Health Uncertainty and Medical Expenditure: A Model of Savings with Endogenous Transitions Authored by: Shooshan Danagoulian Ph.D. Student, Cornell University Discussed by: Donna Gilleskie, UNC-CH Sep 29-Oct 01, rd Annual Health Econometrics Workshop

Author ’s Motivation Extend prevailing structural models of savings by modeling medical expenditure as a choice rather than a draw from an uncertain distribution Allow this choice of medical care expenditure to affect the one-period health transition Model extends DiNardi, French, and Jones (2010) Compare path of savings when stochastic health is exogenous and when it is endogenous Obtain input from you; work is admittedly preliminary

Discussant’s Motivation Make clear the assumptions of the model in order to point out deviations from our understanding of life-cycle health behaviors Suggest areas where we can push our models so as to better understand behaviors Highlight the estimated, econometric model to explain where our econometric knowledge can be incorporated into models of behavior

Author’s timing of elderly savings and medical care expenditure decisions c t, m t, a t+1 s t+1, h t+1 (m t, h t ) beginning of age t beginning of age t+1 consumption, medical care expenditures, and savings decisions survival and evolution of health Ω t = (a t, h t ) Ω t+1 = (a t+1, h t+1 ) unobs’d health determinants

V(a t, h t = h) = max { u (c t, φ(m t, h t )) + β s t+1 ∑ π(h t+1 = h ’ |m t,h t,s t+1 ) V(a t+1,h t+1 = h ’ ) + β (1-s t+1 ) V(a t+1,h t+1 = 0) } Author’s model of elderly savings and medical care expenditures {c t, m t, a t+1 } h’h’ stochastic, but exogenous survival stochastic, and endogenous health transition endogenous medical care expenditure

Author ’s data Health and Retirement Survey(HRS) Asset and Health Dynamics of the Oldest Old (AHEAD) cohort Cohort information: o Cohort born in 1923 or before o Initial wave in 1993/1994 and followed for 9 waves ( ) Medical care expenditure information: o Out-of-pocket expenditures on hospital/nursing home in last 2 years o OOP expenditures on doctor/outpatient/dentist in last 2 years o OOP expenditures on Rx per month (in last 2 years) Health status information: o Self-reported health o Limitations of activities of daily living (and IADLs) Asset information: o Stocks, mutual funds, dividends, bonds, CDs, T-bills, home, etc.

Author ’s sample Health and Retirement Survey(HRS) Asset and Health Dynamics of the Oldest Old (AHEAD) cohort Sample: o Retired, single individuals o 3,728 initial sample size Medical care expenditure alternatives: o Out-of-pocket expenditures; sum of all sources? Annual or over 2 years? o Ultimately 2 alternatives: below and above the median Health outcomes: o Self-reported health o Ultimately 3 outcomes: good, fair, or poor Asset level alternatives: o Not estimated, so data are not needed o Ultimately a simulated assets path

Author ’s challenge -to parameterize and solve the optimization problem Parameterize Per-period utility function Discount factor Survival probability Health production function Health Production Function …or Health Transition Probabilities In order to solve the model, one needs to know how health evolves from one period to the next. How does one more dollar spent on medical care translate into (improved, sustained, or worse) health?

One could regress observed health outcomes in t+1 on observed mc expenditures in t and observed health in t to obtain parameter estimates. – Obviously: biased effects b/c mc expenditure is endogenous – Less obvious: we need counterfactual transition probabilties – Less obvious: perverse effects of medical care What do we want/need? If optimal mc expenditure is solved for as part of the decision making problem, then such expenditure has to increase welfare for it to be chosen. Where does expenditure and health enter the model? – MC expenditures: utility function (+,-), budget constraint (-) and health transition (?) – Health: utility function (+ linear) and health transition (?) Modeling health transitions

Discussant ’s comment h t+1 = (1-δ t ) h t + i(m t,h t ) natural depreciation of current health stock over time investment in future health Consider Grossman’s health production function: (1-δ t ) h t i(m t,h t ) < > ? Bottom line: We want/expect medical care to be productive.

Author ’s response Manski’s partial identification method (2003): Use the data to identify regions (or ranges of probabilities) of the health transition. Simulate optimal savings decisions using the lower and upper bounds of the health transition probabilities, which are health and medical care expenditure state specific.

Author ’s conclusion A model with endogenous health transitions leads to higher or lower savings than a model with exogenous health transitions. It is important to consider how one models the probabilities of health transition.

Comments on the paper… Re-estimate all the parameters Consider health insurance as an alternative (or additional) way to smooth consumption – Other sources of uncertainty: Exogenous health shocks vs. behavior-induced shocks Spousal health shocks Price uncertainty – OOP expenditures does not reflect distribution of MC costs Capture the low probability, high cost events – Model consumption or utilization rather than expenditures – And let prices be uncertain Consider other health inputs that affect health transitions Discuss policy alternatives Discussant’s reflections

Why save in this model? Only b/c of income loss associated with endogenous medical care expenditures. No bequests, no other income uncertainty (prices of other goods, prices of medical care), no spousal health shocks. Why consume medical care in this model? B/c it provides contemporaneous utility. Not clear that it increases probability of maintaining or improving health. But health insurance is another form of consumption smoothing in the face of medical expenditure risk. And health insurance is not endogenous. Unclear why one models OOP medical care expenditure, as opposed to medical care utilization under uncertain prices of medical care. Uncertainty can arise b/c individuals don’t know there true health state when they go to the doctor, doctor doesn’t tell them the price of (similar?) alternatives. Tails of the expenditure distribution. We are spending more and more time on this in single equation models. It is important to capture the tails of the distribution well in models of optimal insurance choice…why not savings too. This is precisely where we need to incorporate those econometric considerations.