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Computational Methods for the Study of Dynamic Economies$
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Ramon Marimon and Andrew Scott

Print publication date: 2001

Print ISBN-13: 9780199248278

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199248273.001.0001

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Optimal Fiscal Policy in a Linear Stochastic Economy

Optimal Fiscal Policy in a Linear Stochastic Economy

(p.197) 9 Optimal Fiscal Policy in a Linear Stochastic Economy
Computational Methods for the Study of Dynamic Economies

Thomas J. Sargent

François R. Velde

Oxford University Press

The Lucas and Stokey (1983) economy without capital is used to exhibit features of the Lucas and Stokey model of optimal taxation, and show how they compare with Barro's (1979) tax‐smoothing model. Computation of optimal fiscal policies for Lucas and Stokey's model requires repeated evaluations of the present value of the government's surplus, an object formally equivalent to an asset price. The functional equation for an asset price is typically difficult to solve. A linear quadratic version of Lucas and Stokey's model is specified, which makes both asset pricing computations and optimal fiscal policy calculations easy. Martingale returns on government debt are discussed, and examples and extensions of Lucas and Stokey's model given. Two appendices describe and discuss: the key steps for two basic kinds of stochastic process (a stochastic first‐order linear difference equation and a Markov chain), and time consistency and the structure of debt. Lastly, details are given of the appropriate MATLAB programs.

Keywords:   asset pricing, Barro's tax‐smoothing model, Computation, dynamic economics models, fiscal policies, government debt, linear quadratic models, linear stochastic economy, Lucas and Stokey's economy without capital, Lucas and Stokey's model of optimal taxation, macroeconomics, Markov chains, Martingale returns, MATLAB programs, optimal fiscal policies, stochastic first‐order linear difference equations, stochastic models, stochastic processes, structure of debt, time consistency, valuation of government surplus

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