“Rational Fatalism”:
Non-Monotonic Choices in Response to Risk
Jason T. Kerwin1
University of Michigan Department of Economics and Population Studies Center
March 2012
Many health behaviors, from chemical exposure to unprotected sex, involve weighing definite
benefits against uncertain costs. Previous empirical research has assumed monotonic, negative
responses to such risks, where people always decrease the number of risks they choose to take
when the per-act chance of a bad outcome rises. This paper shows that this need not be true if
rational agents have a history of risk-taking with a still-unrealized outcome. In that case there
exists a tipping point above which agents switch from negative (self-protective) to positive
(fatalistic) responses to risks, even if they are unsophisticated in thinking about probabilities. I
also demonstrate that the typical test for violations of monotonic responses can yield misleading
results, and develop an alternative approach. I then apply my framework to decisions about risky
sex in Malawi, finding suggestive evidence of non-monotonic behavior, and present preliminary
findings from an RCT designed to test the model.
1
I am grateful to Yusufcan Masatlioglu, Raj Arunachalam, Joe Golden, Emily Nicklett, and seminar participants in
the IGPI conference and the University of Michigan Informal Development Seminar for their invaluable feedback.
Rebecca Thornton, Ajay Shenoy, Shaun McGirr, Isaac Sorkin, and participants at the University of Michigan
Extremely Informal Development Seminar provided helpful comments on an earlier version of this paper. Research
on this project was supported by a Student Global Health Engagement Grant from Center for Global Health, the
Population Studies Center Initiatives Fund, and the Weinberg International Travel Fund. The Situational Analysis of
Sexual Behaviors and Alternative Safer Sex Strategies was funded by a grant from the Eva L. Mueller New
Directions in Economics and Demography Fund. Mr. Kerwin acknowledges fellowship support from the Population
Studies Center and the Rackham Graduate School.
1. Introduction
Life is full of decisions that involve weighing the definite benefits of an act against
uncertain, but potentially large consequences. When people consider everything from smoking
and drinking to exposure to chemicals to risky sex to merely driving to work, they face a
probabilistic chance of a bad outcome, and decide whether it’s worth it to take a chance.
Typically research has assumed “self-protective” responses to risks – that when the per-act risk
goes up, people take fewer chances.2 In this paper, I show that rational actors may also respond
“fatalistically” – by increasing their risk-taking when per-act risks rise, and describe a general
model of “rational fatalism” in which the choice of the number of risky acts is a non-monotonic
function of the per-act risk, so that behavior has a both a self-protective and a fatalistic region.
This leads to a fundamental non-monotonicity in people’s behavior – their responses switch from
downward-sloping to upward-sloping depending on the value of the per-act risk. This nonmonotonicity is driven by a history of past risks taken for which outcome is still unrealized.
Logically, this might apply to HIV infection, contracting cancer from smoking, or lung damage
from asbestos exposure. The logic is fairly straightforward: people who are convinced that the
bad outcome is sure to happen perceive no benefit from reducing their risk-taking. In contrast
with previous research I show that this result holds for any reasonable benefit function for the
risky acts, and for a wide range of risk aggregation functions including those that might be
employed by people with a limited background in mathematics. I also demonstrate that fatalistic
behavior can exist for interior solutions, rather than solely in situations where agents choose the
maximal number of risks allowed in the model.
2
Economists commonly use “risk” or “riskiness” to refer to the volatility of an outcome or asset that has some
upside or downside risk, and focus on the curvature of the utility function as a summary of aversion to this sort of
risk. In this paper I use “risk” in the more colloquial sense of “taking a risk”, in which doing something has a
known (beneficial) outcome and carries some chance of a bad result.
Although theoretical work has acknowledged that fatalism can be rational, an extensive
empirical literature on risky choices has almost uniformly imposed a linear functional form
assumption, therefore ruling out potentially non-monotonic relationships. The portion of this
literature that has studied the relationship between unprotected sex and HIV in Africa has found
perplexingly small responses. Many explanations have been advanced for this limited response,
but rational fatalism suggests another possibility that has yet to be studied. If a negative, selfprotective response by some is balanced by a positive, fatalistic response by others, the average
magnitude of the response will be lower and potentially near zero unless the researcher explicitly
allows for non-monotonic responses. This is rare – only a few studies have allowed for nonmonotonicity, commonly by including a quadratic term in the per-act risk. A conventional
approach is to looking for non-monotonicity is to examine the statistical significance of this
squared term, but this can be misleading. Using data generated by the rational fatalism model, I
show that a parametric test of the presence of a non-monotone relationship also performs poorly.
I develop a method to identify non-monotonic responses that is effective for this model, and then
apply it to preliminary data from Malawi. While the data has is purely observational, and reverse
causality between risk-taking and per-act risks is likely, I do find suggestive evidence of nonmonotone choices, especially among people in rural areas. This implies that research on sexual
behavior and HIV transmission risks should consider the potential of rational fatalism, and look
for possible non-monotonicity in responses.
I begin in Section 2 by looking at the existing body of research on choices in the face of
risk, with a particular emphasis on HIV as well as on models of fatalistic behavior. Section 3 lays
out a general theoretical framework that captures the possibility of rational fatalism, and
discusses the conditions under which we expect fatalistic (as opposed to self-protective)
behavior. In Section 4, I develop an empirical strategy for identifying potential fatalistic behavior
from data on risk-taking and perceived per-act risks. I emphasize that linear models will find
attenuated responses in the face of underlying non-monotonicity, and that standard approaches to
testing for a non-monotonic relationship have important limitations when applied to the rational
fatalism model. Section 5 applies that strategy to preliminary observational data from Malawi’s
Zomba District, and shows that there is suggestive evidence of rational fatalism in that region,
and Section 6 concludes.
2. Background
There is an extensive empirical literature in economics that considers decisionmaking in a
context where actions have a known benefit but carry some risk of a bad outcome (a failure in
the probability terminology). This section gives an overview of that literature, with an emphasis
on what the present work contributes and how it differs from related research. I begin with a
discussion of research on responses to risks in general (Section 2.1), and then turn to a discussion
of the possibility of fatalism as a rational choice (Section 2.2). I then discuss the performance of
standard empirical approaches when used on data that may be non-monotonic due to rational
fatalism (Section 2.3).
2.1.
Measuring responses to risks
Among the earliest studies to examine choices in the face of some per-act risk is Viscusi
(1990), which shows that people who think the risk of acquiring lung cancer from smoking is
higher are much less likely to smoke. Research on responses to other risks has found similar
responses. Using a fixed-effects approach that exploits repeated home sales to reduce omittedvariable bias, Gayer et al. (2002) show that the release of information that cancer risks are lower
than expected leads to increases in home prices, implying a rise in demand for housing. A
positive response of wages to job-related mortality risks is one of the central predictions of the
theory of compensating differentials. Also working with home prices, Linden and Rockoff
(2008) use data from Megan’s Law to show that the arrival of a sex offender in a neighborhood
decreases home prices by about 4 percent, which they attribute to a decline in demand due to the
increased perceived risk of crime. Viscusi (2004) uses variations in pay and risk across
occupations to estimate the statistical value of a human life. He finds a significant and positive
response of wages to occupational mortality risks, consistent with a ceteris paribus reduction in
labor supply in response to the risk of death.
Unprotected sex in the face of potential HIV infection is arguably the most important
risky choice from a public policy perspective. Accordingly, the response of people’s sexual
behavior to risks has received extensive attention from economists, beginning with Philipson and
Posner (1993), who develop a model of “rational epidemics,” wherein infectious diseases are
spread principally by voluntary behavior. This approach led to later work that attempted to
measure the responsiveness of sexual behavior to the risk of HIV. Empirical studies of HIV and
sexual behavior in the United States consistently find strong negative responses. Geoffard and
Philipson (1996) estimate the parameters of a rational epidemic model of HIV using data on
homosexual men from 1980s San Francisco, finding significant differences from a traditional
epidemiological predictions. Based on the same dataset, Auld (2006) uses a structural model of
sexual behavior to show that the rate of sexual partner change dropped rapidly in response to
higher HIV prevalence in the homosexual population of that city, with a 10% rise in the
prevalence decreasing the rate of partner change by 5%. Ahituv et al. (1996) use the National
Longitudinal Survey of Youth to study behavioral responses across the United States as a whole,
and find significant increases in condom use as HIV prevalence rises.
In contrast, there is decidedly less evidence of people responding to the risk of HIV by
curtailing sexual risk-taking in sub-Saharan Africa, where the epidemic is at its worst. A study
of 14 countries in the region using data on HIV prevalence and sexual risk-taking from the
Demographic and Health Surveys (DHS) finds that higher HIV prevalence does decrease risky
sex at several margins, after instrumenting for HIV prevalence using the distance to the origin of
the virus (Oster 2012). However, the reductions are small in magnitude: a doubling of the HIV
infection rate decreases the probability of unprotected sex by just 2 percentage points.
Other research shows similarly limited responses. Also using data from the DHS and
instrumenting for the distance to the origin of the virus, Juhn et al. (2009) estimate separately
both the direct biological effect of HIV infection on fecundity, and the indirect behavioral effect
of higher HIV prevalence through reduced unprotected sex. They find evidence of significant
biological reductions in fecundity but no meaningful change in the fertility rate. Stoneburner and
Low-Beer (2004) argue that with the exception of Uganda, no African country has exhibited
substantial behavioral changes in response to the HIV epidemic. Consistent with this pattern of
limited behavioral change in response to the HIV epidemic, Padian et al. (2010) conduct a
systematic review of RCTs that attempt to reduce HIV transmission, finding that only one in
seven show any impact, either positive or negative. “In fact, the overwhelming majority of
completed RCTs are ‘flat’ – unable to demonstrate either a positive or adverse effect.”
Some recent research in Africa has found more encouraging results. Delavande and
Kohler (2011) use panel data on probabilistic expectations in rural Malawi to study the impact of
beliefs about the HIV transmission rate. Relying on optional HIV testing as a shock to people's
beliefs, they find a significant negative relationship between the perceived risk of HIV
transmission and the decision to have multiple sex partners. Godlonton et al. (2012) run an
experiment in rural Malawi that demonstrates that when people are told that circumcised men
have a relatively lower risk of HIV transmission, circumcised men do not change their sexual
risk-taking but uncircumcised men have significantly less risky sex. A study of Kenyan teenagers
also explored responses to relative risks: Dupas (2011) finds that a program that provided
information on the relative risks of HIV infection by the age of one’s partner prompted large
changes in sexual behavior in that group. Despite these encouraging results, however, the
estimated response of risky sex to per-act risks in Africa is still strikingly smaller than in the
United States. A variety of explanations have been advanced for this difference. . Oster (2012)
argues that the limited response she finds is due in part to lower life expectancy in Africa; if
people expect to live short lives anyway (due to say, malaria), HIV infection may not be as
salient a threat. An alternate view is that condoms and other forms of safer sex are culturally
unacceptable in an African context, thus impeding uptake; for example, in Malawi condom use
in marriage is seen as an accusation or admission of infidelity and is commonly compared to
eating candy with the wrapper still on (Chimbiri 2007). In this paper I argue that a third factor
may also contribute to a limited average response: fatalism. If some people are responding
fatalistically to risks – by increasing their risk-taking when risks rise – then this will cancel out
some of the self-protective responses in the data.
2.2.
Fatalistic responses to risks
Empirical research on responses to risks, whether in Africa or elsewhere, has almost
uniformly assumed that these responses conform to the “self-protection” model in which choices
are a declining linear function of riskiness. In contrast with this is the possibility of the opposite
pattern, in which response are actually positive: as the per-act risk goes up, people take more
risks. This kind of behavior is commonly thought of as an irrational, and referred to as
“fatalism”. The connotation is that it is unreasonable and lies soundly in the realm of behavioral
theories that break with rationality. In the context of HIV, for example, “fatalism” is usually used
to refer to the seemingly irrational pattern of just giving up on avoiding infection due to
hopelessness or a lack of regard for personal safety. This behavior was observed as long ago as
the late 1980s in Uganda: Barnett and Blaikie (1992) discuss men who were aware of the risk of
contracting HIV and simply appeared not to care, asking “Who is never going to die?”
Economists have also focused on non-rational explanations for fatalistic behavior. Leon and
Miguel (2011), for example, demonstrate that travelers in Sierra Leone reveal a lower
willingness to pay for reductions in mortality risk than Americans, despite the fact that they have
comparable incomes and remaining life expectancies; they argue that this may be explained by
the perceived role of fate in determining life outcomes in West African societies.
However, it is not necessarily the case that fatalism must arise from people behaving
irrationally. Fatalistic behavior can actually be perfectly rational: in their early treatise on the
economics of HIV, Philipson and Posner (1993) point out that selfishly rational actors will tend
to demand more risky sex as their probability of already having HIV goes up. In the limit, the
logic is simple: if I already have HIV, I gain no benefit from using a condom and doing so
carries some cost. More generally, O’Donoghue and Rabin (2001) develop a simple model of the
expected cost of risk-taking, showing that for some parameter values the marginal cost of
another risky act actually decreases when the per-act risk rises. While their analysis focuses on
people being unwilling to go below some minimum level of risky choices, in Section 3 I show
that the same logic will apply when people have already engaged in risk-taking in the past and do
not yet know the outcome of that risk-taking. Using a special stepwise functional form for the
benefit of the risky behavior, they show that fatalistic responses can be rational, and note that
along with other potential applications such as drug use, their model may have relevance for the
risk of HIV infection as well. More recently, Sterck (2011) develops a theoretical framework that
uses the same cost function as O’Donoghue and Rabin (2001), but in a dynamic setting. Using
parameter values derived from data on Burundi, he argues that believing the risk of HIV
transmission is high can lead to rises in risky sex.
The idea of rational fatalism can be seen as a specific form of the Mickey Mantle effect,
in which people invest less in their health when their life expectancy is lower for reasons
unrelated to the investment in question (Fang et al. 2007). Fang et al. find that this decline in
health investments is heterogeneous across health behaviors, with smoking being more
responsive than heavy drinking. In a rationally fatalistic model, the specific shifter of life
expectancy is past choices of the very same risk under consideration.
Is rationally fatalistic behavior relevant to the study of responses to risks? It may wall be,
at least in the context of the HIV epidemic in Southern Africa. Qualitative evidence from highprevalence areas in the region suggests that indeed rationally fatalistic behavior is potentially
common there. In research on how rural Malawian men discuss HIV and risky sex, Kaler (2003)
documents many cases in which single “freelancer” men use fatalistic reasoning when thinking
about the disease. One informal conversation on the topic recorded in the Kaler (2003) study
proceeded as follows:
Friend: I don't fear AIDS because I know that I have it already.
Diston: How do you know that you have got AIDS?
Friend: I have malaria and some coughs so I know that I have it.
Diston: Do you use condoms when [sleeping with] these bargirls?
Friend: What for, since I know that I am already infected? (Kaler, 2003)
Kaler describes many cases in which high perceived risks are leading sexually experienced
individuals to fatalism: even though they have never tested positive for HIV, they give up on
safer sex, having decided that they cannot avoid developing AIDS.
2.3.
Measuring the response of risk-taking to per-act risks
The possibility of fatalism as a rational response to increased risks has commonly been
discounted in the literature on estimating risk responses empirically. For example, Viscusi (1990)
uses the one-tailed version of the t-test for his statistical significance calculations, thereby
assuming that responses can only be either negative or zero. In the case of HIV, researchers
typically follow Philipson and Posner (1993) in assuming that the overall prevalence of the virus
is sufficiently low that few if any people believe they are HIV-positive. This justifies the
assumption of a linear risk-response relationship, since for low values of both the number of
risks taken and the per-act risk, the probability of infection is approximately linear in the number
of risks. Given the low prevalence in most US populations, ignoring potential fatalism may be
justifiable in this context. However the prevalence of HIV in Africa is much higher, making this
assumption harder to justify, and as noted above at least some people in Malawi use rationally
fatalistic reasoning to explain their own behavior.
This implies that any empirical study of the response of sexual behavior in Africa to the
risk of HIV prevalence must allow for responses to be potentially non-monotonic. Almost no
existing research on the effect of risks on behavior allows for non-monotone effects. Some
studies have considered heterogeneity in responses, for example by gender and marital status
(Oster 2012) and by level of risk-taking (Auld 2006).3 In an experiment studying the effect of
providing HIV test results to people in Malawi, Thornton (2008) explicitly considers combating
fatalism as one of the mechanisms through which HIV testing could potentially affect sexual
behavior. Selfishly rational people who believe they are HIV positive, and find out they are not
due to a test result, are likely to reduce the amount of risky sex they have. She therefore
3
The Auld (2006) approach comes close to allowing us to directly examine the rational fatalism model laid out in
Section 3, but he explores heterogeneous responses by current level of risk-taking, whereas rational fatalism is
driven by variation in past risks taken.
explicitly looks for heterogeneous effects by HIV status, but finds that only HIV-positive
individuals respond significantly to the test results, and that the effect is small in magnitude. One
study related to HIV and sexual behavior that does not impose linear responses is de Paula et al.
(2009). However, they are examining the impact of beliefs about one’s own current HIV status
on sexual behavior, and so are not directly comparable with the other literature discussed above.
Since almost none of literature on the response of sexual behavior to risks allows for that
response to be non-monotonic, this suggests an additional explanation for the lower estimated
responses to risks in Africa than in the US. If people in Africa are more likely to be fatalistic,
then their positive responses to risks will cancel out some of the negative response on average.
Since a linear regression of risk-taking on per-act risks measures the average slope across the
population, this would tend to attenuate the estimated response.
How can one tell if such a linear regression is likely to be misleading? One common
approach to testing for non-monotonic relationships is to run some regression specifications that
include a quadratic term, which allows for the common technique of examining the statistical
significance of the second-order coefficient to determine whether a relationship is nonmonotonic. However, even this approach may fail to reveal the non-monotone responses typified
by rational fatalism.4 Recent work by Lind and Mehlum (2010) shows that a significant quadratic
term may arise even if the relationship is monotonically negative, and propose a formal
parametric test for a U-shaped relationship. Their technique also has its drawbacks, because it
requires an approximately quadratic functional form for the data. As I discuss in detail in Section
4, if rational fatalism is potentially at work in generating data on responses to risks, careful
analysis is necessary to determine whether the relationship is monotonic.
4
De Paula et al. (2009) also look at heterogeneous effects by quantile of perceived risk, which would perform far
better than the use of a quadratic term in a regression.
3. Theoretical Framework: The Rational Fatalism Model
How can existing approaches to studying behavioral responses to risks be modified in
order to accommodate the possibility of rational fatalism? In this section I will develop a model
of rational fatalism that extends the logic employed in the previous literature in a simple but
powerful way. This model replaces the linear probability function used in most research on risktaking with a risk aggregation function that represents an agent’s belief about the probability of a
failure given the number of risky acts chosen and the perceived riskiness of each act. Using this
model, I will show that a tipping point into fatalistic behavior emerges naturally from a wide
range of possible risk aggregation functions, including the true total probability derived from the
binomial distribution.
I begin this section by laying out the basic form of the model, and the conditions that
must be satisfied for an agent’s chosen number of risky acts to be optimal (Section 3.1). Using a
minimal set of assumptions about the optimization problem, I show the conditions under which
an interior optimum will and will not exist. I demonstrate that a non-zero fixed price for each
risky act (which could also be thought of as a time cost or an emotional cost) will exclude the
possibility that agents just choose as many risky acts as possible. (Section 3.2) I then explore the
model’s general comparative statics, focusing in particular on how the optimal number of risks
taken changes in response to variation in the perceived per-act risk. To explore these
comparative statics, I prove that any risk-aggregation function that satisfies basic conditions will
have a tipping point, above which additional increases in riskiness decrease the marginal cost of
risk-taking. I use this finding to show that there are tipping points in individuals’ behavior as
well: above a certain point, additional risks lead to more risk-taking rather than less (Section
3.3). After showing these tipping points exist, I then discuss two fairly simple heuristics that
people might use to think about how risks add up, and show that despite not being differentiable
they also exhibit the tipping point that is central to my result, implying that the behavior I model
could hold even for unsophisticated agents (Section 3.4). In Section 3.5, I show that the rational
fatalism model implies that risk responses are qualitatively different depending on the domain
being considered: the standard negative response occurs in when individuals face low per-act
risks or have a small amount of previous risk-taking, while individuals facing a combination of
both high perceived risks as well as substantial past risk-taking will tend toward fatalistic
behavior. Finally, I discuss the ways in which this model differs from previous theoretical work,
in particular the fact that it holds for any valid risk aggregation function and that it shows that
fatalistic risk responses can occur for interior solutions, and not just in situations where agents
take the maximum possible number of risks (Section 3.6).
3.1.
Model Basics
In this model, I assume that people weigh the benefits of choosing a level of risk-taking,
, against both any monetary costs as well as the expected cost of a stochastic bad outcome
occurring due to their choice.5 Each risky act carries some perceived per-act risk r (its
“riskiness”) that it will cause the bad outcome to occur.6 The benefit of
by a continuously differentiable benefit function,
, with
risky acts is described
and
so the
marginal benefit of risk-taking is positive with diminishing returns. For simplicity I normalize
. There is some non-probabilistic cost p>0 for each act that might be thought of as a
monetary cost, the cost of the time devoted to the act, or even an emotional cost or guilt, so n
acts cost
5
. The expected cost of the bad outcome is the perceived probability of it occurring,
For the sake of simplicity I will assume that n is continuous, rather than a discrete number of acts. This follows
O’Donoghue and Rabin (2001). The simulations in Section 4 will demonstrate that the qualitative results derived in
this section for continuous n will also hold for discrete-valued n.
6
This perceived risk does not have to equal the true risk; most people overestimate per-act risks across a wide range
of activities from smoking (cf. Viscusi 1990) to unprotected sex (see Section 5 of this paper).
, times its perceived cost, . Given a number of acts and a per-act risk, the true probability can
be computed using the binomial distribution. I reserve this for later discussion, however, and
allow people’s perceived probability of the bad outcome (a “failure”, to use terminology from
probability theory) to be some general (continuously differentiable) risk-aggregation function
. Here r, the perceived per-act risk, is assumed to lie between 0 and 1.
is the
number of previous risks taken for which the outcome has not year been realized, and is weakly
positive. In other words, this model explicitly considers agents for whom some of their risktaking history is still unresolved; for example, people in areas with no accessible HIV testing
who are still in the window period between risky sex they might have had and the point at which
they would develop AIDS symptoms. In order to ensure that
corresponds to well-
formed probabilities, I impose the following basic assumption:
Assumption 1
A.
, , and
B.
if
C.
iff
.
, or both
or
and
.
.
and
iff
.
Probabilities must never be negative or greater than one. The probability of the bad
outcome is zero if either the activity is risk-free or if the individual does not engage in the
activity at all. Taking any risks will lead to the bad outcome occurring with certainty if
the per-act risk is 100%. Likewise, choosing an unbounded number of risky acts will
eventually lead to the bad outcome happening for sure, as long as the act has some nonzero risk associated with it.
This simply imposes that the probabilities produced by the risk-aggregation function start from
zero and rise to one as we increase either the riskiness of an individual act or total risk-taking. In
addition, I assume that P is never decreasing in any of its arguments, and strictly increasing to
begin with. I also impose that additional acts do not raise the total probability of a failure if the
acts are riskless, and that raising the per-act risk does not increase the total probability if no risks
are taken.
Assumption 2
, with
if
and
if
and
;
, with
.
Increasing the per-act risk will never decrease the overall probability of a failure;
likewise raising the number of risky acts chosen or the previous stock of risky acts
always (weakly) increases the total probability of a failure. An initial increase in riskiness
or risk-taking strictly raises the total probability of a failure (as long as total risk taking or
riskiness, respectively, are non-zero). Conversely, increasing the number of riskless acts
chosen, or the riskiness of a risky act that is not chosen, does not affect the total
probability of the bad outcome occurring.
Taken together, these assumptions simply state that people must have a general understanding of
risks, so that they understand that probabilities never fall outside of a 0-100% range and that
additional risk taking is bad, up to the limit imposed by maximal probability of 1. They
immediately lead to an initial lemma:
Lemma 1
A.
B.
The effect of increasing the per-act risk on the total probability of the bad outcome is zero
if the per-act risk is one. The effect of the number of risks chosen or the existing stock of
risks approaches zero as the sum of those variables approaches infinity.
Lemma 1A holds trivially if n+m = 0, and likewise for Lemma 1B if r = 0. To see why they must
hold in the non-trivial case, assume they do not hold. Then P is unbounded. But by assumption P
is bounded above at 1, so we have a contradiction. Therefore Lemma 1 must hold in general.
Note that because P is continuously differentiable, Lemma 1A also implies that
. Conceptually, Lemma 1 says that increasing the riskiness of the act high
enough, or taking a sufficient number of risks, pushes the likelihood of the bad outcome to
100%. Once it has reached that point, additional risk-taking does not increase the probability any
further.
The agent’s optimization problem is therefore the following:
By the assumption that n is continuous, the maximand U(n; m; p; c; r) is the sum of continuously
differentiable functions and therefore continuously differentiable itself.
3.2.
Conditions for a Non-trivial Optimum
Since the object of interest in this analysis is the response of n to changes in r, one concern is
whether the solutions to the problem are purely trivial, with fatalism representing jumps to some
maximal level of risk taking. In this section I show that a non-stochastic price for each risky act
guarantees that we will find interior solutions unless risk-taking is not beneficial at all at the
agent chooses to take zero risky acts.
The above optimization problem admits many conceivable forms for the benefit function
B(n), including some that make little intuitive sense. To restrict the discussion to reasonable
benefit functions, I assume that at some point taking additional risks yields no utility gains.
Assumption 3
. As the number of risky acts chosen approaches infinity, the
marginal benefit from an additional risky act approaches zero.7
Under Assumptions 1-4 the problem still admits trivial corner solutions where n*=0. In order to
discuss interior solutions, I impose one additional assumption.
Assumption 4
. Risk-taking is desirable: given the stochastic and nonstochastic costs of risky acts, agents will choose a non-zero level of risk-taking.
Empirically, Assumption 4 seems reasonable in many applications: for example, a large
proportion of people have had unprotected sex at some point in their lives. If the converse of
Assumption 4 holds, agents will (weakly) prefer to set n=0, and the problem becomes trivial.
Given Assumption 4, however, the model allows a fairly powerful statement to be made:
Proposition 1
if p>0.
An interior solution to the optimization problem described in (1) is guaranteed whenever
the non-stochastic cost (e.g. the price) of a risky act is not zero.
Proposition 1 follows because
Assumption 3 and Assumption 4, and because
7
by
. This, along with
This assumption is substantively identical to the sixth Inada condition used to guarantee the stability of
neoclassical growth models.
the continuity of U, allows me to use the extreme value theorem to state that U has at least one
optimum where
, as long as p>0.
This eliminates the possibility of trivial corner solutions, in which the optimal response
to an increase in risk is always to either choose
or
(where
is some upper
bound on n that prevents it from reaching infinity). Conversely, if p=0, then given the other
conditions the optimal n* will be arbitrarily large: U is initially upward-sloping and its slope
never becomes negative, so additional risk-taking is always weakly beneficial. The other
analyses of optimal risk-taking that admit fatalistic responses (Sterck 2011; O’Donoghue and
Rabin 2001) have shown fatalism only as a corner case, in which the individual pursues the
maximum feasible level of risk-taking. While corner solutions are a fairly intuitive response –
they align with the reasoning that once one is doomed, one might as well indulge as much as
possible – they are not empirically relevant: there is little evidence that individuals ever truly
seek out the maximal level of available risk-taking. Moreover, the reason for this is exactly that
given above – taking additional risky acts, whether that means smoking more or seeking out sex
partners, carries pecuniary costs so that there are tradeoffs with out goods an individual might
desire.
Proposition 1 guarantees that the optimum will be non-trivial if the price of risk-taking is
positive. It does not rule out interior optima in other cases; O’Donoghue and Rabin do have an
interior optimum in their model’s non-fatalistic case, for example. However, it is a fairly
intuitive economic result: people are constrained by resources from pursuing the high extreme in
risk-taking. The results that follow will hold for the commonly-seen case in which people pursue
some intermediate level of risk-taking irrespective of their perception of the per-act risk r. In the
following section I will show that fatalism can occur even for these interior solutions.
3.3.
Comparative Statics
Given that an interior solution exists, the optimal choice of n,
, must satisfy the first-order
condition:
where
and
are the derivatives with respect to
of
and
.
also needs to satisfy the second-order condition that the utility function be concave at that point.
It is not possible to solve for
and
without additional assumptions about the functional form of
, and there will be no closed-form solution for
for most possible
functional forms of the benefit and risk aggregation functions.8
Despite the intractability, in general, of the precise optimum
the response of
, it is possible to explore
to changes in other variables without solving for the optimum analytically by
employing the implicit function theorem (IFT). In particular, there is a function
, and therefore the IFT allows us to compute the
comparative static for changes in
in response to changes in , as well as the way that response
changes when varies.9
For comparative static I the denominator is
. This is precisely the left-
hand side of the second-order condition (1.4), and is therefore weakly negative. It is not possible
8
In particular, if I impose that P be the true risk-aggregation function derived from the binomial distribution and
that B have a logarithmic form, then no closed-form solutions for n* are possible.
9
In Appendix A I derive additional comparative statics with respect to p and c.
to rule out the possibility that the second-order condition is exactly zero in general, so the
optimum occurs at a flat region of the utility function. This would mean that neither comparative
static would exist, and the model would predict neither self-protective nor fatalistic responses.
Since such flat regions of the utility function seem unlikely, I will assume the second-order
condition holds strictly.10 The denominator of comparative static II is just the square of the same
expression and therefore strictly positive. Its numerator is the product of
;
is negative as long as
. As a result, comparative statics I and II
will have the same sign, which is opposite to the sign of
Before deriving the sign of
and
.
in general, I first consider the specific case
where agents use the true risk-aggregation function
. This function comes from the
binomial distribution, and can be constructed as follows. Given a stock of past risk-taking
,a
choice of the number of additional risks to take , and the per-act risk , the probability of a
failure after one act is ; after two acts,
; and after three,
.
The probability of avoiding a failure after three acts is
Likewise the probability of avoiding a failure after
chance of a failure having occurred by after
.
acts is
. Therefore the
acts is:
The relevant second derivative from Comparative Statics I and II for this functional form is then
Interestingly, the expression for
, is weakly positive, but
10
may be positive or negative: the first factor,
is either greater or less than zero
Note that even in the limit as the denominator approaches zero all the results in this section will go through.
depending on the values of ,
, and . It is possible to solve the value of that determines the
sign of the second term.
This result holds even if we assume the agent is at
. Then the threshold value of becomes
. This threshold depends on the level of past and current risk-taking. Using the true riskaggregation function
, as
approaches zero, the value of the per-act risk
which leads to fatalism approaches . As
becomes sufficiently large, the critical value of
can become arbitrarily close to zero. Imagine a decisionmaker who has a long history of taking
chances. If he believes the per-act risk is low, and he finds out it is quite high, then he will be
nearly-certain he is already doomed. Thus the cost of taking one more chance goes down
substantially.
The above proof of the existence of a tipping point for the true risk-aggregation function
is due to O’Donoghue and Rabin (2000). However, whereas they consider only the
true risk-aggregation function
, it is possible to show that the same qualitative result
holds for any credible risk-aggregation function
. To prove this I first show that the
cross-partial is initially positive:
Lemma 2
and
. The cross-partial derivative of the total probability
of a failure with respect to riskiness and number of risky acts chosen is positive when the
number of risky acts
This follows straightforwardly from Assumption 2:
is zero if n and m are both zero and
positive if at least one of n or m is positive, so the initial cross-partial is positive; a symmetric
analysis holds for
.
Given Lemma 2, we can therefore prove that this cross-partial changes sign in general,
for all functions P that meet the conditions laid out above.
Proposition 2
with
if
s.t.
if
and
. For sufficiently high values of the per-act risk, increasing the per-act risk
actually diminishes the marginal impact of additional risk-taking.
To prove this, I consider two functions
with
and
. By Lemma 2,
Assumption 1 also gives us
and
Then these two continuous functions begin at the same value and converge to the same value, but
the slope of
is initially higher than that of
which the slope of
that of
exceeds that of
. This implies that there must be some point at
. If not then the value of
can never catch up with
.
Formally, consider a point
sufficiently close to zero that
, which
must be possible because the second function’s slope is initially higher. Then the average slopes
of the two functions between
and some higher point
are
and
,
so the ratio of the two slopes is
ratio approaches
. Taking the limit as
approaches infinity, this
, which is greater than one. This implies that there is a point above
which the average slope of
exceeds that of
; therefore, by the extreme value theorem
there must be a point where the instantaneous slope
. Figure 1 illustrates why this
must be the case. The solid blue line gives the known initial shape of
red line for
and likewise the solid
. Above the breakpoint at infinity, the two-colored line shows their common
value of 1. The dashed lines show the implied average slopes in the intermediate region; because
is initially shallower, it must be steeper on average over this range.
This ensures that a tipping point must exist in any valid risk-aggregation function
. It does not rule out multiple tipping points, which could conceivably arise from
sophisticated curvature of the risk-aggregation function, but the number of such tipping points
must be odd. I will ignore the possibility of multiple tipping points, motivated by the fact that for
the true risk-aggregation function
the cross-partial derivative changes sign only once.
Because the impact of riskiness on the marginal cost of risk-taking has a tipping point,
responses to riskiness will have tipping points as well. Formally we have the following two
comparative statics:
Proposition 3
if
, and
if
(Comparative Static I)
There exists a threshold value for the per-act risk, , at which rational behavior switches
from self-protection (negative responses to risks) to fatalism (positive responses).
Proposition 4
if
, and
if
(Comparative Static II)
Increasing the cost of a failure will increase the magnitude of the responsiveness of risktaking to per-act risks, making it more negative when agents are self-protective and more
positive when they are fatalistic.
Comparative Static I is my central result, which is that there is a tipping point not just in the
marginal cost of risk-taking (as O’Donoghue and Rabin (2001) show for the true risk aggregation
function
) but also in the optimal choice of n. Comparative Static II is an extension
of the finding of Oster (2012), who shows develops a model of rational responses to HIV risks to
show that agents will respond more to the per-act risk of HIV infection when the costs are
higher, e.g. when non-HIV mortality in their area is lower. In this model, a similar result holds,
but only for self-protective agents - those who face risks below . Above , higher costs will tend
to encourage more fatalism.11
Thus the model implies that under fairly broad and plausible assumptions, rationally
fatalistic responses will occur for sufficiently high combinations of the per-act risk r and the past
stock of risk-taking
. While somewhat surprising, this result is consistent with the intuitive
notion, expressed by the men quoted in Kaler (2003), that having made enough mistakes in the
past can doom you to HIV infection, no matter what you do to protect yourself now. If HIV is
unavoidable, attempting to mitigate your own risk of contracting it is useless.
This applies to any situation where there is a risk from each act chosen, and the outcome
goes unrealized for an extended period of time. Consider an individual who knows he has
engaged in some risk-taking in the past in the past. If his accumulated stock of risky acts, and his
perceived per-act risk, are sufficiently high, then learning that the per-act risk is lower than he
had thought can actually lead him to take fewer risks.
11
Another result from Oster (2012) is that all else equal higher costs will lead to less risk-taking. This also holds for
my theoretical framework. See Appendix A for a derivation.
3.4.
Other Risk Aggregation Functions
The results above hold for a broad range of possible risk-aggregation functions that
satisfy a minimal set of conditions, including the true function
. However, the central
point – that behavior will swing from self-protection to fatalism for sufficiently high values of
– is driven by a tipping point in impact of riskiness on the marginal cost of riskiness. This kind of
tipping point may exist even for far simpler heuristic risk aggregation functions that agents might
employ, in particular ones that are not differentiable and therefore not amenable to the
techniques employed in Sections 3.1-3.3. I therefore cannot prove that an interior optimum exists
for such functions, or that optimal risk-taking will switch from self-protective to fatalistic.
Instead, I demonstrate that two very simple heuristic risk aggregation functions exhibit this
tipping point phenomenon.
It might seem that this sort of tipping point is an esoteric mathematical feature of how
probabilities add up that people cannot be expected to understand, but in fact such tipping points
arise naturally and in a comprehensible way from some fairly basic heuristic risk aggregation
functions. Consider the simple linear function used in much of the literature, where the
assumption is made that levels of risk-taking and per-act risks are sufficiently low that the
probability never approaches 1. Agents might use a similar rule, but also assume that if the
probability does reach 1 then it stays there forever:
This function might appear to lack a tipping point as defined in Proposition 2, but the same basic
behavior actually obtains. Consider two agents, one who believes r = 0 and one who believes
. If both agents increase their risk belief by
, the marginal cost of
increasing n rises for the first agent and falls for the second. Any shift in r that increases its value
to at least
will induce fatalism, with further increases having no additional effect on
behavior.
An even simpler alternative is the "exposed enough" heuristic discussed in MacGregor et
al. (1999), wherein people think they are totally safe as long as they stay below some level of
activity, and then doomed with certainty if they take too many risks:
In this case only the act that shifts an agent over the threshold,
, has a direct
marginal cost – all other acts carry no cost at all. Increasing r will in general push agents closer
to the margin of being “sufficiently exposed” to suffer harm, thus carrying an indirect marginal
cost. But if r reaches or crosses
, the agent believes he or she is already sure to suffer
the bad outcome and hence this decreases the marginal cost of an additional act to zero.
Despite not being amenable to analysis through standard optimization techniques, these
functions both exhibit the crucial tipping-point phenomenon, implying that the results of Section
3.3 could hold even if agents handle the addition of risks in a very simple and heuristic way.
3.5.
Domains of Self-Protection and Fatalism
Comparative Statics I and II identify a threshold value of (that depends on
+
)
above which agents will become fatalistic, and increased per-act risks will lead to more risktaking rather than less. That is, the rational fatalism model implies that risk responses will not be
monotonic, but will shift from negative to positive when reaches . This differs sharply from
much of the empirical literature on risks, in which the expected cost of infection, is linear in the
per-act risk:
. Under the linear model, risk responses will be
monotonic and negative; there is no tipping point. In other words, the rational fatalism model and
the linear model give qualitatively identical predictions for any behavior that occurs below the
tipping point .
As a result, the rational fatalism model implies that we should expect to see three distinct
patterns depending on the domain in which it is applied. In settings that are either low-risk or
low-activity, it predicts negative responses consistent with the conventional linear model. In
settings that are both high-risk and high-activity, it predicts positive, fatalistic responses. Finally,
in heterogeneous settings, we expect to find a roughly U-shaped response, with some amount of
self-protection as well as some fatalism.
The first domain includes the Kenyan teenagers studied by Dupas (2011) - they are
sexually inexperienced, and therefore even fairly high perceived per-act risks still cause them to
behave in a self-protective fashion. The second domain is exactly that discussed in Kaler (2003) men with extensive sexual experience who perceive high per-act HIV risks end up rationally
fatalistic; they are doomed no matter what, so why bother using condoms. The third domain is
the most interesting, and most comprehensive: most populations include both people who think
they have some past exposure and those who think they have never taken a risk. In the majority
of cases I expect observed patterns of risk responses to include both self-protective and fatalistic
behavior.
3.6.
Comparison with Existing Theoretical Work
As discussed in Section 2.2 above, previous theoretical work has studied fatalism as a
potentially rational response to risks, with both O’Donoghue and Rabin (2001) and Sterck (2011)
developing formal mathematical models that predict fatalistic responses at some margins. The
rational fatalism model outlined in the above sections improves on those models in several
valuable ways.
First, previous research has only been able to demonstrate fatalistic behavior as a corner
solution, where agents either pursue a low, self-protective level of risk-taking or jump to a point
where they fatalistically take as many risks as possible. Sterck (2011) shows that without random
mistake or a condom failure, people will choose either no risk-taking or maximal risk-taking and
stay there forever, while O’Donoghue and Rabin use a contrived utility function to show that
agents will sometimes react to increased per-act risks by taking as many risks as they possibly
can. While O’Donoghue and Rabin do discuss the implications of their results for interior
solutions, they do not demonstrate that interior solutions actually exist when responses are
fatalistic, as I did in Section 3.2. In contrast the results of Section 3.3 are explicitly conditioned
on interior solutions; the predictions hold specifically for values of
that are not at a maximum
or minimum allowed value. This is guaranteed to be possible because individual behavior is
constrained by an implicit budget constraint; every risky act carries a cost p. In Section 4 I will
show that a wide range of interior solutions exists for plausible parameter values.
Second, both Sterck (2011) and O’Donoghue and Rabin (2001) combine the number of
risky acts being chosen and the unavoidable minimum number of acts into a single variable, and
neither separates out potential past mistakes from current decisionmaking (although Sterck
portends this line of reasoning when discussing mistakes). The rational fatalism model draws an
explicit separation between the unavoidable number of risky acts,
, and the current number of
acts being chosen, n. It also focuses on the case where the m unavoidable acts probably occurred
in the past, but that the outcome (malaria infection, lung cancer, HIV transmission) has not yet
been revealed.
Third, both previous papers rely on specific, simple benefit functions for the risky acts
that potentially raise questions about the robustness of the results to other functional forms,
whereas the model laid out in this section is robust to any concave, increasing benefit function
with sufficiently strongly diminishing returns.
Finally, the previous theoretical work has used the true risk aggregation function to show
interesting effects of varying per-act risks on choices of risky behavior. This is a valuable line of
inquiry, but extensive research has demonstrated that in addition to overestimating per-act risks,
individuals often do not understand how those risks compound into the total probability of a
failure. O’Donoghue and Rabin (2001) note that evidence on HIV transmission beliefs indicates
that the risk aggregation functions individuals employ tend to be far more concave than the true
function. The rational fatalism model shows that similar non-monotonic behavior can be found
for any valid risk aggregation function that satisfies very simple conditions. In addition, I
illustrate similar tipping point behavior even for very simple, non-differentiable risk aggregation
functions that people might realistically use even if they know very little math.
4. Empirical Approach
Based Comparative Static I above, any analysis of data on risk-taking must consider the
possibility of a non-monotonic response to the per-act risk. In this section I lay out the regression
specifications commonly employed in the literature on risk-taking (Section 4.1). I then use the
model from Section 3 generate simulated data (Section 4.2) in order to examine the effectiveness
of the basic approach. I show that under plausible parameter values, a squared term in per-act
risks can be statistically insignificant even when the underlying model has a tipping point. I also
find that in addition to missing the fact that the relationship has a U shape, running simple linear
regressions will tend to attenuate the magnitude of the measured risk response (Section 4.3). I
then describe two methods that may be more successful – the U-shape test of Lind and Mehlum
(2010) and a semi-parametric technique that lets the user look for non-monotonicity directly
(Section 4.4). I find that the Lind and Mehlum method is not particularly successful unless the
functional form of the relationship is close to quadratic, but that the semi-parametric approach
has promise. I propose a combined method, which uses the Lind and Mehlum test but checks that
the relationship is close to quadratic semi-parametrically. This substantially out-performs the
conventional approaches from the literature: a first-order relationship between risk-taking and
per-act risks can show a significant relationship even when the underlying behavior is nonmonotone, and a second-order term in risks can be insignificant even when non-monotonicity
exists. Finally, in Section 4.5, I move to a discussion of several threats to any attempt to use
observational data to identify the relationship perceived per-act risks and risk-taking, and
solutions to those problems.
4.1.
Regression specification
The standard approach used in the literature is to run regressions of the form
where
is a vector of controls. This is fine so long at the relationship between and
is
monotonic, but as discussed in Section 3 above there is reason to believe it may not be. While
relatively little research has considered the possibility of a non-linear relationship between and
, a typical strategy for doing so is to add a squared term to the above regression (cf. the De
Paula et al. 2009 study of the relationship between people’s own perceived HIV status and risky
sex). This yields the following specification.
One method for determining whether an estimated relationship is non-monotone is to
examine the statistical significance of the quadratic term, r2.
4.2.
Simulated data
To explore the effectiveness of these regression specifications, I construct simulated data
using the model described in Section. Specifically, I draw a pseudorandom sample of 3000
individual-level observations, comparable to the size of many field surveys on sexual behavior in
Africa, with the following parameter value distributions. I set the past level of risk-taking m to 2
acts for all individuals. I then set the mean of t to the threshold value for declining marginal
, and SD(r) arbitrarily to 0.2.12 I use a logarithmic utility function
costs,
, setting
for all observations, and impose the true risk-aggregation function,
. I set the cost of a failure to 1 for all individuals. I
choose the mean of p to be 0.15 and its standard deviation to be 0.03 arbitrarily. Using these
values, I engage in a grid search over possible integer values of n ranging from 0 to some upper
12
Note that this is only the tipping point if agents choose zero risky acts (n=0). This is tautologically never observed
since if n=0 no relationship is present. Since agents will in general choose some level of risk-taking greater than
zero, the observed tipping point in the data will differ for each individual, and will be smaller than 0.3935.
limit (which was selected randomly to lie from 15 to 21 for each individual) in order to find the
highest total utility value. The values picked above generate almost entirely interior solutions:
none of the simulated data points had n* = 0, and only three were at their individual-specific limit
for n.
4.3.
Parametric regression results
The first two columns of Table 1 show the simple linear model and a model with both a
linear and a quadratic term respectively, both without any regression controls. Both
specifications find a significant positive first-order relationship between risk-taking and per-act
risks. The estimated quadratic term in specification 2 is positive but statistically insignificant.
Together with the first-order term this would imply a convex parabola with a minimum below
zero. The only relevant potential control is the cost per risky act, p. Controlling for the per-act
cost does not substantially affect our coefficient estimates, but it does improve the precision with
which they are estimated. While the estimated sign of the first-order term is uniformly positive,
implying a positive average relationship between risks and costs, this is simply the result of the
specific parameter values chosen. Other simulations (not shown) give a negative first-order term
but results that are qualitatively similar to what follows.
The results of this analysis are revealing – although this data was simulated using a
model with a built-in tipping point, an approach that looks at the significance of the second-order
risk term would conclude that the relationship is probably monotonic.
Another notable aspect of these regressions can be seen by comparing the coefficient on
the first-order term in Columns 1-4 to that in Column 5; as I shall discuss in more detail later,
Column 5 does a better job of matching the shape of the curved part of the function. Irrespective
of whether a squared term is included, these regressions estimate first-order coefficients that are
far less than 20% of the magnitude of the true coefficient, and of the opposite sign. This implies
that standard regression specifications may yield misleading results when applied to data where
rational fatalism is possible.
4.4.
Identifying U-shaped relationships
To address this shortcoming, I first explore the formal parametric test for U-shaped
relationships proposed by Lind and Mehlum (2010). They argue that a significant quadratic term
is necessary, but not sufficient, for a non-monotone relationship. The logic is simple: if a
relationship is monotonic, but concave, the best fit to the data will in general involve a
significant second-order coefficient. But the turning point in the predicted parabola might be far
outside the data range. Thus it is necessary to formally test whether the fitted values involve both
a statistically significant upward-sloping and downward-sloping component. Table 1 includes the
p-values for this test in Columns 2 and 4, which in both cases are extremely close to 1.13 For this
dataset, the Lind-Mehlum test concurs with the simpler method of looking at the coefficient on
the squared term, and indicates that there is almost surely no non-monotonicity in the
relationship between n and r. This is unsurprising – the squared coefficient in one case does not
meet the necessary condition of being statistically significant, and in the other just barely crosses
that threshold.
Since the Lind-Mehlum method still relies on the estimated coefficients from fitting a
second-order polynomial to the data, one potential concern is that the model fit is sufficiently
poor that we are drawing false inferences. In many cases the solution would be to derive a
superior regression model based on what is known about the data generating process. However,
as discussed in Section 3, the utility maximization that generated this data has no closed-form
13
Tests conducted using the utest function in Stata, written by Lind and Mehlum. Technically both rejections are
trivial, since the estimated minimum point of the parabola would have been outside the data range regardless.
solution so we would be left with a fairly complex challenge of numerical optimization, that
might yield a wide variety of solutions depending on the parameter values chosen. A natural
approach to this issue is to estimate the relationship non-parametrically, in order to avoid any
issues of model selection. There are two general methods for attempting this.
The first is to simple do a scatterplot of the values of the two variables, and possible fit a
non-parametric curve estimate to that data. Figure 2 presents a simple scatterplot (with no curve
fit to it) of the number of risky acts against the per-act risk. While a possible U-shape is evident,
the bivariate relationship is fairly noisy.
An alternative is to use a semi-parametric approach that relies on parametric regression to
reduce the noise and omitted variable bias induced by other variables. I do this by using the
partially linear model estimator as developed by Yatchew (1997) and implemented by Lokshin
(2006) to plot the conditional relationship of n and r, holding p constant. The results are shown
in Figure 3. The plot also includes a plot of the LOWESS-estimated non-parametric curve, but
the non-monotone relationship is clear without it.14
These results imply that the Lind and Mehlum approach was indeed hampered by poor
model fit; the relationship, while non-monotonic, is also clearly not a parabola. As an additional
check, I repeat the same regression as in Column 4 of Table 1, but apply it to just the portion of
the data between r = 0 and r = 0.4. The results are shown in Column 5 of the same table. Now
the linear and quadratic terms are large and statistically significant, and the sign of the linear
term is negative. The Lind and Mehlum test rejects monotonicity at beyond the 0.001 level.
Given the limitations of the Lind and Mehlum test for analyzing this model, it is sensible
to look for a semi-parametric equivalent. For bivariate non-parametric analysis, options do exist.
14
The lowest observed value of n is 3, implying a tipping point of 0.1813 or less. This is roughly consistent with the
observed values.
One example is Bowman et al. (1998), who develop a formal test for the monotonicity of a nonparametric locally linear regression function. They rely on the use of a critical bandwidth that
flips the estimated relationship from monotonic to non-monotonic, and use it to construct This
has substantial promise for the analysis of risk-response relationships, but unfortunately there is
currently no equivalent for partially linear regressions. That limits the direct applicability of their
method, since confounding omitted variables are likely to substantially bias the observed
relationship between n and r. Adapting the Bowman et al. approach to partially linear regressions
is beyond the scope of this paper, but will be a focus of future work.
Lacking a formal semi-parametric test for non-monotonicity, I will rely on a strategy that
combines the Lind and Mehlum test and partially linear regressions. My formal test for nonmonotonicity will use the Lind and Mehlum approach, but I will confirm that the relationship is
approximately quadratic using semi-parametric regressions. If it is not, but possible nonmonotonicity is evident, I will use the data truncation method described above, applying the Lind
and Mehlum test to the portion of the data that is potentially non-monotone.
The preceding analysis demonstrates that the econometric methods commonly used in the
literature perform poorly when data is generated in a manner consistent with the rational fatalism
model of Section 3. The standard regression specifications for measuring risk-taking as a
function of per-act risks will tend to identify a slope that is too small in magnitude and
potentially of the wrong sign. Moreover, if a regression includes both linear and quadratic terms
in risks, a statistically significant squared term is neither necessary nor sufficient for nonmonotonicity. Correspondingly, the formal parametric test for non-monotonicity from Lind and
Mehlum (2010) can fail to identify the fact that the data has a tipping point if the model is
sufficiently mis-specified. In contrast, the approach outlined above – using the Lind-Mehlum test
along with a semi-parametric approach to check for the model fit – appears to perform much
better. A semi-parametric approach is also advisable for confirming that the estimated regression
coefficients are sensible.
4.5.
Threats to identification
Even if an appropriate approach to measuring potential non-monotonicity is adopted,
using observational data on the relationship between per-act risks and risk-taking can lead to
false inferences for three reasons: the data is affected by two different kinds of reverse causality,
which may bias the results in opposite directions, and also subject to substantial measurement
error, which will attenuate measured effects toward zero.
The first reverse causality issue has to do with cases where the per-act risk is actually the
result of previous risk-taking, which may be correlated with current levels of risky choices. This
is most notably the case in the literature on HIV and sexual risk-taking: the per-act risk depends
on the prevalence of the virus, which in turn depends on how much risky sex people have. Other
infectious diseases share this property - malaria, for example, is likely to be more common in
places where mosquito net use is lower. For this sort of risk, simple cross-sectional comparisons
would find high risk-taking in high-prevalence places, and draw a false inference. This issue will
tend to bias estimates toward positive infinity.
Another sort of reverse causality occurs when individuals form their beliefs about the
risks of various acts through experience with risk-taking. To remain with the example of HIV,
suppose a decisionmaker believes that she will quickly show symptoms after contracting the
virus. After engaging in a sufficient quantity of risky sex over time, and not developing
symptoms, her perceived per-act risk would decline, generating a mechanical, negative
relationship between risk-taking and per-act risks. This reverse causality problem will have the
opposite effect from the first one, tending to bias estimates toward negative infinity. It is possible
that some belief-formation processes might generate positive biases as well.
Separate from reverse causality is the problem of poorly-measured data on sexual risktaking and risk perceptions. Data on sexual behavior may be even more susceptible to recall
errors and biases than other behaviors studied using survey data, and also carries the risk of
“social acceptability bias”, where respondents say what they think the enumerator wants to hear.
Active research in survey methodology has focused on the development of life-history and diarybased methods, in order to reduce these sorts of measurement errors (Luke et al. 2009). Data on
risk perceptions present even more severe measurement problems. People with limited math
backgrounds may have trouble understanding questions about probabilistic expectations, and this
issue is likely to be exacerbated in developing-country settings (Attanasio 2009). Encouragingly,
recent work conducted in Malawi by Delavande and Kohler (2009) has shown that, through
carefully designed questions, it is possible to elicit meaningful beliefs about probabilities even
when individuals have very limited formal education.
Errors in both reported sexual behaviors and risk beliefs are likely to take many forms,
and will often be effectively random. Randomly mismeasured sexual behavior will tend to
decrease the precision of the estimated relationship between n and X, while random measurement
errors in beliefs will attenuate any estimated relationship, biasing estimates toward zero. There is
one particular kind of measurement error in risks that may not be random and is worth observing,
however. A certain fraction of individuals in all contexts will answer any probabilistic question
with “50%”, indicating not that they think it is a 50-50 chance but that they simply do not know
(Lillard and Willis 2001). This is true even if questions are posed deterministically, as in “what
share of your friends owns an iPod”. One crude way of estimating the measurement error in a
probabilistic belief variable is to look at the extent to which there is an anomalously high “50%”
response rate.
One factor that is likely to increase measurement error in probabilistic beliefs is the use
of true probabilities as proxies for beliefs. This has been employed in research on HIV and risktaking in Africa (Juhn et al. 2009, Oster 2012) as well as in the United States (Ahituv et al. 1996,
Auld 2006). Since many individuals will be misinformed, this issue will tend to exacerbate the
attenuation bias problem described above. This kind of measurement error also raises the
question of what structural relationship is being estimated. Individuals are less likely to be aware
of the actual probabilities than policymakers, who may intervene to promote reductions in risktaking. Thus a significant estimated response may not reflect actual behavioral responses by
individual people.
The first two identification threats can best be resolved by instrumental variables
approaches. An exogenous shock to beliefs will allow the causal effect of changes in those
beliefs on risk-taking to be measured. For example, Oster (2012) and Juhn et al. (2009) use the
distance from the origin of the human immunodeficiency virus as an instrument for its
prevalence. To study individual risk beliefs, the optimal instrument would actually be some kind
of quasi-random information campaign, or an outright experiment that provides information
about risks.
Resolving the measurement error issue is somewhat harder. A simple first step is to rely
on individual probabilistic beliefs rather than the true per-act risks, since the two may differ
substantially. Much recent work in HIV and risk beliefs in Africa has begun to do this.
(Godlonton and Thornton 2011, Delavande and Kohler 2011, de Paula et al. 2008). Beyond that,
careful questionnaire design, and variables that can serve as cross-checks within a survey, are
useful tools. Question design should focus on minimizing the “50%” response rate (within
reasonable bounds), for example by asking a followup question about whether respondents are
just unsure (Lillard and Willis 2001). Another approach is to test the sensitivity of the results to
excluding respondents who answer “50%” to the relevant question.
5. Preliminary Results
In this section I apply the empirical strategy laid out in Section 4 to a preliminary
observational dataset on sexual behavior and perceived HIV risks in Malawi. Section 5.1
describes the data used, detailing the construction of variables to capture the number of risks
taken, n, and the perceived per-act risk, r. In Section 5.2 I conduct a basic regression analysis of
the form described in Section 4.1, and show that the standard approach of examining the sign of
a squared term in risks implies at best fairly fragile evidence for a non-monotonic relationship.
Section 5.3 applies the method for testing for a U-shaped relationship described in Section 4.4,
finding that the evidence for a U shape is actually fairly robust. Based on this I argue that the
evidence is broadly consistent with possible fatalism in rural areas on Malawi’s Southern
District, which is in line with the findings of previous qualitative research. In Section 5.4 I
examine the plausibility of fatalism in this population in two different ways: first, I compute the
number of people who would be expected to tip into fatalism based on the true risk-aggregation
function ; second, I explore just the subset of individuals who think their sex partners are HIVpositive. Both explorations suggest that fatalism is plausible for this population. Section 5.5
discusses some important limitations of this analysis and argues that my results are likely to be
smaller in magnitude than the true relationship, and may actually understate the extent of
fatalism in this population.
5.1.
Data
I use data collected in the Zomba District of Malawi’s Southern Region. Malawi is in the
midst of a severe HIV epidemic, with an infection rate of nearly 12%. Its experience has been
typical of countries in Southern Africa in that its high infection rate has been sustained for a long
period, and has declined only slightly from its peak (National AIDS Commission, 2003). HIV is
the leading cause of non-infant mortality in the country, and is responsible for one in every three
adult deaths (PEPFAR 2008).
The data form the peri-urban and rural survey components of the Situational Analysis of
Sexual Behaviors and Alternative Safer Sex Strategies which I helped run as part of a
collaboration with PIs Professor Rebecca Thornton of the University of Michigan and Dr. Jobiba
Chinkhumba of the University of Malawi College of Medicine, and co-investigators Sallie Foley,
LMSW, of the University of Michigan and Alinafe Chibwana, MA, of Catholic Relief Services
(Kerwin et al. 2011). We conducted the surveys in July of 2011 in areas adjoining a major
trading post in Zomba District. The survey enumerators were hired near the survey sites, and all
surveys were conducted in Chichewa, the national language, with female enumerators
conducting all interviews with female respondents and likewise for males.
We drew a geographic representative sample of 447 sexually active adults (age 18-49) in
the area based on the locations of households, with selection rules for picking participants within
each household. Our sampling strategy oversampled urban areas and unmarried individuals, so
we constructed sample weights to match the population proportions by locale and marital status
to the 1998 Malawi census. All reported statistics use these sample weights unless otherwise
noted.
Summary statistics for the sample’s demographics are given in Table 2, below. The
sample is 5% peri-urban, meaning people that live around the major trading post, and about 60%
literate. The average age is 29 and people have completed five and half years of school on
average. Nearly 90% of the weighted sample is married. The sample is also almost 60% female;
anecdotally, people in the region reported that men were more likely to migrate away for work.
Respondents have 3 children on average and want just over one more. The sample is 80%
Christian and 20% Muslim, and is dominated by the Lomwe ethnic group at 55%. Other large
ethnic groups include the Yao (22%) and Chewa (16%).
Table 3 summarizes the data on the perceived risks and costs of HIV for our respondents,
as well as their self-reported sexual behavior. The data contains both a measure of perceived past
exposure to HIV (the number of a respondent’s past partners that, looking back, they now think
were HIV-positive at the time) and of their potential future exposure (the share of attractive
people in the region who the respondent thinks have HIV). The former measure appears to be
more or less uncorrelated with current sexual behavior, so I rely on the latter. Respondents report
that they think that 49% of attractive people, on average, are HIV-positive. The survey also
asked respondents how many out of 100 people who had sex with an HIV-positive person last
night would contract the virus. Over 50% of respondents answered that 100% would become
infected, and the mean response was 85%. I multiply these two variables to construct a measure
of the perceived per-act risk from unprotected sex with a possible sex partner, or the variable X
from the framework described in Section 3. The average value of r in this sample is 43%.
The survey also asks about people’s beliefs about their life expectancy, including without
HIV, if they contracted HIV today but did not have ARVs, and if they contracted HIV today and
did not have ARVs. In addition, it asks them how many out of 100 people from their area they
would expect to have access to ARVs. I use these to construct a measure of the expected cost of
an HIV infection in terms of years of life lost. On average, respondents believe HIV infection
will cost them 18.9 years of life – they expect to live almost 30 years if HIV-free and 11.4 years
if they contract the virus.15 While probably lower than the expected cost of HIV in a developed
country, this is hard to square with the idea that limited responses to the threat of HIV infection
15
These numbers do not add up properly because some data is missing for each variable.
are the result of low expected costs in terms of foregone years of life. I will use this variable as
the equivalent of C from the Section 3 theoretical framework.
Finally, the dataset contains a detailed sex diary that captures detailed information on all
sex acts in the past week. I use this to construct a measure of the total number of sex acts and the
number in which no condom was used. The average respondent had unprotected sex 1.9 times in
the preceding week. In the analyses that follow, I will rely on this variable as the measure of
sexual risk-taking from – n from the theoretical framework in Section 3.
5.2.
Regression Analysis
The focus of this analysis is to explore the relationship between n (Unprotected sex acts
in past week) and r (Average Prob. of HIV Xmission per act, attractive people) for my
representative sample of individuals from Malawi’s Zomba District. As a first pass, I construct a
simple, unweighted scatterplot of the two variables (Figure 4). No obvious bivariate relationship
is evident. A simple bivariate regression does not find a significant coefficient on n either (not
shown).
However, the oversampling of unmarried individuals and people near the trading post
may mask an underlying relationship between n and r. I therefore run a set of weighted
regressions, using the specifications described in Section 4.1. Table 4 presents the results.
Column 1 is a bivariate regression of n on r, but using the sample weights. I estimate a
statistically significant positive first-order relationship between perceived per-act risks and the
number of risks taken. Taken at face value, this would imply that the population is fatalistic on
average. However, this result is not robust to the inclusion of a second-order risk term (Column
2), which yields a negative estimated slope. The coefficient on the quadratic term in risks is
positive but imprecisely measured.
Columns 3 and 4 repeat the specifications from Columns 1 and 2 but include a broad set
of regression controls (suppressed from the tables for space). Again the bivariate relationship
(Column 3) is positive and significant. Including a quadratic term in risks (Column 4) reverses
the sign of the first-order term and decreases the accuracy with which it is estimated. The
quadratic term is statistically significant at the 5% level.
In Columns 5 and 6 I extend the model to capture Comparative Static IV (from Appendix
A), which states that the number of risk acts is declining in the cost of a failure (captured by the
expected years of life lost if the respondent contracts HIV) and Comparative Static II, which
states that the higher the cost of a failure, the stronger the relationship between risk-taking and
per-act risks is likely to be. My results contrast with Oster (2012) in that I do not see a
particularly strong effect of the cost of HIV on the risk-response relationship. Increasing the
number of life years lost to the disease by 10 will decrease the slope of the n-r relationship by
just 0.1 in the quadratic specification of Column 6, just 2% of its overall magnitude. However it
is evident that cost of an HIV infection was an important omitted variable in the other
regressions. The first-order term becomes more negative in both specifications and in the secondorder specification the squared term becomes more positive, and in both specifications the
coefficients are more precisely estimated.
Comparative Static V also states that there should be a tipping point in the effect of the
cost of a failure on the relationship between n and r, and that the two tipping points should be
equal. I therefore include an interaction between the cost of a failure at the square of the per-act
risk in Column 7. This still does not lead to statistically significant results for Comparative
Static V, but it decreases the precision of the estimates for the linear and quadratic terms in risk.
Because Column 7 captures both of the relevant comparative statics that can be measured in this
dataset, I will rely on it as my preferred specification for further analysis.
5.3.
Testing for a non-monotone relationship
Looking just at the squared coefficients in Table 4 would suggest that there is some
evidence of a non-monotone relationship between per-act risks and risk-taking but that it is not
robust to changes in the specification used. However, as shown in Section 4, this method is likely
to be misleading if the underlying data-generating process is based on the rational fatalism model
of Section 3. Instead, I employ the two-step test described in Section 4.4. First, I run the LindMehlum parametric test for a U-shaped relationship. The p-values for this test are given in the
third-to-last row of Table 4. While the unconditional relationship (Column 2) does not display
significant non-monotonicity, the test rejects monotonicity for the other three specifications at
the 0.1 level. In the preferred specification of Column 7, the p-value is 0.096.
To confirm that the Lind-Mehlum test is not misleading due to poor model fit, I run a
partially linear regression of risk-taking on per-act risks, including all the covariates from
Column 7 (with the exception of the squared term in risks, which will be captured by the
LOWESS curve). This regression is plotted in Figure 5. Although the LOWESS curve has a
flattened U shape, no obvious relationship is visually evident from the plotted datapoints.
However, the partially linear estimator employed does not accept sampling weights, meaning
that these results are potentially biased due to the oversampling of certain groups – unmarried
individuals and especially people from rural areas. Because of this, Figures 6 and 7 show the
results split out by peri-urban and rural residents. Since rural residents are 95% of the weighted
sample, I focus on Figure 7 as a basic approximation of the weighted partially linear regression.
This plot shows a more noticeable U-shaped relationship, implying that the weighted relationship
we applied the Lind-Mehlum test to has a reasonably parabolic shape and the test results are
probably trustworthy.
In summary, there is suggestive evidence for a non-monotone relationship between risktaking and per-act risks in this dataset. Moreover, the first-order relationship is consistently
positive, which is the opposite of the prediction of the simple linear self-protection model.
Strikingly, these results are based on a weighted sample that is 95% rural. This is consistent with
the finding of Kaler (2003) that some men in rural areas employ rationally fatalistic reasoning.
People near the peri-urban trading center may have more access to HIV testing, which would
tend to resolve the uncertainty about their HIV status and eliminate the fatalistic effect.
5.4.
Plausibility of Fatalism
While these results imply that risk responses may be fatalistic for some people in Zomba
District, it is not clear how plausible this is – could people conceivably think their risk is really
high enough that they cross the tipping point value for per-act risks, ? As a first pass at this
question, I compare people’s beliefs to a plausible tipping-point: I assume that people use the
true risk-aggregation function
. Then the tipping point value of r is
. If people
think they have just a single unprotected exposure to a partner who is HIV-positive, their tipping
point is about 63%; higher levels of exposure imply a lower tipping point. Looking at the
distribution of beliefs in this population, (which is highly-skewed toward 100%), I find that
78.9% of people have beliefs that would be above the tipping point by this standard: if they have
any past exposure to someone they are sure is HIV-positive at all, their beliefs about per-act risks
are high enough to lead to fatalism.
A more conservative approach is to use people’s beliefs about their past partner’s HIV
status (at the time they had sex) multiplied by their perceived per-unprotected-act risk of
contracting HIV from an infected partner. By this standard, 9.7% of people have risk beliefs that
are consistent with fatalism even if they only had unprotected sex with their past partners a
single time – far lower than the actual figure, since condom use is very rare in Malawi. Thus
even by a very conservative standard, one would expect a non-trivial number of people from
Zomba District to react fatalistically to HIV transmission risks.
An alternative method of examining the plausibility of fatalism in this sample is to isolate
how people behave when they think a sex partner is infected with HIV. For this I rely on a set of
questions on the SASB survey that asked respondents about their primary sex partner, which was
defined to be the person they had sex with the most times in the past week, or, if they had not
had sex in the past week, then the person with whom they had most recently had sex. Although a
large share of respondents are married, we did not restrict this partner to be the respondent’s
spouse (and intentionally did not ask if they were). Respondents were asked about the likelihood
that this partner was HIV-positive; 52 of the 447 respondents in the dataset either reported a high
likelihood or said that they were sure their partner was infected. Figure 10 presents a scatterplot
for these 52 individuals, with their perceived per-act risk of infection from sex with an infected
partner on the x-axis and the number of times in the past month that they had unprotected sex
with this partner on the y-axis. Immediately notable is the large cluster of beliefs at 100%. Many
of these respondents also report positive levels of unprotected sex with their partner. A best-fit
line confirms a positive relationship between risk-taking and perceived riskiness. Due to the
small sample size, this relationship is not statistically significant. It is nevertheless suggestive of
potential fatalism among people who think they are being exposed to HIV.
5.5.
Limitations
In Section 4.5, I lay out three potential identification issues with using observational data
to analyze risk responses. With the present dataset I am unable to address either of the two
sources of reverse causality that are likely to be bias these results. I expect that the first reverse
causality issue is of fairly limited importance. The HIV epidemic in Malawi is fairly mature and
all individuals face very similar true prevalences. Moreover, people’s perceived risks have little
relationship with the actual risk they face. The actual per-act risk of HIV transmission is about
0.1% (Wawer et al. 2005), far below the average belief of 85%. And the true prevalence of HIV
in Malawi’s Southern Region is 17.6%, also substantially less that the mean belief for this
variable (49%). Since people do not actually understand the true risk, the causal positive effect of
behavior on the true risk is unlikely to cause a large bias in my results.
The second issue, in contrast, is more important for these data than for data that employ
the true HIV prevalence as a proxy for risks. Since people develop their beliefs in part through
experience I expect this to introduce a net negative bias in these results. Without an exogenous
source of variation in risk beliefs it is not possible to determine the exact nature of the bias in
these results, but the negative bias from the second issue is probably more important than the
positive bias due to the first one. That would imply that the true relationship would be initially
flatter than what is implied by the partial linear regressions in Figures 5, 6, and 7, and then
steeper after the tipping point. In other words, this observational analysis is likely to
undermeasure the true extent of fatalism in this population. This would not be the case if the
belief formation process worked in the opposite way, with more experience leading to higher risk
beliefs.
The measurement error issue is more tractable within the current dataset. As discussed in
Section 4.5, one simple metric for the measurement error in my risk belief variable is the excess
frequency of “50%” responses. Figure 8 shows a histogram of the per-act risk beliefs of my
respondents. There is substantial heaping at exactly 50%. Unfortunately, no viable alternative
variables are available.16 The survey questionnaire did not ask a followup question about whether
people are simply unsure, so it is not possible to exclude only those people or including a dummy
for being unsure. As a crude approximation to that method, however, I replicate the regressions
from Section 5.3 and 5.4 using only the subset of people who are not “uncertain”, meaning they
did not answer 50% to the per-act risk variable. The results are presented in Table 5 and Figure
9. I find uniformly stronger responses to HIV risks across all specifications, and lower p-values
for the Lind-Mehlum test. The preferred specification in Column 7 finds large and statistically
significant first- and second-order terms, and the Lind-Mehlum test rejects montonicity at the
0.05 level. The semi-parametric plot shows a reasonably clear-cut U shape. While this approach
is not perfect, it implies that measurement error is substantially attenuating these results, so the
true response will be larger in magnitude and more statistically significant than what is seen in
Table 4 and Figures 5 through 7.
16
There is a question about the total prevalence of HIV in the population, but a printing error meant that it was
collected only for males. As mentioned above, the data does have the prevalence among past partners, but this has
no appreciable relationship with risk-taking, either positive or negative.
6. Preliminary experimental results
In the summer of 2012, I conducted a field randomized controlled trial (RCT) in to test the
implications of this model. The experiment took place in Traditional Authority (TA) Mwambo,
in the Zomba District of Malawi’s Southern Region. I sampled roughly 2100 sexually active
adults aged 18-49 chosen randomly from 70 villages selected at random from the . Each
participant was interviewed twice: once for a baseline survey, and again for a followup
conducted 1-3 months later. All participants were provided with basic information about the
sexual transmission of HIV and the benefits of condoms.17 Participants from half of the villages,
chosen at random, were also read an information script that presented the actual annual risk of
HIV transmission in serodiscordant couples that have unprotected sex, based on the Wawer et al.
(2005) estimates and also figures from the Malawi National AIDS Commission.
Because existing evidence indicates that fatalistic individuals often frequent rural trading
centers in order to drink and seek out sex partners, the sample of villages was stratified based on
their distance to the closest major trading center.18 One third of the sample was villages within 2
km of a trading center, which is generally agreed to be the maximal distance people will walk for
nightlife; one third was villages between 2 and 5 km from a trading center; and one third was
17
Knowledge of the basics of HIV transmission and prevention is already high in this population. In the 2010 DHS,
nearly 100% of individuals said that HIV was sexually transmitted and over four fifths knew that condoms were
effective prevention. The latter figure may be an underestimate: in survey questions about the risks of unprotected
and protected sex in the Situational Analysis of Sexual Behaviors data, virtually all respondents stated that condoms
provided at least some risk benefit.
18
Trading centers were identified based on the 2008 Malawi Population and Housing Census, which codes periurban areas outside the main cities with enumeration area numbers from 800 to 899. I included trading centers both
inside the TA as well as in other nearby parts of the Southern Region. Since TA Mwambo adjoins the city of Zomba,
I also included the main markets in that city as trading center equivalents. In addition, based on conversations with
local public transit workers, I added three more trading centers (Govala, Kachulu, and Mpyupyu) that do not have
enumeration area codes between 800 and 899 but that are nonetheless major centers for trade and nightlife. The
informants I spoke to stated that besides the EA800-899 sites I had already identified, there were no other places
people went for trading or nightlife outside of TA Mwambo.
more than 5 km away from the closest center. This compares with overall proportions of 10%,
40% and 50% of all villages in TA Mwambo.
I rely on self-reported sexual behavior at the followup interview as my outcome measure. I also
use purchases of subsidized condoms at the followup as an objective measure of risk avoidance:
all participants were given six coins worth five Malawi Kwacha apiece (30 kwacha total, or just
over ten cents), and allowed to purchase up to six packets of Chishango (local-brand) condoms
for five kwacha apiece. This empirical strategy only allows me to estimate linear local average
treatment effects, because I only have two experimental arms. In lieu of fitting a semi-parametric
model to the experimental data, I explore heterogeneous responses to the information treatment
based on the distance to the nearest TC, gender, sexual experience, and baseline risk beliefs, as
well as interactions between these factors.
[Flesh this out more as data comes in]
Conclusion
I develop a theoretical model that generalizes the linear risk-response relationship
assumed in the literature to the case where responses may not be linear. I do this by allowing
people to employ a subjective risk aggregation function that satisfies several broad conditions
about its shape, and show there is a tipping point above which increases in the per-act risk lead to
more risk-taking rather than less. This result holds for any valid risk-aggregation function that
satisfies a set of simple conditions. Even very simple heuristic risk aggregation functions that
require no sophisticated understanding of probability theory also exhibit the tipping point that is
central to my results. The rational fatalism model implies that responses to risks will have both a
downward-sloping (self-protective) and upward-sloping (fatalistic) region. It advances the
previous literature by showing this effect not just for specific simple benefit functions and the
true risk aggregation function, but for a wide range of plausible choices. The rational fatalism
model also shows that fatalistic responses can occur for interior solutions and not just in
situations where people choose to take as many risks as possible. Based on this model, and
imposing some assumptions about the benefit from risky acts and the risk aggregation function, I
generate simulated data and use it to test the effectiveness of standard econometric approaches to
data on risk-taking a per-act risks. I find that the typical specifications can generate misleading
inferences: they may fail to identify non-monotonic relationships and will generate estimates of
the average response that are attenuated relative to the true value and may also be of the incorrect
sign. I develop my own approach based on the Lind and Mehlum (2010) parametric test for nonmonotonicity and the Yatchew (1996) partially linear regression technique. I apply these
methods to preliminary observational data from Malawi’s Zomba District, and find suggestive
evidence of non-monotonicity in that region. I also show that depending on how we think about
past exposures, between 9.7% and 84.4% of people in the region have beliefs that are above the
tipping point into fatalistic behavior implied by the true risk aggregation function. Looking just
at the subset of 52 individuals who think their primary sex partner is HIV-positive, I find that
risk-taking increases with perceptions about the per-act risk, although the sample is not large
enough to rule out a slope of zero. These data are limited by potential measurement error as well
as reverse causality. A first pass at the measurement error issue confirms that it is probably
attenuating the measured relationship between risk-taking and per-act risks, and that the true Ushape is even more pronounced than observed in this data. I also present preliminary results from
a randomized field experiment conducted in Southern Malawi that is designed to test the
implications of this model.
The results of this paper are subject to several important limitations. First, while the
rational fatalism model substantially extends the usual linear risk response relationship used in
the literature, it abstracts from the possibility of multiple periods. In particular, agents may be
aware of the effect of their current behavior on their future decisions about risky acts. This model
is appropriate for individuals with short planning horizons, or as an abstract model of risky
behavior among adults where the cost of a failure is simply dying before old age (when no risks
will be taken).
Second, while it demonstrates that data generated by the rational fatalism model can
display non-monotone responses, and that conventional methods of looking for that nonmonotonicity may not perform well, this is done only for a single simulated dataset. A superior
approach would be to generate a large number of such datasets under plausible assumptions
about parameter values, and explore the general effectiveness of various methods. This would in
turn necessitate developing a formal and automated way of testing for non-monotonicity that
works for this model, probably by adapting Bowman et al. (1998). An additional difficulty with
doing this is that many combinations of seemingly-plausible parameter values generate only
corner solutions, which are not amenable to any kind of test and hence uninformative.
Third, I cannot resolve the reverse-causality issue in my preliminary data, since it lacks
an exogenous source of variation in risk beliefs. I argue that correcting it is likely to decrease the
extent of self-protection in measured in the data while increasing the extent of fatalism, so that
this preliminary data is probably underestimating the extent to which Malawians from that
district are fatalistic and not overestimating it. However, it is impossible to know what the true
relationship is without an instrument or an experiment. Future work on this topic should focus on
conducting an experiment which provides information about HIV transmission risks to people in
Malawi and in other places where people substantially overestimate the per-act risk of
contracting HIV.
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Kiwanuka, N., et al. (2005). Rates of HIV-1 Transmission per Coital Act, by Stage of HIV1 Infection, in Rakai, Uganda. The Journal of Infectious Diseases, 191, 1403–1409.
Yatchew, A. (1997). An elementary estimator of the partial linear model. Economics Letters,
57(2), 135–143. doi:10.1016/S0165-1765(97)00218-8
Table 1: Results of optimal risk-taking on per-act risk, simulated data
Per-Act Risk
(1)
(2)
(3)
(4)
(5)
2.911***
2.573***
2.870***
2.150***
-16.49***
(0.171)
(0.648)
(0.105)
(0.432)
(0.906)
0.425
0.905*
43.84***
(0.785)
(0.488)
(1.954)
-50.07***
-50.10***
-47.72***
(1.012)
(1.012)
(1.561)
(Per-Act Risk)^2
Cost per act
Constant
p-value(Lind-Mehlum U-Shape Test for n and X)
Adjusted R-squared
n
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
4.114***
4.165***
11.63***
11.74***
12.71***
(0.0734)
(0.122)
(0.169)
(0.197)
(0.289)
-
1.000
-
1.000
<0.001
0.0979
0.0978
0.789
0.789
0.797
3000
3000
3000
3000
1547
Table 2: Summary Statistics for Demographics
Mean
Demographics
Peri-Urban
Female
Married
Age
Years of education
Std.
Dev.
Min.
Max.
N
0.05
0.59
0.88
29.46
5.52
0.22
0.49
0.32
8.25
3.03
0
0
0
17
0
1
1
1
49
13
447
447
447
447
444
Literate
0.60
0.49
0
1
447
# of female children
1.47
1.31
0
7
438
# of male children
1.55
1.21
0
6
445
1.16
1.45
0
20
447
3.44
0.90
1
5
442
Household spending in past month, PPP USD
142
232
0
3852
447
Household income in past month, PPP USD**
247
561
0
19369
447
Catholic
0.23
0.42
0
1
447
CCAP
0.13
0.34
0
1
447
Pentecostal
0.13
0.33
0
1
447
Church of Christ
0.11
0.31
0
1
447
Anglican
0.06
0.24
0
1
447
Other Christian†
0.14
0.35
0
1
447
Muslim
0.20
0.40
0
1
447
Lomwe
0.55
0.50
0
1
440
Yao
0.22
0.41
0
1
440
Chewa
0.16
0.37
0
1
440
Other‡
0.07
0.26
0
1
440
Desired # of additional children
Attractiveness [1-5]
*
**
Religion
Ethnic Group
Data taken from Kerwin et al. (2011). Means and standard deviations constructed using sample weights. Summary statistics for
other regression controls available from the author upon request.
* Enumerators (of the same sex as the respondents) rated respondents on how attractive they are, from 1 to 5.
** Constructed by dividing self-reported values in Kwacha by the World Bank ICP PPP exchange rate for 2011, which is 39.46.
† Other Christian includes indegenous Christian churches (2.0%), Baptist (1.6%), 7th-Day Adventist (0.2%), and miscellaneous
(10.3%).
‡ Other includes Mang'angja (2.7%), Nyanja (2.6%), Ngoni (1.3%), Sena (0.4%), and trace numbers of Tumbuka and Shona.
Table 3: Summary Statistics for Subjective Beliefs and Sexual Behaviors
Mean
Subjective Beliefs
Transmission Risks
Share of people resp. finds attractive who are HIV-positive
Prob. of HIV Xmission per unprotected sex act w/infected partner)
Average Prob. of HIV Xmission per act, attractive people
Cost of HIV Infection
Years of life remaining
Years from HIV infection to death, without ARVs
Std.
Dev.
Min.
Max.
N
0.49
0.85
0.43
0.21
0.26
0.24
0
0.01
0
1
1
1
414
423
413
29.96
4.36
17.48
4.09
0
1
82
80
436
423
15.85
12.19
2
100
423
0.62
0.29
0
1
421
11.43
8.50
1.12
100
421
18.86
16.40
0
78
410
Total sex acts in past week
2.11
2.68
0
13
447
Unprotected sex acts in past week
1.93
2.67
0
13
447
Years from HIV infection to death, with ARVs
Share of HIV-positive people who would receive ARVs
Expected years from HIV infection to death
Expected life years lost if resp. gets HIV
Sexual Behaviors
Data taken from Kerwin et al. (2011). Means and standard deviations constructed using sample weights.
Table 4: Regressions of risk-taking on perceived per-act risks, full sample
Average Prob. of HIV Xmission per act, attractive people
(1)
(2)
(3)
(4)
(5)
(6)
(7)
2.833**
-1.046
1.520**
-3.732
1.524
-5.800**
-4.277
(1.304)
(3.508)
(0.759)
(2.588)
(1.133)
(2.494)
(3.274)
(Average Prob. of HIV Xmission per act, attractive people)^2
4.185
5.598**
7.442***
5.818
(4.222)
(2.638)
(2.592)
(3.577)
-0.00804
-0.0156
-0.00419
(0.0221)
(0.0203)
(0.0260)
-0.0267
-0.0129
-0.0841
(0.0415)
(0.0374)
(0.127)
Expected life years lost if resp. gets HIV
(Cost of HIV)*(Prob. HIV per Act)
(Cost of HIV)*(Prob. HIV per Act)^2
0.0793
(0.128)
Constant
0.753
1.401***
-1.850
-0.551
-1.054
0.506
0.349
(0.547)
(0.453)
(3.255)
(3.337)
(3.896)
(3.912)
(3.942)
X
X
X
X
X
†
Controls Used
Std. Errors Clustered by Area
X
X
p-value(Lind-Mehlum U-Shape Test for n and X)
-
0.385
-
0.075
-
0.010
0.096
0.0633
0.0780
0.524
0.535
0.528
0.546
0.545
413
413
380
380
367
367
367
2
Adjusted R
N
Heteroskedasticity-robust standard errors in parentheses. All regressions run using the sampling weights as pweights.
† Controls include gender, age, age squared, education, education squared, number of male and female children, desired future children, marital status, literacy, attractiveness,
attractiveness squared, and peri-urban location, and fixed effects for area, ethnicity, religion, media exposure (TV/radio/newspaper) and enumerator. Coefficients on controls
suppressed due to space considerations but available from author upon request.
*** p<0.01, ** p<0.05, * p<0.1
Table 5: Regressions of risk-taking on perceived per-act risks, excluding “uncertain” respondents
Average Prob. of HIV Xmission per act, attractive people
(1)
(2)
(3)
(4)
(5)
(6)
(7)
2.685*
-3.134
0.910
-6.182**
1.673*
-7.589***
-6.788*
(1.355)
(3.888)
(0.588)
(2.709)
(0.887)
(2.723)
(3.450)
(Average Prob. of HIV Xmission per act, attractive
people)^2
6.126
7.516***
9.511***
8.672**
(4.524)
(2.846)
(2.758)
(3.610)
0.0109
0.00537
0.0107
(0.0157)
(0.0134)
(0.0197)
-0.0175
-0.00118
-0.0369
(0.0336)
(0.0276)
(0.110)
Expected life years lost if resp. gets HIV
(Cost of HIV)*(Prob. HIV per Act)
(Cost of HIV)*(Prob. HIV per Act)^2
0.0385
(0.112)
Constant
0.698
1.596***
-6.952*
-4.511
-7.416*
-4.654
-4.921
(0.544)
(0.456)
(3.560)
(3.341)
(3.881)
(3.459)
(3.568)
X
X
X
X
X
†
Controls Used
Std. Errors Clustered by Area
X
X
p-value(Lind-Mehlum U-Shape Test for n and X)
-
0.217
-
0.0117
-
0.0029
0.0252
0.0783
0.119
0.661
0.681
0.676
0.706
0.705
312
312
293
293
281
281
281
2
Adjusted R
N
Heteroskedasticity-robust standard errors in parentheses. All regressions run using the sampling weights as pweights.
† Controls include gender, age, age squared, education, education squared, number of male and female children, desired future children, marital status, literacy, attractiveness,
attractiveness squared, and peri-urban location, and fixed effects for area, ethnicity, religion, media exposure (TV/radio/newspaper) and enumerator. Coefficients on controls
suppressed due to space considerations but available from author upon request.
*** p<0.01, ** p<0.05, * p<0.1
Figure 1: Shapes of Risk-Aggregation Functions for Low and High Values of Per-Act Risk
Figure 2: Scatterplot of Optimal Risk-Taking by Per-Act Risk, Simulated Data
Figure 3: Partially Linear Regression of Optimal Risk-Taking on Per-Act Risk, Simulated
Data
Figure 4: Scatterplot of Unprotected Sex by Perceived HIV Transmission Risk from
Attractive People, Unweighted
Figure 5: Partially Linear Regression of Unprotected Sex on Perceived HIV Transmission
Risk from Attractive People, All Respondents, Unweighted
Figure 6: Partially Linear Regression of Unprotected Sex on Perceived HIV Transmission
Risk from Attractive People, Peri-Urban Respondents, Unweighted
Figure 7: Partially Linear Regression of Unprotected Sex on Perceived HIV Transmission
Risk from Attractive People, Rural Respondents, Unweighted
Figure 8: Histogram of Perceived HIV Transmission Risk from Attractive People
Figure 9: Partially Linear Regression of Unprotected Sex on Perceived HIV Transmission
Risk from Attractive People, Excluding “Uncertain” Individuals, Unweighted
Figure 10: Risk-Taking with Primary Partner for Respondents who Think Partner is
Probably HIV+
Appendix A: Additional Comparative Statics
This appendix derives two additional comparative statics based on similar methods to those used
in Section 3.3: the response of the optimal value of n to the per-act price p and the cost of the bad
outcome c. These two comparative statics are both negative in sign. The second is directly
analogous to the Oster (2012) result for a linear risk aggregation function P.
Note that the denominator of each expression is simply the second-order condition for an internal
optimum and is therefore strictly negative, and that
is negative by assumption.. This
immediately yields the following intuitive results:
Proposition B1
(Comparative Static I)
The higher the price of a risky act, the less of it people will do. Conversely, the more
negative the price - that is, the more that one is paid to take risks - the more one is willing
to do.
Proposition B2
(Comparative Static II)
Raising the cost of a failure weakly decreases the number of risks taken, and strictly decreases
the number of risks chosen as long as
.
Corruption and the E↵ectiveness of Imported
Antiretroviral Drugs in Averting HIV Deaths
Willa Friedman
Department of Economics, University of California at Berkeley
PRELIMINARY
December 6, 2012
Abstract
This paper looks at the impact of corruption on the e↵ectiveness of antiretroviral drugs
in preventing deaths due to HIV and the potential channels that generate this relationship.
This is based on a unique panel dataset of countries in sub-Saharan Africa, which combines information on all imported antiretroviral drugs from the World Health Organization’s
Global Price Reporting Mechanism with measures of corruption and estimates of the HIV
prevalence and the number of deaths in each year and in each country. Countries with higher
levels of corruption experience a significantly smaller drop in HIV deaths as a result of the
same quantity of ARVs imported. This is followed up with a single case-study from Kenya
to illustrate one potential mechanism for the observed e↵ect, demonstrating that disproportionately more clinics begin distributing ARVs in areas that are predominantly represented
by the new leader’s ethnic group.
1
Introduction
Today antiretroviral drugs are widely available in sub-Saharan Africa, with 8 million peo-
ple receiving treatment in 2011 according to the World Health Organization. Until the last
decade, this level of provision was considered inconceivable as the drugs were prohibitively
expensive, and this enormous expansion in access has been credited with extending the lives
of millions of people across the continent. At the same time, corruption in governments is
associated with inefficient distribution of public goods, and this could limit the e↵ectiveness
1
of imported drugs in saving lives if the drugs do not reach the intended clinics or individual
recipients, or if they are distributed with insufficient guidance.
This paper addresses the role of corruption in determining the e↵ectiveness of antiretroviral drugs in reducing HIV mortality in sub-Saharan Africa. This is first done using a
cross-country analysis comparing the impact of imported drugs on HIV deaths across countries with di↵erent levels of corruption. This is done using an original panel dataset of
countries in sub-Saharan Africa from 2000-2007. This dataset combines standard measures
of corruption used in economics and political science, information about HIV prevalence and
deaths, and records of the quantities of antiretroviral drugs imported into each country. Using year and country fixed e↵ects, this data provides evidence that HIV deaths are reduced
less in corrupt countries given the same quantity of medicine, and the e↵ect is even larger if
the relevant quantity of drugs is measured in dollars spent.
There are many channels through which corruption could influence the e↵ectiveness of
health investments. For example, drugs can be purchased and then diverted either outside
the country or within the country. The supply chain can fail if governments with higher levels
of corruption are generally less capable of delivering public goods. Additionally, corruption
within a government can facilitate targeting of public goods, not based on need, but based
on political or other motivations.
Diversion of drugs could happen if drugs purchased by governments are resold. This could
be particularly lucrative in sub-Saharan Africa for two reasons. First, in nearly all countries
of sub-Saharan Africa, supply is not nearly sufficient to meet demand and so treatment is
rationed. This makes resale valuable because some of those excluded are likely to be willing
to pay for the treatment. Second, because of international agreements with pharmaceutical
companies, ARVs are sold at an enormous discount to governments and NGOs working in
many countries in sub-Saharan Africa. This variation in price between di↵erent countries
creates a substantial opportunity for arbitrage.
Such diversions prevent the drugs from reaching those who need them most, and they
2
may take them out of the country entirely. It should be noted that if these drugs are sold
to others within the same country, then a change in allocation may not reduce the overall
reduction in mortality. However, if they are diverted to those who need them less - perhaps to
those for whom the disease has not progressed as far and their risk of opportunistic infection
is reduced or to those who have another source and want the security of accumulating a
bu↵er stock - then this will prevent the drugs from having the same national impact on
HIV-related mortality.
Studying the impacts of corruption in the context of ARV provision is particularly appropriate for a few di↵erent reasons. First, many important outcomes may be only indirectly
linked to welfare, whereas the relevant outcome in this study of deaths averted is clearly
of direct importance. Second, during this time period there was virtually no domestic production of Antiretroviral Drugs and there is no substitute for these treatments. The next
best alternative (good nutrition and treatment and prevention of opportunistic infections
through antibiotics) does not have nearly the impact on morbidity and mortality that these
drugs do. Therefore, while other studies that look at corruption and goods provision will be
unable to measure the entire supply of those goods, this is possible in this case.
Corruption in government could also limit the e↵ectiveness of local supply chains in a
number of ways. If promotion within the public sector is not based on performance, there is
less incentive for employees to manage transport or work hard at health facilities. Thus the
drugs may remain in the country, but sit unused. Similarly, if health facilities are plagued by
high absenteeism, drugs may either sit idly or be prescribed with insufficient guidance so that
clients are less likely to adhere. Because of its quick rate of mutation HIV is particularly
susceptible to the development of drug resistance due to low adherence to the prescribed
regimen.1 .
An additional channel through which corruption could influence the impact of imported
drugs is through changing allocations within a country. Guaranteeing treatment to those
1
It should be noted that adherence to HIV treatment regimens is generally measured to be quite high in
developing countries (Mills et al, 2006)
3
who have low CD4 counts and therefore have the most compromised immune system is the
most efficient way to immediately avert deaths using ARVs. However, there is also a benefit
to an individual of treatment before the CD4 count is extremely low, and the World Health
Organization recently increased the recommended CD4 count threshold of eligibility from
200 to 350. With the higher threshold, demand for the drugs increases and without sufficient
supply, other systems of allocation besides targeting those with the lowest CD4 count arise.
One notable alternative system of allocation of any health expenditure is political favoritism,
including, for example, targeting core supporters or co-ethnics.
Using data from Kenya about ARV provision before and after an election, I test for
politically motivated targeting of new ARV clinics in one country with high corruption levels
and high HIV rates. This is done using an original dataset containing all health facilities in
Kenya that provide antiretroviral drugs, along with the year in which they began distribution
and their GPS locations. This information is linked with ethnicity records to look for evidence
of targeting of the placement of ARV clinics in the home area of a newly elected political
leader. I find that there are disproportionate clinics opened in areas of the leader’s ethnic
group. This suggests one mechanism through which corruption reduces the impact of health
inputs. Namely, in a country with high corruption, the assignment of ARV clinics follows a
political criterion rather than a public health criterion. Further, this pattern of allocation
appears to reflect additional clinics added to areas that were already served rather than
expanding access to districts that were underserved previously.
This paper is organized as follows. Section 2 discusses the relevant literature and explains
how this paper contributes to it. Section 3 outlines the data to be used for the main
specification and for the analysis of the case study of Kenya. Section 4 presents the empirical
strategy and the results of the cross-country analysis and section 5 discusses the methodology
and results of the case study. Section 6 concludes.
4
2
Literature review
The consequences of corruption are an important area of study in both political science
and economics. Corruption is associated with a number of poor outcomes including weakened
democracy and reduced economic growth (e.g.: Mauro, 1995; Bardhan, 1997). Another crosscountry literature specifically links corruption with public goods and health outcomes (e.g.:
Rajkumar and Swaroop, 2008; Lewis, 2006). There are many mechanisms through which
corruption can hurt health outcomes, and the popular press provides a number of examples
of diversions in public health systems.
A report in Zambia found that an enormous fraction of the money that was provided to
the country by the Global Fund could not be accounted for (“Zambia”, 2011). This money
could have been used to build clinics and distribution networks to facilitate the distribution
of ARVs, but without it, the ARVs would need to be distributed using fewer resources,
possibly causing some drugs to go unused, preventing interventions to increase adherence,
or hurting the ability of the government to target those who most needed treatment.
A Ugandan newspaper reported that in many areas of Uganda in 2011, ARV clinics had
run out of stocks of drugs (Basudde, 2011). If corruption prevents drugs from being restocked
in a timely matter, this can have disastrous impacts on HIV mortality, even if the stocks
return. First, a lack of consistent adherence to ARVs allows the virus within an individual to
develop immunity to the drugs. When treatment is restarted, it is likely to be less e↵ective
at preventing opportunistic infections and keeping the individual alive. HIV is known to
mutate rapidly, facilitating the development of drug resistance. Second, if this individual is
sexually active, this resistance can be transmitted to others. Both factors will reduce the
e↵ectiveness of future ARVs, because the lack of consistent supply allows the virus to develop
drug resistance.
In another article in the same newspaper, alleged corruption prevented a bill to allocate
28.4 billion Ugandan shillings to purchase CD4 count machines. These machines are used to
monitor the progress of HIV in an individual and the e↵ectiveness of treatment (“Corruption
5
feared”, 2011). With the machines, ARVs could be more efficiently administered. These
machines help doctors and clinical officers to determine whether a person has developed
drug resistance and ought to be switched to second line treatment, which would improve the
e↵ectiveness of the treatment and the likelihood of its prolonging life.
A report from the Ministry of Finance in Swaziland illustrated the scale of money lost
due to corruption by showing that it was nearly double the country’s yearly budget for social
services (“Swaziland”, 2011).
One channel through which corruption could reduce the impact of imported drugs is by
preventing targeting based on need in favor of other motives. In order to maximize the
benefit of the drugs, they would need to be distributed in such a way that those who can
use them have sufficient access that they can begin and successfully adhere to treatment. If
corruption allows targeting based on other criteria, this targeting will be weakened, and the
drugs may not lead to those most likely to be helped.
In Zimbabwe, PlusNews reports that HIV positive patients are asked to pay providers
in order to access drugs which are officially distributed free of charge (“Zimbabwe”, 2010).
With this type of targeting, many who could use the drugs may be denied access in favor of
those who either are less likely to be adherent or in less urgent need of the drugs, resulting
in higher rates of mortality due to HIV, even with the same quantity of drugs distributed.
In order to keep prices high, providers may also restrict access, letting some drugs go unused
in order to maximize profits, again resulting in increased mortality.
3
Data
3.1
Cross-country impacts of corruption and ARVs
The data in this paper comes from many sources. For the first section of the paper, all
data is collapsed to a single observation per year in each country in sub-Saharan Africa. The
sample is restricted to one region of the world in order to avoid some - but not all - of the
6
standard concerns with cross-country analysis, and to focus on the region that is the hardest
hit by the HIV epidemic.
The first datasource is used to measure the quantity of drugs entering each country.
This information comes from the WHO Global Price Reporting Mechanism. This is an
online database of all international purchases of drugs associated with HIV/AIDS, malaria,
and tuberculosis going into developing and middle income countries. For each purchase, the
database reports the date of purchase, the country and company of manufacture, the country
of the purchaser, and the price and quantity of each type of drug. This contains records for
approximately 30,000 purchases of antiretroviral drugs across three categories - antiretroviral
drugs, HIV Diagnostics, and HIV prevention. The same drugs with the same dosages are
listed in each category and combining all three reduces threats from misclassification at
the international level of how drugs will be used at the local level.2 The records includes
purchases on the part of governments, NGOs, and researchers.3
The analysis uses two measures of the quantity of drugs entering each country in each
year. The first measure uses standard doses to calculate the quantity of drugs in terms
of person-years. Because some drugs are used in combination with others, this measure
is imperfect and may be higher in countries that use fewer combination pills. The second
measure is the quantity of money spent on all imported ARVs. This is simply the sum of
the costs of all purchases.
HIV statistics come from the UNAIDS/WHO 2008 Report on the Global AIDS Epidemic,
which for each country in each year reports an estimate of the prevalence, the number of
people living with HIV, and the number of deaths due to HIV. While this information may
be flawed, there is no better source of information about the prevalence in all countries.
2
For example, antiretroviral drugs purchased as HIV prevention may be used for Prevention of Mother
to Child Transmission, and as HIV positive babies typically are overcome by the disease quickly, this should
also show up in preventing future deaths.
3
Agreements between drug companies and developing countries set maximum prices that are low if drugs
are purchased by governments or NGOs, but the prices are higher for the private sector. Partly because
of this, the private sector does not import large quantities of ARVs in these countries, but it minimally
participates in distribution of drugs once they are in the country.
7
Governance indicators for Control of Corruption, Government Efficacy, and Rule of Law
are taken from Kaufmann, Kraay, and Mastruzzi (2010). In each year, each country is given
a score for each of these indexes. In order to not rely on small di↵erences, the analysis uses
binary measures of each of these representing an indicator for a score above the mean in
sub-Saharan Africa. GNI per capita is taken from the World Bank’s Human Development
Indicators.
3.2
Case study
The second section of the analysis uses more detailed data obtained from government and
private sources in Kenya, combined with population data from MeasureDHS. Information on
the placement of ARV clinics is from Kenyapharma, a procurement agency, and the National
AIDS and STI Control Program of the Ministry of Health. These reports were provided
directly to the author in the Fall of 2011. The information about ethnic backgrounds of
populations comes from the 2008/2009 Measure DHS data, in which respondents are asked
to report their own ethnicity. The GPS data used to link the two is from the Kenya Open
Data Initiative.
4
4
Empirical Strategy and Results
4.1
Cross-country impacts of corruption and ARVs
This paper will follow previous analysis of cross-country panel-data, including country
and year fixed e↵ects and estimating the coefficient on the interaction of corruption and
quantities of imported drugs. To ensure some reliability of the data, I will first estimate
the following equation to verify that the quantity of drugs is associated with a reduction in
deaths due to HIV:
4
(opendata.go.ke)
8
deathsjt = ↵j +
t
+
1
⇤ ARV sjt +
2
⇤ prevjt +
3
⇤ P LW Hjt + ej
where deathsj t is the number of deaths in year t in country j due to HIV as reported
by the WHO, and ARV sjt is the total quantity of drugs imported in that year according
to the WHO Global Price Reporting Mechanism. In the first set of specifications, this is
included measured in doses (person-years), and in the second set of estimates, the quantity
is reported in dollars spent. Controls are included for the prevalence of HIV (↵j )and the
number of people living with HIV (P LW Hjt ) as well as country and year fixed e↵ects (↵j
and
t ).
The coefficient
1
shows the association between ARVs entering a country and
deaths due to HIV reported in that year.
As reported in columns 1 and 4 of Table 1, this is large and negative and statistically
significant at all standard levels. Column 1 reports the estimates using the number of person
days of drugs as the quantity of ARVs and Column 4 presents the same with the cost of all
imported drugs as the measure of quantity. In both cases, the coefficient is negative and
significant.
To investigate the role of corruption in changing this e↵ect, I focus on the interaction
between the quantity of ARVs and the level of corruption. To do this, I estimate the following
equation:
deathsjt = ↵t +
+
3
j
+
1
⇤ ARV sjt +
2
⇤ corruptionjt
⇤ ARV s ⇤ corruptionjt + ⌃bij ⇤ Xij + ej
where: ARV sjt is the person*years purchased by country j in year t. Corruptionjt is an
indicator for being below the mean (in Africa) on the Kaufmann, Kraay, and Mastruzzi
Control of Corruption Index. To ease interpretation, the quantity of ARVs are demeaned so
9
that the mean is zero. This way the coefficients on the un-interacted terms are meaningful
and can be interpreted as the impact at the mean.
If corruption does limit the reduction in deaths generated by purchased drugs, then
3
should be positive (reflecting a dampened reduction in deaths).
The estimated parameters from this equation are reported in columns 2 and 4 of table
1. In this table, the coefficients on quantities of ARVs are still large and negative and
significant, showing that in less corrupt countries, ARVs reduce deaths due to HIV. The
coefficient on the interaction term in column 2 is positive, but not significant. A positive
coefficient reflects that the impact of ARVs in corrupt countries is lower, but the fact that it
is not significant means that this is inconclusive. In column 4, using spending as the measure
of quantity, the interaction term is positive and significant, and large enough to nearly wipe
out the impact of ARVs on deaths averted. This suggests that corruption does mitigate the
impact of imported ARVs.
Perhaps the variable for corruption is picking up other measures of good governance that
have an e↵ect through di↵erent channels on the impacts of ARVs on deaths. Columns 3
and 6 of table 1 show the same estimates including the country’s GNI and the interaction
between that and the quantity of ARVs. With this included, the coefficient on the interaction
between ARV quantity and corruption is of a similar magnitude, but significant using both
measures of quantity.
Interestingly, the positive coefficients on the interaction between ARV quantity and GNI
imply that wealthier countries may see fewer deaths averted as a result of the same quantity of
ARVs. One possible explanation is that richer countries have met more of the demand within
their countries and the marginal (and average) return is lower as those with less advanced
infection are treated. Although not estimated in this paper, these countries may be treating
those who would not have died immediately otherwise, but the e↵ects on mortality may show
up after a few years.
Table 2 further investigates whether the variable for corruption is a proxy for other types
10
of governance. This table adds a number of measures of government quality alone and
interacted with ARV quantities. These variables are binary measures constructed in the
same way as the measure of corruption coding above average values as 1 and below average
as 0.
The first column uses person days of treatment as the quantity and the second uses
the price. In column 1, the coefficient on the interaction term of ARVs and Corrupt is
still positive and significant, although Good Rule of Law and E↵ective Governance also
have significant relationships when interacted with ARVs. In the second column, only the
interaction with corruption is significant.
Are corrupt countries di↵erent in other ways? Table 3 shows which countries fall in
which categories. Table 4 compares the countries that are more or less corrupt on a variety
of measures. As seen in table 4, more corrupt countries have lower HIV prevalence rates.
They also spend more on ARVs, but for a lower quantity. One possibility is that more
corrupt countries are buying more expensive drugs that may be less likely to be first or
second line treatments, and therefore more valuable since third line and beyond treatments
are rarely widely available.5 Tables 5 and 6 show the breakdown of types of antiretroviral
drugs purchased by more and less corrupt countries. This is measured as the percentage of
all drugs purchased in each category these quantities by the specific type of drug.
Based on these comparisons, the quantity of ARVs imported is clearly not exogenous and
it is possible that the association shown in this cross-country analysis is not causal. The
inclusion of country and year fixed e↵ects deals with many potential threats to endogeneity,
but it cannot handle all of them.
5
ARV treatment becomes ine↵ective for an individual once the HIV in their system develops resistance
to the treatment they are given. Once this happens, a person is given a di↵erent treatment, referred to as
the second line. In developed countries, this process can repeat many times with those who live with HIV
for many years progressing to third, fourth, etc. line treatments.
11
5
Case study in Kenya
If the relationship measured in the previous section is causal, then looking at the mech-
anisms through which corruption changes e↵ectiveness of imported HIV treatment is a pertinent next step. At the same time, identifying specific mechanisms provides additional
support that the relationship is causal.
The fact that controlling for the role of government efficacy does not eliminate the e↵ect
is suggestive that the channel through which corruption has an influence is not in simply
making government programs less efficient generally with poor incentives for performance or
high absenteeism. Instead, this suggests other channels through which drugs are diverted or
allocated inefficiently.
One channel through which corruption could reduce the impact of imported drugs is by
preventing targeting based on need in favor of other motives. In order to maximize the
benefit of the drugs, they would need to be distributed in such a way that those who can
use them have sufficient access that they can begin and successfully adhere to treatment. If
corruption allows targeting based on other criteria, adequate targeting will be weakened, and
the drugs may not reach those most likely to be helped. In this section, I test whether one
type of targeting exists in Kenya, a country consistently listed as in the top half of corrupt
countries in sub-Saharan Africa.
In particular, I look for evidence of selective placement of ARV clinics in Luo areas after
Raila Odinga became Prime Minister in 2008. Previous research has demonstrated that the
match between the ethnicity of leaders and constituents is a strong predictor of the provision
of public goods (Burgess et al, 2009; Kramon and Posner, 2012). In 2008, after a fiercely
contested election for president, followed by allegations of electoral fraud and eventually
by violence, the opposition leader, Raila Odinga, became prime minister. Jablonski (2012)
looks at government spending in areas populated by Odinga’s core supporters after the same
election. This paper uses a similar method, focusing exclusively on ARV clinics.
One concern that has been raised in the literature about targeting of core supporters after
12
a successful election is that in many settings this could be confounded by an inspiration e↵ect.
For example, Marx, Ko, and Friedman (2009) find that African American children in the
US have higher test scores after Obama was elected, and argue that this reflects - not a
channeling of resources - but greater motivation on the part of children who see a role-model
in such an important position. In the case study in this paper, I will test whether political
changes generate changes in investments in health. In particular, I will look at whether there
are more ARV clinics opening in areas with core supporters of Raila Odinga after he became
Prime Minister in Kenya in 2008.
By using a measure of health inputs rather than outcomes, I am able to isolate the impact
through expenditures and channeling of resources, and avoid contamination from inspiration.
This is similar to Burgess et al (2009) who look at road construction in Kenya as a function
of the ethnic match between the constituents and the government.
If there is targeting based on shared ethnicity, then we would expect to see a relative
increase in ARV clinics in Luo areas after the election. To test this, I construct a dataset
in which each observation represents one division in one year.6 For each year between 2004
and 2010 and each of the 225 divisions covered in the 2003 or 2008/2009 DHS survey, this
dataset contains the number of clinics which disburse antiretroviral drugs and an estimate
of the proportion of the population that self-defines as Luo.
This data is used to look for evidence that Luo areas disproportionately received new
clinics after the election, by regressing the number of clinics on the proportion of the population that is Luo, an indicator variable for whether the observation is after the election,
and the interaction of the two. I also include controls for the local HIV prevalence at both
the district and division levels and year and division fixed e↵ects. The coefficient of interest
is the coefficient on the interaction term. Formally, the equation to estimate is:
6
Kenya has provinces subdivided into districts, further subdivided into divisions.
13
N umClinicsjdt = ↵t +
jd
+
1
⇤ P ercentLuojdt +
+ 3 P ostt ⇤ HIV ratejd +
2
⇤ P ercentLuo ⇤ P ostt
4 P ostt
⇤ HIV rated + ✏j
where N umClinicsjdt is the number of health facilities distributing ARVs in division j
of district d in year t. P ostt is a binary variable that is 1 if the observation is from 2008 or
later and 0 if it is earlier. If there exists ethnically-based targeting, one would expect that
2
would be positive and significant.
Columns 1 and 2 of Table 7 shows the estimates of the parameters from the equation
above. The coefficient of interest is the coefficient on the interaction between being a year
after the election and the percent of the population that is Luo. These are reported in
the first row. The first column includes the basic specification without any controls. The
second column HIV rates interacted with P ostt , the indicator for 2008 and later. In each
specification, the coefficient on the interaction term is large, positive and significant. This
provides evidence that Luo areas saw a disproportionate increase in the number of HIV
clinics after the 2007 election.
To better understand the relationship, I replace the outcome with a binary indicator for
whether the division has any ARV clinics, estimating the following equation:
IC linicjdt = ↵t +
+
3
⇤ P ercentLuo ⇤ P ostjdt +
jd
4
+
1
⇤ P ercentLuojdt +
⇤ HIV ratejdt +
5
2
⇤ P ostt
⇤ HIV ratedt + ✏j
where IC linicjdt is an binary variable which takes on a value of 1 in divisions with an
ARV-distributing facility in a given year and 0 otherwise.
Columns 3 and 4 of Table 7 shows the estimates from this equation. Unlike in the
previous table, the coefficients on these interaction terms are consistently insignificant. The
estimates are imprecise enough that it is not possible to conclusively rule out some impact
14
on this margin, but the di↵erence between the two tables is suggestive of an increase in
intensity rather than an expansion to new areas.
The lack of impact on the extensive margin demonstrated in the last columns of 7 is
suggestive of a reduction in welfare as a result of this misallocation. Arbitrary distribution
of scarce resources may not reduce welfare, but this suggests an increase in distribution
without a corresponding increase in access. The degree to which this is true depends on
the degree to which the previously existing ARV-distributing facilities were able to meet the
local demand.
The response of targeting to the ethnic composition is not likely to be linear as specified
above. The analysis from Table 7 is repeated, replacing the dependent variable percent luo
with an indicator for whether the majority of the population is Luo.7 The results, reported
in Tables 8, are qualitatively unchanged.
One explanation for the estimated result is that before the election, Luo areas may have
been disproportionately underserved and the increase was bringing them to where they would
have been otherwise. Limiting the analysis to the years before the election, Table 9 does not
provide evidence that Luo areas were previously underserved.
6
Conclusion
This paper identifies two interesting patterns. First, using a cross-country panel from
sub-Saharan Africa, it shows that corruption is associated with a reduction in efficiency of
imported antiretroviral drugs. The lack of reduction in mortality from the same expenditure
on treatment in relatively more corrupt countries points to a very dangerous consequence of
corruption. Second, using data from within Kenya, I find evidence of political targeting of
HIV treatment, again suggestive of a reduction in efficiency of important health expenditures.
This is extremely preliminary research, and the future direction depends on the credibility
7
The divisions with Luo majorities are in Homa Bay(Kendul Bay, Lake Victoria, Mbita, Ndhiwa, Oyugis,
and Rangwe), Kisumu (Lower Nyakach, Muhoroni, Nyando, Upper Nyakach, and Winam), Migori (Migori
and Nyatike), and Siaya(Bondo, Boro, Rarieda, Ugunja, Ukwala, and Yala)
15
of each piece and whether they ought to be combined or separated. The cross-country
component fits neatly into a literature on the national impacts of corruption on various
outcomes and adds a new outcome with important consequences. The case-study speaks to
a separate literature on political favoritism and targeting of public goods.
There are also a number of ways in which this work could be extended. For the crosscountry analysis, it would be helpful to use additional measures of corruption for robustness.
Further inclusion of the elements that are incorporated into a corruption index could also
help to identify more specific methods. A better understanding of the di↵erences between
di↵erent antiretroviral drugs could illuminate di↵erences in purchases between di↵erent types
of countries to look for di↵erences between types of countries before the drugs are even
received in the country.
The case study could be extended by looking for evidence of di↵erences in outcomes. Using census data, I could obtain better measures of population densities, which combined with
HIV data from MeasureDHS could demonstrate the degree to which - if it all - this targeting
misses out on increasing access to ARVs. Additionally, information about the quantity of
drugs distributed in each facility is available in the data, but still needs substantial cleaning,
could help flesh out the story. Election data from other countries could be combined with
data from MeasureDHS for a coarser measure of targeting - without the detailed information
about ARV-distributing clinics - to get a sense of how generalizable the pattern is.
At this point, this paper presents evidence of large costs of corruption in reducing the
efficiency of health services that are able to save lives. This is combined with suggestive
evidence of one mechanism which may contribute to this relationship. Future work will
expand the analysis of mechanisms through which corruption limits the e↵ectiveness of health
spending in producing outcomes.
16
References
Bardhan, Pranab (1997), “Corruption and Development: A Review of Issues,” Journal of
Economic Literature, 35(3).
Basudde, Elvis (2011), “Where have all the ARVs gone? World Aids Day Supplement” The
New Vision, Kampala, Uganda, December 2, 2011.
Burgess, Robin, Rémi Jedwab, Edward Miguel, and Ameet Morjaria (2009), “Our Turn to
Eat: The Political Economy of Roads in Kenya,” unpublished working paper.
“Corruption feared in sh28b HIV deal” The New Vision, Kampala, Uganda, December 4,
2011.
Jablonski, Ryan (2012), “How Aid Targets Votes: The Impact of Electoral Incentives on
Foreign Aid Distribution,” unpublished working paper.
Kaufmann, Daniel, Aart Kraay, Massimo Mastruzzi, “The Worldwide Governance Indicators:
Methodology and Analytical Issues,” World Bank Policy Research Working Paper No. 5430.
Kramon, Eric and Daniel Posner (2012), “Ethnic Favoritism in Primary Education in
Kenya,” unpublished working paper.
Lewis, Maureen (2006) “Governance and Corruption in Public Health Care Systems,” CGD
Working Paper 78.
Marx, David, Sei Jin Ko, Ray Friedman (2009) “The ‘Obama E↵ect’: How a salient role
model reduces race-based performance di↵erences,” Journal of Experimental Social Psychology 45(4).
Maura, Paolo (1995) “Corruption and Growth,” The Quarterly Journal of Economics,
110(3).
Mills, Edward, Jean Nachega, Iain Buchan, James Orbinski, Amir Attaran, Sonal Singh,
Beth Rachlis, Ping Wu, Curtis Cooper, Lehana Thabane, Kumanan Wilson, Gordon Guyatt,
David Bangsbert (2006), “Adherence to antiretroviral Therapy in Sub-Saharan Africa and
North America: A Meta-analysis,” JAMA, 296(6).
Rajkumar, Andrew Sunil, and Vinaya Swaroop (2008), “Public Spending and Outcomes:
Does Governance Matter?” Journal of Development Economics, 86(1).
“SWAZILAND: Corruption exceeds social services budget,” IRIN, Mbabane, Swaziland, October 12, 2011.
“Zambia: Corruption scandal rocks ARV programme,” PlusNews, Johannesburg, South
Africa, March 14, 2011.
“ZIMBABWE: HIV patients forced to pay up or go without,” PlusNews, Harare, Zimbabwe,
October 5, 2010.
17
7
Figures
Figure 1: ARV clinics in Kenya
8
Tables
18
Table 1: Impact of corruption on e↵ectiveness of ARVs
VARIABLES
ARVs (person years)
(1)
deaths
(2)
deaths
(3)
deaths
-0.0821***
-0.0915**
-0.0832**
(0.0253)
(0.0392)
(0.0409)
0.0356
0.0346*
(0.0254)
(0.0202)
ARVs*Corrupt
ARVs*High GNI
(4)
deaths
(5)
deaths
(6)
deaths
-0.384***
-0.716***
-0.601***
(0.140)
(0.0876)
(0.108)
0.434***
0.396***
(0.120)
(0.107)
0.168***
(0.0440)
Spending on ARVs (1000s)
Spending*Corrupt
Spending*High GNI
1.456*
(0.834)
Corrupt
4,318**
3,538**
4,705***
3,626***
(1,825)
(1,487)
(1,173)
(1,189)
High GNI
HIV prevalence
PLWH
Observations
R2
4,629***
6,249***
(1,414)
(1,574)
1,076
1,113
2,718**
941.1
636.5
2,416**
(1,805)
(1,875)
(1,291)
(1,710)
(1,501)
(946.5)
0.0766**
0.0801***
0.0540***
0.0653**
0.0807***
0.0555***
(0.0298)
(0.0295)
(0.0170)
(0.0259)
(0.0220)
(0.0113)
142
0.998
142
0.998
142
0.998
142
0.998
142
0.998
142
0.999
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
All estimates include both country and year FEs,
and all SEs are clustered at the country level.
19
Table 2: Impact of corruption and other government indicators on e↵ectiveness of ARVs
VARIABLES
(1)
deaths
ARVs (person years)
-0.0621
(2)
deaths
(0.0982)
Spending on ARVs (1000s)
-0.656***
(0.225)
ARVs*Corrupt
0.0148
(0.0918)
Spending*Corrupt
0.410***
(0.128)
ARVs*High GNI
0.177***
(0.0504)
Spending*High GNI
1.427
(0.855)
ARVs*Good Rule of Law
0.0396
(0.168)
Spending*Good Rule of Law
-0.0832
(0.329)
ARVs*E↵ective Governance
-0.0593
(0.112)
Spending*E↵ective Governance
0.136
(0.302)
Corrupt
High GNI
Good Rule of Law
E↵ective Governance
HIV prevalence
PLWH
Observations
R2
3,064
3,452**
(2,389)
(1,472)
4,659***
6,588***
(1,259)
(1,411)
376.8
-664.0
(3,633)
(2,368)
-1,730
-760.8
(2,568)
(1,636)
2,756**
2,172**
(1,341)
(1,032)
0.0526***
0.0571***
(0.0175)
(0.0118)
142
0.998
142
0.999
Robust standard errors in parentheses
*** p<0.01, **20
p<0.05, * p<0.1
All estimates include both country and year FEs,
and all SEs are clustered at the country level
Never Rich
Sometimes Rich
Table 3: Countries by corruption status
Never Corrupt
Sometimes Corrupt
Always Corrupt
Burkina Faso
Benin
Burundi
Eritrea
Comoros
Cameroon
Ghana
Djibouti
Central African Republic
Lesotho
Ethiopia
Chad
Madagascar
Gambia
Cote d’Ivoire
Mali
Guinea
Guinea-Bissau
Mauritania
Liberia
Kenya
Mozambique
Malawi
Niger
Rwanda
Nigeria
Togo
Sierra Leone
Zambia
Sudan
Uganda
Senegal
Sao Tome and Principe
Always Rich
Angola
Zimbabwe
Botswana
Gabon
Republic of the Congo
Cape Verde
Tanzania
Democratic Republic of the Congo
Namibia
Equatorial Guinea
Seychelles
Somalia
South Africa
Swaziland
Countries categorized as rich if GNI is higher than mean and as more corrupt if the control
of corruption score is below the mean.
21
Table 4: Comparison of more and less corrupt countries
Variable
Less Corrupt More Corrupt
HIV prevalence
7.442
4.456
(8.768)
(4.467)
PLWH
607633.33
444457.65
(1320124.3)
(624440.62)
ARVs (person years)
26416.174
24679.665
(60638.485)
(60317.787)
Money for ARVs (1000s)
5481.701
7041.231
(11247.696)
(15658.17)
Table 5: Drugs purchased by country, by dose
Variable
Less Corrupt More Corrupt
Abacavir (ABC)
1.42
1.77
Combination
32.22
23.17
Didanosine (ddI)
4.05
2.96
Efavirenz (EFV)
2.73
21.77
Indinavir (IDV)
.03
.04
Lamivudine (3TC)
2.14
11.33
Nelfinavir (NFV)
.07
.32
Nevirapine (NVP)
21.52
3.99
Ritonavir (RTV)
.1
1.39
Saquinavir (SQV)
.07
.
Stavudine (d4T)
8.04
24.33
Tenofovir (TDF)
0
0
Zidovudine (ZDV)
27.6
8.94
Table 6: Drugs purchased by country, by money spent
Variable
Less Corrupt More Corrupt
Abacavir (ABC)
2.32
5.36
Combination
66.03
60.29
Didanosine (ddI)
5.71
2.2
Efavirenz (EFV)
7.17
16.14
Indinavir (IDV)
.17
1.65
Lamivudine (3TC)
2.78
1.71
Nelfinavir (NFV)
.55
1.11
Nevirapine (NVP)
8.05
2.29
Ritonavir (RTV)
.15
.43
Saquinavir (SQV)
1.05
.
Stavudine (d4T)
.68
4.17
Tenofovir (TDF)
0
1.26
Zidovudine (ZDV)
5.33
3.38
22
Table 7: Targeting of introduction of ARVs in health facilities in Kenya
(1)
(2)
(3)
(4)
VARIABLES
Num. ARV clinics Num. ARV clinics Any ARV clinics Any ARV clinics
Post*PercLuo
2.079***
(0.528)
1.753**
(0.874)
1.553
(2.565)
0.727
(4.841)
Post*HIVdivision
Post*HIVdistrict
0.0442
(0.0760)
-0.0681
(0.161)
-0.132
(0.306)
0.774
(0.685)
Observations
1,568
1,260
1,568
1,260
R-squared
0.721
0.724
0.747
0.748
Clusters
224
180
224
180
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Standard errors clustered at the division level. All estimates include division and year FEs.
Table 8: Targeting of introduction of ARVs in health facilities in Kenya
(1)
(2)
(3)
(4)
VARIABLES
Num. ARV clinics Num. ARV clinics Any ARV clinics Any ARV clinics
Post*LuoMajority
1.906***
(0.463)
Post*HIVdivision
Post*HIVdistrict
Observations
1,568
R-squared
0.721
Clusters
224
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Standard errors clustered at the division level.
23
1.631**
(0.714)
1.635
(2.588)
0.792
(4.496)
0.0540
(0.0705)
-0.0388
(0.131)
-0.144
(0.296)
0.684
(0.638)
1,260
0.725
180
1,568
0.747
224
1,260
0.748
180
All estimates include division and year FEs.
VARIABLES
LuoMajority
HIVdivision
HIVdistrict
Table 9: Previously underserved?
(1)
(2)
(3)
Num. ARV Clinics Any ARV clinics Num. ARV clinics
0.237
(0.380)
0.130
(0.858)
2.501
(1.630)
-0.0392
(0.163)
-0.0992
(0.383)
1.148
(0.849)
PercLuo
Observations
720
720
R-squared
0.212
0.266
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Standard errors clustered at the division level.
All estimates include division and year FEs.
24
(4)
Any ARV clinics
0.0423
(0.829)
1.847
(1.617)
0.448
(0.404)
-0.125
(0.374)
0.914
(0.896)
0.0288
(0.193)
720
0.215
720
0.266
Parental Health, Child Labor and Schooling Outcomes: Evidence from
Malaria and HIV/AIDS Inflicted Region in Tanzania
Shamma Adeeb Alam
University of Washington - Seattle
Abstract
This study examines the impact of parents’ health on child labor and schooling outcomes in
agricultural societies. Despite the effect of numerous fatal diseases on households, there has been
no prior research that focuses on the effect of illness of adult household members on child
education or child labor. Employing longitudinal data from the Kagera region in Tanzania, a
region severely affected by malaria and HIV/AIDS, this study demonstrates that parental
sickness lead to increased child labor among these agricultural households. Consequently, the
increased child labor leads to lower school attendance and enrollment. Subsequently, it
culminates in children failing their grade and in some cases dropping out of school altogether.
This paper explains how the effect on child labor and school enrollment is especially higher
when single-mothers or both parents are sick. Furthermore, the provision of greater household
wealth acts as a buffer against heightened child labor and lower school enrollment when adults
are ill. In other words, households with greater assets are better able to cope with health shocks,
and hence do not need to increase child labor to weather the shock. Additionally, fathers’ illness
lead to greater hours of outside (including farm) employment, while sickness of mothers or both
the parents lead to greater hours in household chores. There is also a gender-difference in hours
worked as girls work more than boys because of parental illness. This gender difference is
mainly present for household chores but not for outside employment. Lastly, older children are
likely to work more in the farm. The paper concludes with policy implications.
1
Introduction
Child labor continues to be a serious problem in developing countries. It is estimated that
there are still over 200 million children laborers worldwide (ILO, 2010). An important
consequence of increased child labor is reduction in children’s schooling. Edmonds (2005)
summarizes many factors that affect child labor and educational outcomes. Although prior
research examines many factors that affect child labor and educational outcomes (Edmonds,
2005), the effect of parental illness have received very little empirical attention. Diseases like
HIV/AIDS and malaria have devastating impacts on adult health with high levels of morbidity
and mortality. Hence, these diseases are likely to affect parent’s decisions on whether to send a
child to school or whether to use them as a child labor to replace a sick adult labor.
Understanding these family decisions can help us better target policies to reducing child labor
and improve education.
This study examines the influence of parental health on children’s labor and schooling
outcomes. Employing longitudinal data from Tanzania, focusing on children aged 7 to 15, this is
the first study to show that parental illness has a direct impact on child labor and educational
outcomes. Illness of fathers and mothers lead to increased hours of child labor, which
consequently leads to reduced school attendance and enrollment. These effects are especially
higher when single-mothers are ill or if both parents are ill. However we find no other consistent
impact on child labor or school enrollment when other adults, such as siblings, grandparents,
uncles and aunts of the child, are ill. This study further finds that greater household wealth acts
as a buffer against greater child labor. In other words, households with greater assets are better
able to cope with adult health shocks and hence do not need to increase child labor to deal with
the shock.
2
Furthermore, this study shows evidence that parental illness leads to greater gender
difference in housework as girls work more than boys when parents are ill. However, there is no
gender gap in the increase in outside employment. Additionally, hours of outside employment of
children increases when only fathers are ill and hours of household chore increases when only
mothers or both the parents are ill. Lastly, I find that older children are more likely work
increased hours and less likely to enroll in school because of adult illness. We use a child-level
fixed effects model to control for household preferences or birth order effects.
This paper makes four contributions to the literature. First, it contributes to the child labor
literature as it shows that parental illness is a significant determinant of child labor. Although
prior studies have shown that numerous factors affect child labor (Edmonds, 2005), there is only
limited evidence on the effect of parental health on child labor. Dillon (2008) finds that only
illness of mothers in Mali increases child labor. However, as his study is based on cross-sectional
data, it does not control for time-invariant child or household level heterogeneity that can bias
results.1
Second, this study contributes to the education literature as it demonstrates that parental
illness lead to lesser school enrollment, and hence fewer children advancing to the next grade.
The only prior study having examined this relationship is Sun and Yao (2010). They find that
illness of parents causes reduced enrollment and completion of middle school. However, their
study is based on retrospective survey that asks households to recall illness and health
expenditure in the prior 15 years, which may lead to reporting errors arising from such long
1
Certain inherent characteristics can cause households are likely to have more sick people and also more child labor.
If we do not control for unobservable household characteristics, it will lead to a biased result.
3
recall periods.2 Sun and Yao (2010) also does not address potential endogeneity issues as it does
not control for household and child’s unobserved characteristics. I employ child fixed effects
model to address the unobserved heterogeneity and endogeneity issues.
Third, my findings contribute to the consumption smoothing literature and permanent
income hypothesis. This literature states that households use savings and borrowing to adjust
their consumption during economic booms and busts. Several studies (Beegle et al, 2006; Duryea
et al, 2007; Guarcello et al, 2010; Janvry et al., 2006) demonstrate that households increase child
labor to smoothen their consumption during income shocks (i.e. sudden loss of income). Child
labor may also be used to smoothen household consumption during adult illness. Adult illness
affects household budgets in two ways: greater health care expenditure and reduced income
through forgone labor hours. Households can cope with these shocks (i.e. illness) using savings,
credits or buffer stock of assets. However, if households lack buffer stock or are credit
constrained, they are likely to resort to increased child labor to cope with adult illness.
Lastly, it contributes to the health policy literature. The health literature documents the
various consequences of illness, including fatal diseases like HIV/AIDS and malaria. This study
demonstrates the effect of these and other illnesses on children’s labor and educational outcomes,
which did not receive prior attention in the literature.
Data
This study uses a panel data survey, named Kagera Health and Development Survey
(KHDS), from the Kagera region in Tanzania. The survey is conducted by the World Bank and
2
Errors may occur as respondents may forget some illnesses in the last 15 years or may not recall the precise time of
the sickness. The study focuses only on major health shocks. However, smaller health shocks can also have a
significant effect on education as shown by my study.
4
the University of Dar es Salaam in four rounds from 1991 through 1994. It surveyed over 800
households, drawn from 51 communities (49 villages) in the six districts of Kagera. The average
interval between each of the survey rounds was between six and seven months. The sample
selection was based on a variable probability sampling procedure (a two-stage, randomized
stratified procedure) based on expected mortality.3 The Kagera region has suffered the
devastation of both HIV/AIDS and malaria. In some parts of Kagera, the HIV/AIDS rate was as
high as 20 percent of adults during the time of the study. Similarly, for malaria, more than 10
percent of children have an adult member of the family who have been diagnosed with malaria.
And an additional 20 percent think that they have malaria as they have malaria type symptoms,
although they did not approach a medical practitioner. As this area has suffered from these fatal
diseases, this region is an ideal area to study of the effects of adult health on children’s
outcomes.
The data contain detailed information on individual and household level demographic
and socioeconomic characteristics, which makes it suitable for this study. It contains data on
child’s age, education and enrollment status. It also provides detailed data on value of household
asset holdings, which include business equipment, durable goods, land, livestock and personal
savings. Additionally, the survey provides detailed time use data in the past seven days of all
household members aged 7 and above, hence allowing us to find the number of hours worked by
children. Furthermore, household members were asked to report any illness that they have
suffered in the past 4 weeks. They were further asked about the number of days of work, if any,
that they have missed because of their illness. As there can be a huge variation in the severity of
illness, I only consider an individual to be ill, if they have missed at least a day’s worth of work.
3
For further details on the sample selection, please refer to World Bank (2004).
5
Using this data on illness of all adult household members aged 18 and above, I find its effect on
child labor and education of children between the age of 7 and 15. Summary statistics of the data
employed are provided in Table-1.
Results
Table 2 demonstrates the impact of parental illness on child labor. I find that parental
illness causes an increase in children’s hours worked by 2 to 4 hours each week, which
corresponds to an approximately 15 to 25 percent increase. The maximum increase of about 25
percent is when single mothers are ill. To further understand the nature of the child labor, I
disaggregate the total hours worked by household chore hours and time spent at external
employment (such as, in the farm) in table 3. The results show that illness of mothers or both the
parents cause an increase in household chore hours, but father’s illness cause an increase in time
spent working outside home.
Although there is an increase in hours worked on average, it is important to study if
parental illness cause children to enter the labor force, who previously were not working.
Therefore, I employ a dichotomous binary variable which indicates if a child is working (1
represents working and 0 represents not working). The results are presented in Table 4. My
estimates indicate that only in dire conditions, which is when both parents are ill or a single
mother is ill, a child is forced to start working, typically in housework rather than farm-work.
Next, we find the impact of parental illness on children’s schooling outcomes. Table 5
shows that parental illness, i.e. if father, mother or both parents being ill, significant reduces
school attendance among children across different age groups. However, in addition to parents, I
also find that illness of grandparents also cause a reduction in children’s school attendance. Next,
6
in table 6, we find the effect of parental illness on children’s school enrollment. The estimates
shows that if the father or mother is ill, children are significantly less likely to be enrolled in
school. Although, both parents being ill has the correct sign, it is not statistically significant,
probably because only a small sample of children have both parents who are ill.
In the last section, we find the parental illness’ differential impact through gender, age
and household wealth. First I find the impact of parental illness on child labor for three age
groups: 7-9, 10-12, and 13-15. I find that older children are more likely to work when their
parents are ill, which is especially true for the middle age group, 10-12. The increase in hours
worked for children aged 10-12 is greater than the age group 13-15 is probably because the
higher age group already works near their full potential and hence are unable to increase their
hours worked as much as the 10-12 age group. Disaggregating the hours worked by farm work
and household chores, I find that older children are more likely to work in the farm when the
father is ill, and more likely to work for household chores when both parents are ill. Lastly,
school attendance also declines for older children because of parental illness.
I also disaggregate the increase in child labor by gender (Table 8), and find that girls are
likely to work more hours compared to boys, when the mother is ill or both her parents are ill.
Girls work more than boys by as much as approximately 4.5 hours, which is about 30 percent
increase in weekly hours worked. The increase in hours worked is predominantly for household
chores. However, somewhat surprisingly, there is no significant difference between boys and
girls in increase in work at the farm when any of the parents are ill.
Lastly, I examine if household wealth mitigate the effect of health shocks (i.e. parental
illness) on child labor. I control for the wealth in the previous period before the health shock has
occurred, i.e. controlling for wealth 6 months prior to the current survey round. I also include an
7
interaction term between household wealth and parental illness, which could capture the
mitigating effect of wealth when there is parental illness in the household. The results are
presented in Table 9. I find that parental illness continue to have a significant effect on the
number of hours worked, not only at the aggregate level, but also at the household and the farm
level. Furthermore, the interaction terms between illness and household assets have a negative
and significant effect when the father or the mother is ill. It indicates that given that a parent is
ill, greater assets would lead to fewer hours of work. This demonstrates that assets act as a buffer
to increased child labor as wealthier households are better able to weather the shocks.
References
Beegle, K., Dehajia, R., & Gatti, R. 2006. “Child labor and agricultural shocks.” Journal of
Development Economics 81: 80-96.
Dillon, A. 2008. Child labor and schooling responses to production and health shocks in
Northern Mali. IFPRI Working Paper.
Dureya, S., Lam, D., & Levison, D. 2007. “Effects of economic shocks on children's
employment and schooling in Brazil.” Journal of Development Economics 84(1): 188-214.
Edmonds, Eric V., 2008. "Child Labor," Handbook of Development Economics, Elsevier.
Guarcello, L., Mealli, F., & Rosati, F.C. 2010. Household vulnerability and child labor: the effect
of shocks, credit rationing, and insurance. Journal of Population Economics 23: 169-198.
Janvry, A., Finan, F., & Vakis, E.S.R. 2006. “Can conditional cash transfer programs serve as
safety nets in keeping children at school and from working when exposed to shocks?” Journal of
Development Economics 79: 349-373.
Sun, A., & Yao, Y., 2010. “Health shocks and children's school attainments in rural China.”
Economics of Education Review 29: 375-382.
8
Table 1: Summary Statistics:
Variable
Mean
Std. Dev.
Hours worked
Hours worked for children with hours>0
18.3
20.1
14.96
14.5
Only father ill
Only mother ill
- single mother ill
- non-single mother ill
Both parents ill
13%
22%
9%
13%
8%
0.34
0.41
0.28
0.33
0.27
Adult sibling ill
Grand parents ill
Uncle/aunts ill
Other household members ill
14%
3%
3%
4%
0.34
0.18
0.16
0.20
Only father ill x Child ill
Only single mother ill x Child ill
Only non-single mother ill x Child ill
Both parents ill x Child ill
Only mother ill x Child ill
5%
4%
5%
3%
8%
0.22
0.19
0.21
0.18
0.27
165583
39%
11.1
1.6
34%
2016109
0.49
2.6
2.0
0.47
7.8
3.7
Per capita asset owned (in Tanzanian shillings)
Number of child illness
Age
Education
Percentage of crop loss
Number of household members
N
5495
Table 2: Effect of parental illness on child labor hours
(1)
Parents ill
(2)
(3)
(4)
3.05**
2.91**
2.71*
(1.52)
(1.50)
(1.47)
2.55**
2.45**
2.29**
(1.16)
(1.17)
(1.15)
4.53***
4.01***
(1.44)
(1.44)
2.32**
2.17*
(1.15)
(1.13)
1.51
3.65
(2.30)
(2.52)
-0.69
-0.71
(1.04)
(1.00)
0.31
0.37
(2.33)
(2.60)
0.70
-0.79
(1.54)
(2.04)
2.96***
(0.73)
Both parents ill
Only father ill
Only mother ill
3.12***
(0.92)
- Single mother ill
- Non-single mother ill
Grand parents ill
Adult sibling ill
Uncle/aunts ill
Other household members ill
Number of household members
-0.52**
(0.24)
Number of observations
5495
5495
5495
5495
Table 3: Effect of parental illness on hours worked in farm and home
Household chore hours
Only father ill
Only mother ill
0.40
0.39
1.84**
1.76**
(0.71)
(0.71)
(0.75)
(0.75)
2.01***
0.81
(0.56)
(0.61)
- single mother ill
- non-single mother ill
Both parents ill
Grand parents ill
Adult sibling ill
Uncle/aunts ill
Other household members ill
Number of HH members
Number of observations
N
Farming hours
2.19**
1.72*
(0.88)
(0.96)
1.85***
0.26
(0.70)
(0.76)
2.66***
2.64***
0.15
0.01
(0.92)
(0.92)
(1.01)
(1.01)
0.87
0.87
2.00
2.02
(1.39)
(1.39)
(1.83)
(1.82)
-0.30
-0.30
-0.37
-0.38
(0.57)
(0.57)
(0.69)
(0.69)
1.06
1.06
-0.67
-0.71
(1.12)
(1.12)
(2.07)
(2.07)
-1.05
(1.10)
-0.37**
(0.14)
-1.05
(1.10)
-0.37***
(0.14)
0.47
(1.41)
-0.14
(0.16)
0.46
(1.40)
-0.14
(0.16)
5495
5495
5495
5495
Table 4: Effect of parental illness on likelihood of child labor (Child previously not working now coming
into child labor)
Only father ill
Only single mother ill
Only non-single mother ill
Both parents ill
Only father ill x Child ill
Only single mother ill x Child ill
Only non-single mother ill x Child ill
Both parents ill x Child ill
Number of observations
Aggregate
Houseehold chores
Employment work
0.012
0.001
0.035
(0.021)
(0.023)
(0.032)
0.061***
0.042*
0.054
(0.022)
(0.026)
(0.039)
0.013
0.014
-0.021
(0.018)
(0.020)
(0.037)
0.083***
0.071**
0.043
(0.027)
(0.032)
(0.051)
-0.004
-0.020
-0.029
(0.026)
(0.030)
(0.044)
-0.028
-0.031
0.013
(0.027)
(0.029)
(0.052)
0.038
0.014
0.081
(0.026)
(0.031)
(0.046)
-0.093***
-0.059*
-0.17***
(0.035)
(0.036)
(0.054)
5495
5495
5495
Table 5: Effect of parental illness on school attendance
Only school going children
Age group 7-15
Both parents ill
Only father ill
Only mother ill
Uncle/aunts ill
Other household members ill
Number of observations
Age group 7-15
Age group 8-15
-0.059*
-0.061*
-0.060*
-0.074*
-0.073*
-0.022
-0.024
(0.04)
(0.036)
(0.037)
(0.037)
(0.040)
(0.040)
(0.032)
(0.034)
-0.120***
-0.12***
-0.116***
-0.115***
-0.116***
-0.115***
-0.067**
-0.076**
(0.04)
(0.038)
(0.038)
(0.038)
(0.039)
(0.039)
(0.030)
(0.033)
-0.057**
-0.063**
-0.068***
(0.02)
(0.025)
(0.025)
Only non-single mother ill
Adult sibling ill
Age group 9-15
-0.059*
Only single mother ill
Grand parents ill
Age group 8-15
All children
-0.067*
-0.081**
-0.081**
-0.038
-0.058
(0.041)
(0.042)
(0.040)
(0.037)
(0.039)
-0.051*
-0.051*
-0.059*
-0.06**
-0.054*
(0.029)
(0.030)
(0.031)
(0.029)
(0.030)
-0.10*
-0.098*
-0.097*
-0.097*
-0.107*
-0.107*
-0.021
-0.035
(0.05)
(0.054)
(0.055)
(0.055)
(0.061)
(0.061)
(0.038)
(0.044)
0.011
0.011
0.022
0.023
0.018
0.019
-0.023
-0.011
(0.03)
(0.028)
(0.028)
(0.028)
(0.029)
(0.029)
(0.028)
(0.029)
0.152
0.152
0.152
0.152
0.163
0.163
0.098
0.137
(0.10)
(0.096)
(0.098)
(0.098)
(0.106)
(0.106)
(0.096)
(0.116)
0.091
0.091
0.084
0.084
0.085
0.086
0.035
0.044
(0.05)
(0.052)
(0.052)
(0.052)
(0.057)
(0.057)
(0.057)
(0.053)
2987
2987
2886
2886
2704
2704
4590
4046
Table 6: Effect of parental illness on school enrollment
Only father ill
Only single mother ill
Only non-single mother ill
Both parents ill
Adult sibling ill
Grand parents ill
Number of observations
Age group 7-15
Age group 8-15
Age group 9-15
-0.039*
-0.048*
-0.058**
(0.025)
(0.028)
(0.027)
-0.015
-0.031
-0.034
(0.029)
(0.031)
(0.029)
-0.044*
-0.042*
-0.032
(0.026)
(0.027)
(0.027)
0.002
0.008
0.004
(0.026)
(0.026)
(0.024)
-0.018
-0.017
-0.014
(0.020)
(0.023)
(0.023)
-0.019
-0.026
-0.084
(0.029)
(0.042)
(0.053)
4590
4046
3533
Table 7: Effect of age group on child labor and school attendance
Aggregate
Both Parents ill x Age 10-12
x Age 13-15
Only father ill x Age 10-12
x Age 13-15
Only mother ill x Age 10-12
x Age 13-15
House hours
School Attendance
0.27
0.64
-0.30
-0.01
0.55
0.60
-0.072
-0.069
(1.92)
(1.92)
(1.19)
(1.19)
(1.20)
(1.19)
(0.05)
(0.052)
2.28
2.78
-0.15
0.09
2.29**
2.51**
-0.094*
-0.086*
(2.00)
(2.00)
(1.36)
(1.37)
(1.20)
(1.20)
(0.05)
(0.054)
4.15***
4.37***
3.64***
3.84***
0.39
0.43
-0.028
-0.026
(1.42)
(1.42)
(0.94)
(0.95)
(0.95)
(0.96)
(0.05)
(0.046)
2.36*
2.65*
2.60**
2.76**
-0.29
-0.15
-0.087*
-0.081*
(1.62)
(1.62)
(1.09)
(1.10)
(0.98)
(0.98)
(0.05)
(0.051)
1.61
0.75
0.92
0.002
(1.35)
(0.92)
(0.87)
(0.05)
-0.36
-0.12
-0.07
-0.056
(1.33)
(0.94)
(0.82)
(0.05)
Only non-single mother ill x Age 10-12
x Age 13-15
Only single mother ill x Age 10-12
x Age 13-15
Number of observations
Farm hours
5495
3.44*
2.68**
0.76
0.013
(1.96)
(1.29)
(1.18)
(0.058)
1.74
1.00
0.85
-0.008
(1.74)
(1.20)
(1.13)
(0.059)
-0.80
-1.92*
1.17
-0.022
(1.55)
(1.07)
(1.21)
(0.089)
-3.22
-1.75
-1.50
-0.135
(2.01)
(1.46)
(1.13)
(0.095)
5495
5495
5495
5495
5495
2886
2886
Table 8: Effect on girl's hours worked
Aggregate
Both parents ill x Daughter
Only father ill x Daughter
Only mother ill x Daughter
2.45
2.67**
2.41**
0.19
-0.11
(1.73)
(1.76)
(1.13)
(1.14)
(1.11)
(1.13)
-0.44
-0.84
-0.01
-0.19
-0.46
-0.68
(1.34)
(1.34)
(0.85)
(0.85)
(0.89)
(0.90)
1.76*
1.57**
0.19
(1.14)
(0.70)
(0.81)
Only non-single mother ill x Daughter
Only father ill
Only mother ill
4.38**
2.80***
1.56
(1.75)
(1.05)
(1.32)
-0.11
0.70
-0.81
(1.48)
(0.91)
(1.05)
-1.56
-0.90
-1.27
-0.90
-0.14
0.16
(2.75)
(2.79)
(1.74)
(1.78)
(1.93)
(1.96)
3.03
3.53
0.41
0.68
2.52
2.76
(2.41)
(2.42)
(1.42)
(1.42)
(1.71)
(1.72)
0.16
-0.43
0.53
(1.94)
(1.16)
(1.38)
Only single mother ill
Only non-single mother ill
Number of observations
Farm hours
3.0*
Only single mother ill x Daughter
Both parents ill
House hours
5495
-2.75
-2.14
-0.65
(3.19)
(1.64)
(2.48)
2.27
0.76
1.45
(2.43)
(1.56)
(1.65)
5495
5495
5495
5495
5495
Table 9: Breakdown of effects by wealth
Only father ill
Only single mother ill
Only non-single mother ill
Both parents ill
Assets x Only father ill
Assets x Only single mother ill
Assets x Only non-single mother ill
Assets x Both parents ill
Number of observations
Total Hours
Household chores
Farm hours
3.99***
(1.41)
6.35***
(2.30)
4.49**
(1.76)
0.68
(2.15)
0.7081
(0.823)
2.28*
(1.370)
2.68**
(1.045)
1.86*
(1.157)
3.17***
(0.97)
3.94**
(1.60)
1.73
(1.18)
-1.22
(1.40)
-0.03***
(0.00)
-4.25
(4.72)
-0.82**
(0.42)
-0.09
(0.35)
-0.035***
(0.003)
0.364
(2.52)
-0.347
(0.318)
0.229
(0.177)
0.003
(0.003)
-4.54*
(2.570)
-0.458
(0.375)
-0.322*
(0.203)
3568
3568
3568