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OCR for page 112
4
Learning and Lags in Mortality Perceptions
Mark R. Montgomery
Each culture has experts, people of unusual acumen or specialized knowledge,
who detect covariations and report them to the culture at large.
Nisbett and Ross (1980: 1 1 1~.
Every demographer can sketch in two curves the broad outlines of the demo-
graphic transition. One curve depicts high and then falling mortality; the other
shows how fertility, also high at the outset, follows a similar downward course
after a lag. Fertility change depends on many factors other than mortality per se,
but it is reasonable to believe that, as survival prospects improve, the need for
high fertility must be reduced.
Although much empirical research supports the view that mortality decline is
a causal factor in fertility decline (Schultz, 1981; Wolpin, in this volume), the
literature also contains puzzling cases in which considerable mortality decline
fails to evoke any response in fertility, as well as examples in which the usual
sequence is reversed, with fertility decline preceding the decline in mortality
(Matthiessen and McCann, 1978~. In spite of the fundamental role assigned to
mortality change, no theory has yet been formulated to explain the lag in fertility
responses or to show why long lags are to be expected in some circumstances and
rapid response in others.
In assembling the elements of such a theory, it is worthwhile to pose to
ourselves this question: How, in fact, do people learn that mortality has de-
clined? Imagine oneself semiliterate, situated in a rural area of a developing
country, and isolated to a great degree from the media and from the formal
health-care system. Suppose that even in such an environment, a decline in child
mortality is under way. Are the improvements in child survival simply self-
evident? Is it a trivial matter to learn the facts? How would one know of
mortality decline without having been informed of the facts by health personnel
or by those who are better educated?
112
OCR for page 113
MARK R. MONTGOMERY
113
These questions came to mind in the course of a series of focus groups that
Olukunle Adegbola and I conducted in Lagos, Nigeria, in 1989. Lagos is of
course at the opposite end of the spectrum from the situation just described: It is
perhaps Africa's largest urban community, saturated by information from radio,
television, and newspapers, with a population that contains numerous health
personnel and a mixture of the well-educated and the thoroughly uneducated.
Without really expecting much from the question, we asked our focus group
participants in Lagos whether they thought children were more likely to survive
these days than a generation ago. We were somewhat taken aback by the range
and variety of their replies. No consensus existed about mortality decline. The
better-educated expressed confidence that a decline was under way and pointed
to the many medicines and modern treatments that were unknown in their fathers'
time. Some of the less-educated, by contrast, exhibited confusion about the
direction of change, some arguing that children were more likely to die now than
in the past, while others cited improvements in health care. Several participants
observed that currently in Lagos, one sees many more funerals than used to be the
case; to them, this was evidence of rising mortality. They were clearly thinking
of the numerator of a mortality rate, rather than of the rate itself.
Evidently, it is not a simple matter to deduce mortality decline from observa-
tion alone. It may be that few people think naturally in terms of rates or prob-
abilities, and that some training is required to appreciate the distinction between
the number of deaths and the death rate. Perhaps educated Nigerians know of
mortality decline because they have learned about it in school or because they are
more attentive to information presented in the media or by health personnel. In
addition, the mortality decline in Nigeria may have been uneven (Hill, 1993),
with a clearer downward trend for socioeconomically advantaged groups and a
slower change, perhaps too subtle to reach the threshold of perception (McKenzie
1994), among groups that are less well-off.
The aim of this chapter is to explore such issues with the aid of formal
models of learning and decision making under uncertainty. I draw on a diverse
literature that includes studies in economics, demography, and social and cogni-
tive psychology. The chapter is frankly speculative. I know of only three empiri-
cal studies that have directly measured mortality perceptions in developing coun-
tries: Pebley et al. (1979) for Guatemala, Heer and Wu (1978) for Taiwan and
urban Morocco, and Cleland et al. (1992) for five Central and West African
countries. The Pebley et al. study focused on perceived child survival probabili-
ties in four villages in the Institute of Central America and Panama (INCAP)
study of Guatemala. Likewise, Heer and Wu (1978) considered child mortality
perceptions in two Taiwanese townships and for Morocco they gathered data on
perceptions of change. Cleland et al. explored the perceived threat of AIDS to
adult survival and behavior. In developed country settings, recent work by Hurd
and McGarry (1995) for the United States is concerned with the perceptions of
mature and elderly men and women of old age survival prospects. In view of the
OCR for page 114
4
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
prominent causal role thought to be played by child mortality decline in fertility
transitions, it is surprising that the empirical literature on perceptions of survival
remains so thin.
The chapter is organized as follows. In the first section I consider a model of
Bayesian learning about child survival in which individual perceptions are deter-
mined by a prior distribution that summarizes initial subjective beliefs about
mortality probabilities, these beliefs then being updated by reference to a sample
of information on mortality experience, yielding a posterior distribution that
summarizes how beliefs change in the light of experience. Bayesian learning
supplies a natural benchmark for learning models, in that the approach assumes
that individuals process information in an optimal fashion, acting much as statis-
ticians do. In view of the difficulties that individuals may face in thinking in
probabilistic terms, however, to assume Bayesian learning may well be inappro-
priate. An extensive literature in both psychology and economics, which makes
use of experimental evidence on judgment and belief updating, provides strik-
ingly little support for the Bayesian model. It seems that individual reasoning
about uncertainty can and often does depart systematically from Bayesian predic-
tions. In the second section some of the major findings from this experimental
literature are reported, and I speculate about their implications for mortality
perceptions. In the final section I present conclusions and offer suggestions for a
demographic research agenda.
BAYESIAN LEARNING ABOUT CHILD SURVIVAL
The Bayesian approach to learning is perhaps viewed most usefully as an
optimal benchmark, providing a standard against which less precisely formulated
models can be judged. I focus on a type of learning that might be termed social
learning (Montgomery and Casterline, 1996), whereby individuals gather infor-
mation about child survival prospects by observing the experiences of their peers.
Each family is assumed to be linked by way of its social networks to a sample of
other families that provides N observations on child survival in each year. The
true child survival probability will change from one year to the next, following an
upward trend, and each year the family' s beliefs about survival will be updated in
a Bayesian fashion, taking into account that year's sample of size N.
To draw out the implications of survival probabilities for fertility, I rely on a
simple utility maximization model (details are reported in the Appendix) that is
an idealized representation of fertility decision making. Parents are assumed to
choose the number of births they bear, denoted by B. so as to maximize an
expected utility function U(S), where S < B is the number of surviving children. I
explore a specification in which U is a quadratic function of S. that is,
U(S) = aS- bS2,
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MARK R. MONTGOMERY
115
with parameters a, b > 0. In this specification there is an ideal numbers of
surviving children S* that corresponds to the maximum of U(S). Because child
survival is uncertain, parents are not assured of having S* children and will adjust
their fertility B to protect themselves against the possibility of child loss. The
number of surviving children S is assumed to be binomially distributed given the
number of births B and the child survival probability O. In developing the ex-
amples below, I take ~ to be the probability of surviving to age 5, that is, as the
complement of the child mortality probability.2
Known Survival Probabilities
To begin, suppose that the survival probability ~ is known with certainty.
Figures 4-1 and 4-2 illustrate the optimal fertility distributions for a range of
values of the survival probability O. In developing these figures, I assumed that
the desired number of surviving children is fours and that ~ lies in the range that
has been characteristic of the postwar experience in West Africa. To motivate the
example, I take from Hill (1993:Table 5.2) a time series of child mortality esti-
mates for Ghana, a West African country whose mortality decline is well docu-
mented. In the immediate postwar period (circa 1948) the probability of child
mortality was about 0.301 in Ghana. A period of mortality decline then set in,
bringing child mortality to a level of 0.199 by 1967. In the 1970s and 1980s little
further improvement took place, and by 1985 Ghanaian child mortality had fallen
only to 0.163. Figure 4-1 presents illustrative fertility estimates derived from
values that range from 0.699, a number that corresponds to the immediate post-
war years, to a maximum of 0.95, the latter being some 10 points above what
Ghana had achieved as of the mid-1980s.
As can be seen in Figure 4-1, improvement in child survival brings about a
reduction in mean desired fertility. The mean value of fertility declines from 5.5
to 4.2 over the range for 0, a difference of slightly more than one child. The net
reproduction rate, however, remains essentially constant, this being a common
1 For simplicity, I choose parameter values to ensure that there is only one maximum of u(s),
associated with an integer value for s.
Alternatively, one could consider survival to adulthood rather than to age 5. In most developing
country settings in which mortality rates are very low between age 5 and adulthood, there would be
little empirical difference between the two survival probabilities. Where perceptions are concerned,
however, the death an older child or young adult might exert a powerful influence out of proportion
to its empirical likelihood.
3The optimal number of surviving children is produced by making assumptions on the ratio of
utility parameters a and b such that 4 = al(2b) or a = 8b. we can then consider different values for b.
The greater the value for b, the sharper the fall off in utility as the number of surviving children
deviates from four.
OCR for page 116
6
5.6
5.4
5.2 t
.~
.
~ 4.6
4.8
4.4
4.2
4.0
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
\
0.70 0.75
0.80 0.85 O.gO 0.95
Child Survival Probability
FIGURE 4-1 Mean fertility by child survival probability.
0.7
0.6
0.5
.o 0.4
o
2
0.3
0.2
0.1
\
~ I
.g , - l
. · . .
.8
· I
/ -' / ~ 2. ;
J . \ ~
\ .7
_ ~ ~1 ~-~-e ~,1 1
0.0
0 1 2 3 4 5 6 7 8 9 10
Parity
FIGURE 4-2 Distributions of fertility given different survival values.
OCR for page 117
MARK R. MONTGOMERY
117
feature of models that take births themselves to be costless (see the Appendix).
The effects of child survival are perhaps clearer in Figure 4-2, which shows the
distribution of desired fertility for several ~ values.
Uncertain Survival Probabilities
Having sketched the main features of the case in which ~ is known, I now ask
how fertility decisions might differ if the survival probability ~ is an unknown
quantity about which individuals have more or less certain prior beliefs. Two
questions must be addressed. First, how does one represent such prior beliefs?
Second, how does experience cause these beliefs to be revised?
As they enter adulthood, most women and men in developing countries will
have had some exposure, whether direct or indirect, to the risks of child mortality.
Many will have experienced the death of a sibling, an event that must leave a
deep and vivid impression, and the experiences of relatives might figure in as
well.4 Those who have attended school would have acquired some general
information about health and survival, which could also shape initial perceptions
of risk. But for many young adults, childbearing and the risks of child death are
matters that belong to a stage of life that they have not yet entered and about
which they know little. We would therefore expect perceptions of the survival
probability ~ to be hazy and subject to considerable uncertainty.
Imagine two young Ghanaian adults who begin their family building in
1948. In each year, they will have access, through social networks of relatives,
friends, and peers, to a sample of N observations on child survival. Each year the
family assesses the information contained in this sample and revises its subjective
beliefs about ~ accordingly. The size N of this sample will depend on the extent
of social networks in general, the level of fertility in the population, and the
degree of privacy that shrouds matters of birth and death. For example, it may be
that the educated have access to larger social networks than do the less educated
and so possess a larger sample of information. For simplicity, however, I take N
to be a constant and set N= 10 for purposes of illustration.
Returning to the household's fertility choice, the problem is to choose the
number of births B that maximizes
E U(S) = E (aS- bit.
As noted in the Appendix, if the value of the survival probability ~ were known,
this problem could be restated as
4As John Casterline (personal communication, 1996) notes, this supposition forms the basis of the
sisterhood method for estimating adult mortality.
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118
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
max B(a - b) ~ - bB(B - 1)02.
With ~ unknown, however, the values of ~ and 02 must be replaced in the expres-
sion by their subjective expected values, E(~) and E(02), which in turn depend on
prior beliefs and the available sample of child survival observations.
Illustrative Results
11- we take the (]hanaian experience as a guide, Figure 4-3 shows the se-
quence over time of the actual survival probability as compared with the evolu-
tion of subjective beliefs about survivorship. Figure 4-3 shows the subjective
mean E(~) and the 25th and 75th percentiles of the subjective distnbution. It
illustrates the evolution of perceptions for a family beginning in 1948 with a prior
distribution whose mean is identical to the true survival probability (0.699), but
with considerable uncertainty about 0, as evident in the 25th to 75th percentile
range that stretches from 0.57 to 0.86. In 1948 and in each year thereafter, the
family updates its beliefs on the basis of ten new observations, each such sample
being drawn from a binomial distribution characterized by that year's (true)
survival probability. The learning shown here is therefore cumulative; that is,
beliefs in 1980 are influenced to some degree by the initial prior distribution in
1948 as well as by the intervening sequence of social network samples.
As can be seen in the figure, although the uncertainty evident in the initial
~ .0
.
0~9
._
~ 0.8
-
.> 0.7
A}
0.6
0.5
true mean
-
-
subjective mean
1950 1960 - 1970 1980 1990
Calendar Year
FIGURE 4-3 Actual trend versus subjective distribution.
OCR for page 119
MARK R. MONTGOMERY
119
prior distribution is quickly reduced, and even though the initial subjective mean
and the true mean were selected to exactly coincide, the family's perception of
child survival fails to keep pace with the empirical realities. There is an upward
trend in the subjective mean, to be sure, but the year-to-year gain is smaller than
the true improvement in survivorship. By the early 1960s even the 75th percen-
tile of the subjective ~ distribution has fallen below the true value for 0, and by
the end of the period the gap between the subjective mean and the true ~ value has
grown to some eight percentage points.
One might ask whether larger social networks, which contain more annual
observations on children's deaths and survival, would bring the subjective mean
into line with the true survival probability. A change in the sample size N does
have some effect, but the gap shown in Figure 4-3 persists even if N is doubled to
20 annual observations.
The persistent lag in expectations, as compared with the true level of child
survival, is the product of two factors. The first is that the true values for ~ follow
a trend, whereas in the simple Bayesian model outlined above, beliefs are up-
dated without there being a recognition that a trend in survivorship exists. If a
more complex Bayesian model were employed (see Zellner and Rossi, 1984;
Koop and Poirier, 1993; Poirier, 1994) in which both level and trend components
for ~ were updated from sample experience, the subjective values would adhere
more closely to the actual trend. Such Bayesian trend models require greater
sophistication on the part of decision makers, who must now make mental com-
parisons of their social network samples over time.
The second factor is that even with relatively small social network samples
(recall that N = 10), only a few rounds of experience are required to substantially
reduce subjective uncertainty about O. As the distribution of beliefs becomes
ever more concentrated about the subjective mean, upward revision of that mean
is made ever more grudgingly. With time and experience, individuals become
more and more set in their beliefs and begin to resist new evidence of improve-
ments in survival.
Implications for Fertility
How much difference does learning and uncertainty make to fertility deci-
sions? One way to assess the net effect of learning is to compare the mean level
of desired fertility with the survival probability ~ set equal to its true end-of-
period value (see Figure 4-3) to the mean fertility level produced by the subjec-
tive distribution of ~ for that year. The difference in fertility is on the order of 0.6
children. In other words, an objectively correct evaluation of survival prospects
would be predicted to lead to 0.6 fewer desired births than in the case in which
subjective mortality impressions are employed.
The projected difference of 0.6 desired births is in no way an empirical
finding, being simply the outcome of a particular model and set of assumptions.
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120
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
The model itself could be elaborated in any number of dimensions, for example
by incorporating both trend and level components in learning and by adding a
dynamic structure that would permit child replacement effects to be analyzed.
These are worthwhile extensions; they will inevitably lead to a more sophisti-
cated Bayesian model. Before we undertake to construct such an elaborate model,
we should assess the experimental evidence on learning to determine whether any
support exists for the type of optimal learning being considered here.
DEPARTURES FROM BAYESIAN LEARNING
Camerer (1995) has thoroughly reviewed the literature in cognitive psychol-
ogy, social psychology, and economics and found evidence that indicates a de-
parture from Bayesian learning in two principal areas: Individuals employ learn-
ing strategies that are cognitively much simpler than the Bayesian rules; and in
some circumstances, individuals consistently make fundamental mistakes in
probabilistic reasoning, tending to assign too much weight to certain types of
evidence and not enough to others.
Nonexperimental economists have been inclined to dismiss such findings,
arguing that, as individuals gather experience and are repeatedly subjected to the
discipline of the market or other social institutions, their judgments will come to
resemble optimal Bayesian judgments. Such conditions are unlikely to obtain in
respect to mortality perceptions and fertility decision making. In developing
transitional societies, individuals are often called upon to make decisions in novel
situations and in environments that are in flux, where the old rules no longer quite
apply but new rules and institutions have not yet evolved to take their place.
Mistakes and misperceptions are to be expected as individuals traverse such new
terrain.
To begin, it should come as no surprise that individuals prefer to use simple
rules of thumb in making their judgments and updating beliefs, rather than to
engage in complex Bayesian calculations. Such common decision rules usually
involve a simple averaging of prior beliefs and new sample evidence (Lopes,
1985, 1987; McKenzie, 1994~. This need not in itself put the Bayesian perspec-
tive in doubt, as one could argue that individuals often behave as if they were
Bayesians. In the case of updating in mortality perceptions, the main features of
Figure 4-3 above would probably not change greatly if individuals simply split
the difference between their prior beliefs and the latest sample evidence.
However, there is considerable doubt that individuals consistently behave as
if they were Bayesians. As Camerer (1995) and Conlisk (1996) demonstrate,
when economic experiments are designed to reward optimal decisions and punish
mistakes in judgment, as a market would, these incentives do not consistently
lead participants to adopt Bayesian decision rules. A new area of research in
economics, exemplified by El-Gamal and Grether (1995) and Cox et al. (1995),
attempts to discover by statistical means the types of learning rules participants
OCR for page 121
MARK R. MONTGOMERY
121
employ in experimental games. Bayesian decision making emerges as one in the
set of rules employed, but other rules are equally prominent and substantial
heterogeneity in learning evidently exists. Although this literature casts doubt on
Bayesian learning, it has not yet succeeded in identifying a compelling and domi-
nant alternative. Rather, it seems that the type of non-Bayesian reasoning that
individuals employ is situation-specific, depending in a complicated fashion on
the nature of the problem.
Where mortality perceptions are concerned, the experimental literature sug-
gests that, on the whole, perceptions may be even more resistant to change than
was illustrated in the simple Bayesian model above. Not every aspect of the
literature supports such a conclusion, but the bulk of the evidence does.
It may be useful to preface the following discussion by reference to recent
findings on the neurological basis of human learning and memory. The experi-
ments of Knowlton et al. (1996), and the insightful comments on them by Robbins
(1996), provide evidence that memory and learning in tasks related to probability
classification involve a different section of the brain than do other tasks involving
recognition and recall. (Their probabilistic experiments had to do with a weather
forecasting game in which an arrangement of four cards imperfectly predicted the
weather.) Moreover, as Knowlton et al. (1996:1400) observes, "the probabilistic
structure of the task appears to defeat the normal tendency to try to memorize a
solution, and individuals can learn without being aware of the information they
have acquired." Because child survival and death are likewise imperfectly pre-
dictable chance events, one wonders whether humans process information about
them in ways that are fundamentally distinct from other types of learning. Might
individuals over time come to appreciate trends and covariations in child survival
without ever being able to say quite why they know what they do? The anomalies
in probabilistic learning to be discussed below may well have common neuro-
logical roots.
Null Events
Where mortality is concerned, the definition of an event is itself worth con-
sidering. A statistician would note both the occurrence of a child death and the
occurrence of a child survival; both are "events." But for the lay person, only the
former may be noteworthy. There is no news in a child's survival; nothing has
happened; it is a "null event." It may therefore be difficult for the lay person to
give recollections of child survival their fully appropriate subjective weight. The
experimental literature (Estes, 1976) contains numerous examples in which sub-
jects demonstrate their difficulty in retaining information about such null events.
If an event X is always described in an experiment as being "not Y." this trivial
semantic difference appears to have real implications for recall.
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22
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
Use of Base Rates
It is often observed in experimental contexts that when presented with a
statistical portrait of a population, termed by psychologists a "base rate," and a
sample of evidence from that population, individuals tend to give too much
emphasis to the sample evidence and not enough to the base rate. For example,
when told that these days, 90 percent of children survive to adulthood, and when
given a small sample in which only six children in a group of ten survived,
individuals might tend to give the sample evidence too much weight in their
thinking (Grether,1980~. When asked to compare two situations having different
base rates, such as two different mortality levels, individuals will often ignore
these base rates entirely in favor of sample evidence, unless their attention is
specifically directed to the difference in the base rates (Bar-Hillel, 1980; Bar-
Hillel and Fischhoff, 1981; Argote et al., 1986~. It seems that the base rates are
somehow viewed as rather abstract and pallid by comparison with the vividness
and individuality of sample data (Bar-Hillel, 1980~. Perhaps for a developing
country villager, general media presentations on the likelihood of child survival,
or similar presentations by health personnel, lack the immediacy and persuasive
power inherent in a tiny sample of recent village experience. One source of data
is "merely statistical," whereas the other commands attention and demands inter-
pretation.
As Nisbett and Ross (1980:57) remind us, this bias in favor of sample evi-
dence is reinforced by many folk sayings. Statements such as "Seeing is believ-
ing," or "You can prove anything with statistics," which stress the reliability of
one's own experience, are not counterbalanced by other maxims that warn against
the danger of inferring too much from a small sample. The experimental evi-
dence (see Nisbett and Ross, 1980:56-60; Tversky and Kahneman, 1974) shows
that people prefer to rely on sample evidence even when they are made aware that
such evidence has very little diagnostic content.
Strength Versus Weight
Griffin and Tversky (1992) argue that in making judgments about the likeli-
hood of an event, people focus first on the apparent "strength" of an effect (such
as the size of a sample mean) and then make an adjustment, but typically an
insufficient adjustment, for the "weight" of the sample evidence (the sample size
or the standard error of the sample mean). To put this differently, ". . . people are
highly sensitive to variations in the extremeness of evidence and not sufficiently
sensitive to variations in its credence or predictive validity. . ." (Griffin and
Tversky,1992:413~. This bias might cause certain unusual events, such as a case
in which a single family in a rural village lost all of its children, to acquire a
disproportionate influence in mortality perceptions.
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MARK R. MONTGOMERY
127
have been described, this does not necessarily occur. Rather, groups are often
more extreme in their judgments than individuals, sometimes (although not al-
ways) amplifying individual errors into an erroneous group consensus (Argote et
al., 1986, 1990~. Thus, groups as well as individuals may violate Bayes' rule.
Cultural Differences
A small literature explores cultural differences in how uncertainty itself is
viewed and how degrees of uncertainty are expressed. This literature centers on
the concept of probabilistic thinking, which Wright et al. (1978:285) define as
"the tendency to adopt a probabilistic set, discrimination of uncertainty, and the
ability to express the uncertainty meaningfully as a numerical probability." Re-
views and experiments regarding probabilistic thinking are presented in Wright
et al. (1978) and Kleinhesselink and Rosa (1991~. The major conclusions appear
to be as follows. In a study of factual knowledge about geography and other
matters that included students from Hong Kong, Malaysia, Indonesia, and Great
Britain, Wright et al. (1978) found that, as seems to be typical (Fischhoff et al.,
1977), all students tended to be overconfident about their judgments in relation to
true performance (that is, to be wrong too often when confident they are right).
Given this, the Asian students tended to express their evaluations and degrees of
confidence in absolute terms (e.g., O percent or 100 percent confidence in a
judgment) more often than did the British students, who adopted gradations in
language and used nuance to describe their confidence levels. These tendencies
apparently could not be attributed to different levels of substantive knowledge
(for similar findings see Wright and Phillips, 1980~.
It may be, therefore, that the Asian students are less prone to think in proba-
bilistic terms. An alternative explanation is that, however the Asian students may
think, they are less likely to express themselves in terms of degrees of certainty.
This literature hints that cultural differences may exist, but leaves uncertain their
extent and depth.
Summary
If the literature described above can be taken as a guide, I would argue that
on the whole, improvements in child mortality are likely to be perceived with a
greater lag than suggested by optimal Bayesian calculations. There are clearly
many subtleties here, and it may be that recency effects and different types of
adaptive learning could reverse this conclusion. Nevertheless, it seems far from
clear that when mortality improves, individuals will possess the cognitive equip-
ment to correctly and rapidly perceive the trend.
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28
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
CONCLUSIONS
My aim in this chapter has been to point to a gap in the theory of the
demographic transition related to the factors that might induce lags or misper-
ceptions of mortality change. If the wide-ranging literature cited above offers
any basis for generalization, one might extract from it a few general themes.
Social Learning and the Demographic Transition
Economic development is associated with sweeping change in any number
of social and economic arenas. Some of these changes require little effort to
observe and interpret. Others, however, are difficult both to perceive and to
understand. Among these society-wide changes, mortality is perhaps especially
difficult in that some probabilistic thinking is required even to judge the direction
of change. I have argued that individuals, if left to their own perceptual devices,
are unlikely to infer that mortality prospects have improved; more precisely, they
are unlikely to do so rapidly and without some interim period characterized by
error, uncertainty, and debate.
Social learning may also be important in other arenas of behavior, particu-
larly in cases in which individuals are considering the adoption of innovations.
Elsewhere (Montgomery and Casterline, 1996) it has been argued that social
learning is a fundamental element in the diffusion perspective on fertility transi-
tion. Diffusion models lay emphasis on factors affecting the demand for chil-
dren, such as mortality, as well as those that affect the costs of fertility regulation.
Some of the arguments made above with regard to mortality perceptions might
also apply to learning about the properties of modern contraceptive methods or
the risks and expected returns to be derived from educating children.
The role played by exogenous variability and the mediating functions of
social institutions also deserve consideration. High-mortality environments are
likely to be environments in which mortality is highly variable. High variance, in
turn, must surely add to the difficulties that individuals face in learning about the
central tendencies of their environments, that is, in extracting signal from noise.
Stable social institutions can act as buffers against extreme risks, or may play an
insurancelike function in spreading otherwise local risks over wider populations.
When institutions play such roles, they act to dampen variance and may thereby
facilitate individual learning.
Education and the Modern Health Sector
It- mortality misperceptions are likely, it might now be asked how they come
to be corrected. The argument developed above suggests a reconsideration of the
special contribution of education and the provision of information. We do not yet
OCR for page 129
MARK R. MONTGOMERY
129
understand how mortality perceptions are formed and whether they are influ-
enced principally by direct experience, observed experience, or by the acquisition
of learning in school, from the media, or from the health sector itself. Diffusion
of information about mortality improvements from those who were taught the
facts to those who might otherwise not have perceived them may be the funda-
mental source of changes in perceptions.
The roles that are played by national and international organizations charged
with health interventions must surely be important. It is these agencies that
communicate information about mortality and health change to the populations
they serve. They can do so directly through presentations in the media and the
discussions of health personnel. One wonders, in light of the discussion above,
what factors determine the reception of these media messages. Are they typically
judged persuasive, or abstract and irrelevant? The formal health organizations
also communicate information indirectly by insertion of material related to health
in national school curricula. LeVine et al. (1994) have argued that schooling
itself equips individuals with the cognitive skills they need to translate the
"decontextualized language" of the formal health sector into terms that are mean-
ingful to individual experience and decisions.
Perhaps it is in the schoolroom that individuals learn to be attentive to infor-
mation provided by government and the formal health sector. Of course, few
students will emerge from school with an understanding of the germ theory of
disease and the workings of modern medicines. Many will come to know that
such knowledge exists and that it rests in the hands of modern health care person-
nel. They will also have been exposed to the knowledge that mortality is control-
lable, at least to a degree, and this in itself will tend to heighten attention to
information about health (Simons, 1989~.
The Western experience in such matters may be instructive. As Preston and
Haines (1991) argue, citing Dye and Smith (1986), the nineteenth century expe-
rience in the United States was one of a gradually increased emphasis on the
mother's role in protecting her children's health. There was an increasing faith in
the controllability of mortality, although few effective means existed for preven-
tion and even fewer for cure. Until the early twentieth century, the rising belief in
controllability did little but increase anxiety and promote a sometimes frantic
search for cures; when effective medicines finally emerged, however, the net
effect was to improve child survivorship. Interestingly, in this era it was within
the medical and public health professions that diffusion of information and the
combat between traditional and modern health beliefs were important. Not until
the second decade of the twentieth century did physicians fully relinquish nine-
teenth century beliefs in bodily imbalances, innate racial constitutions, and vari-
ous miasmas as explanations for disease.
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130
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
A Research Agenda
To know whether lags and learning are important in today's developing
countries, there is no substitute for basic research aimed at eliciting perceptions
of mortality levels, differentials, and change. This is a challenging area for
research in that the populations whose perceptions are to be studied are not
always fully literate and perhaps have a different vocabulary and understanding
of uncertainty. In highly literate populations, several methods have been used
successfully to elicit subjective probabilities (see Hurd and McGarry, 1995;
Dominitz and Manski, 1994a,b; and Morgan and Henrion, 1990~. The early
study of Pebley et al. (1979) tested simple probability scales in Guatemala, evi-
dently with good results. These methods might be adapted profitably for use in
developing country settings in which mortality and fertility transitions are now
under way.
APPENDIX
In the simple Bayesian fertility decision model, parents are assumed to choose
the number of their births B to maximize the expected value of the utility function
U(S), where U(S) = as- bS2. The U(S) function is symmetric, a specification that
imposes equal penalties for falling short of the target S* and exceeding it. This
form of the utility function has been chosen principally for analytic convenience,
and although I do not do so in what follows, other nonsymmetric specifications
might also be considered.
Note that the number of births B does not enter U(S) directly. The implicit
assumption is that the costs of children that is, the factors that cause U(S) to
slope downward beyond S* are largely the costs associated with surviving chil-
dren. In high-mortality settings, where the probability of death after infancy is
high, such an assumption is not entirely appropriate. An additional term involv-
ing B could be added to the specification above, yielding a more general expected
utility function U(S,B). This addition would certainly affect the fertility predic-
tions derived from the model, but would not directly alter mortality perceptions
and the process of learning. To simplify matters, therefore, I have not included B
directly.
In keeping with Sah (1991), the number of surviving children S is assumed to
be binomially distributed given the number of births B and the child survival
probability O. That is,
P(S = s I B. B) = ( )0s (1 _ o)B-s
The parameter ~ represents the probability of surviving to age 5.
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MARK R. MONTGOMERY
13
Known Survival Probabilities
To begin, suppose that the survival probability ~ is known with certainty. In
this case, parents confront the following maximization problem:
max s=0 U(s) s (1 _ JIB s
B (s)
Although no analytic solution for B is available, the utility-maximizing B is
easily found by numerical means for any given O. Indeed, from the binomial
assumption and the simple form adopted for U(S), the problem reduces to finding
the number of births B that maximizes
E fU(s) I B,0] =B(a- big- bB(B- 1~02.
Without additional structure, the steps taken to this point would lead to a single
utility-maximizing value B* for fertility. It is perhaps more reasonable to allow
for some heterogeneity in the population and to think of B* as the most likely
value for fertility. Heterogeneity is introduced by attaching "disturbance terms"
£B specific to each level of fertility, giving
E f U(s) I B. E, £B] = B(a- big - bB(B- 1~02 + £B
.
Provided that the disturbance terms £B are mutually independent, extreme-value
random variables, we are led to a distribution of the levels of optimal fertility of
the form
exp~B(`a - buff - bB(`B _ 1~02]
Pr(`B I f9) =
~j=oeXptita - buff - bj(` j _ 1~2]
The above is recognizable as the probability derived from a conditional-logit
choice problem.
Subjective Beliefs
It is analytically convenient to summarize prior beliefs regarding ~ by means
of the beta distribution, whose density is
f(~3 1 0C,'(~) = 1 `3a-~`l_~3~-l
where Be~a,b) is the beta function. This distribution is reasonably flexible and
allows for a variety of representations of uncertainty (Lee, 1989; Pratt et al.,
1995~. The mean and variance of the beta distribution are
OCR for page 132
32
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
E(~) =
var (a) =
oc
oc+D'
aD
(~+~)2(~+~+1)
E(~) [1 - E(~) ]
oc+~+1
When or = 13 = l, the distnbution of ~ is uniform over the interval from 0 to l; the
case or = 13 = 2 yields a symmetric distnbution for ~ about the value ~ = 0.5; and
with or > 13, or > 2 a skewed unimodal distnbution emerges. I illustrate this last
case in Figure 4A-l, for which or and 13 have been chosen so that the subjective
mean of the survival probability ~ = 0.699, a value equal to Hill's initial esti-
mated probability of child survival in postwar Ghana.
Social Learning
When beta-distnbuted prior beliefs about ~ are updated by reference to a
sample of N external observations on child survival, this sample being generated
by the binomial distnbution, the posterior distnbution for ~ is also a beta. In
other words, the beta distnbution is the conjugate prior for the binomial. We can
see this as follows. Let pokey represent the prior distnbution for ~ and pap)
represent the updated or posterior distnbution. We then have
2.2
2.0:
1.8
1.6 .
~ ].4
V, 1.2
0
a
1.0
0.8
0.6
0.4
0.2
l
0,0 ~-~ 1 1_ 1 1 1 1
0.0 0.1 0.2 0.3 0.4
FIGURE 4A-1 The beta density (mean = 0.699~.
O.S 0.6 0.7 0.8
1 , 1 ' I ~1 1
0.9 1.0
Theta
OCR for page 133
MARK R. MONTGOMERY
) (I )Os (1 (3)N-s
Bc~c`,0'(3 (1_(3)~ 1( )~35(1_(3)N-s
= 1 (3a+5_1 (1 _ 0)~+N-s-l
Be(oc+s,~+N-s)
so that the posterior distribution is a beta with parameters oh = or + s, p~ = ~ +
N - s.
133
Although flexible, the beta distribution is not an ideal choice for an applica-
tion to child survival in that the distribution always assigns some subjective
probability to values of ~ near 1 and 0. This gives a potentially unrealistic
representation of subjective beliefs, as few individuals believe either that all
children will survive or that none will. However, by selecting values for or and ~
with some care, one can confine most of the subjective distribution for ~ to a
reasonable range.
Note that the principal advantage of the beta distribution is that, when it is
combined with the binomial, the posterior distribution for ~ has the same form as
the prior distribution, both being betas. This is analytically convenient. By
departing from the beta distribution one could represent subjective perceptions in
a more reasonable way, perhaps by confining the perceived ~ to a range, but this
advantage would be offset by greater difficulty entailed in analytic comparisons
when the prior and posterior differ in form.
Desired Fertility with ~ Uncertain
Returning to the fertility choice facing households, the problem is to choose
the number of births B that maximizes
E U(S) = E (aS- by.
As noted above, if the value of the survival probability ~ were known, this
problem could be restated as
max B(a - b) ~ - bB(B - 1~02
With ~ unknown, however, the values of ~ and 02 must be replaced in the expres-
sion by their subjective expectations, E(~) and E(02), which in turn depend on
prior beliefs and the available sample of child survival observations. The utility
maximization problem can be stated as
OCR for page 134
134
where E(~) = oc/(oc + p).
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
max B(a - b) E(~) - bB(B - 1)E(~):E(~) + ~3( ~ ],
ACKNOWLEDGMENTS
This research was supported in part by a grant from the Rockefeller Founda-
tion. I thank John Casterline, Barney Cohen, and two anonymous referees for
their insightful comments.
REFERENCES
Argote, L., R. Devadas, and N. Melone
1990 The base-rate fallacy: Contrasting processes and outcomes of group and individual judg-
ment. Organizational Behavior and Human Decision Processes 46:296-310.
Argote, L., M. Seabright, and L. Dyer
1986 Individual versus group use of base-rate and individuating information. Organizational
Behavior and Human Decision Processes 38:65-75.
Bar-Hillel, M.
1980 The base-rate fallacy in probability judgments. Acta Psychologica 44:211-233.
Bar-Hillel, M., and B. Fischhoff
1981 When do base rates affect predictions? Journal of Personality and Social Psychology
41(4):671-680.
Caldwell, J., P. Reddy, and P. Caldwell
1983 The social component of mortality decline: An investigation in South India using alterna-
tive methodologies. Population Studies 37(2):185-205.
Camerer, C.
1995 Individual decision making. In J. Kagel and A. Roth, eds., The Handbook of Experimen-
tal Economics. Princeton, N.J.: Princeton University Press.
Cleland, J., M. Carael, J.-C. Deheneffe, and B. Ferry
1992 Sexual behavior in the face of risk: Preliminary results from first AIDS-related surveys.
Health Transition Review 2(Suppl.):185-204.
Conlisk, J.
1996 Why bounded rationality? Journal of Economic Literature 34:669-700.
Cox, J., J. Shachat, and M. Walker
1995 An Experimental Test of Bayesian vs. Adaptive Learning in Normal Form Games. Un-
published manuscript, Department of Economics, University of Arizona, Tucson.
Dominitz, J., and C. Manski
1994a Eliciting Student Expectations of the Returns to Schooling. Unpublished manuscript,
Institute for Social Research, University of Michigan, Ann Arbor.
1994b Using Expectations Data to Study Subjective Income Expectations. Unpublished manu-
script, Institute for Social Research, University of Michigan, Ann Arbor.
Dye, N., and D. Smith
1986 Mother love and infant death, 1750-1920. Journal of American History 73:329-353.
OCR for page 135
MARK R. MONTGOMERY
135
El-Gamal, M., and D. Grether
1995 Are people Bayesian? Uncovering behavioral strategies. Journal of the American Statis-
tical Association 90(432): 1137- 1145.
Estes, W.
1976 The cognitive side of probability learning. Psychological Review 83(1):37-64.
Fischhoff, B., P. Slovic, and S. Lichtenstein
1977 Knowing with certainty: The appropriateness of extreme confidence. Journal of Experi
Fiske, S.
mental Psychology: Human Perception and Performance 3(4):552-564.
1993 Social cognition and social perception. Annual Review of Psychology 44:155-194.
Grether, D.
1980 Bayes Rule as a descriptive model: The representativeness heuristic. Quarterly Journal
of Economics 95:537-557.
Griffin, D., and A. Tversky
1992 The weighing of evidence and the determinants of confidence. Cognitive Psychology
24:411-435.
Heer, D., and H.-Y. Wu
1978 Effects in rural Taiwan and urban Morocco: Combining individual and aggregate data.
Pp. 135-159 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility.
New York: Academic Press.
Hill, A.
1993 Trends in childhood mortality. Pp. 153-217 in K. Foote, K. Hill, and L. Martin, eds.,
Demographic Change in Sub-Saharan Africa. Washington, D.C.: National Academy
Press.
Hogarth, R.
1975 Cognitive processes and the assessment of subjective probability distributions. Journal of
the American Statistical Association 70(350):271-289.
Hogarth, R., and H. Einhorn
1992 Order effects in belief updating: The belief adjustment model. Cognitive Psychology
24: 1-55.
Hurd, M., and K. McGarry
1995 Evaluation of the subjective probabilities of survival in the Health and Retirement Study.
Journal of Human Resources 30(Suppl.):S268-S292.
Kleinhesselink, R., and E. Rosa
1991 Cognitive representation of risk perceptions: A comparison of Japan and the United
States. Journal of Cross-Cultural Psychology 22(1):11-28.
Knowlton, B., J. Mangels, and L. Squire
1996 A neostriatal habit learning system in humans. Science 273:1399-1402.
Koop, G., and D. Poirier
1993 Bayesian analysis of logit models using natural conjugate priors. Journal of Economet
Lee, P.
1989 Bayesian Statistics: An Introduction. New York: Halsted Press.
LeVine, R.A., E. Dexter, P. Velasco, S. LeVine, A.R. Joshi, K.W. Stuebing, and F.M. Tapia-Uribe
1994 Maternal literacy and health care in three countries: A preliminary report. Health Transi-
tion Review 4(2): 186- 191.
rics 56(3):323-340.
Lopes, L.
1985 Averaging rules and adjustment processes in Bayesian inference. Bulletin of the
Psychonomic Society 23(6):509-512.
1987 Procedure debiasing. Acta Psychologica 64:167-185.
OCR for page 136
136
LEARNING AND LAGS IN MORTALITY PERCEPTIONS
Matthiessen, P., and J. McCann
1978 The role of mortality in the European fertility transition: Aggregate-level relations. Pp.
47-68 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New
York: Academic Press.
McKenzie, C.
1994 The accuracy of intuitive judgment strategies: Covariation assessment and Bayesian
inference. Cognitive Psychology 26:209-239.
Montgomery, M., and J. Casterline
1996 Social learning, social influence and new models of fertility. Population and Develop-
ment Review 22(Suppl.): 151- 175.
Morgan, M., and M. Henrion
1990 Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analy-
sis. New York: Cambridge University Press.
Nisbett, R., and L. Ross
1980 HumanInference: Strategies and Shortcomings ofHuman Judgment. Englewood Cliffs,
N.J.: Prentice-Hall.
Pebley, A., H. Delgado, and E. Brinemann
1979 Fertility desires and child mortality experience among Guatemalan women. Studies in
Family Planning 10(4): 129-136.
Poirier, D.
1994 Jeffreys' prior for logit models. Journal of Econometrics 63:327-339.
Pratt, J., H. Raiffa, and R. Schlaifer
1995 Introduction to Statistical Decision Theory. Cambridge, Mass.: MIT Press.
Pratto, F., and O. John
1991 Automatic vigilance: The attention-grabbing power of negative social information. Jour-
nal of Personality and Social Psychology 61(3):380-391.
Preston, S.H., and M.R. Haines
1991 Fatal Years: Child Mortality in Late Nineteenth Century America. Princeton, N.J.:
Princeton University Press.
Robbins, T.
1996 Refining the taxonomy of memory. Science 273:1353-1354.
Sah, R.
1991 The effects of child mortality changes on fertility choice and parental welfare. Journal of
Political Economy 99(3):582-606.
Savage, I.
1993 An empirical investigation into the effect of psychological perceptions on the willing
ness-to-pay to reduce risk. Journal of Risk and Uncertainty 6:75-90.
Schultz, T.P.
1981 Economics of Population. Reading, Mass.: Addison-Wesley.
Simons, J.
1989 Cultural dimensions of the mother's contribution to child survival. Pp. 132-145 in J.
Caldwell and G. Santow, eds., Selected Readings in the Cultural, Social and Behavioural
Determinants of Health. Health Transition Series No. 1. Canberra: Health Transition
Centre, Australian National University.
Skowronski, J., and D. Carlston
1989 Negativity and extremity biases in impression formation:
Psychological Bulletin 105(1): 131- 142.
Slovic, P.
1987 Perception of risk. Science 236:280-285.
A review of explanations.
OCR for page 137
MARK R. MONTGOMERY
137
Taylor, S.
1991 Asymmetrical effects of positive and negative events: The mobilization-minimization
hypothesis. Psychological Bulletin 110(1):67-85.
Tversky, A., and D. Kahneman
1974 Judgment under uncertainty: Heuristics and biases. Science 185:1124-1131.
Wright, G., and L. Phillips
1980 Cultural variation in probabilistic thinking: Alternative ways of dealing with uncertainty.
International Journal of Psychology 15:239-257.
Wright, G., L. Phillips, P. Whalley, G. Choo, K. Ng, I. Tan, and A. Wisu&a
1978 Cultural differences in probabilistic thinking. Journal of Cross-Cultural Psychology
9(3):285-299.
Zellner, A., and P. Rossi
1984 Bayesian analysis of dichotomous quantal response models. Journal of Econometrics
25:365-393.
Representative terms from entire chapter:
mortality perceptions
