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Consumption and asset prices with recursive preferences: Continuous-time approximations to discrete-time models

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  • Mark Fisher
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    Abstract

    This paper presents tractable and efficient numerical solutions to general equilibrium models of asset prices and consumption where the representative agent has recursive preferences. It provides a discrete-time presentation of the approach of Fisher and Gilles (1999), treating continuous-time representations as approximations to discrete-time "truth." First, exact discrete-time solutions are derived, illustrating the following ideas: (i) The price-dividend ratio (such as the wealth-consumption ratio) is a perpetuity (the canonical infinitely lived asset), the value of which is the sum of dividend-denominated bond prices, and (ii) the positivity of the dividend-denominated asymptotic forward rate is necessary and sufficient for the convergence of value function iteration for an important class of models. Next, continuous-time approximations are introduced. By assuming the size of the time step is small, first-order approximations in the step size provide the same analytical flexibility to discrete-time modeling as Ito's lemma provides in continuous time. Moreover, it is shown that differential equations provide an efficient platform for value function iteration. Last, continuous-time normalizations are adopted, providing an efficient solution method for recursive preferences.

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    Bibliographic Info

    Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 99-18.

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    Date of creation: 1999
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    Handle: RePEc:fip:fedawp:99-18

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    Keywords: Asset pricing ; Consumption (Economics) ; Interest rates ; Wealth;

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    1. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," NBER Working Papers 4676, National Bureau of Economic Research, Inc.
    2. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    3. John Y. Campbell, 1992. "Intertemporal Asset Pricing Without Consumption Data," NBER Working Papers 3989, National Bureau of Economic Research, Inc.
    4. Campbell, John Y. & Koo, Hyeng Keun, 1997. "A comparison of numerical and analytic approximate solutions to an intertemporal consumption choice problem," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 273-295.
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