The longterm care problem precautionary saving and economic growth.docx

1、The longterm care problem precautionary saving and economic growthJournal of MacroeconomicsVolume 29, Issue 1, March 2007, Pages 60-74doi:10.1016/j.jmacro.2005.04.001|How to Cite or Link Using DOICopyright 2006 Elsevier Inc. All rights reserved.Permissions & ReprintsThe long-term care problem, preca

2、utionarysaving, and economic growthNoriyoshiHemmia,KenTabatabandKoichiFutagamicaFaculty ofEconomics,Hokkai Gakuen University, 4-1-40, Asahi-Machi, Toyohira-Ku, Sapporo 062-8605, JapanbKobe City University of Foreign Studies, Kobe, JapancFaculty ofEconomics,Osaka University, Osaka, JapanReceived 10 D

3、ecember 2003;accepted 26 April 2005.Available online 22 December 2006.AbstractThis paper examines the interaction between decisions about financing after-retirement health shocks and precautionarysavingmotives, and how this interaction affectseconomicdevelopment. We show that at low levels of income

4、, individuals choose not to save to finance the cost of after-retirement health shocks. However, once individuals become sufficiently rich, they do choose to save to finance the cost of these shocks. This change in individualsavingbehavior may give rise to multiple steady state equilibria.Keywords:A

5、fter-retirement health shocks; Precautionarysavingmotives; Multiple steady state equilibriaJEL classification codes:E21; H24; O41Article Outline1.Introduction2.Individuals decision making2.1.Individuals optimization problems2.2.Decisions about paying for ARHS2.3.Thesavingproblem3.Equilibrium4.Conclu

6、ding remarksAcknowledgementsAppendix 1.AppendixAppendix 2.AppendixAppendix 3.AppendixAppendix 4.AppendixAppendix 5.AppendixReferences1. IntroductionThe cost of long-term care threatens the financial health of the elderly.1For example, in the USA, even with Medicare and private health insurance, the

7、risk of a catastrophic medical expense is large. Out-of-pocket medical expenses for the elderly in 1988 were estimated to be $2394 per elderly person or roughly 18% of their average per capita income. Nearly 10% of elderly households spend a fifth or more of their incomes on out-of-pocket medical ex

8、penses (Palumbo, 1999) and 23% incur medical expenses exceeding 40% of their adjusted gross incomes (Feenberg and Skinner, 1994). Nursing home expenses are the most significant long-term care costs for the elderly. According toPalumbo (1999), the likelihood of a typical 65-year-old person entering a

9、 nursing home during his or her lifetime is 43%. Once admitted, the average stay in a long-term care facility exceeds one year. Because nursing home costs are virtually uninsured, admission to a long-term care facility can quickly deplete ones financial wealth.Therefore, after-retirement health unce

10、rtainty should provide young individuals with strong precautionary motives forsaving.Despite this, less attention has been paid to this issue in the literature than to precautionarysavingin response to lifespan and earning uncertainty.Kotlikoff (1989)points out that the lack of research on this topi

11、c may reflect the difficulty of precisely quantifying theeconomicrisk of morbidity. However, recent analyses have begun to investigate this issue rigorously and they show that after-retirement health uncertainty has a strong impact on individual consumptionsavingbehavior. For example,Palumbo (1999)e

12、stimates that the uncertainty of future health expenses alone induces a typical family to spend, on average, 7% less. Furthermore,Hubbard et al., 1994,Hubbard et al., 1995andPalumbo, 1999show that the precautionarysavingmotives arising from future health uncertainty play crucial roles in explaining

13、the observed pattern of individual consumptionsavingbehavior over a life cycle.Recently,Dynan et al. (2000)found that higher (lower) lifetime income households are likely to save a larger (smaller) fraction of their income. This implies that there exists a positive correlation between lifetime incom

14、e andsavingrate. Considering the observed differences in precautionarysavingand bequest behavior by lifetime income groups,Dynan et al. (2000)explain this empirical result as follows. Concerning precautionarysavingbehavior, under the asset-based means-tested public subsidy programs such as Medicaid

15、and Supplemented Security Income, households with lower lifetime income are likely to reduce theirsavingsfor future health expenses so as to qualify for the subsidy program (Hubbard et al., 1995). On the other hand, households with higher (lower) lifetime income spend more (less) for medical treatme

16、nt in the case of costly illness (Newhouse, 1977).2Thus they are likely to save more (less) for future health expenses. Concerning bequest behavior, households with higher (lower) lifetime income are likely to leave larger (smaller) financial bequests to subsequent generations (Becker and Tomes, 198

17、6andMulligan, 1997). Therefore, the combination of these precautionarysavingand bequest behaviors may explain the observed positive correlation between lifetime income and thesavingrate.Caroll and Samwick, 1998andGourinchas and Parker, 2001, and others show that wealth that is held for precautionary

18、savingmotives occupies a larger fraction of total wealth and accounts for at least 50% of total wealth. Moreover, using OECD data,Jitsuchon and Saito (1995)show that cross-country differences insavingand per-capitagrowthrates are closely linked with the degree of heterogenous uninsured idiosyncratic

19、 shocks. These results imply that differences in individual precautionarysavingbehavior according to lifetime income may impact significantly upon the capital accumulation process of the economy. Therefore, it is important to investigate the relationships among after-retirement health shocks, indivi

20、dual choice of medical treatment, and precautionary motives forsavingin aneconomic growthcontext and explore the impact uponeconomicdevelopment.This paper establishes a simplegrowthmodel that explicitly incorporates the interaction between decisions to pay for coping with after-retirement health sho

21、cks and the precautionarysavingmotives. When an economy is underdeveloped, the cost of coping with after-retirement health shocks will prevent them from paying for it. In this case, paying for coping with after-retirement health shocks is not an effective option and people do not make precautionarys

22、aving.However, when the economy develops, people will decide to pay for coping with after-retirement health shocks. This paper shows that this positive correlation may give rise to multiple steady state equilibria in this economy, since higher income causes higher capital accumulation and vice versa

23、.This paper is organized as follows. Section2analyzes the interaction between financing decisions about after-retirement health shocks and precautionarysaving.In Section3, we present the dynamic properties of the economy and show that there exist multiple steady state equilibria. Finally, in Section

24、4, we summarize the results and suggest directions for future research.2. Individuals decision making2.1. Individuals optimization problemsIndividuals face a two-period dynamic programming problem. Individuals derive utility from their own consumption in both young and old periods of life, and have

25、no bequest motives. The utility function,u(c), satisfiesu0,u0, and the Inada conditions. Individuals are endowed with one unit of labor. They work inelastically in the young period and retire in the old period. In the young period, individuals allocate their labor incomewtto consumption andsavingst.

26、 Then, in the old period, they receive (1+rt+1)stand consume all the principal and accrued interest of thesavings.After-retirement health shocks (ARHS) are assumed to be unveiled in the beginning of the old period. Individuals suffer disutility(0) with probabilityp, and nothing with probability 1p.

27、Generally, even if any monetary resources are sacrificed, it is impossible to completely remove any disutility from being sick or handicapped. However, for simplicity, the effects of the shocks are assumed to be removed completely by paying the fixed cost ofdfor medical treatment.3If an individual s

28、uffers disutility(u(1+rt+1)st-d),the individual is not willing to paydfor coping with ARHS. On the other hand, if(2)u(1+rt+1)st)+u(1+rt+1)st-d),the individual is willing to paydfor coping with ARHS.Therefore, the individuals dynamic programming problem is as follows:(3)2.2. Decisions about paying fo

29、r ARHSIn the remainder of this section, we solve the optimization problem defined in(3). First, we consider decisions to pay for ARHS. FollowingFan (2001), we assume that there exists a lower bound on. This lower bound is defined by the following equation:(4)u(0)u(d)+.This reflects the fact that ind

30、ividuals do not paydfor ARHS if their incomes in the second period are less thand. Additionally, we defineas thesavinglevels, which satisfiesu(1+rt+1)s)+u(1+rt+1)sd)=0 givenrt+1. Thus, we have the following lemma.Lemma1 Decisions about paying for ARHSWhen individuals suffer disutility (0) in the sec

31、ond period, they decide to pay for ARHS if. On the other hand, if, they do not pay.ProofSeeAppendix 1.Note that, if. Thus,Lemma 1implies that individuals do not pay for ARHS, when they cannot save enough because of their low income.2.3. ThesavingproblemLemma 1states that individuals do not pay for ARHS, if. Thus, suppose that the inequality constraintholds in the first period, then(3)is rewrit