Skip to main content

Optimal Career Strategies and Brain Drain in Academia


Some areas of science face the problem that many academics prefer the private sector over academia. This negatively affects the quality and the quantity of the research output as well as the availability of competent lecturers in these areas. The present paper investigates by means of an optimal control model how the reward of competencies in research and teaching in the private sector affects investments into these skills as well as the decision on whether and when to optimally leave academia. As the decision between academia and industry is obvious if a scientist has strong preference for either, we focus on scenarios where this is not the case. We notably show that the dynamic trade-off between academia and industry results in various forms of brain drain. In this regard, we first confirm that if academic competencies are well rewarded in the private sector, the most competent academics will leave academia. Further, we find scenarios where a scholar with intermediate competencies will try to improve his or her skills as much as possible before leaving academia and scenarios in which it is optimal to not put much effort into work and let competencies slowly depreciate before leaving. Even if scientists are highly skilled and motivated to stay, if poor working conditions do not support knowledge acquisition, competencies will inevitably fall and academia will consist solely of mediocre scholars. The results suggest that brain drain can be destructive for academia in the long run.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. In the business academic discipline, for instance, doctoral programs give graduates options for professional versatility; see [7].

  2. According to [9], taste for science means a strong preference for freedom to choose research projects, the ability to publish and the desire to conduct basic research.

  3. By “scientist” we actually refer to all kinds of staff doing scientific work including professors, researchers and lecturers. Note that scientists with non-permanent employment contracts might face uncertainty about whether an academic position can be maintained over the course of their career. We assume for simplicity that scientists do not include this uncertainty in their general career planning.

  4. Below we omit time argument \(t\) unless necessary.

  5. Within this paper, we study the case where the scientist can leave the academic sector and join, e.g., a private firm, but switches back are not possible. In general, moving back to academia is possible and leads to interesting questions for further research. However, in this case the second period in the non-academic sector would also have to be modeled with continuous time.

  6. The third and fourth eigenvalues can also be expressed analytically, but they are omitted here because they are not necessary for the proof.

  7. By publication lists, extent of previous teaching activities, rewards, evaluations, etc.

  8. By the term “scientist starts at the dashed (dotted, dashed-dotted) line” we mean that \((x_{10},x_{20})\) lies on the dashed (dotted, dashed-dotted) line.

  9. Here we assume parameters \(b_1\) and \(b_2\) are smaller than the parameters used for the calculations of Fig. 5. For \(b_1=b_2=0.5\), the additional complementary term would simply increase the attractiveness of the private sector such that it would always be optimal to leave.

  10. Parameters \(b_1\) and \(b_2\) are the same as in Fig. 5.


  1. The Royal Society: The scientific century: securing our future prosperity. RS Policy document 02/10 (2010). Accessed 25 Feb 2014

  2. Austin, A.E.: Preparing the next generation of faculty: graduate school as socialization to the academic career. J. High. Educ. 73(1), 94–122 (2002)

    Article  Google Scholar 

  3. Stephan, P.E.: How economics shapes science. Harvard University Press, Cambridge (2012)

    Book  Google Scholar 

  4. Toole, A.A., Czarnitzki, D.: Commercializing science: Is there a university “brain drain” from academic entrepreneurship? Manag. Sci. 56(9), 1599–1614 (2010)

    Article  Google Scholar 

  5. Balsmeier, B., Pellens, M.: Who makes, who breaks: Which scientists stay in academe? Econ. Lett. 122(2), 229–232 (2014)

    Article  Google Scholar 

  6. Fritsch, M., Krabel, S.: Ready to leave the ivory tower? Academic scientists’ appeal to work in the private sector. J. Technol. Transf. 37(3), 271–296 (2012)

    Article  Google Scholar 

  7. AACSB: The promise of business doctoral education: Setting the pace for innovation, sustainability, relevance, and quality. AACSB International Report (2013). Accessed 11 March 2014

  8. Sauermann, H., Roach, M.: Science PhD career preferences: levels, changes, and advisor encouragement. PLoS One 7(5), 1–9 (2012). doi:10.1371/journal.pone.0036307

    Article  Google Scholar 

  9. Roach, M., Sauermann, H.: A taste for science? PhD scientists’ academic orientation and self-selection into research careers in industry. Res. Policy 39(3), 422–434 (2010)

    Article  Google Scholar 

  10. Sauermann, H., Roach, M.: Not all scientists pay to be scientists: PhDs’ preferences for publishing in industrial employment. Res. Policy 43(1), 32–47 (2014)

    Article  Google Scholar 

  11. Agarwal, R., Ohyama, A.: Industry or academia, basic or applied? Career choices and earnings trajectories of scientists. Manag. Sci. 59(4), 950–970 (2013)

    Article  Google Scholar 

  12. Dietz, J.S., Bozeman, B.: Academic careers, patents, and productivity: industry experience as scientific and technical human capital. Res. Policy 34(3), 349–367 (2005)

    Article  Google Scholar 

  13. Levin, S.G., Stephan, P.E.: Research productivity over the life cycle: evidence for academic scientists. Am. Econ. Rev. 81(1), 114–132 (1991)

    Google Scholar 

  14. Thursby, M., Thursby, J., Gupta-Mukherjee, S.: Are there real effects of licensing on academic research? A life cycle view. J. Econ. Behav. Organ. 63(4), 577–598 (2007)

    Article  Google Scholar 

  15. El Ouardighi, F., Kogan, K., Vranceanu, R.: Publish or teach? Analysis of the professor’s optimal career path. J. Econ. Dyn. Control 37(10), 1995–2009 (2013). doi:10.1016/j.jedc.2013.05.007

    Article  Google Scholar 

  16. Sethi, S.P.: Nearest feasible paths in optimal control problems: theory, examples, and counterexamples. J. Optim. Theory Appl. 23(4), 563–579 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sethi, S.P.: Optimal advertising policy with the contagion model. J. Optim. Theory Appl. 29(4), 615–627 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  18. Skiba, A.K.: Optimal growth with a convex-concave production function. Econometrica 46(3), 527–539 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dechert, W.D., Nishimura, K.: A complete characterization of optimal growth paths in an aggregated model with a non-concave production function. J. Econ. Theory 31(2), 332–354 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  20. Grass, D., Caulkins, J.P., Feichtinger, G., Tragler, G., Behrens, D.A.: Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror. Springer, Heidelberg (2008)

    Book  Google Scholar 

  21. Zeiler, I., Caulkins, J.P., Grass, D., Tragler, G.: Keeping options open: an optimal control model with trajectories that reach a DNSS point in positive time. SIAM J. Control Optim. 48(6), 3698–3707 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kiseleva, T., Wagener, F.O.O.: Bifurcations of optimal vector fields in the shallow lake model. J. Econ. Dyn. Control 34(5), 825–843 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Caulkins, J.P., Feichtinger, G., Grass, D., Hartl, R.F., Kort, P.M., Seidl, A.: Skiba points in free end time problems. J. Econ. Dyn. Control 51, 404–419 (2015)

    Article  MathSciNet  Google Scholar 

  24. Grass, D.: Numerical computation of the optimal vector field: exemplified by a fishery model. J. Econ. Dyn. Control 36(10), 1626–1658 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Gustav Feichtinger.

Additional information

This research was supported by the Austrian Science Fund (FWF) under Grants P25979-N25 and P25275-G11.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seidl, A., Wrzaczek, S., El Ouardighi, F. et al. Optimal Career Strategies and Brain Drain in Academia. J Optim Theory Appl 168, 268–295 (2016).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Mathematics Subject Classification