Journal of Health Economics 27 (2008) 1095–1108
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Journal of Health Economics
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Bias and asymmetric loss in expert forecasts: A study of physician
prognostic behavior with respect to patient survival
Marcus Alexandera,∗, Nicholas A. Christakisb,c
aHarvard University, Institute for Quantitative Social Science and Department of Government, CGIS 1737 Cambridge Street, Cambridge 02138, United States
bDepartment of Health Care Policy, Harvard Medical School, 180 Longwood Avenue, Boston, MA 02115, United States
cDepartment of Sociology, FAS, 33 Kirkland Street, Cambridge, MA 02138, United States
a r t i c l e i n f o
Received 23 November 2006
Received in revised form 1 February 2008
Accepted 10 February 2008
I10, I12, I19, D01, D80, C53
a b s t r a c t
We study the behavioral processes undergirding physician forecasts, evaluating accuracy
and systematic biases in estimates of patient survival and characterizing physicians’ loss
functions when it comes to prediction. Similar to other forecasting experts, physicians face
different costs depending on whether their best forecasts prove to be an overestimate or an
underestimate of the true probabilities of an event. We provide the first empirical charac-
terization of physicians’ loss functions. We find that even the physicians’ subjective belief
increased by (1) reduction of the belief distributions to point forecasts, (2) communication
of the forecast to the patient, and (3) physicians’ own past experience and reputation.
© 2008 Elsevier B.V. All rights reserved.
In this paper, we investigate the accuracy of physicians’ forecasts of survival. We ask whether a physician’s prognosis
exhibits systematic biases, and we explore the sources of such biases. Our investigation uncovers a systematic tendency of
physicians to overpredict their patients’ survival at three stages: first, with respect to the survival distributions that doctors
construct, second in their summarization of this distribution through the selection of a point estimate, and third in their
choice about how to further modify this estimate during communication.
The strategic role of communication between physicians and patients has been studied by Caplin and Leahy (2004),
illustrating how the standard model of preferences breaks down once agents draw psychological utility from their beliefs.
Extending this model, Koszegi (2006) also used physician–patient communication to investigate how provision of informa-
tion by experts becomes distorted in the presence of anticipatory feelings. These important theoretical contributions lay
the groundwork for empirically examining the systematic tendencies of physicians to distort their prognosis when both
formulating it and communicating it to their patients.
More specifically, findings from the literature on emotional agency lead us to expect that a closer relationship between
a physician and a patient should be associated with more upwardly biased loss. In this model, the physicians’ utility func-
tion includes their patients’ emotional status, therefore providing an incentive for physicians to formulate an upwardly
biased prognosis. This theoretical framework also sheds light on why we would expect a doctor to be even more upwardly
biased when communicating than when formulating an expectation. It is clearly more emotionally stressful to share bad
news than merely to think about it. Additionally, communication provides for a strategic environment consistent with
∗Corresponding author. Institute for Quantitative Social Science and Department of Government, Harvard University, CGIS, 1737 Cambridge Street,
Cambridge, MA 02138, United States. Tel. +1 617 909 4618; fax: +1 617 432 5891.
E-mail address: firstname.lastname@example.org (M. Alexander).
0167-6296/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
M. Alexander, N.A. Christakis / Journal of Health Economics 27 (2008) 1095–1108
Koszegi’s (2006) model, whereby a physician has an opportunity as an agent to affect the emotional state of the patient as a
Furthermore, as Koszegi (2003) indicates, physician–patient communication may be accompanied by deeper psycholog-
ical biases such as Samuelson’s (1963) fallacy of large numbers—simply defined as accepting a large number of unfavorable
gambles even when the agent is unwilling to take any one individual gamble on its own. In fact, some of the classic biases
in behavioral economics have been first characterized by studying physician behavior. These are most notably associated
with the process by which physicians formulate diagnosis, and they most famously include the role of hindsight in distorting
probability estimates (Arkes et al., 1981; Slovic and Fischhoff, 1977), base rate neglect (Casscells et al., 1978; Kahneman
and Tversky, 1973), and the conjunction fallacy (Tversky and Kahneman, 1983). In all of these situations, agents produce
inaccurate probability estimates given the uncertainty they face over the true state of the world.
of survival, and how they use their own subjective belief distributions to formulate a point forecast. In other words, even
before the strategic component of physician–patient communication enters the picture, we can ask whether systematic
biases characterize the process by which physicians arrive at their own best point forecast of patients’ survival.
In analyzing the asymmetry of physicians’ prognosis, it is useful to draw on the broader economic literature on expert
forecasts. In one of the first studies of asymmetric loss in economics, Varian (1974) documented an important fact that
experts in a market face different costs depending whether their best prediction is an overestimate or an underestimate of
the market price. In his study of the market for single family homes in a 1965 California town, Varian noticed that assessors
faced a significantly higher cost if they happened to overestimate the value of a house. While in the case of an underestimate,
the assessor’s office faced the cost in the amount of the underestimate, conversely, in the case of the overestimate by an
identical amount, the assessor’s office faced a possibility of a lengthy and costly appeal process. Since this classic study, loss
functions have become an important aspect of the study of expert forecasts.
The two key empirical puzzles surrounding the question of expert forecasts became to determine whether forecasters’
loss functions were symmetric, and if not, how optimal forecasts can be made given loss asymmetry, as addressed most
recently by Elliott et al. (2005). For example, government experts making budget forecasts may be influenced by political
incentives, as the costs of wrongly projecting a surplus may lead to public disapproval, while wrongly projecting a deficit
may lead to an impression of exceptional government performance. Artis and Marcellino (2001), as well as Campbell and
Ghysels (1995), document that budget deficit forecasts have asymmetric loss. Furthermore, expert opinion varies greatly and
systematically. For example, research by Lamont (1995) indicates that factors such as forecasters’ experience and reputation
are reliable determinants of experts’ willingness to deviate from consensus forecasts of GDP, unemployment, and prices.
In financial and macroeconomic forecasting, Granger and Newbold (1986) have concluded that economic theory does not
suggest that experts even should have a symmetric loss function. An improved understanding of behavioral biases arising in
agents’ decisions, such as those associated with loss functions, can contribute to answering puzzles about risky behavior in
the labor market and education decisions (e.g., Abowd and Card, 1989; Card and Hyslop, 1997; Card and Lemieux, 2001a,b)
and in health economics (e.g., Koszegi, 2003, 2006).
Because in most economic situations, such as Varian’s (1974) real-estate market, agents formulate and report point
predictions as their forecasts, the agents’ true subjective belief distributions are lost and cannot be recovered from their
forecasts. Hence the problem of characterizing the loss function is compounded by the fact that we do not know anything
about the behavioral process by which agents reduce their belief distributions into single-point predictions, a process which
itself reflects the extent of asymmetry in their unobserved loss function. Furthermore, because of strategic considerations,
the prediction that agents communicate may be different from both the point prediction and the prediction implied by
the agents’ full subjective belief distributions. Unfortunately, due to data limitations, no study has been able to examine all
of these aspects of forecasting simultaneously. To date, the study of loss function asymmetry has been largely limited to
studying point forecasts (e.g., the Livingstone survey), while the study of forecasters’ fuller subjective belief distributions has
been confined to surveys of national output by experts (e.g., Survey of Professional Forecasters), as illustrated by the work
that originated with Victor Zarnowitz’s (1985) study of rational expectations.
Our study addresses the extent of intrinsic bias in forecast predictions and asks how the forecast bias and the symmetry
of the loss function change as agents move from a full subjective distribution to a point prediction and then to commu-
nicating their formulated forecast. We focus on the first part of the processes because psychological research by Tversky
and Kahneman (1973, 1974) has documented that individuals exhibit different types of biases when using probability dis-
tributions to infer a possibility of an outcome. Analogous to the biases that arise from the use of inference heuristics such
as representativeness or availability, agents may also exhibit biases when narrowing their subjective belief distributions
to single-point predictions. In particular, because the standard symmetric loss function requires minimization of the mean
squared error, individuals may show systematic bias due to failure to compute a correct mean or because t have asymmetric
loss. Much like econometric estimators that are biased when certain assumptions fail, the behavioral mechanism leading
to a point forecast from subjective beliefs may be biased due to computational limitations or a misinterpretation of the
optimization problem by agents. We also focus on the latter part of the process – the role of communication – because, with
the exception of independent, disinterested expert forecasters, the communication of an agent’s forecast is likely to play a
strategic role in a market. Therefore, any bias that led to formulation of the forecast may be further compounded by the
agent’s strategic biases in communicating the prediction. To study all of this, we need a record of forecasts that documents
both the process of reduction from subjective beliefs to a point forecast and the process of communication of that forecast.
M. Alexander, N.A. Christakis / Journal of Health Economics 27 (2008) 1095–1108
1995; Bonham and Cohen, 1995; Mankiw et al., 2003). In addition to empirical results that challenge the assumption of loss
symmetry, there have emerged a number of theoretical objections to assuming that economic agents making forecasts have
a symmetric loss function, instead arguing that forecasting should be studied from a decision-making perspective that takes
into account economic incentives that forecasters face (Christoffersen and Diebold, 1997; Christoffersen, 1998; Diebold et al.,
1998; Diebold, 2001; Granger and Newbold, 1986; Granger and Pesaran, 2000; Pesaran and Skouras, 2001; Skouras, 2007;
West et al., 1993).
of inventory and production (Arrow, 1958), the first commonly used asymmetric loss functions, including the quad–quad
loss function, the lin–lin loss function, and the LINEX loss function, appeared subsequently. The quad–quad loss function
simply modifies the MSE loss by assuming that the scaling constants are different on the positive and on the negative side
of the loss (e.g., Elliott and Timmermann, 2002):
Lquad–quad(et) = [a + b × 1(et< 0)] × e2
Granger’s (1969) lin–lin loss function takes a very similar form, but instead of a squared error, it uses the absolute value
of the error:
Llin–lin(et) = [a + b × 1(et< 0)] × |et|.
The third commonly used loss function is Varian’s (1974) LINEX loss function, further studied by Zellner (1986). The
LINEX, or linear-exponential, loss function allows loss on one side to rise approximately exponentially, while the loss on the
opposite side rises linearly as the forecaster moves from the correct prediction. As discussed in introduction, Varian (1974)
motivated his model by the observation that, in the real-estate market, the economic costs of over-assessment of property
are much steeper than under-assessment, due to potential costs of appeals and litigation. The LINEX function takes the form:
LLINEX(et) = b exp(aet) − cet− b,
where b>0, and a, c?=0. Assuming that ab=c, which ensures that the minimum of the LLINEX(et) is at et=0 (Zellner, 1986),
the LINEX loss function is then:
LLINEX(et) = b[exp(aet) − aet− 1],
where b>0, and a?=0.
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