Health Uncertainty and Medical Expenditure: A Model of Savings

with Endogenous TransitionsAuthored by:

Shooshan Danagoulian

Ph.D. Student, Cornell University

Discussed by:

Donna Gilleskie, UNC-CH

Sep 29-Oct 01, 20113rd Annual Health Econometrics Workshop

Author ’s Motivation

Extend prevailing structural models of savingsby 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 modelin 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

ct, mt, at+1 st+1, ht+1(mt, ht )

beginning of age t

beginning of age t+1

consumption, medical care

expenditures, and savings

decisions

survival and evolution of

health

Ωt= (at, ht ) Ωt+1= (at+1,ht+1)

unobs’d health determinants

V(at, ht = h)

= max { u (ct, φ(mt, ht))

+ β st+1 ∑ π(ht+1= h’|mt,ht,st+1) V(at+1,ht+1= h’)

+ β (1-st+1 ) V(at+1,ht+1= 0) }

Author’s model of elderly savings and medical care expenditures

{ct, mt, at+1}

h’stochastic, but exogenous

survival

stochastic, and endogenous

health transition

endogenous medical care expenditure

Author ’s dataHealth and Retirement Survey(HRS)Asset and Health Dynamics of the Oldest Old (AHEAD) cohort

• Cohort information: o Cohort born in 1923 or beforeo Initial wave in 1993/1994 and followed for 9 waves (1993-2008)

• Medical care expenditure information:o Out-of-pocket expenditures on hospital/nursing home in last 2 yearso OOP expenditures on doctor/outpatient/dentist in last 2 yearso OOP expenditures on Rx per month (in last 2 years)

• Health status information:o Self-reported healtho Limitations of activities of daily living (and IADLs)

• Asset information: o Stocks, mutual funds, dividends, bonds, CDs, T-bills, home, etc.

Author ’s sampleHealth and Retirement Survey(HRS)Asset and Health Dynamics of the Oldest Old (AHEAD) cohort

• Sample: o Retired, single individualso 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 healtho Ultimately 3 outcomes: good, fair, or poor

• Asset level alternatives: o Not estimated, so data are not neededo 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

ht+1= (1-δt) ht + i(mt,ht)

natural depreciation of current health stock over time

investment in future health

Consider Grossman’s health production function:

(1-δt) ht i(mt,ht)<>

?

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.