Stability analysis of a delay differential Kaldor's model with government policies
DOI:
https://doi.org/10.7146/math.scand.a-116243Abstract
This paper is devoted to analysis of the stability of the economy according to an extended version of Kaldor's economic growth model. We consider the role of the government and its simultaneous monetary and fiscal policies and we study whether or not a time delay between the recognition and the implementation of its fiscal policy can affect the economic stability. Numerical simulations provide further conclusions about the long-term behavior of the four variables modeled—namely, national income, capacity of production, bonds value and money supply.
References
Barro, R. J. and Sala-i Martin, X., Economic growth, second ed., MIT Press, 2004.
Blinder, A. S. and Solow, R. M., Does fiscal policy matter?, J. Public Econ. 2 (1973), no. 4, 319–337. https://doi.org/10.1016/0047-2727(73)90023-6
Chang, W. W. and Smyth, D. J., The existence and persistence of cycles in a non-linear model: Kaldor's 1940 model re-examined, Rev. Econ. Stud. 38 (1971), no. 1, 37–44. https://doi.org/10.2307/2296620
De Cesare, L. and Sportelli, M., A dynamic IS-LM model with delayed taxation revenues, Chaos Solitons Fractals 25 (2005), no. 1, 233–244. https://doi.org/10.1016/j.chaos.2004.11.044
Gabisch, G. and Lorenz, H.-W., Business cycle theory. a survey of methods and concepts, second ed., Springer-Verlag Berlin Heidelberg, 1989. https://doi.org/10.1007/978-3-642-74715-1
Gandolfo, G., Economic dynamics, fourth ed., Springer, Heidelberg, 2009. https://doi.org/10.1007/978-3-642-03871-6
Goodwin, R. M., A growth cycle, in “Socialism, Capitalism and Economics Growth” (Feinstein, C. H., ed.), Cambridge University Press, 1967, pp. 54–58.
Hale, J. K. and Verduyn Lunel, S. M., Introduction to functional-differential equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993. https://doi.org/10.1007/978-1-4612-4342-7
Ichimura, S., Toward a general nonlinear macrodynamic theory of economic fluctuations, in “Post-Keynesian Economics”, Rutgers University Press, 1954, pp. 192–226.
Kaddar, A. and Talibi Alaoui, H., Hopf bifurcation analysis in a delayed Kaldor-Kalecki model of business cycle, Nonlinear Anal. Model. Control 13 (2008), no. 4, 439–449.
Kaldor, N., A model of the trade cycle, Econ. J. 50 (1940), no. 197, 78–92. https://doi.org/10.2307/2225740
Kalecki, M., A macrodynamic theory of business cycles, Econometrica 3 (1935), no. 3, 327–344. https://doi.org/10.2307/1905325
Krawiec, A. and Szydłowski, M., The Kaldor-Kalecki business cycle model, Ann. Oper. Res. 89 (1999), 89–100. https://doi.org/10.1023/A:1018948328487
Kuang, Y., Delay differential equations with applications in population dynamics, Mathematics in Science and Engineering, vol. 191, Academic Press, Inc., Boston, MA, 1993.
Mankiw, N. G., Macroeconomics, fifth ed., Worth Publishers, 2003.
Sala-i Martin, X., The world distribution of income: falling poverty and \dots convergence, period, The Quarterly Journal of Economics 121 (2006), no. 2, 351–397. https://doi.org/10.1162/qjec.2006.121.2.351
Matsumoto, A., Destabilizing effects on income adjustment process with fiscal policy lags, Metroeconomica 59 (2008), no. 4, 713–735. https://doi.org/10.1111/j.1467-999X.2008.00334.x
Matsumoto, A., Merlone, U., and Szidarovszky, F., Goodwin accelerator model revisited with fixed time delays, Commun. Nonlinear Sci. Numer. Simul. 58 (2018), 233–248. https://doi.org/10.1016/j.cnsns.2017.06.024
Matsumoto, A., Nakayama, K., and Szidarovszky, F., Goodwin accelerator model revisited with piecewise linear delay investment, Advances in Pure Mathematics 08 (2018), 178–217. https://doi.org/10.4236/apm.2018.82010
Matsumoto, A. and Szidarovszky, F., Delay dynamics in a classical IS-LM model with tax collections., Metroeconomica 67 (2016), no. 4, 667–697. https://doi.org/10.1111/meca.12128
Matsumoto, A., Szidarovszky, F., and Asada, T., Essays in economic dynamics: theory, simulation analysis, and methodological study, Springer Singapore, 2016. https://doi.org/10.1007/978-981-10-1521-2
Mircea, G., Neamţu, M., and Opriş, D., The Kaldor-Kalecki stochastic model of business cycle, Nonlinear Anal. Model. Control 16 (2011), no. 2, 191–205. https://doi.org/10.15388/NA.16.2.14105
Takeuchi, Y. and Yamamura, T., Stability analysis of the Kaldor model with time delays: monetary policy and government budget constraint, Nonlinear Anal. Real World Appl. 5 (2004), no. 2, 277–308. https://doi.org/10.1016/S1468-1218(03)00039-7
Wolfstetter, E., Fiscal policy and the classical growth cycle, Zeitschrift für Nationalökonomie 42 (1982), no. 4, 375–393. https://doi.org/10.1007/BF01283644
Zhou, L. and Li, Y., A dynamic IS-LM business cycle model with two time delays in capital accumulation equation, J. Comput. Appl. Math. 228 (2009), no. 1, 182–187. https://doi.org/10.1016/j.cam.2008.09.004
Blinder, A. S. and Solow, R. M., Does fiscal policy matter?, J. Public Econ. 2 (1973), no. 4, 319–337. https://doi.org/10.1016/0047-2727(73)90023-6
Chang, W. W. and Smyth, D. J., The existence and persistence of cycles in a non-linear model: Kaldor's 1940 model re-examined, Rev. Econ. Stud. 38 (1971), no. 1, 37–44. https://doi.org/10.2307/2296620
De Cesare, L. and Sportelli, M., A dynamic IS-LM model with delayed taxation revenues, Chaos Solitons Fractals 25 (2005), no. 1, 233–244. https://doi.org/10.1016/j.chaos.2004.11.044
Gabisch, G. and Lorenz, H.-W., Business cycle theory. a survey of methods and concepts, second ed., Springer-Verlag Berlin Heidelberg, 1989. https://doi.org/10.1007/978-3-642-74715-1
Gandolfo, G., Economic dynamics, fourth ed., Springer, Heidelberg, 2009. https://doi.org/10.1007/978-3-642-03871-6
Goodwin, R. M., A growth cycle, in “Socialism, Capitalism and Economics Growth” (Feinstein, C. H., ed.), Cambridge University Press, 1967, pp. 54–58.
Hale, J. K. and Verduyn Lunel, S. M., Introduction to functional-differential equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993. https://doi.org/10.1007/978-1-4612-4342-7
Ichimura, S., Toward a general nonlinear macrodynamic theory of economic fluctuations, in “Post-Keynesian Economics”, Rutgers University Press, 1954, pp. 192–226.
Kaddar, A. and Talibi Alaoui, H., Hopf bifurcation analysis in a delayed Kaldor-Kalecki model of business cycle, Nonlinear Anal. Model. Control 13 (2008), no. 4, 439–449.
Kaldor, N., A model of the trade cycle, Econ. J. 50 (1940), no. 197, 78–92. https://doi.org/10.2307/2225740
Kalecki, M., A macrodynamic theory of business cycles, Econometrica 3 (1935), no. 3, 327–344. https://doi.org/10.2307/1905325
Krawiec, A. and Szydłowski, M., The Kaldor-Kalecki business cycle model, Ann. Oper. Res. 89 (1999), 89–100. https://doi.org/10.1023/A:1018948328487
Kuang, Y., Delay differential equations with applications in population dynamics, Mathematics in Science and Engineering, vol. 191, Academic Press, Inc., Boston, MA, 1993.
Mankiw, N. G., Macroeconomics, fifth ed., Worth Publishers, 2003.
Sala-i Martin, X., The world distribution of income: falling poverty and \dots convergence, period, The Quarterly Journal of Economics 121 (2006), no. 2, 351–397. https://doi.org/10.1162/qjec.2006.121.2.351
Matsumoto, A., Destabilizing effects on income adjustment process with fiscal policy lags, Metroeconomica 59 (2008), no. 4, 713–735. https://doi.org/10.1111/j.1467-999X.2008.00334.x
Matsumoto, A., Merlone, U., and Szidarovszky, F., Goodwin accelerator model revisited with fixed time delays, Commun. Nonlinear Sci. Numer. Simul. 58 (2018), 233–248. https://doi.org/10.1016/j.cnsns.2017.06.024
Matsumoto, A., Nakayama, K., and Szidarovszky, F., Goodwin accelerator model revisited with piecewise linear delay investment, Advances in Pure Mathematics 08 (2018), 178–217. https://doi.org/10.4236/apm.2018.82010
Matsumoto, A. and Szidarovszky, F., Delay dynamics in a classical IS-LM model with tax collections., Metroeconomica 67 (2016), no. 4, 667–697. https://doi.org/10.1111/meca.12128
Matsumoto, A., Szidarovszky, F., and Asada, T., Essays in economic dynamics: theory, simulation analysis, and methodological study, Springer Singapore, 2016. https://doi.org/10.1007/978-981-10-1521-2
Mircea, G., Neamţu, M., and Opriş, D., The Kaldor-Kalecki stochastic model of business cycle, Nonlinear Anal. Model. Control 16 (2011), no. 2, 191–205. https://doi.org/10.15388/NA.16.2.14105
Takeuchi, Y. and Yamamura, T., Stability analysis of the Kaldor model with time delays: monetary policy and government budget constraint, Nonlinear Anal. Real World Appl. 5 (2004), no. 2, 277–308. https://doi.org/10.1016/S1468-1218(03)00039-7
Wolfstetter, E., Fiscal policy and the classical growth cycle, Zeitschrift für Nationalökonomie 42 (1982), no. 4, 375–393. https://doi.org/10.1007/BF01283644
Zhou, L. and Li, Y., A dynamic IS-LM business cycle model with two time delays in capital accumulation equation, J. Comput. Appl. Math. 228 (2009), no. 1, 182–187. https://doi.org/10.1016/j.cam.2008.09.004
Downloads
Published
2020-03-29
How to Cite
Caraballo, T., & Silva, A. P. da. (2020). Stability analysis of a delay differential Kaldor’s model with government policies. MATHEMATICA SCANDINAVICA, 126(1), 117–141. https://doi.org/10.7146/math.scand.a-116243
Issue
Section
Articles
