Estimating the effect of individual time preferences on the use of disease screening.
Bradford, W. David ; Zoller, James ; Silvestri, Gerard A. 等
1. Introduction
Time preferences are considered a fundamental characteristic of
economic behavior. Standard utility theory, set in a dynamic model, has
strong predictions about the effect of different rates of discounting on
an individual's behavior. In general, we expect that higher rates
of discounting for an individual will lead her to more strongly shift
consumption of economic goods to the present and economic bads to the
future, relative to a person with lower rates of preference for the
present. Preventative health care can be categorized into two types:
primary prevention and secondary prevention and screening. Primary
prevention often requires patients to engage in activities they do not
enjoy today (for example, reducing the intake of high-fat and
high-sodium foods, exercising, losing weight, consuming pharmaceutical
products, etc.) to prevent the onset of disease. Patients who discount
the future more heavily should be less likely to demand primary
preventative health care than patients with low rates of time
discounting. However, secondary prevention involves screening and
medical care intended to detect disease that may already be present and
to prevent its advancement. Thus, while people who have high rates of
discounting would still prefer to shift unpleasant health care into the
future, their past neglect of primary prevention may raise the
likelihood of disease such that the increased clinical need outweighs
the economic tendency toward procrastination. Thus, more complex
interactions between time preferences and the use of secondary
prevention and screening are possible. Despite the potential importance
of this time discounting effect on the demand for preventative medicine,
the issue has not been heavily studied to date.
We investigate the direct impact of higher discount rates for an
individual patient on her utilization of secondary prevention health
screens using a compensating variations method. We evaluate one standard
screening tool for men (prostate exams), two screening tools for women
(PAP smears and mammography), and three general screens (dental exams,
blood pressure tests, and cholesterol tests). To do this, we conducted a
nationally representative survey of 2000 individuals over age 40. In
addition to a set of standard demographic and economic questions and
respondents' recent utilization of health care screening tests,
individual rates of time preference were elicited by asking respondents
to imagine they had won a lottery that will pay them $10,000 one year
from that day, or some higher value six years from that day.
(Respondents were also told the interest rate that a savings account
would pay to generate the offered higher future payment.) They were then
asked whether they would prefer the one-year delayed payout or the
six-year delayed payout. Follow-up questions were asked to permit
tighter bounds on the range of discount rates. All payments (and so,
interest rates) were randomly assigned uniquely to each respondent.
With the data in hand, we model the joint likelihood that a
respondent's latent discount rate lies within the interval
indicated by their responses to the survey questions and that the
respondent uses each of the six screening services; this model is
estimated using a two-step maximum likelihood (LIML) method. We find
that respondents have a discount rate of approximately 25.1% per year,
on average, and that this discount rate increases with age. We find that
discount rates have a generally negative relationship to the likelihood
of screening, though a positive relationship is found for one disease
screen--that for prostate cancer.
The results from these models should be of interest to economists
in general, as well as health policy makers. For economists, this will
be one of the few attempts to integrate a direct estimate of individual
agents' actual discount rates with their demand for a
time-dependant service. Consequently, the results will inform an
important, but understudied, intersection between economic theory and
empirical estimation. For policy makers, the information gain with
respect to the demand for preventative services should be similarly
informative. Clinicians are often frustrated by the difficulty in
convincing patients to consume preventative health care. This reluctance
is typically taken as an indication that patients are poorly informed,
and so education programs are proposed as a solution. These results
suggest, however, that at least some patients are in part making
rational decisions based upon their discounting of the future.
The article proceeds by reviewing the literature on the estimation
of individual rates of time preference and on models that predict the
demand for preventative health care. Section 3 presents the details of
our empirical models. Section 4 presents the results, and section 5
concludes with a discussion of the implications of this work and
suggestions for future research.
2. Discount Rates and the Demand for Preventative Medicine
Michael Grossman (1972) introduced the concept of health as a
component of human capital, which depreciates and in which investments
can be made. Since that seminal contribution, a number of economists
have investigated many dynamic aspects of health production and health
care demand (Wagstaff 1986; van Doorslaer 1987; Wagstaff 1993; Grossman
and Kaestner 1997; Zweifel and Breyer 1997). Theoretically, there have
been a number of contributions that have explicitly modeled the role of
time preferences on general human capital investments, of which health
care is one. The Becker and Murphy (1988) model of rational addiction is
perhaps the most successful of these. In that model, agents have
foresight, and make human capital (and other consumption) decisions
based upon the current utility and future utility generated. They find
that higher rates of time preference tend to lead to lower current
consumption of goods but will increase current consumption of addictive
products. As Grossman (2000) notes, the Becker-Murphy model predicts a
discount rate effect only under certain circumstances (the result is
generally ambiguous in sign, and uncertain in magnitude). Ehrlich and
Chuma (1990) explore the general implications of the Grossman (1972)
model more completely and do pay particular attention to the impact of
time preference. They find that increasing the rate of discounting the
future tends to reduce investments in health capital--though this result
holds only on average. The empirical research we present will test these
"average" predictions from the Grossman (1972) and Ehrlich and
Chuma (1990) models.
While the theoretical guidance is relatively clear with respect to
the impact of time preference in health care demand, direct empirical
tests of these predictions are notably absent from the literature. A
number of authors have tested the effect indirectly, by demonstrating a
schooling--health investment relationship that is consistent with an
inverse relationship between discounting and human capital investment
(Farrell and Fuchs 1982; Berger and Leigh 1989). However, these are only
indirect tests and subject to multiple interpretations. Consequently, in
the words of Grossman (2000, p. 401): "definitive evidence with
regard to the time preference hypothesis is still lacking." While
definitive evidence may be long in coming, we will at least present
direct evidence in this work.
One paper that does examine time and risk preferences impacts on
the use of medical screening exams is Picone, Sloan, and Taylor
(2004)--though again the test with respect to time preferences is
necessarily indirect. The authors propose a simple two-period model of
expected utility maximization over the decision to undergo cancer
screening. They predict that higher rates of discounting would lead to a
reduction in the demand for screening. However, in their model the
likelihood of disease does not depend upon the health state; there is no
long-term clinical benefit from early detection (either in terms of
likelihood of successful treatment or mortality), and they do not
explicitly model time preferences (rather they make inferences about
time preferences by assuming specific functional forms for utility).
From a data perspective as well, the authors lack a direct measure of
time preferences. Using the Health and Retirement Survey, they are only
able to categorize individuals into short time-horizon or long
time-horizon groups, which may or may not be directly correlated with
having high or low time preferences over the long run. Despite these
limitations, which the authors discuss, they find that women with longer
life expectancies and self-identifying as having a long time horizon are
more likely to undergo cancer screening. We will improve upon this work
in two areas. Theoretically, we will expand their model to permit more
direct assessment of the role of time preferences, which generates a
somewhat more complex set of results. Empirically, we will have a direct
estimate of each person's underlying discount rate, which we can
then use as an explanatory variable in models that track their actual
use of several types of screening (not just mammography and PAP smears
among women). Unlike Picone, Sloan, and Taylor, though, we will not have
a measure of respondents' risk preferences.
One reason that direct evidence on the relationship between time
preference and health care demand is scarce is the difficulty in
measuring time preference. Until fairly recently, the art of estimating
individual discount rates has been poorly explored. However, there is
currently a strong, and growing, literature on which to draw. (1) There
are three primary methodologies for assessing individual discount rates.
The first is to use natural experiments in which individuals must choose
between alternatives with differential time dimensions, such that a
discount rate can be inferred. An example of this literature is Warner
and Pleeter (2001), who took advantage of data generated from an early
retirement program in the U.S. military to estimate discount rates for
enlisted men and officers. A second methodology is to present
individuals with hypothetical or real payouts that vary in their time
dimension in an experimental setting. Coller and Williams (1999) and
Harrison, Lau, and Williams (2002) represent examples of this research.
The third methodology employed is to present survey subjects with a set
of hypothetical present and future payouts and estimate discount rates
using a contingent valuation (CV) method. We will employ this latter
approach.
As discussed, economists expect that time preferences will play an
important role in medical decisions that have differential effects
through time. Physicians have a variety of tools at their disposal to
improve health, both current and future. Often, medical care is aimed at
changing health behaviors or providing interventions in the present with
some hope of reducing the incidence of acute conditions in the future.
This type of health care, when no symptoms currently exist, is known as
primary prevention. In addition, physicians may screen for diseases that
the patient may currently have, though no definitive acute symptoms are
present. This type of health care is known as secondary prevention (and
is, technically, the sort that our empirical models will evaluate).
While clinical tools are well validated, physicians often complain that
they cannot convince large numbers of their patients to adopt primary
prevention practices. For examples of such discussion in the
cardiovascular realm, see reports from the 33rd Bethesda Conference Task
Forces #3 (Ades et al. 2002) and #4 (Ockene et al. 2002; Giorgianni,
Grana, and Keith 2003).
While there are a large number of potential health screens
available to clinicians, a much smaller set have built up such a body of
evidence in their favor that clear clinical guidelines exist to promote
their use. For men, this set includes annual prostate exams; the
American Cancer Society currently recommends that all men over the age
of 50 be offered digital rectal exams and prostate specific antigen
(PSA) blood tests for the presence of prostate cancer. For women, the
American Cancer Society recommends annual PAP smears for women beginning
no later than age 21 and mammograms every other year for women aged
40-50 and every year for women over 50. The National Heart Lung and
Blood Institute has facilitated development of a set of criteria,
including annual screening for blood LDL cholesterol levels (National
Heart Lung and Blood Institute 2001). The American Dental Association
recommends annual dental exams for caries and gum disease. We will study
whether respondents in our survey undertook each of these recommended
secondary (and primary, in the case of dental exams and cholesterol
tests) health care screens. Despite the clinical evidence and pressure
from primary care physicians, low rates of adherence suggest that many
patients are not willing to expend effort currently to be screened to
secure some potential health gains in the future (reduced future
mortality associated with early treatment). The degree to which innate
discounting of the future plays a role in this poor adherence is open
because evidence suggests that willingness to seek screening for some
cancers varies by patient characteristics and financial constraints for
example, mammography for breast cancer has been studied by Tudiver and
Fuller-Thomson (1999).
Consequently, we examine data generated from a national survey,
where utilization of primary and secondary screening, willingness to
delay payouts from a hypothetical sweepstakes, and respondent
characteristics were collected. We use interval estimation models to
estimate each respondents' discount rate and dichotomous choice
likelihood models (probits) to estimate the probability of screening
(separately for each type of screening) as a function, in part, of the
latent discount rates. This work will simultaneously add to the
literature that seeks to understand individual time preferences and also
to the literature that models patient utilization of preventative
services.
3. Theory
For the theoretical underpinnings of this research, we will expand
on a simple two-period model of Picone, Sloan, and Taylor (2004). For
our version of the model, we consider a two-period game with the
following rules. In the first period the agent chooses whether to seek a
disease screen. The test is positive with probability [rho](*) [member
of][0, 1], which is also the probability that the person suffers from
the disease in question (we assume no false positive results); if the
test is positive then the patient is treated. One of the distinctions we
make in this research is the difference between primary prevention
(e.g., exercise, sodium intake control, weight management) and screening
for the presence of a disease (e.g., cancer, hypercholesterolemia,
cardiovascular disease), in the former case, existing theoretical models
predict that increases in an individual's discounting of the future
should (on average) decrease the demand for primary prevention (Ehrlich
and Chuma 1990). As will be seen, the relationship between discounting
and screening is not necessarily the same. People will often only seek
screening in response to some symptom that the disease is present. For
example, patients may seek a cardiac stress test only after suffering
from some initial chest pain or shortness of breath. Thus, the
probability that a person has a disease for which they will seek a
screening will be a function of their current health, H, and the
investments in primary prevention that they have made in the past--which
is itself a function of the rate of discounting (in conformity with
Grossman 1972; Becker and Murphy 1988; and Ehrlich and Chuma 1990).
Thus, we posit this probability to be [rho](H, [beta]),where H
represents current known health; [beta] [member of] [0, 1] is the future
discount factor (an inverse function of the individual's discount
rate); and [[rho].sub.H], [[rho].sub.[beta]] < 0.
Treatment in the first period has a probability of success of
[alpha] [member of] [[delta], 1]. If the patient is not screened in the
first period, then their disease state is revealed in the second stage,
and if they have the disease they are treated, with a probability of
success of ([alpha] - [delta]) [member of] [0, 1]. Patients pay for the
screening test and any needed disease treatment out of pocket at a cost
of c and P, respectively.
We assume that patients will seek to maximize the present value of
expected utility. Utility is an increasing function of health state and
income. Full health, H, is reduced by amount L when the patient has the
disease in question. Income is either spent on some numeraire good, x,
or on testing and treatment: U(H, x).
Finally, at the end of the second period the agent receives a
payoff that is the present value of all future utility. This residual
utility will depend upon the health state that obtains as a result of
the two-period game and life expectancy. For simplicity, we will define
two residual present value functions: one when the disease state is
either not present or resolved through treatment
[PV.sup.0] = [[integral].sup.T.sub.t=3] U(H, x) x [beta](t)dt (3.1)
and one where the disease state is present and unresolved.
[PV.sup.L] = [[integral].sup.T.sub.t=3] U(H - L, x) x [beta](t)dt
(3.2)
In this case it is clear that [PV.sup.o] - [PV.sub.L] > 0.
Consistent with expected utility maximization, we assume the agent
will choose to purchase a disease screening of the expected utility from
doing so
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.3)
is greater than the expected utility of not screening in period one
and waiting until period two to resolve the uncertain disease state
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.4)
Thus, the decision rule for whether to purchase screening in period
one is whether NB = [EU.sub.s] - [EU.sub.NS] [greater than or equal to]
0. For ease of exposition and seeing the sign of our derivatives of
interest, we can rewrite this net benefit of screening function as
follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3.5)
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.6)
To see what the impact of increasing an individual's discount
rate, r, would be, recall that if [beta] is the traditional discount
factor, then [[beta].sub.r] < 0 (that is, increasing the discount
rate causes the agent to reduce the weight assigned to future utility,
which is equivalent to reducing [beta]). Thus,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.7)
The second and third terms of this partial derivative are negative;
however, the first term is ambiguous in sign. Thus while Ehrlich and
Chuma (1990) find that increasing the discount rate should (on average)
increase the use of medical care (which corresponds to primary
prevention care in this model), we find that the impact of increasing
the discount rate on the use of disease screening is uncertain. While
one might expect a negative relationship, if the productivity of
preventative health care in staving off disease ([[rho].sub.[beta]]) is
large and the utility loss from income outlays to secure current
treatment is sufficiently outweighed by the expected benefit from
current treatment, then the impact of higher rates of discounting may
well be to increase the value of current screening for acute disease.
Thus, this theoretical model has three implications for how we will
empirically model the marginal effects of individual discount rates on
health decisions.
1. As can be seen in the previous discussion, the marginal effect
of the benefit of screening (and so the decision to screen) will depend
on the price of the screening technology itself, though the direction of
the effect is uncertain. Empirically, this implies an interaction term
between the opportunity cost of screening and the individual discount
rate. While we do not have measures of screening prices, we do have
measures of whether the respondent is insured with a traditional (fee
for service) insurance policy, insured with an HMO, or uninsured
(excluded category); consequently, we include interactions between the
discount rate and insurance indicators in the second stage model
discussed later.
2. The marginal effect of the discount rate on the benefit of
screening will depend positively on the productivity of screening in
leading to treatments that prevent, or at least quickly cure, the
underlying disease. Thus, the marginal effect of discounting will be
positive (less negative) as the effectiveness of the screening in health
production increases. Because the effectiveness of these screens will
change with age, we will include an interaction term between the imputed
discount rate and age.
3. Finally, the marginal effect of the imputed discount on the
screening benefit will depend on the underlying likelihood of the
disease being screened for. Consequently, we will include interaction
effects between the imputed discount rate and measures of the age
gender--race adjusted likelihood of the respective diseases (e.g., the
probability of breast cancer for mammography).
We will test the net effect of discounting on the rates of
screening for breast cancer (mammography), cervical cancer (PAP smears),
prostate cancer (prostate screening), dental caries,
hypercholesterolemia (cholesterol screening), and hypertension (blood
pressure exams). Given the interaction effects that we must include
according to our theoretical model, estimating marginal effects are
complicated. As a result, we will examine the parameters of the model
for significance and then calculate empirical marginal effects by
predicting the estimated probability of each screen separately for each
observation as we change the imputed discount rate from 0.01 to 1.0.
4. Methods
Survey
We conducted a randomized telephone survey of 2000 adults (over 40
years of age) during the second half of 2002 and the first half of 2003.
Random digit dialing was employed. The only exclusion restriction was
age. In addition, we oversampled current and former smokers. After
eliminating observations with incorrect survey administration, and
observations from Alaska and Hawaii (due to outlier status with regard
to costs of living and market interest rate options), we retained a
sample of 1878 individuals. Table 1 presents the demographic information
on our sample.
Contingent valuation (CV) is a widely used method to assess the
valuation for goods not traded in the marketplace. While it has often
been used to value environmental resources, it has also found a home in
health economics in assigning dollar values to many things that are not
traded in the market (such as life-years in the future) and services
that are traded in the market, but for which patients do not naturally
pay the full marginal cost out-of-pocket. The earliest utilized approach
was to survey people, asking how much they would be willing to pay for a
particular good. Often, however, the survey respondents have no direct
experience with purchasing the service being evaluated. Consequently,
answers may be noisy. Additionally, when the survey offered several
examples of value, the responses may also suffer from framing, in that
the value offered by the survey may influence the respondent's
actual expressed valuation (see, for example, Diamond and Hausman 1994).
Many of the problems of this simple survey method can be avoided by
using the dichotomous choice approach. In this approach, participants
are asked whether they would pay a certain amount for the good in
question. The amount asked is varied across participants. In this way,
the question is less strongly "framed" for respondents--at
least they are not asked to consider whether the offered amount
corresponds to their maximum willingness to pay. Further, by asking
whether they will pay $x, respondents can perceive no signal as to
whether "Yes" or "No" is the "preferred"
answer that the surveyor desires. Thus, the elicited response can be
expected to better represent the choices of the survey participant (see
Boardman et al. 1996, pp. 347 9). Typically, the actual dollar amount
offered varies across a small number of values. Less commonly, the value
is varied randomly for each respondent (a method that significantly
raises the difficulty of administering the survey). However, because
there is a potentially large increase in the precision of the estimates
by varying offer amounts for each individual, that is the approach we
take in this study. In addition, rather than asking about willingness to
pay, we will ask about preferences for receiving a payout, where the
magnitude of the payout varies inversely with the time delay in
receiving it.
One disadvantage of a single-bound dichotomous choice method is
that if someone answers "Yes" to the question "Would you
be willing to accept $x in six years rather than $10,000 in one
year?", then the implied discount rate can only be seen as an upper
bound to their true underlying discount rate (or a lower bound, if they
answer "No"). An alternative approach, which has recently been
applied to health economics, takes the elicitation process one step
further (Bradford et al. 2004). This method is known as double-bounded
dichotomous choice contingent valuation (DBDC) (Hanemann 1985; Cameron
and James 1987). When employing the DBDC method, a survey poses
follow-up questions to the initial willingness to pay (WTP) query. If a
person responds "Yes" to the willingness to accept question,
then they are asked a follow-up question where the implied discount rate
is lowered. If the person responds "No" to the first question,
then they are asked the question again, this time with a higher implied
discount rate. Thus, the DBDC approach generates more information
because either the upper or lower bounds are defined more precisely or
the true WTP is clearly bounded on both sides. This information gain
implies that the DBDC approach may be significantly more efficient than
the single-bound method (Hanemann, Loomis, and Kanninen 1991; Kanninen
1993).
The actual discounting questions were as follows:
I want you to imagine that you have just won a sweepstakes prize.
Imagine that you have been offered two choices for how you will take
your prize. Which of the following two choices would you select?
A. In $10,000 cash paid to you one year from now?
B. In $[x.sub.1] cash paid to you six years from today. (This is
like having a savings account that pays an interest rate of [r.sub.1]%
per year.)
The dollar amount $[x.sub.1] was randomized for each survey
respondent, and the respondents were told the implied interest rate,
[r.sub.1], which was calculated based upon the randomly assigned dollar
amount and a five-year time frame (because the second prize, which is
paid in six years, is to be compared to the first prize, which is paid
in one year). The rationale behind the year-long delay in any reward is
to avoid confounding the estimated discount rate if individuals discount
the future differently for payouts that are imminent compared with
payouts that are further in the future. (2)
If the underlying discount rate for the person lies below the
offered rate, [r.sub.1], then this means the money will grow faster by
delaying the prize than the person's rate of discounting the
future--in which case the respondent will choose to delay payment. On
the other hand, if the respondent's innate discount rate is above
[r.sub.1], then he or she will discount the future more quickly than the
prize will grow, and so the person would choose the $10,000 in one year.
Consequently, if the respondent chose to take the $10,000 payment in one
year, an identical question was asked with a new dollar amount,
$[x.sub.2], that was higher (by a random factor) than the initial one,
corresponding to a higher interest rate, [r.sub.2]. Contrarily, if the
person selected the future payment, a new question with a randomly lower
dollar amount, $[x.sub.3], and interest rate, [r.sub.3], was asked.
Figure 1 presents this process schematically, noting the average offer
rates at each node and the numbers (and percentage) of respondents who
followed each of the four possible paths.
In addition to the usual set of socioeconomic characteristics, the
survey also elicited information on respondents' health maintenance
behaviors over the recent past. In particular, the survey asked
respondents whether they had had any of the following health services
within the past two years: mammography, PAP smear, prostate exam, dental
visit or exam, blood pressure check, and cholesterol test (mammography
and PAP smears were only asked of women, and prostate exams were only
asked of men). To be consistent with the range of clinical guidelines,
we measure health habits as dichotomous indicators for whether the
respondent had any of the listed services within the past two years.
[FIGURE 1 OMITTED]
Econometric Model
Considering each health behavior separately, we assume that there
exist two latent variables, which are defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.1)
where [beta] and [theta] are vectors of unknown parameters, [alpha]
is an unknown scalar, [[epsilon].sub.1i] and [[epsilon].sub.i,2] are
vectors of (correlated) errors, and the subscript i references the
individual. The latent individual discount rate, [R.sup.*], and the
health screening behavior demand, [S.sup.*], depend upon a set of
explanatory factors X and Z, respectively, where X contains elements
that are not present in Z, which is necessary for identification.
It is possible that the very act of offering CV questions with
explicit discount rates can frame the responses and further complicate
the process of inferring [R.sup.*] (Frederick, Loewenstein, and
O'Donoghue 2002). To confront this, we will model the framing
process directly. First, assume that the underlying latent variable
[R.sup.*] is stable, but that the answers to the CV questions may be
affected by the values that are offered. In essence, the CV hypothetical
questions are based upon a perceived discount rate, which is a function
of the true underlying rate and the rates offered in the hypothetical
situations. To operationalize this, assume that the first response is
based upon the underlying latent rate [R.sup.*], but that the second
response is based on a perceived discount rate, which is a linear
combination of the true latent rate and the first round offer rate,
[r.sub.1] as in:
[R.sup.1] = [lambda][R.sup.*] + (1 - [lambda])[r.sub.1], (4.2)
where [lambda] [member of] [0,1]. Once the framing has occurred,
the respondent is then offered a second discount rate. This rate is
lower ([r.sub.2]) if the person responded "Present" to the
first CV question; the rate is higher ([r.sub.3]) if they responded
"Future" to the first CV question.
Because the final answer is dependent on this hybrid latent rate
[R.sup.1], the probability that the person has responded to the second
question that they want the money in one year rather than the payoff
$[x.sub.2], which is associated with an annual return of [r.sub.2], is
equal to the probability that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.3)
which, with the appropriate substitution of terms, can be expressed
as:
[r.sub.2] < [X.sub.i][beta] + [[epsilon].sub.li] + [delta] x r
< [infinity], (4.4)
where [DELTA]r [equivalent to] ([r.sub.1] - [r.sub.2]). This
describes the interval under which the true discount (X[beta] +
[epsilon]) must fall if the person prefers $10,000 in one year to
$[x.sub.2] in six years.
Using similar arguments, the intervals for the four possible
responses to the iterated CV time preference questions are as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.5)
These responses can be summarized into the following regression
relationship:
[r.sup.1] < [X.sub.i] [beta] + [delta] x [DELTA]r + dPF x
[delta][r.sub.1] + dFP x [delta][r.sub.2] + [[epsilon].sub.1i] <
[r.sup.u] (4.6)
where dPF = 1 if the respondent answers ("Present",
"Future") to the CV questions and = 0 otherwise; dFP = 1 if
the respondent answers ("Future", "Present") to the
CV questions and = 0 otherwise; and the upper ([r.sup.u]) and lower
([r.sup.l]) bounds on the discount rate are defined by which response
category described earlier the person falls into.
For the latent health screening demand, the observed responses are
the typical dichotomous dependent variable:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.7)
The full log-likelihood function for this two-equation model can be
represented generally as
[ln] L = [N.summation over(i=1)] f([r.sup.l.sub.t],
[r.sup.u.sub.i], [s.sub.i] | [X.sub.i] [Z.sub.i], [beta], [theta] ,
[alpha], [delta]) (4.8)
However, deriving the joint likelihood for the interval defined and
dichotomous dependent variables is complex and so limits the
attractiveness of a full information maximum likelihood approach.
Rather, we will implement a limited information maximum likelihood
(LIML) procedure on our triangular structure by first maximizing
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.9)
where i [member of] LC are those observations for which the implied
rate is below [r.sup.l.sub.i] (and so are bounded above 0 by
construction), i [member of] RC are those observations for which the
implied rate is above [r.sup.u.sub.i] (and so are right censored), and i
[member of] I are those observations for which the implied rate is
between [r.sup.l.sub.i] and [r.sup.u.sub.i] (and so are interval
bounded). After solving the first likelihood function, we then maximize
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.10)
where [??] and [??] are the estimated parameters from the first
stage of the two-step ML (LIML) procedure. Because the joint
distribution was not derived, the standard errors for the two-step ML
estimates are generated using a bootstrap procedure. (3)
Finally, the structure of this latent discount rate model provides
a natural set of instruments for identifying the imputed latent discount
rate from the preventative service use models discussed earlier. As an
instrument, we need variables that are related to the revealed discount
rate but are unrelated to the latent demand for preventative services.
Given the framing arguments derived earlier, we must include [DELTA]r,
dPF x [r.sub.1], and dFP x [r.sub.2] in the grouped regression
likelihood function for the latent discount rate model. Because all of
the offered rates are randomly constructed for the survey questions
only, they must be unrelated to the process that determines the past
actual use of preventative services. Note that if all of our
observations were within the i [member of] I set, then the [delta] x
[DELTA]r + dPF x [Sr.sub.1] + dFP x [delta][r.sub.2] term would be
subtracted out of each observation and thus not identify the model
(because these terms would then not effectively appear in the imputed
value, which would then be perfectly collinear with [Z.sub.i]). However,
with the interval regression model, the expected value of the latent
dependent variable (discount rate) is only equal to the linear
projection through the right-hand side variables when the latent rate is
bounded on both sides. For the observations where [??] is outside the
interval [[r.sub.1], [r.sub.2]], the expected value of the latent rate
is a nonlinear function of the bounds and the right-hand side variables.
Let [??] [equivalent to] [X.sub.i][??] + [??] x [DELTA]r + dPF x
[??][r.sub.1] + dFP x [??][r.sub.2] be the predicted dependent variable
from our first stage, then the imputed discount rate is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4.11)
Thus, these three variables serve as natural identifying variables,
and they pass the usual tests for weak instruments. (4)
Explanatory Variables
We include explanatory variables that fall into several classes.
These are as follows:
* Characteristics of the individual that are expected to influence
general preferences: respondent age, gender, race (indicators for
whether the respondent is African American, and other race if respondent
is not Caucasian or African-American; Caucasian is the excluded
category), marital status, and educational attainment (indicators for
whether the respondent graduated from high school or attended some
college or graduated; did not graduate from high school is the excluded
category).
* Characteristics that reveal underlying preferences with respect
to risk: self-reported health status (an indicator variable for whether
the respondent reported she was in good or excellent health);
self-reported cancer risk (an indicator variable for whether the
respondent reported that she believed herself to have a high or very
high risk of cancer); and smoking status (indicator variables for
whether the respondent has smoked in past, but not in present, and
whether the respondent is a current smoke--never smoked is the excluded
category).
* Characteristics that affect the opportunity costs of medical
care: insurance status (indicator variables for whether the respondent
is covered by Medicare, Medicaid, private, nongroup insurance, HMO
coverage, or some other form of insurance; noninsured is the excluded
category); employment status (indicator variables for whether the
respondent is currently employed or currently retired; nonemployed is
the excluded category); and income (indicator variables for six discrete
income level indicators, plus an indicator variable for whether the
respondent refused to answer the income question; income over $100,000
per year is the excluded category).
* Characteristics required because of the theoretical model: age x
imputed discount rate ([R.sup.*.sub.i]) interaction; individual
probability of breast cancer, cervical cancer, prostate cancer, and oral
cancer (imputed by age, race, and gender using DevCan 6.3.1 from the
National Cancer Society SEER database), and cardiovascular disease
(imputed by age, race, and gender using the National Heart Lung and
Blood 10-Year Risk Assessment Tool [NHLBI 2001] based on data from the
Adult Treatment Panel III study); and imputed discount rate
([R.sup.*.sub.i] x disease risk interaction terms.
The variables listed are expected to affect both the demand for
preventative medical care and the returns to health investments.
Additionally, we include variables that are expected to affect
individuals generally. These include a year indicator for 2003 and a set
of census region indicators (mid-Atlantic is the excluded region).
Table 1 presents descriptive statistics of the variables discussed.
5. Results
Results from the First Step ML Discount Rate
The interval regression estimates of the discount rate model appear
in Table 2. We generate predictions of the latent discount rate for each
individual in the data as outlined in section 4. Figure 2 graphs the
histogram of the imputed individual discount rates. The model yields an
average predicted discount rate of 25.1% per year. While 25% per year is
high relative to market rates of interest paid to savings, CD, or high
quality corporate paper, it is in fact not high relative to the rates
charged for much consumer debt on credit cards. Further, the value of
25.1% falls squarely in the midrange of previous estimates of individual
discount rates (Frederick, Loewenstein, and O'Donoghue 2002).
[FIGURE 2 OMITTED]
As Table 2 shows, men had statistically significantly lower average
discount rates than women--with mean predicted annual discount rates
that were about 1.4% lower than those of women in the sample. (While
perhaps surprising to some readers, this is commonly found in the
literature.) Respondents in good health had imputed rates significantly
lower than those who did not report good health (by 3.6% per year). In
general, individuals with higher socioeconomic standing more education
and higher income had statistically and economically lower discount
rates than individuals with lower socioeconomic standing.
One characteristic of the imputed discount rate that is apparent in
Figure 3 is the steady increase in imputed rates with age. Annual
discount rates for the oldest age group (70 years old) are more than 10%
higher than the rates for the youngest age group (40 year olds). This is
borne out in the parameter estimates, where age is uniformly a positive
and significant predictor of the latent rate. That older individuals
would be less patient is consistent with findings in the literature
(Frederick, Loewenstein, and O'Donoghue 2002) and is often
explained as a risk effect: Older individuals may perceive the
likelihood that they will be alive in six years to collect the award to
be lower, and therefore exhibit less patience with respect to the timing
of the reward.
[FIGURE 3 OMITTED]
The steepness of the age or discount rate curve has another
implication for our model. The discount rates in excess of 50% per year
for the oldest respondents imply that individuals in these age groups
will substantially devalue benefits occurring more than five years in
the future. This is reinforced because the clinical benefits of
screening for prostate, cervical, or breast cancer fall significantly
with advanced age. For this reason, the National Comprehensive Cancer
Network guidelines call for prostate cancer screening only in men with
at least 10 years of remaining life expectancy. Similarly, the NCCN
recommends discontinuing cervical cancer screening (PAP smears) at age
70 for women who have had no abnormal screens in the previous 3 years
and suggests that all women over age 70 discuss with their physician
whether they would benefit from screening (NCCN 2004). While there is no
explicit age limit on breast cancer screening with mammography, the
benefits are clearly lower as life expectancy declines. Consequently,
given the clinically questionable value of many preventative screening
programs in the oldest populations, we will only estimate our models on
the aged 40 to 70 subsample.
Results from Second Step ML Preventative Screening Use
As a baseline for comparison, we estimated our second stage models
assuming separability between the discount and screening decisions,
using a standard probit model for each screening choice. These
coefficients for the key variables (discount rate, disease
probabilities, and interactions) are presented in Table 3 (and the
coefficients for the remaining variables are presented in Appendix Table
A3). Using these naive estimates, we find that the coefficients on the
imputed discount rates have the expected negative and significant sign
for two of the screening tools (PAP smears and cholesterols checks),
while the effect of higher discount rates are positive for prostate
exams.
However, the potential for endogeneity of the discount measure in
the screening decision cannot be ruled out. Consequently, our full model
is presented in Table 4, where screening is estimated using a two-stage
least squares (using the method of two-stage residual inclusion [Terza,
Basu, and Rathouz 2008]) model to account for the potential correlation
in the error terms between the first and second stages. Table 4 presents
the coefficients (not marginal effects) and t-statistics for the key
variables of the screening models, where each column represents separate
implementations of our discount rate-screening LIML model. (Again, the
coefficients for the remaining variables are presented in Appendix Table
A4.) While one may expect correlations between the errors between the
different screening use variables, such that a seemingly unrelated
regressions (SUR) framework would be more efficient, constructing a
full-information maximum likelihood version of our model is beyond the
scope of this work; consequently, our bootstrapped standard errors will
be somewhat larger than they would be for a FIML version, and our
t-tests should be seen as conservative.
The primary results of interest are the parameters on estimated
discount rates and the discount x age and discount x disease probability
interactions. First, for PAP smears and cholesterol tests we find that
the main effect of discounting is negative and significant; however, for
prostate exams the main effect is positive and significant. The
interaction terms between discount and the risk of cervical cancer (for
PAP smear use) and discount and the risk of prostate cancer (for
prostate exams) are significant. (Note, the magnitude of the parameters
attached to the probability of cervical cancer are not anomalous because
even for women in the age range we study, this cancer is quite rare.)
Finally, approximately half of the interactions between the induced
discount rate and insurance indicators are significant. Thus, individual
discount rates would appear to have a significant effect on the
likelihood of screening use.
What is the actual marginal effect of discounting on screening?
Unfortunately, given the multiple interaction terms required by the
theoretical model, calculating the marginal effect becomes complex. As
Ai and Norton (2003) indicate, when interaction terms are present, the
actual marginal effect cannot be calculated using standard methods (for
example, implementing the 'mfx' command in Stata) because both
the sign and net significance may differ from the parameter of the main
effects. Therefore, to illustrate the magnitude of the marginal effects
of imputed discount rates on the probability of screening use, we
predict the likelihood of adopting each screening technology for each
observation in the data, setting the imputed discount rate at 1%, while
keeping the remaining characteristics of each person unaltered, and then
calculating the average likelihood of screening use across all
observations. This process was repeated by replacing the actual imputed
discount with 2%, 3%, and so forth. In this way, we can map out the
density function of screening use as the imputed discount rate moves
through the 1% to 100% per year range, simultaneously accounting for all
interaction terms.
The relationship between the discount rate and screening
probabilities are presented in Figure 4. From this figure, two results
are striking. First, there is the obvious difference in response to
higher individual discount rates between men seeking prostate exams and
all other screening exams studied. Whereas higher discount rates are
associated with lower probabilities of all other screening tests, the
association between discount rates and the probability of prostate
screening is positive. This positive association is stronger for men
with higher probabilities of prostate cancer. Recall that the
theoretical model does permit a positive relationship between individual
discounting and disease screening when the interaction between disease
likelihood and testing efficacy are taken into account. The greater the
efficacy of treatment (in this case, the reduction in mortality from
catching aggressive prostate cancer early), the greater the chance that
the marginal effect of discounting on screening is positive. It is also
the case that the chances of prostate cancer for men in the sample were
among the highest of any--and also had the broadest range, with the
largest upper bound. The second striking result is the magnitude of the
discounting response. Mammography had the lowest range of implied
behavior but still ranged from a probability of around 80% with the
lowest discount rate (1% per year) to a low of around 35% probability of
screening when the discount rate is 100% per year. The probability of
prostate exams essentially spanned the entire [0, 1] range. (Again,
recall that these imputed probabilities take all interaction effects
into account.) Thus, it seems that the economic magnitude of the
complete (fully interactive) impact of individual time discounting on
the probability of disease screening is quite substantial.
[FIGURE 4 OMITTED]
As a practical matter, these results suggest that providers who
wish to persuade high discounting individuals to increase their
adherence to screening recommendations will need some other message than
simply emphasizing the future health benefits. However, it is not at all
clear that increasing the rate of screening among these individuals is
efficient. Because these people care relatively little about future
payoffs, they might be made worse off if society could somehow coerce
them to increase their adherence to screening guidelines. More attention
to theoretical issues surrounding the consistency of choices across
time, the stability of time preferences through the life cycle, or the
importance of such forces as regret in intertemporal decision making is
needed before the welfare consequences of artificially increasing
screening adherence in a high discount population could be stated
unambiguously.
6. Conclusions
Preventative health care is often cited as one solution to the
aging population and the growing share of health care spending in U.S.
gross domestic product. To the extent that individuals can be persuaded
to consume efficacious preventative services today, then their need for
acute services in the future should be reduced. However, one significant
barrier to patient adoption of preventative regimens is that they
generally require the person to forego consumption and activities (or
lack thereof) that they enjoy today for the promise of some future
payoff. The degree to which a person prefers the present relative to the
future should therefore be an important determinant in their decisions
with respect to the consumption of preventative medicine. Despite this
relatively obvious observation, there have been few attempts in the
economic literature to directly assess how individuals' time
preferences affect the demand for preventative service.
This article addresses this gap in the literature by analyzing data
collected in a nationwide survey of adults over the age of 40. In this
survey, we used a contingent valuation method to elicit responses to
questions designed to reveal the individual's rate of time
preference and the utilization of five common disease screens (prostate
exam, PAP smear, mammogram, dental exams, and cholesterol testing). The
results suggest that the average respondent in the survey has an
underlying discount rate of around 25% per year. The likelihood of
screening within the past two years was modeled as a function of the
discount rate (directly and interacted with respondent age) and other
patient characteristics. Completely interacted results indicate that
higher rates of discount are associated with lower use of all studied
screening technologies except prostate exams, where the effect was
positive.
This research has significant implications for clinical care and
for policy making. First, if the estimated discount rates are accurate
(and they are consistent with past literature), one might expect
relatively few patients will voluntarily undertake preventative
activities that entail positive costs if the benefits accrue many years
in the future. Given the average estimated discount rates, even very
large benefits to the individual will be discounted heavily in present
value terms. Consequently, clinical attempts to alter patients'
behavior by stressing the health benefits accruing 10, 15, or 20 years
in the future may not be the most effective messages.
These results suggest that advocacy and education that emphasizes
the future benefits of prevention may not be universally effective tools
at reducing burdens on the health care sector from preventable diseases
or disease states. Further, from a public welfare perspective,
individuals seem to reveal that they discount the future much more
heavily than many market interest rates. While this is a consistent
finding in the literature, why such a state of affairs would persist
over time deserves attention. High rates of discount are consistent with
preferences toward current consumption of health capital and
expectations that any future acute episodes will be treated when they
arise, rather than prevented.
Of course, much research remains to be conducted. It remains to be
seen if the demand for other types of secondary preventative services is
inversely related to individuals' discount rates--or whether other
primary prevention or acute care demand is also related to discounting.
Much research into individual discounting of the future has focused on
potential time inconsistencies. These issues must also be resolved
before the welfare implications of any negative discount--screening
demand relationship are understood. Finally, while this research did
indicate a significant relationship between an individual's rate of
discount for financial instruments (sweepstakes prizes) and some
components of health care demand, if people discount health care itself
at a different rate than they discount money, these results may be
misleading. Nonetheless, the current results do suggest that more
attention should be paid to the consistency between public policies
toward encouraging disease screening and individual preferences that
might work to undermine such evidence-based clinical guidelines.
Aligning public and private preferences in this area should be a matter
of high policy significance.
Appendix
Table A3. Probability of Screening Exams within Past Two Years
Separate Probit Estimator
Mammography PAP Smear
Constant -0.7472 [-0.427] 6.8896 *** [4.293]
male
age -0.0036 [-0.068] -0.0561 *** [-2.584]
goodhealth -0.1760 [-0.962] -0.0660 [-0.331]
currsmoke -0.1586 [-1.085] -0.0227 [-0.121]
formersmoke 0.0111 [0.089] -0.0063 [-0.040]
selfcnrisk 0.2559 [1.245] -0.0127 [-0.056]
black 0.0137 [0.083] 1.5081 ** [2.496]
otherrace -0.0357 [-0.142] 1.6018 * [1.948]
married 0.2010 * [1.714] 0.2979 ** [2.040]
hschool -0.2806 [-1.307] -0.1289 [-0.519]
somecoll -0.0181 [-0.081] -0.1336 [-0.522]
insure 0.3135 [0.618] 0.1440 [0.258]
hmo 0.1687 [0.573] 0.1908 [0.482]
employed 0.0035 [0.025] 0.0895 [0.577]
incl -0.4765 [-1.413] -0.1726 [-0.438]
inc2 -0.3246 [-0.954] -0.4887 [-1.260]
inc3 -0.5222 [-1.619] -0.2903 [-0.749]
inc4 -0.0939 [-0.314] 0.1862 [0.511]
inc5 -0.2765 [-0.914] -0.3381 [-0.929]
inc6 -0.1262 [-0.384] 0.1550 [0.363]
unknowninc -0.2966 [-1.090] 0.0956 [0.286]
newengl -0.3056 [-1.163] 0.1724 [0.418]
southeast 0.0271 [0.193] 0.0184 [0.104]
midwest -0.0076 [-0.051] -0.1347 [-0.735]
plains 0.0393 [0.143] 0.1360 [0.335]
west -0.0019 [-0.011] 0.1108 [0.489]
Observations 909 909
Prostate Exam Dental Visit
Constant -8.7201 *** [-4.640] 1.2990 [1.525]
male -0.1224 [-0.894]
age 0.2126 *** [5.273] -0.0173 [-1.015]
goodhealth -0.4264 ** [-2.232] 0.5286 *** [4.520]
currsmoke -0.3864 *** [-2.855] -0.0786 [-0.780]
formersmoke 0.0770 [0.519] -0.1799 * [-1.816]
selfcnrisk -0.0399 [-0.209] -0.4149 *** [-3.258]
black 0.2361 [1.499] -0.1392 [-1.298]
otherrace -0.4214 ** [-2.300] -0.4575 *** [-3.425]
married 0.0478 [0.391] 0.1708 ** [1.997]
hschool 0.0134 [0.067] 0.1265 [0.933]
somecoll 0.4564 ** [2.264] 0.4658 *** [3.314]
insure -0.5133 [-1.140] 0.0987 [0.315]
hmo -1.4161 *** [-4.698] 0.0650 [0.298]
employed -0.3941 ** [-2.121] 0.0596 [0.557]
incl -0.1730 [-0.466] -0.2954 [-1.173]
inc2 0.2701 [0.661] -0.1802 [-0.704]
inc3 -0.2020 [-0.600] -0.2963 [-1.245]
inc4 -0.2337 [-0.788] 0.2107 [0.934]
inc5 -0.2921 [-0.992] 0.1777 [0.780]
inc6 -0.4911 [-1.614] 0.4164 [1.622]
unknowninc -0.4574 * [-1.667] 0.1027 [0.495]
newengl -0.2088 [-0.796] -0.0753 [-0.361]
southeast -0.0549 [-0.373] -0.1257 [-1.153]
midwest -0.0690 [-0.410] -0.2089 * [-1.756]
plains 0.1946 [0.716] -0.1052 [-0.508]
west -0.1626 [-0.916] -0.2134 [-1.632]
Observations 726 1635
Blood Pressure Check Cholesterol Check
Constant 3.4366 * [1.959] 2.0559 *** [3.041]
male -0.6471 *** [-3.129]
age -0.0226 [-0.637] -0.0035 [-0.276]
goodhealth -0.6230 ** [-2.182] -0.7137 *** [-5.051]
currsmoke -0.5701 *** [-3.031] -0.2955 *** [-3.364]
formersmoke -0.0785 [-0.347] -0.1471 * [-1.678]
selfcnrisk 0.3941 [1.445] 0.0951 [0.717]
black 0.4759 * [1.844] -0.2748 *** [-2.993]
otherrace 0.0478 [0.228] -0.2990 ** [-2.522]
married -0.0952 [-0.567] 0.0771 [0.978]
hschool 0.3700 [1.559] -0.1710 [-1.211]
somecoll 0.4248 * [1.750] 0.1731 [1.197]
insure -0.1987 [-0.317] 0.4371 [1.395]
hmo 0.6597 [1.393] -0.6315 *** [-3.220]
employed 0.1717 [0.873] -0.0623 [-0.609]
incl -0.5307 [-1.193] -0.2636 [-1.121]
inc2 0.1963 [0.381] 0.2891 [1.152]
inc3 0.3242 [0.710] -0.0646 [-0.294]
inc4 0.3382 [0.817] 0.0520 [0.264]
inc5 -0.1424 [-0.368] 0.1151 [0.583]
inc6 -0.0724 [-0.176] -0.0609 [-0.298]
unknowninc 0.1095 [0.295] -0.0837 [-0.468]
newengl 0.2808 [0.696] -0.0611 [-0.350]
southeast 0.0573 [0.277] -0.1224 [-1.257]
midwest -0.1325 [-0.595] -0.1061 [-1.008]
plains 0.0060 [0.016] -0.1266 [-0.693]
west -0.3703 * [-1.691] -0.4421 *** [-3.942]
Observations 1635 1635
Value of t-statistics in brackets.
* Significant at 10%.
** Significant at 5%.
*** Significant at 1%.
Parameters on the key discount variables, interactions and disease
probabilities are presented in Table 3.
Table A4. Probability of Screening Exams within Past
Two Years--2SLS Estimator
Mammography PAP Smear
Constant 0.3965 [0.14] 8.8738 [3.35] ***
male
age 0 [0.00] -0.0547 [2.39] *
goodhealth -0.3199 [1.24] -0.3114 [1.00]
currsmoke -0.1136 [0.71] 0.0333 [0.14]
formersmoke 0.0528 [0.39] 0.0556 [0.36]
selfcnrisk 0.3714 [1.47] 0.1914 [0.58]
black 0.0878 [0.48] 1.5844 [2.63] **
otherrace 0.0928 [0.31] 1.7433 [2.01] *
married 0.1637 [1.17] 0.2312 [1.22]
hschool -0.4847 [1.64] -0.5059 [1.40]
somecoll -0.2372 [0.73] -0.5187 [1.41]
insure 0.4931 [0.871 0.4472 [0.67]
hmo 0.0556 [0.19] 0.0113 [0.02]
employed -0.0519 [0.31] 0.0154 [0.08]
inc1 -0.4716 [1.01] -0.1443 [0.13]
inc2 -0.2056 [0.48] -0.2563 [0.22]
inc3 -0.5111 [1.32] -0.2455 [0.23]
inc4 -0.2178 [0.471 -0.0148 [0.01]
inc5 -0.4095 [0.85] -0.538 [0.46]
inch -0.2057 [0.43] 0.0393 [0.04]
unknowninc -0.5069 [1.051 -0.2276 [0.21]
newengl -0.0716 [0.19] 0.5341 [1.17]
southeast 0.0118 [0.08] 0.0087 [0.05]
midwest -0.0103 [0.07] -0.1282 [0.661
plains 0.1917 [0.54] 0.3681 [0.92]
West 0.0081 [0.03] 0.1465 [0.55]
Observations 909 909
Prostate Exam Dental visit
Constant -10.6613 [4.06] *** 3.8097 [3.45] **
male -0.1448 [0.98]
age 0.2122 [4.42] ** -0.0189 [1.13]
goodhealth -0.2097 [0.92] 0.2357 [1.71]
currsmoke -0.3766 [2.59] ** -0.06 [0.59]
formersmoke 0.0486 [0.34] -0.1227 [1.19]
selfcnrisk -0.2678 [0.99] -0.1435 [0.881
black 0.1533 [0.83] -0.0365 [0.34]
otherrace -0.5979 [2.62] ** -0.261 [1.68]
married 0.0998 [0.68] 0.1037 [0.94]
hschool 0.3061 [1.03] * -0.2534 [1.36]
somecoll 0.7826 [2.42] 0.0689 [0.41]
insure -0.8282 [1.17] 0.4453 [1.05]
hmo -1.3292 [3.70] ** -0.0932 [0.47]
employed -0.2722 [1.53] -0.0408 [0.31]
inc1 -0.1496 [0.39] -0.2888 [1.02]
inc2 0.122 [0.331] 0.0574 [0.16]
inc3 -0.1885 [0.56] -0.2785 [0.921
inc4 -0.0051 [0.02] -0.0424 [0.20]
inc5 -0.0258 [0.08] -0.108 [0.41]
inch -0.3395 [1.06] 0.258 [0.91]
unknowninc -0.125 [0.36] -0.2958 [1.13]
newengl -0.5341 [1.88] 0.3419 [1.35]
southeast -0.0334 [0.24] -0.1432 [1.001
midwest -0.081 [0.52] -0.2026 [1.54]
plains -0.0713 [0.22] 0.1915 [0.69]
West -0.1972 [1.14] -0.1814 [1.49]
Observations 726 1635
Blood Pressure Cholestereol
Check Check
Constant 5.995 [2.49] ** 1.7313 [1.90] *
male -0.6859 [3.69] ** -0.0431 [0.42]
age -0.029 [1.41] -0.0042 [0.31]
goodhealth -0.8443 [2.66] ** -0.6716 [3.93] **
currsmoke -0.5731 [2.77] ** -0.2893 [3.22] **
formersmoke -0.0243 [0.10] -0.156 [1.89]
selfcnrisk 0.6594 [2.22] * 0.0469 [0.29]
black 0.5683 [1.85] -0.2943 [2.67] **
otherrace 0.1977 [0.79] -0.3301 [2.93] **
married -0.1603 [0.901 0.0881 [0.79]
hschoo1 -0.0192 [0.05] -0.1132 [0.63]
somecoll 0.001 [0.00] 0.2365 [1.26]
insure 0.1371 [0.22] 0.3743 [0.981
hmo 0.5595 [1.33] -0.6173 [3.20] **
employed 0.0605 [0.28] -0.0391 [0.31]
inc1 -0.4825 [0.25] -0.2673 [1.02]
inc2 0.4013 [0.20] 0.2436 [0.82]
inc3 0.3127 [0.16] -0.0678 [0.29]
inc4 0.0413 [0.02] 0.0927 [0.43]
inc5 -0.4576 [0.24] 0.1638 [0.73]
inch -0.2215 [0.12] -0.0315 [0.14]
unknowninc -0.2441 [0.13] -0.021 [0.10]
newengl 0.6334 [1.59] -0.1278 [0.58]
southeast 0.0648 [0.271 -0.1189 [1.28]
midwest -0.1019 [0.50] -0.1084 [0.94]
plains 0.3188 [0.78] -0.1761 [0.77]
West -0.3327 [1.53] -0.4457 [3.24] **
Observations 1635 1635
z statistics in brackets.
Parameters on the key discount variables, interactions,
and disease probabilities are presented in Table 4.
* p significant at 5%.
** p significant at 1%.
References
Ades, Philip, Thomas E. Kottke, Nancy Houston Miller, John C.
McGrath, N. Burgess Record, and Sandra S. Record. 2002. Task Force #3:
Getting results: Who, where, how? Journal of the American College of
Cardiology 40(4):615-30.
Ai, C., and E. Norton. 2003. Interaction terms in logit and probit
models. Economic Letters 80(1):123-9.
Becker, G., and K. Murphy. 1988. A theory of rational addiction.
Journal of Political Economy 96(4):675-700.
Berger, M., and J. Leigh. 1989. Schooling, self-selection, and
health. Journal of Human Resources 24(3):433-55.
Boardman, A, D. Greenberg, A. Vining, and D. Weimer. 1996.
Cost-benefit analysis: Concepts and practices. Upper Saddle River, NJ:
Prentice Hall.
Bradford, W. David, Andrew N. Kleit, Marie A. Krausel-Wood, and
Richard N. Re. 2004. Double-bounded dichotomous choice method to assess
willingness to pay for telemedicine. Journal of Telemedicine and
Telecare 10(6):325-30.
Cameron, T., and M. James. 1987. Efficient estimation methods for
use with "closed ended" contingent valuation survey data.
Review of Economics and Statistics 69:269-76.
Coller, M., and M. Williams. 1999. Eliciting individual discount
rates. Experimental Economics 2(1):107-27.
Diamond, Peter, and Jerry Hausman. 1994. Contingent valuation: Is
some number better than no number? Journal of Economic-Perspectives
8(4):45-64.
Ehrlich, I., and H. Chuma. 1990. A model of the demand for
longevity and the value of life extension. Journal of Political Economy
98(4):761-82.
Farrell, P., and V. Fuchs. 1982. Schooling and health: The
cigarette connection. Journal of Health Economics 1(3):217-30.
Frederick, Shane, George Loewenstein, and Ted O'Donoghue.
2002. Time discounting and time preference: A critical review. Journal
of Economic Literature XL:351-401.
Giorgianni, S., J. Grana, and J. Keith. 2003. Heart disease: An
all-out attack. Pfizer Journal 7(4):1-49.
Greene, William H. 2002. Econometric analysis. Upper Saddle River,
NJ: Prentice-Hall.
Grossman, M. 1972. On the concept of health capital and the demand
for health. Journal of Political Economy 80(2):223-55.
Grossman, M. 2000. The human capital model. In Handbook of health
economies, edited by A. Culyer and J. Newhouse. Amsterdam: Elsevier
Science B.V.
Grossman, M., and R. Kaestner. 1997. Effects of education on
health. In The social benefits of education, edited by J. Behrman and N.
Stacey. Ann Arbor, MI: University of Michigan Press, pp. 69-123.
Hanemann, M. 1985. Some issues in continuous-and discrete response
contingent valuation studies. Northeast Journal of Agricultural
Economics 14(1):5-13.
Hanemann, M., J. Loomis, and B. Kanninen. 1991. Statistical
efficiency of double-bounded dichotomous choice contingent valuation.
American Journal of Agricultural Economics 73(4):1255-63.
Harrison, G., M. Lau, and M. Williams. 2002. Estimating individual
discount rates in Denmark. American Economic Review 92(5): 1606-17.
Kanninen, B. 1993. Optimal experimental design for double-bounded
dichotomous choice contingent valuation. Land Economics 69(2): 138-46.
National Comprehensive Cancer Network (NCCN). 2004. Practice
guidelines in oncology screening. Fort Washington, PA: National
Comprehensive Cancer Network.
National Heart Lung and Blood Institute (NHLBI). 2001. Third report
of the national cholesterol education program expert panel on detection,
evaluation, and treatment of high blood cholesterol in adults (adult
treatment panel iii). Washington, D.C.: National Institute of Health,
National Heart Lung and Blood Institute.
Ockene, Ira S., Laura L. Hayman, Richard C. Pasternak, Eleanor
Schron, and Jacqueline Dunbar-Jacob. 2002. Task Force #4: Adherence
issues and behavior changes: Achieving a long-term solution. Journal of
the American College of Cardiology 40(4):365-83.
Picone, Gabriel, Frank Sloan, and D. Taylor. 2004. Effects of risk
and time preference and expected longevity on demand for medical tests.
Journal of Risk and Uncertainty 28(1):39-53.
Terza, Joseph V., Anirban Basu, and Paul J. Rathouz. 2008.
Two-stage residual inclusion estimation: Addressing endogeneity in
health econometric modeling. Journal of Health Economics 27(3):531-43.
Tudiver, F., and E. Fuller-Thompson. 1999. Who has screening
mammography: Results from the 1994-1995 national population health
survey. Canadian Family Physician 45:1901-7.
Van Doorslaer, E. 1987. Health, knowledge, and the demand for
medical care: An econometric analysis. Maastricht, The Netherlands: van
Gorcum and Comp.
Wagstaff, A. 1986. The demand for health: Some new empirical
evidence. Journal of Health Economics 5(2):195-233.
Wagstaff, A. 1993. The demand for health: An empirical
reformulation of the Grossman model. Health Economics 2(2):189-98.
Warner, J., and S. Pleeter. 2001. The personal discount rate:
Evidence from military downsizing programs. American Economic Review
91(1):33 53.
Wooldridge, Jeffrey M. 2002. Econometric analysis of cross section
and panel data. Cambridge, MA: MIT Press.
Zweifei, P., and F. Breyer. 1997. Health economics. New York:
Oxford University Press.
W. David Bradford, James Zoller, [dagger] and Gerard A. Silvestri
[double dagger]
* Department of Public Administration and Policy, University of
Georgia, 201C Baldwin Hall, University of Georgia, Athens, GA 30602,
USA; E-mail
[email protected]; corresponding author.
[dagger] Department of Health Professions, Medical University of
South Carolina, P.O. Box 250961, Charleston, SC 29425, USA; E-mail
[email protected].
[double dagger] Department of Medicine, Medical University of South
Carolina, MSC 630, 812 CSB, 96 Jonathan Lucas Street, Charleston, SC
29425, USA; E-mail
[email protected].
This research was supported by a grant from the U.S. Department of
Defense. The authors would like to thank David Bishai, Richard
Lindrooth, and Peter Thompson, participants at the 3rd Annual
Southeaster Health Economic Study Group meeting held in Miami, Florida,
in October 2006, and participants at the Center for Health Economic and
Policy Studies seminar series at the Medical University of South
Carolina for comments on an earlier version of this research. Michael
Kunz and Olena Verbenko provided able research assistance.
Received February 2008; accepted March 2009.
(1) For a summary of this literature, see Frederick, Loewenstein,
and O'Donoghue (2002).
(2) There is a growing literature that suggests that people may in
fact discount the distant future less heavily than they discount the
proximate future. Most commonly this has been discussed in terms of
hyperbolic discounting. For a summary of the measurement and
implications of nonconstant discounting, including hyperbolic
discounting, see Frederick, Loewenstein, and O'Donoghue (2002).
(3) More complete discussions of the two-step ML method (and the
entire class of M-estimators) can be found in Wooldridge (2002) and
Greene (2002). Note that the LIML model is not subject to the
"forbidden regression" issue--where predicted values from a
first stage are inappropriately inserted into a nonlinear second stage
discussed in Wooldridge (2002, p. 236) for 2SLS applied to nonlinear
models.
(4) The Wald chi-square statistic on a first stage regression
including only the three candidate instruments is 1716 (the nonlinear
analogue to a partial F statistic), and the individual t statistics on
each of the instruments are significant at better than the 1% level.
Table 1. Descriptive Statistics
Number of Standard
Variable Observations Mean Deviation
Imputed discount rate 1635 0.251 0.105
Mammogram within past two years 1635 0.423 0.494
PAP smear within past two years 1635 0.498 0.500
Prostate within past two years 1635 0.188 0.391
Dental visit within past two years 1635 0.791 0.406
Blood pressure exam within the
past two years 1635 0.966 0.182
Cholesterol test within past two
years 1635 0.684 0.465
Pr[Breast cancer I age, race] 909 0.014 0.006
Pr[Cervical cancer age, race] 909 0.0006 0.0002
Pr[Prostate cancer age, race] 726 0.012 0.015
Pr[Oral cancer I age, race,
gender] 1635 0.0008 0.0007
Pr[Cardiovascular disease I age,
gender] 1635 0.014 0.019
Gender (male = 1) 1635 0.444 0.497
Age 1635 51.832 9.013
Respondent in good health 1635 0.888 0.315
Respondent a current smoker 1635 0.303 0.460
Respondent a former smoker 1635 0.245 0.430
High perceived cancer risk 1635 0.095 0.294
Race (African American = 1) 1635 0.172 0.377
Race (other race = 1) 1635 0.096 0.295
Respondent married 1635 0.663 0.473
Respondent graduated high school 1635 0.374 0.484
Respondent has some college 1635 0.547 0.498
Respondent has fee for service
insurance 1635 0.168 0.374
Respondent has HMO insurance 1635 0.554 0.497
Respondent is employed 1635 0.735 0.442
Income: under $20,000 1635 0.075 0.263
Income: $20,000-$30,000 1635 0.048 0.213
Income: $30,000-$40,000 1635 0.067 0.250
Income: $40,000-$60,000 1635 0.127 0.333
Income: $60,000-$80,000 1635 0.121 0.326
Income: $80,000-$100,000 1635 0.082 0.274
Income: unknown 1635 0.438 0.496
New England region 1635 0.045 0.207
Southeast region 1635 0.321 0.467
Midwest region 1635 0.229 0.420
Plains region 1635 0.042 0.200
West region 1635 0.152 0.359
Rate1--Rate2 1635 -0.066 0.144
dPF x Rate1 1635 0.027 0.077
dFP x Rate2 1635 0.023 0.092
Minimum Maximum
Variable Value Value
Imputed discount rate 0.019 0.540
Mammogram within past two years 0 1
PAP smear within past two years 0 1
Prostate within past two years 0 1
Dental visit within past two years 0 1
Blood pressure exam within the
past two years 0 1
Cholesterol test within past two
years 0 1
Pr[Breast cancer I age, race] 0.005 0.256
Pr[Cervical cancer age, race] 0.0005 0.001
Pr[Prostate cancer age, race] 0.0003 0.620
Pr[Oral cancer I age, race,
gender] 0.0001 0.277
Pr[Cardiovascular disease I age,
gender] 0.005 0.080
Gender (male = 1) 0 1
Age 40 70
Respondent in good health 0 1
Respondent a current smoker 0 1
Respondent a former smoker 0 1
High perceived cancer risk 0 1
Race (African American = 1) 0 1
Race (other race = 1) 0 1
Respondent married 0 1
Respondent graduated high school 0 1
Respondent has some college 0 1
Respondent has fee for service
insurance 0 1
Respondent has HMO insurance 0 1
Respondent is employed 0 1
Income: under $20,000 0 1
Income: $20,000-$30,000 0 1
Income: $30,000-$40,000 0 1
Income: $40,000-$60,000 0 1
Income: $60,000-$80,000 0 1
Income: $80,000-$100,000 0 1
Income: unknown 0 1
New England region 0 1
Southeast region 0 1
Midwest region 0 1
Plains region 0 1
West region 0 1
Rate1--Rate2 -0.421 0.313
dPF x Rate1 0 0.348
dFP x Rate2 0 0.496
Table 2. Individual Discount Rate Estimators-Interval Estimator
Variables Coefficients
Age 0.0018 *** [0.0004]
Gender (male = 1) -0.0145 ** [0.01]
Respondent in good health -0.0401 *** [0.01]
Respondent a current smoker 0.0077 [0.01]
Respondent a former smoker 0.0028 [0.01]
High perceived cancer risk -0.0031 [0.01]
Race (African American = 1) -0.0087 [0.01]
Race (other race = 1) -0.0191 * [0.01]
Respondent married -0.004 [0.01]
Respondent graduated high school -0.0245 [0.02]
Respondent has some college -0.0301 * [0.02]
Respondent has FFS Insurance 0.011 [0.90]
Respondent has HMO -0.028 *** [3.99]
Respondent is employed -0.0121845 [1.16]
Income: under $20,000 0.0690 *** [0.02]
Income: $20,000-$30,000 0.0567 ** [0.02]
Income: $30,000-$40,000 0.0451 ** [0.02]
Income: $40,000-$60,000 0.0109 [0.02]
Income: $60,000-$80,000 -0.0034 [0.02]
Income: $80,000-$100,000 -0.0002 [0.02]
Income: unknown -0.0159723 [1.16]
New England region 0.00751 [0.48]
Southeast region -0.0018111 [0.21]
Midwest region -0.0058684 [0.65]
Plains region 0.0005773 [0.04]
West region -0.0129824 [1.36]
Rate1--Rate2 0.9021 *** [32.85]
dFP x Rate1 0.1255 *** [4.16]
dPF x Rate2 -0.1541 *** [4.93]
Constant 0.248 *** [7.21]
Observations 1635
[R.sup.2] robust standard errors in brackets.
* p < 0.1.
** p < 0.05.
*** p < 0.01.
Table 3. Probability of Screening Exams within Past Two Years
Separate Probit Estimator (t-Statistics in Brackets.)
Mammography PAP Smear
Discount rate 1.1020 -9.5797 **
[0.196] [-2.146]
Discount rate * Age 0.0701 0.0737
[0.416] [1.024]
Discount rate * Pr[Breast CN] -334.7819
[-1.330]
Pr[Breast CN] 153.3195 *
[1.842]
Discount rate * Pr[Cervical CN] 5,998.0997 **
[2.262]
Pr[Cervical CN] -4,338.5171 ***
[-2.870]
Discount rate * Pr[Prostate CN]
Pr[Prostate CN]
Discount rate * Pr[Oral CN]
Pr[Oral CN]
Discount rate * Pr[CVD]
Pr[CVD]
Discount rate * FFS Insurance -1.1326 0.5353
[-0.761] [0.330]
Discount rate * HMO Insurance -0.1840 1.3373
[-0.178] [1.000]
Observations 909 909
Prostate Exam Dental Visit
Discount rate 21.2232 *** -2.7790
[3.250] [-1.108]
Discount rate * Age -0.4895 *** 0.0360
[-3.442] [0.686]
Discount rate * Pr[Breast CN]
Pr[Breast CN]
Discount rate * Pr[Cervical CN]
Pr[Cervical CN]
Discount rate * Pr[Prostate CN] 141.0315 *
[1.712]
Pr[Prostate CN] -58.7661 **
[-2.448]
Discount rate * Pr[Oral CN] -204.1541
[-0.326]
Pr[Oral CN] -7.2772
[-0.032]
Discount rate * Pr[CVD]
Pr[CVD]
Discount rate * FFS Insurance 1.7745 0.2878
[1.194] [0.298]
Discount rate * HMO Insurance 4.3041 *** 0.5779
[3.814] [0.751]
Observations 726 1635
Blood
Pressure Cholesterol
Check Check
Discount rate -5.3134 -4.8187 **
[-1.025] [-2.187]
Discount rate * Age 0.0909 0.0776 *
[0.820] [1.743]
Discount rate * Pr[Breast CN]
Pr[Breast CN]
Discount rate * Pr[Cervical CN]
Pr[Cervical CN]
Discount rate * Pr[Prostate CN]
Pr[Prostate CN]
Discount rate * Pr[Oral CN]
Pr[Oral CN]
Discount rate * Pr[CVD] -51.7020 -12.2294
Pr[CVD] [
22.6030 [-10.4775
[1.273] [0.239]
Discount rate * FFS Insurance 1.9021 -1.1328
[0.970] [-1.145]
Discount rate * HMO Insurance 0.2720 1.2482 *
[0.151] [1.758]
Observations 1635 1635
Value of t-statistics in brackets.
* Significant at 10%.
** Significant at 5%.
*** Significant at 1%.
Also included, but not shown: indicator variables for male, age,
good health, current smoker, former smoker, cancer risk,
African-American, other race, high school, some college, FFS
insurance, HMO insurance, employed, income status (6 categories),
unreported income, and census region.
Table 4. Probability of Screening Exams within Past Two Years
2SLS Estimator
Mammography PAP Smear
Discount rate 1.983 -9.0121
[0.25] [1.83] *
Discount rate * Age 0.0436 0.0747
[0.18] [0.96]
Discount rate * Pr[Breast CN] -289.8772
[0.82]
Pr[Breast CN] 147.6453
[1.30]
Discount rate * Pr[Cervical CN] 5,428.51
[1.96] **
Pr[Cervical CN] -4,163.33
[2.80]
Discount rate * Pr[Prostate CN]
Pr[Prostate CN]
Discount rate * Pr[Oral CN]
Pr[Oral CN]
Discount rate * Pr[CVD]
Pr[CVD]
Discount rate * FFS Insurance -1.5579 -0.2036
[0.88] [0.11]
Discount rate * HMO -0.0052 1.6452
Insurance [0.01] [1.01]
Predicted term from 1st Stage -48.6137 -85.3871
[1.12] [1.64] *
Observations 909 909
Prostate Exam Dental Visit
Discount rate 20.6764 -2.7258
[2.76] *** [1.16]
Discount rate * Age -0.4839 0.0435
[2.97] *** [0.85]
Discount rate * Pr[Breast CN]
Pr[Breast CN]
Discount rate * Pr[Cervical CN]
Pr[Cervical CN]
Discount rate * Pr[Prostate CN] 135.9581
[1.57]
Pr[Prostate CN] -58.8215
[2.24]
Discount rate * Pr[Oral CN] -325.3897
[0.49]
Pr[Oral CN] 45.7768
[0.18]
Discount rate * Pr[CVD]
Pr[CVD]
Discount rate * FFS Insurance 2.6646 -0.5766
[1.26] [0.43]
Discount rate * HMO 4.1324 0.8469
Insurance [3.56] *** [1.18]
Predicted term from 1st Stage 77.0192 -97.3898
[1.95] * [3.37] ***
Observations 726 1635
Blood
Pressure Cholesterol
Check Check
Discount rate -5.6227 -4.8626
[1.59] [2.10] **
Discount rate * Age 0.1085 0.0769
[1.45] [1.61]
Discount rate * Pr[Breast CN]
Pr[Breast CN]
Discount rate * Pr[Cervical CN]
Pr[Cervical CN]
Discount rate * Pr[Prostate CN]
Pr[Prostate CN]
Discount rate * Pr[Oral CN]
Pr[Oral CN]
Discount rate * Pr[CVD] -63.5172 -11.8873
Pr[CVD] 27.229 [2.1429
[1.95] ** [0.35]
Discount rate * FFS Insurance 0.9957 -0.9718
[0.56] [0.89]
Discount rate * HMO 0.3976 1.2408
Insurance [0.25] [1.78] *
Predicted term from 1st Stage -90.8521 14.859
[1.76] * [0.59]
Observations 1635 1635
z statistics in brackets.
* Significant at 10%.
** Significant at 5%.
*** Significant at 1%.
Also included, but not shown: indicator variables for male, age,
good health, current smoker, former smoker, cancer risk,
African-American, other race, high school, some college, FFS
insurance, HMO insurance, employed, income status (6 categories),
unreported income, and census region.
