Computational Economics

, Volume 35, Issue 4, pp 355–370 | Cite as

Finite Elements in the Presence of Occasionally Binding Constraints

  • José J. Cao-Alvira


This paper proposes and compares in terms of speed and accuracy two alternative approximation methods employing finite elements to parameterize the true policy functions that solve for the equilibrium of an optimal growth model with leisure and irreversible investment. The occasionally binding constraint in investment is efficiently handled on one algorithm by parameterizing the expectations of the marginal benefit of future physical capital stock and on the other by modifying the planner’s problem to include a penalty function. While both methods benefit from the high speed and accuracy achieved by a finite elements approximation, the algorithm incorporating a penalty function in the planner’s problem proved being of fastest convergence over a whole range of the model’s calibrations.


Finite element method Occasionally binding constraints Irreversible investment Optimal growth model 


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  1. Aiyagari R. (1994) Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics 109(3): 659–684CrossRefGoogle Scholar
  2. Aruoba S., Rubio J., Fernandez-Villaverde J. (2006) Comparing solution methods for dynamic equilibrium economies. Journal of Economic Dynamics and Control 30: 2477–2508CrossRefGoogle Scholar
  3. Christiano L., Fisher J. (2000) Algorithms for solving dynamic models with occasionally binding constraints. Journal of Economic Dynamics and Control 24: 1179–1232CrossRefGoogle Scholar
  4. Collard F., Juillard M. (2001) Accuracy of stochastic perturbation methods: the case of asset pricing models. Journal of Economic Dynamics And Control 25(6): 979–999CrossRefGoogle Scholar
  5. Den Haan W. J., Marcet A. (1994) Accuracy in simulations. Review of Economic Studies 61: 3–17CrossRefGoogle Scholar
  6. Fletcher R. (1987) Practical methods of optimization. Wiley, ChichesterGoogle Scholar
  7. Hansen G. (1985) Indivisible labor and the business cycle. Journal of Monetary Economics 16: 309–325CrossRefGoogle Scholar
  8. Hodrick R., Kocherlakota N., Lucas D. (1991) The variability of velocity in cash-in-advance models. Journal of Political Economics 99: 358–384CrossRefGoogle Scholar
  9. Hughes T. R. J. (2000) The finite element method, linear static and dynamic finite element analysis. Dover Publications, New YorkGoogle Scholar
  10. Huggett M. (1993) The risk-free rate in heterogeneous agent incomplete insurance economies. Journal of Economic Dynamics and Control 17: 953–969CrossRefGoogle Scholar
  11. Judd K.L. (1992) Projection methods for solving aggregate growth models. Journal of Economic Theory 58: 410–452CrossRefGoogle Scholar
  12. Judd K. L. (1998) Numerical methods in economics. The MIT Press, Cambridge, MAGoogle Scholar
  13. Judd K. L., Guu S. M. (1997) Asymptotic methods for aggregate growth models. Journal of Economic Dynamics and Control 21: 1025–1042CrossRefGoogle Scholar
  14. McGrattan E. (1996) Solving the stochastic growth model with a finite element method. Journal of Economic Dynamics and Control 20: 19–42CrossRefGoogle Scholar
  15. McGrattan E. (1999) Application of weighted residual methods to dynamic economic models. In: Marimon R., Scott A. (eds) Computational methods for the study of dynamic economies. Oxford University Press, OxfordGoogle Scholar
  16. Taylor J.B., Uhlig H. (1990) Solving nonlinear stochastic growth models: A comparison of alternative solution methods. Journal of Business and Economic Statistics 8: 1–17CrossRefGoogle Scholar
  17. Wen Y. (2005) Understanding the inventory cycle. Journal of Monetary Economics 52: 1533–1555CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Graduate School of Business AdministrationUniversidad de Puerto RicoSan JuanUSA

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