SID, SAV, and Efficient Use

Chapter 15

© Allen C. Goodman, 2013

Supplier Induced Demand

• Does more providers more treatment?

S1

S2

D1D2

D'2

Price ofServices

Quantity ofServices

P1

Q1

• Suppose S from S1 to S2. You would expect changes to P3, Q3.

Q3

P3

• If physicians can induce demand, however, to D2, or D'2, they can avoid losses.

What kind of evidence do we need.

What kind of evidence do we need.

Big Econometric Identification Problem

Start with model without SID (From earlier editions – not in FGS/5 – 7)QD = a0 + a1P + a2Y + u1 (10.1)QS = b0 + b1P + b2X + b3MD + u2 (10.2)

where MD is number of MDs.In Eq’m:a0 + a1P + a2Y + u1 = QD = QS = b0 + b1P + b2X + b3MD + u2

orP = (b0-a0)/(a1-b1) - a2Y /(a1-b1) +b2X/ (a1-b1) + b3MD/ (a1-b1) Substituting into either (10.1) or (10.2)Q = c0 + c2X + c3Y + c4MD + v (10.3)

This looks like SID, except there was no SID in the model.

Why not induce all the time?

• Perhaps, inducement is a “bad.”

• Gives us unusual indifference curves.

• We see U1 > U2.

Inducement, I

Net IncomeU1

U2 < U1

I2 I1

p = mQ0 + mI

p = mQ0 + mI

• Suppose m falls (due to increased competition).

• It could give us less inducement

• … or more inducement.

mQ0

m Q0

I3

U'2 < U1

m = profit rate

Can not have BOTH U2 and U'2

Can not have BOTH U2 and U'2

• Let’s decompose a decrease in m into income and substitution effects

• Suppose m falls

Inducement, I

Net IncomeU1

U2 < U1

I2 I1

p = mQ0 + mI

p = mQ0 + mI

• Income effect – Drop in m implies more inducement

• Substitution effect – Drop in m makes inducement less effective. We do less inducement.

Income and Substitution Effects

Income Effect

Substitution Effect

m = profit rate

• Suggests that for there to be major increase in inducement, income effects must dominate substitution effects.

• Research findings, at this point are varied.

Inducement, I

Net IncomeU1

U2 < U1

I2 I1

p = mQ0 + mI

p = mQ0 + mI

Income and Substitution Effects

Income Effect

Substitution Effect

m = profit rate

Important Issue

• If you believe in SID, then demand-side policies have little impact because providers can always induce more demand.

• Some people argue that of course providers induce demand – if so, so do mechanics.

SAV – Small Area VariationIs the Right Amount of Treatment Used?

• Usage of technologies may vary. Why?– Provider may not have complete knowledge of

patient’s condition.– May not have complete knowledge of

appropriateness of procedure.– Provider may have preferences among types of

treatment.– Patient may have preferences among types of

treatment.

Wennberg

• Practice style -- Why do practices vary so much?

Medical Care

Hea

lth S

tatu

s

S1

S2

S*

Medical Care

Hea

lth S

tatu

s

S1

S2S*

Mgl. Cost

• Phys. 2 is shown as believing that additional units of medical care are more effective than does Phys. 1

• Rate w/in a market depends on distributions of type 1 and type 2 Phys. M1

M2

Mgl. Product

May vary within same office!

May vary within same office!

An Example

• Cesarean sections.

• Reference: Dartmouth Atlas for Michigan, Pp 8-9.

• What does it mean?

McAllen v. El Paso

• Both cities on Rio Grande River.

• Both with large Hispanic percentages.

• McAllen – 89%• El Paso – 82%

Source: Franzini et al.

Gawande - 2009

What’s going on?

Gawande A. The cost conundrum.New Yorker [serial on the Internet]. 2009 Jun 1 [cited 2010 Nov 3].Available from: http://www.newyorker.com/reporting/2009/06/01/090601fa_fact_gawande

Franzini, Mikhail, Skinner

• Look at medical use and expense data for patients privately insured by Blue Cross and Blue Shield of Texas.

• In contrast to the Medicare, use of and spending per capita for medical services by privately insured populations in McAllen and El Paso was much less divergent, with some exceptions.

• Although spending per Medicare member per year was 86% higher in McAllen than in El Paso, total spending per member per year in McAllen was 7% lower than in El Paso for the population insured by BCBS of Texas.

• Conclude that health care providers respond differently to Medicare incentives compared to private insurance.

Gawande A. The cost conundrum.New Yorker [serial on the Internet]. 2009 Jun 1 [cited 2010 Nov 3].Available from: http://www.newyorker.com/reporting/2009/06/01/090601fa_fact_gawande

How do we test it?

• Education, Feedback, and Surveillance – If by providing education, or by monitoring certain types of

treatments, there is a change Practice Style Hypothesis. Some verification, but not a lot.

• Comparing Utilization Rates in Homogeneous Areas – If you can rule out utilization differences due to

socioeconomic factors, you can say that practice style is important.

• Control by regression analysis. If you do a regression:Utilization = bixi + e,then if you’ve controlled for everything, you get an R2 measure.

Practice style would be the residual.

Three Problems

• How do you know if you’ve controlled for everything?

• What if some of your x’s actually represent practice style.

• Most of this is decidedly ad hoc. You’d like to see some good modeling.

• When done, we explain between 40 and 75% of the variation. This may leave a little, or a lot of variation to be explained by practice style.

SAV and Inappropriate Care

• Can you look at different levels of care, and determine that something wrong is going on.

• A> No! Efficient use of care occurs where marginal benefits = marginal costs. Simplest way to define this is to look at supply and demand curves.

• You may have single demand curve, and differing supply curves, due, e.g. to factor conditions

Medical Care

$

D1

S1

Medical Care

$

D1

S1

D2

S2

Demand?

Supply?

SAV and Inappropriate Care

• OR,• Differing demand curves

due to incomes, preferences, et.

Medical Care

$

D1

S1

D2

+-

Inappropriate Levels of Care

• If Q1 is the “right” level, then

• What are the costs of being at the wrong level,

• Either + or -?Medical Care

$

D1

S1

Q1

Measuring the costs in the aggregate

Fundamentally, we'll assume that marginal cost is constant. If marginal costs are rising, we'll see that these constitute lower bounds to the true costs.

(1) W = 0.5 xi vi Why?

W = welfare loss

xi = utilization of intervention for person i

vi = valuation of incremental unit

IF is the correct utilization,

(2) W = 0.5 (xi - ) vi

Loss triangles !Loss triangles !

If we then multiply and divide (3) by 2, we get [write out]:

W = 0.5 E 2 Nv/W = (0.5 E 2/2 )(Nv/) 2

Coefficient of variation = /, so 2/2 is CV2.

Measuring the costs (2)

Suppose that the valuation function is:

= v/x, or v = (xi - ).

Substituting into (2):

(3) W = 0.5 (xi - ) (xi - ) = 0.5 2 N.

Define inverse elasticity, at the mean, as:

E = (dV/dx)(x/V) = /v = E v/.

x

vx

v

Slope = (2) W = 0.5 (xi - ) vi

xi

That leaves Nv, which equals aggregate spending.W = 0.5 * E * CV2 * Spending Level.

I like working in terms of real Elasticities, so I would use:W = 0.5 * CV2 * Spending Level/E' .

where E' is the true demand elasticity, and CV2 is the coefficient of variation squared.Coefficient of variation is defined as the standard deviation divided by the mean. A good descriptive measure but it doesn't have a lot of statistical theory attached to it.

Measuring the costs (3)

Measuring the costs (4)

So this says that careful study of a medical intervention will have a greater expected benefit when:

- large numbers of people are affected.

- the per-unit cost of the intervention is high.

- the level of uncertainty about correct use is large.

- demand is inelastic.

W = 0.5 * CV2 * Spending Level/E' .

What if we use mean rather than X*?What may happen if we are comparing the actual use

with the mean, when, instead, we should be using X*, the appropriate level?

Consider valuation curves V1 and V2, their average Va, and the appropriate level V*.

If we compute the welfare loss around average Xa, we would include areas A, B, and C. The correct measure has areas A, C, D, E, and F, but not B.

Measured Loss = A + B + C

True Loss = A + D + E + F + C

B

Rate of Use

Incr

emen

tal V

alue

MC

V* VA V2

V1

X1 X* Xa X2

A

CD

E

F

Measured Loss = A + B + C

True Loss = A + D + E + F + C

True - Measured = (A + D + E + F + C) - (A + B + C)T - M = (D + E)

Measured Loss = A + B + C

True Loss = A + D + E + F + C

True - Measured = (A + D + E + F + C) - (A + B + C)

T - M = (D + E)

Region F has the same area as region B, so the missing area has size of regions D and E combined which is a parallelogram. So you are underestimating by (D + E).

Of course, if marginal costs are increasing, the losses are even larger.

What if we use mean rather than X*?