SID, SAV, and Efficient Use
Chapter 15
© Allen C. Goodman, 2013
What kind of
evidence do
we need.
Supplier Induced Demand
• Does more providers
 more treatment?
S1
Price of
Services
S2
• Suppose S  from S1 to
S2. You would expect
changes to P3, Q3.
P1
• If physicians can
induce demand,
however, to D2, or D'2,
they can avoid losses.
P3
D1 D2
Q1 Q3
Quantity of
Services
D'2
Big Econometric Identification Problem
Start with model without SID (From earlier editions – not in FGS/5 – 7)
QD = a 0 + a 1 P + a 2 Y + u 1
(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
or
P = (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.
Can not
Why
have BOTH
U2 and U'2
not induce all the time?
m = profit rate
Net Income
• Perhaps, inducement
is a “bad.”
• Gives us unusual
indifference curves.
• We see U1 > U2.
U1
U2 < U1
p = mQ0 + mI
• Suppose m falls (due to mQ0
increased competition). m Q
0
• It could give us less
p = mQ0 + mI
inducement
• … or more inducement.
U'2 < U1
I2
I1
I3Inducement, I
Income and Substitution Effects
m = profit rate
Net Income
• Let’s decompose a
decrease in m into
income and substitution
effects
• Suppose m falls
U1
U2 < U1
p = mQ0 + mI
• Income effect – Drop in m
implies more inducement
• Substitution effect – Drop
in m makes inducement
p = mQ0 + mI
less effective. We do less
inducement.
Income Effect
Substitution Effect
I2
I1
Inducement, I
Income and Substitution Effects
m = profit rate
Net Income
• Suggests that for
there to be major
increase in
p = mQ0 + mI
inducement, income
effects must dominate
substitution effects.
• Research findings, at
this point are varied.
U1
U2 < U1
Income Effect
Substitution Effect
p = mQ0 + mI
I2
I1
Inducement, I
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 Variation
Is 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
• 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.
Health Status
S*
S1
May vary
within same
office!
Medical Care
Mgl. Product
Health Status
• Practice style -- Why
do practices vary so
much?
S2
Mgl. Cost
M2
S1
S*
M1
Medical Care
S2
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
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
What’s going on?
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
D1
D2
Demand?
$
S1
Medical Care
D1
Supply?
$
S1
S2
Medical Care
SAV and Inappropriate Care
• OR,
• Differing demand curves
due to incomes,
preferences, et.
D1
D2
$
S1
Medical Care
Inappropriate Levels of Care
• If Q1 is the “right”
level, then
• What are the
costs of being at
the wrong level,
• Either + or -?
D1
$
-
+
Q1
Medical Care
S1
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
Loss triangles !
IF  is the correct utilization,
(2) W = 0.5  (xi - )  vi
(2) W = 0.5  (xi - )  vi
Slope = 
Measuring the costs (2)
v
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/.
v
x

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.
xi
x
Measuring the costs (3)
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.
W = 0.5 * CV2 * Spending Level/E' .
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.
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
Measured Loss = A + B + C
V*
Incremental Value
V2
VA
True Loss = A + D + E + F + C
V1
True - Measured = (A + D + E +
F + C) - (A + B + C)
T - M = (D + E)
A
MC
D
E
C
F
X1
X*
Xa
X2
Rate of Use
What if we use mean rather than X*?
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.