3. [15pts] Suppose two manufacturing companies merge and the employees from one

Question

3. [15pts] Suppose two manufacturing companies merge and the employees from one company are switched to the more generous health insurance plan of the other company. Think of "more generous" meaning some combination of more medical procedures being covered and a higher reimbursement rates for covered procedures. Succinctly answer the following in no more than 500 words total. Explain why this provides a natural experiment that could be used to evaluate the effects of a generous health insurance plan on health care usage. a. b. Describe the data that you would want to collect for such a study, and how you would analyze the data. Discuss the validity of the causal conclusions, and the generalizability of the study. What weaknesses might there be? c.

Explanation / Answer

a. Let the two companies be C1 and C2 and their respective health plans be P1 and P2.

Let the 'generosity' of P1 be G1 and the 'generosity' of P2 be G2

Without loss of generality, we assume that G2 > G1 i.e. plan P2 is more generous than plan P1.

Employees incur some expenses when they avail of these plans. Let those expenses be E1 and E2.

In economic terms, the pay-offs of P1 and P2 are PO1 = G1 - E1 and PO2 = G2 - E2.

Now, when employees of C1 migrate to the plan of C2, their payoff will naturally increase since G2 > G1.

So, this increases their incentive to utilise their plan.

Also, employees of C2 who continue to be on P2, will experience no change in their environment.

That is why, they have no additional incentive to utilise their plan and we can expect to see differences

in 2 ways:

i) Employees of C1 using plan P2 more than when they used plan P1

ii) The higher rate of usage of plan P2 from employees of C1 as opposed to employees of C2.

That is why this situation serves as a natural experiment.

b. We would collect two sets of data:

i) For each employee of C1, the number of times that she/ he used plan P1 in a year

For each employee of C1, the number of times that she/ he used plan P2 in a year

ii) For each employee of C2, the number of times that she/ he used plan P2 in a year

The number of times of health care usage u is a parametric variable.

In the first case, it is the same sample (employees of C1) which we test twice.

There are only two groups (employees using plan P1 and employees using plan P2),

so we can apply a paired sample t-test, which will show whether there is significant difference

in the average usage in the 2 groups.

ii) In the second case, they are different samples (employees of C1 and employees of C2).

There are only two groups, both of which use plan P2.

so we can apply a 2-sample t-test, which will show whether there is significant difference

in the average usage in the 2 groups.

c. t-test does not establish causality. Even if there is a statistically significant higher usage,

it does not prove that the cause is the generosity of the plan (i.e. G2 > G1 is the reason).

There could be other factors such as a change in the company policy, increase in the incidence of ailments.

We can generalize the study to n companies. In such a case, t-test is not applicable.

Then, we have to apply 1-way ANOVA.

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