# Numerical Policy Error Bounds for $$\eta$$ η -Concave Stochastic Dynamic Programming with Non-interior Solutions

Listed:
• Huiyu Li

()

## Abstract

This paper derives explicit error bounds for numerical policies of $$\eta$$ η -concave stochastic dynamic programming problems, without assuming the optimal policy is interior. We demonstrate the usefulness of our error bound by using it to pinpoint the states at which the borrowing constraint binds in a widely used income fluctuation problem with standard calibrations and a firm production problem with financial constraints. Copyright Springer Science+Business Media New York 2015

## Suggested Citation

• Huiyu Li, 2015. "Numerical Policy Error Bounds for $$\eta$$ η -Concave Stochastic Dynamic Programming with Non-interior Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 171-187, August.
• Handle: RePEc:kap:compec:v:46:y:2015:i:2:p:171-187
DOI: 10.1007/s10614-014-9460-9
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File URL: http://hdl.handle.net/10.1007/s10614-014-9460-9

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## References listed on IDEAS

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1. Maldonado, Wilfredo L. & Svaiter, B.F., 2007. "Holder continuity of the policy function approximation in the value function approximation," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 629-639, June.
2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, January.
3. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
4. Matteo Iacoviello, 2005. "House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle," American Economic Review, American Economic Association, vol. 95(3), pages 739-764, June.
5. McGrattan, Ellen R., 1996. "Solving the stochastic growth model with a finite element method," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 19-42.
6. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
7. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
8. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
9. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
10. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
11. Virgiliu Midrigan & Daniel Yi Xu, 2014. "Finance and Misallocation: Evidence from Plant-Level Data," American Economic Review, American Economic Association, vol. 104(2), pages 422-458, February.
12. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
13. Den Haan, Wouter J., 2010. "Comparison of solutions to the incomplete markets model with aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 4-27, January.
14. Francisco J. Buera & Joseph P. Kaboski & Yongseok Shin, 2011. "Finance and Development: A Tale of Two Sectors," American Economic Review, American Economic Association, vol. 101(5), pages 1964-2002, August.
15. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
16. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
17. Schechtman, Jack & Escudero, Vera L. S., 1977. "Some results on "an income fluctuation problem"," Journal of Economic Theory, Elsevier, vol. 16(2), pages 151-166, December.
18. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
19. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
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### Keywords

Accuracy test; Computable policy error bound; Noninterior solution; Euler equation error ; C63; E21;

### JEL classification:

• C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
• E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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