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Business cycle fluctuations and learning-by-doing externalities in a one-sector model. (English) Zbl 1260.91149
Summary: We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with [K. Arrow, “The economic implications of learning by doing”, Rev. Econ. Stud. 29, 155–173 (1962)], to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.

MSC:
 91B55 Economic dynamics 91B52 Special types of economic equilibria
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References:
 [1] Arrow, K., The economic implications of learning by doing, Review of economic studies, 29, 155-173, (1962) [2] Asea, P.; Zak, P., Time-to-build and cycles, Journal of economic dynamics and control, 23, 1155-1175, (1999) · Zbl 1016.91068 [3] Bambi, M., Endogenous growth and time-to-build: the AK case, Journal of economic dynamics and control, 32, 1015-1040, (2008) · Zbl 1181.91166 [4] Bambi, M., Licandro, O., 2005. (In)determinacy and time-to-build. EUI Working Paper No. 2004/17. [5] Basu, S.; Fernald, J., Returns to scale in US production: estimates and implications, Journal of political economy, 105, 249-283, (1997) [6] Benhabib, J.; Farmer, R., Indeterminacy and increasing returns, Journal of economic theory, 63, 19-41, (1994) · Zbl 0803.90022 [7] Benhabib, J.; Nishimura, K., The Hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth, Journal of economic theory, 21, 421-444, (1979) · Zbl 0427.90021 [8] Benhabib, J.; Nishimura, K., Competitive equilibrium cycles, Journal of economic theory, 35, 284-306, (1985) · Zbl 0583.90012 [9] Benhabib, J.; Rustichini, A., Vintage capital, investment and growth, Journal of economic theory, 55, 323-339, (1991) · Zbl 0754.90007 [10] Blundell, R.; MaCurdy, T., Labour supply: a review of alternative approaches, (), 1559-1695 [11] Boucekkine, R.; del Rio, F.; Licandro, O., Endogenous vs. exogenously driven fluctuations in vintage capital models, Journal of economic theory, 88, 161-187, (1999) · Zbl 1044.91548 [12] Boucekkine, R.; Germain, M.; Licandro, O., Replacement echoes in the vintage capital growth model, Journal of economic theory, 74, 333-348, (1997) · Zbl 0889.90031 [13] Boucekkine, R.; Licandro, O.; Puch, L., Crecimiento económicos y generaciones de capital, Cuadernos económicos de ICE, 72, 155-176, (2006) [14] Boucekkine, R.; Licandro, O.; Puch, L.; del Rio, F., Vintage capital and the dynamics of the AK model, Journal of economic theory, 120, 39-72, (2005) · Zbl 1120.91024 [15] Campbell, J., Asset prices, consumption and the business cycle, () [16] Chirinko, R., $$\sigma$$: the long and short of it, Journal of macroeconomics, 30, 671-686, (2008) [17] d’Albis, H.; Augeraud-Véron, E., Competitive growth in a life-cycle model: existence and dynamics, International economic review, 50, 459-484, (2009) [18] d’Albis, H.; Le Van, C., Existence of a competitive equilibrium in the Lucas (1988) model without physical capital, Journal of mathematical economics, 42, 46-55, (2006) · Zbl 1142.91655 [19] d’Autume, A.; Michel, P., Endogenous growth in arrow’s learning by doing model, European economic review, 37, 1175-1184, (1993) [20] Diekmann, O.; Van Gils, S.; Verduyn-Lunel, S.M.; Walther, H.O., Delay equations: functional-, complex-, and nonlinear analysis, (1995), Springer-Verlag New York · Zbl 0826.34002 [21] Dufourt, F., Lloyd-Braga, T., Modesto, L., 2009. Sunspot equilibria and the expectations-driven Phillips curve. Working Paper. University of Strasbourg. [22] Fabbri, G.; Gozzi, F., Solving optimal growth models with vintage capital: the dynamic programming approach, Journal of economic theory, 143, 331-373, (2008) · Zbl 1151.91069 [23] Gruber, J., 2006. A tax-based estimates of the elasticity of intertemporal substitution. NBER Working Paper 11945. [24] Guo, J.T.; Lansing, K., Capital – labor substitution and equilibrium indeterminacy, Journal of economic dynamics and control, 33, 1991-2000, (2009) · Zbl 1183.91095 [25] Hartl, R., A simple proof of the monotonicity of the state trajectories in autonomous control problems, Journal of economic theory, 41, 211-215, (1987) [26] Hassard, B.; Kazarinoff, D.; Wan, Y., Theory and application of Hopf bifurcation, (1981), Cambridge University Press Cambridge · Zbl 0474.34002 [27] Kalecki, M., A macroeconomic theory of the business cycle, Econometrica, 3, 327-344, (1935) [28] Mulligan, C., 2002. Capital interest and aggregate intertemporal substitution. NBER Working Paper 9373. [29] Nishimura, K.; Nourry, C.; Venditti, A., Indeterminacy in aggregate models with small externalities: an interplay between preferences and technology, Journal of nonlinear and convex analysis, 10, 2, 279-298, (2009) · Zbl 1173.91425 [30] Ramsey, F., A mathematical theory of saving, The economic journal, 38, 543-559, (1928) [31] Rogerson, R.; Wallenius, J., Micro and macro elasticities in a life cycle model with taxes, Journal of economic theory, 144, 2277-2292, (2009) · Zbl 1195.91080 [32] Romer, P., Increasing returns and long-run growth, Journal of political economy, 94, 1002-1037, (1986) [33] Rustichini, A., Hopf bifurcation for functional differential equations of mixed type, Journal of dynamics and differential equations, 1, 145-177, (1989) · Zbl 0684.34070 [34] Vissing-Jorgensen, A., Limited asset market participation and the elasticity of intertemporal substitution, Journal of political economy, 110, 825-853, (2002)
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