Signature
WL = 0.5 * (p - c * p) * (q_1 - q_0)
| Inputs | Definition | Unit |
|---|---|---|
p | Cost to the health system of providing one unit of care, the price without insurance | currency per unit of care |
c | Share of the resource cost paid by the patient at the point of use, at least zero and less than one | proportion |
q_1 | Units of care used when the patient pays c × p per unit | units of care per person per year |
q_0 | Units of care used when the patient pays p per unit | units of care per person per year |
WL | Resource cost of the extra care minus the value the patient places on it | currency per insured person per year |
|---|
Function
Ex post moral hazard welfare function
Maps the resource cost of care, the share of that cost the insured patient pays and the quantities of care used at the full and insured prices to the welfare loss attributed to insurance-induced use, and maps observed spending under two cost-sharing arrangements to a price elasticity of demand. The welfare measures assume that the demand curve measures the patient's marginal benefit, an assumption that the access motive and behavioural hazard challenge.
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Implementations
Excel
Welfare loss triangle from prices and quantities
With the unit cost in UnitCost, the coinsurance rate in CoinsRate and the quantities in QtyInsured and QtyFullPrice, Excel returns the welfare loss.
=0.5*(UnitCost-CoinsRate*UnitCost)*(QtyInsured-QtyFullPrice)
Assumptions
Demand curve measures marginal benefit
The patient's demand curve is read as the value of care to the patient. Nyman's access motive and the behavioural hazard argument of Baicker, Mullainathan and Schwartzstein both reject this reading for part of the extra use, and then the triangle overstates, or can even reverse, the true welfare effect.
Linear demand between the two prices
Demand is linear between c × p and p, so the area between the cost line and the demand curve is a triangle. With a convex demand curve the triangle is an approximation.
Resource cost constant and fully passed to the uninsured price
Each unit costs p to provide whatever the quantity, and p is the price an uninsured patient would pay. Supplier responses and differences between price and resource cost are excluded.
Worked examples
Outpatient visits under 25 per cent coinsurance
Visits cost 100 pounds each. At the full price a person uses 4 visits a year; with 25% coinsurance the patient pays 25 pounds and uses 5.5. The welfare loss attributed to the extra 1.5 visits is 56.25 pounds per person a year. The figures are illustrative.
p = 100; c = 0.25; q_1 = 5.5; q_0 = 4; WL = 56.25
Same visits under full insurance
With no cost sharing the same linear demand curve gives 6 visits a year, and the welfare loss rises to 100 pounds per person a year.
p = 100; c = 0; q_1 = 6; q_0 = 4; WL = 100
Common errors
Counting the whole cost of the extra care as the loss
In the first example the extra 1.5 visits cost 150 pounds, but the patient values them at between 25 and 100 pounds each. Only the triangle of 56.25 pounds is a loss under the conventional analysis.
Treating all extra use as waste
The triangle values extra care by what patients are willing to pay at the margin. Care that insurance makes affordable, or high-value care that patients underuse, is not captured by that measure, so extra use is not waste by definition.
Sources
Moral hazard as a rational response to a lower price
Pauly MV. The economics of moral hazard: comment. American Economic Review. 1968;58(3):531-537. Insurance that lowers the price of care at the point of use increases use; care valued below its cost is a welfare loss, so full coverage of some uncertain medical expenses may not be optimal.
Handbook review of moral hazard and its welfare cost
Zweifel P, Manning WG. Moral hazard and consumer incentives in health care. In: Culyer AJ, Newhouse JP, editors. Handbook of Health Economics. Vol 1A. Amsterdam: Elsevier; 2000. p. 409-459. Ex ante, ex post and dynamic moral hazard; the welfare loss from insurance-induced demand under coinsurance, measured with the demand curve.
Canonical Identity
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