Wednesday, April 9, 2014

Incentives for three health plans.

Situation:   The table below lists characteristics (deductible, coinsurance rate, and out-of-pocket expense limits) for three different health plans


Three Health Insurance Plans
Plan Number One
Plan Number Two
Plan Number Three
Deductible
$2,500
$4,000
$8,000
Coinsurance Rate
20%
30%
0%
Out of-pocket Expense  Limit
$5,000
$10,000
$8,000


The table below describes total health expenditures (the amount paid by the insured and the amount paid by the insurance company) for a sample of 35,000 people.


Health Expenditures
Number of People
$0
8,000
$500
7,000
$3,000
6,000
$6,000
5,500
$12,000
5,500
$25,000
2,800
$150,000
200
Total
35,000





Questions:

What is the mean and the total health expenditure paid by the insurance firm for the three health insurance plans and this group of individuals?


A company offers all three insurance policies to its employees.  Discuss three reasons why actual health expenditures will differ from expected health expenditures for these three health plans?


Analysis:

We are given total health expenses (both insurance payment and payment by the insured).    We need insurance payments only for each of the three plans.

In order to get the insurance payment function we need the threshold where the insurance company pays 100% of the bill.   I show how to do this in a previous post.




Results for the threshold for the three plans at which total health expenditures trigger insurance company payments equal to 100% of the bill are presented below.

Plan 1
Plan 2
Plan 3
Formula
OUTP_MAX
$5,000
$10,000
$8,000
a1
DEDUC
$2,500
$4,000
$8,000
a2
Coinsurance Rate%
0.2
0.3
NA
a3
THRESH
$15,000
$24,000
$8,000
(a1-a2+a3*a32)/a3
CHECK
$5,000
$10,000
$8,000
a2+a3*(a4-a2)


The insurance plan parameters and the frequency distribution for the data on total health expenditures are used to get figures for insurance payments under the three plans.

The insurance company payout formula differs in three intervals.


Insurance expenditures are zero for health expenditures below the deductible. 
   

When total health expenses are between the deductible and the threshold triggering the maximum out-of pocket expense the insurance payment is

(1-CO_RATE) x (HE-DEDUC)

Where CO_RATE is the coinsurance rate, HE is health expense and DEDUC is deductible.


When health expense is greater than the threshold triggering the maximum allowable out-of expenses the insurance payout is the sum of the payout at the threshold and the difference between total health expenditures and the threshold.

Payment at the threshold is

(1-C0_RATE) x (THRESH-DEDUC)

Add to this (HE-THRESH).

These numbers are fairly easy to program with a single if statement in SAS but much harder to do in EXCEL   I don’t have SAS so I hard wired the three intervals in EXCEL.  (It is probably possible to create this table with the look-up function.)



Health Expenditures
Number of People
Insurance payments plan 1
Insurance payments plan 2
Insurance Payments Plan 3
$0
8,000
$0
$0
$0
$500
7,000
$0
$0
$0
$3,000
6,000
$400
$0
$0
$6,000
5,500
$2,800
$1,400.0
$0
$12,000
5,500
$7,600
$5,600
$4,000
$25,000
2,800
$20,000
$15,000
$17,000
$150,000
200
$145,000
$140,000
$142,000
SUMPRODUCT
$144,600,000
$108,500,000
$98,000,000
Average Insurance Company Expenditure
$4,131.43
$3,100.00
$2,800.00


Discussion:

 The high-deductible health plan is the least expensive of the three health plans. 

More people have an incentive to at least partially economize on health expenditures under the second health plan than under the other two health plans.  (Under health plan two there is some incentive to economize until health expenditures reach $24,000.   The incentive to economize under health plans one and three end at total health expenditures of $15,000 and $8,000 respectively.)

Insurance payouts are lower under health plan three than the other two health plans.  High deductibles are highly effective at reducing total costs because all insured individuals must pay the entire deductible prior to receiving payments.


There are two reasons to believe that the cost differential across health plans will be larger than the ones shown here if an individual is free to choose among all three health plans.

Both health plans two and three provide a greater incentive for individuals to economize on consumption of health care than health plan one. 

Healthier people will tend to sign up for the least expensive health plan.

The cost figures presented here are a lower bound on the reduction in insurance payouts caused by moving away from plan one towards a plan with greater cost sharing.  Actual reduction in payouts is affected by the incentive to economize and adverse selection – the incentive for healthy people to choose the least expensive plan.  






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