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On the Dynamics of Demand for Leisure and theProduction of HealthRobim C. Sickles a & Abdo Yazbeck ba Department of Economics , Rice University , Houston , TX , 77005-1892 E-mail:b World Bank, South Asia Region , Washington , DC , 20433 E-mail:Published online: 02 Jul 2012.

To cite this article: Robim C. Sickles & Abdo Yazbeck (1998) On the Dynamics of Demand for Leisure and the Production ofHealth, Journal of Business & Economic Statistics, 16:2, 187-197

To link to this article: http://dx.doi.org/10.1080/07350015.1998.10524752

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Robj-9 C., $&KLES D ~ ~ ~ - . : - ; ? O - r l o ~ . ~ n t oi Ecocemics, Rice University, Houston, TX 77005-1 894 (ssick!es@rice.eas)

[ ' b d ~ ? y ! ~ z ~ ~ c s < World Bank1 Sou:h Asia Region, Washington, DC 20433 (yaz@pop.access.digne;:(.nei)

Our a~ticle (!evelops and estimates a siructurai modcl of household health production ilia! jointlj Eetemines the dernand for leisure aiid the demand for consumptioll for elderly males. We use a stochastic dynamic progvammiiig lrarne\r.ork based on the assumption that an individual maximizes lifctiine utility subject to budget and time con5!:.ainrs and a health-produciion function by choosing hours oS 1sis;ire and levels of cor?sulnp!ion of health-related and health-neutral goods and ser\'ices. ;V!orcover. we use a wry coinprehensi\e health index that combines four scales measuring a yarlety of di!neniioi~s in the quality of life. 'i'he EuIer equations derived from our model are estlinated Ecing dam from six biennial panels of the Retirement History Sur~re).

KEY V{OXDS: Adult mortality and morbidity: Dynamic programming; Ge~leralized methvd of :nom.ents.

Tvvo o? :he nare imp,oslani issues 912 the economics of health dcal w!Ch labor supply (or its converse. the demand for Pe?st~~e time) and the pocess by which long-run spend- icg on healah-related gcoas and services produces health. F~len tiio~:gh an extensive literahare exists on the relction- ship bemeer, labor supply axd health, especially for the elderly, Llae research has focused primarily on ti?e impact of 14! heslrh OK the aiming of retirement (e.g., see Fuchs 1984: W i x 198, 1389; Kurd 1990: Feinstein 1992). The impact of labor cessarioc and the efecl of iong-run spending gat- 4 ~,,n_s YV on 31eaBth-rei~teci goods and services in the production of good hcallh lzas not been givea as extensive a treatanent . . .. rr t ie 11's~-ate:re. 3ecat1se both 'leisure and healill spending tend io increase as the health of an iadi~~iduai deteriorates, finding a yosithe e8ect of either on health using cross- sectiosal dare or static models has been problematic. The focus of rliis arhicle is on the empirical study of the impact ~f keahth-relared spendi~g and variations in leisure demand oc the pru6uction of good health for a 'growing segment of the U.S. popilietion, the aged. 'We believe that the results presentxi hel-e shcd light on 'he policy debates eoncern- i ~ ~ g ;he determinants of hezlth fior the elderly and the costs of soc i~ l p:ograr?is lo: retirement income and ~ x d i c a l ic- su-ance. In adit ion 'Lo the e~aapi.ric~.,l hndings. we feel that I/* ine strocbiz of the modci we develop can be expanded to EOIC pre",lseiy study inse:~nives in current social programs -e ro-L n . 7 m -eu A bil ,;? t2e elderly a3d to simulate effects of possible

policy changes in those programs. Our article develops and estimates a sarhkctural model

of hwssehoI? health prodxiction that jointly determines she demand for leisure an2 ihe demand for consumption for eIde?y :;;.,ales, We use a sto'chastic dynamic program-

~ P msng xrarnew=rLi based 3c the assa~mption that an indi- vidual maximizes lifetime x~i!ity subject to budget and ~:i;-r~e consrraints an16 a health-production ft~nction by choos- ilrg honi-s of 1eisptl.e and leveks of consumption 01 health- i-elaied end 1Crealth-neutral g o d s and services. Several au-

thors have used this apprcach for modeling labor s u ~ p l y (Heckman E 976: MaCurdy 1981; Hotz, KydIand, and Sed- Tacek 1988). retirement choices, (Earnermesh 1984; Rust 1989) and health prod~action (Wolpin 19884: Rosenrvb.ekg and Wolpin 1988), but they have not formally modeled leisure time and heaith spending as inpus in health production. Moreover, bile use a very comprehensive measure of health. arl index that combi~aes four scales that measure a variety of dimensions in the quality of life. The Euler equations de- rived from our model are estimated using data from six bi- ennial panels of the Retire~a~ent History Survey (RHS), We use a sufhciently flexible form for preferences and health production that allows us to study th-, temporal interaction between health and leisure for t i e elderly as well as i ~ t e . - actions among consranptiom, Icisure. and health.

The remainder of the article is organized as follows. Sec- tion 1 details the issues ir1vo4veii in our choice of model, which is formally developed in Section 2. A description wL' our data and results are presented in Section 3. Section 4 concPudes.

In this sectioim we motivate our empirical model by 'dis- cussing some of the economic determinants of the dcmand for health and labor supply ot- the elderly. We also address the issues of joint health and leisure de~xand, a static versus a dynamic framework. a deterministic versus a stochastic environmentl and the intertemporal separability of prefer- ences.

The relationship between heairh and retirement/ieisure has been the subject of a number of empirical studies, among which are those by Parsons (19XO), Anderson and Burkhauser (2985), Haersrnan and Wise (1985), SicEties

- -

1998 Amerecan StaECsZseal Association Jow~nal of Bus~ness &: Economic Bta'iBstscs

April 1998, 9101. 16, No, 4

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Jouinal of Business & Economic Statistics. April 1998

end Tav.bman_ (1986). and Behrman, Sickles. and Ta.~abmair (6987). Considerable ernpkEcai evidence (Burrless aisd hlof- fir 1984; Dieleep 1986; Rurtless 1987: Sickles and Tawbman 1986, 4997; Bound 8991; Bebrman. Sickles. and Tau'ornan in ~;xssS) s~tpportsttlre ~zotion that I~ealth demand and labor suyply, espesialiy for be elderly. are jointiy determined. Ea- bor su?ply/?eisrzse demand will be affected by health in at least tx;ilo vb7ays. First, the individual's health plays a role in his a'&bilitu/ to work and the type of ivcdrlc Ire can do and ~b.-re- fore is an important factor in Labor-srzpply decisions. Sec- ond, consumptian patterns are ma.jor facie-s -k any labor- sugply decision and thus health-reia:ed consumptioc. espe- ciagly for the elderly. aEec:s leisure demand fhr-ough the budget constrainr. Leisure demand also in8uei;ces l-reaiih in a direct and an indirect way. The direct eEect is caprured in the health-prode~crion func~ion ir? ~;\.l̂ iic!-i leisure is an inpui~ in the production of healin. The indirect effect comes into play through the bndget co:istraini"s eEect on consumption of !aealth-relatesi goods. Given ;;his inreraciion between the two decisions and the ecoinon~etric problems created by Eg- noring depende:~cg~, one mast consider rxodels that expllc- Etiy recognize this joint decern:ination~.

Oi~e by-product of the separate t r e m e n t of ia.bor supply and heailb demand is an uneven development in the eco- nor~ric and econometric rech:~ologies used for estimation. D ~ i r i ~ ~ g the early eighties. major steps were taken toward ;ro~r!.ng labor-supply il~odels away from static one-period models to less restrictive life-cycle m2dels. Meanwhile. empirical health-demand models :For the elderly continued tc be dorfihaied by siunp2e onc-period i~lodels. Tneo~etical ~r,~orl< in labor and healtia econmics has long recognized the life-cycle nat:lr!r-e of labor supply, retirement. and the demanc8 for health decisions, but tlle empirical work. until rece~itly. has typically asscilned a purely static framework. The yeasons usually given for the gap betvieen t!~eoretical end eiilpiricsl work are data a\:aiiabiilta; nild the restric- tiveness of the assur~ptions necessaq to i n i k thc problem more tractable. P77e address ooth of these issues and also presen~t a indriperisd frarnev;ork for joint dete:min~ation es- . .

'LlmaILOn.

Uncertainty about LveaEth accuu;rr!ation. financial needs. heaitk, and job npportun.'zies plays a consider;ible role in de- cisions 02 lagor supply and heaith-services demand. Failing to incorporate lincertalnty ignores very i~xporiant part of the decision-making process that we adhess by rational- expecta"aions srio6,eling in an en~lkonn~eirt of nr~certali~ty in the Joint-determination model.

Two problems associated with life -cycle modeling are siinplifyqling assump~iiocs usrzally employed for tractability- !lameiy, temporal and inierte~:pc.,ril separability. The first refers ts the asscamption that arguments of a l;ti!41y function are not reiated to each other within e time period. This prob- lem can be solved by choosiing f~mctior1a.1 forms iha.t mode! interaction between arguurzlits at each time period. The sec- ond problem refers to treating time as a superficial barrier between an argument in time t and the same argument et :imes i - 1 imd t 1. This is usually sc?ved by breaking thg objecti\ie Ffinction 41910 smaller time-separibie problems,

which allows stacdard dynanaic ~rograini-fifil;g techniqr~es to be used to soY":e the rnaximizetion problem. The price for matken~atical cc:~vecience is the t r e a t n z ~ t of 15e argr~menrs as time separable. A number of authors hrve argued for the use of such preference struc~irres that ii:sorporate forms of state dependence (Kysllalld and Prescott 1982: Eiche~abaum, Hansen, aiid SingPeton 1988: Eorz et 22, 1988). Section 3 presems a i ~ ~ o d c i that iimcol-porates temporal ncnseparabil- ity in leisure, health. and consumption and intertemporal :.ianseparabi?ity in health.

2. THE MODEL AND E!\jjPiRlCAL SPECiFlCiATlBhl

0i"ieegi~ with a :ypical individual, who at each stage of the life c>cie chooses cer~s~~a;~?tisn, leisure, and health to ma~iiinize

where C': is tine reel zons~lrnption of health-neutral goods, T' is hocis of leisure. 2T is health sia,tus, 3 is a discount - - factor equal io 1/'(?1+ ,pj, LE is life exgectancy. and 5 is an e:;pectationr operator. The utility 6~:anc~ior;. C7. is s twice- diiferentizbie concave f~x~zction thar increases in all '01 its arguments.

The per-period budget constraint is

where .it are real assets at the beginning oC period 1 . -'* =

(1 1 . ; ) . rt is the real interest rate, 11; is the real wage :ate, which is assumed to be exogenous. Tt ' is the hours of a~ork. and P,''CIZ are real out-of-pocket health expenditures. As- sume thrr there a e no bequests so that -ALE = 0. and let the numeraire price be 'chat of C!. assume that, as of the beginning cf period t. IT; and r tP l are Icnotvn to the agent but that fciure realizations are not. The time alioca- lion constraii~t is

- rolowing Hotz et al. (1988). interterflporal consepasa.bi1- iry is introduced by equaeing the stock of health capital at <he end of period t j&) with cijrrenl period i invest- ment in health. iit(.)-that is. heaiifi groduc~icp-r, (G~ossman 1972a.)-and a distributed lag of past heaith srocks ( a t ) :

where

- Mere k+ is the ratio of total heaith-Teiated cons:~~nption ic out-of-pocket tealih-related consumption that simply scales out-of-pocket cansalmption :c total health-related conseimption. which iiicludes ~~redical casts paid by rhird- party poviders. a measures the irnpertance of past health on currear hee!ih, and n measures the rare of depreciation oF the influence of past health or, current utlllsy. In this forma- lalion. heaith is coi~posed of two parts. The first is currea?t investment. w%ich is created nsing leisure time ilnd health- related consl~mpticn, The second is the stock sf past health

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" . nrod~>l:ed :1.'ei. ch? ;ife cvc-t-!:I p;..:[icnFar. tfle ii.z:fiahie a t . T~,;nnsra.l ;:?r?fisey:~~::a~i!:~:r il: ir?er;nd;lcc5d by i;lchi";-.,g -;a car- .pq,r %.". . . I ,, .. . !,d?:l-: 2. .:.:~~;i:::~'ieil lag of past healifi ill add.itt.6:~ :o the i.nrrr:2i prTiod'r, i:~:~"s.~~fi-~rai-,~t i.1 health. aiternasiye s9ec.i- ,. . ~ . . :2a::01>. 15 :O mo!e., t::.e :cc:< 5f !:e&;h ii.;ing the ne~-pe;ttel

, 7 " , e T i r p - - .i.. L , . ~ L L 3 - ' r ~ ~ , ~ ; ~ ~ I . o c I I c I ~ LJ :!..,;I ;pe~ii<cslion, the ie;~el gf hea;;il sioc;< at ens ef j : ~ p ~ ; t 8.2 i.!,3&!& Of aeiiod f ia\!es';-

. .~ ~

iseii: :>J 4,ea!&h pli.!r, .!o.:*i per100 s i.epv-ccizred health stock. d;slr:'., - -." 1 - , I I , L C ~ . ~ - : ~ ~ - ;,y?:oach - that U,P : a ~ l o ~ . - is in keegifig

\i:iti;~ ih; EQCL 1: ?( (:SEE) :>-$~dc' ~ ~ ~ C T I I Y ) ~ for der ;i - S L ~ - c,' . . .

Firon 111 !~c&ii ifi~,.r-~?~~rS;:n; 3 7 ' ihe lagged h e a l h ,&ects 011 . . - . ~

current t::iiiti. i'~<.nrec;er. ,r 1.s a cor,\eai~,rii \k7ay lo kcor- . ~ ~;.ori_a:: a Y~rlil? O[ :n'.s::'ei~f;~mh nar;separclbility, This ;~odel

sa.i: L ' .~SG 3~ ;1;;-q.3.: $15 :'j S D ~ C ; ~ I case of tile rationel a & & ~ - 'lion mode: escd tar; Beck-r.. G1-o.ssi~;an, Murphy (199:). in :heii- m,odei. :I 333C i:, d2s;led as a&iciijre if an j~^,crease

. - past c~ulf~.~r; .~~: . ia i~ e:~sers ':he .:nrrertt-perlo8c ~ifiiily f1~l11:- . , . lio-';. i~:ii 112 .Ihc E15ll~ ei ;lj. 1.~~ctde1. past leis;re enlers the

, . . , . CjT-.fi,i-PPl'iGZ; :~ l l l i ; : " r f~ilCS;~:1.

The l~-?;b,y.i.p:-r'lcn ,I ,.,us-- -;or.objec: is fipw~ed in te:.-ii;s of a &!!;alI?ic p7,-ogr27--t ,--:>

. d w,, i i l ~ g 3robe::l. 3 e value f ~ : ~ c t i ~ : ~ i at &.-- a illl la, i IS

- ~F,, iT ,T-k : ( [ )7 ; <:,, (+);+ - 3-,tp;'{)':2-' -1- 31 7771 ,l?(~.,, (f'jjCtj (1"

-7 \

(8)

* " d L\? :lit

- - 7 - 7 - ktLL'7!(~!) -, ;, >. L T ( f ) t j , T ) (c ) - , . j ~ < ~ r - l f ,.,,! l t) - 3-2 lj-,:/-f+l:, = 2, " :' " -4 ,

(9)

7 - :?J>i~s, :.-,- ,[he :;1.,.;3pi. .3.e.r;~;,m x+Ld the lay$: of i~efated ex- . - -

Ip?~$:ti~>:. v"3j5 car! i;;n:t : C L ~ ~ ~ I . - - 1, -' (; 3s .-.

. _ _I 8 I-!=;-,. ( - I - ; ? 321rt+L' ., -- 7 i ; :' ,.( - . - L t T t .I 410)

,..rp G!

7 - 1 - - 7 - \ - , ( t ) + ( l - , , ; ' j~ ' , - ,~*l

- - - E,L:LIq(Lj -1- (1 ~ ,/;:!;~;3tc[,7H(t- l),3:;1-z;

-~~ - - - * L- - - bt(.!L - ,+r( - 7)it1 - ~ 7 ) j!Tpt~ (ii) i,. --

l - I

f- .-,... - *.,,. 11 uln-ng F , , ~ L i a ; i c ~ ~ j1.G) ~>.nd ( 1 : 1 5 ' ; tinlie pei-iocis [. i + 1, ~. * .

cr!d f L 2 !~!.~.nh 'i-~e z:.le~i eq;l,a'c/3cs $7)-(91, b:p, s~Ms':~&~u.';

and

Hquatio:as ( 1 :!), :i 3) , and ( i 4.) can 5e estimated v~hei: e f u x - tion?J form for the ntfliiy fiinciior, an s ilze 2rodta.ction ~LIIX-

tifill I,s speci+jed. P,f3;.ca.er3 5ecause 5qrrations (12). (135, and (14) zero expeclae.;on. rS2hxi:io~s of ?~itl l l .~ T6li-

dom 7:ariabEes 171317?14! tha.1

and

~,vihcse ciTl = ((E~,~,-, . z . , , - ~ . F ~ . ~ _ ~ ) is a wctor of Col~ecis! errors associated ivitl~ the 5;st-order co~:ditions a; period f . 3:a:isnal expec'&oils iT:1ply i.l;at Et(r,,l) = i] an3 ?has +)ha* - c t + i is orthogonal to the i.~fori:iation set of period t, !its where the forecast er-yms for a - eiicn indivi&aS a;e a.1-ially unto:-re!ated.

Wc next ,'or-rnrriate :he geuierali~ed rrxtbodi of liqomcrtz (GPANf) eszir~ato: (Elansen 1982). cqloidng in the choke of iastr:jrne;lts t h ~ , fact ;hat i;be i.zi-izbles ir the inforilialion set 2, are or+hogonal to _r i l l . We assume trans!op fi~nciion.l fcr112.s fo"& the ?.~iiLij:y end pr-duction 5ncrions. 7-he j ~s~ i~~ey faficrfion is

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Jouinal of Business 8 Econom~c Stat~stlcs, Aprll 1998

Lip = ( C 2 + S i In C': + j6 111 I f t + In T;)/T~ ;I; (20)

and

k = ( ~ ~ + ~ ~ l n ~ ~ + ( ~ l ~ ~ ~ ~ ' + < ~ l n ~ Y ~ ) / H ~ . (21)

The health-produc,iior, function is

with marginal products

hc\ = + PS!n 7" 1 1n(ki~,h))/(C',h) (23)

and

h p = (Fz + F3 1n(ktC':j + P5 I ~ T ; ) / T ~ (Zb)

Substitnting these marginal utilities and marginal pxodv.cts into Equations (15)-(17) resnhts in the first-order conditions being parameterized by

00 = (<I% < a j 13. S5,56. i 7 ( 8 . <9.

rl. r3* r4; r5. 0. r,. J ) .

Table 1. Quality of Well-Being: Mobility, Physical Activity, and Socal Activity Scales

Ste,o number Index definition Weight

Mobility scale

No limitations for health reasons Did not drive a car. health related; did not ride in a car; andlor did not use public transporta- tion, health related: or had or would have used more help than usual lor age to use public transportation. health related In hospital

Physical activity scale

No limitation for health In wheeichair, moved or controlled move- ment of wheelchair. moved without help from someone else; or had trouble or did not try to lift, stoop, bend over, or use stairs or in- clines, health related: andlor limped, used a cane, crutches, or walker, health related: andfor had any other physical limitation in walking, or did not try to walk as far or as last as others the same age are able, health related In wheelchair, did not move or control the movement of wheelchair \kfithout help from someone else, or in bed, chair, or couch for most or all of the day, health related

Social activ~ty scale

No limitations for health reasons Limited in other (e.g., recreational) role activ- ity. health related Limited in major (primary) role activity. health relatec! Performed no major role activity, health re- lated, but did perform self-care activities Performed no major role activity, health re- lated, and did not perform or had more help than usual in periormance of one or more self-care activities. health related

Table 2. Sample Summary Stat~sfics

Varizble Mean Stzndard deviation

Desired hourslyr. 4,751.6 i ,561.1 Other consumptioniyr. 2,143.1 3,241.6

(discretionary) Total health-related 1,939.0 10,747.99

expenditures Out-of-pocket health 326.9 701.9

consumpt~on.l~~r. Wealth status inde:: 1.61 .28 Hourly wage 5.01 4.83 Number in the household 2.35 1.46 Expected S.S. benefits 1.570.8 1,64 0.2 Years of education 9.75 3.61 Married .77 .42 Widowed .15 .36 Divorcediseparated .03 .17 Black .09 .29 Professional . I9 .39 Management .16 .36

Letting XZt be the vector of variables entering the ith in- dividual's first-order condi'iions in period i. we can1 express the (1 x 3) system 115)-(17) as f j X 2 t . Bo) = ~ , . ~ + l . Rational- ity and ils Implication that information in R,+ is of no help in forecasting future shacks implies that E [ f ( X Z t . 80) %? ZZt] = 0, where ZZt is a (I x h) aatrix of elements of Q,,. The poplaiation orthogonality condiiioas for the years that the panel data are available can be derived by averaging over time,

Sample analogs are then constructed by averaging over the random sanple of ~ 3 ~ - individaals.

and GMM estimates sf O0 are defined as the

where T'EiA- is the symmetric positive definite weighting ma- trix

and where corlsistent first-step estimates of (3" are based on setting the weighting matrix 11s to the identity matrix.

The asymptotic covariance matrix for the GMM estima- tor is

S

cz, = (LP;-S;~D~\-)-~. n, = (iji,~'~(x,. z,. z = l

3 5FTA AN";19MPlRBCAB RESULTS

Daia from the WHS were used to estimate ow dy~~amic

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S E C ~ ! E S and Vazbeck: Jemand foi Leisure and the Production of Health 191

72bls 3. Parameter Estimates and Standard Errors (consumption and ksisure separable)

<3 -.79?3 r ' ~ (.C322) (.C61?) (.01 93)

i 4 -.'I314 r3 .0026 (.0441) i.0039)

<5 -.3602 r4 .0057 (.I 371) (.0062)

C6 5948 a ,0101 i.391 1) (.0811)

b .0712 '7 ,0876 (.0519) i.0693)

<a ,8874 + 7) ,8966 (.1274) j.5169)

heakth/leisure model. The BHS contains six biennial pan- els taken duris:g the period 1969 through 1979. The RHS is a nationwide random sample of k 1,000 men and women heads of households, aged 58 to 63 in 1969. who were rein- terviewec every two years. We restrict om an2J;lysis to men to reduce heterogeneity. We augment the WHS with data from the Social Security hies cln death and Social Security earnings begincing in 1951 that have been used in previ- o t ~ s analyses by Sickles and Tal.nb~nan (1984) and Behrmar,, Sickles, Taubman, and Yazbeck (1991).

The choice of how to measure health statlas presents a complicated problem. Ideally, a measure of health should reEect the individual's physical and mental well-being using a standardized icdeti. Lrnhrtunateiy, such indexes cannot be constructed horn information in most datasets. forcing researchers to rely on sribjective and objective qual- italive proxies for health status. Subjective measures in- chde information collec~ed from individuals about their awn health, b:st objective measures describe heiilth infor- netion collected from a sonrce oeher than the individual in qnes~ion. Two typical examples of subjective health mea- siares for the eider-ly are answers to questions such as "is health a reasoil for your retirement?" or "would you say that your beal'rh is better, same as, or worse than that of ather people your age?" Several problems exist with these measdres. First, poor "nerPlchz is z. socially acceptable reason for retirement, and therefore it is possible that an individual n a y cite i l as a reason for retiremerat even when it is net. Second, the subjectivity of the answer makes it difficult to c o q a r e results 2~~021g the individuals. Third: some retire-

ment benefits are a function of an individual's well-"oeirzg that creates an incentive for inaccurate description of one's laeaith sta:srs. These problems with the subjective measures lead to biases in estimation but would seem ta pull ir, npp- site directions. The inability to corxpare among Indiviciuz.ls is a measurement error that is likely to e~nderestimare '195 impact of health. Conversely, the other two problems weuld seem to overestimate the irnpzcl of health on retirement.

Objective measures of health are not without their prob- lems. The razost often used objective measure is retrospec- tive mortality information. The fact that an individual died within a follow-up time interval is more objeciive than a self-reported health measure, but it airay not be an accurate description of the impact of health on labor serpply. For e::- a.mp?e, deaths that occur suddenly f ron an accident or a disease h a w little or no impact on iabor/leiserre decisions while the individual was alive. Such objective variables will suPFer from errors-in-variables prablerns and bias the results by underestimating ;he eEect of health on retirement, It is interesting to note that most studies that use objective mea- sures such as mortality data 5nd health to be less importaat in explaining labor-supply decisions than do studies that use subjective measures. This result is interpreted as indicating biases iil thz subjective measures while ignoring the possi- bility of bias in objective measures. One argument for the use of subjective measures is chat they have biases work- ing in opposite directions, whereas objective measures have biases that may not cancel out. Analher argument fur the use of self-reparted measures can be found in the public- health literature, where subjective ratings by the eiderly were found to be highly correlated with their phg~si&~ans' ratings (Ferraro 1980; Mossej7 and Shapiro 1987).

Our study combines subjectkre alrd objective measures of health in an index constructed along the Iines of the Qraal- ity of Well-Being (QWB) index developed by Kaplan and others (Kaplan and B ~ s b 1982; Kaplan and Anderson 4988; Anderson, Kaplaa, Berry, Bush, and Rarn~baut 1989). QWB combines four scales that measure mobility, physical ac- tivity, social activity, and symptorn/problem complexes. 4~ developing QWB, Ka.plan and Anderson (1988) integra~ed morbidity and mortality, building on a considesable body of theory in economics. psychology, medicine, and public health. Three steps describe the index and ics development.

Table 4. Heaith-Reialed Consumplion Elasticity of h'eaith Production--Consumptio~ and Leisure Separabie

Year12ge Cohort 58 Cohort 59 Cohort 60 Cohort 6: Cohort 62 Cohort 63

NOTE- Entr~es a1.e cohort means wth their standard deviations n parentheses

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J~urna l of Business & Economic Statistics, April I998

Table 5. Parameter Esfirnaies and Standard Errors and the Socia\ Security records. The subjective/objectiw (desired leis~tre model)

52 -.2171 f j - . 1 604 (. 1027) (.0246)

53 -1.0573 r2 ,1164 (.7795) j.0855)

i~ -.1 108 r3 ,0051 (.0136) (.0045)

c5 ,0234 r4 ,0405 (.0034) (.0214)

(6 -.0185 f 5 ,2863 (.04 02) (. 1 002)

57 -.0137 a ,0990 (.0033) (,0711)

i 8 .I 220 ri ,3077 (.0395) (.1212)

(9 1.1473 7)!(0 + 11) ,7566 (.I 482) (.2609)

h the firststep, a comprehensive stt?&y kvas undertaken to enumerate the links between disease and injuries and be- havior and role performance. Then three scales were con- structed representing related bmtiiistinct aspects of daily f~~nctioning-mobility, physical activity, and social activ- ity. The second step focused on subjective comp?aints as an important component of a general health measure iead- ing to the development of a fourth index relating to symp- tom/probiem complexes. The third step integrated the tlhree scales and the subjective index into a single index. In con- structing this final expression, weights were assigned to the various levels within each scale and among scales based on lneasured preferences of health states or "quality" judg- ments frop- 2 representative random s a ~ p l e of 866 indi- viduals who were asked to evaluate the relative desirability of specific health condidons. The estimated shadow val- ues of health conditions were found to be quite stable over different stratified subsamples. A description of the empiri- cal svorh- was given by Kaplan and Aflderson (1988). These shadow values were then used as weights in the ,QWB index.

The WHS allows us to construct direcrly the first three scales. The conditions that malie up these scales aa-e given in Table I . Detailed informatioia needed to construct the s.jmptom/prob?em scale is not avaiiable in the RHS $1- rectly. We thus mocPify the subjective in6ex by using the evaluation of heads of houselholds' heaith relative to people their age augmented with death information from the RHS

health-status variables \were discussed at length by Sickles and Taubrnan (1986. 1997). We assigned to ii~ese four health statuses (I-nealth better/same/worse than those the same age and respondent died during the same period) the Kaplan and Anderson symptom/probiern weights using a weight of O for health Che same. the grcup sympia~n/p~oblern c o ~ p l e x weight for health worse, its negative for health better. and an index of -1 (the vaB index ranges from 0 to 1 as health deteriorates) for those who died during the sample period. Vie then scaied the index to vary between 1 a ~ d 2 as health improved.

Several treatmerits for measuring leisme are possibIc (Hurd 1990, 1997). One Is a trichotomous va~-iab!le indi- catifig whether an inldividual is retired. semiretired. or sliI1 kvorking full-time. Another is to drop the sen.-tiretirement observations and construct a c l u m y variable of the remain- ing two outcomes. The most ofien used index in em.pirical labor studies of the elderly, however, is the working-fcll- time/no-i--~n~ouicing-full-~irne dichotomy. Sicliles and Taub- man (1986) tested the aiternalive definitions and chose the last option. They found con~parable eresu.lts when using al- ternative definitions and chose the full-time-work versus less-than-full-time-l~orlc because of simplicity and compa- rability with o t h r stbadies. We choose three digereat treat- ments for the binding leisure constraints that cmse Equa- tion (17) not to hold and that a e computationally feasible and reasonabky straightfornard to im~lement. T i e first is io assume that csnsu~nytion and leisure are separable in the consumer's maxi~ization problem [Eq. (631. W-e then esti- mate the model with leisure choice as a state variable. Tnis yields the system of equations (15)-(161, without the Euier equation for leisure, Equa.tion (17). The second and third treatments modify the leisure data so that the constraint is not binding and use ail three eqeations [(1)-( 6711.

Tne second approach cons'rmcts a reduced-for= measure of the desired leisure variable and uses the observed wage (or wage on last job inflated to the present). We represent the Pevel of ieisure by a continuous variable gotten by sub- tracting the number of hours actually weriied from total available hours. For tilose who have retired. this variable will be limited and the virtual wage to which it corresponds will differ from the observed wage (or wage on last job). We used observed wages '(or. for those ~aot working, wages

Table 6. Desired Leisure Elasbcity of Health Production

Yearlaae C o h ~ r t 58 Cohort 59 Cohort 60 Cohort 61 Cohort 62 Cohort 63

NOTE. Entiles are cohort means with standard dev~atons in parentheses

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Sicltles and 'iazbeck: Denland for ieisuce and the Production of ?eal':h 193

Table 7. i+.eaitn-Relatsd Cor-isurn,oibn Eiaslicity of Hsaiih P r ~ c i u ~ t i o , ~

:/Ear/sge Cohort 51: Cohort 59 Cohori SO Cohoif 6 r Cohort 52 Cohort 63

NOTE. Entries are cohori means w i h r'ler standard devlziions In uarenlhzses

on the last job in cuireni. real dollars) and cc?nsaruc:'.ed the lwei of desired hocrs for those who retired. The RXS a.1- lows us t~ form such a -variable because respendents axe asked about ihe hours of work per week *3 both their px t - tk-sii-, aind full-time jobs. Vie base the leisure vari;ibl"e ou: yearly hwrs of work by estimating 'lcbit reduced-foran re- gressions of zverage desk-ed hoa~rs of leisure. W e notc that health depends on ~-onrnark~,t ' ; h e aliocateel to its produc- "I.on. We have ;lo cEaia in the KHS, however, that lets us constract sir,ch a variable, W e feel that, hi the least. charages in leisure-tl:xe allocations wolpld cq3msre the essentl.a.1 dy- namic of the tirile allocations that provnde the individuals in our sample with the potential fsu heal111 augmertatiofi;_. in this way the constraint in Equation (17) Is no1 biadirmg because the cptii~.ization problem is ~efra~:?ed in terms of desired levels of wcrrk and I7ence leisure, These are a h bou~ded av,ljay fimm coslzcr solutions. T:-ie in~pacts a! :;he leisure variabie 017 our estirnatea will 5e explored Yai-er.

The third approach ~tsed observed ??,ours worked ax$ con- :structe& the vlrlual wage f31. those who had stopped work- ing. Hours for thsse whc retired fuII-time were 3orailded eway from zero hmrs worked. Construction sf the virtrral

-7 wage was based on the .idaies and Woodland (1983) and Lee aad Rtt (1986) ~~~.e:hociology wherein the interiem?o- rai marginal rates ohsubstitution between co~asuinpiion acd leiswe were eq~iated t~ the relative ?rice of consunpt:on goods and tF: virtlial wage rate, With ';he price of con-

Tab! 8. .%rame!si Esiimaleo and Standard Erjrors j!/ifiua! wage model)

-. .-

C2 ., ?- -. tua0 r~ -.2322

(.0557) ( 0291) <3 - 8649 1 2 . I 122

(.4.377) j.0941) GI .1007 : 3 .CC57

- (.O? ~Ifi,) (.0039)

6 ,0278 Ta 0560 (.0039; j.0259)

<6 - 0002 f 5 ,2183 (.0001 '1; (.0777)

C7 -- .o; 4.0 (1 ,0501 (0061) (.004i )

Cs .I 1 d.4 7! t 954 (-033.) ) (.07.1 1)

i s .7391 11/jo -b r j ) 7959 (321 1 ) (.0812)

sunrpdon gocds normalized ro be miry, this meant that the virtt~al wage 1s gi;ien by

The l:i;-taaB wzgr is a fuzctlon of the r:niinown st:-uctural -"-, ,ialdmeters for thsse who have retired and is solxred for

itereti1;ely in an ahg0:-itL11;1 nested \<vithtn the GMIM algo- rithm anC reevalu~tsd at each step in which parameters ase changed Za the search atgou-ith;n, We shall discuss estimates based oil this a;pp-oach later.

The wealth 31: variables in the KF"ISalso allows us to toll-

slruct the ;lonhealtia consarrrpiian and health-related con- sumptior. variables. The itonhealth consumption variable . . , (net of t:":oos~ng expenditures. Food, and cloth317g) consists of expendiiir-es 6n gifts, e~~tertainrnent, charitable srga- nizzcier~s. social orga::izations, rans sport at ion, vacations, trips, urililles, and nocfood grocery pnrclxiises. We thus assume that the :r.tnli';y Fmction is sepxabie in these ex- cluded ~~o@discl.e:,ionari.iscrear sons.cris.ption categories. Beaith- related expendit~~res chat were ovi-of-pocket (Cp) ificl~dec? health insarance. doctors' bills, hospital stays, prescription drugs, anti olher ~meci~cal expenses paid by the respondent or spo.~lse. and total health-releied expei~dituses (kt Cft ) in- ch~ded torai rnediccl. haspltal, an2 doctors' costs not paid ~ I J the 1-csponde~c or sponse. Finally, we excltide edircaiion from ihc poducf on functioc and implicitly take the view of Kusenzweig a d ScbcLrz (1383, 1988, 1991) that edu- cation has ar? ~.IIara:ive bat ml: kt technic21 etfect. Fop a!ternat;eive z~r,roach, see G r a s s ~ n a ~ ~ ar?d Joyce (1990).

The set of variables we rise as instruments ar time i sre contemporene~us 11aiues of the hourly wage rate for thase q~ho work and tine ho~tily iwge on last job for. those who are ,rot wo.k' ~n,. .. r NILI~I ,LL~ - .-- - -- of people in the household; expected

Soci.a.1 Secapily benefits: education: dujminmies for currently ~xarrizd, wi:ls,wed. divozced/separa~ec'r iexcluded sategorp is II~VSJ. ~xrriec?): a d i ~ m m y -for a?cln~r;hite; dunnarnies for Iccgest occspasion In 111. professions or in management; lt~nd age. "Pe d e k e t h s c ?.;hose longesc occupations are iii

~. . farming or in the nairtary. Sample sun.arnary statistics of all ,.I- U.Y ~lihl-iabies 2nd \la:-iabk desc~iiptions are presented ii? ?a- 5 s 2, Social Secarity benefits are those one would expec: to receive i f retirement begins in the respective year. They arc

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194 Journal of Business C? Economic Statistics, April 1998

Table 9. Leish2re Elasticity of Health Production

Yeariage Cohort 58 Cohort 59 Cohort 60 Cohort 61 Cohort 62 Cohort 63

NOTE, Enirles are cohort means wlth standard deviations in warenrheses

compuacd using covered earnings taken from each person's Social Security record, which is part of the RMS. and then replicating the Social Security rules. To do this. we first calciilated each person's avenge monthly earnings JAME) by using the respondent's earnings since 1951: which were truncated at the maximum allowable earnings level. The five lvyvest years of income were dropped, and h e sum of the remzining incomes was divided by the nlnrriber of months worked. The resulting AM", was then used to compute the primary insurance amount (PHA) based on the tables An the Socia! SecuriQ Handbook. These account for Infiation and therefore change over the 1969-1979 sample period. Once PIA was computed, the benefits total was determined on the basis of PliA and marital stati~s. By using benefits available rather than those paid to actual retirees, we woid an obvi- ous selection problem. Missing observations and selection on male heads of household at the beginning of the sam- ple period (1959) reduced the sarnple to 5,359, and sample attrition due to death reduced this number to 4,369 by the end of the sample period ('1 979).

For aTi models the coeficient on the logarithm of con- sumption of nonhealth-related goods and services was nor- malized at unity. The annual discount factor 3 is set equal to ,955, and the real interest rate is equal to the average real three-year treasury-bill rate over each sample period. The GMM estin~ates of the system of Eiiler equations ( 1 5)-(161, assuming that leisure time is separable from consumption,

are presented in Table 3. For this model the parameters ta. c8. Tar and r5 are not identified and are set equal to 0. The number of overidentifying restrictions is h - k = 11: where k = dim(8) = 11 and h = number of orthogonality conditions ( I ? for each of the two remaining equations). The Hansen chi-squared test statistic for the overidentifying restrictions is X 2 = 2.51(x~95,11 = 19.68). The patterns of s a ~ p l e average marginal utilities of health based on Equa- tion (21) are higher than those reported when leisurn ,, 1s ' a choice variable. Estimates in 1969 for the cohorts ages 58- 63 are .639, ,645: ,651, ,652, .664, and .676 and in 1979 for the same cohorts are .638, 557, ,702, .701, ,622, and .626. Sample average estimates (at the median time period) for the marginal utility of a thou-sand-dollar increase in health- neutral consumption are .027 1, ,0194, .0244, .023 1, .Oi98, and .0294 for the 58-53 cohorts (standard errors are .007S, .0059, ,0083, .0079, .OBI, and .06961).

Table 4 reports the health elasticities of health-related consumption, respectively, for each age cohort. The elastic- ities are positive across cohorts and time, indicating a sig- nificantly positive contribution of health-related consump- tion to better health over the life cycles represented in the RMS. Our results are in agreement with two-stage least re- sults of Grossman (1972b), who showed that the sign of the medicai-care coefficient Is reversed when reverse causal- ity is appropriately dealt with, and with Wosenzweig and Schultz (1983, 1988, 1991) and Grossman and Joyce (1990) in the context of birthweight production. The health elas- ticity of health-related consumption ranges between .030

Tabb 10. Health-Related Consumption Elasticity of Health Production

Vear/age Cohort 58 Cohort 59 Cohort 60 Cohort 61 Cohort 62 Cohorr 63

1969 ,0434 ,0423 .0415 ,0433 ,0431 ,041 8 (.00071) (.00093) (.00076) (.00080) (.0008l) (.00089)

1971 ,0392 ,0399 ,0384 ,040-i ,0402 ,0429 (.00066) (.00070) (.00072) (.00074) (.00070) (.00108)

1973 ,0366 ,0372 ,0348 ,031 0 ,0321 ,0476 (.00080) (.00087) (.00086) (.00082) (.00070) (.00125)

1975 ,0451- ,0424 ,041 8 ,0393 ,041 8 ,0424 (.00082) (.00082) (.00083) (.00083) (.00081) (.00086)

1977 ,0420 ,041 4 ,0399 ,0387 ,0431 ,0370 (.00088) (.00094) (.00092) (.00010) (.00092j (.00072)

1979 ,0442 ,0442 ,0433 ,0422 ,0478 ,0327 (.00095) (.00102) (.DO1 03) (.00111) (.001 10) (.00087)

NOTE. Entrles are cohort means with the~r standard deviations In parentheses

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Slckies and \.'azbec!<: Demanc. ini Cei!jure and the Production of IHealth 195

3ild .033. The cstirnaie of cr. which ~neasures the weight of past heelfh in cursent ~~tgllty, ic rather small at ,0101 indi- caiiilg the relaiivedy shnri-lived memory that agents have af pa" health when evaluating (current preferelrces. The es- timate of ii !3 .0876. enii i*1 measures the rate of deprecia- fic~8 of the iniixence of past tt:aEth on current utility, The irn:~lked weight on scrre2t health in current ertility can be assessed by cdcnlaiing liljn 17 ) = .8966. which indicates she iqpxtaoce ?laced 011 currerat health. Tire relative impor- a x e OF past h e ~ l t h to scrrent health, a/?l3 is .P153, which i?dic~bes zi subseaaria! role for dynamics in the health- production function.

GhIh4 estlmaces onsed on our second treatment-the de- sired hours and obsezs-ed wage model and the full system of Equakioixs ( i 5)-( 17)-are presexted in Table 5. The Hansen chi-sqaarcd rest s t ~ r i s t ~ c foclr the overidentifying restrictions is 3L2 = 1.E9i ?c:g,,,, = 28.673. The patterns of sample sv- erage rnal-pinal uriliiies af health based on Equadon (21) show n rather :oasisrenz pattern among coisorts and cver , Llt,le. .*-. - hsiizatcs ir 1569 f a e tile co!:;n:-ls ages 5 8 4 3 are .06159, 2563, .0653, ,065 1. .0453, and .0641, whereas es- iilrnates In 11979 Fsr 3hor t s oi' individuals s:iFE aiivc in- (I:-.- ,k ,~ate a marginal crilily of health of .0579, .63556, .0530.

.65!.71 .0527, a d ,0498, isdicetilag some diminishing re- ,:Firr:ms boih betwces zLnC 5~;fthin cohorts. SaimpEe werage es- ~knates (at she medien time peri3d) for the marginal utility of a Choilscad-duller iccrease ir! health-neentral conscmp- +; .Luln are ,0327. 331 1 , .3235, .C354, .OIP8, and .O461 for the

53-53 coho:es (sta~~dwci errors are .00214, ,00212. .90258, .C0489, .00?4!3, aj:d ..0'0733), Comparable average estimates of ;he ma!-gi:?al utili;;~ of a thouand hours of additionzl

- . . annac. L ~ P S U ~ F , based oq Equation (20) axe ,0238. .3236, ,225 6, :2185, .02$7. and .Oi 8 l (standard errors are ,90094, ,000869, .08@929, .OOGS%!, .J6158, and .000795).

Of particrrI.ar interest are the health-production results that x e swealed in per: 5y th,e ccaeffcient estimates of - : - r;. We analyze bI?e heaI::S~~-prod~~c:io~ resv.;lles as she cohorrs age during :he sample period Tables 6 and 7 report d i ~ hehlth elasticities of desired leisure and health-related coiisor~~ption, respectivel;~, fo'or each age cohort. Both iets of

, . etaticities are Fosrtriie nross cohorts and time, indicating R cig~,Sijcantly psittive contributio~ sf desired leisure and health-rclai:ed coasumnptiolz 10 better health over the life cy- cles represenicci in ihe RHS. We found that the magnitude oi' estmated heabh elasticities with respect to leisure are rather- stable, ~,a.q$ng benvzen .59 and .69 ~ r i t h some slight m~wwra t;e~;d oxre. time. The heai'ih elasticity of health- related constirr~lian is between .03i and ,045. The pattern of cons~srnpricn eiastici:l:s indicates some increase over time for each coh~r t , srrggesting the increased imi3oria1ce aF he~~kh-lrelaied cc:~sun~.p'rio~~ in the roductiora sf health a s ,ndi.l;ids?als reach the ?eru:tiana:e event.

Finsly, the es:irfiate of n is rather small at .093, again in- dicating ,he i-elatKv~_iy sI~oi-t-jit7ec1 memory that agents have o~f past hez l~h 'vihel-i evaluating currenl! preferences. The es- il!nale of q is ,308. 30:h of these have increased from the first treztmeni. The implied weigh; on current health to cur- rent uiility, ~ : ! ( a . ~ 7). is ,757. ?!lough current health is sf11

highly important: this measure has dropped some from [he first treatment. The relative importance of past hcakh 10

current health, a/?/. is .3247, which again indicates a sub- stantial role for dynamics in the production of health.

Estimates based on onr third treatment-imputed virtual wage and obserxled hours of leisure &re provided in Tables 8-10. The Hansen chi-squared lest statistic for the over- identifying res"tictiors is X" 6.77. Owing to the Ehighly nonlinear nature of the vil-tual-wage model, the estimates x e not as: uniform but are comparable to those using the observed wage and iralputed hours. As before in the ofher two treatments, the elasticities indicate that health-related consumption and Ieis~rre contribute positively to the produc- tion of healih. Table 9 suggests a somewhat lower overall health elasticity of leisure with elasticities ranging fro- .23 to .30. Table 10 points to estimates of health elasticities with respect to Z~ealth-related cons~mmption ranging from .031 to .048 that are quite close to those in Table 4.

Again. estimates indicate short-lived memory of past heailla when evaluating current preferences because c - is "05. A relatively large weight on current health to cur- ren? utility Is f w d to be .796, which is similar to the find- ings using the second treatrmen?. The relative importance d past health to current health is ,2564. which f~Els between the findings in the first two treatments.

This article develops a frarneworl< for the estimaiion of a stochas:ic dynamic modei of demand for health. leisure, and consumpiion goo&. T i e model we have de:le!cped al- lows us to study important decisions oC a growing segment of the U.S. papulafion. Choosing a life-cycle framework witla uncertainly creates coinputationel and interpreta*,ionlal complications but presents a richer representation of the dynamic decisioc-making gxocess. Incorporating forms 01 intertemporal nonseparabiility also enl-iches the n~odel by allowing interaction among sample periods.

The RHS presenis us with a data structure suitable for oras model in that it permits us to track h e decisions of elderly citizens over an extended period of time. Our em- pirical results poine to the irnporLani sole tha: dynamics play in life-cycle allocation decisions and to the importance of these dynamics in identifying ihc linkages between %ik- cycle consusnpdon expenditores on health and health out- comes.

Vv'e thank Jere Behrrnan, James N. Brown, Peter Harr- ley. Michael Meane, Thomas Ksmiesner, Ellen Read, loh:~ Rbast, Paul Taubanan, Jennifer Williams, participants of the Eco~lornetrics WorHtshops a.t Michigan State University and Indiana University, arid an anonymous referee for their use- ful and substantive comments. The usual caveat applies.

APPENDIX. DEWIVAT~ON OF EIILER EQUATIONS

The mb~~kmtzatlon p r o b l e ~ I S chzraclerazed as a dynam~c

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196 Journal o i Business & Economic Statistics, April 7998

programming problem. The value function at time t is Next, rewriting (A.3') yields

~ - ~

+ ~?EtVt+l(At+~, a,+l. T?Vt,,). (A.1) From (14.9) and (A.8) we then have

where V t is a function of the state variables At. at. and the wage rate i.T:,. The 5rst-order conditions with respect to Et,3V:+' = EtadVH(t + 1 ) Cf. O;h, and Ti are

E ~ [ ~ ~ c , ~ ( t )hCh (i) - ?7ip/\/::-l + J ~ ~ v ; ~ I ~ ~ ~ ( t ) l = 0. Finally substituting (A.10) Into (A.3') yields

(A.31 r Et PLiH ( t ) / z c n ( t ) - ~ ' , o (LIP: + 3kthch ( f )

and

Et .L-T, ( t ) + C p ~ ( t ) hTr (t)+31/:+~17~~ ( t ) -Jfi!ti~tb-i-l~ = 3 arH(t - 1) - [ ( I - 7);

(A.4)

Using the envelope theorem and the law of iterated expec- tations, we can write k:: and 1,: as

- ~ ~ ~ , j v i + ~ = Et?tqil102irt72 A - .I (A.5) Our last first-order equation (14.4) can be rewritten by sub-

stituting in (A.2) as and

v," = f idYH(t i + (1 - rl)31/2-' Ef [Up (t) + i;l(tjhTz ( i ) - d ~ , ~ , " + ' h ~ ~ ( t ) - I/&Cco(t)] = 0 .

= EtaUH(t, f (1 - q) . i?[Etac~( t - 1) (A.12) +(1 - r i )3~,;-2]

T Rewrite (A.3') as - - E ~ c ~ u ~ ( T ) [ ( ~ - rl)djr- t . (A.6)

r=t

We next show how the value function can be substituted out of the first-order conditions (A.21-@.41. Multiplying jve can substitute (A.13) ~ n t o (A.12) to get our final modi- Equation (A.2) at perbod t + l by yt and 3 yields fied Euler equation

E+8-;tLic~ ( t J, 1 ) = CITco ( t ) I?; hTl ( t )

Combining this with (A.5) allows us to write (A.2) as kt /i,i~ ( t )

[Receil.ed March 1994. Revised Jime 1997.1 Next (A.3) can be written in terms of (A.2) as

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