Optimal control indicators for the assessment of the influence of government policy to business cycle shocks

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January 2014, 1(1): 79-104. doi: 10.3934/jdg.2014.1.79

Optimal control indicators for the assessment of the influence of government policy to business cycle shocks

John Leventides ^1, and Iraklis Kollias ^1,

1.	Department of Economics, Division of Mathematics-Informatics, National and Kapodistrian University of Athens, 8 Pesmazoglou Street, Athens, 105 59, Greece, Greece

Received July 2012 Revised October 2012 Published June 2013

Abstract
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We consider idealised dynamic models isolating the relationship between GDP and government expenditures. In this setting we assess the possibility of smoothing the effect of business cycle shocks via government expenditure alone and propose optimal control indicators measuring the control potential of this government action. This provides with new indicators and indices refining the dynamic relationship obtained by ARMA or similar type of macro - modeling.

Keywords: dynamic macro - modeling and indicators., Control systems, business cycles, stochastic optimal control.

Mathematics Subject Classification: Primary: 93C05, 93E20; Secondary: 49J2.

Citation: John Leventides, Iraklis Kollias. Optimal control indicators for the assessment of the influence of government policy to business cycle shocks. Journal of Dynamics and Games, 2014, 1 (1) : 79-104. doi: 10.3934/jdg.2014.1.79

References:

[1]	A. G. Malliaris and J. L. Urrutia, How big is the random walk in macroeconomic time series: Variance ratio tests, Economic Uncertainty, Instabilities And Asset Bubbles, (2005), 9-12. doi: 10.1142/9789812701015_0002.
[2]	C. Burnside and M. Eichenbaum, Factor Hoarding and the Propagation of Business Cycle Shocks, American Economic Review, 86 (1996), 1154-1174.
[3]	C. R. Nelson and C. I. Plosser, Trends and random walks in macroeconomic time series: Some evidence and implications, Journal of Monetary Economics, 10 (1982), 139-162. doi: 10.1016/0304-3932(82)90012-5.
[4]	D. E. W. Laidler, An elementary monetarist model of simultaneous fluctuations in prices and output, in "Inflation in Small Countries" (ed. H. Frisch), Lecture Notes in Economics and Mathematical Systems, 119, Springer, Berlin-Heidelberg, (1976), 75-89. doi: 10.1007/978-3-642-46331-0_4.
[5]	F. Canova, Detrending and business cycle facts, Journal of Monetary Economics, 41 (1998), 475-512. doi: 10.1016/S0304-3932(98)00006-3.
[6]	F. E. Kydland and E. C. Prescott, Time to build and aggregate fluctuations, Econometrica, 50 (1982), 1345-1370.
[7]	J.-O. Cho and T. F. Cooley, The business cycle with nominal contracts, Economic Theory, 6 (1995), 13-33. doi: 10.1007/BF01213939.
[8]	J. B. Long, Jr. and C. I. Plosser, Real business cycles, Journal of Political Economy, 91 (1983), 39-69.
[9]	J. H. Stock and M. W. Watson, Does GNP have a unit root?, Economics Letters, 22 (1986), 147-151. doi: 10.1016/0165-1765(86)90222-3.
[10]	J. Y. Campbell and N. G. Mankiw, Are output fluctuations transitory?, The Quarterly Journal of Economics, 102 (1987), 857-880. doi: 10.2307/1884285.
[11]	L. J. Christiano and M. Eichenbaum, Current real-business cycle theories and aggregate labor-market fluctuations, American Economic Review, 82 (1992), 430-450.
[12]	L. J. Christiano and M. Eichenbaum, Unit roots in real GNP: Do we know and do we care?, Carnegie-Rochester Conference Series on Public Policy, 32 (1990), 7-62.
[13]	Lutz Arnold, "Business Cycle Theory," Oxford University Press, 2002. doi: 10.1093/acprof:oso/9780199256815.001.0001.
[14]	M. Boldrin and M. Horvath, Labor contracts and business cycles, Journal of Political Economy, 103 (1995), 972-1004. doi: 10.1086/262010.
[15]	N. G. Mankiw and D. Romer, "New Keynesian Economics," Vols. 1 and 2, Cambridge University Press, 1991.
[16]	O. J. Blanchard and S. Fischer, "Lectures in Macroeconomics," MIT Press, Cambridge, 1989.
[17]	Philip R. Lane, The cyclical behaviour of fiscal policy: Evidence from the OECD, Journal of Public Economics, 87 (2003), 2661-2675. doi: 10.1016/S0047-2727(02)00075-0.
[18]	R. Cottle, J. Pang and R. Stone, "Linear Complimentarity Problem," Classics in Applied Mathematics, SIAM, 2009.
[19]	R. E. Lucas, Jr., Econometric policy evaluation: A critique, in "Carnegie-Rochester Conference Series on Public Policy," Elsevier, North Holland, Amsterdam, (1976), 19-46. doi: 10.1016/S0167-2231(76)80003-6.
[20]	R. E. A. Farmer and J.-T. Guo, Real business cycles and the animal spirits hypothesis, Journal of Economic Theory, 63 (1994), 42-72. doi: 10.1006/jeth.1994.1032.
[21]	R. G. King and S. T. Rebelo, Resuscitating real business cycles, in "Handbook of Macroeconomics" (eds. J. B. Taylor and M. Woodford), North Holland, Amsterdam, (1999), 927-1007. doi: 10.1016/S1574-0048(99)10022-3.
[22]	R. G. D. Allen, "Macroeconomic Theory: A Mathematical Treatment," Macmillan, London, 1967.
[23]	R. Neck, The Contribution of Control Theory to the Analysis of Economic Policy, in "Proceedings of the $17^th$ World Congress," The International Federation of Automatic Control, Seoul, (2008), 6-11.
[24]	V. R. Bencivenga, An econometric study of hours and output variation with preference shocks, International Economic Review, 33 (1992), 449-471. doi: 10.2307/2526904.
[25]	S. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, Cambridge, 2004.
[26]	T. Puu and I. Sushko, A business cycle model with cubic nonlinearity, Chaos, Solitons and Fractals, 19 (2004), 597-612. doi: 10.1016/S0960-0779(03)00132-2.

show all references

References:

[1]	A. G. Malliaris and J. L. Urrutia, How big is the random walk in macroeconomic time series: Variance ratio tests, Economic Uncertainty, Instabilities And Asset Bubbles, (2005), 9-12. doi: 10.1142/9789812701015_0002.
[2]	C. Burnside and M. Eichenbaum, Factor Hoarding and the Propagation of Business Cycle Shocks, American Economic Review, 86 (1996), 1154-1174.
[3]	C. R. Nelson and C. I. Plosser, Trends and random walks in macroeconomic time series: Some evidence and implications, Journal of Monetary Economics, 10 (1982), 139-162. doi: 10.1016/0304-3932(82)90012-5.
[4]	D. E. W. Laidler, An elementary monetarist model of simultaneous fluctuations in prices and output, in "Inflation in Small Countries" (ed. H. Frisch), Lecture Notes in Economics and Mathematical Systems, 119, Springer, Berlin-Heidelberg, (1976), 75-89. doi: 10.1007/978-3-642-46331-0_4.
[5]	F. Canova, Detrending and business cycle facts, Journal of Monetary Economics, 41 (1998), 475-512. doi: 10.1016/S0304-3932(98)00006-3.
[6]	F. E. Kydland and E. C. Prescott, Time to build and aggregate fluctuations, Econometrica, 50 (1982), 1345-1370.
[7]	J.-O. Cho and T. F. Cooley, The business cycle with nominal contracts, Economic Theory, 6 (1995), 13-33. doi: 10.1007/BF01213939.
[8]	J. B. Long, Jr. and C. I. Plosser, Real business cycles, Journal of Political Economy, 91 (1983), 39-69.
[9]	J. H. Stock and M. W. Watson, Does GNP have a unit root?, Economics Letters, 22 (1986), 147-151. doi: 10.1016/0165-1765(86)90222-3.
[10]	J. Y. Campbell and N. G. Mankiw, Are output fluctuations transitory?, The Quarterly Journal of Economics, 102 (1987), 857-880. doi: 10.2307/1884285.
[11]	L. J. Christiano and M. Eichenbaum, Current real-business cycle theories and aggregate labor-market fluctuations, American Economic Review, 82 (1992), 430-450.
[12]	L. J. Christiano and M. Eichenbaum, Unit roots in real GNP: Do we know and do we care?, Carnegie-Rochester Conference Series on Public Policy, 32 (1990), 7-62.
[13]	Lutz Arnold, "Business Cycle Theory," Oxford University Press, 2002. doi: 10.1093/acprof:oso/9780199256815.001.0001.
[14]	M. Boldrin and M. Horvath, Labor contracts and business cycles, Journal of Political Economy, 103 (1995), 972-1004. doi: 10.1086/262010.
[15]	N. G. Mankiw and D. Romer, "New Keynesian Economics," Vols. 1 and 2, Cambridge University Press, 1991.
[16]	O. J. Blanchard and S. Fischer, "Lectures in Macroeconomics," MIT Press, Cambridge, 1989.
[17]	Philip R. Lane, The cyclical behaviour of fiscal policy: Evidence from the OECD, Journal of Public Economics, 87 (2003), 2661-2675. doi: 10.1016/S0047-2727(02)00075-0.
[18]	R. Cottle, J. Pang and R. Stone, "Linear Complimentarity Problem," Classics in Applied Mathematics, SIAM, 2009.
[19]	R. E. Lucas, Jr., Econometric policy evaluation: A critique, in "Carnegie-Rochester Conference Series on Public Policy," Elsevier, North Holland, Amsterdam, (1976), 19-46. doi: 10.1016/S0167-2231(76)80003-6.
[20]	R. E. A. Farmer and J.-T. Guo, Real business cycles and the animal spirits hypothesis, Journal of Economic Theory, 63 (1994), 42-72. doi: 10.1006/jeth.1994.1032.
[21]	R. G. King and S. T. Rebelo, Resuscitating real business cycles, in "Handbook of Macroeconomics" (eds. J. B. Taylor and M. Woodford), North Holland, Amsterdam, (1999), 927-1007. doi: 10.1016/S1574-0048(99)10022-3.
[22]	R. G. D. Allen, "Macroeconomic Theory: A Mathematical Treatment," Macmillan, London, 1967.
[23]	R. Neck, The Contribution of Control Theory to the Analysis of Economic Policy, in "Proceedings of the $17^th$ World Congress," The International Federation of Automatic Control, Seoul, (2008), 6-11.
[24]	V. R. Bencivenga, An econometric study of hours and output variation with preference shocks, International Economic Review, 33 (1992), 449-471. doi: 10.2307/2526904.
[25]	S. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, Cambridge, 2004.
[26]	T. Puu and I. Sushko, A business cycle model with cubic nonlinearity, Chaos, Solitons and Fractals, 19 (2004), 597-612. doi: 10.1016/S0960-0779(03)00132-2.

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