An empirical analysis of the factors impacting discount rates: Evidence from the U.S. Marine Corps "i:t. Nayantara Hensel a,*, Martin Deichert b

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1 ELSEVIER Review of Financial Economics 17 (2008) RFE An empirical analysis of he facors impacing discoun raes: Evidence from he U.S. Marine Corps "i: Nayanara Hensel a,*, Marin Deicher b a Graduae Schoo! of Business and Public Policy. u.s. Naval Posgraduole School, Ingersoll Dyer Road, MOII,erey. CA 93943, Unied Saes b Manpower Plans and Polic.y Division. Headquarers. Unied Sales Murine Corps. Uniled Slaes Received 15 May 2006; acceped 1 February 2007 Available online 20 February 2007 Absrac This analysis examines he impac of age, race, marial saus, number of dependens, educaion, rank, years of service, and occupaional code on personal discoun raes. The sudy focuses on 3241 Marine Corps officers! enlised personnel beween 1992 and 1997 who separaed from he Marine Corps hrough he VSI program (an annuiy paymen) or he SSB program (lump-sum paymen). The analysis finds ha, alhough he degree of saisical significance varied beween he officer model and he enlised model, holding oher facors consan, females and individuals wih more years of service or educaion were less likely o ake he lump-sum paymen, and ha blacks and individuals wih more dependens were more likely o ake he lump-sum paymen. Across all demographic facors, enlised personnel had saisically significanly higher average discoun raes han officers, as is consisen wih prior sudies. The esimaed personal discoun raes averaged 14.9% for officers and 24% for enlised Marines. This sudy conribues o he lieraure in ha i is he only sudy o examine he Marines during his ime period. Many of he resuls can be generalized o he civilian secor o assis in fannulaion of savings! reiremen policies. Published by Elsevier Inc. JEL classificaion: GIO; D91; M52; E21 Keywords: Discoun rae; Miliary; Ineremporal choice; Marine Corps * The auhors appreciaed discussions wih Kahy Kocher, Seve Mchay, and John Warner. All errors are enirely he auhors', Please do no quoe or cie wihou permission of he auhors. These views reflec only hose of he auhors, no hose of any insiuion. Corresponding auhor. Tel.: address: ndhensel@nps.cdu (N. Hensel) /$ - sec fron mauer. Published by Elsevier Inc. doi: I I6Ij.rfe

2 RFE f FmanciaJ Economica milocaeleconbase raes: Dyer Road, /es rank, years of :orps officers! :r program (an he degree of cors consan, -sum paymen,.en. Across all 1an officers, as sand 24% for.iarines during on of savings! 1. Inroducion and lieraure review N. Hensel, M. Deicher / Review oj Financial Economics 17 (1008) The U.S. governmen implemened a series of downsizing iniiaives under he Defense Auhorizaion Acs (1991 and 1992) o reduce U.S. miliary forces by 25% by fiscal year 1995 (FY 1995), following he collapse of he Sovie Union in 1989 and he end of he Cold War. The wo programs developed o achieve hese objecives were he Volunary Separaions Incenive (VSI) program and he Selecive Separaion Benefi (SSB) program. The SSB program provided individuals wih a lump-sum paymen of 15% of annual base pay imes years of service. The VSI program, on he oher hand, provided individuals wih an annuiy which was he produc of he service member's years of service (YOS) and 2.5% of heir annual basic pay. These VSI annuiy paymens would be received for a period equal o wo imes he years of service and would no increase over ime o compensae for inflaion, as discussed in Warner and Pleeer (2001). The inroducion of hese wo programs provided a naural experimen o esimae discoun raes since individuals choosing o separae had o decide which of he wo programs o ake. Consequenly, he purpose of his sudy is o esimae discoun raes for he 3241 Unied Saes Marine Corps (USMC) officers and enlised personnel who separaed from he USMC beween 1992 and 1997 under eiher he VSI or he SSB program. This sudy evaluaes he impac of variables such as gender, race, educaion, and years of service on he discoun rae and hence on he choice beween he wo programs. Undersanding he facors impacing discoun raes is imporan in formulaing savings plans, reiremen policies, and reenion policies for boh civilians and miliary since an individual's discoun rae reflecs hislher endency o rade off curren consumpion for fuure consumpion. Higher discoun raes imply a greaer desire for curren consumpion, while lower discoun raes imply a greaer desire for fuure consumpion. This analysis conribues o he lieraure in ha previous sudies have examined discoun raes exhibied by individuals in oher branches of miliary service in various conexs and over various ime periods bu have no examined he Marine Corps. Our analysis focuses on Marine officers and enlised personnel who separaed under he VSVSSB programs beween 1992 and 1997 using Marine Corps Toal Force Daa Warehouse (TFDW) daa.' Consequenly, i complemens Warner and Pleeer's (2001) sudy, which esimaed he discoun raes for 66,000 Army, Navy, and Air Force officers and enlised personnel who were eligible o separae from he miliary using VSI or SSB during 1992 and 1993 using Defense Manpower Daa Cener (DMDC) daa. They did no examine he Marines in heir sudy. Our overall discoun rae esimaes of 14.9% for officers and 24% for enlised personnel are consisen wih Warner and Pleeer's fmdings (as will be discussed laer in greaer deph), as well as hose of oher analyses. For example, Mackin (1995) esimaed discoun raes by examining he choice of Air Force officers/enlised beween VSI and SSB during FY 1992/ 1993 and FY 1994/1995. Mackin found an average personal discoun rae of 21 % for enlised personnel and 14% for officers. Cylke, Goldberg, Hogan, and Mairs (1982) esimaed ha Navy enlised personnel had discoun raes of beween 15% and 18%, based on he change in reenlismen bonus in 1979 from annual insallmens o lump-sum paymens. ely he auhors'. no hose of any I Correspondence wih he Marine Corps library in Quanico, VA, and wih he Manpower Plans and Policy Di vision a Marine Corps Headquarers has indicaed ha he ALMAR documens for he Marine Corps, which conained he VSI and SSB eligibiliy requiremens, were no saved prior o Consequenly, unlike Warner and Pleeer's (2001) daa for he Air Force, and he Navy, which conains infonnaion on hose who were eligible o separae, our daa se only conains infonnaion on hose who acually separaed.

3 _ -----_._ N. Hensel, M. Deicher / Revie}1/ oj Financial Economics 17 (2008) The previous analyses esimaing civilian discoun raes have included boh experimenal and nonexperimenal/field sudies. Examples of experimenal sudies include Thaler (1981), Benzion, Rapopor, and Joseph (1989), Coller and Williams (1999), Chesson and Viscusi (2000), and Heskeh (2000). Nonexperimenal sudies inferring he personal discoun raes from acual raher han experimenal choices include Gilman (1976), Hausman (1979), Gaely (1980), and Ruderman, Levine, McMahon (1986). One of he mos recen civilian sudies, Harrison, Lau, and Williams (2002), esimaed civilian discoun raes in Denmark using survey quesions wih real moneary rewards and found an overall average of 28.1 % across heir sample. Coller and Williams (1999) found discoun raes ranging from 15% o 25%, Chesson and Viscusi (2000) found an II % discoun rae, and Heskeh (2000) found discoun raes ranging beween 4% and 36%. The similariy of our discoun rae esimaes for miliary personnel wih hese civilian esimaes suggess ha our fndings may be helpful in assising in he formulaion of civilian savings and reiremen policies. The mehodology used in his sudy is discussed in Secion 2 of he paper. Secion 3 describes he daa and provides summary saisics. Secion 4 presens he esimaion resuls for boh he officer model and he enlised personnel model, while Secion 5 concludes. 2. MehOdology This analysis fo llowed a similar mehodology o Mackin (1995) and Warner and Pleeer (200 I). Firs, he value of he SSB and he VSI paymen for each individual was calculaed based on hislher base pay and hislher YOS. The SSB paymen was deermined as 15% of he base pay muliplied by he YOS. The VSI paymen was deermined as 2.5% of he base pay muliplied by he YOS muliplied by wo muliplied by he YOS. The analysis deermined he break-even discoun rae (D*) which se he presen value of he SSB paymen equal o he presen value of he VSI paymen such ha PV (SSB)=PV (VSI). PV(lump-sum) = PV(annuiy) or P V(1ump-sum) = {PV(annuiy) = C [~_~(I + /")I]}. The probabiliy of aking he SSB opion - Pr(SSB) - was hen esimaed as a funcion of D* (he break-even discoun rae) and oher variables (age, gender, educaion, marial saus, ec.). Individuals chose he SSB opion if heir personal discoun rae (D) exceeded heir break-even discoun rae (DO). Based on he disribuion of he daa, our analysis used logi specificaions for hese binary choice models. The personal discoun raes (D) for each individual in he sample were esimaed as D; = XdJ + E, where E- N(O, (5 2 ) and fj = ii/". <5 represened he esimaed coefficiens from he model esimaing Pr(SSB) (excep for DO) and 0:= - l / (coefficien on D* from he Pr(SSB) logi model).

4 lal and non- Ill, Rapopor, (2000). Nonenal choices (1986). One ;oun raes in ge of 28.1% 5%, Chesson ~ing beween hese civilian I savings and ibes he daa,r model and 2001). Firs, her base pay Ie YOS. The '0 muliplied. value of he 1). 1 of D* (he Individuals rae (D*). oice models. :1*) and a= r, r I I I ~ N. Hensel, M. Deicher / Review of Financial Economics 17 (2008) Separae logi models wih he Pr(SSB) as he dependen variable were run for he officers and for he enlised personnel because he likelihood raio es beween he unresriced model (wih officers and enlised personnel) and he resriced model (wih jus officers), as well as he es beween he unresriced model (wih officers and enlised personnel) and he resriced model (wih jus enlised personnel) indicaed ha he coefficiens for hese wo groups were in fac significanly differen from each oher and should herefore be evaluaed in separae models. 3. Daa and summary saisics The Marine Corps' Toal Force Daa Warehouse (TFDW) provided he daa used for his sudy. TFDW is he Marine Corps' auhorized sysem for currenlhisorical demographic and service-relaed records and provided he daa on he 494 officers and 2747 enlised Marines who separaed using he VSI or SSB program beween 1992 and Table 1 shows he summary saisics for Marine officers and enlised personnel by gender, race, and age. In addiion, i also shows he percenages wihin he officer caegory and he enlised caegory who chose VSI or SSB, as well as he percenages of hose who chose one opion over he oher by gender, age, and race. Table 1 indicaes ha 61.74% of officers chose he VSI annuiy opion, while 76.34% of enlised personnel chose he SSB lump-sum opion. In Warner and Pleeer's (2001) sudy on VSIISSB separaions during 1992 and 1993 using Army, Air Force, and Navy daa, he auhors found ha over half of he officers wih less han 10 years of service ook he SSB, and ha among E-5 enlised personnel wih less han 10 years, over 90% of he individuals ook he SSE. One of he reasons why a smaller percenage of individuals in our daa se of Marines ook he SSB opion is ha, prior o he FY 1993 Defense Auhorizaion Ac, here were incenives o ake he SSB over he VSI, which were removed in he FY 1993 Ac. 2 Warner and Pleeer's sudy focused on he FY 1992 and FY 1993 ime period, whereas our analysis examines 1992 hrough In our daa se, boh officers and enlised personnel had roughly similar percenages of males relaive o females-wihin boh caegories, abou 95% of he individuals were males. Wihin he officer caegory and wihin he enlised caegory, roughly he same percenage of males as females ook he SSB opion; however, as was consisen wih he percenages wihin he officer/enlised caegory pooled across genders, he percenage of males/females aking SSB among officers was significanly lower han he comparable percenage among enlised. Wihin boh he officer caegory and he enlised caegory, whies dominaed he sample, alhough he percenage of blacks was higher in he enlised caegory han in he officer caegory. Wihin he officer caegory and wihin he enlised caegory, roughly he same percenage of whies as blacks ook he SSB opion; however, as was consisen wih he percenages wihin he officer/enlised caegory pooled across race, he percenage of blacks/whies aking SSB among officers was significanly lower han he comparable percenage among enlised. Alhough he larges percenage of individuals wihin he officer caegory and wihin he enlised caegory were in he age range, he enlised caegory had a much higher percenage in he As discussed in Warner and Pleeer (200 I), SSB required only a hree year commimen in he Ready Reserve, while VSI required ha he recipien be affiliaed wih he reserves during he life of he paymen sream. SSB recipiens received a longer exension of medical coverage, moving benefis, ec. (pp ).

5 N. Hensel, M. Deicher / Review oj Financial Economics 17 (2008) Table I Summary saisics for Marine officers and enlised by gender, race, and age Variable Percen (number) Percen (number) aking SSB Percen (number) Percen (number) aking SSB among officers among officers among enlised among enlised Opion chosen SSB (189) (2097) VSI (305) (650) Gender Male (470) (181) (2599) (1993) Female 4.86 (23) (8) 5.39 ( 148) ( 104) Race Whie (460) (172) (2012) (1510) Black 4.66 (23) (10) (594) (474) Oher (I) (9) (8) Age (48) (25) (989) (855) (332) (127) (1303) (958) (105) (37) (394) (245) (9) (61) (39) age range (36%) han he officers did (9.72%). Wihin boh he officer caegory and he enlised caegory, he younges officers were he mos likely o ake he SSB (he lump-sum paymen), alhough he percenage of individuals in each age range for enlised personnel aking he SSB was almos wice ha of he individuals of comparable age in he officer caegory. The summary saisics for Marine officers and enlised personnel by educaional level, marial saus, and number of dependens are provided in Table 2. In addiion, wihin each of hese caegories and by Table 2 Summary sais ics for Marine officers and enlislcd by educaion level. manlal saus, and number of dependens Variable Percen (number) Percen (number) aking Percen (number) Percen (number) aking among officers SSB among officers among enlised SSB among enlised Educaion level Enlised: < HS 0.51 (14) (10) Enlised: HS or equivalen 9.97 (274) (200) Enlised: > HS (2459) (1887) Officers: (411) (J 73) Bachelors Officers: > Bachelors (83) (16) Marial slaws Married (399) (152) (2240) (1713) Single (95) (37) (507) (384) Number of dependens (385) ( 146) (2115) (1629) > (109) (43) (632) (468)

6 N. Hensel, M. Deicher / Review of Financial Economics 17 (2008) ber) aking SSB :d sed caegory, alhough he wice ha of narial saus, gories and by officers/enlised, he able shows he percenage of individuals who ook he SSB opion (he lump-sum paymen). For enlised personnel, as he educaion level increased from less han a high school diploma o greaer han a high school diploma, he percenage aking he SSB opion increased. On he oher hand, for officers, as he educaional level increased from a bachelors degree o greaer han a bachelor's degree, he percenage aking SSB dropped dramaically. This suggess ha here may be a cerain level of educaion (a high school diploma or higher) prior o which he probabiliy of aking SSB increases as educaion increases, bu ha educaion beyond ha level conribues o a decreasing probabiliy of aking SSB. Wihin he enlised caegory and wihin he officer caegory, he percenage of individuals aking he SSB does no differ significanly beween hose who are married and hose who are single or beween hose who have beween 0 and 3 dependens and hose who have more han 3 dependens. Consisen wih he descripive saisics in Table I, he percenage aking he SSB for enlised personnel, regardless of caegory (educaion, marial saus, or number of dependens), was usually almos wice he percenage of officers aking he SSB opion wihin he comparable caegory. The summary saisics for Marine officers and enlised personnel by rank, occupaional code (MaS), and years of service (YOS) are provided in Table 3. Consisen wih he descripive saisics in Tables I and 2, he percenage aking he SSB for enlised personnel, regardless of caegory (rank, MaS, or YOS), was usually almos wice he percenage of officers aking he SSB opion wihin he comparable caegory. Wihin he rank caegory, as rank increased, he percenage of individuals aking he SSB opion declined wihin boh he enlised personnel caegory and he officer caegory. Alhough he percenage aking he SSB across differen occupaional codes (MOSs) did no differ wihin he enlised caegory, a higher percenage of individuals wihin he officer caegory in he comba arms MaS ook he SSB relaive o Table 3 Summary saisics for Marine officers and enlised by rank, MOS, and yas

7 68 N. Hensel, M. Deicher I Review of Financial Economics J 7 (2008) individuals in he comba anns suppor or he aviaion MOS. As years of service increased, wihin boh he officer and he enlised caegories, he percenage aking he SSB declined, alhough he decline was seeper as years of service increased for officers han for enlised personnel. 4. Esimaion resuls 4.1. A. Officer and enlised esimaion resuls The resuls of he logi model esimaing he probabiliy of aking he SSB (lump-sum) opion by Marine officers are displayed in Table 4. The binary choice regression models in Tables 4 and 5 conribue o our undersanding of he inerplay of various facors on he discoun rae because hey enable an examinaion of he impac of one facor on he probabiliy of choosing he SSB opion, while holding he oher facors consan. Graduae educaion had a highly saisically significan negaive effec (a he 1% level) on a Marine officer's probabiliy of selecing he lump-sum paymen opion. A higher educaional levels, he probabiliy of an officer aking he SSB was lower. Indeed, he parial effecs of a graduae educaion show ha officers wih a level of educaion greaer han a bachelor's degree were less likely o choose he SSB paymen plan. Ou of 83 officers who had educaional levels higher han a Table 4 Marine officer esimaion using logi models wih Pr(SSB) as he dependen variable Variable Parameer esimae Sandard error Pr> x 8 Parial effecs Inercep SEU ' SEP _ " SEP_ SEP_ SEP_ FEMALE BLK OTHEILMINORITY SINGLE NUMBERDEPENDENTS E FIELD_GRADE COMBALSERVICE-SUPPORT AV IATION GRADUATE-EDUCATION " UNEMPLOYMENT.RATE " AGE YOS BEDR R' Max rescaled R Number of observaions 494 Coefficien is Significan aline 0.10 level.. Coefficien is significan al he 0.05 level. Coefficien is significan a he 0.01 level.

8 N. Hensel, M. Deicher I Review oj Financial Economics 17 (2008) wihin boh decline was 1) opion by 5 conribue :y enable an : holding he e (a he 1%. educaional,f a graduae, less igher han a Parial effecs o o , bachelor's degree, 67 of hem, or 80.7%, decided o ake he VSI paymen. This suggess ha beereducaed officers were beer able o recognize ha an annuiy-ype paymen offered hem greaer moneary value relaive o a lump-sum paymen. This rmding is consisen wih Warner and Pleeer's (200 I) officer model of he probabiliy of choosing he SSB opion, which found ha graduae educaion had a saisically significan negaive effec. Harrison e al. (2002), in heir sudy of Danish civilians, also found ha individuals wih higher levels of educaion had saisically significanly lower discoun raes. Gilman (1976) and Black (1984) also found ha discoun raes declined as educaion increased. The unemploymen rae faced by Marine officers a heir ime of separaion had a saisically significan posiive effec on heir decision o choose he lump-sum paymen opion. The parial effecs of he unemploymen rae reveal ha, as he rae of unemploymen increased by 0.1 %, he officers were more likely o ake he SSB paymen han officers who faced he average unemploymen rae of 6.5%. The daa showed ha 121 ou of he 283 officers, who faced a higher han average unemploymen rae upon separaion from he Marine Corps, seleced he lump-sum paymen opion. A number of oher facors which, in he summary saisics ables, suggesed differen propensiies o ake he SSB (lump-sum paymen) had he anicipaed sign bu were saisically insignifican in he binary choice officer model parially since oher facors were conrolled for in he regression. These facors included YOS, gender, number of dependens, and race. Females may have been less likely o ake he SSB opion (negaive sign on he coefficien), alhough he resul was no saisically significan, which is consisen wih Warner and Pleeer's (200 I) negaive, saisically insignifican effec for females. Blacks, as in oher sudies, may have been more likely o ake he SSB opion (posiive sign on he coefficien), alhough he resul was no saisically significan; Warner and Pleeer' analysis had a posiive, saisically significan effec for blacks. As yas increased, he endency o ake he SSB opion declined (negaive sign on he coefficien), alhough he resul was no saisically significan. Finally, as he number of dependens increased, individuals were more likely o ake he SSB opion (posiive sign on he coefficien), alhough he resul was no saisically significan; in Warner and Pleeer's officer model, he number of dependens had a posiive, saisically significan effec. In our analysis, miliary rank served as our proxy for wages/income, and field grade officers had a lower probabiliy of choosing he SSB opion, alhough he effec was no saisically significan. Similarly, Warner and Pleeer's officer model suggesed a negaive, saisically insignifican relaionship beween wages and he probabiliy of aking he SSB opion. Harrison e al. (2002) showed ha average discoun raes for various income brackes declined as income increased. Table 5 displays he esimaion resuls for Marine enlised personnel from he logi model esimaing he probabiliy of aking he SSB (he lump-sum paymen) as a funcion of various characerisics. Several of he effecs which had he sanle sign in boh he officer and he enlised model and which were no saisically significan in he officer model were significan in he enlised model. Gender had a saisically significan negaive effec (a he 10% level) on he probabiliy of aking SSB in ha women were less likely o ake he lump-sum paymen han men. The sign was he same as he corresponding coefficien in he officer model, bu he officer resuls were no saisically significan. Warner and Pleeer's (200 I) sudy similarly found a saisically significan gender effec in heir enlised model, bu no in heir officer model. In our analysis, a female enlised Marine was less likely o choose he SSB paymen plan upon separaion. Possibly his was because female Marines leaving he service may have expeced o earn less in heir civilian employmen, so hey could no afford o ake he lower amoun of money offered by he lump-sum paymen opion. Ehrenberg and Smih (2003) suggesed ha he wages of women in a civilian job are likely o be lower han hose of men.

9 70 N. Hensel, M. Deicher I Review of Financial Economics 17 (2008) Table 5 Marine enli sed resuls using logi models wih Pr(SSB) as he dependen variable Variable Parameer esimae Sandard error Pr>/ Parial effecs Inercep SEP_ SEP_ <0.0001" SEP_ a a SEP_1996 a 0 0 a SEP_ FEMALE ' BLK " OT IIE~MI NOR ITY SINGLE NUMBEILDEPENDENTS ' E E E COMBAT5ERVICE5UPPORT AVIATIO N LT _lis_diploma GLIIS_DIPLOMA UNEM PLOYMENT-RATE AGE ' YOS " BEDR R' Max rescaled Rl Number of observaions 2747 Coefficien is significan a he 0.10 level. Coefficien is significan a he 0.05 level.. Coefficien is significan al he level. Blacks were saisically significanly more likely (a he I % level) o choose he SSB program, despie conrolling for educaional and financial saus (as measured by rank). In he enlised daa, he educaional levels and he disribuion across ranks for blacks and whies were very similar. 3 The sign was he same as he corresponding coefficien in he officer model, bu he officer resuls were no saisically significan. Black enlised Marines were more likely o choose he lump-sum paymen han whie enlised Marines. This finding is consisen wih Warner and Pleeer's (2001) finding ha blacks had a higher propensiy o ake he lump-sum paymen and o have correspondingly higher personal discoun raes. Warner and Pleeer suggesed ha his may possibly occur because blacks may no be able o borrow money a low ineres raes due o educaional or income obsacles. J Approximaely 53.5% of blacks and 4')<'10 of whi les were in he lowes wo ranks - corporal and sergean - in. he enlised daa. Blacks had 0.7% of enlised personnel wih less han a high school diploma, compared o 0. 5% for whies. Abou II % of whie enlised Marines and abou 7% of black enlised Marines had a high school equivalen degree. Abou 92% of black Marines had educaion beyond a hi gh school diploma. compared wih 88% for whie enlised Marines.

10 Parial effecs, I, 1 I! f ~ i , ~ , I , , am, despie educaional he same as significan. lie enlised ad a higher coun raes. ~ o borrow in. he enlised Abou 11 % of 92% of black,. + ~ o. N. Hensel, M. Deicher I Review of Financial Economics J 7 (2008) Table 6a Mean implied PDR or Marine officers/enlised by gender, race, marial saus, number of dependens. and age Variable Mean PDR officers Sandard deviaion Mean PDR enlised Sandard deviaion Gender Male Female Race Whie Black Oher minoriy Marial saus Married Single Number of dependens > Age The number of dependens had a posiive, saisically significan effec (a he 10% level) on he probabiliy of he individual aking he SSB. The coefficien in he officer model was he same sign as in he enlised model bu was no saisically significan. This sudy and Warner and Pleeer's (2001) sudy are among he few which link discoun raes o family size. Warner and Pleeer similarly found a saisically significan posiive effec for number of dependens in heir enlised model. For every increase by one in he number of dependens an enlised Marine had, he likelihood of he SSB opion being chosen increased by Our daa showed ha a each level of number of dependens, which in he daa se ranged from 0 o 12, he percenage of enlised Marines who ook he lump-sum paymen was consisenly higher han hose who oped for he annuiy paymen. 4 This may possibly have been due o Marines wih larger families having greaer financial obligaions during heir ransiion ou of he miliary and herefore needing he money immediaely upon ransiioning ou. Age had a saisically significan negaive effec (a he 10% level) on he probabiliy of an enlised Marine aking he SSB (lump-sum) opion. As a Marine's age increased by I year, he probabiliy of ha person selecing he SSB paymen decreased by The daa showed ha from age 30 hrough 46, here was a decline in he percenage of SSB akers wih every one-year increase in age. Marines in his age bracke consiued 75.8% of he enlised sample. Warner and Pleeer (2001) similarly found a 4 The only excepion is a he eigh-child level, where 50% of he Marines ook. he SSB paymen and he oher half ook he VSI paymen

11 72 N. Hensel. M. Deicher / Review oj Financial Economics 17 (2008) saisically significan negaive age effec in heir enlised model. Moreover, Harrison e al. (2002) also found ha average discoun raes decline wih age for individuals under 50. The number of years of service (YOS) in he Marine Corps had a saisically significan negaive effec (a he 5% level) on he likelihood of an individual choosing he SSB opion. The parial effec for he YOS variable was a negaive One explanaion for his was ha, bolding educaion, race, and gender consan, an individual wih more years of service in he miliary migh have heen more likely o quickly ge a job afer leaving he Marines due o more work experience and hence would have been less likely o need he SSB (lump-sum paymen) o assis financially since he job searching ime would have decreased. Warner and Pleeer's (200 I) enlised model also had a posiive effec for YOS, alhough, unlike our enlised model, he effec was no saisically significan B. Personal discoun rae esimaes for officers and enlised personnel The esimaion resuls from Tables 4 and 5 were used o esimae a personal discoun rae (PDR) for each Marine officer and enlised individual in he sample. Tables 6a and 6b show he average of hese personal discoun raes by characerisic (age, gender, ec.) among officers and among enlised personnel. Tables 6c, 6d, and 6e show he -saisics for he di fferences of he average means by characerisic beween he oflicer group and he enlised group, as well as wihin each group. Tab le fib Mean implied PDR fo r Marine omcers/enlised by rank, MOS. educaional level, and yas Variable Mean POR officers Sandard deviaion Mean PDR enlised Sandard deviaion Rank E E E E E Field grade MOS Comba arms Comba service suppor Avi~ i on Educaion level LT lis diploma EQU IV lis diploma GT lis diploma 0.24! Bachelor's degree Graduae educaion YOS

12 , (2002) also gaive effec ffec for he n, race, and ore likely o ve been less would have 5, alhough, ;., < N. Hensel, M. Deicher! Review of Financial Economics 17 (2008) Table 6c Differences beween mean discoun raes for gender. race, marial saus, and educaion Tes for differences in average discoun T-saisic for wihin T-saisic for wihin T-saisic for differences beween he rae beween various caegories he officer group he enlised group officer group and he enlised group Males vs. females Enlised males vs. officer males Enlised females VS. officer females Blacks vs. whies Enlised whies vs. whie officers Enlised blacks vs. black officers Married vs. single Single officers vs. single enlised Married officers vs. married enlised Lowes educaional level vs. he highes e (PDR) for., < age of hese d personnel. haracerisic., (dard deviaion 39 " " ,. + 64, 98 +.;., Table 6a indicaes ha he average personal discoun rae for enlised personnel was significanly higher han ha of officers across all characerisics lised in he able- gender, race, marial saus, number of dependens, and all age caegories. Tables 6c and 6d confirm ha he average personal discoun raes for enlised personnel were saisically significanly higher, based on he I-saisics, han he average personal discoun raes for officers across gender, race, marial saus, number of dependens, and all age caegories. This suggess ha enlised personnel had a higher rae of ime preference and discouned fuure consumpion a a higher rae; hence, as is consisen wih he daa, hey were more likely o prefer lumpsum SSB paymens han annuiy-like VSI paymens. The saisical significance of differences in average discoun raes by characerisic was largely consisen wih he findings in Harrison e al. 's (2002) civilian sudy. I was difficul o compare hese wih Warner and Pleeer's (200 I) sudy hecause hey did no compare average discoun raes by characerisic or examine he saisical significance of differences in discoun raes. Table 6c suggess ha here was a saisically significan difference in average discoun raes (from Table 6a) beween males and females boh wihin he officer group and he enlised group. Harrison e al.'s (2002) sudy of civilians in Denmark, on he oher hand, did no find a saisically significanly differen Table 6d Differences beween mean discoun raes for number of dependens, age. and rank Tes for differences in average discoun rae beween various caegories Individuals wih 0-3 dependens vs. over 3 Enlised vs. officers wih 0-3 dependens Enlised vs. officers wih more han 3 dependens Younges age group vs. he oldesl age group Enlised vs. officers beween 22 and 30 Enlised vs. officer.i beween 31 and 35 Enlised vs. officers beween 36 and 40 Enlised vs. officers beween 41 and 46 Lowes rank vs. he highes nmk T-saisic for wihin T-saisic for wihin T saisic for differences beween he he officer group he enlised group officer group and he enlised group

13 74 N. Hensel, M. Deicher / Review of Financial Economics / 7 (2008) average discoun raes beween men and women. As is eviden in Table 6a, blacks ended o have a slighly higher average personal discoun rae han whies in boh he officer caegory and he enlised caegory; his resul was saisically significan wihin boh caegories (Table 6c). Among officers and enlised personnel, single and married individuals did no have saisically significanly differen discoun raes, which is consisen wih Harrison e al. 's (2002) Danish sudy. Our analysis did no show a saisically significan difference in average discoun raes wihin eiher he officer caegory or wihin he enlised caegory beween individuals wih 0-3 dependens versus individuals wih over 3 dependens. For boh enlised personnel and officers, as age increased, he average personal discoun raes fell. The difference beween he younges age caegory (22-30) and he oldes age caegory (41-46) was more subsanial wihin he enlised caegory han wihin he officer caegory. Harrison e al. (2002) also found ha average discoun raes declined wih age. The I-saisics in Table 6d suggesed ha he difference in average discoun raes beween he younges age group and he oldes age group was saisically significan, boh wihin he officer group and wihin he enlised group. The average personal discoun rae for enlised personnel was significanly higher han ha of officers across all characerisics lised in he able- rank, occupaional code (MaS), educaional level, and years of service (YOS) in Table 6b. The I-saisics in Tables 6c, 6d, and 6e indicae ha he enlised average personal discoun raes by each demographic characerisic were saisically significanly higher han he comparable average discoun raes for enlised personnel. As rank increased, he average personal discoun rae by rank declined for boh officers and enlised personnel, alhough he difference in average discoun raes beween he highes rank and he lowes rank was much greaer for enlised personnel han for officers (Table 6b). The I-saisics in he las line of Table 6d sugges ha he differences beween in average discoun rae beween he highes rank and he lowes rank were saisically significan, boh wihin he officer group and wihin he enlised group. Rank served as a proxy for income; consequenly, he finding is similar o ha of Harrison e al. (2002), who found ha average discoun raes declined wih income. Table 6e indicaes ha he average personal discoun raes beween occupaional codes or MOSs (from Table 6b) can significanly differ. Wihin he officer group, he difference in he average discoun rae Table 6e T-saislics fo r differences beween mean discoun raes by MOS and VOS Tes for differences in average discoun rale beween various caegories Comba arms MOS vs. he aviaion MOS 4.10 Comba anns MOS vs. he comba anns suppor MOS Comba anns suppor MOS vs. he aviaion MOS Enlised VS. officers in he comba anns MOS Enlised vs. officers in he comba anns suppor MOS Enlised vs. officers in he aviaion MOS Individuals wi h 4-10 yas vs yas Enlised vs. officers wih 4-10 VOS Enlised vs. officers wih vas Enlised \is. offi cers wih y as T-saisic for wihin T-saisic for wi hin T-slaisic for differences beween he he officer group he enlised group officer group and he enlised group l I f ~! +,.

14 N. Hensel, M. Deicher / Review of Finalll:ial Economics J 7 (2008) j o have a he enlised lfficers and m discoun lo show a r wihin he lependens. es fell. The ) was more I also found i fference in saisically of officers.,. I, and years ed average 'ler han he lal discoun ge discoun for officers 10 average I wihin he Ie finding is mcome. loss (from scoun rae s beween he,lisle<! group beween he comba arms MOS and he aviaion MOS was saisically significan, and wihin he enlised group, he average discoun rae beween he comba arms MOS and he comba arms suppor MOS was saisically significan. As years of service increased, he average personal discoun rae fell for enlised personnel, alhough he average personal discoun rae did no differ much for differen ranges ofyos for officers. Indeed, he average discoun rae for he group wih he lowes Y~S range (4-10 YOS) did no differ significanly from he average discoun rae for he group wih he highes YOS range (16-22 YOS) for officers, alhough he difference was saisically significan for enlised personnel. For officers, as educaion increased, he average personal discoun rae declined by educaional level. The difference in he average discoun rae beween he lowes educaional level and he highes educaional level, boh wihin he officer group and wihin he enlised group, was saisically significan (Table 6c). Harrison e. al. also showed a negaive relaionship beween educaion and discoun raes C. Comparison wih previous sudies The resuls of his sudy are consisen wih he findings repored by Warner and Pleeer (1994) and Mackin (1995), who consruced similar models for he oher branches of service. The average personal discoun rae across all YOS for officers and for enlised personnel, as well as a various levels ofyos, are compared across sudies in Table 7. Our average personal discoun rae across all officers was 14.9%, which is comparable o he 19% found in Warner and Pleeer's (1994) sudy and Mackin's (1995) sudy. Wihin he officer group, he average esimaes by Y~S were slighly lower han Warner and Pleeer's sudy and roughly similar o Mackin's sudy. Similarly, our average personal discoun rae wihin he enlised group was 24%, consised wih Warner and Pleeer (23%) and Mackin (20.9%). The resuls of his analysis are compared wih hose in Wamer and Pleeer's (200 I) sudy in Table 8. As discussed earlier, Warner and Pleeer's sudy examined he discoun rales for Navy, Army, and Air Force officers/enlised who were eligible o separae during 1992 and 1993 using DMDC dala while our sudy examines discoun rales for he Marines during who separaed under he VSI/SSB programs using TfDW daa. Our resuls are more comparable o Warner and Pleeer's linear model. Across all Y~S for individuals who separaed, Warner and Pleeer's officer caegory averages 12.9%, which is similar o our 14.9% while heir enlisled caegory averages 36.9%, which is somewhal higher han our 24%. Under Table 7 HenseUDeicher (2006) resuls compared o previous sudies Officer All YOS YOS YOSI Enlised YOS YOSI II All YOS YOS YOSI YOSI YOS Sample Decision Warner and Mackin HensellDeicher HenscVDeicher HensellDeicher number poin Plee!er (1994) (1995) esimaes (2006) sandard deviaions of observaions

15 76 N. Hensel, M. Deicher / Review of Financial Economics 17 (2008) Table 8 HcnscVDeicher (2006) resuls compared o Wamer/Plecer (2001) Sample Decision poin Warner and Pleeer (200 I ) Warner and Pleeer (200 I) HensellDeicher linear model loglinear model esimaes (2006) Officer Leavers all yas (enire sample) (0.104) 0.210(0.187) yas yas Enlised Leavers all vas (enire sample) (0.354) (0.536) yas yas Warner and Pleeer's loglinear model, discoun raes in he 50-60% rae were esimaed for enlised personnel. Our analysis does no esimae discoun raes ha are so high bu, regardless of he ype of model used, buh our srudy and Warner and Pleeer found ha officers had lower discoun raes han enlised personnel. This highlighs he differences in curren and fuure consumpion behavior beween he wo groups. Moreover, he differences in discoun raes beween officers and enlised personnel may parallel Harrison e al. 's (2002) finding in he civilian secor ha skilled workers had a lower average discoun rae han unskilled workers. 5. Conclusion This research deermined he discoun rae ha each individual Marine used o exchange presen dollars for furure dollars during severance from he Marine Corps under eiher he VSI or SSB volunary separaion paymen programs beween 1992 and This analysis also deermined hose professional, personal, and economic facors ha significanly influenced Marines in heir separaion paymen opion decisions. This sudy complemens he sudy done by Warner and Pleeer (200 I) because i esimaes he personal discoun raes of Marines, while Warner and Pleeer examined Anny, Navy, and Air Force officers who separaed during 1992 and The range used in our analysis has an addiional advanage over he period in ha, for hose separaing afier he beginning of FY 1993, he SSB vs. VSI decision was purely based on financial differences beween he wo programs. Neverheless, prior o he passage of he FY 1993 Defense Auhorizaion Ac, SSB recipiens had some advanages relaive o VSI recipiens. s Our analysis used daa provided by he Marine Corps' Toal Force Daa Warehouse on he personal and professional rais of he 494 officers and 2747 enlised Marines who separaed using he VSI or SSB program. The mehodology used o deermine he personal discoun raes for be Marines closely followed ha used by Warner and Pleeer and Mackin (1995). The esimaed personal discoun raes deennined by his sudy averaged 14.9% for officers and 24% for enlised Marines, which is consisen wih prior esimaes from Warner and Pleeer (1994, 200 I), and Mackin (1995). Warner and Pleeer (1994) esimaed 19% for officers and 23.3% for enlised personnel. Warner and Pleeer (2001) esimaed 12.9% for officers and 36.9% for enlised personnel in heir linear model, and Mackin (1995) esimaed 14.6% for officers and 20.9% for enlised personnel. Alhough Warner and Pleeer's (200 I) sudy esimaed much higher discoun raes for enlised personnel under heir loglinear 5 John Wamcr and Saul Pleeer's "The personal discoun rae: Evidence from miliary downsizing programs." American Economic Review, Vol. 91, no. I (March 2001), p. 36.

16 N. Hensel, M. Deicherl / Review of Final/cial Ecollomics 17 (2008) :nsevdeicher.imaes (2006) !40!75!07 for enlised he ype of raes han ior beween sonnel may ver average :sen dollars 3 volunary rofessional, nen opion simaes he I Air Force ysis has an ming offy ) programs. :s had some Toal Force 1arines who scoun raes e esimaed for enlised!od Mackin ne!. Warner near model, Wamerand,ir loglinear 1S," American, model han our analysis found, boh sudies consisenly found ha officers had lower discoun raes han enlised personnel. Moreover, he esimaed discoun raes in his analysis are consisen wih civilian sudies, such as Harrison e al. (2002), which esimaed a discoun rae of 28.1 %. Many of he characerisics impacing he probabiliy of aking he SSB (lump-sum paymen) had coefficiens wih he same sign in he officer model as hey did in he enlised model, alhough he saisical significance differed. For example, boh officer and enlised regression models indicaed ha females were less likely o ake he lump-sum, alhough he effec was only saisically significan for enlised personnel (a he 10% level). Boh models suggesed ha blacks migh be more likely o ake he lump-sum paymen, alhough he effec was only saisically significan for enlised personnel (a he 1% level). As he number of dependens increased, boh models suggesed a greaer endency on he par of individuals o ake he lump-sum paymen, alhough he effec was only saisically significan for enlised personnel (a close o he 5% level). Boh age and yas wihin he enlised model had saisically significan negaive effecs (a he 10% level and a close o he I % level, respecively) on he endency o ake he lump-sum paymen. Rank, marial saus, and miliary occupaional code were no significan in eiher model, once oher effecs, such as age and educaion, were conrolled for. Graduae educaion in he officer model was saisically significan a he I % level, suggesing ha more educaed individuals were less likely o ake he lump-sum paymen; educaion effecs were no significan in he enlised model. The unemploymen rae a he ime of separaion in he officer model was saisically significan a he I % level, suggesing ha higher unemploymen raes conribued o a greaer endency o ake he lump-sum paymen; his effec was no significan in he enlised model, alhough he coefficien had he same sign as in he officer model. Boh his analysis and Warner and Pleeer's (200 I) analysis highlighed he differences in he preference for curren consumpion vs. fuure consumpion beween officers and enlised personnel. Wihin he civilian conex, his may parallel he differences beween skilled and unskilled workers found in Harrison e al. 's (2002) sudy on Danish civilians. Alhough he degree of saisical significance varied beween he officer and enlised models, he signs of he coefficiens suggesed ha females were less likely o ake he SSB opion, blacks were more likely o ake he SSB opion, individuals wih more dependens were more likely o ake he SSB opion, and ha individuals wih more years of service and greaer educaion were less likely o ake he SSB opion. These resuls, consisen wih hose of Warner and Pleeer's (200 I) analysis, also paralleled hose of Gilman (1976) and Black (1984), who found ha individuals wih more educaion and higher income had lower discoun raes, and ha blacks had higher discoun raes han whies. Harrison e al. (2002) found ha individuals wih higher educaion, older individuals, and individuals wih higher incomes had a saisically significanly lower discoun raes. As a resul, many of he relaionships can be generalized beyond he miliary environmen o assis in policy-making. In conclusion, various characerisics impac he endency of individuals o prefer curren consumpion o fuure consumpion. In many cases, conrolling for oher variables, hese endencies may no be saisically significan wihin cerain populaions. Neverheless, an undersanding of he ineracion beween age, gender, educaion, and race, and heir corresponding impac on he fuure earnings sream available o individuals, is key in formulaing reiremen, force shaping, and savings rae policies. References Benzion, U., Rapopor, A., & Joseph, Y. (1989). Discoun raes inferred from decisions: An experimenal sudy. Managemen Science, 35(3),

17 78 N. liensel. M. Deicher / Review of Financial Economics 17 (2008) Black, M. (1984). Personal discoun raes: Esimaes for he miliary populaion. Final Repor of he Fifh Quadrennial Review of Miliary Compensaion, Vol. IB, Appendix I. Washingon. DC: U.S. Depanmen of Defense. Chesson, H., & Viscusi. W. K. (2000). The heerogeneiy of ime-risk radcoffs. Journal of Behavioral Decision Making, 13, Coller, M., & Williams, M. (1999). Eliciing individual discoun raes. rperimenal Economics, 2, Cylke. S., Goldberg. M., Hogan, P., & Mairs. L. (1982). The personal discoun rae: Evidence from miliary career decisions. Washingon, DC: Deparmen of he Navy OP-62. Ehrenberg. R., & Smih, R. (2003). Modern labor economics: Theory and public policy (8h ed.). New York: Addison-Wesley. Gaely, D. (1980). Individual discoun raes and he purchase and uilizaion of energy-using durables: Commen. BeJl Joumal oj Economics. 1/(1) Gilman. H. (1976). Deerminans of implici discoun raes: An empirical examinaion of he paern of volunary pension conribuions 0/ employees in four firms. Arlingon, VA: Cener for Naval Analysis. Harrison, G Lau, M., & Williams, M. (2002). Esimaing individual discoun raes in Denmark: A field experimen. The American Economic ReView, 92(5) Hausman, J. (1979). Individual discoun raes and he purchase and uilizaion of energy-using dumbles. Bell Journal oj Economics, 10(1), Heskeh. B. (2000). Time perspecive in career-relaed choices: Applicaions of ime-discouning principles. Joumal oj Vocaional Behavior, Mackin, P. (1995). The personal discoun rale: Evidence from Air Force loss programs. Mimeo. Rudcnnan, H., Levine, M., & McMahon. J. (1986). Energy efficiency choice in he purchase of residenial appliances. In K. Wille & M. Neiman (Eds.). Energy efficiency: Perspecive."! on individual behavior (pp. 41 ~50). Washingon DC; American Council for an Energy Efficien Economy. Thaler, R. (198l). Some empirical evidence on dynamic inconsisency. Economics Leers, 8(3), Warner, J. T., & Plceer, S. (1994). The personal discoull rale: Evidencefrom miliary downsizing programs. Washingon DC: Office of he Secreary of Defense. Warner, 1. T., & Pleeer, S. (2001). The personal discoun rae: Evidence from miliary downsizing programs. The American Economic Reviel-v, 91, Furher Reading Asch, 8., & Warner, J. (200 I). A! examinaion of he effecs of volunary separaion incenives. Sana Monica, CA: RAND MR SD. Frederick, S. Lowensein, G., & O'Donoghue, T. (2002). Time discouning and ime preference: A criical review. Journal oj Economic Lieraure, 40(2), 35\- 40 I.