# Presentation: 028986

## Michael Dalton
 California State University, Monterey Bay

Stephen Ralston
National Marine Fisheries Service,
Southwest Fisheries Science Center, Santa Cruz

** **California State University, Monterey Bay
**Stephen Ralston**
- National Marine Fisheries Service,
- Southwest Fisheries Science Center, Santa Cruz

**The California Rockfish Conservation Area****and Groundfish Trawlers ****at Moss Landing Harbor**

## Overview and motivation

- Rebuilding stocks of bocaccio, canary, darkblotched, widow, yelloweye rockfish ...
- Bycatch for groundfish trawlers that target dover sole, thorny heads, sablefish ...
- Spatial regulations could protect overfished stocks and allow opportunities for others

## Economic Effects of Spatial Management

- A **=** Net Revenue Per Unit Effort in an Area
- H **=** Fishing Effort in an Area
- Fishery Economic Value in an Area V **=** A H
- Decomposition of Change in Value:
-       A** ́** H** ́ -** A H **=** ( A** ́ **- A ) H** ́** **+** A ( H** ́ -** H )
- Conclusion: Effort shifts *and* changes in RPUE important for evaluating spatial management

## Recent West Coast Spatial Management

- Marine Reserves Processes
- Channel Islands National Marine Sanctuary
- California Marine Life Protection Act
- Pacific Fishery Management Council
- 2003 Groundfish Regulations
- Bycatch and Discard Analysis

## Policy and Management Implications

- Economic analysis for Channel Islands:
- Cost **=** -A H in closed area, claim upper bound
- Ignores effort shift, RPUE change in open area
- PFMC analysis of 2003 regulations
- Estimates effort shift but not RPUE change
- Neither analysis has statistical basis
- Objective here to provide statistical basis for analyzing shifts in effort and changes in RPUE

## PacFIN Data and GIS analysis

- California PacFIN trawler logbook and ticket data
- 1981-2001, north of Point Conception
- GIS by port and DFG fishing blocks
- Query GIS for Moss Landing data on tow hours, catch, and ex vessel prices

## IRI SST and DFG bathymetry data

## California Rockfish Conservation Area (CRCA)

- CRCA
- Inshore zone    **>**3nm and **<**50-60fm
- Offshore zone **>**150fm Pt. Reyes south, **>**250fm north
- Area 1: DFG blocks inside CRCA
- Area 2: DFG blocks outside CRCA

## Data for vector autoregression (VAR) analysis

- Compile time series data for Moss Landing
- Total tow hours for blocks inside and outside CRCA, 1981-2001
- Cumulative ex vessel prices for DTS species at Moss Landing
- Nov-March Average sea surface temperatures (SST) for ENSO index
- Quadrivariate (four variable) VAR
- Data are deviations from means
- Data are covariance stationary
- Second-order restrictions appropriate

## Slide 10

## Slide 11

## Slide 12

## Orthogonalized impulse response functions simulate 1997-98 ENSO
Increase in effort inside CRCA
Decrease outside
Inshore movement of effort from ENSO
Modest increase in ex vessel prices

**Increase in effort inside CRCA**
**Decrease outside**
**Inshore movement of effort from ENSO**
**Modest increase in ex vessel prices**

## Response to a temporary effort reduction in the CRCA equal to total tow hours in 2001 
Reduction inside CRCA followed by rapid return to mean
Increase outside with oscillations
Modest increase in ex vessel prices

**Reduction inside CRCA followed by rapid return to mean**
**Increase outside with oscillations**
**Modest increase in ex vessel prices**

## Granger causality tests

- Multivariate test rejects excluding effort outside CRCA from the VAR at 5% significance level
- Effort outside CRCA could be Granger causing:
- Ex vessel prices
- Fishing effort inside CRCA
- SST (fishermen’s expectations)
- Bioeconomic model here allows 3 only
- Bivariate tests inconclusive
- T-statistics from VAR support 3

## Bioeconomic Model components

- Two area model with stochastic dynamics
- Net RPUE A t depends on
- Effort H t in the area (crowding externality)
- Abundance N t in the area (dynamic externality)
- Ex vessel prices P t  at the port
- A t = f 0 + f 1 H t  + f 2 N t  + f 3 P t

##  Bioeconomic Model components

- Abundance N t depends on
- Effort H t in the area (fishing mortality)
- Lagged abundance N t - 1
- Stochastic recruitment or migration X t
- N t = g 0 + g 1 H t  + g 2 N t - 1  - g 1 g 2 H t - 1 + X t
- Stochastic recruitment depends on
- Sea surface temperature S t
- random factor Y t
- X t = τ S t + Y t

## Bioeconomic model components

- SST and Y t are first order Markov processes
- S t = ρ S t - 1 + ε s t
- Y t = λ Y t - 1 + ε y t
- Ex vessel prices have a first-order form
- P t = φ1 P t - 1 + φ2 S t - 1 + ε p t
- The ε k t  are least-squares residuals with finite variance and zero conditional mean

## Fisherman’s problem

- Dynamic and spatial adjustment costs
- Each fisherman has discount factor 0 **< **β **< **1 and chooses random vectors of fishing effort h t to maximize an expected present value of profits:
-     *E *Σ t β t ( A t h t – ( h t - h t – 1 )** ́** *R *( h t - h t – 1 ) )

## Model solution and regression equations

- Solution given by stochastic Euler equations and transversality conditions
- Solving the fisherman’s problem involves many tedious steps of algebra
- Highlights are
- Factoring characteristic matrix polynomial
- Wiener-Kolmogorov prediction formula
- Construction of orthogonal forecast errors
- End result: system of four regression equations that incorporate parameter restrictions of rational expectations hypothesis

## Maximum likelihood estimates

| Parameter | Equation/Variable | CRCA | Outside | Joint |
| --- | --- | --- | --- | --- |
| f 1 | RPUE/Effort | -0.881 | -0.501 |  |
| f 2 | RPUE/Stock | 0.194 |  0.166 |  |
| f 3 | RPUE/Price | 0.094 | 0.009 |  |
| g 1 | Stock/Effort | -0.013 | -0.233 |  |
| g 2 | Stock/Stock | -0.028 | 0.031 |  |
| r | Adjustment Cost | 0.007 | 0.489 |  |
| τ | Stock/SST | 0.231 | -0.257 |  |
| λ | Random | -0.296 | 0.077 |  |
| φ1 | Price/Price |  |  | 0.963 |
| φ2 | Price/SST |  |  | 0.048 |
| ρ | SST |  |  | -0.126 |

## Likelihood ratio tests of bioeconomic model

- Bioeconomic model tested against less restricted third-order VAR alternative
- First test statistic has asymptotic chi-squared distribution
- Second test statistic modified for small sample bias
- Neither test rejects bioeconomic model at 5% significance level

| Test | Statistic  | Significance |
| --- | --- | --- |
| Asymptotic χ2 | 12.354  | 0.09 |
| Small Sample | 5.491  | 0.60 |

## Conclusions

- VAR analysis shows significant differences inside and outside CRCA
- Inshore movement from ENSO
- Effort displacement from CRCA
- Bioeconomic model gives reasonable results
- RPUE inside CRCA more sensitive to vessel crowding
- RPUE inside CRCA more sensitive to changes in ex vessel prices
- Adjustment costs greater outside CRCA
- Stock/SST effects support VAR results

## Next steps for data and model development 

- Historical regulatory data including trip limits for DTS species from SAFE documents
- Species detail from stock assessments, rebuilding analyses, etc. to identify additional parameters and estimate bycatch
- Relax model assumptions to predict effort shifts
- Adjustment costs
- Stock recruitment and migration
- Address effort and ex vessel prices

## Acknowledgements

- National Marine Fisheries Service, Division of Statistics and Economics
- California Seagrant
- William Daspit (PSMFC/PacFIN),
- Rita Curtis (NMFS), Church Grimes (NMFS), Pat Iampietro (CSUMB), Carrie Pomeroy (UCSC), Rick Starr (CSG), Cindy Thomson (NMFS), Charlie Wahle (NOAA MPA Center), Gina Wade (CDFG), Nancy Wright (CDFG)