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Quantifying the Life-Cycle Benefits of an Influential Early Childhood Program

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Abstract

This paper quantifies and aggregates the multiple lifetime benefits of an influential high-quality early childhood program with outcomes measured through midlife. Guided by economic theory, we supplement experimental data with non-experimental data to forecast the life-cycle benefits and costs of the program. Our point estimate of the internal rate of return is 13.7% with an associated benefit/cost ratio of 7.3. We account for model estimation and forecasting error and present estimates from extensive sensitivity analyses. This paper is a template for synthesizing experimental and non-experimental data using economic theory to estimate the long-run life-cycle benefits of social programs.
Quantifying the Life-cycle
Benefits of an Influential Early Childhood Program
Jorge Luis Garc´ıa
John E. Walker Department of Economics
Clemson University
Social Science Research Institute
Duke University
James J. Heckman
American Bar Foundation
Center for the Economics
of Human Development
The University of Chicago
Duncan Ermini Leaf
Leonard D. Schaeffer Center
for Health Policy and Economics
University of Southern California
Mar´ıa Jos´e Prados
Dornsife Center for
Economic and Social Research
University of Southern California
First Draft: January 5, 2016
This Draft: February 5, 2019
This research was supported in part by grants from the Robert Wood Johnson Foundation’s Policies for Action
program, NICHD R37HD065072, the American Bar Foundation, the Buffett Early Childhood Fund, the Pritzker
Children’s Initiative, NICHD R01HD054702, NIA R01AG042390, and by the National Institute On Aging of the
National Institutes of Health under Award Number P30AG024968. The views expressed in this paper are solely
those of the authors and do not necessarily represent those of the funders or the official views of the National
Institutes of Health. The authors wish to thank Frances Campbell, Craig and Sharon Ramey, Margaret Burchinal,
Carrie Bynum, and the staff of the Frank Porter Graham Child Development Institute at the University of North
Carolina Chapel Hill for the use of data and source materials from the Carolina Abecedarian Project and the
Carolina Approach to Responsive Education. Years of partnership and collaboration have made this work possible.
Andr´es Hojman, Yu Kyung Koh, Sylvi Kuperman, Stefano Mosso, Rodrigo Pinto, Joshua Shea, Jake Torcasso,
and Anna Ziff contributed to analysis related to this paper. We thank Bryan Tysinger of the Leonard D. Schaeffer
Center for Health Policy and Economics at the University of Southern California for help adapting the Future Adult
Model to make the health projections used in this paper. For very helpful comments on various versions of the
paper, we thank the editor, Harald Uhlig, and four anonymous referees, St´ephane Bonhomme, Neal Cholli, Fl´avio
Cunha, Steven Durlauf, David Figlio, Dana Goldman, Ganesh Karapakula, Magne Mogstad, Sidharth Moktan,
Tanya Rajan, Azeem Shaikh, Jeffrey Smith, Chris Taber, Matthew Tauzer, Evan Taylor, Ed Vytlacil, Jim Walker,
Chris Walters, and Matt Wiswall. We benefited from helpful comments received at the Leonard D. Schaeffer Center
for Health Policy and Economics in December, 2016, and at the University of Wisconsin, February, 2017. We thank
Peg Burchinal, Carrie Bynum, Frances Campbell, and Elizabeth Gunn for information on the implementation of
the Carolina Abecedarian Project and the Carolina Approach to Responsive Education and assistance in data
acquisition. For information on childcare in North Carolina, we thank Richard Clifford and Sue Russell. The set
of codes to replicate the computations in this paper are posted in a repository. Interested parties can request
to download all the files. The address of the repository is https://github.com/jorgelgarcia/abccare-cba.
To replicate the results in this paper, contact the first author, who will put you in contact with the appropriate
individuals to obtain access to restricted data. The Appendix for this paper is posted on http://cehd.uchicago.
edu/ABC_CARE.
Abstract
This paper quantifies and aggregates the multiple lifetime benefits of an influential high-
quality early childhood program with outcomes measured through midlife. Guided
by economic theory, we supplement experimental data with non-experimental data
to forecast the life-cycle benefits and costs of the program. Our point estimate of
the internal rate of return is 13.7% with an associated benefit/cost ratio of 7.3. We
account for model estimation and forecasting error and present estimates from extensive
sensitivity analyses. This paper is a template for synthesizing experimental and non-
experimental data using economic theory to estimate the long-run life-cycle benefits of
social programs.
Keywords: Early childhood education, life-cycle benefits, long-term forecasts, program
evaluation, rates of return, cost-benefit analysis
JEL codes: J13, I28, C93
Jorge Luis Garc´ıa James J. Heckman
John E. Walker Center for the Economics
Department of Economics of Human Development
Clemson University University of Chicago
228 Sirrine Hall 1126 East 59th Street
Clemson, SC 29630 Chicago, IL 60637
Phone: 773-449-0744 Phone: 773-702-0634
Email: jorge.ggmenendez@gmail.com Email: jjh@uchicago.edu
Duncan Ermini Leaf Mar´ıa Jos´e Prados
Leonard D. Schaeffer Center for Dornsife Center for
Health Policy & Economics Economic and Social Research
University of Southern California University of Southern California
635 Downey Way 635 Downey Way
Los Angeles, CA 90089 Los Angeles, CA 90089
Phone: 213-821-6474 Phone: 213-821-7969
Email: dleaf@healthpolicy.usc.edu Email: prados@usc.edu
1 Introduction
A large body of evidence documents that high-quality early childhood programs boost the
skills of disadvantaged children.1Much of this research reports treatment effects of programs
on cognitive test scores, school readiness, and measures of early-life social behavior. A few
studies analyze longer-term benefits in terms of completed education, adult health, crime
and labor income.2Rigorous evidence on their long-term social efficiency is scarce.3
This paper investigates the social benefits and costs of an influential pair of closely re-
lated early childhood programs conducted in North Carolina that targeted disadvantaged
children. The Carolina Abecedarian Project (ABC) and the Carolina Approach to Respon-
sive Education (CARE)—henceforth ABC/CARE—were evaluated by randomized control
trials. Both programs were launched in the 1970s. Participants were followed through their
mid 30s. The programs started early in life (at 8 weeks of life) and engaged participants
until age 5. They generated numerous positive treatment effects.4Parents of participants
(primarily mothers) received free childcare that facilitated parental employment and adult
education. We find that the program has a 13.7% (s.e. 3%) per-annum tax-adjusted internal
rate of return and a 7.3 (s.e. 1.84) tax-adjusted benefit/cost ratio.
The program is a prototype for many programs planned or in place today.5About 19%
1See Cunha et al. (2006), Almond and Currie (2011), Duncan and Magnuson (2013), and Elango et al.
(2016) for surveys.
2Examples include: Heckman et al. (2010a), Havnes and Mogstad (2011), and Campbell et al. (2014).
3Belfield et al. (2006) and Heckman et al. (2010b) present a life cycle cost-benefit analysis of the Perry
Preschool Program. Our approach is more comprehensive in terms of the outcomes analyzed, in terms of
providing a general methodology that can be replicated to assess the social efficiency of other programs, and
in the procedure used to obtain standard errors of estimates of the parameters summarizing social efficiency.
4A companion paper, Garc´ıa et al. (2018), reports these treatment effects. Participants in ABC/CARE
benefit in terms of both cognitive and socio-emotional skills, education, employment and labor income, and
risky behavior and health. The parents of participants benefit in terms of labor income and education.
5Programs inspired by ABC/CARE have been (and are currently being) launched around the world.
Sparling (2010) and Ramey et al. (2014) list numerous programs based on the ABC/CARE approach. The
programs are: Infant Health and Development Program (IHDP) in eight different cities in the U.S. (Spiker
et al.,1997); Early Head Start and Head Start. (Schneider and McDonald,2007); John’s Hopkins Cerebral
Palsy Study in the U.S. (Sparling,2010); Classroom Literacy Interventions and Outcomes (CLIO) study.
(Sparling,2010); Massachusetts Family Child Care Study (Collins et al.,2010); Healthy Child Manitoba
Evaluation (Healthy Child Manitoba,2015); Abecedarian Approach within an Innovative Implementation
Framework (Jensen and Nielsen,2016); and Building a Bridge into Preschool in Remote Northern Territory
1
of all African-American children would be eligible for ABC/CARE today.6Implementation
of the ABC/CARE program in disadvantaged populations would be an effective, socially
efficient policy for promoting social mobility.7
This paper addresses a fundamental problem that arises in evaluating social programs.
Few program evaluations have complete life-cycle histories of participants. In our data,
the oldest experimental subject is in his/her mid 30s. At issue is determining the life-cycle
impact of the program. We forecast the full life-cycle benefits and costs of the program using
non-experimental data guided by economic theory.8
As a byproduct, we also address the problem of aggregating evidence from the multi-
plicity of treatment effects found in ABC/CARE. We estimate economically interpretable
aggregates: internal rates of return and benefit/cost ratios that monetize the large array of
benefits and costs generated. In constructing these aggregates, we account for model estima-
tion and forecasting error and the welfare cost of taxation to fund programs. Our estimates
survive extensive sensitivity analyses.
We construct synthetic cohorts from non-experimental samples. The cohorts are chosen
to approximate the life cycles of experimentals in their post-experimental years. To make
these approximations, we formulate and estimate production functions on non-experimental
samples that predict program treatment effects and assess their within-sample forecast accu-
racy in experimental samples. Some of the inputs of the estimated production functions are
Communities in Australia (Scull et al.,2015). Current Educare programs in the U.S. are also based on
ABC/CARE (Educare,2014;Yazejian and Bryant,2012). Appendix A.8 lists these Educare programs, all
of which implement curricula based on ABC/CARE.
643% of African-American children were eligible at its inception.
7Garc´ıa and Heckman (2016) estimate that if ABC/CARE were implemented on the current stock
of eligible children, the intra-black gap (black disadvantaged relative to black advantaged) in high-school
graduation, years of education, employment and labor income at age 30 for females would be reduced by
110%, 76%, 22%, and 30%, respectively. It would eradicate the intra-black high-school graduation gap,
reduce the years of education gap to 0.12 years, reduce the employment gap to 14 percentage points, and
reduce the labor income gap to 4,075 USD (2014). For males, the program would eradicate the intra-black
high-school graduation gap, reduce the years of education gap to 0.18 years, and reduce the employment gap
to 9 percentage points.
8Ridder and Moffitt (2007) discuss data combination methods. These methods are related to the older
“surrogate marker” literature in biostatistics (see e.g., Prentice,1989). However, as noted below, exogeneity
is an integral part of the models we estimate, although it is not considered in the statistics literature. That
literature does not provide testable predictions for validation of its forecasts as we do.
2
changed by treatment and are measured in both experimental and non-experimental sam-
ples. If the production functions mapping inputs to outputs across cohorts are unaffected
by treatment (i.e., are “treatment invariant”), we can safely use them to forecast treatment
effects at older ages provided that we accurately forecast the path of future inputs. We test
and do not reject treatment invariance comparing outcomes in experimental samples with
those forecasted in non-experimental samples that overlap in age.9We forecast experimen-
tal treatment effects using our estimated production functions applied to non-experimental
data with inputs and outputs. We conduct an extensive sensitivity analyses for our baseline
forecasting models including examining, for example, alternative assumptions about cohort
effects that might characterize non-experimental samples. We compare the outcomes of our
approach with a cruder matching procedure. Estimates from it replicate those from our more
sophisticated procedure.
Our analysis is a template for estimating the life-cycle gains of social experiments for
which there is less than full lifetime follow-up. Supplementing experimental data with non-
experimental data enhances the information available from social experiments. Using eco-
nomic theory and econometric methods to generate empirically concordant forecasts en-
hances the credibility of the procedure.
The quest for long-run estimates from experiments with short-term follow-up has recently
led to application of informal procedures for estimating long-term benefits using short-term
measures of childhood test scores (e.g. Chetty et al.,2011;Kline and Walters,2016). We
show by example that these procedures can give very misleading estimates of true life cycle
program benefits by focusing on earnings, not counting the full array of benefits generated,
and relying solely on test scores to predict future earnings.
This paper proceeds in the following way. Section 2describes the ABC/CARE program.
Section 3discusses our methodology for forecasting life-cycle outcomes and the evidence
9See Hurwicz (1962) for the definition treatment (policy) invariance. We build on the methodology of
Heckman et al. (2013), who relate intermediate and long-term outcomes in a mediation analysis. However,
they do not construct out-of-sample forecasts as we do in this paper.
3
supporting our assumptions. We examine in detail how we forecast life-cycle labor income.
Section 4discusses how we forecast other life-cycle outcomes. Section 5reports baseline
estimates of internal rates of return and benefit/cost ratios and reports an array of sensi-
tivity analyses. Section 6uses our estimates to examine the predictive validity of widely
used informal forecasting methods and to examine the reliability of forecasts based only on
measures available early on in the experiment. Section 7summarizes our findings.
2 ABC/CARE: Background
The Carolina Abecedarian Project and the Carolina Approach to Responsive Education
(ABC/CARE) were enriched childcare programs that targeted the early years of disadvan-
taged, predominately African-American children in the area of Chapel Hill, North Carolina.10
Appendix Adescribes these programs in detail. We summarize their main features here.
These early childhood programs went well beyond providing regular care. They were
high-quality, educationally-focused child care centers. Their goal was to enhance the life
skills of disadvantaged children. They supported language, motor, and cognitive develop-
ment as well as socio-emotional competencies considered crucial for school success including
task orientation, the ability to communicate, independence, and pro-social behavior.11 All
treatment children received medical check-ups that conformed with the American Academy
of Pediatrics. Parents were notified if children had medical issues. The first cohort of the
ABC control-group received similar services, but not the later cohorts (Campbell et al.,2014;
Henderson et al.,1982).
The design and implementation of ABC and CARE were very similar. Both had two
phases. The first and main phase lasted from birth until age 5. In this phase, children
were randomly assigned to treatment. The second phase of the study took place in the
first three years of public schooling and supported children’s academic development. It en-
10Both ABC and CARE were designed and implemented by researchers at the Frank Porter Graham
Center of the University of North Carolina in Chapel Hill.
11Sparling (1974); Ramey et al. (1976,1985); Wasik et al. (1990); Ramey et al. (2012).
4
hanced parental involvement in the education of the children. A home visit took place every
two weeks and provided parents home activities to complement the skills taught at school.
The visitor facilitated communication between the teachers and the parents (Campbell and
Ramey,1995). Children were assigned to this treatment through a second-stage randomiza-
tion. The first phase of CARE, from birth until age 5, had an additional treatment arm of
home visits designed to improve home environments.12
ABC recruited four cohorts of children born between 1972 and 1976. CARE recruited two
cohorts of children, born between 1978 and 1980. For both programs, families of potential
participants were referred to researchers by local social service agencies and hospitals at the
beginning of the mother’s last trimester of pregnancy. Eligibility was determined by a score
on a childhood “risk index” of disadvantage.13
Our analysis uses data from the first phase and pools the ABC treatment group with
the CARE treatment group that received center-based childcare. We do not use the data
from the CARE group that only received home visits in the early years. Campbell et al.
(2014) test and do not reject the hypothesis that the CARE data through age 5 (without
home visits) and the ABC data through age 5 come from the same distribution.
The initial ABC sample consisted of 120 families. Due to attrition and non-response, the
study sample was reduced to 114 subjects: 58 in the treatment group and 56 in the control
group. In CARE, the initial sample had 65 families: 23 were randomized to a control group,
25 to a family education treatment group, and 17 to a center-based childcare treatment
group that followed ABC protocols.14 We use standard weighting methodologies to account
for attrition, non-response, and missing data.15
For both programs, data were frequently collected on cognitive and socio-emotional skills,
home environments, family structure, and family economic characteristics from birth until
12Wasik et al. (1990).
13See Appendix A.2 for details on the construction of the “risk index” used to determine eligibility.
14There were no randomization compromises in CARE. During preschool, 5 subjects attrited (3 in the
treatment group, 1 in the family education group, and 1 in the control group). Details on attrition and
non-response are presented in Appendix A.3.
15See Appendix C.2.
5
age 8. Further follow-ups were collected at ages 12, 15, 21, and 30. In addition, there is
information from administrative criminal records, and from a full in-person medical assess-
ment that included a survey and collection of bio specimens and measurements when the
subjects were in their mid30s. Appendix A.7 provides exact details on the timing of the dif-
ference data collections.16 Many control-group children in both ABC and CARE attended
alternative formal childcare arrangements (75% and 74%, respectively).17
3 Forecasting Life-cycle Costs and Benefits: Method-
ology
Our forecasting procedure builds in the methodology of Heckman et al. (2013). Experimental
outcomes are modeled as the outputs of treatment-invariant technologies. Treatment affects
inputs only and not the relationship between inputs and outputs. We measure how treatment
affects inputs within sample and forecast future input paths resulting from experimental
manipulations. We use non-experimental data to estimate the technologies associated with
treatment and use the experimental data to examine the hypothesis of treatment invariance
of the technology and the ability of the estimated technology to reproduce experimental
results using the input changes induced by the experiment. Given policy invariance, these
input changes define the intervention and link it to changes in child environments that occur
outside the experiment.
To formalize our procedure, the following notation is useful. W= 1 indicates that
parents referred to the program participate in the randomization protocol. W= 0 indicates
otherwise. Rindicates randomization into treatment (R= 1) or control (R= 0). Dindicates
16We also document the balance in observed baseline characteristics across the treatment and control
groups after dropping the individuals for whom we have no crime or health information. There is substantial
missing data for these outcomes, which we address using the methodology exposited in Appendix C.
17The alternative arrangements were generally lower quality than ABC/CARE (see Appendix A.6.1 for
details). In our main analysis, we compare treatment- and control-group children, irrespective of take-up of
alternatives. In Appendix F, we address the problem of substitution bias (Heckman,1992;Heckman et al.,
2000;Kline and Walters,2016). We disaggregate our analysis to distinguish treatment effects by type of
alternative selected by the control group.
6
whether or not a family attends the program. D=Rimplies compliance with the initial
randomization protocol. Lowercase variables denote realizations of random variables. We
suppress individual subscripts to avoid notational clutter.
Individuals are eligible to participate in the program if their baseline background vari-
ables B∈ B0, where B0is the set of scores on the childhood risk index that determines
program eligibility. Because all of the eligible individuals with the option to participate
chose to do so (W= 1, and D=R), we can safely interpret the treatment effects gener-
ated by the experiment as average treatment effects for the eligible population and not just
average treatment effects for the treated.18
Define Y1
aas the outcome vector at age afor the treated. Y0
ais the age-aoutcome
vector for the controls. At age athe vector of average treatment effects for the population
for which B∈ B0is:
a:= EY1
aY0
a|W= 1=EY1
aY0
a|B∈ B0.(1)
Randomization identifies this parameter in the experimental sample.
3.1 Using Economic Models to Make Forecasts
This paper uses economic models to generate unbiased, out-of-sample forecasts of a. We
use a structural production function (mediation) model for treatment (D= 1) and control
(D= 0) outcomes at age ain sample k∈ {e, n}, where edenotes membership in the
experimental sample and ndenotes membership in a non-experimental (auxiliary) sample.
The vector of production functions for output Yd
k,a is:
Yd
k,a =φd
k,a(Xd
k,a,Bk) + εd
k,a,(2)
18All providers of health care and social services (referral agencies) in the area of the ABC/CARE study
were informed of the programs. They referred mothers whom they considered disadvantaged. Eligibility was
corroborated before randomization. Conversations with the program staff indicate that all but one of the
referred mothers attended and agreed to participate in the initial randomization (Ramey et al.,2012).
7
d∈ {0,1}, k ∈ {e, n}, a ∈ {1,..., ¯
A}where φd
k,a (·,·) is a vector of structural production
relationships mapping inputs Xd
k,a,Bkinto outputs holding the error term εd
k,a fixed.19,20 Bk
are baseline variables not affected by treatment. Xd
k,a are variables potentially affected by
treatment. ¯
Ais the oldest age through which benefits are projected. In the experiment we
analyze, participants are observed through age a<¯
A.
The relationship between the inputs Xd
k,a,Bkand outputs Yd
k,a can, in principle, differ
between experimental and non-experimental samples although in our data this is not the
case. Equation (2) characterizes the outcomes of the two treatment regimes in any sample,
including a non-experimental sample with no direct empirical counterpart for the case d= 1.
We present conditions for identifying and estimating φd
k,a (·,·) in non-experimental samples.
A crucial condition is that for fixed values of inputs Xd
k,a =x,Bk=bthere are no differences
in the technologies and in the distributions of εd
k,a across treatment regimes and samples.
We first formalize this assumption and then remark on its content.
Assumption A–1 Structural Invariance For all x,bsupp(Xd
k,a,Bk), k ∈ {e, n}, and
a∈ {1,..., ¯
A}
φ0
k,a (x,b) = φ1
k,a(x,b)
=φa(x,b),(3a)
where φa(x,b)is the common structural function (across dand k) generating the determin-
istic portion of the effect of Bk=b,Xd
k,a =xon outcomes and
F0
k,a ·| Fix Xd
k,a =x,Bk=b=F1
k,a ·| Fix Xd
k,a =x,Bk=b
=Fa·| Fix Xd
k,a =x,Bk=b,(3b)
where Fj
k,a (z|Fix =ω)is the distribution of Zfor fixed at ωand Fa(z|Fix =ω)
is the age-adistribution of the errors associated with the production functions, assumed to
be common across treatment regimes and samples given Xd
k,a =xand Bk=b.
We clarify Assumption A–1 with two remarks.
19Fixing and conditioning are fundamentally different concepts. See Haavelmo (1943) and Heckman and
Pinto (2015) for discussions. The “do” operator in Pearl (2009) is an example of fixing.
20If feasible, cross-equation restrictions on Equation (2) should be tested, and, if satisfied, imposed.
8
Remark R–1 There are Two Distinct Aspects of Structural Invariance Assump-
tion A–1 has two distinct aspects that can be resolved further into two separate assumptions:
(i) structural relationships and distributions evaluated at the same arguments have identical
values for treatment and control groups in the experimental sample, and (ii) analogous con-
ditions hold across the experimental and non-experimental samples. Condition (ii) enables
analysts to simulate treatment and control outcomes in non-experimental samples.
Remark R–2 Accounting for Cohort Effects A second aspect of Assumption A–1,
that the structural relationships and distributions are identical in the experimental and non-
experimental samples for aa, embeds an implicit assumption about the absence of
cohort effects in the technology and distribution of errors in the post-sample period for
the experimental sample. In particular, a structural function φd
n,a (x,b)or distribution
Fd
n,a (z|Fix =ω)applied out of sample to subjects who are older than those in the ex-
perimental sample, is a valid tool for forecasting the outcomes in the experimental sample
at ages currently out of the age range of the experiment. Note that this does not mean that
there are no cohort effects in the outcome of interest, Yd
k,a. Instead, it means that there are
no cohort effects in the mapping between Xk ,a,Bkand Yd
k,a,k∈ {e, n}.21
Testing Assumption A–1 using the experimental and non-experimental samples without
imposing parametric assumptions requires common support conditions over the age range
aa. This requirement is captured by Assumption A–2:
Assumption A–2 In-Sample Support Conditions For aaand d∈ {0,1}:
supp(Yd
e,a,Xd
e,a,Be,εe,a )supp(Yn,a,Xn,a ,Bn.εn,a).(4)
To forecast out of sample input paths in order to forecast out of sample treatment effects we
require Assumption A–3:
Assumption A–3 Out-of-Sample Forecast Support
(i) The support of the non-experimental data contains the support of the future values that
experimentals could experience.
(ii) We can accurately forecast the distributions of future values of inputs and errors.
Condition (i) is a version of Assumption A–2 for a>a.
21Note that the function φd
k,a could include polynomial age trends as arguments in order to capture, for
example, work experience (age schooling 6).
9
Remark R–3 Requirements for Accurate Forecasts This assumes that the analyst
can make accurate adjustments for cohort effects. We only require distributions of forecast
variables to make accurate forecasts.
To be specific, we now consider how one can use this framework to forecast life-cycle
labor income.
3.2 Forecasting Labor Income
Step 1. Constructing a Synthetic Cohort. We use the Children of the National Longi-
tudinal Survey of Youth (CNLSY) to construct a synthetic cohort from ages 21 to 29 using
similarity with the baseline variables in the experimental samples (B). We use both the Na-
tional Longitudinal Survey of Youth 1979 (NLSY79) and the Panel Study of Income Dynam-
ics (PSID) to construct a synthetic cohort from ages 29 to 67. Whenever we use the NLSY79
and PSID together, we combine samples. Thus we use three non-experimental datasets to
obtain information across the life cycle. We satisfy support conditions—Equation (4).
Because we do not observe each element of the eligibility index discussed in Section 2,
we approximate Bn∈ B0. We delimit the sample to include observations satisfying the
following criteria: (i) NLSY79: Black, labor income less than $300,000 (2014 USD) in any
given year, birth year between 1957 and 1965; (ii) PSID: Black, labor income less than
$300,000 (2014 USD), birth year between 1945 and 1981; and (iii) CNLSY: Black, labor
income less than $300,000 (2014 USD) in any given year, birth year between 1978 and 1983.
We weight individuals in the non-experimental samples according to their resemblance
to individuals in the experimental sample.22 We match on baseline pre-treatment match
variables: year of birth, gender, and number of siblings at baseline. All are available in
the non-experimental datasets. This procedure generates a synthetic cohort in the non-
experimental sample for subsequent analysis in our structural forecasting procedure.
By design, there is no treatment effect in the non-experimental sample. Matching to the
22We use Mahalanobis’ matching Algorithm 1and weights derived from the Mahalanobis distances that
downweight dissimilar observations. See Appendix Cfor details.
10
experimental sample is executed using baseline variables not affected by treatment in the
experimental sample. Figure 1demonstrates that the synthetic cohort is comparable to the
control group of the experiment. At age 30, average observed labor income for the control
group in the experimental sample coincides with average labor income for the synthetic
cohort.23
Step 2. Establishing Exogeneity of Inputs. Forecasting does not require that we
take a position on the exogeneity of Xd
k,a for k∈ {e, n}and a∈ {1, . . . ¯
A}with respect
to labor income. Estimated structural models with biased parameters can still give reliable
forecasts if relationships between observed and unobserved variables are the same within
sample and in the forecast sample.24 However, exogeneity facilitates the use of economic
theory to interpret treatment effects, to forecast outcomes in samples where inputs are
manipulated differently than in the experimental sample, and to test the validity of the
construction of our synthetic cohort. Exogeneity also makes identification of φd
k,a (·,·) in the
non-experimental sample straightforward. Assumption A–4 formalizes a strong form of the
exogeneity condition.
Assumption A–4 Exogeneity Let {1,..., ¯
A}index the periods of a life cycle. For all
a, a0∈ {1,..., ¯
A}and for d, d0∈ {0,1},
εd
k,a Xd0
k,a0|Bk=b(5)
for all bin the support of Bk, k ∈ {e, n}, where “MN|Q” denotes independence of M
and Ngiven Q.
Below we discuss how this condition can be weakened and unbiased forecasts can still be
obtained.
To appreciate the benefit of Assumption A–4, consider the following example. Suppose
that years of education is a component of Xd0
k,a0. The joint distribution of εd
k,a and Xd0
k,a0can
differ substantially across experimental and non-experimental samples. In the experimental
23We observe labor income in the experimental samples at ages 21 and 30. We use the data at age 21 to
initialize our forecasting model and hence cannot use it for testing our forecast.
24See Liu et al. (2016). Conditions C–1 to C–3 in Appendix C.3 spell out the requirements.
11
Figure 1: Labor Income Profile, Disadvantaged Individuals and Synthetic Cohort Constructed by Matching in the Auxiliary
Samples
(a) Males
ABC/CARE Eligible at a*: 24.91 (s.e. 2.31)
Synthetic Cohort at a*: 27.12 (s.e. 2.24)
10
20
30
40
50
Labor Income (1000s 2014 USD)
20 Interpolation a* Extrapolation 40
Age
ABC/CARE Eligible (B Β0) Synthetic Cohort−Matching Based +/− s.e.
Control Observed Observed +/− s.e.
(b) Females
ABC/CARE Eligible at a*: 22.89 (s.e. 1.84)
Synthetic Cohort at a*: 21.23 (s.e. 1.76)
10
20
30
40
50
Labor Income (1000s 2014 USD)
20 Interpolation a* Extrapolation 40
Age
ABC/CARE Eligible (B Β0) Synthetic Cohort−Matching Based +/− s.e.
Control Observed Observed +/− s.e.
Note: Panel (a) displays the forecast labor income for males in the auxiliary samples for whom B∈ B0, i.e., ABC/CARE eligible, and for the synthetic
cohort we construct based on the method proposed in this section. We combine data from the Panel Study of Income Dynamics (PSID), the National
Longitudinal Survey of Youth 1979 (NLSY79), and the Children of the National Longitudinal Survey of Youth 1979 (CNLSY79). We highlight the
observed labor income at oldest a(age 30) for the ABC/CARE control-group participants. We stop at age 45 for want of data to compute the
childhood risk index defining B∈ B0in the auxiliary samples. Panel (b) displays the analogous figure for females. Standard errors are based on the
empirical bootstrap distribution. ais the oldest age in the experimental sample.
12
sample, years of education are boosted by treatment, which is randomly assigned. In the
non-experimental samples, however, there is no experimental variation and exogeneity does
not hold. Individuals with high observed levels of education could have high values of εd
k,a
due to omitted ability. This creates a fundamentally different dependence between εd
k,a and
Xd0
k,a0in the non-experimental sample. Assumption A–4 avoids this problem when making
forecasts. Below, we establish that our forecasts based on this assumption are concordant
with forecasts from approaches that do not require Assumption A–4.
Step 3. Determining Inputs. Analysis of the non-experimental data reveals that
the inputs determining labor income under Assumption A–4 are: average PIAT achievement
score from ages 5 to 7, completed education, labor income at age 21, and lagged labor income.
Appendix Table C.3 shows that these variables predict labor income. Appendix C.3.6 shows
that there is common support across datasets. We report tests for endogeneity of these
variables in the experimental and auxiliary samples used in this paper in Appendix C.3.7.25
After conditioning on Xd
k,a and Bk, we do not reject the null hypothesis of exogeneity.
Accordingly, we use OLS in making our baseline estimates.
Table 1displays the treatment effects of the program for these inputs.26 Assignment to
treatment has statistically and economically significant causal effects on the inputs generating
final outcome treatment effects. Our forecasted treatment effects are based on these program-
induced changes in inputs. For females, it increases the average PIAT score by almost one
third of a standard deviation.27 For males, the effect is almost half of a standard deviation.
25These tests are based on the assumption that εd
k,a for k∈ {e, n}is characterized by a factor structure.
The factors are predicted by measurements of cognitive and non-cognitive skills. We use estimated factors
as control functions. We do not reject the null of exogeneity. See Appendix C.3.7. Factor structure models
are widely used in structural estimation of production functions of skills during early childhood. See, e.g.,
Cunha and Heckman (2008) and Cunha et al. (2010).
26We first present raw treatment-control mean differences. As we report in Table 1, the treatment effects
are substantial across multiple outcomes. In some cases, this finding is at odds with what other studies report
(Ramey et al.,1985;Clarke and Campbell,1998;Campbell et al.,2001,2002,2008,2014). The difference
is explained, mainly, by the fact that we consider effects by gender. Only Campbell et al. (2014) consider
treatment effects by gender. They focus on health effects and find that men have many more positive effects
especially in cardiovascular and metabolic conditions if compared to women. This is consistent with the
results we report below.
27The test is standardized to an in-sample standard deviation of 15 units.
13
The program substantially boosts high school graduation for females and college graduation
for both males and females. We use years of education attained to summarize both effects
in a measure that is comparable across genders. Labor income at age 21 for girls is not
greatly boosted by the program. This arises in part because treated girls are more likely
to be enrolled in college at age 21 and thus do not work at that age. The program boosts
annual labor income, especially for males, for whom the average treatment effect at age 30
is almost 20,000 (2014 USD).28
Table 1: Summary of Treatment Effects for Inputs Generating Labor Income (Xd
k,a)
Females Males
Control Average Control Average
Inputs Mean Treatment Effect Mean Treatment Effect
PIAT Scores 95.63 4.92 93.46 7.70
High School Graduation 0.51 0.25 0.61 0.07
College Graduation 0.08 0.13 0.12 0.17
Years of Education 11.76 2.14 12.90 0.66
Labor Income at 30 23,443.42 2,547.50 29,340.31 19,809.74
Note: This table shows the control-group level and the raw mean difference between treatment and control
(average treatment effects), by gender. PIAT scores have a sample mean of 100 and a standard deviation
of 15. High school and college graduation are expressed in rates. Labor income is in 2014 USD. Average
treatment effects are bolded when statistically significant at the 10% level.
Step 4. Testing the Empirical Implications of Assumption A–1.Under Assump-
tion A–4, we build on Heckman et al. (2013) to test for invariance. Condition (3a) of As-
sumption A–1 combined with Assumptions A–2 and A–4 and the normalization E(εd
k,a)=0
for all a∈ {1,..., ¯
A}, generates the following testable implications:
EY1
e,a|X1
e,a =x,Be=b, D = 1=EY0
e,a|X0
e,a =x,Be=b, D = 0(6a)
and
EYd
e,a|Xd
e,a =x,Be=b, D =d=E[Yn,a|Xn,a =x,Bn=b],(6b)
for d∈ {0,1}where Yn,a is the counterpart of Ye,a in the non-experimental sample.
28Table 1displays age-21 and age-30 labor income because labor income is observed at ages 21 and 30 in
the experimental sample. Labor income at age 30 is an input in our methodology only after age 30.
14
Note, however, that if the only goal is to construct unbiased forecasts of mean treat-
ment effects, the minimal requirement is that experimental treatment effects should equal
differences in the conditional means of forecasts formed on the non-experimental samples
evaluated at Xn,a =x1and Xn,a =x0respectively:
EY1
e,a|X1
e,a =x1,Be=b, D = 1EY0
e,a|X0
e,a =x0,Be=b, D = 0
=EYn,a|Xn,a =x1,Bn=bEYn,a |Xn,a =x0,Bn=b.(6c)
Rather than imposing Condition (6c), we test sufficient conditions for it to hold: i.e., we
test Conditions (6a) and (6b). We test Condition (6a) across treatment regimes and Condi-
tion (6b) for d= 0 at age 30, where we observe labor income in the experimental sample for
both the treatment and the control groups. Assuming linearity, if Condition (6a) holds, the
coefficient associated with D, denoted by τ, should be zero in
Yd
e,30 =τ·D+Be·γd
e,30 +Xd
e,30 ·βd
e,30 +εd
e,a.(6a)
Failing to reject the null hypothesis H0:τ= 0 is equivalent to failing to reject invariance
across treatment regimes.
Panel (a) of Table 2displays estimates of the coefficients of Equation (6a) for labor
income at age 30 by gender. We do not reject the null hypothesis that the technology is
invariant across treatment regimes for either gender.29 Panel (b) of Table 2reports estimates
for the remaining coefficients in Equation (6a). Years of education is strongly boosted by
ABC/CARE (see Table 1).
Define K=1(k=e) as an indicator of whether an observation comes from the exper-
imental sample. The coefficient on K, denoted by π, should be zero in the following linear
29Note that after accounting for background variables and the intermediate inputs, average labor income
is $2,213 (2014 USD) higher in the control group for females. This value is relatively small in the context of
annual labor income at age 30 and given that the average in the control group is $23,443 (2014 USD). The
same holds for the males, where the treatment-control difference is $232 net of inputs and the average for
the control group is $29,340 (2014 USD).
15
Table 2: Testing Invariance in Technologies φd
k,a (x,b)of Labor Income at Age 30
Females Males
coefficient p-value coefficient p-value
Panel (a). Invariance Across Treatment Regimes
D(treatment indicator) -2,212.806 0.586 231.606 0.969
Panel (b). Precision of Estimated Coefficients of (6a)
Be(baseline variables)
Mother’s Education (at birth) -957.0972 0.387 1,850.201 0.358
Xd
e,30 (age-30 inputs)
PIAT (5-7) 5.726 0.975 327.186 0.338
Years of Education (30) 2,356.143 0.006 4,474.721 0.018
Labor Income (21) 0.218 0.320 0.322 0.175
R20.281 0.207
Observations 52 50
Sample: Experimental Treatment and Control Groups at Age 30
Panel (c). Invariance Across Experimental and Non-Experimental Samples
K(treatment indicator) -142.631 0.965 1,887.575 0.654
Panel (d). Precision of Estimated Coefficients of Counterpart to (6b)
in the Non-experimental Sample
Bk(baseline variables)
Mother’s Education (at birth) -229.481 0.631 427.224 0.459
Xd
k,30 (age-30 inputs)
PIAT (5-7) 266.1971 0.002 219.220 0.044
Years of Education (30) 4,263.156 0.000 4,434.173 0.000
Labor Income (21) 0.355 0.000 0.685 0.000
R20.221 0.182
Observations 829 746
Sample: Experimental Treatment and Control Groups and Non-
Experimental Synthetic Cohort at Age 30
Note for Panel (a) and (b): Estimates of the coefficients in Equation (6a) for labor income at age 30 by
gender within the experimental sample. Ddenotes the treatment indicator (D= 0 for control-group par-
ticipants and D= 1 for treatment-group participants). Beis comprised of baseline variables not affected
by treatment (mother’s education at birth) and Xd
e,30 is age-30 intermediate inputs. We drop labor income
observations above the 95th percentile to avoid precision issues.
Note for Panel (c) and (d): Estimates of the coefficients in Equation (6b) for labor income at age 30 by
gender pooling the experimental treatment and control groups and the synthetic cohort at age 30. Kde-
notes membership to the experimental or non-experimental sample (K= 0 synthetic cohort in the non-
experimental sample and K= 1 experimental sample). Bkis comprised of baseline variables not affected
by treatment (mother’s education at birth) and Xd
k,30 is age-30 intermediate inputs.
16
technology (i.e., H0:π= 0 if Condition (6b) is true):
Yk,30 =π·K+Bk·γk,30 +Xk,30 ·βk,30 +εk,a.(6b)
Panel (c) in Table 2displays estimates of the parameters of Equation (6b) for labor
income at age 30 for males and females. Estimates of πare small and not statistically
significant.30 We do not reject the null hypothesis that the technologies are invariant across
samples so the data are consistent with invariance.
Table 3: Testing Invariance in Distributions of the Error Terms Fd
k,aof Labor Income at
Age 30
Females Males
Panel (a). Invariance Across Treatment Regimes
Equality in means t-stat p-value t-stat p-value
1.075 0.287 -0.0390 0.969
Equality in distributions K-S p-value K-S p-value
0.272 0.632
Sample: Experimental Treatment and Control Groups at Age 30
Panel (b). Invariance Across Experimental and
Non-Experimental Samples
Equality in means t-stat p-value t-stat p-value
0.054 0.957 -0.226 0.822
Equality in distributions K-S p-value K-S p-value
0.481 0.046
Sample: Experimental Treatment and Control Groups and
Non-Experimental Synthetic Cohort at Age 30
Note for Panel (a): Tests for equality in distributions of residuals within the experimental sample across
treatment regimes at age 30 in labor income by gender. Residuals are the relevant outcome net of mother’s
education at birth, average PIAT test from ages 5 to 7, years of education at age 30, and labor income at
age 21. Residuals are adjusted for estimation error as explained in step 6 of Appendix C.7.1. Tests are a
t-test of equality in means and the Kolgomorov-Smirnov test.
Note for Panel (b): Tests for equality in distributions of residuals across the experimental and non-
experimental samples pooling the experimental treatment and control groups and the synthetic cohort at
age 30 for labor income by gender. Residuals are the relevant outcome net of mother’s education at birth,
average PIAT test from ages 5 to 7, years of education at age 30, and labor income at age 21. Residuals
are adjusted for estimation error as explained in step 6 of Appendix C.7.1. Tests are a t-test of equality in
means and the Kolgomorov-Smirnov test.
We use analogous procedures to test Condition (3b) of Assumption A–1. First, we test
30The averages of labor income in the experimental and non-experimental sample for females and males
are $24,584 and $40,007, and $24,098 and $32,717 (2014 USD), respectively.
17
invariance in the distributions of εd
k,a across treatment regimes within the experimental sam-
ple for labor income at age 30. Then, invoking invariance across treatment regimes, we
test invariance across the experimental and non-experimental residual distributions. Resid-
uals are generated from the estimated forecasting model in Equation (2) assuming a linear
technology. We adjust the residuals for model estimation error as explained in step 8 of
Appendix C.7.1.
With the empirical counterparts of εd
k,a in hand, we implement two tests to compare
the distributions in Table 3:t-tests of mean comparisons and Kolgomorov-Smirnov tests of
equality of distributions. We do not reject equality of treatment and control distributions of
εd
k,a for both females and males—Panel (a). As before, we pool the experimental treatment
and control groups and the synthetic cohort to test invariance across samples by gender. Ex-
cept for one hypothesis test of Condition (6b) for males, we do not reject the null hypothesis
of invariance across samples—see Panel (b).
Steps 5. Accounting for Estimation Error, Forecast Error, and Plausible
Ranges of Externally Supplied Parameters. We obtain standard errors from the em-
pirical bootstrap distribution. Our inference accounts for each step of our estimation pro-
cedure, as well as forecast error. We conduct sensitivity analyses for externally supplied
parameters. A step-by-step recipe for accounting for parameter uncertainty is presented in
Appendix C.7. The forecasted present value of the gain induced by treatment using the esti-
mates displayed in Figure 2is $133,032 (s.e. $76,634) in 2014 USD. We explore the estimates
from alternative forecasting models in Appendix C.6.31 When pooling males and females
and when separating the samples by gender, the present value gains remain within a range
that does not change our inference that the program had substantial lifetime benefits.
Step 6. Validating Forecasts. Invariance across treatment regimes and samples is
the essential ingredient for constructing valid forecasts. Figure 2displays our forecasted
31As both a referee and various discussants of our paper have pointed out, our identification and estimation
strategies do not impose cross-sectional restrictions. We use different datasets to identify and estimate the
φa(x,b) for each outcome (e.g., labor income, health, crime). Thus, the predictor variables that we are able
to use differ across outcomes and we cannot conduct joint estimations.
18
labor income profiles. Forecasted and actual labor income are closely aligned in both the
treatment and the control regimes.32 Computing the net present value, the internal rate of
return and benefit/cost ratios is straightforward once age-by-age forecasts are available.33
3.2.1 Alternative Forecasting Models for Labor Income
An alternative non-parametric forecasting method compresses the whole forecasting proce-
dure. Under Assumptions A–1 and A–4, we can use matching on baseline variables and
variables affected by treatment to construct counterparts to the experimental treatment and
control groups in the non-experimental sample.34 Matching is a non-parametric estimation
procedure for conditional mean functions. Matching creates direct counterparts in the auxil-
iary sample for each member of the experimental sample. Instead of estimating a model for
the life-cycle profile of labor income and forecasting from it, we directly use the counterpart
matched profiles.35 This is an intuitively appealing non-parametric estimator of life-cycle
program treatment effects that is valid under exogeneity (Heckman and Navarro,2004).
This is a fundamentally different matching procedure than what is used to construct the
synthetic cohort in Step 1. In the main analysis of this paper, we match on baseline variables
not affected by treatment to construct a synthetic cohort with B∈ B0. Using these samples,
we estimate production functions on this cohort to forecast out-of-sample treatment effects.
In contrast, in the analysis of this subsection, we match both on baseline variables (B)
and on variables affected by treatment Xd
k,acompressing the construction of the synthetic
cohort and the estimation of the production functions for out-of-sample forecasts to a single,
non-parametric procedure.
32The content in Figure 2is sufficient but not necessary to calculate the gain of the program due to
labor income. It would be sufficient to forecast the difference between the treatment and control groups.
Forecasting the levels, however, provides us with additional testable implications. It also allows us to easily
account for forecasting error and to verify that the life-cycle profiles that we estimate are comparable to
observed profiles for similar socio-economic groups. The pattern of life-cycle labor income we generate is
typical for that of low-skilled workers (Blundell et al.,2015;Gladden and Taber,2000;Sanders and Taber,
2012;Lagakos et al.,2016).
33Some practical details involved in doing this are in Appendices C.4 and C.5.
34Heckman et al. (1998) discuss this procedure.
35See Appendix C.3.5 for details.
19
Figure 2: Forecasted Labor Income Profiles for ABC/CARE Participants
(a) Males
Control at a*:
Forecasted, 31.34 (s.e. 4.45)
Observed, 29.34 (s.e. 4.01)
Treatment at a*:
Forecasted, 37.7 (s.e. 9.53)
Observed, 39.01 (s.e. 5.79)
0
10
20
30
40
50
60
Labor Income (1000s 2014 USD)
Interpolation a* Extrapolation 45 55 65
Age
Control Forecasted Treatment Forecasted Forecast +/− s.e.
Control Observed Treatment Observed Observed +/− s.e.
(b) Females
Control at a*:
Forecasted, 19.59 (s.e. 3.24)
Observed, 23.44 (s.e. 2.64)
Treatment at a*:
Forecasted, 26.24 (s.e. 3.98)
Observed, 25.99 (s.e. 3.19)
0
10
20
30
40
50
60
Labor Income (1000s 2014 USD)
Interpolation a* Extrapolation 45 55 65
Age
Control Forecasted Treatment Forecasted Forecast +/− s.e.
Control Observed Treatment Observed Observed +/− s.e.
Note: Panel (a) displays the forecast life-cycle labor income profiles for ABC/CARE males by treatment status, based on the method proposed in
Section 3. We combine data from the Panel Study of Income Dynamics (PSID), the National Longitudinal Survey of Youth 1979 (NLSY79), and the
Children of the National Longitudinal Survey of Youth 1979 (CNLSY79). We highlight the observed labor income at a(age 30) for the ABC/CARE
control- and treatment-group participants. Panel (b) displays the analogous figure for females. Our forecasts go up to age 67, the age of assumed
retirement. Standard errors are the standard deviations of the empirical bootstrap distribution. See Appendix Cfor a discussion of our choice of
predictors and a sensitivity analysis on those predictors. We under-predict labor income for both males and females. These differences, however, are
not statistically significant (and labor income is a relatively minor component of the overall analysis for females).
20
Table C.12 shows that there is close agreement between non-parametric estimates based
on matching and the more parametric model-based approach previously presented. This
reassuring concordance is consistent with exogeneity of inputs and structural invariance.36
4 Forecasting Other Life-cycle Benefits
In this section, we adapt the methodology described in Section 3to forecast the net benefits of
the program arising from enhanced parental income, health, and reduced crime. In the text,
we focus on forecasting health benefits and briefly discuss forecasts of crime and parental
labor income.37 Procedures for forecasting the benefits and costs of education are reported
in Appendix D.
4.1 Health
One contribution of this paper is forecasting and monetizing the life-cycle benefits of the
enhanced health and reduced health costs of participants using a version of Equation (2).
The model recognizes that: (i) health outcomes such as diabetes, heart disease, or death
are absorbing states; and (ii) there is no obvious terminal time period for benefits and costs
except death, which we forecast.
We adapt the Future Adult Model (FAM)—a forecasting model for health conditions
and costs developed by Dana Goldman and coauthors (Goldman et al.,2015).38 We forecast
health outcomes of program participants from their mid 30s up to their projected age of
death.39 Our version of FAM passes a variety of specification tests and accurately forecasts
health outcomes and health behaviors.40
Our methodology has four steps–extensive details are provided in Appendix G: (i) follow
36Note that the non-parametric estimates are more tightly estimated because there are fewer steps in
estimation. We are conservative in using the less precisely estimated forecasts in our main analysis.
37Appendices Eand C.3.8 provide further documentation.
38Appendix Gdiscusses the FAM methodology in detail. It is not a competing risks model, but forecasts
vectors of incidence and costs of disease one category at a time using univariate models.
39The simulation starts at the age in which we observe the subjects’ age-30 follow-up.
40Goldman et al. (2015) present tests of the model assumptions and predictive performance for population
aggregate health and health behavior outcomes.
21
an adapted version of the steps in Section 3to predict the health state occupancy probabil-
ities for the ABC/CARE subjects; (ii) estimate quality-adjusted life year (QALY) models
using the Medical Expenditure Panel Survey (MEPS) and the PSID;41 (iii) estimate medical
cost models using MEPS and the Medicare Current Beneficiary Survey (MCBS), allowing
estimates to differ by health state and observed characteristics; and (iv) forecast the medical
expenditures and QALYs that correspond to the simulated individual health trajectories.42
Our application of FAM uses the information on age-30 observed characteristics and a
mid-30s health survey allowing us to account for components that are important for fore-
casting health outcomes. The models forecast the probability of having any of the major
disease categories and health states at age a+ 1 based on the state of health as summarized
by major disease categories at age a.43
Using the occupancy probabilities for each health outcome at each age, we take a Monte-
Carlo draw for each subject. Each simulation depends on each individual’s health history
and characteristics. For every simulated trajectory of health outcomes, we forecast the life-
cycle medical expenditure using the models estimated from the MEPS and the MCBS. We
estimate the expected life-cycle medical expenditure by taking the mean of each individual’s
simulated life-cycle medical expenditure.
The models estimated using MCBS represent medical costs in the years 2007 to 2010. The
MEPS estimation captures costs during 2008 to 2010. To account for real medical cost growth
after 2010, we adjust each model’s forecast using the method described in Appendix G.2.3.
The same procedure is applied to calculate QALYs. We compute QALY based on a widely-
41QALY is a measure which reweighs a year of life according to its quality given the burden of disease
(Dolan,1997;Shaw et al.,2005).
42As part of step (i), we impute some of the variables used to initialize the FAM models (see Ap-
pendix G.1.6.1).
43See Tables G.1 to G.3 for a summary. Our forecasts are based on two-year lags, due to data limitations
in the auxiliary sources we use to simulate the FAM. For example, if the individual is 30 (31) years old in
the age-30 interview, we simulate the trajectory of her health status at ages 30 (31), 32 (33), 34 (35), and so
on until her projected death. Absorbing states are an exception. For example, heart disease at age adoes
not enter in the estimation for heart disease at age a+ 1 because it is an absorbing state: once a person has
heart disease, she carries it through the rest of her life.
22
used health-related Quality-of-Life measure available in MEPS.44 We then apply this model
to the PSID data. QALYs monetize the health of an individual at each age. Although there
is not a clear age-by-age treatment effect on QALYs, there is a statistically and substantively
significant difference in the accumulated present value of the QALYs between the treatment
and the control groups.45
We estimate three models of medical spending: (i) Medicare spending (annual medical
spending paid by parts A, B, and D of Medicare); (ii) private spending (medical spending
paid by a private insurer or paid out-of-pocket by the individual); and (iii) all public spending
other than Medicare. Each medical spending model includes the variables we use to forecast
labor and transfer income, together with current health, risk factors, and functional status
as explanatory variables.
We also calculate medical expenditures before age 30.46 The ABC/CARE interviews
at ages 12, 15, 21 and 30 have information related to hospitalizations at different ages and
number of births before age 30. We combine this information along with individual and
family demographic variables to use MEPS to forecast medical spending for each age.
4.2 Crime
To estimate the life-cycle benefits and costs of ABC/CARE on crime, we use rich data ob-
tained from public records. Two previous studies consider the impacts of ABC on crime:
Clarke and Campbell (1998) use administrative crime records up to age 21, and find no sta-
tistically significant treatment effects. Barnett and Masse (2002,2007) analyze self-reported
crime at age 21. They lacked access to the longer-term, administrative data that we use and
report weak treatment effects on crime. Our study improves on this research in two ways: (i)
we use administrative data on the accumulated number of crimes that participants commit
through their mid 30s; (ii) we use micro-data specific to the states in which participants
44HRQoL measure EQ-5D.
45Our baseline estimation assumes that each year of life is worth $150,000 (2014 USD). Our estimates
are robust to substantial variation in this assumption, as we show in Appendix H.
46See Appendix G.2.4.
23
grew up, as well as other national datasets, to forecast criminal activity from the mid 30s
to 50. We forecast using methods standard in the criminology literature.47 See Appendix E
for a complete discussion of our crime forecasts.
4.3 Parental Labor Income
ABC/CARE offers childcare to the parents of treated children for more than nine hours a day
for five years, 50 weeks a year. Only 27% of participant mothers of children reported living
with a partner at baseline. This barely changed during the course of the experiment (see
Appendix A). The childcare component generates substantial treatment effects on maternal
labor force participation and parental labor income.48 In addition, subsidized childcare
induced wage growth due to enhanced parental educational attainment and through wage
growth due to work experience.
We observe parental labor income at eight different ages for the participants through
age 21.49,50 To estimate the profile of parental earnings over the entire life-cycle, we use two
different approaches in Appendix C.3.8: (i) an approach based on projections using standard
Mincer equations; and (ii) an approach based on the analysis of Section 3.
Any childcare inducements of the program likely benefit parents who, at baseline, did
not have any other children who were not eligible for program participation. Additional
childcare responsibilities would weaken the childcare effects of ABC/CARE, especially if
younger siblings are present. In Appendix C.3.8, we show that the treatment effect for
discounted parental labor income is much larger when participant children have no siblings
at baseline. Treatment effects weaken when comparing children who have siblings younger
than 5 years old to children who have siblings age 5 years or older.51
47Cohen and Bowles (2010) and McCollister et al. (2010).
48There is also an effect on maternal school enrollment. Some of the mothers of participants decided to
enroll in school and further their education. This could be one of the reasons why they make more money
afterward. We quantify the social cost of additional education in Appendix D.
49The ages at which parental labor income is observed are 0, 1.5, 3.5, 4.5, 8, 12, 15, and 21. At age 21
the mothers of the ABC/CARE subjects were, on average, 41 years old.
50We linearly interpolate parental labor income for ages for which we do not have observations between
0 and 21.
51These patterns persist when splitting the ABC/CARE sample by gender, but the estimates are not
24
4.4 Program Costs
The yearly cost of the program was $18,514 per participant in 2014 USD. We improve on
previous cost estimates by using primary-source documents.52 Appendix Bdiscusses program
costs in detail.
5 Estimates and Sensitivity Analysis
Figure 3summarizes our findings. It displays the discounted (using a 3% discount rate)
life-cycle benefits and costs of the program (2014 USD) pooled across genders, over all
outcome categories, and for separate categories as well.53 These benefits are the inputs of
our baseline estimates for the annual internal rates of return and benefit/cost ratios. We
conduct extensive sensitivity and robustness analyses to produce ranges of plausible values
for the estimates of the internal rate of return (8.0, 18.3) and benefit/cost ratio (1.52, 17.40).
We document that no single component of benefits drives our estimates.
The costs of the program are substantial, as frequently been noted by critics.54 But
so are the benefits, which far outweigh the costs. The individual gains in labor income,
parental labor income, crime, and health are at least as large in magnitude as the costs.
As a consequence, our measures of social efficiency remain statistically and economically
significant even after eliminating the benefits from any one of the four main components
that we monetize.
precise because the samples become too small. See Appendix C.3.8.
52Our calculations are based on progress reports written by the principal investigators and related docu-
mentation recovered in the archives of the research center where the program was implemented. We display
these sources in Appendix B. The main component is staff costs. Other costs arise from nutrition and services
that the subjects receive when they were sick, diapers during the first 15 months of their lives, and trans-
portation to the center. The control-group children also receive diapers during approximately 15 months,
and iron-fortified formula. The costs are based on sources describing ABC treatment for 52 children. We
use the same costs estimates for CARE, for which there is less information available. The costs exclude any
expenses related to research or policy analysis. A separate calculation by the implementers of the program
indicates almost an identical amount (see Appendix B).
53Using discount rates of 0%, 3%, and 7%, the estimates for the benefit/cost ratios are 17.40 (s.e. 5.90),
7.33 (s.e. 1.84), and 2.91 (s.e. 0.59), respectively. We report estimates for discount rates between 0% and
15% in Appendix H.1.
54See, e.g., Fox Business News (2014) and Whitehurst (2014).
25
Figure 3: Net Present Value of Main Components of the Pooled (Over Gender) Cost/Benefit Analysis Over the Life Cycle per
Program Participant, Treatment vs. Control
←… Components of Total Benefits …→
−1
0
1.5
3
4.5
6
100,000’s (2014 USD)
Program Costs Total Benefits Labor Income Parental Labor Income Crime QALYs*
Net Present Value Significant at 10%
Per−annum Rate of Return: Males and Females 13.7% (s.e. 3%).
Benefit−cost Ratio: Males and Females 7.3 (s.e. 1.8).
Note: This figure displays the life-cycle net present values per program participant of the main components of the cost/benefit analysis of ABC/CARE
from birth to forecasted death, discounted to birth at a rate of 3%. By “net” we mean that each component represents the total value for the treatment
group minus the total value for the control group. Program costs: the total cost of ABC/CARE, including the welfare cost of taxes to finance it.
Total benefits: the benefits for al l of the components we consider. Labor income: total individual labor income from age 21 to the retirement of
program participants (assumed to be at age 67). Parental labor income: total parental labor income of the parents of the participants from when the
participants were ages 1.5 to 21. Crime: the total cost of crime (judicial and victimization costs). To simplify the display, the following components
are not shown in the figure: (i) cost of alternative preschool paid by the control-group children’s parents; (ii) the social welfare costs of transfer
income from the government; (iii) disability benefits and social security claims; (iv) costs of increased individual and maternal education (including
special education and grade retention); (v) total medical public and private costs. Inference is based on non-parametric, one-sided p-values from the
empirical bootstrap distribution. Dots () indicate point estimates significant at the 10% level. *QALYs refers to the quality-adjusted life years. Any
gain corresponds to better health conditions until forecasted death, with $150,000 (2014 USD) as the base value for a year of life.
26
Pooling males and females, the program is socially efficient: the internal rate of return
and the benefit/cost ratio are 13.7% and 7.3, respectively. These estimates are statistically
significant, even after accounting for sampling variation and forecast and estimation error in
the experimental and auxiliary samples and the tax costs of financing the program.55
We conduct an extensive set of sensitivity analysis. Table 4displays the results of a
sensitivity analysis of the estimates of the benefit/cost ratio to alternative plausible assump-
tions. Table 5presents the corresponding internal rates of return. Our estimates are not
driven by our methods for accounting for attrition and item non-response, by the condi-
tioning variables, by the functional forms of projection equations used when computing the
net-present values or by values of externally set parameters, such as the value of life intro-
duced in our predictions of crime and health costs.56 Although the internal rate of return
remains relatively high when using participant outcome measures only up to ages 21 or 30,
the benefit/cost ratios indicate that accounting for benefits that go beyond age 30 is impor-
tant. The return to each dollar is at most 3/1 when only considering benefits up to age 30
(see the columns in the forecast span rows).
Accounting for the treatment substitutes available to controls also matters. Males benefit
the most from ABC/CARE relative to attending alternative formal childcare, while females
benefit the most from ABC/CARE relative to staying at home. We explore these differences
futher in Appendix F.
Our baseline estimates account for the deadweight loss caused by distortionary taxes
collected to fund programs, plus the direct costs associated with collecting taxes.57 We
assume a marginal tax rate of 50%.58 Our estimates are robust to dropping it to 0% or
55We obtain the reported standard errors by bootstrapping all steps of our empirical procedure, including
variable selection, imputation, model selection steps, and forecast error (see Appendix C.7).
56See Appendix Cfor a detailed discussion.
57When the transaction between the government and an individual is a direct transfer, we consider 0.5
as the cost per each transacted dollar. We do not weight the final recipient of the transaction (e.g., transfer
income). When the transaction is indirect, we classify it as government spending as a whole and consider
its cost as 1.5 per dollar spent (e.g., public education).
58Feldstein (1999) estimates that the deadweight loss caused by increasing existing tax rates (marginal
deadweight loss) may exceed two dollars per dollar of revenue generated. We use a more conservative value
(0.5 dollars per dollar of revenue generated). In Tables 4,5, and in Appendix H.2, we explore the robustness
27
Table 4: Sensitivity Analysis for Benefit/Cost Ratios
Pooled Males Females
Baseline 7.33 (s.e. 1.84) 10.19 (s.e. 2.93) 2.61 (s.e. 0.73)
Baseline: IPW and Controls, Life-span up to predicted death, Treatment vs. Next Best, 50% Marginal tax 50% (deadweight loss), Discount rate 3%, Parental
income 0 to 21 (child’s age), Labor Income predicted from 21 to 65, All crimes (full costs), Value of life 150,000.
Specification No IPW and No Controls No IPW and No Controls No IPW and No Controls
7.31 7.99 9.80 8.83 2.57 2.82
(1.81) (2.18) (2.69) (2.72) (0.72) (0.68)
Forecast to Age 21 to Age 30 to Age 21 to Age 30 to Age 21 to Age 30
Span 1.52 3.19 2.23 3.84 1.46 1.81
(0.36) (1.04) (0.61) (1.60) (0.36) (0.50)
Counter- vs. Stay at Home vs. Alt. Presch. vs. Stay at Home vs. Alt. Presch. vs. Stay at Home vs. Alt. Presch.
factuals 5.44 9.63 3.30 11.46 5.79 2.28
(1.86) (3.10) (2.95) (3.16) (1.37) (0.76)
Deadweight- 0% 100% 0% 100% 0% 100%
loss 11.01 5.50 15.38 7.59 3.83 2.01
(2.79) (1.37) (4.35) (2.23) (1.04) (0.59)
Discount 0% 7% 0% 7% 0% 7%
Rate 17.40 2.91 25.45 3.78 5.06 1.49
(5.90) (0.59) (10.42) (0.79) (2.82) (0.32)
Parental Mincer Life-cycle Life-cycle Prediction Mincer Life-cycle Life-cycle Prediction Mincer Life-cycle Life-cycle Prediction
Income 7.63 7.73 10.46 10.63 2.98 3.12
(1.84) (1.92) (2.94) (2.95) (0.76) (0.85)
Labor .5% Annual Decay .5% Annual Growth .5% Annual Decay .5% Annual Growth .5% Annual Decay .5% Annual Growth
Income 7.01 7.66 9.58 10.79 2.51 2.71
(1.80) (1.90) (2.66) (3.24) (0.70) (0.75)
Crime Drop Major Crimes Halve Costs Drop Major Crimes Halve Costs Drop Major Crimes Halve Costs
4.24 5.18 7.41 7.12 2.61 2.47
(1.10) (1.22) (3.43) (2.41) (0.67) (0.66)
Health Drop All Double Value of Life Drop Al l Double Value of Life Drop All Double Value of Life
(QALYs) 6.48 8.19 9.14 11.23 2.20 3.03
(1.79) (2.13) (2.73) (3.40) (0.69) (1.04)
Note: This table displays sensitivity analyses of our baseline benefit/cost ratio calculation to the perturbations indexed in the different rows. The characteristics of the
baseline calculation are in the table header. IPW: adjusts for attrition and item non-response (see Appendix C.2 for details). Control variables: Apgar scores at ages 1 and 5
and a high-risk index (see Appendix C.8 for details on how we choose these controls). When forecasting up to ages 21 and 30, we consider all benefits and costs up to these
ages, respectively. Counterfactuals: we consider treatment vs. next best (baseline), treatment vs. stay at home, and treatment vs. alternative preschools (see Appendix F
for a discussion). Deadweight loss is the loss implied by any public expenditure (0% is no loss and 100% is one dollar loss per dollar spent). Discount rate: rate to discount
benefits to child’s age 0 (in all calculations). Parental labor income: see Appendix C.3.8 for details on the two alternative forecasts (Mincer and Life-cycle). Labor Income:
0.5 annual growth (decay) is an annual wage growth (decay) due to cohort effects. Crime: major crimes are rape and murder; half costs takes half of victimization and judi-
ciary costs. Health (QALYs): “drop all” sets the value of life equal to zero. Standard errors obtained from the empirical bootstrap distribution are in parentheses. Bolded
p-values are significant at 10% using one-sided tests. For details on the null hypothesis see Table H.1.
28
Table 5: Sensitivity Analysis for Internal Rate of Return
Pooled Males Females
Baseline 13.7% (s.e. 3.3%) 14.7% (s.e. 4.2%) 10.1% (s.e. 6.0%)
Baseline: IPW and Controls, Life-span up to predicted death, Treatment vs. Next Best, 50% Marginal tax 50% (deadweight loss), Discount rate 3%, Parental
income 0 to 21 (child’s age), Labor Income predicted from 21 to 65, All crimes (full costs), Value of life 150,000.
Specification No IPW and No Controls No IPW and No Controls No IPW and No Controls
13.2% 14.0% 13.9% 13.0% 9.6% 10.0%
(2.9%) (3.1%) (3.7%) (4.3%) (6.0%) (4.9%)
Forecast to Age 21 to Age 30 to Age 21 to Age 30 to Age 21 to Age 30
Span 8.8% 12.0% 11.8% 12.8% 10.7% 11.7%
(4.5%) (3.4%) (4.8%) (4.7%) (5.8%) (5.2%)
Counter- vs. Stay at Home vs. Alt. Presch. vs. Stay at Home vs. Alt. Presch. vs. Stay at Home vs. Alt. Presch.
factuals 9.4% 15.6% 6.0% 15.8% 13.4% 8.8%
(4.2%) (4.3%) (3.6%) (5.0%) (5.7%) (7.0%)
Deadweight- 0% 100% 0% 100% 0% 100%
loss 18.3% 11.2% 19.4% 12.1% 17.7% 7.1%
(4.7%) (3.1%) (6.2%) (3.9%) (12.4%) (4.2%)
Parental Mincer Life-cycle Life-cycle Prediction Mincer Life-cycle Life-cycle Prediction Mincer Life-cycle Life-cycle Prediction
Income 15.2% 14.5% 16.0% 14.5% 13.3% 12.3%
(4.0%) (6.4%) (5.1%) (6.4%) (8.2%) (9.9%)
Labor .5% Annual Decay .5% Annual Growth .5% Annual Decay .5% Annual Growth .5% Annual Decay .5% Annual Growth
Income 13.5% 13.8% 14.5% 14.8% 9.9% 10.3%
(3.4%) (3.2%) (4.3%) (4.1%) (6.0%) (6.0%)
Crime Drop Major Crimes Halve Costs Drop Major Crimes Halve Costs Drop Major Crimes Halve Costs
10.7% 11.6% 12.0% 11.9% 10.1% 9.9%
(4.4%) (3.8%) (5.3%) (4.9%) (6.0%) (6.0%)
Health Drop All Double Value of Life Drop Al l Double Value of Life Drop All Double Value of Life
(QALYs) 12.8% 13.5% 13.5% 14.4% 8.8% 9.3%
(4.6%) (3.6%) (5.6%) (4.6%) (6.4%) (6.1%)
Note: This table displays sensitivity analyses of our baseline internal rate of return calculation to the perturbations indexed in the different rows.
The characteristics of the baseline calculation are in the table header. IPW: adjusts for attrition and item non-response (see Appendix C.2 for de-
tails). Control variables: Apgar scores at ages 1 and 5 and a high-risk index (see Appendix C.8 for details on how we choose these controls). When
forecasting up to ages 21 and 30, we consider all benefits and costs up to these ages, respectively. Counterfactuals: we consider treatment vs. next
best (baseline), treatment vs. stay at home, and treatment vs. alternative preschools (see Appendix Ffor a discussion). Deadweight loss is the
loss implied by any public expenditure (0% is no loss and 100% is one dollar loss per dollar spent). Parental labor income: see Appendix C.3.8 for
details on the two alternative forecasts (Mincer and Life-cycle). Labor Income: 0.5 annual growth is an annual wage growth due to cohort effects;
only benefit assumes labor income is the only benefit of the program. Crime: major crimes are rape and murder; half costs takes half of victim-
ization and judiciary costs. Health (QALYs): “drop all” sets the value of life equal to zero. Bolded p-values are significant at 10% using one-sided
tests. For details on the null hypothesis see Table H.1.
29
doubling it to 100% (deadweight loss columns). Our baseline estimate of benefit/cost ratios
is based on a discount rate of 3%. Not discounting roughly doubles our benefit/cost ratios,
while they remain statistically significant using a higher discount rate of 7% (discount rate
columns).
Parental labor income effects induced by the childcare subsidy are an important compo-
nent of the benefit/cost ratio.59 We take a conservative approach in our baseline estimates
and do not account for potential shifts in parental labor income profiles due to education
and work experience subsidized by childcare (see the discussion in Section 4.3). Our base-
line estimates rely solely on parental labor income when participant children are ages 0 to
21. Alternative approaches considering the gain for the parents through age 67 generate
an additional increase in the gain due to parental labor income (see parental labor income
columns).60
Individuals in ABC/CARE could experience positive cohort effects that might (i) make
them more productive and therefore experience wage growth; (ii) experience a negative shock
such as an economic crisis and therefore experience a wage decline. Our estimates are robust
when we vary annual growth and decay rates in labor income between 0.5% and 0.5%.
This is consistent with the range of values in Lagakos et al. (2016).
We also examine the sensitivity of our estimates to (i) dropping the most costly crimes
such as murders and rapes;61 and (ii) halving the costs of victimization and judiciary costs
related to crime. The first sensitivity check is important because we do not want our esti-
mates to be based on a few exceptional crimes. The second is important because estimates
of this choice of the welfare cost and find little sensitivity.
59There is no inconsistency between the weak female treatment effects on wages at age 30 and the high
lifetime net present value treatment effect for earnings given life-cycle wage growth attributable to enhanced
inputs (education, PIAT scores, etc.).
60If labor markets operate without frictions and the marginal rate of substitution between leisure and
consumption equals the marginal wage rate, parental labor income should not be valued at the margin. The
bottom box of Figure 4shows that the benefit/cost ratio and the internal rate of return remain sizable
in magnitude and statistically significant if we omit parental income from the benefits attributed to the
program.
61Two individuals in the treatment group were convicted of rape and one individual in the control group
was convicted of murder.
30
of victimization costs are controversial because they are subjective (see Appendix E.3). Our
benefit/cost estimates are robust to these adjustments, even though crime is a major com-
ponent of it. We also examine the sensitivity with respect to our main health component:
quality-adjusted life years. This is an important component because healthier individuals
survive longer, and treatment improves health conditions. Since this component is largely
realized later in life and thus is heavily discounted, improvements in future medical care have
a negligible effect on the estimated life-cycle benefits. Dropping this component or doubling
the value of life does not have a major impact on our calculations.
Figure 4: Benefit/Cost Ratio and Internal Rate of Return when Accounting for Different
Combinations of the Main Benefits
3.4%
1.2
2.9%
0.57 5.7%
1.2
4.0%
1.3
4.6%
1.7
10.7%
2.3
6.4%
2.5
6.1%
1.7
4.5%
1.9
8.7%
2.5
8.5%
2.9
6.3%
3.1
11.4%
3.7
8.2%
3.06
13.7%
7.3
Crime
Health
Labor Income
Parental Income
Note: This figure presents all possible combinations of accounting for the benefits from the four major
categories in our analysis. The non-overlapping areas present estimates arising from a single category as the
benefit. Where multiple categories overlap, we account for benefits from each of the overlapping categories.
The other components remain constant across all calculations and are the same as in Figure 3. Health
combines QALYs (quality-adjusted life years) and health expenditure. Inference is based on non-parametric,
one-sided p-values from the empirical bootstrap distribution. We put boxes around point estimates that are
statistically significant at the 10% level.
Figure 4summarizes the results from our extensive sensitivity analyses reported in Ta-
ble H.1 of Appendix H, including the case where only one of the many streams we consider
is the source of the benefit. We calculate the estimates with all possible combinations of
31
the main benefit and cost streams. Our measures of economic efficiency remain statistically
and economically significant even after eliminating the benefits from any one of the four
main components that we monetize. Overall, our sensitivity analyses indicate that no single
category of outcomes drives the social efficiency of the program. Rather, it is the life-cycle
benefits across multiple dimensions of human development.
6 Assessing Recent Benefit-Cost Analyses
We use our analysis to examine the empirical foundations of the approach to benefit/cost
analysis taken in a prototypical study of Kline and Walters (2016), which in turn is based
on estimates used in Chetty et al. (2011).62 Although widely emulated, we show that this
approach offers imprecise approximations of benefit/cost ratios with questionable validity.
Kline and Walters (2016) use data from the Head Start Impact Study (HSIS) and report
a benefit/cost ratio between 1.50 and 1.84.63 Their analysis proceeds in three steps: (i)
calculate program treatment effects on cognitive test scores measured around age 5;64 (ii)
monetize this gain using the return to cognitive test scores measured between ages 5 and
7 in terms of net present value of labor income at age 27 using the estimates of Chetty
et al. (2011);65,66 ,67 and (iii) calculate the benefit/cost ratio based on this gain and their own
calculations of the program’s cost.68,69
To analyze how our estimates compare to those based on this method, we present a series
of estimates in the fourth column of Table 6. For purposes of comparison, the fifth column
62Examples of application of this approach include Attanasio et al. (2011), Behrman et al. (2011), and
Lafortune et al. (2018).
63HSIS is a one-year-long randomized evaluation of Head Start (Puma et al.,2010).
64They use an index based on the Peabody Picture Vocabulary and Woodcock Johnson III Tests.
65The Chetty et al. (2011) return is based on Stanford Achievement Tests.
66For this comparison exercise, we interpret the earnings estimated in Chetty et al. (2011) to be equivalent
to labor income.
67Calculations from Chetty et al. (2011) indicate that a 1 standard deviation gain in achievement scores
at age 5 implies a 13.1% increase in the net present value of labor income through age 27. This is based on
combining information from Project Star and administrative data at age 27.
68Their calculation assigns the net present value of labor income through age 27 of $385,907.17 to the
control-group participants, as estimated by Chetty et al. (2011).
69All monetary values that we provide in this section are in 2014 USD. We discount the value provided
by Chetty et al. (2011) to the age of birth of the children in our sample (first cohort).
32
Table 6: Examining the Validity of Recent Ad Hoc Methods for Forecasting in Light of the
Analysis of This Paper
(1) (2) (3) (4) (5)
Age NPV Source Component Kline and Walters (2016) Authors’ Method
Method
27 Chetty et al. (2011) Labor income 0.58 (s.e. 0.28)
ABC/CARE-calculated Labor income 0.09 (s.e. 0.04) 1.09 (s.e. 0.04)
34 ABC/CARE-calculated Labor income 0.37 (s.e. 0.04) 0.15 (s.e. 0.05)
ABC/CARE-calculated All 1.21 (s.e. 0.05) 3.20 (s.e. 1.04)
Life-cycle ABC/CARE-calculated Labor income 1.56 (s.e. 0.08) 1.55 (s.e. 0.76)
ABC/CARE-calculated All 3.80 (s.e. 0.29) 7.33 (s.e. 1.84)
Note: This table displays benefit/cost ratios based on the methodology in Kline and Walters (2016) and
based on our own methodology. Age: age at which we stop calculating the net present value. NPV Source:
source where we obtain the net present value. Component: item used to compute net present value (all
refers to the net present value of all the components). Kline and Walters (2016) Method: estimate based on
these authors’ methodology. Authors’ Method: estimates based on our methodology. Standard errors are
based on the empirical bootstrap distribution.
of Table 6shows the analogous estimates based on our samples and forecasts.
For the first estimate, we calculate the benefit/cost ratio using both the “return to
IQ” and the net present value of labor income at age 27 reported in Chetty et al. (2011).
This calculation is the same type of calculation as that used in Kline and Walters (2016).
In the second exercise, we perform a similar exercise but use our own estimate of the net
present value of labor income at age 27.70 In this exercise, the standard errors account for
variation in the return because we calculate the return in every bootstrapped re-sample. In
that sense, our approach more accurately accounts for the underlying uncertainties when
compared to the approach of Kline and Walters (2016), who do not account for estimation
error in reporting standard errors. The estimated return is smaller because our sample is
much more disadvantaged than that used by Chetty et al. (2011).
The remaining exercises in Table 6increase the age range over which we calculate the
net-present value of labor income or consider the value of all of the components we analyze
throughout the paper, in addition to labor income. The more inclusive the benefits mea-
70This allows us to compute our own “return to IQ” and impute it to the treatment-group individuals.
33
sured and the longer the horizon over which they are measured, the greater the benefit/cost
ratio. The final reported estimate, 7.3, is our baseline estimate that incorporates all of the
components across the life cycles of the subjects.
Our methodology provides a more accurate estimate of the benefits and costs of the
ABC/CARE program. We better quantify the effects of the experiment by considering the
full array of benefits over the whole life cycle. We also better approximate the uncertainty
of our estimates by considering both the sampling error in the experimental and auxiliary
samples, the forecast error due to the interpolation and extrapolation, and the sensitivity of
the estimates to externally specified parameters.
In the concluding portion of this section we consider how well researchers would do if
they aim to forecast life-cycle benefits applying our methodology but lacking access to data
through the mid-30s. For example, suppose that a researcher had access to inputs of the
production function that are experimentally shifted by the treatment but only up to age
21. Studying the performance of our forecasting procedure in this case is an additional
examination of robustness.
Researchers seeking to implement a formal forecasting methodology may face severe data
limitations. Often, data are lacking beyond early ages (like age 5). Our analysis can inform
researchers on how precise such forecasts might be if they are based only on data from earlier
segments of the life cycle. The first row of Table 6gives information on how well test scores
at ages 5-7 predict the benefit-cost ratio of the program based only on labor income through
age 27. For reasons previously discussed, this produces a poor approximation.
We present two additional analyses. First, we analyze the case where we limit Xd
k,a to
PIAT scores and years of education but only use data up to age 21 (the previous wave of
the survey). As before, we use the average PIAT achievement score from ages 5 to 7. An
analysis based on these two measures only requires data through the age at which education
is completed—generally long before age 30. Second, we conduct an analysis where we limit
Xd
k,a to contain only lagged labor income at age 21. Researchers often have access to a test
34
score as well as a measure of schooling or may only have a measure of labor income early in
life with which they could initialize a forecast of autoregressive labor income. For both of
these cases, we produce forecasts for the entire life cycle of labor income.
In the first analysis, we use PIAT scores and years of education to predict income from
age 21 to age 65 (assumed age of retirement). In the second analysis, we use an autoregressive
model of earnings—see, e.g. Meghir and Pistaferri (2011)—to predict labor income from age
21 to age 65. As in our baseline forecasting procedure, we are able to initialize this forecast in
the experimental sample because we observe labor income at age 21.71 We otherwise follow
the steps in Section 3.2 and re-estimate the forecasting functions in the non-experimental
sample as researchers would do if they were to forecast with these subsets of predictor
variables. We then use the estimated functions to forecast in the experimental sample.
Figure 5shows the results from analyses by displaying labor income forecasts analogous
to Figure 2for the two sets of predictor variables. We do not vary the construction of the
non-experimental samples used for forecasting or the background variables that we include.
The forecasts show that PIAT and years of education used together provide a forecast that is
imprecise but in the ballpark of the baseline forecast in Figure 2. Lagged income alone does
not suffice to accurately forecast treatment-control life-cycle differences. This makes sense
because we initialize the forecast at age 21, where the treatment-control difference in labor
income is not informative because many of the subjects—especially those in treatment—are
still in school. Thus, while a forecast based on a short-term test scores does not produce an
accurate forecast, a short-term test score together with education is close to being on the
mark.
71We do not present results based solely on a short-term test score as the PIAT because the results
are extremely imprecise, which is consistent with the results in Table 4and warns practitioners against
forecasting based on a short-term test score although this is commonly done (e.g. Kline and Walters,2016).
Our test scores are measured later than theirs (at ages 3 to 4) and are likely more precise.
35
Figure 5: Forecasted Labor Income Profiles for ABC/CARE Participants
(a) Males, Based on PIAT and Education
20
30
40
50
60
70
Labor Income (1000s 2014 USD)
25 30 35 40 45 50 55 60 65
Age
Treatment Control +/− s.e.
(b) Males, Based on Lagged Labor Income
10
15
20
25
30
Labor Income (1000s 2014 USD)
25 30 35 40 45 50 55 60 65
Age
Treatment Control +/− s.e.
(c) Females, Based on PIAT and Education
10
20
30
40
Labor Income (1000s 2014 USD)
25 30 35 40 45 50 55 60 65
Age
Treatment Control +/− s.e.
(d) Females, Based on Lagged Labor Income
0
5
10
15
20
Labor Income (1000s 2014 USD)
25 30 35 40 45 50 55 60 65
Age
Treatment Control +/− s.e.
Note: Panels (a) and (b) displays the forecast life-cycle labor income profiles for ABC/CARE males by treatment status, analogous to the forecasts
in Figure 2but using either PIAT (5-7) and years of education as predictors or lagged labor income. Figure 2uses PIAT (5-7), years of education as
predictors, and lagged labor income. Panels (c) and (d) are analogous versions of (a) and (b) for women.
36
7 Summary
This paper presents a template for constructing economically interpretable summaries of the
multiple treatment effects generated from a randomized evaluation of a high-quality, widely
emulated early childhood program with follow-up through the mid 30s. We go beyond the
usual practice of reporting batteries of treatment effects. We report the costs and monetize
the treatments across numerous domains. We estimate the tax-adjusted internal rate of
return and the benefit/cost ratio of the program to assess the social efficiency of the program.
We use auxiliary information and structural economic models to guide monetization of
treatment effects and to extrapolate the measured benefits and costs to the full life cycles
of participants. We account for model estimation and forecast error and conduct extensive
sensitivity analyses of our estimates to alternative assumptions and methodologies. Under a
variety of plausible assumptions, we estimate that the tax-adjusted internal rate of return of
the program ranges from 8% to 18.3%. These estimates demonstrate the social profitability
of ABC/CARE. We show that forecasts from a robust non-parametric matching strategy are
close to those from our structural approach.
We conclude with a cautionary note. The program we study was targeted to a relatively
homogenous, disadvantaged, and predominately African-American population in a university
town in North Carolina. Generalization of our findings to other populations should proceed
with caution.72 In particular, there is no basis for using this study to argue for universal
application of ABC/CARE across all socio-economic groups. However, the essential features
of the ABC/CARE approach are currently in wide use in a variety of early childhood inter-
vention programs that target disadvantaged children. In this sense, our analysis has lessons
of general interest for disadvantaged populations. Our study indicates what is possible and
that the possibilities are substantial.
72Especially problematic are forecasts over the supports of our samples.
37
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... (2010) estimate benefit/cost ratios for Perry that range between 6:1 and nearly 9:1, with benefits driven in roughly equal measure by increases in earnings and reduced crime. In the case of Abecedarian, García et al. (2020) estimate benefit/cost ratios exceeding 6:1, with more than two-thirds of the benefits driven by crime reductions and the remainder reflecting differences in adult health and the labor income of participants and their parents (the five years of full-time childcare enabled parents to establish and maintain more continuous and higher-paying careers). ...
... It is difficult to imagine that the longer-term Boston impacts were not fueled by some kind of short-term improvements, although it is quite possible that the "secret sauce" isn't captured by the administrative data available to evaluators. Attempts are currently underway to develop prediction models that can translate short-run impacts into longer-run projections (Athey et al. 2019, García et al. 2020), but mere prediction is a poor substitute for a conceptual understanding and empirical confirmation of the processes by which recent cohorts of disadvantaged children may achieve upward mobility through targeted early childhood education programs. ...
... At the same time, the literature on specific programs targeting disadvantaged children is mixed at best, with some early studies pointing to large and long-lasting benefits, but most recent studies showing null to negative impacts several years after the end of the programs. To understand this apparent paradox, we need to recognize the challenges of drawing lessons from social experiments when control-group participants can access other, close-substitute programs or a higher-quality home environment(Heckman et al., 2020; Kline and Walters, 2018). In contrast to early Head Start studies, recent program evaluations like the Head Start Impact Study have shown modest initial effects that quickly faded out, which is consistent with the idea that the growth of center-based substitutes has reduced the apparent impacts of the program. ...
... Effect sizes (Hedges' g) were small or negligible, all with confidence intervals including zero. Some level of attrition occurred during the experimental period, mostly due to health-related reasons or to family relocation (see appendix in García et al., 2020). Descriptive statistics of baseline family characteristics were Notes. ...
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Mechanisms translating initial impacts of early childhood education (ECE) programs into longer-term effects are poorly understood. As with astrophysics’ “dark matter” hypothesis, unobserved mediated effects are integral to our understanding of the pathways underlying ECE programs’ long-term impacts. Leveraging two sets of panel data (Study 1: N = 107; 97% African American, 3% White; 52% girls. Study 2: N = 1,251; 44% Black, 25% Hispanic, 31% White; 50% girls), ECE programs’ patterns of indirect effects on completed schooling were examined via bundled mediators measured at age 8 or 10, 12, and 15. We found that, accounting for up to 50% of the impact, patterns of indirect effects in both studies revealed stable patterns of direct effects, indicating that impacts on unmeasured mediators are present throughout the duration of the period after the end of ECE programs and before longer-term outcomes are observed.
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This paper considers the problem of forecasting a collection of short time series using cross‐sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross‐sectional information to transform the unit‐specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that equals the population distribution of the random coefficients. We show that the risk of a predictor based on a nonparametric kernel estimate of the Tweedie correction is asymptotically equivalent to the risk of a predictor that treats the correlated random effects distribution as known (ratio optimality). Our empirical Bayes predictor performs well compared to various competitors in a Monte Carlo study. In an empirical application, we use the predictor to forecast revenues for a large panel of bank holding companies and compare forecasts that condition on actual and severely adverse macroeconomic conditions.
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We study the impact of post- 1990 school finance reforms, during the so- called "adequacy" era, on absolute and relative spending and achievement in low- income school districts. Using an event study research design that exploits the apparent randomness of reform timing, we show that reforms lead to sharp, immediate, and sustained increases in spending in low- income school districts. Using representative samples from the National Assessment of Educational Progress, we find that reforms cause increases in the achievement of students in these districts, phasing in gradually over the years following the reform. The implied effect of school resources on educational achievement is large.
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This paper documents how life cycle wage growth varies across countries. We harmonize repeated cross-sectional surveys from a set of countries of all income levels and then measure how wages rise with potential experience. Our main finding is that experience-wage profiles are on average twice as steep in rich countries as in poor countries. In addition, more educated workers have steeper profiles than the less educated; this accounts for around one-third of cross-country differences in aggregate profiles. Our findings are consistent with theories in which workers in poor countries accumulate less human capital or face greater search frictions over the life cycle.
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This paper empirically evaluates the cost-effectiveness of Head Start, the largest early-childhood education program in the United States. Using data from the Head Start Impact Study (HSIS), we show that Head Start draws roughly a third of its participants from competing preschool programs, many of which receive public funds. Accounting for the public savings associated with reduced enrollment in other subsidized preschools substantially increases estimates of the program's rate of return. To parse Head Start's test score impacts relative to home care and competing preschools, we selection correct test scores in each care environment using excluded interactions between experimental offer status and household characteristics. We find that Head Start's effects are greater for children who would not otherwise attend preschool and for children that are less likely to participate in the program.
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In Project STAR, 11,571 students in Tennessee and their teachers were randomly assigned to classrooms within their schools from kindergarten to third grade. This article evaluates the long-term impacts of STAR by linking the experimental data to administrative records. We first demonstrate that kindergarten test scores are highly correlated with outcomes such as earnings at age 27, college attendance, home ownership, and retirement savings. We then document four sets of experimental impacts. First, students in small classes are significantly more likely to attend college and exhibit improvements on other outcomes. Class size does not have a significant effect on earnings at age 27, but this effect is imprecisely estimated. Second, students who had a more experienced teacher in kindergarten have higher earnings. Third, an analysis of variance reveals significant classroom effects on earnings. Students who were randomly assigned to higher quality classrooms in grades K-3-as measured by classmates' end-of-class test scores-have higher earnings, college attendance rates, and other outcomes. Finally, the effects of class quality fade out on test scores in later grades, but gains in noncognitive measures persist.