back to course page L Karp and C Traeger
Course Outline
ARE 263, Fall 2008
Methods of Dynamic Analysis and Control
Course requirements: (i) Approximately half a dozen problem sets (ii) a final exam.
Books on reserve:
Dynamic Optimization, 2nd ed, M Kamien and N Schwartz, North Holland
Elements of Dynamic Optimization, Alpha Chiang, McGraw Hill.
Dynamic Programming and Optimal Control, D Bertsekas, Athena Scientific Press (1995)
Mathematical Bioeconomics, C Clark 2nd ed, Wiley
Differential Equations, Stability and Chaos, W Brock and A Malliaris, North Holland, 1989
Numerical Methods in Economics, Kenneth Judd, MIT Press 1999.
Applied Computational Economics and Finance, M Miranda and P Fackler, MIT Press, 2002
Recursive Methods in Economic Dynamics, Stokey and Lucas, Harvard University Press, 1989
Other books:
Differential Games in Economics and Management Science, Dockner, van Long and Sorger, Cambridge University Press 2000, (chapter 3 is a nice introduction to continuous time dynamic programming)
Investment under Uncertainty, Dixit and Pindyck, Princeton University Press, 1994.
List of topics (with some readings):
1. Basics of dynamic programming (discrete time). This section examines examples of discrete time dynamic programming problems. MF (= Miranda and Fackler) pp 155 - 163, pp 189 – 208.
2. The linear-quadratic model. MF 223 – 226. This section discusses the solution to the LQ problem, and some of its variations, and examines the dynamic version of the “taxes versus quantities” comparison.
Weitzman (1974), Prices vs. Quantities , Review of Economic Studies 41: 477-491.
Hoel and Karp (2002), Taxes versus quotas for a stock pollutant , Resource and Energy Economcis 24: 367-384.
Newell and Pizer (2003), Regulating stock externalities under uncertainty , Journal of Environmental Economics and Management 45: 416-432.
3. Learning about unknown parameters. This section discusses modeling of anticipated learning about fixed but unknown model parameters, applied to climate change policy.
Clark and Mangel, Stochasticity, Uncertainty, and some Information as a State Variable, Chapter 11 in: Dynamic State Variable Models of Ecology, Oxford Press, 2000.
Gollier, Julien and Treich (2003), Scientific progress and irreversibility: An economic interpretation of the precautionary principle , Journal of Public Economics 75: 229–253.
Application: climate change.
Kolstad (1996), Learning and Stock Effects in Environmental Regulation: The Case of Greenhouse Gas Emissions , Journal of Environmental Economics and Management 31: 1-18.
Ulph and Ulph (1997), Global warming, irreversibility and learning , The Economic Journal 107: 636-650.
Kelly and Kolstad (1999), Bayesian learning, growth, and pollution , Journal of Economic Dynamics and Control, 23: 491-518.
Karp and Zhang (2005), Regulation with Anticipated Learning about Environmental Damages , Journal of Environmental Economics and Management 51: 259–279.
4. Numerical solutions to dynamic problems. This section explains how to obtain numerical solutions for dynamic problems. MF Chapter 6, Chapter 7 pp 163 – 182, Chapter 9.
5. Introduction to continuous time dynamics. This section discusses basics of Ordinary Differential Equations (ODEs) and Phase Plane Analysis. Clark chapter 6; Kamien and Schwartz appendix.
Applications:
Krugman, P. (1991) " History versus Expecation" QJE 651 - 67.
Fukao, K and R. Benabou (1993), History versus Expectations: a comment , QJE vol 108 pp 535-542.
Brander, J and S Taylor (1998) "The Simple Economics of Easter Island: a Ricardo-Malthus Model of Renewable Resource Use ". AER, vol 88 pp 119 - 138.
Chichilnisky, G “North-South Trade and the Dynamics of Renewable Resources ” (1993) Structural Change and Economic Dynamics Vol. 4, pp 219-248.
Karp, Larry S. and Thierry Paul, “Indeterminacy with Environmental and Labor Dynamics ” Structural Change and Economic Dynamics Vol. 18, pp 100 – 119 (2007).
6. The Calculus of Variations (COV). This section derives the continuous time Euler Equation and discusses its intuition. Kamien and Schwartz, part I, sections 1 - 11; or Chiang, chapters 1 - 5.
7. The Maximum Principle. This section discusses analysis of a one-state variable optimal control problem, emphasizes comparative statics and comparative dynamics. Kamien and Schwartz, part II, sections 1 - 9; or Chiang, chapters 7 - 9; Dynamic Envelope Theorem.
8. The dynamic programming equation in continuous time. This section derives the continuous time DPE and discusses its relation to the Maximum Principle.
Applications:
Weitzman (1976), On the Welfare Significance of National Product in a Dynamic Economy , The Quarterly Journal of Economics 90: 156-162.
Weitzman (1999), Pricing the limits to growth from mineral depletion , The Quarterly Journal of Economics 114: 691-706.
9. Event uncertainty. This section shows how to convert a problem with event uncertainty into a deterministic control problem. Kamien and Schwartz pp 61 – 63 and 190 – 193.
Applications: catastrophic damages associated with climate change.
Clarke and Reed. "Consumption/pollution tradeoffs in an environment vulnerable to pollution-related catastrophic collapse " Journal of Economic Dynamics and Control 1994 vol 18 pp 991 - 1011.
Tsur and Zemel (1996), Accounting for global warming risks: Resource management under event uncertainty , Journal of Economic Dynamics and Control 20: 1289-1305.
10. Non-convex control problems. This section discusses the solution to non-convex problems. We discuss optimal economic control in the shallow lake problem.
Brock and Malliaris pp 159 – 168.
Applications: (i) Pollution
Tahvonen and Salo (1996), Nonconvexities in Optimal Pollution
Accumulation
, Journal of Environmental Economics and Management 31: 160-177.
( ii) Shallow lakes
Dasgupta and Maler (2003), The Economics of Non-Convex Ecosystems: Introduction , Environmental and Resource Economics 26: 499–525.
Brock and Starrett (2003), Managing Systems with Non-convex Positive Feedback , Environmental and Resource Economics 26: 575–602.
Mäler, Xepapadeas and de Zeeuw (2003), The Economics of Shallow Lakes , Environmental and Resource Economics 26: 603–624.
11. Time consistency. This section discusses the difference between time consistency and Markov perfection and gives examples.
Applications: tariffs for non-renewable resources, durable goods monopoly, pollution policies with endogenous abatement.
Karp, Larry S., and David M. Newbery. “Intertemporal Consistency Issues in Depletable Resources .” In Handbook of Natural Resources, Vol. III, edited by Allen Kneese and James Sweeny. North Holland, New York, 1993, pp. 881-930.
Horner, J and M Kamien (2004) “ Coase and Hotelling: a meeting of minds ” Journal of Political Economy 112: 718 – 723.
Marsiliani, L and T Renstrom (2001) “Time inconsistency in environmental policy: tax earmarking as a commitment solution ” Economic Journal 110: 123- 138.
Karp, L and I H Lee (2003) “Time Consistent Policies ” Journal of Economic Theory 112: 353- 64.
Karp, L (1996)
"Depreciation
erodes the Coase Conjecture" European Economic Review 40: 473 - 490.
12. Discounting. This section discusses the many issues arises from discounting, emphasizing the problem of climate change.
Heal (2005), Intertemporal Welfare Economics and the Environment , Handbook of Environmental Economics, vol 3 Chapter 21
Heal (2007), Climate Change Economics - A Meta-Review and some suggestions , Working Paper.
Weitzman (1998), Why the Far-Distant Future should be discounted at its lowest possible rate , JEEM 36: 201-208.
Weitzman (2001), Gamma Discounting , American Economic Review 91:260-271.
Weitzman (2007), A Review of the Stern Review on the Economics of Climate Change , Journal of Economic Literature 45: 703-724.
Weitzman (2007), Structural Uncertainty and the Value of Statistical Life in the Economics of Catastrophic Climate Change, NBER Working Paper 13490.
Nordhaus (2007), A Review of the Stern Review on the Economics of Climate Change, Journal of Economic Literature 45: 703-724.
Groom, Hepburn, Koundouri and Pearce (2005), Declining Discount Rates: The Long and the Short of it , Environmental & Resource Economics 32: 445–493.
Chichilnisky (1996), An axiomatic approach to sustainable development , Social Choice Welfare 13:231-257.
Gollier (2002), Discounting an uncertain future , Journal of Public Economics 85 (2002) 149–166
Gollier (2002), Time Horizon and the Discount Rate , Journal of Economic Theory 107: 463–473.
Gollier (2008), Ecological Discounting , Working Paper.
Karp (2005), Global warming and hyperbolic discounting , Journal of Public Economics 89: 261–282.
Karp (2007), Non-constant discounting in continuous time , Journal of Economic Theory 132: 557 – 568.
Fujii and Karp (2008), Numerical analysis of non-constant pure rate of time preference:
A model of climate policy , Journal of Environmental Economics and Management 56: 83–101.
Dasgupta (2007), Commentary: The Stern Review’s Economics of Climate Change , National Institute Economic Review 2007.
Dasgupta (2008), Discounting Climate Change , forthcoming, Journal or Risk and Uncertainty.
Hoel and Sterner (2007), Discounting and relative prices , Climatic Change 84:265–280.
Sterner and Persson (2007), An Even Sterner Review: Introducing Relative Prices into the Discounting Debate , RFF Working Paper.
Traeger (2007), Sustainability, Limited Substitutability and Non-constant Social Discount Rates, Working Paper.
13. (Learning under) Ambiguity. This section extends the framework discussed in section 3 to situations where uncertainty cannot be captured by a unique probability distribution.
Klibanoff, P., Marinacci, M. & Mukerji, S. (2006), Recursive smooth ambiguity preferences, Working Paper 2007.
Klibanoff, P., Marinacci, M. & Mukerji, S. (2005), A smooth model of decision making under ambiguity, Econometrica 73:1849–1892.
Ghirardato, P., Maccheroni, F. & Marinacci, M. (2004), Differentiating ambiguity and ambiguity attitude, Journal of Economic Theory 118:122–173.
Maccheroni, F., Marinacci, M. & Rustichini, A. (2006), Dynamic variational preferences, Journal of Economic Theory 128:4–44
Maccheroni, F., Marinacci, M. & Rustichini, A. (2006), Ambiguity aversion, robustness, and the variational representation of preferences, Econometrica 74:1447–1498
Lange and Treich (2008), Uncertainty, learning and ambiguity in economic models on climate policy: some classical results and new directions , Climatic Change 89:7–21.
Lange (2003), Climate Change and the Irreversibility Effect – Combining Expected Utility and MaxiMin, Environmental and Resource Economics 25: 417–434.
Vercelli (1998), “Hard uncertainty and environmental policy”, in Chichilnisky, Heal and Vercelli: Sustainability: Dynamics and Uncertainty, Springer.
Basilia, Chateauneuf and Fontini (2008), ‘Precautionary principle as a rule of choice with optimism on windfall gains and pessimism on catastrophic losses’, Ecological Economics, in press.
14. Continuous time stochastic control and optimal stopping (if time permits). This section gives a brief introduction to continuous time stochastic processes and Ito calculus. We apply it to questions of optimal control and the optimal timing of investments. The section is based on Dixit and Pindyck 1994, chapters 3-5.
Pindyck (2002), Optimal timing problems in environmental economics , Journal of Economic Dynamics & Control 26: 1677 – 1697.
Pindyck (2000), Irreversibilities and the timing of environmental policy . Resource and Energy Economics 22: 233–59.
Pindyck (1984), Uncertainty in the Theory of Renewable Resource Markets , Review of Economic Studies 51: 289-303.
Pindyck (1980), Uncertainty and Exhaustible Resource Markets , Journal of Political Economy 88: 1203-1225.
15. Disentangling intertemporal substitutability from risk aversion. The standard models of intertemporal expected utility (used so far) assumes that risk aversion is equivalent to the propensity to smooth consumption over time. This section introduces models that distinguish these two a priori different characteristics of preference.
Epstein and Zin (1989), Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns – A Theoretical Framework , Econometrica 57: 937-969.
Epstein and Zin (1991), Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns - An Empirical Analysis , Journal of Political Economy 99: 263-286.
Campbell, J. Y. (1996), Understanding risk and return, The Journal of Political Economy 104: 298–345.
Vissing-Jørgensen, A. & Attanasio, O. P. (2003), Stock-market participation, intertemporal substitution, and risk-aversion, The American Economic Review 93: 383–391.
HaDuong
and Treich (2004), Risk Aversion, Intergenerational Equity and Climate Change , Environmental and Resource Economics 28: 195–207.Epaulard and Pommeret (2003), Optimally eating a stochastic cake - a recursive utility approach , Resource and Energy Economics 25: 129–139.
Howitt, Msangi, Reynaud and Knapp (2005), Estimating Intertemporal Preferences for Natural Resource Allocation , American Journal of Agricultural Economics 87: 969–983.
Lybbert and McPeak (2008): Risk, Intertemporal Substitution & Early Resolution of Uncertainty: Livestock Portfolio Allocations and Off-Take Among Kenyan Pastoralists, Working Paper.
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