Linear-quadratic approximation, external habit and targeting rules.

*(English)*Zbl 1181.91143Summary: We examine the linear-quadratic approximation of nonlinear dynamic stochastic optimization problems. A discrete-time version of M. J. P. Magill [J. Econ. Theory 15, 211–219 (1977; Zbl 0382.90028)] is generalized to models with forward-looking variables paying special attention to second-order conditions. This is the “large distortions” case in the literature. We apply the approach to monetary policy in a DSGE model with external habit in consumption. We then develop a condition for “target-implementability”, a concept related to “targeting rules”. Finally, we extend the approach to a comparison between cooperative and non-cooperative equilibria in a two-country model and show that the “small distortions” approximation is inappropriate for this exercise.

##### MSC:

91B51 | Dynamic stochastic general equilibrium theory |

91A10 | Noncooperative games |

91A12 | Cooperative games |

91B66 | Multisectoral models in economics |

##### Keywords:

linear-quadratic approximation; dynamic stochastic general equilibrium models; utility-based loss function; cooperative and non-cooperative equilibria
PDF
BibTeX
XML
Cite

\textit{P. Levine} et al., J. Econ. Dyn. Control 32, No. 10, 3315--3349 (2008; Zbl 1181.91143)

Full Text:
DOI

##### References:

[1] | Altissimo, F., Curdia, V., Rodriquez, D., 2005. Linear-quadratic approximation to optimal policy; an algorithm and two applications. Presented at the Conference “Quantitative Analysis of Stabilization Policies”, Columbia University, September 2005. |

[2] | Anderson, E.W., Hansen, L.P., McGrattan, E.R., Sargent, T.J., 1996. Methods of forming and estimating dynamic linear economics. Amman, H.M., Kendrick, D., Rust, J. (Eds.), Handbook of Computational Economics. Elsevier Science, Amsterdam. · Zbl 1126.91394 |

[3] | Batini, N., Levine, P., Pearlman, J., 2007. Monetary rules in emerging economies with financial market imperfections. Presented to the NBER Conference on International Dimensions of Monetary Policy, S’Agaró, Catalonia, Spain, June 11-13, 2007, forthcoming in NBER Conference Volume. |

[4] | Benigno, G.; Benigno, P., Designing targeting rules for international monetary cooperation, Journal of monetary economics, 53, 3, 473-506, (2006) |

[5] | Benigno, P., Woodford, M., 2003. Optimal monetary and fiscal policy: a linear-quadratic approach. Presented at the International Research Forum on Monetary Policy in Washington, DC, November 14-15, 2003. |

[6] | Benigno, P.; Woodford, M., Inflation stabilization and welfare: the case of a distorted steady state, Journal of the European economic association, 3, 6, 1185-1236, (2005) |

[7] | Benigno, P., Woodford, M., 2007. Linear-quadratic approximation of optimal policy problems. NBER Working Paper No. 12672, Revised Draft. · Zbl 1258.91134 |

[8] | Choudhary, A.; Levine, P., Idle worship, Economic letters, 90, 1, 77-83, (2006) · Zbl 1254.91405 |

[9] | Clarida, R.; Gali, J.; Gertler, M., Monetary policy rules and macroeconomic stability: evidence and some theory, Quarterly journal of economics, 115, 147-180, (2000) · Zbl 1064.91512 |

[10] | Clarida, R.; Gali, J.; Gertler, M., A simple framework for international monetary policy analysis, Journal of monetary economics, 49, 879-904, (2002) |

[11] | Currie, D., Levine, P., 1993. Rules, Reputation and Macroeconomic Policy Coordination. Cambridge University Press, Cambridge. · Zbl 0794.90012 |

[12] | Fernandez-Villaverde, J.; Rubio-Ramirez, J.F., Solving DSGE models with perturbation methods and a change of variables, Journal of economic dynamics and control, 30, 2509-2531, (2006) · Zbl 1162.91480 |

[13] | Judd, K.L., Numerical methods in economics, (1998), The MIT Press Cambridge, MA, USA · Zbl 0941.00048 |

[14] | Khan, A.; King, R.; Wolman, A., Optimal monetary policy, Review of economic studies, 70, 825-860, (2003) · Zbl 1180.91201 |

[15] | Kim, J.; Kim, S.H., Spurious welfare reversals in international business cycle models, Journal of international economics, 60, 471-500, (2003) |

[16] | Kim, J.; Kim, S.H., Two pitfalls of linearization methods, Journal of money, credit and banking, 39, 4, 995-1001, (2007) |

[17] | Kim, J., Levin, A., Yun, T., 2006a. Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models, forthcoming FRB Working Paper. |

[18] | Kim, J., Levin, A., Yun, T., 2006b. Relative price distortion and optimal monetary policy in open economies. Bank of Korea Working Paper 251. |

[19] | Levine, P., Pearlman, J., Pierse, R., 2007a. Monetary policy revisited in a two bloc DSGE model. Presented at the Conference on “Robust Monetary Rules for the Open Economy” at the University of Surrey, September 20-21, 2007. |

[20] | Levine, P., McAdam, P., Pearlman, J., 2007b. Quantifying and sustaining the welfare gains from monetary commitment. ECB Working Paper No. 759, Presented at the 12th International Conference on Computing in Economics and Finance, Cyprus, June, 2006. |

[21] | Magill, M., A local analysis of N-sector capital accumulation under uncertainty, Journal of economic theory, 15, 2, 211-219, (1977) · Zbl 0382.90028 |

[22] | Magill, M., Some new results on the local stability of the process of capital accumulation, Journal of economic theory, 15, 2, 174-210, (1977) · Zbl 0372.90009 |

[23] | McCallum, N.T., Nelson, E., 2004. Targeting rules vs instrument rules for monetary policy. Mimeo. |

[24] | Pappa, E., Do the ECB and the fed really need to cooperate? optimal monetary policy in a two-country world, Journal of monetary economics, 51, 753-779, (2004) |

[25] | Pierse, R.G., 2001. WinSolve version 3: an introductory guide. University of Surrey \(\langle\)www.econ.surrey.ac.uk/winsolve/⟩. |

[26] | Smets, F.; Wouters, R., An estimated stochastic dynamic general equilibrium model of the euro area, Journal of the European economic association, 1, 5, 1123-1175, (2003) |

[27] | Svensson, L.E.O., What is wrong with Taylor rules? using judgement in monetary policy through targeting rules, Journal of economic literature, 41, 426-477, (2003) |

[28] | Svensson, L.E.O., Monetary policy with judgment: forecast targeting, International journal of central banking, 1, 1-54, (2005) |

[29] | Trentelman, H.L.; Rapisarda, P., Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation, SIAM journal on control and optimization, 40, 3, 969-991, (2001) · Zbl 0997.93082 |

[30] | Woodford, M., Foundations of a theory of monetary policy, (2003), Princeton University Press Princeton, NJ |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.