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Modeling Army enlistment supply for the All-Volunteer Force.

The success of the All-Volunteer Force depends upon the ability of the U.S. military to meet its manpower requirements. The Army alone intends to maintain a total active duty force of 780,000. This target requires approximately 140,000 new accessions each year. Army recruiting has exceeded overall enlistment goals since 1979, but this trend may soon be reversed in wake of the recent economic expansion. The rising demand for labor is reducing youth unemployment and increasing wages, inducing more youths to enter the civilian labor market. In addition, the population aged 17 to 21 is predicted to fall 6.4 percent between 1985 and 1990. The pool of potential recruits is limited even further by higher enlistment standards mandated by Congress in 1983.

The greates recruiting challenge facing the Army is to attract a sufficient number of "high-quality males," particularly those who are high school graduates and score above the 50th percentile on the Armed Forces Qualifying Test (category 1-3A), hereafter referred to as graduate-senior males (GSM 1-3A). Evidence suggests that the number of accessions by such individuals is supply constrained, with total manpower goals being met by accepting lower category or nongraduate males, or women, as needed. The first sign of recruiting difficulty, then, may not be a fall in the total number of accessions, but rather a decrease in the percent of accessions among the GSM 1-3A group. Although such a decline may not have a significant immediate effect on total accessions, the emphasis on maintaining the quality of the force requires that the Army be able to compete successfully for "high quality" males.

The report models the peacetime supply of graduate-senior (1-3A) males with no prior military service, with particular interest in the effects of both unemployment and earnings on the Army enlistment rate. The model is then used to generate short-run forecasts. These projections are useful to manpower planners, not only for developing recruitment policies but also for allocating current accessions to military occupational specialties.

Analytical framework

In a simple one-period model, an individual chooses to enlist if the military wage at least equals his or her reservation wage. This reservation wage is a function of the alternative earnings in the civilian sector, the probability of receiving a wage offer in that sector, and the net utility of the nonpecuniary factors such as military lifestyle, travel, loss of personal freedom, and risk. It is clear that both earnings and unemployment rates in the civilian economy should influence enlistment rates. However, much of the recent research, particularly that research using time-series or pooled cross-sectional data, finds no such effects. These and other anomalous results may be due to model misspecification.

When an individual decides to join the Army, he or she signs a contract. The contract may specify immediate entry, or a delay for up to 12 months. Because the enlistment decision is made at the time of contract, total contracts are the appropriate quantity to use as the dependent variable. Accessions at any time are a combination of past and present contracts, and reflect the loss of those individuals who may not actually enlist despite the contract. Some studies have used accessions rather than contracts as the dependent variable, producing ambiguous results.

The recruiting success in the 1981-84 period has been widely attributed to high youth unemployment rates. Yet the relationship between enlistment and unemployment has been difficult to identify empirically. Many studies have found no unemployment effect, or have reported unemployment significant with lags of 1 and 3, but not 2, months. Previous studies use a wide range of unemployment rate measures, such as aggregate unemployment or the jobless rate for 16- to 19-year-old males. Because most male recruits are from 17 to 21 years old, the readily available unemployment rate for males ages 16 to 21 is intuitively a logical choice. This rate also generates the best fit in the regression equations.

Compensation is now a significant inducement for enlistment, particularly for individuals desiring to save for further schooling. Soldiers currently receive $573.60 per month in basic pay at entry, rising to $620.40 after advanced individual training (or 4 months). In addition, the Services provide food and housing (or subsisitence allowance), a clothing allowance, medical care, social security contributions, retirement benefits after 20 years' service, commissary and exchange benefits, and tax exemption for all allowances. Soldiers may qualify for "special" and incentive pay, and supplemental benefits and allowances. Educational bonuses are also quite substantial. With educational contributions and other related bonuses, a soldier may obtain up to $24,000 in educational benefits for a 4-year tour, and somewhat less for shorter tours. Therefore, the actual compensation package may be quite attractive, particularly for youths just out of high school with little or no work experience.

Not all recruits receive incentive and supplemental pay, nor do all recruits who qualify for enlistment bonuses elect to participate in the program. For simplicity, military compensation is estimated in this analysis as the sum of basic pay, allowances for quarters and subsistence, and the tax advantage derived from the nontaxable status of the allowances. Over time, this series is highly correlated with total compensation. However, the level of military compensation is probbly not as important alone as it is relative to civilian ernings. In a one-period model, the opportunity costs might be considered to be youth earnings, although using this series introducs substantial error into the analysis. When military service affects future earnings or when the individual is comparing enlistment with schooling, the rationale for comparing military with civilian youth compensation is less clear. In this analysis, military pay was compared to earnings estimates for production or nonsupervisory workers on private nonagricultural payrolls obtained from the Bureau of Labor Statistics. This series can be interpreted as an average measure of earnings for jobs which are similar in nature to many Army jobs for the enlisted force.

Compensation enters this model with a slightly different twist. Previous analyses simply included a compensation ratio, usually the ratio of military to civilian pay, as an independent variable. Yet the two series are not comparable. The BLS earnings series are essentially moving averages because wages are continually changing throughout the economy over time. Military compensation, however, usually increases just once each year. Therefore, the ratio of military to civilian compensation rises once each year, and then falls for 11 months. Simple econometric models which include the pay ratio yield anomalous results, and the size as well as the sign of the pay effect varies as alternative lags are chosen. In this analysis, military pay is first converted to a moving average, and is then compared to civilian earnings. It appears that the real wage difference has a larger impact in the model than the wage ratio. Thus, the pay variable of choice is the real diference of the two earnings series expressed as moving averages.

The Army devotes considerable resources of recruiting. In fiscal 1984, the Army spent close to $325 million on recruiting and examining activities alone. Two recruiting factors are easily measured and are statistically significant: (a) the number of recruiters, and (b) the real advertising expenditures on national media.

Finally, the male population ages 16 to 21 is included in the model, albeit indirectly. The dependent variable is number of contracts divided by male population, and recruiters are also expressed as recruiters per eligible male, or recruiter density. The enlistment (contract) forecasts are adjusted by population projections to produce the level of expected contracts.

The model to be estimated takes the form: S/POP = F (Pay, U, Recruit/POP, Adver) where: s = the supply of graduate-senior (1-3a) males; POP = population of eligible males; Pay = real military compensation relative to civilian earnings; Recruit = number of recruiters; U = the unemployment rate for 16- to 21-year-olds; and Adver = Army advertising expenditures.


Because the model initially exhibited a significant amount of serial correlation, the generalized least squares (GLS) technique was used. Various two-stage GLS specifications of the enlistment model have been estimated using quarerly data covering second-quarter 1977 through second-quarter 1984 and are provided in table 1. The results demonstrate that both the earnings and unemployment varialbes exert a sizable and statistically significant effect on army enlistments. In addition, the number of recruiters and national advertising expenditures are also important. The current unemployment rate, although possessing the right sign, is not statistically significant. This is not surprising because individuals would not be expected to respond immediately to an increase in unemployment, wishing to test the civilian job market first before enlisting in the military.

Equation 4 substitutes a pay ratio for the pay difference used in the other equations. While the ratio term is significant, the higher mean squared error demonstrates an inferior fit. This result is particularly interesting because most other studies use such a ratio as the pay variable. Equations 5 and 6 exhibit two of the Almon polynomial lags fit to the unemployment variable. Neither quadratic distributed lag fits the data very well. The final regression includes only those variables which appear to be significant. Unemployment lagged two quarters is significant at the .10 level; all other variables meet the .05 significance test. The coefficients are quite stable across various specifications.

End-point elasticities have been calculated for each of the significant variables from equation 7. Unemployment, with an elasticity of .73 (for both lags combined), has a large impact on the level of contracts. For example, it is estimated that the fall from 17 percent to 16 percent in the unemployment rate for 16- to 21-year-old males would result in a decline of almost 600 GSM 1-3A contracts per quarter. The impact of changes in the unemployment rate is felt after a lag of one to two quarters.

The effect of military compensation is also significant. The pay elasticity based on equation 7 is 2.7, which implies that a military pay increase of approximately $115 will result in an increase of 390 GSM 1-3A contracts per quarter. It is interesting to note that the pay ratio in this study generates an elasticity of 2.1. This is comparable with other enlistment studies which find ratio elasticities of around 2.0.

The recruiter elasticity of .76 implies that 100 additional recruiters will induce 232 "high quality" potential recruits to enlist per quarter, or more than 9 per year per additional recruiter. Additional recruiters will yield more contracts from other recruit categories as well.

Finally, the national avertising elasticity of .044, based on an annual expenditure level of $45.6 million, implies that a $100,000 increase in expenditures per quarter should result in 5.6 additional graduate-senior male recruits per quarter. At this rate, the advertising cost to attract a single additional contract is $17,857. This number appears unduly high, but excludes the associated increase in contracts in other recruit categories.

Enlistment projections

The Army uses enlistment projections to set recruiting goals, allocate recruiting resources, and distribute recruits to various military occupational specialties. The forecasts provided here are generated assuming a constant pay differential and no changes in the number of recruiters per eligible made. Recruiting resources and goals did rise over fiscal 1984, and the projections reflect this recruiting policy change. The forecasts allow the civilian unemployment rate to fall to 6.3 percent by 1988, which is consistent with the August 1984 unemployment projections of the U.S. Congressional Budget Office. The predicted unemployment rate series for 16- to 21-year-old malesis derived from forecasts of the total civilian rate, based on the past relationship between the two series. The rate for young males is therefore assumed to fall 14.5 percent by 1988. Table 2 presents quarterly numbers of contracts and accessions for 1984 and forecasts for first-quarter 1985 through first-quarter 1987.

These results demonstrate the manpower problem facing the Army over the next several years. The forecast contract numbers do not adjust for the delayed entry program loss, which averages approximately 6 percent for graduate-senior males; some persons who sign a contract do not actually enlist when they are due to enter the Army. This effect is illustrated by the forecast accessions in table 2. Given the target about 60,000 accessions per year for the next few years, the Army alone would be facing a shortfall which increases over time if no counteractive discretionary policies are implemented. Data from the U.S. Army Recruiting Command for fiscal 1984--86 illustrate the problem dramatically:

The delayed entry program creates a manpower pool which can be reduced when recruiting becomes difficult. Because recruits have some control over the length of the delay, accessions fluctuate relative to contractss from quarter to quarter. The increase in retention rates experienced by the Army in recent years may reduce the number of accessions needed to maintain the desired manpower levels in the future. However, the latest reenlistment rates may indicate a reversal of this trend.

Error analysis. Because the model has been developed to generate forecasts of enlistment contracts, its forecasting properties are considered here. Because the model is estimated over 28 quarters, leaving only 21 degrees of freedom, relatively few back forecasts can be derived. One-quarter-ahead forecasts for five quarters (1983: II-1984: II) were generated, and the mean squared error calculated on the basis of percent changes over time. The error shares are then allocated among the regression, bias, and disturbance proportions. A good forecasting model should have relatively little bias and regression effor. If the actual numbers of contracts (A.sub.t) are regressed on predicted values (P.sub.t), the regression can be expressed as: A.sub.t = [alpha] + [BETA]P.sub.t

The bias proportion is zero if [alpha] = 0, and the regression proportion is zero if [BETA] = 1. The disturbance proportion remaining is the random error in the regression. Because the forecast error is expressed in terms of percent changes over time, the root mean squared error provides a measure of error in percent terms. The error allocation is provided above:

The root mean squared error is 2.8 percent, well within the range of respectable forecast error. The majority of the error is disturbance error, as expected. The bias proportion is quite reasonable, despite the fact that the number of contracts peaked in first-quarter 1983 and began to decline in the next quarter. The bias proportion should fall even further given a longer forecasting horizon. However, the small number of degrees of freedom prevents using an extended forecast test. In any case, the low bias and regression error and the large disturbance proportion indicate that the forecast model is performing well.

These forecasts may perhaps be more accurately described as simulations. It is expected that the Army will, in fact, increase recruiting resources to meet the potential recruiting difficulties ahead. Therefore, the actual shortfall will most likely differ from current estimates. The latest data show that large increases in recruiting resources, in light of the projected shortfall for fiscall 1984, have indeed resulted in more enlistments. The projections in this report provide information on expected enlistment only if everything else (including relative pay and recruiting resources) is held constant, and if the economy continues strong with unemployment declining. While the number of recruiters and national advertising are the only recruiting variables in the model, it is likely that other variables such as the level of resources available to the recruiters, or pressure on recruiters to produce accesssions, will influence the level of enlistment as well.

The aggregate time-series models are particularly useful for short-term projections and can be updated and estimated quickly and easily. In the long run, however, aggregation problems become important. Parameter estimates cannot be precise for this level of aggregation and must be used with caution for policy analysis. Our model does not control for competition from the other services, nor for the fact that many recruiting districts met or exceeded recruiting goals. These factors may be significant, although experimentation incorporating the demand by other services in the time-series model did not yield satisfactory results. The possibility that the contracts are demand constrained is minimized by modeling "high quality" male contracts. Any such constraint would lead to a negative bias in the estimated coefficients. The contract projections become very tenuous when predicting more than several quarters into the future.


The U.S. Army could face serious recruiting problems throughout the remainder of the 1980's. The two primary causes of this shortfall would be economic gains and the continued decline in the population of eligible males. The model demonstrates that unemployment rates are an important determinant of peacetime enlistment, in contrast with many previous studies, and that military compensation relative to civilian earnings is of paramount importance to potential recruits. The recruitment shortfall can be reduced if appropriate manpower management policies are implemented. The number of recruiters is also significant, as are national advertising expenditures.

The model appears to fit the data well over the entire period, while the one-period-ahead forecasts for the four quarters of 1984 differ from actual contracts by between 1.5 and 3.0 percent. Of course, the forecasts are expected to be less accurate as the projections approach 1990, because they depend upon the state of the economy as well as military personnel policy.
COPYRIGHT 1985 U.S. Bureau of Labor Statistics
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Author:Horne, David K.
Publication:Monthly Labor Review
Date:Aug 1, 1985
Previous Article:The FCMS contribution to nonlabor dispute resolution.
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