Externalities in R&D: a route to endogenous fluctuations

Gomes, Orlando (2007): Externalities in R&D: a route to endogenous fluctuations.

Abstract

Technological progress produces both positive and negative economy wide externalities. Although positive spillovers seem to prevail most of the times, there is evidence and logical arguments revealing that investment in R&D can exceed the corresponding socially optimal level. Taking on board the assumption that the two kinds of externalities are possible and that, therefore, one is able to define the pace of technical progress required to maximize social welfare, we develop a standard two-sector optimal growth model with externalities in the production of technology. The added assumption allows for introducing endogenous business cycles in the Walrasian growth setup. The undertaken stability analysis discusses the local properties of a difference equation two-dimensional system, identifying the occurrence of a flip bifurcation, and looks at global dynamics, through a numerical example, in order to better illustrate and describe the non linear nature of the system.

• Item Type: MPRA Paper
• Institution: Escola Superior de Comunicação Social - Instituto Politécnico de Lisboa
• Language: English
• Keywords: Technology; Externalities; Endogenous business cycles; Two-sector growth models; Nonlinear dynamics and chaos
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles

References

Aghion, P. and P. Howitt (1992). “A Model of Growth through Creative Destruction.” Econometrica, vol. 60, nº 2, pp. 323-351. Arrow, K. J. (1962). “The Economic Implications of Learning-by-Doing.” Review of Economic Studies, vol. 29, pp. 155-173. Barro, R. J. and X. Sala-i-Martin (1995). Economic Growth. New York: McGraw-Hill. Benhabib, J. and R. H. Day (1981). “Rational Choice and Erratic Behaviour.” Review of Economic Studies, vol. 48, pp. 459-471. Brock, W. A. and C. H. Hommes (1997). “A Rational Route to Randomness.” Econometrica, vol. 65, pp.1059-1095. Brock, W. A. and C. H. Hommes (1998). “Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model.” Journal of Economic Dynamics and Control, vol. 22, pp. 1235-1274. Cass, D. (1965). “Optimum Growth in an Aggregative Model of Capital Accumulation.” Review of Economic Studies, vol. 32, pp. 233-240. Cellarier, L. (2006). “Constant Gain Learning and Business Cycles.” Journal of Macroeconomics, vol. 28, pp. 51-85. Christiano, L. and M. Eichenbaum (1992). “Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations.” American Economic Review, vol. 82, pp. 430-450. Christiano, L. and S. Harrison (1999). “Chaos, Sunspots and Automatic Stabilizers.” Journal of Monetary Economics, vol. 44, pp. 3-31. Coury, T. and Y. Wen (2005). “Global Indeterminacy and Chaos in Standard RBC Models.” University of Oxford and Cornell University working paper. Day, R. H. (1982). “Irregular Growth Cycles.” American Economic Review, vol. 72, pp.406-414. Diebolt, C. (2006). “Comments on ‘Constant Gain Learning and Business Cycles’.” Journal of Macroeconomics, vol. 28, pp. 86-89. Evans, G. W. and S. Honkapohja (2001). Learning and Expectations in Macroeconomics. Princeton, New Jersey: Princeton University Press. Goenka, A. and O. Poulsen (2004). “Factor Intensity Reversal and Ergodic Chaos.” Working paper 04-13, Aarhus School of Business, Department of Economics. Gomes, O. (2006). “Local Bifurcations and Global Dynamics in a Solow-type Endogenous Business Cycles Model.”, Annals of Economics and Finance, vol. 7, pp. 91-127. Grandmont, J. M. (1985). “On Endogenous Competitive Business Cycles.” Econometrica, vol. 53, pp. 995-1045. Grossman, G. M. and E. Helpman (1991). Innovation and Growth in the Global Economy. Cambridge, Mass.: MIT Press. Guo, J. T. and K. J. Lansing (2002). “Fiscal Policy, Increasing Returns and Endogenous Fluctuations.” Macroeconomic Dynamics, vol. 6, pp. 633-664. Heer, B. and A. Maussner (2005). Dynamic General Equilibrium Modelling – Computational Methods and Applications. Berlin: Springer. Hommes, C. H. (2005a). “Heterogeneous Agent Models: Two Simple Case Studies.” Tinbergen Institute Discussion Papers 05-055/1, Tinbergen Institute. Hommes, C. H. (2005b). “Heterogeneous Agent Models in Economics and Finance.” Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute. Jones, C. I. (1995). “R&D-Based Models of Economic Growth.” Journal of Political Economy, vol. 103, nº 4, pp. 759-784. Jones, C. I. and J. Williams (2000). “Too Much of a Good Thing? The Economics of Investment in R&D.” Journal of Economic Growth, vol. 5, nº 1, pp. 65-85. Koopmans, T. C. (1965). “On the Concept of Optimal Economic Growth.” in The Econometric Approach to Development Planning. Amsterdam: North Holland. Kurz, M. (1994). “On the Structure and Diversity of Rational Beliefs.” Economic Theory, vol. 4, pp. 877-900. Kurz, M. (1997). Endogenous Economic Fluctuations: Studies in the Theory of Rational Belief, Studies in Economic Theory, number 6, Berlin and New York: Springer-Verlag. Kurz, M.; H. Jin and M. Motolese (2003). “Endogenous Fluctuations and the Role of Monetary Policy.” in Aghion, P.; R. Frydman; J. Stiglitz and M. Woodford (eds.) Knowledge, Information and Expectations in Modern Macroeconomics (in honor of E. S. Phelps). Princeton, New Jersey: Princeton University Press. pp. 188-227. Kydland, F. and E. C. Prescott (1982). “Time to Build and Aggregate Fluctuations.” Econometrica, vol. 50, pp. 1345-1370. Long, J. B. and C. I. Plosser (1983). “Real Business Cycles.” Journal of Political Economy, vol. 91, pp. 39-69. Lucas, R. E. (1988). “On the Mechanics of Economic Development.” Journal of Monetary Economics, vol. 22, nº 1, pp. 3-42. Medio, A. (1979). Teoria Nonlineare del Ciclo Economico. Bologna: Il Mulino. Ramsey, F. (1928). “A Mathematical Theory of Saving.” Economic Journal, vol. 38, pp. 543-559. Romer, P. M. (1986). “Increasing Returns and Long-Run Growth.” Journal of Political Economy, vol. 94, nº 5, pp. 1002-1037. Romer, P. M. (1990). “Endogenous Technological Change.” Journal of Political Economy, vol. 98, nº 5, part II, pp. S71-S102. Romer, D. (2001). Advanced Macroeconomics, 2nd edition. New York: McGraw-Hill. Schmitt-Grohé, S. (2000). “Endogenous Business Cycles and the Dynamics of Output, Hours, and Consumption.” American Economic Review, vol. 90, pp. 1136-1159. Solow, R. M. (1956). “A Contribution to the Theory of Economic Growth.” Quarterly Journal of Economics, vol.70, nº 1, pp.65-94. Stutzer, M. J. (1980). “Chaotic Dynamics and Bifurcations in a Macro-Model.” Journal of Economic Dynamics and Control, vol. 2, pp. 353-376. Weder, M. (2004). “A Note on Conspicuous Leisure, Animal Spirits and Endogenous Cycles.” Portuguese Economic Journal, vol. 3, pp. 1-13.