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MANAGING IMPERFECTLY MANAGING IMPERFECTLY MANAGING IMPERFECTLY MANAGING IMPERFECTLY OBSERVED COMPLEX SYSTEMS OBSERVED COMPLEX SYSTEMS CompSust Conference, Cornell University CompSust Conference, Cornell University June 9, 2009 June 9 2009


  1. MANAGING IMPERFECTLY MANAGING IMPERFECTLY MANAGING IMPERFECTLY MANAGING IMPERFECTLY OBSERVED COMPLEX SYSTEMS OBSERVED COMPLEX SYSTEMS CompSust Conference, Cornell University CompSust Conference, Cornell University June 9, 2009 June 9 2009 June 9, 2009 June 9 2009 Gautam Sethi 1 Chris Costello 2 Gautam Sethi 1 , Chris Costello 2 , Anthony Fisher 3 , Michael Hanemann 3 , and Larry Karp 3 1 Bard Center for Environmental Policy. 2 Donald Bren School of Environmental Science & Management. 3 University of California at Berkeley 3 University of California at Berkeley.

  2. Talk Outline Talk Outline � M � Motivation i i � Roughgarden & Smith’s claim � Optimal policy descriptions � Critique of Roughgarden & Smith � Critique of Roughgarden & Smith � Our Model � Results � Conclusions 2 of 26

  3. enfish.c ? enfish.c 3 of 26

  4. The Real The Real enfish.c enfish.c 4 of 26

  5. Motivation Motivation • Fishery collapse has emerged as a widespread Fi h ll h d id d phenomenon • Many possible causal factors • Overcapitalization of the industry • Politicized catch quotas • Imperfect monitoring and enforcement • Increased stochasticity • Increased stochasticity 5 of 26

  6. Why Fisheries Collapse … � R � Roughgarden and Smith (1996) assume h d d S i h (1996) multiple sources of stochasticity and find that the use of the “economic” criterion leads to the use of the economic criterion leads to fishery collapse “Economic theory for managing a renewable resource, Economic theory for managing a renewable resource, such as a fishery, leads to an ecologically unstable equilibrium as difficult to maintain as balancing a marble on top of a dome. A fishery should be managed marble on top of a dome. A fishery should be managed for ecological stability instead – in the analogy, as easy to maintain as keeping a marble near the base of a bowl”. bowl . 6 of 26

  7. Deterministic Model Deterministic Model � The manager seeks to maximize the present discounted sum of profits, subject to the growth equation: equation: where r is the discount rate p is the price of fish where r is the discount rate, p is the price of fish, h is the harvest, g is the stock-recruit function, and x is the stock of fish 7 of 26

  8. Deterministic Solution Deterministic Solution I hi In this example, optimal target stock equals 400 l i l k l 400 and annual catch equals 60. � What is the intuition behind this result? � What are its properties in terms of stock dynamics? 8 of 26

  9. Alternative Representation Alternative Representation The solution to the deterministic model is given b by 9 of 26

  10. Future Stock Uncertainty Future Stock Uncertainty • Reed (1979) assumes manager can observe stock accurately at the time of announcing catch quota but is faced with recruitment catch quota but is faced with recruitment uncertainty • He shows that the solution to this problem is qualitatively similar • Recruitment uncertainty leads to higher escapement 10 of 26

  11. Current Stock Uncertainty Current Stock Uncertainty • Clark and Kirkwood (1986) assume manager observes pre-spawning stock accurately and b i k l d post-spawning stock with noise 11 of 26

  12. Multiple Uncertainty Multiple Uncertainty � Roughgarden and Smith pose a new problem: � Roughgarden and Smith pose a new problem: What is the implication of following the solution of deterministic economic model when � Th � The stock-recruit relationship is stochastic, k i l i hi i h i � Stock measurements are prone to errors, and � Actual take is prone to error? p � To answer this question, the authors run simulations and find that following the d deterministic economic decision rule leads to … i i i i d i i l l d 12 of 26

  13. … disaster! … disaster! 13 of 26

  14. R&S Optimal Policy R&S Optimal Policy &S O &S O o o c c 14 of 26

  15. R&S Recommendation R&S Recommendation 15 of 26

  16. Our Work Our Work � The deterministic policy recommendation from � The deterministic policy recommendation from the economic model is inapplicable to the highly stochastic world the authors create. � The 3/4 th K solution is a constrained optimum i.e. it is the optimum solution within the class of constant-escapement rules . � This raises two questions: q � What is the optimum solution under three sources of uncertainty mentioned above? � How does the optimum solution compare with � How does the optimum solution compare with Roughgarden and Smith’s solution? 16 of 26

  17. Assumptions Assumptions � Each of the shocks is multiplicative and is p drawn from known independent uniform densities. � The stock-recruit relationship is logistic with Th k i l i hi i l i i i h known parameters. � The only state variable used by the manager is � Th l t t i bl d b th i current period measurement. The control variable is the seasonal catch quota. � “Small” and “large” uncertainty refer to uniform shocks of +10% and +50% around the mean values. l 17 of 26

  18. Problem Formulation Problem Formulation � The manager’s problem is to g p 18 of 26

  19. Solution Algorithm Solution Algorithm � The DPE of this problem is � The DPE of this problem is We solve this dynamic problem using value y p g function iteration, which involves � making a guess of the value function, � finding the conditional solution, � recomputing the value function, and � checking for convergence. h ki f 19 of 26

  20. Results: Results: Recruitment Uncertainty Recruitment Uncertainty Recruitment Uncertainty Recruitment Uncertainty 20 of 26

  21. Results: Results: Small Multiple Uncertainty Small Multiple Uncertainty Small Multiple Uncertainty Small Multiple Uncertainty 21 of 26

  22. Results: Results: One Large Uncertainty One Large Uncertainty One Large Uncertainty One Large Uncertainty 22 of 26

  23. Results: Results: Multiple Uncertainty Multiple Uncertainty Multiple Uncertainty Multiple Uncertainty 23 of 26

  24. Sensitivity Analysis Sensitivity Analysis � To see how robust our results are to the assumptions we make, we conduct sensitivity analyses with respect to: � The stock-recruit relationship, � The value of the intrinsic growth parameter, and Th l f h i i i h d � Search costs � We find that our results are fairly robust with respect to each of these 24 of 26

  25. Summary Statistics Summary Statistics 25 of 26

  26. Conclusions Conclusions � Given our assumptions, we find that the optimal policy is does better than the constant- li i d b h h escapement policy on both counts: commercial profitability as well as extinction probability profitability as well as extinction probability � However, we make a number of simplifying assumptions in this model which makes it assumptions in this model, which makes it inapplicable � In light of this we see this model as an initial � In light of this, we see this model as an initial step towards the development of more complex and realistic models 26 of 26

  27. Thank You! Thank You! 27 of 22

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