1. I. What I do Economic, statistical, and mathematical models relating to environmental management. Dynamic allocation of resources. Decision-making under uncertainty. Value of information. Optimal design of environmental regulations. Search theory problems relating to env. mgt.

2. Examples of kinds of questions I ask (of relevance here) 1.If a forecast of variability is available, how would it affect optimal fishery regulation? 2.Value of improved El Nino forecasts in the management of salmon in Pacific Northwest? 3.Should forecasts become more accurate or have a longer lead-time? 4.How to manage fisheries under multiple sources of uncertainty (profits & stock viability)? 5.How should environmental regulation proceed when firms and regulator have asymmetric information (and update & learn differently)?

3. A few other projects Modeling and management of small-scale fisheries in Baja California – why have some been successful and others crashed? Managing renewable resources under high-grading (a genetic externality). What are good second-best regulations? Modeling the Serengeti ecosystem – how to integrate human activity into ecosystem models. Some project ideas for F 3 …

4. Optimal regulatory instruments under uncertainty Regulators face high uncertainty & variability. Biophysical models developed here help understand sources, but not necessarily resolve uncertainty. Optimal instruments under certainty likely to be highly variable (space & time) quota or effort regulations. Under uncertainty, may prefer other instruments. Models can help determine tradeoffs.

5. Value of Information Biophysical and coupled human/natural models will improve our understanding of the sources of variability facing managers and fishermen. What is the value (typically measured in $) of reducing uncertainty. Important difference between variability and uncertainty.

6. What uncertainty should be resolved? Given a framework for estimating the VOI (the value of resolving different types of uncertainty), we can ask which types of uncertainty are the most important to resolve. E.g. Should we invest in stock surveys or spatial/temporal flow forecasts? –Can get surprising results – not all uncertainty has a high cost – e.g. Information that doesn’t cause you to change behavior has no value.

7. How do fishermen and regulators learn? How to manage under asymmetric information? Asymmetric information could be responsible for management failures (fish stocks are lumpy, fishermen know where lumps are, regulators don’t). Depends largely on how two players learn and update, and on how flexible their approaches are. This could be modeled in a game-theoretic framework.

8. II. Some approaches & tools Economists are obsessed with optimality and with analytical, general solutions (i.e. without simulations). This parsimony often (usually) comes at the expense of reality. Result is: relatively simple, analytically tractable mathematical/statistical models. Bottom line is that economists models look a lot like a model Dave or Bruce would write (and I mean that in the most generous possible way).

9. Value of Information Usually couched in a probabilistic statistical framework that specifically describes source(s) of uncertainty. Identical to the notion of “option value” in finance. Basic idea is to calculate an expected value of information (before the information has been acquired). Can help give policy guidance about which sources of uncertainty are most important to resolve.

10. A Toy Example of VOI Suppose uncertainty is over level of upwelling: Either “good” or “bad”. Have to decide quota (50 or 100) before know. No Forecast: Set Q=100 (370>330). Forecast “Good” – Set Q=100, “Bad” – Set Q=50. With Forecast, expected return is 510. Value of forecast ex ante is 140. Good Upwelling (.3)Bad Upwelling (.7) Quota=1001000100 Quota=50400300

11. Dynamic Optimization To calculate the optimal regulation over time, must account for how actions taken in one period will affect future. Need specialized tools (analytical and computational). Uncertainty makes everything probabilistic – cannot just insert expected values of random variables (due to non-linearities).

12. One method: SDP Stochastic Dynamic Programming –Continuous or discrete time –Any number of state variables (typically 1 or 2) –Any number of control variables (typically 1 or 2) –Works by backward induction to find optimal control at any point in time given the state. –Transitions are Markovian – uses transition probability matrix for uncertainty.

13. Examples Regulator setting quota for an area. Uncertainty over recruitment. Estimate recruitment from surveys, based on estimates, set quota over time. What is optimal quota as function of estimated recruitment? Adaptive management of marine reserves – uncertainty over ecological effects of marine reserve. Set reserve, observe effects (learn), move (or change size of) reserve, etc… What is the best initial reserve design? How should design adapt to what is learned in the process? [Here the adaptive management part is that it may be optimal to set up a reserve that has a low current period payoff, but it facilitates learning that has high value].