The effect of separation bonuses on voluntary quits: evidence from the military's downsizing.

1. Introduction

Despite widespread downsizing of both private firms and government agencies during the last decade, little research has been conducted on the various financial incentives used to encourage voluntary separation. Several studies have analyzed the influences of early retirement programs on an individual's retirement decision and on the optimal age at retirement (Burkhauser 1979, 1980; Fields and Mitchell 1984). Hogarth (1988) analyzed a state government's early retirement bonus program and Lumsdaine, Stock, and Wise (1990) analyzed an early retirement option offered to employees of a private firm. Other studies have developed a general method of analyzing the decision to separate voluntarily (Black, Moffitt, and Warner 1990; Daula and Moffitt 1995). But no study has linked the decision to resign by nonretirement-eligible personnel in response to separation incentives, especially when the incentives are offered during an organizational downsizing. Thus, little is known about the overall effectiveness of buyout programs in inducing voluntary separations of nonretirement-eligible personnel.

During the post-Cold War downsizing that began in the late 1980s, the U.S. military needed to eliminate mid-career personnel, but wanted to avoid involuntary separations. Historically, military personnel have considered the military retirement system an implicit contract. Though the military pension is not vested until 20 years of service, prior to the drawdown, personnel had come to expect that after six to eight years of service they would be allowed to serve 20 years and qualify for a retirement annuity. However, the scale and speed of the military downsizing meant that some nonvested careerists, who in other times would have served until retirement, faced involuntary separation.

To avoid imposing these pension losses on mid-career personnel and creating negative incentive effects for junior personnel, the Department of Defense offered a separation bonus to selected careerists in 1992. Two options were offered. The first, called the Special Separation Benefit (SSB), provided a lump sum payment equal to 15% of annual base pay multiplied by years of service. Unlike private firms, the military also offered an annuity option, called the Voluntary Separation Incentive (VSI), which provided an annual payment equal to 2.5% of annual base pay multiplied by years of service. The annuity would continue for twice the number of years of service. These programs replaced the equivalent of between 29% and 36% (depending on years of service) of the present value of the expected military pension for a person who would have retired after 20 years.

This article examines the decisions of uniformed personnel to leave voluntarily under the military's separation incentive program. It focuses on the effects of the VSI/SSB bonus program on Navy and Air Force enlisted personnel in 1992, the first year of the program. In particular, we estimate the net effect on retention - the reduction in the retention rate that was induced by the program.(1)

Two methods are used to estimate the effect of the VSI/SSB program on retention. The first method approaches the estimation problem from a "program evaluation" perspective in that we use a difference-in-differences design to isolate the program effect. That is, we use a selected period before implementation of the VSI/SSB program and the period during the program and include occupations eligible for the program and a comparison group of occupations that were not eligible. The program effect is estimated using a dummy variable, and the difference-in-differences design controls for occupation and time period fixed effects.(2) The second approach estimates a structural model of retention. The separation bonus is incorporated as a component of the financial incentives influencing the individual's stay-leave decision. We estimate the effect of the separation bonus on Navy enlisted personnel in 1992 within the framework of the annualized cost of leaving (ACOL) model, which has been applied extensively in modeling the effect of pay on separation decisions (Warner and Goldberg 1984; Black, Moffitt, and Warner 1990).

Heckman and Smith (1995) argue that so-called "black box" program evaluation methods - estimation of mean effects using nonstructural models - are inferior to estimation of program effects using structural models, in part because the results provide little general information on fundamental economic behavior. We use both techniques here because an unbiased, relatively precise estimate of the program effect using black box estimation can provide corroborating evidence regarding the estimate from a structural model and provide a useful test of the structural model itself.

The ACOL results provide an estimate of the effect of the financial incentive on the individual's voluntary retention decision. But there is the potential problem that individuals may have believed that if they rejected the buyout they would be involuntarily separated under less favorable financial terms. The Navy announced that involuntary layoffs would not be used. At the other extreme, the Air Force announced that layoffs would be necessary if response to the buyout program was not adequate. Air Force personnel, prior to being offered the bonus, were grouped by occupation into "tiers" based on the probability of future layoff in each occupation. We use the Air Force data to test for the effect of the threat of layoff on the individual's decision to accept the "voluntary" separation incentive. Not surprisingly, acceptance rates for the exit bonus increase with the threat of layoff.

2. Annualized Cost of Leaving Framework

The theory underlying the ACOL model has been developed extensively in the literature (Warner and Goldberg 1984; Hogan and Black 1991; Daula and Moffitt 1995). Here, we briefly summarize the basic form of the model. In the ACOL model of retention, the individual is assumed to compare the utility of leaving the military immediately with the utility of remaining for each possible future period of service. In general, one searches over all possible lengths of stay to determine the optimal length of stay at a given decision point. The financial returns associated with the optimal length of stay are then compared with the financial incentive of leaving immediately. The ACOL value is the net financial incentive to stay. It is calculated as the annualized difference in the financial rewards from staying to the optimal leaving point relative to leaving immediately. Depending upon rank, all personnel are forced into mandatory retirement at various points between 20 and 30 years of service. The utility from staying or leaving depends on both the present value of the income stream and the present value of the monetary equivalent of any nonpecuniary aspects. The latter component is unobserved.

In our analysis, we assume that individuals choose between leaving immediately or leaving after 20 years of service, which is the vesting point for retirement. The exit bonus is incorporated into the ACOL model by including the value of the bonus in the income stream associated with leaving immediately. This assumes (correctly as it turns out) that the separation bonus was perceived as a one-time offer.

The ACOL value is the net financial incentive to stay. We assume that an unobserved component of the decision the net difference between the value of nonpecuniary factors associated with civilian and military life - is distributed normally with mean [Mu] and variance [[Sigma].sup.2]. Then, if the net taste for civilian life for individual i is [[Delta].sub.i], we can define z = ([Delta] - [Mu])/[Sigma], and the retention decision rule becomes:

[Mathematical Expression Omitted] (1)

where [r.sub.i] represents the probability of staying for individual i, [[Lambda].sub.i] and [X.sub.i] are the respective vectors of parameters and individual characteristics, [Mathematical Expression Omitted] is the financial incentive to stay calculated over a period that takes the individual to the 20-year point, and f([center dot]) is the standard normal pdf. The variables in X are assumed to affect unobservable tastes for military and civilian life. In the specification below, these variables include race, sex, marital status, number of dependents, whether one has a military spouse, Armed Forces Qualification Test (AFQT) score, and technical occupation.

Although most prior retention research has focused on the reenlistment behavior of junior personnel, Goldberg (1982) analyzed the effect of military pay on the retention of more senior personnel at approximately 11 to 14 years of service. He assumed that these mid-career personnel [TABULAR DATA FOR TABLE 1 OMITTED] choose between staying to the 20-year point or leaving immediately. Historically, reenlistment rates approach unity with increasing years of service because mid-careerists who remain for 11 to 14 years have exhibited strong preferences for military life. This dynamic self-selection, combined with the increasing attractiveness of the military retirement system with additional service, is hypothesized to be a major factor influencing retention behavior at this career point. In computing ACOL, Goldberg chose the horizon from the date of the retention decision to the date at which the individual could retire (20 years of service) to calculate the military pay stream and the returns from leaving the Navy at the decision point. Because the VSI/SSB incentives were offered only to mid-career personnel, we have adopted a similar assumption.(3)

3. The Bonus Program

The Navy, the main focus of this study, targeted the bonus narrowly to specific (overstaffed) occupations, years of service (10 to 17), and pay grades (5 and 6). These restrictions meant that less than 10% of the enlisted force was eligible for the buyout. Information on the population of 34,032 Navy enlisted personnel who were eligible for the bonus in 1992 was combined with information on which individuals separated under one of the incentive programs. Missing data for some variables reduced the final data set to 31,872 observations. Of these, 3876 (12.1%) accepted a separation bonus; 84.8% of the takers chose the lump sum bonus (SSB) over the annuity (VSI) option. Table 1 provides descriptive statistics for bonus-eligible Navy personnel.

Air Force and Navy personnel were combined in a second data set to analyze the impact of the layoff threat. Data on Air Force personnel eligible for the bonus in 1992 were restricted to individuals who faced a layoff threat, which consisted of enlistees in grades 5 and 6 with 9 [TABULAR DATA FOR TABLE 2 OMITTED] to 14 years of active duty service. After combining Navy and Air Force personnel with these characteristics, the second data set contained 70,116 observations.(4)

Table 2 shows relevant descriptive statistics for bonus-eligible Air Force personnel who were threatened with involuntary separation. Similar to the Navy, Air Force personnel who accepted the bonus were younger with fewer years of service, were less likely to be married, and less likely to be minorities. As was also true for the Navy, females in the Air Force had a significantly higher acceptance rate than males. However, unlike Navy personnel, the Air Force leavers had lower AFQT scores and more dependent children, were less likely to have a military spouse, and were more likely to serve in a nontechnical occupation.

Although the Navy announced reductions in force (RIF) would not occur even if the voluntary program did not meet expectations, Air Force personnel faced an explicit RIF threat, if enough personnel did not accept the separation bonus. As a measure of potential vulnerability to RIF, the Air Force grouped occupations into five "tiers," with the degree of overstaffing and corresponding threat of RIF rising from tier 2 to tier 5. The bonus acceptance rate for Air Force personnel was 15.9%, about 3.7 points (or 30%) higher than for Navy personnel, but varied from 12.1% for tier 2, 17.1% for tier 3, 19.6% for tier 4, to 20.1% for tier 5.(5)

4. Program Evaluation Estimates

In this section, we outline the design used to estimate the program effect for Navy enlisted personnel. The evaluation design identifies a comparison group relevant to those eligible for the bonus, and measures retention in the treatment group and the comparison group before and after the bonus offer. The buyout encouraged people to leave in two ways. It not only offered a financial incentive to leave, but also released takers from their enlistment contracts. That is, some personnel eligible for the bonus were at a normal reenlistment point and therefore could freely choose to leave, whereas others were not at a reenlistment point and, in the absence of the program, would have been obligated to stay until their contracts expired. At issue is whether the comparison group should consist of all personnel or only those who were similarly at a reenlistment point.

Table 3. 1991 Navy Separation Rates by Tenure and Reenlistment
Status

Tenure (years)   At Reenlistment Point   Not-at-Reenlistment Point

10                        0.24                     0.03
11                        0.18                     0.03
12                        0.13                     0.03
13                        0.10                     0.03
14                        0.09                     0.03
15                        0.07                     0.03
16                        0.05                     0.02
17                        0.05                     0.02

Data provided by Navy Bureau of Personnel.

Columns 3 and 4 of Table 3 compare separation rates in 1991, the year before the bonus program, for Navy personnel who were at a reenlistment point and for all Navy personnel. The rates are calculated for the same years of service that were targeted for the bonus program in 1992. It is unclear which category represents the "correct" comparison group. Only those at a reenlistment point could voluntarily choose to leave the Navy. In contrast, most of the targeted personnel prior to being offered the bonus in 1992 were not at a reenlistment point. It is reasonable to assume that in the absence of the bonus their behavior would have mimicked that of other personnel not at a reenlistment point. The weighted average separation rate for those making reenlistment decisions in 1991 (column 1) was 11.2%, whereas it was only 3% for those serving under an obligation (column 2). Thus, if separation rates for VSI/SSB eligibles in 1992 are compared to personnel at a reenlistment point (in 1991), the separation rate for program eligibles is 1.1 percentage points higher (12.3 - 11.2). If, instead, personnel in all reenlistment statuses are used as the comparison group, the program-related differential is 9.3 percentage points (12.3 - 3.0).

These unadjusted differentials are illustrative but inconclusive. For one thing, the separation rates in Table 3 are aggregated over all grades and occupations. Also, two unusual events in 1991 affected retention: the aftermath of the Gulf War created considerable personnel turbulence, and the military's drawdown was already underway. These events are likely to cause 1991 separation rates to be higher than in a steady-state period. Thus, in the analyses below, we use 1988 - the first available predrawdown, pre-Gulf War year - to form part of the control group for assessing the effect of the bonus program.(6)

The program guidelines restricted eligibility to certain occupations, pay grades, and years of service. Because eligibility was not randomly assigned, we were especially concerned about controlling for occupation-specific and grade-specific effects. In the program evaluation, we pool 1988 and 1992 data for personnel in both eligible and noneligible occupations to control for occupation and time period fixed effects. The pooled data allow comparisons of program-eligible personnel in 1992 to otherwise similar personnel in 1988 who were in the same occupations, [TABULAR DATA FOR TABLE 4 OMITTED] grades, and tenure categories. In addition, pooling allows comparisons of program eligibles to noneligibles in 1992 who were in different occupations but were in similar grade and tenure cells.

The approach adopted here is to compare the retention behavior of the targeted group to otherwise similar nontargeted personnel. Within the pooled data, two alternative comparison groups are used. The first "at reenlistment" comparison group includes only bonus-ineligible personnel who were free to leave in the absence of the program (i.e., they were at a normal reenlistment point). The second "all bonus ineligible personnel" comparison group encompasses everyone not eligible for the bonus, including both those at a reenlistment decision point and those serving under a reenlistment contract. Table 4 presents the mean characteristics of individuals in the second comparison group broken out by program eligibility and reenlistment status.

The estimating model is specified as follows. Let [Y.sub.i] = 1 if the individual stays, and [Y.sub.i] = 0 otherwise. The probability that [Y.sub.i] = 1 is:

Pr([Y.sub.i] = 1) = Pr{[X.sub.i][Beta] + [[Alpha].sub.1][ELIG.sub.i] + [[Alpha].sub.2][YEAR.sub.i] + [[Alpha].sub.3]([ELIG.sub.i][multiplied by]REENL) + [[Sigma].sub.j][[Alpha].sub.4j][OCC.sub.ji] + [[Epsilon].sub.i] [greater than] 0} (2)

where [X.sub.i] is a vector of individual characteristics (race, marital status, number of children, AFQT, education, grade, and tenure), [YEAR.sub.i] is a dummy for 1988, [OCC.sub.ji] are occupational dummies, [ELIG.sub.i] is a dummy for eligibility, and ([ELIG.sub.i][multiplied by][REENL.sub.i]) is an interaction term for individuals who are eligible for the bonus and are also at a normal reenlistment point.

We estimate two separate models as probit equations. In the first model, we combine the program-eligible group with the "at reenlistment only" comparison group. In the second, program eligibles are combined with the "all-personnel" comparison group. The results for both models are presented in Table 5. Using the probit results when the comparison groups include only those "at reenlistment" in Table 5 (columns 1-3), we estimate the separation rate with the bonus in effect and compare it to an estimate of the separation rate under otherwise similar circumstances, but without the bonus. The results indicate that when the comparison group [TABULAR DATA FOR TABLE 5 OMITTED] consists of only individuals at a reenlistment point, the quit rate for program eligibles not at a reenlistment point was only 0.2 percentage points higher than the quit rate for otherwise similar noneligible personnel who were at a reenlistment decision point. This statistically insignificant effect represents only about a 1% increase in the loss rate. However, if we consider only bonus-eligible personnel who were at a normal reenlistment point in 1992, the effect is the sum of the program dummy variable and an interaction between eligibility and being at a reenlistment point. Bonus eligibles at a normal reenlistment point in 1992 now have about a 1-percentage-point higher quit rate than noneligible personnel who were also at a normal reenlistment point in 1992, an increase in the underlying separation rate of about 10%.(7)

The second comparison group in Table 5 (columns 4-6) includes all individuals not eligible for the bonus, regardless of whether they were at a reenlistment point. A dummy variable is added to the specification to indicate individuals who were at a reenlistment point. Using this comparison group, the coefficient of the eligibility dummy combines the effect of being released from the enlistment contract with the financial incentive of the exit bonus. As in the first comparison, the interaction term indicates that program eligibles who were naturally at a reenlistment point had a slightly higher quit rate than eligibles who normally would have been under an obligation. Using this second comparison group for noneligible personnel, we distinguish between those at and those not at a reenlistment point. This dummy variable indicates that those free to make a reenlistment decision had separation rates 8.8 percentage points higher than other noneligible personnel. The net financial effect of the bonus on the separation rate is the difference between the eligibility and the reenlistment dummies. In this case, the effect of the financial incentive on the separation probability is 0.6 percentage points, consistent with the magnitude estimated using the first comparison group.

[TABULAR DATA FOR TABLE 6 OMITTED]

5. Structural Estimates

A COL Model Estimates

The results of estimating the ACOL model of Equation 1 with data on Navy enlisted personnel are displayed in Table 6. Construction of the ACOL variable is described in the appendix. The coefficient of the ACOL variable is statistically significant and positive, although its magnitude is small. Column 4 provides the predicted acceptance probabilities with and without the separation bonus. The effect of the bonus was calculated by using the SSB, which was the option selected by more than 85% of takers. The SSB increases the acceptance probability by 0.531 percentage points, a relative increase of 4.29%. Thus, of the 4320 enlistees who accepted the buyout, it is estimated that 4146 would have left without the bonus. This estimate lies midway in the range of estimates using the fixed effects estimators.

Effect of Layoff Risk

In this section, we estimate the effect of the threat of involuntary separation (RIF) on loss rates under the bonus program using the combined data on bonus-eligible Navy and Air Force personnel. The data set included personnel who satisfied both services' buyout eligibility criteria and Air Force personnel subject to a layoff threat. This limited the combined data set to personnel in grades 5 or 6 with 10 to 14 years of service.

To estimate the effect of the RIF threat on program acceptance rates, we use the ACOL model combined with a set of dummy variables to reflect differences in the threat of involuntary separation for Air Force personnel. The construction of ACOL is the same as in the Navy model in Table 6 above. Included in the specification are dummy variables to proxy the involuntary separation threat (TIER2-TIER5) to Air Force personnel. Recall that higher tiers contained occupations with greater overmanning and therefore a higher risk of involuntary layoff.(8) Navy [TABULAR DATA FOR TABLE 7 OMITTED] personnel are the reference group since they faced no such threat and were not assigned to tiers. To the extent that there are fixed differences in the retention rates between the two service branches, a constant average difference will be a component of the tier dummies. This specification also constrains the ACOL coefficient to be the same for Navy and Air Force personnel.

Table 7 presents the results of the probit retention model for bonus-eligible Navy and Air Force personnel. The coefficients of the TIER3-TIER5 dummies are all significant and negative. Also, the magnitude of the coefficients increases from tier 3 to tier 5, indicating a positive relationship between the layoff threat and the acceptance probability. Individuals in tier 2, which represented occupations with the lowest RIF probability, are less inclined to accept the separation bonus than are Navy personnel. Air Force personnel in this tier may have considered themselves as more or less immune from involuntary separation. Moreover, as noted above, the tier dummies also capture average differences in the retention rate of Air Force and Navy personnel. Hence, the positive coefficient may indicate simply that, other things equal, Air Force personnel have slightly higher retention rates than Navy members. The marginal effects in column 4 of Table 7 indicate the difference in acceptance probabilities between Air Force personnel in each tier and Navy personnel who faced no layoff risk. Air Force members in tiers 4 and 5 had the highest program acceptance rates: The probability of leaving was 6.59 points higher for those in tier 4 and 7.35 points higher for those in tier 5, which represents a difference of over 50% for both groups.

The findings illustrate that the layoff threat boosted acceptances of the buyout. Air Force members in tiers associated with higher layoff threats were more likely to resign compared to similar Navy personnel. If the Navy had implemented a system similar to the Air Force's, the layoff threat would have increased total acceptance rates of Navy personnel from 4320 to 5963, a relative increase of about 38%. Thus, the Air Force's higher overall acceptance rate appears to be explained largely by the threat of layoff.

Also of interest in Table 7 is that the estimated program effect has more than tripled in size compared to Table 6. In the combined Navy and Air Force data set, the SSB increases the acceptance probability by 1.8 percentage points, a relative increase of about 15%. This occurs even though the model controls for the threat of layoff among Air Force personnel, and suggests that the severity of the downsizing and the more uncertain climate in the Air Force intensified the effect of the bonus program well above what it was in the Navy. Moreover, this result is more likely to represent the program effect throughout the military where some services faced a layoff threat (Army and Air Force) and others did not (Navy and Marine Corps).(9)

6. Summary and Conclusions

This research represents a first step toward understanding voluntary separation behavior in response to exit bonuses in downsizing organizations. The results show that the effect on quits of the financial incentive alone was positive, but small. This result is perhaps understandable. The program was targeted to individuals with between 10 and 15 years of service. Historically, retention rates in this tenure range are high and inelastic. Moreover, the exit incentive replaced only 30 to 40% of the present value of the retirement annuity the individual would have received if s/he were to remain in the military an additional 5 to 10 years. There was also a substantial effect of the program from simply releasing personnel from their enlistment contracts, though it is likely that these personnel would have left at the expiration of their contract. And, although the program effect was small, it was sufficient to prevent involuntary layoffs of mid-level personnel who in less turbulent times likely would have served until retirement.

The buyout program provided the Defense Department with a flexible policy tool for implementing its downsizing program. A further advantage of the program is that by targeting the bonuses to specific groups the military was able to restructure its work force in terms of skills, experience, and grades. Targeting the bonuses to specific skills, grades, and tenure cells ensured that all takers were in redundant jobs and did not need to be replaced. One problem experienced with civilian buyouts has been the difficulty in targeting specific workers in unneeded jobs. As a result, civilian firms often have been forced to hire replacements for bonus takers, thus increasing the cost per job abolished (Congressional Budget Office 1993).

Nonetheless, it appears that separation bonuses that offer mid-career personnel only a fraction of the present value of expected future retirement pay have only a modest effect in inducing additional quits. This would be particularly relevant to private firms that attempt to adhere to a no-layoff policy. Our results also suggest that the effect of the incentive to separate voluntarily must be carefully distinguished from latent threats of layoff. Since most private firms have offered bonuses only when layoffs were imminent, the Air Force's experience is more relevant than the Navy's to civilian organizations. The "voluntary" quit rate rises substantially when bonuses are offered in an environment of uncertainty about potential layoffs.

We thank an anonymous referee and Charlie Brown for helpful comments. Melissa Potter, Frank Rogge, and Don Sewell provided excellent research assistance. The views expressed are solely those of the authors.

1 Previous studies analyzed the demographic factors affecting the probability of accepting the separation incentive to determine the effect of the downsizing on the quality of personnel choosing to leave (Mehay and Hogan 1996). Also, Warner and Pleeter (1995) used information on the choice of VSI or SSB to estimate an implied personal discount rate.

2 The program effect is estimated as though it were the difference between the change in separation rates for the program-eligible group before and after the program and the change in separation rates for the noneligible (control) group before and after program implementation. In the program evaluation literature, this method is referred to as a difference-indifference estimate.

3 Daula and Moffitt (1995) compared the predictive power of the ACOL model with a dynamic programming model in explaining the reenlistment decision of first- and second-term Army personnel. The effect of a hypothetical VSI program on retention was simulated to compare the predictive power of the dynamic programming model and the simpler ACOL model. Despite many differences between their simulation and the actual VSI/SSB program that was adopted, in simulations where the VSI was offered immediately, the predicted retention effect of VSI in the ACOL model was the same as in the dynamic retention model. Their main criticism of ACOL was its inability to predict the effect on current retention of financial incentives offered at some future point. This criticism is irrelevant here, however, because the actual bonus program offered the incentive during short windows of one to two months, and it had to be accepted or rejected immediately with no guarantee of being reoffered.

4 Note that the unobserved heterogeneity that may bias ACOL estimates of early retention decisions is less important in this context owing to the seniority of personnel who are program eligible.

5 Personnel in tier 1 were not eligible for the separation bonus and, therefore, are omitted from the Air Force data.

6 To ensure comparability of variable definitions, especially for program eligibility and separation, we use data provided by the Defense Manpower Data Center.

7 This is similar to a simulation by Daula and Moffitt (1995) that found separation rates increased 11-12% in response to VSI in both the dynamic retention model and the ACOL model.

8 The Air Force estimated the probability of layoff based on the percent of eligible personnel who would have to be involuntarily separated if there were no bonus takers. On this basis, the Air Force assigned an 80% layoff probability to tier 5, a 60% probability to tier 4, a 50% probability to tier 3, and a 40% probability to tier 2 (U.S. Department of the Air Force 1992).

9 It is noteworthy that the pay elasticities - 0.10 in Table 6 and 0.37 in Table 7 - fall within the range estimated by Goldberg (1982) for reenlistment decisions made by third-term personnel.

Appendix: ACOL Calculations.

ACOL calculations are as follows.

A. Military Pay Stream

Enlisted Master Files for 1992 for the Navy and the Air Force were obtained from the Defense Manpower Data Center and used to estimate the expected future military income stream. The grade distribution for each year of service was computed from these files, which provided the probability of being in a certain pay grade by year of service. This probability was combined with military pay tables for 1992 to obtain information on monthly basic pay and allowances. These data were combined to calculate the expected annual military income for each year of service. The present value of the military income stream was approximated by adding the discounted expected values of annual military pay until 20 years of service and of the military retirement benefits from retirement age until life expectancy. The military retiree's civilian age-earnings profile was calculated using data from the 1990 Census, Public Use Microdata Samples (PUMS). An age-earnings profile was estimated using data on military veterans to generate the individual's civilian pay and retirement after military retirement. The present value of the civilian income stream expected after military retirement was the sum of the discounted annual civilian pay from military retirement age until age 65 plus the discounted annual civilian retirement benefits from age 65 until life expectancy. The values of the military and postmilitary civilian income streams were used to approximate the individual's pecuniary value of staying in the military until 20 years of service. A discount rate of 10% was used for all calculations.

B. Civilian Pay Stream

To obtain the annual expected civilian earnings of military veterans with less than 20 years of service, a postservice log-earnings model was estimated using PUMS data. The model was then used to calculate the age-earnings profile for the civilian alternative. Discounting the individual's annual civilian income and adding these amounts from the current age until life expectancy provides the perceived present value of the civilian income plus retirement stream. Since most of the bonus takers chose the SSB lump sum payment, this option was added to the civilian pay stream to obtain the present value of the returns to be expected if the individual leaves the military immediately. A discount rate of 10% was used for all calculations.

C. The Cost of Leaving

The cost of leaving (COL) was calculated for each individual as the difference between the present value of staying until 20 years of service and that of leaving immediately. Conditioned on the number of years remaining until 20, the COL values were annualized using a 10% personal discount rate to obtain ACOL values.

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