/ 2 November 1982 DETERMINANTS OF REENLISTMENT AND EXTENSION RATES IN THE UNITED STATES MARINE CORPS. Matthew S. Goldberg John T.

Transcription

1 y / #ß-/H*»?'f (CNA) / 2 Nvember 1982 MEMORANDUM DETERMINANTS OF REENLISTMENT AND EXTENSION RATES IN THE UNITED STATES MARINE RPS Matthew S. Gldberg Jhn T. Warner NAVAL STUDIES GROUP Wrk Cnducted Under Cntract N C-0664 This memrandum represents the best pinin f CNA at the time f issue. It des nt necessarily represent the pinin f the Department f the Navy. CENTER FOR NAVAL ANALYSES 2000 Nrth Beauregard Street, Alexandria, Virginia 22311

2 LU >- I < < < > < cm O cm LU n C*3 O M CM CM c c CM X Q. In re: (CNA) / 2 Nvember 1982 MEMORANDUM TO THE ASSISTANT SECRETARY OF DEFENSE, MANPOWER, RESERVE AFFAIRS AND LOGISTICS (Attn: Mr. Paul Hgan) Subj: Center fr Naval Analyses Memrandum; frwarding f Encl: (1) (CNA) , "Determinants f Reenlistment and Extensin Rates in the United States Marine Crps," 2 Nvember 1982, Unclassified Enclsure (1) cntains the analysis that CNA has cmpleted n Reenlistment and Extensin Rates in the United States Marine Crps under cntract N C ^-'"JAMES C. WILSON Directr Special Studies Prgram O CM an affiliate f the University f Rchester

3 EXECUTIVE SUMMARY This paper analyzes the effects f Selective Reenlistment Bnuses (SRB) n retentin rates amng first-term and secnd-term enlisted persnnel in the United States Marine Crps. Our sample cntains the nearly 90,000 first-term and nearly 20,000 secnd-term enlisted persnnel wh made reenlistment decisins during the perid FY 1975 t FY We classified thse individuals int the six ccupatinal clusters shwn in Table I. Each ccupatinal cluster cnsists f tw-digit military ccupatinal specialties that we judged t be similar in terms f skill requirements, tasks perfrmed, and wrk envirnment. Within each ccupatinal cluster and fiscal year we may cmpute the reenlistment rate and the extensin rate. The reenlistment rate is defined as the rati f the number f reenlistment eligibles wh sign cntracts fr three r mre years f additinal service divided by the ttal number f reenlistment eligibles. The extensin rate is defined as the rati f the number f reenlistment eligibles wh sign cntracts fr less than three years f additinal service divided by the ttal number f reenlistment eligibles. The sum f the reenlistment rate plus the extensin rate is less than ne, since many individuals chse t leave the Marine Crps rather than either reenlisting r extending. -l-

4 TABLE I MARINE RPS OCCUPATIONAL CLUSTERS UNCLASSIFIED MBAT 03 - Infantry 08 - Field artillery 18 - Tank and amphibian tractr MBAT SUPPORT 02 - Intelligence 13 - Engineer, cnstructin equipment 25 - Operatinal cmmunicatins 26 - Signals intelligence/grund electrnics warfare 35 - Mtr transprt 57 - Nuclear, bilgical, and chemical ADMINISTRATION AND LOGISTICS 01 - Persnnel and administratin 04 - Lgistics 30 - Supply administratin and peratins 31 - Transprtatin SERVICE 11 - Utilities 14 - Drafting, surveying, and mapping 15 - Printing and reprductin 21 - Ordnance 23 - Ammunitin and explsive rdnance dispsal 33 - Fd service 34 - Auditing, finance and accunting 41 - Marine crps exchange 43 - Public Affairs 44 - Legal services 46 - Audivisual 55 - Band 58 - Military plice and crrectins -li-

5 TABLE I (Cnt'd) TECHNICAL 28 - Data/cmmunicatins maintenance 40 - Data systems 59 - Electrnics maintenance 66 - Avinics 72 - Air cntrller/air supprt/anti-air warfare 73 - Air traffic cntrl and enlisted flight crews AVIATION 60 - Aircraft maintenance (fixed wing) 61 - Aircraft maintenance (hel) 65 - Aviatin rdnance 68 - Weather service 70 - Aviatin peratins -iii-

6 Individuals wh reenlist (but nt thse wh extend) receive an SRB payment. The SRB payment is cmputed as the prduct f: (1) mnthly basic pay at the date f reenlistment, (2) length f reenlistment (measured in years), and (3) an SRB multiple, r level, ranging frm 0 t 6. We used lgit analysis t determine the statistical relatinship between the SRB multiple and the reenlistment and extensin rates. Table II reprts ur results fr first-term persnnel. Accrding t the table, a ne multiple SRB increase t the cmbat cluster wuld increase the reenlistment rate by.0605 but decrease the extensin rate by Since the increase in the reenlistment rate exceeds the decrease in the extensin rate, the ttal prbability f staying in the Marine Crps increases by.0140 ( =.0140). The results fr the ther five ccupatinal clusters have similar interpretatins.* Table II may be used t predict the effects f an SRB decrease as well as an SRB increase. This is accmplished by simply reversing the signs f the numbers in the table. Fr example, a ne multiple SRB decrease t the cmbat cluster wuld decrease the reenlistment rate by.0605, increase the extensin rate by.0465, and decrease the ttal prbability f staying in the Marine Crps by *The standard errrs f the effects in table II range between.001 and.002. Therefre, almst all f the effects are statistically significant. The nly tw insignificant effects are the small increase in the extensin rate in the technical cluster and the decrease in the extensin rate in the aviatin cluster. -iv-

7 TABLE II PARTIAL EFFECTS OF ONE MULTIPLE SRB INCREASE ON FIRST-TERM RETENTION 3 Changes in rates Occupatinal cluster Stay Reenlist Extend (s) (r) (e) Cmbat Cmbat Supprt Administratin/ Lgistics Service Technical Aviatin a Based upn the FY 1982 pay table, a ne level SRB increase crrespnds t an increase in the annualized bnus payment f $820. Table II may als be used t predict the effects f increasing r decreasing the SRB payment by mre than ne multiple. This is accmplished by multiplying the numbers in the table by the change in multiples. Fr example, cnsider increasing the SRB payment t the cmbat cluster by tw multiples (e.g., increasing the SRB multiple frm 1 t 3). Dubling the numbers in Table II, we predict that the reenlistment rate wuld increase by.1210, the extensin rate wuld decrease by.0930, and the ttal prbability f staying in the Marine Crps wuld increase by v-

8 Table III reprts ur results fr secnd-term persnnel.* The interpretatin f table III is identical t that f table II. Hwever, the effects f SRB changes are strnger fr secnd-term persnnel than fr first-term persnnel. Fr example, a ne multiple secnd-term SRB increase t the aviatin cluster wuld increase the reenlistment rate by.1600, decrease the extensin rate by.0512, and increase the ttal prbability f staying in the Marine Crps by TABLE III PARTIAL EFFECTS OF MULTIPLE LEVEL SRB INCREASE ON SEND-TERM RETENTION 3 Changes in rates Occupatinal cluster Stay Reenlist Extend (s) (r) (e) Cmbat Cmbat Supprt Administratin/ Lgistics Service Technical Aviatin Based upn the FY 1982 pay table, a ne level SRB increase crrespnds t an increase in the annualized bnus payment f $1,060. *The standard errrs f the effects in table III range between.002 and.007. All f the effects are statistically significant. -vi-

9 TABLE OF NTENTS Page List f Tables ix Intrductin 1 Data 2 Statistical Techniques 9 Findings 20 Cnclusins 31 References 32 -vi l-

10 LIST OF TABLES Page I Marine Crps Occupatinal Clusters II Partial Effects f One Level SRB Increase f First-Term Retentin III Partial Effects f One Level SRB Increase n Secnd-Term Retentin ii v vi 1 Marine Crps Occupatinal Clusters 3 2 First-Term Retentin Statistics and Average Bnus Multiples Secnd-Term Retentin Statistics and Average Bnus Multiples Prprtinate Distributin f First-Term Sample 10 5 Prprtinate Distributin f Secnd-Term Sample 11 6 Partial Derivatives f the Prbabilities 18 7 Means and Standard Deviatins f First-Term Pay Variables Means and Standard Deviatins f Secnd-Term Pay Variables 22 9 Cefficients and T-Statistics fr First-Term Marines Cefficients and T-Statistics fr Secnd-Term Marines Partial Effects f One Level SRB Increase n First-Term Retentin Partial Effects f $820 RMC Increase n First-Term Retentin Partial Effects f One Level SRB Increase n Secnd-Term Retentin Partial Effects f $1,060 RMC Increase n Secnd-Term Retentin 29 -ix-

11 I. INTRODUCTION This paper analyzes the determinants f reenlistment and extensin rates amng first-term and secnd-term enlisted persnnel in the United States Marine Crps. In particular, we analyze the separate effects f regular military cmpensatin and reenlistment bnuses n the prbabilities f reenlistment and extensin. The decmpsitin f retentin int reenlistments f greater than three years and extensins f less than three years is imprtant fr several reasns. First, these tw cmpnents f retentin respnd differently t varius cmpensatin incentives. Fr example, since nly thse wh reenlist receive reenlistment bnuses, an increase in bnus levels will increase the reenlistment rate but prbably decrease the extensin rate. Mrever, the distinctin between reenlistments and extensins is imprtant because a shift in the mix f retentin tward reenlistments and away frm extensins implies a higher stck f cntracted manyears and hence a larger and mre stable enlisted frce ver time. We have estimated the magnitude f these effects separately fr first-term and secnd-term persnnel in each f six ccupatinal clusters. Sectin II f this paper describes ur data set cnstructin. Sec- tin III presents ur statistical estimatin techniques. Sectin IV reprts ur empirical findings, and Sectin V discusses ur cnclusins. -1-

12 II. DATA The data fr this study were prvided by the Defense Manpwer Data Center (DMDC). DMDC maintains master and lss files that are extracts f the services' master recrds. Frm these files, DMDC cnstructed a lngitudinal data file that tracks every enlisted individual in the Marine Crps wh had mre than 23 mnths f service n 1 July 1974 either t the time f terminatin f service r t 30 September Individuals wh reached their 23rd mnth f service between 1 July 1974 and 30 September 1978 were similarly tracked. Each persn's recrd cntains bth persnal backgrund data and military histry data. Frm these data we identified and extracted all f the individuals wh made first-term r secnd-term reenlistment decisins during the perid FY 1975 t FY The resulting data set cntains nearly 90,000 first-term and nearly 20,000 secnd-term persnnel. We then disaggregated the data int the six ccupatinal clusters shwn in table 1. Each ccupatinal cluster cnsists f tw-digit military ccupatinal specialities (MOS) that we judged t be similar in terms f skill requirements, tasks perfrmed, and wrk envirnment. Tables 2 and 3 present summary retentin statistics by ccupatinal cluster and fiscal year fr first-term and secnd-term persnnel respectively. The prbability f staying, s, is defined as the rati f the number f reenlistment eligibles wh chse t stay in the Marine Crps -2-

13 TABLE 1 MARINE RPS OCCUPATIONAL CLUSTERS UNCLASSIFIED MBAT 03 - Infantry 08 - Field artillery 18 - Tank and amphibian tractr MBAT SUPPORT 02 - Intelligence 13 - Engineer, cnstructin equipment 25 - Operatinal cmmunicatins 26 - Signals intelligence/grund electrnics warfare 35 - Mtr transprt 57 - Nuclear, bilgical and chemical ADMINISTRATION AND LOGISTICS 01 - Persnnel and administratin 04 - Lgistics 30 - Supply administratin and peratins 31 - Transprtatin SERVICE 11 - Utilities 14 - Drafting, surveying and mapping 15 - Printing and reprductin 21 - Ordnance 23 - Ammunitin and explsive rdnance dispsal 33 - Fd service 34 - Auditing, finance and accunting 41 - Marine crps exchange 43 - Public Affairs 44 - Legal services 46 - Audivisual 55 - Band 58 - Military plice and crrectins -3-

14 TABLE 1 (Cnt'd) TECHNICAL 28 - Data/cmmunicatins maintenance 40 - Data systems 59 - Electrnics maintenance 66 - Avinics 72 - Air cntrller/air supprt/anti-air warfare 73 - Air traffic cntrl and enlisted flight crews AVIATION 60 - Aircraft maintenance (fixed wing) 61 - Aircraft maintenance (hel) 65 - Aviatin rdnance 68 - Weather service 70 - Aviatin peratins -4-

15 TABLE 2 FIRST-TERM RETENTION STATISTICS AND AVERAGE BONUS MULTIPLES Rates Average Number f Occupatinal Fiscal Stay Reenlist Extend bnus reenlistment cluster year (s) (r) (e) multiple eligibles Cmbat , , , ,820 Cmbat ,903 Supprt , , ,806 Administratin/ ,129 Lgistics , , ,220 Service , , , ,396 Technical , , , ,183 Aviatin , , , ,082-5-

16 TABLE 3 SEND-TERM RETENTION STATISTICS AND AVERAGE BONUS MULTIPLES Rates Average Number f Occupatinal Fiscal Stay Reenlist Extend bnus reenlistment cluster year (s) (r) (e) multiple eligibles Cmbat Cmbat Supprt ,007 Administratin/ Lgistics ,210 Service Technical ,000 Aviatin

17 t the ttal number f reenlistment eligibles. We further decmpse s int the reenlistment rate, r, and the extensin rate, e. The reenlistment rate is defined as the rati f the number f reenlistment eligibles wh sign cntracts fr three r mre years f additinal service t the ttal number f reenlistment eligibles. The extensin rate is defined as the rati f the number f reenlistment eligibles wh sign cntracts fr less than three years f additinal service t the ttal number f reenlistment eligibles. Nte that s = r + e. Our data exclude individuals declared ineligible t reenlist. Mrever, ur data exclude early reenlistments that ccur mre than 12 mnths prir t the end f the ld enlistment r reenlistment cntract. Bth factrs make it difficult t cmpare ur retentin statistics t fficial statistics, which use a different definitin f eligibility. Individuals wh reenlist (but nt thse wh extend) receive a Selective Reenlistment Bnus (SRB). The SRB is cmputed as the prduct f: (1) mnthly basic pay at the date f reenlistment, (2) length f reenlistment (measured in years), and (3) an SRB multiple, r level, ranging frm 0 t 6. The SRB is set by the Marine Crps n an MOS basis each fiscal year in an attempt t achieve the desired reenlistment rate in each MOS. Tables 2 and 3 present the average bnus multiples that first-term and secnd-term persnnel in each ccupatinal cluster and fiscal year wuld have received had they all reenlisted. The average -7-

18 bnus multiples actually paid t the fractin f persnnel wh chse t reenlist may differ frm the numbers presented in the tables. Nte that SRB levels were equal t zer fr all secnd-term persnnel in cmbat and administratin/lgistics, s that n reenlistment bnuses were available t these individuals during ur sample perid. The Selective Reenlistment Bnus System is the successr t the earlier Regular Reenlistment Bnus (RRB) System that it replaced n 1 July Individuals wh entered the Marine Crps prir t this date but wh executed first-term reenlistment cntracts after this date in an MOS with a level zer SRB still received a level ne RRB. T reflect this fact, we identified all first-term persnnel with active duty service dates prir t 1 July 1974 wh made reenlistment decisins in an MOS with a zer SRB, and we recded their SRB levels frm zer t ne. Mst f the individuals in ur sample wh received an RRB did s in either FY 1975 r FY The phasing ut f the RRB prgram explains mst f the general decline in the first-term average bnus multiples ver ur sample perid. The SRB payments were made in annual installments prir t 1 April Hence, this was the plicy thrughut the entire perid spanned by ur data. Hwever, current plicy is t pay 50 percent f the bnus in a lump-sum at the date f reenlistment and the remaining 50 percent in annual installments ver the duratin f the reenlistment cntract. Since lump-sum bnuses are mre effective than installment bnuses [1], we adjusted ur estimates t reflect the change t the current plicy.

19 Tables 4 and 5 present the prprtinate distributin f the firstterm and secnd-term samples by marital status, educatin, race, and AFQT mental grup. All f these variables are measured at the date f the reenlistment decisin. Nte that the percent f individuals with mre than 12 years f educatin is highest in the Technical cluster, and the percent f individuals in mental grups 1 and 2 is highest in the Technical and Aviatin clusters. Nte als that the percent married is much higher amng secnd-termers than amng first-termers. III. STATISTICAL TECHNIQUES We emplyed a sequential lgit mdel fr the decisin t reenlist, extend, r leave the Marine Crps. That is, we used ne lgit mdel t represent the decisin t stay r leave the Marine Crps, and a secnd lgit mdel t represent the decisin t reenlist r extend amng thse wh stay in the Marine Crps. We assume that the prbability f staying in the Marine Crps is a lgistic functin f the annualized r annuitized difference between the military incme stream frm staying in the Marine Crps and the civilian -9-

20 b C c» SO CN Cl c a^ C^ in SO. t CN. 1 CN H > i a 3 u be <r <r so CN Ov LO ~-< i i 00 t i ~H H O O a 3 M T3 0) 4J O H T) C C 0) e 4 CN I r^ c C^ a> «* r~- 00 ^H -3" a\ ~H >* * LO <r «* CN <r r>» <Ts CN. i lo in r-- 00 LO so LO i i i i ~H CN so sr CA a < M H I H cn tti H En ta O O H H OS H t & E id cn c Ü «u t C H 4J 0 3 T3 w 4-1 CN A CTN <f r-. OS «tf ON in cn -tf h«r«. r^ 00 OS \ c «* CN cn O CN ^r <r CN O c O H i i CTN so so so r^ h«i*» 1-^ Cd 1 H CN i l V T3 0) H M U as h» <r CN u-i cn so LO <r H f». C^ cn cn CN CN O ~H LO r>«s LO i» cn so r^ cn IT) cn <r <r m * M 00.O 3 C 0 H 4J & 3 U u H 4-1 a U H a. 4J a. 3 (J H 4J C <D CJ 0 4J 4J H U H H 0 H c 4-1 J3 J2 H > 4= e s E (J Ü H 0 C T3 0) <U > u CJ < 05 H < -10-

21 1 1 IT) >*0 <r PI a-n ON t^ NO «* <r <tf <r <r cn en a 3 H h ON en f * ON ON O r-l ON 1 1 O w fa a 3 u b T3 a) 4-1 t a H c C e H Ö fa CM CM 00 O-N CM CM CM < 1 CM I/O c NO in 1*» ON ON <N 00 a pa 2 w H I O 2 O CJ fa c fa IB H a H OS a g 0 c H 4J y cfl M fa C H 4-1 Cfl CJ 3 T) W CM CM NO ON 00 CM 00 L/0 CM 00 NO 00 LO ON CM CM ON ON CM ON H Q W H CM V NO r i CM CM NO NO ON fa fa ON CM 00 ON CM NO L/ NO -H r^- I»» p^ r». r H 0) 4J 4-> 01 en H 3 DO u H 4-1 H 3 cfl u O 3 H a 4J H a Cfl M H cfl 3 fa Cfl <U 0 O J H u H H U cfl c H C 4J ja J2 H > a s S SJ y H -a QJ <u > CJ O < H < -11-

22 incme stream frm leaving the Marine Crps.* We will nw discuss the prcedures that we emplyed t cmpute the military and civilian incme streams fr each individual in ur sample. We first cmputed the present value at a 10 percent discunt rate f the military incme stream that each individual culd expect ver the hrizn f a 4-year reenlistment. We included bth regular military cmpensatin (RMC) and any bnus that the individual wuld receive if he reenlisted. Our RMC values incrprated the individual's expected prmtin path given his length f service (LOS) and paygrade at the date f the reenlistment decisin. We next cmputed the present value at a 10 percent discunt rate f the civilian incme stream that the individual culd receive ver the same 4-year time hrizn. T btain variatin in civilian incme by LOS, we began with an age-earning prfile fr white high schl graduates frm the March 1977 Current Ppulatin Survey (CPS). We deflated this prfile t FY 1975 dllars using an index f average hurly earnings f wrkers in the manufacturing industry. We als cmputed the * Cnsider an incme stream Y,,...,Y T. The annualized value f this incme stream at discunt rate d is defined as: T T T* = E Y t (l+d) _t / I (l+d) _t t=l t=l Observe that a cnstant incme stream f Y* ver a T-perid hrizn has the same present value as the riginal incme stream. -12-

23 rati f this index t the cnsumer price index. We nrmalized bth indices t 1.00 in FY The rati f the tw nrmalized indices increases ver time if there is real (i.e., inflatin-adjusted) grwth in civilian wages relative t the base year FY 1975, but decreases ver time if the ppsite is true. We scaled ur FY 1975 age-earning prfile by the rati f indices t btain age-earning prfile fr each f FY 1976 t FY 1978, all expressed in FY 1975 dllars. The age-earning prfiles incrprate variatin in civilian earnings acrss individuals by LOS and fiscal year. T btain further variatin by race and educatin level, we calculated average earnings differences in the March 1977 CPS between whites and nn-whites, and amng individuals with less than 12 years f educatin, thse with exactly 12 years f educatin, and thse with mre than 12 years f educatin. We btained estimate f earnings differences by mental grup frm Rss and Warner [2], These surces prvided the fllwing percentage adjustment factrs: < 12 years f educatin versus 12 years: > 12 years f educatin versus 12 years: Nn-white versus white: Mental grup 1-2 versus mental grup 3: Mental grup 4 versus mental grup 3: percent percent percent percent percent -13-

24 We adjusted each individual's civilian earnings as cmputed frm the age-earnings prfile t accunt fr differences in race, educatin level, and mental grup. We applied the adjustments sequentially t accunt fr each f these factrs. The adjustments added cnsiderable variatin t the civilian earnings values. Fr example, a white individual in mental grup 1 with mre than 12 years f educatin received adjustments f 14.8 percent fr educatin and 3.2 percent fr mental grup. This resulted in a cmpunded upward adjustment f (1.148)(1.032)-1 r 18.5 percent. A black individual in mental grup 4 with less than 12 years f educatin received dwnward adjustments f 16.5 percent fr educatin, 6.8 percent fr mental grup, and 20.0 percent fr race. This resulted in a cmpunded dwnward adjustment f 1-(1-.165)(1-.068K1-.200) r 37.7 percent. Hence, adjustments fr race, educatin, and mental grup served t widen the difference in civilian earnings between these tw individuals by a ttal f = 56.2 percent. Let M dente the annualized value f RMC, B the annualized reenlistment bnus, and C the annualized value f civilian earnings, all cmputed at a 10 percent discunt rate ver a 4-year time hrizn. Als, let Dy^, D77, and Dyg be dummy variables equal t ne if the individual made his reenlistment decisin in the year indicated by the -14-

25 subscript, and zer therwise. Then we express the prbability f stay- ing in the Marine Crps (s) as: lg [s/(l-s)] = a Q + Oj (M+B-C) + a 2 D y6 + a^ + a 4 D^ (1) where lg dentes the natural lgarithm peratr. The maximum likelihd prcedure enables us t estimate the cefficients in equatin (1) using nly the infrmatin n each individual's decisin t stay r leave, his value f (M+B-C), and the year in which his decisin was made. Once the cefficients have been estimated, equatin (1) may be used t predict the prbability f staying fr a new individual drawn frm utside f the riginal sample. The dummy variables fr fiscal year in equatin (1) are included t capture the effects f time-dependent variables such as the civilian unemplyment rate. We have nt estimated the mdel using the unemplyment rate itself in place f the set f dummy variables. Therefre, we have n direct estimate f the effect f civilian unemplyment n Marine Crps reenlistment decisins. Hwever, the dummy variables cntrl fr the effects f civilian unemplyment as well as any ther time-dependent variables that affect reenlistment decisins. Hence, a measures the pure effect f relative pay n the prbability f staying in Marine Crps. -15-

26 We assume, that amng thse wh chse t stay, the prbability f reenlisting rather than extending is a lgistic functin f the annual- ized reenlistment bnus and the dummy variables fr the decisin year: lg (r/e) = S 0 + Bl B + if + e 3 D?7 + ^?Q (2) We adpt this specificatin because, apart frm the higher cumulative prmtin rate, the reenlistment bnus is the majr mnetary incentive t reenlist rather than extend. Once again, althugh equatin (2) is a prbability mdel, it may be estimated using nly infrmatin n each individual's decisin t reenlist r extend, his value f B, and the year in which his decisin was made. In additin t predicting prbabilities fr particular individuals utside f the riginal sample, we may use equatins (1) and (2) t derive the partial derivatives f the prbabilities f reenlisting, extending, staying, and leaving with respect t varius pay changes. The partial derivatives represent the changes in the prbabilities that wuld result frm specified pay changes. In particular, the partial derivatives culd be used by bnus managers t predict the effects f changes in SRB levels n the prbabilities. This wuld enable bnus managers t chse SRB levels that will achieve desired retentin rates and the desired mix between reenlistraents and extensins. -16-

27 The partial derivatives are presented in table 6. The secnd clumn gives the changes in the prbabilities assciated with a ne dllar annual increase in RMC. By cnstructin, the change in the prbability f staying equals the sum f the changes in the prbabilities f reenlisting and extending. Als, the change in the prbability f staying plus the change in the prbability f leaving sum t zer. The third clumn in table 6 gives the changes in the prbabilities assciated with a ne dllar increase in the annualized bnus payment. Once again, the change in the prbability f staying equals the negative f the change in the prbability f leaving and als equals the sum f the changes in the prbabilities f reenlisting and extending. Nte als that, with the sequential lgit mdel represented by equatins (1) and (2), the changes in the prbability f staying are equal fr a ne dllar increase in annual RMC and a ne dllar increase in the annualized bnus payment. Hwever, the mix f reenlistments and extensins amng stayers is quite different fr the tw types f pay increases. An increase in RMC increases bth the reenlistment rate and the extensin rate by the same percentage relative t their base values. This fllws since an increase in RMC des nt imply any increase in B and, frm equatin (2), the mix between reenlistments and extensins is unchanged as lng as B remains cnstant. -17-

28 TABLE 6 PARTIAL DERIVATIVES OF THE PROBABILITIES WITH RESPECT TO PAY Effect f dllar increase in: Prbability RMC Annualized bnus payment Reenlist: r r(l-s)a^ r(l-s)aj + e(r/s)3^ Extend: e e(l-s)cj e(l-s)u - e(r/s)f?^ Stay: s r+e s(l-s)ai s(l-s)ai Leave: Si 1-8 -s(l-s)a^ -s(l-s)a^ The effects are quite different fr an increase in the bnus payment. The prbability f staying increases, as des the prprtin wh reenlist amng stayers. Bth f these factrs cntribute t an increase in the reinlistment rate. Hwever, althugh there are mre stayers, the prprtin f stayers wh extend declines. Hence, the abslute number f extenders may decline as well. Finally, cnsider the effect f increasing the SRB multiple by ne level. If bnuses are paid in annual installments, then the annualized value f the bnus is simply mnthly basic pay times the SRB multiple. Hence, a ne level increase in the SRB multiple implies that the annualized value f the bnus increases by the value f mnthly basic pay. Since the third clumn f table 6 gives the effect f a ne dllar increase in the annualized value f the bnus, the effect f a ne level -18-

29 increase in the SRB multiple is btained by multiplying the numbers in this clumn by the value f mnthly basic pay. T perfrm these cmputatins, we first tk the FY 1982 mnthly basic pay f a typical first-term individual (E-4 at LOS 4) and a typical secnd-term individual (E-6 at LOS 8). These values are $820 and $1,060, respectively. We deflated these values t FY 1975 dllars using the cnsumer price index, and arrived at the deflated values $410 and $530. We als tk accunt f the current bnus payment system in which 50 percent f the bnus is paid in a lump-sum at the date f reenlistment and the remaining 50 percent is paid in annual installments ver the duratin f the reenlistment cntract. Under this system, the annualized value f the bnus is given by: r. 5+ " 4. ) r Z.167 (1 + d) * " * (P)(SRB)(L0R) B ='--^ 4 (3) E t = 1 (1 + d)^ + l where P dentes mnthly basic pay and LOR dentes the length f reenlistment. A ne level increase in the SRB multiple nw implies a larger increase in the annualized value f the bnus than was the case under the ld installment payment system. At a 10 percent discunt rate, the annualized bnus increases by 1.05 times mnthly basic pay. Hence, the effect f the bnus is magnified by 5 percent under the current system. -19-

30 Therefre, we have multiplied ur mnthly basic pay values f $410 and $530 by the factr 1.05 t arrive at the values $431 and $557 that we emplyed in ur cmputatins. Table 7 and 8 present the means and standard deviatins f the pay variables used in ur analysis. Again, B dentes the annualized reenlistment bnus, while M dentes the annualized value f RMC and C dentes the annualized value f civilian earnings. Recall als that SRB levels were equal t zer fr secnd-term persnnel in cmbat and administrative/lgistics thrughut ur entire sample perid, s that B equals zer fr these individuals. IV. FINDINGS Tables 9 and 10 present ur maximum likelihd estimates f the cefficients a and 3, frm equatins (1) and (2), respectively. The lack f variatin in SRB levels amng secnd-term persnnel in cmbat and administratin/lgistics precluded estimatin f 3, fr these tw ccupatinal clusters. Table 11 presents ur estimates f the partial effects n firstterm retentin f a ne level increase in the SRB multiple. These estimates are based upn FY 1982 pay levels and take accunt f the current bnus payment system in which 50 percent f the bnus is paid in the lump-sum and the remainder is paid in annual installments. -20-

31 TABLE 7 MEANS AND STANDARD DEVIATIONS OF FIRST-TERM PAY VARIABLES* 1 Occupatinal cluster B M + B - C Cmbat (193.31) (1,190.72) Cmbat Supprt (265.54) (1,181.42) Administratin/ Lgistics (167.45) (1,116.64) Service (222.39) (1,079.63) Technical (488.76) (993.31) Aviatin (267.72) (1,012.13) a Standard deviatins appear in parentheses. All variables are measured in FY 1975 dllars. -21-

32 TABLE 8 MEANS AND STANDARD DEVIATIONS OF SEND-TERM PAY VARIABLES a Occupatinal cluster B M + B - C Cmbat 0.00 (0.00) Cmbat Supprt (208.31) 1, (1,281.29) (1,143.27) Administratin/ Lgistics 0.00 (0.00) (1,084.34) Service (207.20) Technical (197.27) Aviatin (82.16) 1, (1,183.41) (1,059.23) 1, (966.83) a Standard deviatins appear in parentheses. All variables are measured in FY 1975 dllars. -22-

33 TABLE 9 EFFICIENTS AND T-STATISTICS FOR FIRST-TERM MARINES a Occupatinal cluster a l 3 1 Cmbat (11.34) Cmbat Supprt (20.17) (12.79) (16.56) Administratin/ Lgistics (19.38) (7.70) Service (18.35) Technical (7.06) Aviatin (16.16) (7.86) (1.39) (2.95) T-statistics appear in parentheses, -23-

34 TABLE 10 EFFICIENTS AND T-STATISTICS FOR SEND-TERM MARINES a Occupatinal cluster a l h Cmbat (20.83) Cmbat Supprt (17.98) Administratin/ Lgistics (17.86) Service (15.38) Technical (16.91) Aviatin (16.09) b (1.69) b (4.34) (4.08) (2.04) a T-statistics appear in parentheses. Cefficient is nt estimable due t lack f variatin in bnus levels. -24-

35 TABLE 11 PARTIAL EFFECTS OF ONE LEVEL SRB INCREASE ON FIRST-TERM RETENTION 3 ' b Changes in rates Occupatinal cluster Stay Reenlist Extend (s) (r) (e) Cmbat Cmbat supprt Administrative/lgistics Service Technical Aviatin (.0012) (.0006) (.0007) (.0013) (.0007) (.0006) (.0019) (.0012) (.0007) (.0019) (.0012) (.0007) (.0023) (.0017) (.0006) (.0020) (.0013) (.0007) a Based upn the FY 82 pay table, a ne level SRB increase crrespnds t an increase in the annualized bnus payment f $820. Standard errrs appear in parentheses. We estimate that a ne level SRB increase wuld increase the prbability f staying in the Marine Crps by between.0140 fr the cmbat cluster t.0366 fr the administratin/lgistics cluster. The effects n the mix f reenlistments and extensins amng stayers are much mre varied acrss ccupatinal clusters. With nly tw exceptins, the effects in table II are mre than twice their standard errrs and hence -25-

36 are statistically significant. The tw exceptins are the small in- crease in the extensin rate in the technical cluster and the decrease in the extensin rate in the aviatin cluster. Table 11 may als be used t predict the effects f increasing r decreasing the SRB payment by mre than ne multiple. This is accmplished by multiplying the numbers in the table by the change in multiples. Fr example, increasing the SRB payment t the cmbat cluster by tw multiples wuld increase the reenlistment rate by.1210, decrease the extensin rate by.0930, and increase the ttal prbability f staying by These effects are less precisely estimated than thse fr a single multiple change since they are based upn extraplatin alng a linear apprximatin (cnstant partial derivatives) t the nn-linear equatins (1) and (2). Therefre, cautin shuld be exercised when applying the numbers in the table t large changes in the bnus multiple. Table 12 presents ur estimates f the effects f increasing firstterm pay by means f an RMC increase rather than SRB increase. We cnsider an increase in annual RMC f $820 that is equal in value t the increase in the annualized bnus payment that wuld result frm a ne level first-term SRB increase. With ur sequential lgit mdel, the prbability f staying increases by equal amunts under an RMC increase and an SRB increase. Hence, the secnd clumn f table 12 cincides with the secnd clumn f table 11 (apart frm rundff errr). -26-

37 Hwever, while an SRB increase usually leads t a decline in the exten- sin rate, an RMC increase leads t increases in bth the reenlistment rate and the extensin rate. Tables 13 and 14 present ur estimates f the partial effects f increases in SRB and RMC n secnd-term retentin. While the effects f an RMC increase depend nly upn the sample prbabilities and the cefficients a,, the effects f an SRB increase depend upn the cefficients 3i as well. Recall that gi is nt estimable in the cmbat and administratin/lgistics clusters since SRB levels were equal t zer in these clusters thrughut ur entire sample perid. Hwever, frm tables 9, 11, and 12 it appears that the behavir f first-term persnnel in the cmbat cluster is quite similar t that f first-term persnnel in the cmbat supprt cluster. Mrever, the behavir f first-term persnnel in the administratin/lgistics cluster is quite similar t that f first-term persnnel in the service cluster. We have adpted the assumptin that these similarities carry ver t secnd-term persnnel as well. Therefre, we have emplyed the ß, cefficient in the cmbat supprt cluster t cmpute the partial effects f SRB changes in the cmbat cluster, and the fj, cefficient in the service cluster t cmpute the partial effects f SRB changes in the administratin/lgistics cluster. -27-

38 TABLE 12 PARTIAL EFFECTS OF $820 RMC INCREASE ON FIRST-TERM RETENTION 3 Changes In rates Occupatinal cluster Stay (s) Reenlist (r) Extend (e) Cmbat.0139 (.0012).0066 (.0006).0074 (.0007) Cmbat supprt.0254 (.0013).0136 (.0007).0119 (.0006) Administrative/lgistics.0367 (.0019).0223 (.0012).0144 (.0007) Service.0349 (.0019).0219 (.0012).0130 (.0007) Technical.0162 (.0023).0117 (.0017).0045 (.0006) Aviatin.0316 (.0020).0204 (.0013).0112 (.0007) Standard errrs appear in parentheses. -28-

39 TABLE 13 PARTIAL EFFECTS OF ONE LEVEL SRB INCREASE ON SEND-TERM RETENTION 3 ' b Change In rates Cmbat 0 Occupatinal cluster Cmbat supprt Administatin/lgistics c Service Technical Aviatin Stay Reenlist Extend (s) (r) (e) (.0048) (.0025) (.0023) (.0049) (.0025) (.0024) (.0049) (.0023) (.0024) (.0050) (.0025) (.0024) (.0058) (.0028) (.0030) (.0068) (.0034) (.0034) a Based upn the FY 82 pay table, a ne level SRB increase crrespnds t an increase in the annualized bnus payment f $1060. Standard errrs appear in parenthes s. c Based upn cti cefficient fr Cmbat and 3i cefficient fr Cmbat Supprt. Based upn a, cefficient fr Administratin/lgistics and ß, cefficient fr Service -29-

40 TABLE 14 PARTIAL EFFECTS OF $1,060 RMC INCREASE ON SEND-TERM RETENTION 3 Changes in rates Occupatinal Stay Reenlist Extent Cluster (s) (r) (e) Cmbat (.0048) (.0025) (.0023) Cmbat supprt (.0049) (.0025) (.0024) Administratin/lgistics (.0049) (.0025) (.0024) Service (.0050) (.0025) (.0025) Technical (.0058) (.0028) (.0030) Aviatin (.0068) (.0034) (.0034) Standard errrs appear in parentheses, -30-

41 The effects f a ne level SRB increase n secnd-term retentin are much larger than the effects n first-term retentin reprted earlier in table 11. In part, this result fllws frm the fact that mnthly basic pay is 29 percent higher fr secnd-term persnnel than fr first-term persnnel, s a ne level SRB increase represents a larger increase in the annualized bnus payment fr secnd-term persnnel than fr first-term persnnel. Hwever, since the estimates in table 13 exceed thse in table 11 by mre than 29 percent, secnd-termers appear t be intrinsically mre respnsive t pay than are firsttermers. We find that an SRB increase leads t increases in the reenlistment rate in all six f the ccupatinal clusters. The extensin rate increases in the cmbat and cmbat supprt clusters but decreases in the ther fur clusters. Despite the sign reversals, all f these effects are statistically significant. Finally, table 14 presents ur estimates f the effects f increasing secnd-term pay by means f an RMC increase rather than an SRB increase. We cnsider an increase in annual RMC f $1,060 that is equal in value t the increase in the annualized bnus payment that wuld result frm a ne level secnd-term SRB increase. Again, an RMC increase leads t increases in bth the reenlistment rate and the extensin rate. -31-

42 V. NCLUSIONS We have estimated the effects f increases in reenlistment bnuses and regular military cmpensatin n the reenlistment and extensin rates f first-term and secnd-term persnnel in six Marine Crps ccupatinal clusters. In particular, we find that increases in bnus levels always lead t increases in the reenlistment rate and usually lead t decreases In the extensin rate. Hwever, the increase in the reenlistment rate always exceeds the decrease in the extensin rate, s that the ttal prbability f staying in the Marine Crps increases. Our estimates shuld imprve the ability f bnus managers t set bnus levels that will achieve desired retentin rates and the desired mix between reenlistments and extensins. 32-

43 REFERENCES [1] CNA, Prfessinal Paper 356, "Estimatin f the Persnnel Discunt Rate: Evidence frm Military Reenlistment Decisins," by Steven Cylke, Matthew Gldberg, Paul Hgan and Lee Mairs, Unclassified, Octber 1982 [2] CNA, Research Cntributin 306, "Cmparisns f Military and Veteran Cmpensatin," by Sue Rss and Jhn Warner, Unclassified, December