Income–well-being gradient in sickness and health

Kanninen, Ohto and Böckerman, Petri and Suoniemi, Ilpo (2022): Income–well-being gradient in sickness and health.

Abstract

We propose a method of studying the value of insurance. For this purpose, we analyze well-being of the same individuals, comparing sick and healthy years in German panel survey data on life satisfaction. To impose structure on the income–wellbeing gradient, we fit a flexible utility function to the data, focusing on the differences in marginal utility in the sick and the healthy state, by allowing for a “fixed cost of sickness”. We find that marginal utility of income is higher in the sick state. We use our estimates to gauge the value of sickness insurance for Baily-Chetty type optimal policy calculations. We also show that the income–wellbeing gradient has steepened over time in Germany and we use the fitted model to characterize this change.

• Item Type: MPRA Paper
• Language: English
• Keywords: life satisfaction state dependence risk aversion social insurance optimal benefits sickness absence
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; H - Public Economics > H5 - National Government Expenditures and Related Policies > H55 - Social Security and Public Pensions; I - Health, Education, and Welfare > I1 - Health > I13 - Health Insurance, Public and Private

References

Baily, M.L. (1978). Some aspects of optimal unemployment insurance. Journal of Public Economics, 10, 379–402. doi: 10.1016/0047-2727(78)90053-1

Benjamin, D.J., Heffetz, O., Kimball, M.S. and Rees-Jones, A. (2012). What do you think would make you happier? What do you think you would choose? The American Economic Review, 102, 2083–2110. doi: 10.1257/aer.102.5.2083

Benjamin, D.J., Heffetz, O., Kimball, M.S. and Rees-Jones, A. (2014a). Can marginal rates of substitution be inferred from happiness data? Evidence from residency choices. The American Economic Review, 104, 3498–3528. doi: 0.1257/aer.104.11.3498

Benjamin, D.J., Heffetz, O., Kimball, M.S. and Szembrot, N. (2014b). Beyond happiness and satisfaction: Toward well-being indices based on stated preference. The American Economic Review, 104, 2698–2735. doi: 10.1257/aer.104.9.2698

Bond, T.N., and Lang, K. (2019). The sad truth about happiness scales. Journal of Political Economy, 127, 1629–1640. doi: 10.1086/701679

Böckerman, P., Kanninen, O. and Suoniemi, I. (2018). A kink that makes you sick: The effect of sick pay on absence. Journal of Applied Econometrics, 33, 568–579. doi: 10.1002/jae.2620

Chen, L.Y., Oparina, E., Powdthavee, N., Srisuma, S. (2019). Have econometric analyses of happiness data been futile? A simple truth about happiness scales. IZA Discussion paper, No. 12152.

Chetty, R. (2006). A general formula for the optimal level of social insurance. Journal of Public Economics, 90, 1879–1901. doi: 10.1016/j.jpubeco.2006.01.004

Chetty R. (2008). Moral hazard versus liquidity and optimal unemployment insurance. Journal of Political Economy, 116, 173–234. doi: 10.1086/588585

Chetty, R. and Finkelstein, A. (2013). Social insurance: Connecting theory to data. In Handbook of Public Economics, Volume 5, Amsterdam: Elsevier, 111–193. doi: 10.1016/B978-0-444-53759-1.00003-0

Cohen, A. and Einav, L. (2007). Estimating risk preferences from deductible choice. The American Economic Review, 97, 745–788. doi: 10.1257/aer.97.3.745

Cullen, J.B. and Gruber, J. (2000). Does unemployment insurance crowd out spousal labor supply? Journal of Labor Economics, 18, 546–572. doi: 10.1086/209969

DICE Database. (2017, December 19). Lost working time due to sickness, 2000-2009. Retrieved from http://www.cesifo-group.de/DICE/fb/3Sb8mxDdU

Einav, L., Finkelstein, A., Pascu, I., and Cullen, M. (2012). How general are risk preferences? Choices under uncertainty in different domains. The American Economic Review, 102, 2606–2638. doi: 10.1257/aer.102.6.2606

Engen, E.M. and Gruber, J. (2001). Unemployment insurance and precautionary saving. Journal of Monetary Economics, 47, 545–579. doi: 10.1016/S0304-3932(01)00051-4

Feldstein, M. (1974). Social security, induced retirement, and aggregate capital accumulation. Journal of Political Economy, 82, 905–926. doi: 10.2307/1829174

Finkelstein, A., Luttmer, E.F.P., and Notowidigdo, M.J. (2009). Approaches to estimating the health state dependence of the utility function. The American Economic Review, 99, 116–121. doi: 10.1257/aer.99.2.116

Finkelstein, A., Luttmer, E.F.P., and Notowidigdo, M.J. (2013). What good is wealth without health? The effect of health on the marginal utility of consumption. Journal of the European Economic Association, 11, 221–258. doi: 10.1111/j.1542-4774.2012.01101.x

Geary, R.C. (1950). A note on “A constant-utility index of the cost of living”. The Review of Economic Studies, 18, 65–66. doi: 10.2307/2296107

Gruber, J. (1997). The consumption smoothing benefits of unemployment insurance. The American Economic Review, 87, 192–205. doi: 10.3386/w4750

Jäger, S., Schoefer, B., and Zweimueller, J. (2018). Marginal jobs and job surplus: A test of the efficiency of separations. University of Zurich, Department of Economics, Working Paper No. 314.

Jones, I.J., and Klenow, P.J. (2016). Beyond GDP? Welfare across countries and time. The American Economic Review, 106, 2426–2457. doi: 10.1257/aer.20110236

Kahneman, D. and Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263–291.

Kahneman, D., Wakker, P., and Sarin, R. (1997). Back to Bentham? Explorations of experienced utility. The Quarterly Journal of Economics, 112, 375–405. doi: 10.1162/003355397555235

Kaiser, C., & Vendrik, M. C. (2019). How threatening are transformations of reported happiness to subjective wellbeing research? doi: 10.31235/osf.io/gzt7a

Krebs, T., & Scheffel, M. (2013). Macroeconomic evaluation of labor market reform in Germany. IMF Economic Review, 61(4), 664-701.

Kolsrud, J., Landais, C., Nilsson, P., and Spinnewijn, J. (2018). The optimal timing of unemployment benefits: Theory and evidence from Sweden. The American Economic Review, 108, 985–1033. doi: 10.1257/aer.20160816

Layard, R., Mayraz, G., and Nickell, S. (2008). The marginal utility of income. Journal of Public Economics, 92, 1846–1857. doi: 10.1016/j.jpubeco.2008.01.007

Mata, R., Frey, R., Richter, D., Schupp, J., and Hertwig, R. (2018). Risk preference: A view from psychology. Journal of Economic Perspectives, 32, 155–72. doi: 10.1257/jep.32.2.155

Merton, R.C. (1971). Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory, 3, 373–413. doi: 10.1016/0022-0531(71)90038-X

Meyer, D.J. and Meyer, J. (2005). Relative risk aversion: What do we know? Journal of Risk and Uncertainty, 31, 243–262. doi: 10.1007/s11166-005-5102-x

Meyer, B.D. and Mok, W.K. (2019). Disability, earnings, income and consumption. Journal of Public Economics, 171, 51–69. doi: 10.1016/j.jpubeco.2018.06.011

MISSOC (2017). Mutual Information System on Social Protection in the Member States of the European Union. European Commission.

Palme, M., Persson, M. (2019). Sick pay insurance and sickness absence: Some European cross-country observations and a review of previous research. Journal of Economic Surveys, 34:1, 85–108. Doi: https://doi.org/10.1111/joes.12351

Perets, G. and Yashiv, E. (2016): The Fundamental Nature of HARA Utility. Working paper.

Phlips, L. (1978). The demand for leisure and money. Econometrica, 46, 1025–1043. doi: 10.1016/b978-0-444-86531-1.50017-2

Pichler, S. and Ziebarth, N.R. (2017). The pros and cons of sick pay schemes: Testing for contagious presenteeism and noncontagious absenteeism behavior. Journal of Public Economics, 156, 14–33. doi: 10.1016/j.jpubeco.2017.07.003

Viscusi, W.K., and Evans, W.N. (1990). Utility functions that depend on health status: Estimates and economic implications. The American Economic Review, 80, 353–374.

Viscusi, W.K. (2019). Utility functions for mild and severe health risks. Journal of Risk and Uncertainty, 58, 143–166. doi: 10.1007/s11166-019-09301-9

Weber, E.U., Blais, A.R. and Betz, N.E. (2002). A domain‐specific risk‐attitude scale: Measuring risk perceptions and risk behaviors. Journal of Behavioral Decision Making, 15, 263–290. doi: 10.1002/bdm.414

Zeckhauser, R. (1970). Medical insurance: A case study of the tradeoff between risk spreading and appropriate incentives. Journal of Economic Theory, 2, 10–26. doi: 10.1016/0022-0531(70)90010-4

Ziebarth, N.R. and Karlsson, M. (2014). The effects of expanding the generosity of the statutory sickness insurance system. Journal of Applied Econometrics, 29, 208–230. doi: 10.1002/jae.2317