Bambi, Mauro and Fabbri, Giorgio and Gozzi, Fausto (2009): Optimal policy and consumption smoothing effects in the time-to-build AK model.
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In this paper the dynamic programming approach is exploited in order to identify the closed loop policy function, and the consumption smoothing mechanisms in an endogenous growth model with time to build, linear technology and irreversibility constraint in investment. Moreover the link among the time to build parameter, the maximum capital reproduction rate, and the magnitude of the smoothing effect is deeply investigated and compared with what happens in a vintage capital model characterized by the same technology and utility function. Finally we have analyzed the effect of time to build on the speed of convergence of the main aggregate variables.
|Item Type:||MPRA Paper|
|Original Title:||Optimal policy and consumption smoothing effects in the time-to-build AK model|
|Keywords:||Time-to-build, AK model, Dynamic programming, optimal strategies, closed loop policy.|
|Subjects:||E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations; Cycles
E - Macroeconomics and Monetary Economics > E2 - Macroeconomics: Consumption, Saving, Production, Employment, and Investment > E22 - Capital; Investment; Capacity
O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O40 - General
|Depositing User:||Giorgio Fabbri|
|Date Deposited:||06. Sep 2009 19:01|
|Last Modified:||16. Feb 2013 22:36|
Asea, P.K. and Zak, P.J. (1999), “Time-to-build and cycles”, Journal of Economic Dynamics and Control, vol.23, no.8, 1155-1175.
Barro, R. J., Sala-i-Martin, X., 2004. Economic Growth. Second Edition. The MIT Press.
Bambi, M. (2008), “Endogenous growth and time to build: the AK case”, Journal of Economic Dynamics and Control, vol. 32, 1015-1040.
Bambi, M., and Gori, F. (2009), “Unifying time to build theory”.
Benhabib, J., and Rustichini, A. (1991), “Vintage capital, investment, and growth”, Journal of Economic Theory 55, 323-339.
Bellman, R. and Cooke, K. (1963), Differential-difference equations, New York Academic Press.
Bensoussan, A., Da Prato, G., Delfour, M. C. and Mitter, S. K. (1992), Representation and control of Infinite dimensional system, Birkhäuser Boston.
Boucekkine, R., Licandro, O., Puch, L. and del Rio, F. (2005), “Vintage capital and the dynamics of the AK model”, Journal of Economic Theory, vol. 120, 39-72.
Collard, F., Licandro O., and Puch, L. (2009), “The short-run dynamics of optimal growth models with delays”, Annales d’Economie et Statistiques, forthcoming.
Diekmann, O., Van Gils, S.A., Verduyn Lunel, S.M. and Walther, H.O. (1995), Delay equations, Springer, Berlin.
Edge, R. (2007), “Time-to-build, time to plan, habit persistence, and the liquidity eﬀect”, Journal of Monetary Economics, vol. 54, 1644-1669.
El-Hodiri, M., Loehman, E. and Whinston, A. (1972), “An optimal growth model with time lags”, Econometrica, vol.40, no. 6, 1137-1146.
Fabbri, G. and Gozzi, F. (2008), “Solving optimal growth models with vintage capital: the dynamic programming approach.”, Journal of Economic Theory, vol. 143, no. 1, 331-373.
Kalecki, M. (1935), “A macroeconomic theory of the business cycle”, Econometrica, vol.3, 327-344.
Kolmanovskii, V. and Myshkis, A. (1992), “Applied theory of functional differential equations”, Dordrecht academic publishers.
Kydland, F. E. and Prescott, E. C. (1982), “Time-to-build and aggregate ﬂuctuations”, Econometrica, vol.50, no.6, 1345-1370.
Ortigueira, S., and Santos, M. S. (1997), “On the speed of convergence in endogenous growth model”, American Economic Review, vol.87, no.3, 383-399.
Rustichini, A. (1989), “Hopf bifurcation for functional diﬀerential equation of mixed type”, Journal of Dynamics and Diﬀerential Equation, vol. 1, no. 2, 145-177.
Vinter, R.B. and Kwong, R.H. (1981), “The inﬁnite time quadratic control problem for linear systems with state and control delays: an evolution equation approach”, Siam J. Control Optimization, 19 (1981), 139–153.