Transformative and Subsistence Entrepreneurs: Origins and Impacts on Economic Growth

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1410 June 2025 Transformative and Subsistence Entrepreneurs: Origins and Impacts on Economic Growth Ufuk Akcigit, Harun Alp, Jeremy Pearce and Marta Prato Please cite this paper as: Akcigit, Ufuk, Harun Alp, Jeremy Pearce and Marta Prato (2025). “Transformative and Subsistence Entrepreneurs: Origins and Impacts on Economic Growth,” International Finance Discussion Papers 1410. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2025.1410. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Transformative and Subsistence Entrepreneurs: Origins and Impacts on Economic Growth Ufuk Akcigit Harun Alp Jeremy Pearce Marta Prato* June 26, 2025 Abstract Thispaperexploresthesymbioticrelationshipbetweentransformativeentrepreneurs and inventors, which is crucial for economic growth. We utilize microdata from Denmark to demonstrate that while the relationship between IQ and general entrepreneurship tends to be negative, it is strongly positive among transformative entrepreneurs. Transformative entrepreneurs, often with higher IQ and education levels, significantly drive R&D and business growth, thereby providing substantial opportunitiesforinventors. Incontrast, averageentrepreneursaremoreinfluenced by their family’s entrepreneurship background. Our economic model links these dynamics to overall economic progress, highlighting how higher education influences career paths in entrepreneurship and invention. We identify talent misallocation caused by unequal education access, particularly affecting lower-income families. Our findings indicate the most effective policies strengthen the interplay between higher education, innovation, and entrepreneurship to foster transformative businesses and achieve long-run economic growth. Keywords: Entrepreneurship,R&DPolicy,Innovation,IQ,EndogenousGrowth. JEL Classification: O31, O38, O47, J24. *Author affiliations and contact information. Akcigit: University of Chicago, Department of Economics, NBER, & CEPR (uakcigit@uchicago.edu). Alp: Federal Reserve Board of Governors (harun.alp@frb.gov). Pearce: Federal Reserve Bank of New York (jeremy.pearce@ny.frb.org). Prato: Bocconi University, Department of Economics, IGIER and CEPR (marta.prato@unibocconi.it). We would like to thank Martin Junge and the Ministry of Science and Education for their invaluable supportandassistancethroughouttheproject. Wealsothankourdiscussants,MartaMorazzoniandMorten Sorenson, and seminar and conference participants at the NBER, SED, LAEF, Duke, New York Fed, Philadelphia Fed, St Louis Fed, UPenn, LSE, HBS, HKU, Oxford, Zurich, Stockholm, Vanderbilt, EIEF Pizzanomics, the Swiss Macro Workshop, CEPR Joint IMO & ESF Workshop, Bristol Macroeconomics Workshop, Purdue, and Barcelona Summer Forum for helpful comments. The views in this paper are solelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoard ofGovernorsoftheFederalReserveSystem,theFederalReserveBankofNewYork,oranyotherperson associatedwiththeFederalReserveSystem.

ransformative and ubsistence ntrepreneurs T S E 1 Introduction A symbiotic relationship between entrepreneurs and inventors is essential for technological progress. Yet, this symbiotic relationship depends on the nature of entrepreneurs; unlike subsistence entrepreneurs who focus on day-to-day survival, transformative entrepreneurs push boundaries by turning groundbreaking ideas into realworld applications. Without the visionary drive of transformative entrepreneurs, inventors would lack the commercial pathways needed to bring their innovations to market. Conversely, without inventors, transformative entrepreneurs would not have access to the new technologies that underpin significant market disruptions. In this paper, we explore the career choices of different types of entrepreneurs and inventors and study the dynamic interplay among them. Specifically, we ask: Who becomes a transformative entrepreneur, and how does that path differ from becoming an inventor or subsistence entrepreneur? Is there talent misallocation in the economy? How do policies shape the distribution of talent among these occupations? We address these questions with novel microdata from Denmark on inventors, entrepreneurs, and firms. We build a set of facts using detailed information on individual education, parental background, IQ, and firm performance. We embed thesefacts in an endogenous growth model, where heterogeneous individuals can become production workers, inventors, or entrepreneurs. This process generates the demand and supply for innovative talent, shaping aggregate innovation and economic growth. The quantified model enables us to study innovation and education policies and their interaction with talent allocation, firm growth, and economic growth. igure orker and ntrepreneur by F 1: R&D W E IQ Entrepreneur R&D Worker 7 5 )0 06 )0 1 re p5 4 0 1 re ( e r a4 3 p ( e ra h h S S ru 3 2 re e k n e2 ro W r p e 1 D rtn 1 & R E 0 0 1 2 3 4 5 6 7 8 9 10 IQ Deciles 1

ransformative and ubsistence ntrepreneurs T S E One striking fact at the center of our analysis is the allocation of talent between entrepreneurs and inventors by IQ, illustrated in Figure 1. It shows the share of individuals who choose to become either R&D workers—inventors that are employed in innovation-related occupations—or entrepreneurs by deciles of the distribution of IQ test scores, which we interpret as a proxy for ability. The likelihood of being an R&D workerisincreasinginIQ:thetopdecileis20timesaslikelyasthebottomtobecomean R&Dworker. Onthecontrary, thelikelihoodofbeinganentrepreneurdeclineswithIQ, with the top decile a little over half as likely as the bottom to become an entrepreneur. This surprising finding challenges the common portrayal of entrepreneurs as individuals who drive creativity and growth, a narrative often seen in both academic literature and popular media. A central aim of this paper is to unravel this intriguing puzzle. This exploration not only sheds light on the heterogeneity among entrepreneurs but also investigates the career choices of different talents in society. Next, using multivariate regression analysis, we explore other important determinants that shape the sorting into these professions, such as parental background and individual characteristics. We find that while high IQ and higher education predict becoming an R&D worker, they decrease the likelihood of becoming an entrepreneur. While there is no direct effect of parental income on becoming an R&D worker, there is an indirect effect through schooling, which is highly correlated with parental income even conditioning on IQ and parental education. Interestingly, we find that family entrepreneurship experience has the strongest impact on the likelihood of becoming an entrepreneur. These results pave the way for exploring heterogeneity in entrepreneurial types. Not all entrepreneurs seek to innovate and grow their business (Hurst and Pugsley, 2011). Only a handful of entrepreneurs are transformative and aim to bring new innovations to the market. In our data, we define transformative entrepreneurs as those who hire at least one R&D worker, signaling an intention to innovate. Importantly, we do not define them based on ex-post outcomes such as firm growth, as this would risk excludingentrepreneurswhoaimedtogrowbutultimatelyfailed. Instead, wefocuson their ex-ante incentives by examining their business strategy — specifically, the types of workers they bring into the firm who are likely to drive future growth. According to this definition, only a handful of entrepreneurs are transformative and hire technical personnel for innovation. The likelihood of being a transformative entrepreneur increases with IQ and higher education, and these transformative entrepreneurs lead firms that grow faster, patent more, and have lower exit rates. We collect our results into five main empirical facts on the determinants of initial 2

ransformative and ubsistence ntrepreneurs T S E career choice, entrepreneur type, and firm dynamics. Fact 1 IQ and education negatively predict becoming an entrepreneur. Fact 2 Parental entrepreneurship is the strongest predictor of entrepreneurship. Fact 3 IQ and education are the strongest predictors of becoming an R&D worker. Fact 4 IQandeducationarethestrongestpredictorsofbecomingatransformativeentrepreneur, i.e., an entrepreneur who hires R&D workers. Fact 5 Transformative entrepreneurs grow faster and create more jobs than subsistence entrepreneurs. To link these findings to aggregate economic outcomes, we build an endogenous growth model that incorporates these facts into a theory of talent allocation and occupational sorting with Schumpeterian growth and firm dynamics. Individuals in the model are born with heterogeneous ability and parental income that determines their initial educational choice, as we observe that both are important determinants of college attendance in the data. Education is a necessary prerequisite to becoming an R&D worker (in line with Fact 3). While some individuals choose not to become R&D workers due to personal preferences, others cannot afford to pursue education due to low parental income. This friction in the access to education creates a misallocation that can propagate to the opportunity to become a transformative entrepreneur. After choosing their initial career, both types of workers have the opportunity to become entrepreneurs throughout their lifetime. The arrival of an entrepreneurial opportunity is random, with frequency influenced by childhood exposure to entrepreneurship (Fact 2) and educational attainment (Fact 4). IQ and education may not have a positive impact on selection into entrepreneurship (Fact 1). Importantly, the model distinguishes between transformative and subsistence entrepreneurs, differentiated by levels of talent and education (Fact 4). Transformative entrepreneurs innovate and enhance product quality by employing R&D workers, while subsistence entrepreneurs do not engage in such innovation-oriented activities. As a result, innovative entrepreneurs grow their firms (Fact 5), contributing to overall innovation and growth. The model highlights two key mechanisms that determine an economy’s capacity for innovation and its connection to aggregate growth. The first mechanism involves occupational sorting, specifically how individuals select their initial careers. Workers 3

ransformative and ubsistence ntrepreneurs T S E in R&D represent the supply of innovative talent, and the factors influencing their occupational choices significantly impact the overall level of innovation within the economy. The second mechanism centers on entrepreneurship: without sufficient demand for R&D talent by growing firms, their innovative potential cannot effectively translate into broader innovation, firm dynamics, and growth. Education serves as a critical channelinfluencingboththesupplyofR&Dworkersandtransformativeentrepreneurs. Individuals prevented from obtaining higher education due to low parental income are lesslikelytobecomeR&Dworkers,therebyconstrainingtheeconomy’ssupplyofinnovative talent. Moreover, educated individuals are over 5 times more likely to engage in transformativeentrepreneurship. Consequently,limitedaccesstohighereducationalso diminishes the demand for innovative talent. Given the interdependence between R&D workers and transformative entrepreneurs, each form of educational misallocation can significantly impede innovation and aggregate economic growth. After characterizing the solution of the model, we calibrate the underlying parametersbymatchingkeyfeaturesofthemicrodata,withthetechniqueofSimulatedMethod of Moments. The quantification focuses on the role of career sorting based on individuals’ characteristics and family background, driven by heterogeneous returns to R&D andproductionworkandthelifecycleofsubsistenceandtransformativeentrepreneurship. Using the quantified model, we highlight four main results. First, distortions in educational choices caused by financial frictions create a bottleneck in access to innovative careers, due to the reliance on parental income for higher education, a dynamic that can have significant aggregate implications. To illustrate this point, we study a counterfactual exercise that removes financial barriers in access to education, allowing all individuals to pursue college if they wish to. Eliminating these frictions boosts economicgrowthby11.1%, expandsR&Dworkershareby15%, andraisesthetransformative entrepreneur share by 7.5%. The expansion of R&D workers and transformative entrepreneurs occurs mainly among individuals from the lower end of the income distribution and the upper end of the talent distribution. These results highlight that financial constraints in education create talent misallocation, preventing some highability individuals from becoming inventors or transformative entrepreneurs. Second, there is a symbiotic relationship between R&D workers and entrepreneurs that matters for the effectiveness of policies. To highlight this complementarity, we conduct a partial equilibrium counterfactual exercise with the alleviation of financial frictions, as above, but where we keep the number of entrepreneurs of each type and the firm size distribution fixed to the baseline. If the firm side of the model stays fixed, 4

ransformative and ubsistence ntrepreneurs T S E consistentwithnoeffectonentrepreneurship, growthonlypicksupby6.6%, compared to the 11.1% in the full general equilibrium described above. Thus, the demand side for innovative talent accounts for 40% of the growth increase from alleviating financial frictions. Third, we highlight education subsidies as a superior policy tool to foster transformative entrepreneurship and innovation. We study four policies in the form of subsidies to either (i) all startups, (ii) R&D (incumbent) subsidy, (iii) innovative startups, and (iv) education, which affect different margins of talent allocation and firm dynamics in the economy. A uniform entrepreneurship subsidy proves largely ineffective as it primarily attracts subsistence entrepreneurs who don’t drive innovation. An R&D subsidy for incumbents generates moderate growth by increasing demand for R&D workers but faces diminishing returns at the firm level. The innovative startup subsidy, targeting transformative entrepreneurs who hire R&D workers, more effectively boosts growth-oriented startups and innovation. However, education subsidies emerge as the most effective policy, addressing the foundational issue of human capital developmentbyexpandingboththepoolofpotentialR&Dworkersandtransformative entrepreneurs simultaneously, stimulating increases in both the supply of and demand for R&D talent. Overall, with a 0.05% of GDP budget, education subsidies increase innovation by 16%, against 4% for startup subsidies to transformative entrepreneurs and 2% for R&D subsidies, and 0.1% for general startup subsidies. Finally,weexploretheoptimalmixofthethreesubsidies,andwefindthatapecking order of policies emerges. With a low budget, the entirety of the subsidy should be allocated to education, introducing innovative startup subsidies for mid-range budgets (e.g., 0.4% of GDP), and finally including R&D subsidies only at higher budgets (e.g., 0.7% of GDP). Once the budget is high enough (e.g., greater than 0.7% of GDP), the optimalstrategyistomixthethreepolicies. Thisexercisedemonstratesboththecritical importanceofaddressingbottlenecksinaccesstoeducationtoboostinnovationandthe importance of mixing policies to build an ecosystem of transformative firms and R&D workers. The rest of the paper is organized as follows. After reviewing the literature, Section 2 introduces the data and facts in the data. Section 3 introduces a model that incorporates the main facts, focusing on individual heterogeneity and the innovation production function. Section 4 reports the estimation and discusses the main quantitative mechanisms in the model. Section 5 focuses on the normative aspects of the quantified model, talent misallocation, and policy counterfactuals that address different margins. Section 6 concludes. 5

ransformative and ubsistence ntrepreneurs T S E Literature Review. Dating back to the contribution of Schumpeter (1911), economists have long highlighted the connection between entrepreneurship and aggregate growth. Schumpeter (1911) further noted a core difference between an inventor and an entrepreneur: As long as they are not carried into practice, inventions are economically irrelevant. And to carry any improvement into effect is a task entirely different from the inventing of it, and a task, moreover, requiring entirely different kinds of aptitudes. Although entrepreneurs may be inventors..., but not by nature of their function but by coincidence and vice versa. While economists have understood this connection, data and theoretical tools to unpack this question have been limited. This paper develops this insight on the dual rolesofinventorsandtransformativeentrepreneurs,connectingstrandsoftheliterature on entrepreneurs and inventors. Lucas (1978), Baumol (1990), Murphy et al. (1991), Gennaioli et al. (2013) highlight that the human capital of entrepreneurs is important in determining the productivity of firms and, in turn, the growth rate of entire economies. Decker et al. (2014) document extensively the importance of entrepreneurship in job creation. Hurst and Pugsley (2011) show that only a handful of entrepreneurs have the potential to grow and be transformative, which we incorporate in this paper. The ability of transformative entrepreneurs to scale is a key ingredient in aggregate growth (Akcigit et al., 2021). This finding connects to conceptual insights central to our paper thatreturnstoR&Dworkerswillbelowiftherearenotentrepreneurswhocandemand their services (Michelacci, 2003). We complement this work with a comprehensive empirical and quantitative analysis of the factors shaping entrepreneurial choice and success, integrating inventors into the analysis to explore their symbiotic relationship withentrepreneurs. Thisismadepossiblebyleveragingrichmicro-leveladministrative data from Denmark. Empirically, there is a growing line of research that explores the origins of entrepreneurship and the drivers of entrepreneurial success. Much of this literature studies the forces that determine the decision to become an entrepreneur. Evans and Jovanovic (1989) and Blanchflower and Oswald (1998) find that family background is important for entrepreneurship. Levine and Rubinstein (2016) also argue that human capital and background characteristics play an important role in the choice to become an entrepreneur. We find, in line with Levine and Rubinstein (2016) and Hvide and Oyer (2018), that individuals are more likely to become entrepreneurs if they have parental entrepreneurs. Lindquist et al. (2015) use adoption data to show that both 6

ransformative and ubsistence ntrepreneurs T S E genetic and environmental forces determine the propensity for an individual to become an entrepreneur. Bhandari et al. (2024) find that the non-pecuniary benefits of entrepreneurship are small and their income growth is higher, which is consistent with our framework. This connects to the distinction between subsistence and transformative entrepreneurship — building on Schoar (2010) and Hurst and Pugsley (2011) — and examine how these different entrepreneurial types generate demand for inventors within a general equilibrium framework. Entrepreneurs must be team players, and our paper focuses on how they must hire R&D workers to realize their vision of firm growth. This observation connects to work more broadly on entrepreneurial ability and how entrepreneurs must be balanced in their skills (Lazear, 2004), which incorporates communication and networking ability (Kaplan et al., 2012). Our paper is also related to work focusing on inventor teams (Wuchty et al., 2007; Pearce, 2020), which we extend to entrepreneurs and the inventors they hire, and to the literature showing the importance of entrepreneurial networks (Hochberg et al., 2007, 2010). In this paper, we show that schooling plays an important role for the type of entrepreneur because individuals with college education receive technicaltraining, increasingthelikelihoodofbecomingatransformativeentrepreneur. This result is consistent with evidence that entrepreneurial skill is persistent (Gompers et al., 2010) because it is shaped by both the education and career decisions of individuals (Lerner and Malmendier, 2013; Morazzoni, 2021; Queiró, 2022). In our framework, as in Queiró (2022), entrepreneurial human capital affects firm dynamics, but we further introduce an interaction with the supply of innovative talent through the demand for inventors and life cycle opportunities. One of the main messages of this paper is about connecting the dynamics of firms and entrepreneurs to the canonical literature of inventors producing ideas that lead to economic growth dating back to Romer (1990). This literature varies in terms of its focus on who becomes an inventor (Aghion et al., 2017, Akcigit et al., 2025, Bell et al., 2018), learning (Akcigit et al., 2018), and the interaction with firms (Aghion et al., 2018). In this literature, we advance on two fronts. First, we provide novel empirical evidence on the careers of entrepreneurs and inventors jointly; second, we connect the entrepreneurialcareertoamacroeconomicenvironment,acomponentthathasreceived less attention in the literature. Connecting inventors and entrepreneurs to the macroeconomy requires a new theory of innovation-led growth, which connects the development of human capital to entrepreneurship, innovation, andproduction. Ourtheoryincorporatesamodeloftheallocation of talent between entrepreneurship and work, as in Lucas (1978), into a micro- 7

ransformative and ubsistence ntrepreneurs T S E founded model of Schumpeterian growth following Aghion and Howitt (1992) and Klette and Kortum (2004), which has been used as workhorse theory of firm dynamics (see, e.g., Akcigit and Kerr, 2018; Garcia-Macia et al., 2019; Lentz and Mortensen, 2008). The importance of occupational sorting and talent allocation for economic growth is also highlighted by Hsieh et al. (2019) and Prato (2024). We also contribute to a strand of the literature that uses these frameworks to study the aggregate impact of innovation policies (Atkeson and Burstein, 2019) by studying a rich set of policy tools for innovation. Our model enriches the existing framework by explicitly modeling the role of family background for occupational choice, building on the work of Akcigit et al. (2025), who focus only on inventors, and expanding it to examine the contribution of entrepreneurs and R&D workers to the growth of the firm. 2 Motivating Empirical Evidence We motivate the core features of our model of career choice and firm dynamics by employing individual and firm-level data from Denmark. We start by discussing the data with a main focus on R&D workers, entrepreneurs, and firms. We then discuss the determinants of becoming an entrepreneur, particularly a transformative one, and the firms of transformative and subsistence entrepreneurs. 2.1 Data Environment The empirical and quantitative analysis in this project uses detailed micro-level data from the Denmark Statistical Office (DST) for the years 2001-2013. We rely on four datasets that contain (i) individual background and test information; (ii) matched employer-employee data with detail on wages and occupations; (iii) information on entrepreneur firms and firm-level outcomes; (iv) patent data to link innovative behavior to individuals and firms.1 In the empirical analysis, we group individuals into three categories. Our main sample consists of R&D workers, production workers, and entrepreneurs. We categorize as “R&D workers" those individuals who work in occupations with high patenting rates. More precisely, we select all occupations where at least 1% of workers ever file a patent and classify all individuals in those occupations as R&D workers. By identifying R&D workers based on their occupational classifications, we capture a broader 1MoredetailsondataconstructionandvariabledefinitionsareprovidedinAppendixB. 8

ransformative and ubsistence ntrepreneurs T S E set of contributors to innovation—recognizing that not all R&D workers hold patents, yet still play a vital role in technological development. With this definition, individuals in R&D occupations account for approximately 3% of the working population in our data.2 We categorize production workers as individuals who work but do not have an R&D occupation. Finally,wedefineentrepreneursasindividualsidentifiedintheIVPS/IVPEdatabase as primary founders of a firm with at least one employee. To distinguish transformativeentrepreneurs,weavoidrelyingsolelyonex-postmeasuresoffirmgrowth; instead, we aim to capture entrepreneurs’ ex-ante intention to innovate and expand their businesses through their hiring choices. Specifically, an entrepreneur who intends to grow her business is more likely to hire R&D workers—a behavior we can directly observe in our data. Thus, we categorize an entrepreneur as transformative if they hire at least one R&D worker, whereas a subsistence entrepreneur is one who does not hire any R&D workers. 2.2 Transformative and Subsistence Entrepreneurs As noted in Figure 1, individuals with higher IQ are much more likely to become inventors or R&D workers. On the other hand, entrepreneurs are negatively selected in terms of IQ. In this section, we focus on the determinants of career choice with particular attention to the nature of entrepreneurs. At the center of this analysis are the heterogeneous goals and impacts of entrepreneurs (Baumol, 1990). In the literature, there is a bifurcation across two types of entrepreneurship: subsistence and transformative entrepreneurs (e.g., Schoar, 2010, Hurst and Pugsley, 2011, and Akcigit et al., 2021). Subsistence entrepreneurs focus on maintaining their business and often prefer entrepreneurship to wage employment but do not attempt to grow or innovate. The other types of entrepreneurs are transformative: they attempt to grow and contribute to technological progress. In our data, we define transformative entrepreneurs as entrepreneurs who hire an R&D worker at some point during the life cycle of the firm, consistent with an intention to grow rather than an outcome. Toexamineentrepreneurtypes,wesplitouroccupationalcategoriesintofourgroups: production workers, R&D workers, subsistence entrepreneurs, and transformative entrepreneurs. First, we note that only a handful of entrepreneurs are transformative, accounting for about 17% of firms in our data. Next, to understand the determinants 2AppendixB.3liststhetopR&Doccupations,whichconsistsofoccupationswheremorethan1%of individualshaveapatent. 9

ransformative and ubsistence ntrepreneurs T S E of transformative entrepreneurship, in Figure 2, we plot the share of individuals in each IQ decile who become subsistence entrepreneurs (left axis) and transformative entrepreneurs (right axis). igure and ntrepreneurship F 2: IQ E Subsistence Entrepeneur Transformative Entrepreneur 7 1.4 ) 0 ) 0 06 1.20 1 1 r r e e5 1 p p ( ( e e r r4 0.8a a h h S S e 3 0.6 e v c n e2 0.4 ita m ts r o is fs b1 0.2n u a S rT 0 0 1 2 3 4 5 6 7 8 9 10 IQ Deciles Figure 2 shows a starkly different IQ sorting for subsistence and transformative entrepreneurship. The prevalence of transformative entrepreneurship rises significantly with IQ, while the share of subsistence entrepreneurs declines sharply. Among entrepreneurs in the bottom IQ decile, only 4% are transformative, compared to 33% in the top decile. This sorting mechanism is a crucial part of our framework, determining the allocation of talent in the innovation pipeline. Given the IQ-based sorting patterns in Figures 1 and 2, we next examine empirical specifications that control for additional factors influencing occupational sorting, allowing us to jointly assess the relative importance of various determinants of career choice. We implement a multinomial logistic regression to explore the determinants of career choice for R&D workers, entrepreneurs, and entrepreneur types. We compare the probability that an individual i enters an occupation k against the probability of becoming a production worker 3, as described in equation (1): 3Forindividualswithmultipleoccupationsduringthesampleperiod,weassigneachindividualito the occupation k in which they spend the majority of their observed working years. Our results remain consistent when we instead classify occupations based on cross-sectional career observations from a singleyear. SeeAppendixBforadditionaldetails. 10

ransformative and ubsistence ntrepreneurs T S E (cid:32) (cid:33) P 4 log i,k =β college + ∑ ω I{IQ Quartile = j} 1 i i i P i,p j=2 +β entrepreneur parents +β R&D worker parents 2 i 3 i +β production worker parents +ϕparent income +Λ +ϵ , (1) 4 i i b(i) i where P is the probability that individual i is in occupation k against the probai,k bility of being a production worker, P .4 The independent variables are all binary and i,p indicate individual i’s college attainment, her IQ quartile, whether she has a parent entrepreneur5, a parent R&D worker, a parent production worker, and whether her parents’ income belongs to the top half of the income distribution. We include cohort fixed effects Λ , where b(i) is the birth cohort of individual i. We plot the coefficients b(i) from two regressions with the structure of equation (1) in Figures 3 and 4. The first specification, in Figure 3, examines the likelihood of becoming an entrepreneur, in panel (A), or an R&D worker, in panel (B), against the baseline case of being a production worker. We plot the estimated coefficients ordered by decreasing magnitude for entrepreneurs, with bands for the standard error. igure ultinomial ogit for areer hoice F 3: M L C C Entrepreneur R&D Worker Entrepreneur Entrepreneur Parents Parents R&D Worker R&D Worker Parents Parents High Parental High Parental Income Income Production Worker Production Worker Parents Parents IQ2 IQ2 IQ3 IQ3 IQ4 IQ4 College College -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 a ntrepreneur b orker ( ) E ( ) R&D W 4AppendixCprovidesthefulldetailsunderlyingthisfigure. 5Parent entrepreneur includes if either parent is an entrepreneur. This is measured as registered self-employmentasaprimaryoccupation,aswedonotobservefirmfoundingpriorto2001. 11

ransformative and ubsistence ntrepreneurs T S E Figure 3a shows that the strongest predictor of entrepreneurship is whether an individual has a parent who is an entrepreneur. The estimated coefficient of 0.574 log odds implies that individuals with a parent entrepreneur are 78% more likely to be entrepreneurs, conditional on covariates. Those with more education and higher IQ are less likely to be entrepreneurs overall, as the top IQ quartile is 15% less likely to be an entrepreneur than a production worker, conditional on covariates. Ontheotherhand,asseeninFigure3b,thereisastrongconnectionbetweenschooling and IQ and becoming an R&D worker. The top quartile of IQ has 1.25 higher log odds of being an R&D worker over a production worker. This means they are about 2.5 times more likely to be R&D workers than production workers. College additionally makes an individual almost 4 times more likely to be an R&D worker than a production worker. These results highlight the importance of talent and higher education for becoming an R&D worker. Figure 3 also reveals that high parental income is not a strong factor in determining career choice when controlling for the other covariates. However, parental income could have an indirect impact on occupational sorting through the likelihood of college attendance. In Appendix C, we show that even though parental income does not influence the likelihood of becoming an R&D worker when education is taken into account, it remains a strong predictor of college education, conditional on IQ and parental education levels. This suggests that unequal access to higher education, which is strongly influenced by parental income, serves as a key bottleneck in the pathway to becoming an R&D worker. In the second specification in Figure 4, we separate the entrepreneurial types and examine the likelihood of becoming a transformative entrepreneur, a subsistence entrepreneur, or an R&D worker against the baseline case of being a production worker. Figure 4 presents the coefficients corresponding to the two entrepreneur types. While parental entrepreneurship remains a key factor for transformative entrepreneurs, IQ and education now also play crucial roles, unlike the case of general entrepreneurship. In particular, college education and the highest IQ quartile are associated with an increaseintheprobabilitythatanindividualisatransformativeentrepreneurby55%and 110%, respectively, conditional on covariates. These results deliver Fact 3, that transformative entrepreneurs have higher IQ and obtain higher education. On the contrary, the probability of becoming a subsistence entrepreneur is negatively associated with higher IQ. This result aligns with the model discussed later, which suggests negative selection by talent into subsistence entrepreneurship. An important element for our framework is that unequal access to education, which 12

ransformative and ubsistence ntrepreneurs T S E igure ntrepreneur ype F 4: E T Transformative Entrepreneur Subsistence Entrepreneur Entrepreneur Parents R&D Worker Parents High Parental Income Production Worker Parents IQ2 IQ3 IQ4 College -1 -0.6 -0.2 0.2 0.6 1 is influenced by both individual IQ and parental income, creates a bottleneck for both R&D workers and transformative entrepreneurs.6 Not only does education drastically increase the odds of becoming an R&D worker, but it also doubles the likelihood of being a transformative entrepreneur vis-a-vis a subsistence entrepreneur and production worker. This outsized effect of education, which is itself affected by ability and parental income, is an important channel for opportunities into entrepreneurship. Firms. Are transformative entrepreneurs more likely to produce a successful firm? Figure 5 documents the evolution of employment of firms held by transformative and subsistence entrepreneurs over firm ages. To focus on the differences in their growth patterns, we plot employment, normalizing the initial value to be one, even though transformative entrepreneurs start larger. We find that transformative entrepreneurs start around twice as large as subsistence entrepreneurs and grow more than 9% faster per year, leading to stark differences in the firm size distribution of the two firm types. As a result, even though transformative entrepreneurs account for only 13% of the workforce hired by startups (firms of age 0), by age ten, they account for 34% of the employment of firms of that age. This finding 6Theinfluenceofthefamilyeconomicbackgroundoncollegeattainmentisanimportantingredient in the theoretical model. The literature has documented the link between educational attainment and familyincomeinthecaseofDenmark,despitethegenerousgovernmenteducationsubsidies;seeNielsen etal.(2010)andAkcigitetal.(2025). WedocumentsuchalinkinthecontextofourdatainAppendixC. 13

ransformative and ubsistence ntrepreneurs T S E igure mployment by ntrepreneur ype ge F 5: E E T /A 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 tnemyolpmE dezilamroN Subsistence Transformative Age underscores their important role in the overall business dynamism in the economy and disproportionate impact relative to their smaller share of initial entrepreneurship. In Appendix C, we show that transformative entrepreneurs, in addition to being more likely to be innovative, also have higher revenue growth and lower exit rates than subsistence entrepreneurs. These results are robust to different definitions of a transformative entrepreneur. Empirical Takeaways. Overall, our empirical findings suggest that entrepreneurs are negatively selected on ability and schooling, but those who undertake transformative entrepreneurship—byhiringR&Dworkers—arepositivelyselected,akintoR&Dworkers, and run larger, faster-growing firms. Further, parental background in occupation and income shapes educational and entrepreneurial opportunities. Taken together, these results underscore the importance of jointly considering individual attributes— such as IQ, education, and family background—and entrepreneurial type to understand firm dynamics and economic growth. To further unpack these dynamics and their implications for policy, we next introduce a theoretical framework that integrates individual occupational choice, entrepreneurial heterogeneity, and firm life-cycle dynamics. 3 Model This section develops a life-cycle model of career choice, entrepreneurship, and firm dynamics embedded in an endogenous growth framework, guided by the empirical 14

ransformative and ubsistence ntrepreneurs T S E facts presented earlier. In our model, individuals differ in ability, family income, and exposure to parental entrepreneurship. These differences affect educational decisions and ultimately shape occupational choices, the evolution of firms, aggregate innovation, and economic growth. The model is formulated in continuous time and designed to capture the interplay between talent allocation across occupations and firm growth along a Balanced Growth Path (BGP) equilibrium. In our exposition of the model, we normalize all the growing variables by the final good in the economy to keep the stationary equilibrium values constant, and suppress time subscripts whenever this causes no confusion. Figure 6 illustrates the key elements of the model, from initial career choice between R&D and production worker, to entrepreneurial choice, to the dynamics of firms and innovation. igure odel ap F 6: M M Born with talent parental resources parental entrepreneurship exposure Career and education choice Pay cost of education with parental income Production worker: R&D worker: Exit Exit Entry rate Entry rate Startup cost Startup cost Entrepreneur type Entrepreneur type Entrepreneur Subsistence Transformative Hire production workers Hire production and R&D workers Incumbent Innovation & Aggregate Growth 15

ransformative and ubsistence ntrepreneurs T S E 3.1 Environment and Agent Heterogeneity We consider an economy populated by agents that are heterogeneous in three dimensions: (i) worker ability (z), (ii) parental resources (y), and (iii) exposure to entrepreneurship through parents (f). In every period, a measure m of new agents enters the economy, with characteristics drawn from the joint distribution Ω(z,y, f). Agents die at an arrival rate ψ and are immediately replaced by new agents with the same characteristics such that the distribution of characteristics in the economy remains unchanged. 3.2 Educational Choice and Occupational Sorting When individuals are born, they initially decide on an occupation to begin their working career, choosing either to become a production worker or an R&D worker. Production workers do not attend higher education, while an R&D career requires the acquisition of costly education, where the cost is denoted by the parameter c . We ins terpret this cost broadly — not necessarily as tuition fees, but rather as living expenses, books and supplies, the opportunity cost of foregone income during higher education, and other related expenditures. Importantly, we assume that this cost must be paid in advance through parental resources, reflecting a form of financial friction.7 Therefore, individuals with y < c cannot afford schooling, and they become production s workers. In addition, individuals have preferences over education characterized by an idiosyncratic preference shock ϵ. Wedenotethechoiceofschoolingwiththeindicatorvariable s ∈ {0,1}, whichtakes the value 1 for an individual who acquires education, which also corresponds to being an R&D worker in the model.8 Given this structure, the occupation choice problem of an individual with state (z,y, f) who can afford education can be expressed as: max{W (z,y, f),W (z,y, f)−c +ϵ}. (2) 0 1 s Here, W (z,y, f), s ∈ {0,1}, which will be derived in the next subsection, denotes the s lifetime values associated with a career as a production worker (s = 0) and an R&D 7The literature has documented the presence of financial frictions and the influence of parental incomeonaccesstocollegeeducationinDenmark,despitethelowcostofeducationcomparedtoother countries;seeNielsenetal.(2010)andAkcigitetal.(2025). WewillusetheevidencefromNielsenetal. (2010) to calibrate the magnitude of these financial frictions, which play a central role in the allocation oftalentwithinourframework. 8Accordingly,inourmodel,choosingeducationiseffectivelyequivalenttochoosingbetweenacareer asaproductionworker(s =0)oranR&Dworker(s =1). 16

ransformative and ubsistence ntrepreneurs T S E worker (s = 1), not accounting for education costs and preference shock. We assume the preference shock follows a logistic distribution with mean χ and scale parameter ς.9 Given this distributional assumption, the above decision problem implies that the probability of acquiring education and becoming an R&D worker is given by 1 P(s = 1|z,y, f) = 1(c s < y)× (cid:16) (cid:17). (3) 1+exp W 0 (z,y,f) − W 1 (z,y,f)−cs +χ ς ς This equation highlights two key channels through which initial career selection operates: (i) the direct role of financial resources in restricting education access and (ii) the economic trade-offs between present schooling costs and future career returns. The first component, 1(c < y), is an indicator function that equals 1 if parental resources s exceed the cost of education and 0 otherwise. This represents the financial constraint that individuals face—education is only possible when family resources can cover its costs. This formulation directly captures the credit market imperfections that prevent talented individuals from low-resource backgrounds from obtaining education rather than due to lack of aptitude or preference. The second component, a standard logit function derived from the distribution of preference shocks, reflects the trade-off between the lifetime values of being a production worker W (z,y, f) and an R&D worker 0 W (z,y, f), adjusted for schooling costs c and average preference for schooling χ. A 1 s higher ς increases the role of idiosyncratic preferences, making the decision more dispersed and less deterministic. After making the initial career choice, agents enter the competitive labor market where they start earning wage income ω(z,s) based on their ability z and occupation of production worker or R&D worker, corresponding to s = 0 and s = 1 respectively. We allow for heterogeneity in how ability affects worker productivity across occupations by assuming that a worker with ability z supplies zαs efficiency units in the labor market, where α governs the rate at which productivity increases with ability for a s given occupation of production worker (s = 0) or R&D worker (s = 1). Consequently, the wage income per period is given by ω(z,s) ≡ ω zαs s where ω denotes the wage per efficiency unit for a production worker (s = 0) and s an R&D worker (s = 1), which will be determined in equilibrium by the set of entrepreneurs and their firms, which we turn to in the following section. 9Inthissetting,anegativevaluefor χ canbeinterpretedasdisutilityfromeducation. 17

ransformative and ubsistence ntrepreneurs T S E 3.3 Entrepreneurial Opportunities and Startup Decisions In addition to earning wage income, agents receive random opportunities to become entrepreneurs and earn profits from running a firm over the course of their life cycle. This opportunity arrives at rate λ , which depends on whether the agent comes from f,s an entrepreneurial family (f = 1) or not (f = 0), and on her education level s ∈ {0,1}. When the entrepreneurship opportunity arises, the agent draws an entrepreneur type θ from a distribution Π(θ|z,s) that depends on the agent’s ability and education. The drawntype θ determinestheentrepreneur’sefficiencyinutilizingR&Dworkers, which will be explained further in the next section. We assume θ can take two possible values, θ ∈ {0,θ¯}. The types θ¯ are transformative entrepreneurs: they hire both production workers and R&D workers, and the latter enables them to engage in innovation activity in an attempt to expand their firms. The types θ = 0 are only involved in production and do not innovate, but they may still grow their firms exogenously. Anindividual’sdecisiontotransitionfromworkertoanentrepreneurinvolvescomparing the benefits of starting a firm — net of a stochastic entry cost c — with the e continuing value of remaining a worker.10 If she decides to become an entrepreneur, she leaves the labor force and starts a firm. Thus, an agent can occupy one of three roles at any given time: (i) production worker, (ii) R&D worker, and (iii) entrepreneur. Given this setting, the lifetime value of the workers solves the following equation: ρW (z,y, f) = ω(z,s) (4) s +λ [E (max{V (θ)−c ,W (z,y, f)})−W (z,y, f)] f,s ce,θ e e s s +ψ[0−W (z,y, f)] s where ρ is the discount rate.11 The left-hand side, ρW (z,y, f), represents the required s return on the worker’s lifetime value at the discount rate r, which equals the sum of three distinct components. First, the worker earns a per-period wage, ω(z,s), based on their ability and education. Second, workers have the option to transition into entrepreneurship when opportunities arrive at the rate λ ; the term inside brackets f,s captures the expected additional benefit from potentially becoming an entrepreneur, consideringboththeentrepreneurialpayoffV (θ)(definedexplicitlyinthenextsection) e 10Here, the cost of starting a new firm is orthogonal to family background, which is consistent with ourempiricalevidenceaswellascurrentevidencefromtheliterature(RobbandRobinson,2012). 11Due to the normalization of value functions by the final good, the value function is discounted with ρ rather than interest rate r. For details, see Appendix A.1 for the household decision and A.4 for normalization. 18

ransformative and ubsistence ntrepreneurs T S E net of entry costs c , and the continuation value of remaining a worker W (z,y, f). e s This expectation is taken over the distributions of the entry cost and entrepreneurial type θ. Finally, the last term accounts for mortality: workers exit the economy at rate ψ, at which point their lifetime value drops to zero. We next turn to describe what entrepreneurs do in detail and the resulting firm dynamics. 3.4 Entrepreneurship and Firm Dynamics The firm side of the model builds on the framework of Klette and Kortum (2004) to capture the dynamics of innovation and firm growth. In our setting, each firm is ownedandmanagedbyanentrepreneurandisconceptualizedasaportfolioofproduct lines that generate profits via employing production workers.12 Entrepreneurs start their firms with a single product line, reflecting the minimal initial scale of new firms. Firms invest in innovation—using R&D workers as input—to expand their portfolios by improving product quality. While innovation grows firm value, this growth is offset by competition from incumbents and entrants that displace product lines. As a result, firm value evolves endogenously with the capture of new product lines and the loss of existing ones. Thefirm’sdynamicdecisionischaracterizedbyitschoiceofinnovationeffort,which determines the arrival rate of new product lines. A firm with n product lines and entrepreneur type θ produces innovations at rate X(n,θ) = θlσ nη, (5) rd where l denotes the efficiency units of R&D labor hired by the firm, σ captures the rd elasticity of innovation with respect to R&D labor, and η governs returns to scale in the number of product lines.13 The parameter θ reflects entrepreneurial innovation capability: transformative entrepreneurs have θ = θ¯ > 0 and actively invest in R&D, while subsistence entrepreneurs have θ = 0 and therefore do not attempt to innovate and do not hire any R&D workers. Given this technology, the cost of producing innovation effort X is given by the cost of R&D worker it requires: 12Theseproductlinesareusedasinputstoproducethefinalgoodintheeconomy. Weprovidefurther detailsinAppendixA.2. 13The inclusion of n in the innovation function reflects that firms with more product lines have a larger base of knowledge and resources, enhancing their capacity to generate innovations. We assume σ+η ≤1,i.e.,weallowfordecreasingreturnstoscaleininnovationproductionfunction,motivatedby theevidenceprovidedbyAkcigitandKerr(2018). 19

ransformative and ubsistence ntrepreneurs T S E (cid:18) (cid:19)1 X σ C(X;n,θ) = ω 1 θnη where ω is the wage per efficiency unit of R&D labor. 1 When innovation is successful, the firm improves the quality of a random product by a factor γ and captures it from another firm, thereby increasing its portfolio by one product. Symmetrically, each product line the firm owns is at risk of being displaced byotherfirmsandentrantsattherate τ. Wereferto τ asbusinessreallocationrate, which is endogenously determined in equilibrium and taken as given by the firm. The value of a firm with n product lines and type θ is denoted by V(n,θ) and satisfies the following Bellman equation: ρV(n,θ) = πn (6) +τn[V(n−1,θ)−V(n,θ)] (cid:40) (cid:18) (cid:19)1(cid:41) X σ +max X[V(n+1,θ)−V(n,θ)]−ω X 1 θnη +υn[V(n+1,θ)−V(n,θ)] +ψ[0−V(n,θ)]. The first term on the right-hand side, πn, captures the total flow profits generated by the n product lines.14 The next term reflects the loss in value due to competition by other incumbents and new entrepreneurs, where each product line faces the risk of being displaced at the rate τ. The maximization component represents the change in the firm value through innovation; by choosing an optimal innovation effort X, or equivalently, how many R&D workers to hire, and paying the corresponding cost, the firm expands its portfolio (increasing the number of product lines from n to n+1). The next term captures exogenous factors that may contribute to firm growth at the rate ν per product line. Finally, the last term accounts for the exit due to the death of the entrepreneur, in which case the value of the firm goes to 0. Note that since firms enter with a single product line, the value of choosing entrepreneurship introduced in the previous section satisfies V (θ) = V(1,θ). e Firm exit occurs either through exogenous death of the entrepreneur or endogenously when all product lines of the firm are lost due to competition from other firms. In the latter case, the entrepreneur shuts down the firm and returns to the labor market 14Detailsontheproductmarketandtheresultingprofits πn areprovidedinAppendixA.2. 20

ransformative and ubsistence ntrepreneurs T S E in her previous occupation. Together, the entry and exit processes generate a dynamic equilibrium in which the composition and size of firms continuously evolve, thereby driving aggregate growth and the reallocation of resources across the economy. 3.5 Labor Market Clearing and Stationary Equilibrium Distributions One of the main novel elements of this framework is connecting the origins of the supply and demand sides for innovation. This section discusses the labor market clearing thatenablesthisgeneralequilibriumtreatment. Onthesupplysideofthelabormarket, recall that each individual with ability z who works as a production or R&D worker supplies zαs efficiency units of labor, and the total number of such workers is determined by agents’ educational choices early in life and their entrepreneurial decisions over the life cycle. On the demand side, firms demand 1 efficiency units of produc- ω γ 0 tion worker per product line they own, which is derived in Appendix A.2. Demand for R&D workers, on the other hand, is determined by firms’ innovation effort choice X implied by firms’ dynamic problem (6). Let Φ (z,y, f) denote the density of individual workers with talent z, parental ins come y, family entrepreneurship background f, and schooling s ∈ {0,1}. Let Ψ(n,θ) denote the joint distribution of active firms by number of product lines n and entrepreneurial type θ. Labor market clearing then requires that ∑∑ 1 n Ψ(n,θ) = ∑ (cid:90) (cid:90) Φ (z,y, f)zα 0dzdy (7) 0 ω γ θ n P f z y for production workers, and ∑∑ (cid:18) X(n,θ) (cid:19) σ 1 Ψ(n,θ) = ∑ (cid:90) (cid:90) Φ (z,y, f)zα 1dzdy (8) θnη 1 θ n f z y for R&D workers. To solve for these labor market-clearing conditions, we need to characterizeboththeworkerandfirmdistributions, Φ (z,y, f) and Ψ(n,θ). Weprovide s the derivation of these distributions in Appendix A.5. 3.6 Aggregate Business Reallocation and Innovation The process of business reallocation across firms is central to the dynamics of our model. It is driven by both new entrepreneurs’ and incumbent firms’ activities. The 21

ransformative and ubsistence ntrepreneurs T S E overall rate of business reallocation, denoted by τ, is given by τ = ∑ e + ∑∑ [X(n,θ)+νn]Ψ(n,θ) θ θ θ n where e denotes the entry rate into type-θ entrepreneurship, capturing the contribu- θ tion of entrants to business reallocation, while the second term reflects the incumbent firms’ innovation efforts as well as exogenous factors that contribute to business reallocation across firms. Whereas τ measures the overall flux of business activity—including both new firm entry and incumbent expansion (innovative or otherwise)—only some of those changes lead to direct quality improvements in our model. Thus, τ captures the entire process of reallocation across the economy, encompassing both innovating and non-innovating firms. In contrast, we define τ as aggregate innovation rate, which captures the portion g of these reallocative events that actually raise product quality and thereby contribute to aggregate growth: τ = ∑ sIe + ∑∑ X(n,θ)Ψ(n,θ) (9) g θ θ θ θ n where sI is a parameter representing the share of entry by θ-type entrepreneurs that θ leads to a quality improvement upon entry. This parameter is calibrated using empirical evidence to reflect the relative importance of entrants on the overall growth of the economy. Consequently, τ governs growth via successful innovations, and τ governs g the broader reallocation of resources across the economy. Finally, the aggregate growth rate of the economy is expressed as15 g = ln(γ)τ , g where γ > 1 is the step of product quality improvements achieved through innovation. We finish our model description by defining the equilibrium of this economy. Definition 1 A Balanced Growth Path (BGP) equilibrium is a collection of value functions {W (z,y, f), V(n,θ)}, policy functions (e.g., education choice, entrepreneurial entry, R&D s intensity), wages {ω ,ω }, and distributions {Φ (z,y, f), Ψ(n,θ)} satisfying the following: 0 1 s 1. Workers’ Optimization. Each agent solves the problem (2) and the Bellman equation in (4), choosing whether to pay the education cost and become an R&D worker or to 15ThederivationofthegrowthrateisgiveninAppendixA.3. 22

ransformative and ubsistence ntrepreneurs T S E become a production worker that does not require education, and whether to transition to entrepreneurship upon an opportunity. 2. Firms’ Optimization. Each entrepreneur with state (n,θ) solves the firm problem in (6), determining R&D effort (if transformative) to maximize firm value. 3. Market Clearing. The supply of production and R&D labor—driven by individuals’ occupationalchoices—matchesthetotallabordemandedbyfirms,asspecifiedinequations (7) and (8). Φ Ψ 4. StationaryDistributions. Thedistributions and overindividualsandfirmsremain invariantovertime,consistentwithendogenoustransitionsandentry/exit,satisfying(18) and (20) in Appendix A.5. 5. Balanced Growth. Let γ > 1 be the quality step per successful innovation and τ the g aggregate innovation rate. Output grows at g = ln(γ)τ , g endogenously determined by equilibrium innovation and entrepreneurship. ModelTakeaways. Ourframeworkunifiesthecareerchoicesofindividuals—whether to become a production worker, R&D worker, or entrepreneur—with firm-level innovation and underlines how they jointly shape economic growth through innovation. Specifically, it illustrates that talent allocation across occupations—determined by individual ability, educational opportunities, and family background—critically influences the supply of innovative talent (R&D workers) and the emergence of transformative entrepreneurs. A central implication of this model is that the synergy between higherability transformative entrepreneurs and the supply of educated R&D workers is essential for sustaining growth. Moreover, the model highlights that financial constraints limiting access to education can lead to significant talent misallocation, reducing both the number of transformative entrepreneurs and R&D workers. Consequently, alleviating thesebarriersthrough targetedpolicies cansubstantially boostinnovation, improve occupational sorting, and accelerate overall economic growth. 23

ransformative and ubsistence ntrepreneurs T S E 4 Estimation In this section, we connect the empirical facts to the model framework in order to uncover fundamental parameters driving education choice, occupational choice, and firm dynamics from entrepreneurs. We start by calibrating the model parameters to the data and then provide a set of counterfactual analyses to quantify talent misallocation in the economy and the effectiveness of various policies to alleviate this misallocation and promote innovation. 4.1 Functional Forms and Identification Webeginwithadescriptionoftheestimationprocedure. Ourmodelhas27parameters, 11 of which are calibrated externally and presented in Table 1. able alibrated arameters T 1: C P Parameter Description Value Source ρ Discount rate 0.050 Standard ψ Death rate rate 0.025 40-year career σ Curvature on innovation production function 0.500 Akcigit and Kerr (2018) σ SD of talent distribution 0.224 Data z σ SD of family income distribution 0.619 Data y ρ Correlation of talent and family income 0.144 Data z,y µ Mean of family income distribution 0.461 Nielsen et al. (2010) y p Probability parent entrepreneur 0.080 Data f c Education cost 0.275 Data s γ Innovation step size 1.250 De Loecker et al. (2020) sI Share of entrants with improvement upon entry 0.25 Data θ Notes:Theseparametersareindependentlyidentifiedinthedataorliterature. We set the discount rate ρ to 5 percent. Following the microeconometric literature on innovation, we set the curvature of innovation production function to σ = 0.5, indicating a quadratic cost function; this captures diminishing returns to labor inputs in research.16 The death rate ψ is set to 0.025, implying 40 years of expected working life. The innovation step size (γ=1.25) indicates that successful innovations increase productivity by 25%, calibrated from markup data from De Loecker et al. (2020). The share of innovative entrants sI is directly measured in the data as the share of entering θ 16SeeAkcigitandKerr(2018)andAcemogluetal.(2018),whodiscussthisevidenceinmoredetail. 24

ransformative and ubsistence ntrepreneurs T S E firms that improve upon the median productivity upon entry in their given industry. The education cost parameter (c ) is directly measured in the data as the opportunity s cost from foregone earnings during the years of higher education relative to lifetime earnings. We assume that z and y follow a bivariate lognormal distribution with mean parameters µ and µ , standard deviation σ and σ , and correlation ρ . The standard z y z y z,y deviationsoftalent(proxiedbyIQ)andfamilyincomearemeasureddirectlyfromdata, as is their correlation. The talent mean parameter, µ , is normalized, as its level is not z separately identified. The family income mean parameter, µ , is calibrated to match the y share of individuals who are credit constrained (30%) from Nielsen et al. (2010), who study higher education in Denmark and estimate the number of individuals in the population who face credit constraints for education based on the response of college enrollment to changes in student aid arising from a Danish reform. This moment is central to our quantification of the effect of financial frictions on college access. Finally, the probability of parent entrepreneurship is calibrated to p = 0.08, representing the f baseline rate of entrepreneurship in the previous generation. The remaining 16 parameters are estimated jointly by matching 41 moments from the data to model-generated moments, which are presented in Table 3 and Figure 7. We combine individual-level moments with firm-level moments to connect these two core features of our framework. These moments focus on ability distributions across occupations, the performance of transformative and subsistence entrepreneurs, and the aggregate growth rate. Each set of moments is chosen for its economic relevance to the key mechanisms of the model. To begin with, we target R&D workers and entrepreneurs share by IQ deciles to discipline the parameters that determine the returns to each occupation, such as α . s Motivatedbyourempiricalevidence, theprobabilityofdrawingatype θ¯ andbecoming a transformative entrepreneur depends both on ability z and investment in schooling s, according to the following functional form: φ+ι×s Π(θ¯|z,s) ≡ P(θ = θ¯|z,s) = , 1+exp(−κ(z−ζ)) where φ, κ, ζ, and ι are parameters that we estimate by targeting the share of transformative entrepreneurs by IQ deciles and by education. Overall, φ captures the baseline probability of transformative entrepreneurship, while ι and κ govern the role of education and ability respectively, and ζ represents a threshold parameter. We calibrate θ¯ by matching the life-cycle growth profile of transformative entrepreneurs, captured 25

ransformative and ubsistence ntrepreneurs T S E throughtheaveragefirmsizebyage. Weallowsubsistencefirmstogrowexogeneously at rate ν, which we pin down by comparing the growth trajectories of subsistence and transformative firms by age. We assume that schooling and parental entrepreneurship background interact additively in the arrival rate, λ = λ +λ , f,s f s and we further normalize λ = 0 for uneducated individuals (s = 0) such that we only s estimate the additional entrepreneurial opportunity due to education. The entry cost c e isdrawnfromaParetodistributionwithshapeparameterϖ andascaleparameterfixed at 1.17 We identify these parameters by targeting the share of entrepreneurs with and without entrepreneurial parents and the differences in entrepreneurship rates across education groups. A core component of our firm dynamics framework is the innovation production functioninequation(5). Toidentifythecurvatureoftheinnovationproductionfunction with respect to the size of the firm η, we run the following firm-level regression, which connects the R&D employment to the total workforce for a firm j at time t: ln(R&D Worker ) = β +β ln(Total Worker )+ε . (10) jt 0 1 jt jt This relationship describes how firm-level innovation scales with size and helps us identify the returns to scale pattern in innovation: if β = 1, R&D employment scales 1 proportionallywithtotalemploymentcorrespondingtoσ+η = 1inthemodel. β < 1, 1 on the other hand, indicates decreasing returns to scale in innovation. Therefore, this regressioncoefficienthelpsidentifytheparameter η, whichgovernshowthenumberof productlinescontributestothefirm’sinnovationcapacity, conditionalonthecalibrated valueofσ. Asaresult,ourframeworkallowsfordecreasingreturnstoinnovationatthe firm level, as long as the R&D workforce does not scale one-to-one with firm size. This is consistent with the economy’s need to have a robust pool of entrepreneurs to absorb R&D workers without hitting diminishing returns. We now turn to the estimation results to connect the moments to the underlying parameters. 17The arrival rate λ and the scale parameter of the entry cost cannot be separately identified; hence wesetthelatterto1. 26

ransformative and ubsistence ntrepreneurs T S E 4.2 Estimation Results In this section, we present the internally estimated parameters in Table 2 and the moments that identify them in Table 3 and Figure 7. able stimated arameters T 2: E P Parameter Description Value λ Entrepreneurship arrival rate w/ entrepreneur parent (%) 0.05 f=1 λ Entrepreneurship arrival rate w/o entrepreneur parent (%) 0.02 f=0 λ s=1 Contribution of education to entrepreneurship arrival rate (%) 0.1 θ¯ Scale for innovation function 0.235 κ Entrepreneurial type draw function 1.413 ι Entrepreneurial type draw function 3.358 ζ Entrepreneurial type draw function 3.519 φ Entrepreneurial type draw function 0.354 α Wage function - R&D workers 0.545 1 α Wage function - Production workers 0.495 0 m Entrant cohort mass 0.181 η Product line share in innovation function 0.338 χ Utility from education -3.153 ς Education preference shock scale 0.389 ϖ Pareto shape parameter for entry cost 2.571 ν Exogenous arrival rate of products (subsistence firms) 0.125 Notes:Allparametersareestimatedjointly. We describe some of the key results from our estimation. For the entrepreneurship arrival rate by parent entrepreneurial exposure, λ , we find λ = 0.05% and f f=1 λ = 0.02%, which capture the critical role of family background—individuals with f=0 entrepreneur parents are 2.5-times more likely to have an opportunity to become an entrepreneur. The contribution of education to entrepreneurship arrival rate (λ = s=1 0.1%)alsoindicatesthateducatedworkersaremuchmorelikelytohaveentrepreneurial opportunities. The parameter ι = 3.358 further amplifies the effect of education on entrepreneurialopportunities. Ourestimationofthisparametersuggeststhat,onaverage, education increases the likelihood of being a transformative entrepreneur as opposed to subsistence by about 69 percentage points. The estimated wage parameters for R&D workers (α = 0.545) and production workers (α = 0.495) capture the earnings pre- 1 0 mium for R&D workers, which is part of what draws higher-IQ individuals into an R&D career. The value for the product line share in innovation (η = 0.338) implies that, 27

ransformative and ubsistence ntrepreneurs T S E for each percentage increase in firm size, the innovation rate increases by only about 0.84 percent, resulting in decreasing returns in innovation. Together, these parameters illuminate how family background, education, and labor market structures interact to shape entrepreneurial outcomes and economic mobility. able oments T 3: M Description Model Data R&D workers share by IQ In Figure 7 Entrepreneurs share by IQ In Figure 7 Transformative entrepreneur share by IQ In Figure 7 R&D workers share in highest family income decile 0.027 0.028 Entrepreneur share by entrepreneur parent 0.10 0.10 Entrepreneur share by non-entrepreneur parent 0.06 0.06 Entrepreneur family share 0.08 0.08 Average firm size at age 10 - Subsistence entrepreneur 2.30 2.27 Average firm size at age 10 - Transformative entrepreneur 4.96 5.08 Share of transformative entrepreneurs within production workers 0.006 0.007 Share of transformative entrepreneurs within R&D workers 0.05 0.05 R&D workers log wage premium - highest to lowest IQ decile difference 0.09 0.09 Regression coefficient in equation (10) 0.38 0.36 Aggregate growth rate (%) 1.00 1.00 Notes:Momentsjointlyinputintoestimation.Averagefirmsizemomentsarerelativetoentrysize. The estimation matches the specific moments and the occupational distribution quite well. The key moments in our model are targeted to match empirical regularities in entrepreneurship, innovation, and career dynamics. The shares of R&D workers, entrepreneurs, and transformative entrepreneurs by IQ are matched across the ability distribution (discussed below). We precisely match the impact of parental background, with entrepreneurs’ children being significantly more likely to become entrepreneurs themselves (0.10 vs 0.06 for non-entrepreneurs’ children). Our model accurately captures firm growth dynamics with subsistence entrepreneurs reaching average sizes of 2.30 employees at age 10 (vs 2.27 in data), while transformative entrepreneurs grow substantially larger (4.96 in the model vs 5.08 in the data). The model successfully reproduces the critical role of education in fostering transformative entrepreneurship, with educated entrepreneurs being eight times more likely to build transformative firms (0.05 vs 0.006 for uneducated). We match the change in wage premium over the IQ distribution for R&D workers (0.09 log difference), the relationship between occupation and entrepreneurial outcomes (0.36 regression coefficient in the data vs 0.38 in 28

ransformative and ubsistence ntrepreneurs T S E the model), and the aggregate growth rate (1%). igure alent llocation across ypes F 7: T A T 100 96 92 88 84 80 1 2 3 4 5 6 7 8 9 10 )001 rep( erahS Model Data 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 IQ Deciles a roduction orker ( ) P W )001 rep( erahS Model Data IQ Deciles b orker ( ) R&D W 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 )001 rep( erahS Model Data 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 9 10 IQ Deciles c on transformative entrepreneur ( ) N - )001 rep( erahS Model Data IQ Deciles d ransformative entrepreneur ( ) T On the career choice side, Figure 7 shows the share of individuals by occupation and IQ decile, as calibrated in the model and in the data. Overall, the model provides a close match for the talent allocation pattern across occupations in the data. 4.3 Untargeted Moments In this section, we compare our quantified model against untargeted features of the data with respect to occupational sorting and firm dynamics. First, we examine the transition probability from being a worker to being a transformative entrepreneur split by worker type, which was not directly targeted in the data. Panel A of Table 5 shows that, in the data, 76% of the entrepreneurs with a back- 29

ransformative and ubsistence ntrepreneurs T S E ground as R&D workers are transformative, while the remaining 24% are subsistence entrepreneurs. On the contrary, production workers who become entrepreneurs are much more likely to be subsistence types, while only 11% of them are transformative entrepreneurs. The table indicates that the quantified model aligns closely with the data regarding the higher propensity of entrepreneurs with an R&D background to be transformative compared to those with a production worker background. able ntargeted oments T 4: U M — Career Choice — — Firm Dynamics — Transformative Share Firm Age 5 size Firm Age 10 size Data Model Data Model Data Model R&D Worker 0.76 0.91 3.16 2.99 4.35 4.72 Production Worker 0.12 0.12 2.62 1.81 3.04 2.61 Next, we examine the dynamic evolution of a firm’s size depending on the entrepreneur’s occupation background. Panel B of Table 5 reports the average firm employment at ages five and ten relative to age 0. The table indicates that, in the data, firms with entrepreneurs who have R&D worker background grow by a factor of 3.16 after five years and 4.25 after ten years. Firms run by entrepreneurs with a production worker background tend to grow less instead, by a factor of 2.62 after five years and 3.04 after ten. The quantified model closely matches the data along these dimensions. Finally, we examine the dynamics of firm size by entrepreneurial type. Figure 8 shows the share of firms, in Panel (A), and the share of total employment, in Panel (B), accounted for by transformative entrepreneurs by firm age.18 The pattern is monotonically increasing, as transformative entrepreneurs account for a share of firms that increases from about 13% at age 0 to 18% at age 10, and a share of total employment that increases from about 13% at age 0 to more than 30% at age 10. The model and the data are closely aligned, highlighting the increasing importance of transformative entrepreneurs throughout the firm life cycle, which will be central to understanding misallocation and evaluating policy counterfactuals. 4.4 Education and Entrepreneurship Oneofthenovelcomponentsatthecenterofthisframeworkisthestudyofthepipeline for transformative entrepreneurs. Before turning to the counterfactual analysis, we 18Wenormalizetheinitialcountoffirmstoadjustfortheshareofallindividualsintheeconomy. 30

ransformative and ubsistence ntrepreneurs T S E igure ntargeted oments hare of ransformative ntrepreneurs F 8: U M : S T E 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0 1 2 3 4 5 6 7 8 9 10 erahS tnuoC Model Data 0.34 0.30 0.26 0.22 0.18 0.14 0.10 0 1 2 3 4 5 6 7 8 9 10 Age a hareof ransformative ntrepreneurs ( )S T E erahS tnemyolpmE Model Data Age b mployment hare of ransformative ( ) E S T ntrepreneurs E turn to the importance of education for entrepreneurship and firm dynamics. The quantified model suggests education is not just important for the creation of R&D workers, but also for the role of entrepreneurs. To highlight the role of education, we run a counterfactual exercise where we shut down the effect of higher education on the arrival rate of a transformative entrepreneurial idea. Specifically, we set the parameters λ = 0 and ι = 0, neutralizing the higher education advantage on the frequency of s=1 idea arrival and on the probability of drawing a high-type idea. We then solve for the counterfactual BGP equilibrium under these assumptions. able mportance of ducation for ntrepreneurship T 5: I E E Baseline No Educational Impact Change(%) on Entrepreneurship Growth (%) 1.00 0.92 -7.95 Occupation Shares Production Workers 96.33 96.47 0.15 R&D Workers 1.58 1.44 -8.55 Subsistence Entrepreneurs 1.59 1.63 2.57 Transformative entrepreneurs 0.50 0.45 -9.20 Table 5 presents the results of this counterfactual analysis, illustrating the impact of removing the effect of higher education on transformative entrepreneurship. The 31

ransformative and ubsistence ntrepreneurs T S E findings indicate that shutting down this effect leads to a 7.95% reduction in the overall growth rate. This decline can be attributed to several factors. First, the share of transformative entrepreneurs decreases by 9.20%, while the proportion of subsistence entrepreneurs rises by 2.57%. This shows the crucial role of education in driving growth through entrepreneurship. Second, the share of R&D workers decreases by 8.55%, representing a combination of forces due to the symbiotic relationship between entrepreneurs and R&D workers. The occupational decision of an R&D worker changes because part of the motivation to obtain education and choose an R&D occupation is the expectation that this path increases the likelihood of becoming a transformative entrepreneur. Eliminating the link between higher education and transformative entrepreneurship reduces the perceived benefits of higher education, thereby discouraging individuals from choosing careers in R&D. In addition, the demand for R&D workers declines, given that there are fewer transformative entrepreneurs. These results emphasize the critical role of education in shaping the innovation pipeline within our framework. igure irm ife ycle by chooling and arental ntrepreneurship F 9: F L C S P E 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0 5 10 15 20 25 30 35 40 45 50 noitaerC tnemyolpmE evitaleR f = 0, s = 1 f = 1, s = 0 f = 1, s = 1 Age To further illustrate the role of schooling and family background, Figure 9 presents the impact of education and family exposure to entrepreneurship on the unconditional expected employment creation for an individual by age. The lines represent three groups of individuals: (i) those with parental exposure to entrepreneurship and no higher education (f=1, s=0, solid blue line); (ii) those with education attainment but no parent entrepreneurs (f=0, s=1, dashed black line); (iii) those with education and with parentalentrepreneurshipexposure(f=1, s=1,dashed-dottedredline). Eachlineshows the unconditional expected job creation for an individual from each group, relative to 32

ransformative and ubsistence ntrepreneurs T S E those without schooling or parent entrepreneurs (f=0, s=0). As a result, these lines include both the probability of starting a firm and the expected size of such a firm. The figure shows that individuals who have both parent entrepreneurs and higher education are the largest contributors to job creation. There are three important observations from Figure 9. First, for entrepreneurs without higher education, parental exposure leads to over twice as much job creation throughout the life cycle. This effect is due to the higher propensity of becoming entrepreneurs for individuals with a parent entrepreneur. Second, we observe that individuals with schooling exhibit a steeper job creation profile. Higher education increases the likelihood that these individuals will draw a transformative type, conditional on having an entrepreneurial opportunity. Thus, in the first few years following their education (ages 0-5), they are more likely to delay starting a firm if they draw a low type compared to individuals without higher education. This is because they expect a greater chance of drawing a high type in the future. As a result, individuals with higher education show lower job creation in the early years but higher job creation in the central and later stages of their careers. Finally, the fact that individuals with both higher education and parental exposure to entrepreneurship have the steepest employment creation profile highlights that the interaction of parental entrepreneurship and schooling is central to the contribution of transformative entrepreneurs to job creation. 5 Talent Allocation and Policy Counterfactuals In this section, we use our quantitative framework to examine the allocation of talent in the innovation pipeline, focusing on how individual career choices and firm dynamics interact, as well as the related policy implications. We begin with a positive analysis of the impact of financial frictions on both career choice and firm dynamics. Next, we explore policy tools that can foster growth by improving the allocation of talent across occupations and promoting the development of startups and firms. 5.1 Talent (Mis)Allocation The presence of financial frictions in the access to education produces talent misallocation in the economy: some highly talented individuals who would like to invest in education and pursue an R&D career might be unable to do so if they are born from lower-income families and cannot afford the cost of education. Such barriers can spill over to the rate of transformative entrepreneurship, given the large impact of 33

ransformative and ubsistence ntrepreneurs T S E education on the probability of becoming a transformative entrepreneur. These considerations raise the following questions: Are there missing R&D workers and missing entrepreneurs in the economy due to the inability to pursue education because of family income? To answer this question, we solve for a counterfactual BGP equilibrium, focusing on the alleviation of the financial frictions in schooling by enabling all individuals in the economy to access education if they wish to attend school. We do not subsidize their schooling directly, as they must still pay the education cost, which enters their discounted lifetime earnings, but they are not financially constrained. The results of this exercise are illustrated in Table 6, where we report the share of R&D workers and entrepreneurs in the population, the share of transformative entrepreneurs among all entrepreneurs, and the growth rate for our baseline economy and the counterfactual where all individuals can afford education. able lleviating inancial rictions in ducation ccess T 6: A F F E A Baseline No Financial Frictions Change (%) Growth (%) 1.00 1.11 11.08 Occupation Shares Production Workers 96.33 96.11 -0.23 R&D Workers 1.58 1.82 15.24 Subsistence Entrepreneurs 1.59 1.53 -3.60 Transformative entrepreneurs 0.50 0.54 7.49 Alleviating the frictions in access to education would increase the R&D workers population share by 15.2%, transformative entrepreneurs by 7.5%, and the growth rate by 11.1% relative to the baseline. Unequal access to education represents a bottleneck for various career paths due to the financial frictions that hinder access. As a result, alleviating these frictions can have a significant impact on talent allocation to entrepreneurship and innovation, enabling talented individuals from lower-income families to pursue careers as R&D workers and transformative entrepreneurs. In our framework, the education channel operates on both the demand of R&D talentbytransformativeentrepreneursandthesupplyofR&Dtalentthroughthecareer choice of R&D workers. Alleviating financial frictions increases both the demand and the supply for talent. The supply channel quantitatively dominates, as the R&D wage decreases by 2.01%. To highlight the complementarity between the demand and the supply of innova- 34

ransformative and ubsistence ntrepreneurs T S E tivetalent, weconductapartial equilibriumcounterfactualexercisewith thealleviation of financial frictions, as above, but where we keep the number of entrepreneurs of each type and the firm size distribution fixed to the baseline. We thus focus on the supplyside effect of financial frictions, allowing the share of R&D workers to increase while keeping the demand side fixed at the steady state. Table 7 reports the results from this exercise, showing that the growth rate increases by only 6.6%, compared to 11.1% when both supply and demand adjust. Thus, the supply side can only generate about 60% of the total general equilibrium effect. These results underscore the complementarity of R&D workers and transformative entrepreneurs in the innovation pipeline. Merely increasing the number of inventors is insufficient; there must be a corresponding rise in job opportunities created by transformative entrepreneurs to fully unlock their potential and drive maximum growth. able ynergy between orkers and ntrepreneurs T 7: S R&D W E No Change in Demand and Baseline Entrepreneurship (PE) Supply Adjust (GE) Growth (%) 1.000 1.066 1.111 igure lleviating inancial rictions by amily ackground F 10: A F F F B 5 4.5 )0 0 4 0.54 1 re3.5 0.51 0.56 p ( e 3 ra h S 2.5 0.45 1.67 2.34 1.97 n 2 0.82 o ita1.5 p u c 1 c O 1.64 1.58 1.53 1.48 0.5 0 Baseline Without Financial Baseline Without Financial Frictions Frictions Parental Income Below Median Parental Income Above Median Subsistence Entrepreneur R&D Worker Transformative Entrepreneur Returning to the full general equilibrium effects of alleviating financial frictions, Figure 10 shows the share of individuals who choose an occupation as subsistence entrepreneur, R&D worker, or transformative entrepreneur depending on their parental background. Wegroupindividualsbyparentalincomeaboveorbelowthemedian. The figure compares the occupational shares in the baseline and in the counterfactual with 35

ransformative and ubsistence ntrepreneurs T S E no financial frictions for individuals with low-income and high-income parents. The figure illustrates that, without financial frictions, the share of R&D workers increases for individuals with low parental income, but it decreases for those with high parental income, reducing the gap in access to careers in innovation by family income. A small gap remains due to the underlying differences in talent distribution for individuals with different parental backgrounds, driven by intergenerational talent correlation. In addition, we note that the share of transformative entrepreneurs increases for individuals with both low and high parental income. This result is due to direct and indirect effects. First, alleviating financial frictions improves access to education, which directly increases the arrival rate of transformative entrepreneurship. Second, the increased supply of R&D workers further stimulates transformative entrepreneurship. These results underscore the importance of family background in determining career choice in the innovation sector and as a source of talent misallocation. Finally, we investigate the change in occupational shares along the talent distribution. Figure11showsthechangeintheshareofindividualsineachoccupationbetween the baseline and the counterfactual with no financial frictions. igure lleviating inancial rictions by F 11: A F F IQ 0.3 e c )s tn 0.2 n e re ffID io p e g a 0.1 e tn ra e c h S re p 0.0 ( -0.1 1 2 3 4 IQ Quartile Subsistence Entrepreneur R&D Worker Transformative Entrepreneur Alleviating financial frictions leads to an increase in the share of R&D workers and transformativeentrepreneursintheeconomyacrossalltalentquartiles,buttheincrease ismorepronouncedforhigh-IQindividuals. Inparticular, alleviatingfinancialfrictions increases the shares of R&D workers and transformative entrepreneurs by 0.26p.p. and by 0.06p.p. respectively for individuals in the top IQ quartile, but only by 0.18p.p. and 0.02p.p. in the bottom quartile. On the contrary, the share of subsistence entrepreneurs 36

ransformative and ubsistence ntrepreneurs T S E declines along all segments of the talent distribution. This result highlights that alleviating financial friction improves the allocation of talent to innovative careers in the economy. Firm Dynamics and Financial Frictions. Financial frictions matter not only for talent allocation but also for firm dynamics. The latter effect emerges because entrepreneurs’ backgroundandeducationdecisionsaffecttheirfirms’performance. Figure12explores how talent misallocation affects the dynamics of firms and innovation, comparing the counterfactual BGP without financial frictions discussed above (blue solid lines) to the baseline case (gray dashed lines). Panel (A) shows the average employment of transformative entrepreneurs by firm age relative to the baseline. The alleviation of financial frictions increases average employment for transformative entrepreneurs, which goes up by 1% for firms of age 1 and by almost 3% for firms of age 0. Next, we split this effect into the share of firms of each entrepreneur type and the share of employment. Panel (B) evaluates the share of transformative entrepreneurs with and without financial frictions by firm age. Panel (C) shows the employment share of transformative entrepreneurs in the economy with and without financial frictions. These pictures show that alleviating financial frictions increases both the share of firms that are transformative and the share of employment that they account for. This change in the composition of firms toward transformative types is the driver of the increase in innovation and aggregate growth when financial barriers to education access are lifted. This result complements previous work (Akcigit et al., 2025) in showing the connection between financial frictions and innovation but expands on how the educational channel has a direct impact on entrepreneurship and firm dynamics. This new channel may lend itself to novel policy implications. Motivated by this observation, in the next section, we investigate how different policies can improve the allocation of talent, firm growth, and the innovative capacity of the economy. 5.2 Comparing Alternative Policies This section studies how different policies affect various margins of the career sorting process, the allocation of talent in the economy, and the overall innovation capacity and productivity growth. Keeping fixed the budget of the policymaker, we consider four different possible instruments for innovation: subsidize R&D, entrepreneurship, transformative entrepreneurship, or education. 37

ransformative and ubsistence ntrepreneurs T S E igure lleviating inancial rictions irm utcomes F 12: A F F : F O 1.03 1.02 1.01 1.00 0 1 2 3 4 5 6 7 8 9 10 tnemyolpmE evitaleR No financial frictions 0.20 0.18 0.16 0.14 0.12 0 1 2 3 4 5 6 7 8 9 10 Age a verage mployment of ransformative ( ) A E T irms F erahS tnuoC Baseline No financial frictions Age b hare of ransformative irms ( ) S T F 0.36 0.32 0.28 0.24 0.20 0.16 0.12 0 1 2 3 4 5 6 7 8 9 10 erahS tnemyolpmE Baseline No financial frictions Age c mployment hare of ransformative irms ( ) E S T F We assume that the government levies a lump sum tax to finance the policies by balancing the budget in every period. The four different policies have a specific mappingtothequantifiedmodel: (i)subsidytotheentrycostforallentrepreneurs(Uniform Startup Subsidy), (ii) subsidy to the incumbent firms for their R&D expenses (R&D Subsidy), (iii) subsidy to the entry cost only for transformative entrepreneurs (Innovative Startup Subsidy), and (iv) subsidy to the cost of education for those who cannot afford it (Education Subsidy). We compare alternative BGP equilibria with policies that use the same total government budget. Table 8 reports the results for a government budget equivalent to 0.05% of GDP. The first row of the table reports the change in the growth 38

ransformative and ubsistence ntrepreneurs T S E rate under each policy, while the other rows report the change in the share of each occupation. able olicy utcomes for quivalent udget of of T 8: P O E B 0.05% GDP Uniform R&D Innovative Education Startup Subsidy Subsidy Startup Subsidy Subsidy Growth (% Change wrt Baseline) 0.11 2.31 4.38 16.14 Occupations Shares (% Change wrt Baseline) Production Workers -0.01 -0.04 -0.08 -0.33 R&D Workers -0.02 2.86 4.04 22.26 Subsistence Entrepreneurs 0.76 -0.74 -1.45 -5.27 Transformative Entrepreneurs 0.50 1.49 6.69 10.84 There are several key takeaways from Table 8. First, a uniform entrepreneurship subsidy appears largely ineffective, as it primarily attracts subsistence entrepreneurs, subtracting them from R&D and production, without significantly increasing the number of transformative entrepreneurs. Because subsistence entrepreneurs neither hire R&D workers nor significantly expand, they do not propel the innovation process, so the economy’s long-run growth rate remains only slightly above the baseline. In contrast, an R&D subsidy for incumbents spurs moderate innovation in the economy, increasing the demand for R&D workers and also resulting in a modest increase in the share of transformative entrepreneurs. However, its overall impact on growth is limited compared to some other policies in Table 8 primarily for two reasons. First, there are decreasing returns to innovation at the firm level implied by our estimation results. Second, this policy does not directly affect how many people can become R&D workers or transformative entrepreneurs. Unlike the uniform startup subsidy, the innovative startup subsidy targets transformative entrepreneurs who plan to hire R&D workers. Lowering these entrepreneurs’ startup costs leads to an appreciable increase in the share of transformative firms, fueling faster innovation, greater demand for R&D labor, and higher overall growth. Although this policy does not help incumbents as much as the R&D subsidy, it effectively boosts the formation of growth-oriented, transformative startups, which accounts for a noticeable rise in the growth rate. Both the R&D subsidy and the innovative startup subsidy can stimulate innovation to some extent, but neither tackles the root cause of the primary friction — the unequal access to education faced by those who cannot afford it. In contrast, subsidizing the 39

ransformative and ubsistence ntrepreneurs T S E cost of education proves far more effective given the same budget. By helping more individualsaffordhighereducation, itexpandsboththepoolofpotentialR&Dworkers and the set of individuals who can found transformative firms. The heightened supply of R&D workers supports incumbent innovation, while the broader set of educated individuals fosters more transformative startups in the first place. Because this policy strengthens both sides of the market for innovation (the supply of R&D labor and the demand for it), it creates the largest increase in growth relative to the other three subsidies. Overall, Table 8 highlights that innovation and entrepreneurship respond strongly to policies that expand human capital (education) or that specifically target growthoriented startups. These policies create a more pronounced “multiplier” effect by simultaneously deepening the labor pool for R&D and boosting transformative entrepreneurship, thereby accelerating aggregate productivity growth more effectively than indiscriminate entry or incumbent-only R&D subsidies. Policies and Firm-level Outcomes. Each policy also impacts the growth of firms, and thus, job creation and innovation spillovers at the firm level. This result is illustrated in Figure 13, which shows firm outcomes in the baseline (gray lines), and under the three policies that proved effective in increasing growth: the R&D subsidy (pale blue), innovative startup subsidy (medium blue), and education subsidy (dark blue). Panel (A) shows the average employment of transformative entrepreneurs by firm agerelativetothebaseline. AnR&Dsubsidyachievesanexpansioninaverageemployment of transformative firms of about 2%, which mostly accrues in the early part of the firm life cycle. Education subsidies increase the average employment of transformative firms not just initially (by 2% at age 1) but also as the firm ages, up to 6% at age 10. An innovativestartupsubsidyinsteadreducestheaverageemploymentofinnovativefirms because it increases the share of transformative entrepreneurs more than the share of R&D workers, resulting in less innovation per transformative firm and flatter life-cycle growth. Panels (B) and (C) show, respectively, the share of transformative firms and the employment share of transformative firms under different policies by firm age. All three main policies boost the share of transformative firms and their employment share at any age. The innovative startup subsidy increases the share of transformative firms the most, followed closely by the education subsidy. However, the latter is the most effective instrument to boost the employment share of transformative firms, which increases to about 40% for firms of age 10 compared to about 30% in the baseline. 40

ransformative and ubsistence ntrepreneurs T S E igure irm utcomes under olicies F 13: F O P 1.06 1.04 1.02 1.00 0.98 0.96 0 1 2 3 4 5 6 7 8 9 10 tnemyolpmE evitaleR 0.22 0.20 0.18 0.16 0.14 0.12 0 1 2 3 4 5 6 7 8 9 10 Age Baseline Incumbent R&D Subsidy Innovative Startup Subsidy Education Subsidy a verage mployment of ransformative ( ) A E T irms F erahS tnuoC Age Baseline Incumbent R&D Subsidy Innovative Startup Subsidy Education Subsidy b hare of ransformative irms ( ) S T F 0.40 0.36 0.32 0.28 0.24 0.20 0.16 0.12 0 1 2 3 4 5 6 7 8 9 10 erahS tnemyolpmE Age Baseline Incumbent R&D Subsidy Innovative Startup Subsidy Education Subsidy c mployment hare of ransformative irms ( ) E S T F The overarching takeaway is that education subsidies consistently outperform other policy interventions across all measured outcomes, suggesting that they may be the most effective approach to fostering high-impact entrepreneurship, while direct R&D support and startup subsidies offer more modest but still positive effects. Optimal Policy Mix. So far, a clear hierarchy of policy effectiveness has emerged, based on interventions amounting to 0.05% of GDP. Education policy tends to be the most effective, but innovative entry policies also show high effectiveness. Next, we will consider the potential interactions and complementarity between policies: certain 41

ransformative and ubsistence ntrepreneurs T S E policies may become more effective when implemented alongside others. We explore policy interactions at increasingly larger budgets in Table 9. able ptimal olicy ix at ifferent udget evels T 9: O P M D B L Budget Share, % Budget Incumbent Innovative Education Change in (% of GDP) R&D Startup Subsidy Innovation, % 0.05 0.0 11.6 88.4 20.0 0.10 0.0 52.0 48.0 27.5 0.20 0.0 73.9 26.1 39.4 0.30 0.0 81.5 18.5 48.9 0.40 0.0 85.5 14.5 56.7 0.50 0.0 87.9 12.1 63.4 0.60 5.0 84.5 10.5 69.4 0.70 13.9 76.8 9.3 74.9 Table 9 illustrates the optimal allocation of a given budget across three policy areas to maximize growth as budget levels increase from 0.05% to 0.70% of GDP. Our results reveal a clear prioritization pattern: at lower budget levels (0.05-0.50% of GDP), funding is split between education subsidies and innovative startups, with education receiving the majority share at the smallest budget but steadily decreasing as the budget increases, while support for innovative startups grows substantially. As the budget expands beyond 0.5% of GDP, incumbent R&D begins receiving allocation, from a 5% share at a budget of 0.6 % of GDP to a 13.9% share with a 0.7% GDP budget. Meanwhile, the education subsidy share continues to decline, and innovative startups maintain the dominant share (though slightly reduced from its peak). Thisstrategicshiftinbudgetallocationproducesprogressivelystrongerinnovationoutcomes, with the percent change in innovation growing from 20% at the lowest budget level to 75% at the highest, suggesting that policymakers should prioritize education and innovative startups when resources are constrained, and then move to support established firms’ R&D when substantial funding is available. This result connects to the broad interplay between education and transformative entrepreneurship at the center of our analysis. 42

ransformative and ubsistence ntrepreneurs T S E 6 Conclusion This paper highlights the fundamental role of the symbiotic relationship between entrepreneurs and inventors in driving technological progress, innovation, and long-run economic growth. By examining the distinct pathways to becoming an inventor or an entrepreneur, and the role that entrepreneurs play in hiring and managing inventive talent, we contribute to a deeper understanding of how innovative firms emerge and scale. In particular, we connect the concept of the transformative entrepreneur to the broader literature on talent allocation and economic dynamics. Our contribution is twofold. First, we present new empirical evidence on entrepreneurial careers and firm dynamics. We show that while the likelihood of becoming an R&D worker rises with IQ, the likelihood of becoming an entrepreneur declines with it. However, for transformative entrepreneurs—those who actively hire R&D workers and pursue innovation—IQ and educational attainment are strongly predictive. Parental background remains a powerful determinant of entrepreneurship in general, but talent and education appear to be key filters for the most growth-oriented entrepreneurs. Second, we develop a quantitative endogenous growth model that incorporates these empirical patterns and captures the feedback loop between transformative entrepreneurs and skilled R&D workers. Our analysis reveals that financial constraints in access to education, particularly for talented individuals from low-income backgrounds, represent a key bottleneck for innovation. These frictions limit the development of both the supply of innovative workers and the demand from transformative entrepreneurs. Among various policy tools, we find that education subsidies are more effective in addressing these root frictions than uniform startup subsidy or incumbent R&D subsidies, producing greater gains in both innovation and aggregate growth. In short, unlocking an economy’s innovative potential requires strengthening both sidesofthemarket: thesupplyofskilledR&Dtalentandthedemandoftransformative entrepreneurs. This underscores the importance of policies that promote inclusive access to higher education and improve the allocation of talent in the economy. Although the central role of the entrepreneur has long been recognized, this paper offers a new foundation-empirical, theoretical, andquantitative-tounderstandhowentrepreneurs and inventors jointly shape the future of modern economies. 43

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ransformative and ubsistence ntrepreneurs T S E Appendix A Model Appendix A.1 Representative Household Our economy admits representative households for each cohort of agents with characteristics of ability, parental income, and parental entrepreneurship, (z,y, f). The household values the consumption of the final good of the cohort with the following preferences: (cid:90) ∞ U = e −ρtlnC dt, (11) 0 t 0 where ρ > 0 is the discount factor and C(t) denotes consumption at time t. The representative household earns wage income from production and R&D workers, as well as interest income at rate r from asset holdings A , which correspond to the total t value of firms owned by entrepreneurs within the cohort. Given this specification, the representative household maximizes utility as defined in equation (11), subject to the flow budget constraint, A˙ +C = rA + I + I , t t t p,t rd,t where A˙ is the time derivative of the assets, I and I denote the wage income of t p,t rd,t production workers and R&D workers within the cohort, respectively. This problem delivers the standard Euler equation: C˙ t ≡ g = r−ρ, (12) c C t where g is the growth rate of consumption, which is equal to the growth rate of the c finalgood, g,intheBGPequilibrium. Wenextdiscussfinalgoodproductionandderive its growth rate. A.2 Product Market Structure and Static Profits Consider a representative firm that produces the final good, denoted by Y, using a t continuum of intermediate inputs y . The production technology is Cobb-Douglas in j,t logs: (cid:90) (cid:0) (cid:1) lnY = ln y dj. t j,t j∈N 47

ransformative and ubsistence ntrepreneurs T S E The measure of available product lines is unity, although not all lines are necessarily active at any given time19. N denotes the active set of product lines. We normalize the price of the final good to one without loss of generality. Cost minimization problem implies that the representative final-goods producer allocates an identical expenditure, Y, to each active intermediate variety j t p y = Y, ∀j ∈ N j,t j,t t Intermediate Production. An intermediate goods firm is defined as an entity holding a collection of product lines. These firms are the key objects of interest, which are run byentrepreneursinourtheoreticalframework. Eachintermediategood y isproduced j,t via a linear technology: y = q l , (13) j,t j,t j,p,t where l denotes the effective units of production labor allocated to line j, and q j,p,t j,t is the productivity level at which intermediate good is produced by the firm at date t. w Consequently, the marginal cost of producing line j is 0,t, where w represents the q 0,t j,t wage rate per efficiency unit of production workers. Firms can augment their portfolios by innovating on a product line. Successful innovation upgrades the quality of intermediate j by a factor γ > 1, increasing q to γq . j j We assume Bertrand competition between the latest innovator and the previous incumbent: upon innovating, the entrant captures the entire market for that intermediate and sets a price equal to the former incumbent’s unit cost: γw p = 0,t . (14) j,t q j,t Under this pricing rule, the market is fully served by the new innovator. This implies that each product line j is produced by a single intermediate good firm that has the highest productivity q . j,t Static Profits. The associated static profit for an intermediate line j is γ−1 π = p y − w l = Y. (15) j,t j,t j,t 0,t j,p,t t γ 19Productlinesmaybecomeinactiveduetothedeathofentrepreneurs,forinstance. 48

ransformative and ubsistence ntrepreneurs T S E It follows that the labor demand for line j is 1 l = , j,p,t ω γ 0,t w where we define ω ≡ 0,t. Note that, at any point in time, this static problem is 0,t Yt identical across all product lines a firm owns. If a firm holds n such lines, its total static profit equals π n. There is no heterogeneity in static profits across entrepreneur types t in our framework; differences instead arise in each type’s propensity to innovate and expand the firm’s portfolio. Next, we derive the final good output as a function of aggregates. Let L be the P,t aggregate demand for production labor. It satisfies (cid:90) ϕ L ≡ l dj = P,t j,p,t N ω 0,t γ where ϕ ≡ |N| defines the measure of active product lines. As firms set a price equal to p = γw 0,t, we get j,t q j,t (cid:90) ln(Y) = ln(y )dj t j,t N (cid:90) (cid:90) = ln(p y )dj− ln(p )dj j,t j,t j,t N N (cid:90) = ln(Y)ϕ−ln(w γ)ϕ+ ln(q )dj t 0,t j,t N (cid:90) = ln(Y)ϕ+[ln(L )−ln(ϕ)−ln(Y)]ϕ+ ln(q )dj t P,t t j,t N Y = ϕ −ϕL ϕ Q t P,t t (cid:0)(cid:82) (cid:1) where Q ≡ exp ln(q )dj is the aggregate productivity index. t N j,t A.3 Aggregate Growth Rate In previous section, we show that Y = ϕ −ϕL ϕ Q . Since L and ϕ are constant in t P,t t P,t stationary equilibrium, the growth rate of aggregate output Y equals the growth rate t ∆ of the aggregate productivity index Q. We can express lnQ after an instant t as t (cid:90) 1 lnQ t+∆t = (cid:2) τ g ∆ tln (cid:0) γq jt (cid:1) +(1−τ g ∆ t)lnq jt (cid:3) dj 0 = τ ∆ tln(γ)+lnQ g t 49

ransformative and ubsistence ntrepreneurs T S E where τ is aggregate innovation rate defined in equation (9) and higher order terms g ∆ ∆ in t are omitted. By subtracting lnQ from both sides, dividing by t, and taking the t limit as ∆ t → 0, we get g = Q˙ t = lim lnQ t+∆t −lnQ t = ln(γ)τ . ∆ g Q t ∆t→0 t where Q˙ denotes the time derivative of aggregate productivity index. t A.4 Normalization of Value Functions In this section, we derive the normalized value function for the firms given in equation (6).20 We start with the unnormalized firm value V˜ (n,θ), given by t ∂V˜ (n,θ) rV˜ (n,θ)− t = πnY (16) t t ∂t (cid:2) (cid:3) +τn V˜ (n−1,θ)−V˜ (n,θ) t t (cid:40) (cid:18) (cid:19)1(cid:41) (cid:2) (cid:3) X σ +max X V˜ (n+1,θ)−V˜ (n,θ) −w X t t 1,t θnη (cid:2) (cid:3) (cid:2) (cid:3) +υn V˜ (n+1,θ)−V˜ (n,θ) +ψ 0−V˜ (n,θ) , t t t where the term ∂V˜ t (n,θ) reflects the fact that the value of the firm changes over time. We ∂t normalize the value function with the final good Y such that t V˜ (n,θ) ≡ V(n,θ)Y. t t Substituting the above definition into the left side of the value function above yields the following, ∂V˜ (n,θ) ∂(V(n,θ)Y) rV˜ (n,θ)− t = rV(n,θ)Y − t t t ∂t ∂t Y˙ = rV(n,θ)Y − t V(n,θ)Y t t Y t = (r−g)V(n,θ)Y (17) t = ρV(n,θ)Y, t 20Thenormalizedvaluefunctionsforworkersinequation(4)canbederivedsimilarlyandistherefore omittedforbrevity. 50

ransformative and ubsistence ntrepreneurs T S E where g is the growth rate of the final good and r− g = ρ from the household maximization problem in equation (12). Finally, by substituting the last term into the unnormalized value function, canceling the final good from both sides, and defining normalw ized efficiency wage for R&D workers as ω ≡ 1,t, we arrive at the normalized value 1 Yt function in equation (6). A.5 Firm and Worker Distributions in Equilibrium This section describes the mass of firms and workers across different states. The stationary equilibrium of the model ensures that the distributions of firms and workers remain stable over time. A.5.1 Firm Size Distribution The equilibrium mass of firms is denoted by Ψ(n,θ,s|z,y, f) where firms are indexed by size n ∈ {1,2,3,...}, entrepreneur type θ ∈ {0,θ¯}, entrepreneur’s education s and characteristics (z,y, f). We denote the relevant marginal distribution, i.e., integrated versionovereducationandworkercharacteristics,as Ψ(n,θ). Instationaryequilibrium, the firm mass satisfies a set of conditions that regulate entry, transition, and exit: ∞ τ Ψ(1,θ,s|z,y, f)+ψ ∑ Ψ(n,θ,s|z,y, f) = e(θ,s|z,y, f) (18) n=1 [X(n,θ)+τ+υ+ψ]Ψ(1,θ,s|z,y, f) = τ2 Ψ(2,θ,s|z,y, f)+e(θ,s|z,y, f) [X(n,θ)+(τ+υ)n+ψ]Ψ(n,θ,s|z,y, f) = [X(n,θ)+υ(n−1)]Ψ(n−1,θ,s|z,y, f) +τ(n+1)Ψ(n+1,θ,s|z,y, f), n ≥ 2 where e(θ,s|z,y, f) denotes the density of firm entry, given by: e(θ,s|z,y, f) = λ Π(θ|z,s)×P[V (θ)−c > W (z,y, f)]Φ (z,y, f), (19) f,s e e s s andintegratingitovertheentrepreneur’seducationandworkercharacteristicsgives (cid:90) (cid:90) ∑ ∑ e = e(θ,s|z,y, f)dzdy. θ z y f∈{0,1}s∈{0,1} The first equation in (18) describes the entry of firms, ensuring that the inflow of new firms balances the outflow due to business reallocation τ and the mortality of the 51

ransformative and ubsistence ntrepreneurs T S E entrepreneur ψ. The right-hand side represents the entry flow, which depends on the arrival rate of entrepreneurship and their decision to start a firm. The second equation determines the equilibrium mass of firms of size one. The left-hand side represents the outflow of firms with size one, which can occur either due to firm exit or because they grow into larger firms. The right-hand side captures the inflow into size one, consisting of new firms entering the market and firms that shrink from larger sizes due to business reallocation. The next equation describes a similar evolution of mass of firms with size n ≥ 2, where firms experience growth due to innovation or exogenous reasons and shrink due to competitive forces. Equation (19) defines the density of firm entry with entrepreneur type θ due to individuals with ability z, parental income y, family background f, and education status s. The term λ captures the arrival rate of entrepreneurial opportunities based f,s on family background and education. The term Π(θ|z,s) denotes the probability of drawing entrepreneur type θ conditional on ability and education. The expression P[V (θ)−c > W (z,y, f)] is the probability that the value of starting a firm exceeds e e s the value of remaining a worker. Finally, Φ (z,y, f) is the density of individuals with s characteristics (z,y, f) and education status s. Altogether, the equation gives the mass of individuals who receive an opportunity, draw type θ, find it profitable to enter, and have the corresponding characteristics. A.5.2 Worker Distribution and Occupational Flows The distribution of workers is represented by Φ (z,y, f), the unnormalized probability s density function of worker characteristics (z,y, f) in occupation production worker or R&D worker, corresponding to s ∈ {0,1}. In equilibrium, worker outflows (due to transitions to entrepreneurship and mortality) must be equal to inflows (occupation choice of newborn and transitions out of entrepreneurship). The unnormalized density of workers satisfies: (cid:32) (cid:33) ∑ e(θ,s|z,y, f)+ψ Φ (z,y, f) = m P(s|z,y, f)Ω(z,y, f)+ ∑ τ Ψ(1,θ,s|z,y, f). (20) s θ θ Equation (20) relates the unnormalized density of workers, Φ (z,y, f), in occupas tions of production or R&D, to two distinct inflows: new entrants making initial occupation choices based on their characteristics, represented by m P(s|z,y, f)Ω(z,y, f), and existing entrepreneurs returning to worker status, denoted by ∑ τ Ψ(1,θ,s|z,y, f). θ These inflows must exactly offset occupational outflows in BGP, which occur due to 52

ransformative and ubsistence ntrepreneurs T S E the entry into entrepreneurship—captured by ∑ e(θ,s|z,y, f)—and worker mortality θ at rate ψ. B Data Appendix 21 In the main text, we discussed how to construct data on inventors and entrepreneurs. Thissectionprovidesfurtherdetailsonthedataconstructionandoccupationdefinition. B.1 Dataset Construction and Information For data on individuals, we use the Integrated Database for Labor Market Research (IDA); for employer-employee matched data, we use the Firm-linked IDA (FIDA); for information on business origins, we rely on the Danish Entrepreneurship Database (IVPS/IVPE); for data on patents, we rely on the database of the European Patent Office (EPO). We connect these to IQ data, which is facilitated by the military test, Borge Prien’s Prove, which is required for males in Denmark at age 18. We merge these datasets together, which enables tracking individuals across their lifetime across firms and occupations. B.2 Dataset Details In this section, we expand on the datasets we combine, the occupational and entrepreneurial definitions, and additional statistics on the main variables of interest. Our work in this project combines various datasets from the Danmark Statistical Office. We observe a crosswalk for all individuals to their parents. Given the income and occupation database, we are able to link individuals to parental income and occupation observations. Our measure of entrepreneurs, indicating business founders with at least one registered employee, captures 147,087 firms and 24,281 transformative firms. For firm-level analysis, we leverage the entire firm distribution (including entrepreneurs without IQ information). For IQ× firm analysis, we leverage observations that have both IQ and firm information (17,669 firms). Below, we detail the main datasets used in the DST 21Denmark Statistical Office data were obtained by Ufuk Akcigit under the purview of University of Chicago licenses. The remaining co-authors, Harun Alp, Jeremy Pearce and Marta Prato, did not have anyunauthorizedaccesstothisdatawhileworkingonthispaper. 53

ransformative and ubsistence ntrepreneurs T S E server in an itemized fashion. We proceed by discussing the core datasets and what they provide. The IQ data is provided by the Danish military test, Borge Prien’s Prove, which is required for males in Denmark at age 18. This test provides IQ data on most males entering the workforce or college after 1995. As a result, we observe IQ information for about 30% of males in our data (500,000 total). For internal data to the DST, we leverage the IDA, which assigns a unique identifier to each individual in Denmark. We thus observe a panel dataset on individuals on an annual basis. The variables used from this dataset include annual income, employment status, occupation, and highest completed education level. Leveraging IDA alongside BEF, we connect individuals to their parents’ characteristics, including the income and occupationofparents. ThisdatasetadditionallyincludesinformationonIQforasubset of individuals. The firm-linked (FIDA) dataset connects individuals to their primary place of employment (a unique employer identifier) for each year. Individuals have an occupational code and are linked to their primary firm. On the firm side, we observe industry code, number of employees, sales, profits, and firm age. Thus, we can connect individuals to their firms and occupations over time. We also connect individuals and firms to theirpatentstospeaktoinnovationattheindividualandfirmlevels. TheEPOdatabase provides information on patents assigned to Danish firms or individuals. The patent database is linked to individuals and firms in the DST data with a disambiguation algorithm developed by DST. We use patents as our primary measure of innovation. The link between individual and firm is especially valuable for connecting the individuals behind the firm and their employees. This link is done primarily through the IVPS/IVPE entrepreneurship databases, which provide information on the primary founders of all privately owned firms in Denmark. IVPS contains individuals behind companies, while IVPE contains individuals behind proprietorships. We include both as entrepreneurs. Thus, we can observe the progression of individual firms and the individuals behind them. The dataset covers a wide array of firms and individuals. In total, weobserve305,052uniquefirmsmatchedto3.92millionuniqueindividualsfrom 2001-2013.22 We identify the primary business founders of 28% of the total registered firms. 22Wedefineafirmasanentitywithafirmidentifierandatleastoneregisteredemployee. 54

ransformative and ubsistence ntrepreneurs T S E B.3 Occupations As noted in the main text, our analysis focuses on four distinct occupations. In this section, we provide additional details on occupation definitions, particularly for the R&D category, which determines how R&D workers and transformative entrepreneurs are classified. AnR&DworkerisdefinedasanindividualwhoisinanR&Doccupationforatleast half of their working life. The R&D occupation, in turn, is determined by the patenting intensity of different occupations. Our baseline framework looks at occupations where workers have a 1% patenting intensity rate or higher. Table B1 lists the top five most common R&D occupations in the economy by inventor rate and employment share, respectively. The empirical findings are qualitatively robust to considering alternative cutoffs to classify R&D occupations, such as a patenting intensity of 2% or 0.5%. Next, a transformative entrepreneur is defined as an entrepreneur who hires at least one R&D worker. In the next section, we show that the firm-level results are robust across variations of this definition, such as hiring an R&D worker in the first year since starting the firm, in the first five years, or ever in the life of the firm. able ccupations T B1: R&D O ID Description Inventor Rate Inventor Employment Share 211 Physics and Earth Science Professionals 0.135 0.011 215 Electrotechnology Professionals 0.048 0.007 214 Engineers 0.048 0.188 213 Life Science Professionals 0.041 0.021 231 Professors 0.029 0.083 311 Physics and Engineering Technicians 0.012 0.222 214 Engineers 0.048 0.188 222 Pharmacy and Health 0.011 0.116 200 General Scientist 0.023 0.104 123 Manager (R&D, info, supply) 0.018 0.085 C Empirical Appendix This section extends the analysis from the main text, focusing on robustness and additional facts on career choice, entrepreneurship, and firm dynamics. 55

ransformative and ubsistence ntrepreneurs T S E C.1 Career Determinants This section provides additional results on occupational sorting and transformative entrepreneurship. We start by providing more details on the specification underlying the figures in Section 2. Next, we expand on the role of parental background in education decisions. Finally, we assess the robustness of our empirical findings to alternative definitions of occupations and firms used in the primary specifications. Tables from Main Text Figures. Table C2 displays the coefficients corresponding to the multinomial logistics regressions from the estimation of equation (1) presented in Figures 3 and 4. “Model 1” indicates the first specification, that distinguishes entrepreneurs and R&D workers from production workers. “Model 2" represents the second specification, which additionally includes the split between transformative and subsistence entrepreneurs. Model 1 shows distinct patterns across different occupational choices. For R&D workers, higher IQ is strongly positively associated with choosing this occupation, with coefficients increasing monotonically from quartile 2 (0.434) to quartile 4 (1.252), while parental income on its own has no significant effect. College education has a large positive effect (1.601) on R&D work. By contrast, for entrepreneurs, higher IQ has a negative association, noted in the 3rd (-0.093) and 4th quartile (-0.167), and collegeeducationisstronglynegative(-0.591), suggestingaverageentrepreneursfollow a different human capital accumulation path. Model 2 shows distinct patterns across different occupational choices. For transformative entrepreneurs, higher IQ is strongly positively associated with choosing this occupation, with coefficients increasing monotonically from quartile 2 (0.270) to quartile 4 (0.740), while parental wealth shows a significant positive effect (0.159). College education has a substantial positive effect (0.437) on transformative entrepreneurship. Parental background also plays an important role, with parental entrepreneurship (0.380) and parental R&D work (0.291) both having significant positive effects, while parental business ownership shows no significant association. These results suggest that transformative entrepreneurs represent a distinct group from regular entrepreneurs, with selection patterns more similar to R&D workers regarding human capital requirements but with additional importance placed on parental wealth, indicating that both ability and access to resources are crucial factors for transformative entrepreneurial activity. 56

ransformative and ubsistence ntrepreneurs T S E able ogistic egressions for igures and T C2: L R F 3 4 IQ Quartile (baseline: Q1) Parental Income Occupation Q2 Q3 Q4 High vs. Low R&D Worker 0.434∗∗∗ 0.793∗∗∗ 1.252∗∗∗ 0.036 (0.077) (0.074) (0.071) (0.039) Entrepreneur 0.011 -0.093∗∗ -0.167∗∗∗ 0.025 (0.029) (0.031) (0.034) (0.023) College Parent Entrepr. Parent R&D Production Worker Parent R&D Worker 1.601∗∗∗ 0.205∗∗∗ 0.463∗∗∗ -0.064 (0.048) (0.060) (0.043) (0.050) Entrepreneur -0.591∗∗∗ 0.574∗∗∗ 0.066 0.017 (0.026) (0.033) (0.035) (0.044) Model 2 IQ Quartile (baseline: Q1) Parental Income Occupation Q2 Q3 Q4 High vs. Low R&D Worker 0.436∗∗∗ 0.799∗∗∗ 1.261∗∗∗ 0.038 (0.077) (0.074) (0.071) (0.039) Subsistence -0.003 -0.167∗∗∗ -0.361∗∗∗ 0.005 Entrepreneur (0.030) (0.033) (0.038) (0.025) Transformative 0.270∗∗ 0.537∗∗∗ 0.740∗∗∗ 0.159∗∗ Entrepreneur (0.087) (0.085) (0.084) (0.056) College Parent Entrepr. Parent R&D Production Worker Parent R&D Worker 1.606∗∗∗ 0.203∗∗∗ 0.466∗∗∗ -0.064 (0.048) (0.060) (0.043) (0.050) Subsistence -0.855∗∗∗ 0.609∗∗∗ -0.003 0.084 Entrepreneur (0.030) (0.035) (0.041) (0.053) Transformative 0.437∗∗∗ 0.380∗∗∗ 0.291∗∗∗ -0.132 Entrepreneur (0.056) (0.083) (0.068) (0.077) Notes: Standard errors in parentheses. ∗ p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001. The models are multinomial logit estimations with a production worker as the base category (0). Cohort fixed effects includedinbothmodelsbutnotreported. ParentEntrepr. =parentwasself-employed,ParentR&D =parentworkedinR&D,ProductionWorkerParent=parentwasnotR&Dorself-employed. 57

ransformative and ubsistence ntrepreneurs T S E Schooling. Individuals’ schooling is an essential input to their career development process. In this section, we focus on two core determinants of schooling: family income and IQ. Both covariates may affect an individual’s propensity to obtain education throughabilityandfinancialfrictionsoropportunities. Weperformasimpleregression that examines the propensity of an individual to attend college as a function of their family income and IQ . Equation (21) provides the specification, as follows: s = α+α IQ +α ParInc +Λ +ϵ . (21) i 1 i 2 i b(i) i Equation (21) is a linear probability model, where s is an indicator of individual i’s i college attainment (0 or 1); IQ is the IQ in percentiles (going from 0 to 1); ParInc is i i Λ the parental income is percentile (going from 0 to 1), based on the income in 2000; b(i) is a control for the cohort b(i) of the individual. Table C3 reports the results from the above regression. able robability of ollege ttendance T C3: P C A (1) (2) College College IQ 0.389∗∗∗ 0.359∗∗∗ (0.002) (0.002) Parental Income 0.154∗∗∗ 0.121∗∗∗ (0.002) (0.002) Parent College 0.081∗∗∗ (0.001) Observations 442587 442587 Standarderrorsinparentheses ∗ p <0.05,∗∗ p <0.01,∗∗∗ p <0.001 Table C3 shows that IQ has a substantial positive effect on college attendance, with coefficients of 0.389 and 0.359 in columns (1) and (2), respectively, indicating that a one standard deviation increase in IQ raises college probability by approximately 36-39 percentage points. Parental income also positively influences college attendance, with effects of 0.154 and 0.121, suggesting that higher family resources significantly increase educational attainment opportunities. Column (2) additionally controls for parental education, showing that having college-educated parents independently increases a child’s probability of attending college by 8.1 percentage points while slightly reducing the magnitude of both IQ and parental income coefficients. These results suggest 58

ransformative and ubsistence ntrepreneurs T S E that, while cognitive ability remains the strongest predictor of college attendance, both financial resources and inter-generational transmission of educational preferences play important roles. able robability of becoming an orker T C4: P R&D W (1) (2) R&D Worker R&D Worker IQ 0.021∗∗∗ 0.021∗∗∗ (0.001) (0.001) Parental Income 0.005∗∗∗ 0.005∗∗∗ (0.001) (0.001) Parent College 0.001 (0.000) Observations 442587 442587 Standarderrorsinparentheses ∗ p <0.05,∗∗ p <0.01,∗∗∗ p <0.001 In our model, there is a one-to-one correspondence between college attainment and R&D occupation. Thus, we repeat the regression in equation (21), considering the outcome variable of becoming an R&D worker. Table C4 displays the results for the probability of becoming an R&D worker, with both columns revealing more modest but still highly significant effects. IQ shows a consistent positive effect of 0.021 across both specifications, indicating that higher cognitive ability increases the likelihood of R&D careers, though with a substantially smaller magnitude than its effect on college attendance. Parental income has a small but significant positive effect of 0.005, suggesting that family resources play a minor role in R&D career selection. Interestingly, in column (2), parental college education shows no statistically significant effect on R&D career choice (coefficient of 0.001), unlike its substantial impact on college attendance. This pattern suggests that while cognitive ability remains important for specialized R&Dcareers, theinter-generationaltransmissionofpreferencesandadvantagesmainly operates through increased college attendance rather than directly influencing occupational selection into R&D work. The overall findings indicate that R&D workers are primarily selected based on ability rather than family background characteristics. 59

ransformative and ubsistence ntrepreneurs T S E C.2 Firm Dynamics This section provides more details on entrepreneurship types. We first examine entrepreneurial characteristics across different organizational forms and industries, highlighting the sharp contrasts between transformative and subsistence entrepreneurship. Regressionanalysesrevealthattransformativeentrepreneurspossesssignificantlyhigher cognitive abilities and educational attainment, particularly in knowledge-intensive sectors, while also benefiting from greater parental wealth and education. Industryspecific selection patterns demonstrate considerable heterogeneity, with technology and professional services attracting individuals with the highest human capital, while retailandpersonalservicesshowlesspronouncedselectioneffects. Thedatafurtherreveals how non-corporate and corporate entrepreneurship differ in their selection mechanisms, with corporate ventures typically founded by entrepreneurs with stronger educational backgrounds and industry experience. Thesectionthenanalyzesfirmdynamicsthroughcomparativelife-cyclepatternsbetween transformative firms (those hiring R&D workers) and subsistence enterprises. IllustratedthroughFiguresC1-C3,transformativefirmsdemonstratesubstantiallystronger trajectories in employment growth (increasing five-fold over ten years) and revenue generation (reaching seven times their initial levels), while maintaining lower exit rates in later years compared to subsistence firms that plateau after modest initial growth. Additional analyses explore how founder characteristics correlate with venture performance metrics, including productivity, innovation intensity, and survival rates, documenting significant sorting effects where high-ability entrepreneurs disproportionately select industries with higher returns to ability. This comprehensive approach provides insightsintobothselectionmechanismsandsubsequentfirmperformancepatternsthat characterize entrepreneurial activity. Figures C1-C3 present a comparative analysis of firm life cycles between transformative entrepreneurship (defined as firms hiring an R&D worker) and subsistence entrepreneurship. All figures display measures of growth over the first ten years of operation, with the initial size normalized to one at age zero. In Figure C1, we consider a definition of transformative entrepreneur as hiring an R&Dworkerinthefirstfiveyearsofoperation(asopposedtoeverinthelifeofthefirm, which is our baseline definition in the main text). The figure shows that both transformative and subsistence firms start with the same baseline (normalized) employment at age 0 and diverge in their growth trajectories. Transformative entrepreneurs exhibit substantially stronger employment growth, increasing five-fold by age 10, compared 60

ransformative and ubsistence ntrepreneurs T S E igure irm life cycle with transformative definition based on first F C1: F , 5 years 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 tnemyolpmE dezilamroN Subsistence Transformative Age to subsistence firms, which plateau at approximately twice their initial size after the first year. The growth path for transformative firms shows higher growth throughout the decade, while average subsistence firms maintain relatively flat employment levels after their initial modest expansion. igure irm life cycle evenue F C2: F , R 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 euneveR dezilamroN Subsistence Transformative Age Figure C2 illustrates the revenue performance of both firm types over the same tenyear period. The revenue trajectories closely mirror the employment patterns, with both firm types starting from the same normalized baseline at founding. Transformative firms demonstrate dramatic revenue expansion, reaching more than seven times their initial revenue by year 10. In contrast, subsistence enterprises show only modest revenue growth, reaching approximately 2.5 times their starting level. The revenue gap between the two firm types widens substantially after year 1, with transformative firms 61

ransformative and ubsistence ntrepreneurs T S E exhibiting a steeper, nearly linear growth trajectory throughout the observation period. This revenue differential becomes particularly pronounced in later years, highlighting the cumulative advantage that transformative firms develop over time. These two figures are consistent with the idea that transformative entrepreneurs, through creative destruction, become a larger share of the economy with age. igure irm life cycle xit ates F C3: F , E R 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 tixE Subsistence Transformative Age Figure C3 depicts exit rates for both firm types over the first decade of operation. We define exit as the firm having zero employment or firm records. Both transformative and subsistence firms experience relatively high exit probabilities in their early years, with subsistence firms starting at a higher initial exit rate of approximately 16% compared to 12% for transformative firms. The exit rates for both firm types generally decline with age, reflecting a selection effect where surviving firms become increasingly stable. Subsistence firms show a steeper initial decline in exit rates during the first five years, after which both firm types converge to similar exit probabilities of around 8-9% by year 8. Notably, transformative firms demonstrate slightly lower exit rates overall, suggesting that their investments in R&D and growth are connected to greater firm stability and longevity. Figure C4 illustrates the distribution of entrepreneurs across different industries based on IQ deciles. The graph reveals a clear pattern of industry sorting by cognitive ability, with significant shifts in industry composition moving from lower to higher IQ deciles. In the lowest IQ deciles (1-4), traditional sectors dominate entrepreneurial activity, with Trade/ Transport and Construction/ Agriculture representing the largest shares. As IQ increases, there is a marked decline in these sectors’ representation, with Trade/Transport dropping from nearly 40% in the first decile to only about 12% 62

ransformative and ubsistence ntrepreneurs T S E igure irm ndustry by ntrepreneur F C4: F I E IQ 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 sruenerpertnE fo erahS IQ Deciles Trade/Transport Construction/Ag Other Service Knowledge/Communic. Manufacturing Arts/Education Financial/Real Estate Health in the tenth decile. Construction/Agriculture follows a similar downward trend as IQ increases. Conversely,knowledge-intensiveindustriesshowastrongpositiverelationshipwith IQ. The Knowledge/Communication sector demonstrates the most dramatic increase, expanding from a minimal presence in the lowest IQ decile to becoming the dominant industry category for entrepreneurs in the highest IQ deciles (8-10), where it represents approximately 50% of all entrepreneurial activity. Other high-skill sectors, including Financial/Real Estate, Health, and Arts/Education, also show modest but consistent increases in representation as IQ rises, collectively accounting for a much larger share of entrepreneurship in the top IQ deciles compared to the bottom ones. This pattern suggests significant sorting of entrepreneurial talent across industries based on cognitive ability, with higher-IQ individuals disproportionately selecting into knowledge-intensive sectors that likely offer greater returns to cognitive skills, while lower-IQentrepreneurspredominantlyentertraditionalindustrieswithpotentiallylower barriers to entry and cognitive skill requirements. Figure C5 shows the distribution of entrepreneurs across IQ deciles (1-10) by company type, with blue representing non-corporate entrepreneurs and orange representing corporate entrepreneurs. The y-axis shows the share of entrepreneurs, which always totals to 1 (or 100%) for each IQ decile. We note a stark trend: as IQ decile increases from 1 to 10, the proportion of non-corporate entrepreneurs steadily decreases (from about 60% in decile 1 to about 37% in decile 10), while the proportion of cor- 63

ransformative and ubsistence ntrepreneurs T S E igure orporate and on orporate firms by entrepreneur F C5: C N -C IQ 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 erahS Non-Corporate Corporate IQ Deciles porate entrepreneurs correspondingly increases. This suggests that entrepreneurs with higher IQ are more likely to establish corporate entities, while those with lower IQ are more likely to operate non-corporate businesses. The shift is gradual but consistent across all deciles, indicating a strong correlation between measured cognitive capacity and the formal business structure entrepreneurs choose. This is consistent with our main message of the paper, as transformative entrepreneurs tend to be more formal and serious about firm structure and expansion. 64