1 L Karp and C Traeger Course Outline ARE 263 Fall 2010 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 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 Elements of Dynamic Optimization Alpha Chiang McGraw Hill 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 2 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 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 3 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 535542 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 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 7 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 8 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 4 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 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 Polasky Zeeuw and Wagener Optimal Management with Potential Regime Shifts Working Paper 2010 10 Non convex control problems This section discusses the solution to non convex problems 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 M ler 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