WORKING PAPER
Evaluation of a Female Sterilization Campaign in
Peru
An Application of Propensity Score Reweighting Methods with
Unobserved Participation Status
Tanya Byker and Italo Gutierrez
RAND Labor & Population
WR-1118
September 2015
This paper series made possible by the NIA funded RAND Center for the Study of Aging (P30AG012815) and the NICHD funded RAND
Population Research Center (R24HD050906).
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EVALUATION OF A FEMALE STERILIZATION CAMPAIGN IN PERU:
AN APPLICATION OF PROPENSITY SCORE REWEIGHTING METHODS WITH
UNOBSERVED PARTICIPATION STATUS
Tanya Byker
Department of Economics, Middlebury College
tbyker@middlebury.edu
Italo A. Gutierrez
RAND Corporation
italo@rand.org
September 30, 2015
Abstract
We evaluate the impact of a female sterilization campaign in Peru in 1990s using a
propensity score reweighting (PSR) method that accounts for a contaminated treatment group
problem: while we observe sterilizations, we do not know which sterilizations were part of the
campaign and which would have occurred in the absence of a campaign. Using our PSR method,
we estimate that women sterilized as part of the campaign had on average 1.2 fewer children by
2004. In contrast, women sterilized outside the campaign had 0.6 fewer children by 2004. We
also estimate impacts of the campaign on other household outcomes.
Keywords: female sterilization; fertility; family planning; contaminated data models; propensity
scores.
JEL codes: C21, J13
ACKNOWLEDGEMENTS
We are grateful to Martha Bailey, Robert Garlick, Andrew Goodman-Bacon, David Lam,
and Jeffrey Smith for helpful comments and guidance. We also thank Matthew Cefalu for his
help with the Monte Carlo analysis. This research was supported by an NICHD training grant to
the Population Studies Center at the University of Michigan (T32 HD007339), by a William and
Flora Hewlett Foundation/Institute of International Education Dissertation Fellowship in
Population, Reproductive Health and Economic Development, and by funding from the Center
for Causal Inference at the RAND Corporation.
1. INTRODUCTION
In the late 1995 President Fujimori of Peru initiated an aggressive family planning campaign
with the stated purpose of addressing widespread poverty in the country. Evidence seemed to
support Fujimori’s claim that there was a “vicious circle [of] poverty--unwanted child--poverty”
in Peru.1 In the early 1990s, 35 percent of women reported that their latest birth was not wanted;
this percentage increased to 65 percent among women with three or more children.2 Although the
campaign initially had support from the United Nations (UNFPA), USAID and local and
international NGOs, its implementation remains controversial. Tubal ligation, a form of female
sterilization, was a publicly stated element of the campaign. However, by the year 1998,
controversy erupted regarding whether health workers were given large sterilization quotas and
used “bribes,” coercion, and even physical force to meet them.3 As of today, there are still no
1
Address by President Alberto Fujimori at the United Nations, New York, during the 21st
Special Session of the General Assembly, 30 June - 2 July 1999. URL:
http://www.un.org/popin/unpopcom/32ndsess/gass/state/peru.pdf. Accessed on: Monday,
September 19, 2011.
2
Data from the Peruvian Demographic and Health Survey (DHS II, 1991-1992) from a question
asked of all women who gave birth within the last five years.
3
A report by Tamayo (1999) from the NGO Flora Tristan published in 1999 provides evidence
based on interviews with sterilized women and investigations of rural “health festivals.” The
post-Fujimori government of Alejandro Toledo also produced reports documenting human rights
violations under the Fujimori sterilization campaign. The Toledo government was, however,
reported to be opposed to birth control in general on religious grounds (Boesten, 2007, del
Aguila, 2006).
1
official reports of how the campaign was carried out, what population it targeted and how many
women participated. The purpose of this paper is to provide some initial answers to these
questions. Specifically, we seek to understand which and how many women were affected by the
sterilization campaign and to estimate its causal effect on fertility (family size) and on other
household outcomes.
The main challenge in evaluating the sterilization campaign is the lack of public information
about women who participated in the campaign or how the campaign was implemented. The best
next available data come from the Peruvian Demographic and Health Surveys (DHS). These
surveys ask women 15 to 49 years old whether they have been sterilized and the year of
sterilization. As shown in Figure 1, there is a dramatic spike in female sterilizations in 1996 and
1997 and an equally dramatic fall by 1998 when the controversy erupted and the campaign was
allegedly dismantled. However, no information on participation in sterilization campaigns is
available in the DHS.
It is important to distinguish between women who were sterilized because of the campaign
versus women who would have chosen sterilization even in the absence of the campaign because
the impact of sterilization is likely different for the two groups of women. For example, we
suspect that women who would have chosen sterilization even in the absence of a government
campaign were on average more educated, urban women who had access to a broader set of
contraceptive options compared to the less-educated rural women who were allegedly targeted
by the campaign. The impact of sterilization will likely be different if it is one of several
contraceptive options compared to a situation where few other methods were previously
available and sterilization is presented as a sole alternative. If there are heterogeneous effects of
2
sterilization, simply using the population of women sterilized during the campaign years to
evaluate the effects of the campaign will result in biased estimates.
In this paper we have developed a propensity score estimation strategy that allows us to
separate the population of sterilized women into those who were and were not treated by the
campaign despite the fact that participation in the campaign is unobserved. Our method allows
us to estimate causal effects of the campaign, provided that two probabilities can be estimated: i)
the probability of sterilization during the campaign years (1996-1997) and ii) the conditional
probability that if a woman was sterilized during those years, it happened as part of the
campaign. We find that over one third of the sterilizations that occurred during the years 19961997 were part of the government campaign; or alternatively, the campaign increased the number
of sterilizations by about 62%. We also find that roughly half of the women treated by the
campaign lived in rural areas and a quarter were from rural mountain regions. We estimate that
participation in the sterilization campaign resulted in 0.41 fewer children per woman on average
by 2000, and 1.16 fewer children per woman by 2004. We find small and non- or marginally
significant impacts of the sterilization campaign on women's and children's outcomes, with the
exception of substantial and statistically significant improvements in the height for age (a
measure of health) of girls whose mothers participated in the campaign.
[Insert Figure 1 here]
Our paper also contributes to the literature on estimation of treatment effects with
contaminated data. In contaminated data models, some observations are contaminated, while
3
others are clean (Chen, Hong and Nekipelov, 2011).4 For example, Hotz, Mullin and Sanders
(1997) adapt the method of Horowitz and Manski (1995) for bounding the distribution of a
contaminated random variable to estimate the causal effect of teenage childbearing on the
education and labor market outcomes of women. The key problem is to estimate the mean
counterfactual outcomes for women who gave birth as a teenager. Hotz, Mullin and Sanders
(1997) propose using information from teenagers who experienced a miscarriage to estimate that
counterfactual. However, teenagers that experienced miscarriage form a contaminated control
group. Some of them experience a miscarriage randomly and would have given birth otherwise.
Other teenagers who experience miscarriage would have otherwise decided to abort. And some
miscarriages may occur non-randomly to teenagers who smoke, use drugs or have other adverse
health behavior, which also affect their schooling and labor market outcomes. Only the first
subgroup provides a clean comparison. If the researchers could observe the nature of the
miscarriage (random or not) and what the pregnancy outcome would have been in the absence of
miscarriage (birth or abortion), they could use only the outcomes from teenagers who experience
miscarriages randomly and would have given birth otherwise to estimate the counterfactual-information that is typically unobservable. Hotz, Mullin and Sanders (1997) show that placing a
bound (obtained from epidemiological studies) on the proportion of teen miscarriages that occur
randomly and would otherwise have resulted in births allows them form bounds on the mean
counterfactual, and therefore on the mean casual effect. Our empirical problem is similar, but we
have both a contaminated treatment group and a contaminated control group. Among women
who were sterilized in the years 1996-1997, some of them participated in the sterilization
4
In contrast, in measurement error models all observations can be measured but with errors of
different magnitudes Chen, Hong and Nekipelov (2011).
4
campaign (our group of interest), while others were sterilized outside of the campaign. Similarly,
among women who were not sterilized in those years and form our control group, some of them
had a higher latent-risk of participating in the campaign (the cleaner control group), whereas
some of them had a lower latent risk of participation in the campaign, or a lower risk of any
sterilization at all. Using our methodology, we are able to obtain point identification of the
effects of the Fujimori sterilization campaign (FSC).
Our approach is also related to work by Botosaru and Gutierrez (2014), who develop a
difference-in-difference estimator when treatment status is observed in only one period. Their
methodology uses repeated cross-sections and relies on the ability to predict treatment status in
one period based on knowledge of treatment status in the other period and auxiliary information
available in both cross-sections. Similar to our approach, the Botosaru and Gutierrez (2014)
method provides point estimates of the average treatment on the treated. Our empirical problem
is different, however, in that we aim to estimate impacts for a subgroup of interest whose
membership is not observable. Rather than a pre-post comparison as in Botosaru and Gutierrez,
we rely on cross-sectional data and propensity scores reweighting (PSR) methods. To the best of
our knowledge, this paper is the first that combines PSR methods with contaminated data
models.
The method we develop in this paper can be applied to other situations where researchers are
interested in evaluating the effect of an intervention for a particular subgroup (e.g. individuals
that were more compliant with the intervention, individuals who receive a more intense
intervention, or individuals who received a better quality intervention) but membership to the
subgroup of interest is not observed in the data. If the probability of belonging to the subgroup
5
can be estimated from observable auxiliary information, then it is possible to apply the method
we present here to estimate the average effect of the intervention for the subgroup of interest.
The rest of the paper is organized as follows. Section 2 derives a PSR estimator that
accounts for the issue that sterilization status is known but participation in the sterilization
campaign is not observed. The estimator requires auxiliary information on the probability of
participation in the campaign conditional on being sterilized. Section 3 shows how this auxiliary
information can be obtained from our data and the necessary assumptions. Section 4 presents
evidence from Monte Carlo simulations that our estimator is able to recover the causal effects of
interest. Section 5 presents the impact evaluation results of the sterilization campaign, including
effects on total fertility and on other household outcomes. Finally, Section 6 concludes.
2. ESTIMATING THE EFFECTS OF THE STERILIZATION CAMPAIGN
USING PROPENSITY SCORES REWEIGHTING METHODS
Let ܵ ൌ ሼͲǡͳሽ denote whether a woman was sterilized during the campaign years (19961997), an event observed in our data. Let ‫ ܥ‬ൌ ሼͲǡͳሽ denote participation in the government
sterilization campaign, which is unobserved. Women sterilized during the campaign years (ܵ ൌ
ͳ), can be divided between those who were sterilized because of the campaign, (ܵ ൌ ͳǡ ‫ ܥ‬ൌ ͳ) or
simply ‫ ܥ‬ൌ ͳ, and those who were sterilized outside of the campaign (ܵ ൌ ͳǡ ‫ ܥ‬ൌ Ͳ). Let ܺ
denote other observed characteristics of the household, either time-invariant or measured during
the campaign years. Finally denote by ܻଵ the household potential outcome if the woman was
sterilized during the campaign years, and denote by ܻ଴ the household potential outcome if the
6
woman was not sterilized during the campaign years.5 We are interested in evaluating the
average treatment effect on women treated (ATET) by the campaign, which is given by:
‫ ܶܧܶܣ‬ൌ ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ െ ‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ
(1)
If we knew ‫ܥ‬, then we could estimate ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ directly from the data. Then, we could
estimate the probability of participation in the campaign and use standard propensity score
reweighting (PSR) methods to estimate ‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ from data on women who were not
sterilized during the campaign years (ܵ ൌ Ͳ). However, given that we only observe ܵ and not ‫ܥ‬,
this procedure is not feasible. An alternative would be to approximate ATET by equation (2):
෫ ൌ ‫ܧ‬ሾܻଵ ȁܵ ൌ ͳሿ െ ‫ܧ‬ሾܻ଴ ȁܵ ൌ Ͳሿ
‫ܶܧܶܣ‬
(2)
The term ‫ܧ‬ሾܻଵ ȁܵ ൌ ͳሿ can be directly estimated from the data, whereas the term ‫ܧ‬ሾܻ଴ ȁܵ ൌ Ͳሿ
can be estimated using standard PSR methods because the probability of sterilization can be
෫ would be a biased estimator of if women who participated in
constructed. However, the sterilizations campaign were different on average than those who were sterilized outside of
the campaign and if the effects of sterilization are heterogeneous across women of different
characteristics. Both of these conditions are very likely to be true as we shown in our estimation
results.
5
Note that not being sterilized during the campaign years does not rule out the possibility of
sterilization at later years.
7
However, even if ‫ ܥ‬is uknown we can still obtain unbiased estimates of ATET if we can
estimate the probability that if a woman was sterilized during the campaign window (19961997), it was because she participated in the campaign, or ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺሻ. To see how the
conditional probabilities can be used in the estimation of the ATET, we analyze the two terms on
right-hand side of equation (1) separately. Start by defining ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ as in equation (3). We
then multiply and divide the integrand by the conditional probability density function
݂ሺ‫ݕ‬ଵ ǡ ܺȁܵ ൌ ͳሻ and then apply Bayes rule to the numerator and denominator of the new
integrand to arrive at equation (4).
‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ ൌ ‫ݕ ׬ ׬‬ଵ ݂ሺ‫ݕ‬ଵ ǡ ‫ݔ‬ȁ‫ ܥ‬ൌ ͳሻ݀‫ݕ݀ݔ‬ଵ
௉ሺௌୀଵሻ
௉ሺ஼ୀଵȁ௬ ǡ௫ሻ
‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ ൌ ௉ሺ஼ୀଵሻ ‫ݕ ׬ ׬‬ଵ ௉ሺௌୀଵȁ௬భ ݂ሺ‫ݕ‬ଵ ǡ ‫ݔ‬ȁܵ ൌ ͳሻ݀‫ݕ݀ݔ‬ଵ
ǡ௫ሻ
భ
(3)
(4)
Next we invoke a strong ignorability condition, common in PSR methods:
Condition 1 (Strong Ignorability): After conditioning on ܺ the probability of participation
in the sterilization campaign and the probability of being sterilized outside the campaign are
independent of the potential outcomes ሼ଴ ǡ ଵ ሽ:
ܲሺ‫ ܥ‬ൌ ͳȁ‫ݕ‬ଵ ǡ ‫ݕ‬଴ ǡ ܺሻ ൌ ܲሺ‫ ܥ‬ൌ ͳȁܺሻ
(5)
ܲሺܵ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁ‫ݕ‬ଵ ǡ ‫ݕ‬଴ ǡ ܺሻ ൌ ܲሺܵ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁܺሻ
(6)
ܲሺܵ ൌ ͳȁ‫ݕ‬ଵ ǡ ‫ݕ‬଴ ǡ ܺሻ ൌ ܲሺܵ ൌ ͳȁܺሻ
(7)
8
Condition 1 implies that regardless of potential outcomes, women who are observationally
equal had the same probability of being sterilized within campaign (equation (5)) and of being
sterilized outside the campaign (equation (6)), and therefore of being sterilized in general
(equation (7)). Under Condition 1, equation (4) can be re-written as shown in equation (8) below.
Notice that
௉ሺ஼ୀଵȁ௫ሻ
௉ሺௌୀଵȁ௫ሻ
is equal to the conditional probability ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬ሻ, which
suggests the finite sample estimator for ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ provided in equation (9), where is ߶௜ is the
observation sampling weight and ߣ௜ ൌ ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬௜ ሻ: 6
௉ሺௌୀଵሻ
௉ሺ஼ୀଵȁ௫ሻ
(8)
‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ ൌ ௉ሺ஼ୀଵሻ ‫ݕ ׬ ׬‬ଵ ቀ௉ሺௌୀଵȁ௫ሻቁ ݂ሺ‫ݕ‬ଵ ǡ ‫ݔ‬ȁܵ ൌ ͳሻ݀‫ݕ݀ݔ‬ଵ
௦థఒ
೔ ೔ ೔
‫ܧ‬ሾܻଵ ȁ‫ ܦ‬ൌ ͳሿ ൌ σே
௜ୀଵ ‫ݕ‬௜ ൬σಿ ௦ థ ఒ ൰
(9)
೔సభ ೔ ೔ ೔
Thus, ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ can be estimated with a weighted average of observed outcomes ܻ for
women who were sterilized during the campaign period. The weights ߣ௜ are proportional to the
probability that, conditional on being sterilized during that period, the woman participated in the
campaign.
Next, we derive an estimator for the second term on the right-hand of equation (1), ‫ܧ‬ሾܻ଴ ȁ ൌ
ͳሿ. As before, we start with its definition, shown in equation (10). Then, we multiply and divide
6
௉ሺௌୀଵሻ
௦ థ೔ ఒ೔
൰.
೔సభ ௦೔ థ೔
೔
The finite sample estimator of ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ is given by ௉ሺ஼ୀଵሻ σே
௜ୀଵ ‫ݕ‬௜ ൬σಿ
σಿ ௦ థ
௉ሺௌୀଵሻ
However, the
population value ௉ሺ஼ୀଵሻ can be approximated in finite samples with σొ೔సభ௦ థ೔ ఒ೔ , giving the
౟సభ ೔ ೔ ೔
expression in Equation (9).
9
the integrand by the conditional probability density function ݂ሺ‫ݕ‬଴ ǡ ‫ݔ‬ȁܵ ൌ Ͳሻ, apply Bayes rules
and invoke Condition 1, to obtain equation (11).
(10)
‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ ൌ ‫ݕ ׬ ׬‬଴ ݂ሺ‫ݕ‬଴ ǡ ‫ݔ‬ȁ‫ ܥ‬ൌ ͳሻ݀‫ݕ݀ݔ‬଴
௉ሺௌୀ଴ሻ
௉ሺ஼ୀଵȁ௫ሻ
(11)
‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ ൌ ௉ሺ஼ୀଵሻ ‫ݕ ׬ ׬‬଴ ௉ሺௌୀ଴ȁ௫ሻ ݂ሺ‫ݕ‬଴ ǡ ‫ݔ‬ȁܵ ൌ Ͳሻ݀‫ݕ݀ݔ‬଴
After replacing ܲሺܵ ൌ Ͳሻ with ͳ െ ܲሺܵ ൌ ͳሻ, multiplying and dividing the first term on the
right-hand side by Pሺܵ ൌ ͳሻ, and performing a similar operation for the integrand, we obtain the
result in equation (12). This equation suggests that ‫ܧ‬ሾܻ଴ ȁ‫ ܦ‬ൌ ͳሿ can be estimated with the finite
sample estimator provided in equation (13)7:
‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ ൌ ቀ
ଵି௉ሺௌୀଵሻ
௉ሺௌୀଵሻ
௉ሺௌୀଵሻ
௉ሺ஼ୀଵȁ௫ሻ
௉ሺௌୀଵȁ௫ሻ
ቁ ቀ௉ሺ஼ୀଵሻቁ ‫ݕ ׬ ׬‬଴ ቀ௉ሺௌୀଵȁ௫ሻቁ ቀଵି௉ሺௌୀଵȁ௫ሻቁ ݂ሺ‫ݕ‬଴ ǡ ‫ݔ‬ȁܵ ൌ Ͳሻ݀‫ݕ݀ݔ‬଴ (12)
ሺଵି௦೔ ሻథ೔ ఏ೔ ఒ೔
‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ ൌ σே
௜ୀଵ ‫ݕ‬௜ ൬σಿ
೔సభሺଵି௦೔ ሻథ೔ ఏ೔ ఒ೔
൰
(13)
௉ሺௌୀଵȁ௑ୀ௫ ሻ
Where ߠ௜ ൌ ቀଵି௉ሺௌୀଵȁ௑ୀ௫೔ ሻቁ and ߣ௜ is defined as before. Thus, the expected value
೔
‫ܧ‬ሾܻ଴ ȁ‫ ܦ‬ൌ ͳሿ is a weighted average of the observed outcome ܻ for women who were not
sterilized during the campaign time period. The weights are made up of two components. The
7
The finite sample estimator of ‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ is given by
ଵି௉ሺௌୀଵሻ
ቀ
௉ሺௌୀଵሻ
௉ሺௌୀଵሻ
ሺଵି௦೔ ሻథ೔ ఏ೔ ఒ೔
ቁ ቀ௉ሺ஼ୀଵሻቁ σே
௜ୀଵ ‫ݕ‬௜ ൬σಿ
೔సభሺଵି௦೔ ሻథ೔
൰. However, the population value ቀ
σಿ ሺଵି௦ ሻథ
ଵି௉ሺௌୀଵሻ
௉ሺௌୀଵሻ
௉ሺௌୀଵሻ
ቁ ቀ௉ሺ஼ୀଵሻቁ
೔ ೔
, giving the expression in equation (13).
can be approximated in finite samples with σಿ ೔సభ
ሺଵି௦ ሻథ ఏ ఒ
೔
೔సభ
10
೔ ೔ ೔
first component, ߠ௜ , gives higher weights to women who are observationally more similar to
women that were sterilized during the campaign period. The second factor, ߣ௜ , gives higher
weights to those women who, if they had been sterilized during the campaign period, were more
likely to have been sterilized because of the campaign.
Note that ܲሺܵ ൌ ͳȁܺ ൌ ‫ݔ‬௜ ሻ ൏ ͳ is required for ߠ௜ to be defined. Condition 2 summarizes the
common support or overlap conditions required for our PSR estimator. Because we are
estimating the ATET and not the average treatment effect (ATE), we do not need to restrict
ܲሺܵ ൌ ͳȁܺ ൌ ‫ݔ‬௜ ሻ ൐ Ͳ for all individuals. It is sufficient that a non-zero fraction of women have a
positive probability. Similarly, we only require ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬௜ ሻ being positive for nonzero fraction of women.
Condition 2 (overlap): There is no perfect predictability of sterilization given X:
ܲሺܵ ൌ ͳȁܺ ൌ ‫ݔ‬௜ ሻ ൏ ͳ
for all women
(14a)
ܲሺܵ ൌ ͳȁܺ ൌ ‫ݔ‬௜ ሻ ൐ Ͳ
for some women
(14b)
ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬௜ ሻ ൐ Ͳ
for some women
(14c)
By joining the results of Equations (9) and (13), we can estimate the ATET as in equation
(15). Notice how this estimator differs from a standard PSR estimator. The weights used to
estimate ‫ܧ‬ሾܻଵ ȁ‫ ܥ‬ൌ ͳሿ and ‫ܧ‬ሾܻ଴ ȁ‫ ܥ‬ൌ ͳሿ have been augmented with a new term ߣ௜ that defines the
conditional probability that if a woman was sterilized during the campaign period, it was because
she participated in the campaign.
௦థఒ
ሺଵି௦೔ ሻథ೔ ఏ೔ ఒ೔
೔ ೔ ೔
ே
‫ ܶܧܶܣ‬ൌ σே
௜ୀଵ ‫ݕ‬௜ ൬σಿ ௦ థ ఒ ൰ െ σ௜ୀଵ ‫ݕ‬௜ ൬σಿ
೔సభ ೔ ೔ ೔
11
೔సభሺଵି௦೔ ሻథ೔ ఏ೔ ఒ೔
൰
(15)
So far we have focused on estimating the impact of the campaign. Suppose that we were
interested in estimating the impact of being sterilized during the campaign years for those
women who did not participate in the campaign. The corresponding estimator is given in
equation (16). For this estimator to be defined, we need to strengthen Condition 2 by requiring
that ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬௜ ሻ ൏ ͳ for some women.
௦ థ ሺଵିఒ ሻ
ሺଵି௦೔ ሻథ೔ ఏ೔ ሺଵିఒ೔ ሻ
೔ ೔
೔
ே
‫ܧ‬ሾܻଵ െ ܻ଴ ȁܵ ൌ ͳǡ ‫ ܥ‬ൌ Ͳሿ ൌ σே
௜ୀଵ ‫ݕ‬௜ ൬σಿ ௦ థ ሺଵିఒ ሻ൰ െ σ௜ୀଵ ‫ݕ‬௜ ൬σಿ
೔సభ ೔
೔
೔
൰
೔సభሺଵି௦೔ ሻథ೔ ఏ೔ ሺଵିఒ೔ ሻ
(16)
3. DATA AND ESTIMATION OF ૃܑ AND ીܑ
We investigate the effect of the sterilization campaign using the fourth and fifth waves of the
Demographic and Health Surveys for Peru (hereafter DHS IV and DHS V). Both DHS IV and
DHSV are nationally representative cross sectional surveys and were conducted after the
campaign had ended and thus allow us to look at medium and long-term impacts on fertility and
other household outcomes. DHS IV was conducted in 2000 and has a sample size of 27,843
women aged 15-49; and DHS V was collected continuously over the course of 2004 to 2008 and
has a sample size of 41,648 women. The primary advantage of the surveys for our purposes is
that information is collected on birth control methods including sterilization and the date when
the sterilization occurred. The surveys also contain information on women’s’ marital and birth
histories, place of residence and basic demographic information like age and educational
attainment.
As discussed in the previous section, a key step in our empirical approach is estimating ߣ௜ ,
the probability that if a woman was sterilized during the sterilization campaign years (199612
1997), it was because she participated in the campaign. To estimate ߣ௜ , we use information about
women who were sterilized prior to the campaign to predict the probability that, in the absence
of the sterilization campaign, a woman would have been sterilized during the years 1996 and
1997. To illustrate this strategy, we introduce time subscripts in our notation, such that ܵଵ
denotes sterilization in the period prior to the campaign and ܵଶ denotes sterilization during the
campaign years. The term ‫ ܥ‬continues to denote participation in the sterilization campaign
(during period 2). Denote by ܲሺܵଶ ൌ ͳȁܺ ൌ ‫ݔ‬ሻ the probability that a woman is sterilized during
the campaign period (given that she was not sterilized before). This probability can be
decomposed as the sum of the probability of being sterilized because of the campaign and
because of other factors (i.e. outside the campaign):
ܲሺܵଶ ൌ ͳȁܺ ൌ ‫ݔ‬ሻ ൌ ܲሺ‫ ܥ‬ൌ ͳȁܺ ൌ ‫ݔ‬ሻ ൅ ܲሺܵଶ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁܺ ൌ ‫ݔ‬ሻ
(17)
Assumption 1 below allows us to exploit the information we have about the probability of
sterilization before the campaign was implemented. A similar assumption is made by Botosaru
and Gutierrez (2014) to estimate the probability of treatment for the period where treatment
status is missing.
Assumption 1 (stationarity of the propensity score): The probability of a woman with
observed characteristics ܺ being sterilized during the campaign years but outside of the
campaign is the same as the probability of sterilization in the pre-campaign years for a woman
with similar observable characteristics:
13
ܲሺܵଶ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁܺ ൌ ‫ݔ‬ሻ ൌ ܲሺܵଵ ൌ ͳȁܺ ൌ ‫ݔ‬ሻ
(18)
Under Assumption 1 we can re-write equation (17) to express the probability of participation
in the sterilization campaign as shown in equation (19) and the probability of participating in the
campaign, conditional on being sterilized during the campaign period as shown in equation (20):
ܲሺ‫ ܥ‬ൌ ͳȁܺ ൌ ‫ݔ‬ሻ ൌ ܲሺܵଶ ൌ ͳȁܺ ൌ ‫ݔ‬ሻ െ ܲሺܵଵ ൌ ͳǡ ȁܺ ൌ ‫ݔ‬ሻ
ܲሺ‫ ܥ‬ൌ ͳȁܵଶ ൌ ͳǡ ܺ ൌ ‫ݔ‬ሻ ൌ
௉ሺ஼ୀଵȁ௑ୀ௫ሻ
௉ሺௌమ ୀଵȁ௑ୀ௫ሻ
ൌ
௉ሺௌమ ୀଵȁ௑ୀ௫ሻି௉ሺௌభ ୀଵǡȁ௑ୀ௫ሻ
௉ሺௌమ ୀଵȁ௑ୀ௫ሻ
(19)
(20)
The result in equation (20) is intuitive. It says that the probability of being sterilized because
of the campaign equals to the increase in the risk of sterilization during the campaign years in
comparison to the previous years. In other words, the increases in the incidence of sterilizations
during the years 1996 and 1997 shown in Figure 1 are the result of the campaign. In practice, as
described in our estimation below, we allow for a time trend to capture the underlying national
trend in sterilizations prior to the implementation of the sterilization campaign.
To implement this strategy we use the date of sterilization and other retrospective variables
in the DHS to construct a longitudinal history for each woman describing her fertility and marital
time path from 1990 to the end of the policy period in 1997. Each woman has one observation
for each year (indexed by ‫)ݐ‬. We record sterilization in each year with a dichotomous variable ܵ௜௧
and once a woman is sterilized she drops from the panel. This re-arrangement of the data allows
us to estimate the probability of a woman being sterilized in each year, given that she has not
been sterilized before. We fit the following logit model:
14
݈‫ݐ݅݃݋‬ሾܲሺܵ௜௧ ȁܺ௜௧ ሻሿ ൌ ߙ ൅ ߜ‫ ݐ‬൅ ܺ௜௧ᇱ ߚଵ ൅ ߨ‫݊݃݅ܽ݌݉ܽܥ‬௧ ൅ ሺܺ௜௧ ൈ ‫݃݅ܽ݌݉ܽܥ‬௧ ሻԢߚଶ
(21)
Where ܺ௜௧ is a set of women’s observed characteristics, including: geographic location, age,
age at first birth, education attainment, number of children, whether any of the children is a boy,
whether she gave birth in year ‫ݐ‬, and her mother tongue (Spanish or other). We include a linear
time trend (ߜ‫ )ݐ‬in the specification to account for the observed rising trend in sterilizations prior
to the start of the campaign. The specification also includes a dichotomous variable ‫݊݃݅ܽ݌݉ܽܥ‬௧
that equals one if the year belongs to the campaign period (1996-1997) and zero if it belongs to
the pre-campaign period (1990-1994). We leave the year 1995 out of the estimation sample
because part of this year can be attributed to the pre-campaign period and part to the campaign
period. Finally, we interact the indicator ‫݊݃݅ܽ݌݉ܽܥ‬௧ with the observed characteristics ܺ௜௧ . Using
equation (20) (derived from Assumption 1) and the estimation results of equation (21), we can
predict for women who were not yet sterilized as of 1996 their i) overall probability of
sterilization in the campaign years; and ii) the probability of participation in the campaign
conditional on sterilization. These are shown in equations (22) and (23), respectively:
ܲሺܵ௧ ൌ ͳȁܺ ൌ ‫ݔ‬ሻ ൌ ݁‫ݐ݅݌ݔ‬ሾሺߙ ൅ ߠሻ ൅ ߜ‫ ݐ‬൅ ܺ௜௧ᇱ ሺߚଵ ൅ ߚଶ ሻሿ
ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬ሻ ൌ
ᇲ
ᇲ
௘௫௣௜௧ൣሺఈାఏሻାఋ௧ା௑೔೟
ሺఉభ ାఉమ ሻ൧ି௘௫௣௜௧ൣఈାఋ௧ା௑೔೟
ఉభ ൧
ᇲ ሺఉ ାఉ ሻ൧
௘௫௣௜௧ൣሺఈାఏሻାఋ௧ା௑೔೟
భ
మ
(22)
`
(23)
With these probabilities we can construct the weights ߣ௜ and ߠ௜ that are used in our PSR
estimator. In practice, the estimated difference
݁‫ݐ݅݌ݔ‬ሾሺߙ ൅ ߠሻ ൅ ߜ‫ ݐ‬൅ ܺ௜௧ᇱ ሺߚଵ ൅ ߚଶ ሻሿ െ
݁‫ݐ݅݌ݔ‬ሾߙ ൅ ߜ‫ ݐ‬൅ ܺ௜௧ᇱ ߚଵ ሿ can be negative. Given our assumptions, that would imply that the
conditional probability ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬ሻ, and thus the weight ߣ௜ , are negative. This is
15
problematic since probabilities are bounded between zero and one by definition, and weightedmeans are only defined for non-negative weights. In these cases, we restrict the conditional
probability ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺ ൌ ‫ݔ‬ሻ to equal zero. The rationale is that if such women were
sterilized, the probability that they were sterilized because of the campaign is very small or
virtually zero. Conversely, their probability of being sterilized outside the program is (close to)
one. We achieve this by replacing the overall risk of sterilization in the campaign years with the
predicted counterfactual risk of sterilization in the absence of the campaign, ݁‫ݐ݅݌ݔ‬ሾߙ ൅ ߜ‫ ݐ‬൅
ܺ௜௧ᇱ ߚଵ ሿ in cases where ߣ௜ is negative. This approach and Assumption 1 rule out the probability
that the risk of sterilization went down for any women during the years of the campaign.
Table 1 shows the logit coefficients for DHS IV and DHS V. For each characteristic, we
present the main effects (coefficient ߚଵ from equation (21)) and the incremental difference
during the campaign years (coefficient ߚଶ). Younger women who had fewer children and no
boys, who were from the rural areas in the Andes and the Amazon, had lower education
attainment, for whom Spanish was not their mother tongue, and who did not give birth were less
likely to be sterilized in any given year in the analysis period (1990-1994 and 1996-1997).
However, the logit estimates also indicate that during the campaign years (1996-1997) the risk of
sterilization increased for this group of women. Particularly, it increased for women in the rural
areas of the Andes and Amazon and for younger and less-educated women. The risk of
sterilization also increased for women who did not give birth in the current year, indicating that a
larger share of sterilizations during the campaign time period were not performed at the time of a
delivery.
[Insert Table 1 here]
16
We use these logit models to estimate the probabilities needed to construct the weights that
enter into our PSR estimator. In particular we need to estimate the risk of overall sterilization,
ܲሺܵ ൌ ͳȁܺሻǡ and the conditional probability of participation in the campaign if sterilized,
ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺሻ. Following the methods described above we found negative estimated values
for the conditional probability ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺሻ in 25% of cases for DHS IV and in 11% cases
for DHS V. As discussed, in these cases we set ܲሺ‫ ܥ‬ൌ ͳȁܵ ൌ ͳǡ ܺሻ ൌ Ͳ. Figure 2Figure 2 and
Figure 3 explore the overlap in these two probabilities between women that were sterilized and
women that were not sterilized in 1996 and 1997, for DHS IV and DHS V respectively. We can
observe from these figures that there is a reasonable overlap in both probabilities for both groups
of women.
[Insert Figure 2 and Figure 3 here]
Before presenting the empirical results, we show next a Monte Carlo simulation analysis to
test our proposed estimator and of our approach for dealing with negative estimated weights.
4. MONTE CARLO SIMULATIONS
We use Monte Carlo simulations to study whether our proposed estimator and empirical
approach to calculate the weights ߣ௜ and ߠ௜ deliver unbiased estimates. To mimic our estimation
approach we simulate data for two periods. In each period women have a probability of being
sterilized. We also model an increase in the risk of sterilization in period 2 due to a sterilization
campaign. Importantly, the risk of sterilization in period 2 increases only for some subgroups of
individuals, as evidence suggests it was the case with the sterilization campaign in Peru. We then
model the effect of sterilization on outcomes, in this case family size, which is also
heterogeneous across subgroups. Finally we follow the estimation strategy discussed in the
17
previous section to calculate the weights ߣ௜ and ߠ௜ and implement our PSR estimator. We
perform this simulation for various scenarios. In each scenario there are 50,000 observations and
1,000 simulations.
In each scenario we first generate 5 bivariate covariates ‫ݔ‬௜ with success probability equal to
‫ ݌‬ൌ ሼͲǤͷǡͲǤʹǡͲǤ͵ǡͲǤʹǡͲǤͳሽ. Then, we simulate the probability of sterilization in period 1 (ܵଵ) and
in period 2 (ܵଶ ), using the following logistic models:
ሺଵ ൌ ͳȁሻ ൌ ‡š’‹–ሾȽ଴ ൅ ᇱ Ƚሿ
(24)
ሺଶ ൌ ͳȁሻ ൌ ‡š’‹–ሾȽ଴ ൅ ᇱ Ƚ ൅ ɀšଵ ሿ
(25)
Where ߙ଴ ൌ െʹǤͷ and ߙ ൌ ሼെʹǡ െͳǡͳǡͳǡͲǤͷሽ. The parameter ߛ which increases the
probability of sterilization in period 2 for individuals with ‫ݔ‬ଵ ൌ ͳǡcan take the following values
ሼͲǤͷǡͳǡͳǤͷǡʹǡʹǤͷሽ depending of the simulation scenario. We can further decompose the
probability of sterilization in period 2 as being sterilized due to the campaign (‫ ܥ‬ൌ ͳ) or outside
the campaign (‫ ܥ‬ൌ Ͳ):
ሺ‫ ܥ‬ൌ ͳȁሻ ൌ ‡š’‹–ሾȽ଴ ൅ ᇱ Ƚ ൅ ɀଵ šଵ ሿ െ ‡š’‹–ሾȽ଴ ൅ ᇱ Ƚሿ
(26)
ሺܵଶ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁሻ ൌ ‡š’‹–ሾȽ଴ ൅ ᇱ Ƚሿ
(27)
Using the probabilities in equations (24), (26) and (27) we predict each woman’s sterilization
outcomes in period 1, and conditional on not being sterilized in period 1, sterilization in period 2
either within or outside the campaign. Finally, we define a generating process for family size
according to the following Poisson model:
18
‫ݕ‬௜ ̱ܲ‫݊݋ݏݏ݅݋‬ሺ݁‫݌ݔ‬ሾߚ଴ ൅ ܺ௜ ᇱ ߚ ൅ ߰ܵ௜ ൅ ߰ଵ ሺܵ௜ ൈ ‫ݔ‬ଵ௜ ሻሿሻ
(28)
Where ߚ଴ ൌ1, ߚ ൌ ሼെͲǤͷǡͲǤͳǡͲǤ͵ǡ െͲǤʹͷǡͳሽ, ߰ ൌ െͲǤͲͷ, and ߰ଵ , which imposes
heterogeneous treatment effects, can take the following values ሼെͲǤͷǡ െͲǤʹሽ depending on the
simulation scenario. Notice that sterilization ܵ is modeled to reduce family size more for the
same subgroups of women that are more likely to participate in the sterilization campaign (i.e.
those with ‫ݔ‬ଵ ൌ ͳ). This is important because if the effects of sterilization were not
heterogeneous we could evaluate the effects of the campaign by looking at the average effects of
sterilization. The problem for the econometrician of not observing participation in the campaign
is that women who participate are on average different than those that are sterilized outside the
campaign, and the treatment effects of sterilization are also different for those women.
We implemented our estimation with the simulated data, following the PSR estimator
discussed in Section 2 under two situations. First, participation in the campaign (‫ )ܥ‬is
unobserved but the true probabilities ሺଶ ൌ ͳȁሻ and ሺ‫ ܥ‬ൌ ͳȁ ൌ ͳǡ ሻ are known. Second,
the probabilities are unknown but they are estimated using a logit model approach, as described
in Section 3. Following equation (21), we add a dummy for period 2 and interact all five
covariates with the dummy. We then predict ሺଶ ൌ ͳȁሻ and ሺ‫ ܥ‬ൌ ͳȁ ൌ ͳǡ ሻ, as shown in
equations (22) and (23). These two probabilities are then used to construct the weights in our
PSR estimator. Because we observe campaign participation status (‫ܥ‬ሻ in the simulated data and
we can construct the counterfactual outcomes in the case of sterilization (ܻଵ ) and no sterilization
(ܻ଴ ), we can also compute the bias of our estimator with respect to the real average treatment
19
effect for the subgroup that participated in the campaign (ATET). These results are presented in
Figure 4 and Table 2.
[Insert Figure 4 and Table 2 here]
In each scenario, the probability of sterilization outside of the campaign remains constant at
about 7%, but the probability of overall sterilization during the campaign years ܲሺܵଶ ൌ ͳሻ and
the conditional probability of participation in the campaign if sterilized ܲሺ‫ ܥ‬ൌ ͳȁܵଶ ൌ ͳሻ
increase across the scenarios as ߛ increases. Note also that the true ATET depends on parameter
߰ଵ , and it is either around 1.35 or 2.55 less children.
We draw some important observations from Table 2. First, as expected, the mean bias is
larger as the conditional probabilityܲሺ‫ ܥ‬ൌ ͳȁܵଶ ൌ ͳሻ is smaller. This is because at lower values
of ܲሺ‫ ܥ‬ൌ ͳȁܵଶ ൌ ͳሻ, the estimator becomes more imprecise as shown in Figure 4 and also
evidenced by the larger standard deviations for these scenarios in Table 2. In other words,
precision increases as the size of the subgroup sterilized due to the campaign increases relative to
the total number of women sterilized. However, it is worth noticing that in all cases the mean
bias is not large enough, in comparison to the standard deviation, to be statistically significant.
Second, the mean bias is larger if the weights need to be estimated than if they are known. In
fact, if the weights are known, the mean bias is very small. Notice also that the standard
deviations are similar regardless of whether the weights are known or not, which indicates that
not much precision is lost by estimating the weights. Finally, it is interesting to notice that even
though ܲሺܵଶ ൌ ͳȁܺሻ െ ܲሺܵଶ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁܺሻ ൒ Ͳ for every woman in the simulated data, in about
24% of the cases –stable across all scenarios- we estimate a negative difference. These negative
differences are the result of having to rely on a logit model, without knowing its true
specification, to estimate the weights. As discussed, these negative differences imply negative
20
weights ߣ௜ which cannot be used with the estimator. In those cases, we proceed to set
ܲሺܵଶ ൌ ͳȁܺሻ ൌ ܲሺܵଶ ൌ ͳǡ ‫ ܥ‬ൌ Ͳȁܺሻ, or ߣ௜ =0. Having to deal with estimated negative weights,
and restricting them to be zero, might explain why the average bias is larger when the weights
are unknown and need to be estimated. This outcome of the simulations is important because we
observe in the DHS data that around 11% (in DHS V) to 25% (in DHS IV) of observations also
have negative estimated weights that we set to zero. This is a limitation of having to estimate the
weights rather than a problem with the proposed PSR estimator.
5. ESTIMATION RESULTS
Table 3 and Table 4, based on DHS IV and DHS V respectively, show the sample means of
demographic variables before and after applying the weights we developed in Sections 2 and 3.
Column 1 shows the unweighted sample means for all eligible women (ever married women with
at least one child who were not sterilized as of the start of 1996); column 2 shows the
unweighted sample means for women that were sterilized in 1996-1997; and column 3 shows the
unweighted sample means for eligible women that were not sterilized in those years. We see that
sterilized women are older, have more children, and are slightly less educated and less likely to
live in rural areas.
In columns 4 and 5, we apply the proposed weighs: ߣ௜ for women who were sterilized as a
result of the FSC and ߠ௜ ߣ௜ for women who were not sterilized and will serve as a control group.
As discussed, these weights are designed to up-weight the observations from women more likely
to have participated in the campaign (if they were sterilized), or that are observationally similar
to women more likely to have participated in the campaign (if they were not sterilized). Two
important observations arise after applying the weights. First, we obtain relatively balanced
21
characteristics between sterilized and non-sterilized women. We are particularly encouraged by
the improvement in balance that weighting provides for the variables in the last two rows of
Table 3 which are responses to DHS survey questions about the wantedness of the woman’s last
pregnancy.8 Since these variables are not included in the logit models, this is suggestive
evidence that, while we are matching on observed characteristics, our treatment and control
group also match on typically unobserved characteristics like attitudes and fertility aspirations.
This is reassuring for the causal interpretation of our treatment effects.
Second, there are striking differences in the weighted means in comparison to the
unweighted means that are consistent with the results discussed for the logit models in Table 1.
The women that we find to be more likely to have participated in the sterilization campaign are
younger, considerably less educated, and much more likely to live in rural areas. We further
highlight the differences between women that were sterilized as part of the campaign versus
women that were sterilized outside of the campaign in the last two columns of Table 3 and Table
4. In those columns, we select only the sample of women who were sterilized in 1996 and 1997
and weight them according to their probability of participation in the campaign ߣ௜ (column 6)
and their probability of nonparticipation in the campaign ͳ െ ߣ௜ (column 7). Women sterilized
outside the campaign are older, more educated, and considerably more likely to live in urban
areas and in the coastal region of the country such as Lima.
[Insert Table 3 and Table 4 here]
8
We only make this comparison for women who had pregnancies in the last five years but before
the policy and can thus only do this check in DHS IV.
22
Before presenting average treatment effects of the campaign, we first estimate the number of
women that participated in the campaign. We estimate the number of total female sterilizations
in a given year with the estimator σே
௜ୀଵ ‫ݏ‬௜ ߶௜ and the total number of sterilization due to the
campaign with the estimator σே
௜ୀଵ ‫ݏ‬௜ ߶௜ ߣ௜ . Using information from DHS IV (which has a shorter
recall period) and United Nations age-and-gender-specific population tables (Desa, 2009) we
estimate that about 159,709 women were sterilized in Peru in the years 1996-1997, and of those
about 60,883 women were sterilized because of the campaign. In other words, over one third of
the sterilizations that occurred during the years 1996-1997 were part of the government
campaign; or alternatively, the campaign increased the number of sterilizations by about 62%.
Table 5 shows the estimated impact of the campaign on fertility and other household
outcomes. Columns 1 and 2 give results for outcomes from DHS IV which was collected three
years after the campaign. Columns 3 and 4 show estimates for outcome from DHS V which was
collected seven to eleven years after the campaign. The first column in each section provides
estimates of the impact of the FSC, using the estimator from equation (15). The second column
in each section provides estimates the effects of sterilization for women who were sterilized
during the campaign period, but who were sterilized outside of the campaign, using the estimator
from equation (16). Standard errors are calculated from 500 bootstrap replications.
We find substantially different fertility impacts of being sterilized in the years 1996-1997
depending on whether sterilization occurred as part of the campaign or outside of the campaign
and the differences are highly statistically significant. For women that participated in the
campaign the average effect was 0.4 fewer children by 2000 and 1.2 fewer children by 2004
(both significant at a 1% level). For women sterilized outside of the campaign the effects are
much smaller, on average 0.1 fewer children by 2000 (and not statistically significant) and 0.6
23
(statistically significant at a 1% level) fewer children by 2004. The impact of the sterilization
campaign on fertility is large but plausible given the age of the participating women (on average
30 years old, see Table 3 and Table 4), the amount of time since the policy, and otherwise
limited access to contraception available in the areas of Peru targeted by the campaign.
[Insert Table 5 here]
Turning to other household outcomes, we find that by 2000, the probability of working for
pay among women who participated in the campaign increased by 2.1 percentage points,
although the estimate is not statistically significant. Similarly small and insignificant estimates of
the impact on paid work are obtained for DHS V in 2004-2008. We find that women who
participated in the sterilization campaign are more likely to experience domestic violence (either
physical or sexual) in the last 12 months (this information is only available in DHS V). We
estimate that participation in the campaign increased the likelihood of experiencing domestic
violence by 5.1 percentage points. Given the mean rate of reported domestic violence is 13
percent, the magnitude of this estimate is large though it is marginally statistically insignificant
at standard confidence levels. Since we found that participation in the sterilization campaign led
to a substantial decrease in fertility, we can hypothesize that impacts on other outcomes, for
example the incidence of domestic violence, are the result of lowered fertility. It might be the
case that changes in ability to bear children may impact women's bargaining power within the
household. However, we cannot rule out impacts of the campaign through mechanism other than
fertility. As mentioned in the introduction, there were reports that some of the sterilizations
during the campaign were allegedly performed without proper consent or coercively. This could
lead to trauma and deterioration in mental health, affecting domestic relationships.
24
Next we examine outcomes for children. We focus on children who were born before the
FSC effectively comparing outcomes for children whose mothers were sterilized and therefore
had no additional siblings, to children who may have had additional siblings. First we estimate
impacts on height for age in standard deviations from the reference median. The DHS only
records this biometric information among children under age four. Thus, Table 5 shows only
height for age results for DHS IV, since children born before 1996 in DHS V are over four years
old by the time of the survey. Furthermore, since kids’ characteristics were not included in detail
in the logit models, we use a PSR-regression adjusted estimator controlling for child’s age.9
Impacts on height for age, which is a long-term measure of health, are positive but not
significant. When we examine girls separately, however, we find that daughters of women who
participated in the sterilization campaign had height for age measures that were 0.57 standard
deviations greater than counterfactual girls. This is a substantial and statistically significant
effect. We find a smaller (0.44) effects for women in who were sterilized outside of the
campaign.
We find small and insignificant positive impacts of the FSC on years of schooling for girls
and boys under the age of 15 who were born prior to the policy by 2000 using DHS IV. By
2004, in DHS V we find slightly larger impacts—0.15 additional years of schooling for girls and
0.19 additional years for boys—for children whose mothers were sterilized, with the estimate for
boys reaching statistical significance at a 10% level. We see that for every outcome we examine
9
PSR-regression adjusted estimators are obtained through a weighted ordinary least square
(OLS) regression of the outcome of interest on mother’s sterilization in 1996-1997 (ܵ௜ ሻ and
additional child-level covariates, and weighting observations in the sterilized group (ܵ௜ ൌ ͳሻ by
ߣ௜ and in the non-sterilized group (ܵ௜ ൌ Ͳሻ by ߠ௜ ߣ௜ .
25
the magnitude of the coefficient for women who participated in the FSC is larger in magnitude
than for women sterilized outside of the campaign, though beyond the fertility estimates, the
differences are not always statistically significant.
6. CONCLUSION
We evaluate the impact of a large-scale national female sterilization campaign in Peru in the
years 1996 and 1997. We propose a modified propensity score reweighting (PSR) estimator to
tackle the challenge of a contaminated treatment group—while we know who was sterilized
during the campaign period, we do not know who was sterilized because of the campaign and
who would have been sterilized even in the absence of the campaign. The proposed method can
be applied to other situations where researchers are interested in evaluating the effect of an
intervention for a particular subgroup --for instance individuals that were more compliant with
the intervention-- but the membership to the subgroup of interest is not observed in the data.
The key requirement of our estimator is the ability to construct (from auxiliary data) a
conditional probability of belonging to the (unobserved) subgroup of interest if the contaminated
treatment is observed. This conditional probability is then used as an additional weight in the
PSR estimator. For evaluating the effects of the sterilization campaign, we used available
information to estimate women’s risk (probability) of sterilization in the years prior to the
campaign and the increase in this risk during the campaign years. Then, under the assumption
that the risk of sterilization would have remained constant in the absence of the campaign, we
constructed the conditional probability that if a woman was sterilized during the years of the
campaign, it was because she participated in it. Using this probability, we applied our modified
PSR estimator to evaluate the impact of the sterilization campaign.
26
We estimate that over one third of the sterilizations that occurred during the years 19961997 were part of the government campaign; or alternatively, the campaign increased the number
of sterilizations by about 62%. We also find that the group of women more likely to have
participated in the campaign was different on average from the group of women sterilized in the
same years, but likely outside the campaign. Women that participated in the campaign were
younger, less educated and more likely to live in rural areas in the mountain and jungle regions
of Peru.
We also find that the fertility effects of sterilization were different depending on whether a
woman was sterilized because of the campaign. We estimate that participation in the sterilization
campaign resulted in 0.4 fewer children by 2000, and 1.2 fewer children by 2004, on average.
For women sterilized outside the campaign, the effects are much smaller: 0.1 fewer children by
2000 and 0.6 fewer children by 2004.
Finally, we find small and non- or marginally significant impacts of the sterilization
campaign on women's and children's outcomes, with the exception of substantial and statistically
significant improvements in the height for age of girls whose mothers participated in the
campaign. We also find positive effects in girls’ height for age measures for women sterilized
outside the campaign. Although the point estimates are smaller than those for women that
participated in the campaign, they are not statistically different.
There is a continuing debate about the causal link between access to family planning,
reductions in fertility, and increases in well-being in both the developed and developing world.
Beyond any direct impact on the level of fertility, access to contraception clearly allows women
to control the timing of fertility, which reduces constraints on choices about work and caring for
existing children. Recent research in both the United States (Bailey, 2006) and Colombia (Miller,
27
2010) uses plausibly exogenous variation in access to show that contraception significantly
increases female educational attainment and labor force participation by allowing women to
delay first births. In contrast to these results, our findings in Peru suggest that the mere reduction
in fertility, and without changes in the ability to optimally plan timing and family size, is not
necessarily associated with substantial improvements in measures of household wellbeing (with
the exception of height for age for girls). Also potentially explaining the lack of strong effects is
that women who chose sterilization usually have a large family already (about 4 children), and
that women who participated in the campaign are more likely to live in poor rural areas in the
Andean and jungle regions of Peru, where the economic returns to reduced fertility might be
minimal.
28
REFERENCES
Bailey, Martha J. 2006. "More Power to the Pill: The Impact of Contraceptive Freedom on
Women's Life Cycle Labor Supply." The Quarterly Journal of Economics, 289-320.
Boesten, Jelke. 2007. "Free Choice or Poverty Alleviation? Population Politics in Peru under
Alberto
Fujimori."
Revista
Europea
de
Estudios
Latinoamericanos
y
del
Caribe/European Review of Latin American and Caribbean Studies, 3-20.
Botosaru, Irene and Federico H Gutierrez. 2014. "Difference-in-Differences When Treatment
Status Is Observed in Only One Period." Available at SSRN 2377483.
Chen, Xiaohong; Han Hong and Denis Nekipelov. 2011. "Nonlinear Models of Measurement
Errors." Journal of Economic Literature, 49(4), 901-37.
del Aguila, Ernesto Vasquez. 2006. "Invisible Women: Forced Sterilization, Reproductive
Rights, and Structural Inequalities in Peru of Fujimori and Toledo." Estudos e Pesquisas
em Psicologia, 6(1), 109-24.
Desa, UN. 2009. "World Population Prospects: The 2008 Revision." New York: Department for
Economic and Social Affairs.
Horowitz, Joel L and Charles F Manski. 1995. "Identification and Robustness with Contaminated
and Corrupted Data." Econometrica: Journal of the Econometric Society, 281-302.
Hotz, V Joseph; Charles H Mullin and Seth G Sanders. 1997. "Bounding Causal Effects Using
Data from a Contaminated Natural Experiment: Analysing the Effects of Teenage
Childbearing." The Review of Economic Studies, 64(4), 575-603.
Miller, Grant. 2010. "Contraception as Development? New Evidence from Family Planning in
Colombia." The Economic Journal, 120(545), 709-36.
29
Tamayo, Giulia. 1999. Nada Personal: Reporte De Derechos Humanos Sobre La Aplicación De
La Anticoncepción Quirúrgica En El Perú, 1996-1998. CLADEM, Comité de América
Latina y el Caribe para la Defensa de los Derechos de la Mujer.
30
Figure 1. Number of Reported Sterilizations by Year
Peruvian Demographic and Health Surveys
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
0
100
200
300
400
Sterilizations by Year - Peru DHS IV (2000)
Year of Sterilization
Year of Sterilization
31
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
0
100
200
300
400
500
Sterilizations by Year - DHS V (2004-2008)
Figure 2. Common Support for Weighting Variables by Sterilization Status in 1996-1997 (DHS IV)
Probability of Sterilization
P(S=1|X)
Probability of Participation in Campaign Given Sterilization
P(C=1|S=1,X)
0
Sterilized
0
0
5
10
50
Sterilized
15
0
Density
5
10
15
Not Sterilized
50
Not Sterilized
0
.1
.2
.3
.4
0
Graphs by Sterilization Status
Graphs by Sterilization Status
32
.5
1
Figure 3. Common Support for Weighting Variables by Sterilization Status in 1996-1997 (DHS V)
Probability of Sterilization
P(S=1|X)
Probability of Participation in Campaign Given Sterilization
P(C=1|S=1,X)
10
0
Sterilized
10
0
0
5
20
40
60
Sterilized
15
0
Density
5
20
40
15
Not Sterilized
60
Not Sterilized
0
.1
.2
.3
.4
0
Graphs by Sterilization Status
Graphs by Sterilization Status
33
.5
1
Figure 4. Average Bias in Simulated Scenarios
1
2
3
4
5
6
7
8
9
10
-60
-50
-40
-30
-20
-10
0
10
Bias (%)
If weights known
excludes outside values
34
20
30
40
50
If weights unknown
60
Table 1. Determinants of Sterilization Prior to and During
the Fujimori Sterilization Campaign (Logit Coefficients)
DHS IV
Variables
Number of kids
1
2
3
Rural Coast
Urban Mountain
Rural Mountain
Urban Jungle
Rural Jungle
Primary Education
Secondary Education
Age
under 26
26 to 29
over 36
First language not Spanish
No male children
No birth that year
Year (linear trend)
Campaign
Observations
DHS V
Main effects
Interactions
effects
Main effects
Interactions
effects
-4.602***
(0.000)
-2.089***
(0.005)
-0.973
(0.167)
-0.115
(0.577)
-0.110
(0.469)
-1.448***
(0.000)
0.119
(0.452)
-1.367***
(0.000)
-0.646***
(0.001)
-0.121
(0.514)
-0.937
(0.476)
0.500
(0.619)
0.564
(0.553)
0.149
(0.593)
-0.468**
(0.033)
0.521*
(0.075)
-0.231
(0.303)
0.820***
(0.008)
0.304
(0.279)
-0.151
(0.568)
-6.412***
(0.000)
-1.673
(0.139)
0.200
(0.854)
0.096
(0.679)
-0.420**
(0.026)
-1.204***
(0.000)
-0.107
(0.519)
-1.336***
(0.000)
-0.980***
(0.000)
-0.441**
(0.029)
0.637
(0.716)
-0.546
(0.677)
-0.986
(0.436)
0.310
(0.323)
0.034
(0.891)
0.513*
(0.073)
0.224
(0.323)
0.757**
(0.025)
0.717**
(0.012)
0.063
(0.818)
-1.174***
(0.000)
-0.604***
(0.001)
-0.235
(0.151)
-1.031***
(0.001)
-0.063
(0.782)
-2.443***
(0.000)
0.178***
(0.000)
-0.076
(0.944)
84,717
0.635*
(0.074)
0.582**
(0.011)
-0.225
(0.305)
0.512
(0.145)
-0.182
(0.541)
0.458**
(0.021)
-1.171***
(0.000)
-0.387**
(0.020)
-0.480
(0.152)
-0.623*
(0.061)
-0.742***
(0.002)
-2.568***
(0.000)
0.248***
(0.000)
-1.427
(0.294)
93,734
1.166***
(0.000)
0.578**
(0.010)
0.042
(0.910)
0.216
(0.561)
0.437
(0.159)
0.817***
(0.000)
Notes: Main effects refer to coefficient ߚଵ from equation (21). Interaction effects refer to coefficient ߚଶ. Indicator variables for
number of kids greater than 3 (up to 9) were included in the regressions but are not reported for the sake of space. Coefficient
on the constant term is also omitted for space. P-values are included in parentheses: *** p<0.01, ** p<0.05, * p<0.1
35
Table 2. Monte Carlo Simulations
Bias of Estimator (%)
Scenario
ࢽ
࣒૚
P(ࡿ૛ =1)
P(C|S)
True
ATET
Prob.
Neg.
Weights
If weights
unknown
Mean
Std.
Dev
If weights are
estimated
Mean
Std.
Dev
1
0.50
-0.50
0.07
0.09
-2.59
0.24
0.69
9.28
-11.66
11.18
2
0.50
-0.20
0.07
0.09
-1.35
0.24
3.47
19.60
-8.30
18.29
3
1.00
-0.50
0.08
0.20
-2.58
0.23
0.59
6.32
-4.83
6.88
4
1.00
-0.20
0.08
0.20
-1.35
0.24
1.28
12.93
-3.66
12.14
5
1.50
-0.50
0.10
0.33
-2.57
0.23
0.28
4.91
-2.55
4.79
6
1.50
-0.20
0.10
0.33
-1.35
0.24
0.51
9.33
-2.06
8.87
7
2.00
-0.50
0.12
0.45
-2.56
0.24
0.06
4.09
-1.49
3.72
8
2.00
-0.20
0.12
0.45
-1.34
0.23
0.22
7.78
-1.48
7.01
9
2.50
-0.50
0.15
0.57
-2.54
0.23
-0.01
3.29
-1.04
2.97
10
2.50
-0.20
0.15
0.57
-1.33
0.24
0.01
6.54
-0.96
5.59
36
Table 3. Characteristics of Women Eligible for Sterilization in 1996-1997, DHS IV
All Women Eligible for Sterilization (S) in 19961997
Women Sterilized in 1996-1997 (S=1)
Reweighted to
represent C=1
Not Reweighted
Reweighted to represent:
(6)
(7)
S= 0
P-value
for zero
diff
C=1
C=0
30.68
31.61
0.00
30.68
33.42
4.08
4.08
0.98
4.08
3.80
(1)
(2)
(3)
(4)
(5)
all
S= 1
S =0
S= 1
Age in 1996
31.48
32.36
31.44
# Kids in 1996
2.86
3.91
2.81
Pre-Campaign Characteristics
Years of education
7.85
7.12
7.89
5.21
5.44
0.27
5.21
8.31
Age at first birth
20.69
20.08
20.72
18.63
19.10
0.01
18.63
21.00
rural
0.36
0.35
0.36
0.58
0.57
0.71
0.58
0.21
coast
0.51
0.58
0.51
0.44
0.46
0.68
0.44
0.67
mountain
0.36
0.26
0.36
0.35
0.34
0.67
0.35
0.21
jungle
0.13
0.15
0.13
0.21
0.21
0.97
0.21
0.12
urban coast
0.45
0.48
0.45
0.33
0.35
0.57
0.33
0.57
rural coast
0.06
0.10
0.06
0.11
0.11
0.81
0.11
0.10
urban mountain
0.12
0.09
0.13
0.03
0.03
0.69
0.03
0.13
rural mountain
0.23
0.17
0.24
0.31
0.30
0.75
0.31
0.08
urban jungle
0.06
0.07
0.06
0.05
0.05
0.74
0.05
0.09
rural jungle
0.07
0.08
0.07
0.16
0.16
0.91
0.16
0.03
Wanted last Pregnancy Later
0.22
0.14
0.22
0.16
0.15
0.73
0.16
0.14
Did not Want last Pregnancy
0.33
0.55
0.31
0.55
0.51
0.31
0.55
0.55
Geography
Among pre-1997 pregnancies:
Notes: Columns 1 to 3 give unweighted mean characteristics for the sample of women eligible to be sterilized during the campaign years. Column 1 shows the means for
the full sample; column 2 shows means for women who were sterilized in 1996-1997 (S=1); and column 3 shows means for women not sterilized in that period. In
columns 4 to 7 we apply the weights described in Sections 2 and 3 of the text. Column 4 shows means for women sterilized during the campaign years reweighted (using
ߣ௜ ) to resemble women sterilized because of the campaign; column 5 shows means for women not sterilized during the campaign years reweighted (using ߠ௜ ߣ௜ ) to
resemble women sterilized because of the campaign; column 6 repeats column 4; and column 7 shows means for women sterilized sterilized during the campaign years
reweighted (using ͳ െ ߣ௜ ) to resemble those sterilizations outside of the campaign.
37
Table 4. Characteristics of Women Eligible for Sterilization in 1996-1997, DHS V
All Women Eligible for Sterilization (S) in 19961997
Women Sterilized in 1996-1997 (S=1)
Reweighted to
represent C=1
Not Reweighted
Reweighted to represent:
(6)
(7)
S= 0
P-value
for zero
diff
C=1
C=0
29.53
30.26
0.02
29.53
31.84
3.89
3.96
0.55
3.89
3.63
(1)
(2)
(3)
(4)
(5)
all
S= 1
S =0
S= 1
Age in 1996
29.09
31.11
29.00
# Kids in 1996
2.51
3.71
2.45
Pre-Campaign Characteristics
Years of education
7.96
6.88
8.01
4.51
4.61
0.66
4.51
7.98
Age at first birth
20.52
20.31
20.53
19.58
19.92
0.16
19.58
20.65
rural
0.34
0.36
0.34
0.64
0.60
0.25
0.64
0.24
coast
0.50
0.54
0.50
0.33
0.36
0.39
0.33
0.63
mountain
0.37
0.32
0.37
0.45
0.44
0.55
0.45
0.26
jungle
0.13
0.15
0.13
0.21
0.20
0.66
0.21
0.11
urban coast
0.45
0.44
0.45
0.20
0.23
0.20
0.20
0.55
rural coast
0.05
0.10
0.05
0.14
0.13
0.75
0.14
0.08
urban mountain
0.14
0.11
0.15
0.09
0.08
0.78
0.09
0.13
rural mountain
0.23
0.20
0.23
0.37
0.35
0.65
0.37
0.13
urban jungle
0.07
0.08
0.06
0.08
0.08
0.74
0.08
0.09
rural jungle
0.06
0.06
0.06
0.14
0.12
0.46
0.14
0.03
Geography
Notes: See notes to Table 3.
38
Table 5. Effects of Sterilizations during the Campaign years (1996-1997)
(1)
DHS IV (2000)
(2)
(3)
Sterilized by the
Campaign (C=1)
Sterilized outside
Campaign (C=0)
# of obs.
-0.411***
-0.117
14,430
(0.084)
(0.097)
0.021
0.001
(0.032)
(0.031)
DHS V (2004-2008)
(4)
Sterilized by the
Campaign (C=1)
Sterilized outside
Campaign (C=0)
# of obs.
-1.160***
-0.550***
14,833
(0.109)
(0.108)
0.028
-0.017
(0.033)
(0.033)
Fertility Outcome:
Number of Children
Women's Outcomes
Worked for pay?
14,430
Domestic Violence
0.051
-0.008
(0.033)
(0.022)
16,675
13,383
Children's Outcomes
Height for age
0.219*
0.215*
(0.141)
(0.114)
Girls
0.567***
0.438***
2,898
Boys
(0.204)
-0.099
(0.161)
-0.056
1,457
(0.193)
0.054
(0.172)
0.022
0.164*
0.093
(0.062)
(0.071)
(0.091)
(0.066)
Girls < 15
0.034
-0.032
11,529
0.148
0.101
13,061
Boys < 15
(0.090)
0.020
(0.088)
-0.008
11,005
(0.129)
0.185*
(0.086)
0.092
13,588
(0.082)
(0.089)
(0.106)
(0.083)
0.252
-0.100
(0.364)
(0.262)
Years of Schooling
Girls > 15
26,649
4,302
Notes: Each entry in columns 1 and 3 gives the average treatment effect of being sterilized as part of the sterilization campaign using our modified propensity score reweighting (PSR)
estimator as in equation (15) for the indicated outcome. Each entry in columns 2 and 4 gives the average treatment effect of sterilizations that occurred outside of the campaign using our
modified PSR estimator as in equation (16) for the indicated outcome. In the case of child outcomes we use a PSR-regression adjusted estimator which controls for child’s age as discussed in
footnote 9. Standard errors calculated based on 500 bootstrap replications appear in parentheses. *** denotes p-value<0.01; ** denotes p-value <.05; * denotes p-value <0.1 .
39