W_s , 13
POLICY RESEARCH WORKING PAPER 2153
The Mystery of the This entertaining introduction
to the concepts and methods
Vanishing Benefits of impact evaluation - as
seen through the eyes of Ms.
Ms. Speedy Analyst's Introduction Speedy Analyst-assumes
readers are familiar with basic
to Evaluation statistics up to regression
analysis (as covered in an
Martin Ravallion introductory text on
econometrics).
The World Bank
Development Research Group
Poverty and Human Resources
July 1999
POLIcY RESEARCH WORKING PAPER 2153
Summary findings
The setting for this good-natured training guide for Ms. Speedy Analyst's on-the-job training in how to
impact evaluation is the fictional developing country assess the impact of a social program provides the vehicle
Labas. Twelve months ago the government introduced an through which this paper explains:
antipoverty program in Northwest Labas with support * Methods of evaluating a program's impact-
from the World Bank. The program aims to provide cash randomizing, matching, reflexive comparisons, double
transfers to poor families with school-age children. To be difference (or "difference in difference") methods, and
eligible to receive the transfer, households must have instrumental variables methods.
observable characteristics that suggest they are poor. To * The types of data used for impact evaluation, typical
continue receiving the transfer, they must keep their problems with and uses of data, control variables,
children in school until 18 years of age. The program is instrumental variables, regressions, and so on.
called PROSCOL. * How to form and match comparison groups.
The government wants to assess PROSCOL's impact * Sources of bias.
on poverty, to help decide whether the program should * The value of baseline surveys.
be expanded or dropped. The Finance Minister asks the * Measures of poverty (headcount index, poverty gap
undersecretary, and the undersecretary calls in Ms. index, and squared poverty gap).
Speedy Analyst. * How to compare poverty with and without the
program.
This paper -a product of Poverty and Human Resources, Development Research Group - is part of a larger effort in the
group to provide useful training tools for Bank staff. Copies of the paper are available free from the World Bank, 1818 H
Street NW, Washington, DC 20433. Please contact Patricia Sader, room MC4-773, telephone 202-473-3902, fax 202-522-
1153, Internet address psader@worldbank.org. Policy Research Working Papers are also posted on the Web at http://
www.worldbank.org/html/dec/Publications/Workpapers/home.html. The author may be contacted at mravallion
@worldbank.org. July 1999. (40 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
The Mystery of the Vanishing Benefits:
Ms Speedy Analyst's Introduction to Evaluation
Martin Ravallion*
World Bank
This paper aims to provide an introduction to the concepts and methods of impact evaluation. The
paper assumes that readers are familiar with basic statistics up to regression analysis (as would be covered
in an introductory text on econometrics). For their comments and discussions I am grateful to Judy Baker,
Kene Ezemenari, Emanuela Galasso, Paul Glewwe, Jyotsna Jalan, Emmanuel Jimenez, Aart Kraay,
Robert Moffitt, Rinku Murgai, Pedro Olinto, Berk Ozler, Laura Rawlings, Dominique van de Walle, and
Michael Woolcock.
The setting for our story is the developing country, Labas. 12 months ago, its Government
introduced an anti-poverty program in Northwest Labas, with support from the World Bank. The
program aims to provide cash transfers to poor families with school-age children. To be eligible to
receive the transfer, households must have certain observable characteristics that suggest they are
"4poor"; to continue receiving the transfer they must keep their kids in school until 18 years of age.
The program is called PROSCOL.
The Bank's Country Director for Labas has just asked the Government to assess PROSCOL's
impact on poverty, to help determnine whether the program should be expanded to include the rest of
the country, or be dropped. The Ministry of Social Development (MSD) runs PROSCOL. However,
the Bank asked if the Finance Ministry could do the evaluation, to help assure independence, and to
help develop capacity for this type of evaluation in a central unit of the government - close to where
the budgetary allocations are being made. The Government agreed to the Bank's request. The
Minister of Finance has delegated the task to Mr. Undersecretary, who has called in one of his
brightest staff, Ms Speedy Analyst.
Four years ago, Speedy Analyst graduated from the Labas National University, where she did
a Masters in Applied Economics. She has worked in the Finance Ministry since then. Speedy has a
reputation for combining good common sense with an ability to get the most out of imperfect data.
Speedy also knows that she is a bit rusty on the stuff she learnt at LNU.
Mr. Undersecretary gets straight to the point. "Speedy, the Government is spending a lot of
money on this PROSCOL program, and the Minister wants to know whether the poor are benefiting
from it, and how much. Could you please make an assessment."
Speedy thinks this sounds a bit too vague for her liking; what does he mean by "benefiting",
she thinks to herself. Greater clarity on the program's objectives would be helpful.
"I will try to do my best, Mr. Undersecretary. What, may I ask, are the objectives of
PROSCOL, that we should judge it against?"
2
Mr. Undersecretary does not seem entirely comfortable with such a direct question. He
answers: "To reduce poverty in Labas, both now and in the future."
Speedy tries to pin this down further. "I see. The cash transfers aim to reduce current poverty,
while by insisting that transfer recipients keep their kids in school, the program aims to reduce future
poverty".
"Yes, that's right, Speedy".
"So I guess we need to know two things about the program. Firstly, are the cash transfers
mainly going to low-income families? Secondly, how much is the program increasing school
enrollment rates?"
"That should do it, Speedy. Here is the file on the program that we got from the Ministry of
Social Development."
Thus began Speedy Analyst's on-the-job training in how to assess the impact of a social
program. Note 1 summarizes the methods she will learn about over the following days.
The mystery unfolds
Back in her office, Speedy finds that the file from MSD includes some useful descriptive
material on PROSCOL. She learns that targeting is done on the basis of various "poverty proxies",
including the number of people in the household, the education of the head, and various attributes of
the dwelling. PROSCOL pays a fixed amount per school-age child to all selected households on the
condition that the kids attend 85% of their school classes, which has to be verified by a note from the
school.
3
Note 1: Methods for evaluating program impact
The essential problem of impact evaluation is that we do not observe the outcomes for participants if
they had not participated. So evaluation is essentially a problem of missing data. A "comparison group"
is used to identify the counter-factual of what would have happened without the program. The
comparison group is designed to be representative of the "treatment group" of participants with one key
difference: the comparison group did not participate. The main methods available are as follows:
* Randomization, in which the selection into the treatment and comparison groups is random in some
well-defined set of people. Then there will be no difference (in expectation) between the two
groups besides the fact that the treatment group got the program. (There can still be differences due
to sampling error; the larger the size of the treatment and comparison samples the less the error.)
* Matching. Here one tries to pick an ideal comparison group from a larger survey. The comparison
group is matched to the treatment group on the basis of a set of observed characteristics, or using
the "propensity score" (predicted probability of participation given observed characteristics); the
closer the propensity score, the better the match. A good comparison group comes from the same
economic environment and was administered the same questionnaire by similarly trained
interviewers as the treatment group.
* Reflexive comparisons, in which a "baseline" survey of participants is done before the intervention,
and a follow-up survey done after. The baseline provides the comparison group, and impact is
measured by the change in outcome indicators before and after the intervention.
* Double difference (or "difference in difference") methods. Here one compares a treatment and
comparison group (first difference), before and after a program (second difference). Comparators
should be dropped if they have propensity scores outside the range observed for the treatment
group.
* Instrumental variables methods. Instrumental variables are variables that matter to participation,
but not to outcomes given participation. If such variables exist then they identify a source of
exogenous variation in outcomes attributable to the program - recognizing that its placement is not
random but purposive. The instrumental variables are first used to predict program participation,
then one sees how the outcome indicator varies with the predicted values.
No method is perfect. Randomization is fraught with problems in practice. Political feasibility is often a
problem. And even when selection is randomized, there can still be selective non-participation.
Matching methods only deal with observable differences; there will still be a problem of latent
heterogeneity, leading to a possible bias in estimating program impact. Selective attrition plagues both
randomization and double-difference estimates. It is always desirable to triangulate methods.
The file includes a report, "PROSCOL: Participants' Perspectives", commissioned by MSD
and done by a local consultant. The report was based on qualitative interviews with program
administrators and focus groups of participants. Speedy cannot tell whether those interviewed were
representative of PROSCOL participants, or how poor they are relative to those who were not picked
for the program and were not interviewed. The report says that the kids went to school, but Speedy
wonders whether they might not have also gone to school if the program had not existed.
4
Speedy reflects to herself. "This report is a start, but it does not tell me how poor PROSCOL
participants are and what impact the program has on schooling. I need hard data." Later Speedy
prepares Note 2, summarizing the types of data typically used in impact evaluations.
Note 2: Data for impact evaluation
* Know the program well. It is risky to embark on an evaluation without knowing a lot about the
administrative/institutional details of the program; that information typically comes from the
program administration.
* It also helps a lot to have a reasonably firm grip on the relevant "stylized facts" about the setting.
The relevant facts might include the poverty map, the way the labor market works, the major
ethnic divisions, other relevant public programs, etc.
* Be eclectic about data. Sources can embrace both informal, unstructured, interviews with
participants in the program as well as quantitative data from representative samples.
* However, it is extremely difficult to ask counter-factual questions in interviews or focus groups;
try asking someone who is currently participating in a public program: "what would you be doing
now if this program did not exist?" Talking to program participants can be valuable, but it is
unlikely to provide a credible evaluation on its own.
* One also needs data on the outcome indicators and relevant explanatory variables. You need the
latter to deal with heterogeneity in outcomes conditional on program participation. Outcomes can
differ depending on whether one is educated, say. It may not be possible to see the impact of the
program unless one controls for that heterogeneity.
* Depending on the methods used (Note 1), you might also need data on variables that influence
participation but do not influence outcomes given participation. These instrumental variables can
be valuable in sorting out the likely causal effects of non-random programs (Note 1).
* The data on outcomes and other relevant explanatory variables can be either quantitative or
qualitative. But it has to be possible to organize it in some sort of systematic data structure. A
simple and common example is that one has values of various variables including one or more
outcome indicators for various observation units (individuals, households, firms, communities).
* The variables one has data on and the observation units one uses are often chosen as part of the
evaluation method. These choices should be anchored to the prior knowledge about the program
(its objectives of course, but also how it is run) and the setting in which it is introduced.
* The specific source of the data on outcomes and their determinants, including program
participation, typically comes from survey data of some sort. The observation unit could be the
household, firm, geographic area, depending on the type of program one is studying.
* Survey data can often be supplemented with useful other data on the program (such as from the
project monitoring data base) or setting (such as from geographic data bases).
There is a promising lead in the MSD file. Nine months ago the first national household
survey of Labas was done by the Labas Bureau of Statistics (LBS). It is called the Living Standards
Survey (LSS). The survey was done for a random sample of 10,000 households, and it asked about
household incomes by source, employment, expenditures, health status, education attainments, and
5
demographic and other attributes of the family. There is a letter in the file from MSD to LBS, a few
months prior to the LSS, asking for a question to be added on whetler or not the sampled household
had participated in PROSCOL. The reply from LBS indicates that the listing of income sources in the
survey schedule will include a line item for money received from PROSCOL.
"Wow", says Speedy, and she heads off to LBS.
Speedy Analyst already knows a few things about the LSS, having used tabulations from it
produced by LBS. But Speedy worries that she will not be able to do a good evaluation of
PROSCOL without access to the raw household-level data. But after a protracted and unsuccessful
discussion with the head of the LBS unit in charge of the survey, and seemingly endless follow-up
phone calls, Speedy starts to worry whether she will get the data, and have anything on outcomes
worth showing her boss.
However, after a formal request from the Minister (which Speedy wrote for him to sign), the
Secretary of Statistics finally agrees to give her the micro data. Then, after a few more phone calls,
LBS also gives her a copy of the documentation she needs to read the data.
Speedy already knows how to use a statistics package called SAPS. After a long and painful
day figuring out how to use the raw LSS data, Speedy starts the real work. She uses SAPS to make a
cross-tab of the average amount received from PROSCOL by deciles of households, where the
deciles are formed by ranking all households in the sample according to their income per person. In
calculating the latter, Speedy decides to subtract any monies received from PROSCOL; this, she
reckons, will be a good measure of income in the absence of the program. So she hopes to reveal
who gained according to their pre-intervention income.
The cross-tab suggests that the cash transfers under the program are quite well targeted to the
poor. By the official LBS poverty line, about 30% of Northwest Labas' population is poor. From her
table, she calculates that the poorest 30% of the LSS sample receive 70% of the PROSCOL transfers.
This looks like good news for PROSCOL, Speedy reflects.
6
What about the impact on schooling? She makes another table, giving average school
enrollment rates of various age groups for PROSCOL families versus non-PROSCOL families. This
suggests almost no difference between the two; the average enrollment rate for kids aged 6-18 is
about 80% in both cases.
Speedy then calculates average years of schooling at each age and plots the results separately
for PROSCOL families and non-PROSCOL families. The two figures are not identical, but they are
very close.
"Was there really no impact on schooling, or have I done something wrong?" she asks
herself. The question is just the beginning of the story of how Speedy Analyst solves the mystery of
the vanishing schooling benefits from PROSCOL.
Speedy Analyst visits Mr. Unbiased Statistica
Speedy decides to show her curious results to a couple of trusted colleagues. First she visits
Mr. Unbiased Statistica, a senior statistician at LBS. Speedy likes Statistica, and feels comfortable
asking him about statistical problems.
"Mr Statistica, my calculations from the LSS suggest that PROSCOL kids are no more likely
to be in school than non-PROSCOL kids. Have I done something wrong?"
Statistica tells her bluntly: "Speedy, I think you may well have a serious bias here. To know
what impact PROSCOL has, you need to know what would have happen without the program. The
gain in schooling attributable to the program is just the difference between the actual school
attendance rate for participating kids and the rate for those same kids if the program had not existed.
"What you are doing Speedy is using non-PROSCOL families as the comparison group for
inferring what the schooling would be of the PROSCOL participants if the program had not existed.
This assumes that the non-participants correctly reveal, at least on average, schooling without the
program. Some simple algebra might help make this clear."
7
Mr. Statistica starts writing. "Let Pi denote PROSCOL participation of the i'th child. This can
take two possible values, namely Pi=I when the child participates in PROSCOL and Pi=0 when she
does not. When the i'th child does not participate, her level of schooling is S0i which stands for child
i's schooling S when P=O. When the child does participate her schooling is Sli. The gain in
schooling due to PROSCOL for a child that does in fact participate is:
G, = SIi-So, J Pi=l
"Why do you need this I "? asks Speedy.
"That stands for 'given that' or 'conditional on' if you prefer. The' 'is needed to make
it clear that we are calculating the gain for a child who actually participated. If we want to know
the average gain we simply take the mean of all the G's. This will give you the sample mean
gain in schooling amongst all those who participated in PROSCOL. As long as you have
calculated this mean correctly (using the appropriate sample weights from your survey) it will
provide an unbiased estimate of the true mean gain. The latter is what statisticians often call the
"expected value" of G, and it can be written as:
G = E(SI -Soi I Pi=1)
You can think of this as another way of saying 'mean'. However, it need not be exactly equal to the
mean you calculate from your sample data, given that there will be some sampling error. In the
evaluation literature, E(S1 -So, I Pi=l) is sometimes called the 'treatment effect' or the 'average
treatment effect on the treated'."
Speedy thinks to herself that the government would not like to call PROSCOL a "treatment".
But she is elated by Statistica's last equation. "Yes Mr. Statistica, that is exactly what I want to
know."
8
"Ah, but that is not what you have calculated Speedy. You have not calculated G but rather
the difference in mean schooling between kids in PROSCOL families and those in non-PROSCOL
families. This is the sample estimate of:
D = E(Sli I Pi=l) - E(So0 I Pi=O)
There is a simple identity linking the D and G, namely:
D=G+B
This term 'B' is the bias in your estimate, and it is given by:
B = E(Soj I Pi=1 ) - E(So, I P1=0)
In other words, the bias is the expected difference in schooling without PROSCOL between children
who did in fact participate in the program and those who did not. You could correct for this bias if
you knew E(So0 I P,=l). But you can't even get a sample estimate of that. You can't observe what the
schooling would have been of kids who actually participated in PROSCOL had they not participated;
that is missing data - it is called a 'counter-factual' mean."
Speedy sees that Statistica has a legitimate concern. In the absence of the program,
PROSCOL parents may well send their kids to school less than do other parents. If so, then there will
be a bias in her calculation. What the Finance Minister needs to know is the extra schooling due to
PROSCOL. Presumably this only affects those families who actually participate. So the Minister
needs to know how much less schooling could be expected without the program. If there is no bias,
then the extra schooling under the program is the difference in mean schooling between those who
participated and those who did not. So the bias arises if there is a difference in mean schooling
between PROSCOL parents and non-PROSCOL in the absence of the program.
"What can be done to get rid of this bias, Mr. Statistica?"
"Well, the best way is to assign the program randomly. Then participants and non-
participants will have the same expected schooling in the absence of the program, i.e., E(So0 I P=l) =
E(So, I Pi=O). The schooling of non-participating families will then correctly reveal the counter-
9
factual, i.e., the schooling that we would have observed for participants had they not had access to
the program. Indeed, random assignment will equate the whole distribution, not just the means.
There will still be a bias due to sampling error, but for large enough samples you can safely assume
that any statistically significant difference in the distribution of schooling between participants and
non-participants 'is due to the program."
On recalling what she read in the .PROSCOL file, Speedy realizes that she need look no
further than the design of the program to see that participation is not random. Indeed, it would be a
serious criticism of PROSCOL to find that it was. The very fact of its purposive targeting to poor
families, who are presumably less likely to send their kids to school, would create bias.
She tells Mr. Statistica about the program's purposive placement.
"So, Speedy, if PROSCOL is working well then you should expect participants to have worse
schooling in the absence of the program. Then E(Soi I P, =1) < E(Soi I Pi =0) and your calculation will
underestimate the gain from the program. You may find little or no benefit even though the program
is actually working well."
Speedy returns to her office, despondent. She sees now that the magnitude of this bias that
Mr. Statistica is worried about could be huge. Her reasoning is as follows: Suppose that poor families
send their kids to work rather than school; because they are poor and cannot borrow easily, they need
the extra cash now. Non-poor families send their kids to school. The program selects poor families,
who then send their kids to school. One observes negligible difference in mean schooling between
PROSCOL families and non-PROSCOL families; indeed, E(Sj1 I Pi =1) = E(So i I Pi =0) in
expectation. But the impact of the program is positive, and is given by E(Soi I Pi =0) - E(Soi I Pi =1).
The failure to take account of the program's purposive, pro-poor, targeting could well have led to a
very substantial under-estimation of PROSCOL's benefits from her comparison of mean schooling
between PROSCOL families and non-PROSCOL families.
10
A visit to Ms Tangential Economiste
Next Speedy visits a colleague at the Ministry of Finance, Tangential Economiste. Tangential
specializes in public finance. She has a reputation as a sharp economist in the Ministry, though
sometimes a little brutal in her comments on her colleague's work.
Speedy first shows her the cross-tab of amounts received from PROSCOL against income.
Tangential immediately brings up a concern, which she chastises Speedy for ignoring. "You have
clearly overestimated the gains to the poor from PROSCOL because you have ignored foregone
income, Speedy. Kids have to go to school if the family is to get the PROSCOL transfer. So they
will not be able to work, either on the family business or in the labor market. Kids aged 15-18 can
earn two-thirds or more of the adult wage in agriculture and construction, for example. PROSCOL
families will lose this income from their kids' work. You should take account of this foregone
income when you calculate the net income gains from the program. And you should subtract this net
income gain, not the gross transfer, to work out pre-intervention income. Only then will you know
how poor the family would have been is in the absence of the PROSCOL transfer. I reckon this table
might greatly overstate the program's gains to the poor."
"But why should I factor out the foregone income from child labor? Less child labor is
surely a good thing," Speedy says in defense.
"You should certainly look at the gains from reducing child labor Speedy, of which the
main gain is no doubt the extra schooling, and hence higher future incomes of currently poor
families. I see your next table is about that. As I see it, you are concerned with the two main
ways PROSCOL reduces poverty: one is by increasing the current incomes of the poor, and the
other is by increasing their future incomes. The impact on child labor matters to both, but in
opposite directions. So PROSCOL faces a trade off."
11
Speedy realizes that this is another reason why she needs to get a good estimate of the
impact on schooling; only then will she be able to determine the foregone income that Tangential
is so worried about. Maybe the extra time at school comes out of non-work time.
Next, Speedy tells Tangential about Mr. Statistica's concerns about her second table, to
see what she thinks.
"I think your main problem here is that you have not allowed for all the other determinants of
schooling, besides participation in PROSCOL. You should run a regression of years of schooling on
a set of control variables as well as whether or not the child's family was covered by PROSCOL.
Why not try this regression?" Tangential writes. "For the i'th child in your sample let:
Si = a + bPi + cX, + si
Here a, b and c are parameters, X stands for the control variables, such as age of the child, mother's
and father's education, the size and demographic composition of the household and school
characteristics, while E is a residual that includes other determinants of schooling, and measurement
errors. You can see Speedy that the estimated value of b gives you the impact of PROSCOL on
schooling."
"No, I don't see that," Speedy interjects.
"Well, if the family of the i'th child participates in PROSCOL then P=1 and so its schooling
will be a + b + cX, + si. If it does not participate, then P=O and so its schooling will be a + cX1 + £i.
The difference between the two is the gain in schooling due to the program, which is just b."
This discussion puts Speedy in a more hopeful mood, as she returns to her office to try out
Tangential's equation. She runs the REGRESS command in SAPS on the regression with and
without the control variables Tangential suggested. When she runs it without them, she finds that the
estimated value of b is not significantly different from zero (using the standard t-test given by SAPS).
This looks suspiciously like the result she first got, taking the difference in means between
12
participants and nonparticipants - suggesting that PROSCOL is not having any impact on
schooling. However, when she puts a bunch of control variables in the regression, she immediately
sees a positive and significant coefficient on PROSCOL participation. She calculates that by 18
years of age, the program has added two years to schooling.
Speedy thinks that this is starting to look more convincing. But she feels a little unsure about
what she is doing. "Why do these control variables make such a difference? And have I used the
right controls? I need more help if I am going to figure out what exactly is going on here, and
whether I should believe this regression."
Professor Chisquare helps interpret Speedy's results
Speedy decides to visit Professor Chisquare, who was one of her teachers at LNU. Chisquare
is a funny little man, who wears old-fashioned suits and ties that don't match too often. "It is just not
normal to be so square", she recalls thinking during his classes in econometrics. Speedy also recalls
her dread at asking Chisquare anything, because his answers were sometimes very hard to
understand. "But he knows more about regressions than anyone else I know", Speedy reflects.
She arranges a meeting. Having heard on the phone what her problem is, Chisquare greets his
ex-student with a long list of papers to read, mostly with rather impenetrable titles, and published in
seemingly obscure places.
"Thanks very much Professor, but I don't think I will have time to read all this before my
report is due. Can I tell you my problem, and get your reactions now?"
Chisquare agrees. Speedy shows him the regressions, thinking that he will be pleased that his
ex-student has been running regressions. He asks her a few questions about what she had done, and
then rests back in his chair, ready, it seems, to pronounce judgement on her efforts so far.
13
"One concern I have with your regression of schooling on P and X is that it does not allow
the impact of the program to vary with X; the impact is the same for everyone, which does not seem
very likely."
"Yes, I wondered about that," chips in Speedy. "Parents with more schooling would be more
likely to send their kids to school, so the gains to them from PROSCOL will be lower".
"Quite possibly, Ms Analyst. To allow the gains to vary with X, let mean schooling of non-
participants be ao + coXi while that of participants is a, + c1Xi, so the observed level of schooling is:
Si = (a, + ciXi + sli)Pi + (ao + coX + coi)(1 - Pi)
where &o and si are random errors, each with means of zero and uncorrelated with X. To estimate this
model, all you have to do is add an extra term for the interaction effects between program
participation and observed characteristics to the regression you have already run. So the augmented
regression is:
Si = ao + (al- ao)Pi + coXY + (c] - co)PAX + £i
where &i = cl,Pi + Foi (1 - P,). Then (a, - ao) + (cl - co)X is the mean program impact at any given
value of X. If you use the mean X in your sample of participants then you will have their mean gain
from the program.
"A second concern Ms Analyst is in how you have estimated your regression. The
REGRESS command in SAPS is just Ordinary Least Squares. You should recall from when you did
my Econometrics class that OLS estimates of the parameters will be biased even in large samples
unless the right-hand side variables are exogenous."
"Yes, I think I do recall that; but can you remind me what 'exogenous' means?"
"It means that the right-hand-side variables are determined independently of schooling
choices and so they are uncorrelated with the error term in the schooling regression. Is PROSCOL
participation exogenous Ms Analyst?"
14
Speedy thinks quickly, recalling her conversation with Mr. Statistica. "No. Participation was
purposively targeted. How does that affect my calculation of the program's impact?"
"Your equation for years of schooling is:
Si = a + bPi + cXi + ei
You used a + b + cXi + Fi as your estimate of the i'th household's schooling when it participates in
PROSCOL, while you used a + cXi + si to estimate schooling if it does not participate. Thus the
difference, b, is the gain from the program. However, in making this calculation you implicitly
assumed that ei was the same either way. In other words, you assumed that £ was independent of P.
Speedy now sees that the bias due to non-random program placement that Unbiased Statistica
was worried about might also be messing up her estimate based on the regression model suggested
by Tangential Economiste. "Does that mean that my results are way off the mark?"
"Not necessarily," Chisquare replies, as he goes to his white board. "Let's write down an
explicit equation for P, as, say:
P,= d+eZi+v,
where Z is a bunch of variables that include all the observed 'poverty proxies' used for PROSCOL
targeting. Of course there will also be some purely random error term that influences participation;
these are poverty proxies that are not in your data, and there will also have been 'mistakes' in
selecting participants that also end up in this v term. Notice too that this equation is linear, yet P can
only take two possible values, 0 and 1. Predicted values between zero and one are OK, but a linear
model cannot rule out the possibility of negative predicted values, or values over one. There are
nonlinear models that can deal with this problem, but to simplify the discussion I will confine
attention to linear models.
"Now, there is a special case in which your OLS regression of Son P and Xwill give you an
unbiased estimate of b. That is when X includes all the variables in Z that also influence schooling,
15
and the error term v is uncorrelated with the error term e in your regression for schooling. This is
sometimes called 'selection on observables' in the evaluation literature."
"Why does that eliminate the bias?" asks Speedy.
"Well, you think about it. Suppose that the control variables X in your regression for
schooling include all the observed variables Z that influence participation P and v is uncorrelated
with £ (so that the unobserved variables affecting program placement do not influence schooling
conditional on X). Then you have eliminated any possibility of P being correlated with E. It will now
be exogenous in your regression for schooling.
"To put it another way, Ms Analyst, the key idea of selection on observables is that there is
some observable X such that the bias vanishes conditional on X."
"Why did it make such a difference when I added the control variables to my regression of
schooling on PROSCOL participation?"
"Because your X must include variables that were amongst the poverty proxies used for
targeting, or were correlated with them, and they are variables that also influenced schooling.
"However, Ms Analyst, all this only works if the assumptions are valid. There are two
problems you should be aware of. Firstly, the above method breaks down if there are no unobserved
determinants of participation; in other words if the error term v has zero variance, and all of the
determinants of participation also affect schooling. Then there is no independent variation in
program participation to allow one to identify its impact on schooling; you can predict P perfectly
from X, and so the regression will not estimate. This problem is unlikely to arise often, given that
there are almost always unobserved determinants of program placement.
"The second problem is more common, and more worrying in your case. The error term £ in
the schooling regression probably contains variables that are not found in the LSS, but might well
influence participation in the program, i.e., they might be correlated with the error term v in the
participation equation. If that is the case then the error term £ will not have zero mean given X and P,
16
and so ordinary regression methods will still be biased when estimating your regressions for
schooling. So the key issue is the extent of the correlation between the error term in the equation for
participation and that in the equation for schooling."
Speedy learns about better methods of forming a comparison group
Next Speedy tells Chisquare about her first attempt at estimating the benefits. "How might I
form a better comparison group?"
"You want to compare schooling levels conditional on observed characteristics. Imagine that
you divide the sample into groups of families with the same or similar values of Xand you then
compare the conditional means for PROSCOL and non-PROSCOL families. If schooling in the
absence of the program is independent of participation, given X, then the comparison will give an
unbiased estimate of PROSCOL's impact. This is sometimes called 'conditional independence', and
it is the key assumption made by all comparison-group methods."
Speedy tries to summarize. "So a better way to select my comparison group, given the data I
have, is to use as a control for each participant, a non-participant with the same observed
characteristics. But that would surely be very hard Professor, since I could have a lot of those
variables. There may be nobody amongst the non-participants with exactly the same values of all the
observed characteristics for any one of the PROSCOL participants"
"Ah", says Chisquare, "some clever statisticians have figured out how you can simplify the
problem greatly. Instead of aiming to assure that the matched control for each participant has exactly
the same value of X, you can get the same result by matching on the predicted value of P, given X,
which is called the propensity score of X. You should read the papers by Rosenbaum and Rubin on
the list I prepared for you. Their Biometrika 1983 paper shows that if (in your case) schooling
without PROSCOL is independent of participation given Xthen they are also independent of
participation given the propensity score of X. Since the propensity score is just one number, it is far
17
easier to control for it than X, which could be many variables as you say. And yet propensity score
matching is sufficient to eliminate the bias provided there is conditional independence given X."
"Let me see if I understand you, Professor. I first regress P on Xto get the predicted value of
P for each possible value of X, which I then estimate for my whole sample. For each participant, I
then find the non-participant with the closest value of this predicted probability. The difference in
schooling is then the estimated gain from the program for that participant."
"That is basically right, Ms Analyst. You can then take the mean of all those differences to
estimate the impact. Or you can take the mean for different income groups, say. But you have to be
careful with how you estimate the model of participation. A linear model could give you crazy
predicted probabilities, above one, or negative. It is better to use the LOGIT command in SAPS. This
assumes that the error term v in the participation equation has a logistic distribution, and estimates
the parameters consistent with that assumption by maximum likelihood methods. You remember my
class on maximum likelihood estimation of binary response models don't you Ms Analyst?"
"Yes, I do", says Speedy, as convincingly as she can.
"Another issue you should be aware of Ms Analyst is that some of the non-participants may
have to be excluded as potential matches right from the start. Some will be ineligible according to
the eligibility rules. Others will be eligible, but have observable characteristics that make
participation unlikely. In fact there are important recent results in the literature indicating that failure
to compare participants and controls at common values of matching variables is a major source of
bias in evaluations. See the Heckman et al. (1998) paper on my reading list.
"The intuition is that you want the comparison group to be as similar as possible to the
treatment group in terms of their likelihood of participating in the program, as summarized by the
propensity score. You might find that some of the non-participant sample has a lower propensity
score than any of those in the treatment sample. This is sometimes called 'lack of common support'.
In forming your comparison group, you should eliminate those observations from the set of non-
18
participants to assure that you are only comparing gains over the same range of propensity scores.
You should certainly exclude those non-participants for whom the probability of participating is zero.
It is probably also a good idea to trim a little, say 2%, of the sample from the top and bottom of the
non-participant distribution in terrns of the propensity scores. Once you have identified participants
and non-participants over a common matching region, I recommend you take an average of (say) the
five or so nearest neighbors in terms of the absolute difference in propensity scores."
"What should I include in X?" Speedy asks.
"Well clearly you should include all the variables in your data set that are, or could proxy for,
the poverty indicators that were used by MSD in selecting PROSCOL participants. So again X
should include the variables in Z.
"However, you have touched on a weak spot of propensity score matching. With
randomization, the results do not depend on what Xyou choose. With matching, a different Xwill
yield a different estimate of impact. Nor does randomization require that you specify some model for
participation, whether a logit or something else."
"Yes, Professor, I am convinced that a random experiment is the ideal. Alas, that is clearly
not the case with PROSCOL."
Speedy prepares Note 3, summarizing the steps she needs to follow in doing propsensity
score matching.
19
Note 3: Steps in matching
The aim of matching is to find the closest comparison group from a sample of non-participants to the
sample of program participants. "Closest" is measured in terms of observable characteristics. If there
are only one or two such characteristics then matching should be easy. But typically there are many
potential characteristics. The main steps in matching based on propensity scores are as follows:
Step 1: You need a representative sample survey of eligible non-participants as well as one for the
participants. The larger the sample of eligible non-participants the better, to facilitate good matching. If
the two samples come from different surveys, then they should be highly comparable surveys (same
questionnaire, same interviewers or interviewer training, same survey period and so on).
Step 2: Pool the two samples and estimate a logit model of program participation as a function of all
the variables in the data that are likely to determine participation.
Step 3: Create the predicted values of the probability of participation from the logit regression; these
are called the "propensity scores". You will have a propensity score for every sampled participant and
non-participant.
Step 4: Some of the non-participant sample may have to be excluded at the outset because they have a
propensity score which is outside the range (typically too low) found for the treatment sample. The
range of propensity scores estimated for the treatment group should correspond closely to that for the
retained sub-sample of non-participants. You may also want to restrict potential matches in other ways,
depending on the setting. For example, you may want to only allow matches within the same
geographic area to help assure that the matches come from the same economic environment.
Step 5: For each individual in the treatment sample, you now want to find the observation in the non-
participant sample that has the closest propensity score, as measured by the absolute difference in
scores. This is called the "nearest neighbor". You can find the five (say) nearest neighbors.
Step 6: Calculate the mean value of the outcome indicator (or each of the indicators if there is more
than one) for the five nearest neighbors. The difference between that mean and the actual value for the
treated observation is the estimate of the gain due to the program for that observation.
Step 7: Calculate the mean of these individual gains to obtain the average overall gain. This can be
stratified by some variable of interest such as incomes in the non-participant sample.
This is the simplest form of propensity score matching. Complications can arise in practice. For
example, if there is over-sampling of participants then you can use choice-based sampling methods to
correct for this (Manski and Lerman, 1978); alternatively you can use the odds ratio (pl(1-p), where p is
the propensity score) for matching. Instead of relying on the nearest neighbor you can instead use all
the non-participants as potential matches but weight them differently, according to how close they are
(Heckman et al., 1998).
Troublesome, and not so troublesome, unobservables
"I now have a much better idea of how to form the comparison group, Professor Chisquare.
This should give me a much better estimate of the programs' impact."
"Ah, there is no guarantee of that. Recall my warning that all these methods I have described
to you so far will only eliminate the bias if there is conditional independence, such that the
20
unobservable determinants of schooling-not included in your set of control variables X-are
uncorrelated with program placement. There are two distinct sources of bias, that due to differences
in observables and that due to differences in unobservables; the latter is often called 'selection bias'."
Speedy's Note 4 elaborates on this difference.
Note 4: Sources of bias in naive estimates of PROSOL's impact
The bias described by Mr. Statistica is the expected difference in schooling without PROSCOL
between families selected for the program and those not chosen. This can be broken down into two
sources of bias:
* Bias due to differences in observable characteristics. This can come about in two ways. Firstly
there may not be common support. The "support" is the set of values of the control variables for
which outcomes and program participation are observed. If the support is different between the
treatment sample and the comparison group then this will bias the results. In effect, one is not
comparing like with like. Secondly, even with common support, the distribution of observable
characteristics may be different within the region of common support; in effect the comparison
group data is miss-weighted. Careful selection of the comparison group can eliminate this
source of bias.
* Bias due to differences in unobservables. The term "selection bias" is sometimes confined
solely to this component (though some authors use that term for the total bias in a non-
experimental evaluation). This source of bias arises when, for given values of X, there is a
systematic relationship between program participation and outcomes in the absence of the
program. In other words, there are unobserved variables that jointly influence schooling and
program participation conditional on the observed variables in the data.
There is nothing to guarantee that these two sources of bias will work in the same direction. So
eliminating either one of them on its own does not mean that the total bias is reduced in absolute
value. That is an empirical question. In one of the few studies to address this question, the true
impact, as measured by a well-designed experiment, was compared to various non-experimental
estimates (Heckman et al., 1998). The bias in the naMve estimate was huge, but careful matching of
the comparison goup based on observables greatly reduced the bias.
Chisquare points to his last equation. "Clearly conditional independence will hold if P is
exogenous, for then E(s, I Xi, Pi) = 0. However, endogenous program placement due to purposive
targeting based on unobservables will still leave a bias. This is sometimes called 'selection on
unobservables'."
21
Speedy interjects. "So really the conditions required for justifying the method suggested by
Ms Economiste are no less restrictive than those needed to justify a version of my first method based
on comparing PROSCOL families with non-PROSCOL families for households with similar values
of X. Both rest on believing that these unobservables are not jointly influencing schooling and
program participation, conditional on X."
"That's right, Ms Analyst. Intuitively, one might think that careful matching reduces the
bias, but that is no necessarily so. Matching eliminates part of the bias in your first naYve estimate of
PROSCOL's impact. That leaves the bias due to any troublesome unobservables. However, these two
sources of bias could be offsetting, one positive the other negative. Heckman et al. (1998) make this
point. So the matching estimate could well have more bias than the naYve estimate. One cannot know
on a priori grounds how much better off one is with even a well chosen comparison group. That is an
empirical question."
Speedy regrets that a baseline survey was not done
Speedy is starting to feel more than a little desperate. "Is there any method besides
randomization that is robust to these troublesome unobservables?" she asks the Professor.
"There is something you can do if you have 'baseline data' for both the participants and non-
participants, collected before PROSCOL started. The idea is that you collect data on outcomes and
their determinants both before and after the program is introduced, and you collect that data for an
untreated comparison group as well as the treatment group. Then you can just subtract the difference
between the schooling of participants and the comparison group before the program is introduced
from the difference after the program. This is called the 'double difference' estimate, or just 'double
diff' by people who like to abbreviate things. This will deal with the troublesome unobserved
variables provided they do not vary over time."
22
Chisquare turns to his whiteboard again pointing to one of his earlier equations. "To see how
this works, let's add time subscripts, so schooling after the program is introduced is:
Sia = a + bPi + cXia + Eia
Before the program, in the baseline survey, school attainment is instead:
Sib = a + CXib + Eib
(Of course P=O before the program is introduced.) The error terms include an additive time invariant
effect, so we can write them as:
ci, = 1i + 4it (for t=a,b)
where mi is the time invariant effect, which is allowed to be correlated with Pi, and ,it is an
innovation error, which is not correlated with Pi (or Xi).
"The essential idea here is to use the baseline data to reveal those troublesome
unobservables. Notice that since the baseline survey is for the same households as you have now, the
i'th household in the equation for Si, is the same household as the i'th in the equation for Sib. You can
then take the difference between the 'after' equation and the 'before' equation; you get:
Sia - Sib = bPi + C(Xia - Xib) + -li. - 4ib
So now you can regress the change in schooling on program participation and the changes in X. OLS
will give you an unbiased estimate of the program's impact. The troublesome unobservables - the
ones correlated with program participation - have been conveniently swept away."
Speedy reflects: "If the program placement was based only on variables, both observed and
unobserved, that were known at the time of the baseline survey then it would be reasonable to
assume that the il's do not change between the two surveys."
Professor Chisquare nods. "Yes, as long as the troublesome unobservables are time invariant,
the changes in schooling over time for the comparison group will reveal what would have happened
to the treatment group without the program."
23
Speedy thinks to herself that this means one needs to know the program well, and be able to
time the evaluation surveys so as to coordinate with the program. Otherwise there are bound to be
unobserved changes after the baseline survey that influence who gets the program. This would create
rl's that changed between the two surveys.
Something about Chisquare's last equation is worrying her. "As I understand it Professor,
this last equation means that the child and household characteristics in Xare irrelevant to the change
in schooling if those characteristics do not change over time. But the gain in schooling may depend
on parents' education (and not just any change in their education) and possibly on where the
household lives, as this will determine the access to schools."
"Yes, Ms Analyst, there can be situations in which the changes over time in the outcome
indicator are influenced by the initial conditions. Then one will also want to control for differences in
initial conditions. You can do this simply by adding X, and Xb in the regression separately, so that
the regression takes the form:
Si. - Sib = bPi + CaX.a + CbXib + pLia .- jib
So even if some (or all) variables inXdo not vary over time one can still allow Xto affect the
changes over time in schooling.
"The propensity-score matching method that I told you about can help assure that the
comparison group is similar to the treatment group before you do the double difference. In an
interesting study of an American employment program, it was found that failure to assure that
comparisons were made in a region of common support was a major source of bias in the double
difference estimate when compared to a randomized control group. Within the region of common
support, however, the bias conditional on Xdid not vary much over time. So taking the double
difference makes sense, after the matching is done. See the paper by Heckman et al., in
Econometrica 1998 on my reading list."
24
Speedy has had some experience doing surveys, and is worried about this idea of following
up households. "When doing the follow-up survey, it must not be easy to find all those households
who were originally included in the baseline survey. Some people in the baseline survey may not
want to be interviewed again, or they have moved to an unknown location. Is that a problem?"
"If the drop outs are purely random then the follow up survey will still be representative of
the same population in the baseline survey. However, if there is some systematic tendency for
people with certain characteristics to drop out of the sample then there will be a problem. This is
called 'attrition bias'. For example, PROSCOL might help some poor families move into better
housing. And even when participant selection was solely based on information available at or around
the baseline date (the time-invariant effect Tij), selected participants may well drop out voluntarily on
the basis of changes after that date. Such attrition from the treatment group will clearly bias a double-
difference estimate of the program's impact."
Later Speedy writes up Note 5, on the steps to form a double-difference estimate.
Note 5: Doing a double difference
The "double difference" method entails comparing a treatment group with a comparison group (as
might ideally be determined by the matching method in Note 3) both before and after the intervention.
The main steps are as follows:
Step 1: You need a "baseline" survey before the intervention is in place, and the survey must cover
both non-participants and participants. If you do not know who will participate, you have to make an
informed guess. Talk to the program administrators.
Step 2: You then need one or more follow-up surveys, after the program is put in place. These should
be highly comparable to the baseline surveys (in terms of the questionnaire, the interviewing, etc).
Ideally the follow-up surveys should be of the same sampled observations as the baseline survey. If
this is not possible then they should be the same geographic clusters, or strata in terms of some other
variable.
Step 3: Calculate the mean difference between the "after" and "before" values of the outcome
indicator for each of the treatment and comparison groups.
Step 4: Calculate the difference between these two mean differences. That is your estimate of the
impact of the program.
This is the simplest version of double-difference. You may also want to control for differences in
exogenous initial conditions, or changes in exogenous variables, possibly allowing for interaction
effects with the program (so that the gain from the intervention is some function of observable
variables). A suitable regression model can allow these variations.
25
Chisquare reminds Speedy about instrumental variables
"Double difference is neat, Professor Chisquare. But I don't have a baseline survey of the
same households. I don't think anyone thought PROSCOL would have to be evaluated when they
started the program. Is there anything else I can do to get an estimate that is robust to the troublesome
unobservables?"
"What you then need is an instrumental variable (IV)" he tells Speedy. "You must surely
recall from my classes that this is the classic solution for the problem of an endogenous regressor."
"Can you just remind me, Professor Chisquare?"
"An instrumental variable is really just some observable source of exogeneous variation in
program participation. In other words, it is correlated with P but is not already in the regression for
schooling, and is not correlated with the error term in the schooling equation, s. So you must have to
have at least one variable in Z that is not in X, and is not correlated with s. Then the Instrumental
Variables Estimate of the program's impact is obtained by replacing P by its predicted value
conditional on Z. Since this predicted value depends solely on Z (which is exogenous) and Z is
uncorrelated with e, it is now reasonable to apply ordinary least squares to this new regression."
"I see," says Speedy. "Since the predicted values depend only on the exogenous variation
due to the instrumental variable, and the other exogenous variables, the unobservables are no longer
troublesome, since they will be uncorrelated with the error term in the schooling regression."
"You've got it Ms Analyst. That also suggests another, more efficient, way you can deal
with the problem. Remember that the source of bias in your estimate of the program's impact was the
correlation between the error term in the schooling equation and that in the participation equation.
This is what creates the correlation between participation and the error term in the schooling
equation. So a natural way to get rid of the problem when you have an instrumental variable is to add
the residuals from the first stage equation for participation to the equation for schooling. You still
26
leave actual participation in the schooling regression. But since you have now added to the schooling
regression the estimated value of the error term from the participation equation, you can treat
participation as exogenous and run OLS. Of course, this only works if you have a valid instrument.
If you don't, the regression will not estimate, since the participation residual will be perfectly
predictable from actual participation and X, in a linear model.
"An IV can also help if you think there is appreciable measurement error in your program
participation data. This is another possible source of bias. Measurement error means that you think
that program participation varies more than it actually does. This overestimation in the variance of P
leads naturally to an underestimation of its coefficient b."
"Yes, you called that 'attenuation bias' in your class, as I recall, because this bias attenuates
the estimated regression coefficient."
"That's right. So you can see how useful an instrumental variable can be. However, you do
have to be a little careful in practice. When you just replace the actual participation with its predicted
value and run OLS you will not give the correct standard errors since the computer will not know
that you had to use previously estimated parameters to obtain the predicted values. A correction to
the OLS standard errors is required, though there are statistical packages that allow you to do this
easily, at least for linear models.
"However, if you had a dependent variable that could only take two possible values, at school
or not at school say, then you should use nonlinear binary response model, such as Logit or Probit.
The principle of testing for exogeneity of program participation is similar in this case. There is a
paper by Rivers and Vuong (1988) that discusses the problem for such models; Blundell and Smith
(1993) provide a useful overview of various nonlinear models in which there is an endogenous
regressor. I have written a program, in the programming language called Gauss, that can do a probit
with an endogenous regressor and I can give you a copy."
27
"Thanks. I guess I will cross that bridge when I get to it. But what should I use as an
instrument?" asks Speedy.
"Ah, that you will have to figure out yourself Ms Analyst".
Speedy later summarizes what she has leant about alternative methods, as in Note 1.
Speedy returns to her computer
Speedy is starting to wonder whether this will ever end. "I'm learning a lot, but what am I
going to tell my boss?"
Speedy tries to think of an instrumental variable. But every possibility she can think of could
just as well be put in with the variables in X. She now remembers Professor Chisquare's class; her
problem is finding a valid "exclusion restriction", which justifies putting some variable in the
equation for participation, but not in the equation for schooling.
Speedy decides to try the "propensity score matching method" suggested by Chisquare. Her
logit model of participation looks quite sensible, and suggests that PROSCOL is well targeted.
(Virtually all of the variables that she would expect to be associated with poverty have positive, and
significant, coefficients.) This is interesting in its own right. She then does the propensity score
matching just as Professor Chisquare had advised her. On comparing the mean school enrollment
rates, Speedy finds that kids of the matched comparison group had an enrollment rate of 60%, as
compared to the figure of 80% for PROSCOL families.
She now thinks back on those comments that Ms Tangential Economiste had made about
foregone income. She finds that the Bureau of Statistics did a special survey of child labor that asked
about earnings. (There is an official ban on kids working before they are 16 years of age in Labas,
but the government has a hard time enforcing it; nonetheless, child wages are a sensitive issue.)
From this she can figure out what earnings a child would have had if she had not gone to school.
28
So Speedy can now subtract from PROSCOL's cash payment to participants the amount of
foregone income, and so work out the net income transfer. Subtracting this net transfer from total
income, she can now work out where the PROSCOL participants come from in the distribution of
pre-intervention income. They are not quite as poor as she had first thought (ignoring foregone
income) but they are still poor; for example, two-thirds of them are below Labas' official poverty
line.
Having calculated the net income gain to all participants, Speedy can now calculate the
poverty rate with and without PROSCOL. The "post-intervention" poverty rate (with the program) is
just the proportion of the population living in households with an income per person below the
poverty line, where "income" is the observed income (including the gross transfer receipts from
PROSCOL). This she calculates directly from the LSS. By subtracting the net income gain (cash
transfer from PROSCOL minus foregone income from kids' work) attributed to PROSCOL from all
the observed incomes she gets a new distribution of pre-intervention incomes. The poverty rate
without the program is then the proportion of people living in poor households, based on this new
distribution. Speedy finds that the observed poverty rate in Northwest Labas of 32% would have
been 36% if PROSCOL had not existed. The program allows 4% of the population to escape poverty
now. The schooling gains mean that there will also be both pecuniary and non-pecuniary gains to the
poor in the future.
Speedy recalls a class Chisquare gave on poverty measurement, in which he pointed out that
the proportion of people below the poverty line is a rather crude measure, since it tells you nothing
about changes below the line. Note 6 reproduces (after some tidying up) Speedy's class notes.
When Speedy calculates both the poverty gap index and the squared poverty gap index the results
suggest that these have also fallen as a result of PROSCOL.
29
Note 6: Poverty measures
The simplest and most common poverty measure is the headcount index. In Labas this is the proportion
of the population living in households with income per person below the poverty line. (In other countries,
it is a consumption-based measure, which has some advantages; for discussion and references see
Ravallion, 1994.)
The headcount index does not tell us anything about income distribution below the poverty line: a poor
person may be worse off but the headcount index will not change; not will it reflect gains amongst the
poor, unless they cross the poverty line.
A widely used alternative to the headcount index is the poverty gap index (PG). The poverty gap for each
household is the difference between the poverty line and the household's income; for those above the
poverty line the gap is zero. When the poverty gap is normalized by the poverty line, and one calculates
its mean over all households (whether poor or not), one obtains the poverty gap index.
The poverty gap index will tell you how much impact the program has had on the depth of poverty, but it
will not reflect any changes in distribution amongst the poor due to the program. For example, if the
program entails a small gain to a poor person who is above the mean income of the poor, at the expense
of an equal loss to someone below that mean, then PG will not change.
There are various "distribution-sensitive" measures that will reflect such changes in distribution amongst
the poor. One such measure is the squared poverty gap (Foster et al., 1984). This is calculated the same
way as PG except that the individual poverty gaps as a proportion of the poverty line are squared before
taking the mean (again over both poor and non-poor.) Another example of a distribution-sensitive
poverty measure is the Watts index. This is the mean of the log of the ratio of the poverty line to income,
where that ratio is set to one for the non-poor. Atkinson (1987) describes other examples in the literature.
Speedy also recognizes that there is some uncertainty about the LBS poverty line. So she
repeats this calculation over a wide range of poverty lines. She finds that at a poverty line for which
50% of the population are poor based on the observed post-intervention incomes, the proportion
would have been 52% without PROSCOL. At a poverty line which 15% fail to reach with the
program, the proportion would have been 19% without it. By repeating these calculations over the
whole range of incomes, Speedy realizes that she has traced out the entire "poverty incidence curves"
with and without the program, which are just the same thing statisticians call the "cumulative
distribution function".
Note 7 summarizes the steps Speedy takes in making comparisons of poverty with and
without PROSCOL.
30
Note 7: Comparing poverty with and without the program
Using the methods described in the main text and earlier Notes one obtains an estimate of the gain to each
household. In the simplest evaluations this is just one number. But it is better to allow it to vary with
household characteristics. You can then summarize this informnation in the form of poverty incidence curves
(PICs), with and without the program.
Step 1: You should already have the post-intervention income (or other welfare indicator) for each
household in the whole sample (comprising both participants and non-participants); this is data. You also
know how many people are in each household. And, of course, you know the total number of people in the
sample (N; or this might be the estimated population size, if inverse sampling rates have been used to
"expend up" each sample observation).
Step 2: You can plot this information in the form of a PIC. This gives (on the vertical axis) the percentage of
the population living in households with an income less than or equal to that value on the horizontal axis. To
make this graph, you can start with the poorest household, mark its income on the horizontal axis, and then
count up on the vertical axis by 100 times the number of people in that household divided by N. The next
point is the proportion living in the two poorest households, and so on. This gives the post-intervention PIC.
Step 3: Now calculate the distribution of income pre-intervention. To get this you subtract the estimated
gain for each household from its post-intervention income. You then have a list of post-intervention
incomes, one for each sampled household. Then repeat Step 2. You will then have the pre-intervention PIC.
If we think of any given income level on the horizontal axis as a "poverty line" then the difference between
the two PICs at that point gives the impact on the headcount index for that poverty line (Note 5).
Alternatively, looking horizontally gives you the income gain at that percentile. If none of the gains are
negative then the post-intervention PIC must lie below the pre-intervention on. Poverty will have fallen no
matter what poverty line is used. Indeed, this also holds for a very broad class of poverty measures; see
Atkinson (1987). If some gains are negative, then the PICs will intersect. The poverty comparison is then
ambiguous; the answer will depend on which poverty lines and which poverty measures one uses. (For
further discussion see Ravallion, 1994.) You might then use a priori restrictions on the range of admissible
poverty lines. For example, you may be confident that the poverty line does not exceed some maximum
value, and if the intersection occurs above that value then the poverty comparison is unambiguous. If the
intersection point (and there may be more than one) is below the maximum admissible poverty line then a
robust poverty comparison is only possible for a restricted set of poverty measures. To check how restricted
the set needs to be, you can calculate the poverty depth curves (PDCs). These are obtained by simply
forming the cumulative sum up to each point on the PIC. (So the second point on the PDC is the first point
on the PIC plus the second point, and so on.)
If the PDCs do not intersect then the program's impact on poverty is unambiguous as long as one restricts
attention to the poverty gap index or any of the distribution sensitive poverty measures described in Note 5.
If the PDCs intersect then you can calculate the "poverty severity curves" with and without the program, by
forming the cumulative sums under the PDCs. If these do not intersect over the range of admissible poverty
lines then the impact on any of the distribution-sensitive poverty measures in Note 5 is unambiguous.
Speedy makes an appointment with Mr. Undersecretary, to present her assessment of
PROSCOL.
31
A chance encounter with Ms Sensible Sociologist
The day before she is due to present her results to her boss, Speedy accidentally bumps into
her old friend, Sensible Sociologist, who now works for one of Labas' largest NGOs, SCEF (the
Social Capital for Empowerment Foundation). Speedy tells Sense all the details about what she has
been doing on PROSCOL.
Sensible Sociologist's eyes start to roll when Speedy talks about "unbiased estimates" and
"propensity scores". "I don't know much about that stuff Speedy. But I do know a few things about
PROSCOL. I have visited some of the schools in Northwest Labas where there are a lot of
PROSCOL kids, and I meet PROSCOL families all the time in my work for SCEF. I can tell you
they are not all poor, but most are. PROSCOL helps.
"However, this story about 'foregone income' that Tangential came up with, I am not so sure about
that. Economists have strange ideas sometimes. I have seen plenty of kids from poor families who
work as well as go to school. And some of the younger ones not at school don't seem to be working
either. Maybe Tangential is right in theory, but I don't know how important it is in reality."
"You may be right, Sense. What I need to do is check whether there is any difference in the
amount of child labor done by PROSCOL kids versus a matched comparison group," says Speedy.
"The trouble is that the LSS did not ask about child labor. That is in another LBS survey. I think
what I will do is present the results with and without the deduction for foregone income."
"That might be wise" says Sensible Sociologist. "Another thing I have noticed Speedy is that,
for a poor family to get on PROSCOL it matters a lot which school-board area the family lives in.
All school areas (SBA) get a PROSCOL allocation from the center, even SBAs that have very few
poor families. If you are poor but living in a well-to-do SBA you are more likely to get help from
PROSCOL than if you live in a poor SBA. I guess they like to let all areas participate for political
32
reasons. As a result, it is relative poverty-relative to others in the area you live-that matters much
more than your absolute level of living."
"No I did not know that", replies Speedy, a little embarrassed that she had not thought of
talking to Sensible Sociologist earlier, since this could be important.
"That gives me an idea, Sense. I know which school-board area each household belongs to in
the LBS survey, and I know how much the center has allocated to each SBA. Given what you have
told me, that allocation would influence participation in PROSCOL, but one would not expect it to
matter to school attendance, which would depend more on one's absolute level of living, family
circumstances, and I guess characteristics of the school. So the PROSCOL budget allocation across
SBA's can be used as instrumental variables to remove the bias in my estimates of program impact."
Sensible Sociologist's eyes roll again, as Speedy says farewell and races back to her office.
She first looks into the original file she was given, to see what rules are used by the center in
allocating PROSCOL funds across SBAs. A memo from the Ministry indicates that allocations are
based on the number of school age children, with an "adjustment factor" for how poor the SBA is
thought to be. However, the rule is somewhat vague.
Speedy re-runs her regression for schooling. But now she replaces the actual PROSCOL
participation by its predicted value (the propensity score) from the regression for participation, which
now includes the budget allocation to the SBS. She realizes that it helps to already have as many
school characteristics as possible in the regression for attendance. Although school characteristics do
not appear to matter officially to how PROSCOL resources are allocated, Speedy realizes that any
omitted school characteristics that jointly influence PROSCOL allocations by SBA and individual
schooling outcomes will leave a bias in her IV estimates. She realizes that she will never rule out the
possibility of bias, but with plenty of geographic control variables, this method should at least offer a
credible comparator to her matching estimate.
33
Soon she has the results. Consistent with Sense's observations, the budget allocation to the
SBA has a significant positive coefficient in the logit regression for PROSCOL participation. Now
(predicted) PROSCOL participation is significant in a regression for school enrolment, in which she
includes all the same variables from the logit regression, except the SBA budget allocation. The
coefficient implies that the enrollment rate is 15 percentage points higher for PROSCOL participants
than would have otherwise been the case. She also runs regressions for years of schooling, for boys
and girls separately. For either boys or girls of 18 years, her results indicate that they would have
dropped out of school almost two years earlier if it had not been for PROSCOL.
Speedy wonders what Professor Chisquare will think of this. She is sure he will find
something questionable about her methods. "I wonder if I am using the right standard errors? And
should I be using linear models?" Speedy decides she will order that new program FEM (Fancy
Econometric Methods) that she has heard about. But that will have to wait. For now, Speedy is
happy that her results are not very different from those she got using the propensity-score matching
method. And she is re-assured somewhat by Sense's comments based on her observations in the
field. "They can't all be wrong".
Speedy reports back to her boss
Speedy writes up her results and gives the report to Mr. Undersecretary. He seems quite
satisfied. "So PROSCOL is doing quite well." Mr. Undersecretary arranges a meeting with the
Minister, and he asks Speedy to attend. The Minister is interested in Speedy's results, and asks some
questions about how she figured out the benefits from PROSCOL. He seems to appreciate Speedy's
efforts to assure that the comparison group is similar to PROSCOL families.
"I think we should expand PROSCOL to include the rest of Labas," the Minister concludes.
"We will not be able to do it all in one go, but over about two years I think we could cover the whole
country. But I want you to keep monitoring the program Speedy."
34
"I would like to do that, Minister. However, I have learnt a few things about these
evaluations. I would recommend that you randomly exclude some eligible PROSCOL families in the
rest of Labas. We could then do a follow up survey of both the actual participants and those
randomly excluded from participating. That would give us a more precise estimate of the benefits".
The Minister gets a dark look in his eyes, and Mr. Undersecretary starts shifting in his seat
uncomfortably. The Minister then bursts out laughing. "You must be joking, Ms Analyst! I can just
see the headlines in the Labas Herald: "Government Randomly Denies PROSCOL to Families in
Desperate Need." Do you not want me to get re-elected?"
"I see your point, Minister. But since you do not have enough money to cover the whole
country in one go, you are going to have to make choices about who gets it first. Why not make that
choice randomly, amongst eligible participants? What could be fairer?"
The Minister thinks it over. "What about if we picked the schools or the school board areas
randomly, in the first wave?"
Speedy thinks. "Yes, that would surely make the choice of school or school board area a
good instrumental variable for individual program placement", she says with evident enthusiasm.
"Instrumental what?", says the Minister, while Mr. Undersecretary shifts in his seat again.
"Never mind. If that works for you, then I will try to see if I can do it that way. The Ministry of
Social Development will have to agree of course."
"If that does not work, Mr. Minister, could we do something else instead, namely a baseline
survey of areas in which there are likely to be high concentrations of PROSCOL participants before
the program starts in the South? I would like to do this at the same time as the next round of the
national survey I used for evaluating PROSCOL in north Labas. There are also a few questions I
would like to add to the survey, such as whether the children do any paid work."
"Yes, that sounds like a reasonable request, Speedy. I will also talk to the Secretary of
Statistics".
35
Epilogue
It is three years later. Speedy Analyst is head of the new Social and Economic Evaluation
Unit, which reports directly to the Minister of Finance. The Unit is currently evaluating all of Labas'
social programs on a regular basis. Speedy has a permanent staff of three assistants. She regularly
hires both Professor Chisquare and Sensible Sociologist as consultants. They have a hard time talking
to each other. ("Boy, that Chisquare is just not normal" Sense confided to Speedy one day.) But
Speedy finds it useful to have both of them around. The qualitative field trips, and interviews with
stake-holders, that Sense favors help a lot in forming hypotheses to be tested and assessing the
plausibility of key assumptions made in the quantitative analysis that Chisquare favors. Speedy
reflects that the real problem with MSD's "Participants' Perspectives" report on PROSCOL was not
what it did, but what it did not do; casual interviews can help in understanding how a program works
on the ground, but on their own they cannot deliver a credible assessment of impact.
However, Speedy has also leant that rigorous impact evaluation is much more difficult than
she first thought, and one can sometimes obtain a worryingly wide range of estimates, depending on
the specifics of the methodology used. Chisquare's advice remains valuable in suggesting alternative
methods in the frequent situations of less than ideal data, and pointing out the pitfalls. Speedy has
also learnt to be eclectic about data.
The Finance Minister did eventually convince the Minister of Social Development to
randomize the first tranche allocation of PROSCOL II across school board areas in the rest of Labas,
and this helped Speedy identify the program's impact. Her analysis of the new question on child
labor added to the LBS survey revealed that there was some foregone income from PROSCOL,
though not quite as much as she had first thought.
Tangential Economiste made a further comment on Speedy's first report on PROSCOL, to
the effect that Speedy could also measure the future income gains from PROSCOL, using recent
36
work by labor economists on the returns to schooling in Labas. When Speedy factored this into her
calculations, PROSCOL was found to have quite a reasonable economic rate of return, on top of the
fact that the benefits were reaching the poor.
One big difference from her first PROSCOL evaluation is that Speedy now spends a lot more
time understanding how each program works before doing any number crunching. And she spreads
the evaluation over a much longer period, often including baseline and multiple follow-up surveys of
the same households.
However, everything has not gone smoothly. At first she had a lot of trouble getting the
relevant line ministries to cooperate with her. It is often hard to get them to define the objectives of
each program she is evaluating; Speedy sometimes thinks that getting the relevant line ministry to
define the objectives of its public spending is an important contribution in its own right. But
eventually the line Ministries realize that they can learn a lot from these evaluations, and that they
were being taken seriously by the Finance Minister.
Internal politics within the government is often a problem. Thankfully the data side is now
working well. The Minister had the good idea of making the Secretary of Statistics an Advisor to the
unit, and Mr. Statistica is his representative. Speedy often commissions new surveys from LSB and
advises them on questionnaire design and sampling.
Speedy has also started giving advice to other countries and international agencies (including
the World Bank) embarking on impact evaluations of social programs. And she has found that
swapping notes with other program analysts can be valuable. For example, I learnt about Speedy's
interesting experience with PROSCOL on a recent mission to Labas, and I also told here about recent
work evaluating a World Bank supported anti-poverty program in Argentina (Jalan and Ravallion,
1999; Note 8 summarizes the methods and results of that study). Speedy reckons there are policy
mysteries galore in Labas and elsewhere - mysteries that the tools she has learnt to use might well
throw light on.
37
Note 8: An example for another anti-poverty program
With support from the World Bank, Argentina introduced the Trabajar Program in 1997, in response
to a sharp increase in unemployment, and evidence that this was especially hurting the poor. The
program aimed to provide useful work on community projects in poor areas work for unemployed
workers from poor families. Jalan and Ravallion (1999) assessed the income gains to the families of
participating workers and examined how well targeted the gains were. A survey was done of a
random sample of participating families, at the same time, and using the same survey instrument and
interviewers, as a pre-planned large national sample survey. A logit model of program participation
was first estimated on the pooled sample and the propensity scores were then calculated. The
matching methods described in Note 3 were then used to draw a control group from the larger cross-
sectional survey. The participants sample had a mean propensity score of 0.40, while it was 0.075 for
the national sample. So the national sample is clearly unrepresentative of Trabajar participants. After
matching, however, the comparison group drawn from the national sample also had a score of 0.40.
The results indicated that income gains were about half of the gross wage on the program (the
difference being due to lost income from work that had to be given up to join the program). About
80% of the families of participating workers came from the poorest 20% of all families in Argentina,
in terms of (pre-intervention) income per person. A test for selection bias in the resulting matching
estimator was also done using instrumental variables. The bias in the matching estimates was
negligible.
38
References (including Professor Chisquare's Reading List for Speedy)
Atkinson, Anthony, 1987, "On the Measurement of Poverty", Econometrica, 55: 749-64.
Blundell, Richard W. and R.J. Smith, 1993, "Simultaneous Microeconometric Models with
Censoring or Qualitative Dependent Variables", in G.S. Maddala, C.R. Rao and H.D. Vinod
(eds) Handbook of Statistics Volume 11 Amsterdam: North Holland.
Foster, James, J. Greer, and Erik Thorbecke, 1984, "A Class of Decomposable Poverty Measures",
Econometrica, 52: 761-765.
Grossman, Jean Baldwin, 1994, "Evaluating Social Policies: Principles and U.S. Experience", World
Bank Research Observer, 9(2): 159-80.
Heckman, James, 1997, "Instrumental Variables. A Study of Implicit Behavioral Assumptions Used
in Making Program Evaluations", Journal ofHuman Resources, 32(3): 441-461.
Heckman, James and Richard Robb, 1985, "Alternative Methods of Evaluating the Impact of
Interventions: An Overview", Journal of Econometrics, 30: 239-67.
Heckman, J., H. Ichimura, J. Smith, and P. Todd, 1998, "Characterizing Selection Bias using
Experimental Data", Econometrica, 66: 1017-1099.
Jalan, Jyotsna and Martin Ravallion, 1999, "Income Gains from Workfare and their Distribution",
Policy Research Working Paper, World Bank, Washington DC.
Meyer, Bruce D., 1995, "Natural and Quasi-Experiments in Economics", Journal of Business and
Economic Statistics, April.
Manski, Charles and Irwin Garfinkel (eds), 1992, Evaluating Welfare and Training Programs,
Cambridge, Mass: Harvard University Press.
Manski, Charles and Steven Lerman, 1977, "The Estimation of Choice Probabilities from
Choice-Based Samples", Econometrica, 45: 1977-88.
39
Moffitt, Robert, 1991, "Program Evaluation with Nonexperimental Data", Evaluation Review, 15(3):
291-3 14.
Ravallion, Martin, 1994, Poverty Comparisons, Fundamentals in Pure and Applied Economics
Volume 56, Harwood Academic Publishers.
Rivers, Douglas and Quang H. Vuong, 1988, "Limited Information Estimators and Exogeneity
Tests for Simultaneous Probit Models", Journal of Econometrics, 39: 347-366.
Rosenbaum, P. and D. Rubin, 1983, "The Central Role of the Propensity Score in Observational
Studies for Causal Effects", Biometrika, 70: 41-55.
Rosenbaum, P. and D. Rubin, 1985, "Constructing a Control Group using Multivariate Matched
Sampling Methods that Incorporate the Propensity Score," American Statistician, 39: 35-39.
40
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