The Review of Economics and Statistics

VOL. CIV

JANUARY 2022

NUMBER 1

SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS

N. Meltem Daysal, Marianne Simonsen, Mircea Trandaﬁr, and Sanni Breining*

Abstract—We investigate the effects of early-life medical treatments on
the treated children and their families. We use a regression discontinuity
design that exploits changes in medical treatments across the very low
birth weight (VLBW) cutoff. Using administrative data from Denmark, we
establish that VLBW children have better health and higher test scores. We
ﬁnd that these beneﬁts spill over to other family members: mothers enjoy
better mental health, and siblings have higher test scores. Maternal mental
health improvements seem to be driven by better focal child health and
sibling spillovers by improved interactions within the family and parental
compensating behavior.

Introduction

AN extensive body of research in economics suggests

that early-life conditions have long-lasting impacts on
individual well-being, including health, educational attain-
ment, and labor market outcomes (Almond & Currie, 2011;
Almond, Currie, & Duque, 2018). Growing evidence also in-
dicates that disabled children affect the socioeconomic out-
comes of other family members, such as parental labor supply
(Gunnsteinsson & Steingrimsdottir, 2019; Deshpande, 2016;
Powers, 2003), health (Burton, Lethbridge, & Phipps, 2008),
and marital stability (Kvist, Nielsen, & Simonsen, 2013) and
sibling academic achievement (Black et al., 2017). A natural
question then is whether, and by how much, interventions
that improve child health also affect these spillovers in the
family. In this paper, we address this question by investigat-
ing the spillover effects of early-life medical treatments on
the socioeconomic outcomes of other family members, fo-
cusing on the speciﬁc case of treatments provided to very
low birth weight (VLBW) children—those with birth weight
below 1,500 grams.

Received for publication May 15, 2019. Revision accepted for publication

June 3, 2020. Editor: Brian A. Jacob.

∗Daysal: University of Copenhagen, CEBI, and IZA; Simonsen: Aarhus
University and IZA; Trandaﬁr: University of Southern Denmark and IZA;
Breining: Ramboll Management Consulting.

Doug Almond, Prashant Bharadwaj, Aimee Chin, Gordon Dahl, Nabanita
Datta Gupta, Joe Doyle, Mark Duggan, Bill Evans, David Figlio, Kristiina
Huttunen, Katrine Løken, Bhash Mazumder, and seminar participants at
Bergen, Concordia, Gothenburg, Houston, IZA, Mainz, Michigan, Tilburg,
VIVE, York, Zurich, Second SDU Workshop on Applied Microeconomics,
SFI-Lund Workshop on Health Economics, Essen Health Conference, and
Copenhagen Education Network provided helpful comments and discus-
sions. The activities of CEBI are ﬁnanced by the Danish National Research
Foundation, grant DNRF134. S.B. and M.S. gratefully acknowledge ﬁnan-
cial support from CIRRAU. The authors bear sole responsibility for the
content of this paper.

A supplemental appendix is available online at https://doi.org/10.1162/

rest_a_00982.

Medical interventions targeting VLBW children constitute
an ideal setting to study spillover effects for several reasons.
First, they have been found to substantially improve the health
(Cutler & Meara, 1998; Almond et al., 2010; Bharadwaj,
Løken, & Neilson, 2013) as well as the academic achievement
(Bharadwaj et al., 2013) of treated children. Second, although
VLBW children represent a small share of all births, they
account for a substantial portion of newborn health care ex-
penditures. For example, VLBW babies in the United States
represent around 1.5% of all births, but the neonatal intensive
care unit costs associated with these babies alone account for
30% of all newborn health care costs (Johnson et al., 2013).
Finally, focusing on treatments provided to VLBW children
allows us to overcome identiﬁcation challenges arising from
potentially correlated unobservables within the family, such
as shared genetic factors that affect both the receipt of medi-
cal treatments by targeted children and the outcomes of other
family members. Speciﬁcally, we use a regression discontinu-
ity design that exploits changes in medical treatments across
the very low birth weight threshold to address the nonran-
dom assignment of medical treatments (Almond et al., 2010;
Bharadwaj et al., 2013). We restrict our analysis to the fami-
lies of focal children (deﬁned as the children with birth weight
in a small window around 1,500 grams) with gestational age
above 32 weeks because the medical guidelines prescribe ad-
ditional medical treatments to children with gestational age
below 32 weeks regardless of their birth weight.

Using population-level data from Denmark, we ﬁrst repli-
cate the ﬁnding in the previous literature that VLBW children
are signiﬁcantly less likely to die within the ﬁrst year of life
relative to newborns with slightly higher birth weight. We
also conﬁrm the ﬁnding that these children have higher math
and language test scores in ninth grade. Our estimates are re-
markably comparable in magnitude to the reductions in infant
mortality and improvements in test scores from the previous
studies using data from the United States, Chile, and Norway
(Almond et al., 2010; Bharadwaj et al., 2013). We add to these
studies by expanding the outcome set to include a range of
common childhood disabilities (intellectual disability, atten-
tion deﬁcit hyperactivity disorder, behavioral and emotional
disorders, cerebral palsy, and epilepsy), as well as by inves-
tigating effects on hospital and emergency room (ER) visits
up to ﬁfteen years after birth. Our ﬁndings suggest that chil-
dren slightly below the 1,500 gram threshold have the same

The Review of Economics and Statistics, January 2022, 104(1): 1–16
© 2020 The President and Fellows of Harvard College and the Massachusetts Institute of Technology
https://doi.org/10.1162/rest_a_00982

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THE REVIEW OF ECONOMICS AND STATISTICS

likelihood of a childhood disability by age 10 as compared to
children slightly above the threshold. While there is no im-
pact on child disability, the medical treatments provided to
VLBW children seem to result in better health during school
years as proxied by reduced hospital and ER contacts.

We next turn to investigating the spillover effects of early-
life medical treatments on other family members. We exam-
ine the effects on siblings’ health (hospital and ER contacts)
and academic achievement (ninth-grade math and language
test scores, enrollment beyond compulsory education). For
parents, we focus on labor market outcomes (employment
status, number of days worked), annual gross income, and
mental health as proxied by antidepressant use. Where possi-
ble, we present the short-term effects (one to ﬁve years after
the birth of the focal child) separately from the long-term
effects (six to ﬁfteen years after the birth of the focal child).
We try to address the potential multiple inference issues re-
sulting from the large number of outcomes we study in two
ways. First, we create indices summarizing the relevant vari-
ables in each outcome domain and time horizon, standard-
ized at the level of the birth cohort of the focal child. Second,
we adjust the p-values to take into account the multiple in-
ference problem using a procedure proposed by Anderson
(2008).

Our results suggest that early-life medical interventions
have no impact on parental behavior that affects total house-
hold resources: we do not observe discontinuous changes
across the VLBW cutoff in parental labor force participation
or income in either the short run or the long run. This is per-
haps not surprising given that Denmark has one of the most
generous social safety nets in the world, including 52 weeks
of parental leave, generous cash payments to families with
children, heavily subsidized child care, and free and universal
health care. Our results instead suggest that early-life med-
ical interventions may improve intrahousehold interactions.
In particular, we ﬁnd that the mothers of VLBW focal chil-
dren are signiﬁcantly less likely to use antidepressants soon
after the focal child is born and that these mental health gains
diminish as the focal child ages. We provide evidence sug-
gesting that both focal child survival and improved focal child
health are important drivers of these mental health gains.

Our results also suggest that early-life medical treatments
have substantial positive spillovers on sibling test scores.
We ﬁnd that the siblings of VLBW newborns have ninth-
grade test scores that are on average 0.375 standard devia-
tion higher. Our results further highlight that test score gains
are observed across skill domains: language and math test
scores are higher by 0.386 and 0.255 standard deviations, re-
spectively. These results are economically large, correspond-
ing to a reduction of 33% to 69% in the test score gap be-
tween the children in the top and bottom 10% of the income
distribution. We show that these sibling spillovers are un-
likely to be driven by correlated health shocks within the
family that would result in siblings’ exposure to early-life
medical treatments themselves or by differential focal child
survival at the cutoff. Instead, our evidence points to im-

proved intrafamily interactions as a potential channel behind
the sibling spillovers.

Finally, we provide indirect evidence on the role of parental
reallocation of resources within the family. If the production
of human capital exhibits dynamic complementarities, then
parental investments have higher returns for children with
high initial endowment than for children with low initial en-
dowment. If parents engage in compensating behavior, our re-
sults suggest that the siblings of VLBW focal children should
receive more parental resources than the siblings of focal chil-
dren with birth weight slightly above 1,500 grams. We ﬁnd
that the siblings of VLBW focal children experience higher
test score gains if they have high initial endowments them-
selves (as proxied by their birth weight), a pattern consistent
with compensating behavior by their parents, especially in
the presence of dynamic complementarities in human capital
accumulation.

Our paper makes three contributions. First, we add to the
studies that document spillover effects of child health. The
majority of this research examines the effects of having a
disabled child on parental outcomes, such as labor supply
(Gunnsteinsson & Steingrimsdottir, 2019; Deshpande, 2016;
Powers, 2003) and health (Burton et al., 2008). One notable
exception is Black et al. (2017), who investigate spillovers to
siblings and ﬁnd that the second child in a family has worse
test scores when the third child is disabled.1 Our paper doc-
uments that improvements in child health that do not operate
through child disability status may still result in signiﬁcant
sibling spillovers.

Second, we contribute to the economic literature on the
returns to early-life medical interventions. These studies al-
most exclusively investigate the effects on treated children
(Cutler & Meara, 1998; Chay, Guryan, & Mazumder, 2009;
Field, Robles, & Torero, 2009; Almond et al., 2010; Bharad-
waj et al., 2013; Daysal, Trandaﬁr, & van Ewijk 2015, 2019;
Hjort, Sølvsten, & Wüst, 2017; Bütikofer, Løken, & Kjell Sal-
vanes, 2019).2 The main insight that emerges from our work
is that medical treatments may have far-reaching effects on
family well-being through spillovers even in developed coun-
tries with generous welfare systems.

Third, our results speak to the economic literature that re-
lies on sibling ﬁxed-effects models to account for unobserved
heterogeneity across households in estimating the effects of
various exposures. To the extent that siblings have spillovers

1There is also evidence on sibling spillovers more generally. For example,
Dahl, Løken, and Mogstad (2014) show that take-up of family-friendly poli-
cies affects siblings’ subsequent use of these policies, Joensen and Nielsen
(2018) and Nicoletti and Rabe (2019) ﬁnd that siblings’ education choices
and test scores causally affect younger siblings’ academic outcomes, and
Altonji, Cattan, and Ware (2017) and Heissel (forthcoming) document
that older siblings’ risky behavior have an impact on younger siblings’
outcomes.

2One exception is Adhvaryu and Nyshadham (2016), who examine the
effects of a large-scale iodine supplementation program in Tanzania on
parents’ investments in children and ﬁnd that the siblings of treated children
were more likely to be immunized.

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SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS

on each other, sibling ﬁxed-effects models would not estimate
the true treatment effects.

Our results are also pertinent to the ongoing discussions
about the cost effectiveness of early-life medical treatments.
During the past few decades, medical spending for the very
young increased substantially faster than spending for the
average individual. For example, US annual spending on in-
dividuals aged 1 to 64 increased by 4.7% between 1960 and
1990, while per capita spending on infants under 1 year old
increased by 9.8% per year (Cutler & Meara, 1998). Techno-
logical innovations are widely considered the main driver of
this medical cost growth in general and in the speciﬁc case
of early-life treatments (Newhouse, 1992; Cutler & Meara,
1998). As medical expenditures keep increasing, understand-
ing the beneﬁts of early-life medical interventions becomes
even more important. Our ﬁnding that medical treatments for
VLBW children have positive externalities on other family
members indicates that conventional calculations understate
the net beneﬁts of these treatments.

II.

Institutional Background

The majority of Danish health care services, including
birth-related procedures, are free of charge, and all residents
have equal access (Danish Ministry of Health and Preven-
tion, 2008). The ﬁrst European neonatal intensive care unit
was established in 1965 at Rigshospitalet in Denmark, and
the use of early-life medical technologies has since followed
the international development (Mathiasen et al., 2008). Dan-
ish neonatal medicine textbooks pay particular attention to
VLBW children (those weighing less than 1,500 grams, re-
gardless of gestational age) and very premature newborns
(those with a gestational age less than 32 weeks, regard-
less of birth weight). These birth weight and gestational age
classiﬁcations are frequently found in medical research pa-
pers based on Danish data where the focus is often on their
higher mortality rates (Thomsen et al., 1991; Hertz, Holm, &
Haahr, 1994). Medical handbooks suggest courses of treat-
ment based on either birth weight or gestational age (Schiøtz
& Skovby, 2001). Speciﬁc recommendations in terms of nu-
trition and vitamin supplements exist for VLBW children
(Peitersen & Arrøe, 1991). In addition, papers indicate that
children below 1,500 grams or born before 32 weeks of ges-
tation are more likely to receive additional treatments such as
cranial ultrasound (Greisen et al., 1986), antibiotics (Topp,
Uldall, & Greisen, 2001), prophylactic treatment with nasal
continuous positive airway pressure, prophylactic surfactant
treatment and high priority of breast feeding, and use of the
kangaroo method (Jacobsen et al., 1993; Verder et al., 1994;
Verder, 2007; Mathiasen et al., 2008).

Anecdotal evidence from hospital and regional speciﬁc
notes also outline special services that are provided to fami-
lies with children below 1,500 grams or below 32 weeks of
gestational age. These services include referrals to a physio-
therapist who guides and instructs parents on how to stimulate
the development of the child and on various baby exercises.

It is also mentioned that all children below 1,500 grams or
below 32 weeks of gestational age are routinely checked one
to two months after discharge and again when they are 5
months, 1 year, and 2 years old.3

III. Empirical Strategy

Identiﬁcation of the (spillover) effects of early-life health
interventions is complicated by the nonrandom assignment
of medical treatments. In particular, there may be unobserved
determinants of the outcomes of other family members that
are correlated with the receipt of medical treatments by tar-
geted children, such as shared genetic factors. In order to
address this endogeneity, we follow Almond et al. (2010)
and Bharadwaj et al. (2013) and use a regression discontinu-
ity design that exploits changes in medical treatments across
the VLBW threshold. Speciﬁcally, we estimate
(cid:3)

(cid:2)

yi jt = f

bw j − 1500

+ βVLBWj + δXi jt + (cid:2)i jt ,

(1)

where yi jt is an outcome of family member i of focal child j at
time t after the birth of the focal child, bw j is the birth weight
of focal child j, f (·) is a ﬁrst-degree polynomial in distance
to the VLBW cutoff that is allowed to differ on both sides
of the cutoff, VLBWj is an indicator for focal child j having
very low birth weight (bw j < 1500), and Xi jt is a vector of covariates.4 We start our analysis by replicating and extending the ﬁndings in the previous literature on the impact of medical technologies on focal children themselves: we set i = j in equation (1). We then turn to effects on other family mem- bers. The parameter of interest, β, is an intention-to-treat esti- mate of the effects that additional medical treatments received by VLBW newborns may have on themselves and on their families. Our baseline regressions use a triangular kernel that assigns decreasing weights to observations further away from the cut- off. We choose our bandwidth based on a rule-of-thumb pro- cedure suggested by Calonico, Cattaneo, and Titiunik (2014), which yields optimal bandwidths between 118 grams and 251 grams with an average of 189 grams (see appendix table A2). We choose 200 grams as our preferred bandwidth to ensure that newborns on either side of the VLBW cutoff are nearly identical. This bandwidth is the same as the one used by Bharadwaj et al. (2013) for Norwegian data and reﬂects the relatively small number of observations available in Denmark and Norway. The vector of covariates, Xi jt , includes indica- tors for heaping at multiples of 50 grams in all speciﬁcations unless mentioned otherwise (Barreca et al., 2011).5 Some 3Unfortunately, our data do not include any information on speciﬁc early- life treatments. 4An alternative strategy would rely on the 32-week cutoff for gestational age. This strategy is infeasible with our data because gestational age is recorded in full weeks. 5Given that birth weight is measured in grams, heaping is generally sym- metric around our cutoff point, and hence our strategy is less likely to be l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 4 THE REVIEW OF ECONOMICS AND STATISTICS of our robustness checks additionally control for child and family characteristics (see section IV). We are interested in exploring a variety of outcomes across multiple domains for several family members. This gives rise to a multiple inference problem: we may estimate statistically signiﬁcant effects of the VLBW status on some outcomes simply by chance. We address this issue in two ways fol- lowing the recommendations of Anderson (2008). First, we create indices for each family member and each domain (see section IV and appendix table A1 for details). While this pro- cedure helps with reducing the dimensionality, we are still left with a relatively large number of indices. Hence, as a second step, we adjust the p-values to take into account the multiple inference problem based on a procedure proposed by Anderson (2008).6 Finally, we construct robust conﬁdence intervals follow- ing Calonico et al. (2014, 2019). These conﬁdence intervals are centered on bias-corrected estimates instead of the usual (conventional) estimates and use the standard errors from a speciﬁcation with a higher-order polynomial in the running variable, which in our case is a second-degree polynomial. Therefore, in addition to the coefﬁcient estimates and their robust standard errors, we also report the bias-corrected es- timates that are used to construct these robust conﬁdence intervals. IV. Data Our key data set is the Birth Register, which includes in- formation about the universe of births in Denmark starting from 1970. For each child, the data include information on the exact date of birth, gender, and plurality. Birth weight is recorded in 250 gram intervals between 1973 and 1978, in 10 gram intervals in the period 1979 and 1990, and at the gram level since 1991. Gestational age was added beginning in 1982. Using parental identiﬁers, we are able to link chil- dren to their parents and siblings and determine parity. We also link these data to other register data that provide infor- mation on both parents and children regarding demographic characteristics, labor market outcomes, health outcomes, and academic achievement. We ﬁrst use data on focal children to investigate whether early-life medical interventions have an impact on focal child health and academic achievement. Our mortality index in- cludes two previously studied short-term outcomes, 28-day and 1-year mortality. In addition, we construct two health in- dices. Our short-term health index uses indicators for being hospitalized during each year between the ages of 1 and 5, affected by the criticism raised by Barreca et al. (2011). Indeed, we show in section VC that our results are robust to the exclusion of these controls. 6The false discovery rate (FDR) is the average fraction of true null hy- potheses among the rejected hypotheses, and the q-value is the level of the FDR desired by the researcher (Benjamini & Hochberg, 1995; Benjamini, Krieger, & Yekutieli, 2006). We report the lowest q-value, that is, the lowest sharpened FDR, at which an estimated effect is still signiﬁcant (see Ander- son, 2008, for details). This is conceptually similar to a p-value in that it represents the probability of a type 1 error. while our long-term health index uses separate indicators for being hospitalized and for having an ER visit during each year between the ages of 6 and 15. Given the previous medical lit- erature linking very low birth weight to child developmental disabilities (Schieve et al., 2016), we also construct a disabil- ity index based on separate indicators for being diagnosed by age 10 with one of the following conditions: intellectual dis- ability, attention deﬁcit hyperactivity disorder, behavioral and emotional disorders, cerebral palsy, and epilepsy. Our ﬁrst measure of human capital accumulation is a test score index based on course-speciﬁc test scores from ninth-grade qual- ifying exams in reading and math, available between 2001 and 2010.7 Finally, we create an index of enrollment beyond compulsory education (nine years during our sample period) using indicators for enrollment in high school or vocational school at age 18, enrollment in an academic track at age 18, enrollment in higher education at age 24, and enrollment in a university at age 24. We then turn to spillover effects on the family. The out- comes for siblings mirror the outcomes for focal children with the exception of mortality and disability diagnosis. In particular, we create a short-term health index using indica- tors for being hospitalized during each year when the focal child is 1 to 5 years old and a long-term health index using indicators for being hospitalized or having an ER visit dur- ing each year when the focal child is 6 to 15 years old. We construct a test-score index based on ninth-grade math and language test scores and an index of enrollment beyond com- pulsory education based on siblings’ enrollment in (higher) education at ages 18 and 24. For parents, we focus on mental health and labor market outcomes separately for mothers and fathers. Our two men- tal health indices are based on indicators for having ﬁlled at least one antidepressant prescription during each year when the focal child is 2 to 5 and 6 to 15 years old.8 For labor mar- ket outcomes, we study effects on employment and income. We create two employment indices for each parent based on the number of days worked, as well as indicators for being employed in each calendar year when the focal child is 1 to 5 and 6 to 15 years old. We similarly create income indices based on the log real annual gross income over the same range of focal child age. We construct each index in two steps. We ﬁrst standardize each variable by the birth cohort of the focal child such that it has a mean of 0 and a standard deviation of 1. Next, we take the average of the standardized variables that make up the index, and because some of these variables are correlated, we restandardize the index at the level of the birth cohort of the focal child. Appendix table A1 lists each variable in- cluded in the construction of each index. We provide results 7All exams are graded by the teacher and by an external examiner, who can overrule the teacher. 8The prescription drug register begins recording data from 1995 so we can construct measures of antidepressant use only starting from focal child at age 2. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS 5 using selected outcomes or alternative aggregation strategies in appendix tables A6 to A8. Some of our checks use focal child characteristics (gesta- tional age, indicators for gender, parity, plurality, birth year, and birth region), maternal characteristics at the birth of the focal child (age, years of education, indicators for marital status and immigrant status), and sibling characteristics (ges- tational age, birth weight, and indicators for gender, parity, plurality, and birth year).9 We deﬁne the analysis sample in several steps (see ap- pendix table A3). First, we select focal children born between 1982 and 1993.10 We then exclude observations for which either birth weight or gestational age is missing and restrict the sample to those with birth weight within 1,300 to 1,700 grams. Given that we are particularly interested in sibling spillovers, we further restrict the sample to the 3,677 focal children with siblings.11 As discussed in section II, newborns with a gestational age of less than 32 weeks are always cov- ered by medical guidelines for receiving additional medical interventions, regardless of their VLBW classiﬁcation. Since there is no discontinuity in eligibility for medical treatments (Bharadwaj et al., 2013), we do not expect to observe a dis- continuity in focal child outcomes or the outcomes of their family members. Therefore, we use the 1,521 focal children with gestational age below 32 weeks and their families only in a falsiﬁcation check, and from here on, we focus exclu- sively on the 2,156 focal children with gestational age of at least 32 weeks (hereafter the FC sample) and their families. Parents are identiﬁed from the birth register. Our data in- clude parental identiﬁers for all the mothers. If the mother is married to a man at the time of birth, authorities automatically register the husband as the biological father. When the mother is unmarried, the biological father needs to claim paternity of the child. Parental identiﬁers for the fathers are missing for only forty of the focal children in the FC sample. Thus, the parent sample virtually overlaps with the FC sample. Siblings are deﬁned as children born to the same mother from different pregnancies. We include both older and younger siblings because the receipt of additional medical treatments around the VLBW cutoff does not seem to have an impact on future fertility decisions.12 We focus on sib- 9Maternal education is missing for 315 observations corresponding to 154 mothers. We replace these with the median number of years of education by birth cohort and include an indicator for imputed maternal education. Our results (available on request) are robust to excluding these observations or the indicator for missing mother’s education. 10Our sample includes focal children born after 1982, when both birth weight and gestational age are recorded. We include cohorts born before 1994 for two reasons. First, this allows us to study human capital accumu- lation information for all cohorts, which makes it possible to compare the effects of early-life health interventions on the focal children in our context to those in previous studies. Second, evidence suggests that medical guide- lines around the VLBW cutoff are less likely to be binding in recent years (see, for example, note 20 in Bharadwaj et al., 2013). 11The results for the sample, including the 922 focal children who have no siblings born within our sample period, are quantitatively and qualitatively similar (available on request). 12A focal child may have more than one sibling. We treat each sibling- focal child pair as an independent observation. This is not a concern for lings who are old enough for us to observe their academic outcomes. Tests are administered when children are around 15 to 16 years old, so data on test scores are available for cohorts of siblings born between 1986 and 1997. Enrollment outcomes are measured at ages 18 and 24 and include siblings born between 1970 and 1993. The resulting sample includes 3,311 siblings of focal children with gestational age of at least 32 weeks (the sibling sample).13 V. Results A. Tests of the Validity of the Regression Discontinuity Design The validity of an RD design rests on the assumption that individuals do not have precise control over the assignment variable. Since women cannot precisely predict the birth weight of their children, the variation in birth weight near the VLBW cutoff is plausibly as good as random (Almond et al., 2010; Bharadwaj et al., 2013). The key identiﬁcation assumption of the RD design could be violated if physicians systematically misreport birth weight, especially in the pres- ence of ﬁnancial incentives for manipulation (Shigeoka & Fushimi, 2014; Jürges & Köberlein, 2015). In order to test this assumption, we examine the frequency of births by birth weight within our bandwidth around the cutoff. Appendix ﬁgure A1 plots the distribution of observa- tions in the FC/parent sample and in the sibling sample by birth weight of the focal child. We use 10 gram bins because birth weight is reported in 10 gram intervals for most of our sample period.14 Similar to previous studies (Almond et al., 2010; Bharadwaj et al., 2013), we observe reporting heaps at multiples of 50 and 100 grams but there is no evidence of irregular heaping around the VLBW cutoff. We check this more formally by estimating a local-linear regression similar to our baseline model, using the number of births in each birth our identiﬁcation because parity and total family size are relatively smooth across the cutoff in the FC sample. In addition, we ﬁnd no evidence of a discontinuity at the cutoff when we examine the probability of having a younger sibling, the number of younger siblings, and the birth spacing be- tween focal children and younger siblings (see table 1). Finally, our results are qualitatively similar when we cluster the standard errors at the mother level in order to correct for the bias in standard errors caused by the poten- tial correlation in the error terms between pairs of siblings from the same household (available on request). 13Test scores are missing for approximately 20% of the eligible cohorts in the sibling sample. This is because children can be exempted from taking the test if, for example, they have a documented disability. This could be a concern if medical treatments provided to focal children have an impact on the test taking of siblings. We ﬁnd no discontinuity at the cutoff in the probability that a sibling takes the language test (estimate 0.029, bias- corrected estimate [b.c.e.] 0.051, s.e. 0.070, mean 0.808) or the math test (estimate 0.048, b.c.e. 0.069, s.e. 0.068, mean 0.804), or in the age when they take the test (estimate −0.139, b.c.e. −0.106, s.e. 0.120, mean 16.035). Enrollment information is available for all eligible cohorts. 14Some degree of rounded running variables is common across studies relying on regression discontinuity designs; a prominent example is to use age in quarters (Card, Dobkin, & Maestas, 2008) or years (Oreopoulos, 2006). While rounding can, of course, cause discretization bias (Dong, 2015), we believe this is a minor issue in our case with access to relatively ﬁne-grained data. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 6 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 1.—DISTRIBUTION OF COVARIATES ACROSS THE VLBW CUTOFF A. Focal child characteristics (N = 2,156) Boy Birth order Multiple birth Gestational age Family size Has younger siblings Number of younger siblings B. Sibling characteristics (N = 3,311) Estimate (1) −0.028 0.229 0.065 −0.353** 0.054 −0.066 −0.189 Boy Birth order Multiple birth Gestational age Birth weight VLBW Age difference–older sibling Age difference–younger sibling C. Mother’s characteristics at the birth of the focal child (N = 2,156) −0.003 −0.115 0.026 −0.319 −128.494* 0.012 −0.119 −0.400 Age Education (years) Immigrant Married D. Father’s characteristics at the birth of the focal child (N = 2,116) 1.118 −0.246 −0.021** 0.047 Age Education (years) Immigrant Not reported 2.044** 0.172 0.013 −0.008 Bias-Corrected Estimate (2) Robust Standard Error (3) Sharpened q-Value (4) Mean of Dependent Variable (5) [−0.079] [0.166] [0.092] [−0.508] [0.009] [−0.020] [−0.205] [−0.033] [−0.154] [0.011] [−0.464] [−188.938] [0.019] [−0.397] [−0.691] [1.040] [0.218] [−0.052] [0.003] [2.132] [0.465] [−0.006] [−0.004] (0.077) (0.173) (0.070) (0.258) (0.160) (0.078) (0.133) (0.068) (0.147) (0.017) (0.449) (105.751) (0.033) (0.782) (0.449) (0.800) (0.389) (0.027) (0.080) (0.873) (0.400) (0.039) (0.023) {0.919} {0.919} {0.851} {0.576} {1.000} {1.000} {0.713} {1.000} {0.919} {1.000} {0.919} {0.618} {1.000} {1.000} {0.713} {0.851} {1.000} {0.576} {1.000} {0.507} {0.919} {1.000} {1.000} 0.456 1.911 0.208 34.097 2.937 0.611 0.899 0.520 2.121 0.023 38.209 2,898.7 0.046 6.586 4.515 27.735 11.239 0.068 0.535 30.547 11.608 0.074 0.021 Sample of (family members of) focal children with birth weight within a 200 g bandwidth around the 1,500 g cutoff and gestational age of at least 32 weeks. Column 1 reports the estimated coefﬁcient of the VLBW variable from a separate local-linear regression with a triangular kernel of the characteristic listed in the row for the family member indicated in the panel heading. Column 2 reports the corresponding bias-corrected estimate, column 3 the robust standard error (Calonico et al., 2014, 2019), column 4 the sharpened q-value for the set of tests included in the table (Anderson, 2008), and column 5 the mean of the variable in the row calculated among (family members of) focal children with birth weight above 1,500 g. Asterisks indicate statistical signiﬁcance (signiﬁcant at **5% and *10%), based on robust conﬁdence intervals centered on the bias-corrected estimates (for details, see Calonico et al., 2014, 2019). l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 weight bin as the dependent variable (McCrary, 2008). We do not ﬁnd any evidence of a discontinuity in the frequency of births at the VLBW cutoff.15 These results suggest that birth weight is unlikely to be manipulated in our context. In the remainder of this section, we check if there are differ- ences in observable characteristics across the VLBW cutoff by estimating our baseline model with the covariates as de- pendent variables. If the RD design is valid, then there should be no discontinuities at the VLBW cutoff.16 Table 1 provides the results. Panels A, C, and D use the FC/parent sample and check whether focal child and parental characteristics are balanced, while panel B uses the sibling sample to check for discontinuities in the covariates of siblings. Column 1 pro- vides the conventional point estimate from the local-linear regression, and columns 2 and 3 present the bias-corrected 15The estimates corresponding to appendix ﬁgures A1a and A1b are 0.092 (b.c.e. −7.507, standard error s.e. 6.955) and 0.196 (b.c.e. −12.614, s.e. 17.429). The results are qualitatively similar when using the logarithm of the number of births as the dependent variable instead. In this case, the estimated coefﬁcients are 0.013 (b.c.e. −0.223, s.e. 0.188) and 0.027 (b.c.e. −0.238, s.e. 0.324). 16Visual evidence on selected covariates is provided in appendix ﬁgures A2 to A4. estimate and the robust standard error (Calonico et al., 2019). We report sharpened q-values, that is, p-values based on the numbers in columns 2 and 3 further corrected for multiple inference and in column 4 (see section III and Anderson, 2008, for details). Finally, column 5 reports the mean of the covariate in the sample of (family members of) focal chil- dren with birth weight of at least 1,500 g. The results show that observations just below the VLBW cutoff are generally similar to those just above the VLBW cutoff. There are few characteristics with marginally signiﬁcant discontinuities at the threshold, and none of these survive the adjustment for multiple inference: the lowest q-value is 0.5. Overall, the analyses in this section indicate no evidence of manipulation of the running variable around the VLBW cutoff or of discontinuities in the observable characteristics of focal children, their parents, and their siblings. B. Baseline Results Figure 1 provides visual evidence on the relationship be- tween birth weight and the outcomes of focal children. Fig- ures 1a to 1d focus on child health, while ﬁgures 1e to 1f focus SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS 7 FIGURE 1.—EVOLUTION OF SUMMARY INDICES OF FOCAL CHILDREN AROUND THE VLBW CUTOFF l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Sample of focal children with gestational age of at least 32 weeks. Each dot represents the average of the summary index indicated in the panel for a 40 g bin. Focal children with birth weight of 1,500 g are excluded. The lines plot a ﬁrst-degree polynomial estimated separately on either side of the VLBW cutoff. 8 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 2.—SHORT-TERM EFFECTS OF VLBW CLASSIFICATION TABLE 3.—LONG-TERM EFFECTS OF VLBW CLASSIFICATION Mother (3) — Father (4) — Health Mean outcome Observations Focal Child (1) Siblings (2) Mother (3) Father (4) −0.324*** [−0.437] (0.144) {0.052} 0.039 1,960 0.090 [0.167] (0.155) {0.332} 0.115 3,311 −0.168 0.233 [−0.199] [0.427] (0.293) (0.122) {0.239} {0.293} −0.011 −0.026 2,116 2,155 Focal Child (1) Siblings (2) — −0.508** [−1.011] (0.408) {0.065} 0.726 2,156 0.133 [0.161] (0.190) {0.415} 0.190 1,978 −0.049 [−0.041] (0.142) {0.471} 0.103 3,311 −0.347*** −0.016 [−0.338] [0.098] (0.173) (0.124) {0.415} {0.052} 0.023 0.042 669 689 — — 0.068 0.066 Mortality Mean outcome Observations Health Mean outcome Observations Labor market outcomes Mean outcome Observations [0.211] (0.150) {0.293} −0.060 2,143 0.109* [0.286] (0.153) {0.213} −0.070 2,144 [0.205] (0.156) {0.303} 0.051 2,099 0.112* [0.289] (0.171) {0.239} −0.048 2,100 Income — — Mean outcome Observations Sample of (family members of) focal children with birth weight within a 200 g bandwidth around the 1,500 g cutoff and gestational age of at least 32 weeks. Each cell reports the estimated coefﬁcient of the VLBW variable from a separate local-linear regression with a triangular kernel of the summary index listed in the row for the family member indicated in the column (see appendix table A1 for details on the construction of the summary indices). All regressions control for heaping at multiples of 50 g. Bias- corrected estimates are listed in brackets, robust standard errors in parentheses, and sharpened q-values in braces below the coefﬁcient estimates. The mean of the outcome is reported for (family members of) focal children with birth weight above 1,500 g. Asterisks indicate statistical signiﬁcance (signiﬁcant at ***1%, **5%, and *10%) based on robust conﬁdence intervals centered on the bias-corrected estimates (for details, see Calonico et al., 2014, 2019). on academic achievement. The ﬁgure shows that focal chil- dren with birth weight slightly lower than 1,500 grams have lower mortality than children who weigh slightly more than 1,500 grams. Conditional on survival, however, the short- term health of children seems to be similar across the VLBW cutoff. We also do not observe any discontinuity in the dis- ability index in ﬁgure 1d, but there is some indication of improved long-term health during primary school–age years from the index based on hospital admissions and ER vis- its in ﬁgure 1c. Turning to academic achievement, ﬁgure 1e shows that focal children with birth weight slightly lower than 1,500 grams have visibly higher test scores in ninth grade. The improved test scores, however, do not seem to result in higher enrollment beyond compulsory education (ﬁgure 1f). Column 1 in tables 2 and 3 presents the corresponding regression results from our baseline model. Each cell re- ports the estimated coefﬁcient of the VLBW variable from a separate local-linear regression with a triangular kernel of the summary index. Bias-corrected estimates are listed in brackets, robust standard errors in parentheses, and sharpened q-values in braces. We also report the mean of the outcome for observations above the cutoff. Consistent with the graphical evidence, we ﬁnd that VLBW newborns have lower mortality in the short run and lower hospital and ER visits in the long l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Disability diagnosis by 0.234 — — — age 10 Mean outcome Observations Ninth-grade test scores Mean outcome Observations Higher education Mean outcome Observations [0.246] (0.294) {0.415} 0.249 2,156 0.314** [0.564] (0.234) {0.065} −0.257 952 0.044 [0.146] (0.180) {0.415} −0.380 2,156 0.375*** [0.524] (0.193) {0.052} −0.216 1,539 0.048 [0.086] (0.141) {0.415} −0.211 2,759 Labor market outcomes — — Mean outcome Observations Income Mean outcome Observations See the notes to table 2. — — — — — — 0.093 [0.098] (0.153) {0.415} −0.028 2,124 0.080* [0.252] (0.152) {0.239} 0.037 2,074 0.095 0.076 [0.214] [0.171] (0.149) (0.139) {0.332} {0.293} −0.063 −0.068 2,074 2,125 run: mortality is 0.508 standard deviation lower (table 2), and hospitalizations and ER visits during school years are 0.324 standard deviation lower (table 3).17 We also ﬁnd that focal children just below the VLBW cutoff have on average 0.314 standard deviation higher test scores in the ninth grade, but they are not signiﬁcantly more likely to be enrolled beyond compulsory education. We next turn to spillover effects on the siblings. Figure 2 provides visual evidence while the corresponding regression results are presented in column 2 of tables 2 and 3. Figure 2 shows that the siblings of focal children with birth weight slightly lower than 1,500 grams have visibly higher test scores in ninth grade. On the other hand, there is no evidence of important spillovers on health or enrollment outcomes. The regression results conﬁrm that the early-life medical treat- ments offered to VLBW children have signiﬁcant positive 17As an example, the 95% robust conﬁdence interval for the mortality effect (−0.508) is constructed using the bias-corrected estimate and the robust standard error as: −1.011 ± 0.408 × 1.96 = [−1.811, −0.211]. SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS 9 FIGURE 2.—EVOLUTION OF SUMMARY INDICES OF SIBLINGS AROUND THE VLBW CUTOFF, GA32+ SAMPLE l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Sample of siblings of focal children with gestational age of at least 32 weeks. Each dot represents the average of the summary index indicated in the panel for a 40 g bin. Siblings of focal children with birth weight of 1,500 g are excluded. The lines plot a ﬁrst-degree polynomial estimated separately on either side of the VLBW cutoff. spillovers on the test scores of the siblings without gains in higher education or health outcomes. In particular, we ﬁnd that siblings of VLBW newborns have ninth grade test scores that are on average 0.375 standard deviation higher.18 Finally, in ﬁgures 3 and 4 and in the remaining columns of tables 2 and 3, we examine potential spillovers to parental outcomes. Figure 3 suggests that the mothers of VLBW new- borns have potentially better mental health, as proxied by reduced antidepressant use, than do the mothers of heavier babies. On the other hand, there are no apparent disconti- 18Among the test takers in the sibling sample, the maximum age difference between older siblings and focal children is 7.6 years, meaning that none of the older siblings take the test before the focal children are born. nuities in maternal labor market outcomes or income, and surely not immediately after the birth of the focal child. Fig- ure 4 similarly shows that the distributions of paternal labor market outcomes and income are generally smooth across the VLBW cutoff. However, the fathers of VLBW newborns do not seem to experience the mental health improvements enjoyed by the mothers. The corresponding regression re- sults reported in columns 3 and 4 of tables 2 and 3 conﬁrm the visual evidence. We generally do not ﬁnd signiﬁcant dis- continuities at the VLBW cutoff in the measures of family resources (parental labor market outcomes and income). In the few cases when we ﬁnd marginally signiﬁcant gains, the results do not survive the adjustment for multiple inference: the lowest q-value is 0.213. However, we do ﬁnd evidence 10 THE REVIEW OF ECONOMICS AND STATISTICS FIGURE 3.—EVOLUTION OF SUMMARY INDICES OF MOTHERS OF FOCAL CHILDREN AROUND THE VLBW CUTOFF l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Sample of mothers of focal children with gestational age of at least 32 weeks. Each dot represents the average of the summary index indicated in the panel for a 40 g bin. Mothers of focal children with birth weight of 1,500 g are excluded. The lines plot a ﬁrst-degree polynomial estimated separately on either side of the VLBW cutoff. SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS 11 FIGURE 4.—EVOLUTION OF SUMMARY INDICES OF FATHERS OF FOCAL CHILDREN AROUND THE VLBW CUTOFF l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Sample of fathers of focal children with gestational age of at least 32 weeks. Each dot represents the average of the summary index indicated in the panel for a 40 g bin. Fathers of focal children with birth weight of 1,500 g are excluded. The lines plot a ﬁrst-degree polynomial estimated separately on either side of the VLBW cutoff. 12 THE REVIEW OF ECONOMICS AND STATISTICS of improved maternal mental health soon after the birth of the focal child that dissipates as the child ages. In particular, our results indicate that antidepressant use by the mothers of VLBW newborns is on average 0.347 standard deviation lower. Consistent with the visual evidence in ﬁgure 4, we ﬁnd no evidence of a similar effect for the fathers. C. Robustness Checks In this section we present robustness checks for the in- dices that were statistically signiﬁcant in the baseline regres- sions and survived the adjustment for multiple inference: fo- cal child mortality, focal child long-term health, focal child test scores, sibling test scores, and maternal short-term health (appendix ﬁgures A6 to A8 and A10 to 12 and appendix ta- ble A5 provide the corresponding checks for the remaining indices). Appendix ﬁgure A5 and column 1 of appendix table A4 investigate the robustness of our estimates to the choice of bandwidth. Appendix ﬁgure A5 presents the results for all bandwidths between 100 and 300 grams in 10 gram steps. Our baseline effect is indicated with a square, and the verti- cal bars plot the corresponding 95% robust conﬁdence inter- val following Calonico et al. (2014, 2019). The ﬁgure shows that the magnitudes of the estimates are remarkably consis- tent across different bandwidths. In column 1, we allow the bandwidths to differ across outcomes using the optimal band- widths suggested by the Calonico et al. (2014) strategy. Given the stability of the estimates to alternative bandwidths, it is not surprising that the results are again very robust. We next check the sensitivity of our results to the choice of degree of polynomial in birth weight. The results in column 2 show that our ﬁndings are robust to using a second degree of polynomial. Column 3 investigates the sensitivity of the results to the inclusion of the control variables described in section IV. If the key assumption in our RD design is satisﬁed (i.e., birth weight is as good as random around the cutoff), then including additional relevant covariates should not affect the estimates much but increase precision instead. The results show that this is generally the case. Columns 4 and 5 turn to the role of heaping. Heaping can lead to biased estimates if it does not occur in a symmetric way around the cutoff. Following Barreca et al. (2011, 2016), our main speciﬁcation controls for heaping at 50 gram inter- vals. We conduct two checks to probe this further. First, we estimate models excluding the heaping dummies (column 4). Second, in column 5 we estimate “doughnut” regressions that exclude the (family members of) focal children who weighed 1,500 grams (Barreca et al., 2016). The results are again sim- ilar to the main estimates, suggesting that our baseline results are not driven by heaping. Our baseline model uses a triangular kernel. In column 6, we show that our ﬁndings are robust to using a rectangular kernel that places equal weights on each observation. Col- umn 7 checks the sensitivity of our inference by clustering standard errors at the birth weight level and conﬁrms that the results remain statistically signiﬁcant at conventional levels. Finally, we conduct two falsiﬁcation tests. First, we esti- mate our baseline model in the sample of (family members of) focal children with a gestational age of less than 32 weeks. Since these children are eligible to receive additional medical treatments regardless of their birth weight, any discontinuity in their outcomes or in the outcomes of their family members would suggest a violation of the key identiﬁcation assump- tions underlying the RD design. The results in column 8 indi- cate that the indices studied are relatively smooth across the VLBW threshold in this sample. Second, we check whether we observe similar disconti- nuities in the indices at other points in the distribution of birth weight of the focal child. If the observed gains are in- deed driven by the medical treatments received by focal chil- dren, then we should not observe systematic discontinuities in the outcomes at other potential cutoffs. We examine cut- offs from 1,300 grams to 3,100 grams, keeping the bandwidth ﬁxed at 200 grams. The results presented in appendix ﬁgure A9 indicate that the discontinuities observed at 1,500 grams are indeed distinct. Although the effects at 1,300 grams are more noisily estimated, it is clear in most ﬁgures that the largest and only signiﬁcant discontinuity is found at 1,500 grams.19 Overall, these ﬁndings strongly suggest that the ob- served (spillover) effects are due to the impact of medical treatments provided to the VLBW focal children. D. Discussion In section I, we conﬁrm the ﬁndings in the previous liter- ature that early-life medical treatments have signiﬁcant ef- fects on focal child survival and academic achievement. In order to compare our ﬁndings with the previous literature, we present the results using selected components of the mor- tality and the test score indices in appendix table A6. We show that the probability of death within the ﬁrst 28 days (1 year) of life is 4.1 (5.4) percentage points lower among VLBW newborns. These are large gains when compared to the average mortality rates of those above the cutoff (6.2% and 7.7%, respectively) but they are comparable in magnitude to the reductions in infant mortality from previous studies: 1 percentage point (mean: 5.5%) in the United States (Almond et al., 2010), 4.5 percentage points (mean: 11%) in Chile, and 3.1 percentage points (mean: 3.6%) in Norway (Bharadwaj et al., 2013). We ﬁnd that VLBW newborns have language and math test scores higher on average by 0.229 and 0.315 standard deviations, respectively.20 The estimated effect on math test scores is comparable to those found by Bharad- waj et al. (2013), who estimate effects of 0.152 standard 19In the case of focal child and sibling test scores, we also ﬁnd marginally signiﬁcant discontinuities at 2,500 grams, another birth weight cutoff for specialized medical treatments. These effects are three to four times smaller than the estimated effects at 1,500 grams. 20These results are not driven by delayed school entry as proxied by the age at which focal children take the ninth-grade test (Landersø, Nielsen, & Simonsen, 2017). Indeed, we ﬁnd that the distribution of the age when focal children take the test is smooth across the VLBW threshold (estimate −0.033, b.c.e. −0.115, s.e. 0.127, mean 16.137). l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS 13 deviation in Chile and 0.476 standard deviation in Norway. We add to this literature by investigating effects on focal child human capital accumulation beyond compulsory schooling as well as disability and hospital/ER contacts. We do not ﬁnd effects on enrollment beyond compulsory schooling. Further analyses based on individual components of the index show that there is also no impact on the “intensive” margin, as the share of focal children enrolled in an academic track at age 18 is not signiﬁcantly higher among VLBW children (see appendix table A6). In order to reconcile the test score gains with the lack of effects on enrollment, we estimate a quantile RD speciﬁcation based on the method proposed by Frandsen, Frölich, and Melly (2012). The results presented in appendix table A9 indicate that early-life medical treatments do not improve the test scores of the focal children at the bottom of the test score distribution. This suggests that the children affected by the medical treatments are not on the margin of dropping out or of making the choice between an academic or a vocational track. While we also do not ﬁnd any effects on focal child disability status, our results consistently point to health improvements during the school years, highlighting a potential channel behind the academic achievement results.21 The main novelty in our paper is the investigation of spillover effects to other family members. Our results sug- gest that early-life medical interventions have little impact on parents’ decisions that affect total household resources: we see no discontinuity in the labor market or income in- dices of either mothers or fathers. Since Denmark is a de- veloped country with a particularly generous social safety net, this may not be surprising. We do, however, ﬁnd evi- dence that early-life treatments provided to VLBW children improve maternal mental health. The mental health gains are short-lived and tend to dissipate as focal children age. One natural explanation for this pattern could be improved focal child survival. We check whether this is the case in two ways. First, we estimate our baseline model in the sample of fam- ily members of focal children who survive past the ﬁrst year of life. The estimated effect shown in column 1 of appendix table A10 is smaller than our baseline estimate, suggesting that child survival is indeed a channel through which early- life medical treatments may affect maternal mental health. Second, we consider several groups of focal children whom we expect to be affected differently by early-life medical in- terventions. For example, twins are on average lighter than singletons, meaning that a VLBW singleton may be in poorer health than a VLBW twin. Therefore, we would expect the VLBW singletons in our sample to beneﬁt more from med- ical treatments than twins do. In addition, the large medi- cal literature on the “fragile male” hypothesis states that the male fetus is simply more at risk than the female fetus (Naeye et al., 1971). Hence, we would expect that the VLBW boys in 21In order to shed some light on this, we estimate our baseline model with the focal child test score index as the outcome while additionally controlling for focal child long-term health index. The estimated coefﬁcient of the VLBW variable in this case is 0.260 (b.c.e. 0.496, s.e. 0.233). our sample beneﬁt more than girls from the additional treat- ments provided to VLBW children. Indeed, columns 2 to 5 in appendix table A10 indicate that our mortality results are driven by singletons and by boys. However, there are long- term improvements in health across all four groups, support- ing our earlier conclusion that early-life medical treatments have health beneﬁts beyond just survival. More important, the table shows large improvements in the mental health of the mothers of focal children with no survival beneﬁts (twins and girls). This suggests that general improvements in the health of focal children, and not just their survival, is a chan- nel behind the spillover effects on maternal mental health. Turning to siblings, we ﬁnd that early-life medical in- terventions have economically signiﬁcant long-run gains in sibling academic achievement. The results based on course- speciﬁc test scores presented in appendix table A8 show that the test score gains are driven by both math and language test scores. Siblings of VLBW newborns have on average 0.386 (0.255) standard deviation higher language (math) test scores relative to the siblings of newborn who weigh slightly more than 1,500 grams. One way to gauge the magnitudes of these effects is to compare it to other policy-relevant test score gaps. For example, among all children born during the period covered by our sibling sample, the difference in language (math) scores between the children of nonimmi- grants and immigrants is 0.264 (0.404) standard deviation. Our results imply that medical interventions are equivalent to eliminating the language disadvantage for children of im- migrants and reducing the gap in math scores by more than half. We also calculate that the difference in language (math) test scores among those born in households above the 90th in- come percentile and those born in households below the 10th income percentile is 0.557 (0.769) standard deviation. Our coefﬁcients imply that medical interventions can reduce the income-based test score gap at age 16 by 33% to 69%. These effects are in line with those found by Duncan and Sojourner (2003) for income-based test score gaps at ages 3 through 8 for children exposed to an early-education program targeting low birth weight children in the United States. Similar to the focal child results, we ﬁnd that siblings’ test score gains do not translate into a higher likelihood of pursu- ing education beyond the compulsory level. In contrast to the effects on focal children, however, the results from the quan- tile RD approach indicate that early-life medical treatments improve the test scores of siblings across the entire test score distribution (see appendix table A9). This seems to still not affect the children on the margin of dropping out, likely due to the fact that only 22% of students do not continue beyond compulsory schooling. However, as more students from the lower half of the test score distribution see improvements in their academic achievement, we now ﬁnd effects at the “in- tensive” margin: siblings of VLBW children are more likely to follow an academic track instead of a vocational track (see appendix table A8). These positive spillovers on academic achievement are un- likely to be driven by correlated health shocks within the l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 14 THE REVIEW OF ECONOMICS AND STATISTICS family that make siblings themselves more likely to receive medical interventions early in life. The fact that we do not observe discontinuities in the hospital/ER visits of siblings at the cutoff offers the ﬁrst evidence that this is unlikely to be the case. We conduct two more checks to shed more light on this issue. First, we exclude VLBW siblings and conﬁrm that our main results are not driven by them.22 Second, if the fam- ilies of VLBW focal children are more prone to having health shocks than the families of slightly heavier children, then our human capital achievement results may capture the effects of these unobserved family traits instead of the spillovers from early-life medical interventions. In that case, we may expect to see differences across the VLBW cutoff in the short-term survival rates of older siblings before being exposed to the VLBW focal children. Using the 28-day and 1-year mortal- ity rate of older siblings as outcomes suggests that this is not a concern in our context.23 The sibling spillovers are also not driven by differential focal child survival at the cutoff. In contrast to mother’s mental health, we ﬁnd similar improve- ments in sibling test scores to our baseline results when we estimate the baseline model in the sample of families where focal children survive the ﬁrst year (column 1 of appendix table A10). The fact that we observe signiﬁcant test score gains among siblings of VLBW children without effects on total household resources or sibling health suggests that early-life medical treatments may be changing intrafamily interactions or the intrahousehold allocation of resources. Data limitations do not allow us to investigate these hypotheses directly, but we provide indirect evidence on both. It is well understood in economics that the family, especially parent-child interac- tions, plays a central role in the human capital accumulation of children (Cunha & Heckman, 2007; Cunha, Heckman, & Schennach, 2010; Almond & Currie, 2011). In order to shed further light on this, we estimate our baseline model while controlling for the maternal short-term mental health index and ﬁnd that this reduces the estimated effect on sib- ling text scores by about 50%.24 This suggests that improved parent-child relations may be important for sibling academic achievement. The research also indicates that children’s early-life health endowments have an impact on the academic outcomes of other children in the family by changing parental investments. Evidence of such spillover effects is found in both developing and in developed countries, and the magnitudes of the effects are economically large (Yi et al., 2015; Black, Devereux, & Salvanes, 2007). We can provide some indirect evidence on 22The estimated coefﬁcient of the VLBW variable is 0.401 (b.c.e. 0.466, s.e. 0.205, N = 1,456) for the language test score and 0.263 (b.c.e. 0.416, s.e. 0.183, N = 1,465) for the math test score. After excluding VLBW siblings, only ten siblings with a gestational age below 32 weeks remain in the sample. Dropping these from the sample does not change the results. 23The estimated coefﬁcient of the VLBW variable is 0.016 (b.c.e. 0.027, s.e. 0.020, N = 3,594) for 28-day mortality and 0.021 (b.c.e. 0.031, s.e. 0.022, N = 3,594) for one-year mortality. 24The estimated coefﬁcient of the VLBW variable is 0.182 (b.c.e. 0.437, s.e. 0.250, N = 546). this if we make the assumption that there are dynamic com- plementarities in the production of human capital, as Cunha and Heckman (2007) suggested. In this case, children with high initial endowments would beneﬁt most from parental investments because “skills beget skills.” To illustrate, con- sider two children with low initial endowment, A and B, who are identical in every respect except that A has a sibling with birth weight slightly below the VLBW cutoff while B has a sibling with birth weight slightly above the cutoff. If both sets of parents engage in compensating behavior, then child B has more resources taken away from her and allocated to her sibling than child A does (because the VLBW sibling of child A beneﬁts from the additional medical treatments). Therefore, in the long term, child B ends up with a lower level of skills than child A. Now consider a similar pair of identical children, C (who has a VLBW sibling) and D (who does not), but with high initial endowment. Just as before, child D has more resources taken away from her and so ends up with a lower level of skills in the long term than child C. However, because of dynamic complementarities, child D is harmed even more by the fewer resources she receives be- cause the return to those resources would be higher for her than for child B. Therefore, the difference in skills between children C and D (high initial endowment) is larger than the difference in skills between children A and B (low ability).25 To check whether we observe this pattern in our data, we rely on birth weight as an indicator of initial endowments because the previous literature ﬁnds that it is highly corre- lated with later-life academic, health, and labor market out- comes (Black et al., 2007; Figlio et al., 2014). We deﬁne “high-endowment” siblings as those whose birth weight is higher than the birth weight of the median child born dur- ing our sample period. The results, shown in appendix table A11, suggest that high-endowment siblings beneﬁt more than low-endowment siblings do from the additional medical treat- ments received by VLBW focal children. This suggests that parental compensating behavior (possibly combined with dy- namic complementarities in the production of human capital) may also be one of the factors behind the observed spillover effects. VI. Conclusion This paper investigates the spillover effects of early-life medical treatments provided to VLBW children on other fam- ily members. Using register data from Denmark, we conﬁrm the ﬁndings in the previous literature that VLBW children eligible to receive early-life treatments are less likely to die in the ﬁrst year of life and have higher academic achieve- ment in ninth grade. We add to this literature by showing that focal children’s likelihood of having a childhood disability 25Alternatively, the difference in skills between children C and D can be larger than the difference in skills between children A and B if parents reallocate more resources to the focal child in order to compensate for the larger difference in endowments within the family. This explanation is also consistent with compensating behavior by the parents. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 1 1 1 9 8 0 1 6 1 / r e s t _ a _ 0 0 9 8 2 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 SPILLOVER EFFECTS OF EARLY-LIFE MEDICAL INTERVENTIONS 15 is not affected by early-life medical treatments, but they are still more likely to enjoy better health during school years, as proxied by reduced hospital/ER contacts. The main innovation in our study is that we document the presence of spillover effects to other family members. While total household resources do not differ between the families of VLBW children and the families of slightly heavier new- borns, the mothers of VLBW children are signiﬁcantly less likely to take antidepressants soon after the birth of the chil- dren. These health gains diminish as the focal child ages. Our results suggest that both increased focal child survival and improvements in focal child health contribute to the im- provements in maternal mental health. Turning to siblings, we ﬁnd that the siblings of focal children who were slightly below the VLBW cutoff have better ninth-grade language and math test scores. These gains are not driven by corre- lated health shocks within the family or by differential focal child survival at the cutoff. Instead, we present evidence sug- gesting that improved interactions in the family and parental compensating behavior may be important reasons behind the spillovers to siblings. Our results underscore the importance of health interven- tions targeted to other family members as an important fac- tor in the accumulation of human capital. Our ﬁndings also have important implications for understanding the efﬁcacy of early-life medical interventions. 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