Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model

Lin, Hwan C. and Shampine, L.F. (2014): Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model.

Abstract

The statutory patent length is 20 years in most countries. R&D-based endogenous growth models, however, often presume an infinite patent length. In this paper, finite-length patents are embedded in a non-scale R&D-based growth model, but any patent’s effective life may be terminated prematurely at any moment, subject to two idiosyncratic hazards of imitation and innovation. This gives rise to an autonomous system of mixed-type functional differential equations (FDEs). Its dynamics are driven by current, delayed and advanced states. We present an algorithm to solve the FDEs by solving a sequence of standard BVPs (boundary value problems) for systems of ODEs (ordinary differential equations). We use this algorithm to simulate a calibrated U.S. economy’s transitional dynamics by making discrete changes from the baseline 20 years patent length. We find that if transitional impacts are taken into account, optimizing the patent length incurs a welfare loss, albeit rather small. This suggests that fine-tuning the world’s patent systems may not be a worthwhile effort.

• Item Type: MPRA Paper
• Language: English
• Keywords: Patent Length, Innovation, Delay Differential Equation, Advance Differential Equation, Transitional Dynamics, Endogenous Growth
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O31 - Innovation and Invention: Processes and Incentives; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O34 - Intellectual Property and Intellectual Capital

References

Aghion, P. and P. Howitt (1992). A Model of Growth Through Creative Destruction. 60, 323–351.

Asea, P. K. and P. J. Zak (1999). Time-to-build and cycles. Journal of economic dynamics and control 23, 1155–1175.

Bambi, M., F. Gozzi, and O. Licandroc (2014). Endogenous growth and wave-like business fluctuations. Journal of Economic Theory 154, 68–111.

Bellman, R. (1963). Differential-Difference Equations. Academic Press.

Benhabib, J. and A. Rustichini (1991). Vintage capital, investment, and growth. Journal of Economic Theory 55, 323–339.

Boucekkine, R., D. De la Croix, and O. Licandro (2002). Vintage human capital, demographic trends, and endogenous growth. Journal of Economic Theory 104, 340–375.

Boucekkine, R., M. Germain, and O. Licandro (1997). Replacement echoes in the vintage capital growth model. Journal of Economic Theory 74, 333–348.

Boucekkine, R., O. Licandro, and C. Paul (1997). Differential-difference equations in economics: On the numerical solution of vintage capital growth models. Journal of Economic Dynamics and Control 21, 347–362.

Boucekkine, R., O. Licandro, L. A. Puch, and F. Del Rio (2005). Vintage capital and the dynamics of the ak model. Journal of economic theory 120, 39–72.

Caballero, R. J. and M. L. Hammour (1994, December). The Cleansing Effect of Recessions. American Economic Review 84, 1350–68.

Chu, A. C. (2009). Effects of blocking patents on R&D: a quantitative dge analysis. Journal of Economic Growth 14, 55–78.

Chu, A. C. (2010). Effects of patent length on R&D: a quantitative dge analysis. Journal of Economics 99, 117–140.

Chu, A. C., G. Cozzi, and S. Galli (2012). Does intellectual monopoly stimulate or stifle innovation? European Economic Review 56, 727–746.

Collard, F., O. Licandro, and L. A. Puch (2008). The short-run dynamics of optimal growth model with delays. Annales d’Economie et de Statistique 90, 127–143.

Comin, D. (2004). R&D: A small contribution to productivity growth. Journal of Economic Growth 9, 391–421.

Cozzi, G. and S. Galli (2014). Sequential R&D and blocking patents in the dynamics of growth. Journal of Economic Growth 19, 183–219.

Cozzi, G. and G. Impullitti (2010). Government Spending Composition, Technical Change, and Wage Inequality. Journal of the European Economic Association 8, 1325–1358.

Eicher, T. S. and S. J. Turnovsky (2001). Transitional dynamics in a two-sector non-scale growth model. Journal of Economic Dynamics and Control 25, 85–113.

Furukawa, Y. (2007). The protection of intellectual property rights and endogenous growth: Is stronger always better? Journal of Economic Dynamics and Control 31, 3644–3670.

Futagami, K. and T. Iwaisako (2007). Dynamic analysis of patent policy in an endogenous growth model. Journal of Economic Theory 132, 306–334.

Grinols, E. and H. C. Lin (2006). Global patent protection: channels of north and south welfare gain. Journal of Economic Dynamics and Control 30, 205–227.

Grossman, G. M. and E. Helpman (1990a). Comparative advantage and long-run growth. American Economic Review 80, 796–815.

Grossman, G. M. and E. Helpman (1990b). Trade, innovation, and growth. The American economic review 80, 86–91.

Grossmann, V., T. Steger, and T. Trimborn (2013). Dynamically optimal R&D subsidization. Journal of Economic Dynamics and Control 37, 516–534.

Hale, J. K. (1977). Theory of Functional Differential Equations. New York: Springer.

Helpman, E. (1993). Innovation, imitation, and intellectual property rights. Econometrica 61, 1247–1280.

Iwaisako, T. and K. Futagami (2003). Patent policy in an endogenous growth model. Journal of Economics 78, 239–258.

Iwaisako, T. and K. Futagami (2013). Patent protection, capital accumulation, and economic growth. Economic Theory 52, 631–668.

Jones, C. I. (1995a). R&D-based models of economic growth. Journal of political Economy 103, 759–784.

Jones, C. I. (1995b). Time series tests of endogenous growth models. The Quarterly Journal of Economics 110, 495–525.

Jones, C. I. and J. C. Williams (2000). Too much of a good thing? the economics of investment in R&D. Journal of Economic Growth 5, 65–85.

Judd, K. L. (1985). On the performance of patents. Econometrica: Journal of the Econometric Society 53, 567–585.

Kalecki, M. (1935). A macrodynamic theory of business cycles. Econometrica, Journal of the Econometric Society 3, 327–344.

Kierzenka, J. and L. F. Shampine (2008). A BVP solver that controls residual and error. JNAIAM J. Numer. Anal. Indust. Appl. Math 3, 27–41.

Kwan, Y. K. and E. L.-C. Lai (2003). Intellectual property rights protection and endogenous economic growth. Journal of Economic Dynamics and Control 27, 853–873.

Lai, E. L.-C. (1998). International intellectual property rights protection and the rate of product innovation. Journal of Development economics 55, 133–153.

Lin, H. C. (2010). Technology diffusion and global welfare effects: Imitative r&d vs. south-bound FDI. Structural Change and Economic Dynamics 21, 231–247.

Lin, H. C. (2013a). Creative destruction and optimal patent life in a variety-expanding growth model. Southern economic journal in-press. Southern Economic Journal In-Pres.

Lin, H. C. (2013b). Switching from patents to an intertemporal bounty in a non-scale growth model. MPRA Paper 50205, University Library of Munich, Germany, 1–41.

Nordhaus, W. D. (1969). Invention, growth, and welfare: A theoretical treatment of technological change. MIT Press Cambridge, MA.

Norrbin, S. C. (1993). The relation between price and marginal cost in us industry: a contradiction. Journal of Political Economy 101, 1149–1164.

O’Donoghue, T. and J. Zweimuller (2004). Patents in a model of endogenous growth. Journal of Economic Growth 9, 81–123.

Peretto, P. F. (1998). Technological change and population growth. Journal of Economic Growth 3, 283–311.

Rivera-Batiz, L. A. and P. M. Romer (1991). Economic integration and endogenous growth. The Quarterly Journal of Economics 106, 531–555.

Romer, P. M. (1990). Endogenous technological change. Journal of political Economy 98, S71–102.

Segerstrom, P. S. (1998). Endogenous growth without scale effects. American Economic Review 88, 1290–1310.

Segerstrom, P. S., T. C. Anant, and E. Dinopoulos (1990). A schumpeterian model of the product life cycle. The American Economic Review 80, 1077–1091.

Steger, T. (2003). The segerstrom model: Stability, speed of convergence and policy implications. Economics Bulletin 15, 1–8.

Young, A. (1998). Growth without scale effects. Journal of Political Economy 106, 41–63.