More Demand

© Allen C. Goodman, 2013

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. Time

Severity

Illness

Treatment

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 make-up 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.

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 IncomeIf:

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/(2

p + 2t)] bp + [2

t/(2p + 2

t)] bt. This is a weighted average.

More on Permanent IncomeIt 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 regession 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.

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.

What some people do

PriceIf 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.

Visits

Mon

ey P

rice Effective P

rice

80

60

40

20 20

40

60

80

Money price demand

Effective demand

2 4 6 8 10 12 14

Kinks from Insurance3 sections

1. Deductible - same as before

Health Care

Com

posi

te

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 non-linear, and non-convex.

Students tend to fixate on the kinks. May not necessarily be at a kink.

Students tend to fixate on the kinks. May not necessarily be at a kink.

More kinks

Clearly, the price is negatively correlated with the amount purchased.

Consider the regression:Q = a + bP, ignoring everything else.

The impact is:plim b = (1 - w) b + V.

There are two possible error terms:

More kinks1. The type of errors in variables equation, If this is random, then the coefficient b is biased toward 0, (or upward).

2. V is different. 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.

plim b = (1 - w) b + V.

More kinksThat 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 w takes us toward 0, and V takes us away. It's not clear how they sort out.

plim b = (1 - w) b + V.

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?

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. BorisovaProcter and Gamble Pharmaceuticals, Cincinnati, Ohio

Allen C. GoodmanWayne 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 ModelA = 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 demographicattributes; andε 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 PriceThe 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

QuestionsIf you had to pay here for each visit, what is the MOST money you would be willing to pay?

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?

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?

$10$10

$8$8

$12$12

TT = 40TT = 40

TT = 80TT = 80

TT = 0TT = 0

WTP, butAlso consistency

WTAccept

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 TobitRosett and Nelson (1975) developed the two-limit tobit model to allow both upper and lower censoring at the same time.

1*1

1*58.0*

58.0*58.0

Aif

AifXA

Aif

A

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. x

x x x

x

x x

x x

x

xx

A

x

upper

lower

“True”

x

x x x

x

x x

x x

x

xx

x x

x x x x

• Suppose we have a set of data points.

• The “true values” are the circles.

• We have a true line.

Aupper

lower

x

• We “see” the circles and

squares with the x’s in them.• What do we do?

“True”2LT - Graphically

Three Predictions

E(A* | X) = Xβ , and kkX

XAE

)|*(

.

E (A | 0.58 < A < 1, X) = Xβ + )()(

)()(

LU

UL

,

2

)()(

)()(

)()(

)()(1

),158.0|(

LU

UL

LU

UULL

k

kX

XAAE

E (A | X) = )()()()( LUUULL

)()(

)()(

LU

ULX

)|Pr()()()|(

XUncensoredX

XAEkLUk

k

Table 1 - Treatment Attendance, and Mean Values of Money and Time Prices per Treatment Day

Attendance RateRange

Percent of-Clients

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

Table 2 – Variable

Definitions and Sample Means

Variables Mean 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) 18065. 17853. 18375.

WEEKS IN TREATMENT 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-------

TIME PRICE ($) per day, measured by WAGE 12.27---- 13.85------ 9.98-------

TIME PRICE ($) per day, measured by WTP 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-------

OBSERVATIONS 303---- 180 123*A is a treatment attendance rate

Variables Parameter T-Ratio η†

A | X Latent A* | X

A | 0.58 < A < 1, X

INTERCEPT 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

AGE -6.97E-04---- -0.19+++ 0.0184 0.0367 0.0148

AGE SQUARED 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

FAMILY INCOME (per week) -3.4E-05----- -2.06**+ -0.0061 -0.0122 -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  

Table 3Tobit EstimatesUsing WTP

Money price and time price are BOTH important

Money price and time price are BOTH important