The longterm care problem precautionary saving and economic growth.docx

The longterm care problem precautionary saving and economic growth.docx

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Thelongtermcareproblemprecautionarysavingandeconomicgrowth

JournalofMacroeconomics

Volume29,Issue1,March2007,Pages60-74 

doi:

10.1016/j.jmacro.2005.04.001 | HowtoCiteorLinkUsingDOI

Copyright©2006ElsevierInc.Allrightsreserved.

  Permissions&Reprints

Thelong-termcareproblem,precautionary saving,andeconomicgrowth

Noriyoshi Hemmia, 

 Ken Tabatab and Koichi Futagamic

aFacultyof 

Economics,

 HokkaiGakuenUniversity,4-1-40,Asahi-Machi,Toyohira-Ku,Sapporo062-8605,Japan

bKobeCityUniversityofForeignStudies,Kobe,Japan

cFacultyof 

Economics,

 OsakaUniversity,Osaka,Japan

Received10December2003;  

accepted26April2005.  

Availableonline22December2006. 

Abstract

Thispaperexaminestheinteractionbetweendecisionsaboutfinancingafter-retirementhealthshocksandprecautionary 

saving

 motives,andhowthisinteractionaffects 

economic

development.Weshowthatatlowlevelsofincome,individualschoosenottosavetofinancethecostofafter-retirementhealthshocks.However,onceindividualsbecomesufficientlyrich,theydochoosetosavetofinancethecostoftheseshocks.Thischangeinindividual 

saving

 behaviormaygiverisetomultiplesteadystateequilibria.

Keywords:

 After-retirementhealthshocks;Precautionary 

saving

 motives;Multiplesteadystateequilibria

JELclassificationcodes:

 E21;H24;O41

ArticleOutline

1. 

Introduction

2. 

Individuals’decisionmaking

2.1. Individuals’optimizationproblems

2.2. DecisionsaboutpayingforARHS

2.3. The saving problem

3. 

Equilibrium

4. 

Concludingremarks

Acknowledgements

Appendix1. 

Appendix

Appendix2. 

Appendix

Appendix3. 

Appendix

Appendix4. 

Appendix

Appendix5. 

Appendix

References

1.Introduction

Thecostoflong-termcarethreatensthefinancialhealthoftheelderly.1 Forexample,intheUSA,evenwithMedicareandprivatehealthinsurance,theriskofacatastrophicmedicalexpenseislarge.Out-of-pocketmedicalexpensesfortheelderlyin1988wereestimatedtobe$ 2394perelderlypersonorroughly18%oftheiraveragepercapitaincome.Nearly10%ofelderlyhouseholdsspendafifthormoreoftheirincomesonout-of-pocketmedicalexpenses（Palumbo,1999）and2–3%incurmedicalexpensesexceeding40%oftheiradjustedgrossincomes（FeenbergandSkinner,1994）.Nursinghomeexpensesarethemostsignificantlong-termcarecostsfortheelderly.Accordingto Palumbo（1999）,thelikelihoodofatypical65-year-oldpersonenteringanursinghomeduringhisorherlifetimeis43%.Onceadmitted,theaveragestayinalong-termcarefacilityexceedsoneyear.Becausenursinghomecostsarevirtuallyuninsured,admissiontoalong-termcarefacilitycanquicklydepleteone’sfinancialwealth.

Therefore,after-retirementhealthuncertaintyshouldprovideyoungindividualswithstrongprecautionarymotivesfor 

saving.

 Despitethis,lessattentionhasbeenpaidtothisissueintheliteraturethantoprecautionary 

saving

 inresponsetolifespanandearninguncertainty. Kotlikoff（1989） pointsoutthatthelackofresearchonthistopicmayreflectthedifficultyofpreciselyquantifyingthe 

economic

 riskofmorbidity.However,recentanalyseshavebeguntoinvestigatethisissuerigorouslyandtheyshowthatafter-retirementhealthuncertaintyhasastrongimpactonindividualconsumption–

saving

 behavior.Forexample, Palumbo（1999） estimatesthattheuncertaintyoffuturehealthexpensesaloneinducesatypicalfamilytospend,onaverage,7%less.Furthermore, Hubbardetal.,1994, Hubbardetal.,1995 and Palumbo,1999 showthattheprecautionary 

saving

 motivesarisingfromfuturehealthuncertaintyplaycrucialrolesinexplainingtheobservedpatternofindividualconsumption–

saving

 behavioroveralifecycle.

Recently, Dynanetal.（2000） foundthathigher（lower）lifetimeincomehouseholdsarelikelytosavealarger（smaller）fractionoftheirincome.Thisimpliesthatthereexistsapositivecorrelationbetweenlifetimeincomeand 

saving

 rate.Consideringtheobserveddifferencesinprecautionary 

saving

 andbequestbehaviorbylifetimeincomegroups, Dynanetal.（2000） explainthisempiricalresultasfollows.Concerningprecautionary 

saving

 behavior,undertheasset-basedmeans-testedpublicsubsidyprogramssuchasMedicaidandSupplementedSecurityIncome,householdswithlowerlifetimeincomearelikelytoreducetheir 

savings

 forfuturehealthexpensessoastoqualifyforthesubsidyprogram（Hubbardetal.,1995）.Ontheotherhand,householdswithhigher（lower）lifetimeincomespendmore（less）formedicaltreatmentinthecaseofcostlyillness（Newhouse,1977）.2 Thustheyarelikelytosavemore（less）forfuturehealthexpenses.Concerningbequestbehavior,householdswithhigher（lower）lifetimeincomearelikelytoleavelarger（smaller）financialbequeststosubsequentgenerations（BeckerandTomes,1986 and Mulligan,1997）.Therefore,thecombinationoftheseprecautionary 

saving

 andbequestbehaviorsmayexplaintheobservedpositivecorrelationbetweenlifetimeincomeandthe 

saving

 rate.

CarollandSamwick,1998 and GourinchasandParker,2001,andothersshowthatwealththatisheldforprecautionary 

saving

 motivesoccupiesalargerfractionoftotalwealthandaccountsforatleast50%oftotalwealth.Moreover,usingOECDdata, JitsuchonandSaito（1995） showthatcross-countrydifferencesin 

saving

 andper-capita 

growth

 ratesarecloselylinkedwiththedegreeofheterogenousuninsuredidiosyncraticshocks.Theseresultsimplythatdifferencesinindividualprecautionary 

saving

 behavioraccordingtolifetimeincomemayimpactsignificantlyuponthecapitalaccumulationprocessoftheeconomy.Therefore,itisimportanttoinvestigatetherelationshipsamongafter-retirementhealthshocks,individualchoiceofmedicaltreatment,andprecautionarymotivesfor 

saving

 inan 

economicgrowth

 contextandexploretheimpactupon 

economic

 development.

Thispaperestablishesasimple 

growth

 modelthatexplicitlyincorporatestheinteractionbetweendecisionstopayforcopingwithafter-retirementhealthshocksandtheprecautionary 

saving

 motives.Whenaneconomyisunderdeveloped,thecostofcopingwithafter-retirementhealthshockswillpreventthemfrompayingforit.Inthiscase,payingforcopingwithafter-retirementhealthshocksisnotaneffectiveoptionandpeopledonotmakeprecautionary 

saving.

 However,whentheeconomydevelops,peoplewilldecidetopayforcopingwithafter-retirementhealthshocks.Thispapershowsthatthispositivecorrelationmaygiverisetomultiplesteadystateequilibriainthiseconomy,sincehigherincomecauseshighercapitalaccumulationandviceversa.

Thispaperisorganizedasfollows.Section 2 analyzestheinteractionbetweenfinancingdecisionsaboutafter-retirementhealthshocksandprecautionary 

saving.

 InSection 3,wepresentthedynamicpropertiesoftheeconomyandshowthatthereexistmultiplesteadystateequilibria.Finally,inSection 4,wesummarizetheresultsandsuggestdirectionsforfutureresearch.

2.Individuals’decisionmaking

2.1.Individuals’optimizationproblems

Individualsfaceatwo-perioddynamicprogrammingproblem.Individualsderiveutilityfromtheirownconsumptioninbothyoungandoldperiodsoflife,andhavenobequestmotives.Theutilityfunction, u（c）,satisfies u′ > 0, u″ < 0,andtheInadaconditions.Individualsareendowedwithoneunitoflabor.Theyworkinelasticallyintheyoungperiodandretireintheoldperiod.Intheyoungperiod,individualsallocatetheirlaborincome wt toconsumptionand 

saving

 st.Then,intheoldperiod,theyreceive（1 + rt+1）st andconsumealltheprincipalandaccruedinterestofthe 

savings.

After-retirementhealthshocks（ARHS）areassumedtobeunveiledinthebeginningoftheoldperiod.Individualssufferdisutility θ（<0）withprobability p,andnothingwithprobability1 − p.Generally,evenifanymonetaryresourcesaresacrificed,itisimpossibletocompletelyremoveanydisutilityfrombeingsickorhandicapped.However,forsimplicity,theeffectsoftheshocksareassumedtoberemovedcompletelybypayingthefixedcostof d formedicaltreatment.3 Ifanindividualsuffersdisutility θ（<0）,heorshedetermineswhetherornottopaythecost d.If

（1）u（（1+rt+1）st）+θ>u（（1+rt+1）st-d）,theindividualisnotwillingtopay d forcopingwithARHS.Ontheotherhand,if

（2）u（（1+rt+1）st）+θ

Therefore,theindividual’sdynamicprogrammingproblemisasfollows:

（3）

2.2.DecisionsaboutpayingforARHS

Intheremainderofthissection,wesolvetheoptimizationproblemdefinedin （3）.First,weconsiderdecisionstopayforARHS.Following Fan（2001）,weassumethatthereexistsalowerboundon θ.Thislowerboundisdefinedbythefollowingequation:

（4）u（0）

 asthe 

saving

 level s,whichsatisfiesu（（1 + rt+1）s） + θ − u（（1 + rt+1）s − d） = 0given rt+1.Thus,wehavethefollowinglemma.

Lemma 1DecisionsaboutpayingforARHS 

Whenindividualssufferdisutilityθ（<0）inthesecondperiod,theydecidetopayforARHSif 

.Ontheotherhand,if 

theydonotpay.

Proof

See Appendix1. □

Notethat 

if 

.Thus, Lemma1 impliesthatindividualsdonotpayforARHS,whentheycannotsaveenoughbecauseoftheirlowincome.

2.3.The 

saving

 problem

Lemma1 statesthatindividualsdonotpayforARHS,if 

.Thus,supposethattheinequalityconstraint 

 holdsinthefirstperiod,then （3） isrewrit