MANAGING IMPERFECTLY MANAGING IMPERFECTLY MANAGING IMPERFECTLY - - PowerPoint PPT Presentation

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 Sethi1 Chris Costello2 Gautam Sethi1, Chris Costello2, Anthony Fisher3, Michael Hanemann3, and Larry Karp3

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 i i Motivation Roughgarden & Smith’s claim Optimal policy descriptions Critique of Roughgarden & Smith Critique of Roughgarden & Smith Our Model Results Conclusions

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enfish.c enfish.c?

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The Real The Real enfish.c enfish.c

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Motivation Motivation

Fi h ll h d id d

• Fishery collapse has emerged as a widespread

phenomenon

• Many possible causal factors
• Overcapitalization of the industry
• Politicized catch quotas
• Imperfect monitoring and enforcement
• Increased stochasticity
• Increased stochasticity

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Why Fisheries Collapse …

R h d d S i h (1996) Roughgarden and Smith (1996) assume 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 .

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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

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Deterministic Solution Deterministic Solution

I hi l i l k l 400 In this example, optimal target stock equals 400 and annual catch equals 60.

What is the intuition behind this result? What are its properties in terms of stock dynamics?

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Alternative Representation Alternative Representation

The solution to the deterministic model is given b by

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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

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Current Stock Uncertainty Current Stock Uncertainty

• Clark and Kirkwood (1986) assume manager

b i k l d

• bserves pre-spawning stock accurately and

post-spawning stock with noise

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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 k i l i hi i h i The stock-recruit relationship is stochastic, 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 i i i i d i i l l d deterministic economic decision rule leads to …

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… disaster! … disaster!

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R&S Optimal Policy R&S Optimal Policy &S O

• c

&S O

• c

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R&S Recommendation R&S Recommendation

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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 3/4th 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?

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Assumptions Assumptions

Each of the shocks is multiplicative and is p drawn from known independent uniform densities. Th k i l i hi i l i i i h The stock-recruit relationship is logistic with known parameters. Th l t t i bl d b th i The only state variable used by the manager is 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 l mean values.

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Problem Formulation Problem Formulation

The manager’s problem is to g p

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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

h ki f

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checking for convergence.

Results: Results: Recruitment Uncertainty Recruitment Uncertainty Recruitment Uncertainty Recruitment Uncertainty

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Results: Results: Small Multiple Uncertainty Small Multiple Uncertainty Small Multiple Uncertainty Small Multiple Uncertainty

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Results: Results: One Large Uncertainty One Large Uncertainty One Large Uncertainty One Large Uncertainty

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Results: Results: Multiple Uncertainty Multiple Uncertainty Multiple Uncertainty Multiple Uncertainty

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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, Th l f h i i i h d The value of the intrinsic growth parameter, and Search costs

We find that our results are fairly robust with respect to each of these

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Summary Statistics Summary Statistics

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Conclusions Conclusions

Given our assumptions, we find that the optimal li i d b h h policy is does better than the constant- 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

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Thank You! Thank You!

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