代写EC9790 Health Economics Examinations 2021/22

日期：2024-08-24 07:26

EC9790

May Examinations 2021/22

Health Economics

SECTION A: Answer ONE question ONLY

1. This question has two parts. Please answer both.

Part I

A doctor needs to decide on the treatment to provide to their patients. There are two possible treatments: A and B. Each patient that the doctor sees suffers from one (and only one) of two illnesses: a or b. The probability that a patient suffers from illness a is 0.5 and the probability that they suffer from illness b is 0.5. Assume that treatment A is the “right” treatment for patients with illness a and treatment B is the “right” treatment for patients with illness b. More specifically, if the patient receives the “right” treatment for their illness, the probability that the treatment will succeed is 0.75 and the probability that the treatment will fail is 0.25, whereas if the patient receives the “wrong” treatment, the treatment will fail with certainty. In order for the doctor to diagnose the patient’s illness, they need to invest effort that has a cost of 10. If the doctor invests that effort they will correctly diagnose the patient’s illness, whereas if they do not, the cost they incur will be 0 but they will not be able to diagnose the patient’s illness. Assume that the doctor can choose whether or not to exert the effort, and if they do not, they will choose one of the two treatments randomly. Assume that there is a health plan that contracts with doctors to treat patients. The doctor’s objective is to maximize their expected utility. Assume that the doctor’s utility from treating a patient is given by:

where w is the payment the doctor receives for each patient and ce is the doctor’s cost of effort (that is, ce = 0 if the doctor exerts no effort and ce = 10 if the doctor exerts the effort). Finally, assume that the doctor can always refuse to treat a patient and obtain an expected utility of U = 40  from some other activity.

(a)   Assume that neither the doctor’s effort, nor the treatment outcome is verifiable, and thus the plan can only offer the doctor a lump sum payment per patient. What is the lowest lump sum at which the doctor will agree to treat patents? What is the  probability that the treatment will succeed in this case? (7 marks)

(b)  Assume now that treatment outcome is verifiable but the doctor’s effort is not (that is, the payment to the doctor can depend on whether or not the treatment succeeded but it cannot depend on the doctor’s effort). The health plan’s objective is that the doctors will provide the “right” treatment to every patient at the lowest cost to the health plan. Describe the contract that the health plan should offer the doctor in this case. (7 marks)

(c)   Assume now that the doctor’s effort is also verifiable. Here too assume that the health plan’s objective is that the doctors will provide the “right” treatment to every patient at the lowest cost to the health plan. Describe the contract that the health plan should offer the doctor in this case. (7 marks)

(d)  Assume now that not only the doctor, but also the health plan can invest the effort (incurring the same cost as the doctor) in order to diagnose the patient’s illness and then inform. the doctor. For each of the three cases above, should the health plan invest that effort? (9 marks)

Part II

The Progressive Corporation, the fourth largest insurance company in the United States, filed a patent for a new insurance system for drivers called an autograph. An insured driver who chooses the autograph option transmits information to Progressive about their trips (how many, to where, at what time, and even their speed and acceleration) and the insurance premium is calculated based on this information. Drivers who are not interested in installing a transmitter in their vehicle can continue to pay insurance premiums calculated in the traditional way, that is according to general information held by the insurance company (age, marital status, history of traffic offenses and accidents, etc.). Initial experiments with an autograph system conducted in Houston, Texas, showed that policyholders who opted for an autograph system saved an average of about 25% of their insurance premiums compared to the premiums they would have paid under the traditional insurance method.

(e)   Can the results of the initial experiment be explained by the moral hazard phenomenon? (7 marks)

(f)    Can the results of the initial experiment be explained by the adverse selection phenomenon? (7 marks)

(g)   If Progressive offers the option to pay insurance under an autograph system throughout the United States but also allows drivers to continue paying premiums according to the traditional method, what do you think will be the effect on the insurance premium of those who do not choose to install the autograph system and what proportion of drivers will choose not to install the system? (6 marks)

2. This question has two parts. Please answer both.

Part I

An individual can be either healthy or sick.  With probability 0.75 the individual will be healthy and in this case their utility function will be given by Uh =  10√c , where c is their level of consumption, and with probability 0.25 the individual will be sick and their utility will be given by: Us = 4√c + 2√x where x is the amount of health services they consume. Assume that the market price of each unit of consumption is 1 and that of each unit of health care is also 1. The individual’s income is I = 100 and they can choose any level of consumption they wish (subject to their budget constraint, of course) but they can choose only one of three levels of health services: x= 0 or x=36 or x=64 (that is, they cannot choose any other level of x).  Assume that individuals choose their level of health services only if and after they become ill.

(a)   What level of health care services will the individual purchase if they are not insured? (6 marks)

(b)   What is the actuarially fair premium for full insurance? (6 marks)

(c)   Is there a moral hazard problem if the individual purchases full insurance? (6 marks)

(d)   Will the individual purchase full insurance at the actuarially fair premium if they can choose only between being fully insured or not being insured at all? (6 marks)

(e)   Please provide an intuitive explanation for your result in part (d) above. (6 marks)

Part II

Long-term care insurance pays individuals or their families a monthly amount for all or part of any period in which the individual is defined as a "long-term care" patient. An individual fits this definition if they are unable to perform. a certain number (usually three or four) of basic activities such as: showering or dressing alone; getting up, sitting or lying down on their own, etc. In most Western countries, however, only around ten percent of individuals acquire long-term care insurance privately.

(f) Can you provide an explanation for the low proportion of individuals acquiring long-term care insurance based on the moral hazard phenomenon? (7 marks)

(g) Can you provide one or more explanations based on the adverse selection phenomenon? (7 marks)

(h) Can you offer (no more than two or three) other explanations for why so few people choose to purchase long-term insurance? (6 marks)

SECTION B: Answer ONE question ONLY

3.

(a) A vaccine can cause side effects with probability 0.05 at the time of inoculation t0 and it lowers the probability of contracting a virus in the next period from 0.2 to 0.1. Without side effects or sickness, H = 10. Side effects decrease health by 2, the virus decreases health by 8. Write down the expected health in both periods with and without the vaccine. How do they change with the vaccine? Assuming an individual is risk neutral with U=H and discounts future health at a factor of 0.02, what is total utility with and without the vaccine? What does the individual choose? Now assume that the probability of infection without the vaccine is 0.11. What does the individual choose? (7 marks)

(b) Now assume that the efficacy of the vaccine depends on the state of the world, what is the particular virus strand that becomes dominant in the next period; this is unknown at time 0. What is the minimum efficacy (the decrease in infection probability) that would lead the individual to get vaccinated? (4 marks)

(c) Now assume that there is an additional, final, period, t2 (old age). One only lives to t2 if H1 > 3. In old age, an individual has a 0.3 chance of getting dementia, which yields U=H=-50. Does the individual want to get vaccinated in this case if parameters are as in (a)? Discuss what changed. (7 marks)

(d) Now assume that the individual is risk averse, with utility U  = 2√H. How does your answer to (a) change (assuming probability of infection without the vaccine is 0.11? Discuss. (7 marks)

(e)   From 1908 to 1933, local governments in the United States instituted county-level health departments (CHDs) that provided preventative health services geared towards young children, aged 0-5. The figure below shows effects of living in a county that introduced CHDs for children born in that county around the time of the introduction of CHDs on income earned by those children when they grow up. Results are from a regression that controls for individual characteristics, county, and birth cohort fixed effects. Describe the picture. Suppose that CHDs were introduced  first in counties that were poorer, but were catching up with the rest of the US. Can  you interpret the results causally? Why or why not? Now suppose that CHDs were introduced in random order. What does the graph suggest about the relationship between health and income? (10 marks)

(f)    Minorities have disproportionally worse health and are more likely to live close to pollution sources, like ports. Can you conclude that pollution is the cause of poorer health in minorities by regressing health measures on pollution by race? Now suppose you use an identification strategy that leverages quasi-experimental variation from distant oceanic events several days prior that exogenously shift the vessel tonnage in port to identify the causal effect of daily pollution concentrations on health in port areas. Can you conclude your estimates are causal? Why or why not? Suppose this table summarizes your findings: describe the table. Are blacks more affected by pollution in terms of respiratory, cardiac, and mental health? (5 marks)

(g)   The graph below shows treatment intensity (total expenditure ordered) for physicians who switch to a different group (think of this as employer) with Δpmt defined as the difference in intensity between the destination and the origin group. The regressions estimating these coefficients include physician fixed effects. What can explain these patterns? Do you think there is a causal relationship between the environment where a physician operates and their practicing style based on these graphs? (5 marks)

(h)   Describe the figure below. List at least two mechanism that can explain it. C-section stands for Cesarean section surgery for birth delivery. (5 marks)

4.

(a)   The table below plots estimates of the relationship between several variables and an indicator for whether elderly parents are in a good health using data from Chinese rural villages. Describe the table. (PCE stands for annual per capita household expenditures) Can we interpret the coefficients on spousal and children’s education in Columns 204 causally? Why or why not? (7 marks)

(b)   Now, suppose you want to instrument children’s education with grandparents’ education (so the parents of the individuals whose health you are measuring). Is grandparents’ education a valid instrument in this case? Why or why not? (7 marks)

(c)   Now, suppose you want to instrument children’s education with distance of the family home from the closest high school. Is this a valid instrument in this case? Why or why not? The Table below shows effects of children’s education instrumented in this way on parents’ health in column 1, and the effect of distance from high school on the health of elderly individuals in the survey who do not have children in column 2. How do you interpret column 2? (7 marks)

(d)   Suppose children care about their parents’ health, H, and their own consumption c. They can purchase care for their parents at unitary price p=3, while consumption costs 1 per unit. U = C2  + 30H.

Scenario 1: If children have an income of 100, do they prefer H=95/3 or H=30?

Scenario 2: If children are more educated and have an income of 200, which level of health do they pick of these two? Discuss what changed. (7 marks)

(e)   Scenario 3: An alternative model suggests that better educated children understand the value of preventative care better, so they are able to make more cost-effective   choices (or value it more), even holding income constant. In this different model, p=2. If children have an income of 100, do they prefer H=95/3 or H=30 under this scenario? What changed with education in this case with respect to Scenario 1? Can a researcher disentangle these mechanisms empirically from parental health consumption? (7 marks)

(f)    Minorities have disproportionally worse health and are more likely to live close to pollution sources, like ports. Can you conclude that pollution is the cause of poorer health in minorities by regressing health measures on pollution by race? Now suppose you use an identification strategy that leverages quasi-experimental variation from distant oceanic events several days prior that exogenously shift the vessel tonnage in port to identify the causal effect of daily pollution concentrations on health in port areas. Can you conclude your estimates are causal? Why or why not? Suppose this table summarizes your findings: describe the table. Are blacks more affected by pollution in terms of respiratory, cardiac, and mental health? (5 marks)

(g)   The graph below shows treatment intensity (total expenditure ordered) for physicians who switch to a different group (think of this as employer) with  Δpmt defined as the difference in intensity between the destination and the origin group. The regressions estimating these coefficients include physician fixed effects. What can explain these patterns? Do you think there is a causal relationship between the environment where a physician operates and their practicing style based on these graphs? (5 marks)

(h)   Describe the figure below. List at least two mechanism that can explain it. C-section stands for Cesarean section surgery for birth delivery. (5 marks)