Nonparametric quantile regression analysis of R&D-sales relationship for Korean firms

  • Joon-Woo Nahm
Part of the Studies in Empirical Economics book series (STUDEMP)


This paper applies the nonparametric quantile regression estimation procedure to the analysis of the innovation-firm size relationship using Korean manufacturing firms data. Due to the high asymmetric distribution of R&D expenditure, the mean regression does not capture properly the stylized facts of R&D behavior; hence it underestimates the sales elasticity. Comparing the parametric estimates and nonparametric estimates allows us to see that there exists a nonlinear relationship in innovative activity and sales. Dividing the data into three groups according to the sales volume, the elasticity in the medium-sized firms is the biggest for scientific firms. This result conforms that the findings of Scherer (1965) coincide with findings from Korean manufacturing firms data in the sense that R&D expenditure tends to increase faster than firm size with size up to a point and then more slowly among larger firms. For the non-scientific firms, it steadily increases showing increasing returns to scale

Key words

Quantile regression Nonparametrics Average median derivative 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Acs Z, Audretsch D (1990) R&D, Innovation and technological change, an international comparison. Harvester Wheatsheaf, New YorkGoogle Scholar
  2. Bertschek I, Entorf H (1996) On nonparametric estimation of the schumpeterian link between innovation and firm size: Evidence from Belgium, France, and Germany. Empirical Economics 21: 401–426Google Scholar
  3. Bound J, Cummins C, Griliches Z, Hall B, Jaffee Z (1984) Who does R&D and who patents? In: Griliches Z (ed.) R&D, patents, and productivity. The University of Chicago Press, pp. 21–54 Comanor W (1967) Market structure, product differentiation, and industrial research. Quarterly Journal of Economics 81: 639–657Google Scholar
  4. Fan J, Gijbels I (1996) Local polynomial modelling and its application. Chapman and Hall, LondonGoogle Scholar
  5. Gasser T, Müller H (1984) Estimating regression function and their derivatives by the kernels method. Scandinavian Journal of Statistics 11: 171–185Google Scholar
  6. Griliches Z, Mairesse J (1984) Productivity and R&D at the firm level. In: Griliches Z (ed.) R&D, patents, and productivity. The University of Chicago Press, pp. 339–374Google Scholar
  7. Hamberg E (1964) Size of firms, oligopoly, and research: The evidence. Canadian Journal of Economics and Political Science 30: 62–75CrossRefGoogle Scholar
  8. Härdle W (1985) On robust kernel estimation of derivatives of regression functions. Scandinavian Journal of Statistics 12: 233–240Google Scholar
  9. Härdle W (1990) Applied nonparametric regression. Cambridge University Press, New York Härdle W, Stoker T (1989) Investigating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association 84: 986–995Google Scholar
  10. Holmes J, Patricia P, Webber E (1991) A functional-form-free test of the research and develop-ment/firm size relationship. Journal of Business and Economic Statistics 9: 85–90Google Scholar
  11. Kamien M, Schwartz N (1975) Market structure and innovation: A survey. Journal of economic literature 13: 1–37Google Scholar
  12. Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46: 33–50CrossRefGoogle Scholar
  13. Magee L, Burbidge J, Robb A (1991) Computing kernel-smoothed conditional quantiles from many observations. Journal of the American Statistical Association 86: 673–677CrossRefGoogle Scholar
  14. Nadaraja E (1964) On regression estimators. Theory of Probability and Its Application 9: 157–159Google Scholar
  15. Link A, Seaks T, Woodbery S (1988) Firm size and R&D spending: Testing for functional form. Southern Economic Journal 54: 1027–1032Google Scholar
  16. Nahm J (1989) Nonparametric Least Absolute Deviations Estimation. Unpublished Ph.D. thesis, University of Wisconsin-MadisonGoogle Scholar
  17. Nahm J (1996) R&D Expenditure and Sales: A Nonparametric Approach. Journal of Economic Theory and Econometrics 2: 103–124Google Scholar
  18. Pagan A, Ullah A (1999) Nonparametric econometrics. Cambridge University Press, Cambridge Samarov A (1993) Exploring regression structure using nonparametric functional estimation. Journal of the American Statistical Association 88: 836–847CrossRefGoogle Scholar
  19. Scherer F (1965) Size of firm, oligopoly, and research: A comment. Canadian Journal of Economics 31: 256–266Google Scholar
  20. Schumpeter J (1942) Capitalism, socialism and democracy, Harper, New YorkGoogle Scholar
  21. Stoker T (1991) Equivalence of direct, indirect, and slope estimators of average derivatives. In: Barnett W, Powell J, Tauchen G (ed.) Nonparametric and semiparametric methods in econometrics and statistics. Cambridge University Press, Cambridge, pp. 99–118Google Scholar
  22. Sung, M (1993) Nonparametric average median derivatives estimation of index coefficients, manuscriptGoogle Scholar
  23. Yu, K and Jones M (1990) Local linear quantile regression. Journal of the American Statistical Association 93: 228–237CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Joon-Woo Nahm
    • 1
  1. 1.Department of EconomicsSogang UniversitySeoulKorea

Personalised recommendations