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OCR for page 90
5
Determining Optimal Levels of
Advertising and
Recruiting Resources
r—enerally, econometric approaches are the most suitable research
t. ~ designs for assessing the optimal levels of recruiting programs
_ and resources. They can be applied to both natural and experi-
mental data. Because they often can be applied successfully to natural
data, they can save the often significant costs associated with a formal
experiment. This can occur, however, only for resources and programs
that have been implemented and for which there is variation cross-
sectionally, over time, or preferably both.
Econometric methods can be used to isolate and identify the effects of
existing resources, policies, and external factors affecting recruiting out-
comes as well as their costs. There is by now a relatively well-developed
body of econometric research that has identified some of the most important
determinants of enlistment supply as well as the cost and effectiveness of
various recruiting resources and the trade-offs among them. Estimates
are based on the natural variation in key recruiting resources and out-
comes (usually aggregated) that occur over time and across geographic
locations.
In this chapter we first review current approaches as described in the
recent literature and then suggest practical areas in which the research
design can be improved (with best data sources) and that promise to
produce the most reliable results. An implicit theme is that one cannot
approach design issues in isolation. That is, to obtain better estimates of
the effect of advertising, for example, improvements must be made in
models that already account for other factors affecting supply in a solid
way, and vice versa. Hence, it is probably a mistake to think in terms of
90
OCR for page 91
ADVERTISING AND RECRUITING RESOURCES
91
the best model for estimating recruiter effects, the best model for estimat-
ing advertising effects, and so forth. In this multivariate framework of the
actual recruiting market, one must adequately control for all factors to
isolate the effect of a single factor.
ECONOMETRIC APPROACH TO ENLISTMENT SUPPLY
From the beginning of the All-Volunteer Force, enlistment supply has
been an ongoing topic of research.2 Econometric studies of enlistment
supply have used either aggregate national time-series data or panel
data that is, data over time disaggregated by some geographic level
(e.g., state, county, Service-specific recruiting area). Early studies typi-
cally focused on highly qualified enlistments (H) and modeled H as a
function of exogenous economic factors (X) and recruiting resources (R):
H = h(X, R).3 These studies implicitly assumed that the supply of recruits
with low qualification levels (L) was unlimited and that these recruits are
costless to recruit.
Dertouzos (1985) and Polich, Dertouzos, and Press (1986) introduced
the current generation of recruiting supply models. These models are
distinguished by accounting formally for the role of recruiters' prefer-
ences, the recruiting technology, and recruiter incentives. Dertouzos
(1985) argued that because it takes time and effort on the part of the
recruiter to attract and process even walk-in recruits, a more appropriate
formulation of the supply of highly qualified recruits adds L to the high-
quality enlistment supply function: H =f(X,R,L). L should have a negative
effect on H in this formulation.
Recruits do not simply appear off of the street. Recruiters must seek
them out and provide information about military service opportunities
that may convince them to join. This activity requires recruiters to expend
effort. The high-quality enlistment function is thus further modified to
include recruiter effort: H =f(X,R,L,E). Recruiter effort is unobservable to
researchers. But Polich, Dertouzos, and Press assume that it depends on
how high H and L are relative to the quotas that recruiters are given for
these two qualification categories of recruits (QH and QL, respectively).
This can be tempered somewhat by noting that a particular specification designed to
measure advertising effects, for example, may control for other factors in a way that is not
designed to produce structural estimates of their effects, but simply control for variation
from that source. The point here is that this other variation must be accounted for.
2Nelson (1986) provides a useful survey of the voluminous studies conducted prior to the
mid-1980s.
3High-quality enlistments are enlistments of high-school diploma graduates who score 50
or above on the Armed Forces Qualification Test.
OCR for page 92
92
EVALUATING MILITARY ADVERTISING AND RECRUITING
When H (L) is low relative to QH (Qr), recruiting is more difficult and
recruiters must work harder. Therefore, E = gRQH,Qr). Substituting this
expression into the function above for H gives H =f(X,R,L,QH,Qr). Most
enlistment supply studies operationalize this general function by assum-
ing that the natural logarithm of H. log(H), is a log-linear function of the
other variables:
log(H) = logy + Eulogy + Eulogy + ~QHlogQH + ~Q~IogQ~ + £
The random error £ in this equation accounts for unobservable influ-
ences on log(H). The coefficients in this equation are elasticities of H with
respect to the variables in the equation. Elasticities show the percentage
change in H due to a given percentage change in a given variable. For
example, a recruiter elasticity of 0.4 indicates that a 10 percent increase in
the recruiter force would lead to a 4 percent increase in H.
Warner, Simon, and Payne (2002) provide a detailed review of 15
econometric studies of enlistment supply conducted between 1985 and
1996. Some of the elasticity estimates from these studies are summarized
below. Models are usually estimated with panel data that is, data that
vary by time (e.g., month, quarter, year) and cross-section unit (e.g.,
Service recruiting area, state).4
The log-linear model rationalizes the inclusion of quotas as factors
affecting highly qualified enlistment. It implies that an increase in quotas
will, by stimulating recruiter effort, increase enlistments. It is possible,
however, that the effect of quotas depends on whether H is above or
below QH and L is above or below Qr Daula and Smith (1985) and Berner
and Daula (1993) pursue a different modeling strategy based on the con-
cept of "switching" regression. Their approaches break the restriction of
linear relationships between log(H) and logtQH) and logtQr) and permit
changes in quotas to have different effects depending on how high they
are relative to H. Daula and Smith (1985) allowed log(H) to switch between
"supply-constrained" regimes (H < QH) and "demand-constrained"
regimes (H > QH). Studying Army recruiting battalions, Berner and Daula
(1993) allowed H to fall into three regimes: those that were highly supply-
4 The proper estimation method with panel data depends on the form of the residual in
the model. In panel data, the residual £ may be composed of three different factors. The first
is a state effect, which is constant over time. The second is a time effect, which captures the
influences of unobservable influences that are common to all states at a point in time. The
third is an idiosyncratic factor, which varies randomly by state and time. Models with panel
data can be estimated by using one-way or two-way fixed-effects models that control for
unobservable state and time effects (Greene, 2002~.
OCR for page 93
ADVERTISING AND RECRUITING RESOURCES
93
constrained, those that were producing around the quota, and those that
were producing well above their quota.
Issues in Estimation of Advertising Effects
Two key issues in estimating the effects of advertising are (1) func-
tional form, the shape of the relationship between expenditures or impres-
sions and enlistments, and (2) dynamics, how advertising in one period
affects recruiting in subsequent periods. The simplest form of relation-
ship is a semilogarithmic relationship in which log(H) is related linearly to
current or lagged expenditures or impressions. The semilogarithmic rela-
tionship imposes the restriction that each dollar increase in advertising
gives the same percentage change in H. Another frequently assumed form
of relationship is the log-log relationship, in which log(H) is related to the
natural logarithms of current or lagged advertising. This form of relation-
ship imposes the restriction that the elasticity of enlistment with respect
to advertising is constant regardless of the level of advertising. A short-
coming of this specification is that the logarithmic transformation requires
excluding those observations for which the advertising measure has a
value of 0, often the case with military advertising.5
Dertouzos and Garber (2003) argue that the functional relationship
needs to be flexible in order to estimate the effects of advertising over a
wide range of levels of advertising. Furthermore, they argue that adver-
tising must reach a minimum critical level before it has any impact on
enlistment. Beyond this critical minimum level, increases in advertising
increase highly qualified enlistments, first at an increasing rate and later
at a decreasing rate. Finally, beyond some saturation level, advertising
ceases to have any impact on highly qualified enlistments. A form that
allows regions of both increasing and diminishing returns is the logistics
function. Figure 5-1 illustrates logistics and linear relationships between
the log of highly qualified enlistments and advertising expenditures.
The second important specification issue raised by Dertouzos and
Garber is the timing of the relationship between advertising and enlist-
ment. Advertising in a particular month is likely to affect highly qualified
enlistments in future months, and the problem is how to specify the timing
of the advertising-enlistment relationship. Some studies have imposed
specific distributed lag relationships. One popular form of distributed lag
relationship, the Koyck lag, imposes a geometrically declining relation-
5Alternatively, one can set the advertising measure equal to some small number. How-
ever, Hogan, Dali, Mackin, and Mackie t1996' reported that results were sensitive to this
choice of number. For this reason, they entered advertising linearly in levels.
OCR for page 94
94
1.0
0.9
0.8
0.7
In
0.6
0.5
. _
0.4
0.3
0.2
0.1
0.0
EVALUATING MILITARY ADVERTISING AND RECRUITING
0 5 10
15 20 25
Advertising Expenditures
(in thousands)
30 35 40
FIGURE 5-1 Hypothetical relationships between log of highly qualified enlist-
ment and advertising: Logistics and linear cases.
ship between past advertising and current enlistments. That is, advertis-
ing has a larger near-term effect than far-term effect. Specific lag forms
such as the Koyck are often assumed when time-series are short and there
are insufficient data to accurately estimate a large number of lag parameters.
Despite this virtue, they run the risk that the true relationship is not of the
assumed form. With a long enough time series, it is possible to simply
include a sufficient number of lags of advertising in the model and esti-
mate the parameters by regression.
Estimates from Econometric Studies
Table 5-1 outlines the empirical strategies of 16 enlistment studies of
male highly qualified recruits carried out between 1985 and 2001.6 Eleven
of these studies focused on a single Service. The factors that determine
high-quality enlistment supply fall into three categories: (1) recruiting
market factors (relative military pay, unemployment rate, youth popula-
6Nelson (1986) summarizes studies performed with data from the 1970s.
OCR for page 95
ADVERTISING AND RECRUITING RESOURCES
95
lion); (2) recruiting resources (number of recruiters, advertising budgets);
and (3) recruiting policy variables (recruiting goals, enlistment bonuses,
college benefits). Table 5-2 summarizes the findings from the studies in
Table 5-1 with respect to recruiters and advertising.
Excluding Warner's (1990) negative estimate for the Air Force, esti-
mates of the elasticity of highly qualified enlistments with respect to
recruiters range from a low of 0.090 for the Air Force (Fernandez,1982) to
1.65 for the Army (Dertouzos, 1985~. The Fernandez and Dertouzos esti-
mates were obtained from data that spanned very short time periods.
Estimates from longer time periods and periods over which recruiters
exhibit more variation are more reliable. Furthermore, because the allocation
of recruiters to geographic areas is likely to be correlated with unobserv-
able factors that vary systematically across geographic areas, estimates
based on models that include fixed geographic effects are probably less
biased than are other estimates. In fact, studies with panel data employ-
ing fixed effects for geographic area or time (or both) have tended to yield
smaller recruiter elasticity estimates.7 The mean of the recruiter elasticity
estimates in Table 5-2 is 0.55, implying that a 10 percent change in the
recruiter stock changes enlistment of highly qualified recruits by about
5.5 percent.
As Table 5-2 shows, there are many fewer estimates of the effects of
advertising than of recruiters. In the only experimental study of advertis-
ing effectiveness, Dertouzos (1989) reanalyzed the Ad Mix Test data.
Unlike the original analysis by Carroll (1987), Dertouzos estimated posi-
tive but modest effects of advertising. However, flaws in the design of the
test limited the usefulness of the data produced by that experiment. The
table reveals the paucity of econometric estimates of advertising effects. A
primary reason is the lack of data. The Navy, through a contract with PEP
Research, Inc., was the only Service to systematically collect advertising
data at any geographic level of detail throughout the 1980s.8 Through a
contract with the Department of Defense (DoD), PEP collected advertis-
ing data on all four Services by month by county for the period 1988-1997.
Warner (1991) provided an early analysis of the PEP data. Using
annual data at the Navy Recruiting District level, he estimated the elasticity
of enlistments of highly qualified recruits with respect to all Navy adver-
tising to be about 0.05. That is, doubling Navy advertising would raise
Estimation procedure may account for the different recruiter elasticities estimated by
Fernandez (1982) and Dertouzos (1985~. Fernandez (1982) used a fixed-effects estimator in
his dataset of 67 Military Entrance Processing stations MEWS; Dertouzos (1985), who used
a 33-MEPS subset of Fernandez (1982) dataset, did not.
8PEP estimates military advertising expenditures and impressions at the county level for
many categories of advertising.
OCR for page 96
96
EVALUATING MILITARY ADVERTISING AND RECRUITING
TABLE 5-1 Empirical Strategies
Beginning Ending Cross-Sectional # X- Services
Date of Date of Frequency Unit of Sec Includec
Study Study Study of Data Observation Units in Study
Berner and Oct-80 Jan-90 Monthly Battalion 55 Army
Daula
(1993)
Bohn and Oct-92 Sep-95 Monthly NRD 31 Navy
Schmitz
(1996)
Buddin Oct-86 Sep-90 Monthly Battalion 53 Army
(1991)
Daula and Oct-80 Jun-83 Monthly Battalion 54 Army
Smith
(1985)
Dertouzos Dec-79 Sep-81 Monthly AFEES 33 Army
(1985)
Dertouzos Oct-83 Sep-84 Monthly ADI 210 All
(1989)
Fernandez Dec-79 Sep-81 Monthly AFEES 66 Army,
(1982) Air Forc
Navy
Goldberg Ju1-71 Dec-77 Quarterly Nation
(1979)
Navy
OCR for page 97
ADVERTISING AND RECRUITING RESOURCES
97
# X- Services
Sec Included Study Theoretical Estimation Fixed Log or
Units in Study Type Framework Procedure Effects? Linear
55 Army Econometric Recruiter 3-regime Yes Log
utility switching
maximization regression model
31 Navy Navy College Reduced OLS No Linear
Fund form
53 Army Army's 2+2+4 Recruiter Nonlinear No Log
Experiment utility 3SLS
. . .
max~m~zahon
54 Army Econometric Supply and 2-regime Some Log
demand switching models
regression
model
33 Army Econometric Recruiter 2SLS and No Log
utility maximum
maximization likelihood
210 All Advertising Reduced SUR with No Log
Mix Test form correction for
serial
correlation
66 Army, Educational 12-month first Yes Log
Air Force, Assistance Reduced difference using
Navy Test Program form LS with
correction for
heteroskedasticity
1 Navy Econometric Reduced Maximum No Linear
form likelihood
corrected for
heteroskedasticity
Continued
OCR for page 98
98
TABLE 5-1 Continued
EVALUATING MILITARY ADVERTISING AND RECRUITING
Beginning Ending Cross-Sectional # X- Services
Date of Date of Frequency Unit of Sec Includec
Study Study Study of Data Observation Units in Study
Hogan Jan-90 Dec-94 Monthly NRD 31 Navy
et al.
(1996)
Kearl
et al. Oct-80 Dec-89 Quarterly Brigade 5 Army
(1990)
Murray and Oct-82 Sep-93 Monthly PUMA 911 All
McDonald
(1999)
Polich Ju1-81 Jun-84 Monthly MEPS 66 Army
et al.
(1986)
Smith Oct-80 Sep-89 Monthly Battalion 55 Army
et al.
(1990)
Warner Oct-80 Sep-87 Quarterly NRD 41 All
(1990)
Warner Oct-80 Sep-90 Annual NRD 41 Navy
(1991)
Warner, Oct-89 Oct-97 Monthly State 51 All
Simon and
Payne
(2001)
NOTE: ADI = areas of dominant influence; AFEES = armed forces entrance examination
station; MEPS = military entrance processing station; NRD = Navy recruiting district; PUMA
= public-use microdata areas. FIML = full information maximum likelihood; IV = instru-
OCR for page 99
ADVERTISING AND RECRUITING RESOURCES
99
# X- Services
Sec Included Study Theoretical Estimation Fixed Log or
Units in Study Type Framework Procedure Effects? Linear
31 Navy Econometric Reduced LS with Yes Both
form correction for
serial correlation;
IV for advertising
in some models
Reduced GLS No Log
5 Army General form heteroskedasticity
911 All Econometric Hybrid OLS corrected for Yes Log
structural heteroskedasticity
and reduced and serial
form correlation; IV
for some variables
66 Army Enlistment Recruiter Two-stage No Log
Bonus utility procedure
maximization using 3SLS
55 Army Econometric Enlistee OLS found that Yes Log
utility correcting for
maximization serial correlation
did not affect
estimates
41 All Econometric Reduced Effects Yes Log
form
41 Navy Econometric Recruiter OLS and Yes Log
utility fixed
maximization effects
51 All Econometric Recruiter Fixed effects with Yes Both
utility IV for some
maximization variables
mental variables; LS = least squares; GLS = generalized least squares; 0LS = ordinary least
squares; 2SLS = 2-stage least squares; 3SLS = 2SLS followed by SUR; SUR = seemingly
unrelated regressions.
OCR for page 100
100
EVALUATING MILITARY ADVERTISING AND RECRUITING
TABLE 5-2 Econometric Estimates of Advertising Elasticities
Elasticiti
Study Sample
S.
ervlce
Advertic
Berner and Daula (1993)
Bohn and Schmitz (1996)
OLS
NRD dummies included
NRD and month dummies included
Buddin (1991)
Daula and Smith (1985)
'~Pooled,,
Supply-Constrained
Demand-Constrained
Dertouzos (1985)
Reduced form, 1980 goals included
Reduced form, 1981 goals included
Structural model 1980 2SLS
Structural model 1981 2SLS
Structural model 1980 FIML
Structural model 1981 FIML
Dertouzos (1989)
Army
Navy
Air Force
Marines
Fernandez (1982)
Army
Navy
Air Force
Goldberg (1979)
Hogan et al. (1996~: Median estimates
TV
Radio
Mailings
0.208
NA
NA
NA
NA
0.089
0.107
0.156
NA
NA
NA
NA
NA
NA
0.028
-0.005
0.071
-0.001
0.140
0.028
0.021
0.038
OCR for page 101
ADVERTISING AND RECRUITING RESOURCES
101
Elasticities
Service Joint Recruiters Advertising Measure
Advertising Advertising National Impressions
0.208 NA
0.274
NA NA 0.221
NA NA 0.346
NA NA 0.139
NA NA 0.238 Expenditures
Impressions and
0.089 NA 0.585 expenditures
0.107 NA 0.959
0.156 NA 0.826
NA NA 0.842
NA NA 0.466
NA NA 1.193
NA NA 1.086
NA NA 1.647
NA NA 1.529
0.028
-0.005
0.071
-0.001
0.016
0.028
0.008
0.023
0.227
0.526
0.303
0.470
0.295
0.274
0.090
Expenditures
0.140 1.270 Dollars
0.286
0.028 0.031 Impressions
0.021 0.009 Impressions
0.038 0.029 Impressions
Continued
OCR for page 102
102
TABLE 5-2 Continued
EVALUATING MILITARY ADVERTISING AND RECRUITING
Elasticiti
Study Sample
S.
ervlce
Advertic
Kearl et al. (1990)
Model 1
Model 2
Model 3
Murray and McDonald (1999)
Army early (1983-87)
Army late (1990-93)
Marine Corps early (1983-87)
Marine Corps late (1990-93)
Air Force early (1983-87)
Air Force late (1990-93)
Navy early (1983-87)
Navy late (1990-93)
Polich et al. (1986)
Smith et al. (1990)
Warner (1990)
Army, time trend included
Navy, time trend included
Air Force, time trend included
Marine Corps, time trend included
Warner (1991)
Warner, Simon, and Payne (2001)
Army
Navy
Air Force
Marine Corps
SUMMARY STATISTICS
Mean
Standard deviation
Coefficient of variation
0.430
0.580
0.720
0.056
0.050
0.103
0.015
-0.034
-0.017
0.050
0.136
0.084
-0.013
-0.065
0.114
0.186
1.625
NOTE: 2SLS = 2-stage least squares; FIML = full information maximum likelihood; NRD =
Navy recruiting district; 0LS = ordinary least squares.
OCR for page 103
ADVERTISING AND RECRUITING RESOURCES
103
Elasticities
Service Joint Recruiters
Advertising Advertising
Advertising Measure
National Impressions
0.430
0.580
0.720
0.480
0.680
1.150
0.51
0.60
0.53
0.62
0.49
0.59
0.33
0.24
Expenditures
0.056 0.597 Expenditures
0.050 0.150 Expenditures
Expenditures
0.103 0 0.371
0.015 -0.004 0.412
-0.034 0.004 -0.045
-0.017 0.001 0.487
0.050 -0.028 0.527 Expenditures
0.136 0.008 0.410 Impressions
0.084 -0.003 0.640 Impressions
-0.013 0.015 0.480 Impressions
-0.065 0.022 0.470 Impressions
0.114 0.010 0.551
0.186 0.015 0.368
1.625 1.545 0.667
OCR for page 104
104
EVALUATING MILITARY ADVERTISING AND RECRUITING
enlistments of highly qualified recruits by 5 percent. Despite the appar-
ently low response, advertising was found to be cost-effective in com-
parison to recruiters because Navy advertising was a very low part of the
overall recruiting budget in the 1980s (see the cost estimates section below).
Hogan et al. (1996) examined the impact of Navy advertising with
more recent data. Furthermore, they estimated the effects of various sub-
categories of advertising. Using a fixed-effects model, they estimated a
TV elasticity of 0.03, a radio advertising estimate of 0.02, and a magazine
advertising elasticity of 0.04. Elasticities were also estimated for joint-
Service TV (0.031) and radio advertising, and mail advertising (own
Service, 0.038; joint-Service mail, 0.029~.
Warner, Simon, and Payne (2001) utilized PEP data to estimate an
overall advertising elasticity for the Army of 0.13 and for the Navy of 0.08.
In models that separated advertising into TV and non-TV advertising,
they obtained TV elasticity estimates of 0.09 and 0.05 for the Army and
Navy, respectively, and non-TV estimates of 0.07 and 0.05 for those Services.
But no relationship was found between Air Force and Marine Corps
enlistments of highly qualified recruits and advertising. Those Services'
advertising programs are much smaller than the Army and Navy pro-
grams, so the insignificance of the estimates could reflect the smaller scale
of those programs. Furthermore, there was some doubt about the quality
of the data for those Services.
Because these studies all imposed log-log or semilog functional rela-
tionships between log(H) and advertising, one should not use these esti-
mates to infer the effects of advertising over a wide possible range of
advertising expenditures. Dertouzos and Garber (2003) recently reanalyzed
the Ad Mix Test data imposing the logistic relationship between log(H)
and four forms of advertising: TV, radio, magazine, and newspaper. Esti-
mates were consistent with the theory and suggested different S-shaped
curves for the different media types. Newspaper spending did not appear
to have an impact on log(H) at any level of advertising. Magazine adver-
tising had an effect at a very low level but reached the saturation level at
a very low level of spending. Radio advertising had larger minimum
effectiveness and larger saturation levels than magazine advertising. TV
advertising had the largest minimum effectiveness and the largest satura-
tion levels.
Dertouzos and Garber report extreme difficulty in estimating their
models with more recent (fiscal year 1993-1997) data.9 Service-specific
estimates were not, in their opinion, very reliable. They therefore aggre-
9In particular, the logistic advertising model must be estimated with nonlinear regres-
sion, and they had difficulty getting nonlinear regression procedures to converge. And
when they did, estimates did not seem to be very plausible.
OCR for page 105
ADVERTISING AND RECRUITING RESOURCES
105
gated their data to the DoD level and estimated models of total DoD
enlistments as a function of advertising and other control variables. Some
models contained total advertising, while others contained TV and non-
TV advertising. These models yielded significant positive effects of total
advertising and of TV advertising, but not of non-TV advertising.
Recruiting Cost Function
The concept of recruiting cost functions (RCF) is taken from the eco-
nomic theory of production. The RCF provides an estimate of the optimal
(i.e., cost minimizing) resource levels to achieve a given set of recruiting
goals. They can be derived directly from the enlistment supply models,
which may be interpreted as recruiting production functions.
The RCF is derived as the outcome of the following cost-minimization
problem:
choose X to min C = Id= piXi subject tof(H*, L*, X, Z*, E) = 0.
where the It's are the prices or unit costs of n resources over which there is
choice, the X's, and He and Lo are particular values for highly qualified
and less-well-qualified recruits, respectively. The vector Z consists of
factors over which the Services do not have control but that affect recruit-
ing. It includes the civilian unemployment rate and civilian wages as well
as, arguably, the aggregate military pay raise. The vector X includes
recruiters, bonuses, advertising, and college benefits, among other things.
As a result of solving the minimization problem and solving the first
order equations for a minimum, we obtain the recruiting cost function:
C = C(p,H,L,Z)
where C is the minimum total cost of recruiting H highly qualified recruits
and L recruits with low qualification levels, and p is a vector of resource
prices and Z are factors affecting cost that are beyond the control or choice
of the Service. In addition to providing an estimate of the minimum total
cost, the RCF also provides an estimate of the optimal levels of resources
that constitute the cost. That is, a product of the cost function is an esti-
mate of the optimal amount of each resource, given the overall goals,
where "optimal" is the cost-minimizing amounts. Moreover, by differen-
tiating with respect to H or to L, one obtains an estimate of the marginal
cost of highly qualified and less-well-qualified recruits.
A RCF was developed for each Service by Hogan and Smith (1994~. A
version of the RCF is currently in use by the Office of the Secretary of
OCR for page 106
106
EVALUATING MILITARY ADVERTISING AND RECRUITING
Defense and the Chief of the Naval Recruiting Command. In these appli-
cations, the RCF uses a log-log specification of the underlying enlistment
supply model. The model provides the cost and levels of resources for a
given set of recruiting goals and for a given economic environment.
Marginal Resource Cost Estimatesi°
Once the responsiveness of enlistment to recruiting resources has been
estimated, estimates can be used to calculate the marginal cost of enlist-
ment. A greater responsiveness of enlistment to recruiting resources im-
plies lower marginal cost. Consider the marginal cost of highly qualified
enlistments brought about by an expansion of the recruiter force. The
marginal cost of highly qualified enlistment via recruiters can be calcu-
lated as C*(R/H)/~R where C is the cost of a recruiter, R is the ratio of
recruiters to highly qualified enlistments, and OR iS the elasticity of H with
respect to R. If C = $45,000 (DoD recruiter cost factor), R/H = 0.1 (late 1990s
ratio for the Army, the Navy, and the Marine Corps), and OR = 0 5, then
the marginal cost of H via additional recruiters would be $9,000. Since OR
is 0.5, the marginal cost is twice the average cost ($4,500~. The most plau-
sible estimates of OR range from 0.3 to 0.6 (Table 5-2~. This range of esti-
mates implies marginal recruiter costs for the Army, the Navy, and the
Marine Corps in the range of $7,500 to $15,000. Because Air Force recruit-
ers average about 25 highly qualified contracts per recruiter, marginal
recruiter cost for the Air Force is much lower (about $3,400~.
The marginal cost of highly qualified enlistments brought about by
an expansion in advertising can be calculated similarly. At 1997 budget
levels, Warner, Simon, and Payne calculated the marginal cost of recruits
via an expansion of Army advertising to be about $10,700. Because they
Submarginal cost estimates reported here are inclusive of "rents." Rents are the amounts
over and above that amount necessary to obtain the recruits. They are more important for
some ways of obtaining additional recruits than others. For example, additional recruits
will be attracted to enlist if there is an increase in first-term pay. But because all recruits,
even those who would have enlisted without the increase in first-term pay, would receive
the pay increase, rents from this method of increasing recruits supplied are large. In con-
trast, rents associated with increasing recruits through the efforts of additional recruiters
are negligible. From the perspective of the economy as a whole, rents are approximately a
transfer payment, neither a cost nor a benefit. They represent resources transferred from
some to others in the economy, although there may be additional costs if the resources are
taxed from some, and this taxation affects behavior. Nonrent costs are always costs to the
economy. They represent resources used up in the production of some good or service.
Hence, if two or more ways of increasing the supply of qualified recruits have the same
marginal cost when rents are included, the one with the lower marginal cost excluding
rents is preferred from the perspective of the economy as a whole.
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107
estimated a larger responsiveness of enlistment to advertising than those
obtained in some of the studies summarized in Table 5-2, marginal adver-
tising costs could in fact be greater.
The logistics functional form employed by Dertouzos and Garber
implies high marginal advertising costs at low levels of enlistment fol-
lowed by declining marginal costs in the midrange of advertising outlays
and then by high marginal costs as advertising reaches a saturation point
(which may depend on the target market and the advertising message
strategy). Dertouzos and Garber calculated that, at 1993-1997 advertising
budget levels, the marginal cost of a DoD highly qualified male enlist-
ment via total advertising to be about $37,000. But FY 1993-1997 was a
period of relatively low advertising; advertising outlays rose dramatically
in the FY 1998-2000 period. Dertouzos and Garber (2003) calculated that,
at an advertising spending level roughly double the average level prevail-
ing in the FY 1993-1997 period, marginal advertising costs for highly
qualified male contracts would fall to about $10,500. Furthermore, accord-
ing to their calculations, marginal costs of the recruits obtained via TV
advertising would continue to fall over a much higher range of spending
before beginning to increase.ll
Estimates of the Effects of Other Resources
Econometric methods can be applied to estimate the effects of other
resources not often considered in the traditional enlistment supply model.
An example is an econometric estimate of the effect of the number and
location of recruiting stations on recruit supply (Hogan, Mehay, and
Hughes, 1998~. In this analysis, an enlistment supply model was estimated
that was not dissimilar from the models described above. It consisted of a
pooled time series of cross-sections. The dependent variable was specified
as enlistments in a given zip code area. Explanatory variables included,
among other things, distance to the nearest recruiting station. This per-
mitted assessment of the effect of recruiting station location on enlistment
supply. Estimates indicated that the number and location of recruiting
stations had a significant effect on recruiting.
Econometric methods can often be applied to include additional
resources or factors that could potentially affect recruiting. The data for
the additional resource or factor must be available for the same cross-
1lThese cost estimates are dependent on the assumed functional (logistic) form. While
certainly the most plausible functional form found in the recruiting literature, more work
clearly needs to be done to verify that it fits the data better than other forms. Given the
difficulty of estimating the model and the probable fragility of their estimates, Dertouzos
and Garber stress the need for more work in this area.
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sectional and time-series dimensions as the other variables included in
the model. What is important is that the effect of the additional variable
be included in a model that also includes all other resources or factors
affecting recruiting. Failure to include all other variables increases the
likelihood of obtaining a biased estimate of the effect.
IMPROVEMENTS IN DOD RECRUITING RESEARCH
Effects of Recruiters
Aspects of the econometric estimates of the effects of recruiters on
enlistment supply can be improved by a relatively straightforward exten-
sion of existing models. First, an individual recruiter's productivity varies
with experience. Newly assigned recruiters typically produce few or even
no recruits in their first six months on station. Over the next 18 months,
productivity rises and reaches a plateau. Then productivity begins to
decline as the recruiter prepares to rotate back to his or her primary skill
area.l2 Hence, one can expect the productivity of recruiters to vary sys-
tematically with experience. When the recruiting force increases signifi-
cantly in a short period of time, average experience declines. Similarly,
when the recruiting force declines rapidly, it is usually by a dispropor-
tionate decline in new recruits, increasing average experience and pro-
ductivity.
Failure to account for the effect of these changes on the average expe-
rience and average productivity of recruiters as a whole may bias the
measured recruiter productivity toward zero. By measuring the average
experience or tenure of recruiters in the estimation equation, it may be
possible to improve the precision of estimates and perhaps eliminate a
bias in the estimation of recruiter effects on supply. Moreover, by estimat-
ing econometric models for which the dependent variable is a measure of
individual recruiter productivity, insights can be gleaned regarding fac-
tors affecting individual productivity.
A second issue in measuring the effects of recruiters is to expand the
analysis of recruiter incentives beyond the effects of aggregate quotas.
This would attempt to capture econometrically the more sophisticated
Service "point" systems and other complex incentive structures (see Asch,
1990, for an early analysis of the Navy recruiter point system).
Finally, a third issue that has not been addressed in the literature is to
include the effects of reserve force competition on active-duty recruiting.
While other Service competition has been included in several econometric
12 This is described for a cohort of recruiters in McCloy et al. (2001)
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specifications, no models have incorporated reserve force component
competition for nonprior service recruits. For the selected reserve force,
the proportion of nonprior-service recruits is likely to rise relative to those
who affiliate while leaving active-duty service, simply because active
strength has declined and retention has increased. This may foster greater
competition with active recruiting, in that in many instances they are
competing for recruits from the same set of high school seniors and others.
Incorporating reserve force recruiting into active-duty recruiting models
may help explain the potential interactions, while providing estimates of
the factors affecting reserve force recruiting.
Advertising Content
Econometric estimates that incorporate the effect of advertising have
measured advertising largely as homogenous counts of "impressions"-
the number in relevant populations who see or hear the advertisement-
or expenditures by period and geographic location. They have not
attempted to get inside the expenditure or impression to measure differ-
ences in effects by specific advertising content.
Data could be constructed for television advertising that distinguished
the content of the advertisement as well. That is, if there are one or two
dominant advertising themes for a campaign for a given Service in time
period 1, but this changed in time period 2 and again in time period 3, the
advertising variable itself could be constructed to allow for different
effects for the same ostensible level of advertising (impressions or expen-
ditures) over each of these three periods.
Previous econometric models have separately distinguished the
effects of various types of advertising on recruiting. Radio, magazine, or
print advertising and television advertising have been distinguished, for
example. If the time periods for major television advertising themes or
campaigns can also be distinguished in the data, it is not difficult to specify
the model to allow them to have separate effects. Distinguishing different
effects for television advertising based on the content of the advertise-
ments themselves, however, would be difficult because one would be
attributing a portion of the variation over time in recruiting to the shift
among advertising themes or specific advertisements. The model specifi-
cation and supporting data must be solid to isolate the effects.
An alternative approach to allowing separate estimates by advertis-
ing campaign would be to try and isolate essential elements of an adver-
tising theme and measure them in continuous variables. This would
undoubtedly entail some subjectivity. One could, however, classify ads
by the seconds devoted to three or four themes training, postservice
education, compensation, adventure, and patriotism, for example. This
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would be an interesting exercise, but it would not distinguish differences
in the quality of a given message within a given theme. That is, it would
not distinguish between good advertisements that feature training as a
theme from bad advertisements that feature training as a theme.
Hence, we suggest that initial attempts in this area try to test for
differences in effects of advertising campaigns by allowing distinguish-
able campaigns to have different effects. Then, if it is established that
effects do appear to vary significantly by content and not just dollars or
expenditures, a second step would be to try to understand how content
variation affects recruiting.
More Flexible Functional Forms
A limitation of much of the empirical research is that the functional
forms of the econometric specifications have been relatively restricted.
Perhaps one way to understand some of the implications of the particular
functional forms is to consider an enlistment supply equation as analo-
gous to a production function for recruits. The log-log form of the supply
curve that has been popular forces elasticity estimates to be constant,
regardless of level of recruiting activity or of the particular recruiting
factor. Moreover, when the RCF is derived from such estimates, it is
readily seen that the factor shares of each price resource the proportion
of total cost of production attributable to each resource are constant
regardless of how the prices of resources change.
More flexible functional forms would provide less restrictive con-
straints on parameter estimates. In the literature reviewed, this is particu-
larly important for the measurement of the effects of advertising and for
modeling the effects on recruiter incentives. But it is also important to
obtain more precise and useful estimates of the effects of resources in
general. The more flexible functional forms, such as the trans-log formu-
lation, typically require richer data for estimation. This is in part because
these forms allow the data to determine whether the effects of factors may
vary with scale or with relative proportions of other factors, rather than
imposing them as constraints in the mathematical formulation. As panel
data become more refined and become available over longer periods,
application of more flexible functional forms can perhaps provide new
sets of insights on factors affecting recruiting.
A theme underlying all of the suggested areas for improvement is the
need for better data, consistently collected and retained over time. Sug-
gested improvements in estimates of the effects of advertising, recruiters,
and other incentives will require more sophisticated functional forms and
more detailed specification of effects. This places greater demands on
data than has historically been the case.
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Ideally, these data should include enlistment contract and accession
data, by level of qualification and Service, at the lowest reasonable level of
aggregation and time period. Data at the individual recruit level, coupled
with information regarding timing of enlistment, home (zip code) of the
recruit, and recruiting station should be maintained over time. Impor-
tantly, the data should also include information on the resources and
incentives that have been applied and the external factors that were in
effect during the period, as well as indications of recruiting policies,
incentives, quotas, and so forth. Advertising data, which we discuss in
several places, should contain information not simply on impressions or
dollar expenditures, but also include a systematic characterization of
advertising content, if these are to be evaluated. These data should, again,
be able to be tied to the recruiting data at the lowest reasonable level of
aggregation.
Representative terms from entire chapter:
recruiting resources
