Enlistments into the U.S. Army from the Colorado/Wyoming area

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Enlistments into the U.S. Army from the Colorado/Wyoming area an econometric analysis
Kerns, Kevin J
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Includes bibliographical references (leaves 121-122).
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Submitted in partial fulfillment of the requirements for the degree, Master of Arts, Department of Economics.
Statement of Responsibility:
by Kevin J. Kerns.

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Full Text
Kevin J. Kerns
B.A., University of California, Los Angeles, 1977
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Masters of Arts
Department of Economics

This thesis for the Masters of Arts degree by
Kevin J. Kerns
has been approved for the
Department of Economics
W. James Smith
Wanda I. Griffith

Kerns, Kevin J.
Enlistments into the U.S. Army from the Colorado/Wyoming
Area: An Econometric Analysis
Thesis directed by Associate Professor Mei-Chu W. Hsiao.
This thesis develops an econometric model to es-
timate the number of high school senior or graduate males
scoring in the upper 50% on the entrance examination en-
listing into the U.S. Army from the Colorado/Wyoming
area. Model development is preceded by a review of the
literature from the draft era (1956-68) through recent
times (1988). Variables, models and ideas suggested by
the literature review are evaluated and examined. Those
that were found relevant are used in the local models'
development. Variables fall into several major
catagories: external environment such as unemployment
rate, civilian pay, population size; resource levels such
as number of recruiters, monetary expenditures in a
variety of areas; internal environment such as assigned
mission, number of members waiting to leave for basic
training; and dummy variables to indicate quarter of fis-
cal year or existence of supply limiting periods of con-
tracts. Monthly data from October 1984 through

September 1988 (fiscal year 1985 through fiscal year
1988) was used. The econometric model finally settled on
was estimated by use of the ordinary least squares method
using asigned mission, civilaian pay, quarter and supply
variables. The model provided estimates for third
quarter, fiscal year 1988 and fourth quarter, fiscal year
1988 that were better than 90 percent accurate when the
estimate was compared to the actual figure. A discussion
of the estimated results follow the model's development.
Policy implications indicated by the results are also
discussed. The discussion centers around adjustment of
the United States Army Recruiting Command's model to in-
clude a civilian pay variable; quicker reaction to high
unemployment rates, and the "stair-step" relationship un-
employment rates and enlistment supply have; relooking
the awards system, and constraining resources. Lastly
potential areas for future research are highlighted.
Recommendations here include exanmination of the effects
and timing of advertising and the motivation of the in-
dividual recruiter.
Ihe form and content of this abstract are approved. I recommend
its publication.

This thesis is dedicated to my wife, Cathi, and my daughter,
Lindsey, who put up with so much for so long and gave me en-
couragement when it was needed. Also my thanks to Lieutenant
Colonel Michael Dickson who gave me advice, insight and in-
terest into recruiting.

I. INTRODUCTION........................................1
Purpose of Study...................................1
Special characteristics of Army Recruiting.........4
II. LITERATURE REVIEW..................................11
Early Works.......................................11
Post Draft/Early All Volunteer Works..............16
Recent Works......................................45
Literature Summary................................70
Proposed Data Period..............................74
Proposed Variables................................75
Proposed Econometric Models...................87
Model Summaries...................................89
Discussion and Evaluation of the Results..........93
Unused Variables.................................100
Forecasts.................................... 110
Policy Implications..............................113

VI. SUMMARY AND CONCLUSIONS...........................117
Future Areas of Research.........................119
A. Data Statistics...............................123

2-1 Hanssens & Levien/s Coefficients for the Delayed
Entry Program......................................25
2-2 Ash, Uddis, & McNown's Coefficients for Army
2-3 Dale & Gilroy's (1983a) Coefficients for Army
2-4 Dale & Gilroy's (1983b) Coefficients for Army
2-5 Brown's Coefficients for Army Contracts.............48
2-6 Goldberg's Estimates from Alternate (TSCS) Army
Enlistment Models..................................53
2-7 More Goldberg Estimates from Alternate Switched
Regression Army Enlistment Models..................58
2^8 Hosek & Peterson's Supply Effects...................63
2-9 Daula & Smith's Estimates of Enlistment Supply......68
2- 10 Literature Summary............................. .71
3- 1 Variable and Data Source...........................77
4-1 Developed Models' Results

Purpose of Study
The purpose of this thesis is to build an
econometric model to estimate the monthly number of
quality male Army enlistment contracts possible from the
Colorado/Wyoming region. A quality male Army enlistment
contract is defined as a high school senior or graduate
male scoring in the upper 50% on the armed forces voca-
tional aptitude battery, an entrance examination.
A variety of models dealing with the estimation
of enlistments have been built on the national level
using fiscal year 1986 and earlier data. However, in-
herent in any national model is the assumption that
recruiting in New York City responds to resource inputs
or endogenous variables as does Casper, Wyoming; or,

that the sharp decline in unemployment in
Colorado/Wyoming during 1987 will have the same impact
as past gradual declines. The preceding propositions do
not follow intuitive reasoning and require continued ex-
ploration and research. The Army spends hundreds of
millions of dollars annually for recruiting. It is es-
sential to allocate resources available as effectively
and efficiently as possible. Allocation of these
resources also become important to the 160 men and women
involved with recruiting in the Colorado/Wyoming area
whose careers are directly affected by their success or
lack of it. To have an accurate technique for estimat-
ing the outcome of their efforts can help guide future
Research into this area started in the mid
1960's as President Johnson began to look for ways to
end the draft. However, the more advanced models did
not appear until the early 1980's. These models,
largely developed at the government's request, appear
mostly in government publications. The United States
Army Recruiting Command (USAREC), Army Research In-
stitute (ARI), Office of Economic and Manpower Analysis,
Department of Defense (DOD) and RAND Corporation studies
comprise the bulk of this literature. Studies have also

appeared in the general economic literature such as
American Economics Review. Atlantic Economic Journal and
Management Science.
The first major part of this thesis will be the
development of the enlistment supply model. This will
be attempted in three steps. Chapter II, the first step
will contain a review of literature in this area. The
review will focus primarily on the model used, its vari-
ables and their measurement, the estimation method, and
the results obtained. Chapter III will focus on the
significance of variables used in the above models and
propose variables to be used in developing a regional
model. Lastly, in chapter IV, the Colorado/Wyoming en-
listment models will be developed, with the results ex-
The second major part of this thesis will begin
in Chapter V where the model's forecasting ability is
examined. The optimum resource level or a desired en-
listment goal given the available resources is also ad-
dressed. Chapter V also will focus on policy recommen-
dations that stem from the previous chapters. Chapter
VI will provide a summary and outline areas of
future research.

Special Characteristics of U.S. Army Recruiting
Before the literature review is undertaken, a
general overview of how and who the U.S. Army recruits
in the Colorado/Wyoming area is important to understand-
ing the business of recruitng in the armed forces. The
organization responsible for Army recruiting in the
Colorado/Wyoming area is the United States Army Recruit-
ing Battalion, Denver (USARB, Denver). USARB, Denver is
one of 56 such organizations throughout the United
States. While the geographical size and population
within a battalion's area differ greatly, the how and
what remain roughly the same regardless of which bat-
talion is examined. The Denver battalion is divided
into six subregions; east and west Denver metropolitan
areas, Colorado Springs/southeast Colorado area,
Colorado western slope area, northeast Colorado area,
and all but a small portion of Wyoming. Subregions are
determined by demographic similarities, geography, and
supervisory span of control. Within each subregion
there exist anywhere from 5 to 9 recruiting stations or
"stores". Each "store" has from one to six recruiters

or "sales personnel" whose sole goal, like any other
salesperson, is to meet or exceed their mission or
The words used in quotes, "store", "sales
personnel","quota" are the civilian equivalent of the
preceding military term. However, their use should also
convey to the reader that from top to bottom, the United
States Army Recruiting Command (USAREC), besides being
an Army organization comprised of soldiers responsible
for recruitng young men and women, is also a sales or-
ganization striving to be number one in the enlistment
industry just as Ford is in the auto industry.
Recruiters are supported by an organization that
conducts up to $100 million in national advertising
(fiscal year 1988) and publishes sales pamphlets for lo-
cal distribution. In addition, this headquarters
provides either directly or with Congressional approval
many "options" to make the basic enlistment more attrac-
tive. These options include educational incentives, a
written guarantee for training in a particular job, a
dollar bonus, or guaranteed place of assignment, just to
name a few.

The recruiter works potential leads to sell the
dream or opportunity to travel, train, to develop
oneself for the future, to serve, etc. The buyer in
turn "purchases" the above by enlisting,repaying "Uncle
Sam" with time. Simplistic as the above is, it should
help one to realize that the number of enlistments sold
is not unlike, and subject to many of the same aspects
that effect other big ticket item sales.
Recruiters are trained in sales techniques and
the particular Army requirements before they are sent to
a recruiting station. Like any salesperson, they have a
target audience. Here, in recruiting, the target
audience is primarily the male 17-21 year old high
school senior or diploma graduate. Female high school
seniors and graduates and college students make up a
smaller secondary market, but a market that is still
worked. Recruiters actively seek out their potential
buyer by phone, postal or personal contact. As in any
large item purchase, the buyer, once sold, must go
through a qualification process before the goods are
delivered. So while many are called, in reality few
will be chosen (qualified).

Once chosen, the buyer may wait up to 365 days
before product delivery, or shipping to basic training.
The actual delay is mutually determined by buyer and
seller. The exact shipping date, or accession date as
it is called, is dependent upon the availability of the
applicant and the desired training. While waiting, the
buyer is considered to be in the delayed entry program
(DEP). Very few applicants sign up and then immediately
ship out.
For future reference, in reviewing the litera-
ture it is important one understand the hierarchy of ef-
fects in the recruiting process. First comes the lead
generation, that is instilling interest about the armed
forces in an individual to the point he or she is will-
ing to sit down and discuss the options and oppor-
tunities. If enough interest is established, the in-
dividual agrees to process for possible enlistment; that
is they take the mental and physical entrance examina-
tions. If they pass the two examinations, meet the moral
requirements, and decide to enlist they are shown
specific job opportunities for which they may wish to
sign up. At that time the individual signs a legally
binding (but seldom enforced) contract to ship out (go
to basic training) at some later date to be trained in a

specific skill. At the time the contract is signed the
individual is said to have joined the delayed entry
program (DEP). When the anticipated day of reckoning
comes and he, the enlistee or "DEPer" goes to basic
training he or she is said to have accessed or shipped
The "what" the US Army recruits was partly iden-
tified above. More specifically, the Army now recruits
for 6 different categories of enlistments. Two key
determinates which establishes the category an in-
dividual belongs to are education level and mental
category. The most desirable of the two possible educa-
tion levels is the high school senior or graduate. (The
senior is only desirable if they in turn graduate while
in delayed entry program before serving in the Army).
The second and least desirable education level is the
nongraduate. Because of the nongraduate's high attri-
tion rate (and thus high replacement cost), their number
is restricted.
All enlistees take the armed services vocational
aptitude battery (ASVAB) test before coming into the
service. This test places the enlistees in one of 5
mental categories and determines their aptitude for dif-
ferent military skills, such as mechanical, clerical, or

communications. The higher the mental category, the
faster the learner. Category V individuals, the slowest
learners, are excluded by law from military service.
Most recently, only 3-5 % of all enlistees come from the
next to lowest category, the category IV range.
The bell shape distribution of categories is
such that categories I, II, and IIIA fall in the upper
50% of the population, while IIIB, IV and V fall in the
bottom 50%. The Army seeks individuals who score 50 or
greater on the armed forces vocational aptitude battery
(category I-IIIA) because they are the more successful
in completing their initial period of service and are
easier to train. This means that as a group the category
I-IIIA individuals require less replacement and train
So it is that the most sought after enlistment
is the graduate or senior male category I-IIIA (GSMA).
Other mental category individuals beside the I-IIIA will
also be enlisted as a result of the recruiter's search
for the GSMA. As a matter of policy, no nonhigh school
graduate males in category IIIB or below are allowed to
enlist, nor are nongraduate females of any category al-

lowed. The last category not covered is the prior serv-
ice enlisted those who previously served, were dis-
charged and would like to re-enter the military.
In overall terms, an average recruiter will have
a yearly quota of approximately 30 contracts in the fol-
lowing category distribution: 8-11% prior service, 45-
52% graduate or senior male I-IIIA, 18-22% graduate or
senior male IIIB-IV, 3-5% high school nongraduate male
I-IIIA, 9-15% graduate or senior female I-IIIA, and less
than 3% graduate female IIIB.
As GSMA enlistees are the most prized in terms
of defining success and gaining reward, it is toward
that category that most recruiting efforts are directed
and expended. Because of this, the supply model is con-
cerned with high quality male high school senior or
graduate enlistees, the GSMA. To put the importance
placed on quality male enlistments in perspective, a
1984 study by the Office of Economic and Manpower
Analysis at West Point found in examining 1,100 tank
crews that a category I tank crew scored 75.2% higher
than a category IV tank crew. Therefore, not only do
high quality male enlistments save money, but they also
save lives and make for a stronger Army.

Early Works
Early works in the enlistment supply modeling
field are those which use data from the Vietnam
War/Draft period or earlier. As expected, the further
one moves away from this period the less relevant the
draft/war influenced work becomes.
One such draft influenced work, Altman and Fech-
ter (1967), examined the supply of military personnel in
the absence of the draft. Altman and Fetcher looked at
the number of high quality male enlistments and officers
projected for the period 1970-71 in the absence of the
draft. The forecasts are based largely on 1954-65 data,
with 1963 being the dominate data period for modeling
One of their first discoveries, which still
plagues researchers today, was "that there were many
legal and administrative constraints on recruiting prac-
tices. These made it difficult to separate variations
in the number of enlistees or officers recruited caused

by supply factors from those caused by demand factors".
(Altman & Fetcher, 1967, p.19) Altman and Fetcher ex-
amined voluntary ROTC enrollment and Army enlistments,
arriving at the intuitively logical conclusion that:
In general, whatever a policy was implemented that
tended to reduce the likelihood of a potential ROTC
student being drafted or resulted in his having to
serve a longer tour of obligated duty, the enroll-
ment fell....voluntary enrollments in ROTC would
vary proportionately with variations in enrollment.
(Altman & Fetcher, 1967, p.22)
The draft itself prompts many to enlist in order
to choose the service and specific job rather then have
no option. In times of high draft pressure such as the
Berlin Crisis the number of volunteers was significantly
higher than during times of low draft pressure. A
Department of Defense survey of active duty military
personnel as of 31 October 1964 found "38% of the en-
listed men and 41% percent of the officers indicated
that they "definitely" or "probably" would not have en-
tered service in the absence of a draft". It is not
surprising then that data obtained during the draft
years should provide inaccurate projections for the
1980's and beyond.

Altman and Fetcher's model in its original
Cobb-Douglas form was subsequently transformed by the
double log transformation into a single equation log
linear function of the form:
log ci = + b2(log Y^) + b3(log U^)
where c^ = [ 1 ((D^E^}/p^)], the number of Category
I-IIIB males in the Category I-IIIB male population not
enlisting and
E^ = 1963 enlistments in the i*"*1 region in mental
groups I-III [I-IIIB].
= the proportion of draft motivated volunteers
within mental group I-III in the ith region as
measured by the DOD survey.
p^ = the estimated number of 17-20 year old physi-
cally and mentally qualified males (mental group
I-III) in the civilian labor force.
Yj = relative earnings in the ith region, the ratio
of (a) average annual military pay over the first
term to (b) full-time civilian earnings of 16-21
year old males not enrolled in school in the ith
= Unemployment rate of 16-21 year old civilian
males not enrolled in school in the ith region.
(Altman & Fetcher, 1967, p.26)
1 . 1
For the Army, the ordinary least squares estimation of
the above equation resulted in the following (based on
1. For a discussion of the Ordinary Least Squares method
of estimation see Judge, Hill, Griffiths, Lutkepohl,
and Lee, 1982, chapter 6.

1963 data):
Log = 4.7825 .04297 log .01183 log
(.00940) (.00574)
The standard error is in parenthesis, with only Y being
significant at the 10 percent level. The above equation
tells us that as unemployment rises or the relative pay
of the military increases the population not enlisting
declines, or the number of enlistments increase. A cross
sectional study found "the negative signs for the pay
and unemployment variables signify i^*1 regions with
relatively high military to civilian income and high un-
employment rates have higher than average enlistment
rates" (Altman & Fetcher, 1967, p.27).
The above behavior is one seen in all but one
article in this review. Altman and Fetcher also found
that pay elasticities were higher when enlistments were
adjusted to eliminate the draft effects. Specifically,
they estimated a pay elasticity of 1.17 without the;
draft. That is if civilian pay was held constant, a ten
percent increase in military pay would increase enlist-
ments 11.7 percent. With the draft they found the pay
elasticity in 1963 to be nearly half the above rate at

.62. This can be explained as more pay is needed to
move more people out of the civilian labor force in the
absence of the draft.
Finally, Altman and Fetcher, as they recognized
own admission, did not address the effects of the
military employing first term enlisted and officers at
less than a competitive wage. Because of the powerful
motivating effects associated with the draft, articles
written in this time frame tend to lessen the impact of
exogenous resource expenditures such as military pay.
Instead, articles of this time frame have to measure the
effects resulting from an individual's assessment of his
personal probability of being drafted and possibly sent
into a hostile conflict.
Although these early models led others in the
70's and 80's, this thesis will not rely heavily on
their findings. The idea is not to disregard this
period of research but rather to provide the reader
standing of why certain data periods should be

Post Draft/Early All Volunteer Force (AVF) Work.
After the decision to end the draft in 1973 and
during the late 70's, the services explored the pos-
sibility of recruiting an all volunteer force, but not
with a great deal of success. Sales experience and
market understanding were not on the level of other in-
dustries. Many of the articles written during the early
80's; Ash, Udis and McNown (1983), Dale and Gilroy
(1983), Hanssens and Levien (1983), and Brown (1985),
inherently reflect the service's inexperience in the
late 70's. The literature written in the early 1980's
however did provide some early insight into recruiting,
and gives us our first look at a wide range of variables
and models.
Two 1983 studies represent our first look at
models that utilize a wide range of variables. The
first article, Hanssens and Levien's (1983) ,
"Econometric study of Recruitment Marketing in the Navy"
attempts to look beyond unemployment levels and relative
pay. Besides the normal examination of environmental
variables such as pay and unemployment, Hanssens and
Levien carefully examine the effect of recruitment
marketing efforts such as advertising. They estimate

three equations in the hierarchy of effects. The first
equation estimates the number of leads, LEADj^, in-
dividuals who showed enough interest to talk to a
recruiter. The second equation estimates the number of
monthly enlistments by 17-21 year old nonprior service
males into the delayed entry program, DEPj^. The third
equation estimates the number of contracts written for
direct ship with no time spent in the DEP, DSHIP^t. The
variables are defined after the three equations of the
Cobb-Douglas form below:
DRAbli, t-lMASSb2 itMASSb3 i; ^MAIL*14 i, (t_s
RAE)b6i, t_iPRINTb7itDTvb8itLAMb9i, t-lD0Dblit
The equation to estimate DEP has the same environmental
variables as LEAD, as well as the marketing variables of
the LEAD equation itself. In addition to other marketing
variables, DEP has the number of recruiters and direct
ship requirement incorporated into it.

LEAD131! (; t_lLAMb41 f t_lEADb5* ^
The equation to estimate DSHIP is of the identical form
of the DEP equation.
LEADbli ^jADV^ ltADVb3 t_lLAMM (^KAD^i t_1
RECb6it-DSREQb7iteU3 *
All variables are expressed in per capita
(xlOOO) figures, except unemployment rates and propen-
sity variables. Advertising values were rescaled by ad
ding one dollar to insure that at zero advertising a
zero dependent variable did not result.
Hanssens and Levien's study focused on the vari
ables described below, covering 43 Navy recruiting dis-
tricts over a 36 month period, from January 1976 to
December 1978. This period was a transitional one for
all the services as the realization that aggressive'
marketing, and personal salesmanship would be necessary
to make an all volunteer force work.

One major difference in this study compared to
others reviewed is that Hanssens and Levien do not dis-
tinguish between quality and nonquality male nonprior
service contracts in their dependent variable. For
clarity and simplification, the subscripts i for which
Naval Recruiting district and t, for month, are omitted
from all variables discussed. Hanssens and Levien ex-
amine two effects, environmental and marketing, in
developing their model. Under environmental effects,
Hanssens and Levien had the variables discussed belpw in
the order of their appearance.
UNEMP, as measured by the general unemployment
rate in the Navy recruiting district, was studied and
hypothesized to have a positive effect. PBLACK indi-
cates the percentage of blacks in the total 17-21 year
old male population.. The idea is that the recruiting
efforts are more successful the greater the representa-
tion of blacks in the population.
The third environmental effect considered is UR-
BAN, the percentage of target population living in urban
areas. Hanssens and Levien felt the higher the percent-
age of urbanization the more effective the recruiting
process; yet, perhaps, the fewer the eligible candidates
due to lower quality education systems and increased

likelihood of disqualifying involvement with the law.
For instances in today's environment an individual must
obtain a moral waiver if they are convicted of two or
more misdemeanors.
EARN is a variable indicating the ratio of
civilian income to military compensation. The civilian
income level, as measured by the average weekly dollar
earnings by production or nonsupervisory workers in the
district, was anticipated to have a negative effect in
that the higher the relative civilian to military wage
rates, the less attractive is military service.
PROPM, represents the propensity toward enlist-
ing in the military as measured in the semiannual youth
attitude tracking survey conducted by the Office of the
Secretary of Defense. Because the sample size was so
small for any one district, Hanssens and Levien pooled
the total sample of 2000 individuals for their use.
PROPN, is the propensity toward enlisting in the
Navy measured as above.
SENIOR is defined much as PBLACK in that it is
the percentage of high school seniors in the target
population of 17-21 year old males. The last environ-
mental variable was composed of quarterly dummy inter-
cepts, q^, assigned to indicate Fall, Winter, Spring or

Summer; and Gil and GI2 dummy variables to indicate the
presence or absence respectively of the Viet Nam era GI
bill benefits. In this case Gil is equal to one in
December 1976, the last month of the Viet Nam era GI
Bill, and equal to zero in all other months. GI2 is
equal to one for January and February 1977, to indicate
the onset of a new GI Bill, and zero in all other
The marketing variables are breifly described
REC = number of recruiters assigned.
RAD = expenditures on recruiter aids i.e. brochures
fliers etc. Quarterly data used only.
TV = expenditures on TV advertising.
RA = expenditures on radio.
MAIL = expenditures on mail.
OD = expenditures on outdoor advertising (not used
by the Army at the local level since early
PRINT= expenditures on print media i.e. newspapers
and magazines.
MASS = total mass media expenditure (TV & RA & PRINT
& OD) .
= total advertising expenditures (MASS & MAIL).

LAM = expenditures by local district commanders on
local media such as want ads.
SREQ = the requirement for direct ship enlistees;
that is the number of individuals who must
ship immediately and not stay in the DEP.
(The Army has not had such a requirement on
local commands during the 1980's.)
POOL = number of previously written contracts waiting
to ship out at a later time. This variable
tries to capture word of mouth sales.
Any variable independent variable indicated in
the three equations with a "D" in front of it is the log
of the variable.
Hanssens and Levien thoroughly examined the ad-
vertising effects to determine if diminishing effective-
ness in advertising could be discerned. That is,
if the simple assumption is made that some teen-
agers are more likely to join the Navy then others,
the wearout phenomena of a recruitment advertising
campaign can be expected for two reasons: (1) as
potential candidates enlist in response to the cam-
paign, the size of the target market shrinks, and
(2) the remaining candidates are less prone to join
services. (Hanssens & Levien, 1983, p.1173).

As a result of the above, one of Hanssens and
Levien's more interesting hypothesis is that "the
response of leads to media advertising is asymmetric: an
increase in spending has an immediate impact which
levels off over time" (Hanssens & Levien, 1983, p.1173).
The base model used by Hanssens and Levien was
estimated using ordinary least squares. They estimated
the full sample in a time series then compared the
results for the first 18 monthly periods to the results
for the second 18 monthly periods. Similarly they con-
ducted a cross section analysis2 of the 44 Naval
Recruiting Districts, comparing the top 22 districts to
the bottom 22 districts. The coefficient of
determination3 (R2) was higher in the time series
analysis for the sample containing the first 18 months
(also a period of higher unemployment) compared to the
second 18 month period; and in the cross section
2. For a brief explanation of time series and cross sec-
tion analysis see Kelejian and Oates, 1981, p52.
3. Ibid., chapter 2 for a discussion of coefficient of

analysis for the sample containing the top 22 districts
compared to the bottom 22 districts. The use of ordi-
nary least squares was justified as the residuals ap-
peared to be uncorrelated. The complete listing of
coefficients and standard errors for the full sample
appear below in Table 2-1.

Constant 2.540a 1 0.713
UNEMP 367a 0.051
PBLACK -0.040a 0.016
URBAN -0.160a 0.048
EARN -0.091 0.075
PROPN 0.313a 0.088
SENIORS 0.202b 0.101
Q2 -0.325a 0.037
Q3 -0.152a 0.040
Q4 -0.052 0.040
Gil 0.966a 0.075
GI2 -0.158a 0.054
LEAD(-l) 0.105a 0.020
ADV 0.027b 0.012
ADV(-l) 0.010 0.014
REC 0.618a 0.074
SREQ -0.154a 0.012
LAM(-l) 0.005 0.014
RAD(-l) R^ Sample size F-test 2 0.093a 0.423 1505 61.41 0.015
Adapted from Hanssens and Levien, 1981, p.1177.
1. Significance levels, a at the 1% level, b at the 5%
2. See Kelej ian and Oates, 1981, chapter 5 appendix B
for a discussion of the F-test.

Two special issues examined by Hanssens and
Levien included multiple equations and lag structures.4
They found that the three measures of recruiting perfor-
mance: LEAD, DEP, and DSHIP contracts (the number of
contracts that must ship out immediately after signing
up) respond to fairly similar sets of explanatory vari-
However, contracts are expected to respond to num-
ber of leads generated as in the traditional
hierarchy of effects model, which would introduce
simultaneity and the need for two or three-stage
least squares estimation. Because of the short data
interval, no simultaneous effects were found in
same attempts at simultaneous-equation estimation.
Instead a one period delay between leads and con-
tracts was observed. Also, as the single equation
residuals in this recursive system appeared to be
uncorrelated across equations, the model was
parameterized by ordinary least squares (Hanssens
& Levien, 1983,
In terms of lag structures, Hanssens and Levien
found all advertising had a zero and one month lag (with
the exception of direct mail which had a one and two
month lag).
4. See Judge, Hill, Griffiths, Lutkepohl, and Lee,
1982, chapter 25 for a discussion of lag structures.

The results of Hanssens and Levien work can be
summarized in four general areas. Economic factors
were found to have a strong influence in that the higher
the unemployment the higher the number of enlistments.
Although, unlike the Altman and Fetcher (1983) study,
Hanssens and Levien did not find relative
civilian/military earnings significant.
Sociodemographic factors were found to be as important
as the economic variables in impact. PBLACK and URBAN
had a positive impact on leads and DSHIP had a negative
impact on DEP as recruiters were concentrating on the
immediate goal and not worrying about the future re-
quirement. SENIORS had a positive impact on all three
recruiting performance measures. Other environmental
factors such as seasonality impacts were consistent with
prior hypotheses in impact on LEAD and DSHIP, but less
so on DEP. Propensity towards military service improved
throughout the study period, and suggested long run
positive benefits are being gained from the advertising
Marketing variables provided a potpourri in
terms of impact. Local advertising was found to have a
markedly lower impact than national advertising; and to
some extent competed with national advertising for the

same leads. Mass advertising was found to have a four
times greater effect per dollar expenditure than direct
mail expenditures. Word-of-mouth sales were also found
to have a significant positive effect in terms of their
impact on LEAD. (Word-of-mouth sales were not directly
a part of the DEP equation.)
The diminishing effects of advertising
hypothesized was confirmed, although with low magnitude.
Hanssens and Levien thought wearout may be related to
advertising intensity within a medium, but concluded
more study and detailed data was needed. One of their
major problems in this area was determining exactly what
constituted an "increase" in advertising. The desire of
Hanssens and Levien was to measure an increase in terms
of the number of exposures to a given medium's message.
However, in practice the above measurement became dif-
ficult to separate as advertising campaigns were intro-
duced with new messages on somewhat the same theme on a
constant basis throughout this period.
Overall changes in the environment have a more
drastic impact on recruiting than changes in marketing.
The number of leads was found to be highly sensitive to
environmental variables. As a lead implies low be-

havioral commitment compared to an accession or con-
tract, the LEAD equations higher coefficient of deter-
mination is not counterintuitive.
Hanssens and Levien's study is the first to in-
troduce a wide range of variables. Because of the heavy
use of marketing variables, it is hard to compare their
work to other reviewed works. Although the necessary
statistics were not published, one would expect multi-
collinearity problems by the repetitive inclusion of
market variables in the basic equation for DEP.
The second major work to appear in 1983 was
"Enlistments in the All Volunteer Force: A Military Per-
sonnel Supply Model and it's Forecast" by Colin Ash,
Bernard Udis, and Robert McNown. The theory behind Ash,
Udis, and McNown's work may be summarized as follows:
Each individual, traditionally a male over the min-
imum school leaving age faces a choice between
civilian and military occupations, and there exists
a military reservation wage at which each in-
dividual is indifferent between the two. This
reservation wage is equal to the individual's
highest alternative discounted earnings stream in
civilian life, plus or minus a compensating dif-
ferential reflecting the individuals relative taste
for nonpecuniary aspects of military service....
Enlistment supply is thus defined by the cumulative
frequency distribution of reservation military
wages to be a general function of military and
civilian earnings and tastes. Ceteras paribus, as

Where A* denotes applications to enlist and P, WM,
Uw_, Ow_, Ut, and 0^. denote respectively, the
relevant population, military pay of enlisted
men...the mean and standard deviation of expected
civilian earnings, and the mean and standard devia
tion of relative tastes. (Ash, Udis, and McNown
Ash, Udis, and McNown assumes no variance in
civilian earnings or tastes, and "that the form of in-
dividuals preference functions and their distribution
across the population supports a relative pay
hypothesis" (Ash, Udis, and McNown, 1983, p.146).
Based on research completed in the late 1970's,
their's and others', Ash, Udis, and McNown felt the
above relationship existed. They primarily used semian
nual data from the 2d half of 1967 to the 2d half of
1976 in estimating the accessions of 18-19 year old non
prior service males. The linear supply function Ash,
Udis, and McNown proposed was as follows:
AiVpi=f (Wci/WM^ ,Ui,H,T)
where the variables are defined as follows:
Aj^ = the accessions from the ith racial group
for the jth branch of the armed forces.
P^ = the 18-19 year old male population in ith
racial group.

WC^ = median civilian pay for 18-19 year old
males in ith racial group.
WmD = average military pay of enlisted men E-l
to E-4 (the first and lowest four enlisted pay grades)
including basic pay, living quarters allowance, subsis-
tence allowance and tax advantages.
= unemployment rate for 18-19 year old males
in ith racial group.
H = the probability of not being inducted into
the armed forces. This variable captures the effect of
the threat of being drafted. Measured as one minus the
total number of Department of Defense inductions divided
T = a time trend intended to proxy a sys-
tematic change in tastes with respect to military serv-
By using the two stage least squares estimation
method5 of a linear supply function, Ash, Udis, and
McNown found rather low pay elasticities, no significant
effect of unemployment, a positive impact from the draft
5. See Judge, Hill, Griffiths, Lutkepohl, and Lee,
1982, chapter 13 for a discussion of two stage least

and a weak pervasive change in tastes away from military
service. Although this article was published in the
same time frame as Hanssens and Levien (1983), the data
period used by Hanssens and Levien is more recent and
thus the difference in tastes toward the military. The
complete list of coefficients for the estimation of Army
accessions is at Table 2-2 below.

Constant 0.545 0.084
Pay -0.196 0.060
Unemployment rate 0.215 0.257
Draft threat -0.079 0.057
Time trend -0.006 0.001
R2 .714
Adapted from Ash, Udis, and McNown, 1983, p.150.
Although the level of significance for each
coefficient was not published, one can see from the
above table only unemployment and perhaps the draft
threat appear to be insignificant. Several major flaws
are found in Ash, Udis, and McNown's work. First, their
study includes draft year data with the peculiarities
discussed previously in the Altman and Fechter (1967)
article. The effects of the draft and the transition to
an all volunteer force seems to downplay unemployment
influences and heighten relative pay differentials.

More significantly, this is one of the few
studies to suggest that unemployment has little impact.
Although Ash, Udis, and McNown do offer a possible ex-
planation, indicating the quality content of enlistments
may increase with a rise in the unemployment rate and
not the overall number of enlistments. This finding is
a result of their second serious shortcoming, using ac-
cessions for a dependent variable. Accessions are
largely dependent on the needs of the service and its
ability to train individuals in a fairly evenflow
process. They should have used contract data which ac-
cording to most researchers is strongly determined by
the seasonality and unemployment rates. With a delay of
up to 365 days between contract and shipping,
(accessions) it is difficult to establish any relation
between the variables included and accessions. By using
semiannual periods, Ash, Udis, and McNown largely
obliterate any seasonal distinctions one would expect to
In comparing forecasted enlistments to actual
enlistments for the period 1977 (first half) to 1979
(second half), Ash, Udis, and McNown found they overes-
timated nonwhite enlistments into all services except
the Navy where white male enlistments were overes-

timated. The overestimation may be a result of a market
strategy to seek out quality male high school seniors or
diploma graduates and limit the number of nongraduates
and lower mental groups as mandated by Congress and re-
quested by the services themselves. The data gathered
during the draft period would favor higher minority en-
listment rates as that group is less likely to obtain
draft deferments. The overestimation of whites is
partly explained by the Navy's conscientious effort to
recruit minorities. To this day the Navy is the only
service with written minority recruiting goals. Unfor-
tunately, Ash, Udis, and McNown spend a great amount of
effort in estimation and very little in interpretation
of the data.
In a rebuttal of sorts to Ash, Udis, and
McNown's work, Charles Dale and Curtis Gilroy (1983a)
indicate "Ash et al failed to find an unemployment ef-
fect on enlistments because they did not have the most
appropriate data for estimating their equations" (Dale
and Gilroy, 1983, p.547). Ash, Udis, and McNown (1983)
analyzed draft and post draft era data for 20 semiannual
points (1967: II through 1976: II), whereas Dale and
Gilroy used 78 monthly observations of only post draft
data (1975-82) with the number of male nonprior service

high school graduate contracts signed as their dependent
variable. The difference being contracts are supply
determined, somewhat based on an individual desire;
while accessions are demand determined, based upon serv-
ice needs and training capabilities.
Dale and Gilroy studying only male nonprior
service high school graduates enlistment contracts found
a significant relationship between contracts and the
16-19 year old male unemployment rate. As youth un-
employment rises so too does the number of contracts
written. However, when the unemployment rate was com-
pared to accessions, no such relationship was seen given
the service determined monthly accession rates. Never
stating the exact model as Dale and Gilroy felt it was
not crucial to their argument, the function later es-
timated appeared to be of the following form:
A/P = f(UM, W-l, W+4, GI, Bill, VEAP, KICK, TARGET, Q3).
As alluded to earlier, the dependent variable is
A, the number of Army contracts of male nonprior service
high school graduates, divided by P, the male 16-19 year
old population. This translates into the proportion of
the 16-19 year old male nonprior service high school
graduate population that contracts.

The first independent variable, UM, included in
the Dale and Gilroy study is the unemployment rate of
16-19 year old males. Most researchers avoid using the
teenage unemployment rate as it is highly correlated to
national unemployment rate, and it is an awkward number
for policy makers to grasp due to their unfamiliarity
with its range and relation to national unemployment
The ratio of military pay and compensation to
civilian earnings both lagged one month and led four
months to capture the delayed effects of pay changes and
enlistees anticipatory outlook toward future earnings
are also included as W-l and W+4 respectively. GI, was
a dummy variable indicated by one in December 1976 when
the G.I. bill (a benefit package that among other items
carries tuition subsidies for post high school educa-
tion) expired. The BILL variable is the maximum monthly
benefit for the G.I. bill. After December 1976 this
variable was set to zero. The variable VEAP, the
veterans education assistance program, captures the max-
imum monthly benefits under the program that replaced
the G.I. bill. Before January 1977 this variable was
set to zero. KICK similarly captures the additional
education benefits beyond VEAP the Army was offering to

individuals who contracted for hard to fill job
specialties. TARGET was a binary variable equal to one
between November 1979 and August 1981 to capture the
special recruiting policies in place aimed at the high
school graduate population. A seasonal dummy equal to
one for the summer months of July, August, and Septem-
ber, Q3 was also added.
The estimation method used was generalized least
/r , ,
squares The results are listed in Table 2-3 below. 6
6. See Judge, Hill, Griffiths, Liitkepohl, and Lee, 1982
chapter 10 for a discussion of this estimation method.

Constant 207.3 0.3 -2637.1a -4.1
UM 34.7a1 4.8 18.3a 2.7
W-l 0.2 0.0 NA NA
W+4 NA NA 58.5a 4.8
GI 755.2a 6.9 824.2a 7.3
BILL -36.0 -0.2 407.0b 2.3
VEAP -205.0 -0.7 527.9b 1.7
KICK 4.0 1.3 7.8a 2.7
TARGET 27.9 0.5 158.6a 2.8
Q3 Adjusted 170.1a R2 .75 5.1 77.5b .81 2.0
Adapted : from Dale and Gilroy, 1983a, p.549.
1. Significance levels, a at 1%, b at 5% level.

Using contract data Dale and Gilroy estimate a
significantly higher pay elasticity of 3.9 versus the
.881 that Ash, Udis, and McNown (1983) estimated. A
similar picture also appears in unemployment elas-
ticities where Dale and Gilroy reported an estimate of
.81 versus Ash, Udis, and McNown7s .133. While the
specific functional form Dale and Gilroy used is not
cited in their rebuttal they claim only a 2% error rate
in forecasted enlistments for 1982. As Ash, Udis, and
McNown did not provide future projections no comparison
can be accomplished. However, like Ash, Udis, and
McNown, and Altman and Fetcher (1967), Dale and Gilroy
found "it is important to maintain the comparability of
military pay relative to civilian pay" (Dale and Gilroy
1983a, p.551).
In Dale and Gilroy's (1983b) Atlantic Economic
Journal article, "The Effects of the Business Cycle on
the Size and Composition of the US Army", Dale and Gil
roy give us a more detailed look at projecting the en-
7. Elasticities taken from article and not shown in
table 2-3.

listment rate of the available population. In this ar-
ticle Dale and Gilroy use a single equation model of the
Y = f (U^T^.. .XN) .
Y is a measure of the military enlistment rate
further defined as A/P per the above article. U is a
proxy for the business cycle. In this case U was repre-
sented in three ways in the final equation (not
published). The first way it is represented is by UM,
the unemployment rate of 16-19 year old nonprior service
males, secondly by UM lagged for two months, and thirdly
by UM lagged four months. The inclusion of three un-
employment variables was an attempt to capture the ex-
tended effects of unemployment on contract rates. P is
a measure of military to civilian pay rates again repre-
sented by W-l and W+4, the ratio of military pay and
compensation to civilian earnings lagged one month and
led four months respectively. T is a time trend which
in this case is monthly. X-^.-Xj^ is a variety of ex-
ogenous variables which happen to be the same variables
as listed and defined in the previous article; GI, BILL,

Unlike Dale and Gilroy's (1983a) first equation,
this one was estimated by ordinary least squares instead
of generalized least squares. As no serial correlation
is present in the current article, use of ordinary least
squares is justified. The results of Dale and Gilroy's
current model is summarized below in Table 2-4.

Constant -1901.22a 1 -3.16
UM 19.38c 2.93
UM-2 5.37c 1.02
UM-4 4.31c 0.72
W+4 37.32a 2.94
GI 889.66a 8.79
BILL 336.09b 2.18
VEAP 448.62b 1.74
KICK 6.78a 2.79
TARGET 155.55a 3.15
Q3 104.09b 2.74
Adjusted R2 .82
Adapted from Dale and Gilroy, 1983b, p.46.
1. Significance levels, a is significant at 1% level, b
is significant at 5% level and c is jointly significant
at 1% level

Dale and Gilroy found that a one percentage
point decrease in the unemployment rate, e.g. from 9% to
8%, would result in an 8.8% decrease in high school
graduate enlistments. It is interesting to note that
Dale and Gilroy tried their model out on the other serv-
ices but "because the OLS equation showed appreciable
serial correlation in the disturbance terms [for the
other services only], these equations were re-estimated
using generalized least squares (GLS) with the
Cochrane-Orcutt method" (Dale and Gilroy, 1983b, p.47).
The Navy contracts could be estimated much in
the same way as the Army is, while the Marine Corps male
and Army female enlistments showed very poor estimates.
This suggests for those groups, nonquantifiable factors
may weigh more heavily on their motivation for contract-
ing. Dale and Gilroy also found that a one time pay
freeze would have a more lasting detrimental effect on
enlistments than slow pay increases. It is worth noting
that in this article Dale and Gilroy included the ex-
tended outlook for unemployment in a better way than
before by the inclusion of UM-2 and UM-4. As such,
while the effect of relative pay was still significant,
as in previous articles, its effect was lessened by al-
most fifty percent. Dale and Gilroy also find educa-

tional benefits to be very important and significant in
determining the number of contracts written. Dale and
Gilroy are among the first authors to explore the ef-
fects of education benefits upon enlistments in an ef-
fort to explain why a given number of individuals en-
list. In no article reviewed did any author evaluate
the effects of both an aggressive marketing
plan and education benefits.
Recent Works
In Brown (1985), "Military Enlistments: What can
We Learn from Geographic Variations", Brown found that
"the combination of sizable unemployment elasticities
and major swings in regional concentration of unemploy-
ment had significant effects on regional distribution of
Army enlistees". (Brown, 1985, p.233).
Brown estimated four different dependent vari-
ables; (1) contracts from category I-IIIA high school
graduates as a portion of high school graduates in the
last three years; (2) contracts from all category
I-IIIA7s as a portion of the 18-20 year old population;
(3) contracts from all high school graduates as a por-

tion of high school graduates in the last three years;
and (4) all contracts as a portion of the 18-20 year old
Although not explicitly specified in the paper
it appears that the Cobb-Douglas function used by Brown
and later estimated was of the form:
C = bl (BMC + ED) b2Wcb3URb4UR2 b5Tb6eut.
This function was subsequently transformed by taking the
natural logarithm of both the left and right side of the
equation before estimation. C is one of the four dif-
ferent categories of contracts described above. BMC is
basic military compensation as measured by base pay al-
lowances and tax advantages. ED is the average estimate
of educational benefits an individual might and could
receive. Because of the uncertain value applicants
place on education benefits they may or may not use in
the future, Brown felt using an average of the high and
low estimates various researchers placed on education
benefits would provide more explanatory power. Wc is
the civilian pay variable as measured by the quarterly
average of monthly earnings of private workers based on
unemployment insurance records. UR is the state un-
employment rate. T is a time trend from 1 to 28 repre-

senting the 28 quarters of data from 1976 through 1982.
The data period chosen also avoids the influence of the
draft and helps provide a clearer picture of the supply.
Brown estimated contracts by state using the or-
dinary least squares method in a cross section analysis.
Brown felt this provided more precision
than time series analysis because,
The impact of both the draft and the Vietnam
war would be expected to influence supply, yet
they are difficult to hold constant statisti-
cally. Because the Vietnam war years were a
time of low military (relative to civilian) pay
and low unemployment rates, inadequate control
for the effect of the draft and the war are
likely to bias estimates of the effects of
military pay and
civilian unemployment. (Brown, 1985, p.228)
He also estimated the equation by using generalized
least squares, but felt it added little as the serial
correlation coefficient had to be estimated. The results
for Category I-IIIA high school graduate contracts are
shown below in Table 2-5.

BMC 0.61 2.5
ED 10.8 38.2
WC -1.04 -3.8
UR 0.17 9.7
UR2 0.34 3.3
Trend 0.019 13.3
Adapted from Brown, 1985, p.231.
Again as in other studies, Brown found the
ratio of military to civilian pay to be significant. He
also found that a one percentage point drop in unemploy-
ment lowered enlistments by 10 percent. This estimate
is in the same range as Dale and Gilroy (1983a) and
other later authors7 estimates on the effects of un-
employment, but goes against Ash, Udis, and McNown
(1983) assessment of unemployment's impact. Brown found
the independent variables more explanatory when looking
at category I-IIIA contracts then total contracts. This
suggests that category I-IIIA contracts are supply
determined while total contracts are demand determined
and can be held at a given level by changing the stan-

dards of enlistment. While not explored in this article
the advantages of knowing what states in the country
could provide more contracts in the demand determined
categories could be a powerful piece of knowledge in the
hands of policy makers.
One of the few studies available that looks at
battalion level enlistment supplies using recent data
was done by Lawerence Goldberg, Brian Goldberg and Ellen
Goldberg in July 1987 for the United States Army
Recruiting Command.
A battalion level model has many useful
purposes. TSCS [time series cross section] models
forecast poorly at the district [Battalion] level
because they assume the same parameters, i.e. con-
stant terms and elasticities in each district. In
reality, economic structure, district configuration
management practices, and attitudes toward the
military probably cause the effects of parameters
to differ across districts. Thus, the models are
misspecified, and this causes autocorrelation and
large errors at the district level. The errors tend
to cancel so that ceteras paribus, national level
forecast are reasonably accurate and useful for
forecasting and planning. Unfortunately, the
models are relatively useless to services recruit-
ing commands for allocating resources or distribut-
ing goals among recruiting
districts. (Goldberg et al., 1987, p.2).
The Goldbergs' model is a log linear function in
the form:

LnGSA = aQ + a^LnPAY + a2LnCUNEM + a3LnAUNEM + a^LnACF +
a5LnEBT8K + agLnEBT84K + a^LllBRIDGE + agLnMSREC +
a9LnRECS + error. Where,
PAY relative military compensation for an individual during their first four years of service divided by civilian earnings of youth, both discounted to present value.
CUNEM = cyclical unemployment rate, equal to average FY81-85 unemployment rate minus current rate.
AUNEM = long run average regional unemployment rate.
ACF army college fund educational incentive dollars. (ACF replaced VEAP which replaced the old G.I. bill).
EBT8K = enlistment bonus to entice men to enlist in hard to fill jobs by offering $8,000 for a four year enlistment.
EBT84K = same as above but also offered $4,000 bonus for 3 year enlistments. This was used in certain test battalions, although later not adopted.
BRIDGE = an inspired leadership and policy change dummy variable.

MSREC = mission each recruiter carries (sometimes
not used in different models).
RECS = number of recruiters available.
The Goldbergs felt there was insufficient inde-
pendent variation in the explanatory variables to obtain
reliable estimates on a battalion basis. Instead, a
model was estimated using battalion data with supply
factor elasticities constrained to equal those obtained
from analysis of annual battalion data. Their focus was
on estimating the number of graduate and high school
senior category I-IIIA contracts based on FY81-85 data
using ordinary least squares, first differences (FD),
fixed effects (FE)8, Hidreth-Lu (HL)9, and switching
8. Fixed effects is the change of the observation from
the average observation, while first differences is the
change of the observation from the previous fiscal
year's observation for the same time period.
9. See Judge, Hill, Griffiths, Lutekpohl, and Lee,
1982, chapter 9, for a discussion of this estimation
technique which is also known as an autoregressive
linear regression model.

regression (SR)10 methods of estimation. The Goldbergs7
wanted to explore alternative methods of estimation
before presenting any recommendations. Goldberg et al.
attempted to use a population factor but reportedly
found too many econometric problems with its use. The
Goldbergs' basic objection was that population data was
a crude proxy for other more precise demographic
measures such as percent black population, percent
renters or average education levels. Despite their mis-
givings, the coefficient of determination in one model
estimated by ordinary least squares that used a popula-
tion variable was quite high at .940. They also looked
at local advertising expenditures and found "Its effect
was small and insignificant, with suspect data as a
result of uncertain and unequal time delays in adver-
tisement billing? and poor data collection procedures by
local agencies" (Goldberg et al.,1987,p.8). Table 2-6
reflects the result for supply limited models.
10. Ibid., chapter 17 for a discussion of switching

(with & with out recruiter missions)
VARIABLES with w/o with w/o
CONSTANT 0.71a 2.14b -1.10 -2.03
PAY -0.002 1.05b 3.33b 3.90b
CUNEM 0.065b 0.074b 0.052b 0.050b
AUNEM 0.046 0.24b 0.21 0.29
ACF -0.072a 0.25 0.029 0.035
EBT8K -0.10 0.08 0.027 0.029
EBT84K 0.001 0.027 0.046 0.043
BRIDGE 0.074a 0.075 0.071a 0.061a
MSREC 0.81b NI 0.14a NI
RECS 1.04b 1.09b 0.78b 0.71b
W to 0.925 0.810 0.852 0.855
SEE 0.134 0.213 0.099 0.100

Table 2-6 continued
VARIABLES with w/o with w/o
PAY 2.86b 3.17b 1.95b 2.65b
CUNEM 0.061b 0.060b 0.067b 0.066b
ACF 0.050 0.054 0.106b 0.109b
EBT8K -0.001 0.003 0.024 0.032
EBT84K 0.037 0.036 0.044 0.044
BRIDGE 0.056a 0.052a 0.043 0.040
MSREC 0.063 NI 0.14 NI
RECS 0.67 0.65 0.73a 0.71
R2 0.859 0.859 0.915 0.913
SEE 0.101 0.101 0.089 0.090
Adapted from Goldberg < et al.,1987 , p.17.
1. NI means not included, w/o means without
2. Signicance levels, a is significant at the 5% level,
b at the 1% level

Of all the variables only PAY, CUNEM, BRIDGE,
MSREC and RECS appear to be significant at the .05
level. The ordinary least squares method reflects an
increasing marginal productivity for additional
recruiters of 1.04 which of course is counterintuitive
as one would think there is less and less available
qualified applicants to contract per recruiter past a
certain point. The Hidreth-Lu method corrects for the
increasing marginal productivity of recruiters with a
correlation coefficient11 (rho) of .98. The first dif-
ferences and fixed effects with models had the best fit
with a coefficient of determination of .859 and .915,
respectively. They also had the highest accuracy rate
based upon the percent of error of past year production
to actual past year production. The effects of bonus
dollars and the long run regional unemployment (AUNEM)
were found to be insignificant in all models. Bonus
dollars have been found to guide job selection but not
11. See Wonnacott and Wonnacott, 1972, chapter 14 for a
discussion of the correlation coefficient.

the initial enlistment decision. While PAY and REC were
found to have the largest effect on enlistments as seen
by the size of their coefficients.
For demand limiting models Goldberg et al. used
the following switched regression estimation equation:
LnGSA = aQ + a^nPay + a2LnCUNEM + a3LnAUNEM +
a4LnACF + a5LnEBT8K + agLnEBT84K + ayLnBRIDGE +
PROBS = probability of being supply limited (i.e. the
supply of enlistments falls short of the
missioned goal.)
a^ = elasticities (selected by the authors based
on an assessment of unkown criteria of all
TSCS models) if battalion is demand limited
(i.e. the supply of enlistments exceeds the
missioned goal but is constrained by the
service's desire.)
b^ = elasticities if battalion is supply limited,
c^ = b^ a^, that is the difference in

elasticities, supply minus demand.
Probabilities were first obtained by estimating
a probitJ-s model including all explanatory variables.
Results from alternative switched regression models
using ordinary least squares, first differences, and
fixed effects procedures are reflected in Table 2-7
below. 12
12. See Judge, Hill, Griffiths, Lutkepohl, and Lee,
1982, chapter 18 for a discussion of the probit model.

PAY -0.43 3.14b 1.85b
CUNEM -0.021 0.054b 0.049a
AUNEM 0.046 0.0037 NI
ACF -0.072a 0.029 0.21b
EBT8K o H 0 1 0.068 0.12
EBT84K 0.0014 -0.076 -0.015
BRIDGE 0.074 0.072 0.076
MSREC 0.81b 0.16 0.25a
RECS 1.04b 0.63b 0.71b
PROBS 2.27a 0.88 0.66
PR*PAY 0.44 -0.34 0.023
PR*CUNEM 0.080a -0.002 0.007
PR*ACF -0.49b 0.018 -0.18
PR*EBT8K -0.39a -0.12 -0.18a
PR*EBT84K -0.070 0.12 0.045
PR*BRIDGE 0.20 -0.012 -0.027
PR*MSREC -0.10 -0.11 -0.071
PR*RECS 0.19 0.082 0.044
PSAI -0.019 -0.012 -0.020
R2 0.941 0.866 0.924
SEE 0.119 0.098 0.083
Adapted from Goldberg et al.,1987, p.20.
Note: a is significant at the 5% level, b at 1%.

In the above estimation only PAY, CUNEM,
ACF, MSREC and RECS appear significant at the .05
level. The basic SR model yields implausible
supply factor elasticities: the estimate of the pay
elasticity in supply-limited districts is essen-
tially zero; for ACF and EBT8K, the effects are
negative; for recruiters, it is 1.11. The effect
of missions in supply-limited battalions is 0.82
rather than zero. There is evidence of autocor-
relation, and the aggregate prediction error for FY
1984 is the largest of all methods (7.5%). The
residuals display evidence of nonnormal pattern.
The basic SR model is not supported by evidence
et al 1987, p.19).
Additionally, "the SR model estimating using the
fixed effects procedure does not yield plausible
results" (Goldberg et. al. 1987, p.23). The switched
regression/first differences however does provide
plausible results with some very small improvement.
Goldberg et al. found using the fixed effects model
a 10 percent increase in pay would increase enlist-
ments by 19.5 percent [ from pay coefficient table
2-1]; a one point increase in unemployment would
increase enlistments by 6.7 percent [from the CUNEM
coefficient table 2-1]...the bonus programs had
only small incremental effect on supply. Instead,
the impact of the latter has been to distribute en-
listments into hard to fill occupations and in-
crease the average term of service (Goldberg et al.
The Goldbergs7 study is one of the few to es-
timate enlistments at the battalion level and by a
variety of estimation methods. The Goldbergs7 finding
of autocorrelation in the ordinary least squares es-

timate is not unique in models with a large number of
variables. Dale and Gilroy (1983a) also found autocor-
relation in ordinary least squares estimates of a model
with a large number of variables. The main objection I
have to heavy use of the fixed effects and first dif-
ferences estimation methods is they exclude all series
that vary over time which otherwise might be included
such as unemployment rates.
One of the interesting recent studies to appear
was done by James R. Hosek and Christine E. Peterson for
the RAND Corporation under contract MDA-903-83-C-0047.
(This study also appears in Army Manpower Economics
(AME) edited by Curtis L. Gilroy, Westview Press,
Boulder Colorado, 1986).
, I O ,
Hosek and Peterson used the logit function in
their maximum likelihood estimation14 .
13. See Judge, Hill, Griffiths, Lutekpohl, and Lee,
1982, chapter 18 for a discussion of the logit model.
14. Ibid, chapter 3 for discussion of the maximum
likelihood estimation method.

The enlistment probability of an individual
with characteristics X is defined as P = 1/(1+
eAx). From the logit function we create a
likelihood function for each observation adjusted
for choice base sampling. The individual
likelihoods are then multiplied to form the
likelihood to be maximized over the sample. The log
likelihood of the sample...has the following form:
In L = [sum of] W^ln(p^) + [sum of]
W^ln(l-p^)(Hosek and Peterson, 1986, p.48).
As p^ is the probability of enlistment, (1-p^)
becomes the probability of not enlisting. For the en-
listed sample, is the inverse sample weight for an
observation multiplied by the ratio of the population
proportion enlisting to the sample proportion enlisting.
For the sample not enlisting, is the inverse sample
weight for an observation multiplied by the ratio of the
population proportion not enlisting to the sample
proportion not enlisting. Hosek and Peterson segmented
the market into high school seniors and graduates. The
basis of their model was that each group was further
looked at in terms of either a: planning on continuing
their education or b: not planning on continuing their
education. Each group was also examined in terms of
high armed forces qualification test score (AFQT) (>50),
and low AFQT (<49). Then, based on 25 variables, en-
listment probabilities for given characteristics of each
group were determined. Variables affecting enlistment

range from age, months working, ethnic group to number
of siblings and mother's education level. Fourteen of
the more relevant variables are listed in table 2-8. By
looking at each group in terms of education plans and
AFQT's certain conclusions where reached as to which in-
dividual characteristics indicated the higher propensity
to enlist. Table 2-8 also indicates if the effect was
positive or negative. Data came from a 1979 Department
of Defense survey of enlistees and a 1979 National Lon-
gitudinal Survey of Labor Force Behavior, youth survey
of nonenlistees.

Seniors Graduates
Coefficent & Effect
Learning Proficiency
Age when HS senior -.602 +1 .098*~ >+
AFQT percentile -.011 _2 .002* 0
Ability to Finance School
Lives on home .208* - .042* +
Family income -.028 - .002 0
Numbered Siblings .104 + .102 +
Educational Expectations
Expects more education -.598 - .465 +
Mothers Education . 109 + .034* +
Hourly civilian wage -2.416 -1.026
Weekly hours .017 + -.012* -
Months since school n/a -.395 -
Months on current job -.156 - -.236 -
Months not employed .234 + .252 +
Black .465 + .467 +
Hispanic .431* + -.214* +
Demand Factors
Recruiter Density .592 0 -.257 +
Share of Srs & Grads -4.772 0 -24.543 -
in local market Notes:
Adapted from Hosek and Peterson, 1986, p. 11.
1. "+" means impact enhances probability of enlistment
if more of variable is present.
2. ,,-n means impact lessens probability of enlistment if
more of variable is present.
3. ,,*n Found not to be significant at the .05 level, all
other coefficients were found significant at the .05
4. "O'1 means no effect.

In the above table all senior variables were
found significant at the .05 level except the live at
home and hispanic variables. The same is not true for
the graduates where the age, AFQT, family income,
mother's education, weekly hours, and hispanic variables
are insignificant at the .05 level.
The learning proficiency variables' impact sug-
gest that the better one's alternatives to continue his
or her education or gain skills (as indicated by AFQT)
the less likely one is to enlist. Ability to finance
school had the expected effect; in that the more money
one had available, the more likely the individual is to
seek alternatives other than enlist. The graduates,
being comprised of individuals not currently attending
school and somewhat more independent from their parents,
demonstrated weaker effects than seniors with respect to
ability to finance school.
Education expectations showed opposing effects
between seniors and graduates. The coefficient for
seniors desiring more education was -.598 as opposed to
the graduates who desired more education at .465. This
was explained as the nonstudent graduate faced with

reality and more independence saw enlistment as a chance
to continue his education; while the senior saw enlist-
ment as a detractor and postponement of his education.
Employment variables showed the authors7
hypothesized impact except for hours worked. It was
felt the more the graduate worked, the more money and
human capital investment in a firm he possessed and thus
the less likely he was to enlist. On the other hand,
the senior who worked was felt to be more disposed
toward work than education as an alternative and thus
saw enlistment as a possibility. Race variables may in-
dicate that the opportunities in the Army for blacks are
greater than civilian life and thus the higher
predisposition to enlist.
The demand factors were included to see if in
fact recruiters turned off once they made goal, as they
had higher incentives not to fail in this and subsequent
periods than they had incentives to overachieve in the
current period, and risk possible failure in the next
period. What was observed in the share of seniors and
graduate population of the total youth population was
that the recruiter only worked whom he had to and didn't
try to harvest the bigger population.

Hosek and Peterson7s study looks at behavior and
as such requires costly yearly surveys in order to make
estimates of enlistment supplies. However, it does show
areas where policy could influence allocation of
resources. In fact, since this article was published,
the Army has looked at and focuses itself toward two
market segments, those oriented toward work and those
desiring to continue their education.
Thomas V. Daula and D. Alton Smith (1986) fur-
ther explored the idea of recruiter goals and enlistment
demand in their article "Recruiting Goals, Enlistment
Supply, and Enlistments in the US Army".
Daula and Smith estimate the double log-linear
enlistment supply function in the form:
lnSit = b0 + bllnXit + b2lnYif*+ eit*
S is the supply of high school graduate males with an
AFQT score of 50 or better. X and Y represent factors
affecting enlistments. The factors which Daula and
Smith include fall into four categories: (1) relative
military compensation (military compensation and average
civilian earnings in the manufacturing sector); (2)
sociodemographic factors (youth population, percent
minority, percent of population voting republican); (3)
recruiting resources (number and experience level of

recruiters, number of exposures to national advertising,
local advertising expenditures) and (4) enlistment com-
petition (other services contracts of high school
graduate males with an AFQT score of 50 or better,
demand constrained category requirements).
To estimate this function Daula and Smith util-
ize the maximum likelihood technique. One major dif-
ference in Daula and Smith's article from the other ar-
ticles previously reviewed is the inclusion of the
recruiter's goal. Table 2-9 below compares the results
of supply limited battalions without and with the
recruiter goal considered, and demand constrained bat-
talions with the goal considered.

without goal with goal with goal
Constant -3.21 -2.64 -3.08
Mills ratio -.779 -.647 .846
Recruiter goal NA .150* .186
Constrained contracts -. 201** 1 -.194* -.082*
Other service contracts -.727* -.584* -.717
Relative military pay 1.89 1.60 .824
Unemployment rate 1.36 1.15 .995
Youth population .257* .203* .232
Percent minority -.191 -.163 -.089
Number recruiters 1.11 .959 .826
Recruiter experience . 092* . 078* . 080*
Local ad expenditures .093* .080* .051*
National ad exposures . 134 . 107* .156
Percent republican voters .378* .278* .384
Fourth quarter .724 .619 .368
Army college fund .275 .242 .046*
Adapted from Daula and Smith, 1986, p.110 and p.117.
1. * indicates not significant at the .05 level, all
other coefficients were found to be significant at the
.05 level.

When enlistment supplies were estimated using
recruiter goals, it was found they over estimated in
periods of decreasing unemployment based upon a com-
parison of forecasts and actual enlistments. This sug-
gests the direction as well as the level of the un-
employment rate itself is also important. One of the
principal benefits of this model is the inclusion of
contracts written by services other than the Army and
contracts of low quality written by the Army. By in-
cluding the competition's contracts in the equation a
more realistic picture of what the total market can
supply is seen. Daula and Smith are also the first
researchers in this area to use instrumental variables.
As in other articles, relative pay, unemployment, and
this time the number of recruiters are seen to have a
positive impact. It should also be noted that while the
impact of advertising is limited, particularly at the
local level, some shift of effort out of demand con-
strained areas into supply limited areas could prove to
be the more prudent use of resources. The inclusion of
recruiter goals slightly lowers the coefficients of the
other variables as expected, however there is an ap-

preciable difference when comparing the supply limited
results to the demand constrained results. The impor-
tance of recruiter goal considerations should not be
over looked in developing supply estimates.
Literature Summary
To assist in the development of a battalion
model, Table 2-10 below briefly summarizes the relevant
and more widely used variables. As the models, func-
tions, estimation techniques and definition of the many
variables do no coincide exactly, no one to one com-
parisons can be made from the table below. However,
some general idea of impact and significance of widely
used variables can be gained for future examination.
Coefficients are indicated as significant if known.

TABLE 2-10
Early Models
Study (year) A&F(67) H&L(83) AU&M(83)
Data period 1963 1976-8 1967-76
Estimation method OLS OLS/TSCS 2SLS
Dependent variable Male C MNPS C MNPS A
Relative earnings .043*c/m -.091c/m -.196c/m
Unemployment rate .0118 .367* .215
Season (Q3) NA -.15* NA
Recruiter NA NA NA
Mission NA NA NA
National Advertising NA .027** NA
Available Population NA .202** NA
R2 .73 .423 .714
Study (year) D&G(83a) D&G(83b)
Data period 1975-82 1975-82
Estimation method GLS OLS/TSCS
Dependent variable GSM C % MNPS
Relative earnings 58.5*m/c 37.32*m/c
Unemployment rate 18.3* 19.38*
Season (Q3) 77.5** 104.1*
Recruiter NA NA
Mission NA NA
National Advertising NA NA
Available Population NA NA
R2 .81 .82

Table 2-10 continued
Recent Models
Study (year) BROWN(85) GOLDBERG(87)
Data period 1976-82 1980-86
Estimation method OLS/TSCS FD
Dependent variable % MNPS GSMA C
Relative earnings -1.04 c/m 2.86*m/c
Unemployment rate .17* .061*
Season (Q3) NA NA
Recruiters NA .67*
Mission NA .063
National Advertising NA NA
Available Population NA NA
Study (year) H&P(86) D&S(86)
Data period 1979 1980-83
Estimation method Logit/MLE MLE
Dependent variable GM C GMA C
Relative earnings -1.03c/m 1.60m/c
Unemployment rate -.252* 1.15**
Season (Q3) NA .182**
Recruiters -.257 .959**
Mission NA .150
National Advertising NA . 107
Available Population- -24.54* .203
*=significant at .01, **=significant at .05,
m/c=military/civilian pay ratio, c/m=civilian/military
pay ratio, C=contracts, A=accessions, NA=not available,
MNPS=Male Non-prior Service GSM=graduate senior male,
GSMA=graduate senior male I-IIIA, GM=graduate male,
A&F=Altman and Fetcher, H&L=Hanssens and Levien,
AU&M=Ash, Udis, and McNown, D&G=Dale and Gilroy,
H&P=Hosek and Peterson, D&S=Daula and Smith.

From Table 2-10 at the end of Chapter II, it be-
comes apparent that some variables play a fairly consis-
tent role in any enlistment supply model, while others
do not. Other variables, such as advertising, face the
problem of data collection. In this chapter, the
relevant period of data to use and the recommended vari-
ables based on the literature review above are dis-
One problem that needs to be addressed regard-
less of the variables chosen is the identification
problem between supply limited periods of GSMA produc-
tion and demand constrained periods of GSMA production.
The current process of assigning quarterly production
missions to recruiting battalions in the Army is largely
based on the GSMA production one achieved in the same
quarter last year. This gives rise to demand con-
strained situations once the mission is achieved.

That is, the true potential GSMA production is not
reached; but instead curtailed until the start of the
next period, in order to avoid higher potentially un-
achievable missions in the future. In the business ver-
nacular this is called the "communist plot".
In supply limited periods no such curtailment of
production takes place. The potential GSMA production
is obtained in effort to make the assigned mission. As
I want to examine the supply of male I-IIIA high school
senior and graduate contracts possible in the
Colorado/Wyoming area, any variable variable needs to be
available to this area, accurate in nature, and
and worthwhile to explore.
Proposed Data Period
As a point of departure any variable should use
1981 (or later) to present data in order to eliminate
the problems associated with the draft period and/or
early management problems as discussed previously. As I
am familiar with the personnel who manage and gather
data for recruiting in the Colorado/Wyoming area, and
have an understanding of the reliability of that data
since 1985 I will restrict myself to the monthly data
from 1985 though 1988. Additionally, many of the

records kept before 1985 have been destroyed making ex-
amination of some of the local level variables prior to
1985 next to impossible. Fortyeight monthly observa-
tions from October 1984 to September 1988 will be
used. This amounts to fiscal years 1985 through 1988.
Proposed Variables
National advertising, while desirable to study,
has too many data collection and accuracy problems
beyond the scope of this work to research and correct.
Enlistment bonuses have shown little significant effect
and need not be further explored. Many articles
reviewed explored the impact of the percent of
minorities or urban areas. While those two variables
are informative in a cross section analysis, I'd submit
they are relatively constant to the Colorado/Wyoming
area over the last four years. At any rate, given the
nonstandard demographic census taking that cities and
states conduct it would be hard to gather accurate data.
The model should use instrumental variables where pos-
sible to eliminate the multicollinearity problems in-
herent in the recruiting business. For example the num-
ber of Army recruiters assigned to a battalion is re-
lated to available population and to past production by

Army directive. For each 500 male high school senior
and past two years graduates there is supposed to be one
assigned recruiter. Table 3-1 summarizes the proposed
variables and data source. Following Table 3-1 is the
rational and hypothesized effect for each variable.

Graduate senior male I-IIIA net
contracts written monthly as
indicated by USAREC data base
maintained at Chicago Illinois.
Monthly GSMA contract mission
assigned as indicated by USAREC data
Size of combined Colorado and
Wyoming labor forces as reported
monthly by state labor departments.
Used as the denominator in weighted
average measurements while the
respective individual state labor
size was used as numerator.
Weighted average of unadjusted
Colorado and Wyoming state monthly
unemployment rates as reported by
the Colorado Department of Labor and
Employment and Employment Security
Commission of Wyoming.

Table 3-1 continued
PAY = Weighted average of weekly wage for the monthly observation of Colorado manufacturing sector and Wyoming all industry wage rates as reported by the states7 labor departments.
CASH = The total monthly dollar obligation for expenditures on recruiter and applicant travel, and recruiter expense allowance as reported by USARB, Denver's budget technician.
VEHICLE = Monthly dollar obligation for expenditures on vehicles as reported by USARB, Denver's budget technician.
AWARD = Number of recruiter Gold Badge awards awarded monthly as recorded by USARB, Denver's awards noncommissioned officer-in-charge.
DEP = Number of individuals in the Delayed Entry Program waiting to ship to training the end of the month as indicated by the USAREC data base.

Table 3-1 continued
RECRUITER = Number of on-production recruiters assigned to the USARB, Denver carrying a positive mission of any contract category as indicated on the end of month progress reports kept by the USARB, Denver.
COI & DEP = Monthly dollars obligated on DEP and Centers of Influence (for instance high school principals) functions as reported by the USARB, Denver budget technician.
TRAINING = Monthly dollar obligation for training expenditures as recorded by USARB, Denver7 s budget technician.
QUARTER = Dummy variable equal to one to indicate fiscal year quarters two and four, and equal to zero in fiscal year quarter one and three.
SUPPLY = Dummy variable equal to one in periods of supply limited production as indicated by consistent shortfall

Table 3-1 continued
in mission, and equal to zero in
periods of overachievement, which
for our purposes here is from
October 1986 to June 1987.
Notes: Data statistics are reported in appendix A.
The dependent variable should be high school
graduate senior male I-IIIA (GSMA) contracts. This is
appropriate because first, contracts are the goal of the
USARB, Denver; not accessions which are artificially
controlled by the Army and are not related to the
seasonality of contracting. Second, GSMA are the least
influenced by Army controlled demand constraints. Third,
GSMA contracts provide the greatest source of reward and
Any model should have both environmental vari-
ables, and market variables. For environmental vari-
ables, besides including the obvious measures of a
seasonal dummy (QUARTER), unemployment (UNEMPLOYMENT),
and civilian pay (PAY); there needs to be a dummy vari-
able to account for supply limited periods (SUPPLY), and
an "award" variable (AWARD) to gauge the morale.

Relative pay has a consistent impact throughout
the discussed literature, in having a positive effect on
contracts as military to civilian pay ratio increases.
The hypothesis is that the higher the ratio of military
compensation to civilian compensation the more attrac-
tive the military becomes as an alternative. I would
imagine some areas of the country are more sensitive to
the relative pay factor than are other parts. While I
have no other specific regions to compare the local
coefficient to, knowledge of any response to this vari-
able would be useful.
Unemployment shows mixed results in the previous
studies. In some studies such as Altman and Fetcher
(1967) the lack of effect of unemployment rates can be
explained away by the presence of the draft. In the
Hosek and Peterson (1986) study the finding of unemploy-
ment being of little concern to high school seniors
strikes us as intuitively logical. In some case the
lack of significance can be attributed to the functional
form as in Ash, Udis, and McNown (1983) where they found
a negative relationship between the unemployment rate
and accessions for all of Department of Defense.
However, personal experience as the recruiting battalion
operations officer, responsible for day to day running

of the organization for the last 3 years suggests as un-
employment rises so does the number of contracts writ-
ten. I would hypothesize a 1 to 2 month lag in effect
has it takes that long for the perception of "good
times" or "bad times" to sink in. The unemployment rate
for all ages will be used as it is more easily measured
and form the basis of youth's opinions and perceptions
about their future.
Season of the year has a great deal to do with
recruiting given the timing of an individual's decision
process. Do I go to college or not? What do I do after
high school graduation? Do I like my summer job as a
full time job? The results of an individuals decisions
or desire to postpone a decision gives rise to the fol-
lowing hypothesis in terms of seasons more productive to
writing high quality contracts; (all quarters are fiscal
year quarters) Summer (Q4, July through September) is
more productive than the Winter (Q2, January through
March) which in turn is more productive than the Spring
(Q3, April through June) which in turn is more produc-
tive than the Fall (Qlf October through December). Sum-
mer and Winter quarters are historically ten to fifteen
percent better than either the Spring or Fall quarters.

The recruiter also has his or her own idea of
success. The more he perceives he has a reasonable
chance to succeed the harder he'll try and the more en-
listment contracts likely to be signed. The hypothesis
is the higher the recruiter gold badge award rate
(AWARD) the more contracts likely to be seen in future
periods. This is to capture the morale of a unit which
when successful feels no mountain is too high to climb.
Secondly it will help asses the effects of peer pressure
as young recruiters strive to be recognized as success-
ful experienced recruiting experts.
Market variables should also be included. I
would anticipate the more recruiters (RECRUITERS) the
more contracts. However, I would not expect the same
for available population (LABOR). While on the surface
a population of ten thousand people should supply more
contracts than a population of one thousand would
supply, I believe there is some optimum size desired. A
recruiter can harvest only a certain size population ef-
fectively, any more and they then go to waste, any less
and the supply is then not great enough to provide the
needed guota on a regular basis. This helps explains
the mixed effects indicated in previous studies reviewed
in chapter II concerning population size. Hanssens and

Levien (1983) indicated population had a positive effect
while Hosek and Peterson (1986) indicated population
available had a negative effect.
National and local advertising expenditures,
despite their desirability, will not be included because
the data are too unreliable in that the period of pay-
ment often has no relation to the period of advertise-
ment. More specifically a measure of number of ex-
posures the target audience receives is needed. This in
itself is difficult as often times the media will
provide free bonus spots for a certain amount of paid
advertising. The only studies done in this area were by
Daula and Smith and the N.W. Ayer advertising firm who
held the Army advertising contract until 1987. Besides
being skeptical of the study done by a firm trying to
win a $100 million annual advertising contract, the fact
the Army has taken that same firm to court due to over
payments, makes me leery of any data they would publish.
Previously reviewed studies such as Hanssens and Levien,
and Daula and Smith indicate local advertising has a
negligible effect and so while a by media by exposure
variable would be informative it will not be included.

The model should be run both with and without
recruiter missions included (MISSION). During the early
years, production was demand constrained and so missions
would be highly correlated to production. But as the
Army's demand for quality contracts was raised the
USARB, Denver was pushed into the supply limited mode,
consistently failing to achieve its mission. Missions,
it's hypothesized, take a significantly reduced ex-
planatory power the longer a unit is in a supply limited
mode. The inclusion of the MISSION variable will also
test the importance of recruiter goals in the local
Colorado/Wyoming area. The MISSION variable can also be
viewed as past achievement for the same period last year
given the way in which missions are assigned. Ideally,
when missions are used some total Department of Defense
number could be found as the instrumental variable.
However, the other local recruiting services were reluc-
tant to cooperate and only the Army mission will be
Some sort of local resource level (CASH) should
also be included if reasonably reliable data can be ob-
tained. The CASH variable measures the expenditures in-
curred by recruiters for their and their applicants'
travel and incidental expenses. A separate dollar

figure to indicate a vehicle mileage figure (VEHICLE)
should be examined separately given its large relative
size in the overall budget. Miles driven become a large
part of a recruiter's day and equate to time expendi-
tures. The more money and time spent in a vehicle the
less contracts a recruiter is able to write. This makes
sense as he or she is unable to spend their time in
productive activity if in a vehicle.
Also to judge word-of-mouth sales the number in
the delayed entry program (DEP) should be used as a
variable (DEP). As DEP pool size is controllable by the
Army, insight here might prove to be beneficial in that
letting the number of contracts in the DEP grow could
improve the number of contracts written. It is
hypothesized the larger the DEP the more word-of-mouth
selling and thus contracts.
The last variable to include is monthly expendi-
tures on recruiter training (TNG). The idea is that the
more funds spent on training the more effective the
recruiting force and thus the more contracts
that can be written.

Proposed Econometric Models
The function, a Cobb-Douglas form, which I will
initially estimate using the OLS method is:
The model should be estimated as a log linear
one to easier incorporate assumption of diminishing mar-
ginal returns and provide the estimation of elas-
ticities. The advantage of assuming diminishing mar-
ginal returns is that it takes into account the observed
diminished returns additional resources bring. For ex-
ample, if we increase the number of recruiters available
to work the current population by one percent, we would
not expect to see a one percent increase in the amount
of contracts. Instead we would expect to see somewhat
less then a one percent increase in the number of con-
tracts due to diminishing marginal returns each
recruiter brings.
The additional advantage to using a double-log
function is that coefficients of elasticity are repre-
sented in the equation. If we call the elasticity of
output Y, with respect to a change of input X, as e,

where e = d(ln Y) divided by d(ln X). Then the double
log transformation gives us the elasticity in the coef-
ficient. The elasticity is then also equal to the mar-
ginal function divided by the average function or
(dY/dX) multiplied by (X/Y). In the recruiting business
more so than most other business's concerned with the
bottom line, the number of contracts and measures of
success are relative. That is relative to the amount of
resources given or past efforts. For that reason elas-
ticities are preferred as they show the percentage of
change of output per one percent change in input. Elas-
ticities fit the prescription as leaders are concerned
with where the biggest payoff for the least effort can
be obtained, not necessarily the absolute change of out-
put for an increase of one input.

Model Summaries
As expected, there were many surprises and ad-
justments before a final model was decided upon. The
variables not chosen gave as much insight as those that
were. Two ordinary least squares estimates were ob-
tained. The first estimate is the original hypothesized
Model 1: LnGSMA = bQ + b-jLnMISSION + b 2 LnUNEMPLO YMENT +
b3LnPAY + b4LnCASH + b^LnVEHICLE + bgLnAWARD + byLnDEP +
b^2SUPPLY + error.
Model 1 is also estimated using first order serial cor-
relation by the Cochrane-Orcutt method. The second or-
dinary least squares estimated model, the one yielding
the most plausible results and best fit is
Model 2: LnGSMA = bQ + b-^nMISSION + b2LnPAY(t_1j +
b3QUARTER + b4SUPPLY + error.

Finally, a stepwise regression estimate of Model 1, with
a significance level of .05, and with the PAY variable
lagged one monthly period is applied. That model is
Model 3; LnGSMA = bQ + b-^nMISSION + b2LnUNEMPLOYMENT +
b3LnPAY(t_1) + b4LnCASH + b5LnVEHICLE + bgLnAWARD +
b7LnDEP + b g LnRE CRUITER + bgLnLABOR + b1QTNG +
bnQUARTER + b12SUPPLY + error.
Table 4-1 below summarizes the estimated results
of Model 1, Model 2, and Model 3 obtained by using the
Regression Analysis of Time Series (RATS) microcomputor

Constant -318.515 (1.043) 1 -832.056 (1.540)
Mission .955 (5.752) 1.118 (5.572)
Unemployment : rate 5.230 (1.473) 13.304 (2.150)
Pay .312 (0.736) 15.106 (.107)
PaY(t-l) NA NA
Cash -.0001 (0.844) -.0002 (1.378)
Award -.955 (.683) -1.015 (.514)
DEP .04 (2.291) .045 (1.376)
Recruiters -.807 (1.451) -1.979 (2.109)
Labor .100 (.899) .370 (2.563)
COI & DEP .0005 (.312) -.001 (.693)
Training -.337 (.515) -.0002 (.261)
Quarter 6.813 (1.325) -3.167 (.845)
Supply -18.003 (3.007) 14.037 (1.337)
Adjusted R2 2 .717 .776
SEE 3 10.832 12.276
Durbin-Watson 4 1.975 1.956

Table 4-1 continued
Constant 19.561 (5.525) -5.140 (5.455)
Mission .995 (6.053) 1.056 (7.772)
Unemployment rate NA NA
PaY(t-l) -2.260 (2.131) -3.220 (5.596)
Cash NA NA
Vehicle Miles NA NA
Award NA NA
Recruiters NA NA
Labor NA NA
Training NA NA
Quarter .040 (.992) NA
Supply -.176 (5.208) -.172 (5.036)
Adjusted R* 1 2 3 4 .736 .730
SEE . 109 .109
Durbin-Watson 2.147 1.936
1. Number in parenthesis is the absolute value of the
2. See Judge, Hill, Griffiths, Lutkepohl, and Lee,
1982, chapter 6 for a discussion of adjusted R .
3. SEE is the standard error of the estimate.
4. See Kelejian and Oates, 1981, chapter 6 for a
discussion of the Durbin-Watson test.