Long-Term Care: Is There Crowding Out of Informal Care, Private Insurance as Well as Saving?

Peter Zweifel; Christophe Courbage

doi:10.1515/apjri-2015-0012

Article

Long-Term Care: Is There Crowding Out of Informal Care, Private Insurance as Well as Saving?

Peter Zweifel and Christophe Courbage

Published/Copyright: December 24, 2015

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal Asia-Pacific Journal of Risk and Insurance Volume 10 Issue 1

Abstract

Publicly provided long-term care (LTC) insurance with means-tested benefits is suspected to crowd out either private LTC insurance (Brown and Finkelstein 2008. The Interaction of Public and Private Insurance: Medicaid and the Long-Term Care Insurance Market. American Economic Review 98(3):1083–102), private saving (Gruber and Yelowitz 1999. Public Health Insurance and Private Saving. Journal of Political Economy 107(6):1249–74; Sloan and Norton 1997. Adverse Selection, Bequests, Crowding Out, and Private Demand for Insurance: Evidence from the Long-term Care Insurance Market. Journal of Risk and Uncertainty 15:201–19), or informal care (Pauly 1990. The Rational Non-purchase of Long-term Care Insurance. Journal of Political Economy 95:153–68; Zweifel and Strüwe 1998. Long-term Care Insurance in a Two-generation Model. Journal of Risk and Insurance 65(1):13–32). This contribution predicts crowding-out effects for both private LTC insurance and informal care on the one hand and private saving and informal care on the other. These effects result from the interaction of a parent who decides about private LTC insurance before retirement and the amount of saving in retirement and a caregiver who decides about effort devoted to informal care. Some of the predictions are tested using a recent survey from China.

Keywords: long-term care; insurance; saving; crowding out; means testing; China

JEL Classification: D19; H51; J14

Acknowledgment

The authors are grateful to Chunli Chen (Bonn University) for calling their attention to the importance of filial piety in China, Shuji Tanaka (Nihon University) and other participants of the World Risk and Insurance Economics Conference (WRIEC) 2015 in Munich, and two anonymous referees for their painstaking checking of the manuscript.

References

Andreoni, J. 1990. Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving. Economic Journal 100(401):464–7.10.2307/2234133Search in Google Scholar

Banthrope, P. 2013. The development of impaired annuity markets in the UK and elsewhere. Presentation at the 10th Geneva Association Health and Ageing Conference, “Insuring the health of an ageing population”, Rüschlikon/Zurich (Switzerland), 18–19 Nov. 2013, www.genevaassociation.org/Publications/Conference Papers.Search in Google Scholar

Blinkert, B. and Klie, T. 2004. Die Sicherstellung der Versorgung von pfllegebedürftigen Menschen (Ensuring the provision of care to persons in need of LTC). Sozialer Fortschritt 53(11–12): 319–25.Search in Google Scholar

Brown, J., and Finkelstein, A. 2008. The Interaction of Public and Private Insurance: Medicaid and the Long-Term Care Insurance Market. American Economic Review 98(3):1083–102.10.3386/w10989Search in Google Scholar

Colombo, F., Llena-Nozal, A., Mercier, J., and Tjadens, F. 2011. Help Wanted? Providing and Paying for Long-Term Care. OECD Policy Studies, Paris: OECD Publishing.10.1787/9789264097759-enSearch in Google Scholar

Chang, W., and Kalmanson, L. 2010. Confucianism in Context. Classic Philosophy and Contemporary Issues, East Asia and Beyond. Albany: State University of New York Press.10.1353/book164Search in Google Scholar

Courbage, C., and Zweifel, P. 2011. Two-sided Intergenerational Moral Hazard, Long-term Care Insurance, and Nursing Home Use. Journal of Risk and Uncertainty 43(1):65–80.10.1007/s11166-011-9120-6Search in Google Scholar

De Montesquieu, L. 2013. Long-term care insurance products: standards and innovations. Presentation at the 10th Geneva Association Health and Ageing Conference, “Insuring the health of an ageing population”, Rüschlikon/Zurich (Switzerland), 18–19 Nov. 2013, www.genevaassociation.org/Publications/Conference Papers.Search in Google Scholar

Dionne, G., and Eeckhoudt, L. 1984. Insurance and Saving: Some Further Results. Insurance: Mathematics and Economics 3(2):101–10.10.1016/0167-6687(84)90048-9Search in Google Scholar

Evans, W. N., and Viscusi, W. K. 1991. Estimation of State Dependent Utility Function Using Survey Data. Review of Economics and Statistics 73:94–104.10.2307/2109691Search in Google Scholar

Finkelstein, A., Luttmer, E., and Notowidigdo, M. 2009. Approaches to Estimating the Health State Dependence of the Utility Function. American Economic Review 99(2):116–21.10.1257/aer.99.2.116Search in Google Scholar

Gruber, J., and Yelowitz, A. 1999. Public Health Insurance and Private Saving. Journal of Political Economy 107(6):1249–74.10.3386/w6041Search in Google Scholar

Halek, M., and Eisenhauer, J. G. 2001. Demography of Risk Aversion. Journal of Risk and Insurance 68:1–24.10.2307/2678130Search in Google Scholar

Meier, V. 1996. Long-term Care Insurance and Savings. Finanzarchiv N. F. 53:561–81.Search in Google Scholar

Pauly, M. V. 1990. The Rational Non-purchase of Long-term Care Insurance. Journal of Political Economy 95:153–68.10.1086/261673Search in Google Scholar

Schoder J., and Zweifel, P. 2011. Flat-of-the-curve Medicine: A New Perspective on the Production of Health. Health Economics Review 1(2):1–10.10.1186/2191-1991-1-2Search in Google Scholar

Schonbee, J. 2013. Other silver products to insure the health of an ageing population. Presentation at the 10th Geneva Association Health and Ageing Conference, “Insuring the health of an ageing population”, Rüschlikon/Zurich (Switzerland), 18–19 Nov. 2013, www.genevaassociation.org/Publications/Conference Papers.Search in Google Scholar

Sloan, F. A., and Norton E. C. 1997. Adverse Selection, Bequests, Crowding Out, and Private Demand for Insurance: Evidence from the Long-term Care Insurance Market. Journal of Risk and Uncertainty 15:201–19.10.1023/A:1007749008635Search in Google Scholar

Tao Young, D., Zhang, J., and Zhous, S. 2011. Why are saving rates so high in China? NBER Working Paper No. 16711, New York: National Bureau of Economic Research.Search in Google Scholar

Xu, X., and Zweifel, P. 2014. Bilateral Moral Hazard: Evidence from China. The Geneva Papers on Risk and Insurance – Issues and Practice 39:651–67.10.1057/gpp.2014.28Search in Google Scholar

Zweifel, P., and Strüwe, W. 1998. Long-term Care Insurance in a Two-generation Model. Journal of Risk and Insurance 65(1):13–32.10.2307/253489Search in Google Scholar

Zweifel, P., Felder, S. and Meier, M. 1999. Ageing of Population and Health Care Expenditure: A Red Herring?. Health Economics 8:485–96.10.1002/(SICI)1099-1050(199909)8:6<485::AID-HEC461>3.0.CO;2-4Search in Google Scholar

Appendix: Four exogenous changes and their impact on the reaction functions

In this appendix, the model is subjected first to two exogenous changes on the parent’s side, viz. an increase in his or her initial wealth (dw0>0) and an increase in the degree of cost sharing in LTC expenditure (dα>0,∂r/∂α>0). Two more changes relate to the child, viz. an increase in his or her opportunity cost of caregiving (dθ>0)and a lower amount of inheritance (this is thought to be caused by an increase in its taxation (dt>0).

(1) Higher initial wealth of the parent (dw0>0)

From eqs [2] and [1], the crucial mixed derivative determining the first parental reaction function is given by

(A.1)∂2EU∂I∂w0=−π¯{u1''(.)+(1−s)u2''(.)}+π(e)(1−π¯){−rw''s(1+i)p⋅υ'i+(1−rw'p)2s(1+i)⋅υ''i(.)} −(1−π(e))π¯s(1+i)⋅υ''o(.) =−π¯{u1''(.)+(1−s)u2''(.)} +s(1+i){π(e)(1−π¯){(−rw''p)⋅υ'i+(1−rw'p)2⋅υ''i(.)}−(1−π(e))π¯⋅υ''o(.)} <> 0 .

As to the parent’s second reaction function, eqs [6] and [1] imply

(A.2)∂2EU∂s∂w0=−(1−s)u2''(.)+(1+i){−π(e)(rw''p)⋅υ'i(.)+π(e)(1−rw'p){s(1+i)−rw's(1+i)p}⋅υ''i+(1−π(e))⋅υ''o(.)} =−(1−s)u2''(.)+(1+i){π(e){−rw''p⋅υ'i(.)+s(1+i)(1−rw'p)2⋅υ''i}+(1−π(e))⋅υ"o} <> 0 .

For the child, one has from eqs. (9) and (8)

(A.3)∂2EU¯∂e∂w0=π'(e){{k(1−t)s(1+i)−rw's(1+i)p}⋅υ¯'i−k(1−t)s(1+i)⋅υ¯'o} =π'(e)s(1+i){(k(1−t)−rw'p)⋅υ¯'i−(k(1−t)υ¯'o} =π'(e)s(1+i){(k(1−t)(υ¯'i−υ¯'o)−rw'p⋅υ¯'i} > 0 since υ¯'i<υ¯'o .

(2) Increase in cost sharing (dα>0, ∂r/∂α>0)

An increase in cost sharing is equivalent to an increase in α causing a change in the function r(w0s(1+i),α) such that ∂r(w0s(1+i),α)∂α :=rα'>0. To make this a pure upward shift of the cost-sharing schedule without a change in its progressiveness, rαw″=rwα″=0 is imposed.

On the parent’s side, an exogenous change dα>0 affects the FOC given by eq. [2], resulting in a shift of his or her first reaction function as follows [see also eq. (1)],

(A.4)∂2EU∂I∂α=π(e)(1−π¯) {(−rwα''p)⋅υ'i(.)+(1−rw'p)(−ra'p)⋅υ''i(.)} =−π(e)(1−π¯)(1−rw'p)(ra'p)⋅υ''i(.) < 0 if rw'p>1 (stringent means testing) > 0 if rw'p<1 (lenient means testing).

To determine the displacement of the second parental reaction function, one has from eqs [6] and [1],

(A.5)∂2EU∂s∂α=(1+i){π(e){(−rwα''p)⋅υ'i(.)+(1−rw'p)(−rα'p)⋅υ''i(.)}} =−(1+i){π(e)(1−rw'p)(rα'p)⋅υ''i(.)} < 0 if rw'p>1 (stringent means testing) since rwα''=0 > 0 if rw'p<1 (lenient means testing) since rwα''=0 .

With regard to the child, the direction of the displacement is given by [see eqs. (9) and (8)],

(A.6)∂2EU¯∂e∂α=π'(e)k(1−t)(−rα'p)⋅υ¯'i> 0 .

Now two exogenous changes on the child’s side are considered.

(3) Increased opportunity cost of the child (dθ > 0)

From eqs. (2), (6), and (1), it is evident that the parent is not affected, hence

(A.7)∂2EU∂I∂θ=0, ∂2EU∂s∂θ=0 .

As to the child, eqs. (9) and (8) yield

(A.8)∂2EU¯∂e∂θ=−u¯'(.)+eθ⋅u¯''(.)<0 ,

indicating an inward movement of the reaction curve which becomes more pronounced for higher values of e.

(4) Increased taxation of inheritance (dt > 0)

An increased rate of taxation (dt > 0) has the effect of reducing the net share of the caregiver in the bequest. According to eqs. (2), (6) and (1), this does not affect optimization on the part of the parent, thus

(A.9)∂2EU∂I∂t=0, ∂2EU∂s∂t=0 .

Therefore, there again is no displacement of the parental reaction functions. Concerning the child’s reaction function, one obtains from eqs. (9) and (8),

∂2EU¯∂e∂t=π'(e){−k{w0s(1+i)+I(1−π¯)−r(⋅)p}⋅υ¯'i+k{w0s(1+i)−π¯I}⋅υ¯'o} =−k{π'(e){w0s(1+i)−π¯I}⋅(υ¯'i− υ¯'o)−π'(e){I−r(⋅)p}⋅υ¯'i}.

Using π'(e){υ¯i(⋅)−υ¯o(⋅)}=θu¯'(⋅)from the FOC of eq. (9), this boils down to

(A.10)∂2EU¯∂e∂t=−k{{w0s(1+i)−π¯I}⋅θu¯'(⋅)−π'(e){I−r(⋅)p}⋅υ¯'i} <> 0 .

In sum, several comparative-static results are ambiguous, precluding predictions concerning the displacement of Nash equilibria. However, they prepare the ground for analyzing the case of China in greater detail.

Published Online: 2015-12-24

Published in Print: 2016-1-1

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/apjri-2015-0012

Keywords for this article

long-term care; insurance; saving; crowding out; means testing; China