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  • Juan Carlos Parra-Alvarez (a1)

This study evaluates the accuracy of a set of techniques that approximate the solution of continuous-time Dynamic Stochastic General Equilibrium models. Using the neoclassical growth model, I compare linear-quadratic, perturbation, and projection methods. All techniques are applied to the Hamilton–Jacobi–Bellman equation and the optimality conditions that define the general equilibrium of the economy. Two cases are studied depending on whether a closed-form solution is available. I also analyze how different degrees of non-linearities affect the approximated solution. The results encourage the use of perturbations for reasonable values of the structural parameters of the model and suggest the use of projection methods when a high degree of accuracy is required.

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Address correspondence to: Juan Carlos Parra-Alvarez, Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark; e-mail:
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I would like to thank the editor and two anonymous referees for extremely useful comments and suggestions, as well as the participants of the 18th Annual Conference on Computing in Economics and Finance in Prague, the 6th CSDA International Conference on Computational and Financial Econometrics in Oviedo and the CDMA Workshop on DSGE models in St. Andrews for their helpful comments. I would also like to thank Olaf Posch, Bent Jesper Christensen, Jesús Fernández-Villaverde, Kenneth Judd, Martin Møller Andreasen, Willi Semmler and seminar participants at CREATES for useful suggestions and insights. CREATES (Center for Research in Econometric Analysis of Time Series) is funded by the Danish National Research Foundation.

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E. W. Anderson , E. R. McGrattan , L. P. Hansen , and T. J. Sargent (1996) Mechanics of forming and estimating dynamic linear economies. In H. M. Amman , D. A. Kendrick , and J. Rust (eds.), Handbook of Computational Economics, vol. 1, chap. 4, pp 171252. Netherlands: Elsevier.

S. B. Aruoba , J. Fernández-Villaverde , and J. F. Rubio-Ramírez (2006) Comparing solution methods for dynamic equilibrium economies. Journal of Economic Dynamics and Control 30 (12), 24772508.

P. Benigno and M. Woodford (2012) Linear-quadratic approximation of optimal policy problems. Journal of Economic Theory 147 (1), 142.

A. Bergstrom (1984) Continuous time stochastic models and issues of aggregation over time. In Z. Griliches and M. D. Intriligator (eds.), Handbook of Econometrics, vol. 2, chap. 20, 11451212, Netherlands: Elsevier.

J. v. Binsbergen , J. Fernández-Villaverde , R. S. Koijen , and J. Rubio-Ramírez (2012) The term structure of interest rates in a DSGE model with recursive preferences. Journal of Monetary Economics 59 (7), 634648.

O. Blanchard (2009) The state of macro. Annual Review of Economics 1 (1), 209228.

M. J. Brennan (1998) The role of learning in dynamic portfolio decisions. European Finance Review 1 (3), 295306.

M. K. Brunnermeier and Y. Sannikov (2014) A macroeconomic model with a financial sector. American Economic Review 104 (2), 379421.

D. Caldara , J. Fernández-Villaverde , J. Rubio-Ramírez , and W. Yao (2012) Computing DSGE models with recursive preferences and stochastic volatility. Review of Economic Dynamics 15 (2), 188206.

F. Collard and M. Juillard (2001) Accuracy of stochastic perturbation methods: The case of asset pricing models. Journal of Economic Dynamics and Control 25 (6–7), 979999.

W. J. Den Haan and A. Marcet (1994) Accuracy in simulations. Review of Economic Studies 61 (1), 317.

U. Doraszelski and K. L. Judd (2012) Avoiding the curse of dimensionality in dynamic stochastic games. Quantitative Economics 3 (1), 5393.

J. Fernández-Villaverde , J. F. Rubio-Ramírez , and M. S. Santos (2006) Convergence properties of the likelihood of computed dynamic models. Econometrica 74 (1), 93119.

F. Furlanetto and M. Seneca (2014) New perspectives on depreciation shocks as a source of business cycle fluctuations. Macroeconomic Dynamics 18, 12091233.

F. Gourio (2012) Disaster risk and business cycles. American Economic Review 102 (6), 27342766.

E. L. Grinols and S. J. Turnovsky (1993) Risk, the financial market, and macroeconomic equilibrium. Journal of Economic Dynamics and Control 17 (1–2), 136.

B. Heer and A. Maussner (2009) Dynamic General Equilibrium Modeling: Computational Methods and Applications, 2nd ed. Heidelberg: Springer-Verlag.

K. L. Judd (1996) Approximation, perturbation, and projection methods in economic analysis. In H. M. Amman , D. A. Kendrick , and J. Rust (eds.), Handbook of Computational Economics, vol. 1, chap. 12, pp. 509585. Netherlands: Elsevier.

K. L. Judd and S. M. Guu (1993) Perturbation methods for economic growth models. In H. R. Varian (ed.), Economic and Financial Modeling with Mathematica, chap. 2, pp. 80103. New York: Springer-Verlag.

M. S. Kimball (2014) Effect of uncertainty on optimal control models in the neighbourhood of a steady state. Geneva Risk Insurance Review 39 (1), 239.

T. Kompas and L. Chu (2012) A comparison of parametric approximation techniques to continuous-time stochastic dynamic programming problems: Applications to natural resource modelling. Enviornmental Modelling and Software 38, 112.

F. E. Kydland and E. C. Prescott (1982) Time to build and aggregate fluctuations. Econometrica 50 (6), 13451370.

M. J. P. Magill (1977a) Some new results on the local stability of the process of capital accumulation. Journal of Economic Theory 15 (1), 174210.

M. J. P. Magill (1977b) A local analysis of n-sector capital accumulation under uncertainty. Journal of Economic Theory 15 (1), 211219.

O. Posch (2011) Risk premia in general equilibrium. Journal of Economic Dynamics and Control 35 (9), 15571576.

E. T. Swanson (2012) Risk aversion and the labor margin in dynamic equilibrium models. American Economic Review 102 (4), 16631691.

C. S. Tapiero and A. Sulem (1994) Computational aspects in applied stochastic control. Computational Economics 7 (2), 109146.

J. B. Taylor and H. Uhlig (1990) Solving nonlinear stochastic growth models: A comparison of alternative solution methods. Journal of Business & Economic Statistics 8 (1), 117.

S. J. Turnovsky and W. T. Smith (2006) Equilibrium consumption and precautionary savings in a stochastically growing economy. Journal of Economic Dynamics and Control 30 (2), 243278.

J. Wachter (2013) Can time-varying risk of rare disasters explain aggregate stock market volatility? Journal of Finance 68 (3), 9871035.

K. Wälde (2011) Production technologies in stochastic continuous time models. Journal of Economic Dynamics and Control 35 (4), 616622.

Y. Xia (2001) Learning about predictability: The effects of parameter uncertainty on dynamic asset allocation. Journal of Finance 56 (1), 205246.

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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
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