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.
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
enfish.c ? enfish.c 3 of 26
The Real The Real enfish.c enfish.c 4 of 26
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
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
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
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
Alternative Representation Alternative Representation The solution to the deterministic model is given b by 9 of 26
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
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
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
… disaster! … disaster! 13 of 26
R&S Optimal Policy R&S Optimal Policy &S O &S O o o c c 14 of 26
R&S Recommendation R&S Recommendation 15 of 26
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
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
Problem Formulation Problem Formulation � The manager’s problem is to g p 18 of 26
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
Results: Results: Recruitment Uncertainty Recruitment Uncertainty Recruitment Uncertainty Recruitment Uncertainty 20 of 26
Results: Results: Small Multiple Uncertainty Small Multiple Uncertainty Small Multiple Uncertainty Small Multiple Uncertainty 21 of 26
Results: Results: One Large Uncertainty One Large Uncertainty One Large Uncertainty One Large Uncertainty 22 of 26
Results: Results: Multiple Uncertainty Multiple Uncertainty Multiple Uncertainty Multiple Uncertainty 23 of 26
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
Summary Statistics Summary Statistics 25 of 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
Thank You! Thank You! 27 of 22
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