ncdnumericaljune1 - Numerical Analysis of Non-constant...

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Numerical Analysis of Non-constant Discounting with an Application to Renewable Resource Management Tomoki Fujii Larry Karp May 31, 2006 Abstract The possibility of non-constant discounting is important in environmental and resource management problems where current decisions affect welfare in the far-distant future, as with climate change. The difficulty of analyzing models with non-constant discounting limits their application. We describe and provide software to implement an algorithm to numerically obtain a Markov Perfect Equilibrium for an optimal control problem with non-constant discounting. The software is available online. We illustrate the approach by studying welfare and observational equivalence for a particular renewable resource man- agement problem. Keywords: Non-constant discounting, numerical methods, non-renewable resources, observational equivalence. JEL classification numbers: C63, Q20 School of Economics and Social Sciences, Singapore Management University, 90 Stamford Road, 178903 Singapore email:fujii@smu.edu.sg Department of Agricultural and Resource Economics, 207 Giannini Hall, University of California, Berkeley CA 94720 email:karp@are.berkelely.edu
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1I n t r o d u c t i o n Recent research on models with non-constant discount rates explores the causes of non-constant discounting, examines how agents with non-constant discount rates behave, and attempts to de- termine empirically whether discount rates change with the planning horizon. Non-constant discounting (hereafter “NCD”) increases the complexity of dynamic models, making their anal- ysis more difficult. Numerical methods have proven useful in many areas of economics, both to solve old problems and to suggest new ones. Numerical methods can be similarly useful in NCD models. Here we introduce and illustrate a numerical package that solves a fairly general NCD model. Our model is stationary; in particular, it has an infinite horizon. This kind of model has an “incomplete transversality condition”, a feature that also occurs in some differential games, but not in standard optimal control problems. Our numerical approach must confront this feature. We illustrate our methods by examining the extent to which a decision rule induced by NCD is observationally equivalent to a decision rule associated with a constant discount rate. We also calculate the loss in steady state welfare resulting from the inability to make binding commitments. The rest of this Introduction explains why NCDmaybeanimpor tan tfea tureineconom ic problems, and we explain what we mean by the “solution” to such a model. We review the reason for the incomplete transversality condition, and discuss how this feature complicates the analysis of NCD problems. We then explain the importance of the question of observational equivalence between models with constant versus non-constant discounting. In the process, we discuss some of the relevant literature; Groom, Hepburn, Koundouri, and Pearce (2005) provide a recent review of much of this literature.
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This note was uploaded on 08/01/2008 for the course ARE 263 taught by Professor Karp during the Fall '06 term at University of California, Berkeley.

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ncdnumericaljune1 - Numerical Analysis of Non-constant...

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