Precocious inventors: early patenting success and lifetime inventive performance

ABSTRACT Precocious inventors have a higher inventive productivity during their remaining career. Inventors who have their first patent either applied for extraordinarily fast or a first patent of especially high quality are regarded as precocious. This paper systematically includes individual and employer characteristics that can drive career productivity beside an early patenting success to reveal the true productivity effect of precociousness. We show that early patenting success reveals dimensions of inventive ability that are not captured in individual characteristics that are predetermined at the start of the career such as the school education level. The favourable work environment precocious inventors enjoyed also has a relatively low explanatory value for career productivity. Precocious inventors also do not benefit from cumulative advantage. Although also rival firms can use early patenting success as indicator for a high career productivity, early employers can retain a high share of their precocious inventors. We propose several reasons for this surprising phenomenon.


Introduction
An inventoŕs ability is hard to observe (Merton 1973b;Dasgupta and David 1994).In the absence of transparent and reliable indicators, inventor ability may have to be revealed during an employment relationship (Lange 2007;Schönberg 2007).Especially employers who attract talented inventors right at the start of their career may gain an information advantage on ability.They can observe ability before it is publicly revealed by higher lifetime productivity or other observable career successes.Employers can use these information advantages to retain the most able and productive inventors because outside employers are not certain about true ability.The current employer therefore can fend off poaching attempts by offering a higher wage than rival employers (Lazear 1986).
Only a very small share of inventors achieves a high inventive productivity during their career (Lotka 1926).Therefore, the distribution of inventive success is highly unequal (Price 1965;Levine 1986;Huber 2002;Narin and Breitzman 1995;Sapsalis, van Pottelsberghe de la Potterie, and Navon 2006;Toivanen andVäänänen 2012, 2016;Blomkvist, Kappen, and Zander 2014;Lawson and Sterzi 2014).The few truly prolific inventors not only contribute to corporate success by obtaining more patents than their peers, also the average economic value of their patents is higher (Almeida and Kogut 1997;Gay, Latham, and Le Bas 2010).In addition, prolific inventors are a source of ideas and inspiration for their peers, colleagues, and network members.Finally, prolific inventors can act as knowledge integrators between communities and institutional contexts (Subramaniana, Limb, and Pek-Hooi 2013).Their knowledge-enabling function, therefore, has a positive external effect on the overall innovativeness of their employers (Zucker, Darby, andBrewer 1998, 2002;Gambardella, Harhoff, and Verspagen 2008;Bercovitz and Feldman 2008;Azoulay, Graff Zivin, and Wang 2010;Akcigit et al. 2018).Consequently, the few highly productive inventors seem to be the main source of sustained competitive advantage of employers that rely on innovations (Blomkvist, Kappen, and Zander 2014;Arts and Fleming 2018).
Most papers on the determinants of inventive career productivity concentrate on information that is predetermined at the start of the career such as education level, family background, or personality traits (Dietz and Bozeman 2005;Hunter, Cushenbery, and Friedrich 2012;Lawson and Sterzi 2014).Inventors with an early patenting success ('precocious inventors') may have a systematically higher career productivity (Huber 1998).The extra value of an early patenting success for the prediction of future inventive productivity in addition to predetermined individual productivity determinants however is unclear.Exploration that proves successful provides the basis for future exploitation and the chance on higher inventive productivity in this field.However, chance may have had a strong influence on an early success and with each creative search episode, the fundamental conundrum reappears.The correlation between early and later inventive productivity therefore may be weak (Arts and Fleming 2018).
Career productivity depends not only on individual ability but also on the work environment (Bhaskarabhatla and Hedge 2014; Conti, Gambardella, and Mariani 2014).Precocious inventors may have played a junior role in their early achievement and profited from a positive work environment.In addition, employers may reward precocious inventors by providing them with more resources, a leading role in inventor teams or a high-quality inventor network.Therefore, career inventive productivity may be driven by the so-called cumulative advantage effect.In the extreme case, early patenting success has positive long-term effects on inventive productivity because it is the indirect consequence of employer-provided resources instead of being driven directly by the early success (Merton 1973a).Consequently, also the early work environment and changes in resources over the career have to be included in a systematic analysis of the informational value of early patenting success.
This paper empirically assesses whether patenting successes early in the career are a good predictor of later career inventive success.Specifically, we analyse the informational value of early patenting successes on lifetime productivity in addition to predetermined individual characteristics and the work environment in which they were achieved.We also analyse whether cumulative advantage during the later career drives productivity of precocious inventors (Allison, Long, and Krauze 1982;DiPrete and Eirich 2006).Patented inventions are a scrutinised and publicly observable form of creativity (Audia and Goncalo 2007) and a good indicator for individual inventive productivity in those sectors that use patents (Griliches 1990).Nevertheless, the informational value of the timing and quality of an early patenting success for inventive career productivity considering predetermined individual productivity drivers, the work environment, and cumulative advantage has hardly been assessed.
Our main contribution to the literature is the systematic assessment of the relative importance of early patenting success on lifetime inventive productivity.The empirical literature on the drivers of inventive performance so far concentrates either on individual ability or the work environment.The main reason for the respective focus on either dimension seems to be the lack of data that link longitudinal inventive performance with longitudinal individual and work environment information.Disambiguated patent data are a key data source for lifetime qualitative and quantitative patent productivity (Hoisl 2007b;Audia and Goncalo 2007;Akcigit et al. 2018).However, patent applications do not include predetermined individual information and information on the work environment.To the best of our knowledge there are only three papers that look at the correlation between early patenting success and inventive productivity: Dietz and Bozeman (2005), Audia and Goncalo (2007), and Lawson and Sterzi (2014).Although these papers use linked patent and survey evidence on individual and employer characteristics, they hardly include (changes in) the work environment or indicators for cumulative advantage.The few papers on indicators for cumulative advantage for inventors mainly concentrate on case studies and the analysis of career patenting patterns.They hardly include individual and employer characteristics (Huber 1998;2002;DiPrete and Eirich 2006).
We exploit a rich dataset that combines survey data for 1240 German academic and industry inventors on their career between the years 1978 and 2010 with their patent history over this period.Patent information is drawn from the official PATSTAT patent data provided by the European Patent Office.The survey data comprise important individual information.Inventors in addition answered questions about the central characteristics of their work environment.They used a unique calendar function that allows us to differentiate between the work environment during the first and later career years.
We show that the speed and the quality of the first patent are independent drivers of overall career inventive success.Precocious inventors whose first patent application speed is in the first quartile of all inventors have a career productivity that is about 50% higher compared with their comparison group.The inventive career productivity after the first patent is about 20% higher for inventors whose first patent is in the top citation quartile.We also find that early patenting success adds prediction power about lifetime inventive productivity to predetermined individual information.We in addition show that precocious inventors work in an environment conducive to higher patenting productivity during their first career years.Controlling for the information about the work environment during the years in which the first patent is applied for however does not remove the informational value of the first patent on lifetime productivity.We also find that precocious inventors cannot increase their productivity further in later career years.The productivity change declines from the first career years to the following career years, albeit at a lower rate for precocious inventors.Therefore, there is no indication of cumulative advantage over the career.We also find no evidence for specific cumulative advantage mechanisms that would reduce the explanatory power of early patenting successes.More specifically, precocious inventors cannot increase their share of working time devoted to R&D activities, nor do they have a higher number of co-inventors in later career years compared with the first career years.However, precocious inventors experience a stronger increase in the size of their employers during their career than inventors without early successes.This increase mainly stems from the growth of the employer that precocious inventors worked for during their first patent application instead of a switch to larger employers, however.We finally find a low employer switch rate for precocious inventors that goes hand in hand with strong wage increases at the early employer.

Early patenting success as an indicator for ability
Lifetime inventive productivity can be predicted by individual characteristics that are predetermined before the inventor enters the labour market.During the first labour market years, however additional information can be gathered that is helpful to predict future productivity (Greenwald 1986).This information usually can be revealed easier by the early employer in comparison to rival employers for example by supervising the inventor on the job (Lange 2007).The information however also may become publicly available (Schönberg 2007).
There are several reasons that the information value of an early patenting success for lifetime inventive productivity indeed is public.First, a patent is easily observable for everybody.For a patent to be issued, the invention must be new, useful, and not obvious to persons reasonably skilled in the specific technology.This minimum requirement is applied uniformly to all patents, and thus each patent has a minimum information value about the individual input necessary to obtain it (Griliches 1990;Huber 1998).In addition, a substantive conceptual contribution by the inventor is a legal requirement for an attribution on a patent and violating this requirement may invalidate the patent (Häussler and Sauermann 2013).Consequently, the information value of a patent can be transferred to all inventors listed on a patent.Second, it is costly and time-consuming to reach the knowledge frontier in a field; however, this achievement is a necessary requirement for innovative activity (Jones 2009;2010).It can be assumed that it is less costly for inventors with a higher inventive productivity potential to obtain the human capital necessary to apply for a patent (Melero, Palomeras, and Werheim 2020).Third, there is a strong financial incentive to apply for a patent when an inventor has a suitable inventive idea because a fixed amount of financial income generated from patents is typically shared among all listed inventors (Häussler and Sauermann 2013).Applying for a patent accordingly provides the chance to obtain large and sustained earnings increases (Harhoff and Hoisl 2007;Toivanen and Väänänen 2012).
Inventive activity can be characterised as a contest of priority of discovery.Speed in patenting is rewarded because usually only the first patent applicant gets the reputation and financial rewards for an inventive idea (Merton 1973a;Dasgupta and David 1994).Speed in a patent application, therefore, is decisive especially in cases of multiple independent invention (Voss 1984;Laplume et al. 2015).A quick patenting success however is costlier to obtain for inventors with a lower inventive productivity potential because it is harder for them to speed up the invention.Young inventors in particular need time to acquire the necessary background knowledge and they cannot spend the time needed for training or education on their invention project (Jones 2010).Thus, a higher productivity potential allows inventors to complete the patenting process faster than their peers (Dietz and Bozeman 2005).
Jones (2010) points out that young inventors must decide how to divide their time between education/training and inventive activity.If they spend more time working on their inventive idea, this may allow them to apply for a patent sooner, but it may also reduce the quality of the patent.Therefore, we assume that it is harder to obtain many citations for the first patent if it is applied for quicker.Thus, a fast first patent and a high-quality first patent may be independent drivers of inventive career performance.Consequently, we control separately for speed and quality of the first patent.Conti, Gambardella, and Mariani (2014) and Arts and Fleming (2018) note that young inventors and novices to a scientific field relatively often achieve a breakthrough invention that leads to a high-quality patent.Their early patenting success may however induce young inventors to exploit their first idea instead of exploring new fields (Audia and Goncalo 2007).Their exploitation strategy may lead to an increase in the number of patents during subsequent years but reduce the quality of the following patents.Thus, the consequences of an early patenting success for career patent quantity and patent quality may differ.We, therefore, measure inventive career productivity by the number of patents but also by the number of their forward citations as a measure of patent quality.
There is a rich body of literature on determinants of individual inventive productivity (Huber 1998;Hoisl 2007a,b;Giuri et al. 2007;Mariani and Romanelli 2007;Walsh and Nagaoka 2009;Toivanen and Väänänen 2012;Zwick et al. 2017).However, we are aware of only a few papers that analyse the quality of early career achievements as predictors of inventive career productivity 1 .These papers only control for a limited number of individual productivity drivers, respectively.Audia and Goncalo (2007) show that inventive success measured in rolling 2-year periods leads to a higher probability of generating another invention during the following year. 2  Audia and Goncalo (2007) include not only early patents but all patents applied for during their 20-year observation period.They concentrate on the hard disk drive sector and they examine the immediate patent impact instead of career productivity.Dietz and Bozeman (2005) analyse some CV information 3 merged with patent data of research scientists and engineers working for the US Department of Energy, the Department of Defense, and the National Science Foundation.They find that scientists who had many publications before obtaining their doctoral degree have a higher number of patents per career year on average.Finally, Lawson and Sterzi (2014) look at the patenting record of 500 British academic inventors.Based on CV information 4 , they show that the number of citations the first patent received is the most important predictor for the number of patents inventors obtained during their career.
Early inventive success is only a valuable predictor of lifetime productivity if it does not lose its predictive power when predetermined individual characteristics are added in a multivariate productivity estimation.Predetermined individual characteristics however may be closely related with early patenting success.Thus, we add family background, risk aversion, and the so-called Big Five personality characteristics in addition to birth cohort, gender, technology field, and education level.We in addition check whether the size and significance of the coefficients of early success indicators are influenced by the addition of the individual background information.
Summing up, these are our first two hypotheses: Hypothesis 1: Inventors who apply for their first patent faster than their peers have a higher inventive performance for the remainder of their career after controlling for predetermined individual characteristics.
Hypothesis 2: Inventors whose first patent is of higher quality than those of their peers have a higher inventive performance for the remainder of their career after controlling for predetermined individual characteristics.

Early patenting success as an indicator for an invention-friendly work environment
The image of the young, independent great mind making critical inventions is iconic (Simonton 1988;Jones 2010;Jones and Weinberg 2011;Laplume et al. 2015).Most papers only include individual characteristics as determinants of individual inventive productivity.However, the work environment may be more decisive for the inventive effort´s success than the individual.Audia and Goncalo (2007) hypothesize that collaboration and other exchanges with inventors and the norms in the organisation an inventor works for influences individual inventive performance.Conti, Gambardella, and Mariani (2014) for example point out that an employer that sets specific research goals may induce inventors to conduct exploitative instead of explorative inventive endeavours.Laplume et al. (2015) show that corporations can speed up the individual patenting process.Perry-Smith and Shalley (2003) stress that there may be a reinforcing relationship between social networks and creativity.If an inventor works in an environment conducive to inventions during the first career years, the state-dependent nature of strong and weak ties in inventor networks may induce a long-term advantage for precocious inventors.Inventors with early successes also may move quicker from the fringe to the centre of their network.A central network position however may also enhance productivity in the long run.The work environment therefore may enable an inventor to establish a productive and sustainable network with other inventors or develop the mindset and skills that allow them to increase inventive performance.Precocious inventors however may have a higher chance to get their first job in a work environment conducive to higher inventive productivity.To measure the information value of early patenting success and correct for this potential endogeneity, we therefore additionally control for the work environment in which the first patent has been achieved.
Not only the work environment during the first career years but also changes in the work environment over the career may drive career productivity.More specifically, so-called cumulative advantage may be an important driver of career productivity of precocious inventors.Cumulative advantage is explained in Merton's famous definition of the Matthew effect: 'the accruing of greater increments of recognition of particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark ' Merton (1973b, 446).Cumulative advantage therefore means that early success induces employers to provide resources as well as rewards.The additional resources facilitate continued higher performance given the inventive potential (Owen-Smith and Powell 2001;DiPrete and Eirich 2006).In other words, cumulative advantage may turn fortuitous early patents into lasting inventive productivity advantages (Cole and Cole 1967;Allison, Long, and Krauze 1982).We therefore control for changes in the work environment in addition to the work environment during the first career years to measure the information value of an early patenting success on career productivity.
Previous empirical papers that analyse the correlation between early and lifetime inventive productivity include few selected indicators for the work environment in which the early patents are obtained.Audia and Goncalo (2007) use the number of patents and the proportion of patents with new citations and new technology classes in the organisation in which an inventor previously worked as an indicator for the work environment.Dietz and Bozeman (2005) include the characteristics of the first job, such as industry sector or employer type (business, administration, or academia).Lawson and Sterzi (2014) control for the employer characteristics during the first job (large or small firm, new or established firm, university).These papers find that early inventive success and early job environment characteristics are both significant predictors of lifetime inventive success.However, no paper so far analyses the effect of a change in work environment indicators on career productivity and the change in the predictive power of early patenting success.
The empirical literature on the role of cumulative advantage for the productivity of inventors is tenuous and equivocal, Allison, Long, and Krauze (1982) and DiPrete and Eirich (2006).Most papers show an increase in inequality in publications and citations over the life cycle of the entire population or certain birth cohorts of scientists, Cole and Cole (1967), and Allison and Stewart (1974).These papers do not control for the work environment or individual inventor characteristics however (DiPrete and Eirich 2006).In addition, these analyses may suffer from fallacy of composition (Simonton 1997). 5The resulting patenting patterns may, for example, be biased if inventors who are more productive are active longer in R&D than those who are less productive (Huber 2002).Hence, some authors propose a direct test of whether precocious inventors have a higher productivity rate during the rest of their career (Lotka 1926;Levine 1986).To the best of our knowledge the only paper with a direct cumulative advantage test based on changes in individual inventor productivity over the career is Huber (1998).The author does not find indicators for cumulative advantage.We, therefore, extend on this literature and analyse specific cumulative advantage mechanisms based on the correlation between changes in the work environment over the career and changes in individual inventor productivity to assess whether and how strong the early work environment and cumulative advantage reduce the information value of early patenting success on lifetime productivity.
Our next two hypotheses are as follows.
Hypothesis 3: The positive correlation between early and lifetime inventive productivity is driven by a work environment conducive to inventions during the first career years.
Hypothesis 4: The positive correlation between early and lifetime inventive productivity is driven by cumulative advantage.

Methodology
First, we measure the correlation between speed and quality of the first patent and inventive productivity during the remaining career.Then we add controls for predetermined individual productivity determinants to test hypotheses 1 and 2. In the next step, we add the work environment characteristics for the period when the first patent is applied to test hypothesis 3. Our empirical model is: Career productivity Y i of inventor i is estimated in a Poisson regression model and measured for the entire career excluding the first patent.Early patenting success is denoted by the dummy variables fast and highquality based on the speed and quality of the first patent (denoted by subscript p1).We include a broad range of individual characteristics in vector W i and first patent characteristics in vector X ip1 .Vector Z it1 captures work environment characteristics during the period in which the first patent was applied for (t1).The exceptional wealth of individual and employer information in our data reduces the risk that the correlation between early and lifetime inventive productivity is biased by unobserved variables that are correlated with our early success indicators and productivity.Variables β and δ are the regression coefficients and ɛ is the idiosyncratic error term.
To test hypothesis 4, we check whether there is a positive correlation between inventive productivity during the period t1, and inventive productivity during the remainder of the career (t2). 6 We use a differential equation of exponential growth (Yule process) as a formal empirical test of the presence of cumulative advantage 7 : (2) Cumulative advantage means in Equation ( 2) that a high productivity during t1 (Y it1 ) increases the difference in productivity between t1 and t2 (Y it2 − Y it1 ) measured by a positive slope parameter, β.If, according to hypothesis 4, precocious inventors enjoy a stronger cumulative advantage than their peers, this can be measured by higher β values for inventors with early patenting success than their peers.
Our second test on hypothesis 4 analyses actual cumulative advantage mechanisms.We use difference-in-differences estimations that show whether precocious inventors enjoy a better attribution of resources during the remainder of their career.Specifically, we argue that the share of R&D activities during working time, the size of the patent applicant, the probability of a voluntary job change, and the number of co-inventors are characteristics of a work environment that is conducive to higher inventive productivity.We empirically test whether these four work environment characteristics increase more strongly from t1 to t2 for precocious inventors.The changes in resources between periods t1 and t2 are calculated separately for the four dimensions of indicator Z.We include indicators for the four resources available for both periods for each inventor and control for individual fixed effects γ i besides the interaction terms between the early success indicators and t2.We also include a dummy for t2 to capture the average change in resources between t1 and t2: (3) Cumulative advantage for precocious inventors predicts positive coefficients β 1 and β 2 .

Data
Our dataset combines patent and individual survey data.The patenting activity of the inventors is measured using PATSTAT data for patents of German inventors filed between 1978 and 2010 at the European Patent Office.The patent data include the first filing date of a patent, the status of the patent application, number of co-inventors, number of forward citations per patent received during a specific period, type of patent applicant, and technology sector.According to for example Hoisl (2007a) or Akcigit et al. (2018), we aggregate the number of all patents by applicant to calculate applicant size.We in addition assume that the applicant is the employer of the inventor.
The application date of the first patent 8 determines individual age at first patent and the number of years since obtaining the highest educational degree (both derived from the inventor survey).
The patent data are merged with inventor survey data that contain predetermined individual characteristics.In addition, we use a calendar function in the survey to describe changes in the work environment during the career.The calendar captures key career characteristics, such as the share of R&D activities in the working time, during 5-year spells between 1965 and 2014.Because our patent information ranges from 1978 to 2010, seven spells from the calendar can be used. 9According to our estimation strategy, we differentiate between the period in which the first patent is applied for (t1) and the remainder of the career (t2).We define the last (observable) career period as the period in which the inventor reaches age 65, the period with the last observable patent for those 41 inventors who applied for patents when they were older than 65 years, or the period 2005-2010.Thus, the number of periods included in t2 depends on the application date of the first patent.On average, t2 spans 2.3 calendar periods (11.5 years).In other words, we can observe the work environment for on average 3.3 periods or 16.5 years.The distribution of the observed number of calendar periods is shown in Table A1 in the Appendix.
We calculate career productivity in Equation ( 1) by the number of patents and their citations.In the cumulative advantage Equations ( 2) and (3), we compare average inventive productivity and resources for t1 and t2.The periodicity of t1 and t2 is determined by the (mainly) 5-year periods given in our survey calendar.Five-year brackets are useful for measuring inventive productivity to examine differences in inventive productivity over time because patents tend to be applied for in waves (Huber 1998;Hoisl 2007b).There is a risk of measurement errors incurred by attrition bias with short productivity measurement brackets.Accordingly, most extant papers measure inventive productivity and its changes in time brackets of between 4 and 10 years (Zwick and Frosch 2017).
The patent data are from an administrative source; thus, we have robust, non-biased information on patent quantity and quality. 10Almost all additional information used as dependent variables comes from the survey data.We therefore can rule out a common method bias.Information on the education and family background can be assumed plausibly to pre-date the start of the career, even though the information was collected at the end of the observation period.However, some survey information on personality traits, such as self-assessment on risk-taking, might not reflect the situation at career start.
We draw a random sample of inventors with at least one European patent in clean technology or mechanical elements in the period 2004-2008.Given that most inventors in this sample applied for patents in different technology sectors, the patent portfolio in our sample covers a broad spectrum of technologies (see our descriptive statistics below).We contacted 11,357 German inventors.Some inventors could not be reached because we had an incorrect or no address and some inventors had died.Altogether, these factors reduced our basic sample to 8313 individuals.We received 1851 answers, yielding an acceptable corrected response rate of more than 20%. 11For the 298 inventors who started their career before 1978, the first patent cannot be identified with certainty and these inventors are excluded from the dataset.In addition, we only know the year in which the highest educational degree was obtained for 1492 inventors.From this group, 252 inventors only applied for one patent in their recorded PATSTAT patenting activity.They are excluded from our estimations to allow the effect of the first patent on later career productivity to be identified. 12Consequently, our basic sample consists of 1240 inventors (67% of the original sample). 13  Dependent variables: inventive productivity Reputation, visibility, and economic value of a patent increase with the number of references made to it, typically calculated by forward citations in other patents or scientific work (Trajtenberg 1990;Henderson, Jaffe, and Trajtenberg 1998;Harhoff et al. 1999;Hall, Jaffe, and Trajtenberg 2005; Sapsalis, van Pottelsberghe de la Potterie, and Navon 2006; Gambardella, Harhoff, and Verspagen 2008;Czarnitzki, Hussinger, andSchneider 2009, 2012).The quality of each patent therefore can be measured after several years by its number of citations (Häussler, Harhoff, and Müller 2014).To account for differences in the career length between more and less prolific inventors, the productivity measures are standardised by years of job experience, and thus they are independent of total career length (Huber 1998(Huber , 2002;;Dietz and Bozeman 2005).We, therefore, measure patent quantity and quality as follows: Patent quantity: Patent quantity is measured by the total number of patents applied for per inventor minus the first patent divided by the number of career years, c, after the first patent in the productivity equation.In the cumulative advantage regressions according to Equation (2), patent quantity is measured by the total number of patents applied for per inventor in t1 and in t2, respectively, divided by the period lengths of t1 and t2.
Patent quality: We use forward citations of patents within 5 years of its filing to measure the quality of a patent (Trajtenberg 1990;Albert et al. 1991;Harhoff et al. 1999;Lawson and Sterzi 2014;Bakker et al. 2016).Our measure for patent quality is the total sum of citations without the citations of the first patent in the productivity estimations.In the cumulative advantage regressions, the sum of the citations of all patents applied for during t1 and t2 is divided by the period lengths of the corresponding periods.

Explanatory variables: early patenting success
We use dummy variables instead of continuous indicators for early patenting success because this approach imposes less structure on the correlation between early and lifetime success and measure precocity as follows: High-quality first patent: We define a high-quality first patent as a dummy that equals 1 if the first patent is in the best quartile of first patents of our sample, ranked by the total number of forward citations (within 5 years of filing).
Fast first patent: We define a first patent as being filed fast if an inventor belongs to the fastest quartile of inventors in our sample to file the first patent after obtaining the highest degree of education.We use the time span between the end of education and first patent instead of age to include the trade-off between education and inventive effort as well as differences in educational attainment (Jones 2010).

Control variables
Predetermined individual information.We control for gender differences because career strategies and inventive productivity may differ between men and women (Jung and Ejermo 2014;Hunt et al., 2012;Ding, Murray, and Stuart 2006;Whittington 2011;Whittington and Smith-Doerr 2005;Frietsch et al. 2009;Naldi et al. 2005).We also use controls for birth cohorts because patenting behaviour may have changed over the years, given the so-called 'patent explosion' (Hall 2004;Lawson and Sterzi 2014;Akcigit et al. 2018) and the increase in average age at first patent (Jones 2009).The strong increase in the number of patent applications during the last few decades and the increasing burden of knowledge in many technology areas may imply differences in the chance of patenting an inventive idea quickly after obtaining the highest education at different years during our observation period (Levin and Stephan 1991;Jones 2009;Jones 2010;Allen and Katz 1992;Simonton 1988;Harhoff and Wagner 2009;Dietz and Bozeman 2005).We, therefore, add period dummies.We also control for education level because a higher education, particularly a PhD degree, increases lifetime inventive productivity (Hoisl 2007a;Mariani and Romanelli 2007;Onishi and Nagaoka 2012;Toivanen and Väänänen 2016;Giuri et al. 2007;Akcigit et al. 2018).Baumol, Schilling, and Wolff (2009) argued however that extensive education in a certain field can impede cognitive insight.Paradigms and institutional pressures to conform therefore also may stifle inventive ideas of the more formally educated young inventors.An engineering specialisation during schooling may be a boon for inventive productivity (Gruber, Harhoff, and Hoisl 2013).Therefore, we include a dummy variable for inventors who have an engineering specialisation in their academic education or a technical occupation for those without academic training.Finally, family background may influence inventive productivity; academically educated parents may foster an inventor's achievement (Caldas and Bankston 1997).Hence, we include dummy variables that have a value of 1 if an inventor has a father or a mother with academic education, respectively.Previous studies on inventive productivity find a relationship between personality traits and inventive performance (Dodds, Smith, and Ward 2002).In particular, the personality dimension 'openness to new experiences' seems to be positively related to productivity (McCrae 1987;King, Walker, and Broyles 1996;Furnham and Bachtiar 2008;Sung and Choi 2009;Silvia et al. 2009;Furnham et al. 2011;Furnham, Hughes, and Marshall 2013;Lin et al. 2013;Grosul and Feist 2014;Batey, Furnham, and Safiullina 2010;Zwick et al. 2017).We include the Big Five personality inventory (openness to new experiences), agreeableness (compliance, straightforwardness), conscientiousness (order, dutifulness, competence), extraversion (warmth, sociability, activity), and neuroticism (anxiety, depression), compare McCrae and Costa 2006).Willingness to take risks is also a personality characteristic that seems to be positively related to inventive performance (Dewett 2007;Audia and Goncalo 2007;Zwick et al. 2017).Baumol, Schilling, and Wolff (2009) argues that inventors who seek fast recognition and access to resources frequently pursue riskier innovation strategies.Thus, precocious inventors may be especially risk prone.
Work environment.We control for the employer type that applies for the patent because it may make a difference whether the inventor works for a private firm, a university, or a public research institute (Dietz and Bozeman 2005;Van Looy, Callaert, and Debackere 2006;Zucker et al. 2007;Crescenzi, Filippetti, and Iammarino 2017).The literature is unclear on whether basic or applied research activities have a stronger positive relationship with inventive productivity (Mansfield 1980;Griliches 1986;Lichtenberg and Siegel 1991).Specific knowledge contributes to innovation and generalist knowledge facilitates recombination of ideas.Previous research shows ambiguous results on whether working as a specialist or as a generalist is related to a higher inventive productivity (Jones 2009;Goetze 2010;Melero and Palomeras 2015;Arts and Fleming 2018).We control for the type of research activities an inventor pursues and whether the inventor mainly is a specialist or a generalist in t1.Following Griliches (1990) and Hoisl (2007aHoisl ( , 2009)), we also control for the status of the first patent application, which may be pending, refused, withdrawn, or granted.The reason is that the value of an inventive idea may be lower if the patent application was withdrawn or refused by the patent officer.Finally, we measure the quality of the work environment by the number of patents an employer applied for (Czarnitzki, Hussinger, and Schneider 2012;Mariani and Romanelli 2007;Chabchoub and Niosi 2005;Harhoff and Hoisl 2010;Mansfield 1986;Scherer 1999;Lawson and Sterzi 2014).
Technology fields have different R&D and patenting activity levels (Klevorick et al. 1995;Gruber, Harhoff, and Hoisl 2013;Mansfield 1986;Levin et al. 1987).Therefore, we control for the main technology sector in which an inventor is active during their entire career.We use the information provided by the inventor when asked about the main technology field in which they have been active.

Cumulative advantage mechanisms
We test whether there are specific mechanisms that document cumulative advantage for precocious inventors, that is, their employers attributing additional resources to their precocious inventors (Owen-Smith and Powell 2001; Toivanen and Väänänen 2012): Precocious inventors may have a better chance of working mainly on R&D projects later in their career, and they are encouraged to invest time in research instead of management or organisation tasks (Merton 1973a).This cumulative advantage mechanism assumes that employers put their best researchers on the most promising inventive projects and grant them enough time and resources to complete these projects (Zucker, Darby, andBrewer 1998, 2002).
Job mobility may increase individual productivity because it allows employees to increase the quality of their job match, exchange their knowledge with new colleagues, build more experience, and enlarge their research network (Song, Almeida, and Wu 2003;Dietz and Bozeman 2005;Hoisl 2007a).
Precocious inventors may also benefit from research cooperation opportunities with other inventors (Baldini, Grimaldi, and Sobrero 2007).There is empirical evidence that high-impact scientists enjoy more extensive exchange and better cooperation opportunities with other inventors, and thus they may have more co-inventors mentioned on their patents (Goetze 2010;Blomkvist, Kappen, and Zander 2014).Akcigit et al. (2018) argues that precocious inventors become team leaders more quickly.In contrast to team members, leaders reap the inventive performance of the entire team.Consequently, they are more productive than team members and their productivity increases with the number of members in their team.Thus, an increase in the number of co-operators may be a cumulative advantage mechanism.(Simonton 1992(Simonton , 2003a;;Dunbar 1995;Breschi and Lissoni 2009;Dietz and Bozeman 2005;Jones 2009).
Summing up, we measure the following potential cumulative advantage mechanisms precocious inventors may enjoy:

Descriptive statistics
Table 1 shows that during their career, inventors in our sample file 0.61 patent applications per working year and obtain 0.55 citations per working year.The share of male inventors is 97.7% 14 .Around 92% of inventors in the dataset hold an academic degree including a PhD.More than two-thirds of the inventors are engineers.About 10% of the inventors' mothers and 24% of the inventors' fathers have an academic degree.When filing their first patent, inventors are on average nearly 40 years old 15 (not shown in the descriptive statistics).Less than 30% 16 of the inventors have a first patent that was cited at least twice within 5 years, and thus qualify for our first indicator of early patenting success ('high quality').More than 30% of the inventors are in the fastest quartile of inventors who applied for their first patent within 4 years of obtaining their highest education degree and therefore are labelled as 'fast first patent' inventors.The speed and quality of the first patent is distributed equally in the main technological areas, and consequently, the share of precocious inventors does not vary greatly between technological sectors (Table A2 in the Appendix).We do not expect many changes in the assignment of precocity and therefore do not calculate sector-specific early patenting indicators.
The Big Five personality dimensions of an inventor are measured on a 15-item short version of the Big Five inventory (seven-point Likert scale; compare Schupp and Gerlitz 2014).The personality dimensions are aggregated by principal components factor analysis with varimax rotation (negatively defined items are rescaled; compare Zwick et al. 2017).About 40% of the inventors opt for a score of 7 or higher on a Likert scale that ranges from 0 (highly risk averse) to 10 (highly risk seeking) (compare Dohmen et al. 2011).These inventors are labelled as having a positive risk attitude.
The first patent of an inventor is filed with about three co-inventors on average (the maximum is 24 co-inventors).For first patents, 60% are granted, around 21% are pending, fewer than 18% are refused, and the rest are withdrawn by the applicant.The first patent applicant is almost always a private firm (95%).Most of the inventors in our sample were working in applied R&D instead of basic R&D when they applied for their first patent (83%).About 64% of the inventors report an R&D working time share of more than half when their first patent was applied for.The ratio of inventors who are specialists to those who are generalists is about 1:2 during this period.
Figure A1 in the Appendix shows that the number of patents and their citations per inventor are right-skewed and only few inventors are truly prolific, also compare Huber (1998), Toivanen & Väänänen (2012, 2016) Azoulay, Graff Zivin, and Wang (2010), Blomkvist, Kappen, and Zander (2014), Akcigit et al. (2018).Consequently, the individual shares of the total number of patents and citations closely match Lotka's law. 17The skewed distribution of the dependent variables requires a negative binomial model (count model) in our empirical inventive productivity estimations (Allison, Long, and Krauze 1982;Huber 2002).Therefore, we use a Poisson regression model 18 with parameter λ (Baruffaldi, Visentin, and Conti 2016; Sapsalis, van Pottelsberghe de la Potterie, and Navon 2006) and our estimation Equation (1) can be specified as where γ is the vector of parameters associated with the vector of explanatory variables Y i (W i , X ip1 , Z it1 , fast, and highquality) and α is the overdispersion parameter.The econometric model of the inventive productivity estimation accordingly is where l i is the estimator of the Poisson parameter.Table A4 summarises the correlations between the most important variables.Our two indicators for early inventive success have a strong positive correlation with the two inventive productivity measures.Qualitative and quantitative inventive productivity are highly positively correlated with each other (also compare Bakker et al. 2016;Zwick et al. 2017).However, the two early success measures have almost no correlation with each other and appear to be independent drivers of lifetime inventive productivity.
Our descriptive analysis shows that precocious inventors have more patents and more citations per career year than inventors without early success.Average patent number increases slightly from t1 to t2 for inventors with early success, but this number decreases for inventors without early success.Average patent quality is higher in t1 than in t2 for all four groups (see Figure 1).The decrease in patent quality from t1 to t2 supports the idea of a decrease in inventive capability with age (Jones 2010;Akcigit et al. 2018).This decrease however does not seem to apply to precocious inventors.
The higher productivity of precocious inventors is matched by the better resource endowment of this group of inventors during t1 (Table A5).Inventors with a fast and/or a high-quality first patent have more co-inventors, larger employers, and a higher share of R&D time in their early career years than their peers without an early success.We also find that a higher number of precocious inventors voluntarily move to another employer in t1.However, we do not know whether this move occurs before or after the first patent application.These results suggest that according to hypothesis 3, a more favourable work environment in t1 could explain (part of) the lifetime patenting success of precocious inventors.

Correlations between early success and career inventive productivity
We now assess the relationship between early patenting success and inventive career productivity in a multivariate Poisson regression according to Equation (4) for patent quantity (Table 2) and patent quality (Table 3).In models 1 and 2 of each regression table, only one of the two indicators for early patenting success is used as an explanatory variable.In model 3, both early success variables are included.Controls are added in a stepwise manner in models 4 and 5; first individual characteristics Without any further controls, inventors with a high-quality first patent file 25.9% more patents per working year during their further career (Table 2, column 1; p < 0.01). 19A fast first patent results in more than twice as many patents compared with the reference group (Table 2, column 2; p < 0.01).The covariates in the models 4 and5 in Table 2 give us results previously found in the inventor productivity literature, compare our literature review.Male inventors and inventors with a PhD have significantly higher career productivity.A specialisation in engineering and parents with an academic degree do not additionally drive productivity, however.Inventors with a positive risk attitude and with a high openness to new ideas have a higher productivity, whereas extrovert and conscientious inventors have a lower productivity.Generalist work experience and a high R&D share when the first patent is applied for increase career productivity.Mid-sized patent applicants for the first patent have a stronger positive correlation with inventor career productivity than small and very large applicants.An industrial applicant for the first patent is correlated with a higher career productivity than a university, public research institute, or individual applicant.The number of co-inventors and mainly working in basic or applied research activities when applying for the first patent do not have a productivity effect.Including individual and work environment characteristics more than doubles R 2 from 5% to 11%.
The most important result for our study is that the coefficients of the early success indicators remain significant if we include predetermined individual information.These empirical results support hypotheses 1 and 2. The strength of the correlation also remains relatively constant for a high-quality first patent when we compare the results of models 4 and 5 with those of model 1.However, the coefficients of a fast first patent in our lifetime patent quantity and quality estimations decrease considerably when we add individual characteristics to model 2. We also find that both indicators are independent drivers of career productivity because an interaction term between both success variables is insignificant.
If we add work environment characteristics in t1 in addition to the individual characteristics, there still is a sizeable effect of 59.4% more patents (p < 0.01) for fast inventors, and of 19.4% more patents for inventors with a high-quality first patent (Table 2, model 5).The effects of early patenting success on patenting quality during the career are similar: a highly cited first patent increases the average number of citations received per work year by 66% after including all controls (Table 3, model 6, p < 0.01).Likewise, a fast first patent results in an increase in patent citations of 81% (p < 0.01).The strength of the early success indicators, therefore, decreases somewhat but remains highly significant if we consider that precocious inventors enjoy a relatively invention-friendly environment during their first career years.Thus, hypothesis 3 is not supported.It is interesting to note that the measured impact of early patenting success on career productivity decreases stronger for patent quality than for patent quantity if we include our work environment indicators.This result seems to be in accordance with the finding that the work environment may stronger affect patent quality and the chances to achieve a breakthrough invention than the patent quantity (Audia and Goncalo 2007;Conti, Gambardella, and Mariani 2014).

Robustness checks
We first vary the definitions of the dependent variables.We use fractional counts or, in other words, we divide inventive productivity by the number of co-inventors instead of absolute numbers (Table A6, columns 1 and 2).In addition, we extend the period for citations from 5 to 10 years for our quality measure (Table A6, column 3).Finally, we divide the number of citations by the number of patents instead of by work years (Table A6, column 4).
We also use alternative indicators for early patenting success.We first extend the period in which citations are counted from 5 to 10 years (Table A7, columns 1 and 2).Second, we use a dummy for inventors who applied for their first patent before the start of their career instead of within 4 years of the end of their education (Table A7, columns 3 and 4). 20Third, we reduce the share of inventors who are considered as precocious by increasing the number of citations necessary for the first patent from two to three and to four.We also reduce the number of years between education and first patent application from four years to three and to two years.The results show the expected increase in career productivity for the higher selective samples; compare the coefficients for high-quality and fast first patent in columns 6 in Tables 2 and 3 and the respective coefficients in Table A8.Finally, we use the number of citations per year of all patents applied for during t1 instead of the number of citations of the first patent.The highest quartile of inventors has at least two citations per year in t1.If we use this early high-quality indicator, the coefficients are 1.234*** for patent quantity and 1.688*** for patent quality in regressions that are identical to columns 6 in Tables 2 and 3. 21  Lawson and Sterzi (2014) emphasised that birth cohort effects may drive the results given differences in the share of inventive ideas patented for inventors over time.Therefore, we re-run our regression separately for inventors born before and after the year 1964.The results remain robust for both sub-groups of birth cohorts (Table A9).Jones (2009;2010) and Jones and Weinberg (2011) argue that young inventors may have to reduce the time they can devote to their inventive activity to obtain the education and training needed to reach the frontier of knowledge in their technology field.Therefore, the maturity of a technology field may be a decisive factor in the speed and quality of the first patent.Inventors in technology fields with less accumulated knowledge may have a smaller 'burden of knowledge'.In addition, inventions in technology fields in which experimentation is more important take more time than inventions in mainly conceptual technology fields.Therefore, having a fast or high-quality first patent 22 in a field in which experimentation is important or the burden of knowledge is high may be a stronger indicator of inventive ability compared with other technology fields.Our data give us little information about the importance of experimentation versus theory or the amount of accumulated knowledge in the technology field in which the first patent was applied for.If we however assume that factors that allow quick inventive progress also allow early completion of the education period, age at education completion may be a good indicator of the burden of knowledge and the importance of experimentation.Figure 5 in Jones and Weinberg (2011) supports this hypothesis by showing a positive correlation between age at highest education degree and age at great achievements for Nobel prize laureates.We, therefore, calculate the median age at which the highest education was obtained for each of the 14 main technology fields.We find substantial variation, for example, between mechanical elements (25 years) and pharmaceuticals (31 years).Next, we determine the correlations between early patenting success and career inventive productivity separately for inventors in technology fields below and above the median age of 28 years for completing education.Again, there are no differences in the productivity effect of early inventive success between inventors in both groups (Table A10).
We reproduce all productivity estimations using ordinary least squares (OLS) instead of the Poisson regressions presented (not shown).The OLS coefficients are like the Poisson estimates; for example, a fast (high-quality) first patent is correlated with a 51% (16%) higher career productivity in an OLS estimation according to the specification in Table 2, column 6.
Summing up, we find in all specifications that early patenting success has a large additional informational value for career inventive productivity after controlling for predetermined individual characteristics and indicators for the work environment quality in t1.

Cumulative advantage induced by early career success
We now test whether high early patenting productivity leads to a stronger increase in inventive productivity during period t2 compared with productivity in period t1, compare Equation (2).There is a significant negative correlation between the inventive productivity in t1 and the change between the productivity in t1 and t2 (Table 4, column 1).Instead of cumulative advantage, we find a regression to the mean in a random process.In other words, inventors with a high productivity during their first patenting period cannot increase their productivity further compared with this high level.A high-quality first patent is positively correlated with the difference between t1 and t2 (Table 4, columns 2 and 3).However, a fast first patent and both early success indicators together are not correlated with the productivity difference between t1 and t2 in most estimation specifications.Instead, the sum of the difference effects is negative for all inventor groups.We obtain the same results qualitatively for inventive productivity changes measured by the number of citations (compare Table 5).To test the robustness of our results and reduce the risk of endogeneity 23 , we also estimate Equation ( 2) in levels instead of differences (compare Equation ( 7) in DiPrete and Eirich 2006).In this robustness check, again all inventors experience a regression to the mean effect.This effect is lower for precocious inventors, but also this group of inventors does not enjoy a sustained productivity advantage in t2 (compare Tables A11 and A12).These results suggest that there are no cumulative advantage effects for precocious inventors and hypothesis 4 cannot be supported.Now we analyse whether precocious inventors are offered more resources in t2 in comparison to t1.We show whether inventors with early patenting success can increase the share of R&D activities, the number of co-inventors, the size of the employer, and their chance of moving to another employer voluntarily, see Equation (3).For three resource dimensions, precocious inventors cannot improve their work environment in t2 in comparison to t1 relative to inventors without early success (Table 6).Only the increase in the size of the employer as measured by the number of patents applied for is moderately stronger for precocious inventors.The employer size increase is not a consequence of successful inventors voluntarily changing to larger employers, however.The increase in employer size is larger for inventors with a fast first patent who stay with their early employerthe increase is almost 50 patents for employer stayers in comparison to less than 20 for employer movers (Table A13, columns 1-3 and columns 13-15). 24We also find a lower voluntary job move incidence of precocious inventors after t1 in comparison to inventors without early patenting successes (see Table 6).Consequently, the increase in the number of patents applied for by employers of precocious inventors in t2 cannot be interpreted as an indicator for cumulative advantage.The stronger increase in patent applications of the early employer of precocious inventors instead may partly be driven by the successful patenting activity of the precocious inventors themselves.We, therefore, conclude again that hypothesis 4 must be declined.

Discussion and conclusion
Our results show that precocious inventors have a higher quantitative and qualitative career inventive productivity than inventors without early patenting success.Speed and quality of the first patent have an independent and significantly positive influence on productivity.We cannot be certain to identify a causal relationship between precocity and career inventive productivity in our structural model.We however find that precocity has information value in addition to predetermined individual characteristics and information about early work environment characteristics.We do not find cumulative advantage for precocious inventors: High productivity during the first career years does not lead to a higher (increase in) productivity during the remaining career.Instead of a productivity boost for precocious inventors, we observe a regression to the mean for both precocious and non-precocious inventors.As the decline is smaller for precocious inventors, they can increase their productivity advantage compared to other inventors.In addition, inventors with an early patenting success cannot attract more resources during their career.Consequently, also changes in the work environment during the career cannot explain the higher inventive career productivity of precocious inventors.
Although outside employers can use early patenting success of a young inventor as an indicator for future high career productivity, we find that the share of precocious inventors who voluntarily change their employer after the period in which they achieved their first successes is lower than the share of their less successful peers.Given that highly productive inventors are a central resource in high demand for many inventive employers, it is of key interest how early employers can retain their precocious inventors.We propose several reasons: First, our data suggest that early employers of precocious inventors offer an invention-friendly environment.Inventors may not put this environment at stake when moving to another employer whose work environment they do not know.
Second, early employers of precocious inventors increase the number of patents applied for stronger between t1 and t2 than other employers.This patenting success may be partly driven by the precocious inventors themselves, but it also may be a sign of a general positive development.Precocious inventors therefore may be attracted to stay with their successful employers.
Third, the early employer may restrict the transfer of knowledge and thereby appropriate the inventor's idea (Kim and Marschke 2005;Melero, Palomeras, and Werheim 2020).The employer for example may either apply non-compete clauses or assert intellectual property rights as applicant of the first patent (Conti 2014;Younge and Marx 2016).Restrictions to use the intellectual capital outside the present employer may make it attractive for precocious inventors to stay with the early employer.
Fourth, the early employer could quickly promote precocious inventors to team leaders.The promotion may induce a positive spill-over effect between the team members (Akcigit et al. 2018).A new employer also may offer the inventor a team leader position but with new team members this offer may be unattractive.
Fifth, the early employer can provide wage counter-offers to avoid poaching (Lazear 1986).Precocious inventors indeed enjoy a stronger wage increase during t2 than other inventors (see columns 'salary' and 'salary for stayers' in Table A13).This wage increase is comparable for inventors who stay with the early employer and inventors who change their employer.Employers may share the rents derived from the early invention with their precocious inventors to retain them.
This paper establishes that a fast or a high-quality first patent has an outstanding predictive value for life-time inventive productivity.Future studies with access to a larger pool of prolific inventors may analyse the additional information value of including the characteristics of more than the first patent.In tentative regressions, we find evidence for a decrease in the predictive value for future productivity with the number of patents included in t1.If we define t2 as all patents after the first two years (3,4 or 5) of patent activity, the IRR of the highest quality quartile on patent quality during the remaining career decreases from 1.66 (Table 3, column 6) to 1.51 (1.47, 1.39, and 1.30) (all coefficients are significant at the 5% level).Also, the increase in the incidence of spin-offs from t1 to t2 may explain part of the higher career inventive productivity of precocious inventors. 25Future studies also may analyse in more depth the characteristics of the team precocious inventors work during their first years.Especially the presence of experienced inventors in these teams may play a crucial role for the formation of successful careers.
Although we control for more individual and employer characteristics than previous papers on inventive lifetime productivity, there may be additional predetermined individual characteristics future studies could control for such as education marks or the prestige of the educational institute (DiPrete and Eirich 2006).There are also further work environment characteristics that should be included such as the promotion of risk-taking, autonomy, external competition, or collaborative and supportive leadership styles (Perry-Smith and Shalley 2003) as well as autonomy with respect to invention goals (Conti, Gambardella, and Mariani 2014).
Our study has several implications.First, our results support the interpretation of inventive productivity being characterised by a variation-selection process (Simonton 2003b;Arts and Fleming 2018).Useful and useless variations seem to be randomly distributed within individual careers and there is no indication of cumulative advantage.Thus, productivity differences between inventors are independent of age and experience.The most prolific inventors at the beginning of their career continue to be higher productive for the rest of their career (Huber 1998).Therefore, information about early patenting success reduces uncertainty about future inventor productivity (Long 2002).The impact of an early patenting success however is substantially over-estimated if predetermined individual characteristics and the quality of the early work environment are not controlled.Second, employers that have hired precocious inventors before their employees achieved their early patenting success have a fair chance of retaining them although the first patent provides public information on future productivity.To attract high-ability inventors, employers should put more effort on identifying them before their ability is revealed than to try to hire them later during their career.

Notes
1.The early literature on the impact of early success on productivity shows that more productive scientists and inventors start their career earlier (Zuckerman 1967;Blackburn, Behymer, and Hall 1978).Another persistent finding is that higher inventive productivity during the first career years is correlated with higher productivity in the following career years (Lightfield 1971;Clemente 1973;Reskin 1977).2. Audia and Goncalo (2007) only include patent-specific information such as the number of (new) technology classes, the number of co-inventors or the year in which the patents were applied for.They do not include any individual inventor characteristics.3. Dietz and Bozeman (2005) additionally include the science area of the doctorate and the doctorate year, the type of employment (academia, industry of government), several indicators of the employment patterns over time in these three areas, the number of grants and whether the inventor held a Post-Doc position.4. Lawson and Sterzi (2014) mainly control for education discipline and PhD institution type, gender, age at first patent, number of prior patent applications of first patent applicant, experience of co-inventors on first patent, and further characteristics of the first patent (number of citations and whether it was granted).5.The fallacy of composition describes aggregation errors if inferences about individual experience-productivity patterns are derived from average statistics across many individuals, such as birth cohorts or other groups of people.6.The career productivity indicators in t2 are measured for the period after t1 until the end of the career or the end of the observation window.7.This test is proposed by Allison, Long, and Krauze (1982), also compare Equation (3) in DiPrete and Eirich (2006).8.No inventor applied for more than one patent on the day of the first patent application.Therefore, we can determine the first patent with certainty.9.The seven spells are 1978-1979; 1980-1984; 1985-1989; 1990-1994; 1995-1999; 2000-2004; and 2005-2010.10.In contrast to other studies, we cannot exclude potential self-citations at inventor level.This might imply that some results for patent quality are overestimated.11.For details of the data collection and matching process, see Frosch et al. (2014) and Zwick et al. (2017).12.We also exclude one inventor who applied for all (two) patents within one 5-year period.All remaining inventors have at least one patent in at least one period after the first application period.13.According to our hypothesis that early patenting success is a good predictor of future inventive productivity, inventors with only one patent less frequently had an early success with it.14.The small share of 2.3% female inventors is consistent with other studies (Jung and Ejermo 2014;Hunt et al., 2012).15.This value is close to the 41.4 years reported for the first patent of Swedish inventors (Jung and Ejermo 2014).16.As the number of patents and their citations as well as the years between highest education and first patent are discrete numbers, we determine the numbers that are closest to a quarter in the distributions of the indicators of precocious inventors.17.Lotka's law can be expressed as p n = p 1 /n k , where p n is the proportion of inventors with n patents in all inventors, p 1 is the number of inventors with one patent, and k is a constant (Huber 2002).The goodness of fit values, R 2 , for all regressions on the distributional form of our sample are higher than 0.94.Thus, the empirical distributions closely match the theoretical distributions for the number of patents and their citations.18.Our dependent variables fit a Poisson distribution according to a chi 2 goodness-of-fit test (Table A3).A Jacques-Bera and a Shapiro-Wilk test for normal distribution indicate that our dependent variables deviate significantly from a normal distribution.19.We can interpret the coefficients in terms of incidence rate ratios (IRRs).The coefficients of a Poisson regression represent the log changes of the dependent variables after a change of the independent variable.The interpretation of these coefficients is not always straightforward.IRRs are an alternative representation.These ratios show the expected change in the incidence of the outcome variable after increasing the dependent variable by one unit.For dummy and categorical variables, the IRR represents the relative incidence relative to the reference category.The IRRs are obtained by using the exponential form of the coefficients, that is, the IRR of coefficient is calculated as .IRRs are interpreted as multiplicative.An IRR above 1 represents an increase and an IRR below 1 represents a decrease of the dependent variable after a change in the independent variable.20.We also find robust results if we use the application of the first patent before the end of the PhD period as an indicator for a fast first patent in a subsample of PhDs, compare Dietz and Bozeman (2005).21.We obtain similar results when we take the first five years of the career instead of t1 as period in which the number of citations is counted for all patents applied for.22. Jones (2009) mentions that the burden of knowledge may either decrease the number of ideas and/or their quality (i.e. the 'size of ideas').23.In Equation ( 2), Y it1 is used as an explanatory variable and is part of the dependent variable Y it2 -Y it1 .24.The differences in employer size changes are not significantly different for inventors with and without a high quality first patent.25.The share of entrepreneurs significantly increases from 2.5% to 5.5% for precocious inventors, it however remains flat for the other inventors (4.9% in t1 and 5.5% in t2).

Appendix
(a) An increase in the share of the working time an inventor can spend on R&D tasks in later career years.(b) The probability of moving voluntarily to another employer in later career years.(c) The probability of working for an employer with a better research environment in later career years.(d) An increase in the average number of co-inventors in later career years.

Figure 1 .
Figure 1.Average productivity in t1 and t2 of inventors with and without early success (n = 1240).
Poisson regression.Table shows incidence rate ratios.Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.1.ECONOMICS OF INNOVATION AND NEW TECHNOLOGY are added, then we control for characteristics of the work environment during the first patent application.

Table 4 .
Test of cumulative advantage in productivity.

Table 5 .
Test of cumulative advantage in productivity.

Table 6 .
Test of cumulative advantage in resources.

Table A1 .
Number of periods observed after the first patent.

Table A2 .
Share high quality and share fast first patent applications by main technology field.

Table A3 .
Poisson distribution goodness of fit tests for inventive productivity (n = 1240).

Table A7 .
Productivity estimations with alternative early patenting success measures.

Table A8 .
Robustness tests with alternative definitions of precocious inventors.

Table A9 .
Productivity estimations, results for inventors born before and after 1964.Poisson regressions.

Table A10 .
Productivity estimations, results for inventors by the median age at the highest educational degree in technology field of first patent.Table shows incidence rate ratios.Robust standard errors are shown in parentheses.Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.1.

Table A12 .
Test of cumulative advantage in productivity.