An empirical analysis of the impact of semiconductor engineer characteristics on outflows and inflows: evidence from six major semiconductor countries

The impact of cross-border migration of semiconductor engineers has become an important concern for many countries’ economic policies. There has been limited large-scale data analysis regarding the movement of semiconductor engineers between countries. This study creates an original engineer database for six major semiconductor countries (U.S., China, Taiwan, Japan, Korea, and Germany) using bibliographic information on patents and papers to analyze their transnational migration. Multiple logistic analysis is conducted on the impact of engineers’ characteristics such as age, skills, and areas of expertise on outflows and inflows. The analysis reveals that (1) the United States, Taiwan, Japan, and Germany have excess outflows of engineers, while China and South Korea have excess inflows, (2) the movement of engineers between the United States and China is the most frequent, and (3) there is a significant outflow of engineers from semiconductor fields in which each country specializes.


Introduction
In recent years, securing semiconductors has become a life-and-death national security policy for countries, and governments and companies worldwide are competing to secure the semiconductors they need. In 1971, the American company Intel invented the microprocessor (central processing unit), and its sales grew rapidly thereafter (Wicht 2021). Until the 1970s, the United States was the top semiconductor country, but in the 1980s, Japanese semiconductors became the world's number one. Nevertheless, in the 1990s, Japan's semiconductor industry began to decline (Sekiguchi and Okada 2021), and Korea, Taiwan, and China have been growing to replace Japan's position. Japanese and American semiconductor manufacturers are now overtaken by Taiwan Semiconductor Manufacturing Company (TSMC) Ltd. in terms of technology and South Korea's Samsung in terms of sales volume (Wicht 2021). Ohota (2021) explained that the strength of TSMC, a major semiconductor company in Taiwan, is that it attracts incredibly talented people and huge amounts of money to the company. According to Ohota (2021), Chinese semiconductor companies, such as HiSilicon, have gathered the best and brightest talents to form a group of brains that can develop breakthrough technologies at an astonishing speed, thus creating the world's top-level technological capabilities. In other words, the semiconductor industry is dominated by countries and companies that have acquired the best brains.
Such cross-border movement of human resources is typically analyzed using immigration data (Beine et al. 2011). Testing the brain exchange hypothesis requires uniform statistical data from each country on outflows and inflows, but in practice, countries use different criteria to classify migrants, making it difficult to test (Milio et al. 2012). Consequently, in an attempt to conduct an empirical analysis of brain drain and brain exchange, the analysis of the outflow and inflow of workers with specific skills and knowledge, rather than mere migrants, has not been examined on a systematic and global level due to data limitations.
Therefore, this study investigates the cross-border inflows and outflows of semiconductor engineers worldwide. Specifically, bibliographic information from three data sources (patent data, article data, and grant data) is used to extract engineers' affiliations and research themes, and the status of the flow of engineers to and from semiconductor companies in different countries is analyzed. Particularly, this study focuses on the six major countries in the global semiconductor market, namely, the United States, China, Taiwan, Japan, South Korea, and Germany.
The structure of this paper is as follows. Section 2 presents the previous studies. Section 3 provides an overview of the data, and Sect. 4 discusses the global mobility of semiconductor engineers. Section 5 presents the analysis results on the relationship between the characteristics of engineers and the outflow/inflow of engineers. Finally, Sect. 6 presents the discussion and conclusion.

Theory and hypothesis
The term "brain drain" was coined in the 1950s to describe the phenomenon of highly skilled, qualified, and competent people leaving their home countries and migrating to other countries (Baruch et al. 2007;Docquier and Rapoport 2012;Giannoccolo 2009;Godwin et al. 2009;Grubel 1994;Johnson 1967;Subbotin and Aref 2021). In the late 1960s, research on brain drain showed that the flow of people was biased in one direction, from emerging countries to rich countries (Baldwin 1970;Carrington and Enrica 1999;Carrington 1996;Reynolds and McCleery 1988). In the 1970s and 1980s, brain drain analysis was conducted from the perspective of sending countries (Enke 1969;Joyce and Hunt 1982) and receiving countries (Agarwal and Winkler 1985;Reynolds and McCleery 1988), respectively. Furthermore, recently, studies on the phenomenon of the outflow of talented people from developed countries (e.g., New Zealand and Italy) to other countries have been conducted (Altbach 2013;Carr et al. 2005;Duch et al. 2019;Glass and Choy 2001;Le 2008;Milio et al. 2012).
In the 1990s, the other side of the brain drain phenomenon, that is, "brain gain," began to be pointed out (Tung and Lazarova 2006). Research on "brain gain" can be divided into three main categories. First, traditionally, it refers to the so-called reverse migration, in which countries that have experienced an exodus of skilled human resources acquire an increasing number of highly skilled human resources by, for example, welcoming returnee immigrants as highly trained and competent (Carr 2006;Inkson et al. 1997). Second, it refers to the education effect, where the average education level of the rest of the population who did not migrate rises because of the increased educational acquisition level of the sending country's citizens who wish to work in the international market (Beine et al. 2011;Dodani and LaPorte 2005;Stark et al. 1997;Stark 2004). Third, accepting high-skilled workers will also receive knowledge and skills embedded in the heads of high-skilled workers, leading to knowledge spillovers (Straubhaar 2000).
As described above, previous studies have demonstrated that brain drain used to be biased toward the movement of people from poorer to richer countries; however, in recent years, the brain drain from developed countries to other countries has been confirmed, and brain gain is considered to contribute to knowledge spillover and higher education levels. This leads to the idea that the ratio of brain drain to brain gain may be balanced, as the top six countries in the semiconductor industry all have high technological and economic levels. The first hypothesis is as follows.
H1: Brain drains and brain gains in the major semiconductor countries are balanced. Chambers et al. (1998) pointed out that "brain gain" is also important in relation to "learning-by-doing" and "learning-by-hiring". The term "learning-by-hiring" refers to acquiring knowledge by hiring experts from other companies (Song et al. 2003). For example, a Korean electronics manufacturer hired many engineers who were transferred from Japanese electronics manufacturers (Fujiwara and Watanabe 2021). The reason behind hiring outside engineers and experts is effective for knowledge spillover is that the mobility of engineers serves as an effective channel for organizations to acquire outside knowledge and technology (Palomeras and Melero 2010). There have been many previous studies on the migration of engineers and scientists and knowledge spillover, most of them are concerned with the impact on the organizations and researchers in the destination countries (Lacetera et al. 2004;Slavova et al. 2016;Tzabbar 2009). For example, Fujiwara and Watanabe (2017) analyzed the characteristics of engineers who moved from Japanese electronics manufacturers to Korean and Chinese firms and found that semiconductor-related engineers moved to Korean firms and smartphone-related engineers moved to Chinese firms, that those moving to Korean firms were older and those to Chinese firms were younger; moreover, engineers with strong ties to central figures were more likely to move. The following hypotheses are derived from these previous studies.
Hypothesis 2: The characteristics of engineers flowing in and out of each country differ in terms of age, field of expertise, etc.

Data
This study builds an original data set by aggregating information on affiliations, research themes, and achievements for each engineer and researcher using a combination of three data sources: the European Patent Organisation PATSTAT database (approximately 100 million records), publication database (approximately 180 million records), and grant database (approximately 700,000 records) built by ASTA-MUSE Corporation. PATSTAT is a patent database provided by the European Patent Organisation, which contains application data since January 1964 and is updated twice a year. Patent data have been used in various previous studies because they contain detailed information on the characteristics of patents, such as the name of the inventor, filing date, technical field, and name of the organization to which the patent belongs (Rosenkopf and Almeida 2003;Scherer 1982). Specifically, tracking inventors and their organizational affiliations in patents over time can be used to infer inter-firm mobility (Singh and Agrawal 2011). This heuristic tracking of patents by the same person also allows for the construction of a dataset on the career history of each inventor (Breschi and Lissoni 2009;Marx et al. 2015;Trajtenberg et al. 2009). Moreover, the affiliations of the organizations will be confirmed by the article and grant databases for the accuracy of the career history construction of engineers and researchers. The grant data are from four North American, 16 European, 12 Asian, and 2 Oceanian organizations, for example, the National Science Foundation, United Kingdom Research and Innovation, and European Research Council. The article database includes major articles from Nature, ScienceDirect, Springer Link, and Wiley Online Library. From these data, information such as researcher name, ID, DOI, e-mail address, title, affiliation, category, and coauthor was extracted and compared with patent data to construct a more accurate original database of engineers and researchers. For each person in the database, information on affiliation and year of application/publication is linked to create a time series data. PATSTAT provides 17.4 billion names of people and 2.5 million organizations, whereas the papers and grants database yields 61 million names of people and 20,000 organizations. The first step is to simply extract the person's names and then link them to organizations, dates, and collaborators. The text was then extracted by natural language processing and vectorized. In addition to preprocessing, such as lowercasing, stopword deletion, and stemming, term frequency-inverse document frequency is used to calculate the feature degree of the word vectorization. Moreover, latent semantic indexing is used to compress the dimension. Additionally, the same process is applied to the title keywords, and the words whose feature value exceeds the threshold are considered keywords. After these cleansing processes, candidates with a high possibility of being identical are connected. In doing so, the rule engine is run for the combinations of the proximities of dates, text vectors, and title keywords, commonality of organization names, and agreement of collaborators. The scores are then calculated. Each combination is weighted according to the rule, and the weighted average is used to calculate the total score. The combinations whose total score exceeds the threshold are considered as the same person. This is represented as an undirected graph in graph theory. To ensure accuracy, the maximum flow and minimum cut theorems were used to cut people with low overall scores to be included in a different graph, and cases of clearly different organizations and people were separated. As a result, the fit rate, reproducibility, and F value were 95.2%, 86.6%, and 90.7%, respectively, for the person name, and 94.3%, 94.3%, and 90.7%, respectively, for the tissue name. 86.0%, F value 90.0%. Thus, very high accuracy of name identification and classification was achieved. The database of engineers completed because of this name-gathering process includes the following information: name of each engineer, the transition of the organization to which he or she belongs, research in which he or she was involved, the citations and other evaluations of each research, and the names of co-authors. These processes allow us to track which organizations individual engineers belonged to over a certain period, how well they performed there, with whom they collaborated, and to which organizations they subsequently moved.
Using the database of engineers and researchers obtained through data processing, engineers belonging to semiconductor companies and their subsidiaries were narrowed down by company name. Furthermore, changes over time in the companies they belong to were tracked. In this study, focusing on outflows to and inflows from overseas, domestic and overseas migrations were distinguished based on the address of each company in the transition of the companies they belonged to.

Methods
The dataset is constructed by extracting engineers who have changed their organizations in the semiconductor industry. To test Hypothesis 1, that is, are the outflowing and incoming engineers in equilibrium, the target data will be divided into two groups, the inflow and outflow groups, and an inter military comparison will be performed. Specifically, among engineers in the six major semiconductor countries, those engineers who have moved out of the country and those who have moved in from outside the country are classified into two datasets, the outflow group and the inflow group, respectively. Subsequently, the characteristics of the engineers, such as age and field of expertise, are examined to see if they differ between the two groups.
To test Hypothesis 2, odds ratios were obtained for the outflow and inflow groups using multiple logistic regression analysis with outflow as the objective variable. Multiple logistic regression is a statistical method that explains and predicts the likelihood of an "outcome" (the target variable) occurring from many factors (explanatory variables). Only data with complete information on all variables among the mobile engineers were used for the analysis. Meanwhile, the statistical analysis software Stata 15 was used for statistical processing, and the significance level was set at 5%.
Extant studies have used variables such as age, previous performance, and centrality as determinants of engineer migration (Fujiwara and Watanabe 2017;Tzabbar 2009). Following previous studies, this study classifies explanatory variables into three categories: personal skills, previous work experience, and semiconductor field of expertise as factors affecting the outflow and inflow of engineers to foreign countries.
In terms of the relationship between personal attributes and skills and migration, previous studies have shown that age (Plane 1993), education (Carrington and Enrica 1999), and social connections (Reher and Silvestre 2009;Singh and Agrawal 2011) influence migration decisions. Therefore, factors related to personal skills include estimated age at times of mobility, research productivity skills, and communication skills. Estimated age at times of mobility is a continuous variable that indicates the estimated age at which a person moves from a previous job to the current job. Research productivity may also influence the decision to move. Marx et al. (2015) noted that brain drain is more pronounced for personnel doing higher-impact work. Therefore, the number of papers and patents published up to the point of migration was used as a variable indicating research productivity skills. Additionally, Marx et al. (2015) specified that collaborative people with connections to many collaborators tend to flow out. This is because they can receive offers and increase their visibility through their collaborative ties. Therefore, the communication skills of engineers were measured by the degree of centrality of social network analysis. The degree centrality is calculated for each person (node) by networking the joint application and joint research relationships at each institution every 5 years. The larger the value of degree centrality, the more experience the person has in collaborating with many researchers in the organization.
Next, concerning the relationship between the migration of an engineer and previous employment, hiring firms are significantly more likely to refer to patents of the migrating engineer's previous organizational affiliation ( Almeida and Kogut 1999;Rosenkopf and Almeida 2003;Song et al. 2003). Additionally, as engineers move between firms, a knowledge spillover occurs, in which the knowledge and skills that engineers acquired in their previous jobs are embedded in the individual and transmitted to the hiring firm (Rosenkopf and Almeida 2003;Zucker et al. 1998). Therefore, two variables, the estimated length of employment at a previous job and the evaluation of the works were established as proxy indicators of what the engineer experienced in the previous job. Estimated length of employment at a previous job indicates the length of time the engineer was employed at the previous institution before moving organizations. Meanwhile, the evaluation of the works is a scoring of the engineer's patents and papers in his or her previous job. Astamuse calculates the value of a patent on the basis of the number of citations, the number of years required from the filing of the application to the acquisition of the patent, and the ratio of the effective remaining life of the patent from the evaluation reference date.
The fact that a patent is often cited in a later patent application means that the patent has significant technical value (Youngberg and Hall 2020).
For the engineer's field, logic, foundry, and memory were selected. Wafers were excluded from the semiconductor fields because of the lack of applicable data. Furthermore, manufacturing equipment and photoresist were excluded from the analysis because they were highly correlated with other explanatory variables, causing multicollinearity. The field of the engineer's affiliation is a binary variable that depends on whether the engineer belongs to the category or not.
Thus, the dependent variable is a binary variable indicating the outflow and inflow of engineers to foreign countries.

Status of outflow and inflow of semiconductor engineers from various countries
This section provides an overview of the migration status of engineers. For engineers who are confirmed to have moved multiple times, the last move will be used More than 8 years as the target of judgment. Table 1 presents a summary of the original data set used in this study. The total number of confirmed inter-organizational mobility among engineers in the semiconductor industry is approximately 22,000. Moreover, the timing of mobility indicates when the mobility took place, and inter-organizational transfer indicates whether the movement is a cross-border movement or not. The table shows that many engineers move within domestic firms, but many also move to overseas semiconductor companies. The field of expertise of the engineers was estimated on the basis of the company they belonged to before moving. Logic includes communication chips (fabless), microcontroller units, and analog. For example, Intel, Qualcomm, HiSilicon, and UniSoc were classified as companies in the logic field. For foundries, companies such as TSMC, Global Foundries, and HLMC were included in the classification. However, the memory includes SK hynix, CXMT, and YMTC for DRAM and NAND, and ASM and Shin-Etsu Chemical for wafers. The manufacturing equipment includes the AMAT, ASML, and AMEC, whereas photoresists include JSR and Fujifilm. Lastly, "others" include automobile and electric manufacturers. From this data set, it is clear that many engineers belong to the field of memory and logic. The estimated age during mobility assumes that the first time the engineer applied for and published a patent or a paper was at the age of 28, which is the average age of completion of a doctoral course. Results show that the engineers who move are young, in their 20 s and 30 s. Lastly, the estimated length of employment at a previous job shows that the experience of the mobile engineers in their previous jobs is dispersed from less than 1 year to more than 8 years. Table 2 shows the cross-tabulation results of the countries with the largest number of people for the country of affiliation of the following: engineers who moved to another company, company before the move, and company after the move. Other countries include France, the Netherlands, Italy, and Finland.
This table allows us to determine whether each country is experiencing a net outflow of semiconductor engineers (i.e., more outflow than inflow) or a net inflow (i.e., more inflow than outflow). A horizontal view of the graph shows that 2,329 engineers moved from the U.S. to overseas in the first row, while a vertical view of the graph shows that 1724 engineers moved from overseas to the U.S., providing a net outflow situation. Similarly, the table shows that China and South Korea have a net inflow, whereas Taiwan, Japan, and Germany have a net outflow.
Next, the sending and receiving countries of the technicians are as follows. As shown in Table 2, the largest number of engineers moved from the United States to China, followed by the move from China to US companies and from Germany to US companies. For the movement from Taiwanese companies to companies in other countries and regions, China shows the largest number. Although the United States is the second-largest recipient of outflows from Taiwan, notably, almost no outflows exist from Taiwan to countries other than the United States and China.
Furthermore, the status of each host country is as follows. The largest number of engineers from other countries hired by Japanese companies is from the United States. The top countries from which Chinese companies recruit are the United States, Taiwan,  and Germany, and the number of engineers from these countries is also enormous. Most engineers from other countries hired by US companies are from China, but a relatively large number of engineers moved from Germany, South Korea, and Japan. The largest number of engineers accepted by Taiwanese companies is from Chinese companies, but this number is small compared with the number of engineers hired by Chinese companies from Taiwanese companies. Table 3 provides a detailed look at the semiconductor fields of mobile engineers. The largest number of inter-organizational mobility is in the memory field, followed by the logic field. In many countries, such as China, Japan, South Korea, and Germany, the number of incumbent engineers in the logic field is high, whereas, in the United States and Taiwan, the number of engineers in the logic field is small. Meanwhile, the mobility of engineers in the wafer field is overwhelmingly dominated by Japan, followed by Germany and the Netherlands. Table 4 provides an overview of the dataset used for the analysis. The data show that both the inflow and outflow are dominated by relatively young engineers in their 20 s and 30 s; moreover, the fields with large outflows and inflows differ by country. Table 5 shows the comparison results between the inflow and outflow groups for each of the six major semiconductor countries. The estimated age of both the outflow group and the inflow group is approximately 30 years, indicating that most engineers move overseas at a relatively young age, approximately 30 years. Additionally, the evaluation of the work at the time of migration tends to be higher for engineers who flow out from Japan, Korea, and Taiwan. Table 6 shows the multiple logistic regression analysis results with the outflow to foreign countries as the objective variable in six major countries in the semiconductor industry. For the United States, research productivity skills, communication skills, and logic fields were significantly higher in the outflow group than in the inflow group (p < 0.01). Particularly, being in the logic field was significantly higher with an odds ratio of 5.33 (p < 0.01). Next, looking at China, the research productivity skills, logic, foundry, and memory variables were significantly lower in the outflow group than in the inflow group (p < 0.01). In Taiwan, logic, foundry, and memory were all significantly higher in the outflow group than in the inflow group (p < 0.01). The odds ratios were 26.4, 199.6, and 12.51 for logic, foundry, and memory, respectively, with significantly higher outflows in all major IC fields. For Japan, the outflow group was significantly higher than the inflow group in terms of the number of days of employment at the previous job (p < 0.01). For Korea, the outflow group was significantly higher than the inflow group for estimated age and memory (p < 0.01 or p < 0.05). Particularly, the odds ratio for memory is 232.3, which is significantly higher for outflow. Finally, looking at Germany, we can see that the variables of estimated age, number of days in the previous job, and memory were significantly higher for the outflow group than for the inflow group (p < 0.01 or p < 0.05).

Discussion
Traditionally, the outflow of highly skilled and talented brains has been considered a major economic loss for sending countries that have invested in their education (Saxenian 2002). However, this analysis of the international mobility of engineers from six major semiconductor countries confirmed that the flow of human resources is not biased in one direction, and there is an exchange of ideas with inflows and outflows in both directions. In other words, it was shown that in the semiconductor industry, not only is one country in a state of loss due to the outflow of human resources, but human resources are fluid between countries. However, the flow of human resources is not completely balanced, with some countries, such as the U.S., Taiwan, and Japan, having more outflows than inflows, while other countries, such as China and South Korea, have more incoming engineers than outflows. Particularly in today's knowledge-intensive economy, preventing brain drain is an important policy issue (Marx et al. 2015;Zucker et al. 1998), and governments have begun focusing on efforts to prevent brain drain and to attract the best brains from abroad (Carr et al. 2005;Le 2008;Welch and Zhen 2008). Particularly, Welch and Zhen (2008) specified that East Asian countries, especially South Korea and Taiwan, have been making early efforts to change the flow of brain outflow. Following their example, China has been trying to prevent brain outflow and to acquire brains recently. The results of this study show this point in the data.
Moreover, until recently, the flow of skilled professionals was still heavily skewed from south to north, with the United States considered the main beneficiary (Ellerman 2006;Giannoccolo 2009). However, net flows are particularly high between the United States and China, indicating a juxtaposition of outflows and inflows. Moreover, the movement of human resources between other countries is frequent, indicating that the United States is no longer the only beneficiary, but that a multilateral exchange of brains is occurring.
The study analyzed the impact of characteristics, such as the quality and composition of engineers on the inflow and outflow. Results reveal that for factors related to personal skills, the influx of engineers had higher research productivity skills than the outflow of engineers in China and Germany. Saxenian (2007) named foreign-born immigrants from China, Taiwan, India, and other countries who were educated in the United States or gained experience in high-tech companies as new Argonauts. He also pointed out that they maintain connections with companies in their home countries and contribute to the economic and technological development of their countries. For example, China has promoted a policy called the Hai Gui policy, which encourages talents to migrate abroad to gain advanced knowledge and skills and then return home to contribute to the development and R&D of their home country (Hao and Welch 2012;Hu and Cairns 2017;Welch and Zhen 2008). This study showed that in China, engineers with relatively low research productivity are flowing out and those with high research productivity are flowing in. Hence, the effects of these policies may be manifested.
On the other hand, regarding Germany and Altbach (2013) pointed out that although it is a major academic power, a serious brain drain exists in this country. However, the results of this study reveal that Germany appears to be succeeding in attracting an influx of talented people.
In terms of communication skills, in the United States (Japan), outgoing (incoming) engineers have higher communication skills. Fujiwara and Watanabe (2017) pointed out that engineers who move from Japanese firms to foreign firms, such as China and Korea, are not necessarily central and prominent figures; those are only personnel who shadow the central figures, which is consistent with their findings.
Next, the analysis of engineers classified by field showed that in Taiwan, the outflow of foundry engineers was far greater than the inflow. This is followed by the engineer outflow in the logic field and then in the memory field. Meanwhile, the United States engineers in the logic field are notably more likely to flow out. For Korea, the outflow of engineers in the memory field is significantly more significant than the inflow. However, for China, engineers in logic, foundry, and memory are more likely to flow in than out.
The analysis revealed that the outflow of engineers tends to be greater than the inflow from abroad in the semiconductor fields in which each country excels. Taiwan's outflow of engineers is higher in the foundry field, the United States in the logic field, and Korea and Germany in the memory field. For example, the outflow of engineers in the foundry field in Taiwan is much higher than the inflow. Meanwhile, in the foundry field, Taiwan has an overwhelming 71% global market share (Ohta 2021). The acquisition of engineers in the foundry field in Taiwan is presumed to be a learning-by-hiring process, as specified by Fujiwara andWatanabe (2017, 2022), where engineers are hired from outside to acquire the technology they want to obtain (Song et al. 2003). Regarding the US semiconductor industry, Wicht (2021) specified brain drain as a reason for Intel's fall from being the world's largest chip maker, and the present study confirmed this with data. However, China tends to see an inflow of engineers rather than an outflow in logic, memory, and foundries, suggesting that this is closely related to the inflow from Taiwan.
As described above, a simple observation of the number of engineers flowing in and out of the semiconductor industry shows that engineers are moving in and out of the industry as a whole, but with some bias. However, an analysis of the technical content suggests that the movement of engineers who are considered to possess cutting-edge technology is biased in one direction. The results suggest that the winners in this case are the countries that have developed policies to attract the best and the brightest.

Conclusion and policy implications
To the best of our knowledge, there has been no study that has analyzed the landscape of transnational migration of human resources, especially engineers with the critical technology of semiconductors, using large-scale data. This is because obtaining timely and detailed statistical data on the outward migration of human resources has been considered difficult with traditional data sources (Milio et al. 2012). In this study, however, a unique data set was constructed by carefully tracking the affiliations and research achievements of many engineers in the semiconductor field to empirically analyze the status of brain exchange. The findings of this study provide new insights that governments can use to develop policies for migrating highly skilled people, especially in the semiconductor field.
Although each country will differ in terms of which of the semiconductor fields (logic, foundry, memory, etc.) are important, each country should critically consider policies to prevent the outflow and promote the inflow of engineers in the fields where they are needed. Thus, policymakers should keep in mind that young engineers in their 30 s or so who belong to fields in which their country excels and have high research productivity are likely to leave the country. For example, Fujiwara (2016) pointed out that Japan was slow to take action on policies to prevent the outflow of engineers overseas, resulting in the outflow of many talented people to neighboring Asian countries, causing significant losses. Additionally, to promote the inflow of talented engineers, higher salaries and other institutional arrangements should be taken into account.
The methodological contributions of this study can also be applied to other countries and industries as an analytical framework for examining the impact of engineer migration on human resource policies in a country's priority sectors. This study used the semiconductor industry as a case study to analyze the international mobility of engineers, and by applying similar methods to other industries, it should contribute to the formulation of policies to prevent the outflow of engineers in important industries in each country and to attract talented engineers from abroad. Furthermore, while most previous studies on engineer migration have focused on post-migration effects (Lacetera et al. 2004;Palomeras and Melero 2010;Slavova et al. 2016;Tzabbar 2009), this study is a new perspective, focusing on the relationship between engineer characteristics and the flow of engineers into and out of foreign countries. The results are also useful for managers of companies involved in semiconductors. This is because it reveals the tendency of engineers who are likely to leave the company. If managers want to retain talented people, they should manage young researchers who have high research productivity in each technical field and are close to key personnel to ensure that they are not dissatisfied with their work environment.
Despite this study's contributions, it has some limitations. First, this study focused on the international mobility of engineers in the semiconductor sector. It would be more substantial if the same method could be extended to other industries to learn about the actual situation in other industries and to make comparisons between industries. Second, this study focused on the semiconductor industry and the dataset was constructed focusing on countries with many mobile engineers; thus, all the countries included in the analysis were economically rich. Future studies can consider outflows and inflows from developing countries where the number of mobile engineers is small. International mobility of engineers in other industries and between countries with economic disparities is a topic for future research. discussions with the Ministry of Economy, Trade and Industry and seminar participants during the research process. I would like to thank all parties involved in this research.
Author contributions This paper was written by one author. Rie Osawa and Yuki Nakatsuka of Astamuse, Inc. assisted in the preparation of the data.

Data availability
The patent data used in this study is PATSTAT, published by the EPO, and is available on the Internet. The data that support the findings of this study are available from Astamuse but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are, however, available from the authors upon reasonable request and with permission of Astamuse. This study uses patent data that is publicly available information. This data is available at The official website of the European Patent Office. (https:// www. epo. org/) The article and grant data are owned by Astamuse, and the final data set is also owned by Astamuse.

Declarations
Conflict of interest This manuscript has not been published or presented elsewhere in part or in entirety and is not under consideration by another journal. The study used publicly available data and, thus, no informed consent was required. I have read and understood your journal's policies, and I believe that neither the manuscript nor the study violates any of these. There are no conflicts of interest to declare.
Ethical approval This research is based on the bibliographic information of patents and papers that are publicly available. It is a study that created an original database from bibliographic information. Therefore, it does not fall under the category of research requiring ethical approval or informed consent.
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