A structural study of Big Tech firm-switching of inventors in the post-recession era

The original CPN ($C_{1}$) consisting of 74,637 inventors (as nodes) is connected by 372,245 edges or unique co-authorships⁵⁵5Because the CPN is undirected, a co-authorship relation is counted only once. In the future, we will also consider the weighted version of this network.. The degree distribution of $C_{1}$ follows a power-law distribution with a gamma value of -2.32. Despite the large number of inventors, only a small fraction ($\sim$2.5% or 1,900 nodes) are singletons, indicating a relatively well-connected network. The average inventor in this network has co-authored patents with approximately 10 other inventors, with the most prolific inventor having co-authored with 460 others. The network is divided into 3,598 connected components (including singletons), with the largest connected component consisting of 66,818 inventors. The density of the network is relatively low ($\sim$0.000134), implying that it is still quite sparse, despite the inventors being divided only among five unique organizations. However, as expected from the social nature of such collaborations, the average clustering coefficient is moderately high ($\sim$0.675), which indicates substantial clustering and transitivity among the inventors.

We also computed the degree distribution of the nodes corresponding to the 1,340 inventors who transitioned only once from 2010 to 2022 within the network graph $C_{1}$. Figure 2 (a) and (b) illustrate the overall degree distribution (all nodes) in $C_{1}$ as well as the degree distribution of the subset of 1,340 nodes in $C_{1}$. We then ranked these degrees and compared the ranks with respect to the overall network. We found that 80.61% of the transitioning inventors are in the top quartile (25%) of all nodes, and 95.07% of the transitioning inventors are within the top half (50%) of all nodes. These are significantly higher than would be expected for a random sample of 1,340 nodes selected from the network. These numbers suggest that the majority of transitioning inventors have high degree centrality, indicating some degree of influence (at least in a local sense) within the network. However, by calculating the clustering coefficient for each of the transitioning inventors in $C_{1}$ and subsequently averaging these coefficients, we derive an average local clustering coefficient of approximately 0.379 for the these transitioning inventors, which is lower than the network average of 0.675. This suggests that transitioning inventors are structurally embedded in a more star-like structure: all collaborators of transitioning inventors do not themselves collaborate on the same patents as often. In other words, transitioning inventors are co-authoring patents with groups of inventors between whom the only connection is the transitioning inventor themselves.

Recall that we had also constructed the subgraph $C_{2}$ that only contains as nodes the 1,340 inventors who transitioned just once from 2010 to 2022. We found that $C_{2}$ is denser ($\sim$0.000791) than $C_{1}$ while having lower average clustering coefficient (0.0986) than $C_{1}$. Among the 1,340 inventors, there are 710 co-authorship connections, but nearly half of the 1,340 inventors have not co-authored patents with any others in $C_{2}$ (although they have co-authored patents with inventors in the larger network $C_{1}$). These transitioning inventors therefore have fewer co-authorship connections on average, as evidenced by an average degree of approximately 1.06 and a maximum degree of 13. The shape of this degree distribution is illustrated in Figure 2 (c). While the data is too small to conclusively interpret the shape as that of a scale-free distribution, it is also not inconsistent with such a distribution.

The ‘remaining’ network, $C_{r}$, which mainly consists of inventors who have not transitioned, has a slightly lower average number of co-authorship connections per inventor compared to $C_{1}$. Additionally, the number of inventors without any co-authorship increases, suggesting that the removal of transitioning inventors led to some inventors in $C_{1}$ becoming isolated. We explore fragmentation due to the removal of these nodes in more detail subsequently. As expected, the density of $C_{r}$ is lower than that of $C_{1}$, indicating less intense collaboration among the remaining inventors.

We evaluated the fragmentation caused by the removal of these 1,340 inventors on the CPN by comparing the number of connected components and the average clustering coefficient between the original network ($C_{1}$) and $C_{r}$ (the network after removing the transitioning inventors), as well as a network generated by randomly removing 1,340 inventors from the original network. Compared to $C_{1}$, the average number of connected components in $C_{r}$ increases to 3,952. This indicates that transitioning inventors play a bridging role in the innovation ecosystem, which was also suggested earlier by their lower clustering coefficient (but higher degree centrality) compared with the overall network. There are now (i.e., after removing the transitioning inventors) more isolated groups of inventors who are interconnected within their groups but not connected to other groups in the network.

Note that this fragmentation is greater than would be expected by chance, lending an affirmative answer to the second part of RQ1. To quantify this, we performed an experiment where we randomly removed an equivalent number of inventors (1,340) from the network $C_{1}$, as noted above. We repeated this process independently 100 times, and averaged the number of connected components across these 100 iterations. This average (3,897.1 connected components) is found to be significantly lower than 3,952 (N=100, p = $1.46\times 10^{-9}$, one-sided Student’s t-test). This suggests that transitioning inventors play a greater role in maintaining the network’s global connectivity than a random group of inventors embedded in the same environment (the five Big Tech firms), as their removal results in slightly increased fragmentation compared to the removal of a random set of inventors.

Similarly, the average clustering coefficient exhibits interesting behavior upon the removal of inventors. The average clustering coefficient in the remaining network ($C_{r}$) is 0.674. This suggests that, on average, the remaining inventors in $C_{r}$ still tend to form moderately interconnected groups. Despite the network fragmentation caused by the removal of the 1,340 inventors, collaboration among groups of inventors remains largely unaffected, as indicated by the similar average clustering coefficient in $C_{r}$ and $C_{1}$.

In contrast, when we repeatedly remove a random set of 1,340 inventors from the network, the average clustering coefficient of the nodes in the remaining network is slightly lower, at 0.660. This value is also found to be significantly lower than 0.674 (N=100, p = $4.074\times 10^{-20}$, one-sided Student’s t-test). This indicates that the removal of the specific group of transitioning inventors results in a network ($C_{r}$) that maintains slightly higher transitivity as compared to the network resulting from the random removal of inventors.

The primary focus of RQ2 is to examine if the rate of transition of the 1,340 inventors from 2010 to 2022 is relatively stable over the period of study, or if it peaks (or shows other irregularities) during some periods. We also seek to investigate if transitioning occurred uniformly often between the five organizations, or if some organizations are, in fact, over-represented in terms of out-transitions or in-transitions than would be expected through chance alone. As a first step toward these investigations, we determined an estimator for the transition time $T_{t}$ when an inventor transitioned from the first organization to the second organization. To do so, we identified when a transitioning inventor filed their last patent with the first assignee organization and when they filed their first patent with the second assignee organization. The estimate of $T_{t}$ was then calculated the midpoint between these two points in time⁶⁶6In a slight abuse of terminology, we continue to refer to this estimator as $T_{t}$, rather than the unknown variable itself (mathematically representing a more ‘exact’ time when the inventor transitioned from the first to the second organization) that is being estimated.

Figure 3 illustrates the number of inventors transitioning from their initial assignee organization to their second assignee organization each year. We show company-segregated distributions for both incoming and outgoing transitions (and for each year) to gain deeper insights into the trend. Among the 1,340 inventors who transitioned just once from 2010 to 2022, Microsoft, on average, had the most significant outflow of inventors, while Meta had the lowest. Regarding transitions into the companies, Google, Amazon, and Meta have the highest average influx of inventors. Therefore, outflowing transitions were significantly more skewed than incoming transitions, which were more evenly divided. Furthermore, the annual rate of inventor transitions suggests that there is a peak from 2015 to 2017 for both outgoing and incoming transitions. Together, the figure shows a concentrated transitioning period between the assignee organizations, which further implies that the innovation ecosystem within these organizations underwent a non-trivial shift (with the greatest changes suggested for Microsoft) during a relatively brief 3-year period.

While the results in Figure 3 are illustrative, they are tabulated at the granularity of years. To gain further insight into these transitions at a finer granularity (which is also useful because the rate of transition increases during a relatively narrow time period of 2-3 years), we compute two additional variables for each transitioning inventor: first, we record the time when they first filed a patent with their first assignee organization as their ‘innovation start’ time $T_{s}$. Similarly, we marked the time when they last filed a patent with their second assignee organization as their ‘innovation end’ time $T_{e}$. This period between the start and end times is referred to as the ‘innovation period’⁷⁷7It bears noting that these terms should only be interpreted in the context of this study and time period e.g., some inventors may have been innovating in other organizations (e.g., startups acquired by some of these organizations, or research labs) before or after the time period of study. The ‘innovation end’ time therefore should not be ‘literally’ taken to imply that the inventor has stopped innovating or filing patents.. Given these additional variables, we sought to identify the periods during which transitions occurred most frequently at a finer granularity (quarters or 3-month periods, rather than years). To achieve this, we utilized a moving three-month window that starts from January 2010 and is incrementally rolled (in increments of one day) all the way until December 2022. Within each such window, we determined how long each inventor was associated with either the first or second assignee.

Formally, this calculation may be described as follows: first, for every inventor $i$ in each window, we calculated the length of time spent innovating in the first assignee organization. We do so by measuring the time from the window’s start (or from $T_{s}$ if it commenced after the window began) to either the window’s end or $T_{t}$ (the time of transition), whichever was sooner. This quantity represents the duration that $i$ filed patents with, when they were employed by their first assignee organization. We denote this duration as $D^{1}_{i}$. Similarly, we can compute such a duration ($D^{2}_{i}$) where $i$ filed patents with their second assignee organization, by measuring the length of time from the later of the window’s start, or $T_{t}$, and ending at the earlier of the window’s end or $T_{e}$. An example of this procedure using actual data is illustrated for a small set of transitioning inventors in Figure 4 (a).

Using this procedure, we calculate the total ‘duration’ of innovation in the first organization within a window, by summing all individual durations (namely., the ‘blue’ bars in Figure 4 (a) within a ‘red’ window, but for all transitioning inventors rather than just the ones shown in the figure) for the first organization. We denote this total duration as $D1$. Similarly, we can compute the total duration for the second job (the sum of all the green bars in a red window) for all inventors within a window, as $D2$. Denoting the number of all transitioning inventors as $I=1340$, we can now compute the proportion $\frac{D2}{D1}$ within each window, and plot this proportion against the mid-point of the window (which spans 3 months).

The results are illustrated in Figure 4 (b). We can use the plot to determine when transition, as a measure of this relative proportion of innovation activity in the first versus the second assignee organization, exhibits the most significant change. We do so by examining the slope of this curve. We are specifically interested in identifying a two-year span with the steepest slope. A steeper slope indicates a more rapid change in the ratio $\frac{D2}{D1}$. Our analysis indicated that the derivative of the segment from December 2014 to November 2016 remains high (with a short blip in late summer 2016) before declining secularly afterward. This supports the previous result that the most pronounced transition happened in this period, but it also shows that rates had been increasing leading up to this period, before declining continuously after this period. Further investigation of this period, as well as hypothetical causes for a sustained high transition rate, could be an interesting area for further sociological research exploring innovation patterns in Big Tech.

RQ3 aims to investigate whether the transition between assignee organizations has had a positive impact on the inventors’ ability to produce more high-impact inventions. We note at the outset that determining impact of an innovation, especially in the technology industry, is a controversial topic [25], because the impact could occur over long time horizons, be an indirect enabler of other technologies, and is not always measurable using simple metrics. Nevertheless, one way of examining the impact is by considering the citation count of an inventor’s patents before and after an inventor transitions. Done in aggregate across all patents filed by the 1,340 transitioning inventors from 2010 through 2022, this count allows us to gauge (in a limited, but still reasonable, manner) the potential association between transition and innovation impact.

One bias that must be accounted for before computing such an association is that patents filed earlier will obviously be expected to receive higher citation counts. Hence, we standardize or ‘normalize’ the citation count $P_{t,o}$ for a patent filed in year $t$ and by an inventor currently in organization $o$ by adopting the following methodology: for each unique combination of year ($t$) and organization ($o$), we calculate the mean ($\bar{P}_{t,o}$) and standard deviation ($s_{t,o}$) of citation counts for all the patents filed within that timeframe and in that organization. We can then normalize $P_{t_{o}}$ and represent it as a new variable $Z_{t,o}$ using standard Z-score normalization:

By implementing such a Z-score normalization, we are now able to derive a normalized citation count, or estimated impact, for each patent within our dataset. Similarly, we can calculate the estimated impact for an inventor over a given time period by averaging the estimated impacts of all patents filed in that time period where that inventor was a co-author. With these measures of estimated impact, we investigated RQ3 by first calculating the average estimated impact for each inventor using the patents filed in the entire time period before the inventor transitioned⁸⁸8Using the terminology introduced earlier for RQ2, this would be the average estimates impact of all patents where the inventor was a co-author in the period $T_{t}-T_{s}$; recall that both of these estimators apply individually to each inventor., as well as the inventor’s average estimated impact after the transition. Because these two estimates are obtained for each of the 1,340 transitioning inventors, we obtain two ‘paired lists’ (representing before and after impacts for the same inventor). Subtracting the ‘before transition’ estimated impact from the ‘after transition’ impact, we obtain a single vector containing the estimated excess impact (due to transition) for each of the 1,340 inventors. We plot the distribution of this estimated excess impact as a histogram in Figure 5. A paired Student’s t-test showed evidence in favor of the research hypothesis that the after-transition impact is greater than the before-transition impact (i.e., we were able to reject the null hypothesis convincingly; N=1,340; p= 0.00025).

While this result would need to be replicated for other measures of estimated impact, and other normalization procedures, it does suggest that the innovation potential of Big Tech has likely been improved, rather than diminished, due to such switching activity (whether voluntarily intended⁹⁹9Transitioning or switching does not always imply volition on the worker’s part. In some cases, the first assignee organization may have terminated the worker, while in other cases, the worker may have been induced to leave and join the second organization. Controlling for volition in such analyses is an important, but difficult, study that future sociological research may want to consider. by the worker or not).