Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-27T01:29:11.472Z Has data issue: false hasContentIssue false
  • English
  • Français

BROKEN-HEART, COMMON LIFE, HETEROGENEITY: ANALYZING THE SPOUSAL MORTALITY DEPENDENCE

Published online by Cambridge University Press:  20 April 2017

Yang Lu
Yang Lu*
Affiliation:
Aix-Marseille School of Economics, Aix-Marseille University, 2 Rue de la Charite, 13001 Marseille, France
*
E-Mail: luyang000278@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Using data on joint annuities, we conduct an analysis of the inter-couple lifetime dependence. We estimate a mixed proportional hazards model with treatment effects, which disentangles the broken-heart syndrome from the spurious risk dependence induced by unobserved heterogeneities. We use a flexible semi-parametric distribution for the unobserved heterogeneities to allow for either positive or negative spurious risk dependence. We find that the effect of losing one's spouse is asymmetric for the two sexes. Moreover, although the broken-heart syndrome explains a large portion of the dependency, there is evidence of positive spurious risk dependence. These findings have important implications for the pricing of joint insurance products. Failure to take into account either of these two effects leads to pricing error that can be either positive or negative, depending on the characteristics of the couple.

Keywords

Broken-heartjoint survivor annuitymixed proportional hazards competing risks modeltreatment effectunobserved heterogeneities
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 837 - 874
Copyright
Copyright © Astin Bulletin 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbring, J. and van den Berg, G. (2003a) The identifiability of the mixed proportional hazards competing risks model. Journal of the Royal Statistical Society: Series B, 65 (3), 701–710.CrossRefGoogle Scholar
Abbring, J. and van den Berg, G. (2003b) The nonparametric identification of treatment effects in duration models. Econometrica, 71 (5), 1491–1517.CrossRefGoogle Scholar
Abbring, J. and van den Berg, G. (2007) The unobserved heterogeneity distribution in duration analysis. Biometrika, 94 (1), 87–99.Google Scholar
Baker, M. and Melino, A. (2000) Duration dependence and nonparametric heterogeneity: A Monte Carlo study. Journal of Econometrics, 96 (2), 357–393.CrossRefGoogle Scholar
Bierens, H.J. (2008) Semi-nonparametric interval-censored mixed proportional hazard models: Identification and consistency results. Econometric Theory, 24 (03), 749–794.Google Scholar
Blake, D., Cairns, A., Coughlan, G., Dowd, K. and MacMinn, R. (2013) The new life market. Journal of Risk and Insurance, 80 (3), 501–558.Google Scholar
Brown, J.R. and Poterba, J.M. (2000) Joint life annuities and annuity demand by married couples. The Journal of Risk and Insurance, 67 (4), 527–554.CrossRefGoogle Scholar
Canals-Cerdá, J. and Gurmu, S. (2007) Semiparametric competing risks analysis. The Econometrics Journal, 10 (2), 193–215.Google Scholar
Carriere, J. (2000) Bivariate survival models for coupled lives. Scandinavian Actuarial Journal, 2000 (1), 17–32.Google Scholar
Clayton, D. (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65 (1), 141–151.CrossRefGoogle Scholar
Deng, Y., Quigley, J. and Order, R. (2000) Mortgage terminations, heterogeneity and the exercise of mortgage options. Econometrica, 68 (2), 275–307.CrossRefGoogle Scholar
Drefahl, S. (2010) How does the age gap between partners affect their survival? Demography, 47 (2), 313–326.Google Scholar
Espinosa, J. and Evans, W.N. (2008) Heightened mortality after the death of a spouse: Marriage protection or marriage selection? Journal of Health Economics, 27 (5), 1326–1342.CrossRefGoogle ScholarPubMed
Fallick, B. and Ryu, K. (2007) The recall and new job search of laid-off workers: A bivariate proportional hazard model with unobserved heterogeneity. Review of Economics and Statistics, 89 (2), 313–323.Google Scholar
Finkelstein, A. and Poterba, J. (2004) Adverse selection in insurance markets: Policyholder evidence from the UK annuity market. Journal of Political Economy, 112 (1), 183–208.CrossRefGoogle Scholar
Frees, E., Carriere, J. and Valdez, E. (1996) Annuity valuation with dependent mortality. Journal of Risk and Insurance, 63 (2), 229–261.CrossRefGoogle Scholar
Gouriéroux, C. and Lu, Y. (2015) Love and death: A freund model with frailty. Insurance: Mathematics and Economics 63 (1), 191–203.Google Scholar
Gribkova, S. and Lopez, O. (2015) Non-parametric copula estimation under bivariate censoring. Scandinavian Journal of Statistics, 42 (4), 925–946.Google Scholar
Heckman, J. and Singer, B. (1984) A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica, 52 (2), 271–320.Google Scholar
Hougaard, P., Harvald, B. and Holm, N.V. (1992) Measuring the similarities between the lifetimes of adult danish twins born between 1881–1930. Journal of the American Statistical Association, 87 (417), 17–24.Google Scholar
Iachine, I. (2004) Identifiability of bivariate frailty models. University of Southern Denmark Working Paper.Google Scholar
Jarrow, R. and Yu, F. (2001) Counterparty risk and the pricing of defaultable securities. The Journal of Finance, 56 (5), 1765–1799.Google Scholar
Ji, M., Hardy, M. and Li, S. (2011) Markovian approaches to joint-life mortality. North American Actuarial Journal, 15 (3), 357–376.CrossRefGoogle Scholar
Klein, J.P. and Moeschberger, M.L. (2003) Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer Science & Business Media.Google Scholar
Lancaster, T. (1979) Econometric methods for the duration of unemployment. Econometrica, 47 (4), 939–956.Google Scholar
Lopez, O. (2012) A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models. Insurance: Mathematics and Economics, 51 (3), 505–516.Google Scholar
Lu, Y. (2015) Large duration asymptotics in multivariate survival models with unobserved heterogeneity. CREST DP. Aix-Marseille University working paper.Google Scholar
Luciano, E., Spreeuw, J. and Vigna, E. (2008) Modelling stochastic mortality for dependent lives. Insurance: Mathematics and Economics, 43 (2), 234–244.Google Scholar
Marshall, A.W. and Olkin, I. (1988) Families of multivariate distributions. Journal of the American Statistical Association, 83 (403), 834–841.CrossRefGoogle Scholar
Parkes, M., Benjamin, B. and Fitzgerald, R. (1969) Broken heart: A statistical study of increased mortality among widowers. British Medical Journal, 1 (5646), 740–743.Google Scholar
Prentice, R.L., Kalbfleisch, J.D., Peterson, A.V. Jr, Flournoy, N., Farewell, V. and Breslow, N. (1978) The analysis of failure times in the presence of competing risks. Biometrics, 34 (4), 541–554.Google Scholar
Reichling, F. and Smetters, K. (2015) Optimal annuitization with stochastic mortality probabilities. American Economic Review, 105 (11), 3273–3320.CrossRefGoogle Scholar
Ridder, G. (1990) The non-parametric identification of generalized accelerated failure-time models. Review of Economic Studies, 57 (2), 167–181.CrossRefGoogle Scholar
Simeonova, E. (2013) Marriage, bereavement and mortality: the role of health care utilization. Journal of Health Economics, 32 (1), 33–50.CrossRefGoogle ScholarPubMed
Spreeuw, J. (2006) Types of dependence and time-dependent association between two lifetimes in single parameter copula models. Scandinavian Actuarial Journal, 2006 (5), 286–309.Google Scholar
Spreeuw, J. and Owadally, I. (2013) Investigating the broken-heart effect: A model for short-term dependence between the remaining lifetimes of joint lives. Annals of Actuarial Science, 7 (2), 236–257.Google Scholar
van den Berg, G.J. and Drepper, B. (2012) A unique bond: Does losing your co-twin affect your remaining life-span? University of Mannheim working paper.Google Scholar
Van den Berg, G.J. and Drepper, B. (2016) Inference for shared-frailty survival models with left-truncated data. Econometric Reviews, 35 (6), 1075–1098.Google Scholar
van den Berg, G.J., Lindeboom, M. and Portrait, F. (2011) Conjugal bereavement effects on health and mortality at advanced ages. Journal of Health Economics, 30 (4), 774–794.Google Scholar
Vaupel, J., Manton, K. and Stallard, E. (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16 (3), 439–454.Google Scholar
Wang, H.C. and Yue, J.C. (2015) Mortality, health, and marriage: A study based on Taiwan's population data. North American Actuarial Journal, 19 (3), 1–25.Google Scholar
Youn, H. and Shemyakin, A. (1999) Statistical aspects of joint life insurance pricing. Proceedings of the Business and Statistics Section of the American Statistical Association, pp. 34–38. American Statistical Association.Google Scholar