ECON 4200 Senior Seminar in Economics and Finance Population and Technological Growth Evidence from Roe v. Wade

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ECON 4200 Senior Seminar in Economics and Finance

Population and Technological Growth: Evidence from Roe v. Wade

John T. H. Wong, 3035592600

Matthias Hei Man, 3035552375

Alex Li Cheuk Hung, 3035492288

1 Introduction

Some economists have argued that a greater population base causes higher technological growth and therefore higher

per capita income, whether that is due to network eﬀects such as intellectual contact and specialization spurring

innovation or due to the need to sustain a larger population. Meanwhile, others have argued that per capita

income decreases as population grows, due to competition over a ﬁxed set of resources and greater dependency.

Furthermore, it is commonly known that cross-sectional empirical evidence shows countries with higher population

growth having lower income. This paper will attempt to validate the ﬁrst position by providing evidence that a

greater population leads to more technological growth in the form of patent production.

We ﬁnd that for cohorts born between 1931-1984, a higher starting population at birth is correlated with higher

patents per thousand residents between 1996-2012. In order to rule out the endogeneity of fertility decisions and

estimate the causal eﬀect of cohort births1on patent production, we exploit the heterogeneous impact of the US

Supreme Court’s ruling on Roe v. Wade, which ruled most abortion restrictions unconstitutional. Our identifying

assumption is that states which had not liberalized their abortion laws prior to Roe would experience a negative

birth shock of greater proportion than states which had undergone pre-Roe reforms. We estimate the diﬀerence-

in-diﬀerence in births and use estimated births as an exogenous treatment variable to predict patents per capita.

Our results show that one standard deviation increase in cohort’s starting population (70,608 births) increases per

capita patents by 0.23 (which is 24 percent of the outcome’s standard deviation). These results suggest that at the

margins, increasing fertility can increase patent production. Insofar as patent production is a suﬃcient proxy for

technological growth, increasing births has a positive impact on technological growth.

Our paper builds on two ﬁelds of research: the ﬁrst is theories on the relationship between population and innovation,

whose contributors include Michael Kremer, Simon Kuznets, and David Weil. Second, we add to the study of

determinants of innovation in the US by Bell et al. Here, we would also like to acknowledge Bell et al. for making

the data set of their study open-source and allowing this instance of alternative use. We should also note that

although our research uses changes in abortion policy as an exogenous change in births, this paper and its results do

not pertain to the issue of abortion itself. Insofar as we prove that fertility has a positive impact on technological

growth (which we will argue is the case), we establish that states have good reason to promote births. We are silent

on the optimality of abortion policy as a natalist tool for increasing technological growth.

Before we proceed, we should also take stock of the limitations of our paper. First, as it will become clear in

Section 4, our use of Roe as an exogenous change in births is subject to limitations. Although states with pre-Roe

bans on abortion see births decrease, this drop is not statistically signiﬁcant, making our IV quite weak. Our

diﬀerence-in-diﬀerence estimations of patents per capita (without using cohort births as a treatment variable) also

contradict our hypothesis, which we think is most likely due to confounding factors that may have occurred in

non-reform states after Roe, which we could not control for due to our limited research capacity.

Second, our results (insofar as they are valid) are estimated with instrumental variables, which make them estimated

local average treatment eﬀects (LATE). We can only estimate the eﬀect of births on innovation for individuals of

cohorts who became able to undergo abortions as a result of the repeal of abortion laws following the Roe ruling.

This means, we cannot know the eﬀect of births on patent production for individuals who would have sought

abortions regardless of the procedure’s legality in their home state (by travelling out-of-state), or individuals who

would not have sought abortions regardless, i.e. all eventual parents after Roe. Furthermore, we can only estimate

LATE through the compliers’ inﬂuence on their cohorts’ average level of births and patents.

1We use cohort starting population and cohort births interchangeably throughout this paper.

arXiv:2211.00410v1 [econ.EM] 1 Nov 2022

Finally, it is also beyond our research capacity to account for the heterogeneity in patent utility across patents. This

could be done by merging patents per capita of a cohort to how much the cohort’s patents were cited. However,

our data set on patent outcomes do not track patent utility by cohort and state. To our knowledge, the US Patent

and Trademark Oﬃce (USPTO) also does not release public data of such kind. As a result, we can only assume all

patents granted are equal in their contribution to technological growth, however ﬂawed that assumption might be.

Our paper will proceed as follows. Section 2 discusses the background of our research. We will review the relevant

theoretical literature on population, technological growth, and income. We also will discuss what determines an

individual’s chance of becoming patent holders in the US context. Section 3 describes the various data sets we

combine and use, and estimate the correlation between births and patents. Section 4 covers the institutional setting

of abortion laws in the US and attempts to justify the use of the Roe ruling as an exogenous shock in births. In

Section 5, we will describe our methodology for and results from estimating the causal eﬀect of births on patents.

We will also analyze where our methodology falls short and discuss its major limitations. Section 6 concludes.

2 Background

2.1 Theoretical Framework and Literature

Our hypothesis that population and technology have a positive relationship follows Kremer’s model and evidence

on this subject. Kremer oﬀers two main views. First, he co-opts the “Malthusian assumption that technology

limits population” (Kremer 1993, 681) to argue that high population forces the adoption of “new” technology

to replace “old” technology (i.e. technology insuﬃcient for supporting a given level of population). Research

productivity, under this view, would depend on the level of existing population and we should see proportionality

between the growth of these two variables (Kremer 1993, 681-682). To support this, Kremer shows that eras

with greater population bases also have higher population growth rates. In other words, because of the positive

eﬀect of population base on technological growth, humanity has been able to aﬀord super-exponential population

growth. Second, Kremer rejects the view that subsequent rises in income would have reduced eﬀorts to invent

new technologies (Kremer 1993, 684). Instead, he argues that research productivity depends positively on income

(Kremer 1993, 687). That high population without income is insuﬃcient for achieving technological growth also

explains why densely populated countries such as China had (as of 1990) low research productivity.

Kremer’s model and results contradict the general view that population growth reduces per capita income. Thomas

Malthus has argued that larger populations will eventually fail due to the inadequacy of resources. Kremer’s

arguments are also contrary to economic growth models such as the Solow and Harrod-Domar models, which both

predict that societies with higher population growth will see lower levels of per capita income (Williamson 2014,

222-5; 248-9; Ray 1998, 51-6). More recently, Weil has argued that as the populations of developing countries age,

increasing fertility could actually lead to less per capita income in the short-term as dependency increases (Weil

1999, 253).2Galor and Weil (1999) have argued that even if Kremer is correct that a greater population base leads

to more technological growth, this growth will subsequently reward investments in human capital that will (i) have

a greater role driving subsequent technological growth and therefore (ii) lead households to prioritize the quality

of children over quantity, explaining low levels of population growth in developed economies. Our task is to argue

that the population-induced growth is still signiﬁcant even in the context of a developed economy. However, it is

beyond the scope of this paper to compare the size of population eﬀects to the size of human capital investment’s

eﬀect on innovation.

Separately, Kuznets has argued that productivity per capita, and by extension innovation per capita, should increase

with a larger population. For example, consider country A with population size 10 and country B with a larger

population, say 20. All else equal, the productivity per capita of B should be greater than A because higher

2There is also a strand of literature on demographic transition which argues that as economic development improves, income

increases, and child mortality decreases, households require less children as an investment into old-age security and therefore desire less

children. However, here, the focus is on the relationship from income to population, rather than from population to income. We focus

on the latter as our main interest is in determining what drives technological (and therefore economic) growth. For more, see Robert

J. Barro and Gary S. Becker. ”Fertility Choice in a Model of Economic Growth.” Econometrica 57 (1989): pp. 481-501.

population density allows for greater division of labor and specialization, and the “possibility of more intensive

intellectual contact” (Kuznets 1960, 325-327). Furthermore, Kuznets notes that growing population increases the

size of the market and improves its responsiveness to new goods (a proxy of innovation) (Kuznets 1960, 334-347).

In other words, a greater population acts as a greater ﬁnancial incentive for productivity growth. Such network

eﬀects suggest that population growth and patent production is non-linear (i.e. greater populations see higher

patents per capita and exponentially more patents), which is precisely the hypothesis we aim to prove in the US

context.

Bell et al. provides a recent examination of innovation in modern US. The authors evaluate individuals who end up

as innovators in the US and delve into the backgrounds of these innovators (deﬁned as those who produce patents)

in terms of race, gender, income, and other birth characteristics to obtain explanatory factors. For example, they

highlight how higher percentile income is linked to an exponentially higher number of inventors per thousand,

showing that “rates of innovation rise by 22 percent between the 95th percentile ($193,322) and 99th percentile

($420,028) of the parental income distribution” (Bell et al. 2018, 12). We illustrate this relationship by plotting

the number of inventors per capita across quintiles in Figure 1. Race or ethnicity is another factor highlighted,

with evidence that “1.6 per 1,000 white children and 3.3 per 1,000 Asian children who attend NYC public schools

between grades 3-8 become inventors,” relative to only 0.5 for Black Children and 0.2 for Hispanics (Bell et al.

2018, 13-14). Finally, there is also a gap in innovation between genders, with men more likely to become inventors.

In 1980, the fraction of female inventors is only around 20 percent, and Bell et al. estimate that, given the current

rate of convergence estimated from linear regression, it would approximately take until 2100 to reach a 50 percent

female share (Bell et al. 2018, 14).

Figure 1

Bell et al. also highlight the importance of spatial determinants. Evidence on spatial determinants of innovation

shows that commuting distances have signiﬁcant impacts on patent productivity–both in terms of commuting during

childhood and adulthood. This makes sense as longer commuting times decrease time available to be productive.

Research by Xiao et al. shows that the distance between an individual’s home and their workplace versus their

patent productivity is negatively correlated. An increase of ten kilometers in the worker’s commuting distance

corresponds to a “5% decrease in patents per inventor–ﬁrm pair per year and an even greater 7 percent decrease

in patent quality” (Xiao et al. 2021, 1; 13). Bell et al. further show that neighbourhoods where children grow up

in are also signiﬁcant. Bell et al. argue that children growing up in areas where innovation activity is higher are

more likely to become innovators themselves thanks to exposure to innovation. Their regression shows that a one

standard deviation increase in a neighbourhood’s (or community zone’s) patent rate corresponds with an increase

in the fraction of children who become inventors, having lived in the same neighbourhood, by 28.5 percent (Bell et

al. 2018, 24-28). The results of these papers highlight that ﬁnancial incentives are not the only motivating factor in

patent production, as exposure and geography itself from birth, childhood, to adulthood can impact an individual’s

probability of becoming an inventor.

3 Data and Baseline Results

3.1 Data

In order to estimate the eﬀect of births on innovation, we assemble, construct, and merge several data sets. We use

Bell et al.’s open-source panel data on patent outcomes. The panel data tracks patent outcomes across three units

of observations. First, patent outcomes are tracked for each cohort born between 1916-1984; as patent outcomes

are clustered by cohort (rather than at an individual level), cohorts are also the main unit of observation. Second,

patent outcomes for each cohort are reported once per year, between 1996-2014. For example, we separately know

how many patents the 1970 cohort were granted in 1996, 1997, and so forth. The data set only includes cohorts

aged 25-80 each year. We track outcomes by year because a given cohort’s propensity to produce patents is highly

dependent on the cohort’s age (see Figure 2). Finally, patent outcomes for each cohort in each year are reported

separately for each US state. To extend on the previous example, one row in the data set tells us how many patents

were granted in 1996 to the 1970 cohort in California (versus, say, in Oregon). Patents granted in a year refer to

patents that were applied in that year and subsequently granted even if the latter occurs in later years. Because

the data only captures patent records from 1996-2014, patents applied in latter years that are granted after 2014

are not included as granted. Thus, compared to USPTO national data, the aggregate of patents granted in our

data set tapers after 2011 (Figure 3). We have estimated our results without observations in 2012-2014 and found

no signiﬁcant diﬀerence. We therefore retain all years of observations despite the discrepancy.

Figure 2

Table 1 reports summary statistics. Our outcome of interest is patents granted per thousand people by cohort,

state, and year. The mean of the outcome is 0.887. We use patents adjusted by population as an outcome as a

proxy for research productivity. For two groups with a given number of people, if group A is granted more patents

than B, then group A has higher research productivity. Other variables of interest from the data set include each

cohort’s estimated population in each year in a given state. If having a larger cohort population at birth causes the

cohort to later create more patents, all else equal, then a larger population base would be causing higher research

productivity. The mean count of residents by cohort, state is 60,075.

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ECON4200SeniorSeminarinEconomicsandFinancePopulationandTechnologicalGrowth:EvidencefromRoev.WadeJohnT.H.Wong,3035592600MatthiasHeiMan,3035552375AlexLiCheukHung,30354922881IntroductionSomeeconomistshavearguedthatagreaterpopulationbasecauseshighertechnologicalgrowthandthereforehigherpercapitaincome,wh...

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ECON 4200 Senior Seminar in Economics and Finance Population and Technological Growth Evidence from Roe v. Wade

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