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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

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 & 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.  Google Scholar

[2]

C. Burnside and M. Eichenbaum, Factor Hoarding and the Propagation of Business Cycle Shocks, American Economic Review, 86 (1996), 1154-1174. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

F. Canova, Detrending and business cycle facts, Journal of Monetary Economics, 41 (1998), 475-512. doi: 10.1016/S0304-3932(98)00006-3.  Google Scholar

[6]

F. E. Kydland and E. C. Prescott, Time to build and aggregate fluctuations, Econometrica, 50 (1982), 1345-1370. Google Scholar

[7]

J.-O. Cho and T. F. Cooley, The business cycle with nominal contracts, Economic Theory, 6 (1995), 13-33. doi: 10.1007/BF01213939.  Google Scholar

[8]

J. B. Long, Jr. and C. I. Plosser, Real business cycles, Journal of Political Economy, 91 (1983), 39-69. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

L. J. Christiano and M. Eichenbaum, Current real-business cycle theories and aggregate labor-market fluctuations, American Economic Review, 82 (1992), 430-450. Google Scholar

[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. Google Scholar

[13]

Lutz Arnold, "Business Cycle Theory," Oxford University Press, 2002. doi: 10.1093/acprof:oso/9780199256815.001.0001.  Google Scholar

[14]

M. Boldrin and M. Horvath, Labor contracts and business cycles, Journal of Political Economy, 103 (1995), 972-1004. doi: 10.1086/262010.  Google Scholar

[15]

N. G. Mankiw and D. Romer, "New Keynesian Economics," Vols. 1 and 2, Cambridge University Press, 1991. Google Scholar

[16]

O. J. Blanchard and S. Fischer, "Lectures in Macroeconomics," MIT Press, Cambridge, 1989. Google Scholar

[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.  Google Scholar

[18]

R. Cottle, J. Pang and R. Stone, "Linear Complimentarity Problem," Classics in Applied Mathematics, SIAM, 2009. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[22]

R. G. D. Allen, "Macroeconomic Theory: A Mathematical Treatment," Macmillan, London, 1967. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[25]

S. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, Cambridge, 2004.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[2]

C. Burnside and M. Eichenbaum, Factor Hoarding and the Propagation of Business Cycle Shocks, American Economic Review, 86 (1996), 1154-1174. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

F. Canova, Detrending and business cycle facts, Journal of Monetary Economics, 41 (1998), 475-512. doi: 10.1016/S0304-3932(98)00006-3.  Google Scholar

[6]

F. E. Kydland and E. C. Prescott, Time to build and aggregate fluctuations, Econometrica, 50 (1982), 1345-1370. Google Scholar

[7]

J.-O. Cho and T. F. Cooley, The business cycle with nominal contracts, Economic Theory, 6 (1995), 13-33. doi: 10.1007/BF01213939.  Google Scholar

[8]

J. B. Long, Jr. and C. I. Plosser, Real business cycles, Journal of Political Economy, 91 (1983), 39-69. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

L. J. Christiano and M. Eichenbaum, Current real-business cycle theories and aggregate labor-market fluctuations, American Economic Review, 82 (1992), 430-450. Google Scholar

[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. Google Scholar

[13]

Lutz Arnold, "Business Cycle Theory," Oxford University Press, 2002. doi: 10.1093/acprof:oso/9780199256815.001.0001.  Google Scholar

[14]

M. Boldrin and M. Horvath, Labor contracts and business cycles, Journal of Political Economy, 103 (1995), 972-1004. doi: 10.1086/262010.  Google Scholar

[15]

N. G. Mankiw and D. Romer, "New Keynesian Economics," Vols. 1 and 2, Cambridge University Press, 1991. Google Scholar

[16]

O. J. Blanchard and S. Fischer, "Lectures in Macroeconomics," MIT Press, Cambridge, 1989. Google Scholar

[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.  Google Scholar

[18]

R. Cottle, J. Pang and R. Stone, "Linear Complimentarity Problem," Classics in Applied Mathematics, SIAM, 2009. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[22]

R. G. D. Allen, "Macroeconomic Theory: A Mathematical Treatment," Macmillan, London, 1967. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[25]

S. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, Cambridge, 2004.  Google Scholar

[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.  Google Scholar

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