More Demand
© Allen C. Goodman, 2016
Fundamental Problems with Demand
Estimation for Health Care
• Measuring quantity, price, income.
• Quantity first. It is typically very difficult
to define quantity.
• We usually look at the stuff that is
easiest to measure. Things like visits,
days of service, and the like.
Problems w/ Quantity
• The problem here is that the measures may
not be meaningful.
• 5 days of inpatient care for substance abuse
is not the same as 5 days of inpatient care for
brain surgery.
• We could argue that 5 visits reflects more
treatment than 4 visits, but it could simply
indicate that the first 4 visits were not
effective.
Episodes
• Episodes represent what
may be a more
theoretically desirable
measure of output in a
number of ways.
• An episode starts when
someone starts to need
treatment, and ends when
they no longer need it.
• For example, an episode
may include a few visits to
the doctor, some inpatient
hospitalization, and maybe
some follow-up clinic visits,
and some drug therapy.
Severity
Illness
Treatment
Time
Episodes
• It is usually defined chronologically. In
principle, this is the best way to measure both
instances of demand, and the costs of
treatment.
• Particularly useful, for example, if the makeup of treatment has changed. If, over time,
we have substituted outpatient for inpatient
care, and we have a few more tests, but they
are cheaper, then what is really important is
not the number of visits, or the number of
days, but the cost of the episode.
Episodes
• These seem great. What are the problems?
– They are necessarily arbitrary. We must determine when the
episode starts, and when it ends. Does a certain visit represent
more of the same episode, or the beginning of another episode?
– Less helpful for chronic conditions than acute conditions.
– Might have 2 episodes (e.g. respiratory, mental health) going on
at the same time.
– We must look much more carefully into the process that defines
the episode, and at behavior within the episode.
– We need complete data on individuals. If individuals go to
several providers, or take considerable out-of-plan coverage, it
may be very difficult to create episodes with any real
confidence. Insurance data often make this issue more
tractable.
Income
• Most elementally, it is often difficult to find incomes. If
we are looking at insurance claims, they often don't
have people’s incomes on them. You can get an
expenditure elasticity, but you'll have lots of trouble
getting an income elasticity.
• Given that you have income, there are other
concerns. Many economists, myself included, feel
that many types of expenditures are more
appropriately related to long-term, or permanent
income, than to measured, or current income. If we
try to estimate demand with current income, we get
some problems with the demand elasticity.
Permanent Income
If:
Q = bp YP + bt YT + 0, is the true regression,
and we estimate:
Q = bY + ε1, then set:
Q = bp YP + bt YT + 0 = bY + 1
and we get:
1 = (bp - b) YP + (bt - b) YT + 0.
This gives us:
b = [2p/(2p + 2t)] bp + [2t/(2p + 2t)] bt.
This is a weighted average.
More on Permanent Income
It is very difficult to come up with appropriate
measures of permanent income. The ideal way is to
have some sort of panel data for individuals over
time. If we believe that permanent income is related
to the return to human and non-human capital, then
we would get the identity:
Y = YP + YT.
YP = H + N
where H is human capital, and N is nonhuman capital.
More on Permanent Income
Suppose that H is a function of
Age, Education, Training, Health, etc.
Then we can estimate:
YP = a(Age) + b(Education) + c(Training), etc. + N
In a single period, we can substitute this to get:
Y = a(Age) + b(Education) + c(Training) + N + YT.
Here, the fitted value of the regression of Y, on these
covariates is YP, and the residual is YT.
With cross-sectional data this is about as good as you
can do, although it is hard to identify fixed effects
(ambition, skill).
What some people do instead …
Consider an estimation that looks like:
Q =  idi + Y (ignore error term)
This gives us a set of estimated parameters. Go back
to permanent income:
YP =  bidi, and insert into:
Q = ap YP + at YT
Now, use Y = YP + YT.
We substitute  bidi for YP, and Y -  bidi for YT, to get:
Q =  ap (bidi) + at Y - at  (bidi), or
Q =  (ap - at) (bidi) + at Y.
Difference between econometrics
and running regressions.
What some people do
Q =  (ap - at) (bidi) + at Y.
Key point, here.
Estimates of demographics are likely to be biased,
probably downward. What people think are estimates
of income elasticities, are probably biased severely
downward.
Price
80
Effective demand 80
60
Money Price
60
Effective Price
If we treat coinsurance as
simply a fraction, then
the econometrics should
not be too difficult.
Rather than measuring
price P, we are
measuring net price rP.
A 10 % change in
coinsurance rate is
simply the same as a 10
% change in net price.
Even this simple example
suggests that insurance
is only important IF price
is important.
40
40
Money price demand
20
20
2
4
6
8
Visits
10
12 14
Kinks from Insurance
Students tend to
fixate on the kinks.
May not necessarily
be at a kink.
Composite
3 sections
1. Deductible - same
as before
2. Coinsurance Other Goods trade
off for more health
care.
3. Limit - Insurer won't
pay more. Back to
previous slope.
Budget constraint is
now decidedly nonlinear, and non-convex.
Health Care
More kinks
Clearly, the price is
negatively correlated
with the amount
purchased.
There are two possible
error terms:
More kinks
1. The type of errors in
variables equation, If
this is random, then the
coefficient b is biased
toward 0, (or upward).
2. It reflects the
correlations of price to
the error term of the
demand equation itself.
Since individuals with
large values of the error
term are likely to
exceed a deductible,
and conversely, V will
be negative.
More kinks
That is, a large positive (+)
error is correlated with a
low price, because after
the deductible, we're
thrown into a low
copayment (and vice
versa).
This is noted by error terms in
graph. This suggests that
the demand curve is more
elastic (more negative).
So one form of error takes
us toward 0, and the other
takes us away. It's not
clear how they sort out.
Rand Experiment
• The Rand experimental data randomly
assigned people to insurance
coverages, thus addressing at least
some of the problem.
• Generally these estimates gave
coinsurance elasticities of about -0.2.
What does this mean?
Some More Demand – 1
• Handbook of Health Economics has some
summaries and sources.
• Use of prescription drugs is more price sensitive (Hsu et al., 2006; Huskamp et al., 2003;
Joyce et al., 2002). In general, the literature
finds elasticities of about -0.2 to -0.6.
Source: Who Ordered That? The Economics of Treatment Choices in
Medical Care Amitabh Chandra, David Cutler, and Zirui Song, in
Handbook of Health Economics, Oxford, Elsevier, 2012: 397-432.
Sources – 1
• Hsu, J., Price, M., Huang, J., Brand, R., Fung, V., Hui, R.,
et al. (2006). Unintended consequences of caps on
Medicare drug benefits. New England Journal of
Medicine, 354(22), 2349-2359.
• Huskamp, H. A., Deverka, P. A., Epstein, A. M., Epstein,
R. S., McGuigan, K. A., & Frank, R. G. (2003). The effect
of incentive-based formularies on prescription-drug
utilization and spending. New England Journal of
Medicine, 349(23), 2224-2232.
• Joyce, G. F., Escarce, J. J., Solomon, M. D., & Goldman,
D. P. (2002). Employer drug benefit plans and spending
on prescription drugs. JAMA, 288(14), 1733-1739.
Some More Demand – 2
• People seem to cut back on both
necessary and unnecessary care.
• When cost sharing increases (price ↑),
people use fewer services, but the
services foregone are neither uniformly
valuable nor wasteful (Buntin et al.,
2011; Chandra et al., 2010).
Sources – 2
• Buntin, M. B., Haviland, A. M., McDevitt, R., & Sood,
N. (2011). Healthcare spending and preventive care
in high-deductible and consumer-directed health
plans. American Journal of Managed Care, 17(3),
222-230.
• Chandra, A., Gruber, J., & McKnight, R. (2010).
Patient cost-sharing and hospitalization offsets in the
elderly. American Economic Review, 100(1), 193213.
More Demand – 3
• Higher cost sharing (higher prices) deters
recommended preventive and chronic care,
which may lead to undesirable “offsets” in
greater use and spending on other services,
such as hospital care (Trivedi et al., 2010;
Chandra et al., 2010; Hsu et al., 2006).
• Trivedi, A. N., Moloo, H., & Mor, V. (2010).
Increased ambulatory care copayments and
hospitalizations among the elderly. New
England Journal of Medicine, 362(4), 320-328.
More Demand – 4
• There are complementarities across types of
care (Buntin et al., 2011). Raising costs
(prices) for prescription drugs increases
hospital costs.
• Lowering costs for preventive care has only a
modest effect on utilization if people need to
see their primary care physician before
accessing preventive care.
Time Prices
• Acton's work gets quoted a lot here, although it’s OLD.
This type of analysis has been problematical because of
difficulties in imputing valuations of time. The table in
FGS/7 (P. 180) looks at his findings for outpatient visit
demand, and physician services.
• We see that the own-price elasticity for travel time (-0.958)
of a public outpatient department is about 4 times as large
as for a private physician (-0.252), presumably because
there are numerous substitutes. The cross-price
elasticities are positive, indicating that the two types of care
are substitutes rather than complements
The Effects of Time and Money
Prices on Treatment Attendance
for Methadone Maintenance
Clients
Natalia N. Borisova
Procter and Gamble Pharmaceuticals, Cincinnati, Ohio
Allen C. Goodman
Wayne State University, Detroit, Michigan
Journal of Substance Abuse Treatment 2004
Methadone treatment
• Methadone maintenance is an unusual and
possibly unique health care model.
• First, clients are required to visit a clinic very
often (it used to be every day), so treatment
attendance becomes essential for clients’
compliance and treatment effectiveness.
• Second, treatment attendance has
implications for waste of resources in terms
of staff time and the underutilization of
equipment.
Barriers to Treatment
• Out-of-pocket treatment fees are modest due to
extensive private and public insurance coverage,
but …
• Out-of-pocket transportation costs, and, more
importantly, daily travel and waiting time costs
may be substantial, and possibly prohibitive.
• Clients who face higher treatment fees, related
transportation and childcare costs, and longer
travel and waiting times may be less likely to
attend treatment regularly.
Estimating the Model
A = β0 + β1PM + β2PT + β3Y + β4Z + ε
(1)
where:
PM is the average daily money price;
PT is the average daily time price;
Y is gross household income;
Z is a vector of variables that may influence treatment
attendance including socioeconomic and demographic
attributes; and
ε is an error term
Demand v. Willingness to Pay
• Demand
– Call out price
– Determine quantity
• Willingness to Pay (WTP)
– Call out quantity
– Determine maximum amount people would
pay.
Time Price
The travel time price measured by WTP was based on
a contingent valuation analysis (CVA) in which clients
were offered two hypothetical choices:
(1) spend twice as long as the actual travel time to the treatment
program and (24 - 2T travel – T clinic) amount of time at either work or
leisure, where T travel is travel time and T clinic is time spent at the
treatment program; or
(2) spend no time on travel to the treatment program
and (24 - T clinic ) amount of time at either work or leisure.
WTP
TT = 40
Questions
$10
If you had to pay here for each visit, what is the MOST
money you would be willing to pay?
TT = 80
$8
If it took you twice as long as usual to travel to this clinic
and if you had to pay, what is the MOST money you would
be willing to pay for each visit?
TT = 0
$12
If this clinic were moved right NEXT DOOR to where you
live for your convenience and if you had to pay, what is the
MOST money you would be willing to pay for each visit?
WTP, but
Also consistency
WTAccept
WTP and WTA
• In principle, they should be the same, but most
people feel that they are not.
• Interviews were conducted with 451 subjects at six
health centers (four urban and two rural) in areas with
different socioeconomic characteristics. A payment
card was used to measure the WTP and WTA.
• The WTA/WTP quotient showed a median of 1.55
(interquartile range 1-3.08) and a mean of 3.30 (IC
95%: 2.84-3.75).
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2883536/
WTP and WTA
• “Loss aversion". The basic idea behind loss aversion
is that losses are weighted far more heavily than
gains. The point of reference for the loss and gain is
an "endowment point".
• Valuations of gains and losses are always relative to
the reference or endowment point, losses are valued
more heavily than gains, and the valuation function
exhibits diminishing marginal valuation the further
away from the reference point one gets.
Methods
• Perhaps the key feature of methadone
maintenance is the requirement that clients
demonstrate regular attendance to stay in the
treatment – otherwise they will be discharged for
a noncompliance.
• Thus it is very unlikely for any client to have an
attendance rate less than 0.5. In fact, the lowest
attendance rate reported in the study sample is
0.58 and it is considered as the lower bound for
the attendance rate.
• Because treatment attendance is measured as a
rate rather than a count, it is censored below at
0.58 and above at 1.00.
Two Limit Tobit
Rosett and Nelson (1975) developed the two-limit tobit model to allow
both upper and lower censoring at the same time.
0.58


A   A*  X  

1

if
A*  0.58
if
0.58  A*  1
if
A*  1
where A is the observed treatment attendance rate derived from
latent effect A*,
X is a vector of explanatory variables,
β is a vector of parameters to be estimated, and
ε is an error term that is IID
2LT - Graphically
• Suppose we have
a set of data points.
• The “true values”
are the circles.
• We have a true
line.
“True”
A
upper
x
x
x
x
x
x
x
lower
x
x
x
x
x
x
2LT - Graphically
• Suppose we have
a set of data points.
• The “true values”
are the circles.
• We have a true
line.
“True”
A
x
upper
x
x
x
x
“OLS”
lower
• We “see” the circles and
squares with the x’s in them.
• What do we do?
x
x
x
x
x
x
x
x
x
xx
x
x
x
Three Predictions
E ( A* | X )
 k
E(A* | X) = Xβ , and
X k
E (A | 0.58 < A < 1, X) = Xβ +
E ( A | 0.58  A  1, X )
X k

 ( L )   ( U )
 ( U )   ( L )
 . L  ( L )   U  ( U )   ( L )   ( U )  2
  k 1 



( U )  ( L )

(

)


(

)

U
L 


,
E (A | X) =  L( L )  U (U )  (U )  ( L )  X    ( L )   ( U ) 

E ( A | X )
  k ( U )  ( L )   k Pr(Uncensored | X )
X k
( U )  ( L ) 




Table 1 - Treatment Attendance, and Mean Values of
Money and Time Prices per Treatment Day
Attendance Rate
Range
Percent ofClients
Money Price (dollars)
Time Price (dollars)
TREATMENT
FEES
TRAVEL
COST
CHILD
CARE
COST
WTP
WAGE
A = 1.00
40.6
5.04
2.80
0.16
5.45
-9.98
1.00 > A ≥ 0.99
15.8
3.61
3.24
0.75
5.55
-9.97
0.99 > A ≥ 0.98
14.2
4.56
3.31
0.81
5.69
11.77
0.98 > A ≥ 0.95
12.5
3.61
3.90
1.39
5.56
13.37
0.95 > A ≥ 0.85
10.6
4.13
3.92
1.31
6.45
18.06
0.85 > A ≥ 0.58
16.3
4.21
5.32
3.82
6.87
22.19
Total mean
-
4.42
3.36
0.85
5.71
12.27
Variables
Table 2 –
Variable
Definitions and
Sample Means
Mean* (A |A<1)
Mean (A |A=1)
ATTENDANCE RATE
0.97----
0.95------
1.00-------
AFRICAN-AMERICAN
0.33----
0.44------
0.17-------
WOMEN
0.47----
0.48------
0.45-------
EMPLOYED
0.45----
0.41------
0.52-------
MARRIED
0.24----
0.24------
0.24-------
AGE
41.80----
42.05------
41.43-------
AGE SQUARED
1807.82-
1828.49-----
1777.57-----
CLINIC IN MACOMB COUNTY
0.32----
0.19------
0.50-------
CLINIC IN OAKLAND COUNTY
0.33----
0.31------
0.36-------
FAMILY INCOME (yearly)
WEEKS IN TREATMENT
18065.
17853.
18375.
80.51----
83.17------
76.67-------
NUMBER OF PREVIOUS TREATMENTS
1.00----
1.19------
0.72-------
BUS
0.18----
0.21------
0.15-------
OTHER TRANSPORTATION
0.02----
0.02------
0.01-------
MONEY PRICE ($) per day
8.63----
9.05------
8.00-------
12.27----
13.85------
9.98-------
5.71----
5.88------
5.45-------
TRAVEL TIME (in minutes)
81.37----
91.64------
66.34-------
WAITING TIME (in minutes)
30.99----
33.92------
26.71-------
TIME PRICE ($) per day, measured by WAGE
TIME PRICE ($) per day, measured by WTP
*A is a treatment attendance rate
Mean
OBSERVATIONS
303----
180
123
Variables
Table 3 Money price
Tobit
and time
Estimates price are
Using WTPBOTH
INTERCEPT
Parameter
η†
T-Ratio
A|X
Latent
A* | X
A|
0.58 < A < 1, X
0.9586-----
12.25***
-
-
-
AFRICAN-AMERICAN
-0.0347-----
-3.13***
-0.0179
-0.0358
-0.0144
WOMEN
-0.0071-----
-0.77+++
-0.0036
-0.0073
-0.0029
EMPLOYED
0.0181-----
1.81*++
0.0093
0.0187
0.0075
MARRIED
0.0082-----
0.77+++
0.0042
0.0085
0.0034
-6.97E-04----
-0.19+++
0.0184
0.0367
0.0148
01.84E-05----
0.41+++
-
-
-
CLINIC IN MACOMB COUNTY
(OUTSIDE CENTRAL CITY)
0.1118-----
7.82***
0.0577
0.1152
0.0464
CLINIC IN OAKLAND COUNTY
(OUTSIDE CENTRAL CITY)
0.0896-----
6.32***
0.0462
0.0924
0.0372
-0.0061
-0.0122
AGE
important
AGE SQUARED
FAMILY INCOME (per week)
-3.4E-05-----
-2.06**+
-0.0049
WEEKS IN TREATMENT
-5.5E-05-----
-1.04+++
-0.0023
-0.0046
-0.0018
PREVIOUS TREATMENT
0.0065-----
1.65*++
0.0033
0.0067
0.0027
BUS
0.0109-----
0.89+++
0.0056
0.0112
0.0045
OTHER TRANSPORTATION
0.0354-----
1.03+++
0.0183
0.0365
0.0147
MONEY PRICE (per week)
-1.9E-04-----
-1.68*++
-0.0051
-0.0103
-0.0041
TIME PRICE - WTP (per week)
-4.2E-04-----
-2.84***
-0.0044
-0.0087
-0.0035
OBSERVATIONS
303
Pr (UNCENSORED)
0.5004
E (A* | X)
0.9974
E (A | X)
0.9634
E (A | 0.58 < A < 1, X)
0.9396