American Political Science Review Vol. 103, No. 2 May 2009
doi:10.1017/S0003055409090212
From Violence to Voting: War and Political Participation in Uganda
CHRISTOPHER BLATTMAN Yale University
W
hat is the political legacy of violent conflict? I present evidence for a link from past violence
to increased political engagement among excombatants. The evidence comes from northern
Uganda, where rebel recruitment generated quasiexperimental variation in who was conscripted
by abduction. Survey data suggest that abduction leads to substantial increases in voting and community
leadership, largely due to elevated levels of violence witnessed. Meanwhile, abduction and violence do
not appear to affect nonpolitical participation. These patterns are not easily explained by conventional
theories of participation, including mobilization by elites, differential costs, and altruistic preferences.
Qualitative interviews suggest that violence may lead to personal growth and political activation, a
possibility supported by psychological research on the positive effects of traumatic events. Although the
generalizability of these results requires more evidence to judge, the findings challenge our understanding
of political behavior and point to important new avenues of research.
W
hat is the political legacy of a violent civil
war? Can perpetrators and victims become
productive citizens once the fighting stops?
Policy makers are pessimistic. A recent World Bank
report sees the individual impacts of civil war as so
adverse that they lead to social disintegration (Collier
et al. 2003). The French foreign minister recently spoke
of young exsoldiers as “a time bomb that threatens
stability and growth” (BBC 2007). A New York Times
editorial lamented that such youth return as “dam-
aged, uneducated pariahs” (Editorial, 2006). Mean-
while, reintegration experts worry that excombatants
face a life of crime and banditry, and remain alienated
and “at war” in their own minds (Richards et al. 2003;
Spear 2006). If these commentators are correct, then
the rebuilding of s ociety may be all the more challeng-
ing and unlikely after war, and could contribute to the
well-known “conflict trap” (Collier 2007).
Not all evidence is so gloomy. Psychologists con-
sistently find that victims of violence are in general
resilient, and a growing psychological literature finds
that experiences of personal growth are more com-
mon than distress in the aftermath of violent trauma
(Tedeschi and Calhoun 2004). A handful of studies also
tie victimization by war violence to greater collective
action. Wood (2003), for instance, argues that govern-
ment violence in El Salvador prompted its victims to
Christopher Blattman is Assistant Professor, Department of Political
Science, Yale University, 77 Prospect Street, P.O. Box 208209, New
Haven, CT 06520-8209 (christopher.blattman@yale.edu).
I thank Jeannie Annan, my co-Investigator on the Survey of War
Affected Youth (SWAY). For comments, I also thank Robert Bates,
Khristopher Carlson, Macartan Humphreys, David Leonard, Dyan
Mazurana, Edward Miguel, Betsy Levy Paluck, G
´
erard Roland,
David Roodman, Cyrus Samii, Chris Udry, and Jeremy Weinstein,
several anonymous referees, and seminar participants at Yale Uni-
versity, Columbia University, ECARES, and CGD. For data collec-
tion, I thank Roger Horton, Okot Godfrey, the SWAY field research
assistants, AVSI Uganda, and UNICEF Uganda. Military escorts dur-
ing data collection were provided by the Uganda People’s Defense
Force (UPDF). The survey was funded by grants from UNICEF (via
AVSI Uganda), the John D. and Catherine T. MacArthur Foundation
(via the UC Berkeley Human Rights Center), the Russell Sage Foun-
dation, the International Peace Research Association Foundation,
the UC Berkeley Center for African Studies, and the UC Berkeley
Institute for Economic and Business Research.
support and even join opposition forces out of moral
outrage, whereas Bellows and Miguel (2006, 2008) find
that displacement and family deaths from war lead to
greater political participation and awareness in Sierra
Leonean households.
Little of this evidence, however, proves a causal link
from violence to political engagement, and even less
concerns the perpetrators. Yet, violence is endemic in
the developing world; civil conflict has afflicted more
than half of all nations since 1945, with one-fifth suf-
fering ten or more years of war (Blattman and Miguel
N.d.). In the burgeoning conflict literature, however,
the impact of voting on violence receives more atten-
tion than the reverse (Snyder 2000; Wilkinson 2004).
I employ new data and a tragic natural experiment
in northern Uganda to quantify the sociopolitical im-
pacts of combat experiences and war violence. Patterns
of rebel abduction during Uganda’s twenty-year war
appear to have generated nearly exogenous variation
in recruitment. If so, causal estimates of its impact on
later-life outcomes such as political participation can
be identified.
The results defy expectations and suggest that
forced recruitment leads to greater postwar political
participation—a 27% increase in the likelihood of vot-
ing and a doubling of the likelihood of being a com-
munity leader among former abductees. A bduction,
however, does not generally affect nonpolitical forms
of social activity, suggesting that the effects of war on
participation may be uniquely political.
1
Of course, conscription simply represents a package
of war experiences: violence, military training, indoc-
trination, time away, and so forth. Analysis of self-
reported experiences suggests that exposure to vio-
lence, in particular, violence witnessed, accounts for
most of the impact of abduction on participation. No
other war experiences have similar explanatory power.
This finding is good news for policy makers in
wartorn nations. For social scientists, however, it
presents a puzzle: why would violence lead to positive
1
Blattman and Annan (2008) use the same data and empirical strat-
egy to assess the long-term economic and psychosocial impacts of
abduction.
231
From Violence to Voting May 2009
political engagement? I argue that conventional
explanations—ones that focus on the costs of voting,
or elite mobilization—find little support in the data.
Personal interviews with local leaders and former com-
batants, however, reveal narratives of personal trans-
formation that echo a psychological literature on in-
dividual growth and activation after trauma (Tedeschi
and Calhoun 2004). I explore the alternative empirical
and theoretical links between violence and voting and
set out an agenda for research in political behavior and
psychology.
WAR, ABDUCTION, AND POLITICS
IN NORTHERN UGANDA
In 1988, a spirit medium named Joseph Kony assem-
bled the remnants of several failed insurgent groups
from northern Uganda into a new force, the Lord’s
Resistance Army, or LRA.
2
Locally, Kony is believed
to possess great spiritual powers, and his stated goal
is to seek a spiritual cleansing of the nation. Kony’s
movement, however, is also rooted in a long-standing
political, economic, and ethnic divide. Following in-
dependence, northern peoples (including the Acholi,
to which Kony and the LRA belong) dominated the
military, whereas southerners dominated the commer-
cial sector. For more than two decades, this martial
power enabled a series of brutal northern dictators to
govern the nation. In 1986, however, a young politician
named Yoweri Museveni led a southern rebel force to
overthrow the Acholi-dominated government. Several
guerrilla forces in the north initially resisted Musev-
eni’s takeover, but for the most part settled for peace
or were defeated by 1988. The handful of fighters that
would not settle for peace gathered under Kony to
continue the fight.
Despite widespread antipathy for Museveni, the
LRA attracted limited support from other Acholi, and
the poverty and unpopularity of the movement led to
nearly complete r eliance on forced recruitment. From
its earliest days, the rebels looted homes and abducted
youth to obtain supplies and recruits. In 1994, the
Sudanese government began supplying the LRA with
supplies, weapons, and territory on which to build
bases—support that enlarged and invigorated a small
and weak LRA. Abduction from 1995 to 2004 was
large scale and indiscriminate, with 60,000 to 80,000
youth estimated to have been taken by the LRA for
at least a day (Annan, Blattman, and Horton 2006;
Pham, Vinck, and Stover 2007). The majority were
adolescent males, although men and women of all ages
were commonly taken.
Twenty percent of male abductees did not return
and, sadly, can be presumed perished (as few remain
with the LRA). The remaining 80% escaped, were
released, or were rescued after periods of 1 day to
ten years. Roughly half of these “returnees” were de-
mobilized by the Ugandan army (the UPDF), and two
2
This account is based on Allen (2005), Beber and Blattman (2008),
Behrend (1999), Doom and Vlassenroot (1999), Finnstr
¨
om (2008b),
Lamwaka (2002), and Omara-Otunnu (1994).
in five returnees passed through a “reception center”
that provided basic health services, family relocation,
and reinsertion. In 2006, the Government of Uganda
and the LRA reached a fragile truce. Peace talks broke
down in 2008.
The two decades of instability and economic destruc-
tion in the north stand in stark contrast to the success
and stability of the rest of Uganda. Outside Acholiland,
violence has abated, infrastructure has expanded, HIV
infection rates have fallen, and economic growth has
been a robust 6% for the past decade (Government of
Uganda 2007).
DATA AND MEASUREMENT
To assess the effects of combat and war violence on par-
ticipation, this article compares the social and political
participation of (exogenously) abducted and nonab-
ducted youth in northern Uganda, as well as by spe-
cific war experiences within each group. Quantitative
data come from Phase I of the Survey of War Affected
Youth (SWAY), a representative survey of male youth
(ages 14–30) in eight rural subcounties of the districts of
Kitgum and Pader. Data were collected in 2005–06 by
the author, a psychologist, and local research assistants.
To account for migration and mortality, the survey
selected respondents from a sample frame of youth
living in the region before the conflict. A total of
1,162 households were sampled from World Food Pro-
gramme lists compiled in 2002, and 93% of house-
hold heads were located and interviewed. Enumerators
worked with household heads to develop a roster of all
youth living in the household in 1996—a year chosen
because it was easily recalled as the date of the first
election since 1980.
A sample of 881 surviving male youth was drawn
from these retrospective rosters. Nearly half of the
youth had moved since 1996 and were tracked across
the region. Surveyors located 741, or 84%. Former ab-
ductees were oversampled, with 462 interviewed in to-
tal. Absentee questionnaires were conducted with the
families of young men that had died or were not found
to correct for observable determinants of attrition.
3
Survey summary statistics are listed in Table 1.
Measuring Participation
The survey includes three indicators of political par-
ticipation. First, two weeks prior to the survey a na-
tional referendum was held on the question of opening
Uganda to multiparty politics.
4
Forty-six percent of
survey respondents older than age 18 say they Voted
3
There are two types of unfound youth: absentees that could not
be tracked down, and those that did not return from abduction.
Enumerators interviewed the families of all but about 11 absentees,
and virtually all were reported to be engaged in work or school. Those
that did not return from abduction comprise 20% of all abductees,
95% of which can be presumed perished given the small number of
abductees still with the armed group.
4
This referendum asked voters: “Do you agree to open up the
political space to allow those who wish to join different organiza-
tions/parties to do so to compete for political power?”
232
American Political Science Review Vol. 103, No. 2
TABLE 1. Summary Statistics
All Youth Abducted Only Nonabd Only
Mean SD Mean SD Mean SD Obs
War Experiences
Months abducted (total) 9.3
[16.2]
741
Age abducted 15.3
[4.7]
462
Violent acts total (of 25) 7.9
[4.7]
11.0
[4.6]
5.2
[2.9]
737
Violent acts witnessed (of 6) 3.0
[1.7]
3.9
[1.5]
2.2
[1.5]
739
Violent acts on family (of 5) 2.1
[1.4]
2.2
[1.4]
2.0
[1.4]
739
Violent acts received (of 6) 2.1
[1.8]
3.3
[1.6]
1.0
[1.2]
739
Violent acts perpetrated (of 9) .7
[1.4]
1.5
[1.8]
.1
[.3]
738
Leadership position (indicator) .09
[.29]
462
Carried own firearm (indicator) .32
[.47]
462
Passed through reception center .39
[.49]
462
Received NGO services .22
[.42]
462
Sociopolitical Indicators
Voted in 2005 (if 18 or older) .46
[.50]
.51
[.50]
.40
[.49]
533
Community mobilizer .051
[.22]
.072
[.26]
.032
[.18]
741
Political employment .007
[.08]
.011
[.11]
.003
[.06]
741
Any community group member .42
[.49]
.43
[.50]
.41
[.49]
741
Peace group member .06
[.24]
.07
[.26]
.05
[.21]
741
Water committee member .016
[.12]
.009
[.10]
.021
[.14]
741
Cultural group member .16
[.36]
.17
[.37]
.15
[.36]
741
Sporting group or team member .11
[.31]
.08
[.27]
.13
[.33]
741
Farmer’s cooperative member .11
[.31]
.11
[.32]
.10
[.31]
741
School club/committee member .06
[.23]
.06
[.24]
.05
[.22]
741
Church or bible group member .18
[.38]
.17
[.38]
.18
[.38]
741
Attends church .78
[.41]
.77
[.42]
.79
[.41]
741
Volunteer .05
[.21]
.06
[.23]
.04
[.20]
741
Disobeys elders .07
[.25]
.08
[.27]
.06
[.23]
741
Bottom quartile of prosocial
distribution
.23
[.42]
.18
[.38]
.27
[.44]
741
Physical fight .07
[.25]
.07
[.25]
.07
[.25]
741
Ever quarrelsome .05
[.21]
.03
[.17]
.06
[.24]
741
Ever threatens to hurt others .02
[.14]
.03
[.17]
.01
[.11]
741
Note:
Sample means weighted by inverse sampling and inverse attrition probabilities.
in the 2005 referendum, a rate comparable to national
turnout levels. Second, 5% of youth report that they
are a Community mobilizer—elected members of the
community who are responsible for organizing the
community for daily or weekly meetings.
5
Finally, four
respondents (.4%) hold a Political job, such as a village
councilperson.
The survey also sought indicators of community
participation. Forty-two percent report Membership
in any community group, including peace groups
(6%), water management committees (1.6%), cultural
groups (16%), sports teams (11%), farmer’s coopera-
tives (11%), school clubs and committees (6%), and
church or bible study groups (18%). Seventy-eight per-
cent also Attend church regularly, and 5% of youth
Volunteer for a community organization.
Last, the survey measured self-reported prosocial
and aggressive behaviors. Acholi culture stresses obe-
5
The mobilizer is the most common form of youth leadership and is
an unpaid community service. Every few years, communities hold a
meeting and solicit nominations. Nominees give a short speech and
are elected by a show of hands.
dience to elders, and 7% indicated that they Disobey el-
ders. The survey also measured 11 self-reported proso-
cial behaviors (e.g., enjoying working with peers, or
being helpful to the community), and we construct an
indicator for those in the Bottom quartile of the proso-
cial distribution.
6
Finally, the survey asked whether
respondents had been in a Physical fight in the past
six months (7%), whether they were Ever quarrelsome
(5%), and whether they Ever threatened to hurt others
(2%).
Measuring War Experiences
More than two in five male youth reported an Ab-
duction of any length. Many of these abductions were
short, especially among abductees younger than 11 or
older than 20. Such youth were often released after
giving directions or carrying loot (Beber and Blattman
6
The psychosocial survey questions are based on an adapted version
of the Northern Ugandan Child and Youth Psychosocial Adjustment
Scale (Loughry and MacMullin 2002)
233
From Violence to Voting May 2009
2008). Months Abducted ranged from 1 day to 10 years,
averaging 9.3 months for a youth’s longest abduction.
The LRA routinely used violence to intimidate and
control civilians and abductees. To gauge respondents’
levels of exposure to violence, the survey asked about
25 of the most common Violent acts experienced,in-
cluding 6 acts witnessed,6received,8perpetrated by
the respondent, and 5 inflicted on family members of
the respondent by the LRA.
7
The average abductee
reported 11 different violent acts versus nonabductees’
5.2 acts. Most youth, for example, witnessed killings, ex-
perienced their homes being raided, or took cover from
gunfire. Among the abducted, forced labor, thrashings,
and imprisonment were commonplace. Attempts to es-
cape were punished with beatings or death, a sentence
other abductees were often forced to carry out with
machetes or clubs. Initiation to the LRA also involved
forced violence: 25% of abductees were made to harm
or kill a civilian, and 23% were made to desecrate
dead bodies—a deeply held taboo. Finally, 13.5% of
abductees report being forced to beat or kill family or
friends. Such violence served to break down a youth’s
defenses, desensitize him to violence, and dissuade him
from escape (Beber and Blattman 2008).
Other war experiences recorded include indicators
for whether the youth held a Leadership position or
rank (9%), ever Carried his own firearm (32%), and
whether he Passed through a reception center (39%).
Such centers were set up by local and international
nongovernmental organizations (NGOs) after 1999 to
receive youth returning from long abductions. Just 22%
of abductees Received services from NGOs after re-
turning home.
Qualitative Data
Following the survey and preliminary quantitative
analysis, in 2007, I conducted semistructured interviews
to explore the meaning and validity of the sociopoliti-
cal survey results. Interviews were conducted in three
of the eight enumeration areas and included all sur-
vey respondents recorded as community mobilizers or
having political jobs, all former abductees holding any
rank, as well as a random sample of 20 respondents
(half of whom voted in the 2005 referendum and half
of whom did not). Interviews began with a r epeat of
the abduction and sociopolitical modules of the ques-
tionnaire, whereupon respondents were asked to elab-
orate on their closed-ended answers to explore key
themes, including reasons for voting/not voting, the his-
tory of group participation and community leadership,
7
The survey recorded an indicator for ever experiencing each act,
and each index is a sum of these indicators. Acts received include
gunfire, forced labor, beatings, armed attacked, being tied up, and
receiving a war. Acts witnessed include regular gunfire, beatings or
torture, attacks or battles, killings, massacres, rape, and the torch-
ing of occupied homes. Acts perpetrated include beating a civilian,
beating family or friends, killing a soldier, killing a civilian, killing
family or friends, forcible sex, and abuse of dead bodies. Violence
on family includes abducted parent, other abducted family, family
member with war injury, violent death of a parent, and violent death
of other family.
and reasons for/for not becoming a particular group
member or community leader.
8
Also interviewed in a less structured fashion were
five reception center workers, six local political opera-
tives, and two poll workers from the same three enu-
meration areas. These interviews focused on the role
of formerly abducted youth in local politics (without
revealing the positive association between abduction
and participation).
Furthermore, prior to the survey in 2005, I conducted
two months of unstructured interviews with approxi-
mately 120 youth (including 80 abductees), plus more
than 60 community members and leaders. The inter-
views focused on abduction patterns, LRA organiza-
tion, and return and reintegration experiences. Inter-
views aimed to understand the conduct of the war,
investigate the validity of the causal identification strat-
egy, and develop reintegration metrics and hypotheses.
Interview subjects were typically contacted through
community leaders and reception center staff. fifteen
former LRA junior officers (e.g., a lieutenant) were
also purposefully located via these channels.
Finally, concurrent with the survey, a psycholo-
gist and a local social worker conducted system-
atic, semistructured interviews and psychosocial as-
sessments of a nonrandom subsample of 30 youth and
their families. The details of this qualitative psychoso-
cial study are reported in Annan, Brier, and Aryemo
(2008), and relevant results are highlighted in this
article.
THE IMPACT OF ABDUCTION
ON PARTICIPATION
Empirical Strategy
Estimating the impacts of military service and war vio-
lence is a difficult task. Combatants are usually unlike
noncombatants in unobservable ways, and so any com-
parison will conflate the impacts of war with preexisting
differences that led the youth to join or be selected by
the armed group. This is especially true if the character-
istics associated with being a combatant (e.g., poverty,
social exclusion, or malleability) are traits that also
affect social consciousness or political activity.
One solution is the counterfactual approach, where
a relevant control group is found for recruits. The
estimated impact, however, is only as reliable as the
counterfactual. Causal estimates will be unbiased only
when recruitment is “conditionally unconfounded” or
exogenous—that is, when all selection is on observed
traits (Imbens 2004; Rosenbaum and Rubin 1983;
Rubin 1978).
8
Questionnaires are available at www.sway-uganda.org or by re-
quest. Relevant modules include Sections VII (Community Involve-
ment & Political Attitudes) and IX (Abduction and Return Experi-
ences). The interview was predicated as a follow-up of survey quality
and responses, typically with the original e numerator present. Addi-
tional topics explored included war and abduction experiences, voter
registration status, the qualities of good leaders, election processes,
and the role of former abductees in the community and community
politics.
234
American Political Science Review Vol. 103, No. 2
In most wars, such stringent conditions would not
hold. Evidence from Uganda, however, suggests that
the most common types of selection into armed groups
are not present in the case of the LRA. First, volunteer-
ing (or self-selection) into the LRA was virtually un-
known. What few volunteers did exist tended to join be-
fore 1991, and most come from a neighboring district,
Gulu (and so do not influence this article’s s ample).
Second, interviews with the leaders of LRA raiding
parties suggest t hat by neither design nor accident
did they abduct a select group of youth. From their
Sudanese bases, rebels ventured into Uganda for
weeks at a time in groups of roughly 15 fighters.
Raiding parties had two aims: ambushing government
forces and raiding homesteads along their path for
food and recruits. Abduction targets tended to be
unplanned and arbitrary, and homesteads were raided
regardless of wealth or makeup. Typical of East Africa,
rural Acholi households live in relatively isolated
homesteads in their fields, arrangements that made
them particularly vulnerable to LRA raids. Rebels
usually invaded such homesteads at night, abducting
all able-bodied people to carry looted goods. These
abduction parties were under instruction to release
only young children and older adults, but to keep all
adolescent and young adult males.
The data support these claims. The survey gath-
ered data on prewar household wealth (including land
and livestock) and parent’s education, occupation, and
death—traits that are believed to be reliable predictors
of participation in armed groups in Africa (e.g., Cohn
and Goodwin-Gill 1994; Honwana 2005; Humphreys
and Weinstein 2008). If we compare the abducted and
nonabducted along such prewar traits, we observe little
difference in conditional mean differences at even the
10% significance level (Table 2, Column 1). Abducted
youth differ only by year of birth (as expected) and
prewar household size.
9
These same household t raits, however, help predict
participation in a voluntary government militia, imply-
ing that if abduction were associated with these prewar
traits we would have the statistical power to observe it.
Five percent of youth were current or past militia mem-
bers. A comparison of prewar traits shows that mili-
tia members came from poorer and more agricultural
households (Table 2, Column 2), and collectively, the
prewar covariates strongly predict government militia
membership—the effects are larger than in the abduc-
tion case and jointly significant at the 5% level.
A remaining concern is selective attrition. There
are two main types of “attritors”: nonsurvivors and
unfound migrants. The 84% tracking success r ate
meets or exceeds the rates achieved by several “gold-
standard” youth tracking surveys in poor countries
9
The significance is driven by households greater than 25 in number,
perhaps because small bands of raiders were hesitant to raid large,
difficult-to-control groups. Otherwise, differences in the distribu-
tions of predicted abduction probabilities among abducted and non-
abducted youth are driven by year and location of birth alone. In a
logit regression of abduction on prewar traits, omission of household
traits does not affect the distribution of the predicted probabilities,
and they are jointly not significance (p = .18).
(Hamory and Miguel 2006; Thomas, Frankenberg, and
Smith 2001). Also, similar proportions of abducted and
nonabducted youth were found (29.7% vs. 28.3%).
Even so, differential attrition patterns raise concern:
nonabducted youth are more like to have migrated
and gone unfound, whereas abductees are uniquely
likely to have been abducted and not returned (and
can be assumed perished given the small number of
abductees still with the LRA). Estimates of the impact
of abduction will be biased if qualities that determine
migration or s urvival also shape political action.
To correct for attrition on observables, we collected
demographic data and data on current activities and
well-being from the surviving family members. Follow-
ing Fitzgerald, Gottschalk, and Moffitt (1998), these
data were used to calculate attrition probabilities, and
regression estimates are weighted by the inverse of
these attrition probabilities to eliminate bias from at-
trition on observed traits.
Results
Assuming conditional unconfoundedness, consistent
estimates of the causal impact of abduction can be cal-
culated using an index model such as a l ogit, weighted
by a nonparametric estimate of the selection probabil-
ity, or propensity score (Hirano, Imbens, and Ridder
2003).
10
The results are displayed in Table 3.
To begin, abduction leads to an 11.0 percentage point
increase in the probability a youth older than 18 voted
in the 2005 referendum (Column 2), significant at the
1% level. Because just 40% of eligible nonabducted
youth voted (Column 1), this ATE represents a 27%
increase in voter turnout (Column 3).
Abduction also leads to a 3.4 percentage point in-
crease in the likelihood that a youth is a community
mobilizer, significant at the 1% level. Just 3% of non-
abducted youth are leaders, and so the impact of abduc-
tion represents a 106% increase in levels of leadership.
Abduction is also associated with a 190% increase in
the likelihood of holding a political job such as a com-
munity council member or appointee. The estimate,
however, is not statistically significant due to sample
size: only four respondents reported such employment,
three of whom are former abductees. But the direction
and magnitude of the result is consistent with the other
political results.
10
In this case, Y
∗
is a latent variable describing an individual i’s
propensity for participation, observed as a binary outcome, Y.The
treatment effect, τ, can be estimated by the following regression:
P(Y
i
= 1) = (τ · T
i
+ X
S
i
· β
1
),
where the treatment (i.e., abduction) indicator T equals 1 if
youth i was abducted, and the X
S
are the subset of observed
covariates X that are significantly correlated with Y, conditional on
treatment. The weights used are
ω
i
= ω(T
i
, v
i
,ρ
i
) = ρ
i
· π
i
·
T
i
ˆe(v
i
)
+
1 − T
i
1 − ˆe(v
i
)
,
where ρ
i
and π
i
are sampling and attrition weights, and
ˆ
e(v
i
) is
a nonparametric estimate of the propensity score. The v
i
are the
subset of the covariates X
i
that have substantial correlation with the
treatment.
235