March 6, 2006

Chris L. Peterson

Specialist in Social Legislation

Domestic Social Policy Division

Congressional Research Service ˜ The Library of Congress

Alternatives for Modeling Results from the RAND

Health Insurance Experiment

Summary

The RAND Health Insurance Experiment (HIE) was ongoing from the mid-

1970s to the early 1980s. Two thousand nonelderly families from six urban and rural

areas were randomly assigned health insurance plans with different levels of cost-

sharing (that is, with various levels of deductibles, coinsurance, and out-of-pocket

maximums). The results from this unprecedented health insurance experiment

showed that people facing higher cost-sharing (that is, they had to pay a higher

proportion of total health care costs out of their own pockets) had lower health care

spending than those in plans with lower cost-sharing. No similar experiment has

been performed since the HIE, so it remains the epochal analysis for understanding

the link between health insurance cost-sharing and total health care spending. This

report examines the methods used to apply the HIE results in health policy analyses.

The key variable used to try to explain health care spending in the HIE was the

plans’ coinsurance — that is, the percentage of total health care costs that the

individual must pay. Understanding these results from the HIE was complicated by

the fact that for each coinsurance rate, there were multiple plans, each with a different

out-of-pocket maximum (although the maximum never exceeded $1,000). For

example, a person may have been enrolled in the “25% coinsurance plan,” but after

that person had spent $1,000 (or less) out of pocket, the plan effectively became a 0%

coinsurance plan. Thus, the nominal coinsurance could not be used as the sole cost-

sharing variable for explaining the impact of cost-sharing in the HIE plans.

The HIE results have been particularly useful for policy analysts estimating what

effect changes in cost-sharing might have on health care spending — in public health

insurance programs, for example. Microsimulation modeling is one tool used by

health policy analysts to estimate the impact of cost-sharing changes. “Micro” refers

to the fact that the modeling takes place on an individual level rather than an

aggregate level, based on a database of individuals representative of a certain

population (the U.S. population or a smaller subset, such as individuals enrolled in

Medicaid). If one wanted to estimate the impact of an increase in coinsurance, for

example, a microsimulation model would apply that increase to every person in the

data along with a concomitant drop in total health care spending.

In most health insurance modeling, the HIE results remain the basis for

adjusting total health care spending in response to cost-sharing changes. However,

applying those results in a model is not always straightforward. One of two methods

is typically used — elasticities, generally preferred by health economists, and

induction, preferred by actuaries. Each has benefits and shortfalls, but little

comparative analysis has been done. This report begins by generally describing and

comparing elasticities and induction factors. The report then summarizes key

findings from the HIE and discusses how elasticities and induction factors can be

used to replicate those results. Because of the limitations of these methods in

modeling, this report offers a third alternative that appears to better replicate the HIE

results. This method, called the cubic formula, is simply a formula that produces

HIE-reported spending levels from the experiment’s four coinsurance levels.

Contents

Theoretical Explanation of Cost-Sharing Methods........................2

Elasticity of Demand...........................................2

Health Insurance Applications................................4

Induction Factors..............................................5

Health insurance applications................................7

Additional Comparisons........................................8

RAND Health Insurance Experiment.................................12

Selected Results..............................................12

Calculating and Applying Cost-Sharing Methods Based on HIE Results......17

Arc Elasticities...............................................17

Predicting Quantity with Point-elasticity and Arc-elasticity

Formulas ...........................................18

Effect of Arc Elasticity’s Lack of Path Neutrality................20

Induction Factors.............................................22

Predicting Quantity with Induction Formulas...................22

Cubic Formula...............................................26

Estimating Free-Plan Spending..................................28

Predicting Spending From Estimated Free-Plan Spending.............30

Pure Coinsurance Plan.....................................30

Typical Plan Structure.....................................31

Predicting Spending by Type of Care.............................35

Constant Induction Factors.................................36

Inpatient and Outpatient Care...............................36

Prescription Drugs........................................40

Conclusion ......................................................43

List of Figures

Figure 1. Predicted Expenses Using Various Cost-Sharing Methods, from

Example Case.................................................9

Figure 2. Predicted Expenses Using Various Cost-Sharing Methods and

Values, from Example Case Results at 15% Coinsurance..............11

Figure 3. Effect of Nominal Coinsurance on Annual Per-Person Medical

Expenses, in Dollars, from RAND Health Insurance Experiment........13

Figure 4. Effect of Nominal Coinsurance on Annual Per-Person Medical

Expenses, as a Percentage of Free Plan Expenses....................14

Figure 5. Effect of Average Coinsurance on Annual Per-Person Medical

Expenses, as a Percentage of Free Plan Expenses....................15

Figure 6. Analysis of Arc Elasticity’s Lack of Path Neutrality in HIE

Results: Predicting Quantity Varying By Beginning HIE Data Point.....19

Figure 7. Illustration of Arc Elasticity’s Lack of Path Neutrality:

Predicting Quantity Varying Whether Beginning Data Point Was an

Original HIE Point............................................21

Points from HIE..............................................23

Figure 9. Predicting Quantity of Inpatient Care, By Induction Factor and

Beginning HIE Data Point......................................24

Figure 10. Comparison of Results of Constant Induction Factor from

Free-Plan Spending with Induction Factors and Original Data Points

from HIE...................................................25

Figure 11. Predicting Quantity Using Cubic Formula, Compared to Ideal

Arc Elasticities and Induction Factors, From Original HIE Data Points...27

Figure 12. Effect of Average Coinsurance on Spending, by Type of Service...35

Figure 13. Effect of Coinsurance on Annual Per-Person Total Medical

and Prescription Drug Expenses, as a Percentage of Free Plan Expenses..42

List of Tables

Table 1. Estimated Pure Price Effects of Coinsurance on Medical Expenses,

as a Percentage of Free Plan Expenses............................16

Table 2. Arc Elasticities Between Average Coinsurance Amounts, by

Type of Service..............................................17

Table 3. Predicted Free-Plan Spending Using Arc Elasticities, by Elasticity

Formula for Predicted Spending.................................19

Table 4. Induction Factors Between Average Coinsurance Amounts, by

Type of Service..............................................22

Table 5. Predicted Spending of Example Person in Plan With $1,000

Deductible and 25% Coinsurance, Based on Predicted Free-Plan

Spending, By Cost-Sharing Method..............................34

Table 6. Example Person’s Predicted Spending at 95% Coinsurance, by

Type of Service and Factor.....................................36

Table 7. Average Predicted Spending, by Plan and Factor, Based

on 2002 MEPS...............................................38

Changes in health insurance plans’ cost-sharing (for example, the deductible and

coinsurance) affect the quantity of health services used, according to results from the

seminal RAND Health Insurance Experiment (HIE) of the 1970s and 1980s.

Generally speaking, if a person’s cost-sharing increases, less health care will be used;

if cost-sharing decreases, more health care will be used. Economists account for such

changes with a measure called a demand elasticity; actuaries have a related measure,

called induction factors.

These two methods are used in health insurance models, usually with the

purpose of replicating the HIE results. Neither of these methods is perfect or even

perhaps inherently preferable. Moreover, converting the HIE results into appropriate

elasticities or induction factors is not always straightforward. The use of each has

benefits and shortfalls, but little comparative analysis has been done.

The Congressional Research Service (CRS) has partnered for more than a

decade with actuaries from the Hay Group to formulate microsimulation models that

provide estimates of the actuarial value of health insurance plans. To account for

changes in cost-sharing, these models use induction factors. CRS and Hay are in the

process of a significant overhaul of these models. As part of that process, the

application of the models’ induction factors was assessed and compared to elasticities

and another alternative presented in this report, the cubic formula. This report is the

documentation of that assessment.

This report begins with a basic explanation of elasticities and their health

insurance applications. Induction factors are similarly described then contrasted with

elasticities from a theoretical standpoint. Such an elementary explanation is intended

to ensure that the key distinctions and limitations of elasticities and induction factors

are not missed, particularly for their applications in modeling. The next section of

the report reviews some of the key findings from the RAND Health Insurance

Experiment. Finally, the report discusses how best to replicate HIE results using

elasticities, induction factors, and the cubic formula.

In short, this report assesses the ability of the three methods to consistently

replicate certain RAND Health Insurance Experiment results. Because health care

and people’s responsiveness to its costs may have changed in the decades since the

HIE’s implementation, the method that best replicates the HIE results may not in fact

best represent current responsiveness to health care cost-sharing. Whether people’s

responsiveness has changed is difficult to know without another experimental study

like the HIE. However, on the specific question of which method is best for

replicating the HIE results, this report points to the cubic formula.

Theoretical Explanation of Cost-Sharing Methods

Elasticity of Demand

The elasticity of demand is a number that approximates the effect that a change

in price has on the quantity purchased of a good or service. In other words,

elasticities are used to answer this question: If the original quantity (Q

service is purchased at the original price (p

(Q

For two given prices (p

the elasticity is defined as the percentage change in quantity resulting from a one

percent change in price. Starting from a particular point (p

algebraically as follows:

Q

(1) E p p

p

For example, a car dealership knows that if its price on a particular model is

$30,000, it will sell 500 of those cars in the year; however, if it drops its price to

$27,000, it will sell 600. The point elasticity would then be calculated as follows:

600 500−

500 20% 2===−

(2) E 27,000 30,00010%

30,000

Because the absolute value of the elasticity is greater than one, it denotes that

people are very responsive to price changes for this model. Specifically, a 10% drop

in price would yield a 20% increase in quantity demanded.

Those dealing with elasticities aspire to apply a particular value, say -2, to all

different prices and quantities for that good. However, point elasticities do not yield

consistent results; as a cost-sharing factor, they lack certain desirable properties. One

such property is reversibility, which means that the calculation of a cost-sharing

factor (based on two points) yields the same result regardless of which point is

considered the starting point (p

demonstrated below by using the same two points used in Eq. (2) but switching the

starting point. The elasticity below, -1.5, does not match the previous one, -2:

500 600−

(3) E60030,000 27,000 1.5

27,000

To obtain the same elasticity from a given pair of points, arc elasticities are used

instead of point elasticities. In other words, arc elasticities are reversible. Arc

elasticities are calculated as (change in quantity divided by average quantity) /

(change in price divided by average price), or:

Q Q

(Q Q)/2

(4) E p p

(p p)/2

Using the prior example, the arc elasticity is the following, and does not vary

regardless of which is chosen as (p

600 500−

(600 500)/2+

(5) E27,000 30,000 1.73

(27,000 30,000)/2+

As in this example, the arc elasticity (-1.73) is often close to the average of the

point elasticities (-1.75).

In addition to reversibility, another advantage of the arc elasticity is that it is

defined even if any of the parameters equals zero. In the point-elasticity formula, if

either p

elasticities are generally favored by health economists over point elasticities.

Although the arc elasticity may be nearly as easy to calculate, the point elasticity

is often easier to apply when predicting quantity (Q

results from solving the point-elasticity formula in Eq. (1) for Q

(6)

Q

Eq. (7) shows the formula that results from solving the arc-elasticity formula in

Eq. (4) for Q

(7)

Q

The temptation is to take an arc elasticity and predict Q

elasticity formula in Eq. (6). However, this does not yield proper results. To

illustrate, apply the previously calculated arc elasticity (-1.73) to predict Q

is $27,000 and the starting point is ($30,000, 500). Although the actual Q

the point-elasticity version of Q

yield 600, the original point elasticity of -2 would have to be used. Although it is

more unwieldy, the arc-elasticity version of Q

this case, 600) when applying the arc elasticity.

In other words, when predicting quantity using elasticities, it is critical to use the

Q

additional complication of applying the point elasticity is that, because it is not

reversible, one must determine which point elasticity to use; when predicting Q

a particular (p

point closest to the one it is being applied to.

Health Insurance Applications. Calculating elasticities when individuals

are covered by health insurance is complicated by the fact that the price paid by

consumers for health care (that is, their cost-sharing) is usually not the full price of

that care. For example, the average price of a hospital stay may be $5,000, but the

insured’s effective “price” would be only the cost-sharing — a $750 deductible, for

example. This effective price, the person’s out-of-pocket liability, is what influences

their behavior rather than the total price. Thus, when looking at elasticities for health

insurance purposes, the prices (p

individual out of pocket rather than the actual total price for the good or service.

In addition, it is often difficult to measure the quantity of health care purchased.

When deriving an elasticity for health care, what should be used for “quantity”?

Fortunately, there is a way around this dilemma, using the fact that the total amount

spent on health care (i.e., the person’s out-of-pocket payments plus payments by

insurance) is the actual price of the good or service (not just the out-of-pocket

amount) multiplied by the quantity used. Therefore, the percentage change in total

spending would be as follows, with P

good or service, not just the out-of-pocket amount:

PQ PQ

(8) % ) in total spending = PQ

However, in calculating elasticities based on cost-sharing changes, we assume

that the actual price of the health good service does not change — that is, that P

P

in total spending is equivalent to the percentage change in quantity demanded:

PQ PQQ Q

(9) % ) in total spending = = % ) in quantity demandedPQ Q=

Thus, the easiest way empirically to calculate an elasticity for health care is to

use the percentage change in total spending as the percentage change in quantity

demanded. This applies to all of the uses of “quantity” for the remainder of this

report.

For example, an insurance company contracts with physicians so that a typical

office visit is $100, or P. On average, its enrollees make three visits per year, for

appropriate Q

cumbersome than simply using the appropriate formula in Eq. (7).

total spending of $300 per enrollee for the office visits. The enrollees must pay a

copayment per visit of $5 (a coinsurance of 5%). The following year, the plan keeps

its contract arrangements the same with physicians but increases its copayments to

$25 for office visits (a coinsurance of 25%). The result is that the average number

of visits drops to 2.25, for total average spending of $225. From these figures, the

arc elasticity is calculated as follows:

225 300−

(225 300)/2+

(10) E 25 5 0.21429

(25 5)/2+

Because the absolute value of this elasticity (0.21429) is less than one (and

closer to zero), one would say the demand for this type of care is relatively inelastic.

That is, a substantial change in the effective price of care led to a relatively small

change in the amount of care demanded.

Nevertheless, the example is a much-simplified version of the cost-sharing

structure for the range of services in most health insurance plans, which have

deductibles and out-of-pocket maximums in addition to copayments and coinsurance

that may vary by type of service. As a result, precisely determining p

health insurance plans is not straightforward; p

new cost-sharing structure but of Q

of this simultaneous (some might say circular) relationship, elasticities appear to be

limited outside of applications to plans with only coinsurance cost-sharing.

Induction Factors

Induction factors are not discussed as commonly as elasticities in health policy

circles. A thorough literature review on the topic came up with only a handful of

references, all several years old.

($100) remained the same, the arc elasticity would yield the same result whether using that

quantity or total spending, affirming what was shown in Eq. (9). From the two data points

in this example, the point elasticities would be -0.0625 and -0.4167, depending on which

point was chosen as the start. This is quite a large range for describing the impact of cost-

sharing changes.

which is discussed later in this report.

with Adverse Selection,” Journal of Health Economics, volume 18 (1999), pp. 195-218.

(Hereafter cited as Zabinski, et al., Medical Savings Accounts.) Edwin Hustead et al.,

“Medical Savings Accounts: Cost Implications and Design Issues,” American Academy of

Actuaries’ Public Policy Monograph No. 1, May 1995, at

[http://www.actuary.org/pdf/health/msa_cost.pdf]. Hustead is also the principal actuary at

the Hay Group for the CRS contract on the valuation models. Documentation on those

models regarding induction factors is very similar to the write-up in the MSA monograph.

(continued...)

predict the impact of cost-sharing changes on total health care spending. The key

advantage of induction often touted over elasticities is that its factors are relatively

easy to apply on all plan types, even those with complicated cost-sharing structures.

“Moving beyond the simplified case of pure coinsurance, the actuarial method [of

induction] offers a tractable, albeit imperfect, approximation to the actual change in

medical care.”

sharing structure to the original spending. It does this by calculating the dollar

amount of out-of-pocket payments (OOP) under the old and the new cost-sharing

structures, holding total spending (Q

OOP

structure but the old quantity demanded, Q

(11)

Q

Solving this equation for the induction factor yields the following:

(12)

I = (Q

Eqs. (11) and (12) illustrate that an induction factor is a very different measure

from an elasticity, even though both may try to replicate similar impacts of cost-

sharing changes on total health care spending. The value of an elasticity represents

the percentage change in quantity resulting from a one percent change in price. The

value of an induction factor is the percentage of the difference in two plans’ out-of-

pocket payments that directly affects total health care spending.

For example, a person has total health care spending of $5,000, of which $4,000

is paid by a health insurance plan and $1,000 out of pocket. Another plan in which

the person had total spending of $5,000 may require $1,500 out of pocket, a $500

increase. An induction factor of 70%, or 0.7, means that total health care spending

would be reduced by 70% of the out-of-pocket difference between the plans (70% of

$500, or $350). Thus, under the new plan with higher cost-sharing, total health care

spending for the person would be predicted to drop to $4,650 (that is, $5,000 - $350).

Although induction factors and elasticities are very different measures, there are

cases in which they can be shown to be closely related. For example, in plans where

the cost-sharing can be represented as a pure coinsurance, the induction formula’s

OOP

as shown in Eq. (13), which can be solved for the induction factor, as shown in Eq.

(14):

“Methodological Description of Health Care Reform Premium and Discount Estimates,”

addendum to The White House Domestic Policy Council, “Health Security Act: The

President’s Report to the American People,” Oct. 1993, at

[http://www.ibiblio.org/ pub/academic / me d i c i n e / H e a l t h -S e c u r i t y-A c t / s upporting

-documents/method2.txt].

(13) Q

Q Q

Q

(14) I p p=−

The following emerges by dividing both the numerator and denominator of the

right-hand side of Eq. (14) by -p

Q Q

Q 1

(15) = - E

p p

Through similar algebraic manipulations, the induction factor can also be

written as follows:

(16)

I = - E

These last two equations may not have widespread practical applications.

However, they both illustrate that induction factors can be expressed as a function of

elasticities, both point and arc, in their pure coinsurance forms.

an issue that is indicated by the Q

denominator of Eq. (14) — that induction factors are not reversible. That is,

induction factors calculated from two points will yield different values depending on

which of the two points was chosen as the starting point. This is the same

shortcoming that point elasticities have, and Eq. (15) does not fix this. Arc

elasticities do not have this shortcoming, thus the induction-factor equation as a

function of the arc elasticity in Eq. (16) necessarily places Q

introduce it. Because two values for the induction factor result from any two price-

quantity data points, care must be taken to choose the correct one, depending on the

Q

plan.

Health insurance applications. Using the office-visit example presented

earlier, Eq. (14) yields the following induction factor:

225 300−

(17) I 300 1.25==

5% 25%−

as a function of the arc elasticity.

Induction factors’ lack of reversibility is demonstrated once more by reversing

the parameters of the office-visit example and calculating that induction factor:

300225−

225 1.67==

(18) I

25%5%−

In sum, although induction factors appear to enable a better analysis of a greater

variety of health insurance plans, compared to arc elasticities, they are not

unambiguously superior — one reason being that they are not reversible.

Specifically, the use of induction factors could lead to flawed results if a single value

is being used across a domain of coinsurance levels.

Additional Comparisons

In elementary algebra, the slope of a line is defined as rise over run —

specifically, the change in the dependent variable (y) divided by the change in the

independent variable (x). Thus, the equation for the linear slope between two price-

quantity data points is (Q

formulas previously discussed yields the following:

(19) E

(20) E

(21) I = slope / -Q

Interestingly, if the predicted quantity (say, Q

calculated from a starting point (p

calculate the factors above, the equation is reduced to the following for both point

elasticities and induction factors:

(22) Q

This results in a straight line with the original slope and passing through the

original data points.

coinsurance yields an induction factor of 1.25 and a point elasticity of -0.0625.

Applying these factors in the domain of 5% to 25% coinsurance to predict quantity

yields the straight line in Figure 1, as Eq. (22) would predict.

curve with a slope that is the reciprocal of this one. For this report, traditional graphs and

slopes are used, with apologies to economists who would prefer straightforward demand

curves.

Figure 1. Predicted Expenses Using Various Cost-Sharing Methods,

from Example Case

300

Straight line resulting from point-elasticity

and induction-factor equations

280

s

260nse

ExpeArc resulting from

edarc-elasticity equation

240dict

Pre

220

200

5%10%15%20%25%

Coinsurance

This characteristic has important implications for applying the RAND HIE

results, discussed later.

quantity formula for arc elasticities, Eq. (7), does not yield a simplified equation of

any sort.

curve — an arc. That arc will pass through the original pair of data points if the

starting point (p

when using the appropriate, other point elasticity or induction factor.

form for the predicted quantity based on the arc-elasticity formula. Let Eq. (7) predict a Q

based on some p

derivative of Q

equation is that p

consistent with the arc that results from applying Eq. (7), as in Figure 1.

arc in Figure 1 illustrates this for the coinsurance domain of 5% to 25%, using (5%,

300) as the starting point and -0.21429 as the arc elasticity.

The concavity of the arc also indicates that responses to cost-sharing will not be

constant, as is the case using point elasticities and induction factors. Specifically, the

concavity results in greater responsiveness at lower prices than at higher prices,

within the applicable domain. Whether this is preferable to a constant responsiveness

probably depends on the good or service being analyzed. With respect to the demand

for health care, this concavity is consistent with the HIE results discussed later —

that people are more responsive to cost-sharing changes when their cost-sharing is

relatively small, compared to the response when their cost-sharing is higher.

Another desirable property of cost-sharing factors in addition to those

mentioned earlier is path neutrality — that is, when using a factor’s particular value

(based on two data points), the predicted quantity for a given price should be

identical regardless of which point is chosen as the start (p

straight line in Figure 1 (from induction factors and point elasticities) results whether

using (5%, 300) or (25%, 225) as the starting point. However, in spite of the

reversibility of the underlying factor, arc elasticities are not path neutral. The arc in

Figure 1 would be slightly different had (25%, 225) been used as the starting point.

Beginning at the higher price, the resulting arc would not bulge as much from the

straight line. At 15% coinsurance, for example, the quantity at the straight line is

262.5; on the arc in Figure 1, it is 241.9; if the starting point had been (25%, 225),

the quantity on the arc would have been at 250.5. At 15% coinsurance, the difference

in the estimated quantity between the arc-elasticity results is approximately 3.5%.

In the previous examples, the starting point (p

always been one of the two original points used in calculating the cost-sharing factor.

However, when applying a given cost-sharing factor, the data may require beginning

from a known point that is not one of the original points (if those original points were

even known). In the office-based example — given the induction factor of 1.25, the

point elasticity of -0.0625, and the arc elasticity of -0.21429 — assume a plan has

15% coinsurance (p

on changes to that coinsurance. If a cost-sharing factor is path neutral, then the

predicted quantities in this example should be the same as illustrated in Figure 1.

Assuming this would be the case, the Q

taken from the points on the lines in Figure 1 — 262.5 for the point-elasticity and

induction formulas, and 241.9 for the arc-elasticity formula.

Figure 2 shows the predicted quantities generated from a beginning coinsurance

of 15% and applying the various cost-sharing methods. The dark lines are the

original ones from Figure 1 with which the results would coincide if they were path

neutral. However, none of the three cost-sharing methods — point elasticities,

induction factors or arc elasticities — is path neutral. The dashed lines show the

predicted quantities based on the elasticities, with the straight line based on the point

elasticity and the arc based on the arc elasticity; the light, solid line shows the

came up with this name for the concept.

predicted quantities based on the induction factor. All of the methods reproduce the

Q

Only the arc elasticity matches the original data point (5%, 300). Note that none of

the methods obtains the original point of (25%, 225).

is a serious limitation of all these cost-sharing methods, the implications of which are

discussed in detail in the section on the methods’ ability to replicate HIE results.

Figure 2. Predicted Expenses Using Various Cost-Sharing Methods and

Values, from Example Case Results at 15% Coinsurance

300

280

Predicted based on

spoint elasticity

260

d ExpensePredicted based

on induction

240edicte

Pr

220Predicted based on

arc elasticity

200

5%10%15%20%25%

Coinsurance

the factor’s original points as the starting point for predicting quantity. The other predicted

quantity associated with 15% coinsurance (Q

distinct arc in Figure 2, this one passing through the original point of (25%, 225) but not

(0%, 300).

RAND Health Insurance Experiment

The RAND Health Insurance Experiment (HIE) was ongoing from the mid-

1970s to the early 1980s. Two thousand nonelderly families from six urban and rural

areas were randomly assigned health insurance plans with different levels of cost-

sharing. The results from this unprecedented health insurance experiment showed

that people facing higher cost-sharing (that is, they had to pay a higher proportion of

total health care costs out of their own pockets) had lower health care spending that

those in plans with lower cost-sharing. No similar experiment has been performed

since the HIE, so it remains the epochal analysis for understanding the link between

health insurance cost-sharing and total health care spending.

The key variable used to explain health care spending in the HIE was the plans’

coinsurance — that is, the percentage of total health care costs that the individual

must pay. Four coinsurance rates were used: 0% (called the free plan, in terms of

there being no cost-sharing), 25%, 50%, and 95%. However, for each coinsurance

rate, there were three plans, each with a different out-of-pocket maximum: 5%, 10%,

or 15% of family income, up to a maximum of $1,000. A person may have been

enrolled in the “25% coinsurance plan,” but after that person reached the out-of-

pocket maximum, the plan effectively became a 0% coinsurance plan. Thus, the HIE

results need to be understood in the context of other variables besides the nominal

coinsurance, particularly the out-of-pocket maximum.

Selected Results

From the HIE data, the RAND authors calculated annual per-person medical

spending, controlling for factors such as location and factors that affect likelihood of

having a medical expense.

coinsurance levels (incorporating all the out-of-pocket maximums), with the four

points connected by line segments.

As shown in the figure, average free-plan spending was $1,019 (in 1991

dollars). Plans with a nominal coinsurance of 25% averaged $826 in spending,

significantly less than in the free plan (p<0.001). At the 50% nominal coinsurance

level, spending averaged $764, significantly less than in the 25% plans (p=0.05,

t=1.97). Plans with a nominal coinsurance of 95% averaged $700 in spending, less

than in the 50% plans (p=0.06, t=1.93). Note that for the remainder of this report,

many results are shown rounded, even if their usage later on is based on the

unrounded amounts. This may cause others’ results to differ slightly.

including Joseph P. Newhouse et al., Free for All? Lessons from the RAND Health

Insurance Experiment (Cambridge, Massachusetts: Harvard University Press, 1993).

(Hereafter cited as Newhouse, Free for All?). Authors of the HIE often refer to the out-of-

pocket maximum as the Maximum Dollar Expenditure (MDE). There were a couple other

plans with slightly different cost-sharing designs, but they received less attention in the HIE

results.

spending based on the four-equation model, described in Chapter 3 of Newhouse et al.

Figure 3. Effect of Nominal Coinsurance on Annual Per-Person

Medical Expenses, in Dollars, from RAND Health Insurance

Experiment

(0%, $1,019)1,000

(25%, $826)$)

800991

(1

(50%, $764)

(95%, $700)enses

600 Exp

an

) Me

400icted

red

(P

ual

200n

An

0

0% 20% 40% 60% 80% 100%

Nominal Coinsurance (before out-of-pocket maximum)

Because the dollar amounts are for 1991, it is useful to standardize the results,

with the free-plan spending ($1,019) as the base for comparing health care spending.

Spending in the 25% coinsurance plan would be represented as having 81% of the

free-plan spending, and so on. This is shown by the points connected by the heavy

solid line segments in Figure 4.

As previously mentioned, the effect of the plan’s coinsurance is diminished by

its particular out-of-pocket maximum. The RAND authors noted, for example,

“individuals who exceeded the [out-of-pocket maximum] tended to increase their

spending on all [health care] episode types.”

estimate the “pure price effect” of the coinsurance, estimating how much spending

would occur in each coinsurance in the absence of any deductibles or out-of-pocket

maximums. This is shown in Figure 4 by the points connected by the lighter solid

line segments.

As expected, average health care spending at a given coinsurance rate is lower

if there is no out-of-pocket maximum, compared to levels with an out-of-pocket

maximum. These estimates are from Table 4.17 of Newhouse et al., in which

Chapter 4 provides a detailed description of how these estimates were obtained.

Figure 4. Effect of Nominal Coinsurance on Annual Per-Person

Medical Expenses, as a Percentage of Free Plan Expenses

100%

(0%, 100%)

With out-of-pocket maximum

(25%, 81%)

80%

(95%, 69%)(50%, 75%)ng

(25%, 71%)pendi

S

60%lan

(50%, 63%)

(95%, 55%)ee PWithout out-of-pocket maximum

40% of Fr

centage

er

20%P

0%

0% 20 % 4 0 % 60 % 8 0% 1 00 %

Nominal Coinsurance

Using only the nominal coinsurance from plans with an out-of-pocket maximum

to estimate total spending raises concerns, since it overlooks the plan’s out-of-pocket

maximum, which can have a large impact on total spending, as illustrated in Figure

4. An alternative is to calculate the average coinsurance individuals faced in the

plans. For example, a person with $10,000 in spending in the typical HIE 25% plan

would not have had $2,500 in out-of-pocket spending; because the HIE plans limited

out-of-pocket expenditures, the most the person would have spent out of pocket was

$1,000. Had the person’s out-of-pocket expenditure been $1,000, the average

coinsurance would have been 10%, not the nominal 25%. Because it reflects all cost-

sharing (nominal coinsurance as well as deductibles and out-of-pocket maximums),

the average coinsurance, rather than the nominal coinsurance, is arguably a preferable

single value for representing a plan’s overall cost-sharing.

Figure 5. Effect of Average Coinsurance on Annual Per-Person

Medical Expenses, as a Percentage of Free Plan Expenses

100%

(0%, 100%)

Dark line is with out-of-

(16%, 81%)pocket maximum

(24%, 75%)80%ng

i

(31%, 69%)(25%, 71%)end

Sp

60%

(50%, 63%)Plan

(95%, 55%)ree Without out-of-pocket maximum

f F

40% o

ge

ta

20%Percen

0%

0% 20% 40% 60% 80% 10 0%

Average Coinsurance

Using the HIE data, the 25% plans’ average coinsurance is 16%, the 50% plans’

is 24%, and the 95% plans’ is 31%. This is shown by the points connected by the

heavy solid line segments in Figure 5, along with the previous points from the pure

price effects (that is, for pure-coinsurance plans) from Figure 4. Over its applicable

domain, the average coinsurance for plans with an out-of-pocket maximum yields

spending in line with the pure price effects from pure-coinsurance plans.

The concordance of these results is what one might have expected. It also

makes applying these results convenient. First, microdata on health care

expenditures rarely provide cost-sharing information like a plan’s nominal

coinsurance. The results in Figure 5 suggest that such information may not be

necessary — that the average coinsurance paid by a person, even in a plan with a

complicated cost-sharing structure, should be as reliable in deriving and applying

cost-sharing factors as that of a pure-coinsurance plan.

In addition, the average coinsurance of the typical HIE plans did not exceed

31%. However, in dealing with individuals’ expenditure data, some people may have

faced high cost-sharing. For example, many people may have had health care

expenses that never reached their plan’s deductible, thus facing an average

coinsurance of 100%. Cost-sharing factors calculated from the HIE at an average

coinsurance of 31% may not be appropriate when applied at 100% coinsurance.

Because the pure price effects are estimated for coinsurance up to 95% and are

consistent with the typical HIE plans through their average coinsurance domain of

31%, one can justify using cost-sharing factors from the pure price effects for

application to all average coinsurance levels, regardless of the complexity of a plan’s

underlying cost-sharing structure.

Because of the potentially broader application of the HIE’s estimated pure price

effects, Table 1 is provided, which shows these effects for outpatient and inpatient

care as well as the total. It is worth noting that for up to 25% coinsurance, spending

does not differ by outpatient versus inpatient care, relative to free-plan spending.

Table 1. Estimated Pure Price Effects of Coinsurance on

Medical Expenses, as a Percentage of Free Plan Expenses

Calculating and Applying Cost-Sharing Methods

Based on HIE Results

In this section of the report, cost-sharing factors (arc elasticities and induction

factors) are calculated from the HIE results in Table 1.

elasticities and the induction factors are calculated, variations in their application and

the results are discussed.

One goal of this analysis is to demonstrate how the factors might be applied in

a microsimulation model, using the structure of the CRS/Hay models as an example.

The CRS/Hay models use expenditure data from individuals who are enrolled in

health insurance plans with innumerable (and unknown) cost-sharing structures.

Using the expenditure data by source of payment (that is, out-of-pocket versus

insurance-paid expenses), the first step is to standardize the data, applying cost-

sharing factors to produce expenditure levels as if everyone were in a free plan. The

estimated free plan data then becomes the baseline against which cost-sharing

arrangements are applied.

Table 2. Arc Elasticities Between Average Coinsurance

Amounts, By Type of Service

Average

coinsurance rangeOutpatientInpatientTotal medicalDental

0% - 25%-0.17-0.17-0.17-0.12

0% - 50%-0.27-0.19-0.23-0.19

0% - 95%-0.34-0.25-0.29-0.33

0% - 25%-0.17-0.17-0.17-0.12

25% - 50%-0.30-0.06-0.18-0.22

50% - 95%-0.27-0.20-0.22-0.49

25% - 95%-0.31-0.14-0.22-0.39

Arc Elasticities

Table 2 displays the arc elasticities calculated according to Eq. (4) and based

on the coinsurance (p

three rows show the arc elasticities when compared to the free plan. The next three

display the arc elasticities between consecutive coinsurance rates. The last row

shows the arc elasticity between 25% and 95% coinsurance.

four coinsurance levels used in the HIE is 0%, a value which makes the point-elasticity

formula undefined. When the point elasticity performs best, its results coincide with those

using induction factors. Otherwise, as illustrated in Figure 2, the application of the point

elasticity is far from optimal.

The key column in Table 2 is the shaded one showing elasticities for “total

medical.” These values vary, depending on the average coinsurance range used.

Even if an analyst were to carefully select an elasticity according to these results,

choosing a value is not always straightforward. Consider a person in a plan with

15% pure coinsurance on $5,000 total spending ($750 out of pocket). Which

elasticity should be used if estimating the impact of moving to a 40% coinsurance

plan? An elasticity of -0.22 would predict total spending at $4,097, using Eq. (7).

If an elasticity of -0.17 were used, total spending in the new plan would be estimated

at $4,284, nearly 5% higher. Thus, even the most fastidious analysts can reasonably

use different elasticities and come up with different results on that basis alone.

Predicting Quantity with Point-elasticity and Arc-elasticity

Formulas. Earlier in this report, it was noted that “when predicting quantity using

elasticities, it is critical to use the Q

used, whether arc or point.” This point merits repeating in the context of the HIE

results because arc-elasticity factors are so often applied in the point-elasticity

formula for predicting quantity. That is, arc-elasticity factors like those in Table 2

are often applied in Eq. (6) instead of the more appropriate Eq. (7).

Based on the total medical elasticities in Table 2, Table 3 shows the results if

one were to use those elasticities to estimate free-plan spending from the other three

coinsurance rates. Specifically, for each row in Table 3, the appropriate elasticity is

taken from the first three rows of Table 2. Since the purpose of the calculation is to

estimate free-plan spending, the result should be 100%. Because the arc-elasticity

formula is rarely written in terms of Q

point-elasticity formula in Eq. (6). Those results are shown in Column A of Table

3 and do not yield the target amount of 100% shown in Column C. Column B shows

the results of using the arc elasticities with the formula for Q

yields the targeted results. Eq. (23) illustrates how these results were calculated,

applying the 0%-95% elasticity to the point-elasticity formula; Eq. (24) does the same

but applies the elasticity in the arc-elasticity formula. The results in Table 3 again

illustrate why arc elasticities should not predict quantity using the point-elasticity

formula. Although the arc-elasticity formula for predicting quantity is more

complicated than the point-elasticity one, it is the correct one.

(23)

Q

= 55% (1 + 0.29) = 71%

(24)

Q

= - 55% (-0.29 - 1) / (-0.29 + 1) = -55% (-1.29)/(0.71)

= 100%

The total medical elasticities reflect the combination of outpatient and inpatient spending

and therefore have the result of tempering the differences in those elasticities.

Table 3. Predicted Free-Plan Spending Using Arc Elasticities,

by Elasticity Formula for Predicted Spending

ABC

Applying point-Applying arc-

Beginningelasticity formulaelasticity formulaTarget amount for

Coinsurance (p

25%83%100%100%

50%77%100%100%

95%71%100%100%

Figure 6. Analysis of Arc Elasticity’s Lack of Path Neutrality in HIE

Results: Predicting Quantity Varying By Beginning HIE Data Point

100%

(0%, 100%)

Predicted based on

higher p

80%g

(25%, 71%)

(50%, 63%)

60%an Spendin

PlPredicted based

(95%, 55%)reeon lower p

F

40%

rcentage of

20%Pe

0%

0% 20% 40% 60% 80% 100%

Average Coinsurance

Effect of Arc Elasticity’s Lack of Path Neutrality. As previously

mentioned, the arc-elasticity formula for predicting quantity is not path neutral —

that is, when using a factor’s particular value (based on two data points), the

predicted quantity for a given price will vary depending on which point is chosen as

the start (p

between consecutive points yields the two curves in Figure 6.

The dashed line in the figure is predicted quantity based on the higher of two

consecutive HIE data points. For example, if predicting quantity at a coinsurance

price of 70%, this is between the HIE data points of (50%, 63%) and (95%, 55%),

where the arc elasticity for total medical care is -0.22.

63%) as (p

beginning point of (95%, 55%) predicts a quantity of 58.8%. This is a relatively

small difference. In fact, over the domain of 25% to 95%, the difference in the

predicted quantities, varying which pair of consecutive points is chosen as (p

averages about two-tenths of one percent.

by the nearly imperceptible difference between the lines over the 25% to 95%

domain.

Figure 6 also illustrates a serious limitation of predicting quantity using an arc

elasticity when the price is zero (that is, free), as was the case in the RAND Health

Insurance Experiment. Applying the free-plan data from Table 2 to predict quantity

between a price of 0% and 25% coinsurance causes Eq. (7) to be reduced as follows:

(25)

Q

= (- Ep

1E+

= , where E = -0.17

1E−

= 71%

The constant predicted quantity of 71% is shown by the horizontal solid line

over the 0% to 25% domain in Figure 6 for the predicted quantity based on the lower

p

zero yields a constant quantity across the domain of prices. This is unacceptable for

the present structure of the CRS/Hay models, which derive their results from a

baseline of free-plan values.

cope with this issue where a person’s average coinsurance is 0%.

alternating the consecutive pairs of HIE points for the beginning point:

I Q

where E, Q

HIE data points.

making Eq. (6) undefined. It is also not advisable to use, for example, (1%, 99%) instead

of (0%, 100%) because the shape of the resulting curve is not intuitive.

It was illustrated in Figure 2 that using a (p

data points created a separate arc that did not line up with either of those based on the

original data points. This is another potential area of concern for applying the arc

elasticities. However, this appears to be less of a practical concern when using arc

elasticities derived from the HIE results. The dashed line in Figure 7 is the same one

in Figure 6. The difference between the figures is that in Figure 7 the solid line is

based on the (p

Figure 7. Illustration of Arc Elasticity’s Lack of Path Neutrality:

Predicting Quantity Varying Whether Beginning Data Point Was an

Original HIE Point

100%

Predicted based on

points as shown

80%

(13%, 79%)

Predicted

(38%, 66%)ndingbased on

(73%, 58%)60%n Speoriginal HIE points

la

e P

40%ge of Fre

centa

er

20%P

0%

0% 20% 40 % 60 % 8 0 % 1 00%

Average Coinsurance

The biggest differences between the curves occur when price p

13% used for p

beginning point of (13%, 79%), the free-plan value is predicted at 111% of the actual

HIE free-plan value. Over the domain from 13% to 95%, the largest difference

between the curves is two-tenths of one percentage point. Thus, even when the

beginning data point is not one of the original points used to calculate the elasticity,

applying the arc elasticity to predict HIE results yields relatively consistent results,

except when predicting based on small coinsurance rates. In other words, even

though arc elasticities are generally not path neutral, their application for HIE results

produces curves that appear relatively path neutral, except at smaller coinsurance

levels. Except when dealing with free-plan levels, arc elasticities appear useful in

reasonably replicating HIE results.

Induction Factors

Table 4 displays the induction factors calculated according to Eq. (14) and

based on the coinsurance (p

previously mentioned, the value of an induction factor is the percentage of the

difference in two plans’ out-of-pocket payments that directly affects total health care

spending. Table 4 expresses these percentages as decimals (for example, 1.16 rather

than 116%). As in Table 2, which shows the arc elasticities, the first three rows of

Table 4 show the factors when compared to the free plan. The next three display the

factors between consecutive coinsurance rates. The last row shows the factors

between 25% and 95% coinsurance. As previously discussed, induction factors are

not reversible — their value depends on which of the two data points in the

calculation is chosen as the starting point (p

coinsurance rates, there are two induction factors — one using the lower coinsurance

as p

Table 4. Induction Factors Between Average Coinsurance

Amounts, By Type of Service

Predicting Quantity with Induction Formulas. Induction factors are path

neutral (that is, they consistently predict quantity, using Eq. (13)) when the following

conditions hold:

was used in calculating the induction factor;

starting point; and

factor was based (p

(p

p

quantity is being predicted are both greater than or are both less than

p

Figure 8 shows the results when abiding by these conditions for total medical

(solid line) and inpatient care (dashed line). They are simply line segments drawn

between the original data points in Table 1.

Figure 8. Predicting Quantity Using Induction Factors and Original

Data Points from HIE

100%

(0%, 100%)

80%gInpatient care

(50%, 68%)din

(25%, 71%)(95%, 60%)

n Spen

(50%, 63%)60%la

(95%, 55%)ree P

Total medical

f Fcare

40%ge o

a

20%Percent

0%

0% 20% 40% 60% 80% 100%

Average Coinsurance

Figure 9. Predicting Quantity of Inpatient Care, By Induction Factor

and Beginning HIE Data Point

100%

Inpatient care using HIE

induction factors

80%

Inpatient care with 0.3 induction

ingfactor, from lower p

nd

Spe

60%

PlanInpatient care with 0.3

e

induction factor, from

f Frehigher p

40% o

age

nt

rce

Pe

20%

0%

0% 20% 40% 60% 80% 100%

Average Coinsurance

The induction factors in the CRS/Hay models, however, do not vary by

coinsurance. For each type of care, the induction factors are held constant across the

domain of coinsurance levels. The CRS/Hay models use the induction factors most

commonly cited: 0.3 for inpatient hospitalization, 1.0 for prescription drugs, and 0.7

for all other medical care.

(p

induction factor of 0.3. The thin line is predicted quantity based on the lower HIE

Implications and Design Issues,” American Academy of Actuaries’ Public Policy

Monograph No. 1, May 1995, at [http://www.actuary.org/pdf/health/msa_cost.pdf].

(Hereafter cited as Hustead, et al., Medical Savings Accounts: Cost Implications.)

coinsurance between two points; the heavier solid line is based on the higher HIE

coinsurance. The dashed line is the same as in Figure 8.

When using the 0.3 induction factor, the lines that result in Figure 9 have

relatively constant slopes (not counting the graph’s vertical lines that link the line

segments). Solving Eq. (21) for the slope and holding the induction factor I constant

illustrates why the slope is relatively flat and constant. Based on the four original

HIE data points (for Q

resulting two lines is between -0.18 and -0.30. This is consistent with the slope of

the line segments between the HIE data points where the coinsurance is not zero.

However, between the HIE data points of (0%, 100%) and (25%, 71%), the slope is

-1.16. As a result, the two lines based on the 0.3 induction factor vary substantially

from the line based on the HIE data points, although each of the two lines based on

the 0.3 induction factor passes through one original HIE point — the one that served

as (p

Figure 10. Comparison of Results of Constant Induction Factor from Free-

Plan Spending with Induction Factors and Original Data Points from HIE

100%Inpatient care predicted from

0.3 induction factor and

(0%, 100%)

80%

ng

ndi

pe

SInpatient care predicted

60%nfrom HIE induction

e Plafactors and HIE data

points

40% of Fre

ntage

ce

Per

20%

0%

0% 20% 4 0% 60% 80% 100%

Average Coinsurance

There are two lines predicted from the original HIE points and the 0.3 induction

factor because the use of a constant induction factor effectively assumes the factor

is reversible. Of course, it is not reversible, as illustrated by the two lines that emerge

between two data points when holding the induction factor constant.

The dissimilarity between the slopes of the lines based on the HIE factors versus

the 0.3 factor causes particular concern for the CRS/Hay models, which produce

results based on cost-sharing additions to a free plan. Along with the same dashed

line in the previous two graphs based on the HIE data, Figure 10 shows predicted

inpatient care from a constant 0.3 induction factor and from the free-plan spending

data point of (0%, 100%). Where average coinsurance is 25%, the difference

between the two lines is greatest: The predicted quantity of inpatient care is 30%

higher than the HIE results. These results suggest that, if induction factors are to be

used, they should not be constant against the entire domain of cost-sharing.

Cubic Formula

Both arc elasticities and induction factors have limitations when trying to apply

them to replicate HIE results. These limitations are severe when doing analyses

based on free-plan levels, as illustrated in Figure 6, or when using a constant factor

for all levels of cost-sharing, as in Figure 10. This has huge implications for the

CRS/Hay models because they are built on a base dataset that represents free-plan

spending and uses constant factors regardless of cost-sharing. These findings suggest

the need for another method to estimate the impact of cost-sharing on demand for

health care.

Some other method that yields better model results may lack otherwise desirable

characteristics not critical in modeling. For example, an arc elasticity has

applications for analyzing all kinds of goods and services. It produces a standardized

value for comparing people’s price sensitivity for all kinds of goods and services.

Standardization is obtained by taking the slope of the line (or of the demand curve)

and applying the original or average price and quantity combinations so that the units

are no longer a part of the factor, as demonstrated in Eq. (19) and Eq. (20). For

modeling purposes, however, such standardization is not only unnecessary but is also

problematic in that it leads to the problems observed in Figure 6. A better method

for replicating the HIE results may not ultimately produce factors that are

standardized for comparing other goods and services. It is more important, however,

that the method produce values that are reversible, path neutral and consistent with

the HIE results.

The HIE results of interest for our modeling purposes are the four price-quantity

data points, in terms of average coinsurance and percentage of free-plan spending:

(0%, 100%), (25%, 71%), (50%, 63%), and (95%, 55%). With only four points, a

cubic formula can be calculated using least squares fit, which will create a curve

passing through all four HIE points. For the remainder of this report, this formula is

referred to as “the cubic formula,” where Q is the percentage of free-plan spending

predicted from a particular average coinsurance, p:

(26) Q = -1.5546p

Figure 11 shows the results of this formula as a heavy line, along with the ideal

arc-elasticity and induction results presented earlier. The dashed line is based on the

arc elasticities, and the lighter solid line is based on the induction factors. All three

are for total medical care.

Figure 11. Predicting Quantity Using Cubic Formula, Compared to Ideal

Arc Elasticities and Induction Factors, From Original HIE Data Points

100%

(0%, 100%)

80%g

(25%, 71%)din

(50%, 63%)

Spen

60%

(95%, 55%)

Free Plan

40%e of

tagArc elasticities

Induction factors

ercenCubic formula:

20%P

Q = -1.5546p

R

0%

0% 20% 40% 60% 80% 100%

Average Coinsurance

The cubic formula has several improvements over the other methods. For

example, because (p

inherent in the cubic formula), path neutrality and reversibility are not concerns. The

quantity predicted based on a particular price will always be the same using the cubic

formula. Moreover, calculating the slope (that is, change in quantity / change in

price) at any point along the curve is quite simple, using the derivative of Q with

respect to p:

(27) slope of Q at a given coinsurance (p) = Q’(p) = -4.6638p

A potential concern one might note in Figure 11 is the difference between the

cubic formula and the other two curves between 50% and 95% coinsurance.

Although the arc-elasticity and induction curves are close to one another in this

domain, the cubic-formula curve appears much higher. The difference between the

cubic-formula curve and the induction curve is 3.1%.

coinsurance, the cubic-formula curve is lower than the induction-factor line segments

so that, overall, the area under both curves is nearly identical — 64.6% and 64.7%

respectively. The area under the arc-elasticity curves is 63.3%, approximately 2%

less than the area under the other two curves.

four data points, it is not known which of the three curves best reflects the impact of

cost-sharing between those points. Considering this as well as the relatively small

overall differences between the curves, the shape of the curves should not be an

overriding criterion in determining which method to use.

Estimating Free-Plan Spending

As presented here, each of the methods take a particular average coinsurance to

predict the percentage of free-plan spending associated with that coinsurance. This

section discusses how these results would be applied to create free-plan spending

levels, such as those used in the CRS/Hay models, and how their results vary.

The example case is a person who was enrolled in a high-deductible health plan.

The deductible was $1,000, after which a 25% coinsurance applied. During the year,

the person had total medical expenses of $1,500.

$1,125, or 75%. If this person had been in a free plan, her spending would likely

have been more than $1,500.

the area under the straight line created by the ideal induction-factor results:

1 - I(-1.5546p + 2.8459p - 1.7743p + 1 )dp / [(95%-45%)(55% + ½ (63% - 55%))]

where p ranges from 50% to 95%.

cubic formula and the area under the straight lines for the induction factors.

consecutive pairs of HIE points, using the higher coinsurance of each pair as p

I Q

where E, Q

HIE data points.

expenses.

To calculate free-plan spending using the arc-elasticity formulas, the appropriate

elasticity for total medical spending is needed from Table 2. Because the intent is

to predict free-plan spending (that is, p

should be based on a coinsurance of zero, as in the first three rows of Table 2. The

other value relevant for choosing the appropriate elasticity is the other coinsurance

of 75%. In the table, the nearest coinsurance rates to 75% are 50% (with an elasticity

of -0.23) and 95% (with an elasticity of -0.29). Based on its distance between 50%

and 95% coinsurance, the 75% coinsurance is estimated through simple imputation

to have an elasticity of -0.26333.

$1,500) given in the example, predicting free-plan spending as follows:

(28)

Q

= Q

1E−

= , where E = -0.26333

1E+

= $1,500 (1+0.26333) / (1-0.26333)

= $2,572

As shown in Eq. (28), predicting free-plan spending — that is, predicting Q

where p

variable remaining that reflects the original plan’s 75% coinsurance. As a result,

when dealing with free-plan information, constant results can be avoided only by

calculating precise elasticity values. The results are quite sensitive to the value of the

elasticity. An arc elasticity of -0.23 would have yielded free-plan spending of

$2,396. An arc elasticity of -0.29 would have yielded free-plan spending of $2,725.

When dealing with a free plan, the use of a continuous arc elasticities is required

to predict spending that is not constant over a given domain. In other words, the arc

elasticity must be used to create unique elasticities at each given point, like a point

elasticity. Obviously, this is not the role of the arc elasticity. The approach applied

in Eq. (28) to work around the factor’s limitation when dealing with a free plan is

arguably a misuse of its factors. Thus, when applying arc elasticities to free-plan

information, an analyst must choose between possibly misusing the factors or

predicting constant spending regardless of cost-sharing. Neither is desirable.

In applying the induction-factor formulas, not only should the factor be chosen

from the first three rows of Table 4 but should also be taken from the penultimate

column, for “higher coinsurance as starting point.” This matters because induction

factors are not reversible. As with the elasticities, there are two induction factors to

choose between — 1.17 (based on coinsurance from 0% to 50%) or 0.86 (based on

coinsurance from 0% to 95%). These constant factors would predict unique amounts

of spending for every coinsurance in the domain, unlike elasticities. As a result,

difference in the results when the starting point for predicting quantity was not one of the

original HIE points. However, those results were calculated between consecutive HIE

points with the corresponding elasticity. In this example, there is greater variation due to

the larger coinsurance domain used.

calculating an induction factor for a given coinsurance is not as crucial, but doing so

produces continuous factors that seem more accurate than the factors at 50% and

95%. Based on its distance between 50% and 95% coinsurance, the 75% coinsurance

is estimated to have an induction factor of 0.9978. The free-plan spending level is

then calculated using both Eq. (11) and Eq. (13) respectively below:

(29)

Q

= $1,500 + 0.9978 ($1,125 - $0)

= $2,623

(30)

Q

= $1,500 (1 + 0.9978 (75%-0%))

= $2,623

This is 2% higher than the comparable arc-elasticity amount. These results are

also sensitive to the value of the factor. An induction factor of 0.86 would have

yielded free-plan spending of $2,468. An induction factor of 1.17 would have

yielded free-plan spending of $2,816.

Applying the cubic formula to the same example is more straightforward in that

there are no factors to decide among. Thus, the free-plan spending level is calculated

by applying the price of 75% coinsurance as follows:

(31)

Q = -1.5546p

= -1.5546(75%)

= 61.4%

In other words, the cubic formula estimates that an average coinsurance of 75%

yields a quantity that is 61.4% of free-plan spending. Thus, the $1,500 in total

spending is 61.4% of free-plan spending, and this free-plan spending results:

(32)

$1,500 / 61.4% = $2,442

Although there is a range of possible results from the other two methods, the

cubic formula produces a single result. That result is 5% lower than the arc-elasticity

result in Eq. (28) and 7% lower than the induction-factor result in Eq. (30).

Predicting Spending From Estimated Free-Plan Spending

Pure Coinsurance Plan. Based on the free-plan spending estimates above,

one can predict spending in a plan with nominal coinsurance of 75% and no

deductible or out-of-pocket maximum. In this case, of course, the nominal

coinsurance also serves as the average coinsurance. A priori, one might expect total

spending to be predicted at $1,500 because the average coinsurance of 75%, as

before. Once more, the arc elasticity of -0.26333 is used in Eq. (7), with p

Q

(33)

Q

= Q

= Q

= $2,572 (1 - 0.26333) / (1 + 0.26333)

= $1,500

As illustrated in Figure 6, using constant arc elasticities to predict spending

from free-plan values (that is, p

formula causes spending to be predicted based solely on the value of the elasticity,

with its impact on the free-plan spending of $2,572. Calculating continuous

elasticities is not only problematic, as was mentioned before, but it is also

complicated, requiring one to add a methodology to a methodology.

Predicting spending from the estimated free-plan level using the induction

factors requires choosing a different induction factor than was used in estimating the

free-plan value, even though the analysis is of the same coinsurance amounts. A new

factor must be chosen because induction factors are not reversible and, in this case,

the analysis is of moving from no cost-sharing to substantial cost-sharing of 75%

rather than vice versa. The applicable induction factors from Table 4 are 0.47 and

0.74. For this example, the induction factor is calculated as 0.59 and is applied in Eq.

(13) as follows, with p

(34)

Q

= $2,623 (1 + 0.59(0%-75%))

= $1,462

This result is approximately 2.5% less than the $1,500 total spending that should

have been produced, in spite of the precise calculation of the induction factor. The

difference is due to induction factors’ lack of path neutrality and the issues

surrounding the calculation of the induction factor itself. An induction factor of

0.571 would have predicted quantity of $1,500.

The cubic formula produces the percentage of free-plan spending from the

coinsurance. Eq. (31) already predicted that a 75% coinsurance yields quantity that

is 61.4% of free-plan spending. Since this led to a free-plan value of $2,442 (shown

in Eq. (32)), the predicted spending in a 75% coinsurance plan would be calculated

as $2,442 * 61.4% = $1,500. This is not surprising considering that the $2,442 was

calculated as $1,500 / 61.4%, so $1,500 emerges by necessity when multiplying it by

61.4%. This demonstrates the cubic formula’s path neutrality.

Typical Plan Structure. Pure coinsurance plans are virtually nonexistent.

Today’s health insurance plans have not only coinsurance but copayments,

deductibles and out-of-pocket maximums. This example illustrates how the

formula when dealing with a free plan. The arc elasticities become path neutral, as

demonstrated in this example by the predicted spending of $1,500 emerging by identity.

estimated free-plan spending can be used to predict spending for the same person in

a plan with a deductible of $500 followed by coinsurance of 62.5%, with an out-of-

pocket maximum of $2,000. Although not a pure coinsurance plan, this plan would

also have 75% average coinsurance at $1,500 total spending. Thus, assuming

average coinsurance is an accurate predictor of total spending, one might expect the

methods to predict $1,500 of total spending from the free-plan level for this person.

In this instance,$1,500 may be the desired total spending under the new plan.

However, the only information that would be known in the CRS/Hay models is the

free-plan spending for this person. Because applying the elasticities to predict

spending requires an average coinsurance, the only information for calculating this

is the free-plan spending level of $2,572. In other words, calculating the average

coinsurance of a plan that does not have pure coinsurance requires using the given

spending level as the basis. In this example, the first step would be to calculate out-

of-pocket spending under the new plan given total spending of $2,572. This is the

same calculation that would be done for the induction-factor formula, as follows:

(35)

OOP

The average coinsurance based on free-plan spending (Q

follows, requiring the introduction of a new variable (p

(36)

p

The actual average coinsurance will likely be different once quantity is adjusted

downward because of the cost-sharing. Nevertheless, in lieu of any other known

number, one must then decide which elasticity to use based on Table 2. Again,

because calculating the elasticity is critical when dealing with a free plan, a precise

elasticity is used, -0.25639, based on the average coinsurance. This produces total

spending of $1,523, approximately 1.5% higher than $1,500:

(37)

Q

= Q

= $2,572 (1 - 0.25639) / (1 + 0.25639)

= $1,523

Using induction factors to predict spending is relatively straightforward using

Eq. (11), since it uses OOP

Eq. (35) because the free-plan spending estimated from the induction factors in Eq.

(29) is different than the free-plan spending based on the elasticities, as shown in Eq.

(28). The induction factor’s free-plan spending of $2,623 for this person produces

the following:

(38)

Q

= $2,623 + I ($0 - $1,827)

The challenge is deciding the value of the induction factor, I. Again, the average

coinsurance will likely be different once quantity is adjusted downward because of

the cost-sharing, but in lieu of any other known number, one must use p

an induction factor based on Table 4. (The CRS/Hay models, and most other models

using induction factors for modeling purposes, use constant induction factors

regardless of cost-sharing level, already shown to be problematic.) The average

coinsurance (p

approximately 69.6%. Based on where 69.6% falls between 50% and 95%

coinsurance, the induction factor is estimated at 0.6221. Plugging this value into Eq.

(38) then yields $1,486, which is 1% smaller than the $1,500 expected a priori.

Alternatively, predicting quantity by directly applying the 69.6% average

coinsurance in the induction-factor formula (based on Eq. (13)) based on free-plan

spending also yields $1,486:

(39)

Q

= $2,623 (1+0.6221(0%-69.6%))

= $1,486

This should not be surprising, since setting the first line in Eq. (38) equal to the

first line in Eq. (39) yields an identity:

(40)

Q

Q

Q

Thus, when using induction factors, the average coinsurance derived from

applying a plan structure to a given price-quantity combination yields the same

results as using the nominal out-of-pocket dollar amounts. One of the most common

arguments for using induction factors is that it enables one to handle complex plan

designs by virtue of the nominal out-of-pocket amounts. In actuality, its

methodology is no different than using the average coinsurance. As a result, the

limitations of the arc elasticity from calculating the average coinsurance in a typical

plan structure are the same limitations faced by the induction-factor formulas. This

point is typically obscured, however, because the induction factors rely on the

nominal dollar amounts.

As with arc elasticities and induction factors, the cubic formula also relies on

the average coinsurance of the new plan calculated from the spending levels of the

old plan (Q

70.2%, based on its free-plan spending level, produces the following:

(41)

Q = -1.5546p

= 61.9%

Applying this percentage-of-free-plan spending to the free-plan spending of

$2,442 (from Eq. (32)) yields $1,512, not quite 1% higher than $1,500.

Using the same approaches to predict spending in the original plan, which had

a $1,000 deductible and 25% coinsurance, based on the free-plan spending levels

shown in Eqs. (28-32) yields the values shown in Table 5. The target amount is

$1,500. Once again, the cubic formula produces results closest to the target amount.

To re-emphasize the point, the induction-formula results were calculated using the

first line of both Eq. (38) and Eq. (39). As expected, the results were identical.

Although induction factors are not reversible, this added complication was

previously justified by the factors’ capacity to predict spending based on a new plan’s

cost-sharing structure as applied to the original plan’s spending. The arc-elasticity

and cubic formulas work best when the new plan is only pure coinsurance. Any other

plan structure forces one to resort to calculating an average coinsurance based on the

original plan’s spending level, which introduces some error. However, it was shown

above that the induction factor’s methodology is no different than using the average

coinsurance calculated from the original plan’s spending level, introducing the same

kind of error. This seems to nullify the case for tolerating the induction factors’ lack

of reversibility and the concomitant complexity. Moreover, the induction-factor

methodology is the only one of the three that does not replicate a plan’s original

spending level when modeling a pure-coinsurance plan, as shown in Eq. (34). This

is because the induction-factor results are based on p

Table 5. Predicted Spending of Example Person in Plan With

$1,000 Deductible and 25% Coinsurance, Based on Predicted

Free-Plan Spending, By Cost-Sharing Method

Arc elasticityInduction factorCubic formulaTarget amount

Average 54.2% 53.6% 55.7%

coinsurance (p

Value of factor-0.235540.7184Not applicable

P redicted $1,592 $1,613 $1,529 $1,500

spending (Q

Difference from6.1%7.5%1.9%

target amount

The quantity predicted by the cubic formula was closer to the desired amount

than the quantity predicted by the other methods. This is even after taking extreme

care to calculate seemingly the best possible values for the induction factors and arc

elasticities. If such care is not taken (that is, if constant factors are used across cost-

sharing levels), then the cubic formula would certainly produce results more

consistent with the HIE. Not having to calculate values for a factor makes the cubic

formula preferable from a practical standpoint as well.

Predicting Spending by Type of Care

Most of the preceding discussion has focused on how the methodologies can be

used to predict total medical care spending. One might expect, however, that the

effect of cost-sharing will vary depending on the type of service — whether inpatient

or outpatient, for example. One of the most interesting HIE results is that spending

in the 25% plan averaged 71% of free-plan spending for both outpatient and inpatient

care, as shown in Table 1 and illustrated in Figure 12. Because of this concordance,

the corresponding arc elasticities (Table 2) and induction factors (Table 4) do not

vary by type of care between 0% and 25% coinsurance. Between 25% and 95%

coinsurance, spending does differ by type of care, as do the factors.

Figure 12. Effect of Average Coinsurance on Spending, by Type of

Service

100%

80%

ing

Spend

60%lanTotal medical

PInpatient

reeOutpatient

f FDental

40%

tage o

en

rc

Pe

20%

0%

0% 20% 40% 60% 80% 100%

Average Coinsurance

Constant Induction Factors. Although the CRS/Hay models do not vary

the induction factors by cost-sharing levels, the factors do vary by type of service:

0.3 for inpatient hospitalization, 1.0 for prescription drugs, and 0.7 for all other

care.

not always line up well with the HIE. It is arguable that medical care has changed

so that the constant factors are more in line with current utilization patterns than the

HIE results. However, that is not the argument made. These constant factors “were

based largely on the RAND study.”

factors were obtained from the range of HIE-based induction factors in Table 4.

A decade ago, a team of actuaries reexamined these constant factors, since “the

management, delivery, and mix of health care services have changed dramatically

since the study was performed.” Some of the workgroup members thought the

factors should be higher, while others thought they should be lower. Ultimately they

decided to leave the constants unchanged but noted that “(o)ne set of factors is not

appropriate for all uses. The factors used should be carefully considered in the

context of the specific situation.”

CRS/Hay models still have these values.

Inpatient and Outpatient Care. For practical modeling purposes, one must

consider whether the differences in the HIE results by type of care would

substantially affect model results. If not, it is probably not worth varying the factors

by type of care. Again, between 0% and 25% coinsurance, there is no difference

between inpatient and outpatient care whatsoever, in terms of percent of free-plan

spending. The largest difference is at 95% coinsurance. Differences at the 95%

coinsurance are compared in this section.

From the example person above, a 95% pure-coinsurance plan predicted from

free-plan levels would produce total medical spending shown in the gray column of

numbers in Table 6. The table also shows what spending would be predicted if all

spending had been either outpatient or inpatient care, and varying the factors

accordingly. The table also shows the results for dental care.

Table 6. Example Person’s Predicted Spending at 95%

Coinsurance, by Type of Service and Factor

FactorOutpatientInpatientTotal medicalDental

Elasticity $1,267 $1,543 $1,416 $1,296

Induction $1,277 $1,576 $1,452 $1,302

Cubic formula$1,196$1,465$1,343$1,221

models, based on their health care utilization by type of care.

Although this section focuses on variation by type of service, the differences

in the total medical column merit some discussion, even if it is somewhat repetitive.

First, these amounts are based on the predicted free-plan values, which were based

on the total spending of $1,500 in the original plan with an average coinsurance of

75%. The three approaches produced different free-plan values. Applying the

factors to the estimated free-plan spending to a 95% coinsurance should yield total

medical spending that is 55.0% of the free-plan spending. This was so for the

elasticity and cubic formulas; for the induction formula, it was 55.4%. Thus, the bulk

of the difference among the factors was due to the difference in creating the free-plan

values. As mentioned in that section, the results from the arc elasticities and the

induction factors vary widely depending on the values chosen for the factors.

Moreover, as illustrated in Figure 11, the methods’ functions yield dissimilar results

between the HIE coinsurance levels, and which one is superior is not known.

The cubic formula does not require the calculation of factors when predicting

quantity. Because it does not have factors of its own, predicting spending by various

types of care requires estimating new formulas. For each type of care, a different

cubic formula must be estimated to be consistent with the HIE results. This is one

practical limitation compared to elasticities and induction, which use the same

formulas but different factors for different types of care. For inpatient care, the

formula is estimated as Q = -2.2764p + 3.7873p - 1.9645p + 1. For outpatient care,

it is Q = -0.8662p

1.3865p - 1.1377p + 1. For inpatient care in particular, the resulting curve is not

ideal. Between 41.4% and 69.6%, the slope of the curve is actually positive.

the HIE results are not known between the four original data points, it is

counterintuitive that higher levels of cost-sharing would lead to higher inpatient

spending. In spite of its other advantages, the cubic formula is problematic for

producing spending levels by type of service, at least for inpatient care. The results

in Table 6 are not affected, however, because the coinsurance is 95%, one of the

original HIE data points, which is replicated by the cubic formulas.

If the example person’s spending were all inpatient, each of the three approaches

would predict total spending that is 22%-23% higher than if it were all outpatient.

Though large, this difference does not by itself merit accommodating type-of-service

factors. First, this difference occurs at the 95% coinsurance level, an unusual amount

of cost-sharing for a plan. When calculating average coinsurance on individual

records, many may be at this coinsurance level, or even 100% if they are still in the

plan’s deductible range. Of course, in the deductible range, dollar amounts are

relatively small. This leads to the second point that, in the aggregate, the differences

resulting from using separate factors by type of care may largely offset. For example,

the total medical spending amounts are based on the HIE data in which outpatient

care made up 46% of the total and inpatient care made up 54%. Applying those

percentages to the numbers for outpatient and inpatient in Table 6 yields $1,416 in

total medical for the elasticities, $1,439 for the induction factors, and $1,342 for the

cubic formulas. Only the calculated results using the induction factors vary from the

predicted total medical amount in Table 6 by more than a dollar. Thus, as long as

solving it for Q’(p)=0.

one is predicting total spending, rather than by type of care, it is arguable that the

total medical factors produce adequate results.

Example Using Actual Data. The preceding hypothesis was tested

informally by using person-level expenditure data from the 2002 Medical

Expenditure Panel Survey (MEPS) for those under age 65 with any health care

spending. These results are shown in Table 7.

Table 7. Average Predicted Spending, by Plan and Factor,

Based on 2002 MEPS

Using the total-medical cubic formula, free-plan values were calculated,

producing an average of $2,186. Based on those estimates, total medical spending

was predicted to average $1,202 in a 95% coinsurance plan, or 55% of the free-plan

average.

cubic formulas, yields total plan spending of $1,161, a difference of 3.5% from the

total-medical cubic formula result. This result emerges by outpatient spending being

49% of the free-plan level and inpatient spending being 60% of the free-plan level,

replicating the result in Table 1. The total-medical result of $1,202 differs from

$1,161 to the extent that the ratio of outpatient-to-inpatient spending in MEPS

differed from that in the HIE.

These results will also vary depending on which services are included in each

respective category. For example, if prescription drugs were not modeled separately

but were lumped into outpatient care, which is a reasonable decision, the difference

in predicted total spending would be 5.7%, depending on whether type-of-service

formulas were used instead of the total medical formula.

including zero-night stays and separately billing doctor expenses) and outpatient care

(office-based, outpatient-hospital and emergency-room visits).

separate effect of cost-sharing on prescription drugs is discussed separately, which would

suggest they were not included in outpatient care. The next section of this report discusses

those results separately as well, so prescription drugs are left out of outpatient care here.

As was previously mentioned, when applying elasticities with a free plan, one

must decide whether to misuse the factors, calculating quasi-point elasticities, or

whether to use the constant elasticity values and thus predict constant spending

across a broad domain of cost-sharing. For this example (and for simplicity’s sake),

the constant elasticities in Table 2 will be used to predict free-plan values based on

the MEPS data.

To create the free-plan values, the three elasticities from the gray column of the

first three rows in Table 2 were used. All records in the MEPS data with an average

coinsurance between 0% and 25% had their total expenditures increased by 41% to

create the free-plan spending level.

coinsurance was 0%, 25% or anything in between, which is a flaw in the arc elasticity

when dealing with free-plan information. For coinsurance above 25% to 50%, the

increase to the estimated free-plan spending was 60%. For coinsurance above 50%,

the free-plan adjustment was 82%. This led to average free-plan spending estimated

at $2,764, 26% higher than the free-plan level predicted by the cubic formula.

Beginning with the free-plan spending estimated using the elasticity formula,

flawed as it is, predicting total spending in the 95% coinsurance plan is less

problematic. Even though a constant adjustment emerges, this is acceptable since the

elasticity on which that adjustment is based relies on the same coinsurance levels (0%

and 95%) used to create the elasticities from the HIE. As with the cubic formula, the

elasticity in this case will predict 55% of the free-plan value using the total-medical

elasticity. The outpatient and inpatient elasticities will yield 49% and 60% of free-

plan spending for those services, respectively. Based on the free-plan estimates, the

total-medical elasticity for a 95% coinsurance plan predicts average spending of

$1,520. At the same coinsurance level, applying the outpatient and inpatient

elasticities to those types of care separately produces an average value of $1,473.

The arc elasticities’ estimate of the 95% coinsurance vary by 3% depending on

whether the type-of-service elasticities are used versus the total-medical elasticity.

Of course, these results still differ dramatically from the cubic formula’s largely

because of the flawed nature of the arc elasticity’s formula for creating free-plan

values. Predicting total spending from free-plan spending is also problematic except

when the coinsurance is at one of the HIE levels, which is the case here.

As with elasticities, continuous induction factors can be calculated over a range

of coinsurance levels in an attempt to improve precision, though its impact on

accuracy may be questionable. In applying induction factors to the MEPS data, the

factors given in Table 4 are used, turning to the next induction factor once the upper

coinsurance level of the pairs is exceeded. For example, to create free-plan levels

using the total-medical induction factors, 1.63 is used for coinsurance between 0%

and 25%. For coinsurance above 25% to 50%, 1.17 is used. For coinsurance above

50%, 0.86 is used. This led to average free-plan spending estimated at $2,161, about

1% lower than the free-plan level predicted by the cubic formula and substantially

lower than that predicted by the arc elasticity.

Although the arc-elasticity and cubic formula replicate 55.0% of free-plan

spending at 95% coinsurance, the induction-factor results are slightly different for

total medical, at 55.4%. Thus, spending in the 95% coinsurance plan using the 0.47

induction factor averages $1,196. Calculating spending using the inpatient and

outpatient factors (0.42 and 0.54 respectively) instead yields an average of $1,145,

a difference of more than 4%. Had an inpatient induction factor of 0.3 and an

outpatient induction factor of 0.7 been used, spending would have averaged $1,031

in the 95% coinsurance plan, illustrating once again that the induction factors of 0.7

for outpatient care and 0.3 for inpatient care do not replicate HIE results consistently.

Based on the MEPS data, average spending in a 95% coinsurance plan varies

by 3% to 4%, depending on whether the total-medical or type-of-service formulas

and factors are used. However, these differences are also affected by what is

classified as outpatient versus inpatient care. It is important to note that this is the

coinsurance level where the difference by type of service would be greatest. Since

most plans would likely be at lower levels of coinsurance, where there is little or no

difference by inpatient versus outpatient care according to the HIE results, individual

analysts must decide whether such a type-of-service analysis is merited.

Prescription Drugs. Prescription drugs are a component of health care

spending that has received increasing attention from those who follow health

insurance issues. This is not surprising considering the growing proportion of health

care spending that it comprises. In 1980, around the time of the HIE, prescription

drugs made up 6% of health care spending. By 2003, that percentage had doubled,

to 12%. Not much attention was given to prescription drugs in the original HIE

results, but a reexamination of the available information is merited in light of

prescription drugs’ growing prominence as a feature of health care coverage. One

caveat of this analysis is that because of the changes over the past 25 years — that is,

the increasing number, variety, price and utilization of prescription drugs — the HIE

results regarding prescription drugs may be particularly out of date and inapplicable.

Considering the popular notion that demand for prescription drugs is most elastic

among health care goods and services, the section examines whether the HIE results

affirm that notion and, to the extent the difference is measurable, whether it should

be accounted for in microsimulation modeling.

Newhouse, et al., presented their finding on the effect of a plan’s cost-sharing

on prescription drugs in this way: “[O]ther than through its effect on [physician]

visits, plan did little to alter drug use; that is, plan did not much affect either the

physician’s tendency to prescribe for a patient in the office or the patient’s tendency

to fill the prescription. ... [A]lthough we saw evidence of medically inappropriate

overprescribing, the proportion of inappropriate prescribing did not vary much by

plan design. ... [C]ost-sharing reduced the use of both prescription and

[http://www.congress.gov/erp/rl/pdf/RL31374.pdf]. The HIE plans covered prescription

drugs which at the time had “traditionally been poorly covered by health insurance plans.

... (A)bout 8 percent of total spending [in the HIE] was for drugs” (from Newhouse, et al.,

p. 365). This may have been higher than the average for that time because of the HIE

coverage.

nonprescription drugs; there was no evidence of substitution of over-the-counter

drugs for prescription drugs as cost-sharing increased” (p. 365).

These statements would suggest that the effect of cost-sharing on prescription

drug spending would be similar to that of total medical care, or outpatient care more

specifically. Other HIE results indicate that prescription drugs are quite different,

depending on one’s interpretation. To understand this, it is helpful to recall the

discussion of the effect of cost-sharing on total medical care in the section presenting

selected HIE results. Figure 4 showed the association between cost-sharing and

spending in the original HIE plans, which had out-of-pocket maximums. However,

because of the out-of-pocket maximums, the nominal coinsurance failed to capture

all of cost-sharing in the plan. A separate estimate was derived by the HIE authors

to determine the “pure price effects” associated with the HIE coinsurance levels,

shown as “Without out-of-pocket maximum” in Figure 4. The adequacy of these

numbers was affirmed by how they lined up with the average-coinsurance results,

shown in Figure 5, although the analysis was limited in that the average coinsurance

levels did not exceed 31%.

All three sets of estimates — based on nominal coinsurance, average

coinsurance, and pure coinsurance (or pure price effects) — are not available for

prescription drugs. For purposes of this report, the last would seem most important,

which is the piece not contained in the HIE results. The other two sets of estimates

for prescription drugs are shown in dashed lines in Figure 13 along with the original

total-medical lines from Figure 5. The lighter dashed line in shows the relation

between nominal plan coinsurance and prescription-drug spending. The darker

dashed line uses the same prescription-drug spending levels but is based on the

average plan coinsurance. The points labeled in the figure are only for the

prescription-drug lines. No amounts were given for pure coinsurance, or pure price

effects, for prescription drugs. Lacking this, the other two sets of estimates must be

used to judge whether the total-medical values are adequate estimators for

prescription drugs.

As shown in Figure 13, the nominal coinsurance for prescription drugs

corresponds with the average- and pure-coinsurance levels for total medical

spending. Prescription-drug spending based on the average coinsurance appears

much different than for total medical spending. This would seem to lead one to a

different conclusion than that of the HIE authors. The comparisons in the figure may

be suspect, however. For example, the average coinsurance for the dark, dashed line

in the figure is for all medical spending, not specifically for prescription drugs. This

is problematic because the average coinsurance specifically for prescription drugs

may be different, particularly if a disproportionate share of prescription-drug

spending took place below the out-of-pocket maximum, which is believable. If most

prescription drug spending took place below the out-of-pocket maximum, then the

nominal coinsurance would be closer to the actual average cost-sharing for

prescription drugs than would the plan’s total average coinsurance. In that case, the

lighter dashed line may be preferred. This would be consistent with the HIE authors’

conclusions. It would also make calculating the effects of cost-sharing simpler, since

the total-medical values could be used for all types of care, including prescription

drugs.

It is difficult to determine from the HIE what the pure price effects are on

prescription drug spending. Even if it were possible to determine, it would be

questionable as to its applicability today. In lieu of any more recent experimental

information, it is arguable that using total medical factors is no worse than any of the

other options, especially considering the potential challenges of appropriately

applying additional factors in microsimulation modeling.

Figure 13. Effect of Coinsurance on Annual Per-Person Total Medical and

Prescription Drug Expenses, as a Percentage of Free Plan Expenses

100%

(0%, 100%)

80%

(25%, 76%)ing

(16%, 76%)

(95%, 57%)60%n Spend

(50%, 60%)(31%, 57%)(24%, 60%) Pla

e

FreTotal medical, based on average

40%ge ofcoinsurance

aTotal medical, based on pure

centcoinsurance

PerPrescription drugs, based on

20%nominal coinsurance

Prescription drugs, based on

average coinsurance

0%

0 % 20 % 40 % 6 0% 8 0% 10 0%

Coinsurance

Conclusion

Arc elasticities and induction factors are used in health policy circles to replicate

results from the RAND Health Insurance Experiment (HIE). This report showed how

both methods have serious limitations, particularly for their practical applications in

microsimulation modeling.

Results based on arc elasticities are problematic when dealing with a plan, or

even a record in a dataset, in which there is no cost-sharing. (Results from point

elasticities are not even calculable from a plan with no cost-sharing, which is one

reason why point elasticities were quickly dispensed with in this report.) If such a

free plan is used in applying a particular arc elasticity, total spending will be adjusted

by a constant percentage, regardless of the cost-sharing in the non-free plan. A

workaround was presented, adding another level of complexity to the application of

arc elasticities, but its appropriateness is questionable.

Induction factors can handle such free-plan information. Unfortunately, their

values are not reversible. Between two price-quantity points, two induction factors

emerge rather than one. This complicates the appropriate application of induction

factors.

One purported advantage of induction factors is that they can better handle

complicated plan structures. This is because they are calculated and applied based

on the dollar amounts of cost-sharing that individuals face in a plan. In addition,

induction factors predict spending by applying the new cost-sharing structure to the

old total spending, which also makes its application easier. The analysis in this

report showed, however, that the induction factors essentially rely on the average

coinsurance calculated from applying the original total spending to the new cost-

sharing structure. Arc elasticities do so as well with concomitant limitations

acknowledged. That induction factors effectively do the same thing, with the same

concomitant limitations, is typically obscured because the induction factors rely on

the nominal dollar amounts. Thus, in actuality, induction factors have no inherent,

substantive advantage for handling complicated plan structures. Indeed, because of

their use of dollar cost-sharing based on the original total spending, the induction

factor is arguably inferior when dealing with pure-coinsurance plans, upon which the

HIE results in this report were based. This removes the primary rationale for

tolerating the induction factors’ lack of reversibility.

The CRS/Hay models create and use a baseline of free-plan values for thousands

of records/individuals. Although arc elasticities and induction factors can be used

for this purpose, their sensitivity to the specific factors’ values in such circumstances

is additional cause for concern. Special care must be taken to use the appropriate

values. Because the CRS/Hay models currently use induction factors, which are not

reversible, using the appropriate values is even more important and involved.

Presently, however, the models use constant values for the induction factors

regardless of coinsurance levels. Either new factors should be used that vary by

(continued...)

coinsurance or a new method should be applied. Arc elasticities are not superior for

this purpose, given the method’s limitations and the models’ use of free-plan values.

In an effort to apply some method that would be particularly useful for

microsimulation modeling, the cubic formula was derived. Its legitimacy is based

on the notion that a person’s experience in a plan as captured by their average

coinsurance is appropriate for replicating HIE results. The cubic formula has many

of the desirable qualities that arc elasticities and induction factors sometimes lack.

The cubic formula is path neutral. Because it does not have separate factors that

must be calculated, the cubic formula has no issues regarding reversibility. The cubic

formula faces no diminution of predictive power when dealing with free-plan

information. In addition, from a practical standpoint, it is much simpler to

appropriately implement in microsimulation modeling.

The key flaw of the cubic formula is that if one wants to separately model the

impact of cost-sharing changes by type of service (for example, inpatient versus

outpatient), new cubic formulas must be derived, as was done in this report. At least

one of these cubic formulas produced quite undesirable results. The cubic formula

for inpatient care estimated that as coinsurance rises between 41.4% and 69.6%, there

would be higher inpatient spending. While there are no HIE results between its four

original data points, this result is counterintuitive.

The HIE results also showed that, for most cost-sharing levels, there is little or

no difference in total spending resulting from separate application of cost-sharing

factors for certain types of medical care. Even for prescription drugs, the type of

health care popularly believed to be most affected by cost-sharing changes, the HIE

does not provide evidence that people respond dramatically different to changes in

cost-sharing compared to other types of care. This being the case, it is arguable that

the cubic formula for total medical is adequate for predicting all kinds of cost-sharing

changes. Moreover, because predicted values can vary more from the cost-sharing

method used rather than the type-of-service variation, the choice of cost-sharing

method is arguably more important than dealing with type-of-service variations.

None of these methods — arc elasticities, induction factors, the cubic formula

— is perfect. Each has its advantages. Each has its flaws. Analysts face the

decision, given the advantages and flaws of each, of which is best for their purposes.

For the CRS/Hay models, which are presently built on a baseline of free-plan values

and use constant induction factors regardless of cost-sharing, the cubic formula

appears better able to replicate HIE results than the current approach.

but this should have little or no impact on replicating the HIE results (or if there were an

impact, it would not be for this purpose), which vary by coinsurance regardless of the

nominal dollar amounts of cost-sharing.