Re-Evaluating the Knowledge Production Function for the Regions of the Russian Federation


The present study picks up on the aspect of knowledge generation—a key part of every national innovation system—in the context of the Russian Federation. Following Fritsch and Slavtchev (2006), a knowledge production function can be used to account for the efficiency of an innovation system. In detail, this study implements a panel quantile regression estimation approach and thus presents a novel approach in studying national innovation system and, more specifically, their efficiency. In particular, a non-linear knowledge production function is estimated to quantify for a possible non-linear impact of knowledge inputs on domestically—sing patents from the Russian Patent Office—and internationally—using patents from the European Patent Office—oriented knowledge output. Using regional data, it is shown that a non-linear impact of the inputs especially on Russian domestic patents can be found. The results offer new insights into the structure of the Russian innovation system as a threshold is identified where the innovation system switches from increasing returns of researcher input to decreasing returns. This implies that only smaller research systems work efficiently, and starting from a size of approximately 900 researchers, their efficiency steadily decreases.

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  1. 1.

    A comprehensive analysis of the knowledge generation and transmission process can be found in Perret (2013).

  2. 2.

    At least, if transition statistics of the EBRD’s transition reports are considered, e.g., EBRD (2016), and one acknowledges that the transition process by far has not been successfully concluded, as fitting shown by Kasparov (2015).

  3. 3.

    Audretsch et al. (2014) provide a concise overview on the links between knowledge and innovation.

  4. 4.

    Note that Mathew (2012) provides an analysis, using quantile regressions, that is comparable in the same aspects to the one done in this study.

  5. 5.

    For example, Bitzer (2003) suggests a different approach to modeling a KPF and Kang and Dall’Erba (2015) argue on the importance of including spatial effects in the analysis.

  6. 6.

    Perret (2013) has shown that if both researchers and expenditures on R&D are included, biases due to high multi-collinearity arise. A large share of expenditures on R&D are spent on paying researchers, and thus, a high correlation between both variables arises.

  7. 7.

    See Griliches (1979).

  8. 8.

    Fritsch (2002) and Fritsch and Franke (2004) advocate the use of either researchers or R&D expenditures as knowledge inputs, though not both at the same time. As a large share of the R&D expenditures is used to pay for the researchers including both would lead to biases in the regression results.

  9. 9.

    In some sectors, like pharmaceuticals, the time frame might be much longer, while in other sectors, like food products, it can be much shorter.

  10. 10.

    See WIPO (2012b)

  11. 11.

    Officially, an application should be processed after 18 months.

  12. 12.

    While Fritsch and Slavtchev (2006) suggest that a 3-year lag offers the best alternative; Perret (2013) finds for the Russian Federation a lag of 2 years to provide the best results.

  13. 13.

    Note that in cases where a logarithm, aside from logarithm naturalis, has been implemented, the exponential function needs to be subsidized by a corresponding power function.

  14. 14.

    Even though it is recognized that limiting the study to the year 2012 does exclude recent development trends from a purely formal perspective, it is very convenient to stop in 2012. Until 2012, the regional layout across the Russian Federation has been relatively stable and all changes that did occur were only intra-regional or of an nominative nature. Stopping in 2012 excludes the regional re-allocations between Moscow city and the Moscow Oblast as well as having to argue the exclusion of the two de facto objects of Crimea and Sevastopol—if data were available at all—as they would significantly bias the results.

  15. 15.

    Furthermore, this high correlation might be considered a first indicator that both parts of the Russian NIS are connected.

  16. 16.

    The Nenetsia Autonomous Okrug is considered part of the Arkhangelsk Oblast and the Yamalia and Khantia-Mansia Autonomous Okrugs are considered parts of the Tyumen Oblast.

  17. 17.

    All variables implemented in this section enter the regression in logarithmized terms, except for shares. It can be argued that scaling the researcher variable by using per capita values would be more suitable for the overall validity of the estimation, to ensure comparability with other studies of KPF; however, absolute numbers are considered.

  18. 18.

    Integrating the GRP also allows one to control for business cycle effects.

  19. 19.

    See, for example, Kim (2010).

  20. 20.

    Imports impact innovativeness as it relieves pressure from domestic firms to innovate and provide products for their home market. Lichtenberg and van Pottelsberghe de la Potterie (1998) stresses that it is not so much the intensity of imports but the distribution of the countries of the origin of imports that matters; however, these effects are not accounted for in this study.

  21. 21.

    It is noted that a feedback relation between the generation of knowledge via patents and FDI flows seems highly likely even though respective tests do not yield corresponding results in this context.

  22. 22.

    The link between the market structure and the innovative output, the innovativeness of a region, is argued in detail already by Mansfield (1981), Cohen et al. (1987), Rothwell (1989), and Levin et al. (1991).

  23. 23.

    See respective reports by Yuri Levada Analytical Center (2012) or Russian Public Opinion Research Center / VCIOM (2012).

  24. 24.

    See Netter and Megginson (2001).

  25. 25.

    As with the researchers, it can argued that it might be more prudent to use per capita values instead.

  26. 26.

    Leite and Weidmann (1999) argues that corruption depends on natural resources, while Tompson (2006), a little less drastically, links corruption to large state-owned firms, which in Russia in particular persist in the oil and gas industry. Additionally, Verisk rates the Russian oil and gas sector as a sector of extremely high risk of corruption, going hereby in a similar direction as the EY report (EY 2014). It can, rightfully, be argued that in recent times, corruption also persists in other high-yield sectors like the defense industry or high-tech industries like the nano-tech industry; however, on the one hand, this study focusses on a period up to 2012, and thus, recent trends are only of partial interest. Also on the other hand, data has been available comprehensively for the full time period only for the oil and gas sector.

  27. 27.

    Note, in this context, also the proclaimed negative relation between resource endowments and economic growth which, in the literature, is referred to as the resource curse. See for a discussion of this phenomenon for example Auty (1993).

  28. 28.

    The indicator is calculated as the relation of the sum of exports and imports against the GRP. Even though the exports are as well part of the openness indicator, multicolinearity is no problem in this context.

  29. 29.

    The inclusion of the openness indicator might, however, not generate significant additional information as it basically replicates the effects of exports, imports and GRP in a composite form.

  30. 30.

    All monetary variables including the GRP, the exports, and imports as well as the FDI enter the model in real terms with the base year 1995.

  31. 31.

    Estimations have been carried out for a 2- and a 3-year time lag. In both cases, the results look almost identical. Therefore, only the results for 2-year time lag are presented herein.

  32. 32.

    Note that while the international perspective with patents from the EPO is mainly skipped due to the fact that the coefficients are nearly constant, a preliminary analysis of the residual deviation shows it to be highly non-linear and comparable to either a polynomial of the fifth order or a trigonometrical function. As both cases are not exactly solvable, this study restricts itself solely to the domestic perspective.

  33. 33.

    A figure for the case with a break at 25 patents has not been presented separately as the results would more or less copy Figs. 1114. Table 1 furthermore underlines the similarity of both cases.

  34. 34.

    Asterisks are used to signify significance. * is an error margin of 10%, ** of 5% and *** of 1%.

  35. 35.

    It is taken into account that piecewise functions are regularly defined via the independent variable and not as has been the case here via the dependent variable.

  36. 36.

    While this procedure makes the KPF continuous at the value R = 897.188, it still remains non-differentiable. This design flaw needs to be remarked upon as the basic KPF has been noted in its log-linear form, and the logarithm as well as the first order derivative are linked to the growth rate of the function. This problem, however, will not be treated in the present study.

  37. 37.

    Note that in both cases, a fixed effects estimator has been implemented and thus the resulting KPFs are comparable.

  38. 38.

    Note that these observations relate mostly to specific smaller regions which report consistently small values and are not limited to the years of the 1990s and thus to effects of the transition recession.

  39. 39.

    This development can be seen from ongoing political decisions but also from the studies by Chebankova (2008) and Solnick (2016).


  1. Abdih, Y., & Joutz, F. (2005). Relating the knowledge production function to total factor productivity: an endogenous growth puzzle. IMF Working Paper, WP/05/74.

  2. Acs, Z., Braunerhjelm, P., Audretsch, D., & Carlsson, B. (2009). The knowledge spillover theory of entrepreneurship. Small Business Economics, 32, 15–30.

    Article  Google Scholar 

  3. Andersson, M., & Ejermo, O. (2003). Knowledge production function in swedish functional regions 1993–1999. CESPRI Working Paper, 139.

  4. Anselin, L., Varga, A., & Acs, Z. (1997). Local geographic spillovers between university research and high technology innovations. Journal of Urban Economics, 42, 422–448.

    Article  Google Scholar 

  5. Asheim, B., & Gertler, M. (2005). The geography of innovation: regional innovation systems In J. Fagerberg, D. Mowery, & R. Nelson (Eds.), The Oxford handbook of innovation, 1st edn, (pp. 291–317). Oxford: Oxford University Press.

  6. Audretsch, D., & Stephan, P. (1999a). How and why does knowledge spill over in biotechnology? In D. Audretsch, & R. Thurik (Eds.), Innovation, industry evolution, and employment, (pp. 216–229). Cambridge: Cambridge University Press.

  7. Audretsch, E., Lehmann, D.B., & Hinger, J. (2014). From knowledge to innovation—the role of knowledge spillover entrepreneurship In C. Antonelli, & A. Link (Eds.), Routledge handbook of the economicy of knowledge, 1 edn, (pp. 20–28). Evanston: Routledge.

  8. Auty, R. (1993). Sustaining development in mineral economies: the resource course thesis, 1 edn. New York: Routledge.

    Google Scholar 

  9. Ayyagari, M., Beck, T., & Demirgüç, A. (2003). Small and medium enterprises across the globe: a new database. Worldbank Policy Research Working Paper, 3127.

  10. Bakhtizin, A., & Akinfeeva, E. (2010). Comparative estimates of innovation potential of the regions of the russian federation. Studies on Russian Economic Development, 21, 275–281.

    Article  Google Scholar 

  11. Bitzer, J. (2003). Technologische Spillover-Effekte als Determinanten des Wirtschaftswachstums, volume 532 of Volkswirtschaftliche Schriften, 1 edn. Berlin: Duncker & Humblot.

    Google Scholar 

  12. Branstetter, L. (2001). Are knowledge spillovers international or intranational in scope?: Microeconometric evidence from the U.S. and Japan. Journal of International Economics, 53, 53–79.

    Article  Google Scholar 

  13. Buesca, M., Heijs, J., Martinez Pellitero, M., & Baumert, T. (2006). Regional systems of innovation and the knowledge production function: the spanish case. Technovation, 26, 463–472.

    Article  Google Scholar 

  14. Buesca, M., Heijs, J., & Baumert, T. (2010). The determinants of regional innovation in europe: a combined factorial and regression knowledge production function approach. Research Policy, 39, 722–735.

    Article  Google Scholar 

  15. Carlsson, B. (2007). Innovation systems: a survey of the literature from a schumpeterian perspective In H. Hanusch, & A. Pyka (Eds.), Elgar companion to neo-Schumpeterian economics, 1st edn, (pp. 857–871). Cheltenham: Edward Elgar.

  16. Chebankova, E. (2008). Adaptive federalism and federation in Putin’s Russia. Europe-Asia Studies, 60, 989–1009.

    Article  Google Scholar 

  17. Cohen, W., Levin, D., & Mowery, R.C. (1987). Firm size and R&D intensity: a re-examination. The Journal of Industrial Economics, 35, 543–565.

    Article  Google Scholar 

  18. Conte, A., & Vivarelli, M. (2005). One or many knowledge production function? Mapping innovative activity using microdata. IZA Discussion Paper, 1878.

  19. Cooke, P., Uranga, M., & Etxebarra, G. (1997). Regional innovation systems: institutional and organisational dimensions. Research Policy, 26, 475–491.

    Article  Google Scholar 

  20. EBRD (2016). Transition Report 2016. EBRD Publications, 1st edn.

  21. EY (2014). Managing bribery and corruption risks in the oil and gas industry. EY, 1st edn.

  22. Fischer, M., & Varga, A. (2003). Spatial knowledge spillovers and university research: evidence from austria. The Annals of Regional Science, 37, 303–322.

    Article  Google Scholar 

  23. Fritsch, M. (2002). Measuring the quality of regional innovation systems: a knowledge production function approach. International Regional Science Review, 25, 86–101.

    Article  Google Scholar 

  24. Fritsch, M., & Franke, G. (2004). Innovation, regional knowledge spillovers and R&D cooperation. Research Policy, 33, 245–255.

    Article  Google Scholar 

  25. Fritsch, M., & Slavtchev, V. (2006). Universities and innovation in space. Industry and Innovation, 14, 201–218.

    Article  Google Scholar 

  26. Griliches, Z. (1979). Issues in assessing the contribution of R&D to productivity growth. The Bell Journal of Economics, 10, 92–116.

    Article  Google Scholar 

  27. Griliches, Z., & Mairesse, J. (1998). Production functions: the search for identification In S. Strom (Ed.), Econometrics and economic theory in the 20th century: the Ragnar Frisch centennial symposium, 1st edn, (pp. 169–203). Cambridge: Cambridge University Press.

  28. Kang, D., & Dall’Erba, S. (2015). Exploring the spatially varying innovation capacity of the us counties in the framework of Griliches’ knowledge production function a mixed GWR approach. REAL Working Paper, 16-T-7.

  29. Kasparov, G (2015). Winter is coming: why Vladimir Putin and the enemies of the free world must be stopped. Atlantic Books, 1st edn.

  30. Khvatova, T (2008). Russia’s national system of innovation: strengths and weaknesses. studying the business sector of russia’s nsi. In Proceedings of the 5th international Ph.D. school on innovation and economic development, Tampere.

  31. Kim, M. J. (2010). Corruption and economic growth. EACGS Conference.

  32. Koenker, R. (2004). Quantile regressions for longitudial data. Journal of Multivariate Analysis, 91, 74–89.

    Article  Google Scholar 

  33. Koenker, R., & Bassett, J. G. (1978). Regression quantiles. Econometrica, 46, 33–50.

    Article  Google Scholar 

  34. Komkov, N., Eroshkin, S., & Kravchenko, M. (2005). Transition to a knowledge-based economy: analysis and appraisal. Studies on Russian Economic Development, 16, 570–580.

    Google Scholar 

  35. Lee, H.-Y., & Park, Y.-T. (2005). An international comparison of R&D efficiency: Dea approach. Asian Journal of Technology Innovation, 13, 207–222.

    Article  Google Scholar 

  36. Leite, C., & Weidmann, J. (1999). Does mother nature corrupt? Natural resources, corruption, and economic growth. IMF Working Paper WW/99/85.

  37. Levin, R., Klevorick, A., Nelson, R., Winter, S., Link, A., & Bozeman, B. (1991). Innovative behavior in small-sized firms. Small Business Economics, 3, 179–184.

    Article  Google Scholar 

  38. Lichtenberg, F.R., & van Pottelsberghe de la Potterie, B. (1998). International R&D spillovers: a comment. European Economic Review, 42, 1483–1491.

  39. Lundvall, B.-A. E. (2010). National systems of innovation: toward a theory of innovation and interactive learning, 1st edn. Anthem Press.

  40. Madsen, J. (2008). Semi-endogenous versus schumpeterian growth models: testing the knowledge production function using international data. Journal of Economic Growth, 13, 1–26.

    Article  Google Scholar 

  41. Mansfield, E. (1981). Composition of R&D expenditures: relationship to size of firm, concentration and innovative output. The Review of Economic and Statistics, 63, 610–615.

    Article  Google Scholar 

  42. Masso, J., & Vahter, P. (2008). Technological innovation and productivity in late-transition estonia: econometric evidence from innovation surveys. The European Journal of Development Research, 20, 240–261.

    Article  Google Scholar 

  43. Mathew, N. (2012). Drivers of firm growth: micro-evidence from indian manufacturing. LEM Working Paper Series, 2012/24.

  44. Nelson, R. E. (1993). National innovation systems: a comparative analysis, 1st edn. Oxford: Oxford University Press.

    Google Scholar 

  45. Netter, J., & Megginson, W. (2001). From state to market: a survey of empirical. Journal of Economic Literature, 39, 321–389.

    Article  Google Scholar 

  46. Ó hUallacháin, B., & Leslie, T.F. (2007). Rethinking the regional knowledge production function. Journal of Economic Geography, 7, 737–752.

    Article  Google Scholar 

  47. OECD (1999). Managing national innovation systems, 1st edn, OECD.

  48. Pardey, P. (1989). The agricultural knowledge production function: an empirical look. The Review of Economics and Statistics, 71, 453–461.

    Article  Google Scholar 

  49. Perret, J. (2013). Knowledge as a driver of regional growth in the Russian Federation, 1st edn. Heidelberg: Springer.

    Google Scholar 

  50. Podmetina, D., Vaatanen, J., & Smirnova, M. (2011). Open innovation in russian firms: an empirical investigation of technology commercialization and acquisition. International Journal of Business Innovation and Research, 5, 298–317.

    Article  Google Scholar 

  51. Ponds, R, van Oort, F., & Frenken, K. (2010). Innovation, spillovers and university-industry collaboration: an extended knowledge production function approach. Journal of Economic Geography, 10, 231– 255.

  52. Portal, GAN Business Anti-Corruption Portal (2017). Russia corruption report.

  53. Ramani, S., El-Aroui, M.-A., & Carrère, M. (2008). On estimating a knowledge production function at the firm and sector level using patent statistics. Research Policy, 37, 1568–1578.

    Article  Google Scholar 

  54. Ranga, L., Debackere, K., & von Tunzelmann, N. (2004). Entrepreneurial universities and the dynamics of academic knowledge production: a case study of basic vs. applied research in Belgium. Scientometrics, 58, 301–320.

    Article  Google Scholar 

  55. Roper, S., & Hewitt-Dundas, N. (2015). Knowledge stocks, knowledge flows and innovation: evidence from matched patents and innovation panel data. Research Policy, 44, 1327–1340.

    Article  Google Scholar 

  56. Rothwell, R. (1989). Small firms, innovation and industrial change. Small Business Economics, 1, 51–64.

    Article  Google Scholar 

  57. Roud, V. (2007). Firm-level research on innovation and productivity: Russian experience. ISSEK Working Paper.

  58. Russian Public Opinion Research Center / VCIOM (2012). About Us.

  59. Savin, I., & Winker, P. (2012). Heuristic optimization methods for dynamic panel data model selection: application on the russian innovative performance. Computational Economics, 39, 337–363.

    Article  Google Scholar 

  60. Schumpeter, J (1911). Theorie der wirtschaftlichen Entwicklung, eine Untersuchung über Unternehmergewinn, Kapital, Kredit, Zins und den Konjunkturzyklus, 2nd edn, Harvard University Press, Cambridge.

  61. Silva, A., Afonso, O., & Africano, A. (2010). Learning-by-exporting: what we know and what we would like to know. The International Trade Journal, 26, 255–288.

    Article  Google Scholar 

  62. Solnick, S. (2016). The political economy of russian federalism: a framework for analysis. Problems of Post-Communism, 43. doi:10.1080/10758216.1996.11655701.

  63. Stephan, P., Audretsch, D., & Hawkins, R. (2000). The knowledge production function lessons from biotechnology. International Journal of Technology Management, 19, 165–178.

    Article  Google Scholar 

  64. Tompson, W. (2006). A frozen Venezuela? The resource curse and Russian politics In M. Ellman (Ed.), Russia’s oil and natural gas: bonanza or curse? 1st edn (pp. 189–212). London: Anthem Press.

  65. Torkkeli, M., Podmetina, D., Ylä-Kojola, A.-M., & Väätänen, J. (2009). Knowledge absorption in an emerging economy—the role of foreign investments and trade flows in russia. International Journal of Business Excellence, 2, 269–284.

    Article  Google Scholar 

  66. Varga, A. (2000). Local academic knowledge spillovers and the concentration of economic activity. Journal of Regional Science, 40, 289–309.

    Article  Google Scholar 

  67. Verspagen, B., & Schoenmakers, W. (2004). The spatial dimension of patenting by multinational firms in europe. Journal of Economic Geography, 4, 23–42.

    Article  Google Scholar 

  68. Wagner, J. (2002). Exports and productivity: a survey of the evidence from firm-level data. The World Economy, 30, 60–82.

    Article  Google Scholar 

  69. Wagner, J. (2006). International firm activities and innovation evidence from knowledge production functions for german firms. MPI Discussion Papers on Entrepreneurship, Growth and Public Policy, 1506.

  70. Wang, E., & Huang, W. (2007). Relative efficiency of R&D activities: a cross-country study accounting for environmental factors in the dea approach. Research Policy, 36, 260–273.

    Article  Google Scholar 

  71. WIPO (2012b). Patent System in Russia. WIPO.

  72. Wu, Y.-M. (2009). An empirical analysis of R&D cooperation and regional knowledge spillovers based on knowledge production function. Studies in Science of Science, 2009-10.

  73. Yuri Levada Analytical Center (2012). Levada Center.

  74. Zabala-Iturriagagoitia, J.M., Voight, P., Gutiérrez-Gracia, A., & Jiménez-Sáez, F. (2007). Regional innovation systems: how to assess performance. Regional Studies, 41, 661–672.

    Article  Google Scholar 

  75. Zucker, L., Darby, M., Furner, J., Liu, R., & Ma, H. (2007). Minerva unbound: knowledge stocks, knowledge flows and new knowledge production. Research Policy, 36, 850–863.

    Article  Google Scholar 

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The author would like to thank Mr. David Hanrahan for editorial support.

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Perret, J.K. Re-Evaluating the Knowledge Production Function for the Regions of the Russian Federation. J Knowl Econ 10, 670–694 (2019).

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  • Russian federation
  • Knowledge
  • Knowledge production function
  • Knowledge generation
  • Quantile regression
  • Regional economics