to actuals in Table 6. PS

accessions match exactly because they are a direct user input.

The NPS accessions are underestimated, but that is because

overall losses are underestimated. With increased losses to

match the actuals, EPICC will predict the appropriate number of

accessions. (In fact, we reran the model with retirements and

nonETS losses increased to compare favorably with actuals, and

the number of NPS accessions equaled 70,000).

60
Tables 6

ELIM-COMPLIP FY93 Actual Gains and EPICC FY93 Predicted Gains

ELIM-COMPLIP (FY93 actuals) EPICC (FY93 predicted)

Immediate Reenl 73,906 Reenlistments 71,935

NPS Accessions 70,080 NIPS Accessions 5,6

PS Accessions 7,732 PS Accessions 9,328

RTMC 1,437

from RC 159

Finally we compare predicted costs with FY93 estimated costs

as contained in the FY94 President's Budget. 3 1 As can be seen

in Table 7 below, the estimates are reasonably close. In Table 8

we focus on recruiting costs using data from USAREC. Because the

Army maintains a minimum level endstrength of recruiters in

anticipation of surges and because EPICC costs out optimally

allocated recruiting resources (see Appendix C), the number of

recruiters estimated by EPICC is relatively low while the

estimated use and cost of bonuses, educational benefits, and

advertising are relatively high. These differences offset each

other and we find that the total cost estimate of the program is

close to USAREC's figure, as is the estimated number of

3'This validation was conducted in late November 1993 and

FY93 actual costs were not available at that time.

61
Table 7

Comparison of the FY94 President's Budget (FY93 Costs, $000) with

EPICC Predicted Costs

FY94 PB EPICC t Difference

Basic Pay 7,944 7,979 .44%

Retired Pay 2,892 2,904 .41%

BAQ/VHA 1,206 1,008 -16.42%

BAS 778 772 -. 77%

SRBs 65 80 23.08%

PCS 790 789 -. 13%

Special Pays 568 525 -7.57%

Other 1,364 1,142 -16.28%

VSI/SSB 262 217 -17.18%

Table 8

Comparison of FY93 Actual Costs for Recruiting with EPICC Predicted

Costs ($M)

FY93 Actuals 31 EPICC Predicted

Number of Recruiters 4700 2723

Total Enlisted Bonus 11.5 21

Total Educational Benefits 8.6 22

Advertising 32 15

Number of Contracts 80300 81484

Total Cost 512 484

The next chapter discusses our conclusions.

3 2

Source: U.S. Army Recruiting Command.

62
CONCLUSIONS

Single Integrated Tool for Personnel Policy Analysis

EPICC assists Army personnel planners in their assessment of

the cost and inventory implications of the alternative Army-wide

policies that may be under consideration. It is the ideal tool

for this purpose because it is composed of three modules that do

the following:

1. Inventory Droiection module. The inventory projection module predicts how the inventory of the Army will change over

time as individuals enter and leave the force under different

Army-wide personnel policy scenarios. The inventory model also

predicts losses, determines accession requirements, and

identifies changes in the composition of the enlisted force.

2. Cost estimation module. Any change in personnel

policies has cost as well as inventory implications. The cost

estimation module determines the budget cost of a particular

inventory by applying appropriate cost factors to the stocks and

flows associated with the inventory.

3. Compensation-retention module. Changes in military compensation affect reenlistment rates, which are the key input

in assessing the year-to-year losses from an inventory. The

compensation-retention module provides the quantitative link

between compensation policy changes and reenlistment rates while

controlling for differences between demographic groups.

EPICC provides the Army for the first time, a single model

in which inventory, cost estimation, and compensation-retention modules are linked. This advantage significantly improves decision-making since the analysis of multi-dimensional issues

often requires the interaction of the three activities described

above. Therefore, the integration of these three personnel analysis tools in EPICC facilitates the complete evaluation of

policy alternatives by eliminating the often difficult task of

working with three different, and sometimes inconsistent, models.

A Valuable Training Tool

EPICC can be run quickly and easily. This lends itself to

using the model as a training device for all new personnel policy

analysts being assigned to the ODCSPER staff. New analysts will

be able to learn to operate EPICC easily. Then, by running several scenarios, an analyst can quickly learn how various

policy parameters impact on the enlisted force. We believe that

EPICC will facilitate the process of learning the Army's personnel system. In this way the model will fill a definite

need on the Army staff.

63
REFERENCES

Eichers, D. (1994, January). EPICC technical documentation.

(Contract MDA903-92-D0021, D.O. 0004). Arlington, VA:

Systems Research and Applications Corporation.

Eichers, D., Sola, M., & McLernan, G. (1994, January). EPICC

user's manual. (Contract MDA903-92-D0021, D.O. 0004).

Arlington, VA: Systems Research and Applications Corporation.

Fifth Quadrennial Review of Military Compensation, Executive

Summary. (1984, January). Department of the Defense, Office

of the Secretary of Defense.

Hogan, P. F., Black, M., Hunter, R. W., Rose, D. E., &

Zuckerberg, J. A. (1986, September). Army manpower cost

system: Concept paper #1. (Contract MDA 903-86-C-0106).

Arlington, VA: Systems Research and Applications Corporation.

Hogan, P. F., & Goon, M. (1989, June). The retention of Air

Force officers: A reestimation of the DOPMS model. (Contract

F49642-88-D0001). Arlington, VA: Systems Research and

Applications Corporation.

Hogan, P. F., Eichers, D., Hunter, R. W., Mairs, L. S., Rose,

D. E., & Smith, D. A. (1993, June). The Army Manpower Cost

System (AMCOS) active component cost estimation model, version

7.0 information book. (Contract MDA 903-92-D-0021).

Arlington, VA: Systems Research and Applications Corporation.

Smith, D. A., Slywester, S., & Villa, C. (1991, February). Army

reenlistment models. In Gilroy, Horne, & Smith (Eds.),

Military ComDensation and Personnel Retention--Models and

Evdnce. Alexandria, VA: U.S. Arm! Research Institute for

the Behavioral and Social Sciences.

65
APPENDIX A

DISCUSSION OF COST POLICY MODULES

This appendix contains an extract of the AMCOS Information

Book which explains the methodologies used to calculate costs.

This extract does not include a discussion of recruiting costs

since EPICC is using the methodology described in Appendix C.

A-1
CHAP=ER 3

DISCUSSION OF COST POLICY MODULES

3.0 CHAPTER INTRODUCTION

The sections of this chapter discuss the AMCOS policy modules individually. Each section

may contain the following information:I

"* Cost Composition - A discussion of the specific policy that generates the manpower cost.

"* Average Cost Computation - A discussion of the methodology used to calculate the

average cost for a specific policy. In most cases you will want to use average costs to

estimate the life-cycle costs of a weapon system.

"* Marginal Cost Computation - A discussion of the methodology used to calculate marginal

costs. Marginal costs are used when using the budget analysis to evaluate changes to the

budget.

"* Discussion - A general discussion of the policy module calculations.

"* Notation - Lists the definitions of variables used in the text.

"* Structured Cost Database Variables - Lists the definitions of variables as seen in the

structured cost database.

"* Underlying Variables - Lists die definitions of variables as seen in the underlyirg

database. You need not be concerned with these variable definitions unless you will be

maintaining the AMCOS models' software.

The current list of policy modules includes:

"* Military Compensat;on

"* Enlisted Recruiting

"• Officer Acquisition

" Training

" Permanent Change of Station

"* Retired Pay Accrual

"• Selective Reenlistment Bonus

"* Separations

'This same information is embedded in the AMCOS software and can be accessed through the Help mnm.

A-2
* Special Pays

* Medical Support

* Other Benefits

* The New GI Bill

With the exception of the Selective Reenlistment Bonus, Recruiting, and Training policy

modules, marginal costs are assumed to be equal to average costs. Therefore, in-depth discussions

regarding marginal cost calculations may be absent from the remaining policy module sections.

3.1 MUMRY COMQSAON

COMPOSITION: Consists of all variable costs that provide Basic Pay, quarters (BAQ) and

subsistence (BAS) allowances, and variable housing allowances (VHA).

"* Basic pay is defined as a direct variable cost that provides basic compensation and length

of service increments for members on active duty. The amount of basic pay a member

receives is a function of pay grade and length of service.

" Basic Allowance for Quarters (BAQ) is paid to military members who do not occupy

government housing or who occupy government housing that is not adequate. There are

two rates: one for "with dependents* and one for "without dependents." The cost of

providing BAQ varies with grade and category of dependents. Members who reside in

quarters, on the other hand, receive BAQ-in-kind.

" Basic Allowance for Subsistence (BAS) represents both the cost of food for personnel

eating in government messes and the cash payments to military members in lieu of food.

BAS varies as a function of the number of people receiving cash in lieu of mess privileges

and the cost of food to DoD. To properly cost BAS, the model should include the cost to

the government for food. For this iteration of the model, however, we will assume that

the average cost to the government for providing rations is equal to the BAS rate.

" Variable Housing Allowance (VHA) is paid to military members receiving BAQ whose

families reside in high cost housing areas of CONUS. Cost varies as a function of the

number of member families residing in high cost areas in CONUS, the cost of local

housing relative to BAQ rate, and the pay grade. For the purposes of this model,

however, a weighted average across all locations is used.

AVERAGE COST: Average basic pay is determined by first multiplying the inventory of members?

for all grades and YOS by the appropriate basic pay rate. It is then summed across YOS for each pay

grade and divided by the total inventry for that pay grade. This yields the average annual basic pay

for each pay grade. The longevity increments for a grade are weighted by the inventory in that

grade.

To calculate average BAQ assuming all members receive BAQ in cash, the model multiplies

the BAQ rates, both with and without dependents, by the percentage of members in each grade with

and without dependents. The sum of these two numbers is the average BAQ for that pay grade.

2

Ail invemories reflect Army surgths as of September 30, 1992.

A-3
.1) , F- Er

E Elf

0.2) ACj6" - (wje,%Xbql1 ) + (1-(wdVp)Xbq2)

We use the average VHA by grade as calculated in the MPA Budget Justification Book, which

records the average rate of VHA actually paid to members.

AC'Wj EU EE -W

C

To calculate average BAQ assuming some members receive BAQ-in-kind, the percentages of

all members by grade (with and without dependem) who receive BAQ in cash (mcash and s.cash)

are summed. This percentage is then subtracted from unity and multiplied by the percentage of

members with dependents to calculate the percentage of members receiving BAQ-in-kind. A similar

calculation is used to calculate the percentage of members without dependents receiving BAQ-in-kind.

We assume that re-kind + s-kind + m cash + s cash equals I.

(3.4) ujnd (I-(usca* + s-ca&)Xw% epV%)

s_ - (0 -(m.cah + S.cah)Xl -(w.de,%))

The average BAQ, assuming some members receive BAQ-in-kind and some in-cash, is simply

the percentage of members by grade, with and without dependents, who receive BAQ in cash

multiplied by the BAQ rate.

(3.5) ACjb4 - (nm-cuA bqlj) -f (.whj- bq2) + bq3

Similarly, the VHA rate assuming a mix of BAQ-in-kind and cash is the fraction of those

receiving VHA multiplied by the average VHA rates.

(3.) ACj2 - ft.)*Bj(1*GJ)

Average BAS is determined by calculating the weighted average of all who receive BAS using

the information hfom the MPA Budget Justification Book. To determine total military compenation

paid to the member the model simply adds the pieces already calculated.

0.7) AC"w - AVe + AC641 + ACv'a + ACO

MARGINAL COST: Marginal cost of military compensation is equal to the average cost with a

maximum rate of VHA per grade being substituted for VHA. The model assumnes that at the margin

quarters at each installation always will be filled. Rather than calculate an expected location the

model will pay VHA at the maximm rate to a new space.

A-4
DISCUSSION: The data for military compensation will be extracted from the appropriate OSD pay

tables, allowance tables, or RMC/BMC tables, using a pay table look-up procedure. In addition, we

have obtained tables of allowances based upon Army-specific data on the number of dependents.

A pay table look-up procedure, as opposed to using a snapshot of the JUMPs file, provides

the user with the ability to avoid random fluctuations in the amount of pay received by a member that

has nothin to do with his personnel characteristics. In addition it provides the user the flexibility to

simply update the pay tables when appropriate so that changes in manpower costs can be reflected

immediately. This methodology also allows the user the flexibility of costing a given force under

alternative wage scenarios. For example, if pay is assumed to grow at a real rate of 5 % per year, the

pay table 10 years in the future can be increased to

(3.) ARC, + 10 - ARC(l . 0.05)M10

as specified by the user. To do this, SRA would have to make a special run of this policy module

creating a separate cost data file to be used for simulating the alternate wage scenario.

NOTATION:

E =- Inventory of members in YOS i and grade j

AC'w = Average annual compensation paid to a member

bp, = Basic pay for an individual member in YOS i and gradej

Ecj = Number of members in city C and in grade j

ACQP - Average annual basic compensation paid to members in grade j

bqlj - Rate of BAQ for members drawing w/dependents in grade j

bq2j = Rate of BAQ for members drawing w/o dependents in grade j

bq3j = Rate of BAQ for members drawing partial BAQ (single, living in

government quarters)

m cash - % of married, or single with dependents, members actually drawing BAQ

in cash

s-cash - % of single members actually drawing BAQ in cash

m-kind - % of married members drawing BAQ-in-kind

s kind - % of single members drawing BAQ-in-kind

AC:* - Average BAQ for grade j assuming all members receive BAQ in cash

ACjb* = Average BAQ for grade j assuming some members receive BAQ-in-kind

ACj" = Average BAS for grade j

A-5
AC1'* - Average VHA for grade j assuming all members receive BAQ/VHA in

cash

ACka - Average VHA for grade j assuming some members receive

BAQ/VHA-in-kind

w_dep% - % of members with dependents

fract vhas - Fraction of those receiving VHA

vha..yrcj - Average VHA yearly rate for members in grade j who do not live in

government quarters

STRUCTURED COST DATABASE VARIABLES - Definitions

acbp - Average annual base pay

ac baql - Average cost of baq paid in-cash

ac vhal - Average cost of vha paid in-cash

acbaq2 - Average cost of baq paid in-kind

ac vha2 - Average cost of vha paid in-kind

"aebas - Average basic allowance for subsistence

actax - Average annual tax benefit

ac-rmc - Average annual compensation

UNDERLYING VARIABLES

VARbALE DEFINMON LOCATION SOURC

bp basic pay by grade and YOS mcparms.enl Pay Tables

bql BAQ w/dependents mcparms.enl MPA J-BOOK

bq2 BAQ w/o dependents mcparms.enl MPA J-BOOK

bq3 partial BAQ w/o dependents mcparms.enl MPA J-BOOK

bas basic allowance for subsistence mcparms.enl MPA J-BOOK

ginv grade inventory enlisted.dat or officers.dat

inv inventory (master files) inv.enl DMDC

rmc regular military compensation mcparnms.enl MPA J-BOOK

vha variable housing allowance mcparms.enl MPA J-BOOK

w1dep% % drawing w/dependets mcparms.enl MPA J-BOOK

m cash % wldep receiving BAQ in cash mcpanms.enl MPA J-BOOK

a cash % w/o dep receiving BAQ in cash mcparms.enl MPA J-BOOK

fract va % receiving VHA in cash mcpamn.enl MPA J-BOOK

A-6
3.2 RETIIED PAY ACCRUAL

COMPOSiTON: Provides the funds for DoD's contribution to its military retirement fund under

the provisions of 10 UsC 1466 of the FY84 Defense Authorization Act, P.L. 98-94. Under the

accrual concept (effective in FY85), each Service budgets for retired pay in the Military Personnel

account and transfers funds on a monthly basis to the Military Retirement Trust fund from which

payments are made to retirees.

AVERAGE COST: Retired pay accrual average per capita cost is determined by multiplying the

basic pay (determined earlier by grade) by a fixed normal cost percentage rate obtained from the DoD

umy.

(3.•9) ACP - AC.r*

AN ALTERNATIVE ESTIMATE This next discussion provides an alternative estimate of military

retirement pay accrual for Army officers and enlisted personnel. The DoD Actuary estimates an

accrual change based upon all-DoD retention rates and retirement probabilities. The computations

used in this alternative estimate are based upon Army retention rates only.

There are currently three different retirement systems in effect: (1) for those who entered

prior to October 1, 1980, retirement pay is based upon their terminal base pay and is equal to 2.5

percentage points for each year of service (a minimum of twenty years of service is required for

retirement); (2) for those who entered after October 1980, but before August 1986, retirement pay is

based upon an average of the three highest years of basic pay and is equal to 2.5 percentage points

for each year of service; and (3) for those who enter after August 1986, retirement pay is again based

upon an average of the three highest pay grades, but is limited to 40% of basic pay after twenty

years, rising annually to a maximum of 75 % if the member retires after completing 30 years of

service.

Under the first two systems, retirement pay is, nominally, indexed for inflation. Under the

third system, the member receives an adjustment to his retirement pay that is one percentage point

less than a full indexation each year. However, the real value -f retirement pay is restored upon

reaching age 62. Also at age 62, the member receives the percentage of retirement pay that is offered

under the pre-1986 system.

In this policy module option, the retirement accrual is computed using an approximation to

the entry-age normal method. Certain simplifying assumptions are made that make this an

approximation to the accrual cost. We assume:

"* All enlisted personnel ter at age 18;

"* All officers enter at age 22; and

"* All members live until age T.

Define Pk(i) to be the probability that a member entering MOS k leaves the service after

completing i years. It is computed as

where Ctk is the continuation rate for MOS k between the end of year of service t-W and t. Define

BP as the average pay attained by those leaving at year of service i.

A-7
(3.10) P) (-C~*)fC&,

gel

Pre-1980 System. The following computations apply to those who entered before October 1980. The

present value of the expected retirement annuity for an individual is:

0.11) •_53 1 ,-1 (- 

PV'k is the present value of retirement for MOS k.

Now calculate the expected present value of basic pay that will be paid out to the member

over his career:

(3.) E - E-C& Bpi, (1 +rY

The accrual percentage, then, is defined as the ratio of the expected present value of

retirement outlays to the expected present value of basic pay over the member's career:

(3.13) A .,lM- PyK Pv,"

Finally, the accrual amount for a member under the system in effect before 1980 is:

(3.14) ACL, a AC*A,

High-Three Averaging. The system in effect for those entering after 1980, but before 1986, is similar

to the system just discussed, except that a member's retirement pay is based upon an average of her

highest three years of basic pay. Hence, we can simply modify equation 3.11 to read:

3015 T-18 PA#) . Mj j~p.p-2

,.3. ( I+r 3 ,(1 w)1 (1 +w)

where "w" is the expected anmnal basic pay raise, expressed as a decimal.

Pon-1986 System. Estimation of the accrual percentage on the new retirement system again requires

only a modification to equation 3.11:

The new system offers a retirement anmuity of 40% of basic pay after 20 years of service, rising to

75% after 30 years of service. However, the annuity as a proportion of basic pay is increased to

what it would have been under the older system after the retired member reaches age 62. The annuity

is indexed to one percentage point less than the inflation rate, w. However, the real value is restored

A-8

l in I l HI -
M+ + =4 BP6 +P30161-1 p*QX.4+.O3L M-L IW_01,([ #2 4(1 +?) I+lW )

+ (I + 'r6- 11t P5(O.02SJ~i) 1 +W-.01 y-Is

when the retired member reaches age 62. It again increases a one percentage point less than the

inflation rate. The retirement annuity is based upon an average of a member's highest three years of

basic pay.

DISCUSSION: The default accrual costs estimated in the model are based solely on the OSD

Actuary's analysis. She uses the aggregate entry-age normal method. Alternative methods and

assumptions produce different costs for the Army. The equations discussed in this policy module

option approximate the entry age normal method of retirement accrual used by the DoD Actuary, but

with Army specific retention rates. Using the Army specific probabilities of reaching retirement

reduces the accrual cost to the Army. The Army could use these calculations to argue for a lower

accrual rate than the current overall DoD rate.

These equations permit the use of a retirement accrual percentage that varies by:

- CM(F - Retirement System

- Quality.

NOTATION:

AC7 - Average cost per capita of retired pay accrual for grade j and MOS k

Aq - Average annual basic compensation paid to members in grade j and MOS

k

r. - Fixed normal cost rate obtained from DoD actuary tables

C- Continuation rae for MOS k between the end of year service t-W and t

Pk(i) - Probability that a member entering MOS k will leave after completing i

years of service

BP - Average pay attained by those leaving at YOS i

PVk - Present value of retirement for MOS k

PVr - Present value of basic pay paid to a member in MOS k over his or her

A-9
career

A, - Accrual percentage calculated using Army specific retention data

w - Expected annual basic pay raise expressed as a decimal

sTRUCTURED COST DATABASE VARIABLES - Definition

&rp - Average cost per capita of retired pay accrual

&cjrphi - Average cost per capita of retired pay accrual-high quality

•jpTjo - Average cost per capita of retired pay accrual-low quality

Arp.av - Average cost per capita of retired pay accrual-weighted average

UNDERLYING VARIABLES

VRZL 2ERM LOCATION DATA SOURCE

inv inventory inv.enl DMDC

BP base pay mcparms.enl PAY TABLES

CR continuation rates con rate.enl DMDC

r act DoD actuary rpa factor rpapanns.enl MPA J-Book

"hiQual % high quality accessions by MOS rechqtot.enl DMDC

A-10
3.3 SaUlTED REENLSMM O T BONUS

COMPOSITION: Consists solely of the Selective Reenlistment bonus. The bonus offer is computed

as:

SRB = Award Level x Monthly Basic Pay x Years of Reenlistment

Reenlistment bonuses are offered to members in an MOS on a discretionary basis, at zone A (for our

purposes, we assumed that zone A equates to grades E4-E6) and zone B (grades E5-E7). These

bonuses correspond to the first and second term reenlistment decision points. The "award level" may

vary from zero to six. Currently, 50% of the SRB is paid to the member as a lump-sum at the time

of the reenlistment, while the remainder is paid in equal, annual installments over the period of the

reenlistment contract.

This computation is concerned with estimating the average cost of Selective Reenlistment

Bonuses. Less than 100% of those in a pay Wade within zone A or B will receive the bonus, because

some may not be at an estimated time of seraration (ETS) point, and some may chose to extend

rather than reenlist. Therefore, the bonus amount is calcudated conditional upon receiving it. Then

the bonus amount is multiplied by the probability of receiving it.

AVERAGE COST: The average cost of reenlistment bonuses will vary by MOS because the award

level (A1,) and basic pay (bp*) at each zone vary by MOS. The average cost of a reenlistment bonus

for MOS k at zone z in pay grade j for a member who reenlists for Yh years is given by:

(3.17)E r

SRBD O.5A(Y.X)Q4") + 

This calculates the average cost of the bonus for those in pay grade j and MOS k at zone z,

assuming that they get the bonus. Then the unconditional average cost is

(3.18) - )SRB

where ETSj is the proportion at an ETS point in year of service i and r& is the reenlistment rate at

year of service i in MOS k. This computation is made for all relevant zones and pay grades.

MARGINAL COST: The marginal cost computation of the reenlistment bonus includes the cost of

the infra-marginal rents that would be paid to those who would reenlist anyway. The equation for the

marginal cost of an SRB in grade j and MOS k at Zone z is given by

(3.19) MC; - (ix + SR1"4{ Sze.)-

A-I1
P is the relevant measure of non-bonus pay for which the elasticity is computed.3 It is subtracted

because we are including only the SRB costs of the marginal reenlistees.

DISCUSSION:

"The methods used here discounted the present value of the bonus payments to the

reenlistment decision point at the government's discount rate. It computes discounted

obligations. One could assume that the government's discount rate is zero and compute

undiscounted obligations. Alternatively, one could compute actual outlays, rather than

obligations, since the outlays occur over the reenlistment contract.

" The SRB itself is a function of basic pay at the time of reenlistment. If basic pay

increases, bonus costs also will increase. This function is an advantage of explicit

modeling of bonus costs.

" The SRB award levels can be changed for each MOS, zone, and year, at the option of the

user. The default option for all years is the bonus policy in effect for FY 1990, or the

most recent database update.

nTo understand this formulation, note that:

Total Cost - PQ - Price * Quantity

cc .- &-

S' ,todo mb ,=he. P -Jr..¢-- 1

A-12
NOTATION:

SRBW = Average cost of a reenlistment bonus for pay grade j and MOS k at zone z

for a member who reenlists for Y, years

Aj. = Award level for MOS k at zone z

AC' - Unconditional average cost of an SRB bonus for grade j and MOS k

MCju' - Marginal cost of an SRB bonus for grade j and MOS k

E* = Inventory of enlisted soldiers in YOS i, grade j, and MOS k

ETS1 = Proportion of members at estimated time of separation (ETS) at YOS i

r. = Reenlistment rate at YOS i in MOS k

Sý = Supply elasticity at zone z

bpjb - Basic pay in grade j and MOS k at zone z

'k. - Average non-bonus pay for MOS k at zone z

Yb = Average reenlistment contract length, in years, for MOS k and zone z

STRUCTURED COST DATABASE VARIABLES - Definitions

ac srb - Average SRB cost weighted by probability of receiving bonus

srb - Value of SRB, conditional upon receipt

mc srb - Marginal cost of paying an SRB to a soldier

UNDERLYING VARIABLES

V ABALE 1DENIDMk LOCA7ON 2AT SO~URE~

r discount rate srbparms.enl OMB Circ A-76

lengthl avg term of reup, zone A srbparms.enl Assumed - 4

Iength2 avg term of reup, zone B srbparms.enl Assumed = 4

ave.paya meas of pay for supply elast, zone A srbparms.enl Update Prgm

ave.payfb meas of pay for supply elast, zone B srbparms.enl Update Prgm

Se.a supply elasticity, zone A arbparm.enl Assumed - 2

Se b supply elasticity, zone B srbparms.enl Assumed = I

awardl SRB award level 1 srb data.enl DAPE-MPE

award2 SRB award level 2 arb-data.enl DAPE-MPE

baspay basic pay mcparm.enl MPA J-BOOK

inv inventory by grade & yos inv.enl DMDC

A- 13
3.4 SPECIAL PAYS

COMPOSITION: Includes hazardous duty, sea/foreign duty, medical personnel, diving duty,

overseas allowances, language proficiency pay, family separation allowance, and special duty

assignment pay. Special duty assignment pay is authorized only for a selected population of enlisted

members assigned to demanding and/or duties with higher degree of responsibilities such as special

forces or recruiting assignments and overseas extensions.

AVERAGE COST/MARGINAL COST: The average cost of special pays in the sea/foreign duty

category varies by grade. The cost is calculated using' an historical probability for foreign duty pay

multiplied by current probability of foreign duty by grade multiplied by the foreign duty pay rate.

The average cost of special pays in the overseas allowance category varies by grade. The

average cost for pays in pay grade j is computed by multiplying percent of Army personnel overseas

times percent OCONUS by MOS times overseas rates by grade.

The average cost of special pays in the language proficiency and diving duty category will be

assigned only to certain MOSs. Certain MOSs will receive the predetermined amount and all other

MOSs will receive zero for special pays in this category.

The average cost of special pays in the medical pays category is calculated by MOS and

grade. MOSs in the medical, dental, or veterinary fields are given a weighted average by grade of

total medical pays.

Family separation pay is paid to members with dependents on duty outside the United States

or in Alaska when travel of dependents is not authorized and the member maintains two homes. The

average cost is calculated by multiplying the family separation rate for each grade as shown in the

budget by the probability of family separation.

(3.20) ACjp" - FSAj - P*

Average cost of spJal duty pay is calculated by dividing the total amount of special duty pay

by the number of recipients. This "rate" is applied directly to those MOSs (CMF 79) that receive

special duty pay.

Average cost of hazardous duty is the total amount of hazardous duty pay, less that paid to

specific MOSs, divided by the total Army. The exception to this is that specific MOSs always receive

certain hazardous duty pays and, in such cases, are given the set amount rather than the average. A

member can receive at most two hazardous duty pays per year.

NOTATION:

AC~js - Average cost of family separation pay for grade j

FSAj - Family separation pay rate for grade j

I* - Probability of family separation

STRUCTURED COST DATABASE VARIABLES - Definitions

A- 14
ac dive - Average cost of diving duty pay

ac lang - Average cost of language proficiency pay

ac-acip - Average cost of aviation career incentive pay

ac sd - Average cost of special duty assignment pay

ac-fd - Average cost of foreign duty pay

ac os - Average cost of overseas duty pay

ac•az - Average cost of hazardous duty pay

acrmed - Average cost of medical professional pay

acfsa - Average cost of family separation allowance

acsp - Average cost of special pay

UNDERLYING VARIABLES

freq foreign pay frequency foreign.enl JUMPS FY85

oconus percent of MOS oconus oconus.enl PERSCOM

os.perc percentage overseas spparms.enl MPA J-BOOK

haz-pay hazardous duty pay spparms.enl MPA J-BOOK

totdiv total diving duty pay spparms.enl MPA J-BOOK

totlang total language proficiency pay spparms.enl MPA J-BOOK

totsd special duty assignment pay spparms.enl MPA J-BOOK

langinv total inv for 97E, 98G, 18F spparms.enl DMDC

fsa family separation allowance spparms.enl MPA J-BOOK

fd # receiving foreign duty pay spparms.enl MPA J-BOOK

ginv grade inventory by MOS enlisted.dat

sp-names special pay names spparms.enl MPA J-BOOK

sprates special pay rates spparms.enl MPA J-BOOK

A-I5
COMPOSITION: Includes all variable costs of individual training, including initial training (recruit

training, initial skill training, and one station unit training), other specialized skill training of

individuals, and NCO professional training.

" Recr7u •'aining. Provides for basic training to individual recruits. An eight-week

introductory and combat turvival skill training course given to enlisted personnel upon

their initial entry into military service. It includes training to prior service personnel in

need of refresher training. Enlisted training only.

"* inill 7/01& Training. Includes all formal training normally given immediately following

recruit training and leads to the award of a military occupational specialty (MOS) at the

lowest level. Enlisted training only.

* One Station Unit Training (OSU0). Combines recruit training and initial skill training for

enlisted personnel in the combat arms and certain combat skills into a single course.

Training is conducted at a single station under a single cadre. Enlisted training only.

"* S•ill Progression Training. Provides specialized skill training to enlisted members

subsequent to initial skill training. Through skill progression training, students gain the

knowledge to perform at higher skill levels or in superior positions. Enlisted training and

officer training.

"* Flight Training. Includes courses in the Army's flight training programs, categorized as

either Undergraduate or Graduate Pilot Training. Undergraduate Pilot Training (UPT)

qualifies both commissioned and warrant officer aviation students to perform duties and

assume the responsibilities of Army pilots. Graduate Pilot Training includes courses for

instructor pilots, insument flight examiner, gunnery, and specific pilot qualifications

courses in various aircraft. Officer training only.

"* Acadmies and Seior ROTC. Provides initial trang for officer accessions (see Officer

Acquisition Module).

" Professional Training. Provides education to selected military and civilian personnel

DoD-wide to prepare them to perform increasingly complex tasks that become their

responsiiilities as they progress in their careers (e.g. NDU, AWC, C&GSC, DSMC,

USASMA, and NCOES training).

AVERAGE COST: The traditional source of this data is the Reource Management Office of USA

TRADOC. They produce the ATRM-159 report which displays course costs for TRADOC schools.

A similar report is provided by the Army HEalth Services Command for medica courses. The

rqe t display calculated co mse cosbased on instuctor contact hours, udn load, cots of

supplies, ammunition, the flying hour program and cots based on medical support, base support, and

fanily houing.

MPA Cos. The ATRM-159 determines MPA costs by calculating the pay and the

allowamces of both the students and the istructors for each course. The ATRM-159 determines

instructor contact hours converted to man-years and multiplies it by the average military omp ation

for each grade. Student pay and allowances is determined by first averaging student input and output

A-16
and nmltiplying by the course length to get student manyears. Then manyears are multiplied by the

average military compensation for the modal grade to get student pay and allowances. A pro rata

share of the pay and allowances for the military working in Base Support and Medical Support also

are added to the MPA cost factor.

OMA Costs. The ATRM-159 reports costs that reflect the actual O&M costs spent for

individual training courses. It includes instructors' materials, flying hour costs (where applicable),

and overhead costs. Again, a pro rata share of the O&M piece of Base Support and Medical Support

are included in the cost factor. The OMA costs include pay for civilians. Costs are allocated per

training man-week.

Other Costs. These costs include support costs (e.g., procurement of training devices and

training swmunition) other than MPA and OMA. The ATRM-159 computes equipment depreciation

costs by amortizing procurement costs over a 10 year period. Ammunition costs are computed by

dividing the total cost of ammunition per course by trainee per course. This equals ammunition cost

per trainee.

In each of the above appropriations, AMCOS will read the direct, variable costs per MOS

directly into the structured cost database.

Average cost of training is the variable cost per MOS course as calculated by ATRM-159.

However, AMCOS calculates a weighted average variable cost for all enlisted using the average costs

per MOS and the baseline inventories as weights. The costs displayed in the structured database are

as follows:

"* average cost of basic training

"* average cost of initial skill (or AlT) training

"* average cost of one station unit training

"* average cost of career training (reflected in grades five through nine)

"* average cost of all training by grade

MARGINAL COST: Marginal cost is equal to average cost of training. For those MOSs that have

a choice between OSUT and basic and AIT, the marginal cost will be equal to the cost of basic and

AIT.

STRUCTURED COST DATABASE VARUABLES - Definitions

ae btr - Average cost of basic training

acOtK - Average cost of one station unit training

ac-ir - Average cost of initial skill training (AlT)

accaztr - Average cost of career trtming

cmg - Average cost of all training combined for a given grade

racing - Marginal cost of all training combined for a given grade

acproftr - Average cost of professional training

ac.Up - Average cost of undergraduate pilot training

acpofhtr - Average cost of other flight training

A-17
UNDERtLYING VARIABLES

VAUAL DEFNMO OATMDASUC

pecfraction of MOS given OSUT tr osut.enl TRADOC

sujp a PeotofOU rsuciTAO

osutompa OMA cost of OSUT tr osutzen TRADOC

osut ocher OTHER cost of OSUT tr-osut-eni TRADOC

cr-3 1 skill level of course tr cartr.enl TRADOC

cr-num course number or name tr~canr.enl TRADOC

crmpa MPA cost of course tr-cartr.enl TRADOC

cr ottia OMA cost of course cr-carz.enl TRADOC

cr~other OTHER cost of course tr-cartr.enl TRADOC

A-18
3.7 NMICAL SUPPORT

COMPOSITION: Consists of all fixed and variable non-pay costs that provide health care to the

member and his or her family. It includes the Civilian Health and Medical Program for the

Uniformed Services (CHAMPUS) and the care provided by the military hospital system.

AVERAGE COST/MARGINAL COST: Health care support costs are broken into two pieces, the

cost of CHAMPUS and the cost of care in the military hospitals.

" CHAMPUS costs vary as a function of family size and age of dependents. Family size

tends to vary directly with grade. Average cost, then, is estimated by using the total

government cost for CHAMPUS (inpatient and outpatient care) multiplied by the average

family size per grade to give us average CHAMPUS cost by grade.

(3.21) AC"J w = ACCaO'BA (IFSj - 1)

"* Military health care support costs are a function of the size and number of military

hospitals and the medical force structure. Military medical force structure is sized to

provide for an orderly transition to wartime status in the event of mobilization. The

medical facilities are for providing training to medical personnel filling the force structure.

Secondary is the care provided to members and their families. The medical force structure

is independent of the size of the current Active Army End Strength and current personnel

compensation issues. To count this as a manpower cost of the current force is

questionable, therefore, calculation of average costs will not include cost of facilities or the

military pay of doctors and other military medical personnel. The Army would incur

these costs regardless. To calculate the cost of direct care in the military health care

system the following equation is used:

(3.22) ACJA" - ACa0w'k + AC"m (AFSj - 1)

ACmaxmu=• and AC"=Aw represent the average cost of medical and dental care for military members

and their dependents, respectively; ACj' is the average cost of military hospital care; and AFSJ

represents the average family size by grade. The values for these variables are based on information

obtained from the Medical Expense and Performance Reporting System (MEPRS).

NOTATION:

AC~mNPI - Average CHAMPUS cost per member in grade j

A` - Average CHAMPUS cost per dependent

AFSj - Average family size of a member in grade j

ACrImI - Average cost of medical and dental care per member in grade j

ACE""" - Average cost of medical and dental care for military members

AC'mE.' - Average cost of medical and dental care for dependents of military

members

A-19
STRUCTURED COST DATABASE VARIABLES - Ddinitiam

ac mdsp - Average medical support costs per member by grade

a_champ - Average cost of CHAMPUS per member per grade

UNDERLYING VARIABLES

cc tot total CHAMPUS costs imdbparms.enl OMA J-BOOK

omam total p8m medical costs mdbparms.enl OMA J-BOOK

omaýd total p8m dental costs mdbparms.enl OMA J-BOOK

afs average family size mdbparms.enl AFCSC

A-20
3.3 iBENETS

COMPOSITION: Consists of all fixed and variable costs that provide miscellaneous benefits. It

includes death gratuities paid to beneficiaries of military personnel who die during active duty,

apprehension of deserters, unemployment compensation paid to eligible ex-servicemen, survivor

benefits paid to spouses and children of deceased service members, separation pay, family separation

allowance, clothing allowances, benefits provided under the MWR program, and government

contribution to social security tax.

AVERAGE COST/MARGINAL COST:

Miscellaneous. Average cost of death gratuities, apprehension of deserters, and unemployment

compensation are determined by dividing their total cost by the total member inventory. This average

then can be applied to all members.

ACn 0'8w (3.23) 9

F Ej

J-1

Here, OB,. equals total MPA costs for death gratuities, apprehension of deserters, and unemployment

compensation.

Clothing Allowance. Each member is authorized an initial issue plus a cash payment of a basic

maintenance allowance through her or his 36th month and a cash payment of a standard maintenance

allowance from the 37th month through the end of her or his enlistment. Rates are found in the

Army's budget justification books for MPA. The model uses three clothing rates, each a weighted

average across sex.

FICA. The FICA tax represents the funds paid (employer's tax) to the Social Security Administration

as required by the Federal Insurance Contribution Act. The FICA tax is developed by multiplying the

members annual base pay (up to $54,600 for FY91) by the applicable percentage. The model will

apply the current FICA tax rate to the average cost of basic pay.

(3.24) ACC A - %FICA -AC7A

Srwvvors' Benefi•. Survivors' benefits represent the cost of providing payments of Social Security

benefits to widows and orphans of active military members. The costs are averaged over all service

members.

AC" - SB"

J.1

Morale, Welfare, and Recreation Benou. These benefits are paid for with OMA dollars. A review

of service member use of MWR activities indicates tha there is little or no variation across grade or

MOS, therefore average cost of MWR is applied equally to each member by AMCOS. To calculate

A-21
the average cost of MWR activities, OMA costs are totaled and then divided by the total Army

inventory to determine a per capita cost for each member.

AC"" OMASI"

0.26) 9

j-1

NOTATION:

ACm' -- Average cost of miscellaneous pay paid to members

Ej - Inventory of enlisted soldiers in grade j

%FICA - Current FICA tax rate

ACr = Average annual basic pay paid to members in grade j and MOS k

SBW = Total cost of survivor benefits

OMAr' = Total OMA costs of morale, welfare, and recreation benefits

OB.t - Total cost of other benefits

ACjF-" - Average cost of FCA tax for grade j and MOS k

ACsB = Average cost of survivors' benefits per member

AC"R = Average cost of providing morale, welfare, and recreation activities per

member

STRUCTURED COST DATABASE VARIABLES - Definitions

ac cloth - Average cost of clothing allowance

ac-fica - Average cost of government contribution to FICA

acsurvben - Average cost of survivors' benefits

actmis - Average cost of miscellanou benefits (death gratuities, apprehension of

deserters, and unemployment c pensation)

ac mwr - Average cost of MWR

acob - Average cost of other benefits

A-22
UNDERLYING VARIABLES

ob total MPA costs for misc lenefits obparms.enl MPA J-BOOK

bp base pay enlisted.dat PAY TABLES

ai average monthly leave obparms.enl MPA J-BOOK

amlfreq frequency of cash for lea.e obpams.enl MPA J-BOOK

sev-pay total Army severance pay obparms.en MPA J-BOOK

fica FICA percentage for base year obparms.enl SOCIAL SEC ADMIN

ficalimit maximm pay that is taxed obparms.enl MPA J-BOOK

surv ben total Army survivor benefits obparns.enl MPA J-BOOK

,;lcoth I clothing allowance for El-E2. obparnms.enl MPA J-BOOK

cloth:2 clothing allowance for E3 obparms.enl MPA J-BOOK

cloth)3 clothing allowance for E4-E9 obparms.enl MPA J-BOOK

tot mwr total oma cost of MWR obparms.enl OMA J-BOOK

A-23
3.9 PERMANENT CHANGE OF STATION

COMPOSITION: Divided into five categories of moves: rotational, operational, accession,

training, and separation moves. This module calculates the costs for each of these categories but

reflects only the cost of rotational, operational, and separation moves in the totals for this cost

element. Accession moves and training moves reflected in the totals of other cost elements (recruiting

and training respectively).

AVERAGE COST/MARGINAL COST: PCS costs are a function of the weight allowance per

grade, tour length, and inventory of the MOS requirements overseas. Before costs can be calculated,

however, weight allowances must be adjusted to take into account the rules that apply to E-4s and

below. Two rules apply: 1) whether or not the member has dependents and 2) whether or not the

member has less than two years of service. To calculate a single weight allowance each for E-4s and

E-1I/E-3s, we applied the current distribution of married/unmarried members with less than two years

of service and calculated a weighted average.

(3.27) WA (M0 00EV 1 ) + (200 EU + 15001V

(3.n) WA, - ooxy,• + 7000(x4 + y + Uxdy + 35W(1-X)(1-y.4)

Then we calculated the weighted average weight allowance for each grade.

(3.29) WA5 7000(1- -) + 900Qr1

(3.30) WA6 . 8000(1 -6) + 1 100X6

(3.31) WA7 105001 -x7) + 1250Qz7

(3.32) WA, - 1100(1-00 + 1350.;i.

(3.33) WA, - 12000(-l + 14500xg

Accession. The cost factor for accession moves is the average cost per accesion move.' We

apply this factor against the number of accessions in a projection year.

Separadon. The cost factors for separation moves equal the estimated average costs per

separation move by grade. We use weight allowances by grade to expand the all-Army average cost

of a separation move into a per-grade cost,

where ACs'm is the Army average cost of a separation move, WA, is the average weight allowance in

grade j, and EF and E are the grade j and total baseline strengths, respectively.

'Per-move average costs, by type of move, are available from ODCSPER.

A-24
SAC - ACSOW WA

(3.34) E

flau'ng. The training move cost factors are defined as the average cost of a training move

by grade. They are calculated in an analogous fashion to the separation move factors, so that

A~~maAC~w WA1

E ~ J

where AC"m is the Army average cost for a training move.

Rotational and Operatonal. AMCOS calculates and displays the cost per OCONUS and

CONUS moves just as it does for the other categories of moves. However, for CONUS and

OCONUS moves AMCOS also calculates the probability of a move prior to calculating the average

cost of any PCS moves M number in a particular grade.

The average cost of an OCONUS move, given that a move is made, is

(3.36) ACj= - AC E WAE

W £

The average cost of a CONUS move, given that a move is made, is

(337) ACj" - AC0" WA

I E

In calculating the average cost of CONUS and OCONUS moves member the probability

of making a move is taken into account. The key assumption in calculating this probability is that

operational moves are generated as a residual, after moves out of OCONUS fill the empty CONUS

posiions and separations and accessions are accounted for. This mems tht the average cost of a

rotational move can be eVpressed as

ACa * pwACj=

Whaere P a n0 - [OCO - "c)] - o(Acc)

where the term p0 is the probability of a service member making a rotational move, which varies by MOS as denoted by the subscript k. The per capita moves required to move members from overseas

and to replace those departing overseas i given by two times the proportion of members stationed

a-25
overseas, 2OC, divided by the expected OCONUS tour length, TL-, less the per capita moves

required to rotate members who will be separating from the Army, the second term in brackets, less a

percentage that represents accession moves to OCONUS positions, OC,(Acc), where Acc is the

percentage of the total force that are accessions. The per capita moves value for those members

whose OCONUS tour has ended is achieved by multiplying the proportion of members stationed

oversees by the average continuation rate, ce, to avoid double counting moves associated with

separations.

The average cost of an operational move per member is then calculated as

(3.39) A 'r . -O~ct 0'S,

03)where p (71-4) [- f - ( OO - C ] (I -O C&Xcc)

The term pc is the probability of making an operational move, which equals the per capita moves

required to fill CONUS positions (the proportion of CONUS members divided by the average

CONUS tour length, TLC), less the number of positions that will be filled by members rotating back

from OCONUS, the second term in brackets, and less the proportion of those accession moves made

to CONUS positions.

The structured cost database, then, displays an average cost of a PCS move that is calculated

as shown below.

(3.40) ACm~ = AC~' +AC

DISCUSSION: Missing from the equations is an equation describing the equilibrium tour length.

Our simplifying assumption is that there are sufficient CONUS billets such that the number of

operational moves adjust to whatever tour lengths for CONUS and OCONUS are specified.

NOTATION:

WAX - Composite weight allowance for grade j and MOS k

ACj'km - Average cost of a permanent change of station for grade j and MOS k

AA" - Average cost of a separation move for grade j and MOS k

AC;" - Average cost of a training move for grade j and MOS k

ACw°k - Average cost of a rotational move for grade j and MOS k

ACj - Average cost of an operational move for grade j and MOS k

OC - Percentage of members OCONUS in MOS k

TL - Tour length (either OCONUS or CONUS) for members in MOS k

EB - Member inventory in grade j and MOS k

A-26
E - Total member inventory

- Average continuation rate

Arc - Percentage of total force that are accessions

- Expected number of rotational moves per member (varies by MOS as

denoted by the subscript k)

- Probability of an operational move

- % mwbers with dependes in grade j

yj - % members in grade j with GTE 2 YOS

STRUCTURED COST DATABASE VARIABLES - Definitions

ac amov - Average cost of an accession move

ac_-op - Average cost of an operational move

ac rots Average Cost of a rotational move

ac smov Average cost of a separation move

aicov Average cost of a training move

ac-ps - Average cost of pcs moves

UNDERLYING VARIABLES

ops composite cost of an operational move pcpams.enl DAPE-MB

rots composite cost of a rotational move pcsparms.enl DAPE-MB

sep composite cost of a separation move pcsparm.enl DAPE-MB

acc composite cost of an accession move pcq ms.enl DAPE-MB

Mg composite cost of a training move pcsIpam.eul DAPE-MB

deed % members w/depeudets pcparms.eal MPA J-BOOK

percen % Eft with less tam 2 YOS pcsdatLew Calculatd

loss S members sepaaing by grade pcsdM.en Calculated

tc tour length in CONUS pcs PC.Cl DAPC-249

toc tour length in OCONUS pca_da.Me Assumed - 3

Weig* weigh allowance by grade pcuparms.enl JOINT TVL REG

ocos p of members oconus ocomn.enl PERSCOM

A-27
3.10 O IQ E ACOUIS ON

COMPOSITION: Includes costs associated with the acquisition of officers into the Army such as

advertising; scholarships (HPSP and ROTC); initial training; military pay and allowances for cadets

and officer candidates; and operations and support costs for the U.S. Military Academy, Branch

Immaerial Officers' Candidate School, and Reserve Officers' Training Corps.

" United States Military Academy. The curriculum is oriented primarily toward academics

during the school year and intensive military training during the unmer months. Each

July approximately 1,450 new cadets are trained and equipped to enter the Corps of

Cadets, bringing it up to its authorized strength of 4,500 cadets. The four-year course of

instruction, which results in a Bachelor of Science degree, is designed to produce careeroriented officers for the Army.

" The Branch Immaterial Officer Candidate Course. This course trains selected enlisted

persons to serve as commissioned officers in the units of the active and reserve

components. With an average load of approximately 210 students, this 14-week course

commissions officers in all the accession specialties.

" Senior ROTC. The objective of ROTC is to attract, motivate, and prepare selected college

students with potential to serve as commissioned officers in the active and reserve

components. The program consists of ether a two-year basic course or a six-week basic

camp, followed by a two-year advanced course at ROTC locations throughout the United

States and its territories. Between their junior and senior years, ROTC cadets typically

attend an advanced camp where they receive military training under field conditions.

After successful completion of this program, the cadets are conmissioned as second

lieutenants.

" Health Professionals Scholarship Program. The Army presently is authorized 1,850

students in the HPSP. Students are enrolled in the disciplines of Medical Care,

Psychology, and Optometry as authorized by Public Law 92-246. Costs reflect payment

for tuition and other education expenses (school supplies, microscope rental, text books,

etc.) incuned by the participants.

AVERAGE COST: Officer acquisition costs are computed for both MPA and OMA appropriation.

MPA costs are determined by combining student pay and allowances with instructor pay and

alowanes and dividing by the number of graduates and then adding the average cost of a training

move. OMA costs are determined in a similar manner, combining advertising costs, scholarship

costs, and ope• iona wpport costs. These costs them are divided by the nmnber of graduates.

ACp,?'"(MPA) - M1."" * ACj + 17 . AC + ACJ, ,,,d

0.41) o0

ACP"'(OMA) -~f + ,?"+&U

MARGINAL COST: Marginal cost is the average cost of acquiring the OCS student. During

periods of expansion, the Army traditionally uses OCS to meet the increased officer demands.

A-28
Besides the fact that West Point enrollment is fixed by law, OCS is also the cheapest of the four

methods of acquiring officers.

NOTATION:

AC.D.&M - Average cost of officer acquisition into grade j from source of commission

n

MYr - Student manyears in grade j from source of commission n

Myr - Instructor manyears in grade j from source of commission n

0jr' - Officer graduates into grade j from source of commission n

OS' - Operations and support costs for source of commission n

Adv, = Cost of advertising for source of commission n

Schl.= Cost of scholarships for source of commission n

A~j"Gm - Average cost of a training move for grade j

AC'j - Average annual compensation for grade j

STRUCTURED COST DATABASE VARIABLES - Definitions

ac ocs - Average cost of training an OCS candidate

acwp - Average cost of training a West Poit cadet

ac rotc - Average cost of training an ROTC cadet

acWhp - Average cost of an HPSP cholaship

acoff - Average cost of accessing an officer

mc off - Marginal cost of accessing an officer

A-29
UNDERLYING VARIABLES

-AIAL -EIITO LOAnQAI, SURCE

stmy~l USMA stuident manycars, WAP&an.off OMA J-BOOK

stiny2- OCS student manycars, acqparins-offa

stmy_3 ROTC student mmnycars acqparms-off Assumed - 0

stmy.4 HPSP souen manycar acqpams.off OMA i-BOOK

grad1 USMA graduate AcqParns-off

grad); OCS graduates cqpeM=.off

grad3 ROTC graduates WAVqpriS.off

grad_ 4 HPSP graduates wacparms.off OTSG

oswtgj USMA operational support costs acqpams-off OMA i-BOOK

ostmg_2 OCS operational support costs acqparins-off OMA i-BOOK

osý_wgj ROTC operational support costs acqparms.off OMA i-BOOK

cs..tng 4 HPSP operational support costs acq~arins off Assumed - 0

a& I USMA advertising costs acqparins.off DAPE-ZXA

adv72 OCS advertising costs acqparms-off Assumed - 0

adv73 ROTC advertising costs acqparms-off DAPE-ZXA

adv74 HPSP advertising costs acqparzns-offa

imy off 1 USMA OFFICER instructor costs acqparm.off OMA i-BOOK

imyoff) OCS OFFICER instructor costs acqparns-off OMA i-BOOK

imyoffL3 ROTC OFFICER instructor costs acqparzns.off

imyoff4 HPSP OFFICER instructor costs acqparms-off

imyenhl USMA ENLISTED instructor costs WAcVaMS.off Assumed - 0

imyenl_2 OCS ENLISTED instructor costs acqparns-off

lzny ;*3 ROTC ENLISTED instructor costs acqparzns-off

imyenl4 HPSP ENLISTED instrutor costs acqparins.off

pay_03 average annua pay for 03 Wacqprm.Off AMCOS

SCD)BpayO4 avernge annul pay for 04 acqparms.off AMCOS SCDB

pay-E6 average annual pay for E6 acaparnis.off AMCOS SCDB,

payE7 average annual pay for E7 acqparnis-off AMCOS SCDB

sch I USMA scholarshp costs acqparms.off Assumed - 0

sch) OCS scholarship costs acqparms-off Assumed - 0

sch3 ROTC scholarship, costs acqparnis-off OMA I-BOOK

sch74 HPSP scholarship costs Wacpa=n.off OMA i-BOOK

A- 30
3.11 NEW GI BILL

COM•POSTION: Estimates the expected present value of the basic benefit associated with the New

GI Bill. The basic benefit is actually funded by the Veteran's Administrton and does not appear in

either the Army's nor the Department of Defense's budget. However, this module computes the

expected present value, at the time of enlistment, of the net govermnent outlays associated with the

basic benefit. (The estimated cost of "kickers" are included in the recruiting cost module.)

To participate in the basic benefit of the New GI Bill, a member must be a high school

graduate and must deci: to participate in the beneit shortly after her enlistment. The program is

conatmory, and if a member chooses to participate, $100 per month for twelve consecutive months

is deducted from the participant's pay check.

The basic benefit is equal to $300 per month for up to 36 months for an enlistment of three or

more years, and $230 per mouth for 36 months for an enlism of two years. The stipend is

payable to individuals who enroll in full-time college programs. Partial payments are awarded to

members who enroll in part-me programs.

F.peaed Presen Value Coimpaaons:

Let EPVi(4) be the expected present value of the Army College Fund for four-year

enlistments in year of service i. Then,

12 -o57 00I - +0UWE 300 +U• a" 

EV4 MEt I

0.42) 11)1)(+L2t

1 is

++ ÷ 0

In this equation P.. is the participation raw in the program among four-yer enlistees in MOS k; U, 4,.

is the usage rate for four-year recruits in MOS k, t years after completing thei initial contract; and r

is the discount rate. Note that the maximm for U14.1 is I minus the first term reenlistment rue for

four-years enlistment in MOS k. Then, EPVu is th expected presut value of the Sovernent

outlays for thrw-year enlistments in MOS k.

A-31
43 300 5

Eu M +] °( +UWE +

4+ -4 I1

12) 12

Finally, the expected present value for a two-year enlistme in MOS k is

,Evo .- f F -10 -'- 9 + U.,, 33 2 500+u +u o

Ial + EP1 12) (1 I+I+ -2)1r2 

7 250,÷ 0. 250

4PAJUW EM + - I

K" (i e)

Then, the expected present value of the goverunent outays for the basic benefit is

0.4%) EPVA - aEVO ai 4 +EVA WtEVA

where a-, a2, and a% are, respectively, the proportions of two-, three-, and four-year enlistment in

MOS k.

SIMMIJ)FCATION: Becaue so many of the basic parameters of this cost equation are unknown,

the actual module we will program for in the nitial version of the model will be much simler.

Fks, calcuate

0(1 1

2 ) -+

T1en, let f be the compounded parnclpatdo and usage rate among al patdici who are not eliglible

for 'kickers, and let cp be the compounded participatdio and usage rate for those eligible for

"kickas." Thn the expected present value for MOS k is

ROeM,, , Is the proportio of recruits in MOS k not eligible for educational benefit "kickers"

A-32
04)PVj .s,&1 (PV) + SA(pXPV) 0.47)

under the New G1 Bill, and sk is the proportion eligible for *kickers.

DISCUSSION: Because the New GI Bill is in fact new, there is little information on usage rates.

One can make an informed guess concerning what they are likely to be, however, we have avoided

going into great detail concerning parameters of which we are ignorant.

It is likely that usage rae for the New GI Bill will be significantly greater for those who are

eligible for educational beefit kickers. The simple equations allow one to take this into account.

Also note that the New GI Bill is funded through the Veteran's Administration budget. It is likely

tha it will be suppresse in most applications of the life-cycle model.

NOTATION:

EPVU - Expected present value of educational incentives in MOS k for enlistmemn

conamt lngth I

r - Discount rate

PV - Present value of educational incentives

Puj - Participation rate of recruits in the New 01 Bill

Uk - Usage rate for individuals in MOS k, with conact length 1, in year s after

completing their initial term of service and leaving the active Army

S10 - Proportion of recruits to MOS k who are eligible for kickers

k2 - Proportion of recruits to MOS k who are not eligible for kickers

f - m participation and usage rate for those who are not eligible for

kickers

CP CM pounded participation and usage rate for those who are eligible for

STRUC COST DATABASE VARIABL, - Definitions

acjlb - Average cost of providing GI Bill bMfts to each member

MDERLYING VARIABLXS

YARIAM DEIr- LOCA71ONDAASUC

w percm of high qual rcruits recdata.edl FORECAST

A-33
•.t mmn•TONCOSTS

COMPOSMrTON: There are three types of separation benefits that service members may receive,

depending upon their qualification. These benefits are (1) accrued leave benefits; (2) involuntary

separation benefits; and (3) voluntary separation benefits.

Accnd Leaw. Each service member that is separated from the Army is entitled to receive payment

for the amount of unused leave she or he has accumulated.

nvobuwa Sepamrmto. Any member forced out, regardless of when he or she emered the service,

who has been on active duty at least six years receives a one-time, lump-sum payment. If a member

is not qualified for retention - e.g., QMP, overweight, past a RCP - she or he may receive only a

partial payment. Those members separated for misconduct are not eligible for separatio pays.

Vokgy Separaion. The services are offering bonuses to selected members with between 6 and 18

years of service to leave active duty voluntarily. The bonuses may be offered to members who have

more than six years active service as of December 5, 1991. Members may choose between an

ammuity (VSJ) or a lump sum (SSB). This program is effective through FY95.

In addition to the benefits noted above, each service member that separates is entitled to a separation

move.

AVERAGE COST/MARGINAL COST: To calculate the average cost of providing separation

benefits to members, we first calculate the cost of each of the three types of payments. Either the

payment is a lump sum or it is an ammuity. To calculate the cost of the lump sum payment, regardless

of the reason for separation, we use the calculation

(3.48) Past?. - (rateh(L&=.X12BPO jL

where i equals a member's YOS, index c indicates the category of separation (i.e., c w 1 indicates

volumtary separation, c - 2 indicates involuntMry separation with eligibility for full benefits, and c =

3 indicates involuntary separation with only partial payment authorized), rate, is the percentage of

basic pay used depending on the category of separation (rates'" - .15, rate', - .10, rate•, -

.05, and ratesm - .025 for each YOS), los& is the number of losses experienced in category c by

members in YOS i and MOS k. 12BPI is the annual basic pay for a member in YOS i and gradej.

The last term in the equation represents the assumption that losses are distnibuted across grades in

proportion with inventory.

To estimate the net present value of providing an annuity to eligpble members voluntarily separating,

we use the following calculation:

where n is the year that the annuity is paid, minus the current year, and r is the anual discount rate

A-34
(.10). To estimate the average cost of separation, then, we divide the total cost of providing the

separation benefits by the population by grade.

0.-0) A¢• '- C I

where pww and p are the probabilities of a voluntary separatee opting for the lump sum benefit or

annuity, respectively, and pim equals (1-p-).

Other Searadon Pay. (Lump sum leave paymmes plus severanceMdisability pay plus separation

move).

a. When a service member leaves the service, the member is authorized to cash in any

unused leave at the rate of basic pay to which he or she is entitled at the time of separation. The

average cost of the lump sum leave payment is calculated by multiplying average number of month.,

leave accrued for each grade by base pay by the probability of separation.

0.1)AC~r4 mACA'P. AM1~j pv

b. A service member is authorized severance pay for disability retirement. The average cost

of disability severance is calculated by dividing the total severance pay by the numbers of separatees

by grade.

(3.32) AC 1

11'V,

c. Average cost for other separation pay is the sum of the above costs plus the cost of a

separation move.

(.53) ACJ;"v - AC,"w4 + ACj' ' A3 + 

A-35
Thus, total separation costs equal the sum of the average costs for separation incentives and other

sepaaion costs.

NOTATION:

Pmt.' -= Lump sum payment cost for separation benefits for separation category c,

YOS i, and MOS k

c - Category of separation (c- i, voluntary separation; c-2, involuntary

separation but eligible for full benefits; c-3, involuntary separation with

partial payment of benefits)

rate, = Percentage of basic pay depending on category of separation

loss,& - Percentage of losses experienced in separation category by members in

YOS i and MOS k

BPi - Basic pay for a member in YOS i and grade j

F.* = Soldier inventory for YOS i, grade j, and MOS k

PmtK - Annuity payment cost for separation benefits for separation category c,

YOS i, andMOS k

ph"n - Probability of a voluntary separatee opting for a lump sum benefit

po - Probability of a voluntary separatee opting for an annuity

ACj " Average cost of separation for grade j and MOS k

AC"j, -=1m Average cost of separation incentives for grade j and MOS k

Aq°hw - Average cost of other separation pay for grade j and MOS k

AC;Pm- - Average cost of a separation move

STRUCTURED COST DATABASE VARIABLES - Definitions

ac vsi - Average cost of voluntary separation incentive

acisi - Average cost of involuntary separation incentive

ac othuep - Average cost of accrued leave and separation move

asepcost - Average cost of all separation costs

UNDERLYING VARIABLES

A-36
W LOCATION DAI& SURC

bwspay basic pay by grade and YOS mcparms.en] Uniformed Svcs

Almanac

inv inventory of grade, MOS, and YOS inv.enl DMDC

losses losses receiving vsi or full or partial sepparms.enl PERSINCOM

isi by YOS

discountrate annual discount rate srbparms.enl assumed - .10

prob_hlmp probability of receiving a lump sum sepparms.enl assumed - .98

incentive pint rather than an annuity

probann probability of receiving an annuity pint calculated

rather than lump sum pint anMnal rate vsi multiplier for annuity pmts sepparms.enl DCSPER

aml avg months of leave by grade sepparms.enl MPA J-Book

tot othsep total cost of accrued leave & sep move MPA J-Book

cost by grade

luhp~pint lump sep incentive pnts by grade calculated

npvamann. t net present value of annual pmt calculated

ac vsi average cost of vsi by grade calculated

ac-isi average cost of isi by grade calculated

A-37
APPENDIX B

DISCUSSION OF THE INVENTORY PROJECTION MODULE

DATA REQUIREMENTS

This appendix will discuss the data requirements for the EPICC

inventory module, our source for the data, our method of extracting

the data, and our methodology for adjusting the raw data, where

appropriate. The discussion will be organized by data element. In

general our data came from the Enlisted Master File and the ODCSPER

Gains and Loss Tapes using SAS programs to extract the data. The

raw data was then modified for the EPICC model by SRA. We

initially drafted the SAS program then ODCSPER modified the

programs and conducted the data retrieval "in-house" to expedite

the process.

STRENGTH CONSTRAINTS:

Baseline Inventory. The model requires a baseline starting

inventory that reflects the most recent year end position of actual

enlisted strength. The inventory should be dimensioned by grade,

YOS, and subinventory. To measure grade we sorted by the data

element PAYGRADE. We measured YOS as the difference between the

end fiscal year date and the basic pay entry date (BPED) measured

in years. We counted the inventory within subinventories by using the following variables; SEX, REDCAT, a combination of AFQT score

and AFQT category', and level of civilian education (HSDG or NHSDG).

Using SEX we sorted the inventory by male and female; using REDCAT

we sorted by white and other2 ; using AFQT Score and AFQT we sorted

by CAT I-IIIA, CAT IIIB, and CAT IV; finally, using CIVED we sorted

by HSDG and NHSDG. We also added one cell as a catch-all for

collecting records that do not match the above definitions. There

will be a total of 25 sub-inventories (2x2x3x2 + 1).

Reauirements/Endstrength. The model requires that the user

provide force structure requirements by grade for each projection

year. These by grade requirements are used as targets by the

model. In effect the model minimizes the difference between

projected inventory and force structure requirements. The default

force structure requirements used in EPICC were provided by DAPEMPE.

Accession Distribution. The model requires that the user

specify a distribution for allocating NPS accessions across

subinventories. The default file reflects the distribution from

the most recently completed fiscal year. In that file, NPS

I As renormed for faulty test scores from previous years.

2 The data element REDCAT was chosen so that hispanics would

be grouped with blacks. Our assumption is that hispanic behavior

is more closely aligned with blacks than with whites.

B-I
Accessions were measured using ODCSPER's Gain/Loss Tapes. We

measured the number of NPS accessions from each month's tape and

accumulated the totals over the whole year for the previous fiscal

year. We also accumulated the accessions for each subinventory. The distribution was obtained by dividing totals for each

subinventory by the total number of accessions.

Ouarterlv Timing of Accessions/Accession Losses. To develop

some notion of the flow of accessions over a year, the model uses

a quarterly distribution of NPS accessions. This distribution is

provided by the user; however, the model will use a uniform

distribution in the default file. To determine Accession losses

(or NPS accession attrition), we measured the following information

about the FY90 accession cohort - for each sub-inventory: total

number of NPS accessions in FY90; number of soldiers leaving

service with 0-3 months of service (m/s); number of soldiers

leaving with 4-6 m/s; number of soldiers leaving with 7-9 m/s; and

number of soldiers leaving with 10-12 m/s. These numbers, divided

by the quarterly cohort endstrength, provide the module with the

quarterly attrition rates.

PROMOTION PARAMETERS:

Minimum Promotion Rates. Although the model will first

promote to fill vacancies, it also checks promotions against a

minimum promotion rate provided by the user. This is the desired

minimum rate to maintain reasonable promotion opportunity. They

are calculated by DAPE-MPE. The default file reflects the DAPE-MPE

rates.

Promotion Rate Adjustment Factors, Default adjustment factors

are set at 1.0, however the user may change these factors. The

model applies the product of the adjustment factors and the minimum

promotion rates to the grade requirements to determine promotion

floors.

Primarv/Secondarv Zones. The default file sets beginning and

end points for early and normal promotions in accordance with AR

600-200. The user may also specify a percentage of the total

promotions that determines the number of early promotions. These

parameters are specified for the grades being promoted fJrm.

PRIOR SERVICE ACCESSIONS: EPPIC uses prior-service data broken two

different ways. From the gain/loss tapes we accumulated accessions

from each month to build matrices dimensioned 1) by grade and YOS,

and 2) by subinventory and term of service. The user must also add

the desired number of prior service accessions for each projection

year. The default file will reflect PS numbers as determined by

DAPE-MB.

RETENTION RATES: The EPICC model uses retention rates that reflect

the flow of inventory from one fiscal year to another. As such,

the rates are generated by comparing the ending inventories for two

successive fiscal years. The model accepts three different types

of retention rates; reenlistment rates, extension rates, and nonB-2
ETS continuation rates.

Reenlistment Rates. Baseline reenlistment rates are measured

by counting the numbers of reenlistments recorded in the gain/loss tapes for each month, totaling that number over twelve months, and

dividing by the number of soldiers on the end FY89 EMF with less

than 12 months to ETS. Another input data file contains adjustment factors dimensioned by projection year, subinventory, and ranges of

YOS (1-5, 6-10, 11-31). The default file will contain factors of

1.0.

Extension Rates. Baseline extension Rates are measured in a

similar manner by counting the number of recorded extensions on the

gain/loss tape and dividing by the number of soldiers in the end

FY89 EMF with less than 12 months to ETS. As with reenlistment

rates another input data file contains adjustment factors

dimensioned by projection year, subinventory, and ranges of YOS (1- 5, 6-10, 11-31). The default file will contain factors of 1.0.

Non-ETS Continuation Rates. We defined a continuation as any soldier who was not at ETS, continued on to the next year. The

baseline continuation rates are measured by comparing EMF snapshots for end FY89 and FY90. The denominator is the number of records in

the FY89 snapshot with a time-to-ETS of greater than 12 months.

The numerator is the number of FY89 records remaining in the FY90

snapshot. Here too there is an additional input data file that

contains adjustment factors dimensioned by projection year, subinventory, and ranges of YOS (1-5, 6-10, 11-31). The default

file will contain factors of 1.0.

Allocation rates for Non-ETS Reenlistment. and Exte

Still using the gain/loss tapes, we extract the numbers of non-ETS

reenlistments and extensions. These numbers divided by the non-ETS

population provides the model with the appropriate allocation

rates.

INVOLUNTARY LOSSES: Involuntary losses are those losses that occur

when the soldier is determined to be unqualified to continue in the

force. There are two ways this can occur:

Retention Control Points. These are the maximum numbers of

years of active federal service authorized for a soldier in a

specific grade. The default file will set control points as

specified in AR 600-200 for each projection year, however the user

may change these control points in anticipation of policy changes.

Oualitative Manaaement Program Losses. These are losses that

occur as a result of DA screening boards. The input file accepts anticipated numbers of QMPlosses for each projection year by grade

as well as a distribution for these losses across YOS.

DISTRIBUTION OF BASELINE INVENTORY BY TIME-TO-ETS: This

distribution allows the model to set the baseline inventory across

the time-to-ETS dimension. The default data reflects a matrix

dimensioned by YOS, time-to-ETS, and subinventory. For each

B-3
subinventory the SAS program calculated the percentage of records

in each of six time-to-ETS cells defined as 0-12 months to ETS; 13-

24 months to ETS; 25-36 months to ETS; 37-48 months to ETS; 49-60

months to ETS; and 61-72 months to ETS. This distribution is

automatically set at the beginning of a run and can not be modified

by the user.

DISTRIBUTION OF TERM LENGTHS: To keep track of numbers of soldiers

as they transition across the time-to-ETS dimension, there are

three files of that will distribute initial enlistments,

reenlistments, and extensions.

Initial Enlistments. When measuring NPS accessions using the

ODCSPER gain/loss tapes, we accumulated accessions by initial terr

of service. This generated a vector of NPS accessions by term of

service and is used as the default data for each projection year in

the input file. The user may modify this to reflect anticipated

policy changes.

Reenlistments. Using the gain/loss tapes and the EM? for both

end FY89 and FY90 we identified reenlistments and then conducted a

"crosstabs" comparing time-to-ETS. This generates a matrix

dimensioned by old time-to-ETS and new time-to-ETS. The default

file reflects this transition matrix for each projection year. The

user may adjust the matrix to reflect any anticipated policy

changes.

Extensions. In a similar way we used the gain/loss tapes and

the EMF for both end FY89 and FY90 we identified extensions and

then conducted a "crosstabs" comparing time-to-ETS. This generates

a matrix dimensioned by old time-to-ETS and new time-to-ETS. The

default file reflects this transition matrix for each projection

year. The user may adjust the matrix to reflect any anticipated

policy changes.

B-4
APPENDIX C

LINKING ACCESSION SUPPLY TO EPICC: DESIGN CONCEPT PAPER

I. Introduction

Given compensation and other personnel policies, the

Enlisted Personnel Inventory, Compensation, and Cost (EPICC)

Model estimates the number of non-prior service accessions

required to meet specified endstrength targets. The EPICC

prototype also estimated the cost of obtaining those accessions

using a methodology developed for the Army Manpower Cost System

(AMCOS). Specifically, the average cost of recruiting a high

quality (AFQT categories 1-3A, high school diploma graduate) and

a non-high quality soldier, which is calculated from recruiting

resources expended in a base year, is applied to the required

number of high quality and other accessions to derive total

costs.

While this costing approach is adequate for many

applications, it ignores the empirical evidence that the average

cost of recruiting high quality individuals rises with the high

quality recruiting mission. Therefore, accession cost estimates

using constant average costs will understate the cost of

recruiting more individuals than were accessed in the base year

and overstate the costs of recruiting fewer. This is a

potentially serious problem when EPICC is used to evaluate

significant changes in accession levels, as in analyzing alternatives for downsizing the enlisted force.

This paper describes an alternative approach to estimating

accession costs using a cost function. The recruiting cost

function describes the minimum cost& associated with achieving a

given recruiting mission specified by quality level. It is

derived directly from an enlistment supply function, which

describes how recruiting resources, such as advertising and

recruiters, and market factors, such as unemployment and the

level of military pay, affect the number of high quality

enlistments. This approach offers several analytical advantages

over the methodology used in the prototype:

Because the enlistment supply function now

used in EPICC displays decreasing marginal

returns to recruiting resources, the cost

function will generate marginal and,

therefore, average costs that rise with the

level of accessions. This will improve the

estimate of recruiting costs when the level

of accessions varies from the base year.

Because the enlistment supply function

includes market factors, accession cost

estimates will vary with the assumed

C- 1
unemployment rate and level of relative

military pay. Thus, the two principal

avenues by which the civilian labor market

affects enlisted personnel policy -- accession costs and reenlistment rates -- will be incorporated into EPICC projections.

Because the recruiting cost function

calculates the minimum cost of achieving a

particular recruiting mission, it implicitly

solves for the optimal mix of recruiting

resources. Thus, the resource implications

of alternative accession missions can be

expanded from the current information on

total costs to include estimates of the

required number of recruiters, the optimal

amount of advertising, and the best size for

the enlistment bonus pool.

The key parameters of the new cost function are simply enlistment

supply elasticities, the percent change in high quality contracts

for a percent change in recruiting resources/incentives or market

factors. Our implementation of the recruiting cost function in

EPICC will allow the analyst to change these elasticities,

providing a way for new information on enlistment supply to be

easily incorporated into the recruiting cost estimates provided

by the model.

Section II of this paper describes the cost function

approach in detail. In Section III, we demonstrate the approach

using FY90 data. Section IV discusses implementation of the cost

function in the EPICC model.

II. A Recruiting Cost Function

Our approach is a direct application of the microeconomic

theory of production costs.' We derive the recruiting cost

function from the enlistment supply function and the prices of

recruiting resources using the mathematics of constrained

minimization. To begin, we assume that the number of high

quality contracts signed in a given time period can be described

by an enlistment supply function of the form

where

* A,,, AA. and Ak are high quality, "medium"

'Similar methods have been used to determine the recruiting

costs of alternative quality distributions for the Navy (Deborah

Clay-Mendez, A Recruiting Cost Function for Male High School

Graduates, Center for Naval Analyses, 1982) and in the OSD

Accession Quality Cost-Performance Tradeoff Model currently under

development.

C-2
InA. - ao ÷ M. AV "-Aý+ ÷. (A _AF'AJ+1: Is nR,)

+IZj(aj lnlj) +-k(aklnFk)

quality (AFQT category l-3A non-graduates), and "low" quality (all others) accessions,

respectively; 2

* R's are recruiting resources, such as the

number of recruiters and the amount of

advertising;

* I's are recruiting incentives, such as the

average enlistment bonus and the average value of the Army College Fund (ACF);'

* F's are factors that affect the recruiting market, such as the unemployment rate, and

the level of military pay relative to

civilian pay; and

a's and A-•s are parameters of the

enlistment supply function.

The form of this enlistment supply function, log-log, is

similar to that commonly used in the enlistment studies. The a's

represent the elasticity of high quality enlistments with respect

to recruiting resources, incentives, and market factors., The

only difference is in our treatment of the tradeoff between high quality and other enlistments, which is typically captured by including ln(A,) and ln(Ak) directly, rather than relative to a

maximum accession amount. The standard approach, however,

implies an improbable tradeoff in which the increase in high quality contracts associated with an decrease in the medium or

2While the high quality definition is standard, "medium" and

"low" are our choice of labels for the accession groups defined

in parentheses. We use these groupings simply because the

associated supply parameters have been estimated in the

literature.

3In our terminology, recruiting resources are inputs to the

recruiting process that have prices attached to them while

incentives are benefits paid to high quality recruits.

'Equation (1) can also be interpreted as the logarithmic form of a Cobb-Douglas production function, a functional form

which places certain restrictions on the substitution of inputs in the production process. In principle, recruiting cost

functions can be developed from more flexible production functions. In practice, our empirical knowledge about recruiting production functions is, for the most part, limited to the CobbDouglas form.

C-3
low quality mission is largest when the number of non-high quality contracts is small, rather than large. In economic

terms, the production possibility frontier in equation (1) has

the expected convex shape; the standard approach produces a

frontier that is concave to the origin.

The minimum costs associated with recruiting a given number

of high quality contracts, A, is given by the answer to the

constrained minimization problem

Min [E (pR,) + A;jIj - Aq - A;] (2)

The first term in brackets represents the variable cost portion of the recruiting budget; it has two components. The first is

the sum of expenditures on recruiting resources, determined by multiplying the level of resource use, Ri, by the resource price, pi. The second shows the expenditures on recruiting incentives,

which equals the average cost of these incentives multiplied by

the number of high quality contracts. The second term in

brackets assures that costs are minimized subject to the

constraint of recruiting X high quality individuals.

The first order conditions for equation (2) describe the

solution to the cost minimization problem -- the levels of

recruiting resources, R , and incentives, I:, required to

R- ( ) and Am

where

and a =

recruit 4 at minimum cost.

Substituting these equations for the levels of resources into the

cost equation yields a recruiting cost function of the form

C. = + Ajr; + C, (4)

where CT is total recruiting costs and Cr is the fixed costs

associated with recruiting.

This cost function has four conceptual advantages over the

methods typically used to estimate recruiting budgets. First, the marginal cost of recruiting a high quality soldier rises with

the mission, as implied by enlistment supply research. Unit or

average-cost estimation methodologies incorrectly assume constant

C-4
Table C-1: Inputs to FY90 Cost Function

FaZMO~ Sup&Iy Ehscd. Rmurce Prim

Production recruiters 0.25 Production recruiters $,825

Advertising 0.05 Advertising $1

Enlisment bonus 0.07

Army College Fund 0.14 Fixed Recrmiti Costs $118M

Unemployment 0.70

Relative military pay 0.80 FY90 Market Factors

Constant 1.49 Unaemployment rate 5.3%

Relative military pay 0.89

Quwft Tradeoff Parameters FY0 Contcts

High-to-medium 1:2 AFQT 1-3A, HSDG 63,100

High-to-low 1:6 AFQT 1-3A, NHSDG 1,100

AFQT 3B, 4 25,200

marginal costs.s

Second, the cost function shows how changes in the

recruiting environment will affect the costs of recruiting a

given mission. Unemployment, for example, is positively related

to high quality enlistments which means that the minimum costs to

recruit a given mission will decrease when unemployment

increases. Methods based on historical costs alone implicitly

assume that the recruiting environment is static.

Third, because costs are based on an optimal allocation of

recruiting resources, the cost function is superior to

determining changes in recruiting costs by varying only one

resource, such as the number of recruiters. In general, these

"one resource" approaches will overstate the required change in

costs.

Fourth, most recruiting cost estimation methodologies assume

that the costs of recruiting a given high quality mission are not

affected by the size of non-high quality mission. This

contradicts recent enlistment supply research which demonstrates

that increasing the non-high quality mission, without increasing

the number of recruiters, "crowds out" some high quality

production. Because the cost function is based on an enlistment

supply function which includes non-high quality enlistments, it

recognizes that interaction.

III. An Application to FY90 Recruiting Costs

To validate the methodology, we developed an Army recruiting

cost function for FY90. Table 1 lists the values of the

parameters and variables in the cost function.

'Formulas for the marginal costs of recruiting high quality

and other soldiers are shown in an addendum to this paper.

C-5
The supply elasticities are drawn from the following

studies:

0 Recruiter, advertising, unemployment, and relative pay:

Thomas V. Daula and D. Alton Smith, "Estimating

Enlistment Supply Models for the U.S. Army," in R.

Ehrenberg, ed. Research in Labor Economics, Volume 7.

Greenwich, CT: JAI Press, 1985.

* Enlistment bonus: J.M. Polich, et al. The

Enlistment Bonus Experiment. RAND Corporation (R3353-FMP), 1985.

* Army College Fund: D. Alton Smith et al. Army

College Fund Cost-Effectiveness Study. SRA

Corporation, 1990.

While there is a fairly wide range of supply elasticities in the

research literature, these are typical of the findings in the

better studies.'

The constant, a., is calculated so that the enlistment

supply function predicts the actual FY90 high quality contracts,

given the level of FY90 recruiting resources/incentives and

market factors. Choosing the constant this way assures that the

cost function is based on a reasonably accurate enlistment supply

function when one study cannot provide the best estimate of all

required parameters. It does not, however, force the costs

predicted for FY90 to equal actual costs, as the Army may not

have used the mix of resources estimated to be optimal by the

cost function.

The parameters measuring the tradeoff between high quality

and other enlistments are set so that in FY90 a reduction in one

high quality contract, other factors held constant, yields either

two additional medium quality contracts or 6 additional low

quality contracts.' The available evidence suggests a high-toA•A of these studies use regression analysis to estimate

the supply elasticities. Other approaches to estimating

production functions, such as Data Envelopment Analysis (DEA) or

frontier production functions, could also be used to provide the

supply elasticities for the cost function.

7The formula for a. is

AAX( AN-.

Using a maximum of 25,000 medium quality contracts and setting A9

and A9 at FY90 levels, a. is 0.23 for a 1:2 tradeoff. Using an

analogous formula with a maximum of 75,000 low quality contracts,

al is 0.12 for a 1:6 tradeoff.

C-6
low tradeoff of between 1:4 and 1:8; the high-to-medium tradeoff

is simply an extrapolation of these results. 8

The price information is determined as follows. Advertising

is measured in dollar terms, so we set the price to $1. The

recruiter price includes both the military compensation and

support costs (such as transportation and office expenses) of

adding a production recruiter. We calculate it by dividing 85%

of field recruiting costs in FY90 by the number of production

recruiters. The remaining 15% of field costs are assumed to be

fixed management expenses and are included along with

headquarters costs in the estimate of fixed recruiting costs. 9

Table 2 compares the resource levels and recruiting budget

predicted from this methodology with the actual numbers.

Table C-2: FY90 Predicted v. Actual Resource Levels and Costs

cod FY0

Function Actua

Resource Levels

Production recruiters 5,508 5,700

Advertising (variable costs in M$) 46.6 55.6

Enlistment bonus ($ per HQ recruit) 1,035 935

Army College Fund ($ per HQ recruit) 425 272

Recruiting Budget

Variable costs $459M $444M

- ACF costs 18M 0

+ Fixed costs 118M 118M

Total costs 559M 562M

Predicted values are calculated by substituting the values in

Table 1 into equations (3) and (4). We include the ACF in

determining the minimum budget but subtract its total cost for

comparison with the actual budget. In FY90, the accrual charges

for the ACF were set at zero to compensate for previous

overcharges. Both the enlistment bonus and the ACF value are

expressed in dollars per high quality enlistment. Because only a

fraction of high quality recruits receive a bonus or ACF benefit,

OSee Daula and Smith, op cit, and J. Dertouzos, Recruiter

Incentives and Enlistment Supply. RAND Corporation, R-3065-MIL,

1984.

'These cost data were obtained from ODCSPER.

C-7
these numbers are smaller than the statutory amounts. 10

The cost function results imply that a reallocation of

resources away from the recruiters and towards advertising and

the enlistment bonus would have achieved the same mission of high

quality and other enlistments at a slightly lower variable cost.

The difference, however, is relatively small and probably within

the range of measurement error associated with the enlistment

supply elasticities. In general, there is a remarkable

correspondence between the cost function predictions and the

actual budget for FY90.

Table C-3: FY90 Marginal Cost Estimates

Mlargina Costs

Accession Category

AFQT 1-3A, high school diploma graduate $16,185

AFQT 1-3A, non-graduate 7,725

AFQT 3B and 4 (bjth graduate and non-graduate) 2,575

Recntuin Enviroamment

Half point increase i unemployment rate -$66M

Two percentage point increase in relative military pay -$15M

Table C-3 displays two types of marginal cost estimates that

can be derived from the cost function. The first section shows

the estimated marginal costs of recruiting three different

categories of individuals. High quality recruits, of course, have the highest marginal costs. Altnough not shown in the

table, the marginal costs in this example depend upon the

mission. High quality marginal costs, for example, increase with

either the high quality or other mission. Increasing marginal

costs with the high quality mission follows from an upward

sloping supply curve for high quality individuals. Increasing marginal costs of high quality recruits with increases in the

other missions is an implication of the interaction between

missions in the production function.

The second section displays the estimated budget impacts of

two favorable changes in the recruiting environment -- an

increase in unemployment and an increase in military pay relative

to the private sector. Both changes reduce the cost of

recruiting a given mission.

" 1°The cost of the ACF is less than the benefit level because

benefits are paid in the future and not all eligibles decide to

use their benefits. We multiply the total benefits paid, AIAU, by the ratio of the accrual charge in FY90 ($1,342) to the 3-year benefit level ($12,000) to estimate ACF costs.

C-8
IV. Implementing a Recruiting Cost Function in EPICC

The recruiting cost function described in the previous two

sections replaced the AMCOS methodology for calculating accession

costs in EPICC. We discuss the implementation in two parts: the

inputs to the cost function and the cost/resource outputs.

I Table C-1 organizes the required inputs into six

categories. The inputs in each category will be determined as

follows:

* Enlistment supply elasticities. A screen was

developed displaying the elasticities in

Table C-1 as default values which, with the

exception of the constant, can be changed by

the user. If any of the elasticities are

changed, EPICC will recalculate the constant

to assure that the enlistment supply function

is still accurate for FY90.

* Quality tradeoff parameters. The recruiting

cost screen also allows the analyst to change

the assumed tradeoff between high quality and

other recruits. EPICC will automatically

recalculate the underlying enlistment supply

function parameters.

Resource prices and fixed recruiting costs.

Base year values for these prices can be

changed in the recruiting cost screen. To

estimate projection year costs in then-year

dollars, EPICC will inflate the recruiter

price using the MPA inflation rate,

advertising using the OMA rate, and fixed

recruiting costs using an average of the MPA

and OMA rates.

* Market factors. The unemployment and

relative military pay assumptions by

projection year are the same as those used in

the compensation-retention module to adjust

reenlistment rates.

* Contracts. The number of high, medium and

low quality contracts to be used in

estimating recruiting costs will be generated

by the inventory module.

To facilitate the evaluation of alternative supply elasticities,

quality tradeoffs, and resource prices, a pop-up screen accessed

from the primary recruiting cost screen will duplicate the

information in Table 2, showing the optimal resource mix and

costs associated with new parameters for FY90 for comparison with

the actual results.

C-9
Outputs, The cost function will generate the following

items for each projection year in an EPICC run:

Total recruiting costs, by appropriation.

Total costs are given by equation (4). We

will allocate these costs by appropriation as

follows:

- Advertising: OMA

- Recruiter costs: MPA and OMA in

proportion to base year appropriation

shares

- Enlistment bonus: MPA

- Army College Fund: MPA

- Fixed recruiting costs: Base year

MPA/OMA shares

Minimum-cost resource/incentive mix,

including the number of production

recruiters, the amount of advertising, the

average enlistment bonus, and the average

value for the ACF.

C-10
Addendum: Mazrginal Recruiting Costs

The marginal cost of a high quality recruit is determined by

differentiating equation (4) with respect to A.,

(Ama-A.) - (Arx-AL) A "

Marginal costs rise with the number of high quality contracts if

the exponent of Ak is positive, or (l+Ejo,) > (Ejj+Eiaj) . This

will be true if the sum of the elasticities on recruiting

resources is less than one, a condition which holds for

reasonable values of these elasticities.

C-1I
APPENDIX D

USER'S GUIDE TO MODIFYING PAY LEASTICITIES IN EPICC

As part of the input to the compensation module, EPICC users

can modify pay elasticities defined by year of service (YOS) and

by quality categories (AFQT I-IIIA high school graduates, AFQT IIIIA nongraduates, and all others). The compensation module uses

these elasticities to calculate the parameters in the

compensation-retention equations that relate changes in the

annualized cost of leaving fACOL) to changes in reenlistment

rates.

The default pay elasticities included with EPICC are derived

from the results of the Army Compensation Models Project (Smith

et al.), which studied the reenlistment decisions of enlisted

personnel from 1976 through 1987. An important question is

whether these estimates are still appropriate for use in

projecting the reenlistment effects of compensation policy

changes in the 1990's. With the end of the Cold War, and the

subsequent reduction in the size of the Army, the characteristics

of and opportunities associated with an enlisted career in the

Army have changed markedly, potentially affecting the

responsiveness of reenlistment decisions to compensation changes.

A definitive answer to this question can only be provided through

new reenlistment research using recent data.

Until those results are available, however, it is important

to understand how the existing elasticities should be modified

when evaluating compensation policy changes to reflect the new

environment . We offer two insights: one derived from ACOL

theory and the other from practical considerations in evaluating personnel policies.

Insight #1: If you believe that soldiers today place a lower

value on the nonpecuniary aspects of a military career, as

compared with the 1980's, then the pay elasticities in EPICC

should be increased.

This insight is derived from ACOL theory. To review, the

ACOL decision rule states that a soldier will reenlist if

ACOL > (NC-JM) (1)

where ACOL is the maximum value (across different military career

horizons) of the annualized difference between military and

civilian compensation streams and NC and M are the annual value

of the nonpecuniary characteristics of a civilian and military

career, respectively.

The first panel in Figure 1 shows how the decision rule is

used to predict the reenlistment rate for a group of soldiers

who, because of similar service characteristics, have the same

D-1
ACOL. Because we can't explicitly value the nonpecuniary factors

in equation (1), we assume

that (NC - Wf) is a random

variable distributed

according to the triangular

distribution shown in Figure

D-1. According to the ACOL

decision rule, then, the LhIWteStmdbWbimi

reenlistment rate for these AM.

soldiers is the area of the a.W.•

civilian-military "taste"

distribution to the left of sm

the ACOL line.

The ACOL parameter in a

retention-compensation model L hmmsyp lm

measures the change in the

reenlistment rate for a given

change in ACOL, oý: the shaded

area in each of the panels.

In the second and third

panels, we have varied the

mean of the taste

distribution. Because we OLD A"P AN

also keep the shift in ACOL

values the same as in the

first panel, any change in

the shaded area represents a ARM

similar change in the ACOL

parameter. For example, the

taste distribution in the

second panel has a smaller

mean than that of the first,

indicating that the

nonpecuniary characteristics

of a civilian career are

valued less on average. The Figure D-1. Taste distribution

size of the shaded area and, and the ACOL parameter.

therefore, the ACOL parameter

decreases. Conversely, when

average military preferences decrease as shown in the third

panel, the ACOL parameter and the sensitivity of reenlistments to

pay changes increases.

(Differences in the taste distribution explain two common

empirical findings about pay elasticities. First, because of

self-selection, we would expect preferences for the military to

increase with years of service, implying decreasing pay

elasticities, which are found by Smith et al. and others.

Second, if military and civilian jobs have similar attributes,

the variance of the taste distribution will be smaller,

increasing the pay elasticity. Confirming this hypothesis, Smith

et al. find that first-term pay elasticities for the Mechanical

Maintenance and Administration MOSs are larger than those for the

Infantry MOSs.)

D-2
We can only speculate how differences in the current

enlisted career environment would change the taste distribution

from that represented in the estimated pay elastiticies supplied

with the compensation module. It seems, however, that most of

the environment changes-reduced nonpay benefits, leaner operating

and training budgets, more nontraditional missions, more social

diversity-will make the nonpecuniary aspects of a military career

less attractive. In this case, ACOL theory predicts that today's

pay elasticities will be higher than those measured from

reenlistment decisions made in the 1980's.

Insight #2: The estimated effect on total reenlistments of a

compensation policy change is most sensitive to changes in the

pay elasticities for early years of service.

The estimated change in reenlistments for a compensation

policy change is given (approximately) by

30

AReenlistments = Y. (ETSInventory1 ) x (ETSReupRate1 ) (2)

x (Percentage Change Pay1 ) x (PayElas tici ty1 )

Equation (2) shows that variation in pay elasticities has the

greatest effect on total reenlistments where the ETS inventories

and the default reenlistment rates are largest. Inventories

decrease with years of service, while reenlistment rates

increase. The inventory effect is greater, however, as

demonstrated in Table 1. Using selected data from EPICC, it

shows the range of additional reenlistments predicted for a 5%

pay increase when the default pay elasticity is decreased by 50t

from the expected value and increased by 50%. About 60% of the

variation between the high and low reenlistment estimates is due

to variation in the YOS 2-4 elasticity.

That pay elasticities for the early year of service are most

important in estimating voluntary losses also suggests where the

research effort should be placed in obtaining new elasticity

estimates. Simple ACOL models of first-term reenlistment

decisions are not only the easiest to estimate; they will also

yield the greatest benefits for policy evaluation.

Table D-1

Variation in Estimated Reenlistments with Elasticity Variation

VOS 41 Xgh-low -Rate -Py UlauZ1tiLGtY 3mginuistmm

2 - 4 49,100 .24 .95 - 2.9 1709 - S59 1 1150

6 - a 19,200 .54 .63 - 1.9 986 - 327 a 659

10 - 12 6,900 .70 .31 - .94 229 - 76 = 153

D-3
Referenoes

Smith, D. Alton et al. "Army Reenlistment Models," in Curtis

L.Gilroy, David K. Home, and D. Alton Smith, eds. Military

Compensation and Personnel Retention: Models and Evidence.

United States Army Research Institute for the Behavioral and

Social Sciences, 1991.

D-4