Yagi and Managi (2018, EAP)



Yagi, M. and Managi, S., “Shadow price of patent stock as knowledge stock: time and country heterogeneity,” Economic Analysis and Policy, vol.60, pp.43-61, 2018. doi: 10.1016/j.eap.2018.09.001





This study compares the shadow price (marginal cost) and shadow value (total cost) of patent stock (as knowledge stock) in each of 92 countries between 1992 and 2010. Two specifications are considered in the data envelopment analysis approach. One specification considers population, capital, patent stock, energy use (four inputs), greenhouse gas (undesirable output), and gross domestic product (desirable output). The other uses human capital and natural capital instead of population and energy use. Under these two specifications, respectively, the shadow price of the patent stock (on weighted average) for the whole period is −0.106 and −0.054 million US dollars per patent in the entire sample. Similarly, the shadow value of the patent stock (by the ratio of gross domestic product) in the entire sample is −5.8% and −2.9%, respectively. As the standing position of patent stock, the patent stock is less valuable than human capital and (produced) capital but more valuable than population, energy use, and natural capital. The patent stock also is likely to be valuable in developing countries. In addition, the shadow value of the patent stock is relatively high in certain large countries and nearly flat in most of the countries.


  • Amess, K., Stiebale, J., Wright, M., 2016. The impact of private equity on firms׳ patenting activity. European Economic Review 86, 147–160. doi:10.1016/j.euroecorev.2015.08.013
  • Arrow, K.J., Dasgupta, P., Goulder, L.H., Mumford, K.J., Oleson, K., 2012. Sustainability and the measurement of wealth. Environment and Development Economics 17, 317–353. doi:10.1017/S1355770X12000137
  • Arrow, K.J., Dasgupta, P., Goulder, L.H., Mumford, K.J., Oleson, K., 2013. Sustainability and the measurement of wealth: further reflections. Environment and Development Economics 18, 504–516. doi:10.1017/S1355770X13000193
  • Balasubramanian, N., Sivadasan, J., 2011. What Happens When Firms Patent? New Evidence from U.S. Economic Census Data. Review of Economics and Statistics 93, 126–146. doi:10.1162/REST_a_00058
  • Benz, S., Larch, M., Zimmer, M., 2014. The structure of the German economy. Applied Economics 46, 3274–3283. doi:10.108000036846.2014.927568
  • Berbegal‐Mirabent, J., Sabaté, F., Cañabate, A., 2012. Brokering knowledge from universities to the marketplace. Management Decision 50, 1285–1307. doi:10.110800251741211247012
  • Bertoni, F., Tykvová, T., 2015. Does governmental venture capital spur invention and innovation? Evidence from young European biotech companies. Research Policy 44, 925–935. doi:10.1016/j.respol.2015.02.002
  • Blind, K., Jungmittag, A., 2008. The impact of patents and standards on macroeconomic growth: a panel approach covering four countries and 12 sectors. Journal of Productivity Analysis 29, 51–60. doi:10.1007/s11123-007-0060-8
  • Bottasso, A., Castagnetti, C., Conti, M., 2013. And yet they Co-move! Public capital and productivity in OECD. Journal of Policy Modeling 35, 713–729. doi:10.1016/j.jpolmod.2013.02.007
  • Bottazzi, L., Peri, G., 2007. The International Dynamics of R&D and Innovation in the Long Run and in The Short Run. The Economic Journal 117, 486–511. doi:10.1111/j.1468-0297.2007.02027.x
  • Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444. doi:10.10160377-2217(78)90138-8
  • Chen, J.-R., Yang, C.-H., 2005. Technological knowledge, spillover and productivity: evidence from Taiwanese firm level panel data. Applied Economics 37, 2361–2371. doi:10.108000036840500309262
  • Chung, Y.H., Färe, R., Grosskopf, S., 1997. Productivity and Undesirable Outputs: A Directional Distance Function Approach. Journal of Environmental Management 51, 229–240. doi:10.1006/jema.1997.0146
  • Cohen, W.M., 2010. Fifty Years of Empirical Studies of Innovative Activity and Performance, in: Hall, B.H., Rosenberg, N. (Eds.), Handbook of the Economics of Innovation. Elsevier B.V., pp. 129–213. doi:10.1016/S0169-7218(10)01004-X
  • Collins, R.D., Selin, N.E., de Weck, O.L., Clark, W.C., 2017. Using inclusive wealth for policy evaluation: Application to electricity infrastructure planning in oil-exporting countries. Ecological Economics 133, 23–34. doi:10.1016/j.ecolecon.2016.11.013
  • Cook, W.D., Seiford, L.M., 2009. Data envelopment analysis (DEA) – Thirty years on. European Journal of Operational Research 192, 1–17. doi:10.1016/j.ejor.2008.01.032
  • Crespi, G., D’Este, P., Fontana, R., Geuna, A., 2011. The impact of academic patenting on university research and its transfer. Research Policy 40, 55–68. doi:10.1016/j.respol.2010.09.010
  • Czarnitzki, D., Kraft, K., 2010. On the profitability of innovative assets. Applied Economics 42, 1941–1953. doi:10.108000036840701749019
  • Desyllas, P., Hughes, A., 2009. The revealed preferences of high technology acquirers: An analysis of the innovation characteristics of their targets. Cambridge Journal of Economics 33, 1089–1111. doi:10.1093/cje/bep004
  • Emrouznejad, A., Yang, G., 2018. A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences 61, 4–8. doi:10.1016/j.seps.2017.01.008
  • Falagas, M.E., Kouranos, V.D., Arencibia-Jorge, R., Karageorgopoulos, D.E., 2008. Comparison of SCImago journal rank indicator with journal impact factor. The FASEB Journal 22, 2623–2628. doi:10.1096/fj.08-107938
  • Färe, R., Grosskopf, S., Tyteca, D., 1996. An activity analysis model of the environmental performance of firms—application to fossil-fuel-fired electric utilities. Ecological Economics 18, 161–175. doi:10.10160921-8009(96)00019-5
  • Fenichel, E.P., Abbott, J.K., Bayham, J., Boone, W., Haacker, E.M.K., Pfeiffer, L., 2016. Measuring the value of groundwater and other forms of natural capital. Proceedings of the National Academy of Sciences 113, 2382–2387. doi:10.1073/pnas.1513779113
  • Fujii, H., Managi, S., 2016. Research and development strategy for environmental technology in Japan: A comparative study of the private and public sectors. Technological Forecasting and Social Change 112, 293–302. doi:10.1016/j.techfore.2016.02.012
  • Fujii, H., Managi, S., 2018. Trends and priority shifts in artificial intelligence technology invention: A global patent analysis. Economic Analysis and Policy 58, 60–69. doi:10.1016/j.eap.2017.12.006
  • Gera, S., Gu, W., Lin, Z., 2001. Technology and the demand for skills in Canada: an industry-level analysis. Canadian Journal of Economics/Revue Canadienne d`Economique 34, 132–148. doi:10.11110008-4085.00066
  • Ghadimi, H., Harris, T., Warner, T., 2015. A geospatial approach to measuring regional and sub-regional inclusive wealth: the case of resource rich West Virginia, USA. Regional Science Policy & Practice 7, 199–224. doi:10.1111/rsp3.12067
  • Griliches, Z., 1981. Market value, R&D, and patents. Economics Letters 7, 183–187. doi:10.10160165-1765(87)90114-5
  • Griliches, Z., 1990. Patent Statistics as Economic Indicators: A Survey, Journal of Economic Literature. Cambridge, MA. doi:10.3386/w3301
  • Grimpe, C., 2012. Extramural research grants and scientists’ funding strategies: Beggars cannot be choosers? Research Policy 41, 1448–1460. doi:10.1016/j.respol.2012.03.004
  • Hall, B.H., Jaffe, A., Trajtenberg, M., 2001. The NBER Patent Citation Data File: Lessons, Insights and Methodological Tools, NBER Working Paper 8498. Cambridge, MA. doi:10.3386/w8498
  • Hall, B.H., Jaffe, A., Trajtenberg, M., 2005. Market Value and Patent Citations. The RAND journal of economics 36, 16–38. http://www.jstor.org/stable/1593752
  • Ikeda, S., Tamaki, T., Nakamura, H., Managi, S., 2017. Inclusive wealth of regions: the case of Japan. Sustainability Science 12, 991–1006. doi:10.1007/s11625-017-0450-4
  • Jang, S.-L., Chen, J.H., 2011. What determines how long an innovative spell will last? Scientometrics 86, 65–76. doi:10.1007/s11192-010-0247-z
  • Johnstone, N., Managi, S., Rodríguez, M.C., Haščič, I., Fujii, H., Souchier, M., 2017. Environmental policy design, innovation and efficiency gains in electricity generation. Energy Economics 63, 106–115. doi:10.1016/j.eneco.2017.01.014
  • Kumar, S., Fujii, H., Managi, S., 2015. Substitute or complement? Assessing renewable and nonrenewable energy in OECD countries. Applied Economics 47, 1438–1459. doi:10.108000036846.2014.997922
  • Kuosmanen, T., 2005. Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs. American Journal of Agricultural Economics 87, 1077–1082. doi:10.1111/j.1467-8276.2005.00788.x
  • Kuosmanen, T., Matin, R.K., 2011. Duality of weakly disposable technology. Omega 39, 504–512. doi:10.1016/j.omega.2010.10.008
  • Kurniawan, R., Managi, S., 2017. Sustainable Development and Performance Measurement: Global Productivity Decomposition. Sustainable Development 25, 639–654. doi:10.1002/sd.1684
  • Lach, S., 1995. Patents and productivity growth at the industry level: A first look. Economics Letters 49, 101–108. doi:10.10160165-1765(94)00618-C
  • Lee, J.-D., Park, J.-B., Kim, T.-Y., 2002. Estimation of the shadow prices of pollutants with production/environment inefficiency taken into account: a nonparametric directional distance function approach. Journal of Environmental Management 64, 365–375. doi:10.1006/jema.2001.0480
  • Leleu, H., 2013. Shadow pricing of undesirable outputs in nonparametric analysis. European Journal of Operational Research 231, 474–480. doi:10.1016/j.ejor.2013.05.028
  • Lin, C.-H., Jang, S.-L., 2010. The impact of M&As on company innovation: evidence from the US medical device industry. Scientometrics 84, 119–131. doi:10.1007/s11192-009-0096-9
  • Madsen, J.B., 2008. Economic Growth, TFP Convergence and the World Export of Ideas: A Century of Evidence. Scandinavian Journal of Economics 110, 145–167. doi:10.1111/j.1467-9442.2008.00530.x
  • Mahlich, J.C., 2010. Patents and performance in the Japanese pharmaceutical industry: An institution-based view. Asia Pacific Journal of Management 27, 99–113. doi:10.1007/s10490-008-9128-x
  • Mukherji, N., Silberman, J., 2011. Idea generation: the performance of U.S. States 1997–2007. The Journal of Technology Transfer 36, 417–447. doi:10.1007/s10961-010-9158-7
  • Park, G., Park, Y., 2006. On the measurement of patent stock as knowledge indicators. Technological Forecasting and Social Change 73, 793–812. doi:10.1016/j.techfore.2005.09.006
  • Roman, P., Thiry, G., 2016. The inclusive wealth index. A critical appraisal. Ecological Economics 124, 185–192. doi:10.1016/j.ecolecon.2015.12.008
  • UNU-IHDP and UNEP, 2012. Inclusive Wealth Report 2012 – Measuring Progress Toward Sustainability. International Journal of Sustainability in Higher Education 13. doi:10.1108/ijshe.2012.24913daa.006 http://inclusivewealthindex.org/
  • UNU-IHDP and UNEP, 2014. Inclusive Wealth Report 2014 Measuring progress toward sustainability, Cambridge: Cambridge University Press. < http://inclusivewealthindex.org/>
  • van Zeebroeck, N., 2007. Patents only live twice: a patent survival analysis in Europe. Working Papers CEB No. 07-028.RS. Universite Libre de Bruxelles. < https://ideas.repec.org/p/sol/wpaper/07-028.html>
  • van Zeebroeck, N., 2011a. Long Live Patents: the Increasing Life Expectancy of Patent Applications and its Determinants. Review of Economics and Institutions 2, 37. doi:10.5202/rei.v2i3.41
  • van Zeebroeck, N., 2011b. The puzzle of patent value indicators. Economics of Innovation and New Technology 20, 33–62. doi:10.108010438590903038256
  • Vera, L., 2017. In search of stabilization and recovery: macro policy and reforms in Venezuela. Journal of Post Keynesian Economics 40, 9–26. doi:10.108001603477.2016.1273069
  • Schankerman, M., Pakes, A., 1986. Estimates of the Value of Patent Rights in European Countries During the Post-1950 Period. The Economic Journal 96, 1052. doi:10.23072233173
  • Schmoch, U., 2008. Concept of a technology classification for Country comparison. Final report to the World Intellectual Property Organization (WIPO). http://www.wipo.int/export/sites/www/ipstats/en/statistics/patents/pdf/wipo_ipc_technology.pdf
  • Schmoch, U., Schubert, T., Jansen, D., Heidler, R., von Görtz, R., 2010. How to use indicators to measure scientific performance: a balanced approach. Research Evaluation 19, 2–18. doi:10.3152/095820210X492477
  • Streb, J., Wallusch, J., Yin, S., 2007. Knowledge spill-over from new to old industries: The case of German synthetic dyes and textiles (1878–1913). Explorations in Economic History 44, 203–223. doi:10.1016/j.eeh.2005.11.002
  • Tamaki, T., Shin, K.J., Nakamura, H., Fujii, H., Managi, S., 2018. Shadow prices and production inefficiency of mineral resources. Economic Analysis and Policy 57, 111–121. doi:10.1016/j.eap.2017.03.005
  • Thompson, M.J., 2016. Measuring patent quality: A claim and search report approach. World Patent Information 45, 47–54. doi:10.1016/j.wpi.2016.03.003
  • Tyteca, D., 1996. On the Measurement of the Environmental Performance of Firms— A Literature Review and a Productive Efficiency Perspective. Journal of Environmental Management 46, 281–308. doi:10.1006/jema.1996.0022
  • Uehara, T., Mineo, K., 2017. Regional sustainability assessment framework for integrated coastal zone management: Satoumi, ecosystem services approach, and inclusive wealth. Ecological Indicators 73, 716–725. doi:10.1016/j.ecolind.2016.10.031
  • Walker, B., Pearson, L., Harris, M., Maler, K.-G., Li, C.-Z., Biggs, R., Baynes, T., 2010. Incorporating Resilience in the Assessment of Inclusive Wealth: An Example from South East Australia. Environmental and Resource Economics 45, 183–202. doi:10.1007/s10640-009-9311-7
  • Wang, B., Hsieh, C., 2015. Measuring the value of patents with fuzzy multiple criteria decision making: insight into the practices of the Industrial Technology Research Institute. Technological Forecasting and Social Change 92, 263–275. doi:10.1016/j.techfore.2014.09.015
  • Yagi, M., Fujii, H., Hoang, V., Managi, S., 2015. Environmental efficiency of energy, materials, and emissions. Journal of Environmental Management 161, 206–218. doi:10.1016/j.jenvman.2015.06.054
  • Yamaguchi, R., 2014. Inclusive wealth with a changing but aging population. Economics Letters 124, 21–25. doi:10.1016/j.econlet.2014.04.011
  • Yueh, L., 2009. Patent laws and innovation in China. International Review of Law and Economics 29, 304–313. doi:10.1016/j.irle.2009.06.001
  • Zhou, P., Ang, B.W., Poh, K.L., 2008. A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research 189, 1–18. doi:10.1016/j.ejor.2007.04.042
  • Zobel, A.-K., Balsmeier, B., Chesbrough, H., 2016. Does patenting help or hinder open innovation? Evidence from new entrants in the solar industry. Industrial and Corporate Change 25, 307–331. doi:10.1093/icc/dtw005
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