Available via license: CC BY 4.0
Content may be subject to copyright.
1
MULTIGENERATIONAL EFFECTS OF SMALLPOX VACCINATION
Volha Lazuka* and Peter Sandholt Jensen**
Abstract
Can the effects of childhood vaccination extend across three generations? Using
Swedish data spanning 250 years, we estimate the impact of smallpox vaccination
on longevity, disability, and occupational achievements. Employing mother fixed-
effects, difference-in-differences, and shift-share instrumental-variables designs,
we find that vaccination improves health and economic outcomes for at least two
subsequent generations. Causal mediation analysis reveals that these benefits arise
from improved health behaviors and epigenetic factors. Even in milder disease
environments as seen today, vaccination delivers lasting advantages,
demonstrating its long-term benefits beyond epidemic contexts. These findings
highlight the benefits of early-life health interventions lasting for subsequent
generations.
Keywords: intergenerational transmission of health; smallpox vaccination; shift-
share instrumental-variables.
JEL codes: I18; J24; J62; N33.
* Corresponding author: vola@sam.sdu.dk, University of Southern Denmark,
Lund University, and IZA.
** Linnaeus University.
2
Funding and Acknowledgements
We are grateful to the participants of the EEA Annual Congress, ASSA
Annual Meeting, PAA Annual Meeting, Economic Society of Population
Economics Conference, and of the seminars at the UC Davis, London School of
Economics, and the University of Southern Denmark. Volha acknowledges
funding from the Marie-Curie Individual Fellowship (grant No 101025481).
3
1. Introduction
The recent global disruptions caused by emerging infectious diseases
underscore the critical importance of vaccines in protecting populations against
these diseases (Patel et al. 2022). Live vaccines may also protect against unrelated
diseases, with childhood vaccination enhancing the immune system through
epigenetic and metabolic changes (for reviews see Benn et al. 2023, de Bree, et al.
2018). Recent randomized control trials confirm these “non-specific” positive
effects of vaccines on health during childhood (Schaltz-Buchholzer et al. 2021;
Lund et al. 2015; Kleinnijenhuis et al. 2014). Inspired by epidemiological findings,
economic studies have explored childhood vaccination’s impact on adult labor
market outcomes in a human capital framework (Barteska et al. 2023; Atwood
2022; Bütikofer and Salvanes 2020). However, the overall effects of vaccination
remain underestimated, as these effects theoretically persist in health and
economic outcomes across an individual’s lifetime and over multiple generations
(Collado, Ortuño-Ortín, and Stuhler 2023; Momota, Tabata, and Futagami 2005).
The historical context and availability of detailed demographic microdata for
Sweden present a unique opportunity to investigate the causal effects of
vaccination across generations. Smallpox was a severe and widespread disease in
Sweden, as in the rest of the world, during the eighteenth century. The introduction
of the smallpox vaccine in 1801—the first known vaccination globally—marked
a significant reduction in child mortality, offering a source of variation valuable
for causal identification. Notably, following this development, life expectancy at
birth began to increase significantly in Sweden and other Nordic countries. An
additional advantage is the method of vaccine distribution in Sweden, which relied
primarily on churches and church assistants who did not typically engage in public
4
health activities. This unique aspect enables the implementation of causal
inference strategies to estimate both intention-to-treat effects and average
treatment effects. Finally, Swedish parish registers, which include family-based
records of all demographic events, along with annual censuses, allow us to trace
individuals across three full generations—until their premature death or their 100th
birthday.
In this study, we estimate the impact of smallpox vaccination on the longevity
and economic well-being of three generations, spanning the period from 1790 to
2016. We examine the entire lifespans of three generations to evaluate their health,
behavioral, and socio-economic outcomes, including disability, literacy, and
occupational scores. We leverage the smallpox vaccination campaign in Sweden
as a quasi-experiment. Given the ambitious scope of this research, a substantial
portion of the paper is dedicated to deriving causal and interpretable variation in
the smallpox vaccination status of the first generation (referred to as Generation
1), those vaccinated during childhood and exposed to the positive vaccination
shock. To achieve this, we employ mother fixed effects, difference-in-differences
(DID), and shift-share instrumental-variables (SSIV) strategies within both linear
and hazard models. To address the potential impact of selective migration, we
adjust our estimates using Heckman’s two-stage selection procedure. Furthermore,
we apply the SSIV strategy to estimate the intergenerational effects of smallpox
vaccination on the outcomes of the two subsequent generations. Finally, we
decompose these intergenerational effects into components driven by behavioral
and epigenetic factors.
We find that smallpox vaccination in early childhood enhances both
longevity and occupational achievements of Generation 1 as well as of their
5
children (Generation 2) and grandchildren (Generation 3). Smallpox vaccination
adds 11 years of life to the first generation and 2 and 1 years to the second and
third generations. To put such results in perspective, vaccination in childhood in
historical Sweden produces similar effects for longevity as quitting smoking in
today’s context. All three generations that we study died primarily from causes
other than smallpox, but we also establish explicit “non-specific” vaccination
effects: while mortality from smallpox is reduced the most, there are negative
effects on mortality from other causes. We also find that vaccination improves
economic outcomes across generations—in terms of disability and occupational
achievements, with these effects with a reduced magnitude being transmitted to
subsequent generations. More than half of the transmitted effects are attributed to
nurture, as vaccinated individuals are more likely to vaccinate their children across
generations, while epigenetic factors account for the remainder. Our results
withstand a large number of robustness checks.
In addition to being the first to establish vaccination effects across multiple
generations, our paper contributes to two strands of economic literature. Firstly,
our knowledge on whether health shocks for one generation determine the
outcomes of the subsequent generations causally is extremely scarce. There are
several studies that attempt to derive the causal impacts of health transmission by
relying on environmental shocks as a source of exogenous variation (East et al.
2023; Cook, Fletcher, and Forgues 2019). We contribute to this literature by
tracing the effects of a positive health shock over the full life cycles of three
generations.
Secondly, while there exists an extensive body of literature on the long-term
health and economic effects of recent interventions, there is a smaller, yet steadily
6
expanding, literature focused on interventions that occurred further back in history.
Based on causal designs, economists have recently studied the establishment of
epidemical and modern hospitals (Hollingsworth et al. 2024; Lazuka 2023), the
impacts of licensed midwifery (Kotsadam, Lind, and Modalsli 2022; Anderson et
al. 2020; Lazuka 2018), of tuberculosis dispensaries (Egedesø, Hansen, and Jensen
2020; Clay et al. 2020; Anderson et al. 2019), and of mid-twentieth-century
antibiotics and vaccinations (Atwood 2022; Bütikofer and Salvanes 2020; Lazuka
2020). The focus on historical interventions has helped us better understand their
effects on individuals. We contribute to this literature by examining the
vaccination campaign, which is the world’s first documented public health
initiative and an intervention that has received limited attention in previous
research.
2. The Context of Smallpox Vaccination in Sweden
2.1 Introduction of Smallpox Vaccination
In 1798, Edward Jenner published a book outlining his successful smallpox
vaccination method, where he initially vaccinated a boy with cowpox. After an
eight-week interval, he administered smallpox to the same boy without any
adverse effects, confirming the vaccine’s efficacy (Baxby 1985). Vaccination
against smallpox reached Sweden a few years later and was first mentioned on 7
December 1801 by the Medical Board of Sweden (Riksarkivet 1802-1812).
Vaccination against smallpox was considered by the Swedish reformers as “among
the greatest inventions ever, which—when it has increased in confidence—will be
the supreme happiness of the human race and the triumph of medicine.” (Hedin
1802). The first vaccinations in Sweden were carried out at the end of 1801, and
7
starting from 1803, the Inoculation House of Stockholm maintained a fresh
vaccine available to facilitate nationwide vaccination efforts.
Before the introduction of vaccination, inoculation—a deliberate infection
with smallpox (rather than cowpox) via the skin—was used as a preventive
measure against smallpox. Even though inoculation was introduced in Britain in
1721, it was not until 1756 that it was first used in Sweden. The historical narrative
suggests that inoculation never gained wide acceptance because of, for instance,
the risk of dying from the procedure (Pettersson 1912). Both the country records
on the number of inoculations and our data confirm that inoculation had low uptake
in Sweden: less than 0.01% of parishioners were inoculated between 1769 and
1800 (Riksarkivet 1769-1801).
The introduction of vaccination in Sweden in the 1801 had several
remarkable features that we exploited in our empirical design. First, vaccination
efforts primarily focused on children, typically aged around 2 years old
(Riksarkivet 1802-1812). Starting in March 1816, parents were required to have
their children under the age of 2 vaccinated, with fines imposed for non-
compliance. If parents were unable to pay the fine, they would be subject to
imprisonment and would receive only a diet of water and bread.
Second, vaccination was nearly free of charge. Vaccinators were not
permitted to charge parents for vaccinating children. Local solutions for
compensation included the salary from the parish, small fees charged from the
wealthiest parents, a payment from poor relief, or medals (Sköld 2000). Naturally,
there were no discernible differences in the practice of vaccination in Sweden
based on social class (Dribe and Nystedt 2003).
8
Finally, in 1804 every parish was instructed to appoint a vaccinator. The state
authorities did not allow local physicians to monopolize the vaccination process,
fearing the low uptake and voluntary fee charges. However, the vaccine could be
safely administered by non-medical individuals — “anyone, without prior
experience but with good interpersonal skills, common sense, and the ability to
read and write, who would simply need to acquire a few skills” (Ekelund 1804).
As a solution, starting in 1805, low-skilled church personnel, commonly with no
prior involvement in health or epidemic matters, were obliged to attain the skill of
vaccination. Data from the 1810s indicate that over 60% of those administering
vaccinations were church assistants or church musicians, followed by priests
(12%), upper-class women (10%), and midwives, physicians, and other people
(each accounting for 5%) (Sköld 1996a). In contrast to the local demographic and
cultural factors, the availability and employment of church personnel emerges as
the sole factor highly correlated with vaccination uptake (Sköld 1996b).
2.2 Disease Environment and Vaccine Uptake
Smallpox was the main disease and cause of death among children in the pre-
vaccination era. In Sweden, an ordinary, Variola major was widespread, a highly
contagious type, spread through the air, which affected children or persons lacking
natural immunity against smallpox. The virus remained unchanged throughout
history, causing a two-week period of suffering characterized by symptoms such
as headache, fever, backache, vomiting, and diarrhea, followed by the
development of pustules (Fenner et al. 1988). Case fatality rate reaches 20%
among all infected persons and 55% among children below age 2 (Sköld 1996b).
Survivors often bore life-long pitted scars (pockmarks) and could experience
9
various complications, such as blindness, baldness, limb deformities, infertility,
and conditions in respiratory, gastrointestinal, and central nervous system.
There is no effective treatment against smallpox due to the virus’s resistance
to temperatures below 60 degrees and its independence from nutrition, leading to
losses regardless of access to food or other family conditions (Lunn 1991).
Pregnant women transmit infection, rather than protective antibodies, to fetuses,
leading to premature neonatal death (Hassett 2003). Therefore, the children must
eventually develop their own immunity or receive vaccination to achieve
protection. Vaccination, including earlier iterations, offers approximately 95%
effectiveness (Fenner et al. 1988).
The age pattern of smallpox mortality in Sweden has changed dramatically
with introduction of vaccination in 1801, as shown in Figure A1 Appendix A. We
calculated the rates based on population counts for the regions we further analyze;
these numbers are similar to those for the entire country (Pettersson 1912). Even
though among causes of death the proportion of unknown cases is significant, the
symptoms of the primary infectious diseases were recognizable to death registrars
(i.e., priests and doctors); consequently, in relative terms, the age pattern of
smallpox deaths has a high degree of accuracy (Bengtsson and Lindstrom 2000).
Between 1790 and 1800, smallpox mortality followed an L-shaped pattern, with
approximately 3% of children under the age of three succumbing to the disease
(16% of all causes), a decreasing rate among older children, and relatively few
deaths among adults. This pattern is indicative of a society where older individuals
acquired natural immunity but did not pass it on to their children. In a few decades
after 1801, in a scale with the previous decades, age pattern has almost flattened.
During this period, less than 0.2% of children died due to smallpox.
10
Figure 1 shows the share of the cohort vaccinated by age two for the
nineteenth-century Sweden, encompassing all the generations explored in this
study. Vaccine uptake was gradual for the first few decades after 1801 and then
stabilized at 85%. Mandatory vaccination in 1816 only resulted in a modest
increase in uptake among small children, suggesting that most of the uptake is
associated with other factors, suggestively the number of vaccinators, rather than
the mandatory law. No one died from smallpox in the 1890s, causing the
vaccination rate to decline. The mortality and vaccination patterns are similar to
development presented by Sköld (1996b) for the whole of Sweden.
[Figure 1 about here]
A question that naturally arises is why vaccination rates did not reach 100%
since vaccination was mandatory. The historical narrative suggests that the
compulsory vaccination law was a threat, which made most parents comply with
vaccination (Pettersson 1912). Yet, it is very difficult to find historical examples
of fines being executed. Anti-vaccination opposition was very low in Sweden
compared to other European countries, with the first known petition presented a
half a century after the start of the vaccination. Nevertheless, some people were
spreading the message that smallpox was a religious sin, and the local authorities
were reluctant to bring in the policy and start a conflict with people who had
religious reasons for refusing to vaccinate their children (Sköld 1996b). Another
source of vaccine hesitance was that (false) stories about
the negative consequences from vaccines were spread by vagabonds and beggars.
Regarding parents who did not vaccinate their children, one local doctor classified
cases as follows: laziness, pleasure from defying the law, and fears of the
consequences of vaccination (Landsarkivet i Lund 1805-1827).
11
2.3 Non-Specific Vaccination Effects in the Historical Narrative
Many contemporaries of smallpox vaccination believed that little would be
gained by the elimination of smallpox since other diseases would take over
(Hofsten and Lundström 1976). But the historical narrative for Sweden and other
countries suggests the opposite — the vaccine combated both smallpox and other
infectious diseases, known in the current literature as “non-specific” health effects
of vaccination. Mayr (2004) cites circumstantial evidence from German and
Austrian vaccinators, who reported, for example, that “eye and ear disorders not
only improved but also disappeared, and that chronic diseases vanished amongst
the vaccinees.” He also notes that, as found, vaccinated persons are less susceptible
to infectious diseases such as measles, scarlet fever, whooping cough, and even
syphilis, than non-vaccinated persons. For Sweden, we searched in the annual
reports from provincial and city doctors from different regions and found several
indications of a close association between high vaccination rates and less
infectious disease, not just smallpox (Riksarkivet 1796-1820).
Moreover, the lifetime gains for the vaccinated children may emerge from
the improved disease environment. About 1% of smallpox survivors develop vivid
life-long complications, such as blindness, limb deformities, infertility, and
conditions in respiratory, gastrointestinal, and central nervous system (Sköld
1996b). But smallpox can affect much larger fractions of population, as confirmed
by extensive empirical literature findings that being born in epidemic years reduces
longevity and labor-market performance (Almond, Currie, and Duque 2018).
Respiratory infections in childhood are causing atopy, reversible airway
obstruction, chronic mucus hypersecretion, and irreversible airflow obstruction,
affecting working capacity (Kuh, Ben-Shlomo, and Ezra 2004). Early exposure to
12
infectious diseases may prime the immune system to remain chronically alert,
leading to chronic inflammation, which in turn increases the risk of various chronic
diseases (Finch and Crimmins 2004). Today, the marker of chronic inflammation,
C-reactive protein, is a well-established risk factor in the clinical assessment of
cardiovascular disease, and it is also associated with diabetes, mental health issues,
atherosclerosis, and the disability uptake (Arnett et al. 2019).
3. Data
3.1 Microdata for Three Generations
We aim to investigate if vaccinating Generation 1 against smallpox positively
affects their lifelong well-being, as well as the well-being of Generation 2 and
Generation 3. To do this, we use high-quality data spanning a long time and age
range, with connections across multiple generations.
Our data come from unique register-based datasets containing health,
demographic, and socio-economic information on residents from 79 different
parishes in Sweden, spanning from the 18th to the 21st centuries, including their
descendants. We accessed the data from two sources: for northern and central
Sweden, we obtained them from the Demographic Data Base (CEDAR 2021;
CEDAR 2022), and for southern Sweden, from the Scanian Economic-
Demographic Database (Bengtsson et al. 2021). Both sources share essential
features for our study: The parishes selected into the datasets are built on high-
quality archival records and represent geographically compact areas, which
reduces biases stemming from regional differences. These datasets represent the
reconstructed life and family histories of parish residents. Moreover, the data are
homogeneous in terms of sources and structure, providing variables at the
individual level in the same metrics across cohorts. The quality of data has been
13
confirmed by over 250 articles that rely on it (Dribe and Quaranta 2020; Edvinsson
and Engberg 2020).
Out of the datasets, we chose parishes that contained both pre- and post-
vaccination cohorts. Figure A2 in Appendix A presents the parishes used in the
analysis. The analytic sample for Generation 1 includes individuals born in
between 1790 and 1820, a period roughly equivalent to the general definition of
generation – the mean age difference between parents and children. In the
succeeding generations, we adhered to the same definition, with the latest cohort
for the descendants corresponding to the last reproductive age of the latest born
mother. Specifically, Generation 2 includes the children of Generation 1, born
between 1805 and 1865 (with mothers in reproductive ages 15-45 years), and
Generation 3 includes the grandchildren of Generation 1, born between 1820 and
1910. In total, we tracked the full life cycles of three generations, which amounts
to 141,067 individuals, up until their death, out-migration, or reaching the age of
100.
The datasets collectively represent the economic and health development of
Sweden well. For our analytic sample, Figure A3 in Appendix A presents below-
10 mortality rates by the cause of death aggregated into smallpox, other infectious,
and non-infectious groups from 1790 to 1920. In the data, the causes of deaths are
available as codes of the tenth version of the international classification of diseases,
which is based on the encoding of historical causes of death performed by medical
experts. As shown in the figure, the influence of smallpox declined with the
inception of vaccination, but perhaps surprisingly, child mortality reduced only
slightly. This observation, namely, led economic historians to argue for the
absence of vivid vaccination effects. However, the potential gain in survival for
14
children becomes apparent when looking at the cohort life expectancy at age two.
After a period of no improvement, life expectancy surged by 14 years for cohorts
born between 1801–1820 as compared to 1790–1800, and it continued to grow for
the succeeding generations.
3.2 Individual Vaccination
Our key treatment variable is whether an individual belonging to Generation
1 was vaccinated against smallpox by the age of 2 years. From the microdata, we
observed that the first years of life are the most common vaccination age for
cohorts born after 1801, with the median age among those eventually vaccinated
being 2.04 years. We did not opt for the continuous measure of the vaccination
date because it could be somewhat imprecise. For instance, Dribe and Nystedt
(2003) have suggested that the changing frequency of vaccinated children in the
first post-vaccination years, which we also observe in the data, might indicate
inaccuracy in the exact age of vaccination.
The control group includes individuals who were never vaccinated. This
group includes individuals who obtained natural immunity (i.e., recovered from
smallpox and are alive by the age of 2 years) or had neither vaccination nor
immunity. Smallpox vaccination status is available in the data as a mark and a date
of the mark, recorded by the priests in the church books during censuses and on
many occasions, such as at birth, baptism, vaccination, in- and out-migration. Later
ages of vaccination may therefore be associated with the period of the family’s
absence from the parish rather than the first vaccination date. This observation
reinforces our prior decision to exclude migrant families from the estimation
sample, and we additionally exclude children vaccinated after the age of 2 from
15
the control group. A few vaccination cases mention natural immunity, but they are
rare and unsystematic to constitute a separate control group.
We conducted two checks to assess measurement errors in vaccination status.
First, we compared the number of vaccinated children in the microdata with the
aggregated parish censuses (The Demographic Data Base 2022). Local medical
reports often mention that the aggregated parish records of vaccinees, which were
reported by the priests to the state during census years, provide the most accurate
counts (Riksarkivet 1796-1820). While our microdata also include linked census
data, it is possible that some parish books, which serve as the foundation for family
reconstitutions, have been lost, leading to the underutilization of the available
census data. We found that the counts between the datasets matched perfectly.
3.3 Lifetime Outcomes
The data provide information on the time of an individual’s death or
outmigration from the studied area. For southern Sweden, records have been linked
to the data from Swedish Death Index, which includes most deaths in Sweden
(Släktforskarförbund 2019). For central and northern Sweden, we have
information on death dates for 54% of the sample. Our preferred indicator of
longevity is a linear count of the number of years lived after the age of two (i.e.,
after the smallpox vaccination). This measure also indicates the latest point in time
individuals are observed within the area for a portion of the sample. As we
demonstrate in the results section, our findings remain similar even when these
observations are treated as censored.
We used rich information on occupation from the datasets, employing it as
an outcome measure, a control variable, and in construction of the IV. The original
sources contributing to the occupational information in the microdata are rich and
16
include church books, poll-tax, and examination registers, facilitating cross-
checking and complementarity. Information on the occupations of individuals and
household heads is available in the form of annual records and is coded into
historical social stratification, represented as an occupational score on a continuous
scale (Lambert et al. 2013). This classification enables systematic comparisons
across different cohorts. For the instrument, we selected specific occupations, such
as church assistants and church musicians, and augmented the microdata with
parish and county annual examination records that report the counts of clergy in
these roles (The Demographic Data Base 2022).
Finally, we had access to two additional socio-economic outcomes, which are
unique for such distant cohorts as we study. For the data from northern and central
Sweden, we employ a variable indicating an onset of disability, such as blindness,
deafness, mental and behavioral disorders (insanity, epilepsy, and speech
disorder), and general weakness (“crippleness”). The variable is derived from the
church records and encoded to ensure consistency across different cohorts
(Wisselgren and Vikström 2023). For the northern parishes, we have also obtained
an individual’s literacy until the year of 1870 (for Generation 1). Annual literacy
test was a time when villagers held confidential talks with a priest and spend some
time together, and the occasion was often rounded off with a party (CEDAR 2022).
Literacy is registered annually as a test on the catechism and on reading ability, on
a categorical scale.
The outcomes available for the offspring cohorts include life expectancy,
disability-free life expectancy, and occupational score. We refrain from estimating
the effects for literacy rates, as the offsprings’ literacy is almost perfectly
(positively) collinear with the vaccination status of parents.
17
3.4 Selective Attrition
Our sample comes from the historical longitudinal datasets that are likely
prone to selective migration but not false linkage. In this section, we highlight
exceptional qualities of the data and present the ways we deal with selective
migration.
Digitized family links and demographic events form the foundation of our
dataset, ensuring its high qualities. First, the Swedish household-based
longitudinal parish registers offer a continuously updated record of demographic
events, maintaining family units on a single page as long as they lived together.
Second, the records were continuously updated based on the events registers when
new demographic events occurred. This double- bookkeeping system enables
accurate tracking over individuals (for example, when they out-migrate and then
in-migrate). Finally, due to their role as Sweden’s official registration system until
1990, these records offer complete population coverage, regardless of church
affiliation. In Table A1 in Appendix A, we confirm high quality of digitization by
detecting no significant associations between the vaccination status and seasons of
birth – the common marker of data inaccuracy.
However, a disadvantage of Swedish data sources is that they record
individuals only within parish borders. For the population we focus on (born in
1790–1910), two important strategies helped mitigate this limitation: a portion of
the data (10%) was linked to national death records. Moreover, the data were
collected from clusters of neighboring parishes, and individuals were tracked
within these clusters. This strategy improved coverage, as most movements
occurred within a 15-kilometer radius, with people typically relocating within the
same or nearby parishes rather than moving long distances (Dribe 2003b). In the
18
sample, we observe that the median age of the leavers is 18.1 years, coinciding
with the typical age at which youth left the household and began working, likely
in a nearby parish not included in the sample.
The sample of Generations 2 and 3 includes the full population of children of
all individuals observed in the study area, including return migrants. Offspring
from 37% of individuals in Generation 1 are observed. Figure A4 Appendix A
illustrates differences in observable characteristics between Generation 1
individuals with and without observed children. Notably, the likelihood of having
observed children is uncorrelated with individuals’ socio-economic traits, such as
family occupational scores, literacy, or maternal marital status, suggesting that we
are not selectively observing healthier children. The association with year of birth
is marginally statistically significant. Substantial disparities are observed among
parishes, but identifying their sources is challenging, as they are not linked to
geographic factors like the south-north or urban-rural divide. Perhaps more
importantly, Generations 2 and 3 are represented across all 70 parishes and 31
cohorts, identical to those studied in Generation 1.
In general, the direction of bias related to selective migration is difficult to
predict in our context. Many families, such as those who were landless, had many
children, or included widows, lacked the resources for long-distance moves; at the
same time, farmers were likely to stay due to extensive local social networks and
access to other resources (Vikström, Marklund, and Sandström 2016). Perhaps the
only coherent factor driving local out-migration was high grain prices, which
negatively impacted much of the population by making basic food increasingly
unaffordable (Dribe 2003a). The appeal of this factor is that it is exogenous to
19
individual decisions before migration, serving as a predictor of migration and
helping us address potential bias from selective migration.
To correct for selective migration, we adjust our models using the Heckman
correction procedure (Heckman 1979). In the first stage, the probability of being
included in the estimation sample is modeled as a function of rye prices (rye being
the most common grain) and month of birth (a common predictor of data accuracy)
in a probit model. We interact these variables with birth year dummies to follow a
DID structure (see related discussion in Sant'Anna and Zhao 2020). Rye prices are
taken from Jörberg (1972) and set based on the median cohort for each generation
when they turn 18: years 1825 (Generation 1), 1860 (Generation 2), and 1910
(Generation 3). We then predict an inverse Mills ratio for each individual and
include it as a covariate in the estimation model. We also tested an alternative
correction strategy—inverse probability weighting, with weights derived based on
predictions using the same factors (Weuve et al. 2012); however, our results were
nearly identical to those obtained with the Heckman correction. We report our
Heckman-adjusted estimates for each outcome and each generation.
4. Empirical Strategy
4.1 Selection into Vaccination
We begin with the analysis of selection for vaccination against smallpox by the
age of two for Generation 1. From the microdata, we obtained various background
characteristics of the individual, measuring parental wealth (occupational score
and marital status), literacy, parenting style (survival history of the family and
death of a sibling due to an external cause), as well as the year and parish of birth.
Figure A5 in Appendix A presents the OLS estimates for these variables. The
results show that most variables measuring family conditions correlate weakly or
20
not at all with the probability of children being vaccinated. For instance, paternal
literacy and church attendance does not influence the probability, and a one-
standard deviation change in paternal occupation score increases the probability
by only 0.012 percentage points. These results align well with the fact that
vaccination was free for parents and did not face opposition in Sweden.
The results also indicate that differences in a child’s vaccination status
primarily stem from the parental parish of residence in the first years of the child’s
life. The differences across parishes in the proportion of children vaccinated by the
age of two vary between -1.1 to 0.16 percentage points compared to the baseline.
Previous research has shown that the availability of vaccinators, such as the ratio
of clergy, church assistants, and church musicians per population, explains such
geographical differences (Sköld 1996b). Another significant factor is the year of
birth, as vaccination was first introduced in 1801, and the vaccination rate steadily
rose in the subsequent years. The findings therefore suggest that the factors driving
vaccination of a child by the age of two appear at the regional and cohort level.
Even with no indication of selection into vaccination at the family level based
on observables, selection could still appear from unobservable factors. For
instance, parishes with a higher share of vaccinated children may also be
characterized by higher levels of trust to authorities, which, in turn, are eager to
implement health policies that benefit parishes’ residents, such as employ licensed
midwives or practice isolation of sick residents before it became a widespread
health measure (Lazuka, Quaranta, and Bengtsson 2016). On the individual level,
families that decide to vaccinate their own child may also be more cooperative and
such social norms could affect the child’s future outcomes and the outcomes of the
next generations regardless of initial vaccination (Lazuka and Elwert 2023;
21
Acemoglu and Jackson 2015). To address selection into treatment for Generation
1, we apply three methods: mother fixed effects, DID, and SSIV. As we show
below, we need all three methods to ensure that we obtain quasi-random variation
in individual vaccination status that we can use to explore the intergenerational
transmission of this vaccination’s benefits to the outcomes of Generations 2 and 3.
4.2 Mother Fixed Effects
As a first strategy to address unobservable selection into a child’s smallpox
vaccination, we employ mother fixed effects. Mother fixed effects will allow us to
compare biological siblings, one of whom received the treatment while the other
did not. This effectively removes all fixed, unobservable family-related factors that
may affect both the treatment and long-term outcomes in life. The model is as
follows:
(1) Yiprt = βVaccinatediprt + μm + (ηt + γp + δrt + Xi(p)t Γ) + εirpt
The index i denotes individuals in Generation 1, μm is a set of mother fixed effects.
The dependent variable, Yiprt, is an individual’s outcome, such as years lived after
the age of 2, disability-free years lived after the age of 2, literacy, and occupational
score. In an additional specification, we will add a set of controls to effectively
control for time-varying factors at the family and area levels, such as changes in
parish of residence, local health policies, or family-specific disease events.
Vaccination here can be treated as a positive external shock to one sibling but not
the other, occurred because at that time family resided in the parish where
vaccination was provided or the child was born when vaccine became available,
even though the family decisions were orthogonal to the decision to vaccinate both
of their children.
22
4.3 DID Approach
Our second strategy to deal with selection is to adapt a DID design previously used
to identify the outcomes of exposure to certain infectious diseases targeted by
nationwide rapid interventions (Lazuka 2020, Ager, Hansen, and Jensen 2017).
We exploit two sources of variation: (i) the varying exposure of different cohorts
to the introduction of the smallpox vaccine in 1801, and (ii) the relatively larger
benefits for individuals born in parishes with greater availability of church
assistants and musicians compared to those born in parishes with lower
availability. As explained in Section 3.2, our sample includes individuals who
were either vaccinated by age 2 or never vaccinated; thus, the arrival of the vaccine
in 1801 serves as a clear watershed, nearly perfectly distinguishing treated and
untreated cohorts. Pre-vaccine availability of church assistants and musicians
serves as a measure of a parish’s readiness to perform vaccinations (or local
demand)—the higher the availability, the greater the vaccine uptake. To capture
pre-treatment variation, we thus do not use the smallpox infection rate, as our focus
is ultimately on the impact of the vaccination itself, not the disease.
We estimate the following model:
(2) Yiprt = βPostXCpost-1,p + ηt + γp + δrt (+ Xi(p)t Γ) + εirpt
The index i denotes individuals in Generation 1, p denotes parishes, and t is
cohort. Post refers to individuals born from 1801 onward and belonging to
Generation 1. For Generation 1, we analyze a panel of 31 cohorts, born between
1790 and 1820, across 70 parishes. Cpost-1‚p is pre-1801 availability of church
assistants and musicians at the parish level. ηt is cohort (i.e., year of birth) fixed
effects. γp is parish fixed effects. r denotes six geographic regions (counties), and
we include region-by-cohort fixed effects, δrt, into the main model to capture the
23
potential impact of the divergent development of regions on the outcomes: In the
period of study the county was governed by a county governor with sole
responsibility, including the control of vagrants and hospitals, and the stipulation
of smallpox vaccination campaign (Sköld 2000). The dependent variable, Yiprt, is
an individual’s outcome, such as years lived after the age of 2, disability-free years
lived after the age of 2, literacy, and occupational score.
Pre-1801 vaccinator availability is measured as the average number of church
assistants and musicians in each parish from 1790 to 1800, as shown in Figure 2.
To facilitate interpretation of the estimates, we normalized these availability
indicators by dividing by the interquartile range (9.6 assistants/ musicians),
representing the difference between the 75th and 25th percentiles of the indicator
distribution. The resulting indicator is a continuous variable ranging from 0 to 2,
with values at both endpoints covering more than 15% of the distribution, while
the remaining values fall in between. Note that the availability indicator starts at 0
because it does not account for priests: each parish was part of a pastorat and had
a priest serving (Högberg 2004).
[Figure 2 is about here]
The parameter β in Equation 1 captures the (reduced-form, intention-to-treat)
effect of smallpox vaccination. We expect β to be positive, as a higher availability
of church assistants and musicians should lead to increased vaccination rates and,
ultimately, better outcomes. Following recent methodological developments in the
DID literature (review of Roth et al. 2023), we impose the following assumptions
for β to have a causal interpretation: no anticipation, the stable unit treatment value
assumption, and the conditional parallel trends assumption. The no anticipation
assumption is satisfied due to the sudden arrival of the vaccine and the
24
community’s lack of prior knowledge of its benefits (Sköld 2000). The stable
treatment value assumption is ensured by the parishes’ regulated vaccine
distribution process: the vaccine was provided to priests in quantities sufficient to
vaccinate all parishioners and then distributed locally by vaccinators (Sköld
1996b).
Since the parallel trends assumption could be potentially violated in our
setting, we impose it conditionally, controlling for group-specific pre-trends. We
assume that only groups of parishes with similar pre-treatment characteristics must
exhibit parallel pre-trends. First, Equation 1 already includes county-by-cohort
fixed effects. In an additional specification, we also introduce interactions between
cohort dummies and group-level observable characteristics (measured at the parish
or individual level), in Equation 1 denoted as Xi(p)t.
Among group-level characteristics, we include factors that influence
families’ decisions to vaccinate, related to the changing behavior and outcomes of
parish residents (as discussed in Section 4.1). We also consider local measures
(i.e., at the group of parishes level) of wealth, religiosity, and health policies to
capture regional differences in responses to the mandatory vaccination campaign.
Specifically, we include the number of midwives (interacted with cohort dummies)
to account for healthcare development and the composition of vaccinators in the
area; the smallpox death rate to control for demographic and disease conditions;
the share of urban population and university students per capita to account for
urbanization and social progress; the number of priests to control for religiosity;
and the price of rye as an economic development indicator. To address potential
correlations in local shocks, we cluster standard errors at the parish level in each
specification.
25
Finally, to detect non-parallel pre-trends and examine the effect dynamics,
we will estimate an event-study model:
(3) Yiprt = βt
pre Cpost-1,p
1799
t=1791 + βt
post Cpost-1,p
1820
t=1801 + ηt + γp + δrt + εirpt
In this model, all terms are defined as before. The coefficients βt
pre a are estimated
for pre-vaccine cohorts by interacting the availability indicator Cpost-1,p (i.e., the
same as in Equation 1) (as in Equation 1) with each cohort born before 1801, using
the 1790 and 1800 cohorts as reference categories. The coefficients βt
post are
estimated for each post-vaccine cohort.
4.4 SSIV Approach
4.4.1 Intuition and Equations
The smallpox vaccination evolved gradually and even stepwise from 1801
across Swedish parishes; therefore, we adopt an SSIV approach that allows us to
capture exogenous variation in children’s smallpox vaccination in Generation 1,
better fitting its nonlinear progression. Our ultimate goal is to use this variation to
explore its impact on the outcomes of Generations 2 and 3.
Following a SSIV methodological literature, we use the instrument’s formula
that best describes the impact of the shock (Borusyak, Hull, and Jaravel 2022). Our
instrument is Cp(t-1) x Ct: it is based on the interaction between the number of church
assistants and church musicians at the parish level and their ratio at the country
level. Previously, in a DID approach, we defined Cpost-1‚p as the pre-1801
availability of church assistants and musicians at the parish level. With the SSIV
approach, we aim to measure availability for each cohort, introducing Cp(t-1) as the
number of church assistants for each parish in the previous year (cohort). Ct
represents the national ratio of church assistants and musicians compared to the
previous year, capturing the yearly progression of vaccination as mandated by
26
national laws (in contrast to the DID approach, where Ct was essentially a binary
indicator turning to 1 for post-vaccine cohorts). The interaction term mirrors the
logic of the SSIV method applied to panel data, where Cp(t-1) serves as shares and
Ct as national shifts (shocks).
Figure 3 presents the development of the national number of church assistants
and musicians between 1790 and 1820, along with the rate of change. As shown,
the rate of change captures large shifts in vaccine supply in the years 1805 and
1815, coinciding with national laws mandating the employment of church
assistants for vaccination and the mandatory vaccination of young children. There
is a small shift in the pre-vaccine years as well, which, however, would not impact
the capture of children’s smallpox vaccination since no children were vaccinated
in those years.
[Figure 3 is about here]
We plot the interacted instrument for each year and parish (covering the years
1790-1820 and 70 parishes) in Figure C1 Appendix C. To facilitate interpretation,
we have rescaled the instrument using its interquartile range between the 5th and
95th percentiles (14 persons or units). As a result, the rescaled instrument is a
continuous variable ranging from 0 to 4.2. For nearly every parish, we observe that
the size of the instrument increases after 1801, reflecting local demand and the
availability of the vaccine. For half of the sample, the instrument’s value is 0; we
retain these observations as the null group, which reflects the never-treated group.
To remind, the parishes with zero values of the instrument did not employ church
assistants and musicians, but they had priests and other vaccinators to perform
vaccination. Due to the identifying assumptions that we describe below, we would
like to capture only the variation due to church assistants and musicians as
27
vaccinators. The overall ranking of counties based on this instrument’s quantity
perfectly aligns with the county ranking observed across the entire country (Sköld
1996b).
For Generation 1, our first- and second-stage equations are as follows:
(4) Vaccinatediprt = α(Cp(t-1) x Ct) + Xi(p)t Γ + ηt + γp + δrt + εirpt
(5) Yiprt = βVaccinatediprt
+ Xi(p)t Γ + ηt + γp + δrt + νirpt
The Cp(t-1) x Ct term is the interacted instrument, representing the number of
church assistants and musicians in each parish in the previous year multiplied by
the national rate of change in the number of church assistants and musicians.
Vaccinatediprt indicates the individual smallpox vaccination status before age 2 for
Generation 1. All other terms are defined as previously.
We will also present the results of the reduced form because they have a clear
interpretation as an intention-to-treat effects. The reduced-form equation is as
follows:
(6) Yiprt = ά(Cp(t-1) x Crt) + Xi(p)t Γ + ηt + γp + δrt + uirpt
For Generation 2 and 3, the second-stage equation is as follows:
(7) Yjiprt = βVaccinatedjiprt
+ Xji(p)t Γ + ηt + γp + δrt + νjirpt
The index j denotes children (Generation 2) and grandchildren
(Generation 3). We stack individual observations for the sample of mothers and
fathers (grandmothers and grandfathers from the mother’s and father’s side)
because, as we find, the effects are similar regardless of the parent’s
(grandparent’s) gender.
For Generation 1, we analyze a panel of 31 cohorts, born between 1790 and
1820, for 70 parishes. Generation 2 consists of biological children of Generation 1
28
(and who are born between 1805 and 1865), and Generation 3 consists of
biological grandchildren of Generation 1 (and who are born between 1820 and
1910). Equation 3 models the outcomes of children and grandchildren, Yjiprt, as a
function of variables from Generation 1, aiming to estimate the total vaccine effect
transmitted across generations. In Section 6.2, we will further explore the
mechanisms behind this transmission by applying causal mediation analysis,
incorporating the characteristics of children and grandchildren.
4.4.2 Identifying Assumptions
The estimates of the instrument’s effects on the vaccination and the
outcomes, α and ά, should be positive in every equation. Their interpretation
resembles that of the DID strategy, where we compare pre- and post-vaccine
arrival cohorts and parishes with varying availability of church assistants and
musicians, which reflects the parish’s readiness to vaccinate or the local demand
for vaccination. With the SSIV approach, we compare cohorts experiencing
different national shifts (reflecting vaccine supply) across parishes with varying
readiness or local demand, measured as changing across cohorts. For causality, α
and ά must satisfy assumptions that we mentioned for DID.
However, our main interest is in obtaining causal estimates of the effects of
Generation 1’s individual smallpox vaccination, β. The causality requires four
assumptions (Imbens 2014). If these assumptions hold, our SSIV estimates reflect
the average effect for the observations that comply with the instrument, i.e., a local
average treatment effect (Angrist, Imbens, and Rubin 1996). Even though
smallpox vaccination is individual, our instrument captures its group variation by
construction. In our setting, compliers are therefore parishes with higher
proportions of vaccinated children that responded to the interacted instrument.
29
Those parishes that did not respond to the instrument do not contribute to the
estimate. We will address the assumption of instrument relevance in Section 5.3.1,
and here, we will focus on the remaining three assumptions.
First, the instrument has no direct effect on the outcomes other than through
its influence on the assignment to vaccination (exclusion restriction). To address
this assumption, we chose to focus on church assistants and church musicians as
the only subgroup of vaccinators. Historical sources highlight that Church workers
were trustworthy and literate yet lacking knowledge on medicine (Sköld 1996b).
The law of 1804 stipulated that each parish must employ a church assistant or
musician for vaccination, thereby blocking the potential monopolization of the
process by doctors. Vaccinations were easy to learn, following the instructions
distributed by the state and short training by the priest (Banggaard 2002). As an
illustration, a church musician who assisted at choirs became the first vaccinator
in Kävlinge, one of the parishes in southern Sweden, and vaccinated against
smallpox as his second part-time job; he did not participate in other health-related
matters (Landsarkivet i Lund 1805-1827). In the neighboring parish, initially, a
licensed midwife vaccinated children (Landsarkivet i Lund 1785-1857). Although
the means of preventing disease were very limited in the beginning of the 19th
century, some were practiced by doctors, such as cause-of-death counting and
isolation of the sick, or by midwives, such as proper assistance at labour. In these
two parishes, our instrument will capture the vaccination efforts of a church
musician but not of a midwife.
Second, conditional on controls, we assume that there are no omitted
common factors affecting both the instrument and the outcome (random
assignment). In our case, the series of lagged church assistants and musicians in
30
the parish along with the shocks in current church assistants and musicians in the
region (which constitute two components of the interacted IV) are likely to be
correlated with both fixed and varying characteristics of the parish (region), such
as wealth or religiosity, for instance, which influence the outcomes too. In practice,
this is not a serious problem for our estimates for several reasons. Parish fixed
effects in the baseline specification control for all permanent factors at the parish
level affecting the employment of church assistants and musicians. We also
introduce families’ characteristics affecting families’ decision to vaccinate
children interacted with cohort dummies (as in section 4.1), which account for the
parish shocks related to the changing parish residents’ behavior and outcomes. To
identify any unobserved time-varying parish shocks, we examine pre-trends and
find none, as we further elaborate on in Section 5.3.2.
In relation to the regional shocks, they similarly can reflect regional health
policies, other than vaccination. The region-year of birth fixed effects in our
baseline specification account for any such effects, observed and unobserved. Our
analysis also introduces interactions between cohort (i.e., year of birth) dummies
and local (i.e., for the group of parishes) measures of wealth, religiosity, and health
policies, which capture differential responses of regions to the mandatory
vaccination campaign. In particular, we include the number of midwives
(interacted with cohort dummies) that will control for development of healthcare
and composition of the vaccinators’ group in the area; smallpox death rate will
control for demographic and disease conditions; the share of urban population and
university students per capita will control for the urbanization and progressivity;
the number of priests will difference out the effects of religiosity; and the price of
31
rye will control for economic development. Finally, to account for the mutual
correlation of the local shocks, we cluster standard errors at the parish level.
Third, the instrument must ensure that treatment becomes a more attractive
option (monotonicity). We have searched the local vaccination reports
(Riksarkivet 1796-1820) to identify the possibility of “defiers”, i.e., cases in which
parishes reduce the vaccination rate when there is a positive regional employment
influx of church assistants and church musicians, and increase it when the influx
is negative; we have not found any such cases. Under the presence of
heterogeneous treatment effects, as discussed in Borusyak, Hull, and Jaravel
(2022), a causally interpretable IV estimand is guaranteed as long as the treatment
(i.e., individual vaccination) is correctly specified, shares are non-negative, and the
true effects of shocks on each treatment are monotone (i.e., there are no “defiers”).
We have already discussed that the error in the treatment variable is unlikely in
Section 3.2. The shares cannot be negative by construction.
5. Results for Generation 1
5.1 Mother Fixed-Effects Estimates of the Impact of Smallpox Vaccination
We begin by presenting the results of the mother fixed-effects estimations, shown
in Table 1. The mother fixed-effects results indicate positive and highly
statistically significant effects of smallpox vaccination in childhood on both health
and economic lifetime outcomes of Generation 1, regardless of specification. In
the models with only mother fixed effects, vaccination by age two increases the
number of remaining years lived after age two by 14 years, disability-free years by
13 years, raises the probability of possessing good literacy skills by 12 percentage
points, and improves occupational scores by 4.3 units. In the models with
additional controls that account for time-varying effects, the vaccination estimates
32
adjust slightly, depending on the outcome, but remain sizable and highly
statistically significant (at the 99% significance level). Regarding the Heckman-
correction procedure, we find it reduces the effect on years lived to 11 years,
disability-free years to 10 years, with only small adjustments for good literacy and
occupational scores. Therefore, we will rely on Heckman-adjusted effect estimates
in our future comparisons with DID and SSIV estimates.
[Table 1 about here]
Mother fixed-effects produce the local average treatment effects of
vaccination for families that have a varying treatment status of their children
(Miller, Shenhav, and Grosz 2023). To analyze a mothers’ complier population, in
Figure B1 Appendix B, we assess the differences between the families with and
without varying vaccination status of their children. We also provide the “naïve”
OLS regression results—without mother fixed effects—in Table B1 Appendix B.
Mothers who choose to vaccinate some children but not all have a higher
proportion of children who die and husbands who are illiterate. However, our
mother fixed-effects estimates are not significantly different from those obtained
through a naïve control-for-observables strategy, suggesting that heterogeneity due
to socio-economic factors does not drive our mother fixed-effects results. Instead,
a more significant difference emerges based on the child’s year of birth. This
suggests that, for mothers with varying vaccination status of their children,
smallpox vaccination varies primarily due to the unavailability of the vaccine for
children born before 1801, which is the variation we need.
5.2 DID Estimates of the Impact of Vaccine Arrival
We then turn to the DID results for the impact of smallpox vaccine arrival, which
we introduce to fully capture the intuition behind the SSIV estimates. We present
33
the DID estimates for the Generation 1’s outcomes in Table 2. Both baseline and
Heckman-corrected estimates are shown for specifications following Equation 2,
with and without additional controls. We also present the event-study estimates in
Figure 4.
[Table 2 and Figure 4 are about here]
The DID results indicate that the arrival of the vaccine significantly
improved Generation 1’s lifetime outcomes. The most conservative estimate of the
impact on remaining years lived at age 2 is 4.5 years, and for disability-free years
lived, it is 4.4 years—both statistically significant at the 1% level. For socio-
economic outcomes, the estimate is 7.2 percentage points for good literacy and 1.6
units for occupational score, each also statistically significant at the 1% level. For
most outcomes, the introduction of controls for pre-trends in observable
characteristics yields estimates like those in the baseline specification. Finally, the
Heckman correction procedure slightly reduces the estimates for health outcomes,
likely accounting for the selection of families before age 15. However, the
estimates with and without Heckman correction are not statistically different from
each other.
The event-study results—which demonstrate the evolution of the vaccine
arrival effect across cohorts—indicate the appearance of the vaccine effect for the
outcomes of post-vaccine cohorts (i.e., born from 1801 onward), coinciding with
the vaccine’s inception. For these cohorts, the effects remain consistently positive,
with a tendency to rise. There is a slowdown around the year 1805: in this year,
parishes, following the national law, began actively employing vaccinators among
church assistants and musicians, which may have interacted with an effect
stemming from the pre-treatment number of vaccinators. For the pre-vaccine
34
cohorts, we do not find any significant effects, suggesting that parishes with
different numbers of church assistants and musicians were on the same pre-trends
and supporting our main identification assumptions. These results align with the
finding that DID estimates remain stable after adding controls.
To align the DID results with the mother fixed-effects results, we calculate
the indirect least squares estimates for individual smallpox vaccination. We do this
by dividing the DID estimates by the proportion vaccinated among Generation 1,
which is 35%. The final effects, based on the conservative estimates, are as
follows: 12.8 years for remaining years lived at age 2 (4.5/0.35), 12.6 years for
disability-free years lived at age 2 (4.4/0.35), 21 percentage points for good literacy
(7.2/0.35), and 4.6 units for occupational score (1.6/0.35). These effect sizes
closely align with our mother fixed-effects estimates, suggesting that we are
capturing the effects of the same phenomenon. However, the indirect least squares
provide only effect sizes, not the variation in smallpox vaccination within
Generation 1 that could be used to explore the outcomes for Generations 2 and 3.
For this, we implement an SSIV strategy.
5.3 Linear SSIV Estimates of the Impact of Smallpox Vaccination
5.3.1 Descriptive Analysis
We begin the SSIV analysis with the relationships between the interacted
instrument and the probability of being vaccinated by the age of two (first-stage)
and the lifetime outcomes (reduced-form), shown in Figure 5, Panel A. We
aggregate the estimation sample by the birth cohort and plot the observations and
the fitted line, weighted by the number of individuals in each cohort. To interpret,
recall that we have rescaled the instrument using its interquartile range between
the 5th and 95th percentiles. Therefore, in our context one unit change in the
35
instrument means its maximum impact. The results show a strong positive
association: one unit change in the interacted instrument increases the share of
vaccinated children by 31%.
[Figure 5 about here]
The reduced-form relationships are shown on Figure 5 Panel B, for each
lifetime outcome separately. All outcomes are positively associated with the
instrument. One unit change in the instrument is associated with 1.45 more years
lived and 1.25 more disability-free years lived after the age of two. The relationship
with economic outcomes in adult ages is also strong: the share of individuals with
good literacy skills increases by 7 percentage points and occupation score by 1.13
units, because of one unit change in the instrument. The figures are rough
approximations of the first-stage and reduced-form estimates, because they do not
consider control variables, important for the identification of the causal effects.
5.3.2 Reduced-form and 2SLS estimates
We turn to the SSIV estimates of the impact of vaccination by the age of two on
lifetime outcomes in later ages. For completeness, we will report both baseline and
Heckman-corrected estimates.
To start with, for all outcomes and specifications, the Kleibergen-Paap F-
statistic, which is robust to heteroskedasticity and clustering in errors, in the first
stage is close to 50, meaning that the interacted instrument yields a strong impact
on the probability of being vaccinated in the first ages of life (Keane and Neal
2023). The first-stage results imply that a unit change in the interacted instrument
increases the probability of being vaccinated by the age of two by 15.4 percentage
points, when considering a sample of individuals for years lived as an outcome,
for instance. In comparison to the results of the descriptive analysis, we observe a
36
reduction in the impact of the instrument on the vaccination rate, due to the
inclusion of the control variables necessary for causal identification.
The baseline 2SLS estimates are shown in Panel A and Heckman-corrected
2SLS estimates are in Panel B, Table 3. Regarding the impact on the outcomes,
the 2SLS estimates show a positive and statistically significant impact of
vaccination on health variables and an occupational score. Here the reduced-form
estimates are also strong. The Anderson-Rubin 2SLS test statistic draws a similar
conclusion about the impact of vaccination as the 2SLS t-statistic, indicating that
the latter is unbiased (Keane and Neal 2023). Regarding the reduced-form effects,
a one unit increase in the instrument (recall: the maximum impact) increases the
number of years lived by 1.8 and the number of disability-free years by 1.7 years.
The 2SLS estimate for the impact of vaccination on years lived and disability-free
years lived is 12 years each. The Heckman-corrected estimates are one year larger
than the baseline.
[Table 3 about here]
Turning to economic outcomes, the reduced-form impact of the instrument
is 0.5 units of occupational score in adult ages, and the 2SLS impact of vaccination
is 3 units, which is statistically significant at the 1% level. For literacy, the 2SLS
impact of vaccination loses statistical significance but remains in a similar
magnitude, with a 11-percentage-point increase in the probability of having good
literacy skills in adult ages. For this outcome, our 2SLS estimates are thus not
informative about the causal vaccination effect, which, however, does not imply
that there is no such effect. Since we further find vaccination effects on mental
disability, the absence of statistically significant SSIV results for literacy is likely
37
due to the noisiness of the literacy measure. For the economic outcomes, the
Heckman-corrected estimates are not different from the baseline.
We observe that our results are robust to the inclusion of additional parish-
and time-varying controls, but the estimates tend to become less precise when
more controls are added. This happens because many controls in the extended
model are also strongly correlated with the vaccination variable, so adding these
controls reduces variation in the vaccination variable induced by the instrument
and increases standard errors. The point estimate of the vaccination effect is
smaller in the instrumental-variables compared to the controlling-for-observables
estimations but remains similar in statistical terms. However, even the lowest, a
10-year increase in years lived due to smallpox vaccination in the 2SLS
estimations is large enough to account for most of the cohort improvements in life
expectancy after the age of two.
5.3.3 Parallel Pre-Trends
It is possible to validate the shift-share instrument by examining whether
observations with different exposure shares exhibit parallel trends prior to the
shock (Borusyak, Hull, and Jaravel 2022). This follows from that linear
instrumental-variables with shift-share as an instrument varying by year of birth
and parish of birth are analogous to the DID with continuous treatment, with
underlying “parallel trends” restrictions. Any evidence for significant pre-trends
would signal that a set of cohorts in particular parishes with different levels of the
instrument would have evolved differently from each other even in the absence of
the vaccination campaign.
To assess the plausibility of the parallel trends, we create the leads of the
instrument and estimate the reduced-form effects with these leads instead of the
38
instrument. The results for the models with two sets of covariates are presented on
Figure C2 Appendix C. Overall, there is no evidence of significant pre-trends in
the outcomes. However, note that the evidence for no pre-trends points to the
absence of the time-varying shocks, sufficient for the causality claim of the
reduced-form estimates.
5.4 Nonlinear SSIV Estimates on Mortality and Disability Risks
5.4.1 2SRI Estimates
This section examines when the health benefits of smallpox vaccination
appear for Generation 1 and whether they are due to non-specific vaccination
effects. We use nonlinear instrumental-variables models because an individual’s
risk of death changes over their lifetime, and death from one cause competes with
others. Nonlinear (duration) models also account for censoring from outmigration
and test the Heckman correction procedure. Appendix D includes results from
mother fixed-effects estimations and robustness checks for nonlinear models.
We apply duration SSIV models using Cp(t-1) x Ct as the instrument, and a
two-stage residual inclusion (2SRI) model (Palmer 2024; Wooldridge 2015; Terza,
Basu, and Rathouz 2008). The second equation is:
(8) hiprt = exp (βVaccinatediprt + Xi(p)t Γ + ηt + γp + δrt + εirpt
+ νirpt)
Here, hiprt(a) is the all-cause hazard of death (disability) for individual i born
in parish p, observed at age a. The first stage uses logistic regression, saving
Anscombe residuals for unbiased average treatment effect estimates (Basu and
Coe 2017). In the second stage, we add the residuals from the first stage and
estimate a proportional hazard model, preferred for including control-function
residuals (Palmer 2024). Both a survival function and age-specific life expectancy
are derived post-estimation.
39
The SSIV results in Table D1 show that vaccination reduces mortality risk
by 68%. For disability, vaccination reduces risk by 73-80%. The first-stage
residual is small but insignificant, indicating no omitted variable bias, similar to
linear models. From the 2SRI models, we derive survival functions and life
expectancy, with vaccination improving survival at all ages (see Figure D.1).
Vaccination adds 0.06 years of life expectancy between ages 2-15, 0.15 years
between ages 15-70, and 0.08 years afterwards, totaling 11.6 extra years at age 2
(51.8 years for vaccinated vs. 40.2 years for unvaccinated). For disability, the
patterns are similar to mortality, with vaccination adding 12.5 disability-free years.
Vaccination increases disability-free life expectancy primarily after age 20, adding
2.8 years (Figure D.1, Panel B).
5.4.2 Cause-Specific Mortality and Disability
We further assess the vaccination effect on the hazards of death and disability
by cause. An ideal way to obtain such effects is to model cause-specific hazards
by treating events due to competing causes as censored observations. Therefore,
we apply an approach by Lunn and McNeil (1995): stack the events with as many
rows as there were causes of death (disability) and fit a 2SRI model (i.e., with
controls and a first-stage residual) stratified by cause. The controls and the first-
stage model are the same as in section 5.3.1.
Table D.1 Appendix D shows the results for cause-specific mortality and
disability. Vaccination reduces the risk of death from smallpox to almost null,
implying high efficiency of the historical vaccine. But it also reduces the mortality
risk from other causes by 79%. This finding for mortality suggests the presence of
“non-specific” vaccination effects. For disability, we distinguish two causes—
those known as a consequence of smallpox infection (blindness, mental
40
retardation, and general weakness) and other causes (deafness and mixed causes).
Our results show that smallpox primarily reduces the risk of disability due to
smallpox-related causes (by 42%), linking smallpox to the individual’s ability to
learn and physical fitness.
5.5 Influence of Epidemics and Other Interventions
In this section, we explore the role that positive and negative shocks, aside
from vaccination, played in generating our results.
Presumably, smallpox epidemics severely affected the cohorts in question,
particularly before the introduction of the vaccine, and left behind a negatively
selected group of children who serve as a comparison. If this is the case, our
findings on lifetime effects should be interpreted as the combined result of the
vaccine’s positive impact and the benefits of avoiding the detrimental effects of
epidemics. Previous research has demonstrated that airborne disease epidemics,
including smallpox, left long-term scars on survivors, manifesting in lower
survival rates (Quaranta 2014).
The institutional context of the vaccination campaign suggests that no
beneficial interventions took place in parallel. Medicine was underdeveloped at
that time, and epidemiological hospitals helpful in isolating infectious disease were
built much later (Lazuka, Quaranta, and Bengtsson 2016). One potential
intervention to consider was the practice of midwives—they improved maternal
survival and could influence infant health, with long-term health consequences.
However, previous research has found no effects on infant health prior to the
acceptance of the germ theory of disease and re-education of midwives at the late
nineteenth century (Lorentzon and Pettersson-Lidbom 2021; Lazuka 2018).
Another intervention to contemplate is the introduction of potatoes around 1805.
41
At that time, farmers began growing potatoes in arable fields, which increased the
production of nutritious food, potentially benefiting the growth and health of the
population (Lazuka, Bengtsson, and Svensson 2023).
We assess the influence of smallpox epidemics and other interventions on
vaccination against smallpox and lifetime outcomes by introducing an interaction
of child smallpox mortality, the ratio of midwives to population, and the quantity
of potato seeds per square kilometer (observed at the parish level) with an
interacted IV into Equation 3 (the reduced-form equation). Table E1 in
Appendix E reports the results.
The reduced-form estimates of the interacted instrument on all outcomes
remain largely unchanged after accounting for interactions with other shocks,
suggesting a strong and unbiased direct effect of vaccinators’ efforts on lifetime
outcomes. Moreover, there is an additional beneficial effect for individuals who
are positively affected by vaccination efforts and born during smallpox epidemic
years, amounting to an increase of one year in lifespan and two units of
occupational score. Since the early smallpox vaccine was highly effective (Hedin
1802), this additional effect likely arises from the detrimental outcomes
experienced by unvaccinated individuals, whose lives were significantly impacted
by the disease. Therefore, two-thirds of the effects we observe are likely due to
analyzing a historical population severely affected by epidemics.
For positive cointerventions, we do not find any interactive effects. For
midwives, the absence of the interaction effect aligns with the observation that
midwives or doctors did not serve as the primary group of vaccinators. Regarding
the impact of potatoes, the results reinforce the notion that smallpox is a disease
with a low correlation to nutritional intake (Fenner et al. 1988).
42
6. Results for Generation 2 and Generation 3
6.1 The Effects on Longevity, Disability, and Occupational Score
We next consider the results for Generation 2 and 3, having shown that the
SSIV strategy provides us with a vaccination effect for Generation 1 that is likely
causal and similar to alternative causal identification strategies. In this section, we
turn to the effects of the Generation 1’s childhood vaccination status on the
outcomes of Generation 2 (to whom Generation 1 are parents) and Generation 3
(to whom Generation 1 are grandparents). We stack individual observations for
the sample of mothers and fathers (grandmothers and grandfathers from the
mother’s and father’s side). As explained in Section 4.4.1, we model the outcomes
of Generation 2 and 3 as a function of variables from Generation 1, aiming to
estimate the total vaccine effect transmitted across generations. We also provide
the Heckman-corrected effects, as detailed in section 3.4.
Table 4 presents the SSIV results for the outcomes of Generation 2 and 3 in
Panels A and B. Smallpox vaccination of Generation 1 improves the health
lifetime outcomes of both Generation 2 and 3, and the effects are statistically
significant at least at the 5% level. If to rely on the magnitude with a more extended
set of controls, life expectancy at birth increases by 2.2 years for Generation 2 and
1.1 years for Generation 3. Regarding occupational score, we find the marginally
statistically significant effect for Generation 2 only, with a 1-point increase on a
continuous scale, while Generation 3 does not benefit from grandparents’
vaccination status. The relative magnitudes of the effects on life expectancy and
occupational score are around 20% and 10% for Generation 2 and 3, when
compared to the effects observed in Generation 1. The increase in disability-free
life expectancy—a measure of morbidity—is even more substantial, with gains of
43
8 years for Generation 2 and 4.3 years for Generation 3, which is more than a half
of disability gain for Generation 1. As with Generation 1’s results, a Heckman
correction procedure updates the coefficients only slightly.
[Table 4 about here]
Narrowing the birth cohorts to individuals born close to 1845 and 1890, with
these years serving as the median for Generation 2 and 3, does not alter the results.
Our findings regarding the health of succeeding generations therefore suggest
potential mediation (i.e., reinforcement) by other influential factors, such as health
interventions against infectious disease implemented from the 1880s, for instance.
The absence of transmission of socio-economic relationship to the distant
generations is consistent with increased social mobility among cohorts born
around the 1890s in early industrializing Sweden. We further explore these
possibilities in the causal mediation analysis.
6.2 Mechanisms of Intergenerational Transmission
In the final section, we conduct a causal mediation analysis of the impact of
Generation 1 vaccination on the outcomes of subsequent generations. While there
are numerous potential mediators in these long-term relationships, our primary
focus is to distinguish between factors related to nature and nurture. Specifically,
we aim to determine whether smallpox vaccination induces people to transmit
knowledge through nurturing and/or if there is a direct biological transmission of
past environments (i.e., epigenetic inheritance) (Collado, Ortuño-Ortín, and
Stuhler 2023; Vågerö et al. 2018).
We select mediators based on their relevance to nurturing and natural
influences. To measure nurture, we analyze variables such as the childhood
smallpox vaccination status of Generation 2 (and Generation 3), whether the child
44
was assisted by a midwife at birth, and the parental occupational score. For nature,
we use the fixed component derived from the mothers of Generation 2 and 3.
Specifically, we run mother fixed effects regressions on the outcomes of
Generation 2 and 3 (i.e., years lived, disability-free years lived, and occupational
score) and predict a part of each outcome shared within mother for each
individual—our measure of epigenetic factors.
To perform the causal mediation analysis, we follow the causal inference
literature, which proposes to decompose the total effect into the natural direct
effect and natural indirect effect (Imai, Keele, and Tingley 2010). In our case, the
natural direct effect is comparing Vaccinatediprt at 1 and 0 intervening to fix the
level of mediator to 0, and the natural indirect effect is comparing the effects at
different levels of mediator, intervening to fix Vaccinatediprt at 1. Both effects are
identified under the assumptions of no unmeasured confounders between the
combinations of treatment, outcome, and mediator, given a set of observables. To
improve the plausibility of these assumptions, we perform the analysis on a set of
covariates that we used in a 2SRI model.
We follow Imai, Keele, and Yamamoto (2010) and estimate the direct and
indirect natural effects by fitting a parametric regression model for the outcome of
Generation 2 (Generation 3) and a parametric regression model for mediator in the
following ways:
(9) Y2(3)ijprt = βVaccinatedijprt + μM2(3)jprt + Xi(p)t Γ + ηt + γp + δrt + εijrpt
+ νijrpt,
(10) M2(3)ijprt = βVaccinatedijprt + Xi(p)t Γ + ηt + γp + δrt + εijrpt
+ ϵijrpt,
where Y2(3) is the outcome for Generation 2 (Generation 3), and M2(3) is the mediator
for Generation 2 (Generation 3). All other terms are defined as before. After fitting
the models (4) and (5), the method then uses simulations to calculate natural direct
45
and natural indirect effects. Robust standard errors are clustered at parish of birth
of Generation 1 and retrieved by bootstrapping.
Table 5 displays the results for direct and mediated effects on offspring’s
outcomes, in relation to four mediators. To interpret the importance of the
mediator, we need to multiply the estimate for the natural indirect effect by the
mediator’s mean. For the health outcomes, our results point to the importance of
both nurturing and epigenetics. The propensity of parents to vaccinate their
children against smallpox emerges as a significant, reinforcing mediator: because
parents (grandparents) were vaccinated against smallpox before age two and
vaccinated their children, Generation 2 and 3 experience gains of 1 and 0.8 years
of life, as well as 2.8 and 2.5 disability-free years, respectively. The impact of
epigenetic factors is also sizable but emerges only for Generation 2: the mean of
epigenetic factors (shared life expectancy) is 0.05, meaning that the estimate for
the mediated effect of epigenetic factors is 0.3 added years of life expectancy. The
impact of other mediators, like parental occupational score and assistance at birth
by a licensed midwife, is low or marginally statistically significant. In total, the
impact of both parental vaccination and epigenetic factors fully explains the
transmitted effect of the Generation 1’s vaccination effect on health of subsequent
generations.
[Table 5 about here]
For the occupational scores of subsequent generations, the mediated results
show a different pattern. Occupational score of Generation 2 increases by 2.2 units
due to parental smallpox vaccination directly. However, the natural indirect effect
of parental occupational scores amounts to 0.07 per unit and is statistically
significant at the 5% level. With a range of parental occupational scores of 61.8
46
units, the maximum mediated effect amounts to 4.5 units (61.8 x 0.072), which is
even larger than the direct effect. Previously, we did not find any significant total
effects of grandparental smallpox vaccination on the occupational scores of
Generation 3. We now observe a substantial indirect effect through parental
occupational scores: individuals belonging to Generation 3, whose grandparents
were vaccinated against smallpox by age two, receive a gain of 0.09 per unit of
their own occupational score, or 5.4 units at the maximum (61.8 x 0.087).
Overall, a positive shock to health of Generation 1, such as smallpox
vaccination, operating through various channels, enhances both health and socio-
economic outcomes for at least two more generations.
7. Conclusions
In this study, we investigated whether smallpox vaccination in early
childhood enabled individuals to live longer and become prosperous as adults, and
whether such vaccination effects were transmitted to their two consecutive
generations. To obtain the causal effects of smallpox vaccination, we applied a
SSIV approach, using the fact that vaccination in Sweden was carried out by low-
skilled clergy who otherwise did not perform public health duties. We leveraged
unique historical microdata from different areas across Sweden, covering the full
lifespans of three generations.
Our study leads us to draw several important conclusions. First, we find
evidence consistent with both specific and non-specific vaccination effects.
Smallpox vaccination increases the total and disability-free life expectancy of
Generation 1 by 11 years and enhances their occupational achievements by 10%.
Such effects emerged due to decreases in mortality from smallpox and other
causes, but also appear to have reduced disability associated with ailments that
47
could hinder human capital accumulation. Second, these effects persist across
generations. Smallpox vaccination of Generation 1 increases the life expectancy
of Generation 2 by 2 years and of Generation 3 by 1 year, as well as improving
their occupational scores. More than half of the transmitted effects are attributed
to nurture, as vaccinated individuals are more likely to vaccinate their children
across generations, while epigenetic factors account for the remainder. Finally, we
obtain similar results when utilizing different causal strategies, such as linear and
non-linear SSIV, DID, and mother fixed-effects. The results withstand a large
number of robustness checks.
Our findings are potentially important for policy as they underscore the
power of vaccination. The evidence that smallpox vaccination offers protection
not only against smallpox but also against other diseases makes vaccination a
powerful health intervention. Our findings, which highlight very long-term,
intergenerational health and economic benefits from vaccination, suggest that the
total benefits of smallpox vaccination were much larger than the existing literature
suggests. We demonstrate that while a significant portion of the effects can be
attributed to the analysis of a historical population severely affected by epidemics,
vaccination remains beneficial in the very long term, even in milder disease
environments like those seen today. Whether these findings are applicable to other
vaccines is beyond the scope of this paper but remains an important topic for future
research.
References
Acemoglu, Daron, and Matthew O. Jackson. 2015. “History, Expectations, and
Leadership in the Evolution of Social Norms.” Rev Econ Stud 82 (2 (291)):
48
423–56.
Ager, Philipp, Casper Worm Hansen, and Peter Sandholt Jensen. 2017. “Fertility
and Early-Life Mortality: Evidence from Smallpox Vaccination in Sweden.”
J E E A 16 (2): 487–521.
Almond, Douglas, Janet Currie, and Valentina Duque. 2018. “Childhood
Circumstances and Adult Outcomes: Act II.” J Econ Lit 56 (4): 1360–1446.
Anderson, D. Mark, Ryan Brown, Kerwin Kofi Charles et al. 2020.
“Occupational Licensing and Maternal Health: Evidence from Early
Midwifery Laws.” J Political Econ 128 (11): 4337–83.
Anderson, D. Mark, Kerwin Kofi Charles, Claudio Las Heras Olivares et al.
2019. “Was the First Public Health Campaign Successful?” Am Econ J Appl
Econ 11 (2): 143–75.
Angrist, Joshua D., Guido W. Imbens, and Donald B. Rubin. 1996.
“Identification of Causal Effects Using Instrumental Variables.” J Am Stat
Assoc 91 (434): 444–55.
Arnett, Donna K., Roger S. Blumenthal, Michelle A. Albert et al. 2019. “2019
ACC/AHA Guideline on the Primary Prevention of Cardiovascular Disease:
Executive Summary: A Report of the American College of
Cardiology/American Heart Association Task Force on Clinical Practice
Guidelines.” Circ 140 (11): e563-e595.
Atwood, Alicia. 2022. “The Long-Term Effects of Measles Vaccination on
Earnings and Employment.” Am Econ J Econ Policy 14 (2): 34–60.
Banggaard, Grethe. 2002. “Sygdom Og Sundhed: Offentlige Indgreb Og Deres
Virkninger I Sydsverige, Ca. 1750-1894.” Lund Papers in Economic History
76.
49
Barteska, Philipp, Sonja Dobkowitz, Maarit Olkkola et al. 2023. “Mass
Vaccination and Educational Attainment: Evidence from the 1967–68
Measles Eradication Campaign.” J Health Econ 92:102828.
Basu, Anirban, and Norma B. Coe. 2017. “2SLS Vs 2SRI: Appropriate Methods
for Rare Outcomes And/or Rare Exposures.” Health Econ 26 (8).
Baxby, D. 1985. “The Genesis of Edward Jenner's Inquiry of 1798: A
Comparison of the Two Unpublished Manuscripts and the Published
Version.” Med Hist 29 (2): 193–99.
Bengtsson, Tommy, Martin Dribe, Luciana Quaranta, and Patrick Svensson.
2021. The Scanian Economic Demographic Database, Version 7.2. Machine-
readable database.
Bengtsson, Tommy, and Martin Lindstrom. 2000. “Childhood Misery and
Disease in Later Life: The Effects on Mortality in Old Age of Hazards
Experienced in Early Life, Southern Sweden, 1760-1894.” Popul Stud 54 (3):
263–77.
Benn, Christine Stabell, Nelly Amenyogbe, Anders Björkman et al. 2023.
“Implications of Non-Specific Effects for Testing, Approving, and Regulating
Vaccines.” Drug Safety 46 (5): 439–48.
Borusyak, Kirill, Peter Hull, and Xavier Jaravel. 2022. “Quasi-Experimental
Shift-Share Research Designs.” Rev Econ Stud 89 (1): 181–213.
Bütikofer, Aline, and Kjell G. Salvanes. 2020. “Disease Control and Inequality
Reduction: Evidence from a Tuberculosis Testing and Vaccination
Campaign.” Rev Econ Stud 87 (5): 2087–2125.
CEDAR. 2021. The Demographic Data Base, U20003. Machine-readable
database, no. http://dx.doi.org/10.17197/U20003.
50
CEDAR. 2022. The Demographic Data Base, U20019. Machine-readable
database, no. http://dx.doi.org/10.17197/U20019.
Clay, Karen, Peter Juul Egedesø, Casper Worm Hansen et al. 2020. “Controlling
Tuberculosis? Evidence from the First Community-Wide Health
Experiment.” J Dev Econ 146:102510.
Collado, M. Dolores, Ignacio Ortuño-Ortín, and Jan Stuhler. 2023. “Estimating
Intergenerational and Assortative Processes in Extended Family Data.” Rev
Econ Stud 90 (3): 1195–1227.
Cook, C. Justin, Jason M. Fletcher, and Angela Forgues. 2019.
“Multigenerational Effects of Early-Life Health Shocks.” Demography 56 (5):
1855–74.
de Bree, L C J, Koeken, Valerie A C M, Leo A. B. Joosten et al. 2018. “Non-
Specific Effects of Vaccines: Current Evidence and Potential Implications.”
Semin Immunol 39:35–43.
Dribe, Martin. 2003a. “Dealing with Economic Stress Through Migration:
Lessons from Nineteenth Century Rural Sweden.” Eur Rev Econ Hist 7 (3):
271–99.
Dribe, Martin. 2003b. “Migration of Rural Families in 19th Century Southern
Sweden. A Longitudinal Analysis of Local Migration Patterns.” Hist Fam 8
(2): 247–65.
Dribe, Martin, and Paul Nystedt. 2003. “Information, Trust and the Diffusion of
Smallpox Vaccination: The Case of Scania in Sweden, 1802–1835.” Scand
Econ Hist Rev 51 (1): 9–28.
Dribe, Martin, and Luciana Quaranta. 2020. “The Scanian Economic-
Demographic Database (SEDD).” Hist Life Course Stud (2).
51
East, Chloe N., Sarah Miller, Marianne Page et al. 2023. “Multigenerational
Impacts of Childhood Access to the Safety Net: Early Life Exposure to
Medicaid and the Next Generation's Health.” Am Econ Rev 113 (1): 98–135.
Edvinsson, Sören, and Elisabeth Engberg. 2020. “A Database for the Future:
Major Contributions from 47 Years of Database Development and Research
at the Demographic Data Base.” Hist Life Course Stud (1).
Egedesø, Peter Juul, Casper Worm Hansen, and Peter Sandholt Jensen. 2020.
“Preventing the White Death: Tuberculosis Dispensaries.” Econ J 130 (629):
1288–1316.
Ekelund, Johan Martin. 1804. Om Skyddskoppor Eller Vaccinen: Säkert Och
Bepröfwadt Medel Emot Kopporne. Med Anledning Af Kongl. M Och
Vaccinations-Föreståndare Uti Södermanland. Nyköping: Pehr Winge.
Fenner, F., D. Henderson, I. Arita et al. 1988. “Smallpox and Its Eradication:
World Health Organization.”.
Finch, Caleb E., and Eileen M. Crimmins. 2004. “Inflammatory Exposure and
Historical Changes in Human Life-Spans.” Sci 305 (5691): 1736–39.
Finkelstein, Maxim, and James W. Vaupel. 2009. “Survival as a Function of Life
Expectancy.” Demographic Research S8 (29): 879–84.
Hassett, Daniel E. 2003. “Smallpox Infections During Pregnancy, Lessons on
Pathogenesis from Nonpregnant Animal Models of Infection.” J Reprod
Immunol 60 (1): 13–24.
Heckman, James J. 1979. “Sample Selection Bias as a Specification Error.”
Econometrica 47 (1): 153–61.
Hedin, S. 1802. Kopporna Kunna Utrotas Eller Vaccinationen Til Sina
Lyckligaste Följder. Kort Afhandling Med Illuminerade Tabeller. Stockholm.
52
Hofsten, E., and H. Lundström. 1976. Swedish Population History. Main Trends
from 1750 to 1970.
Högberg, Ulf. 2004. “The Decline in Maternal Mortality in Sweden: The Role
of Community Midwifery.” Am J Public Health 94 (8): 1312–20.
Hollingsworth, Alex, Krzysztof Karbownik, Melissa A. Thomasson et al. 2024.
“The Gift of a Lifetime: The Hospital, Modern Medicine, and Mortality.” Am
Econ Rev 114 (7): 2201–38.
Imai, Kosuke, Luke Keele, and Dustin Tingley. 2010. “A General Approach to
Causal Mediation Analysis.” Psychol Methods 15 (4): 309–34.
Imai, Kosuke, Luke Keele, and Teppei Yamamoto. 2010. “Identification,
Inference and Sensitivity Analysis for Causal Mediation Effects.” Stat Sci 25
(1): 51–71.
Imbens, Guido W. 2014. “Instrumental Variables: An Econometrician's
Perspective.” Stat Sci 29 (3): 323–58.
Jörberg, Lennart. 1972. A History of Prices in Sweden, 1732-1914. 2 vols. 2.
Lund: Lund University.
Keane, Michael, and Timothy Neal. 2023. “Instrument Strength in IV Estimation
and Inference: A Guide to Theory and Practice.” J Econom 235 (2): 1625–53.
Kleinnijenhuis, Johanneke, Jessica Quintin, Frank Preijers et al. 2014. “Long-
Lasting Effects of BCG Vaccination on Both Heterologous Th1/Th17
Responses and Innate Trained Immunity.” Journal of Innate Immunity 6 (2):
152–58.
Kotsadam, Andreas, Jo Thori Lind, and Jørgen Modalsli. 2022. “Call the
Midwife. Health Personnel and Mortality in Norway 1887–1920.”
Cliometrica 16 (2): 243–76.
53
Kuh, D., Y. Ben-Shlomo, and S. Ezra. 2004. “A Life Course Approach to
Chronic Disease Epidemiology.” Oxford Schol Online.
Lambert, Paul S., Richard L. Zijdeman, Marco H. D. van Leeuwen et al. 2013.
“The Construction of HISCAM: A Stratification Scale Based on Social
Interactions for Historical Comparative Research.” Hist Methods 46 (2): 77–
89.
Landsarkivet i Lund. 1785-1857. Halmstads Kyrkoarkiv. Sockenstämmans
Protokoll och Handlingar. Landsarkivet i Lund.
Landsarkivet i Lund. 1805-1827. Kävlinge Kyrkoarkiv. Sockenstämmans
Protokoll och Handlingar. Landsarkivet i Lund.
Lazuka, Volha. 2018. “The Long-Term Health Benefits of Receiving Treatment
from Qualified Midwives at Birth.” J Dev Econ 133 (July): 415–33.
Lazuka, Volha. 2020. “Infant Health and Later-Life Labor Market Outcomes:
Evidence from the Introduction of Sulpha Antibiotics in Sweden.” J Hum
Resour 55 (2): 660–98.
Lazuka, Volha. 2023. “It's a Long Walk: Lasting Effects of Maternity Ward
Openings on Labor Market Performance.” Rev Econ Stat 105 (6): 1411–25.
Lazuka, Volha, Tommy Bengtsson, and Patrick Svensson. 2023. “The Causal
Effects of Enclosures on Production and Productivity.” IZA Working Papers
16397.
Lazuka, Volha, and Annika Elwert. 2023. “Life-Cycle Effects of Comprehensive
Sex Education.” IZA Working Papers 16622.
Lazuka, Volha, Luciana Quaranta, and Tommy Bengtsson. 2016. “Fighting
Infectious Disease: Evidence from Sweden 1870–1940.” Popul Dev Rev 42
(1): 27–52.
54
Lorentzon, Louise, and Per Pettersson-Lidbom. 2021. “Midwives and Maternal
Mortality: Evidence from a Midwifery Policy Experiment in 19th-Century
Sweden.” J E E A 19 (4): 2052–84.
Lund, Najaaraq, Andreas Andersen, Anna Sofie K. Hansen et al. 2015. “The
Effect of Oral Polio Vaccine at Birth on Infant Mortality: A Randomized
Trial.” Clin Infect Dis 61 (10): 1504–11.
Lunn, M., and D. McNeil. 1995. “Applying Cox Regression to Competing
Risks.” Biometrics 51 (2): 524–32.
Lunn, P. G. 1991. “Nutrition, Immunity, and Infection.” In The Decline of
Mortality in Europe, edited by R. S. Schofield, D. Reher, and A. Bideau, 131–
57. Oxford: Claredon.
Mayr, A. 2004. “Taking Advantage of the Positive Side-Effects of Smallpox
Vaccination.” Journal of veterinary medicine. B, Infectious diseases and
veterinary public health 51 (5): 199–201.
Miller, Douglas L., Na'ama Shenhav, and Michel Grosz. 2023. “Selection into
Identification in Fixed Effects Models, with Application to Head Start.” J
Hum Resour 58 (5): 1523–66.
Momota, Akira, Ken Tabata, and Koichi Futagami. 2005. “Infectious Disease
and Preventive Behavior in an Overlapping Generations Model.” Journal of
Economic Dynamics and Control 29 (10): 1673–1700.
Palmer, Christopher J. 2024. “An IV Hazard Model of Loan Default with an
Application to Subprime Mortgage Cohorts.” NBER Working Paper 32000.
Patel, Minal K., Heather M. Scobie, Fatima Serhan et al. 2022. “A Global
Comprehensive Vaccine-Preventable Disease Surveillance Strategy for the
Immunization Agenda 2030.” Vaccine.
55
Pettersson, A. 1912. “Smittkopdödeligheten I Sverige Under Åren 1776-1875.”
Hygiensk Tidskrift, 1–17.
Quaranta, Luciana. 2014. “Early Life Effects Across the Life Course: The Impact
of Individually Defined Exogenous Measures of Disease Exposure on
Mortality by Sex in 19th- and 20th-Century Southern Sweden.” Soc Sci Med
119:266–73.
Riksarkivet. 1769-1801. Collegium Medicum: Årsberättelser Från
Provinsialläkare.
Riksarkivet. 1796-1820. Collegium Medicum: Provinsial- Och Stadsläkares
M.Fl. Årsberättelser.
Riksarkivet. 1802-1812. Collegium Medicum: Vaccinationsrapporter.
Roth, Jonathan, Pedro H.C. Sant’Anna, Alyssa Bilinski et al. 2023. “What’s
Trending in Difference-in-Differences? A Synthesis of the Recent
Econometrics Literature.” J Econom 235 (2): 2218–44.
Sant'Anna, Pedro H. C., and Jun Zhao. 2020. “Doubly Robust Difference-in-
Differences Estimators.” J Econom 219 (1): 101–22.
Schaltz-Buchholzer, Frederik, Peter Aaby, Ivan Monteiro et al. 2021.
“Immediate Bacille Calmette-Guérin Vaccination to Neonates Requiring
Perinatal Treatment at the Maternity Ward in Guinea-Bissau: A Randomized
Controlled Trial.” J Infect Dis 224 (11): 1935–44.
Sköld, Peter. 1996a. “From Inoculation to Vaccination: Smallpox in Sweden in
the Eighteenth and Nineteenth Centuries.” Popul Stud 50 (2): 247–62.
Sköld, Peter. 1996b. “The Two Faces of Smallpox: A Disease and Its Prevention
in Eighteen- and Nineteenth-Century Sweden.” Umeå University.
Sköld, Peter. 2000. “The Key to Success: The Role of Local Government in the
56
Organization of Smallpox Vaccination in Sweden.” Med Hist 44 (2): 201–26.
Släktforskarförbund. 2019. Swedish Death Index 1860-2017. Machine-Readable
Database.
Tchetgen Tchetgen, Eric J. 2014. “A Note on the Control Function Approach
with an Instrumental Variable and a Binary Outcome.” Epidemiol Methods 3
(1): 107–12.
Terza, Joseph V., Anirban Basu, and Paul J. Rathouz. 2008. “Two-Stage
Residual Inclusion Estimation: Addressing Endogeneity in Health
Econometric Modeling.” J Health Econ 27 (3): 531–43.
The Demographic Data Base. 2022. CEDAR, Umeå University (2022) U22002.
Vågerö, Denny, Pia R. Pinger, Vanda Aronsson et al. 2018. “Paternal
Grandfather’s Access to Food Predicts All-Cause and Cancer Mortality in
Grandsons.” Nat Commun 9 (1): 5124.
Vikström, Lotta, Emil Marklund, and Glenn Sandström. 2016. “Demographic
Outcomes During Colonisation: Migration and Mortality Among Indigenous
and Non-Indigenous Populations in Nineteenth-Century Sweden.” J Migr Hist
2 (1): 148–76.
Weuve, Jennifer, Eric J. Tchetgen Tchetgen, M. Maria Glymour et al. 2012.
“Accounting for Bias Due to Selective Attrition: The Example of Smoking
and Cognitive Decline.” Epidemiology 23 (1): 119–28.
Wisselgren, Maria J., and Lotta Vikström. 2023. “Behind the Numbers:
Authorities’ Approach to Measuring Disability in Swedish Populations from
1860 to 1930.” Hist Methods 56 (2): 63–76.
Wooldridge, Jeffrey M. 2015. “Control Function Methods in Applied
Econometrics.” J Hum Resour 50 (2): 420–45.
57
Figure 1 – Percentage of vaccinated by the age of 2 (bars) and of dying from smallpox
by age 100 (line), cohorts 1790–1910.
Source: own calculations based on the estimation sample.
Percentage vaccinated by age 2 /
Percentage dying from smallpox by age 100
Figure 2 – Distribution of the pre-1801 church personnel availability indicator by its
values, parish-level indicators.
Source: own calculations based on the estimation sample.
Figure 3 – The number and rate of change in church assistants and musicians in
Sweden, 1790–1820.
Source: own calculations based on TABVERK.
Figure 4 – Event-study and 95% confidence interval estimates of the effects of the
arrival of the smallpox vaccine in 1801 on lifetime outcomes of Generation 1, using
Cpost-1 as a treatment intensity (pre-1801 availability of church assistants and musicians
at the parish level).
Note: Estimated according to Equation 2.
Figure 5 – First stage and reduced form: The relationship between the SSIV (Cp(t-1) x
Cr) and the share vaccinated by age 2 (Panel A) and the individuals’ lifetime outcomes
(Panel B), average by birth cohort weighted by the number of individuals.
Source: own calculations from the estimation sample.
Table 1 – The effect of smallpox vaccination on lifetime outcomes of Generation 1:
Mother fixed effects
Remaining years
lived at age 2
Disability-free years
lived at age 2
Has good literacy,
after age 15
Occupational score,
max in ages 15-100
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Panel A: Baseline estimates
Vaccinated by age 2
13.585***
18.495***
13.265***
17.746***
0.118***
0.0769***
4.273***
4.474***
(0.225) (0.349) (0.226) (0.352) (0.00551) (0.00779) (0.109) (0.359)
Rsq
0.074
0.173
0.071
0.155
0.062
0.234
0.0025
0.142
Panel B: Heckman-corrected estimates
Vaccinated by age 2
11.067***
18.386***
10.286***
17.806***
0.0814***
0.0646***
4.648***
4.499***
(0.233) (0.346) (0.233) (0.350) (0.00536) (0.0074) (0.205) (0.358)
Rsq
0.091
0.185
0.096
0.173
0.148
0.278
0.0790
0.141
Observations
43,450
43,450
42,021
42,021
28,614
28,614
30,806
30,806
Mother FEs
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Parish of birth F Es
No
Yes
No
Yes
No
Yes
No
Yes
Year of birth FEs No Yes No Yes No Yes No Yes
Region of birth x Y ear of birth FEs No Yes No Yes No Yes No Yes
Families’ Xs x Year of birth FEs
No
Yes
No
Yes
No
Yes
No
Yes
Parish of birth Xs x Year of birth FEs
No
Yes
No
Yes
No
Yes
No
Yes
Note: Observations are individuals. Panel A reports the estimates based on Equation 1. Panel B
reports the estimates with a Heckman correction (see section 3.4 for the procedure). The controls
included are indicated in the table by Yes and No. “Families’ Xs” include child characteristics at
birth: sex, paternal occupational score, maternal occupational score, paternal literacy, maternal
literacy, proportion of non-surviving children in the family, maternal marital status, the presence of
siblings deceased due to external or unknown causes. “Parish Xs” include time-varying parish of
birth characteristics: the number of midwives, the number of priests, smallpox death rate, university
students per capita, price of rye, and the share of urban population.
*** p<0.001, ** p<0.01, * p<0.05
Table 2 – The effect of the arrival of the smallpox vaccine in 1801 on lifetime
outcomes of Generation 1: DID estimates using Cpost-1 as a treatment intensity
Remaining years
lived at age 2
Disability-free years
lived at age 2
Has good literacy,
after age 15
Occupational score,
max in ages 15-100
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Panel A: Baseline estimates
PostXCpost-1‚p
4.573**
4.937**
4.442**
4.647**
0.0976**
0.0715**
1.590***
1.666***
(1.513)
(1.501)
(1.540)
(1.565)
(0.0248)
(0.0291)
(0.419)
(0.645)
R sq
0.123
0.130
0.115
0.128
0.427
0.433
0.122
0.132
Panel B: Heckman-corrected estimates
PostXCpost-1‚p
4.463**
4.558**
4.197**
4.187**
0.0967**
0.0716**
1.591***
1.668***
(1.509)
(1.494)
(1.535)
(1.565)
(0.0235)
(0.0293)
(0.427)
(0.646)
R sq
0.137
0.143
0.131
0.143
0.427
0.433
0.122
0.132
Individuals
43,450
43,450
42,021
42,021
28,614
28,614
30,806
30,806
Parish of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Region of birth x Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Families’
X
s x Year of birth fixed effects
No
Yes
No
Yes
No
Yes
No
Yes
Parish of birth
X
s x Year of birth fixed effects
No
Yes
No
Yes
No
Yes
No
Yes
Note: Panel A reports the estimates based on Equation 2. Panel B reports the estimates with a
Heckman correction (see section 3.4 for the procedure). The controls included are indicated in the
table by Yes and No. “Families’ Xs” include child characteristics at birth: sex, paternal occupational
score, maternal occupational score, paternal literacy, maternal literacy, proportion of non-surviving
children in the family, maternal marital status, the presence of siblings deceased due to external or
unknown causes. “Parish Xs” include cohort-varying parish of birth characteristics: the number of
midwives, the number of priests, smallpox death rate, university students per capita, price of rye, and
the share of urban population. Standard errors are clustered at the parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Table 3 – The effect of smallpox vaccination on lifetime outcomes of Generation 1:
SSIV estimates with Cp(t-1) x Ct as an instrument (2SLS)
Remaining years
lived at age 2
Disability-free years lived
at age 2
Has good literacy,
after age 15
Occupational score,
max in ages 15-100
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Panel A: Baseline 2SLS Estimates
I: First-Stage Estimates (on Vaccinated by age 2)
Cp(t-1)
x
Ct
0.154***
0.163***
0.150***
0.155***
0.181***
0.177***
0.187***
0.196***
(0.0351)
(0.0279)
(0.0349)
(0.0267)
(0.0396)
(0.0295)
(0.0392)
(0.0311)
II: Reduced-Form Estimates
Cp(t-1)
x
Ct
1.768**
1.869**
1.667***
1.489**
0.0192
0.0161
0.564**
0.711**
(0.509)
(0.667)
(0.463)
(0.535)
(0.0278)
(0.0312)
(0.167)
(0.212)
R sq
0.109
0.118
0.100
0.115
0.330
0.347
0.169
0.205
III: 2SLS Estimates
Vaccinated by age 2
11.483***
11.471**
11.791***
11.041**
0.106
0.091
3.009**
3.617**
(3.172)
(3.664)
(3.248)
(3.516)
(0.0691)
(0.0518)
(1.079)
(1.129)
R sq
0.154
0.162
0.145
0.158
0.330
0.348
0.141
0.171
Kleibergen-Paap F-statistic
51.999
52.999
48.001
48.999
45.999
45.999
52.001
52.999
Anderson-Rubin F-statistic
6.940
3.290
7.530
6.860
0.600
0.850
6.450
4.352
Panel B: Heckman-corrected 2SLS estimates
Vaccinated by age 2
12.912***
12.257**
12.428***
12.999***
0.104
0.102
3.262***
3.049**
(3.044)
(4.468)
(2.168)
(2.374)
(0.0679)
(0.0718)
(0.919)
(1.201)
R sq
0.152
0.158
0.143
0.156
0.348
0.350
0.171
0.186
Individuals
43,450
43,450
42,021
42,021
28,614
28,614
30,806
30,806
Parish of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Region of birth x Year of birth fixed effects Yes Yes Yes Yes Yes Yes Yes Yes
Families’
X
s x Year of birth fixed effects
No
Yes
No
Yes
No
Yes
No
Yes
Parish of birth
X
s x Year of birth fixed effects
No
Yes
No
Yes
No
Yes
No
Yes
Note: Panel A reports the estimates based on Equations 3, 4, and 5. Panel B reports the estimates
with a Heckman correction (see section 3.4 for the procedure). “Families’ Xs” include child
characteristics at birth: sex, paternal occupational score, maternal occupational score, paternal
literacy, maternal literacy, proportion of non-surviving children in the family, maternal marital
status, the presence of siblings deceased due to external or unknown causes. “Parish Xs” include
time-varying parish of birth characteristics: the number of midwives, the number of priests, smallpox
death rate, university students per capita, price of rye, and the share of urban population. Standard
errors are clustered at the parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Table 4 – The effect of smallpox vaccination of Generation 1 on lifetime outcomes of
Generation 2 and 3: SSIV estimates with Cp(t-1) x Ct as an instrument for Generation 1
(2SLS)
Remaining years
lived at birth
Disability-free years
lived at birth
Occupational score,
max in ages 20-100
(1)
(2)
(3)
(4)
(5)
(6)
(A) Generation 2
Parent Vaccinated
1.171**
2.204***
6.836***
8.015***
1.531**
1.099*
(0.401)
(0.652)
(1.517)
(2.008)
(0.599)
(0.556)
R sq
0.0564
0.0689
0.00610
0.0455
0.126
0.178
Reduced Form
0.180**
0.359***
1.025***
1.242***
0.286**
0.215**
(0.0794)
(0.0514)
(0.216)
(0.308)
(0.111)
(0.0928)
Parent Vaccinated w. Heckman correction
1.201**
2.186***
6.707***
9.246**
1.508**
1.263**
(0.400)
(0.652)
(1.517)
(2.780)
(0.599)
(0.504)
Observations
109,112
109,112
29,748
29,748
90,294
90,294
(B) Generation 3
Grandparent Vaccinated
1.236***
1.057**
4.503***
4.262**
-1.0278
-0.715
(0.361)
(0.497)
(0.916)
(1.886)
(0.836)
(0.445)
R sq
0.116
0.187
0.00830
0.0316
0.0831
0.0846
Reduced Form
0.190***
0.172***
0.675***
0.661**
-0.192
-0.140
(0.0578)
(0.0481)
(0.0199)
(0.300)
(0.171)
(0.159)
Grandparent Vaccinated w. Heckman correction
1.308***
1.124***
4.089***
4.298**
0.927
-0.128
(0.295)
(0.281)
(0.704)
(1.635)
(0.524)
(0.205)
Individuals
116,544
116,544
40,324
40,324
70,920
70,920
Parish of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Region of birth x Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Families’
X
s x Year of birth fixed effects
No
Yes
No
Yes
No
Yes
Parish of birth
X
s x Year of birth fixed effects
No
Yes
No
Yes
No
Yes
Note: Observations are stacked individuals (54,506 unique individuals for generation 2 and 58,272
unique individuals for generation 3 in total). First-stage regression is the same as in Table 3. The
controls included are indicated in the table by Yes and No. “Families’ Xs” include child
characteristics at birth: sex, paternal occupational score, maternal occupational score, paternal
literacy, maternal literacy, proportion of non-surviving children in the family, maternal marital
status, the presence of siblings deceased due to external or unknown causes. “Parish Xs” include
time-varying parish of birth characteristics: the number of midwives, the number of priests, smallpox
death rate, university students per capita, price of rye, and the share of urban population. Standard
errors are clustered at the (parental) parish-of-birth level. *** p<0.001, ** p<0.01, * p<0.05
Table 5 – Direct and mediated effects of smallpox vaccination of Generation 1 on lifetime outcomes of Generation 2
and 3: SSIV estimates with Cp(t-1) x Ct as an instrument for Generation 1 (2SRI)
Years lived at birth
Disability-free years lived at birth
Occupational score, max in ages 20-100
Generation 2(3) Mediator:
Generation 2(3) Mediator:
Generation 2(3) Mediator:
Vaccinated
in
childhood
Parental
occupation
at birth
Midwife-
assisted
birth
Epigenetic
factors
Vaccinated
in
childhood
Parental
occupation
at birth
Midwife-
assisted
birth
Epigenetic
factors
Vaccinated
in
childhood
Parental
occupation
at birth
Midwife-
assisted
birth
Epigenetic
factors
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(A) Generation 2
Parent Vaccinated (natural direct effect)
0.772**
1.743***
1.994***
1.411***
4.097***
6.854***
6.571***
6.896***
1.752***
2.161***
2.291***
1.610**
(0.303)
(0.316)
(0.338)
(0.426)
(1.469)
(1.517)
(1.139)
(1.548)
(0.381)
(0.595)
(0.594)
(0.602)
Mediated Effect (natural indirect effect)
1.042***
-0.00587*
-0.00788***
0.261**
2.749***
-0.00266
-0.00585*
0.175
0.0636**
0.0720**
0.00279
-0.101
(0.0881)
(0.00342)
(0.00171)
(0.099)
(0.405)
(0.00993)
(0.00328)
(0.226)
(0.0255)
(0.0289)
(0.00346)
(0.066)
Observations
109,112
109,112
109,112
109,112
29,748
29,748
29,748
29,748
90,294
90,294
90,294
90,294
(B) Generation 3
Grandparent Vaccinated (natural direct effect)
0.691
1.469***
1.307***
1.334***
2.690**
5.161***
5.185***
4.510***
0.0819
0.0334
0.0925
0.358
(0.426)
(0.440)
(0.441)
(0.363)
(1.0781)
(1.124)
(1.126)
(0.919)
(0.332)
(0.331)
(0.332)
(1.056)
Mediated Effect (natural indirect effect)
0.838***
-0.00684
-0.00209
-0.014
2.504***
0.00561
-0.00501
0.0244
0.0308**
0.0866***
0.0161
0.00739
(0.124)
(0.00535)
(0.0139)
(0.362)
(0.363)
(0.0114)
(0.0530)
(0.0663)
(0.0148)
(0.0309)
(0.0137)
(0.0611)
Individuals
116,544
116,544
116,544
116,544
40,324
40,324
40,324
40,324
70,920
70,920
70,920
70,920
Parish of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Region of birth x Year of birth fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Note: Observations are stacked individuals (54,506 unique individuals for generation 2 and 58,272 unique individuals for generation 3 in
total). First-stage regression is the same as in Table 3. The effects are estimated for each mediator separately. Bootstrapped standard errors
are clustered at the (parental) parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Online Appendices
to the paper “Multigenerational Effects of Smallpox Vaccination”
by Volha Lazuka and Peter Sandholt Jensen
Appendix A – Selection into Treatment and Data Accuracy
Figure A1 – Age pattern of smallpox mortality before and after the introduction of
vaccination, 1790–1820.
Source: own calculations based on the estimation sample.
Figure A2 – Parishes under analysis, a snapshot of Sweden in 1820
Source: Based on the estimation sample and administrative boundaries from Riksarkivet (2016).
Figure A3 – Mortality rate below age 10 by cause and cohort life expectancy at age 2,
1790–1920
Source: own calculations based on the estimation sample.
Figure A4 – Differences in the observable characteristics between individuals belonging
to Generation 1, with children and grand-children (Generations 2 and 3) observed and not
observed in the sample.
Figure A5 – Selection into vaccination status by the age of 2 for Generation 1
Note: The estimates are obtained from an OLS multivariate regression with a vaccination by age 2 as an
outcome, cohorts born in 1790-1820. Point estimates and 95% confidence intervals. Robust standard
errors are clustered at the parish of birth. Continuous variables (year of birth, year of birth squared,
maternal and paternal occupational scores) are divided by their standard deviation.
Table A1 – Check for the data inaccuracy – on the whole sample
Vaccinated by age 2
Spring
ref
Summer
0.007*
(0.004)
Autumn
0.007
(0.004)
Winter
0.007*
(0.004)
Constant
0.130***
(0.005)
Individuals
43,450
R-squared 0.670
Note: OLS regression estimates with parish and year of birth fixed effects for the first generation.
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Appendix B – Additional Results with Mother Fixed Effects.
Figure B1 – Differences in the share of mothers with varying vaccination status of their
children across children’s observable characteristics (versus mothers with unvarying
status).
Note: 14.5% of mothers have both vaccinated and not-vaccinated children.
Table B1 – OLS estimates of the effect of smallpox vaccination on lifetime outcomes
of Generation 1: Controlling-for-observables
Remaining years
lived at age 2
Disability-free years
lived at age 2
Has good literacy,
after age 15
Occupational score,
max in ages 15-100
(1) (2) (3) (4) (5) (6) (7) (8)
(I) FULL SAMPLE
Panel A: Baseline estimates
Vaccinated 11.697**** 17.423**** 11.147*** 17.429*** 0.188*** 0.108*** 3.802*** 4.481***
(0.198) (0.341) (0.197) (0.347) (0.00432) (0.00438) (0.169) (0.177)
Rsq
0.074
0.170
0.070
0.168
0.062
0.148
0.0016
0.0211
Panel B: Heckman-corrected estimates
Vaccinated 9.266*** 17.224*** 8.348*** 17.514*** 0.0381*** 0.0390*** 4.961*** 4.983***
(0.214) (0.339) (0.211) (0.344) (0.00772) (0.0071) (0.345) (0.344)
Rsq 0.091 0.182 0.096 0.183 0.221 0.221 0.130 0.130
Observations 43,450 43,450 42,021 42,021 28,614 28,614 30,806 30,806
(II) MOTHER FE SAMPLE
Panel A: Baseline estimates
Vaccinated 15.042**** 17.267*** 14.885*** 16.882*** 0.0906*** 0.0604*** 2.449*** 3.547***
(0.491) (0.654) (0.481) (0.655) (0.00754) (0.011) (0.413) (0.580)
Rsq 0.129 0.223 0.132 0.210 0.017 0.242 0.0037 0.143
Panel B: Heckman-corrected estimates
Vaccinated 15.085*** 17.270*** 14.763*** 16.882*** 0.0914*** 0.0553*** 2.581*** 3.604***
(0.492) (0.654) (0.482) (0.655) (0.00758) (0.0106) (0.471) (0.576)
Rsq 0.129 0.223 0.133 0.210 0.017 0.293 0.0036 0.144
Observations
6,313
6,313
6,258
6,258
28,614
28,614
2.668
2.668
Parish of birth FEs No Ye s No Yes No Yes No Yes
Year of birth FEs No Ye s No Yes No Yes No Yes
Region of birth x Year of birth FEs No Yes No Yes No Ye s No Yes
Families’ Xs x Year of birth FEs No Yes No Ye s No Yes No Yes
Parish of birth Xs x Year of birth F Es No Yes No Yes No Ye s No Yes
Note: Observations are individuals. Panel A reports the estimates based on Equation 1. Panel B
reports the estimates with a Heckman correction (see section 3.4 for the procedure). The controls
included are indicated in the table by Yes and No. “Families’ Xs” include child characteristics at
birth: sex, paternal occupational score, maternal occupational score, paternal literacy, maternal
literacy, proportion of non-surviving children in the family, maternal marital status, the presence of
siblings deceased due to external or unknown causes. “Parish Xs” include time-varying parish of
birth characteristics: the number of midwives, the number of priests, smallpox death rate, university
students per capita, price of rye, and the share of urban population.
*** p<0.001, ** p<0.01, * p<0.05
Appendix C – Additional Results with SSIV.
Figure C1 – The values of the SSIV (Cp(t-1) x Ct) across parishes and cohorts.
Source: own calculations from the estimation sample.
Figure C2 – 2SLS estimates of the leads of the interacted IV for all outcomes.
Note: 2SLS point estimates and 95% confidence intervals. We estimate the models with all 30
leads (the year of 1790 is the reference) but report the first five estimates, which is conventional
in the difference-in-differences literature (Roth et al. 2023). “Baseline” controls include year of
birth fixed effects, arish of birth fixed effects, and county of birth-by-year of birth fixed effects.
“All controls” additionaly include interactions between year of birth and child characteristics at
birth (sex, paternal occupational score, maternal occupational score, paternal literacy, maternal
literacy, proportion of non-surviving children in the family, maternal marital status, the presence
of siblings deceased due to external or unknown causes) and interactions between year of birth
and parish of birth characteristics (the number of midwives, the number of priests, smallpox death
rate, university students per capita, price of rye, and the share of urban population). Standard
errors are clustered at the parish-of-birth level.
Appendix D – Assumptions and Robustness Analysis for the Survivor
Models
In this Appendix, we provide the results for SSIV duration models, mother fixed-effects
estimations, and robustness analysis in relation to the assumptions of the SSIV in duration
models.
SSIV duration models: Based on the 2SRI models, we obtain the average survival
function and life expectancy (total and disability-free) after the age of two for the whole life
and at different ages and present them in Figure D1.
We further assess the vaccination effect on the hazards of death and disability by cause.
Table D1 shows the results for cause-specific mortality and disability.
Mother Fixed Effects: We start with reporting our results on the hazards as an outcome
from the mother fixed-effects estimates. When estimating a large number of incidental
parameters for mothers, duration models can produce an “incidental parameter problem” and
bias the estimates. We therefore implement a common solution to solve the problem—apply a
stratified partial likelihood model, in which a set of baseline hazards, separate for each mother
(strata), get absorbed into the unspecified function of age, hm(a):
(7) himprt(a) = hm(a) x exp(βVaccinatediprt + Xi(p)t Γ + ηt + γp + δrt + νimprt),
Here hiprt(a) denotes the all-cause hazard of death (disability) for individual i born in
parish p in the birth year b to the mother m and observed at age a. All other terms are defined
as before. Equation (7) thus eliminates the effects for the mothers from the likelihood
function, in analogy with linear mother fixed effects (Ridder and Tunalı 1999).
The results for the duration mother fixed-effects models are presented in Table D3. For
completeness, we also include the results from controlling-for-observables models in Table D4.
The mother fixed-effects estimates show large and statistically significant effects on the hazard
of death and disability, each reduced by 88 percent. Adding further time-varying controls only
improves the estimates. Similar to the linear estimates, we find that the mother fixed-effects
estimations yield results comparable to models with a full set of controls, suggesting that there
is no upward bias in the individual vaccination variable.
Identifying Assumptions and Robustness: Nonlinear instrumental-variables estimations
rely on the same assumptions as linear instrumental-variables do. As with linear IVs, we foresee
that there might be violations of exclusion restriction and of random assignment, i.e. the presence
of the direct effects of the instrument on the outcome and the common factors between the
instrument and the outcome. Regarding exclusion restriction, our reasoning for the linear models
applies for nonlinear models too. To avoid violation of random assignment, our models included
an extended set of controls. We additionally conduct a bounds test. In the controlling-for-
observables model, the duration models also assume random censoring. This additional
assumption is relaxed in the nonlinear instrumental-variables model (MacKenzie et al. 2021).
In the context of duration models, we compute a so-called e-value that shows how robust
the effect to potential unmeasured selection, without assuming any particular form of the
relationship between the treatment, unobservable, and the outcome (VanderWeele and Ding
2017). Figure D2 shows the e-value and its lower 95% confidence interval for the vaccination
effect of Generation 1 across the life cycle. These two measures suggest that any potential
selection effects should be linked to both vaccination and survival with a hazard ratio of at least
5.3 (5.1) to nullify the vaccination effect. Such an effect would be considered unlikely to diminish
the vaccination’s impact in a modern context, but it should be evaluated in the context of
nineteenth-century Sweden.
To benchmark the effects, we estimate the effects of family conditions, in particular those
associated with misery, neglect and poor prospects in life–being born out of wedlock or born to
family with a high proportion of children dying (Edvinsson et al. 2005). Table D5 reports the
estimates. Indeed, illegitimate children and children whose older siblings died prior to their birth
carry a disadvantage in terms of survival throughout their lifetime. However, the strength of these
associations amounts to not more than 1.3 on a hazard-ratio scale, which is four times lower than
the ratio suggested by the sensitivity analysis. None of the other individual-level covariates
indicate strong effects in childhood, nor do they suggest any lasting consequences. We also show
the estimates for the parishes of birth, among which the largest hazard ratio amounts to 2.7 (for
the parish of Gällivare). Therefore, in our context, any unmeasured factors could not eliminate
the impact of vaccination.
Figure D1 – Survivor functions (bold lines) and lifetime added due to
vaccination (bars) for mortality and disability.
Source: Estimates are based on the estimations from the 2SRI models, with the SSIV (Cp(t-1) x
Ct) as an instrument. Lines denote point estimates for survivor functions and their 95-%
confidence intervals. Bars denote point estimates for the added lifetime in ages.
Figure D2 – E-value for the effect of smallpox vaccination by age 2 across the life
cycle, Generation 1
Note: E-value and lower 95%-CI are presented.
Table D1 – The effect of smallpox vaccination on mortality and disability by
cause for Generation 1: SSIV estimates with Cp(t-1) x Ct as an instrument (2SRI)
Mortality risk
Disability risk
(1)
(2)
(3)
(4)
Vaccinated by age 2 X Death due to smallpox
0.0261***
0.0193***
(0.0178)
(0.0123)
Vaccinated by age 2 X Other cause of death
0.334**
0.244***
(0.117)
(0.0774)
Vaccinated by age 2 X Smallpox-related causes
0.571**
0.506***
(0.113)
(0.0963)
Vaccinated by age 2 X Other cause of disability
0.781
0.744
(0.145)
(0.189)
First-stage residual
0.857
0.868
1.0375
1.0284
(0.0991)
(0.260)
(0.0337)
(0.0447)
Log pseudolikelihood
-53,889
-53,886
-2,779
-2,125
Individual time spells
189,334
189,334
183,022
183,022
Parish of birth fixed effects
Yes
Yes
Yes
Yes
Year of birth fixed effects
Yes
Yes
Yes
Yes
Region of birth x Year of birth fixed effects
Yes
Yes
Yes
Yes
Families’
X
s x Year of birth fixed effects
No
Yes
No
Yes
Parish of birth
X
s x Year of birth fixed effects
No
Yes
No
Yes
Note: Observations are individual time spells. Time splits exist for those individuals who
migrated in and out of the parishes. First-stage estimates are the same as in Table 3. The
estimates are exponentiated and should be interpreted as hazard ratios. The controls included
are indicated in the table by Yes and No. “Families’ Xs” include child characteristics at birth:
sex, paternal occupational score, maternal occupational score, paternal literacy, maternal
literacy, proportion of non-surviving children in the family, maternal marital status, the
presence of siblings deceased due to external or unknown causes. “Parish Xs” include time-
varying parish of birth characteristics: the number of midwives, the number of priests,
smallpox death rate, university students per capita, price of rye, and the share of urban
population. Standard errors are clustered at the parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Table D2 – The effect of smallpox vaccination on the hazard of death and
disability of Generation 1: IV estimates with Cp(t-1) x Crt as an instrument (2SRI)
Mortality risk
Disability risk
Panel A: 2SRI Estimates
Vaccinated
0.320**
0.319**
0.273***
0.201***
(0.113)
(0.119)
(0.0875)
(0.0543)
First-stage residual
0.858
0.853
0.857
0.806
(0.0997)
(0.104)
(0.0869)
(0.212)
Log pseudolikelihood
-53,952
-53,926
-52,040
-52,005
Observations
94,061
94,061
91,463
91,463
Panel B: First-stage ML estimates (on Vaccinated by age 2)
Cp(t-1)
x
Crt
0.141***
0.154***
0.137***
0.138***
(0.0382)
(0.0399)
(0.0381)
(0.0395)
Kleibergen-Paap F-statistic
51.999
52.999
48.001
48.999
Anderson-Rubin F-statistic
6.940
3.290
7.530
6.860
Individual time spells
23,802
23,802
22,965
22,228
Parish of birth FEs
Yes
Yes
Yes
Yes
Year of birth FEs
Yes
Yes
Yes
Yes
Region of birth x Year of birth FEs
Yes
Yes
Yes
Yes
Families’
X
s x Year of birth FEs
No
Yes
No
Yes
Parish of birth
X
s x Year of birth FEs
No
Yes
No
Yes
Note: Observations are individual time spells. Time splits exist for those individuals who
migrated in and out of the parishes. ML denotes maximum likelihood. The estimates for
Panel A are exponentiated, represent hazard ratios. The estimates for Panel B are from
generalized linear models with a logistic link. The controls included are indicated in the table
by Yes and No. “Families’ Xs” include child characteristics at birth: sex, paternal
occupational score, maternal occupational score, paternal literacy, maternal literacy,
proportion of non-surviving children in the family, maternal marital status, the presence of
siblings deceased due to external or unknown causes. “Parish Xs” include time-varying
parish of birth characteristics: the number of midwives, the number of priests, smallpox death
rate, university students per capita, price of rye, and the share of urban population. Standard
errors are clustered at the paris-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Table D3 – The effect of smallpox vaccination on the hazard of death and
disability of Generation 1: Mother fixed-effects (Cox proportional hazards model)
estimates
Mortality risk
Disability risk
(1)
(2)
(3)
(4)
(5)
(6)
Vaccinated
0.114***
0.0939***
0.0962***
0.119***
0.0924***
0.0971***
(0.0309)
(0.00955)
(0.00986)
(0.0323)
(0.00978)
(0.0103)
Log pseudolikelihood
-3,509
-6,989
-6,980
-3,512
-3,444
-3,411
Observations
108,749
108,749
108,749
106,899
106,899
106,899
Parish of birth FEs
No
Yes
Yes
No
Yes
Yes
Year of birth FEs
No
Yes
Yes
No
Yes
Yes
Region of birth x Year of birth FEs
No
Yes
Yes
No
Yes
Yes
Families’
X
s x Year of birth FEs
No
No
Yes
No
No
Yes
Parish of birth
X
s x Year of birth FEs
No
No
Yes
No
No
Yes
Note: Observations are time spells for all individuals. Time splits exist for those individuals who
migrated in and out of the parishes. ML denotes maximum likelihood. The estimates are
exponentiated. The controls included are indicated in the table by Yes and No. “Families’ Xs”
include child characteristics at birth: sex, paternal occupational score, maternal occupational
score, paternal literacy, maternal literacy, proportion of non-surviving children in the family,
maternal marital status, the presence of siblings deceased due to external or unknown causes.
“Parish Xs” include time-varying parish of birth characteristics: the number of midwives, the
number of priests, smallpox death rate, university students per capita, price of rye, and the share
of urban population. Standard errors are clustered at the parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Table D4 – The effect of smallpox vaccination on the hazard of death and
disability of Generation 1: Controlling-for-observables
Mortality risk
Disability risk
(1)
(2)
(3)
(4)
(5)
(6)
Vaccinated
0.477***
0.205***
0.199***
0.456***
0.184***
0.172**
(0.0494)
(0.0359)
(0.0367)
(0.0485)
(0.0302)
(0.0314)
Log pseudolikelihood
-81,671
-80,418
-80,225
-79,230
-80,118
-79,855
Observations
122,528
122,528
122,528
122,098
122,098
122,098
Parish of birth FEs
No
Yes
Yes
No
Yes
Yes
Year of birth FEs
No
Yes
Yes
No
Yes
Yes
Region of birth x Year of birth FEs
No
Yes
Yes
No
Yes
Yes
Families’
X
s x Year of birth FEs
No
No
Yes
No
No
Yes
Parish of birth
X
s x Year of birth FEs
No
No
Yes
No
No
Yes
Note: Observations are time spells for all individuals. Time splits exist for those individuals who
migrated in and out of the parishes. ML denotes maximum likelihood. The estimates are
exponentiated, represent hazard ratios. The controls included are indicated in the table by Yes and
No. “Families’ Xs” include child characteristics at birth: sex, paternal occupational score,
maternal occupational score, paternal literacy, maternal literacy, proportion of non-surviving
children in the family, maternal marital status, the presence of siblings deceased due to external
or unknown causes. “Parish Xs” include time-varying parish of birth characteristics: the number
of midwives, the number of priests, smallpox death rate, university students per capita, price of
rye, and the share of urban population. Standard errors are clustered at the parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
Table D5 – The Cox proportional hazard model estimates for individual-level
covariates, Generation 1.
Mortality risk
Mother married
(ref)
Mother unmarried
1.222*
(0.132)
No siblings dead
(ref)
50% dead
0.902
(0.0927)
100% dead
1.313***
(0.137)
Sibling died due to other cause
(ref)
Siblings died to e xternal/unknown causes
1.279
(0.378)
Unknown
1.071**
(0.0306)
Male
(ref)
Female
0.926***
(0.0271)
Mother literate
(ref)
Mother illiterate
1.046
(0.0729)
Father literate
(ref)
Father illiterate
0.994
(0.0811)
Father: Higher-skilled managers
(ref)
Lower managers, professionals, clerical
1.133
(0.110)
Foremen, medium skilled workers
1.294**
(0.151)
Farmers, fishermen
1.228**
(0.112)
Lower skilled workers, farm workers
1.131
(0.119)
Unskilled workers , farm workers
1.279**
(0.146)
Hög
(ref)
Kävlinge
1.060
(0.0614)
Halmstad
1.236***
(0.0648)
Sireköpinge
0.979
(0.0474)
Linköping Domkyrka
1.490
(0.372)
Linköping Sankt Lars
1.380
(0.342)
Kärna
1.309
(0.324)
Kaga
1.231
(0.298)
Slaka
1.349
(0.333)
Skeda
1.030
(0.255)
Landeryd
1.087
(0.269)
Vist
1.074
(0.267)
Törnevalla
0.834
(0.207)
Östra Harg
1.617*
(0.399)
Rystad
1.485
(0.366)
Vreta Kloster
1.114
(0.275)
Stjärnorp
0.868
(0.212)
Ljung
0.830
(0.206)
Ledberg
1.655**
(0.406)
Grebo
0.860
(0.211)
Värna
1.096
(0.269)
Örtomta
0.850
(0.208)
Askeby
0.907
(0.224)
Åtvid
0.883
(0.221)
Svinstad
0.949
(0.235)
Vårdsberg
1.323
(0.329)
Björsäter
0.974
(0.242)
Nykil
1.114
(0.277)
Gammalkil
0.920
(0.226)
Rappestad
1.128
(0.274)
Sjögestad
1.333
(0.330)
Vikingstad
1.337
(0.328)
Vilhelmina
0.898
(0.202)
Umeå Stadsf.
1.332
(0.930)
Umeå Landsf.
1.223**
(0.505)
Nysätra
0.978
(0.222)
Lövänger
0.974
(0.242)
Sorsele
0.777
(0.180)
Stensele
0.429***
(0.104)
Skellefteå Landsf.
1.035
(0.235)
Byske
0.135
(0)
Norsjö
1.228
(0.278)
Burträsk
0.995
(0.238)
Jokkmokk
2.207***
(0.622)
Kvikkjokk
1.226
(0.365)
Gällivare
2.763***
(0.813)
Jukkasjärvi
1.406
(0.396)
Karesuando
1.608*
(0.455)
Ljustorp
0.948
(0.277)
Hässjö
0.870
(0.302)
Tynderö
1.153
(0.320)
Lögdö Bruksf.
0.840
(0.242)
Lagfors Bruksf.
2.169**
(0.735)
Skön
1.059
(0.335)
Alnö
1.271
(0.394)
Timrö
1.856*
(0.593)
Selänger
0.908
(0.290)
Sättna
0.612*
(0.178)
Sundsvall
1.862
(0.720)
Indal
0.657
(0.194)
Njurunda
1.116
(0.369)
Tuna
1.016
(0.298)
Attmar
0.769
(0.218)
Undersäker
0.773
(0.319)
Undersäkers Lappf.
1.281***
(0.318)
Föllinge
0.735
(0.250)
Föllinge Lappf.
1.077
(0.479)
Hotagen
0.840
(0.380)
Frostviken
0.607
(0.226)
Frostvikens L appf.
0.803
(0.358)
Log pseudolikelihood
-81,217
Observations
122,528
Parish of birth FEs
Yes
Year of birth FEs
Yes
Region of birth x Year of birth FEs
Yes
Note: Observations are time spells for all individuals. Time splits exist for those individuals who
migrated in and out of the parishes. The estimates are exponentiated. The controls included are
indicated in the table by Yes and No. “Families’ Xs” include child characteristics at birth: sex,
paternal occupational score, maternal occupational score, paternal literacy, maternal literacy,
proportion of non-surviving children in the family, maternal marital status, the presence of
siblings deceased due to external or unknown causes. “Parish Xs” include time-varying parish of
birth characteristics: the number of midwives, the number of priests, smallpox death rate,
university students per capita, price of rye, and the share of urban population. Standard errors are
clustered at the parish-of-birth level. *** p<0.001, ** p<0.01, * p<0.05
Appendix E – The Influence of Overlapping Interventions
Table E1 – The interaction effects of vaccination with cointerventions, Generation 1: Reduced-form estimates with Cp(t-1) x Crt
as an instrument
Remaining years lived, at age 2 Disability-free years lived, at age 2 Occupational score, max in ages 15-100
Epidemics
Midwives
Potatoes
Epidemics
Midwives
Potatoes
Epidemics
Midwives
Potatoes
(1)
(2)
(3)
(4)
(5)
(6)
(10)
(11)
(12)
Cp(t-1)
x
Crt
1.698***
1.567***
1.687***
1.695***
1.465**
1.603***
3.116***
3.419***
4.164***
(0.600)
(0.602)
(0.521)
(0.573)
(0.621)
(0.402)
(0.777)
(0.747)
(1.877)
Cp(t-1)
x
Crt
X Cointervention
1.021**
-0.0142
-0.121
0.951**
0.0935
-0.123
2.329***
-0.0567
0.367
(0.424)
(0.0515)
(0.122)
(0.432)
(0.725)
(0.268)
(0.809)
(0.0465)
(0.297)
R sq
0.112
0.113
0.113
0.103
0.106
0.103
0.158
0.158
0.158
Observations
32,120
32,120
32,120
30,930
30,930
30,930
22,823
22,823
22,823
Parish of birth FEs
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year of birth FEs
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Region of birth x Year of birth FEs
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Note: “Epidemics”: The cointervention variable is smallpox mortality among children under age 10. “Midwives”: The cointervention variable is the
ratio of midwives to the population. “Potatoes”: The cointervention variable is the quantity of potato seeds per square kilometer. All variables are
divided by their means to facilitate interpretation. Standard errors are clustered at the parish-of-birth level.
*** p<0.001, ** p<0.01, * p<0.05
References (in Appendices)
Edvinsson, Sören; Brändström, Anders; Rogers, John; Broström, Göran (2005): High-Risk
Families: The Unequal Distribution of Infant Mortality in Nineteenth-Century Sweden. In
Popul Stud 59, pp. 321–337.
MacKenzie, Todd A.; Martinez-Camblor, Pablo; O’Malley, A. James (2021): Time dependent
hazard ratio estimation using instrumental variables without conditioning on an omitted
covariate. In BMC Methodology 21 (1), p. 56. DOI: 10.1186/s12874-021-01245-6.
Ridder, Geert; Tunalı, İnsan (1999): Stratified partial likelihood estimation. In J Econom 92
(2), pp. 193–232. DOI: 10.1016/S0304-4076(98)00090-6.
Riksarkivet (2016): Historiska GIS-Kartor (Information om Territoriella Indelningar i Sverige
från 1500-Talets Slut till 1900-Talets Slut) [Historical GIS Maps (Information on Territorial
Divisions in Sweden from the 1500s to the 1900s)]. Shape-file.
Roth, Jonathan; Sant’Anna, Pedro H.C.; Bilinski, Alyssa; Poe, John (2023): What’s trending
in difference-in-differences? A synthesis of the recent econometrics literature. In J Econom
235 (2), pp. 2218–2244. DOI: 10.1016/j.jeconom.2023.03.008.
VanderWeele, Tyler J.; Ding, Peng (2017): Sensitivity Analysis in Observational Research:
Introducing the E-Value. In Ann Int Med 167 (4), pp. 268–274. DOI: 10.7326/M16-2607.
