Preliminary Disabiliy Insurance Applicaions near Reiremen Age Hugo Beníez-Silva SUNY-Sony Brook Na Yin Baruch College, CUNY Sepember 2011 Absrac The lieraure esimaing he effec of benefi levels on he Social Securiy Disabiliy Insurance (DI) applicaion decisions has no been able o separae he effec of Medicare coverage provided by he program on applicaion decisions from he effec of cash-benefis, and herefore previous esimaes are likely o be oversaed. In his research we compue he elasiciy of DI applicaions wih respec o cash benefi levels focusing on he special age window beween he Early Reiremen Age (ERA) and Normal Reiremen Age (NRA) in which Medicare incenives are virually non-exisen. This approach allows us o more accuraely esimae he effec of cash benefis on he decision o file for disabiliy benefis. The responsiveness of DI applicaions o policy variable changes is simulaed in a life cycle srucural framework ha characerizes in deail he rules of he Social Securiy programs. We find ha he benefi elasiciy of DI applicaions a age ERA-NRA is much higher han ha a younger ages. We also find some ineresing dynamic effecs, such as he changing age srucure of applicans and he applicaion iming shif when here are changes in policy variables. We acknowledge very helpful commens from Rober Weahers, David Sapleon, Selcuk Eren, and Wilber van der Klaauw. Beníez-Silva acknowledges he financial suppor from Gran Number 5 P01 AG022481-04 from he Naional Insiue on Aging, he Universiy of Michigan Reiremen Research Cener (sponsored by he Social Securiy Adminisraion), he Spanish Minisry of Science and Technology hrough projec number SEJ2005-08783-C04-01, and he Fundación Ramón Areces on relaed projecs. Na Yin wans o hank he financial suppor from PSC-CUNY hrough projec number 63887-0041 and hank he Cener for Reiremen Research a Boson College for heir suppor on a relaed projec.
1. Inroducion The Social Securiy Disabiliy Insurance (DI) program is he primary cash ransfer program for he disabled in he Unied Saes. I provides parial earnings replacemen o workers who los earnings capaciy due o severe and long-erm disabiliies. There is an exensive lieraure esimaing he effec of disabiliy benefi levels on DI applicaion decisions. Exising sudies mosly focus on older workers a ages below 62. 1 One reason for his is o avoid modeling he complex program incenives and individual decisions when he Social Securiy Old Age (OA) benefis sar o be available a age 62. These sudies have come o differen conclusions abou he magniude of he responsiveness (elasiciy) of DI applicaion wih respec o DI benefi levels. The esimaed elasiciy varies widely from 0.35 (Leonard, 1979) o 1.3 (Halpern and Hausman, 1986). Anoher imporan benefi provided by he DI program is Medicare coverage wo years afer he cash benefis are awarded. However, i is almos impossible o disinguish he effec of Medicare coverage from he financial incenives. This imporan in-kind benefi is rarely modeled while esimaing he effec of DI benefis on DI applicaion. Since Medicare is a federally-adminisered program, is benefis are sandard for disabiliy beneficiaries. There are few variaions in is benefis across saes or across individuals as noed in Bound and Burkhauser (1999). No being able o measure he effec of Medicare coverage on DI applicaion will lead o bias in he esimaion of he effec of DI cash benefis on DI applicaion. 2 In he paper, we re-esimae he elasiciy of disabiliy applicaion probabiliy wih respec o DI cash benefi levels focusing on he special age window beween he Early Reiremen Age (ERA) and he Normal Reiremen Age (NRA). This is a quasi-experimen o esimae he effec of cash benefis on DI applicaions wihou having o worry abou poenial biases caused by no considering he effec of Medicare incenives on applicaions. According o he Social Securiy Adminisraion (SSA) Annual Saisical Supplemen (2009), approximaely 142,817 workers 1 The sample in Lahiri, Song and Wixon (2008) includes age 18 o 64. 2 One excepion is he work by Lahiri, Song and Wixon (2008) ha predic he expeced value of Medicare coverage for DI applicans.
aged 62-64 applied for DI benefis in 2008 and 54,842 of hem were awarded he benefis. 3, 4 DI applicaions beween ERA and NRA, (age [62, NRA)), are mainly driven by DI cash benefis when Medicare coverage is probably no he main reason for hese ages o apply for disabiliy. The reasoning is as follows: The DI program grans Medicare coverage o disabiliy awardees only wo years afer he dae of award. Thus, a disabiliy applican beween ERA and NRA, if approved, will ge Medicare coverage only afer saying wo years on he DI rolls, a which poin hey will almos surely have reached age 65 when Medicare coverage is auomaically made available, regardless of wheher hey applied for disabiliy. 5 Therefore an individual who applies for DI benefis beween ERA and NRA does so mainly for cash benefis of he DI program. Thus, esimaing he elasiciy of DI applicaion beween he ERA and he NRA, when Medicare incenives of he DI program are virually non-exisen, helps separae ou he Medicare incenive effec from he cash incenive effec. This empirical design allows us o ge more precise esimaes of he elasiciy of DI applicaions wih respec o DI cash benefi levels. In an empirically grounded life-cycle srucural model ha characerizes in deail he DI program incenives as well as he OA program rules, we simulae he effec of changes in policy variables, such as benefi amoun and award probabiliy, on DI applicaion probabiliy. I is appropriae o simulae such behavioral effecs in a dynamic srucural framework, especially if i is possible ha he policy changes aler oher parameers ha govern people behavior, and according o Lucas criique (1976), reduced form models can hardly capure he whole effec (direc effec from he change in he policy of ineres and indirec effec from he change in oher parameers caused by ha policy change) of policy changes on behavior. I is also imporan o characerize no only he DI rules bu also he OA program rules in he model in order o predic individuals behavior. A an age beween ERA and NRA, boh OA and DI benefis are available. Before ERA, only DI is available o apply. DI benefis will conver o OA rolls a NRA. The ineracion beween OA and DI will be discussed in deail in Secion 3 and 5. 3 We have calculaed his using he number of beneficiaries a age 62-64 (54,842 according o he SSA Annual Saisical Supplemen Table 6.C2) and raio of awards o applicaions (38.4% in 2008 according o he SSA Annual Saisical Supplemen Table 6.C7). We assume ha he award probabiliy is consan for all he ages, which may resul underesimaion of he award probabiliy a older ages such as age 62-64. This underesimaion would cause overesimaion of he number of applicans a older ages. 4 The number of disabiliy awardees, once including heir eligible dependens, will be larger. 5 On average i akes abou one year for he disabiliy applican o hear abou he decision on heir saus from he Social Securiy Adminisraion.
Based on he simulaion resuls from our dynamic srucural model, we calculae he elasiciy of DI applicaions wih respec o he policy variable changes. Wha we find are summarized as follows: - Our esimaed benefi elasiciy (and award probabiliy elasiciy) a age 62 o NRA, when Medicare incenives are virually non-exisen, is much higher han ha a younger ages (age 21 o 61). - In general he DI award probabiliy elasiciy is higher han he DI benefi elasiciy. Tha is, people are more responsive o changes in he approval probabiliy han changes in benefi amouns. - DI applicaion probabiliies do no respond symmerically o benefi (or award probabiliy) reducions and increases of equal amouns. - We also find some ineresing dynamic effecs in our life cycle srucural framework, such as he changing age srucure of applicans and he applicaion iming shif when here are changes in policy variables. There are advanages of using life cycle srucural model over reduced-form model in simulaing he behavioral responses o changes in policy measures and esimaing he elasiciy. We ll discuss wo main aspecs here. Firs, he simulaion exercise in a reduced-form conex is essenially o keep all he oher covariaes consan while changing he benefi amoun (or he approval probabiliy) and see how DI applicaion propensiy will respond. However, changes in benefi amouns or approval probabiliies may likely lead o changes in oher covariaes. For example, if benefi amoun is increased, i will probably arac more applicans, and herefore he socioeconomic composiion of he new sample (a pool of he original sample and he newly enered applicans) will be differen. If ha is he case, he simulaion using he reduced-form model on he original sample will lead o biased esimaion. The issue could be addressed poenially by a well-designed social demonsraion projec or a well-buil life cycle srucural model. In he paper, we aemp o apply he second approach and conduc he simulaion exercises. Second, he elasiciy of DI applicaion probabiliy esimaed by a reduced-form model (e.g. probi) is he average responsiveness a all ages in he sample o changes in policy parameers. I
averages ou he differen behavioral responses a differen poin of he life cycle. While some sudies focus on some specific age group and esimae he elasiciy of DI applicaion, i may have missed he applicaion iming effec. For example, if a sudy sample is resriced o age 55-60, he simulaion using such an age-resriced sample o predic he applicaion response o benefi changes implicily assumes ha he benefis are unchanged for he ages ha are ou of he age range of he sample, in his example, ages younger han 55 and ages older han 60. When he benefis increase for he sample (age 55-60), besides he direc behavioral response from he individuals in he sample, individuals a oher ages, mainly hose younger han 55, are likely o wai o apply for higher benefis. The elasiciy esimae from a reduced model is mosly a shor-run responsiveness o benefi changes bu hardly capure he long-run effec due o he induced enry (apply a age 55-60) from oher ages. This could be addressed by simulaions conduced in a life cycle srucural model where he iming effec of DI applicaion could be examined. Disenangling he effecs of DI cash benefis incenives and he effecs of DI healh insurance incenives is informaive for policymakers. The SSA has implemened a series of policy changes since he incepion of he DI program o improve work incenives among he disabled, including changing he financial incenives (such as Trial Work Period, changing Subsanial Gainful Aciviy level), and modifying he Medicare incenives (such as Expanded Availabiliy of Healh Care Services and he currenly conduced demonsraion projec called Acceleraed Benefis for DI beneficiaries). However, he effecs of hose wo ypes of policy changes have been very difficul o differeniae, and he effeciveness of hose disabiliy policy changes has been hard o evaluae. The analysis of DI applicaion beween ERA o NRA will shed some ligh on he effec of DI cash benefi and is informaive for policy makers while gauging he effeciveness of disabiliy policy reforms. The organizaion of he paper is as follows: Secion 2 discusses he specificaion and soluion of he life-cycle srucural model; Daa used o calibrae he model and he calibraion resuls are presened in Secion 3; Secion 4 discusses he simulaion resuls of he effec of policy changes on DI applicaions.
2. A Life-Cycle Srucural Model 2.1. Model Specificaion An individual chooses how much o consume, how much o work, and wheher o apply for Social Securiy OA/DI benefis in each period o maximize he expeced presen value of uiliy over his life ime. Time. Time is discree and each period is one year. The model sars from age 21 when an individual is assumed o begin o decide wheher or no o ener he labor force. There is a finie horizon, age 100, when deah is cerain. Healh and moraliy. Healh saus, indexed by h, is assumed o be exogenous. h =0 denoes excellen/good healh; h =1 denoes fair/poor healh; and h =2 denoes being disabled. 6 One s healh saus evolves beween he hree sauses. Survival probabiliies π ( age, h ) are age and healh specific. Survival probabiliies decrease as age increases and healh deerioraes. Labor supply. An individual makes decisions on how much o work in each period. We define labor supply (leisure) a discree choice variable. 7 The leisure choice (labor supply choice) akes five values. The amoun of waking ime one spends in leisure is normalized o 1. Tha is, l =1 when one is no working a all. One ha works 2080 hours per year 8 is defined as full-ime working and he proporion of awake ime he allocaes o leisure per year is l = 0.525, while he oher levels of leisure, 0.644, 0.763, 0.881, correspond o par-ime working. 9 Social Securiy decisions. Le period. This choice variable akes hree values: Social Securiy OA benefis; ssd be he Social Securiy decision of an individual a ssd =1 when an individual chooses o claim ssd =2 when he decides o apply for DI benefis; ssd =0 denoing 6 Being disabled is referred o being prevened from work compleely by severe healh condiions or funcional limiaions. 7 The probabiliy of being laid off or becoming unemployed is no modeled. 8 An individual is assumed o work 40 hours per week and 52 weeks per year. 9 l = (12*365 2080) /(12*365) = 0.525 corresponding o full-ime work; l = (12*365 1560) /(12*365) = 0.644 corresponding o par-ime work (75% of full-ime work); l = (12*365 1040) /(12*365) = 0.763 corresponding o par-ime work (50% of full-ime work); and corresponding o par-ime work (25% of full-ime work).
applying o neiher of he programs. Social Securiy choice ses are differen by ages, as shown in he able below. Age Social Securiy Choice Se age < ERA ssd {0, 2} ERA age < NRA ssd {0,1, 2} NRA age < MRA ssd {0,1} age MRA ssd {1} The Early Reiremen Age (ERA), which is 62, is he earlies age when individuals can claim heir Social Securiy OA benefis bu he benefis are subjec o an acuarial reducion. The Normal Reiremen Age (NRA) is when o claim and receive 100 percen Primary Insurance Amoun (PIA). The NRA is age 65 in he model. 10 Individuals who claim OA benefis laer han heir NRA will receive higher benefis hrough Delayed Reiremen Credis (DRC) unil age 70, he Maximum Reiremen Age (MRA), when no furher credi will be allowed o laer claiming. An individual makes decision o apply for DI benefis before reaching his NRA, a or above which age DI benefis are no available anymore, and he DI beneficiaries auomaically conver o OA benefis. A ages beween ERA and NRA, an eligible individual could choose o apply o he DI program or OA program. 11 (A deailed discussion will be provided shorly on he ineracion of OA and DI programs for his age range.) An individual a or above his NRA and sill below he MRA faces only one program opion: o claim OA benefis, if an individual has no done so by hen and his OA benefis will be increased permanenly hrough DRC. The MRA, age 70, is assumed o be an absorbing sae and everybody is assumed o have already been on he OA rolls by hen, since here s no furher benefi from delaying claiming afer he MRA. Noice ha he iniial OA benefi claiming is an irreversible choice. Tha is, an individual won leave he OA roll once he is on i, alhough he benefi can vary over ime due o he earnings es and poserior adjusmens for benefis los due o earnings es. 10 The majoriy cohors in he daa reach heir NRA a age 65. 11 The SSA allows eligible individuals o file for OA and DI benefis a he same ime. In ha case, individuals receive heir early reiremen benefis while waiing for deerminaions on heir DI applicaions, and hey could ransfer o he DI roll if he laer awards higher benefis.
Social Securiy benefis. The DI and OA benefis ssb are deermined by a funcion ssb( AIME, age, wage ). As discussed earlier, Average Monhly Indexed Earnings (AIME) summaries one s earnings hisory and is used in a piece-wise linear formula o compue he Primary Insurance Amoun for OA and DI beneficiaries. Age is one argumen in he benefi funcion for wo reasons: firs, he firs age when an individual claims OA benefis will decide wheher he ges his full Primary Insurance Amoun (PIA) or reduced PIA by acuarial adjusmen facor or increased PIA hrough delayed reiremen credi; second, earning ess for OA benefis are age specific. Wage earnings affec AIME compuaion, DI eligibiliy, and he earnings es for OA benefis. Following Beníez-Silva, Buchinsky and Rus (2003), we approximae he evoluion of he annual average wage, aw (aw = AIME * 12) a age using aw a age -1, annual earnings y a age -1, and age. log( aw ) = α + α log( y ) + α log( aw ) + α + α + ε (1) 2 0 1 1 2 1 3 4 Given he above parameer esimaes, he annual average wage aw a age can be prediced as 2 2 aw ˆ α ˆ 0 α1 y ˆ ˆ ˆ 1 α2 aw 1 α3 α4 σε = exp( + log( ) + log( ) + + + / 2) (2) Annual earnings y is hen esimaed using he prediced aw sequence in a log-normal regression model. log( y ) = α + α log( aw ) + α + α + η (3) 2 0 1 1 2 3 The esimaed annual earnings are for full-ime workers and par-ime workers annual earnings are pro-raed accordingly. The DI award probabiliy p (, ) 1 wage h is a funcion of wage and healh saus. If wage while applying is higher han he SGA level, he award probabiliy becomes zero. Being in worse healh saus has a higher chance o be acceped o DI program. An audi probabiliy for DI recipiens is denoed by p 2 ( h ). I is he probabiliy of being audied by periodic reviews and being erminaed from he DI roll due o healh improvemens. The audi probabiliy depends on healh saus. Worse healh has lower probabiliy o be audied.
Social Securiy sae variables. The Social Securiy sae variable ss =0 denoing no on Social Securiy program, eniled o OA benefis. Two variables, age and on DI program: ss akes en values: ss =62, 63,, 70 denoing nine ages firs ss, are used ogeher o define he sae being ss =NRA and age<nra, denoing receiving full PIA a an age younger han NRA. We are allowed o do so because DI benefis are compued using he same formula as OA benefis and DI recipiens can receive around 100 percen PIA before heir NRA while OA beneficiaries can receive 100 percen PIA only when hey reach heir NRA. 12 We keep rack of he age when one is firs eniled o OA benefis because OA benefis are subjec o differen adjusmens a differen ages beween 62 and 70. Tax funcion τ ( y, w ). We include in our model he Social Securiy payroll ax, Medicare ax and progressive federal income ax (he negaive ax indicaes he Earned Income Tax Credi, or EITC). Federal income axes are also imposed on Social Securiy benefis when one s combined income (including Social Securiy benefis) is higher han some hreshold. Uiliy funcion. Insananeous uiliy funcion akes he form: γ u = ( c 1) / γ + φ( age, h, aw )*log( l) h sigma( w, age ) (4) The sigma funcion is equal o zero if one does no apply for DI benefis. φ ( age, h, aw ) is defined as disuiliy from work, which increases in age, decreases in average wage, and increases as healh ges worse. Healh affecs uiliy boh direcly and indirecly hrough is effec on disuiliy from work. We assume ha a sigma from applying for DI benefis exiss and i increases in wealh and decreases in age. 13 Uncerainies in he model are from age and healh specific survival probabiliies, healh ransiion, wage earnings, DI award probabiliy, and DI audi probabiliy. 12 The difference beween DI and OA benefis compuaion lies in he requiremen of quarers of coverage and how he wage hisory is impued while calculaing AIME. Quarers of coverage are no modeled explicily here. 13 There has no any formal analysis o es wheher sigma effec exiss for DI applicans. Here we include a sigma funcion in he model o specify some unobserved facors ha may explain why some people do no apply for DI benefis.
Based on our model, we d like o discuss a bi he ineracions beween he DI and OA program incenives for ages beween ERA and NRA. 14 On he one hand, a DI applican beween age 62 o NRA has usually accumulaed a leas 40 quarers of coverage o be eligible for boh DI and OA benefis, and he has already dropped ou of labor force or reired due o disabiliies. Especially considering ha early reiremen benefis could provide insurance agains possible DI benefi denial, a DI applican will be probably beer off claiming his early reiremen benefi a he same ime as DI applying. However, he radeoff will be, once he claims early reiremen benefi, his OA benefis could be locked a a lower level. If his DI applicaion is denied, he will have o fall back on his reiremen benefi which is a a reduced level almos permanenly. So from a life-ime perspecive, an individual s decision o apply OA or/and DI depends on he comparison of he presen values of he expeced life-ime benefi flows which accoun for benefi amouns in he fuure years and expeced moraliy risks, as modeled in our framework. On he oher hand, an early reiremen benefi claimer will probably be beer off applying for DI benefis a he same ime as filing for reiremen, given ha he has had quarers of coverage ha saisfy boh programs requiremens, and his DI benefis will be higher han his early reiremen benefis. If his DI applicaion is approved, he could enjoy a higher level of benefis possibly in he res of his life (DI benefis will auomaically conver o OA rolls a NRA). If his DI applicaion is denied, he could jus fall back on his reiremen benefis. However, an individual may no be able o apply for DI and OA simulaneously (or will be rejeced of DI benefis for sure) if 1) he coninues o work afer claiming reiremen benefis and earns higher han SGA level, which disqualifies him from DI benefis, or 2) he does no say ou of he labor force for a leas five monhs o demonsrae his disabiliy o work as required by he DI program eligibiliy, or 3) his earned quarers of coverage does no saisfy he recency requiremen of he DI program, or 4) his healh does no qualify him for DI benefis, or 5) he is deerred from applying by he relaively high uncerainy of geing approved, or 6) he sigma is relaively high for him o apply o DI program. Anoher imporan reason ha is no modeled here is he lack of knowledge abou he possibiliy of applying for DI and early OA benefis a he same ime beween ERA and NRA. 14 Leonesio, Vaughan, and Wixon (2003) had grea descripion abou he healh and financial saus of people aged 62-64 who received early Social Securiy reiremen benefis.
Alhough our model does no explicily have a separae choice variable of applying for DI and OA benefis simulaneously, he model allows people who are on he OA roll o apply for DI benefis, and allows DI applicans and beneficiaries o claim OA benefis. 15 I provides a heoreical predicion of people s opimal decision making o apply for Social Securiy programs assuming ha hey have full informaion on he Social Securiy rules especially he rule on he simulaneous filing. 2.2. Solving he Model: The value funcion in period is he sum of curren uiliy and he expeced presen value of uiliy from period onward: V ( S ) = max{ u ( S ) + * EV ( S S, D )} (5) β + 1 + 1 D if one is alive a period +1; or V ( S ) = max{ u ( S ) + * EB( S S, D )} (6) β + 1 D if one dies a period +1, where EB is he expeced presen value of beques. In he Markovian sochasic decision problem described in (5) and (6), he vecor of sae variable S + 1 represens he sae a he beginning of period +1 and i depends on he sae in he previous period S and he decision D made in he previous period. The vecor of sae variables S = { w, aw, ss, h} includes wealh, annual average wage, Social Securiy sae (being on OA or DI program) and healh saus. The vecor of decisions (choice variables) D = { c, l, ssd } includes decisions on consumpion, labor supply and Social Securiy OA/DI applicaion. β is he discoun facor. The expeced condiional value funcion in equaion (7) 2 E V ( S S, D ) k ( h h ) f ( y aw ) V ( S )* P ( S S, D ) dy = (7) + 1 + 1 1 1 + 1 + 1 + 1 + 1 h = 0 y 15 For DI beneficiaries, claiming OA benefis is a choice in principle bu rarely an opimal one because of he higher disabiliy benefis han reiremen benefis.
where P+ 1( S+ 1 S, D) represens he ransiion probabiliies beween Social Securiy saes. This conrolled sochasic process is subjec o uncerainies from healh ransiion k( h h 1) and wage earnings f( y aw 1). The law of moion of one of he sae variables, wealh w, is characerized as follows: w = 1 R*( w + y + ssb( aw, y)* I( ss > 0) c + τ ( y, w)) (8) where R is he reurn on savings. I ( ss > 0) is an indicaor funcion for being on he Social Securiy roll. We solve he Markov sochasic decision problem expressed in (7) and (8) via numerical compuaion of he Bellman recursion for V since here is hardly any analyical soluion o i. The opimal decision rule can be saed as follows: D * ( S ) = argmax V ( S ) (9) D To compue he condiional expecaion of he value funcion expressed in equaion (9), we apply Gaussian quadraure algorihm o approximae he inegral. 16 A each period he opimizaion in (9) is performed over he (w, aw) sae space. Wealh w is discreized ino 15 grid poins and average wage aw ino 8 grid poins. So he oal grid poins of he (w, aw) sae space is 120. Due o he discreizaion of coninuous variables and he sochasic process, nex period s value funcion s value will no always fall in he predefined grid poins. We use wo-dimensional simpicial inerpolaion algorihm o find he value for he value funcion a he neares grid poin as an approximaion of he rue value. 17 Bren s rouine o find a zero of a funcion uses he code from Numerical Recipes in C and modifies i o rack he zero of derivaive of he value funcion and compue he opimal decisions of consumpion, labor supply and Social Securiy decisions for all he (w, aw) grid poins, 10 Social Securiy saes, 3 healh saes and he 80 periods. The procedure is repeaed unil he soluion of he firs period problem is obained. 16 For a deailed discussion of quadraure mehods, refer o Rus (1996) and Judd (1998). 17 Refer o Algorihm 6.5 by Judd (1998) pp. 243.
3. Daa and Calibraion Daa used o calibrae he benchmark model are from a number of sources, including he Annual Saisical Repor on DI program produced by he SSA, saisics on employmen and populaion published by U.S. Census Bureau, and he U.S. Life Table produced by U.S. Ceners for Disease Conrol. Values of key variables in he model are esimaed from he Healh and Reiremen Sudy (HRS) daa se. The HRS is a longiudinal sudy ha follows persons aged 51-61 in 1992 and heir households The HRS provides rich informaion on respondens demographics, healh saus, employmen, income, wealh, and Social Securiy programs paricipaion. The resriced daa on earning hisories of HRS cohors are used o esimae he AIME, he base used o calculae he Primary Insurance Amoun (PIA) ha Social Securiy beneficiaries receive. 18 Self-repored work limiaions in he HRS daa se are used o define he hree disabiliy sauses (good healh, parially disabled, and fully disabled) in he model: 1) Do you have any impairmen or healh problem ha limis he kind or amoun of paid work you can do? ; 2) Does his limiaion keep you from working alogeher? Individuals who answered no o he firs quesion are defined as being in good healh. Defined as being parially disabled are hose who answered yes o he firs quesion and no o he second quesion. Tha is, he parially disabled are hose who self-repored o have work limiaions ha do no keep hem from work compleely hough. The fully disabled are hose who repored work limiaions ha keep hem from work compleely (who answered yes o boh quesions). One s healh ransiions beween he hree healh sauses. One issue is ha he healh ransiion marix esimaed using daa from he HRS is no age-specific bu he average healh ransiion probabiliies. As far as I know, here is currenly no available daa ha allows esimaion of age-specific disabiliy ransiion probabiliies for younger ages according o he parial/full work disabiliy definiions specified above. I is herefore very likely ha he disabiliy probabiliies for younger ages have been overesimaed (esimaed from hose of he HRS cohors) due o he fac ha younger ages likely have lower probabiliies o develop disabiliies han older ages. Then he DI applicaion and award raes for younger ages have probably also been overesimaed. 18 Wealh and wage levels of HRS cohors are lower han he populaion average. So in calibraion we see ha he benefis of older beneficiaries are lower han average benefis of populaion.
Moraliy risk in he model is exogenously deermined and is comparable o he deah rae in he Unied Saes Life Table. 19 The survival probabiliies are firs esimaed from he HRS daa for ages above 50. Then we use he survival probabiliies from he U.S. Life Table for boh older ages and younger ages, adjus i in an ad hoc way according o healh saus and indexed i off from he basic survival probabiliy in he Life Table. To be consisen, we jus use he healh adjused survival probabiliies based on he Life Table for all he ages. The weighed oal survival probabiliy by healh disribuion a each age for age above 50 esimaed from he HRS 20 21 daa is very similar o ha in he Life Table. Following previous lieraure, he discoun facor β akes value 0.96, and he consan relaive risk aversion parameer (1-γ) is 1.37. The healh ransiion marix is esimaed from he HRS daa (k_11=0.95, k_12=0.04, k_13=0.01; k_21=0.25, k_22=0.68, k_23=0.07; k_31=0.05, k_32=0.10, k_33=0.85). The DI award probabiliies for he hree healh saus (from beer o worse) are esimaed from he HRS daa, and hey are 0.62, 0.52, and 0.42, respecively. Esimaed from he HRS daa are also he DI audi probabiliies for he hree healh saus, 0.01, 0.02, and 0.05, respecively. A form of he sigma funcion sigma( w, age ) in he uiliy funcion is chosen o help simulaion resuls beer mach he observed age profile of DI enilemen, DI rolls, average monhly DI benefis, and employmen. Beques is simply he wealh lef when an individual dies. Parameers of incenives under curren DI program and OA program (benchmark model) include he Subsanial Gainful Aciviy (SGA) earnings level ($980/monh in 2009 for nonblind), DI waiing period (one year), Early Reiremen Age (ERA, 62), Normal Reiremen Age (NRA, 65), Maximum Reiremen Age (MRA, 70), earnings es and earnings ax rae for reirees beween ERA and NRA ($12,960/year and 0.5), earnings es and earnings ax rae for reirees in year reaching NRA ($34,440 and 0.33), maximum axable Social Securiy earnings 19 The survival probabiliies are aken from he U.S. Life Table, Naional Vial Saisics Repor, vol. 54, no. 14, 2006, produced by U.S. Cener for Disease Conrol. 20 Reliabiliy of curren moraliy rae and assumpion of fuure moraliy projecion are criical o make sound policy planning and predicion. The model in he paper could be improved by relaxing he assumpion ha moraliy risks are exogenously deermined. 21 My experimens show ha using healh adjused age-specific survival probabiliies or only age-specific survival probabiliies do no really affec he model resuls. De Nardi, French and Jones (2006, page 32-33) also draw similar conclusions.
($97,500/year), Social Securiy ax rae, acuarial reducion facor on early reiremen benefis, and delayed reiremen credi. The srucural model was solved by backward inducion and he numerical soluion was used o simulae life cycle pah for 5,000 arificial agens. Figure 1-6 illusrae he fi of he model o he age profile of key variables. Figure 1 compares he simulaed age profile of percenage of DI beneficiaries wih he acual age profile. We see ha he model fis he age disribuion of DI rolls well, alhough here is a less han 3 percen overesimaion for age group 45-49 and 50-54 and less han 4 percen underesimaion for hose aged 60-64. Figure 1 illusraes he sock of he DI beneficiaries, he proporion of survivors a each age receiving DI benefis. In Figure 2, we see he age disribuion of he flow of DI recipiens, ha is, he age disribuion of all he new awardees. The flow of DI rolls illusraed in Figure 2 shows an overesimaion for age 40-44 and age 45-49, and an underesimaion for age older han 50-54, which represens a similar paern as in Figure 1, excep ha he over-esimaion appears a bi earlier in he flow (Figure 2) han in he sock (Figure 1). Despie some discrepancies beween simulaion resuls and real daa, he model capures he general age paern of DI enilemen reasonably well. The above discrepancies beween he simulaed and he acual age profile of DI beneficiaries is very likely due o he fac ha he disabiliy ransiion marix used in he model are age-consan and was esimaed from he HRS daa se, a relaively older sample of general populaion, while younger ages probably have lower probabiliies o develop disabiliies han older ages. Moreover, in he model he DI award probabiliy is an increasing funcion in healh (higher values of healh denoes worse healh and worse healh has higher chance o ge awarded), and he audi probabiliy is a decreasing funcion in healh (worse healh has lower chance o be audied and removed), i is likely ha we have overesimaed he award probabiliy and underesimaed he audi probabiliy for he younger ages due o he age-consan disabiliy ransiion marix. Tha could possibly help explain par of he overesimaion of percenage of DI recipiens among he young ages. 22 22 We ried he simulaion wih some arificial age-specific disabiliy ransiion probabiliies (smaller probabiliies for younger ages and larger probabiliies for older ages) and he resuls did seem o beer mach he acual age profile of DI enilemen.
In Figure 3 and Figure 4, he model reproduces he age profile of average monhly DI benefis. The average monhly benefis are a funcion of he AIME which is a summary of one s earnings hisory. The model predics he age profile of average monhly DI benefis quie well, implying a relaively well-prediced age profile of earnings hisories. Figure 3 illusraes he benefis of he sock of DI beneficiaries, while Figure 4 shows he benefis of he flow of DI recipiens. Boh figures have capured he general paern of increasing monhly benefis wih age alhough here are some discrepancies in he slope of age profile of benefis. Those discrepancies are mosly due o he way we esimae he annual earnings and he way we approximae he average wage (aw). We esimae one s annual earnings using he observed sequence of average wages calculaed from he earning hisories of HRS cohors aken from he SSA resriced daa. However, HRS cohors have generally lower earnings levels han curren general populaion. Therefore he annual earnings esimaed from HRS cohors earning hisories are likely o be lower han ha of acual populaion. Figure 5 illusraes he age profile of median monhly wages for full-ime workers. The simulaed populaion has a generally lower wage level han he acual populaion. The wages levels for age 55-64 are undersaed by abou 2,200 dollars. This may be par of he reason ha he simulaed average monhly DI benefis are underesimaed for he older recipiens. Figure 6 illusraes he age profile of employmen rae. The general employmen paern prediced by he model maches he acual daa alhough he simulaed employmen rae is higher han he acual rae. The oal employmen rae of he acual male populaion is 0.72, compared o he simulaed oal employmen rae, 0.80. Par of he reason for his discrepancy could be ha unemploymen risk and lay-off risk are no considered in he model and herefore employmen rae has been overesimaed. 4. Simulaion Resuls and Discussion In our life-cycle srucural model, we change he value of DI policy variables, such as he DI benefi amouns and he DI award probabiliy and simulae he effec of hose changes on DI applicaion decisions. According o he simulaed DI applicaion raes, we are able o calculae he elasiciy of DI applicaion wih respec o he benefi amoun and he award probabiliy. The calculaed elasiciies are presened in Table 1 and Table 2. The age group of our main ineres
is 62-NRA. This sudy akes advanage of his special age window, separaes ou he effec of Medicare coverage provided by he DI program on applicaion behavior, and herefore more accuraely measures he effec of cash benefi incenives on DI applicaion decisions. For comparison purpose, he younger age group 21-61 and also he age groups used in he previous lieraures are examined. Our esimaed benefi elasiciy (and award probabiliy elasiciy) a age 62-NRA is much higher han ha a younger ages, for example, age 21-61, as shown in Table 1 (and Table 2). In oher words, individuals a age 62-NRA are more responsive o DI benefi changes (and he award probabiliy changes) han younger individuals when hey are making decisions o apply o he DI program. Since Medicare incenives do no have much effec for his age range, he financial incenive dominaes in one s decision o apply o DI program. A his age range, OA benefis become available and creae compeing financial incenives wih DI benefis, as discussed in deail earlier in he Model Secion. DI benefis are around 100% of one s Primary Insurance Amoun. When DI benefis decrease by 20% or 40% (or when he DI approval probabiliy decreases), OA benefis, even hough a reduced level (20% of he full Primary Insurance Amoun a age 62 for mos cohors in our model), will look more aracive in comparison, especially considering here is also uncerainy of geing DI benefis afer applying. 23 However, claiming early reiremen benefis has he risk of locking he reiremen benefis a a reduced level possibly permanenly. 24 25 So from a life ime perspecive, an individual s decision o apply OA or/and DI depends on he comparison of he presen values of he expeced life-ime benefi flows which accoun for benefi amouns in he fuure years and expeced moraliy risks, as modeled in our framework. For a Social Securiy covered individual wih cerain earnings hisory, his DI benefis are usually higher han his early reiremen benefis. DI benefis can become even more appealing 23 A DI applican who has accumulaed he required quarers of coverage a age 62 or over will mos probably saisfy he quarers of coverage requiremen of OA program. The DI eligibiliy requires 40 Social Securiy credis for age 62 or over and unless he applican is blind, a leas 10 of he credis mus have been earned in he 10 years immediaely before he onse of disabiliy. The OA eligibiliy requires 40 Social Securiy credis for hose born in 1929 or laer such as HRS cohors in our sample. 24 Unless he coninues o work and earns above cerain amoun o have his benefi recalculaed laer. Deailed discussion in his aspec could be found in Beniez-Silva and Heiland (2008) and Mancheser and Song (2007). 25 We are currenly calculaing he elasiciy of DI applicaion wih respec o he raio of DI benefis over OA benefis o conrol for he confounding effec of OA benefis. In Duggan, Singleon, and Song (2007), hey found a modes effec of increases in NRA, herefore he raio of DI benefis o OA benefis, on DI applicaion.
han OA benefis when he former are raised by 20% or 40% (or when he DI approval probabiliy increases). However, he decision o apply also accouns for he rejecion risk from DI program, he work resricion and he audi risk once on he DI program, as characerized in our srucural model. In shor, as in he model, he decision is made afer an individual compares he presen values of expeced life-ime benefis flows which accoun for Social Securiy benefis, work earnings, all he uncerainies (healh ransiions, survival probabiliies, DI rejecion risks for applicans and audi risks for beneficiaries, earning flucuaions), and oher facors. In he simulaion, we do observe an increase in DI applicaion propensiy afer he benefis rise (or he approval probabiliy increase). In comparison, younger individuals DI applicaion decisions are less responsive o benefis amoun changes (and he award probabiliy changes). One reason is ha hey do no have a comparable benefi opion such as OA benefis as he age beween 62 o NRA group has, which makes heir DI applicaion decisions less elasic o any change in he DI policy variables. The oher reason ha DI applicaion decisions are less elasic among younger people is ha besides cash benefis, Medicare coverage is anoher imporan benefi hey are afer when deciding o apply o he DI program. The effec on DI applicaion of any change in cash benefis alone can be diminished by he effec of Medicare incenives. For example, a cash benefi cu will probably no have as big an impac on DI applicaions as when individuals ake ino accoun he value of he Medicare coverage provided by he DI program. The benefi elasiciy shown in Table 1 is generally lower among younger ages (below age 62) han among near reiremen ages (beween 62 o NRA). The benefi elasiciy esimaed in our model ha does no ye characerize he Medicare incenive (we will discuss he limiaion of our model shorly) is conjecured o be lower when he Medicare incenives are properly modeled. One issue wih our model is ha we do no ye model he Medicare coverage provided by he DI program. As menioned earlier, Medicare is an imporan in-kind benefi for disabled individuals. People younger han age 62 apply o DI program for no only cash benefis bu also Medicare coverage. Our curren esimaes of he cash benefi elasiciy for younger ages (below age 62) are likely oversaed due o he limiaion of he model wihou modeling Medicare benefis. We conjecure ha once we include Medicare in he model, he benefi elasiciy of DI applicaion for younger ages (age 21-61 and oher younger age groups) we esimae in his sudy will probably be lower. Tha is, individuals DI applicaion decisions will be less sensiive o
changes in cash benefis alone when hey ake ino accoun he Medicare coverage benefi offered by he DI program. Especially when he DI benefi drops, we would speculae ha disabled individuals would less likely change heir minds o apply o DI program considering he value of Medicare coverage. For example, in Table 1, for people before reaching heir NRA (hose a age 21-NRA, which is age group 21-61 plus age group 62-NRA, a mixed pool of possible applicans who should be affeced by Medicare incenives and who should no be affeced, and he pool is dominaed by he former), our esimaed benefi elasiciy when benefis drop by 20% or 40% (1.847 and 2.181) is more han hree imes he esimae by Lahiri, Song and Wixon (2008) who predic expeced Medicare values for a sample aged 18-64 in heir model while esimaing he elasiciy of DI applicaions. 26 Nex we discuss some oher ineresing resuls found in he sudy. Comparing he resuls in Table 1 and Table 2, in general he DI award probabiliy elasiciy is higher han he DI benefi elasiciy. Tha is, people are more responsive o he changes in he approval probabiliy han he changes in benefi amouns. I is consisen wih he resuls of Lahiri, Song and Wixon (2008). In Table 1, unlike he elasiciy esimae based on an average applicaion probabiliy in previous lieraure ha conduced simulaion in a reduced-form model, 27 he responses are no symmeric o benefi increases and reducions of equal amouns. I is also rue for he award probabiliy elasiciy esimaes in Table 2. For example, a age 62-NRA, he responsiveness o 40% increase in benefi amouns (1.959) is only half of ha o 20% benefi increase (3.946). A age 45-59, he elasiciy (1.193) when benefi amouns drop by 40% is more han half of ha (0.513) when benefi amouns drop by 20%, ha is, more han 40% of individuals a his age range will choose no o apply o DI program when benefis drop by 40%, while only abou 10% of individuals will choose no o apply when benefis drop by 20%. 26 Once Medicare is included ino he model, he incenives o apply for DI benefis a younger ages (han 62) would be sronger, and he sensiiviy of DI applicaion propensiy o policy changes a older ages would probably be smaller. 27 Halpern and Hausman (1986) esimae a benefi elasiciy of 1.3 using a 1972 male sample younger han age 50. Kreider (1998) esimaes a benefi elasiciy of 0.7 using a 1978 sample a age 45-59. Kreider and Riphahn (2000) esimae a benefi elasiciy of 0.51 for men and 0.75 for women using a 1992 sample a age 50-61. Lahiri, Song and Wixon (2008) esimae a benefi elasiciy of 0.5 for men using a 1990-92 sample a age 18-64.
We also find some ineresing dynamic effecs in our life cycle srucural framework. Wha seems unusual in our esimaes resuls are he benefi elasiciy a age 45-59 and age 50-61 when benefis drop by 40%, -0.264 and -0.494, respecively. I seems puzzling: when benefis increase, why would DI applicaions decrease? This has o do wih us puing he research quesion in a life cycle framework. As illusraed in Figure 7, when DI benefis increase by 40%, a lo more individuals choose o apply a younger ages. So when we look a he older age groups, for example, age 45-59 or age 50-61, we see fewer DI applicans han in he benchmark model, ha is, before he benefis rise. This effec can be analyzed only in a life cycle srucural model. A simulaion on a reduced-form model could provide a shor-run elasiciy esimae bu will probably average ou such dynamic effec as he changing age srucure of applicans and he applicaion iming shif when here are changes in policy variables. Similar dynamic effecs are also seen in Figure 8-10. In Figure 8, when DI benefis are cu, here are bigger drops in DI applicaions among younger people, and some of hem pospone heir DI applicaion decisions. So we see ha he decreases in DI applicaions a laer ages are no as dramaic as a younger ages, and we even see an increase in DI applicaions a age 56-58. Figure 9 and 10 illusrae similar dynamic effecs when he DI approval probabiliy changes.
References [1] Beníez-Silva, Hugo, Moshe Buchinsky, and John Rus (2003): "Dynamic Srucural Models of Reiremen and Disabiliy," manuscrip. [2] Beníez-Silva, Hugo, and Frank Heiland (2007): The Social Securiy Earnings Tes and Work Incenives, Journal of Policy Analysis and Managemen, 26 (3), 527-555. [3] Beníez-Silva, Hugo, and Frank Heiland (2008): Early Claiming and Social Securiy Benefis and Labour Supply Behaviour of older Americans, Applied Economics, 40 (23), 2969-2985. [4] Bound, John and Richard Burkhauser (1999): Economic Analysis of Transfer Programs Targeed on People wih Disabiliies, in Orley Ashenfeler and David Card, eds., Handbook of Labor Economics, volume 3c (Amserdam: Norh-Holland). [5] Duggan, Mark, Perry Singleon, and Jae Song (2007): Aching o Reire? The Rise in he Full Reiremen Age and Is Impac on he Disabiliy Rolls, Journal of Public Economics. [6] Halpern, Janice and Jerry A. Hausman (1986): "Choice under Uncerainy: A Model of Applicaions for he Social Securiy Disabiliy Insurance," Journal of Public Economics, 31, 131-161. [7] Judd, Kenneh (1998). Numerical Mehods in Economics. MIT Press. [8] Kreider, Bren (1998): "Workers Applicaions o Social Insurance Programs When Earnings and Eligibiliy Are Uncerain," Journal of Labor Economics, 16, 848-877. [9] Kreider, Bren and Regina T. Riphahn (2000): "Explaining Applicaions o he U.S. Disabiliy Program: A Semi-Parameric Approach," Journal of Human Resources, 35, 82-115. [10] Lahiri, Kajal, Jae Song, and Bernard Wixon (2008): "A Model of Social Securiy Disabiliy Insurance Using Mached SIPP/Adminisraive Daa," Journal of Economerics, 145, 4-20. [11] Leonard, Jonahan (1979): The Social Securiy Disabiliy Program and Labor Force Paricipaion, NBER working paper No. 392. [12] Leonesio, Michael, Denon Vaughan, and Bernard Wixon (2003): Increasing he Early Reiremen Age under Social Securiy: Healh, Work, and Financial Resources, Healh and Income Securiy for an Aging Workforce, No. 7, Naional Academy of Social Insurance. [13] Lucas, Rober E. (1976): Economeric Policy Evaluaion: A Criique, Carnegie-Rocheser Conference Series on Public Policy, 1, 19-46. [14] Nardi, Mariacrisina De, Eric French, and John Bailey Jones: Differenial Moraliy, Uncerain Medical Expenses, and he Saving of Elderly Singles, NBER working paper 12554. [15] Press, William H., Brian P. Flannery, Saul A. Teukolsky, and William T. Veerling (1992): Numerical Recipes in C: The Ar of Scienific Compuing, 2ed., Cambridge Universiy Press. [16] Rupp, Kalman and Charles G. Sco (1996): "Deerminans of Duraion on he Disabiliy Rolls and Program Trends," in Kalman Rupp and David C. Sapleon, eds., Growh in Disabiliy Benefis: Explanaions and Policy Implicaions, W.E. Upjohn Insiue for Employmen Research, Kalamazoo, MI, 139-176. [17] Rus, John (1996): Numerical Dynamic Programming in Economics. In he Handbook of Compuaional Economics, Vol. 1. 619 729. H.M. Amman, D.A. Kendrick, and J. Rus (eds.). Elsevier Science. The Neherlands. [18] Song, Jae G., and Joyce Mancheser (2007): New evidence on earnings and benefi claims following changes in he Reiremen Earnings Tes in 2000, Journal of Public Economics, 91, 669 700.
Figure 1: Percenage of DI worker-beneficiaries by age percenage 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 age acual simulaed Noe: The acual percenage is auhor's calculaion based on populaion esimaed produced by US Census Bureau and Table 4 of Annual Saisical Repor on he DI program, 2006. We canno calculae he acual award rae for age 65-66 since we don' have he saisics for populaion a ha age range. Figure 2: age disribuion of DI awardees percenage 30 25 20 15 10 5 0 30-34 35-39 40-44 45-49 50-54 55-59 60-61 62-NRA age acual simulaed Noe: The acual saisics are from Table 39 of Annual Saisical Repor on he DI program, 2006. We include only disabled workers. Their dependens are no included in he calculaion.
Figure 3: average monhly DI benefis by age dollars 1400 1200 1000 800 600 400 200 0 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-NRA age acual simulaed Noe: The acual saisics are from Table 4 of Annual Saisical Repor on he DI program, 2006. We include only disabled workers. Their dependens are no included in he calculaion. Figure 4: average monly DI benefis, by basis of enilemen and age dollars 1600 1400 1200 1000 800 600 400 200 0 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-NRA age acual simulaed Noe: The acual saisics are from Table 36 of Annual Saisical Repor on he DI program, 2006. Benefis are in 2006 dollars. NRA=Normal Reiremen Age.
Figure 5: Median monhly wage for FT workers dollars 4500 4000 3500 3000 2500 2000 1500 1000 500 0 20-24 25-34 35-44 45-54 55-64 age acual simulaed Source: The acual wage is auhor's calculaion based on U.S. BLS Tables of he Usual Weekly Earnings of Wage and Salary Workers, 2006. Figure 6: employmen rae by age proporion 1.20 1.00 0.80 0.60 0.40 0.20 0.00 20-24 25-34 35-44 45-54 55+ age acual simulaed Noe: The acual employmen raes are auhor s calculaion based on BLS Employmen Siuaion Summary Table A-6, 2007 and Populaion Division, U.S. Census Bureau Table 1: Annual Esimaes of he Populaion by Sex and Five-Year Age Groups for he Unied Saes released in May 2006.
Table 1: Benefi Elasiciy of DI Applicaion Change in DI Benefis Amoun 40% 20% Benchmark 20% 40% Age 62 NRA 3.201 2.912 3.946 1.959 Age 21 61 2.180 1.856 0.353 0.299 Age ranges used in previous lieraure Age 21 50 a 3.707 2.755 0.481 0.622 Age 45 59 b 1.193 0.513 0.073 0.264 Age 50 61 c 0.391 0.358 0.101 0.494 Age 21 NRA d 2.181 1.847 0.362 0.306 a. Halpern and Hausman (1986) esimae a benefi elasiciy of 1.3 using a 1972 male sample younger han age 50. b. Kreider (1998) esimaes a benefi elasiciy of 0.7 using a 1978 sample a age 45-59. c. Kreider and Riphahn (2000) esimae a benefi elasiciy of 0.51 for men and 0.75 for women using a 1992 sample a age 50-61. d. Lahiri, Song and Wixon (2008) esimae a benefi elasiciy of 0.5 for men using a 1990-92 sample a age 18-64. Table 2: Award Probabiliy Elasiciy of DI Applicaion Change in DI Award Prob. 40% 20% Benchmark 20% 40% Age 62 NRA 5.000 8.026 6.811 3.750 Age 21 61 3.796 3.397 1.551 1.312 Age ranges used in previous lieraure Age 21 50 a 4.579 4.873 1.620 1.356 Age 45 59 b 3.520 2.220 1.117 0.768 Age 50 61 c 2.776 1.247 1.368 1.150 Age 21 NRA d 3.798 3.402 1.584 1.329 a. Halpern and Hausman (1986) esimae an award prob. elasiciy of 0.2 using a 1972 male sample younger han age 50. b. Kreider (1998) esimaes an award prob. elasiciy of 0.6 using a 1978 sample a age 45-59. c. Kreider and Riphahn (2000) esimae an award prob. elasiciy of 0.67 for men and 0.26 for women using a 1992 sample a age 50-61. d. Lahiri, Song and Wixon (2008) esimae an award prob. elasiciy of 1.64 for men and 1.43 for women using a 1990-92 sample a age 18-64.
Figure 7 Figure 8
Figure 9 Figure 10