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5 Determining Optimal Levels of Advertising and Recruiting Resources renerally, 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

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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.

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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~.

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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.

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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.

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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.

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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

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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

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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-

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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.

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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

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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

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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.

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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

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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.

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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

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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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ADVERTISING AND RECRUITING RESOURCES 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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108 EVALUATING MILITARY ADVERTISING AND RECRUITING 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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ADVERTISING AND RECRUITING RESOURCES 109 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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110 EVALUATING MILITARY ADVERTISING AND RECRUITING 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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ADVERTISING AND RECRUITING RESOURCES 111 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.