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Stochastic continuous time growth models that allow for closed form solutions

Author

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  • Francesco Menoncin

    (University of Brescia)

  • Stefano Nembrini

    (University of Brescia)

Abstract

We find a closed form solution that maximises the expected utility of an agent’s inter-temporal consumption subject to a stochastic technology, which is a linear combination of AK and Cobb–Douglas technologies. Additionally, we consider two cases of agent preferences: (i) Constant Relative Risk Aversion (CRRA) preferences, which treat optimal consumption as a linear function of capital, and (ii) Hyperbolic Absolute Risk Aversion (HARA) preferences, which treat optimal consumption as an affine function of capital. By establishing a minimum (subsistence) level of consumption in the HARA model, we are able to create a framework that more accurately represents real-world circumstances than previous studies have done. Furthermore, for both the CRRA and HARA cases we show the suitable, consistent stochastic differential equation which describes the capital dynamics. Finally, we perform a numerical simulation based on the CRRA case and calibrate US data for the HARA case.

Suggested Citation

  • Francesco Menoncin & Stefano Nembrini, 2018. "Stochastic continuous time growth models that allow for closed form solutions," Journal of Economics, Springer, vol. 124(3), pages 213-241, July.
    • Handle: RePEc:kap:jeczfn:v:124:y:2018:i:3:d:10.1007_s00712-017-0567-z
    DOI: 10.1007/s00712-017-0567-z
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    References listed on IDEAS

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    More about this item

    Keywords

    Dynamic stochastic general equilibrium models; Closed-form solution; HARA preferences; CRRA preferences; Autonomous consumption;
    All these keywords.

    JEL classification:

    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

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