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Discounting, cognition, and financial awareness: new evidence from a change in the military retirement system.

I. INTRODUCTION

This paper uses new field data derived from a change in the U.S. military retirement system to estimate the personal discount rate (PDR). Military personnel in their 15th year of service were offered the choice between staying with their current retirement plan, called REDUX (Provisions of 1986 Military Retirement Reform Act), and receiving an immediate $30,000 Career Status Bonus (CSB), and receiving an enhanced future retirement annuity, called High-3. The relative values of the two future retirement annuity streams varied as a function of expected years of military service, terminal rank, age, and length of life, information that permits us to estimate the PDR.

Because individuals have at least some ability to smooth consumption over time, the question arises whether the PDRs estimated from choices between cash flows are related to individuals' underlying degrees of patience. We have access to unusually detailed survey data that allow us to relate the estimated PDRs to a variety of financial behaviors that have been linked to impatience, including participation in the U.S. Government's tax-favored Thrift Savings Plan (TSP), saving habits, financial difficulties, and car loan and credit card interest rates. (1)

Financial illiteracy has been implicated in the suboptimality of financial decisions and low levels of accumulated wealth (Behrman et al. 2010; Lusardi and Tufano 2008). Although our survey data do not include information on financial literacy per se, they include information on the Armed Forces Qualification Test (AFQT) scores as well as whether individuals were aware of key features of the CSB/REDUX and High-3 retirement systems, thus permitting examination of whether better-informed individuals are more likely to exhibit patience, as well as the extent to which cognitive ability operates via knowledge of the provisions of the systems. To foreshadow our findings, there is no simple relationship between awareness of program features and PDRs. Rather, the results suggest that individuals tend to acquire information that is consistent with their behavioral preferences, be it patience or impatience.

Warner and Pleeter (2001) studied a similar choice between a current cash payment and future annuity among military personnel who agreed to separate from the military voluntarily during the drawdown period of the early 1990s. Both the current and earlier studies involve stakes that dwarf those that have been used in laboratory experiments with salient payoffs in the United States (Harrison and List 2004, 1042). As in the earlier study, the military went to great lengths to explain the CSB/REDUX program, thus "making the comparison of personal and threshold discount rate relatively transparent" (Harrison and List 2004, 1043). However, a number of factors complicated interpretation of the earlier study, the most important being that individuals who opted not to separate faced the prospect of involuntary termination prior to vesting with only a small separation payment. Moreover, the drawdown occurred during a recession in which the unemployment rate rose to more than 8%. The prospect of a spell of unemployment could have increased the demand for liquidity among separatees and caused patient individuals to appear to be impatient. (2) There were a number of additional factors that complicated the interpretation of the earlier findings. (3)

By contrast, the CSB/REDUX choice faced by military personnel in the 2000s does not involve an unanticipated, involuntary career change. Nor are moral hazard issues arising from questions of eligibility for means-tested assistance that might have arisen in the study by Butler and Teppa (2007) likely to affect our analysis. In addition, because all individuals in their 15th year must make a decision, selection issues that arise in many studies of the decision to annuitize--not all individuals are equally likely to contribute to annuities--pose less of a problem. In addition, the fact that the benefit stream is defined means that it is subject to little if any uncertainty, and hence reduces the potential role for risk preference to contaminate estimates of the PDR.

Of course, not everyone is equally likely to join the military in the first place, much less make it a career. In order to get an idea of how the individuals in our sample compare with the population as a whole, we analyzed data from a recent Financial Industry Regulatory Authority (FINRA 2009, 2010) survey given to civilians and military personnel. Career military personnel exhibit somewhat more "patient" behavior than otherwise comparable civilians. Although our data do not permit us to draw conclusions about the PDR for civilians, we are able to carry out a back-of-the-envelope exercise, calculating the PDRs for military personnel whose distribution of "patience" more closely resembles that of the population as a whole.

The remainder of the paper is organized as follows.

Section II describes the policy environment, paying particular attention to how well service members understood the $30,000 CSB/REDUX versus High-3 annuity choice. Section III describes the calculation of the breakeven discount rate. Section IV lays out our empirical framework. The current study, based on Warner and Pleeter (2001), implements a number of methodological and analytical improvements suggested by Harrison and List (2004) and Harrison (2005), including accounting for uncertainty in the estimated PDRs. Section V shows how the PDR is related to cognitive ability, education, and other personal characteristics, relationships that we use to construct individual-level measures of the PDR. Section VI presents confirmatory evidence by relating our estimated PDRs to a variety of other financial behaviors. Section VII examines the role of awareness of program features and how they relate to cognition and educational attainment. Section VIII concludes with a brief summary and suggestions for future research.

II. POLICY ENVIRONMENT

A. Background

Prior to 1986, military retirees with 20 or more years of service (YOS) received a monthly retirement annuity equal to 0.025 times YOS times the average monthly basic pay for the highest (typically final) 36 months of service. This system, known as "High-3," was fully adjusted annually for changes in the Consumer Price Index (CPI). A retiree with 20 YOS would therefore typically receive an annuity equal to 50% of basic pay.

In order to reduce retirement costs, the Military Reform Act of 1986 replaced the High-3 system with a less generous military pension system known as REDUX. The REDUX system applied to personnel who entered service on August 1, 1986, and featured:

* a 2nd-career annuity between separation and age 61 equal to 40% of basic pay plus 3.5% of basic pay for every year of service beyond 20;

* a one-time adjustment upward to a pension based on the High-3 formula at age 62; and

* an annual, incomplete inflation adjustment equal to CPI growth minus 1 percentage point.

REDUX reduced the second-career annuity from 50% to 40% of basic pay for 20-year retirees, and from 62.5% to 57.5% for 25-year retirees. A 30-year retiree would receive the same initial second-career annuity--75% of basic pay--under either system. However, because of its incomplete inflation adjustment, the real value of REDUX would decline by 1% per year between separation and age 61, and after the age 62 reset.

Figure 1 illustrates the real lifetime annuity streams under the two systems for three ranks of enlisted personnel: E-7 with YOS equal to 20, E-8 with YOS = 25, and E-9 with YOS = 30, assuming individuals entered service at age 20 and using the 2008 military basic pay table. For instance, the annual retirement benefit for an E 7 with 20 YOS is about $23,000 under High-3 and, nominally, about $18,400 under REDUX. Between the age of separation age and age 61, the real value of the pension under REDUX declines to about $15,000 in constant 2008 dollars. The REDUX annuity resets at age 62 to what it would have been under High-3, after which it again declines in real value at the rate of 1 % per year.

The National Defense Authorization Act of 2000 reversed the REDUX provision of the Military Reform Act of 1986. All personnel who entered the military after the year 2000 are enrolled in the High-3 retirement system. To address those already in the armed forces, the Act gave individuals who entered military service between 1986 and 2000 the option of either (1) returning to the High-3 pension system or (2) remaining in REDUX and receiving a $30,000 bonus, called the CSB, in their 15th year of service. Because the relative values of the two retirement systems vary across individuals with different ages, rank, and expected retirement dates, the interest rate at which the two choices have equal present value--called the breakeven discount rate--varies as well.

B. Data

Two datasets were provided and linked by Defense Manpower Center (DMDC): an Administrative dataset and a Survey dataset.

Administrative Data. DMDC identified all active duty personnel eligible to receive CSB as of December 31, 2007, that is, who had entered service on or after August 1, 1986 and had completed 15 years (180 months) of service since October 1,2000, along with the year they became eligible. DMDC also attached information on gender and race, as well as information as of 30 September of each year on age, rank, education, marital status, the number of dependents, military service, occupation, and, for enlisted personnel, AFQT. These personnel records were supplemented with data provided to DMDC by the Defense Financial Accounting Service (DFAS) on calendar-year total military pay, CSB receipt, and participation in the TSP. DMDC then matched these administrative records to the survey data. Each of the individuals in the resulting dataset, about 198,000 observations, was assigned an identification number.

Survey Data. From the Administrative dataset, DMDC created a stratified random sample of 46,566 active duty members who were administered a survey in October 2008 (Defense Manpower Data Center [DMDC] 2008, 2009). DMDC received 19,272 completed surveys, defined to be a survey with answers to more than 50% of the questions in the survey. After eliminating individuals who were not in fact eligible to receive CSB and individuals with other missing information, we had 13,461 usable survey observations: 12,025 enlistees and 1,436 officers. (4) Because DMDC purposely oversampled personnel who elected to receive the CSB at a rate of about 3 to 1, all of our analyses use the weight provided by DMDC. These survey data were then linked to the Administrative data using the assigned identification code.

The key data element provided by the Survey Data is the number of years the service member expects to serve over the course of their military career, needed to construct the breakeven discount rate. Therefore, we are only able to analyze individuals who are included in both surveys. The survey data also include a wealth of information on service members' financial situations, as well as their awareness of various features of the CSB/REDUX program.

C. Awareness of Program Features

The Department of Defense (DoD) publicized the major features of the two retirement systems extensively, thus making the differences between the two systems fairly clear. (5) Evidence on individuals' knowledge is available in the form of survey questions about four key provisions of the retirement systems. The responses, seen in Table 1, indicate that individuals were generally well informed about key features of the two retirement systems. More than 9 in 10 survey participants knew that retirement pay was equal to 40% of basic pay under REDUX and equal to 50% of basic pay under High-3. About three-quarters knew that staying to 30 years yielded the same initial retirement pay under both systems (75% of basic pay), and about as many knew that the REDUX annuity reset at age 62. The least understood feature of the program was the incomplete inflation adjustment under REDUX; even so, more than 65% of officers and nearly 70% of enlistees were aware of this feature. Nearly 6 in 10 survey participants reported being aware of all four features and only about 5% reported being aware of none.

III. THE BREAKEVEN DISCOUNT RATE

A. Construction

The breakeven discount rate [D.sup.*] is the interest rate that equates the present value of the $30,000 CSB and the difference in the value of the annuity under High-3 and REDUX discounted to the 15th year of military service. (6) The breakeven rate is a function of the dollar value of retirement pay, expected YOS at retirement, and lifespan. About 40% of individuals expected to serve 20 years, 32% between 22 and 24 years, and 13.5% for 25 years or more. DoD and other actuarial data were used to assign to each individual an expected lifespan as discussed in Appendix SI (Supporting Information). The information on rank was taken from the Administrative Data and the data on expected career length are taken from the Survey Data. Each participant was assigned a terminal rank based on current rank and current and expected terminal YOS. For the plurality, this amounted to assuming one more career promotion, but a substantial number were assigned to two more. We corrected for inflation by converting the CSB into 2008 dollars and assigning terminal salary using the 2008 pay table. The terminal salary determines the annuity amount and expected lifespan determines the duration of the annuity. The breakeven discount rate is adjusted for federal and state taxes on the CSB and retirement annuities as described in Appendix S2.

Figure 2 shows the effects of expected rank and career length on the breakeven discount rate for a White, male 35-year-old enlistee, absent taxes. Notice that choosing the up-front CSB does not by itself mean that an individual is impatient. In particular, [D.sup.*] is lower for those with longer (expected) military careers. For example, [D.sup.*] for an E-5 is 3% at 30 YOS and 9% at 20 YOS because the High-3/REDUX annuity differential is 0% at 30 YOS and 25% at 20 YOS. In addition, a shorter career translates into a larger number of years of incomplete (CPI - 1%) REDUX inflation adjustment before the age-62 reset. The breakeven discount rate is also higher for those with higher rank because the REDUX penalty is larger at higher levels of pay. For example, [D.sup.*] at 20 YOS is 14% for an E-9 compared with just 9% for an E-5. Similar relationships hold for officers, not shown to save space. [D.sup.*] is also positively related to lifespan because those with longer lives must endure the incomplete inflation adjustment of REDUX for more years. Finally, because the CSB is fixed in nominal terms at $30,000, inflation erodes the value of CSB relative to the High-3 pension, raising [D.sup.*].

B. Distribution of the Breakeven Rate

Table 2 shows the percentage of the 14,231 individuals in our data choosing each option. About 52% of enlisted personnel chose High-3, compared with 86% of officers. Naturally the question is whether differences in the breakeven rate can account for this difference. Indeed, the mean breakeven discount rate is just 7.5% for enlisted personnel, compared with 10.2% for officers. The fact that the breakeven rate is higher for officers than enlisted personnel implies that, other things the same, one would expect officers to be less likely to choose CSB/REDUX and more likely to choose High-3. In addition, officers are better educated on average, which could be correlated with patience. However, as will be seen shortly, differences in the breakeven discount rate and other observable factors only explain part of the difference in choices.

Histograms of the breakeven rate are graphed in the upper half of Figure 3. The breakeven rates have wide dispersion among enlistees as well as officers, the distribution for enlisted personnel being single-peaked, and for officers, bimodal.

IV. EMPIRICAL FRAMEWORK

A. Basic Approach

We estimate a generalized version of Warner and Pleeter's (2001) model. Like Harrison and List (2004), we calculate the PDR as the weighted sum of breakeven discount rates, where the weights are the change in probability of choosing the up-front cash CSB. This frees us from needing to identify the PDR purely off of normality, and allows us to choose a functional form that best fits the data. We assume that individuals choose the up-front cash CSB with probability given by:

(1) Prob (i chooses CSB/REDUX)

= [THETA]([X.sub.i][beta] + [[beta].sub.1]f ([D.sup.*.sub.i]))

where [THETA] is the normal cumulative distribution function and f ([D.sup.*.sub.i]) is a monotonically increasing function determined by model fit. (7) Because individuals who choose the CSB must have a PDR no lower than the breakeven rate, the expected PDR is equal to

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [DELTA][THETA]([D.sup.*]) is the change in the proportion of individuals estimated to choose CSB/REDUX when the breakeven rate is [D.sup.*], the operator [DELTA] refers to the change when [D.sup.*] declines by 0.001 (1/10 of 1%), and the upper limit, [D.sup.*.sub.MAX], is chosen so that [THETA] ([D.sup.*.sub.MAX]) [approximately equal to] 0, here 1.0, well beyond the breakeven rates observed in the data. The median PDR is equal to the value of [D.sup.*] at which the probability of taking the up-front cash is just equal to the probability of taking the delayed annuity, that is, where [THETA]([D.sup.*]) = 0.5. (8) Another advantage of this approach is that it is straightforward to impose a zero lower bound on the PDR.

Harrison and List (2004) criticized Warner and Pleeter (2001) on the grounds that "the distribution of estimated discount rates is much wider than the distribution of offered [that is, breakeven] rates" (italics in original), and that "for enlisted personnel, the distribution of estimated rates is almost entirely out-of-sample in comparison to the offered rates" (p. 1044). Histograms reveal that this is much less of a problem in our data. Harrison and List (2004) also argued that, taking uncertainty in the estimates into account, the results for enlisted personnel were too imprecise to be used to "draw reliable inferences about discount rates," (pp. 1045-46). In the current paper, we construct standard errors based on 1,000 bootstrap replications.

B. Functional Form

We experimented with three formulations of f ([D.sup.*.sub.i]): linear, [D.sup.*.sub.i]; quadratic, [D.sup.*2.sub.i], and logarithmic, 1n ([D.sup.*.sub.i]). In order to save space, we relegate the details to Appendix S3. The quadratic form fit best for enlistees and the log form fit best for officers, and so only these results are shown. The log specification overpredicts the probability of choosing CSB/REDUX at higher breakeven rates, especially for enlistees. The import of this fact is that estimates of the expected PDR using the log specification will tend to be biased upward; estimates of the median PDR are less affected.

V. COGNITIVE ABILITY AND OTHER DETERMINANTS OF CSB/REDUX CHOICE

There is little consensus how patience should vary as a function of observable personal characteristics. Warner and Pleeter (2001) found that their estimated PDRs varied as a function of race, income, and education. Borghans et al. (2008) suggest that the rate of time preference might also vary as a function of time-dependent variables, including children (p. 1029), and Nguyen (2011) suggests that time preference may be affected by the environment in which one is raised.

A. Cognitive Ability

Recently, Dohmen et al. (2010) and Burks et al. (2009) found evidence that individuals with higher levels of cognitive ability are more patient. Cognitive ability could work through a number of channels. For example, individuals with higher levels of cognitive ability may be able to perceive delayed options more precisely, thus making delayed options more attractive. As Borghans et al. (2008) put it, an individual with low cognitive ability may find that the costs of making calculations of present value exceed the expected benefit, which might cause the individual to "choose by default the immediate, certain reward" (p. 1001). Individuals with higher cognitive ability may also be better able to control their emotions and impulses and take a longer view of intertemporal problems--to "imagine the future"--(Borghans et al. 2008, 997, 1037; Burks et al. 2009, 7746). In addition, Burks et al. (2009) hypothesized that more patient individuals may be more sensitive to the potential social consequences of one's actions.

We have for enlisted personnel a single indicator of cognitive ability in the form of an aggregate AFQT score. (9) We estimate the CSB/REDUX probit as a function of the breakeven discount rate and AFQT, and report the results in column (1) of Table 3. Each 10 percentage point increase in the AFQT--about one-half of a standard deviation--is estimated to reduce the probability of choosing CSB by 2.6%, with a standard error of 0.4%.

B. Educational Attainment

Column (2) augments the CSB/REDUX probit equation for enlisted personnel with indicators for educational attainment. Relative to dropouts (the omitted group) high school graduates are estimated to be 6.5% less likely to choose CSB, with a relatively large standard error of 4.3%. (10) Associate degree holders are 12.6% (SE = 4.3%), and college graduates 15.6% (SE = 4.3%) less likely to choose CSB/REDUX. The estimated effect of AFQT falls slightly from -0.0026 to -0.0022 and the standard error is essentially unchanged. Our results are consistent with Becker and Mulligan (1997), who suggested that, "educated people should be more productive at reducing the remoteness of future pleasures" (p. 736). Alternatively, causality could run in the reverse direction, with more patient individuals being more likely to invest in projects that involve delayed benefits. Assessing the direction of causality would require instrumenting for education, not possible with the data available to us.

The estimated effects of educational attainment on CSB/REDUX choice for officers are seen in column (4). The small fraction of officers with less than a college degree are 11.7% (SE = 5.2%) more likely than BA holders to choose CSB/REDUX. The substantial fraction with an advanced degree are 5.2% (SE= 1.5%) less likely to choose CSB/REDUX.

C. Identifying the PDR

To estimate each individual's PDR, we augment the CSB/REDUX probit equation with a comprehensive set of control variables that are exogenous, or at least arguably predetermined. All models control for age, education, gender, race and ethnicity, marital status, number of dependents, the number of months spent in a combat zone in the last year, branch of service, decision year, and 2-digit DoD occupation. (11) Because the incentive to acquire information may be a function of patience, we have not included the awareness indicators (see Table 1), although to the extent that one is interested solely in characterizing the distribution of the PDR, there is no reason for not including them. We return to the issue of awareness in Section VII. (12)

Before turning to the PDR estimates, we first examine how the controls affect the estimated effects of AFQT and educational attainment. The results for enlisted personnel are reported in column (3) of Table 3. The estimated effect of AFQT is now about one-third that in columns (1) and (2) but remains statistically significant. Among enlistees, the estimated marginal effect of having a high school degree is reduced by two-thirds (only 6% have less than a high school degree); the marginal effects of higher educational attainment are only slightly smaller and less precise. Among officers, the marginal effects of education are slightly larger in magnitude.

The estimated marginal effects of the control variables are presented in Table 4. Borghans et al. (2008) suggest that the rate of time preference might vary predictably as a function of age or family circumstance. We find that older individuals are more patient, a finding that is consistent with models of learning in which individuals behave in a financially more sophisticated, less impulsive manner as they acquire knowledge about themselves (Agarwal et al. 2009; Ali 2011). Months spent in a combat zone are associated with a higher probability of choosing CSB/REDUX for enlistees, but the estimated effect is only 1.4 times its standard error. The estimated effect of combat zone months is negative for officers, but its standard error is larger than the point estimate. Black enlistees are estimated to be 14% (SE = 2%) more likely to choose CSB/REDUX, and Black officers 8.9% (SE = 3.4%) more likely. Each additional child (dependent) is estimated to increase the probability of choosing CSB/REDUX by 4.8% (SE = 0.6%) among enlistees and by 1.5% (SE = 0.5%) among officers.

D. PDR Estimates

Estimates of the expected and median PDRs, along with bootstrapped standard errors, are contained in Table 5. Flarrison and List (2004) and Harrison (2005) traced the imprecision of Warner and Pleeter's (2001) PDR estimates for enlistees to the fact that much of the fitted PDR distribution fell well to the right of the support of the breakeven distribution. The histograms in the second row of Figure 3 reveal that this is not a problem in our data.

We estimate a mean expected PDR for enlisted personnel of about 7.2% (SE = 0.15%), and a considerably lower expected PDR for officers of 4.3% (SE = 0.24%). Similarly, the estimated median PDR for enlistees is 6.7% (SE = 0.2%), compared with just 1.9% (SE = 0.35%) for officers. The lower estimated PDRs for officers indicates that the 35.1% difference in CSB/REDUX take-up (see Table 2) cannot be traced to differences in the distribution of the breakeven discount rate. (13)

The low-estimated median PDR for officers is not implausible. For example, Barsky et al. (1997) asked respondents in the Health and Retirement Study to choose the preferred path amongst different consumption profile charts with constant present value at various interest rates. They found that at a zero interest rate, the modal preference was for a flat consumption path, but an upward slope was chosen more often than a downward slope (p. 564). In their review of the discounting literature, Frederick et al. (2002) noted that studies tend to find that people often prefer improving consumption sequences to declining sequences (p. 363).

It is noteworthy that our estimated PDRs are in line with those estimated using very different field data using a framework of compensating differences for fatality risk (Viscusi and Moore 1989; Scharff and Viscusi 2011). For example. Scharff and Viscusi (2011) estimated implicit rates of discount ranging from 6.4% to 10.8% (Table 7, p. 971).

E. PDR Estimates by Demographic Category

Table 5 contains PDR estimates for a number of demographic groups of interest. (14)

We estimate an expected PDR of 6.8% for enlistees in the upper half of the cognitive distribution (AFQT>50) and of 8.0% for those in the lower half. With independent samples and standard errors of just 0.2% and 0.1%, the null hypothesis that the 1.2 percentage point difference is equal to zero is rejected at the better than the 1% level. Dohmen et al. (2010) estimated that each standard deviation increase in their measure of cognitive ability was associated with a 14.6% decrease in the individual's discount rate (p. 1250). To compare our estimated effects with theirs, note that the mean AFQT among those in the upper half of the distribution was 71, and in the lower half about 39, for a difference of 32 points, or 1.7 standard deviations. The difference in estimated expected PDRs is 8.0%-6.8% = 1.2%, or about 17% of the mean. Thus, our estimates imply that each standard deviation increase in AFQT is associated with a 9.8% decrease in the expected PDR. A similar computation implies a 17.6% decrease in the median PDR. Considering the differences in populations studied, the differences in the choice experiments, and the differences in the measures of cognitive ability used, the estimates are remarkably close.

The mean expected PDR for Black enlistees is estimated to be equal to 9.2%, compared with just 6.5% for Whites; the estimates for officers are 8.6% and 3.9%, respectively, differences that are statistically as well as economically significant. The expected PDR is estimated to be higher for individuals with more children (dependents). More educated personnel are estimated to have lower PDRs. The expected PDR for enlistees who had deployed to a combat zone during their CSB/REDUX was higher than those who had not: 7.8% versus 6.9%, a difference that is statistically significant. However, the expected and median PDR for officers who had served in a combat zone is estimated to be slightly and statistically insignificantly lower than for those who had not: 4.4% versus 4.2%. (15)

F. Comparison with Warner and Pleeter (2001)

Using the log-linear model, Warner and Pleeter (2001) estimated enlistees' expected PDR to equal 38.9% and their median PDR to equal 30%. (16) Using their formulas on our sample of enlistees, we estimate a higher expected PDR of 47.7% but a much lower median PDR of just 8.9%. This apparent incongruity is a result of the fact that our estimated coefficient on the breakeven rate is smaller in magnitude (see Appendix S3). (17) The median PDR is much less sensitive to this key parameter than is the mean. The linear model is also more robust to this parameter, and using this model, we estimate enlistees' PDR at 7.1%, compared with the 29.4% estimated by Warner and Pleeter (2001). We also estimate significantly lower PDRs for officers than did Warner and Pleeter (2001): 5.6% versus 9.9% (expected PDR) and 1.9% versus 5.6% (median PDR) using the log model, and negative 7% versus 0% using the linear model.

Taken as a whole, the results indicate that the individuals in the current study are measurably far more patient than in the earlier study. The most likely explanation for the differences is that the current study is less affected by potential confounds, and, in particular, the fact that individuals in the earlier study were faced with an unexpected change in career during a recession. (18) By contrast, the individuals in the current paper are all virtually guaranteed pension vesting within 5 years. The relative lack of confounds described in the Introduction (note 3) provides a better environment in which to estimate the PDR.

VI. CONFIRMATORY EVIDENCE

We estimated the PDR based solely on the choice between cash flows received at different points in time. Because individuals have at least some ability to smooth consumption over time, the question arises whether our PDRs are related to individuals' true underlying degrees of patience. We therefore relate the estimated expected PDRs to a variety of other financial behaviors and outcomes. Each outcome for a given individual is regressed on that individual's estimated median PDR. Year dummies are included to control for, among other things, the possibility that financial problems might be more likely to emerge as time passes.

Validation of the estimated PDRs in this fashion is less convincing to the extent that other financial outcomes coincide closely in time with the CSB/REDUX decision, in which case all such decisions may reflect short-term shocks. For example, an individual with high credit card balances may save little, exhibit financial difficulties, and choose CSB/REDUX because he or she "needs the money." We therefore tried allowing the strength of the relationship to vary with distance in time elapsed from the CSB/REDUX decision via an interaction of the PDR with time. Because the estimated interaction terms were virtually always statistically insignificant, we only present the statistically more efficient results that exclude them.

Thrift Saving Participation. Since FY 2002, military personnel have had the opportunity to save on a pretax basis in the federal government's TSP. The data on Thrift Savings contributions are collected administratively and so are unusually accurate and not subject to subjects' estimation and recall errors. We define our TSP saving variable as the average rate of saving over the period 2002-2008, equal to the sum of real TSP (CPI base year 2008) contributions divided by the sum of real total cash pay over the period, which should measure individuals' longer-term propensities to save.

Columns (1) and (2) of Table 6 contain zero-inflated negative binomial (ZINB) estimates of the average TSP saving rate in basis points on the PDR. (19) The positive estimated coefficients in column (1) indicate that individuals with higher PDRs are less likely to save through TSP (more likely to have zero TSP saving), while the negative estimated coefficients in column (2) indicate that, conditional on participating in TSP, individuals with higher PDRs have lower rates of TSP saving.

To reduce further the chance that the negative relationship between TSP saving and the PDR is merely picking up the effects of a transitory financial shock, we reestimated the TSP saving-PDR relationship, restricting the sample to individuals who reported zero financial problems (see part C of Table 7) and described their financial condition as either "very comfortable and secure" or "able to make ends meet without much difficulty" (part B of Table 7). The estimated relationships between the PDR and TSP for this selected sample, relegated to Appendix S5 to save space, are substantively similar.

Overall Saving Habits. The DMDC survey included a question about individuals' overall saving habits, responses to which are displayed in part A of Table 7. Nearly 53% of enlistees and 81% of officers reported saving regularly each month. Only 2% of enlistees and 0.4% of officers reported spending more than their income. Just 10.8% of enlistees and 4.3% of officers reported spending all of their income. Ordered probit estimates of saving habits as a function of the PDR, seen in column (3) of Table 6, indicate that higher estimated PDRs are associated with lower overall tendencies to save, thus reinforcing the findings for TSP saving in columns (l)-(2). This finding is important because it suggests that the negative estimated relationship estimated between TSP saving and the PDR is not offset by other forms of saving.

Financial Instability. The DMDC questionnaire asked individuals about their overall financial stability, responses to which are contained in part B of Table 7. About 20% of enlistees and 38% of officers reported being very comfortable, and another 51 % of enlistees and 48% of officers reported being able to make ends meet without much difficulty. Just 22% of enlistees and 11% of officers reported having occasional difficulties, with the remaining 7.5% of enlistees and 2% of officers reported being over their head or having trouble making ends meet. The ordered probit estimates in column (4) of Table 6 show that individuals with higher estimated PDRs tend to report higher levels of financial instability, although the estimate for officers is statistically imprecise.

DMDC also asked individuals whether they experienced a variety of financial difficulties, seen in part C of Table 7. Only 4.5% of enlistees and 1.2% of officers reported having bounced two or more checks twice in the past year, but 16% of enlistees and 6% of officers reported having paid overdraft fees two or more times. About 3.5% of enlistees reported having had telephone, cable, or internet shut off, and 3.3% reported having missed a car payment, compared with less than 1% of officers. About 24.4% of enlistees reported having at least one financial problem, and 8.1 % of officers. Column (5) of Table 6 shows that individuals with higher PDRs tend to report more financial problems.

Finally, the regressions in columns (6) and (7) show that individuals with higher estimated PDRs tend to report higher credit card and car loan interest rates. However, the estimated effect for officers' credit card interest rates is not statistically significant at conventional levels.

Taken as a whole, the results suggest that our estimated PDRs are correlated with other financial behaviors that reflect longer-term time preference. (20)

A. Comparisons between Military Personnel and Civilians

Unfortunately, we are not aware of any studies that would permit us to externally validate our PDR estimates with estimates for the U.S. population as a whole, nor do we have any way of calculating the PDR for civilians with our data. However, recent survey data from the National Financial Capability Survey (NFCS) carried out by FINRA (2009, 2010) make it possible to compare the saving habits and financial stability of military personnel and civilians. (21) Details of our analysis, including a discussion of recent work on payday lending, are relegated to Appendix S5. Here, we note merely that military personnel in their 30s and early 40s are more inclined to save and less inclined to spend more than their income than are civilians, and military personnel are less likely to have difficulty paying their bills.

Our analysis cannot be used to estimate PDRs for civilians. We can, however, obtain a rough estimate of the PDR for military personnel that exhibit saving habits and financial stability characteristics similar to those of the overall population, which the confirmatory analysis suggests should be higher. (22) We twice reestimated the CSB/REDUX choice model, once augmented to include dummy variables for saving habits and once augmented to include dummy variables for financial stability, the categories defined so as to correspond to those in the NFCS. (23) We then calculate averages of the PDR using the civilian distributions as weights.

The effect of reweighting for enlistees is modest. The mean PDR for enlistees weighted by civilian saving habits is 8.1%, and weighted by civilian financial stability, 7.8%, compared with 7.2% in the CSB/REDUX sample. The effect of reweighting for officers is considerable. The mean PDR for officers weighted by civilian saving habits is 8.0%, reflecting that although only 0.4% officers in the CSB/REDUX sample spend more than they save, 18.4% of those in the civilian NFCS sample do so. The mean PDR for officers weighted by civilian financial stability is also modestly higher at 5.5%.

VII. PDR AND AWARENESS OF PROGRAM FEATURES

Financial illiteracy has been implicated in the suboptimality of financial decisions and low levels of accumulated wealth (Behrman et al. 2010; Lusardi and Tufano 2008). Unfortunately, our survey data contain no questions about financial literacy. We do, however, have unusually detailed information about individuals' awareness of four key retirement program features (see Table 2). Borghans et al. (2008) suggested that cognitively more able individuals are able to make more precise present value assessments and thus value "patient" choices more highly. In this case, one might hypothesize that higher AFQT scores and educational attainment should be associated with greater levels of awareness. One might further hypothesize that if awareness variables are included in the CSB/REDUX probit--they were excluded on the grounds that they are likely endogenous--that greater awareness would translate into lower PDRs and attenuated estimated effects of education and AFQT.

First, we examine whether higher levels of cognitive ability as measured by AFQT and education are associated with greater levels of program awareness. We estimate ordinary least squares (OLS) models in which the dependent variable equals the sum of the awareness dummies (zero to four). On average, individuals were aware of three of four program features with a standard deviation of about 1.2. The results appear in Table 8. Among enlisted personnel, cognitively more able individuals exhibited statistically significantly greater program awareness, but the estimated effects are tiny: each 10-point increase in AFQT is associated with knowledge of just 0.06 more features. Men were aware of 0.22 (SE = 0.06) more features than women, and married individuals were aware of 0.16 (SE = 0.08) more features than unmarried. Black enlistees (-0.29, SE = 0.05) and officers (-0.40, SE = 0.18) were significantly less well informed than Whites; Hispanics were also less well informed than non-Hispanics, significantly so among enlistees (-0.25, SE = 0.08), insignificantly so among officers (-0.18, SE = 0.26).

Although better-educated enlistees were more aware than those less educated, better-educated officers were estimated to be less aware than those less educated. The small fraction of officers with less than a college degree were aware of an imprecisely estimated 0.2 more features than those with a four-year college degree, and those with an advanced degree were aware of 0.2 (SE = 0.10) fewer features, the latter effect statistically significant at the 4.5% level. That better-educated officers were less aware of program features suggests that the effects of education do not operate purely via better understanding of the program. (24)

The notion that greater awareness does not always translate into greater patience is reinforced when the CSB/REDUX probit equation is augmented to include the four awareness indicators. The estimated marginal effects of interest--the other effects are suppressed to reduce clutter--appear in Table 9. For both enlistees and officers, awareness of three of the four program features is associated with a higher likelihood of choosing the CSB/REDUX, and thus implies higher estimated PDRs. The one exception is incomplete inflation indexation of REDUX, which estimated effect is negative and statistically significant. The estimated effect of AFQT for enlisted personnel is largely unaffected by inclusion of the awareness indicators, and the estimated effects of education are largely intact. (25)

Our results suggest that individuals acquire information in a selective fashion. (26) Such biases have been detected in experimental (Jones and Sugden 2001) and field (Park et al. 2010) settings. According to the selective information story, the provisions for the age-62 reset and equality of retirement pay at 30 YOS make the impatient choice appear more attractive and hence should have been of more interest to impatient individuals; the incomplete indexing provision, which makes the patient choice appear more attractive, should have been of more interest to patient individuals. Selective acquisition of information could also explain why better-educated officers were generally less aware of program features, despite being more likely to opt for the patient choice (i.e., High-3). Individuals who acquire advanced degrees may have such a strong preference for deferred consumption that they may not have found it worth expending the effort to learn about the relative merits of the impatient choice.

VIII. CONCLUSION

We estimated the PDR using new field data on the choice of military personnel between accepting an immediate cash payment equal to $30,000 and remaining in the less generous REDUX retirement system and changing to the more generous High-3 annuity. Despite the similarity of the current choice to the one examined by Warner and Pleeter (2001), our PDR estimates are on the order of a quarter to a half those estimated in the earlier study. Part of the difference can be traced to methodology, but the bulk of the difference can likely be traced to the fact that the current environment is relatively free of confounds. In contrast to Warner and Pleeter (2001), who studied individuals who were separating from the U.S. military involuntarily during a recession, and who had not become vested in a pension, the individuals we study are virtually guaranteed at least five more years in the military and full vesting in a pension.

Although we were not able to observe consumption flows, we found that our estimated PDRs were correlated with a range other financial behaviors. Individuals with higher PDRs tended to save less, were more likely to experience financial difficulties, and faced higher average credit card and car loan interest rates. Hopefully, future work will allow researchers to examine behaviors that are temporally more distant than we were able to examine in this paper.

This paper confirms that cognitively more able individuals are measurably more patient. However, the channel through which cognitive ability operates appears to be subtle. Although cognitively more able individuals were better informed about their retirement choices, such knowledge was not always associated with being more patient. Rather, individuals seem to acquire information selectively, with impatient individuals tending to pick up on facts that make the impatient choice look more attractive, and patient individuals on facts that make the patient choice look more attractive. More work is needed to examine the link between cognition, financial literacy, and investment choices. Hopefully, too, subsequent surveys will contain questions to elicit information about financial literacy.

We also wish that we had information--available in principle, but not to us--on ASVAB component scores in addition to the overall AFQT. Also, as noted by Andersen et al. (2010), researchers should regard field and laboratory evidence as complementary. Future surveys could include questions designed to elicit time preference parameters. One would also like to relate our estimated PDRs to nonfinancial behaviors associated with impatience, impulsivity such as tobacco use or obesity, or lack of self control (Ameriks et al. 2007).

Unusually, our survey data included information on whether individuals felt that, in retrospect, they had made the correct decision. Space limitations led us to place this analysis in Appendix S4. We found that individuals who were more cognitively able, more aware of the provisions of the retirement systems, and with fewer financial difficulties were less likely to report having made a mistake--regardless of whether they chose CSB/REDUX or High3. (27) Individuals who chose CSB/REDUX were, at a 40% rate, overrepresented among those who believed that they had made the wrong choice. More work is necessary to understand the relatively high rate of dissatisfaction among CSB/REDUX takers, especially those with financial difficulties. Perhaps individuals envisioned using the cash for one purpose--for example, to pay off loans--but failed to follow through. Adding survey questions that follow up on the reason for individuals' dissatisfaction could help resolve this. Finally, researchers have begun to identify the psychological factors that may lie at the root of higher-level factors such as the discount rate (Borghans et al. 2008). Adding questions about individuals' psychological outlook on life could prove fruitful in understanding the patterns we found in our data.

ABBREVIATIONS

AFQT: Armed Forces Qualification Test

CPI: Consumer Price Index

CSB: Career Status Bonus

DFAS: Defense Financial Accounting Service

DMDC: Defense Manpower Center

DoD: Department of Defense

FINRA: Financial Industry Regulatory Authority

NFCS: National Financial Capability Survey

OLS: Ordinary Least Squares

PDR: Personal Discount Rate

REDUX: Provisions of 1986 Military Retirement Reform Act

TSP: Thrift Savings Plan

YOS: Years of Service

ZINB: Zero-Inflated Negative Binomial

doi: 10.1111/ecin.12146

Online Early publication September 2, 2014

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Appendix S1. Expected Lifespan

Appendix S2. Calculation of the Breakeven Discount Rate

Appendix S3. Methodology

Appendix S4. Financial Mistakes

Appendix S5. Supplemental Analyses

(1.) Researchers now commonly provide evidence of internal reliability (Borghans et al. 2008, 1037). For example, Tanaka et al. (2010) linked experimental and household survey data from Viet Nam. Chabris et al. (2008) examined whether individuals with higher laboratory-measured discount rates were more prone to engage in 15 field behaviors that reflect impulsivity and impatience. Meier and Sprenger (2007) examined the link between credit constraints and survey-derived measures of discount rates and present bias. Hastings and Mitchell (2011) examined whether survey-derived measures of impatience or present bias help explain suboptimal financial decisions using data on Chilean participants.

(2.) Card et al. (2007) studied the Austrian unemployment insurance system, which provided a lump-sum payment at the start of an unemployment spell that was independent of the spell's duration. They estimated that the lump-sum benefit positively affected the duration of unemployment and consumption during unemployment, neither of which would occur in the absence of a liquidity constraint.

(3.) First, annuity recipients were required to affiliate with a reserve component for the life of the payment whereas bonus recipients required only a 3-year commitment to the Ready Reserve. Second, bonus recipients were given extended commissary and exchange privileges, extended medical coverage for up to 120 days, shipment of household goods, and possibly extended housing benefits while annuity recipients were not. Third, bonus recipients who found jobs in civil service were permitted to include military time toward federal civil service retirement; annuity recipients were not.

(4.) We have relegated analysis of 770 warrant officers, estimates for which are statistically unreliable, to Appendix S3. Estimates of the expected personal discount rate for this group ranged from 6.4%, with a standard error of 1.2% to 30.4% with a standard error of 4 x 1023.

(5.) For example, a web page of the Office of the Secretary of Defense included a table showing annuity multipliers under REDUX and High-3 year-by-year from 20 to 30 years of service, (http://militarypay.defense.gov/retirement/ad/06_rc_thechoice.html, last accessed on March 22, 2011, Google date of February 1, 2001). The official website of the U.S. Navy ran a story entitled, "Do a Reality Check Before Taking Career Status Bonus/REDUX," complete with links to an April 2001 study by the Center for Naval Analyses (Quester et al. 2004) and a DoD-sponsored retirement pay calculator (http://www.navy.mil/search/display.asp?story_id= 1614, last accessed on March 22, 2011, Google date of July 8. 2002). A similar story ran in the Air Force publication, Airman, in July 2003 (Roberts 2003). We were also able to locate a Powerpoint presentation (Army Retirement Services 2001) that included a discussion of how the money from the CSB might be used, including being designated for individuals' Thrift Savings Plan accounts and how it might be allocated among various asset classes, but we do not know how widely the presentation was disseminated.

(6.) Quester and Shuford (2005) attempted to estimate the PDR for Navy enlisted personnel, but lacked information on career length. Brown and Moskowitz (2007) estimated the PDR for a subset of individuals (E-5s in their 15th year) whose career length was surmised by virtue of having exhausted their promotion opportunities and thereby facing mandatory separation at 20 years of service.

(7.) Logit-based estimates of the PDR are highly correlated (0.999 for enlistees and 0.996 for officers) and within 0.01-0.02 percentage points of the probit estimates. We prefer probit on empirical grounds: the logit model predicts a counterfactually slightly higher probability of choosing CSB/REDUX than the probit model at higher breakeven rates.

(8.) The median PDR is defined for each individual in the sample; it is not merely the median across individuals. A mass of individuals with median PDR equal to 0 can arise if [lim.sub.D*[right arrow]0][THETA]([D.sup.*]) < 0.5. In our sample, with our preferred specification, 13% of enlisted personnel were massed at the smallest discount rate (0.001), but only 0.3% of officers. The lowest estimated probability of choosing CSB/REDUX at 0.1% was 21% for enlistees and 36% for officers.

(9.) There are a number of limitations of AFQT as a measure of cognitive ability. First, it may reflect both accumulated experience as well as innate ability. Second, Borghans et al. (2008) argue that such achievement tests measure crystallized intelligence, that is knowledge and developed skills, as opposed to fluid intelligence, which is the "ability to solve novel problems" (p. 979, italics in original). Although, like Dohmen et al. (2010), we cannot establish an unambiguous causal connection between AFQT and impatience, AFQT is unlikely to be related to time-varying influences such as shocks to preferences and opportunity sets, and more likely to be related to factors of fixed quality.

(10.) Hurd and Panis (2006) found a negative, but statistically insignificant relationship between education and the propensity to cash out pensions.

(11.) Nguyen (2011) proposed that occupational environment could affect risk or time preference. He found that Vietnamese fishermen, who "constantly make risky decisions" (261), were "likely to build up a high level of reference for risk and patience which makes the agents more willing to make risky and patient choices" (p. 247). Occupation will also capture differences in cognitive and noncognitive ability.

(12.) Tanaka et al. (2010) found that Vietnamese households with higher incomes were more patient (pp. 567-68). However, we see no compelling reason to include income or rank in our model. Moreover, those variables determine the future annuity stream and hence the breakeven rate, raising issues of interpretation were they to be included.

(13.) To make the point another way, we predicted the probability that officers choose CSB/REDUX using the estimates for enlistees (not shown to save space). Accounting solely for the breakeven rate, between 62% and 84% of the difference in CSB/REDUX take-up is unexplained. Accounting for all covariates except AFQT, which is not available for officers, the unexplained difference ranges from 36% to 50%.

(14.) The estimates are not partial effects, but reflect averages for the group in question.

(15.) In a different setting, Anderson and Stafford (2009) found subjects to be less patient in the presence of risk. Nguyen (2011) posited that the occupational environment affects risk and time preference. Perhaps the environmental effect is at work for both enlistees and officers, but is outweighed by survival probability concerns for enlistees, who are at far more risk in a combat zone than are officers.

(16.) Median PDRs are calculated for Warner and Pleeter's (2001) log-linear estimates by dividing the expected values in their Table 6 by exp (0.5[??]2), where [??] = 0.8496 for officers (their Table 4) or 0.663 for enlistees (their Table 5).

(17.) In the log-linear formulation, the expected PDR equals the median estimated PDR, exp [[X.sub.i][??]). multiplied by exp (0.5[??]2), and [??] equals minus the inverse estimated coefficient on the log breakeven rate.

(18.) The retirement policy that we study changed in a recession year, 2001, but our data start in 2002. The annual dummies included all models, not reported to reduce clutter, help control for any recession effects. In practice, the estimated coefficients on the year dummy variables are imprecise and display no pattern.

(19.) In the ZINB model, TSP saving, [S.sub.i], is governed by E([S.sub.i]) = (1 - Pr([S.sub.i] = 0))[[lambda].sub.i] where [[lambda].sub.i] = exp([[theta].sub.0] + [[theta].sub.1], [1nPDR.sub.i]) equals expected saving conditional on [S.sub.i] > 0, and the probability that [S.sub.i] = 0--more than 50% in our data--is given by the probit model Pr([S.sub.i] = 0) = [THETA] ([[theta].sub.0] + [1nPDR.sub.i]).

(20.) Harrison, Lau, and Williams (2002) found no evidence that individual long-run discount rates were correlated with borrowing. However, Meier and Sprenger (2010) found that present bias was associated with higher debt levels (p. 17), a higher incidence of credit market delinquencies and defaulted balances (2007, 19-20), and lower Fair Isaac Corporation (FICO) scores (p. 21).

(21.) We are grateful to Gary Mottola of FINRA for making available confidential versions of the data, which contain detail and information not available in the public use files.

Dohmen et al. (2010) noted that confusion alone should not be systematically related to impatience. However, they found that individuals who thought about interest rates at the time that they made their decisions exhibited more patience, and that cognitive ability retained explanatory power even after controlling for whether individuals had done so (p. 1255).

(22.) The military samples are restricted to active duty Army. Navy, Air Force, and Marine Corps. The civilian samples are limited to households in which at least one member is employed. Separate comparisons are made for enlistees and officers. Officers are compared to samples of civilians in which the respondent holds at least a college degree. About 14% of enlistees and 11.2% of officers spend more than their income in the NFCS survey, compared with 21% and 18% of civilians, respectively. About 52% of enlistees and 72% of officers are savers, compared with 43% and 50% of civilians. Only 7% of enlistees and 0% of officers found it very difficult to pay their bills, compared with 16.7% and 11 % of civilians.

(23.) The expected PDR for enlistees who spend more than their income is estimated at 11.1%, for those who save nothing, 8.9%, and for those who spend less than their income, 5.9%. The estimates for officers are 19.1%, 8.8%, and 3.5%. The expected PDRs for enlistees who find it very difficult, somewhat difficult, and not at all difficult to pay their bills are 8.7%, 8.5%, and 6.6%, and for officers 7.9%, 6.9%, and 3.9%.

(24.) Alternatively, earning an advanced degree may be a noisy indicator of general (as opposed to occupation-specific) human capital.

(25.) We hasten to point out that our evidence is silent regarding the relationship between financial literacy and knowledge of specific program features, much less between financial literacy and patience.

(26.) Another interpretation is that individuals are more aware of factors that are more relevant to them (Benjamin and Dougan 1997; Benjamin, Dougan, and Bushena 2001). Borghans et al. (2008) and Becker and Mulligan (1997) proposed that the incentive to collect information about the future is greater for more patient individuals (p. 746).

(27.) Recently, also using data on military personnel, Agarwal and Mazumder (2013) found higher-AFQT individuals were less likely to make two types of financial mistakes.

CURTIS J. SIMON, JOHN T. WARNER and SAUL PLEETER *

* Support for the collection of the data analyzed in this study was provided by the Office of the Undersecretary of Defense for Personnel and Readiness. We are grateful to the many individuals in the Defense Manpower Data Center and elsewhere who participated in the data collection and assembly. They include Peter Cerussi, Mark Gorsak, Brian Lippan, Fred Licari, Robert Tinney, Matt Torres, and Deborah West. Jon Pennington of SRA Corporation oversaw the fielding of the CSB survey to over 40,000 military personnel. We are also indebted to Gary Mottola of FINRA, who generously provided us with confidential versions of the National Financial Capability Study. We thank seminar participants at RAND and the 2010 meetings of the Western Economic Association for their comments, particularly our discussant, Mike Strobl. We benefited from the insights of Scott Baier, Bill Dougan, Jim and Susan Hosek, Ed Keating, Paco Martorell, Raymond Sauer, Robert Tamura. Chuck Thomas, Kevin Tsui, Patrick Warren, and Dan Wood. Finally, we are grateful to two referees and the Editors for their careful reading and helpful suggestions. The authors are, of course, solely responsible for all errors and omissions.

Simon: Department of Economics, Clemson University, 228 Sirrine Hall, Clemson, SC 29634-1309. Phone 864-6563966, Fax 864-656-4192, E-mail cjsmn@clemson.edu

Warner: The Lewin Group, Falls Church, VA 22042. Phone 864-506-5800, Fax 703-269-5501, E-mail john.warner@ lewin.com

Pleeter: Department of Economics, American University, Washington DC. Phone 301-493-6481, Fax 202-8853790, E-mail pieeters@gmail.com

TABLE 1
Awareness of CSB/REDUX and High-3 Retirement Systems (a)

                                                Percent Aware

                                        Enlisted   Officers

Staying 20 years in the military         92.6%      94.6%
  provides 40% of my basic pay in
  retired pay under REDUX, as
  compared to 50% under High-3
  Staying 30 years under REDUX           74.1%      76.3%
  provides the same retired pay
  as High-3
Under REDUX, retired pay is              69.5%      66.4%
  increased annually, but less than
  the increased cost of living.
  Under High-3, retirement pay is
  increased annually by the full
  increase in the cost of living.
Under REDUX, retirement pay is           73.6%      78.2%
  reset at age 62 to the same amount
  as under High-3
Aware of all of the above                57.6%      59.0%
Aware of none of the above                5.5%       4.6%
Observations                             11,826     1,411

Figures weighted by survey final weight.

TABLE 2
Summary Statistics (a)

                         Enlisted   Officers

CSB/REDUX                 0.485      0.134
High-3                    0.515      0.866
Breakeven rate            0.075      0.102
Demographics             (0.024)    (0.039)
Male                      0.881      0.890
Married                   0.840      0.900
Divorced                  0.080      0.033
Hispanic                  0.079      0.062
Black                     0.234      0.082
High school degree        0.619      0.001
Associate degree          0.229      0.015
Bachelor degree           0.107      0.364
Advanced degree           0.014      0.584
Months in combat zone     1.463      1.440
                         (2.836)    (2.709)
Age                       35.019     37.202
                         (2.754)     (3.29)
AFQT                      61.845       --
                         (18.761)
Dependents                2.805      2.843
                         (1.503)    (1.415)
Observations              12,025     1,436

(a) Weighted by survey final weight.
Standard deviations are in parentheses.

TABLE 3
CSB Probit Estimates: Estimated Marginal Effects of
Cognitive Ability and Educational Attainment

                     Enlisted (Quadratic)        Officers (Log)

               (1)         (2)        (3)         (4)        (5)
               AFQT     Education     All      Education     All

Breakeven    -29.0774   -30.0444    -27.8566    -0.1445    -0.1083
  rate       (1.9334)   (2.3078)    (2.555)    (0.01792)   (0.0171)
AFQT         -0.0026     -0.0022    -0.00086      --          --
             (0.0004)   (0.0004)    (0.0004)
HS degree                -0.0651    -0.0247       --          --
                        (0.0430)    (0.0445)
Associate                -0.1261    -0.1020       --          --
  degree                (0.0430)    (0.0457)    0.1174      0.1233
Less than
  college                                      (0.0516)    (0.0554)
College                  -0.1562    -0.1380
  degree
Advanced                (0.0433)    (0.0460)    -0.0523    -0.0588
  degree                                       (0.0149)    (0.0158)

Notes: Each column represents a separate probit regression
for the probability of choosing CSB/REDUX as a function of
the breakeven rate and other variables. The specification in
column (1) contains only AFQT, a constant, and year dummies.
The specifications in columns (2) and (4) add indicators for
education. The specifications in columns (3) and (5) contain
a full set of controls, the same as reported in Table 4.

TABLE 4
CSB Probit Estimated Marginal Effects, Full
Model

                       Enlisted
                     (Quadratic)    Officers (Log)

Breakeven rate         -27.8566        -0.1083
                       (2.5551)        (0.0171)
Combat zone mos.        0.0039         -0.0021
                       (0.0028)        (0.0023)
Age                    -0.0054         -0.0158
                       (0.0028)        (0.0025)
AFQT                   -0.0009            --
                       (0.0004)
HS degree              -0.0249            --
                       (0.0249)
Associate degree       -0.1024            --
                       (0.0457)
Less than college         --            0.1233
                                       (0.0554)
College degree         -0.1380            --
                       (0.0460)
Advanced degree           --           -0.0588
                                       (0.0158)
Male                    0.0359         -0.0098
                       (0.0227)        (0.0252)
Married                 0.0153         -0.0239
                       (0.0288)        (0.0388)
Divorced                0.0447          0.0411
                       (0.0359)        (0.0589)
Dependents              0.0475          0.0147
                       (0.0055)        (0.005)
Hispanic               -0.0170         -0.0260
                       (0.0292)        (0.0239)
Black                   0.1383          0.0890
                       (0.0196)        (0.0343)
Asian                  -0.0062          0.0209
                       (0.039)         (0.0487)
Other race              0.0984          0.1654
                       (0.0582)        (0.0953)
Unknown race           -0.0784         -0.0896
                       (0.0649)        (0.0124)

Notes: Each column represents a separate probit regression
for the probability of choosing CSB/REDUX. The omitted
education categories are: high school dropout for enlisted
personnel and college degree for officers.

TABLE 5
Average Median and Expected PDRs by Demographic Group

                          Expected PDR          Median PDR

                    Enlisted   Officers   Enlisted   Officers

All                  0.0717     0.0430     0.0669     0.0192
                    (0.001)    (0.002)    (0.002)    (0.003)
AFQT < 50            0.080        --       0.081        --
                    (0.002)               (0.003)
AFQT > 50            0.068        --       0.061        --
                    (0.001)               (0.003)
White                0.065      0.039      0.055      0.016
                    (0.001)    (0.002)    (0.003)    (0.004)
Black                0.092      0.086      0.100      0.045
                    (0.003)    (0.012)    (0.004)    (0.012)
Hispanic             0.068      0.032      0.062      0.013
                    (0.004)    (0.006)    (0.007)    (0.004)
Male                 0.073      0.042      0.068      0.019
                    (0.002)    (0.002)    (0.002)    (0.003)
Female               0.064      0.048      0.055      0.023
                    (0.003)    (0.007)    (0.005)    (0.006)
Married              0.073      0.043      0.070      0.019
                    (0.002)    (0.002)    (0.002)    (0.003)
Divorced             0.074      0.073      0.070      0.038
                    (0.004)    (0.015)    (0.007)    (0.015)
No dependents        0.051      0.031      0.029      0.013
                    (0.002)    (0.008)    (0.004)    (0.005)
One dependent        0.059      0.033      0.042      0.014
                    (0.002)    (0.004)    (0.004)    (0.004)
Three dependents     0.071      0.048      0.067      0.022
                    (0.002)    (0.004)    (0.003)    (0.004)
Dropout              0.086        --       0.088        --
                    (0.007)                (0.01)
< College              --       0.095        --       0.052
                               (0.004)               (0.004)
Associate degree     0.064                 0.054
                    (0.002)               (0.004)
BA degree            0.059      0.050      0.044      0.023
                    (0.003)    (0.004)    (0.005)    (0.004)
Advanced degree      0.063      0.034      0.051      0.014
                    (0.004)    (0.003)    (0.007)    (0.004)
Non-Comb zone        0.069      0.044      0.063      0.020
                    (0.001)    (0.003)    (0.003)    (0.004)
Combat zone          0.078      0.042      0.077      0.018
                    (0.002)    (0.003)    (0.003)    (0.004)

TABLE 6
Confirmatory Analysis: Estimated Coefficients on Expected PDR

                                TSP Saving

                           (1)           (2)            (3)
Dependent                  Zero      Conditional       Saving
Variable                  Saving       Saving          Habits

Enlisted                  3.490        -6.012          -4.505
                         (0.905)       (0.812)        (0.870)
Officers                  4.222        -3.744          -4.818
                         (1.341)       (0.814)        (1.172)
Estimation Procedure     Zero-inflated binomial    Ordered probit

                             (4)         Number of
Dependent                 Financial      Financial
Variable                 Instability     Problems

Enlisted                    3.774          8.171
                           (0.768)        (0.824)
Officers                    0.905          2.210
                           (1.223)        (0.594)
Estimation Procedure    Ordered probit      OLS

                        Interest Rate on

                          (6)       (7)
Dependent               Credit      Car
Variable                 Card      Loan

Enlisted                17.143    38.162
                        (3.658)   (3.878)
Officers                 2.522    11.865
                        (5.677)   (7.558)
Estimation Procedure      OLS       OLS

Notes: Each element of the table represents a separate
regression of the dependent variable seen in each column
heading on the expected PDR and a set of year dummy
variables. The numbers shown are the estimated coefficients
on the expected PDR, with standard errors based on 1,000
bootstrap replications seen in parentheses.

TABLE 7
Saving Habits, Financial Stability, and Financial
Difficulties

                                                    Enlisted
                                                    Officers (%)

A. Which of the following statements comes
  closest to describing your saving habits?
Don't save, usually spend more                  2.1     0.4
  than income
Don't save, usually spend about                10.8     4.3
  as much as income
Save whatever is left over at the              29.1     9.8
  end of the month, no regular plan
Spend regular income, save other income         5.3     4.9
Save regularly by putting money                52.8    80.6
  aside each month
Total B. Which of the following best           100.0   100.0
  describes your financial condition?
Very comfortable and secure                    19.7    38.3
Able to make ends meet without                 50.8    48.4
  much difficulty
Occasional difficulties                        22.0    11.2
Tough to make ends meet but keeping             6.2     2.0
  head above water
Over your head                                  1.3     0.1
C. In the past 12 months, did any of
  the following happen to you?
Bounced two or more checks                      4.5     1.2
Paid overdraft fees 2 or more times            16.0     6.1
Missed payment on credit card account           8.9     2.0
Missed rent or mortgage payment                 4.1     0.5
Pressured to pay bills by stores,               9.3     1.2
  creditors, or collectors
Had telephone, cable, or internet shut off      3.5     0.7
Had water, heat, or electricity shut off        1.2     0.3
Had a car or other durable repossessed          0.7     0.0
Failed to make a car payment                    3.3     0.1
Filed for personal bankruptcy                   0.7     0.0
Foreclosure initiated or completed on home      1.3     0.3
Had at least one of the above                  24.4     8.1

TABLE 8

OLS Estimates of Awareness (a)

                        Enlisted    Officers

AFQT                     0.0066        --
                         (0.001)
High school degree       0.0107        --
                        (0.0953)
Associate degree         0.1131        --
                        (0.1008)
College degree           0.2436        --
                        (0.1042)
cCollege degree            --         0.212
                                     (0.194)
Advanced degree            --       -0.2107
                                    (0.1049)
Male                     0.2179      0.5748
                        (0.0632)    (0.2041)
Married                  0.1581      0.2902
                        (0.0827)    (0.2228)
Dependents               0.0159      -0.0506
                        (0.0126)    (0.0395)
Black                    -0.2890     -0.4002
                        (0.0456)     (0.184)
Hispanic                 -0.2484     -0.1773
                        (0.0852)    (0.2548)
# Financial problems     -0.0777     -0.0366
                         (0.013)    (0.0701)
[R.sup.2]                0.0778      0.0708
Observations             11,824       1,411

(a) The dependent variable is equal to the sum of the number
of features of the REDUX and High-3 retirement systems
listed in Table 2 of which the individual was aware, and ranges
from 0 to 4. The models for enlisted personnel and officers
control for the same demographic characteristics as appear in
the CSB/REDUX probit models.

TABLE 9
CSB/REDUX Probit Estimated Marginal Effects (a)

                         Enlisted   Officers
Aware of
40% at 20                 0.1142     0.0252
                         (0.0292)   (0.0224)
75% at 30                 0.0349     0.0651
                          (0.02)    (0.013)
Age 62 reset              0.2084     0.0667
                         (0.019)    (0.016)
REDUX CPI--1             -0.2940    -0.1731
Selected demographics     (0.02)    (0.039)
AFQT                     -0.0009       --
                         (0.0004)
HS degree                -0.0463       --
                         (0.046)
Associate degree         -0.1218    -0.0271
                         (0.047)    (0.047)
College degree           -0.1452       --
                         (0.047)
BA degree                   --      -0.0698
                                    (0.029)
MA or PhD                           -0.1476
                                    (0.044)

(a) Probit models for CSB/REDUX choice control
for the same variables as Table 4.
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Author:Simon, Curtis J.; Warner, John T.; Pleeter, Saul
Publication:Economic Inquiry
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2015
Words:12518
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