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Structural estimation of jump-diffusion processes in macroeconomics

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  • Posch, Olaf

Abstract

This paper shows how to solve and estimate a continuous-time dynamic stochastic general equilibrium (DSGE) model with jumps. It also shows that a continuous-time formulation can make it simpler (relative to its discrete-time version) to compute and estimate the deep parameters using the likelihood function when non-linearities and/or non-normalities are considered. We illustrate our approach by solving and estimating the stochastic AK and the neoclassical growth models. Our Monte Carlo experiments demonstrate that non-normalities can be detected for this class of models. Moreover, we provide strong empirical evidence for jumps in aggregate US data.

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  • Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    • Handle: RePEc:eee:econom:v:153:y:2009:i:2:p:196-210
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    Cited by:

    1. Ascari, Guido & Fagiolo, Giorgio & Roventini, Andrea, 2015. "Fat-Tail Distributions And Business-Cycle Models," Macroeconomic Dynamics, Cambridge University Press, vol. 19(2), pages 465-476, March.
    2. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    3. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
    4. Liao, Zhong-Wei & Shao, Jinghai, 2024. "Stability and mean growth rate of stochastic Solow model driven by jump–diffusion process," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. Olaf Posch & Andreas Schrimpf, 2012. "Risk of Rare Disasters, Euler Equation Errors and the Performance of the C-CAPM," CREATES Research Papers 2012-32, Department of Economics and Business Economics, Aarhus University.
    6. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
    7. Parra-Alvarez, Juan Carlos, 2018. "A Comparison Of Numerical Methods For The Solution Of Continuous-Time Dsge Models," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1555-1583, September.
    8. Olaf POSCH & Klaus WALDE, 2009. "On the non-causal link between volatility and growth," LIDAM Discussion Papers IRES 2009025, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    9. Christian Bayer & Klaus Waelde, 2011. "Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models," Working Papers 1111, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
    10. Md. Azizul Baten & Anton Abdulbasah Kamil, 2013. "Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, March.
    11. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    12. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    13. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.
    14. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
    15. Christensen, Bent Jesper & Posch, Olaf & van der Wel, Michel, 2016. "Estimating dynamic equilibrium models using mixed frequency macro and financial data," Journal of Econometrics, Elsevier, vol. 194(1), pages 116-137.
    16. Guerrini, Luca, 2010. "A closed-form solution to the Ramsey model with logistic population growth," Economic Modelling, Elsevier, vol. 27(5), pages 1178-1182, September.
    17. Motoh Tsujimura & Hidekazu Yoshioka, 2023. "A robust consumption model when the intensity of technological progress is ambiguous," Mathematics and Financial Economics, Springer, volume 17, number 2, December.

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    More about this item

    Keywords

    Jump-diffusion estimation Continuous-time DSGE models Closed-form;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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