We estimate grouped-time (discrete) duration models to study the determinants of

Are more able inventors more mobile? Alfons Palangkaraya Melbourne Institute of Applied Economic and Social Research, The University of Melbourne +61 3 8344 2119 +61 3 8344 2111 alfonsp@unimelb.edu.au Abstract We estimate grouped-time (discrete) duration models to study the determinants of Australian inventor institutional mobility using U.S. patent data. We find that the institutional mobility of Australian inventors is consistent with the prediction of standard labour mobility model: (i) it increases with the expected marginal productivity from the move (measured by past performance) and (2) it decreases with reservation wage or moving cost (measured by the extent of current job match). However, while there is robust evidence that more able inventors are more mobile, we find the relationship to be sensitive to how the sample is drawn when cross-sectional analysis is used. Keywords: Inventor mobility; Australia; Patent; Discrete-time duration models JEL Classifications: F24; F60; O31; O34

1. Introduction This paper empirically investigates the importance of distinct factors that may influence the decisions of Australian inventors to move across different employers. Past research has emphasised the importance of knowledge diffusion for innovation and the crucial role of innovation in economic growth (Romer, 1986 and 1990; Lucas, 1988; Grossman and Helpman, 1991). It has been argued that a good understanding of inventor mobility is crucial to knowledge diffusion and thus to promoting and sustaining innovation activities. Labour mobility serves as an important mechanism of knowledge transfer, especially when tacit knowledge is important (Dosi, 1988). Studies have indicated, for example, that the movements of inventors across firms would result in knowledge transfer (Arrow, 1962; Almeida and Kogut, 1999; Agrawal et al., 2006). The literature on inventor mobility is relatively new and most studies that have been done utilised the inventor information provided in patent documents (for examples, Trajtenberg et al., 2006; Hoisl, 2007; Thoma & Torrisi, 2007). One major research area within this literature has identified a possible two-way relationship between inventor mobility and inventive performance. That is, one may expect that not only more mobile inventors facilitate knowledge diffusion better, but they can also end up with better job match and higher productivity (Topel and Ward, 1992). In fact, there is evidence that supports this hypothesis that inventor mobility can lead to higher inventor performance (Hoisl, 2007), even if the relationship between mobility and productivity appears to depend on what motivated the inventors to move at the first place (Schankerman et al., 2006; Hoisl, 2009; Cabagnois, 2010). 2

The underlying driver of the two-way relationship is that, on the one hand, more productive inventors are more likely to be head hunted and thus they are relatively more likely to move to different employers. On the other hand, mobility may be associated in the inventors desire to get a better match and thus resulting in observations of their relatively better performance after the move. While such driver may also apply to other types of employees, they could be more significant for the case of inventors due to the important role of knowledge spillovers, especially because tacit knowledge is often important. Despite this clear prediction, the relatively scarce empirical evidence for the case of inventors is mixed. In the case of the mobility of academic scientists, better scientists have been found to be more mobile and qualitatively measured ability dominates quantitatively measured one (Zucker et al., 2002). In contrast, studies such as Hoisl (2007) and Geuna et al. (2006) found more able inventors to have lower probability to move. The latter also found that for the case of academic inventors, quantitative factors appeared to dominate. On the other hand, more recent studies such as Lenzi (2009), Nakajima et al. (2010) and Palomeras and Melero (2010) found better inventors were also more mobile. The focus of this paper is on the first part of the relationship and the objective is to provide more robust evidence by utilising a more intuitive analytical framework, incorporating more complete model specifications guided by insights from standard labour mobility models and providing comparisons across different model specifications and sample selection. In line with many of the existing studies, this paper also utilises the inventor information in patent database. While patent application data provide necessary 3

information to investigate the effects of past performance on inventor mobility study, they present a particular endogeneity problem because the inferred institutional mobility depends on the productivity of the inventors. The higher the number of patents produced by an inventor, the higher the probability we observe that inventor to move. The duration analysis framework employed in this paper makes it possible to address such limitation directly since it allows us to estimate the effects of the determining factors on any specific sequential move at any period for each inventor. That is, the estimated probability of a move is independent from the way the movement is measured. In contrast, a cross-section analysis based on a binary dependent variable (of a move or no move) or count dependent variable (of the number of moves) is more prone to be affected by the endogeneity-by-definition problem unless a simultaneous model setting or an appropriate sample selections method is used. In this paper, we also investigate whether or not the estimated relationship between inventor ability and mobility is sensitive to the way the study sample is selected within a cross-section empirical framework. This paper is not the first in applying duration analysis on the study of inventor mobility. Recent studies such as Geuna et al. (2006), Lenzi (2009), Palomeras and Melero (2010), and Nakajima et al. (2010) have all used duration analysis to estimate the determinants of inventor mobility. However, compared to this paper, these studies are relatively more restricted in terms of either the sample of the study, the set of determinants being investigated, or model specifications. For examples, Geuna et al. (2006) and Lenzi (2009) focused only on academic inventors; whereas Palomeras and Melero (2010) focused only on inventors working in a single firm (IBM). Furthermore, the models in these studies appear to be incompletely specified compared to a widely cited study on the mobility of 4

knowledge workers (Zucker et al., 2002). As a result, in terms of the role of past performance on inventor mobility, their findings vary significantly and may appear counterintuitive. Therefore, it is not clear how generalisable the findings of these existing studies are. In specifying the discrete-time duration model, this paper follows the main insights used in the specification of Zucker et al. (2002) s model. The specified models are then estimated using Australian inventors U.S. patent records granted between 1975 and 1999 obtained mainly from the NBER U.S. Patent Database (Hall, et al., 2002). The use of Australian inventors is helpful in various ways. First, the sample size is significantly lower than, for example, the use of American or European inventors. Second, the names of the inventors are relatively easier to manipulate and given our access to the complete patenting Australian inventor names data from the Australian Patent Office (IP Australia) administrative database, the problem of tracing inventors can be minimized. Finally, a study of Australian inventors as opposed to inventors from different European countries avoids any potential inference difficulty arising from institutional heterogeneity across the regions and due to the geographical location of Australia helps in interpreting proxy variables which may capture more than one inventor mobility s determining effects as discussed in the text. The rest of this paper is structured as follows. Section 2 briefly discusses some of directly relevant studies. Section 3 sets up the empirical framework and describes the data. Section 4 presents and discusses the findings. Section 5 concludes. 5

2. Recent relevant studies on inventor mobility Polanyi (1958) claimed that [w]e know more than we can tell due to the tacit characteristic of knowledge. More recently, Breschi et al. (2009) stated that [k]nowledge always travels along with people who master it. In other words, the mobility of the person(s) with the (tacit) knowledge can be a key mechanism for knowledge transfer. Because of that, firms that are trying to catch up with their competitors may find it necessary for them to attract inventors working for other firms (Almeida and Kogut, 1999; Song et al. 2003). However, depending on the characteristics of the knowledge in question, not all knowledge transmission requires inventor mobility. Researchers have found that the mobility of inventor plays a stronger role in knowledge transfer when the related invention is more valuable, the underlying knowledge is more tacit and there is a higher degree of scarcity of people with the knowledge (Breschi et al., 2009). A major part of the recent relevant literature is concerned with the relationship between mobility and inventive performance. Trajtenberg (2005, 2006), for example, studied the relationship between the mobility and productivity of Research and Development (R&D) personnel using the name of inventors listed in U.S. patents and found that inventor mobility and performance are positively correlated. As summarised by Hoisl (2007), institutional mobility can lead to higher inventive performance and better performance can lead to higher probability for an institutional move. For the former, mobility can lead to improved job match between the inventors and his/her new work environment resulting in better performance. For example, Topel and Ward (1992) argued that as in 6

other types of labour inventor mobility may improve the match between inventors and their employers. For the latter, there is evidence that because of knowledge spillovers, the incentive to recruit highly productive inventors from other companies is very high (Arrow, 1962; and Song, et al. 2003). Interestingly, however, Hoisl (2007) found that while more mobile inventors were relatively more productive than inventors who were not mobile, more productive inventors were less likely to move. Furthermore, Schankerman et al. (2006) did not find any evidence that matching is an important incentive for movement in the software industry. They found instead that the asymmetry in information between employer and employee on the value of an invention as an important determinant of a move. Unlike other studies of inventor mobility based on cross-section analysis, Geuna et al. (2006) followed Zucker et al. (2002) and utilised a discrete-time duration analysis approach to study the determinant of mobility of academic European inventors using inventor survey data (PatVal) and the corresponding patent level data. They found the value of invention and inventor age as significant determinants of mobility from academia. Counterintuitively and opposite to the findings of Zucker et al. (2002) for the case of academic scientists, but similar to Hoisl (2007), they did not find the quantity or the quality of scientific and technological research output as significant drivers of mobility. In fact, they found that academic inventors with higher number of publications, patents and citations as less likely to move another university or to a private company. They further found similar results when binary and multinomial logit models are used 7

instead (Crespi et al., 2007). However, it is not clear if their findings can be generalised due to the small sample used and the use of academic inventors only. A recent closely related study using duration analysis approach is Palomeras and Melero (2010). They investigated three potential determinants of inventor mobility: the quality of the inventor s knowledge, the degree of complementarities between that knowledge and the knowledge of other inventors in current employer, and the inventor s expertise relative to a potential employer s core expertise. Using discrete-time duration analysis estimated with probit random effect models based on patent data from inventors working at IBM, unlike the two previous studies they found that the probability of institutional mobility increases with the quality of work, decreases with knowledge complementarity with current employer, and increases when the inventor s expertise is in the new employer s core areas in which it is not a dominant player. Unfortunately, because of the use of inventors from one specific firm from a specific industry, the authors cautioned about the generalisability of their findings. Nakajima et al. (2010) also estimated duration models using Weibull hazard regression estimation approach and U.S. patent data to investigate whether or not networked inventors have longer tenure. An inventor is networked in period t if his/her coinventors before period t are affiliated with his/her current employer at the beginning of current employment spell. They found that such networked inventors had longer tenure than nonnetworked inventors. More importantly for our discussion, they also found evidence that more able inventors are more mobile. Unfortunately, given their specific interest, their specified models appear to have inadequate control variables commonly used in other similar studies and thus it is not clear how robust and unbiased their findings are. 8

In terms of the reliability of patent data to study inventor mobility, Lenzi (2009) provides some interesting insights based on her comparisons of inventor mobility measured by the listed assignees in the patent document and inferred from inventor survey. As expected, she found that patent data understated the extent of inventor mobility. Even among inventors with only one patent, about half of them actually moved to different employers. She also found that inventors were not always affiliated with the listed assignees, especially for the case of university or public research institutions. The most relevant part of her study is that she used Cox semiparametric approach to estimate duration analysis models with multiple failures to study the determinants of academic inventor mobility using her data. She found mobility to be positively correlated with age and being male and negatively correlated with working at a university. Furthermore, unlike Zucker et al. (2002), she found the quantity of past performance (measured by the number of patents) as more important drivers of mobility than the quality (measured by the number of citations). However, while her use of survey data is beneficial since it allows for a more precise definition of inventor mobility, the small sample size and the limitation of the sample on only including academic inventors reduce the generalisability of her findings. Researchers have also attempted to characterise the sources of the link between inventor mobility and performance. For example, Hoisl (2009) differentiated the inventors along their inventive performance dimension. Using German inventor survey data, she found that the link between inventor mobility and productivity is not linear: only inventors at the upper end of the productivity distribution who benefit from the move relative to nonmovers. At the lower end, she found educational background as a more important determinant of productivity. 9

Another interesting study, Cabagnois (2010) looked at the impact of French, British, and German inventors' institutional mobility on their productivity using USPTO patent applications data from 1968 to 2002, differentiating between internal movements to an institution that they had worked in the past and external movement to an institution that the inventor had never worked for before. He found the overall impact of the mobility on inventor productivity (measured by the number of USPTO patents produced) is positive but weak. More interestingly, he found the distinction he made external mobility is associated with a reduction in inventor productivity; whereas internal mobility is associated with an increase in research productivity to be important. Other related studies focus on the link between inventor mobility and knowledge flows. For example, Singh and Agrawal (2011) found that when firms hired inventors, they were not only able to use the skills of the inventors for new research project, but they were also able to access the inventors stock of knowledge from past inventions. Their finding that hiring firms significantly increased their exploitations of the new hires prior patents after the recruitment highlights the importance of job matching incentive from the hiring firms point of view as another significant determinant of institutional mobility which may be linked to post-hiring performance of both the firms and the inventors. Finally, instead of institutional mobility, geographical mobility of inventors has also become the focus of recent research. For example, Miguélez et al. (2010), for example, studied the geographical mobility of inventors across European regions. Similar to other studies in this area, they also utilised patent data to trace the movements of inventors across Europe. Their findings confirmed the findings of earlier studies on the spatial mobility of highly skilled individuals (Maier et al., 2007). More interestingly, similar to 10

the findings of Fallick et al. (2006) on the close relationship between labour mobility and geographic agglomeration, Miguélez et al. found that the localised nature of knowledge flows identified by earlier studies such as Breschi and Lissoni (2009) was related to the localised aspect of inventors geographical mobility. 3. Empirical model and data 3.1 Model specification Our empirical modelling strategy follows Zucker et al. (2002) s duration model specifications, which are in turn based on insights from standard labour mobility theoretical and empirical models such as Spence (1973), Topel (1986) and Topel and Ward (1992). The underlying intuition of the duration model is that labour mobility decision is an outcome driven by observed signals which reflect the underlying labour quality and reservation wage. Following Zucker et al. s notations, if Q represents a vector of indicators of expected value of marginal product of an inventor, then the probability an inventor receives a wage offer z from a potential new employer that is higher than any given value is increasing in Q (that is, Pr( w o z; Q) G( z; Q), G Q ( z; Q) 0 ). Furthermore, since inventors wages are not observed from the patent database, we follow Zucket et al. in assuming that current wage is also a function of Q and that higher values of the elements in Q would shift G by more than they would shift the reservation wage R. Under such assumption, the probability of an acceptable offer from a new employer can be specified as Pr( w R; Q) G( R; Q), G ( z; Q) 0 o Q. 11

Therefore, denoting the probability of moving to a different employer at time t+1 conditional on reaching time t with the current employer (that is, the hazard rate of institutional mobility) as t, we can specify Q H it it ; it 1 it 1 as a function of the expected value of marginal product ( Q it 1 ) from the move and other factors that may also affect the hazard rate of a move ( H it 1 ), both of which are measured based on period t-1 observation in order to avoid any endogeneity problem during estimation (Zucker et al., 2002). More specifically, Q it 1 captures the effects of observed inventor heterogeneity in terms of ability proxied by past performance including inventive productivity (number of inventions) or the quality of inventions (number of citations received) and the characteristics of the knowledge field of the inventors (such as the role of tacit knowledge or the supply of people with relevant knowledge). On the other hand, H it 1 captures factors that affect the reservation wage including the costs of moving (such as current job match, age or gender or the characteristics of previous workplace). To estimate the effects of Q it 1 and H it 1, institutional mobility is inferred from a change in the listed patent assignee between two sequentially granted patents sorted according to the date of the application. However, by definition, we do not observe the exact time of the move and if two sequential patents list two different assignees, we can only assume that the inventor move sometime between the reported dates of application of those two patents. It is this censored nature of the underlying continuous duration data that directs our choice of estimation method (Han and Hausman, 1990). That is, as in Zucker et al. (2002), Nakajima et al. (2010) and Palomeras and Melero (2010), we use grouped discrete-time duration approach by imposing a discrete time structure on the data. More An inventor i s move is assumed to occur between periods t and t+1 if Assignee it 12

Assignee it+1 where t and t+1 refers to a discrete unit time corresponding to inventor i s patent application dates. In this paper, we use year as the unit time interval as explained in more details below. Strictly speaking, a change in the assignee name may not always mean that the inventor moves to different employees (Geuna et al., 2006). It may also result, for examples, from research collaborations, strategic alliances, mergers, or spin offs. Unfortunately, due to the lack of any further information, it was not possible for us to identify which assignee changes corresponded to actual job moves. However, Zucker et al. (2002), for example, distinguished between these two sources of academic scientists institutional mobility and found similar findings with regards to the determinants of mobility. Also, in the regression models we include the number of listed assignees as a control variable to control for such specific cases of institutional mobility. Another common problem in inferring inventor s institutional mobility from granted patent data as described above involves multiple changes in assignees that imply movement from and back to the same assignees. While it is possible for people to move from one employer to another employer and then move back to the original employer, the use of patent documents to infer such movement may suffer from over estimation of mobility. Here, the most common remedy taken is to employ a strict mobility definition where only a complete change in affiliation is allowed and any implied period of overlapping employment or spell within spell is not allowed (Hoisl, 2007; Nakajima et al., 2010). Other alternatives include the use of a more loose definition of mobility on the argument that the overlapping spells reflect part-time employment or, as mentioned earlier, collaboration relationship (Zucker et al., 2002) or by avoiding the multiple moves 13

problem altogether (focusing only on the first move or a single randomly selected move). 1 However, each of these steps may introduce sample selection bias in an unclear direction. Because Lenzi (2009) found that patent data underestimate mobility and because we want to assess the sensitivity of the findings or earlier studies which imposed such data adjustments, we decided to just clean the names of the inventors and the assignees as best as we could and use the implied mobility as is. 2 Furthermore, as discussed earlier, because our measure of inventor mobility is inferred from at least two patents produced by the inventors, by definition the more patents produced the higher the probability to be observed as mobile. As result, researchers who used standard mobility measures such as the number of moves or whether or not a an inventor has moved, were forced to look at only a single employment change (usually either the first change or a randomly selected change) in order to avoid the spurious relationship between inventor mobility and performance. 3 In contrast, by specifying a duration analysis model to study the determinants of inventor s institutional mobility we can actually model the complete history of inventor employment mobility, even when mobility can only be inferred from patent data. 4 1 Laforgia and Lissoni (2006) discussed the implications of listed multiple assignees when patent data are used to measure mobility. 2 In the rare event that an inventor s patents indicated multiple changes in employment within the unit time interval (one year), we followed Nakajima et al. (2010) s correction by imposing the restriction that there is only one employment change in a year at maximum. Also, when multiple assignees are listed in sequential patents, the assignee chosen as the employer is the one that maintain the employment spell of the inventor. 3 Hoisl (2009), for example, selected one employment change randomly when the inventors being studied move multiple times during the study period. 4 Furthermore, with the duration analysis, we do not need to exclude inventors with only one patent in the database and let the model handles the censoring during the estimation. However, given that by definition it is impossible to observe a move for inventors with only one patent and in order to allow for comparisons with earlier studies, in this paper we restrict our sample to inventors with at least two patents. 14

There are other advantages from modelling the complete history of inventors employment spells as opposed to just modelling a single spell. For example, we can investigate the role of observed characteristics which change with time. We can also specify a model that is better in taking into account duration dependence (how likely an inventor moves as he/she works for a longer period with their current employer). In addition, allowing for multiple spells means that we can investigate if the order of the move is important and investigate if each move is associated with a risk restart that is consistent with single spell modelling. In this paper, we model the complete history of inventor mobility provided by our U.S. patent data. We allow repeated mobility in the sense that all employment spells across different employers are considered and assume that the time at risk resets after each move. We also include dummy variables of the overall spell sequence and cluster the standard error on inventor ID in order to allow for more flexibility in the model while recognising that each period is subject to a decision of the same inventor. We create a sequence of time intervals from beginning to end of spell and assume year as a unit of interval. For each interval, we create a binary variable moved to indicate movement from current employer to a different employer in the next period as described earlier. We model the probability of move to occur in period (t, t+1] (the probability that assignee t assignee t+1 ) as a function of information in t-1 in order to avoid any possible contemporaneous endogeneity between the dependent and independent variables. We estimate the models using GLM model estimation approach with binary distribution family and cloglog-link to mimic proportional hazard model (Stewart, 1996; Jenkins, 1995 and 1997). 15

Table 1 lists the proxy variables we use for each determinant of inventor mobility that can be constructed using our patent data and their expected signs. As discussed above, we consider a number of determinants to control for both variations in the expected marginal productivity from a move ( Q it 1 ) and variations in reservation wages or moving costs ( H it 1 ). For the former we use measures of past inventive performance (number of patents produced in the immediate and in all periods prior to the move to capture the quantity aspect of performance and the (normalised) number of citations received by past patents to capture the quality aspect of performance). 5 It is possible that the number of citations captured both inventor ability and the tacitness of the inventor s knowledge. In particular, there is evidence that it both proxies the value of patent and reflects the quality of the invention (Harhoff et al., 2003). Based on Zucker et al. (2002) s argument, with a higher value of the invention and the level of natural excludability of the underlying knowledge (through a combination of a higher level of tacitness and scarcity of the new knowledge), the mobility of the inventors becomes an even more important mechanism for technology transfer (see also Zucker et al. 1998a and 1998b). We use an additional measure of tacitness of knowledge by including the total number of coinventors in the past. In addition to Zucker et al. (2002) s argument above, Agrawal (2006) and Agrawal et al. suggested that the importance of tacit knowledge may come from the possibility that the complementary knowledge to realise the invention is too costly or impossible to codify in the patent application or that it was not necessary to claim priority over the invention. Zucker et al. (2002) used coauthoring as indicator of 5 The citing propensities vary across technological fields, thus a simple count of received citations may be biased against patents in fields in which patent citation practice is less intensive. Our normalised measure of received citation count is adjusted for patent citation intensity at the three digit paten class level following Marini (2004). 16

bench-level collaboration and thus a measure of tacitness. They argued that a higher degree of tacitness is expected when more new authors in an area of research are publishing with at least one old author as the coauthor. In our model, we simply argue that as research project involves more collaborative partners, the importance of tacit complementary knowledge increases. Thus, the higher the number of inventor i s past coinventors, the higher the probability that inventor i is possessing knowledge with a high tacit component. In other words, following Almeida and Kogut (1999), inventors who collaborated with other inventors may be more likely to tacitly held an important component of the knowledge underlying the patented invention. Table 1: Determinants of inventors institutional mobility Determinants Proxy Expected sign Inventor ability Inventor s recent productivity (Number of patents in year t-1) + Inventor s past productivity (Number of all patents up to year + t-1) Tacitness of Inventor s quality of work (Average number of citations + knowledge received up to year t-1 (normalised)) Average number of co-inventors up to year t-1 + Outside opportunity Inventor s fields of expertise (Average number #of IPC 4 + technology class of past patents up to year t-1) Match quality with Refereed to current assignee before being affiliated with it - current assignee (Has co-inventors who were affiliated with current assignee in the past) Known by current assignee before being affiliated with it (Has - patents in the past which were cited by other inventors affiliated with current assignee) Inventor Age (year of inventor s 1 st US patent) - demographics Female - Current employer characteristics Other control variables Assignee s age (Year of current assignee s 1 st US patent)? Assignee s size (Log number of inventors with US patents affiliated with current assignee) Co-workers age (Average age of co-workers in the current assignee = average year of co-workers 1 st US patents) Co-workers heterogeneity (standard deviation of co-workers age) Number of assignees and claims in past patents, technology area dummy, annual career sequence dummy? - -? 17

We should note that the number of co-inventors in a single patent can also be interpreted as capturing team size and reflecting the value of resources allocated to the project and thus the value of the patent (Hoisl, 2009). However, what we use in the estimation is the average number of co-inventors in all past patents that an inventor has instead of just the number of co-inventors in any particular patent. Furthermore, to some extent, the value of the patent is captured by the number of citation received. Thus, it is plausible that our measure can be interpreted more as reflecting the scope of the inventor s network than the value of his/her research project. We posit that as the importance of tacit knowledge increases in an inventor s field of research, the higher the needs of him/her as collaborator and the higher the average number of co-inventors in past patent. Furthermore, we also constructed two coinventorship measures depending on the nationality of the inventor. Palomeras and Melero (2010) use coinventorship as a proxy of complementarities between a given inventor and his/her co-workers. In that case, instead of capturing the inventors tacit knowledge, our average number of coinventors may also capture moving costs (the extent of current job match). In order to distinguish between the two effects, we also split the number of coinventors into the number of domestic (Australian) and foreign (American, European and Japanese) coinventors. We expect that the effects captured by foreign coinventorship reflect more of the inventor s tacit knowledge than the complementarity between his/her knowledge and that of his coworkers. In contrast, the domestic coinventors may reflect more of the complementarity of knowledge with current co-workers. In other words, it is plausible that if collaboration reflects the importance of tacit knowledge of an inventor then an international collaboration should reflect it even more than domestic collaboration. 18

The last measure of expected marginal productivity ( Q it 1 ) is outside opportunity. Here we assume that inventor i s outside opportunity is positively correlated with the breadth of his/her research area as captured by the number of different technology class across all past patents. In other words, inventors with less diverse patenting areas are more likely to have their research that is more firm-specific and less valued by other firms (Hoisl, 2007; Palomeras and Melero, 2010). It can also be argued that the technology breadth of one s inventions reflects the scarcity of his/her knowledge. In terms of reservation wage or moving costs, we consider the level of matching with the current employer and a number of individual characteristics which may determine inventor i s individual preference with regards to institutional mobility. Here, the key channel from preference to mobility is the reservation wage. The lower the moving costs, the lower the reservation wage would be and the higher the probability of a move. We use two measures of the level of current job match. The first one, Refereed to current employer is an indicator variable with a value of one if inventor i collaborated in the past (that is, prior to being affiliated with his/her current employer) with other inventors who worked for inventor i s current employer (Nakajima et al., 2010). Here we assume that inventor i was matched with his/her current employer and because of that he/she has a relatively higher level of match than those who had not receive such a matching service. The idea of the second measure is similar, except that the matching service is more passive. If inventor i s current employer is more familiar with his/her past works by citing his/her patents, then the level of inventor i s current job match is more likely to be higher (Singh and Agrawal, 2011). 19

Other individual characteristics that are positively correlated with moving costs include age (older inventors are more likely to be settled for personal/family reason and thus are less likely to move), gender (females face more constraint for personal/family reason) and career stage (those in the later stage of their career the earlier their first U.S. patent is are less likely to move). One may argue that age may also capture experience (Hoisl, 2009), so that it is not clear if experience and mobility would be positively correlated or not. Finally, we also include firm specific factors and other control variables which may affect institutional mobility through both Q it 1 and H it 1 with less clear expected sign of the direction of the effect. These include the size of the employer, the average and standard deviation of inventors age, the breadth of employer s fields of research, and the number of years in the last spell. For example, a larger employer may be able to provide better employment benefits and security and thus is positively associated with moving costs. 3.2 Data The main source of the data used in the empirical analysis of this paper is the NBER U.S. Patent Citations Database (Hall et al. 2002). This database contains all granted U.S. Patents from 1975 to 1999. In addition to the NBER database, this paper also uses the National University of Singapore (NUS) U.S. patent database which provides information on the actual date of application of the granted U.S. patents. From the patent database, all Australian inventors are identified based on the country code of the residential address of the listed inventors. 20

In order to identify the institutional mobility of Australian inventors, a number of data cleaning steps were taken following some of the common practices in the literature such as the ones advocated by Lissoni et al. (2010). These include, for example, addressing the names game problem names are the same, but the persons are different or names are different but the persons are the same arising from the lack of any standard inventor identification number in U.S. patent administrative data. The resulting sample consists of 9,676 Australian inventors accounting for a total of 17,002 U.S. patents granted in 1975-1999. On average, a single Australian inventor has 2.3 U.S. patents granted in that period. Further data cleaning steps were taken for the names of the institution where the inventors work. Here we follow the literature by assuming that the listed patent assignee(s) are the employer(s) of the listed inventor(s). In reality, this may not always be true and thus we need to further assume that in that case the error is random with respect to the relationship that we are estimating. 6 After all the data cleaning steps and the exclusions of inventors with missing values in any of the proxy variable, we end up with a sample size of 2016 inventors with at least two U.S. patents. Table 2 provides a summary of univariate statistics of the various variables used in the estimation of the discrete duration models. From Table 2, for example, only 3.8 per cents of 2016 Australian inventors in the sample are female. On average, they have 4.8 U.S. Patents granted between 1975 and 1999, with an average grant year of 1984. In terms of mobility, the average number of institutional 6 Hoisl (2007) checked the assumption that the listed assignee on the patent document was in fact the employer of the listed inventor by comparing patent documents of European inventors and the employment information from a survey of European inventors. She found that 92% of survey respondents were employed by the assignees indicated in the patent document. 21

moves (assignee changes) is 1.5. The maximum number of assignee moves is 53 and the maximum number of U.S. patents is 71. The former appears to be excessive; however, 98 per cent of the inventors in the sample have less than 13 moves and, therefore, we do not expect that our model estimates would be biased by a spuriously high number of moves of a few inventors. Table 2: Sample descriptive summary Variables Mean Min. Max. Std. Dev. Inventor characteristics Age (Year of first US patent) 1984.2 1966 1997 6.968 Female 0.038 0 1 0.192 Number of assignee moves 1.507 0 53 3.847 Number of US patents 4.816 2 71 5.458 Average number of (non-self)citations received per patent 16.127 0 346 22.142 Average number of inventors per patent 2.846 1 19 1.732 Number of IPC4 technology class per patent (normalised) 0.924 0.167 1 0.153 Has ever been previously refereed to assignee 0.214 0 1 0.410 Has ever been previously cited by assignee 0.035 0 1 0.184 Assignee characteristics Average age of assignees (based on year of assignees 1980.0 1909 1998 8.945 first US patent) Average size of assignees (based number of inventors 38.611 0.667 1391 118.143 with US patents who are affiliated with the assignee) Average age of employees (average years of first US 1988.3 1974 1998 4.530 patent of all other inventors affiliated with the assignee) Std. Deviation of age of employees 3.902 0 10.536 2.447 Average number of 3-digit IPC of all patents of the 38.918 1 275 51.454 assignee Other control variables Have US patent in each of the following technology area: electricity 0.089 0 1 0.285 instruments 0.186 0 1 0.389 chemical 0.277 0 1 0.448 proces 0.190 0 1 0.392 mechanical 0.193 0 1 0.395 Highest number of assignees in a patent 2.806 1 43 3.211 Average number of claims per patent 19.294 1 338 16.693 Sample size (number of inventors with non-missing observation used in the full history discrete duration model estimations) Source: Processed from NBER U.S. Patent Database 1975-1999. 2016 22

4. Results and discussions Table 3 presents the estimated coefficients, the standard errors and the corresponding marginal effects of the determinants of Australian inventor s institutional mobility. Two sets of estimates are presented depending on which average number co-inventors is used. Model 1 uses the total average number of co-inventors in past patent as a proxy for knowledge tacitness. Model 2 disaggregates the measure according to specific countries of the co-inventors, namely the United States of America (US), Japan (JP), European countries which are contracting states to the European Patent Convention (EU), and Australia (AU). From the first set of columns under the label of Model 1 presented in Table 3, inventor ability is positively correlated with inventor mobility. Inventors with a higher number of patents in the immediately preceding period are, on average, around ten percentage points more likely to move to a different employer between period t and t+1. Interestingly, when past performances are considered, it is their quality instead of quantity that matters the most as shown by a much higher estimated marginal effects from the average number of citations to past patents (0.042) than from the number of past patents (0.002). To some extent, this finding that it is the quality of past performance rather than the quantity that is the more important determinant of inventor institutional mobility is consistent with the finding of Zucker et al. (2002) for the case of star scientists. One possible reason is because, as discussed earlier, our measure may capture both the quality of the inventors and the value of the invention (that is, the tacitness and scarcity of the knowledge). Also, 23

note that our finding that inventor quality is more important is opposite to the finding of Lenzi (2009) for the case of academic inventors. 24

Table 3: Discrete duration analysis estimates of the determinants of inventors institutional mobility (Dependent variable: Moved = 1 if assignee it+1 assignee it ; 0 otherwise) Determinants Model 1 Model 2 Inventor s characteristics Coeff. Std. Err. dy/dx Coeff. Std. Err. dy/dx No. of patents in year t-1 0.031 0.017 0.010 * 0.027 0.017 0.008 No. of all patents up to year t-1 0.005 0.003 0.002 * 0.006 0.003 0.002 * Average no. citations received up to t-1 0.138 0.026 0.042 *** 0.113 0.028 0.035 *** Average no. of co-inventors up to t-1-0.007 0.017-0.002 Average no. of US co-inventors up to t-1 0.077 0.026 0.025 *** Average no. of JP co-inventors up to t-1 0.290 0.061 0.092 *** Average no. of EU co-inventors up to t-1 0.113 0.035 0.036 *** Average no. of AU co-inventors up to t-1-0.174 0.026-0.055 *** Average no. of IPC4 patent class up to t-1 0.085 0.263 0.032 0.169 0.272 0.054 Refereed to current employer -0.098 0.082-0.031-0.181 0.083-0.056 ** Cited by current employer 0.008 0.185 0.002-0.048 0.188-0.015 Age -0.023 0.006-0.007 *** -0.013 0.006-0.004 *** Female -0.059 0.161-0.019 0.094 0.177 0.031 Number of years in current spell (log) -0.287 0.034-0.092 *** -0.288 0.035-0.092 *** Current assignee s characteristics Size of assignee (log) 0.172 0.044 0.055 *** 0.123 0.043 0.039 *** Age of assignee -0.004 0.006-0.001-0.007 0.005-0.002 Mean age of co-workers -0.088 0.009-0.028 *** -0.088 0.009-0.028 *** Std. dev. of age of co-workers 0.003 0.018 0.001 0.005 0.018 0.001 Number of 3 digit patent class of assignee -0.002 0.001-0.000-0.001 0.001-0.000 Other control variables Highest no. of assignees in past patents -0.112 0.022-0.036 *** -0.107 0.021-0.034 *** Average no. of claims in past patents 0.007 0.003 0.002 *** 0.009 0.003 0.003 *** Number of observations 6607 6607 Pred. Pr[Moved=1] 0.432 0.426 Log pseudolikelihood -3618-3507 Note: *, **, *** indicate statistical significance at the 10, 5, and 1% level respectively. Regressions also include unreported control variables in the form of annual career sequence dummy variables and technology dummy variables which indicate if the inventor has patents in broad technology areas: electricity, instruments, chemicals, process, and mechanical. Robust standard errors are adjusted for clustering by inventor ID. 25

However, unlike our expectation, the results of Model 1 indicate that the inventor s tacit knowledge does not appear to be statistically significantly related to the probability of an institutional move. On the other hand, inline with our expectation, the results of Model 2 seem to support our conjectures that if collaboration reflects the importance of tacit knowledge that an inventor has, then his/her international collaboration would reflects it even more strongly. Interestingly, the estimated effect for the number of Australian (that is, domestic) co-inventors is negative. As discussed earlier, one other possible aspect of invention characteristics that can be captured by the number of co-inventors beside the tacitness of the underlying knowledge of the inventor is the value of the invention. 7 If that is the case, we still expect a positive correlation between the number of co-inventors and the probability of a move since a higher invention value reflects a higher ability of the inventor. The fact that only the number of Australian co-inventors is negatively correlated with mobility seems to suggest that research collaborations with other domestic researchers in Australia (relative to those with inventors from other developed countries) are, on average, not correlated with either the underlying value of the invention or how tacit is the underlying knowledge or both. Instead, the above finding may reflect our earlier conjecture that the number of Australian co-inventors also captures more of the moving costs aspect associated higher knowledge complementarity with coworkers. 8 In fact, Palomeras and Melero (2010) found that the probability of move is lower for IBM inventors who had more coinventors and attributed the finding to the effects of higher knowledge complementarities between 7 That is, patents with a higher number of co-inventors are usually thought of as revealing a higher valuation of the invention. 8 Another possibility is that domestic collaboration captures Australians working with mates culture effect.this finding probably deserves further analysis in the future. Also, we should note that the estimated models include the number of inventors working for the same employer to capture the moving costs. 26

the inventors and their coworkers (coinventors). It is plausible if that this is what we found from our domestic coinventors effects. In terms of the costs of moving, the estimates shown in Table 3 s second column show that inventors who have a better match with their current employer are less likely to move. Those who were refereed to their current employer are between 3.1 (Model 1) and 5.6 (Model 2) percentage points lower in the average probability of moving to a different employer in the next period. However, being known to the current employee through less formal engagement such as through prior citations does not appear to capture the same extent of employer-employee match. For other more standard proxies for moving costs, inventor s age and the length of current tenure are negatively correlated with the probability to move. Lastly, for employer characteristics, inventors working with older inventors as their coworkers are less likely to move. This probably captures the stocks of knowledge and experience available within current employer s environment that reduce the attractiveness of outside opportunities. However, employer s age and firms technological diversities do not appear to be important. Thus, if our previous interpretation is correct, co-workers age instead of employer s age appears to be a better measure of knowledge and experience of a company that is relevant to a particular employee s level of job match. In order to assess the robustness of our findings, particularly with regards to the possible spurious relationship between the number of patents and institutional mobility, and to allow for direct comparisons to existing studies and thus provide an assessment of the merits of duration analysis in the study of inventor mobility, we re-estimate Model 2 27

using four different subsamples drawn the same sample used earlier. The estimated marginal effects for each model are summarised in Table 4. The first two models in Table 4 (Models 3 and 4) are the single spell versions of the full history models presented in Table 3. Their estimation purpose is to further rule out any systematic feedback from the underlying patent data that leads to a positive but possibly spurious relationship between productivity and mobility. We ask whether or not our findings presented earlier are robust when only a single spell is considered. To operationalise the idea, we randomly select a spell for each inventor (Model 3) and consider only the first spell (Model 4). As can be seen from the first two sets of estimated marginal effects in Table 4, our earlier findings are relatively robust on the number of spells being included in the discrete duration analysis. If the positive correlation between past performance and mobility is purely driven by how mobility is measured, then we expect the single spell estimates of marginal effects should be both less significant statistically and, more importantly, in magnitude than the estimates from the full employment history data. 28