Summer Flounder Allocation Analysis 

Brad Gentner, James Kirkley, Paul R. Hindsley and Scott Steinback 

U.S. Department of Commerce 

National Oceanic and Atmospheric Administration 

National Marine Fisheries Service 

NOAA Technical Memorandum NMFS-F/SPO-111 

October 2010 

Summer Flounder Allocation Analysis 

Brad Gentner1

, James Kirkley2, Paul R. Hindsley3 and Scott Steinback4

 

NOAA Technical Memorandum NMFS-F/SPO-111 

October 2010

U.S. Department of Commerce 

Gary Locke, Secretary of Commerce 

National Oceanic and Atmospheric Administration 

Jane Lubchenco, Ph.D., Administrator of NOAA 

National Marine Fisheries Service 

Eric C. Schwaab, Assistant Administrator for Fisheries

 

1

 Gentner Consulting Group, 9007 Eton Road, Silver Spring, MD 20901, www.GentnerGroup.com. 2

 Department of Fisheries Science, College of William and Mary, Virginia Institute of Marine Science, 

School of Marine Science, Gloucester Point, VA 23062, jkirkley@vims.edu 

3

 Eckerd College - BES, 4200 54th Avenue South St. Petersburg, FL 33711, hindslpr@eckerd.edu 

4

 Northeast Fisheries Science Center, NMFS, Social Sciences Branch, 166 Water Street, Woods Hole, MA 

02543, scott.steinback@noaa.gov 
ii 

Suggested citation: 

Gentner, Brad, James Kirkley, Paul R. Hindsley, and Scott Steinback. 2010. Summer 

Flounder Allocation Analysis. U.S. Dep. Commerce, NOAA Tech. Memo. NMFSF/SPO-111, 93 p. 

A copy of this report may be obtained from: 

Scott Steinback 

Northeast Fisheries Science Center, NMFS 

Social Sciences Branch 

166 Water St. 

Woods Hole, MA 02543-1026 

scott.steinback@noaa.gov 

Or online at: 

http://spo.nmfs.noaa.gov/tm/ 
iii

Table of Contents

List of Figures.................................................................................................................... iv

List of Tables ...................................................................................................................... v

1.0 Abstract........................................................................................................................ vi

2.0 Introduction................................................................................................................... 1

2.1 Background and Trends ............................................................................................ 1

2.1.1 Commercial Trends............................................................................................ 2

2.1.2 Recreational Trends ........................................................................................... 5

2.2 Basis for Economic Allocation Analysis ................................................................ 10

3.0 Commercial Valuation................................................................................................ 12

3.1 Estimation of Trip Costs and Data Manipulation ................................................... 12

3.2 Model ...................................................................................................................... 21

3.2.1 Literature Review............................................................................................. 22

3.2.2 Theoretical Model Specification...................................................................... 23

3.2.3 Empirical Model .............................................................................................. 24

3.3 Results..................................................................................................................... 26

3.4 Conclusions............................................................................................................. 28

4.0 Consumer Valuation ................................................................................................... 30

4.1 Methodology........................................................................................................... 30

4.1.1 The Synthetic Inverse Demand System ........................................................... 31

4.1.2 Statistical Estimates of the SIDS Model.......................................................... 34

4.2 Prices, Revenues, and Compensating Variation ......................................................... 36

5.0 Recreational Valuation................................................................................................ 38

5.1 Unweighted Methodology ...................................................................................... 38

5.1.1 Nested Logit..................................................................................................... 39

5.1.2 Data Manipulation ........................................................................................... 41

5.1.3 Expected Keep Rates ....................................................................................... 43

5.1.4 Unweighted Model Results.............................................................................. 44

5.2 Weighted Model...................................................................................................... 46

5.2.1 Weighted Methodology ................................................................................... 47

5.2.2 Random Utility Model ..................................................................................... 49

5.2.3 Data Manipulation ........................................................................................... 49

5.2.4 Expected Keep Rates ....................................................................................... 50

5.2.5 Propensity Score Results ................................................................................. 52

5.2.6 Model Results .................................................................................................. 57

5.2.6 Model Results .................................................................................................. 57

5.3 Recreational Valuation Discussion......................................................................... 59

6.0 Allocation Discussion ................................................................................................. 60

7.0 References................................................................................................................... 67

Appendix 1: Model Estimation Results ............................................................................ 73
iv 

List of Figures 

Figure 2.1. Landings by Gear Type, 1997-2007................................................................. 3

Figure 2.2. Summer Flounder Commercial and Recreational Landings (Terceiro, 2006) . 3

Figure 2.3. Summer Flounder Spawning Stock Biomass (Terceiro, 2006)........................ 4

Figure 2.4. Total and Directed Effort for Summer Flounder in Millions of Trips, 2002-

2006..................................................................................................................................... 6

Figure 2.5. Total Summer Flounder Catch by Fishing Mode in Thousands of Fish, 2002 – 

2006..................................................................................................................................... 7

Figure 2.6. Summer Flounder Harvest (A+B1) by Mode in Thousands of Fish, 

2002-2006 ........................................................................................................................... 7

Figure 2.7. Summer Flounder Weight per Fish, 2002-2006............................................... 8

Figure 2.8. Trends in Summer Flounder Catch Per Unit Effort (CPUE), 2002-2006 ........ 9

Figure 3.1. Actual Total Trip Cost Versus Predicted Trip Cost ....................................... 17

Figure 3.2. Number of Trips Landing in Each County, 2005-2007.................................. 19

Figure 3.3. Simulated Marginal Quota Value for Summer Flounder Quota Pounds (2007 

dollars) .............................................................................................................................. 29

Figure 3.4. Summer Flounder Commercial Total Net Benefits (2007 dollars) ................ 30

Figure 5.6. Absolute Standard Effect Size: This plot depicts the absolute standard 

difference for variables in the CHTS and intercept samples before and after propensity 

score weighting ................................................................................................................. 17

Figure 6.1. Marginal Willingness to Pay (compensating variation) Schedule for 

Recreational and Commercial Summer Flounder Fishermen (2007 dollars) ................... 62
v

List of Tables 

Table 2.1. Summer Flounder Regulations since 1993 ........................................................ 9

Table 3.1. Otter Trawl Cost Model Parameters (Jin 2008)............................................... 13

Table 3.2. Means and Descriptive Statistics for the Dependent Variables....................... 15

Table 3.3. Nonlinear GMM Parameter Estimates............................................................. 16

Table 3.4. Actual Trip Costs and Predicted Trip Costs .................................................... 17

Table 3.5. Trip Data Set Characteristics, 2005 - 2007...................................................... 17

Table 3.6. Total Pounds, Value, Costs, and Profit per Trip 2005 - 2007 (2007 dollars).. 18

Table 3.7. Pounds Landed per Trip by Species Group, 2005 - 2007................................ 20

Table 3.8. Landed Price per Trip by Species Group, 2005 -2007 (2007 dollars)............. 20

Table 3.9. Landed Value per Trip by Species Group, 2005 - 2007 (2007 dollars)........... 21

Table 4.1. Parameter Estimates of the SIDS Model for Floundera................................... 35

Table 4.2. Log Likelihood Ratio Test Results for Inverse Demand Structure ................. 35

Table 4.3. Mean Compensated Own and Cross Price and Scale Elasticities.................... 36

Table 4.4. Changes in Ex-vessel Prices, Revenues, and Compensating Variation for a 

10% Reduction in Demand for Summer Floundera .......................................................... 37

Table 4.5. Prices, Revenues, and Compensating Variation for a One Unit Increase in 

Demand for Summer Floundera

........................................................................................ 38

Table 5.2. Descriptive Statistics for all Variables............................................................. 43

Table 5.3. Negative Binomial Expected Keep Rate Model Results ................................. 44

Table 5.4. Parameter Estimates and Model Fit................................................................. 45

Table 5.5. Compensating Variation Estimates for the Current Keep Levels (Unweighted 

2007 dollars) ..................................................................................................................... 46

Table 5.6. Descriptive Statistics for CHTS Variables ...................................................... 50

Table 5.7. Descriptive Statistics for all Variables in Intercept Dataset ............................ 50

Table 5.8. Zero Inflated Negative Binomial Expected Keep Rate Model Results ........... 52

Table 5.9. Means before Propensity Score Weighting ..................................................... 54

Table 5.10. Means after Propensity Score Weighting ...................................................... 54

Table 5.11. Individual Site Choice Frequencies and Standard Effect Sizes between the 

CHTS Sample and the Intercept Sample before Propensity Score Weighting ................. 55

Table 5.12. Weighted Individual Site Choice Frequencies and Standard Effect Sizes 

between the CHTS Sample and the Intercept Sample after Propensity Score Weighting 56

Table 5.13. Parameter Estimates and Model Fit for Conditional Logit Model ................ 58

Table 5.14. Compensating Variation Estimates for the Current Keep Levels (Unweighted 

2007 dollars) ..................................................................................................................... 58

Table 5.15. Compensating Variation Estimates for the Current Keep Levels (Weighted 

2007 dollars) ..................................................................................................................... 59

Table 6.1. Recreational Summer Flounder Trip Expenditures and Income Impacts (2007 

dollars) .............................................................................................................................. 63

Table 6.2. Proxy For-Hire Mode Producer Surplus per Pound of Summer Flounder (2007 

dollars) .............................................................................................................................. 64
vi 

1.0 Abstract

This report examines the current summer flounder allocation and makes 

recommendations as to the optimal allocation between recreational and commercial users 

based on the equimarginal principle. Commercial estimates of the marginal value of a 

pound of summer flounder are generated using a dual revenue model of this multi species 

fishery. On the recreational side, several random utility site choice models are estimated 

for summer flounder harvest using data collected from the Marine Recreational Fisheries 

Statistical Survey (MRFSS), including a model weighted to account for choice based 

sampling in the MRFSS survey. Proxy estimates are generated for the for-hire 

recreational industry because no cost and earnings data exists for this sector. Consumer 

marginal values are estimated from an almost ideal demand system using dockside prices. 

The modeling results indicate that the total value to society would increase if the 

allocation shifted further in the direction of the recreational sector. Unfortunately, 

uncertainty in the recreational estimates and limitations in the recreational demand 

modeling make it impossible to define the optimal allocation point. 
1

2.0 Introduction

The summer flounder stock has been under a rebuilding plan since 1993 and stocks are 

increasing. At the same time the stocks are increasing recreational and commercial catch 

limits have been regularly exceeded. This has lead to increasingly restrictive 

management for both sectors while each sector advocates for the relaxation of restrictions 

in the face of improving stocks. Compounding this problem, the recreational sector 

believes the current allocation to be unfair and has advocated increasing their quota share. 

Recreational effort has been on the rise in all recreational fisheries including the summer 

flounder fishery. Total catch and harvest have increased due to increased effort and 

increased catch per unit effort (CPUE). Increasing CPUE suggests that the stock is 

indeed improving. While not addressed in this report anglers are attracted to improved 

catch rates, which at least partially explains the increasing effort. However, increasing 

effort and increasing CPUE means that it is easier to exceed harvest targets, and summer 

flounder harvest targets have been exceeded during two of the last five years, with 

overages in both years exceeding 25%. 

This two edged sword of increasing harvests on one side and a rebuilding plan with strict 

harvest limits on the other side, is a recipe for further ratcheting down of regulations on 

summer flounder anglers. Increased restrictions have lead for calls by the recreational 

community to revisit the commercial recreational split which currently stands at 60% 

commercial and 40% recreational 

While the resource is not in serious trouble, the Atlantic States Marine Fisheries 

Commission and the Mid-Atlantic Fishery Management Council are concerned about the 

allocation of the resource among competing user groups including commercial fishermen 

and recreational anglers. Based on the reported or estimated landings and catch of 

summer flounder, it is clear that summer flounder is an important species for the two user 

groups. A major question, therefore, is whether or not there is an allocation between the 

two groups, which might enhance overall net benefits to society. This report details the 

calculation of marginal benefits across the private recreational anglers, consumers, and 

commercial fishermen. This report begins with a review of catch and effort trends in the 

fishery followed by commercial valuation, consumer valuation, and recreational 

valuation chapters. 

2.1 Background and Trends 

Summer flounder, Paralichthys dentatus, is an important commercial and recreational 

species. Summer flounder is also known as fluke, and may occasionally be misidentified 

as a southern flounder (Paralichthys lethostigma). Both species are left-eyed flounder, 

which means its eyes are on the upper surface of the head when the fish is facing left. 

Summer flounder are distributed from the coastal waters of the southern gulf of Maine to 

Florida, with large concentrations in the Mid-Atlantic region of the northwest Atlantic. 

They grow up to 32 inches in length and may weigh up to approximately 15 pounds. 

Their approximate maximum age is 10 years. 

The most recent stock assessment for summer flounder indicates that although summer 

flounder are not overfished, the biomass has not recovered to desired levels (Terceiro, 
2 

2006)1

. The assessment also indicated, however, that overfishing was occurring in 2005, 

and that the current level of fishing mortality (0.407) was above the target and threshold 

fishing mortality rates of 0.280. The abundance of most age classes did increase over the 

past ten years, but the 2005 year class was estimated to the be the smallest since 1988—

approximately 15.0 million fish (Terceiro, 2006). 

 

Of the total volume (weight in pounds) caught and landed or retained between 1981 and 

2006, the recreational sector accounted for 39.0 % of the total summer flounder caught 

and retained. In four of the years (1997, 1998, 2000, and 2001) between 1981 and 2006, 

recreational harvest accounted for more than 50 % of the total weight of all summer 

flounder caught and retained by commercial fishermen and recreational anglers. Over the 

entire 1981 through 2006 period, the recreational sector has accounted for 39.0 % of the 

total landings, while the commercial sector has accounted for 61.0 % of the total landings 

of summer flounder. 

2.1.1 Commercial Trends 

Summer flounder is an important commercial species from Cape Hatteras to Cape Cod. 

The summer flounder stock migrates from inshore waters to offshore waters, and they are 

concentrated in coastal bays and estuaries from late spring through autumn when they 

move to the outer continental shelf for the winter. Spawning occurs offshore and larvae 

are pushed into estuaries by prevailing water currents. This seasonality is an important 

part of the commercial fishery. 

The otter trawl is the predominate gear type in the summer flounder fishery and Figure 

2.1 displays summer flounder landings by gear type. There are two major trawl fisheries; 

a winter offshore fishery and a summer inshore fishery. The percentage of landings 

coming from the otter trawl fishery has ranged from almost 93% to a low of 64% in 2007 

with other gear use increasing dramatically since 2003. There are a number of other 

gears used in the fishery including; pots, dredges, pound nets, gill nets, hoop nets, fyke 

nets, hand lines, long lines, beam trawls, and others. Only dredge (5.9%), line (3.5%), 

and pound net (1.6%) gear types exceeded one percent of landings in 2007. For gears 

other than otter trawl, their catch of summer flounder is better characterized as bycatch 

whereas the otter trawl gear, while a multi-species fishery, catches a higher proportion of 

summer flounder. 

Harvests for summer flounder peaked in 1983 at 57.5 million pounds and has declined 

since (Figure 2.2). Recognizing a declining harvest trend after 1983, summer flounder’s 

first management plan was put in place. 1991 saw the definition of overfishing and it 

was found that the summer flounder stock had been undergoing overfishing since 1982. 

A rebuilding schedule was developed in 1993 requiring limited entry, reporting 

requirements and input regulations mainly focusing on mesh size. Recreational harvest 

limits were also established in 1993 along with size limits. Currently, recreational and 

 

1

Since the first submission of this work as a grant ending report, an updated stock assessment has been 

completed (Terceiro, 2009). The author’s chose to not update this section of the report with the updated 

stock assessment as the data underlying all the analysis in this report is tied to the same year (2006) as the 

previous stock assessment. Because all analysis results are conditional on the stock in 2006, it was decided 

to leave the stock information from the 2006 assessment. 
3

commercial total allowable catches (TACs) are assigned to the states for management and 

the states can transfer quota to each other. 

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

14,000,000

16,000,000

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Pounds

All Other Gear Otter Trawl

Figure 2.1. Landings by Gear Type, 1997-2007 

Figure 2.2. Summer Flounder Commercial and Recreational Landings (Terceiro, 

2006) 

Currently the summer flounder fishery is not a directed fishery but a bycatch fishery. 

This is mainly driven by low TACs during the rebuilding phase. As the stock rebuilds, 

abundance increases causing commercial fishermen to catch summer flounder in areas 

where they haven’t been in years. As a result, commercial fishermen feel they are being 
4 

kept out of this fishery unnecessarily. This is same stock recovery trap felt by the 

recreational anglers. Bycatch of summer flounder is high for otter trawl caught fish and, 

as abundance increases, more and more summer flounder are caught in the indiscriminate 

otter trawl gear. Due to the low TACs, less fish are being landed but mortality is still 

high. 

As of the most recent stock assessment, summer flounder is not overfished and not 

experiencing overfishing, but the stock is not rebuilt yet. The current rebuilding schedule 

has the stock rebuilt by 2013 (Terceiro 2006). 2007 represents the first year the stock 

was not overfished since 1982. Figure 2.3 shows the spawning stock biomass threshold 

and target. The stock has been below the threshold since 1982. In 2001, the stock 

climbed above the threshold, but is still well below the target. Current spawning stock 

biomass target is 132 million pounds and the stock is at 72% of that level. Recent stock 

assessments used a new model that allows a higher TAC. The 2009 TAC was up 2.68 

million pounds from the 2008 TAC to 18.45 million pounds split 11.07 million pounds 

for the commercial sector and 7.38 million pounds for the recreational sector. 

Figure 2.3. Summer Flounder Spawning Stock Biomass (Terceiro, 2006) 

The remainder of the commercial analysis will focus on the otter trawl commercial gear 

type for a number of reasons. All other gear types harvest a very small portion of the 

catch. Also, all the other gear types are very different from the otter trawl and different 

from one another with regards to their cost structures. The other gear types are more 

aptly described as by-catch fisheries while summer flounder makes up a significant 

percentage of the otter trawl catch. Finally, and most importantly, cost data is far better 

for otter trawls. The National Marine Fisheries Service (NMFS) uses the observer 

program to collect trip cost information and many of the other gear types operate in state 

waters only. Boats operating in state waters are not required to carry observers, and, as 

such, no trip costs information is collected for those gear types. 
5

2.1.2 Recreational Trends 

Summer flounder is caught recreationally from North Carolina through New Hampshire, 

with the majority of the harvest coming from Virginia northward. During the last ten 

years, no summer flounder landings have been reported in Maine. Summer flounder 

fishing is very popular in the Northeast accounting for 22% of all recreational effort for 

all species. Figure 2.4 details total effort and two definitions of summer flounder directed 

effort. The American Fisheries Society (AFS) defines directed effort as any trip that 

caught and/or targeted summer flounder. This definition is used to estimate the line in 

Figure 2.4 entitled “Targeted and Caught.” NMFS occasionally defines directed effort as 

only those trips where summer flounder was caught. This definition is also included in 

Figure 2.4. While summer flounder effort has increased 14% under the more 

conservative definition and 15% under the AFS definition, total effort is up 24%. 

Summer flounder is considered an excellent food fish which increases it attractiveness as 

a target for recreational anglers. Figure 2.5 displays total catch trends from 2002 to 2006. 

The Marine Recreational Fisheries Statistical Survey (MRFSS) has three types of catch: 

harvest measured and weighed by an interviewer (type A); catch not seen by an 

interviewer but released dead or otherwise dead but not observed by an interviewer (type 

B1); and catch released alive and not observed by an interviewer (type B2). The summer 

flounder stock assessment assumes 10% recreational release mortality (Terceiro 2006). 

For the purpose of this report, total catch is defined as A + B1 + B2 catch while harvest is 

defined as A + B1. It is important to note that both types B1 and B2 represent self 

reported data. 

In 2006, 22.2 million summer flounder were caught. Total catch during over the five 

years in Figure 2.5 has gone up 33% with a sharp rise in 2005 where catch was up 62% 

since 2002. The private boat mode dominates all fishing modes catching 18.8 million 

fish, or 85% of the harvest. Shore and for-hire fishing modes are distant followers with 

the for-hire mode overtaking the shore mode in 2006 with 2.4 million fish and 11% of the 

total. 

Figure 2.6 details summer flounder harvest (A + B1) by mode. In 2006 4.2 million fish 

were harvested. Looking back at Figure 2.5, this means that 81% of all summer flounder 

caught are released because regulations forced the release or the fish were released for 

conservation reasons. It is no longer possible in the MRFS to separate released fish into 

fish released for regulatory reasons or fish released for conservation reasons. In 2004 the 

MRFSS eliminated the use of the disposition code in the intercept survey that indicates 

whether the fish released alive was large enough to keep. Trends in release vary 

considerably by mode. The shore mode has the smallest release percentage at 65% 

released followed by the private boat and for-hire modes with 80% and 95% release rates 

respectively. Again, the private boat mode dominates 2006 harvest with 3.7 million fish 

followed by the shore and for-hire modes with 381,053 and 129,701 fish respectively. 

Looking at harvest weight per fish (Figure 2.7) and catch per unit effort (CPUE) (Figure 

2.8) fishing quality is on the rise for every mode except the shore mode. Harvest weights 

are up, except for the shore mode: up 17% in the private boat mode, up 4% in the for-hire 

mode; and down 17% in the shore mode. This of course is partially driven by higher 

minimum size limits, but when coupled with increasing CPUE, it suggests quality is on 
6 

the rise. There is an unexplained drop in weight per fish for the for-hire mode in 2004. 

CPUE is also up in all modes except the shore mode. CPUE is a direct measure of 

quality and is up 33% for the for-hire fleet, up 16% for the private boaters, but is 

completely flat for the shore mode since 2002. In 2005, the shore mode was up 32% over 

2002, potentially indicating that other factors besides stock size and availability reduced 

CPUE in 2006. 

30.8

35.2 34.4

36.9 38.3

5.6

6.1 7.4 7.2 7.9 7.0

4.2 4.8 5.1 4.8 0

5

10

15

20

25

30

35

40

45

2002 2003 2004 2005 2006

Total Caught Targeted & Caught

Figure 2.4. Total and Directed Effort for Summer Flounder in Millions of Trips, 

2002-2006 
7

1,077 1,152 1,376 2,025

17,777 17,642

22,700

18,752

1,691 1,627 1,973 2,270 1,122

16,698

20,555 20,991

26,996

22,288

2,415

13,930

-10,000

0

10,000

20,000

30,000

2002 2003 2004 2005 2006

For-Hire Private Boat Shore Total

Figure 2.5. Total Summer Flounder Catch by Fishing Mode in Thousands of Fish, 

2002 – 2006 

262 389 495 478

3,982 3,936

3,461

3,717

161 207 222 172 130

3,281

4,578 4,653

4,110 4,227

381

2,858

-500

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

2002 2003 2004 2005 2006

For-Hire Private Boat Shore Total

Figure 2.6. Summer Flounder Harvest (A+B1) by Mode in Thousands of Fish, 2002-

2006 

 
8 

As the stock recovers, CPUE will increase. This in turn may attract additional effort 

which will catch fish more efficiently with increased CPUE. These factors decrease the 

likelihood of recovering the stock and increase the regulations needed to achieve harvest 

goals. As a result the recreational summer flounder fishery has become a highly 

regulated fishery and Table 2.1 details the progression of regulations since 1993. Also, 

as regulations have been tightened, they have become increasingly complex with each 

state having its own bag and size limits. 

Looking at Table 2.1, size limits have consistently gone up with some states currently 

using a 20.5” minimum size limit. Using a length/weight calculator from NMFS a 20.5” 

summer flounder weighs 4.7 pounds, which is considerably higher than the average 

weight per fish in Figure 2.7 (NMFS 2008a). This brings up another interesting point; as 

minimum size limits go up it takes fewer fish to reach a harvest quota. Bag limits have 

also been falling and fishing seasons have also been reduced. To take into account the 

increases in effort, total allowable harvest was increased in 2002, dropped in 2003, 

increased in 2004 and 2005, and dropped again in 2006. Over the 16 years in Table 1 

landings exceed the harvest limit during nine years. During the last five years, the 

harvest limit has been exceeded twice. In both overage years, the harvest limit was 

exceeded by 26%. 

2.6

2.8

1.4

2.8

2.5 2.5

2.6

2.8

2.3

2.2 2.1

1.8

1.9

2.7

2.4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

2002 2003 2004 2005 2006

For-Hire Private Boat Shore

Figure 2.7. Summer Flounder Weight per Fish, 2002-2006 
9

8.8

7.6

8.6

7.7

11.7

8.0

7.0

7.6 7.8

9.3

3.1 3.0 3.3

4.1

3.1

0

2

4

6

8

10

12

14

2002 2003 2004 2005 2006

For-Hire Private Boat Shore

Figure 2.8. Trends in Summer Flounder Catch per Unit Effort (CPUE), 2002-2006 

Table 2.1. Table 1Summer Flounder Regulations since 1993 

Regulation 1993 1994 1995 1996 1997 1998 1999 2000 

Harvest Limit (m lb) 8.38 10.67 7.76 7.41 7.41 7.41 7.41 7.41 

Landings (m lb) 8.84 9.33 5.42 9.82 11.87 12.52 8.37 16.52 

Possession Limit 6 8 6 to 8 10 8 8 8 8 

Size Limit (TL in) 14 14 14 14 14.5 15 15 15.5 

5/15 - 4/15 - 1/1 - 1/1 - 1/1 - 1/1 - 5/29 - 5/10 - 

Open Season 30-

Sep 15-Oct 31-Dec 

31-

Dec 

31-

Dec 31-Dec 11-Sep 2-Oct 

Regulation 2001 2002 2003 2004 2005 2006 2007 2008 

Harvest Limit (m lb) 7.16 9.72 9.28 11.21 11.98 9.29 

Landings (m lb) 11.66 8.03 11.66 10.99 11.17 11.74 a 

Possession Limit 3 4 to 8b 4 to 8b 3 to 8b 2 to 8b 2 to 8b 2 to 8b 1 to 8b

Size Limit (TL in) 15.5 15.5 - 

18b

14 - 

17.5b

14 - 

17.5b

14 - 

17.5b

14 - 

18b

14 - 

19.5b

14 - 

20.5b

4/15 - 

Open Season 15-

Oct 

Variesb Variesb Variesb Variesb Variesb Variesb Variesb

a

Projected using 2005 landings proportions by wave and 2006 waves 1-5 data. 

b

State-specific conservation equivalency measures. 

Summer flounder is an important food fish and an important target species for the party 

boat fleet. While the angling community sees the improvements in the stock through 

their increased catches, they see the regulations getting tighter and tighter. As the 

seasons get shorter, the for-hire industry’s bottom line is directly impacted. As a result, 

the recreational community has criticized the MRFSS data collection program and called 

for harvest limits to be raised for the recreational sector. Many have suggested that the 
10 

additional fish needed to increase the harvest limits come from the commercial sector 

through a reallocation. 

2.2 Basis for Economic Allocation Analysis 

Broadly defined, economists use two different metrics to examine the implications of 

policy decisions on society: economic value and economic impacts. The first, economic 

value, also known as economic benefit or welfare, monetizes the value society places on 

resources or activities. Economic value should be the metric used to decide between one 

course of action and another (Freeman 1993, Edwards 1990, and others). Economic 

value, however, is not the only criteria that should be examined when focusing on 

resource allocation questions. Equity, fairness, distributional concerns, and other social 

impacts are important (Edwards 1990), but will not be addressed in this report. 

The second, economic impacts, examines the flow of expenditures on fishery resource 

activities and products as that spending moves through a community. While economic 

impact measures should not be used to choose a course of action, they can be used to 

examine what particular sectors in the economy are hurt or helped by a particular policy 

and to what degree. Economic impact analysis examines the distribution of value 

changes identified when comparing benefits, making both types of analysis 

complementary. 

Edwards (1990) developed a guide for the allocation of fishery resources and this 

discussion follows his framework. Very few allocation studies have been conducted for 

saltwater recreational fishing. Kirkley, et al. (2000) conducted a study for striped bass 

allocation in Virginia examining total value in each sector. Carter, Agar, and Waters 

(2008) conducted an allocation analysis for the red grouper fishery in the Gulf of Mexico 

using the equimarginal principle. 

For both the recreational and commercial sectors, total value is the sum of consumer and 

producer surplus. Producer surplus is measured by examining the supply curves for 

commercial producers of seafood, including harvesters, processors, wholesalers, and 

distributors, as well as the supply curves for for-hire recreational service providers. 

Essentially, producer surplus is the difference between the cost of producing the good and 

the dollar value generated by the sale of the good. Consumer surplus is measured by 

examining the demand for goods at the consumer level including the demand for fish at 

markets and restaurants and the demand for recreational fishing trips. Consumer surplus 

is the difference between the amount society would be willing to pay for the good in 

question and what consumers actually paid for the good in the marketplace. 

For the recreational sector, total value or net benefits is the sum of the consumer surplus 

from recreational fishing participants and producer surplus from for-hire charter and head 

boat operators. For the commercial sector, total value is the sum of consumer surplus 

from the purchase of seafood products in markets and restaurants and the producer 

surplus from harvesters, processors, wholesalers, and distributors of those fishery 

products. 

Value is not static across all allocations, and, as any consumer obtains more of a good, 

the marginal value of obtaining the next unit of that good falls. That is, there are 
11

diminishing returns to additional consumption of any good and this is a fundamental tenet 

of consumer demand, which has important implications for allocation decisions. A 

similar tenet exists for producers, but does not always hold depending on the character of 

the industry. As a result, it is important to examine the schedule of these marginal values 

in each sector. Societal benefits are maximized at the allocation where commercial sector 

marginal value is equal to the marginal value from the recreational sector. This is known 

in economics as the equimarginal principle. Using the equimarginal principle is widely 

recognized as the best way to maximize societal value in an allocation analysis Freeman 

1993, Edwards 1990). 

Estimating producer surplus and the marginal value of a pound of summer flounder 

harvest for the commercial fleet requires data on the costs and earnings of all the various 

businesses involved in the production and sale of seafood or recreational services. Very 

little of this type of information exists, making the calculation of producer surplus 

difficult at best and impossible at worst. Multi-species fisheries, like summer flounder 

otter trawl fishery complicate estimation. For this effort, data on trip costs from a sample 

of otter trawl trips will be used to estimate the trip costs for all otter trawl trips taken 

between 2005 and 2007. 

Estimating consumer surplus entails estimating demand curves for both the angling 

experience and for consumer purchases of seafood. On the recreational side of the 

equation, estimating consumer surplus involves specialized surveys of anglers. NMFS 

periodically collects the data necessary to estimate site choice recreational demand 

models. NMFS has spent considerable time and effort developing site choice models2

and, currently, site choice models are the agency’s preferred recreational valuation 

technique.3 

On the seafood consumer side, data on the prices and quantities of seafood purchased in 

markets and restaurants is needed. Unfortunately this type of data rarely exists. Instead 

there are techniques that utilize landings data to estimate consumer demand functions that 

can be used to calculate the marginal value of summer flounder consumption at the retail 

level. Those techniques will be used here. 

In summary, the equimarginal principle is the preferred method to examine allocations. 

Often, it is difficult to develop a complete schedule of marginal values across all possible 

allocations. In this case, it is appropriate to examine total value, recognizing, however, 

that total value may not take diminishing marginal returns into account. 

 

2

 A partial list of the research in recreational site choice models conducted or sponsored by NMFS or using 

Marine Recreational Fisheries Statistical Survey data include: Gautam and Steinback (1998); Gentner 

(2007); Gentner and Lowther (2002); Gillig, Woodward, Ozuna, T., and Griffin (2000); Haab, Hicks, 

Schnier, and Whitehead (2008); Haab, Whitehead, and McConnell (2000); Haab and Hicks (1999); 

Whitehead and Haab (1999); Hicks, Gautam, Steinback, and Thunberg (1999); and Hindsley, Landry, and 

Gentner (2008). 

3 See the Center for Independent Experts evaluation of NMFS’ recreational economic program. Center for 

Independent Experts. (CIE 2006). 
12 

3.0 Commercial Valuation 

This chapter estimates commercial harvesters’ marginal value for summer flounder. 

Typically, cost and earnings information for commercial harvesters is sparse or nonexistent. In this case, trip cost data was collected from a sample of otter trawl fishermen 

and those trip costs are used in a regression model to estimate trip costs for the entire 

fleet. Estimated trip costs are then used to model input compensated supplies for summer 

flounder and four other species groups harvested by otter trawl fishermen. From these 

input compensated supply equations, it is possible to estimate the current marginal value 

for a pound of summer flounder and simulate that marginal value across the entire range 

of potential allocations. 

3.1 Estimation of Trip Costs and Data Manipulation 

This study uses data from 2005, 2006, and 2007. Estimation of commercial harvester 

profits requires data on both harvester revenues and harvester costs. NMFS collects 

revenue information from a combination of self-reported logbook entries and seafood 

dealer data. To collect cost information, NMFS uses the observer program to collect very 

accurate trip cost data across a sample of otter trawl and other vessels. Because the 

observer program samples commercial trips, NMFS does not have trip costs for all 

reported trips. 

To address the need for trip costs for all trips, NMFS contracted with the Woods Hole 

Oceanographic Institute to develop a regression based model to predict trip costs for 

boats not included in the observer sample. That work is detailed in Jin (2008). His 

model used trip cost data from the 2006 observer year. Jin’s (2008) work estimated 

regression models for fixed costs, labor costs, and trip costs. While the trip cost data is 

considered to be very accurate as it is collected by the observer during the trip, the fixed 

cost data, collected using a separate survey, is felt to be problematic. 

The 2006 data contained a large number of available data points. Generally, trip costs are 

influenced by gear typed, vessel characteristics, days at sea, fishing location, fishing time, 

the value of landings, and other characteristics. To develop a regression relationship 

using the observer, logbook, and dealer data, Jin created the following independent 

variables; monthly dummies, vessel age, engine age, total horsepower, total landed value, 

total landings in pounds, principle port dummies, vessel ownership dummies, vessel 

construction type, fuel type, trip duration in hours, fishing time in hours, squares and 

square roots of vessel length, horsepower, and age, and area fished dummies. The 

dependent variable, trip costs, was the sum of ice, food, fuel, damaged gear, supplies, 

water, oil, and bait costs. All dollar values were converted to 2007 dollars using the 

producer price index. 

While Jin estimated a number of models, the focus here is on the otter trawl gear type. 

Jin’s otter trawl modeling was performed in two phases. The first phase used a stepwise 

linear regression to select the relevant variables. This was performed in SAS using the 

Proc REG procedure, and that procedure adds independent variables to the model one at a 

time. The decision rule for inclusion is maximizing r-square while retaining only those 

variables with a significance level of 0.15 or better. This process yielded the following 

variables; total trip duration, steam time, gross tons, gross tons squared, April monthly 

dummy, and North Carolina and Rhode Island principle port dummies. 
13

Heteroscedasticity (HSK) was found in these initial selection regressions. To address the 

HSK, Jin used SAS Proc MODEL to estimate the final regressions. This procedure 

utilizes a generalized method of moments (GMM) estimator using instrumental variables 

to control for HSK. With this procedure, if HSK is present, the ordinary least squares 

parameters are unbiased and efficient, but the covariance matrix used is White’s. Jin’s 

original coefficients are found in Table 3.1. 

Because this effort had access to two additional years of data (2005 and 2007), it was 

decided to follow Jin’s procedure to estimate another otter trawl cost model. Following 

the exact same data creation and modeling steps as Jin, an updated otter trawl cost model 

was developed. Table 3.2 contains the means and descriptive statistics for the variables 

created and used in the stepwise regression. 

Across all three years, total trip duration was almost 66 hours on average; they steamed 

for almost eight hours and fished for 58 hours. On average, the captains are very 

experience with nearly 22 years of commercial fishing experience. On average, the boats 

are; 70.5% steel, 64.4 feet in length, displaces 90.6 gross tons, and is 30 years old. For 

power, almost 93.9% have one diesel engine and that engine has on average has 484 

horsepower. The most frequent month for trips is July, followed by May and January. 

The lowest activity month is October, although November and December aren’t far 

ahead. Massachusetts (29.5%) is the most popular principle port followed by Rhode 

Island (22.5%) and New Jersey (17.3%). Principle port is different from landing port that 

will be used later in the analysis. Principle port is considered the boat’s home port 

whereas the port of landing is where the boat sold its catch for that trip. 

Table 3.1. Otter Trawl Cost Model Parameters (Jin 2008) 

Variable Estimate Approximate 

Standard Error 

Approximate Pr 

>|t| 

Intercept -105.925 102.8 

Trip Duration 43.65556 2.8352 0.3031 

Steam Time 69.44759 22.0714 <.0001 

Gross Tons Sqrd 0.193516 0.0279 0.0017 

Age*Gross Tons -0.54886 0.0963 <.0001 

April Dummy 896.9853 406.1 <.0001 

North Carolina -1207.29 418.2 0.0274 

Rhode Island -578.67 233.8 0.004 

Adjusted r-square 0.8039

Table 3.3 contains the results of the GMM estimation and, by inference, the stepwise 

selection model. With the additional years of data, the r-square increases to 0.8695. 

Some of the same variables were significant, however there were some changes. Trip 

duration and steam time where both positive, although only total trip duration was 

significant. Steel vessel construction decreases cost as does length, to a point, as length 

squared is positive. Additional horsepower also increases cost. Two monthly dummies 

were selected in to the model and both January and March reduce costs although March 

is only significant at the 0.15 level. Both state dummies were significant with boats 

having an NC principle port having higher lower costs and boats from MA having higher 
14 

costs. Both White’s test and the Breusch-Pagan test indicate that the HSK was remedied 

using the GMM estimator. 

Figure 3.1 plots the actual costs versus the predicted costs and the model predicts quite 

well. With the exception of a few extremely high actual cost values, the predictions are 

very close to the actual values. Also, since the data was sorted by year, notice the upward 

shift in costs in 2007 around observation 600. Table 3.4 compares the predictive 

accuracy of both sets of parameters. The trip cost average across the data used was 

$3,681.64 and the model estimated here (Table 3.3) predicts costs, on average, only 

$10.06 higher while Jin’s parameters (Table 3.1) predicts cost, on average, $87.53 higher. 

Interestingly, the confidence interval on the predicted cost from the model in Table 3.3 is 

tighter than the actual cost confidence interval, so while it predicts slightly higher, it 

predicts less volatility. Both models predict negative trip costs; 26.4% for the parameters 

in Table 3.1 and 17.0% for the parameters in Table 3.3. When the parameters in Table 

3.3 are applied to all otter trawl trips from 2005, 2006, and 2007, only 6.46% of the trip 

costs were negative. Those observations were subsequently dropped from the analysis. 
15

Table 3.2. Means and Descriptive Statistics for the Dependent Variables 

Variable Mean StdErr 

95% Lower 

Confidence 

Limit 

95% Upper 

Confidence 

Limit 

ATRIPDUR 65.94 2.62 60.81 71.08 

CAPTYRS 21.72 0.39 20.96 22.48 

STEAMTIM 7.76 0.29 7.20 8.32 

TIMELOST 1.62 0.23 1.16 2.08 

XTRIPDUR 87.50 3.14 81.34 93.66 

age_eng1 19.56 0.51 18.57 20.56 

LEN 64.36 0.49 63.40 65.31 

VHP 483.60 8.64 466.64 500.56 

GTONS 90.58 1.75 87.15 94.01 

tonage 2,636.46 51.21 2,535.95 2,736.98 

age 30.32 0.36 29.61 31.03 

ENG2EXIST 6.05% 0.87% 4.35% 7.75% 

M1 12.27% 1.16% 9.99% 14.54% 

M2 8.39% 0.98% 6.46% 10.31% 

M3 5.63% 0.82% 4.03% 7.23% 

M4 7.26% 0.92% 5.46% 9.06% 

M5 14.64% 1.25% 12.19% 17.10% 

M6 9.39% 1.03% 7.36% 11.41% 

M7 18.27% 1.37% 15.59% 20.96% 

M8 8.39% 0.98% 6.46% 10.31% 

M9 8.26% 0.97% 6.35% 10.17% 

M10 2.38% 0.54% 1.32% 3.44% 

M11 2.50% 0.55% 1.42% 3.59% 

M12 2.63% 0.57% 1.52% 3.74% 

CORP 73.29% 1.62% 70.10% 76.47% 

soleown 64.58% 1.69% 61.26% 67.90% 

partner 17.15% 1.33% 14.53% 19.77% 

firmown 8.14% 0.97% 6.24% 10.03% 

CT 4.63% 0.74% 3.17% 6.09% 

ME 1.50% 0.43% 0.66% 2.35% 

MD 2.13% 0.51% 1.12% 3.13% 

MA 29.54% 1.61% 26.37% 32.71% 

NJ 17.27% 1.34% 14.64% 19.90% 

NY 15.77% 1.29% 13.24% 18.30% 

NC 4.51% 0.73% 3.06% 5.95% 

RI 22.53% 1.48% 19.63% 25.43% 

VA 1.38% 0.41% 0.57% 2.19% 

fiberg 12.14% 1.16% 9.87% 14.41% 

steel 70.46% 1.61% 67.29% 73.63% 

diesel 99.62% 0.22% 99.20% 100.05% 

GOM 0.25% 0.18% -0.10% 0.60% 

GB 2.50% 0.55% 1.42% 3.59% 

SNE 9.64% 1.04% 7.59% 11.69% 

spec124 2.38% 0.54% 1.32% 3.44% 

spec818 3.00% 0.60% 1.82% 4.19% 

spec5240 12.02% 1.15% 9.76% 14.27% 

spec8009 0.50% 0.25% 0.01% 0.99% 
16 

Table 3.3. Nonlinear GMM Parameter Estimates 

Approximate Variable Estimate Approximate 

Std Err t Value 

Pr > |t| 

Intercept -177729 93629.2 -1.9 0.058 

ATRIPDUR 52.37899 2.7307 19.18 <.0001 

STEEL -99.6791 88.9099 -1.12 0.2626 

STEAMTIM 18.01961 21.579 0.84 0.4039 

LEN -6636.37 3360.5 -1.97 0.0486 

LEN2 20.03945 9.7026 2.07 0.0392 

LENSQRT 64825.78 33619.9 1.93 0.0542 

VHP 2.944961 1.0896 2.7 0.007 

VHP2 -0.00029 0.000486 -0.6 0.5516 

M1 -375.077 179.1 -2.09 0.0365 

M3 -499.643 344.5 -1.45 0.1474 

NC -1817.2 411.1 -4.42 <.0001 

MA 498.7661 206.3 2.42 0.0158 

R-Square 0.8695 

Original plans included estimating profit models at the annual level, but that proved 

problematic because of missing information on vessel characteristics or trip 

characteristics necessary for modeling cost for 373 boats across the three year period. 

Initially, all trips for all vessels that landed summer flounder in each year were included. 

That data set included 71,746 trips distributed as follows: 25,138 trips across 427 vessels 

in 2005; 24,511 trips across 414 vessels in 2006; and 22,097 trips across 398 vessels in 

2007. After estimating trip cost information those numbers fell to 55,066 trips with valid 

cost data. Most of the loss in observations was due to fishing time that exceeded total 

time away from port or missing vessel characteristics (combined 16.8%) and negative 

predicted trip costs (6.5%). For an annual model, this poses problems as the trip time and 

missing vessel characteristics made it impossible to aggregate all trips across all vessels. 

To estimate an annual model with only those vessels with good trip cost data for all trips, 

over 78% of the trips would have to be thrown out affecting 250 vessels in 2005, 76 

vessels in 2006, and 47 vessels in 2007. 

As a result, the remainder of this analysis will focus on the trip level. Across the three 

years, there were 36,413 trips that landed summer flounder and 33,773 of those trips 

allowed estimation of trip costs. The loss of observations were due to the following 

reasons: 3,452 trips were missing vessel characteristics (9.5%), 918 had fishing time 

greater than total trip time (2.52%), and 2,534 trips had negative estimated trip costs 

(7.0%). Table 3.5 contains the descriptive statistics for this data set. The number of 

vessels ranged from 379 in 2007 to 419 in 2005. Average trips per vessel ranged from 

29.1 in 2007 to 36.9 in 2005. Overall, this data set represents the vast majority of 

summer flounder harvested in the otter trawl gear type, ranging from 89% to 95% of the 

summer flounder harvested by otter trawls in each year. As a result, this data still 

represents the majority of summer flounder harvest across all gear types. 
17

Figure 3.1. Actual Total Trip Cost Versus Predicted Trip Cost 

Table 3.4. Actual Trip Costs and Predicted Trip Costs 

Variable N Mean StdErr 

95% Lower 

Confidence 

Limit 

95% Upper 

Confidence 

Limit 

Trip Cost 799 $3,681.64 $172.14 $3,343.73 $4,019.54 

Prediction from Model 

Reported in Table 3.3 795 $3,691.70 $161.13 $3,375.41 $4,007.99 

Prediction Using Jin’s 

Parameters (Table 3.1) 791 $3,769.17 $163.22 $3,448.78 $4,089.57 

Table 3.5. Trip Data Set Characteristics, 2005 - 2007 

Percent of Total Otter Trawl Summer 

Flounder Harvest Year Number of 

Trips 

Number of 

Vessels 

Average Trips 

per Vessel 

Pounds Value 

2005 12,110 419 36.8 89.0% 88.2% 

2006 11,924 403 35.2 93.9% 93.2% 

2007 9,739 379 29.1 95.0% 94.1% 
18 

Table 3.6 details the average per trip total pounds landed, total landed value (revenue), 

estimated trip cost, and profit across this sample by year. Profit was calculated by 

subtracting estimated trip costs from total landed value. From the table, profits are quite 

low per trip but have been increasing. Total landed pounds have been decreasing but so 

have costs. Across the entire data set, 55.4% of all trips lose money (negative profits). 

When only those trips that make 25% or better of their revenue from summer flounder 

are examined, 63.9% of those trips lose money. 

Table 3.6. Total Pounds, Value, Costs, and Profit per Trip 2005 - 2007 (2007 dollars) 

Year Variable Number of 

Trips 

Mean per 

Trip 

95% Lower 

Confidence 

95% Upper 

Confidence 

2005 Estimated Trip Cost 12,110 $3,115.82 $3,054.02 $3,177.62

2005 Profit 12,110 $2,157.78 $2,013.18 $2,302.38

2005 Total Landed Pounds 12,110 5,198.65 5,019.91 5,377.39

2005 Total Landed Value 12,110 $5,019.20 $4,863.86 $5,174.53

2006 Estimated Trip Cost 11,924 $2,956.40 $2,897.18 $3,015.61

2006 Profit 11,924 $2,191.86 $2,071.34 $2,312.37

2006 Total Landed Pounds 11,924 4,835.54 4,674.66 4,996.43

2006 Total Landed Value 11,924 $5,024.62 $4,884.07 $5,165.17

2007 Estimated Trip Cost 9,739 $2,857.43 $2,793.06 $2,921.80

2007 Profit 9,739 $1,871.32 $1,750.72 $1,991.92

2007 Total Landed Pounds 9,739 4,284.50 4,119.68 4,449.31

2007 Total Landed Value 9,739 $4,706.60 $4,558.46 $4,854.73

 

Port of landing and principle port have both proven to be important descriptors of costs 

and therefore profits. In this data set, there are 83 individual landing ports with Point 

Judith, RI the single most important port in terms of summer flounder landings with 

30.0% of all trips landing in Point Judith. A distance second is Belford, NJ with 10.5% 

of all trips landing there. Unfortunately, including 83 port dummies in the profit model is 

too many. As a result both state of landing and county of landing dummy variables were 

created. Figure 3.2 contains the distribution of trips by landing county. The city counties 

in the Virginia Beach area have been aggregated into one landing county creating 33 

landing county dummies. There were a large number of landing counties with very few 

trips (less than 0.03% of the total trips) and those have been aggregated into a category 

called “All Other Counties.” Again, the single biggest landing county is Washington 

County, RI (10,399 trips), followed by Suffolk County, NY (6,182 trips), and Monmouth 

County, NJ (3,553 trips). 

Otter trawls catch a variety of species. In this data set there are over 21 including two 

miscellaneous categories with an unknown number of species in each. For the profit 

model, it is necessary to aggregate these species into fewer species groups. For this 

study, five species groups were developed: summer flounder; bait which includes 

menhaden, herring, butterfish, mackerel, and skate; other bottomfish which includes 

scup, black sea bass, monkfish, tilefish, small mesh species, and other flat fish; shellfish 

which includes shrimp, loligo squid, lobster, scallops, and illex squid; and other species 

which includes others species, highly migratory species, and bluefish. 
19

Figure 3.2. Number of Trips Landing in Each County, 2005-2007 

Table 3.7 details the total landed pounds by each species group across the time series. 

Summer flounder, by definition, is landed in every trip as are shellfish and bait. On 

average, more shellfish are landed in this data set than summer flounder. Other 

bottomfish are not landed on every trip, but when landed, make up a significant portion 

of the catch. 

Table 3.8 details the average price for each species group, per trip, for each year. In all 

years, summer flounder obtains the highest prices ranging from $2.40 to $2.95 per pound. 

Shellfish prices are the second highest ranging from $1.70 to $2.33 per pound. The 

lowest priced species group in all years is the bait category that ranges from $0.63 to 

$0.74 per pound. 

Table 3.9 details the average landed value by species group and year. Across trips that 

land summer flounder, which includes all trips in this database, summer flounder is the 

highest value landed product. When other bottomfish are landed, they constitute a 
20 

significant portion of revenue, but they are not landed on every trip. Both bait and other 

species make up very small portions of landed value. 

Table 3.7. Pounds Landed per Trip by Species Group, 2005 - 2007 

Year Species Group Number 

of Trips 

Mean Pounds 

per Trip 

95% Lower 

Confidence 

95% Upper 

Confidence 

2005 Bait 12,110 864 800 928 

2006 Bait 11,924 836 768 904 

2007 Bait 9,739 828 755 901 

2005 Other Bottomfish 3,789 1,584 1,498 1,671 

2006 Other Bottomfish 4,531 1,313 1,254 1,372 

2007 Other Bottomfish 3,730 1,280 1,219 1,340 

2005 Other Species 3,789 1,134 929 1,339 

2006 Other Species 4,531 954 763 1,144 

2007 Other Species 3,730 1,245 1,030 1,459 

2005 Shellfish 12,110 1,303 1,192 1,415 

2006 Shellfish 11,924 1,375 1,273 1,476 

2007 Shellfish 9,739 883 789 976 

2005 Summer Flounder 12,110 1,074 1,029 1,120 

2006 Summer Flounder 11,924 933 888 977 

2007 Summer Flounder 9,739 807 766 847 

Table 3.8. Landed Price per Trip by Species Group, 2005 -2007 (2007 dollars) 

Year Species Group Number 

of Trips 

Mean Price 

per Trip 

95% Lower 

Confidence 

95% Upper 

Confidence 

2005 Bait 4,295 $0.64 $0.63 $0.65 

2005 Other Bottomfish 8,644 $1.73 $1.71 $1.75 

2005 Other Species 3,789 $1.24 $1.20 $1.27 

2005 Shellfish 5,602 $2.33 $2.27 $2.40 

2005 Summer Flounder 12,110 $2.40 $2.38 $2.41 

2006 Bait 4,865 $0.63 $0.62 $0.64 

2006 Other Bottomfish 9,006 $1.74 $1.72 $1.76 

2006 Other Species 4,531 $1.37 $1.34 $1.41 

2006 Shellfish 6,480 $1.74 $1.69 $1.79 

2006 Summer Flounder 11,924 $2.71 $2.70 $2.73 

2007 Bait 4,512 $0.74 $0.69 $0.78 

2007 Other Bottomfish 7,411 $1.74 $1.72 $1.76 

2007 Other Species 3,730 $1.23 $1.20 $1.26 

2007 Shellfish 4,566 $1.70 $1.65 $1.75 

2007 Summer Flounder 9,739 $2.95 $2.93 $2.97 

As is often done in multi-product fisheries models when one species is the focus, the use 

of a revenue cut off is explored here. All trips were removed from the data if the percent 

of summer flounder revenue was less than 25%. This drops the total number of 

observations 28.0% from 33,773 trips to 24,323 trips. Interestingly profit per trip is ten 

times lower for this subset, costs per pound go up $1.34 per pound, and summer flounder 

profit per pound drops $1.32 per pound. 
21

Table 3.9. Landed Value per Trip by Species Group, 2005 - 2007 (2007 dollars) 

Year Species Group Number 

of Trips 

Mean 

Value per 

Trip 

95% 

Lower 

Confidence 

95% Upper 

Confidence 

2005 Bait 12,110 $242.02 $223.51 $260.53 

2005 Other Bottomfish 12,110 $2,017.71 $1,907.24 $2,128.19 

2005 Other Species 3,789 $436.12 $378.42 $493.81 

2005 Shellfish 12,110 $1,378.81 $1,277.19 $1,480.44 

2005 Summer Flounder 12,110 $1,899.68 $1,834.20 $1,965.17 

2006 Bait 11,924 $219.11 $199.88 $238.34 

2006 Other Bottomfish 11,924 $1,787.24 $1,703.58 $1,870.89 

2006 Other Species 4,531 $368.41 $326.69 $410.13 

2006 Shellfish 11,924 $1,305.83 $1,217.02 $1,394.64 

2006 Summer Flounder 11,924 $1,859.68 $1,784.25 $1,935.11 

2007 Bait 9,739 $286.18 $260.30 $312.06 

2007 Other Bottomfish 9,739 $1,598.21 $1,521.42 $1,675.01 

2007 Other Species 3,730 $534.19 $466.24 $602.15 

2007 Shellfish 9,739 $859.27 $775.19 $943.35 

2007 Summer Flounder 9,739 $1,815.70 $1,738.14 $1,893.26 

3.2 Model 

There has been considerable work on multiproduct fisheries models in the literature. 

Generally, these models use similar specifications and assumptions. In this body of work 

commercial fishermen are profit maximizers that face a two stage problem (Kirkley and 

Squires 1991). In the first stage, the fishing trip, the vessel operator chooses the revenue 

maximizing output bundle subject to fixed inputs, weather, resource quotas, and relative 

product prices. It is important to note that, for the commercial fisherman, inputs are fixed 

once they leave the dock. Because of this characteristic, the input bundle can be 

specified as a single composite input. There have been some detractors of this 

assumption (McConnell and Price 2006) due to the share system used in fisheries to 

compensate labor. Under the share system, labor cost is an endogenous function of 

harvest. Often effort, expressed as days at sea or gross tonnage, is used as the quasi fixed 

input because trip cost information is typically lacking. In the second stage, firms adjust 

their levels of effort to minimize production costs by selecting the optimal vessel size or 

capital stock. This second stage takes place over a 3-14 month horizon (Squires and 

Kirkley 1991). 

Typically, these dual revenue models are estimated using translog or generalized Leontief 

functional forms, with the generalized Leontief used most frequently (Kirkley and Strand 

1988, Squires and Kirkley 1991, Vestergaard 1999, Carter et al 2008, and others). The 

generalized Leontief is usually selected because it places few restrictions on the 

underlying technology. The generalized Leontief also allows the analysis of input 

separability and non-jointness, but at the cost of imposing linear homogeneity in prices 

(Carter et al 2008). Also, the generalized Leontief allows the estimation of output levels 

directly instead of output shares like the translog making the result more intuitive and 

improving the ease of estimation of the derived demands. 
22 

The generalized Leontief requires a series of sometimes limiting assumption. First, profit 

must be non-decreasing in output prices and fixed factors. Profit must also be nonincreasing in input prices, linearly homogeneous in prices and convex in prices. It also 

must be concave in fixed quantities, continuous, and twice differentiable (Carter et al 

2008). Additionally, input and output separability are important testable assumptions 

regarding the underlying technology. Separability implies that there are no interactions 

between any one input and any one output. If this assumption holds, it allows the use of 

composite inputs and composite outputs in the function being estimated. 

Jointness in inputs is another testable assumption. Jointness in inputs implies that it takes 

all inputs to produce all outputs. That is, harvesting processes are interrelated. If 

jointness is not found, it means that there is a separate production function for each 

output or groups of outputs. While this assumption does not often hold, it is suspected 

that is might for a gear like the otter trawl. 

3.2.1 Literature Review 

Kirkley and Strand (1988) were one of the first to apply a dual revenue function to look 

at the Georges Bank multiproduct trawl fishery. The main goal of their work was to test 

general assumptions about the typical multiproduct specification that requires separability 

and non-jointness in production. They estimated a revenue function using a generalized 

Leontief function using the product of days at sea and gross tons as their quasi-fixed 

input. Their analysis used NMFS data containing 175,000 trips taken on Georges Bank. 

They used eight species groups including; cod, haddock, yellowtail flounder, pollock, 

winter flounder, other flounder, miscellaneous, and a catch all group equal to the total 

landed pounds minus the sum of the seven above. They estimated firm level annual input 

compensated supply functions using an iterated Zellner approach. Zero outputs by 

species groups can pose problems for these models. In this case, they left the zero 

outputs as zero as less than 11% of the trips contained zero outputs for any one species 

group. Their analysis showed that the assumptions of separability and non-jointness do 

not hold, but also felt gross tons and days absent may not have had enough variation or 

enough systematic variation to use as their quasi fixed input. 

Squires and Kirkley (1991) used a dual revenue function to examine quota management 

in the multiproduct sablefish fishery. They used a generalize Leontief revenue function 

using total revenue as the dependent variable and output prices, composite input, landing 

port dummy and quarterly dummies as the independent variables. Similar to this 

analysis, they chose to include only those trips that landed more than 1,000 pounds of 

sablefish. Instead of allowing zero outputs to remain zero, they replace zero outputs with 

a trivial value of 0.1. The found the input output separability was rejected but that 

jointness overall was a valid assumption. 

Squires and Kirkley (1996) used a dual revenue function to estimate the virtual prices in a 

multi-species fishery for the purpose of analyzing an individual transferable quota. 

Under the same assumptions as the above work, they used gross tonnage as their single 

composite input and measure of effort. Again they used a generalized Leontief imposing 

symmetry, linear homogeneity in prices and assuming input separability. Also, zero 

outputs were replaced with a small value of 0.1. The focus of this paper was to estimate a 

firm’s input compensated supply equations so that they could derive the virtual price for 
23

quota. As will be done below, they horizontally sum the firm inverse derived demands to 

obtain the market inverse demand. Since the overall quota equals a perfectly inelastic 

supply of quota they equate the market inverse demand to overall quota and solve for the 

equilibrium market price for quota. From a static model, this price is equivalent to the 

price from an open auction. Integrating under these curves estimates producer surplus. 

Vestergaard (1999) examined a multiproduct fishery with joint input production. With 

joint technology, as is the case with the otter trawl fishery, there are spillover effects on 

other output when one output is controlled through regulation. An allocation change, 

which is essentially a change in a sector’s TAC or quota, is a perfect example of an 

output control. In this analysis Vestergaard assumes a multiproduct firm faces a perfectly 

elastic demand for its outputs and input supply curves as assumed perfectly price elastic. 

The study estimates a profit function to measure the quasi-rent. Quasi-rent is the return 

to the fixed factors and is more useful than profit functions for obtaining producer’s 

surplus. An important point posited by Vestergaard is that these types of models as short 

run only and conditional both on the existing biomass and the available biomass. 

Vestergaard’s goal is to estimate producer surplus. To do this, he assumes production is 

joint in inputs with technology interdependence. He also posits that there may be one 

output for which zero production is possible, if and only if, no production takes place at 

all (Just et al 1982). He calls this the necessary output. Most multispecies fisheries fit 

this model well with joint production and little ability to adjust output composition, 

which is certainly the case with otter trawls (Kirkley and Strand 1988, Squires 1987, 

Squires and Kirkley 1991, 1996). 

3.2.2 Theoretical Model Specification 

Recently Carter et al (2008) performed a comprehensive analysis of both recreational 

consumer surplus and commercial producer surplus in the red grouper fishery in the 

South Atlantic and Gulf of Mexico. Their analysis follows the above literature closely 

and the structure of their model will be used here. Fulginiti and Perrin (1993) describe 

the linkage between quota constrained quasi-rent and the unconstrained quasi-rent using 

the concept of a virtual price. Under this structure, the virtual price is the output price 

that induces the firm to produce at a given quota level. Virtual price is defined as: 

1

1

q

pv

= ∂

∂π 3.1) 

where 1 q is the quota for output 1, pv1 is the virtual price for output 1, and π is profit in 

this multiproduct fishery. Furthermore: 

( ) 11 1v pp −= λ 3.2) 

where p1 is the output price and λ1 is the rent per unit of quota or the marginal value of 

output 1. At the virtual price for quota 1, the quota quasi-rent function must equal the 

quota free quasi-rent function: 

( ) ( KwppKqwpp ) h hv ;,,,;,, π 1 1 = π 3.3) 
24 

where ph is the price vector for all other output prices in this multiproduct fishery, w is a 

vector of input prices, and K is the quasi fixed input. Quasi rent can be expanded and 

rewritten as follows for a two output single quasi fixed input case: 

( ) ∑ ( ) ∑ ( ) = =

= − −+ −

m

j

h jj h

n

i

h ii KwppxwqKwppypKqwpp

1

11 11 11

2

1 1 π ,;,, λ ;,, λ λ ;,, 3.4) 

where xj is the single quasi fixed input, wj is the single input price, yi is a vector of the 

two output quantities. Using Hotellings lemma: 

( ) 2;,, 1 −= ≥∀

∂

∂ iKwppy

p

i hi

i

λ π 3.5) 

( ) Kwppx

w j hi

j

;,, 1 λ π −−= ∂

∂ 3.6) 

Where 5) is the output supply and 6) is the input demand. Inverse derived demand for 

quota found by differentiating 4) above with respect to quota 1: 

( ) Kqwp

q

,;, 1 1

1

λ π = ∂

∂ 3.7) 

Market output price (landed price) less the virtual price is the marginal quota rent. This 

expression for the inverse demand captures the optimal adjustment in inputs used and 

captures optimal adjustments in other outputs (Carter et al 2008). As such, it is the 

marginal value of the next unit of quota in fishery 1. While it is possible to calculate 

producer surplus by integrating below the market price and above the output supply, 

producer surplus can be derived using the input demands as the area under the implicit 

derive derived demand for quota measures quasi rent (Carter et al 2008). 

( ) ( ) KqwpdyKqwpPS

q

,;, ,;, 1

0

1 1 1

1

= λ = π ∫ 3.8) 

The total derived demand for the commercial sector is simply the horizontal sum of the 

individual firm and trip level demands. Therefore, commercial quota rental price for the 

last unit of quota is found by setting the total demand equal to the perfectly inelastic 

supply curve for quota, also known as the TAC. Quasi rent is estimated by integrating 

under different levels of the TAC at each level of allocation change being considered. 

3.2.3 Empirical Model 

The general specification of a non-homothetic generalized Leontief quasi-rent function is: 

∑∑ ( ) = ≠

= +

ij

jiij

n

i

ii KpKp Kpp

2/1

1

2 π );( α β 3.9) 
25

where pi is output price of species i, and K is the quasi-fixed input. Symmetry is imposed 

by restricting βij =βji for each i not equal j. Using Hotellings lemma, the inputcompensated unconstrained supplies are 

∑≠ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

++==

∂

∂

ij i

j

ii ii ij

i

K

p

p KKy

p

2/1

2 ββα π 3.10) 

The specification used for estimation is: 

( )

∑∑

∑ += ∑∑ +∑∑ +∑∑ +

i m

imim

i k i l

ikik iiil

i j

ii jiij

Kpf

KpKp KpeKpdKpp

φ

απ β δ ε

2/1 2 );(

 3.11) 

where pi is the landed price for species i, K is the total estimate trip costs, d is a set of 

monthly dummies from January to December, e is a set of dummies for the three years in 

the data, and f is a set of landing county dummies. This study is fairly unique in that the 

data contains total estimated trip costs. These costs are quasi fixed since once a trip has 

started, the inputs available, both capital and labor, are fixed. Applying Hotellings 

lemma the input compensated supplies are: 

( ) ∑ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

++==

∂

∂ KK

p

p KKq

p

Kp

i

j

ii ii ij

i

ββα ρ

π

2/1

2 ; 3.12) 

where 

∑ ∑ ++= ∑

m

mim

k l

kik lil φεδρ fed

Demand for quota is derived for the unconstrained output supply equations using the 

virtual prices. Virtual prices relate unconstrained output supply and factor demand 

functions by substituting the virtual price expression into 12). 

2

11

2

11

1

2/1

1

11

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

−−− −=

∑≠

KKKq

pK

p j

jj

ρβα

β

λ 3.13) 

λ, the input compensated marginal quota rent rises the closer the quota comes to binding. 

The above expression is the inverse derived demand function for additional summer 

flounder quota (Squires and Kirkley, 1996). 

Simulating the quota market involves horizontally summing the individual firm level trip 

demand functions. The market equilibrium lease price for quota is found by setting 

market derived demand equal to the TAC. The expression for the equilibrium quota 

market is: 
26 

( ) ( ) ∑ ∑ ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− = ++

k ≠

k

kk

k

j

j

j

k k KK

p

p Q KK ρ λ βα β

2/1

1 11

11 1

2

1 1 3.14) 

where Q1 is the overall quota for summer flounder and k is the number of trips in the 

year. 

3.3 Results 

Model estimation was handled in SAS using Proc Model (SAS 2003). Each input scaled 

output supply function, summer flounder, baitfish, shellfish, bottomfish, and other, was 

estimated individually and tested for heteroscedasticity using White’s test (White 1980). 

Table 3.10 contains the results of those tests. In each case the null hypothesis of 

homoscedasticity is rejected in favor of a heteroscedastic error structure. 

Heteroscedasticity stemming from the square of the quasi fixed input was anticipated 

(Squires and Kirkley 1991, Carter et al 2008), and it was found with this specification. 

To remedy the heteroscedasticity, the following systems regression was weighted by the 

quasi fixed input. 

Table 3.10. Results of White’s Test for Heteroscedasticity for Individual Equations. 

Equation Statistic Degrees of 

Freedom 

Pr > 

ChiSq Variables 

Summer Flounder 8,399 492 <.0001 Cross of all variables 

Bait 2,686 492 <.0001 Cross of all variables 

Shellfish 9,374 492 <.0001 Cross of all variables 

Bottomfish 3,839 492 <.0001 Cross of all variables 

Other 2,619 492 <.0001 Cross of all variables 

The full system of input scaled output supply functions were estimated using FIML 

estimators (SAS 2003). Symmetry was maintained for the regression result reported 

here. Initially, the Atlantic cyclonic index by month was tried, but for the northern 

Atlantic, there was not enough variation in the index to provide additional explanatory 

power. 

For this regression, the functional form is assumed exact rather than an approximation 

(Squires and Kirkley 1996). As such, the errors are then assumed to arise from 

optimization rather than the approximation. Zero outputs in any species group in the 

regression create a limited dependent variable problem that introduces bias and nonnormality of the regression residuals. As a result, zero outputs were replaced with the 

value of 0.1. See Squires and Kirkley (1991) and Carter et al (2008) for a more complete 

discussion of the impact of this replacement and other potential solutions that weren’t 

possible due to computational feasibility or assumptions that would impact the analysis 

negatively. 

Parameter estimates and regression diagnostics are detailed in Appendix 1. The summer 

flounder equation (parameters a1-a42) had the highest R-squared at 0.7594, which was to 

be expected. Also as expected, trip costs, the quasi fixed input, was positive and 

significant and trip cost squared was negative, small, and significant. Additionally, the 

prices of the other four species groups were positive and significant. Landings during the 
27

late winter (January, February, and March) and fall (October and November) had positive 

effects in the regression and were significant with the exception of the parameter on 

November. The spring and summer months had negative and significant impacts on the 

regression, with the exception of September which was negative, but not significant. 

There are far too many ports modeled to discuss each individually. Many of the port 

variables were insignificant. 

The second best R-squared, 0.2427, came from the bottomfish output supply equation 

(parameters d1-d42). Unexpectedly, trip cost and trip cost squared are both negative and 

significant. All prices for other species were positive and significant. The months of 

January through April have positive and significant impacts on quantity supplied while 

the remainder of the year has a negative impact. 

The third highest R-square, 0.1591, came out of the shellfish model (parameters c1-2. As 

expected, trip cost is positive and trip cost squared is negative. Price of other fish is 

positive but insignificant. Summer flounder price and bait price are both positive and 

significant. The price of bottomfish however has a negative and significant effect on the 

output supply of shellfish. Seasonally, shellfish follows similar pattern as bottomfish. 

The fourth highest R-square, 0.1566, comes out of the baitfish output supply (parameters 

b1-b42). Both trip cost and trip cost squared are negative and significant. Prices of other 

species are all positive and significant except for other fish price which is positive but 

insignificant. The lowest R-square, 0.0842, comes out of the other fish output supply 

(parameters e1-e42). Trip cost was negative and significant while trip cost squared was 

negative and insignificant. All other species groups prices were positive, but only 

bottomfish and summer flounder prices were significant. 

The technology tests included nonjointness and symmetry and the results are displayed in 

Appendix 1. Overall non-jointness in inputs was rejected suggesting that all inputs are 

required to produce all outputs, and, by broader extension, that harvesting processes for 

each species are connected. Species specific non-jointness tests were also rejected for 

each species grouping. This suggests that the production of one group relative to the 

other groups is interrelated to the harvest and relative prices of the other species groups in 

this joint production function. Separability was also rejected indicating that neither 

inputs nor outputs can be represented by composite goods. That is, a specific output 

bundle is required to produce a specific input bundle. 

Detailed cost data of the type used here for the otter trawl fleet was not available for the 

other gears that harvest summer flounder. In 2007, there were 33 other gears that 

harvested summer flounder with a percentage of total landings ranging from well less 

than 0.1% to 4.8% of the total summer flounder commercial harvest. Additionally, the 

otter trawl fleet is probably the closest gear type to a directed fishery for summer 

flounder, whereas the other gear types are bycatch fisheries. 

In order to examine what the possible quota market would look like for the entire quota, 

the following simulation assumes that the marginal quota values that are generated for the 

otter trawl fleet are equivalent to the marginal quota values for quota across other gear 

types that harvest summer flounder. In 2007, 64% of the quota was harvested by the otter 
28 

trawl fleet. Also in 2007, summer flounder dockside prices were $1.49/pound less 

(36.3% lower) for the other gears than the prices obtained from otter trawls. Because of 

this price difference, the marginal quota values presented here represent an upper bound 

on the true estimate. For this not to hold, the cost structure across the other gear types 

would need to be significantly lower than the otter trawl cost structure. This is possible 

given that the otter trawl gear is probably one of the more costly gear types compared to 

the other gears. 

Two methods were tried to simulate the entire 17.1 million pound TAC. The first 

involved randomly sampling additional observations from the otter trawl data set until 

predicted harvests equaled the total TAC (Carter et al 2008). The other involved scaling 

the simulated values upwards to the total TAC holding prices constant. The two methods 

produced virtually equivalent marginal quota value schedules. 

Equation 3.14 was simulated between the total TAC of 17.1 million pounds (100% 

commercial allocation) and zero pounds. By running the simulation across a different 

range of values for λ, the input compensated quota rent, the annual supply function for 

each vessel can be traced and the horizontal sum of those individual supplies produces a 

marginal willingness to pay (WTP) for quota schedule across a range of allocations. The 

results of this simulation are displayed in Figure 3.3. Additionally, only well-behaved 

observations or those observations that did not violate monotonicity requirements were 

used in the simulation (Squires and Kirkley 1996, Carter et al 2008). At the current total 

commercial summer flounder harvest of 10.3 million pounds, summer flounder 

commercial fishermen are willing to pay $1.06 for an additional pound of summer 

flounder quota. At a zero percent commercial allocation, summer flounder fishermen 

would be willing to pay $2.45/pound to participate in the summer flounder fishery. 

3.4 Conclusions 

Commercial WTP for summer flounder quota is $1.06/pound. Figure 3.4 charts the total 

commercial benefit at different allocation levels. At the current allocation, the fishery is 

worth $10.9 million and maximum commercial benefit of $12.0 million occurs at a quota 

of approximately 13.5 million pounds. Estimation of value in this section does not 

include fixed costs or labor costs. Since the trip decision is a short run decision, this is 

typical for the literature. However, if these two cost categories were included in the 

modeling they could significantly alter the long-run profitability and demand for quota. 

Long-run decision making has not been included in this analysis. 

Looking closely at Figure 3.3, one notices that across high allocation values, the inverse 

derived demand for quota is actually upward sloping for across a narrow range of values 

implying upward sloping quota demand function. That is, it appears that there are two 

values for the dependent variable (marginal quota value) for a single value of the 

independent variable (pounds of quota). There are many possible explanations for this 

apparent violation of economic theory. The generalized Leontief functional form is a 

flexible functional form. Flexible functional form models do not forecast well outside the 

mean and have the potential to be unreliable for projections as far outside the mean 

predicted landings. 
29

Second, the otter trawl fleet has high fixed costs. This could possibly explain the upward 

sloping quota demand. High allocations of the TAC would drive summer flounder 

dockside prices downward. At low dockside prices and high fixed costs, operators may 

be willing to pay more for more quota over a certain range. Examining this issue further 

is beyond the scope of this analysis. As a result, caution is warranted when making 

recommendations based on the shape of this function too far outside of the current mean 

landings. 

Finally, the results of the technology tests have implications for potential allocation 

changes that may be examined. Because overall nonjointness in and individual species 

group tests were rejected, changing allocations for summer flounder may have spillover 

effects on other species. While it seems intuitive in a multispecies fishery such as the 

otter trawl fishery, this result quantifies that if summer flounder allocations go up or 

down it may increase exploitation of other species. 

Figure 3.3. Simulated Marginal Quota Value for Summer Flounder Quota Pounds 

(2007 dollars) 
30 

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

14.0015.5017.0015.5014.0012.5010.50

9.508.006.505.003.502.000.50

Millions of Pounds of Quota

Total Benefit in Millions of Dollars

Figure 3.4. Summer Flounder Commercial Total Net Benefits (2007 dollars) 

4.0 Consumer Valuation 

Determining an allocation that maximizes benefits to the nation is extremely complicated. 

Estimates of net benefits from the fishery must include producer benefits, recreational 

angler benefits, for-hire industry benefits, and summer flounder consumer benefits. In 

this brief report, we provide a broad overview of a framework to estimated consumer 

benefits for the commercial sector using compensating variation as the benefits metric. 

We also provide a framework for estimating changes in prices associated with changes in 

landings. Using the models developed, this report provides estimates of changes in 

prices, nominal and real revenues, and compensating variation corresponding to a 10 % 

reduction in commercial landings of summer flounder; and estimates of compensating 

variation per pound landed for the period 1991 through 2006. 

4.1 Methodology 

The body of literature describing approaches for estimating both market and non-market 

values for various goods, services, and states of the environment is rich (see, for example, 

Freeman, 1989 and Bockstael and McConnell, 2007). Our primary focus here, however, 
31

is estimating how changes in commercial landings affect commercial prices, ex-vessel 

revenues, and compensating variation for consumers. Further attention is focused, then, 

on estimating market values for summer flounder. 

4.1.1 The Synthetic Inverse Demand System 

There is an extensive literature of estimating commercial demand functions. This 

includes literature on functional form specification as well as whether or not fish demand 

models should be price or quantity dependent. There is no precise answer, but the 

available literature suggests that the demand for many agricultural and fishery 

commodities should be expressed as price dependent equations (Barten and Bettendorf, 

1989; Barten, 1993; Brown et al., 1995; and Park et al., 2004). 

One approach gaining favor by empirical researchers is the synthetic inverse demand 

system (SIDS). This is a flexible functional form specification of an inverse demand, 

which facilitates testing various restrictions to determine if other alternative 

specifications of demand can be used. These alternative specifications include the 

inverse Rotterdam demand model (IROT), the inverse almost ideal demand system 

(IAIDS), the inverse Central Bureau of Statistics (ICBS) demand model, and the inverse 

National Bureau of Research (INBR) demand model.4

 All these models maintain 

desirable properties of demand theory and facilitate estimation of changes in prices, 

revenues, and consumer benefits associated with changes in the demand (landings) of 

agricultural and fishery commodities. 

Within the SIDS framework, a system of demand equations can be estimated by 

seemingly unrelated regression or, if there are cross equation constraints, maximum 

likelihood estimation techniques. The basic specification used in the analysis contained 

in this paper follows Park et al. (2004): 

it it i ij

j

n

jt i t it t it

it

w v q Q w Q w it

q

Q

it

t

Δ Δ ln = + ln ln + − ΔΔΔ ln − ln ,

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟ + =

απ π θ θ ε ∑1 1 2 4.1) 

where ln ln . t jt

j

N

Q w it = q =

∑1

In this specification, qi is the per capita quantity demanded for the ith quantity; vi is a 

normalized price for the ith commodity (i.e., vi = pi/m, where pi is the price of the ith

commodity, and m is the per capita level of total expenditures for all commodities under 

consideration); αi, πi, and πij are coefficients to be estimated; Δ is a change operator; εit is 

the error term, which is assumed to be normally distributed with a mean of zero and 

constant variance; and θ1 and θ2 are estimable parameters. θ1 and θ2 are further assessed, 

via parametric restrictions, to determine if one of the four basic inverse demand models 

best describe the demand for seafood. If θ1 = θ2 = 0, the model reduces to the inverse 

Rotterdam model; if θ1 = θ2 = 1, the model becomes the inverse almost ideal demand 

system (IADS) model; if θ1 = 1 and θ2 = 0, the model becomes the ICBS model; and if θ1

= 0 and θ2 = 1, the SIDS model becomes the INBR model.5

 The inverse demand system 

of equations requires several constraints consistent with demand theory: (1) symmetry in 

 

4

 Park et al. (2004) provide a comprehensive discussion and illustration of the SIDS model. 

5

 See Park et al. (2004) for a detailed discussion of the SIDS and related inverse demand models. 
32 

which πij = πji, (2) adding up in which Σi πij = 0.0, (3) homogeneity in which Σj πij = 0.0, 

and (4) Σi πi = 0.0. 

Excluding halibut, there are approximately 11 species of flounder landed in the United 

States: (1) arrowtooth flounder, (2) pacific sanddab, (3) southern flounder, (4) starry 

flounder, (5) summer flounder, (6) windowpane, (7) winter flounder, (8) witch flounder, 

(9) yellowtail flounder, (10) plaice, and (11) righteye flounder. Based on some simple 

analyses of correlations and preliminary regressions, it was decided to aggregate 10 of the 

species into two groups: (1) other flounder 1, which consists of arrowtooth, southern, 

starry, winter, and plaice flounder, and (2) other flounder 2 containing windowpanes, 

witch flounder, and yellowtail flounder. We also include imports of all flatfish and 

flounder as another group to consider in the demand analysis. Therefore, we have four 

equations in our system of demand: (1) summer flounder, (2) other flounder 1, (3) other 

flounder 2, and (4) imports. 

No retail data exists for seafood at the species level. As a result these species groups 

were constructed using a review of the literature, simple correlation analysis from 

landings data, and through discussions with retailers. No models were run examining 

different aggregations among the flatfish species other than the aggregation detailed 

above. Also, data on all other protein expenditures, while important in explaining 

seafood protein expenditures were not included due to data and modeling limitations. It 

is very time consuming to set up each species group and most modeling programs are 

limited in the number of simultaneous equations that can be supported. It has been the 

author’s experience that adding additional sectors adds little to change the parameter 

estimates, after a certain point. Asche et al (2005), Parks et al (2004) and others find that 

focusing on a narrower range of species thought to be substitutes or complements a priori 

has little effect on overall estimates. 

NMFS suggested that anecdotal information indicated that tilapia may be used as a 

summer flounder substitute. No attempt was made to examine this for a number of due 

to data limitations. During the period included in this analysis, there has been a structural 

change in the tilapia industry and, early in the time series, tilapia is not well identified in 

the data. 

Although most researchers estimate the system of demand equations using iterative 

Zellner (1962), Greene (2003) demonstrated that maximum likelihood should be used to 

estimate the system of equations when cross equation constraints are imposed. We, 

therefore, apply the maximum likelihood routine available in LIMDEP to estimate the 

system of seemingly unrelated demand equations. 
33

The cross equation constraints used include: 

( )

( )

( )

ij i ij i j i ij i

i i i

ij i ij i j

j

ij

j

ij ji

w w w

w

w w w

adding up

adding up

ogeneity

symmetry

πθ δθ π

π θ

πθ δθ π

π π

− + ==

− =

− + ==

=

∑ ∑

∑

∑ ∑

2 2

1

2 2

0

1

0 hom 4.2) 

The SIDS model is quite convenient because it easily facilitates calculation of various 

compensated and uncompensated price flexibilities or elasticities and measures of 

welfare, which include compensated and equivalent variation and consumer surplus. 

Calculations of the elasticities are as follows:6

scale elasticity

compensated cross quantity elasticity

compensatedown quanitity elasticity

uncompensated quantity elasticity

i

i

i

ij

ij

i

j

ii

i

i

ij j i

f w

f w

w

w

w

f w f

== −

− = = +

− = −

= +

π θ

π θ

π θ

1

2

2

,

,

,

.

*

*

 4.3) 

In the analysis contained in this report, we consider only compensating variation. 

Typically, there is little difference between compensating variation, equivalent variation, 

and consumer surplus. Moreover, Freeman (1979) suggests that the Marshallian 

consumer surplus measure is without economic foundation, and thus, recommends using 

compensating variation as the preferred measure of welfare or benefits. Compensating 

variation is simply the level of compensating payment or offsetting change in income, 

which is necessary to make an individual indifferent between an original situation and 

new situation. It may also be interpreted as the maximum amount an individual would be 

willing to pay for the opportunity to consume the same quantity of goods at a new price, 

as consumed under the original price. 

 

Park et al. (2004) provide three convenient formulas for calculating all three welfare 

measures. While we present all three formulas, we stress that we estimate only 

compensating variation. The three are as follows: 

 

6

 The elasticities and respective calculations are further derived in Park et al. (2004). The scale flexibility 

or elasticity is often equated to the income elasticity in demand. As shown by Park and Thurman (1999), 

however, they are not equivalent. Scale flexibility is defined to be the proportional change in a normalized 

price, vi in our model, resulting from a scalar expansion of all commodities in the consumption bundle (i.e., 

all qi in our analysis). The scale flexibility is restricted to a radial expansion from the origin to the 

indifference curve or utility function. 
34 

( ) ( )

( ) ( )

( ) ( )

equivalent iation q x compensated flexibility q

compensating iation q x compensated flexibility q

consumer surplus q x uncompensated flexibility q

v

v

q

v

v

q

v

v

q

var .

var .

.

=− −

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

=− −

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

=− −

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

Δ Δ

Δ Δ

Δ Δ

1

0

0

0

0

0

0

0

0

05

05

05

 4.4) 

 

For welfare gains, the estimates of compensating and equivalent variation are negative, 

and for welfare losses, the estimates are positive. 

A remaining concern is estimating changes in demand price and corresponding revenues. 

Park et al. (2004) provide a convenient equation for estimating the demand price 

corresponding to a change in demand: 

v

1

 = v

0

 + Δv = v

0

[1-(flexibility)x(Δq/q)], 4.5) 

where p is the normalized price (price divided by total expenditures); v1

 and v0 represent 

normalized prices at time 1 and time 0; flexibility is the compensated quantity elasticity; 

and Δq = q1

 – q0. In this particular situation, we define q to equal the reported quantity 

landed divided by the U.S. population. 

4.1.2 Statistical Estimates of the SIDS Model 

The previously discussed SIDS model was estimated by the method of maximum 

likelihood. As shown by Greene (2002), maximum likelihood is preferred over iterative 

seemingly unrelated regression when cross equation restrictions are imposed, and 

estimation requires dropping one equation from the estimation to avoid singularity. 

There are four equations: (1) an inverse demand for summer flounder, (2) the inverse 

demand for other flounder, group 1, (3) the inverse demand for other flounder, group 2, 

and (4) the inverse demand for imports. One equation must be omitted to avoid 

singularity. For the purpose of estimation, we omit imports from the system of equations. 

Parameter estimates for imports are directly obtained via restrictions imposed on the 

system of equations (e.g., homogeneity and adding up constraints). 

Data on annual landings and ex-vessel values were obtained from NOAA Fisheries, 

electronic databases. Landings data came from the commercial landings data files, and 

data on imports were derived from NOAA’s international fisheries statistics. These data 

were used to construct prices and expenditures, with the latter equaling the sum of the 

price times the quantity of each of the species under consideration in the grouping. All 

landings and expenditure data were converted to per capita statistics by dividing by the 

resident civilian population. Data covered the period 1989 through 2006. Data for 1989 

and 1990, however, were omitted because it was necessary to take first differences of all 

variables. 
35

The system of equations contained 26 parameters. The statistical results were mostly 

significant, and all equations had relatively good fit (Table 4.1). Adjusted R-squared 

values ranged from a low of 0.63 for other flounder (group 1) to 0.82 for other flounder 

(group 2). The adjusted R-squared for summer flounder equaled 0.69. Based on the 

Durbin-Watson statistics, autocorrelation did not appear to pose a problem. Spurious 

correlation was also not a problem because all equations were specified as first 

differences. We accept the original restrictions on the SIDS model regarding symmetry, 

homogeneity, and adding up. The Wald chi-squared statistic testing all restrictions is 

9.65 with 10 degrees of freedom. 

Table 4.1. Parameter Estimates of the SIDS Model for Floundera

Group Constant Summer 

Flounder 

Other 

Flounder

GRP 1 

Other 

Flounder

GRP 2 

Imports

A Divisia 

Quantity 

Index-Q 

θ1 θ2

Summer 

Flounder 0.0003 -0.033* 0.002 -0.005* 0.037* 0.057* 1.41* 0.21* 

Other 

Flounder 1 -0.0017 0.002 -0.104* 0.014* 0.088* -0.054* 1.41* 0.21* 

Other 

Flounder 2 -0.0015 -0.005* 0.014* -0.050* 0.041* 0.034* 1.41* 0.21* 

Imported 

Flounder 0.0029 0.037* 0.088* 0.041* -0.166* -0.037 1.41* 0.21* a

All variables, except constant are expressed in terms of change in natural log values. All landings data 

(each species or composite output) are expressed in terms of per capita consumption. 

* indicates significant at 5 % level of significance. 

The best model estimated was the SIDS model with unrestricted θ values, and these 

results are typical of many SIDS modes where the unrestricted values perform the best 

(Parks et al 2004). The IROT model restrictions (θ1 = θ2 = 0) yields a Wald of 1651.79; 

the ICBS model restrictions (θ1 = 1 and θ2 = 0) yields a Wald of 1380.54; the IAIDS 

model restrictions (θ1 = θ2 = 1) yield a Wald of 1346.23; and the INBR model restrictions 

(θ1 = 0 and θ2 = 1) yield a Wald of 1483.07. This suggests that none of the restrictions 

are appropriate. While the mixing parameters, θ1 and θ2, are close to the ICBS values of 

1 and 0, they are not statistically the same. Furthermore, likelihood ratio test results for 

these same restrictions are shown in Table 4.2 (Brown et al 1995). These tests also 

indicate that the unrestricted model provides the best fit. 

Table 4.2. Log Likelihood Ratio Test Results for Inverse Demand Structure 

Log Likelihood Ratio Model Chi-squared DF Critical Value 

179.77 SIDS 5% 0.50% 

172.32 IROT 14.90 2 5.99 7.88 

172.93 ICBS 13.68 2 5.99 7.88 

172.94 IAIDS 13.66 2 5.99 7.88 

172.40 INBR 14.74 2 5.99 7.88 
36 

4.2 Prices, Revenues, and Compensating Variation 

In this assessment, we initially present estimates of the scale elasticities and all 

compensated own and cross price elasticities (Table 4.3). We next consider a 10 % 

change in landings of summer flounder, and assess changes in ex-vessel prices, nominal 

and real revenues (revenue adjusted for inflation using the producer price index for 

finfish), and compensating variation. We also present estimates of the compensating 

variation on a per pound basis, and the compensating variation corresponding to a one 

unit increase in the demand for summer flounder (i.e., the marginal value of a one unit 

change in demand). 

Table 4.3. Mean Compensated Own and Cross Price and Scale Elasticities 

Group Summer 

Flounder 

Other 

Flounder-1

Other 

Flounder-2 Imports Scale Elasticities

Summer Flounder -0.225 0.004 -0.084 0.305 -0.71

Other Flounder-1 0.003 -0.770 0.114 0.653 -1.91

OtherFlounder-2 -0.093 0.170 -0.487 0.409 -0.94

Imports 0.033 0.097 0.041 -0.171 -1.46

Estimates of the scale elasticities were similar to those obtained in numerous other 

studies in which the values are near 1.0, which simply depict the percentage change in 

price as the quantity of each good in the system is changed by 1.0 % (Table 4.3). The 

scale elasticities for other flounder, group 1 and imports, however, were relatively high at 

1.91 and 1.46 respectively. For example, if the quantity of all flounder species increased 

by 1%, the price of summer flounder would fall 0.71%, other flounder-1 would fall by 

1.91%, other flounder-2 would fall by 0.94%, and import prices would fall by 1.46%. 

The compensated own and quantity elasticities were similar to those obtained in other 

studies on fisheries; the elasticities were all less than 1.0 % (Table 4.3). Note that 

positive cross-price elasticity indicates complementarity, while a negative cross price 

elasticity indicates substitutability. For summer flounder that means that other flounder-1 

and imports are complements while other flounder-2 is a substitute. That is, as price for 

summer flounder decreases, the prices of other flounder1 and imports also fall and the 

price for other flounder-2 rises. Also observe that imports are complements to all three 

other species or aggregate outputs. 

We next examine how prices, revenues, and compensating variation would change for a 

hypothetical 10 % reduction in landings of summer flounder. As is suggested by the 

quantity elasticities, prices are not very sensitive to changes in demand. In 2006, a 10 % 

reduction in demand induced only a 1.57 % increase in ex-vessel price, but ex-vessel 

revenues declined by 8.59 % (Table 4.4). Compensating variation or consumer benefits 

equaled $2.9 million or roughly $0.23 per pound in 2006. On average, compensating 

variation equaled $3.2 million and $0.27 per pound per year between 1991 and 2006. 
37

Table 4.4. Changes in Ex-vessel Prices, Revenues, and Compensating Variation for a 

10% Reduction in Demand for Summer Floundera

Year Observed 

Landings 

10 % 

Reduction 

Observed 

Price 

Price for 

10 % 

Reduction

Reported 

Revenue 

Revenue 

For 10 % 

Reduction

Change in 

Revenue Total CV CV Per Pound 

91 13,868,625 12,481,763 2.18 2.24 30,289,341 27,989,269 -2,300,072 2,842,752 0.23

92 16,635,703 14,972,133 2.11 2.14 35,022,834 32,068,152 -2,954,682 3,634,058 0.24

93 13,000,319 11,700,287 2.25 2.31 29,307,502 27,073,089 -2,234,413 2,931,849 0.25

94 14,572,895 13,115,606 2.44 2.48 35,589,417 32,523,143 -3,066,274 3,821,593 0.29

95 15,410,322 13,869,290 2.48 2.51 38,188,269 34,813,602 -3,374,666 3,951,534 0.28

96 12,656,451 11,390,806 2.33 2.37 29,438,656 26,988,626 -2,450,031 3,465,009 0.30

97 8,591,554 7,732,399 2.49 2.57 21,382,031 19,845,482 -1,536,549 2,441,433 0.32

98 10,984,327 9,885,894 2.29 2.34 25,103,058 23,159,392 -1,943,666 2,736,853 0.28

99 10,490,449 9,441,404 2.25 2.31 23,552,180 21,777,707 -1,774,473 2,523,956 0.27

00 11,019,193 9,917,274 2.14 2.21 23,569,837 21,870,650 -1,699,187 2,282,761 0.23

01 10,716,200 9,644,580 2.01 2.07 21,539,782 19,979,152 -1,560,630 2,413,921 0.25

02 14,227,332 12,804,599 1.84 1.88 26,129,954 24,096,394 -2,033,560 2,765,085 0.22

03 14,328,342 12,895,508 1.96 2.01 28,151,780 25,962,574 -2,189,206 2,729,797 0.21

04 17,883,808 16,095,427 1.85 1.88 33,029,025 30,264,644 -2,764,381 3,080,958 0.19

05 17,261,958 15,535,762 1.88 1.91 32,445,617 29,631,367 -2,814,250 3,182,719 0.20

06 13,960,339 12,564,305 2.05 2.08 28,647,306 26,186,987 -2,460,319 2,917,766 0.23

Mean Value Per Year 3,232,628 0.27 a

All dollar values are in 2006 constant dollars. 

 

A major concern for managers is the allocation of allowable harvests among competing 

user groups, which in this case consists of commercial fishermen and recreational 

anglers. A typical economic allocation rule is to allocate the resource until the marginal 

benefit of one user group equals the marginal benefit of the other user group. In this 

case, we consider the compensating variation for a one unit increase in the landings of 

summer flounder. 

Not surprising, a one unit increase in summer flounder landings does not generate much 

additional revenues or consumer benefits. Table 4.5 contains the model results for a one 

unit increase in landings. Revenues increase by $1.73 in 2006, and consumer surplus, at 

the margin, equaled only $0.15 per pound; the corresponding ex-vessel price was $2.05 

per pound. On average, revenue and compensating variation, respectively, increases by 

approximately $1.67 and $0.16 per year for a one pound increase in landings between 

1991 and 2006. 
38 

Table 4.5. Prices, Revenues, and Compensating Variation for a One Unit Increase in 

Demand for Summer Floundera

Year Reported 

Landings 

One Unit 

Increase 

in Landings 

Reported

Price 

Price for 

One 

Unit 

Increase 

Reported 

Revenue 

Revenue for 

One Unit 

Increase in 

Landings 

Change 

in 

Revenue

CV 

Per 

Pound 

91 13,868,625 13,868,626 2.18 2.18 30,289,341 30,289,343 1.60 -0.01

92 16,635,703 16,635,704 2.11 2.11 35,022,834 35,022,836 1.74 -0.13

93 13,000,319 13,000,320 2.25 2.25 29,307,502 29,307,504 1.66 -0.17

94 14,572,895 14,572,896 2.44 2.44 35,589,417 35,589,419 2.07 -0.18

95 15,410,322 15,410,323 2.48 2.48 38,188,269 38,188,271 2.16 -0.16

96 12,656,451 12,656,452 2.33 2.33 29,438,656 29,438,658 1.89 -0.21

97 8,591,554 8,591,555 2.49 2.49 21,382,031 21,382,033 1.71 -0.32

98 10,984,327 10,984,328 2.29 2.29 25,103,058 25,103,060 1.71 -0.22

99 10,490,449 10,490,450 2.25 2.25 23,552,180 23,552,182 1.63 -0.22

00 11,019,193 11,019,194 2.14 2.14 23,569,837 23,569,838 1.48 -0.18

01 10,716,200 10,716,201 2.01 2.01 21,539,782 21,539,783 1.39 -0.20

02 14,227,332 14,227,333 1.84 1.84 26,129,954 26,129,955 1.38 -0.13

03 14,328,342 14,328,343 1.96 1.96 28,151,780 28,151,782 1.48 -0.13

04 17,883,808 17,883,809 1.85 1.85 33,029,025 33,029,027 1.51 -0.09

05 17,261,958 17,261,959 1.88 1.88 32,445,617 32,445,619 1.60 -0.11

06 13,960,339 13,960,340 2.05 2.05 28,647,306 28,647,308 1.73 -0.15

a

All dollar values are in terms of 2006 constant dollar values. Note that compensating variation for a one 

unit increase is negative, which is a result of the calculation. For ease of interpretation, the compensating 

variation may be converted to positive values. 

5.0 Recreational Valuation 

This section details the calculation of unweighted and weighted recreational marginal 

value estimates using Marine Recreational Fisheries Statistical Survey (MRFSS) data. 

This chapter begins with a description of the unweighted methodology used to generate 

recreational value estimates and a discussion of the results of the modeling effort. Next, 

the weighted methodology and results are discussed. This report only contains marginal 

value estimates for the consumer side of recreational fishing. At this time there is 

insufficient data on for-hire industry’s costs and earnings to calculate the marginal values 

of summer flounder harvest for the for-hire fleet. 

5.1 Unweighted Methodology 

Random utility models (RUM) rely on observed data on recreational site choices. The 

observed data for this study comes from the 2006 MRFSS intercept survey. In this 

section we will specify the RUM model and present the data manipulation process 

necessary to run a RUM for summer flounder using the Marine Recreational Fishery 

Statistics Survey (MRFSS) angler data. 

This report relies on data from the National Marine Fisheries Service’s MRFSS. The 

National Marine Fisheries Service (NMFS) is mandated by law to analyze the benefits, 

costs, and economic impacts of the recreational fisheries policies it promulgates. Since 

1994, NMFS has used the Marine Recreational Fishing Statistics Survey (MRFSS) to 
39

gather the travel cost data necessary to estimate the value of access and the value of 

changes in catch rates. 

The analysis presented here will utilize data collected by the MRFSS. The MRFSS 

consists of two independent and complementary surveys; a field intercept survey and a 

random digit dial (RDD) survey of coastal households. The intercept survey is a creel 

survey used to estimate mean catch-per-trip by species across several strata including, 

fishing wave (2-month period), fishing mode (shore, private or rental boat, or for-hire 

fishing vessel), and state. Data elements collected during the base part of the intercept 

survey include state, county, and zip code of residence, hours fished, primary area fished, 

target species, gear used, and days fished in the last two and 12 months. The creel 

portion of the survey collects length and weight of all fish species retained by the angler 

and the species and disposition of all catch not retained by the angler. 

Because the MRFSS constitutes the best nationwide sample frame for marine recreational 

angling and offers considerable savings over implementing a new program, economic 

data collection is added-on to the MRFSS effort. During March through December of 

2006, an intercept add-on survey was conducted to obtain data on angler trip 

expenditures. Upon completion of the base MRFSS survey in 2006, anglers were asked 

to complete a short add-on questionnaire. The intercept add-on survey was designed to 

collect the minimum data necessary to estimate RUM’s of anglers’ site choice decisions. 

The intercept survey is designed to be a random sample of trips. As such the probability 

of being sampled is linked to the number of times an angler fishes with more avid anglers 

being intercepted more frequently. This is a type of choice-based sampling, also known 

as an endogenously stratified sample, and it impacts the estimation of metrics 

denominated by individual anglers. Thompson (1991) identified the impact this type of 

sampling has on recreational value estimates. Also, during a 2006 Center for 

Independent Experts (CIE) review of the NMFS economic data collection program, 

choice based sampling’s impact on valuation estimates was identified as an area needing 

further examination (CIE 2006). Recent strides have been made to use weights from the 

RDD survey to eliminate this bias including work by this author (Hindsley et al 2008). 

Developing and using these weights to eliminate the choice based sampling bias require 

the estimation of the unweighted model first and the rest of this report will focus on the 

estimation of the unweighted model. The weighted model will be developed in a 

subsequent section. 

5.1.1 Nested Logit 

RUM’s use all of the substitute recreational sites facing an angler to value attributes of 

the site chosen by an angler. In this case, we are interested in valuing summer flounder 

harvest rates. NMFS has sponsored a good deal of research into RUM’s of recreational 

site choice to value site closures and angling quality (Hicks et. al, 1999, McConnell et al, 

1994, Haab et al, 2000, Gentner 2007, to name a few). The majority of this work has 

involved specifying nested logit model of recreational site choice using expected catch 

rates as the measure of angling quality. This exercise follows previous NMFS RUM 

specifications as closely as possible given the data limitations described below. The 

specification of the nested logit model for recreational choices has been adapted from 

Haab and McConnell (2003). 
40 

Angler utility is specified as: 

jkjkjk vu += ε 5.1) 

where vjk is an angler’s indirect utility and εjk is a random error term for site j in mode k. 

For this exercise, it is assumed that the decision to fish for summer flounder is exogenous 

to the model. Subsequent to the choice to participate in summer flounder fishing, the 

angler is assumed to make a fishing mode choice and then a site choice conditioned on 

the mode choice. The upper level nesting structure includes the choice of fishing mode 

across shore fishing, for-hire fishing, and fishing from the private/rental boat mode. In 

this case, the global site list includes the same 63 aggregated sites as used in Hicks et al 

(1999), with some slight modifications discussed below. 

An angler chooses a fishing site from the set of all alternative site and fishing mode 

combinations if the utility of visiting that site in that mode is greater than the utility of 

visiting any other site in any other mode in the global choice set. 

',' ''kjjk ∀≥ kjuu 5.2) 

Furthermore, summer flounder angler indirect utility is specified by: 

( ) β β γ kjkjk jkjky k − ,, = − + + sqcsqcyv 5.3) 

where y is income, cjk is the cost of traveling to the site, qjk is a vector of quality attributes 

that vary by site and mode choice, and sk is a set of attributes that vary only by mode 

choice. Since income is an additive constant across all sites combinations in the choice 

set, it falls out of the nested logit probability. Following Hicks et al (1999), the vector q 

contains travel cost (travelc), the log of the number of MRFSS intercept sites aggregated 

into the sites used in this model (lnm), and the expected keep rate (ekarate). The keep 

rate was used to model mortality and not total catch. While the keep rate includes 

observed catch it also includes self reported mortality not seen by a MRFSS interviewer. 

It does not include any mortality of released fish unless the fish was dead before release. 

It is felt that this measure most closely approximates commercial mortality. The vector, 

s, contains two variables pr_boater and north_shore, which will be described below. 

The nested logit probability is: 

∑ ∑

∑

= =

−

=

⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

= K

m

J

l m

lmm

J

l k

lkk

k

jkk

m m

k k

v

v v

kj

1 1

1

1

exp

exp exp

),Pr( θ

θ

θ

α

θ

α

θ

α

 5.4) 

where K is the total number of upper level nests, Jk is number of lower level sites for 

upper level k, m = (1,....,J), l = (1,....,K), αk is the location parameter, and θk is the 
41

inclusive value parameter. This study is concerned with estimating the marginal net 

benefits of summer flounder harvest. The appropriate benefit metric in this case is 

compensating variation (CV) (Haab and McConnell, 2003). Within the nested logit 

model, indirect utility is specified as: 

 

( ) ( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − = ∑ ∑ = =

m K m

m

J

l m

mlmlm

m

sqcyv aysqcV

θ

1 1 θ

,, , ln,, exp 5.5) 

CV is calculated by differencing the indirect utility before an allocation change to the 

indirect utility after an allocation change and is represented by: 

( ) = −WTPysqcVysqcV )*,*,*,(,,, 5.6) 

where the star (*) denotes the changed indirect utility attributes. If V(*) >V(original) 

then CV is greater than zero. For quality changes that are the same for all sites, such as 

an allocation change, the CV calculation collapses to: 

( )

travelc

ekarate ekarate

WTP

β

Δ β = 5.7) 

or the change in the expected keep rate times the parameter estimate for expected keep 

rate divided by the parameter estimate for travel cost. Please see Haab and McConnell 

(1999) for further details of this specification and the mechanics of the CV calculation. 

5.1.2 Data Manipulation 

Data for this effort comes from the MRFSS intercept survey. In 2006, NMFS conducted 

an expenditure survey that also collected the bare minimum number of additional 

variables for estimation of the site choice model. During 2006, 3,262 anglers caught 

summer flounder, finished the intercept add-on containing the necessary variables, and 

gave the interviewer a home zip code necessary for travel cost calculation. By wave, 

1.7% of all anglers were intercepted in wave 2, 35.9% were intercepted in wave 3, 52.4% 

were intercepted in wave 4, 10% were intercepted in wave 5, and only 0.2% were 

intercepted in wave 6. No MRFSS sampling is conducted in wave 1. By fishing mode, 

5.6% of all intercepts were in the shore mode, 41.2% were in the for-hire mode, and 

53.2% were intercepted in the private rental mode. 

Developing a data set for the nested logit model involves a series of steps. Initially, all 

sites were aggregated using the Hicks et al (1999) methodology. It was found during the 

estimation of keep rates that summer flounder has never been caught or targeted from 

Maine sites during the previous ten years, so all Maine sites were dropped leaving 55 

sites in the model. 

This model diverges from the model specified in both Hicks et al (1999) and Haab et al 

(2000) because less data was collected during the intercept add-on survey. A number of 

variables that have been collected in previous intercept add-on surveys, including boat 

ownership, income, and time off work without pay, were not collected during the 
42 

intercept add-on in 2006 to make room for trip expenditure questions. As a result, travel 

cost does not contain calculations for time taken off work without pay as in Hicks et al 

(1999) and Haab et al (2000). Instead, two measures of travel cost are used here: travel 

cost only and travel cost plus the opportunity cost of time calculated using census income 

data. Travel cost is simply the round trip travel distance multiplied by the current federal 

government travel reimbursement rate of $0.585/mile. The opportunity cost of time was 

calculated by taking the travel time (calculated miles/40 mph average travel speed) and 

multiplying it by one-third the wage rate. Wage rates were calculated by taking median 

household income by zip code and dividing it by 2,000 work hours per year (U.S. Census 

Bureau, 2002). 

CV estimates presented in this report that are based on travel cost alone represent a lower 

bound when compared to methodologies previously used by NMFS. On the other hand, 

CV estimates using U.S. Census income estimates to develop the opportunity cost of time 

likely represent an upper bound when compared to previous NMFS studies. 

While boat ownership has shown to be an important explanatory variable when 

describing mode choice, that question was not asked on the intercept survey. Instead, a 

proxy for boat ownership was defined as taking the value of one if an angler purchased 

boat fuel during their intercepted trip and a value of zero otherwise. This variable was 

crossed with a dummy set to the value of one if an angler was intercepted in the private 

rental boat mode. This variable, pr_boater was used to explain mode choices in the upper 

level nest. The other variable describing the upper level nest mode choice, north_shore, 

took the value of one if an angler was intercepted in the shore mode in any state north of 

New York. 

Following Hicks et al (1999) a keep rate matrix for all sites by mode was developed by 

taking the five year average keep at each site by mode. As described by Hicks et al 

(1999), these matrices contain many zero values that may indicate the site is not used as a 

summer flounder site or that may indicate that summer flounder has never been 

encountered by MRFSS interviewers at the site. Zeros were replaced using the nearest 

neighboring site in the same mode, if replacement was deemed appropriate based on 

examination of the harvest data and the site’s location. Table 5.2 contains the descriptive 

statistics for all variables used in the modeling. 
43

Table 5.2. Descriptive Statistics for all Variables 

Variable 

Name Description Mean Standard Error 

Lower 

Confidence 

Limit 

Upper 

Confidence 

Limit 

Hrsf Hours Fished 4.032 0.026 3.980 4.083 

Pr Dummy for Private/Rental Mode 0.532 0.009 0.515 0.549 

Charter Dummy for Charter Mode 0.412 0.009 0.395 0.429 

Shore Dummy for Shore Mode 0.056 0.004 0.048 0.064 

ffdays12 12 Month Avidity – number of days 25.331 0.601 24.154 26.509 

Travel Calculated Travel Cost $51.88 $1.04 $49.84 $53.91 

travel_opp 

Travel Cost Plus Opportunity Cost of 

Travel Time $75.420 1.460 $72.44 $78.28 

Boater Proxy for Boat Ownership 0.286 0.008 0.271 0.302 

North Equals 1 If Site is North of NY 0.413 0.001 0.411 0.414 

Lnm Log of Number of Aggregated Sites 2.924 0.001 2.921 2.926 

Karate Harvest per Trip – numbers of fish 0.356 0.001 0.355 0.357 

Ekarate 

Expected Harvest per Trip – numbers of 

fish 0.448 0.002 0.444 0.452 

pr_boater 

Private/Rental Mode Crossed with 

Boater 0.095 0.000 0.094 0.096 

north_shore North Crossed with Shore 0.114 0.000 0.114 0.115 

wave3 Intercepted in Wave 3 0.357 0.008 0.340 0.373 

wave4 Intercepted in Wave 4 0.524 0.009 0.507 0.541 

wave5 Intercepted in Wave 5 0.100 0.005 0.090 0.110 

5.1.3 Expected Keep Rates 

To conform to current theories on the calculation of welfare effects stemming from 

quality changes, expected keep rates, rather than actual keep rates, were used as the 

quality variable in the nested logit model. Typically, a poisson regression is used to 

estimate expected keep rates. However, if over-dispersion is found in the data the zero 

alter poission (ZAP) or the negative binomial models are more appropriate. Initial runs 

using a poisson indicated over-dispersion in the data so both ZAP models and negative 

binomial models were estimated. The negative binomial model performed far better than 

the ZAP and was used here for expected keep rates. The specification of the negative 

binomial is: 

( )

i x

i

i

i i

i

i

x

x

x

⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎝

⎛

⎟ + ⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎝

⎛

⎟ +

⎠

⎞ ⎜

⎝

⎛ Γ+Γ

⎟

⎠

⎞ ⎜

⎝

⎛ +Γ

=

λ

α

λ

λ

α

α

α

α

α

11

1

1 1

1

)Pr(

1

 5.8) 

Whereλi = exp( ) ziβ , xi equals harvest, in numbers of fish, of individual i on the 

intercepted trip, and zi contains variables describing the site and the individual including 

a constant term, karate, ffdays12, hrsf, wave3, wave4, and wave5. In previous studies 

(Hicks et al 1999, and Haab et al 2000), years of fishing experience was used to describe 

angler experience. This variable was not collected in the 2006 add-on, so 12 month 

fishing avidity was used as a proxy for fishing experience. 
44 

Table 5.3 contains the parameter estimates from the negative binomial expected keep 

model. All variables were significant at the 90% level except hours fished. All 

parameter estimates are significantly different from zero with a chi-squared test statistic 

of 619.1. The value of alpha, the over-dispersion parameter is 2.05 and significant 

indicating that over-dispersion was indeed a problem in this data set. All parameters had 

a positive and significant impact on the expected keep rate except for hours fished, which 

had a small, negative, and insignificant impact on expected keep. As expected, wave 4 

keep had the strongest influence of the temporal dummies and the private/rental mode 

had the largest impact of the mode dummies, but just barely. This result shows the keep 

rates are very similar between the charter and private/rental modes. The parameters from 

this model were used construct the expected keep rates for all potential choices in the 

model. 

Table 5.3. Negative Binomial Expected Keep Rate Model Results 

Variable Parameter 

Estimate 

Standard 

Error T-ratio P-value 

constant -4.5935 0.6226 -7.3774 0.0000 

Karate 1.4892 0.1434 10.3869 0.0000 

ffdays12 0.0061 0.0012 4.9769 0.0000 

Hrsf -0.0011 0.0010 -1.0406 0.2981 

Pr 1.5823 0.3850 4.1095 0.0000 

Charter 1.5819 0.3918 4.0376 0.0001 

wave3 0.8419 0.5118 1.6450 0.1000 

wave4 1.3314 0.5093 2.6140 0.0089 

wave5 0.9249 0.5258 1.7591 0.0786 

Alpha 2.0460 0.1658 12.3386 0.0000 

Log Likelihood -2,436.9190 

5.1.4 Unweighted Model Results 

The nested logit model was estimated in SAS using proc MDC (SAS 2003). Proc MDC 

utilizes full information maximum likelihood estimation techniques. Table 5.4 contains 

the parameter estimates and model fit information. Overall model fit was good with a 

McFadden’s R of 0.44 and a Cragg-Uhler value of 0.99. Nested logit models collapse to 

the conditional logit model if all inclusive value parameters are equal to one. A test of 

this restriction rejects the hypothesis that the conditional logit is more appropriate which 

also indicates that a conditional logit model using this data would violate independence 

of irrelevant alternatives property of the conditional logit model. 

Additionally, the inclusive value parameter for the shore mode nest was 1.2 from the 

initial estimation of the model. Inclusive value parameters greater than one indicate 

potential problems with utility maximization (Haab and McConnell, 2003), therfore this 

parameter was restricted to 0.9 for the final estimation. A likelihood ratio test for this 

restriction fails to reject the restriction (Table 5.4). As expected, travel cost is negative 

and significant suggesting that closer sites are preferred to more distant sites. The 

aggregation parameter is positive and significant suggesting that aggregated sites that 

contain more individual MRFSS sites are preferred to aggregated sites containing fewer 

MRFSS intercept sites. Also as expected, the parameter on expected keep is positive and 

significant suggesting that sites with higher expected keep rates are preferred to sites with 

less expected keep. 
45

Table 5.4. Parameter Estimates and Model Fit 

Opportunity Cost of Time Not 

Included 

Opportunity Cost of Time 

Included Parameter 

Estimate Standard 

Error 

PValue Estimate Standard 

Error 

PValue 

Lower Level Nest 

travelc -0.0333 0.0006 <.0001 -0.0229 0.0004 <.0001 

lnm 0.5305 0.0233 <.0001 0.5317 0.0233 <.0001 

ekarate 0.2216 0.0347 <.0001 0.2211 0.0348 <.0001 

Upper Level Nest 

north_shore -3.0300 0.3645 <.0001 -3.1070 0.3618 <.0001 

pr_boater 5.3111 0.3576 <.0001 5.3189 0.3577 <.0001 

Inclusive Value Parameters 

Shore Mode 0.9000 * 0.9000 * 

Charter Mode 0.4202 0.1446 0.3923 0.1424 

Private/Rental Mode 0.2335 0.1443 0.2037 0.1421 

UnModel Fit 

Log Likelihood -9569.50 -9304.29 

McFadden's R 0.4435 0.4414 

Cragg-Uhler 0.9892 0.9892 

IIA Test 132.8458 <.0001 

*Restricted parameter. Likelihood ratio statistic = 0.3943 p-value = 0.532. Fail to reject restriction 

Table 5.5 contains the CV estimates for one summer flounder and one pound of summer 

flounder as calculated using the parameters in Table 5.4. Confidence intervals were 

estimated using the method of Krinsky and Robb (1986). The marginal value of a 

summer flounder pound was calculated by dividing the CV for one fish by the average 

weight per fish of 2.77 pounds from the MRFSS web queries (NMFS 2008). Using the 

Northeast Fisheries Science Center length/weight/age conversion web site, this translates 

into a 17.5” summer flounder (NMFS 2008a). When opportunity cost of time 

calculations are included, CV estimates are 46% higher. Aggregating the per fish CV 

value across the current catch of summer flounder in 2006 (11.7 million pounds) the total 

value of the recreational summer flounder fishery was between $28.7 and $42.0 million 

in 2007 dollars. 

Estimating a schedule of recreational marginal CV is not possible for two reasons. First, 

the standard RUM model does not have a flexible functional form and does not allow for 

diminishing marginal returns from increasing catch rates. Currently, there are not 

functional forms that allow the testing of actual demand curvature properties necessary to 

get a decreasing demand as a function of catch. Estimating a RUM that included 

curvature terms was beyond the scope of this project. Second, the actual catch rate 

increase that might manifest from an increase in recreational quota is dependent on the 

amount of additional effort attracted to the fishery as a result of improved catch quality. 

Even with a downward sloping catch demand function, the WTP function could be 

horizontal or upward sloping over the relevant range depending on the effort response. If 

effort stayed exactly the same, the WTP function would maintain the typical downward 

slope. If effort increased to the point where no actual catch rate increase was realized, the 

WTP function would be horizontal at the current point estimate. If effort increased 

enough such that catch rates actually declined, the WTP function would be upward 
46 

sloping. The only way to properly estimate this relationship is using a full bioeconomic 

model of the fishery, which was beyond the scope of this analysis. Because the intercept 

data is collected after an angler has decided to take a trip, changes in effort cannot be 

modeled. Using the standard RUM, it is therefore impossible to estimate a full 

bioeconomic model of this relationship. As a result, it is impossible to trace out a 

recreational quota demand function as done for the commercial sector above. 

Table 5.5. Compensating Variation Estimates for the Current Keep Levels 

(Unweighted 2007 dollars) 

Model Compensating Variation Mean Standard 

Error 

95% Lower 

Bound 

95% Upper 

Bound 

One Summer Flounder $9.65 0.0477 $9.53 $9.72 Opportunity Cost 

of Time Included One Pound of Summer 

Flounder $3.48 0.0172 $3.44 $3.51 

Opportunity Cost One Summer Flounder $6.59 0.0329 $6.52 $6.65 

of Time Not 

Included One Pound of Summer 

Flounder $2.38 0.0119 $2.35 $2.40 

5.2 Weighted Model 

On-site sampling introduces potential biases in RUM model parameters that impact 

welfare estimates for summer flounder harvest rates. The RUM model presented in the 

previous chapter used the Marine Recreational Fisheries Statistical Survey (MRFSS) onsite sample of summer flounder anglers. In this section, Gentner Consulting provides: 1) 

an explanation of the potential consequences of onsite sampling when estimating 

recreation site choice models, 2) a method for addressing these biases, 3) correction 

methods applied to biases associated with on-site sampling, and 4) a discussion on the 

limitations of this approach. 

In the empirical application of recreation site choice models, intercept samples, such as 

the MRFSS, result in two separate types of non-random sample selection bias, 

endogenous stratification and size-biased sampling. Endogenous stratification can be 

characterized by conditions where the endogenous variable (site choice) becomes an 

integral facet of a stratified sample selection process. Samples with endogenous 

stratification may also be referred to as choice-based samples. A thorough literature 

exists related to endogenous stratification in discrete choice models (Manski and Lerman, 

1977; Manski and McFadden, 1981; Cosslett, 1981a; Cosslett, 1981b; Hsieh, Manski, and 

McFadden, 1985; Imbens, 1992; McFadden 1999; and Bierlaire, Bolduc, and McFadden 

2008). In general terms, the MRFSS intercepts saltwater anglers at their chosen site and, 

as a result, the process of choosing an angler for the sample is directly linked with the 

behavioral process driving that angler’s choice. In this scenario, unknown parameters 

associated with the choice process become part of the sample selection process. 

The second type of bias, size-biased sampling, results when the probability of sample 

selection is a function of the size of one of the sample characteristics (Patil and Rao 

1978). In single site recreation demand models, endogenous stratification and size-biased 

sampling are one in the same since the endogenous variable, trip frequency, is directly 
47

tied to angler avidity. The economics literature has outlined methods for addressing this 

type of bias in single site recreation demand models (Shaw 1988; Englin and Shonkwiler 

1996). In recreation site choice models, angler avidity is an exogenous variable. 

Consequently, avidity may bias estimation, but this bias remains exogenous to the choice 

process. In the context of recreation site choice modeling, the MRFSS sample selection 

process represents what Bierlaire, Bolduc, and McFadden (2008) call Exogenous and 

Endogenous Sampling since bias results from both endogenous (site/mode choice) as 

well as exogenous sources (avidity). 

5.2.1 Weighted Methodology 

As discussed earlier, an extensive literature exists which depicts methods for addressing 

endogenous stratification in RUMs. In most cases, the literature focuses on what are 

called “pure choice-based samples.” Pure choice-based samples do not suffer from sizebiased sampling. In pure choice-based samples, within site characteristics are randomly 

assigned. In the context of recreation site/mode choice, this means that the share of 

anglers making site/mode choices in the sample may not equal those made in the 

population, but those anglers making a given site/mode choice are selected at random. 

Since estimation routines using intercept samples suffer from both endogenous 

stratification and size-biased sampling, we apply a method previously proposed by 

Hindsley et al. (2008) to address non-random sample selection biases in the MRFSS. 

This method combines the pseudo-likelihood estimators used to address endogenous 

stratification with propensity score methods. The propensity score methods, which we 

describe in more detail later, allow analysts to address non-random selection of anglers 

within a given site/mode choice. 

The two most common methods for addressing endogenous stratification are Conditional 

Maximum Likelihood (CML) and Weighted Exogenous Sample Maximum Likelihood 

Estimation (WESMLE). Bierlaire, Bolduc and McFadden (2008) generalize these two 

methods into one convenient form. This formula divides the qualification probability 

(i.e. the probability of selection into the sample) into two separate functions, such that 

β sziAsziQszir β),,,(),,(),,,( ns = n n 5.9) 

 

where () sr represents the qualification probability. Note that Q )( contains no unknown 

parameters. Bierlaire, Bolduc and McFadden then utilize the segmented qualification 

probability within a pseudo-likelihood estimator 

∑

= ∑ ≠

− =

N

n ij

n n ESS n szjPszjA

sziPsziA LL sziQ

1

1

),,|(),,,(

),,|(),,,( ln),,()( ˆˆ

β β

β β β . 5.10) 

when ) n ziA ,,( β = 1, the estimator depicts Manski and Lerman’s (1977) WESMLE and 

when 1 ),(

− n ziQ = 1 the estimator represents CML. When applied to multinomial logistic 

regression, both estimators are consistent, but not necessarily efficient. In both cases, 

estimation necessitates a robust sandwich estimator for the calculation of the variancecovariance matrix. Failure to utilize the robust sandwich estimation leads to downward 

bias in the standard errors. 
48 

In our application, we utilize WESMLE. The WESML estimator was first developed by 

Manski and Lerman (1977) for instances where the sample is a “pure” choice-based 

sample and the population proportions of choices are known a priori. In this application, 

Manski and Lerman use the known population proportions and the sample proportions to 

develop an inverse probability weight. Cosslett (1981a) later devised a weight which 

could be estimated when population probabilities are not known, a priori. Much like 

Manski and Lerman’s method, Cosslett’s method also dealt with pure choice-based 

sampling. Hindsley et al (2008) extend Cosslett’s estimated weighting strategy by 

utilizing propensity score based weights. Hindsley et al (2008) validate the use of 

propensity score based weights based on Wooldridge’s (2002) finding that Inverse 

Probability Weights (IPW) can be used with M-estimators to address non-random sample 

selection. IPWs account for the observed components of non-random selection. 

Propensity scores represent a convenient method for estimating these probabilities. 

Propensity scores represent a scalar probability value depicting observed differences 

between two groups. More specifically, the propensity score represents the conditional 

probability of assignment to a particular treatment given a vector of covariates 

(Rosenbaum and Rubin 1983). In our application we estimate a value depicting observed 

differences between the onsite sample and the Coastal Household Telephone Survey 

(CHTS) as an auxiliary sample. This propensity score can then be used to “quasirandomize” the onsite sample based on the observed characteristics of the auxiliary 

sample.

Ridgeway (2006) gives a concise depiction of this weighting methodology where the two 

samples are divided such that 

== tszifsziQtszif = )0|,,(),,()1|,,( nn nnnnn 5.11) 

Where ) tszif = 1|,,( nn are angler choices and characteristics conditional on being in 

the random sample, tszif = 0|,,( ) nn are angler choices and characteristics conditional 

on being in the intercept sample, and ) nnn ,,( sziQ is a weight that allows the joint 

distributions of the two samples to be equal. By solving for ) nnn ,,( sziQ and using Bays 

Law, the above can be rewritten as 

 

),,|1(1

),,|1( ),,( szitf

szitf KsziQ

nn

nn nnn =−

= = . 5.12) 

During estimation, the constant K cancels out, allowing the weight to be depicted as 

),,Pr(1

),,Pr(

szi

szi Q nn

nn n − = , 5.13) 

 

which represents the odds that that an angler sampled onsite would be a member of the 

random sample. This odds ratio can be conveniently represented using binary models 
49

such as logit and probit models. See Hindsley et al. (2008) for a more detailed depiction 

of this weight. 

5.2.2 Random Utility Model 

In this section, we represent saltwater recreational anglers’ site/mode choices through the 

application of the Random Utility Maximization (RUM) model. Assuming that anglers 

are utility maximizers, our model dissects angler choice behavior so that the probability 

of a choice is: 

 

 P( )

 P( )

combinatio site/mode chooses( P(i)n )

VV ij

V ijV

nP ijUU

ninjnjni

njnjnini

njni

≠∀−>−=

≠∀+>+=

= > ∀ ≠

εε

ε ε 5.14) 

where U ni represents utility, Vni the systematic portion of utility, and ε ni represents the 

unobserved portions of utility. We assume that the systematic portion of utility, Vni , is 

linear in attributes such that 

ni β XTCV β Xnn γ 1111 ...+++= 5.15) 

where TC represents travel costs and X represents other site or choice characteristics. 

We estimate the RUM using the conditional logit model. The conditional logit model has 

a random component assumed to be independently and identically distributed Type I 

extreme value (McFadden 1974). Train (2003) identifies the limitations of the 

conditional logit as 1) an inability to represent random taste variation, 2) restrictive 

substitution patterns due to the IIA property, and 3) an inability to be used with panel 

data when unobserved factors are correlated over time for each decision maker. In this 

study, we feel these limitations are outweighed by difficulties associated with addressing 

endogenous stratification with other types of discrete choice models, such as the nested 

logit model used in the previous chapter. The nested structure was chosen in the 

previous chapter because failing to account for substitution between modes has 

potentially large impacts on marginal CV estimates for harvest (Haab et al 2008). At this 

time, it is not possible to estimate nested models that account for biased sampling. We 

estimate an unweighted model as well as a model Hindsley et al. (2008) refer to as 

balanced WESMLE. 

5.2.3 Data Manipulation 

As with the MRFSS intercept survey, our use of the Coastal Household Telephone 

Survey (CHTS) was constrained due to data limitations associated with the sampling 

process. Table 5.6 contains all the descriptive statistics for all the variables used in this 

analysis from the CHTS data set. Table 5.7 contains the descriptive statistics for all the 

variables used in this analysis from the MRFSS intercept data set. First, the CHTS no 

longer collects certain types of data, including fish type targeted and 12 month avidity, 

variables that proved important in Hindsley et al (2008). In addition, the CHTS only 

surveys individuals living in coastal counties. As a result, the CHTS represents a 

geographically truncated version of the true angler population. The CHTS dataset 

includes 6,546 anglers in its entirety. By wave, 5.4% of all anglers were intercepted in 
50 

wave 2, 24.8.9% were intercepted in wave 3, 32.3% were intercepted in wave 4, 26.2% 

were intercepted in wave 5, and only 11 % were intercepted in wave 6. No MRFSS 

sampling is conducted in wave 1. By fishing mode, 34.6% of all intercepts were in the 

shore mode, 10.9% were in the for-hire mode, and 54.4% were intercepted in the private 

rental mode. 

Table 5.6. Descriptive Statistics for CHTS Variables 

Variable 

Name Description Mean Standard Error 

Lower 

Confidence 

Limit 

Upper 

Confidence 

Limit 

Pr Dummy for Private/Rental Mode 0.544 0.006 0.531 0.555 

Charter Dummy for Charter Mode 0.110 0.004 0.102 0.117 

Shore Dummy for Shore Mode 0.347 0.006 0.335 0.358 

ffdays2 2 Month Avidity 5.817 0.092 5.636 5.998 

wave3 Intercepted in Wave 3 0.248 0.005 0.238 0.259 

wave4 Intercepted in Wave 4 0.322 0.006 0.311 0.334 

wave5 Intercepted in Wave 5 0.261 0.005 0.251 0.272 

Table 5.7. Descriptive Statistics for all Variables in Intercept Dataset 

Variable 

Name Description Mean Standard Error 

Lower 

Confidence 

Limit 

Upper 

Confidence 

Limit 

Hrsf Hours Fished 4.032 0.026 3.980 4.083 

Pr Dummy for Private/Rental Mode 0.532 0.009 0.515 0.549 

Charter Dummy for Charter Mode 0.412 0.009 0.395 0.429 

Shore Dummy for Shore Mode 0.056 0.004 0.048 0.064 

ffdays12 12 Month Avidity 25.331 0.601 24.154 26.509 

ffdays2 2 Month Avidity 5.897 0.131 5.641 6.153 

Travel Calculated Travel Cost $51.88 $1.04 $49.84 $53.91 

travel_opp 

Travel Cost Plus Opportunity Cost of 

Travel Time $75.420 1.460 $72.44 $78.28 

Boater Proxy for Boat Ownership 0.286 0.008 0.271 0.302 

North Equals 1 If Site is North of NY 0.413 0.001 0.411 0.414 

Lnm Log of Number of Aggregated Sites 2.924 0.001 2.921 2.926 

Karate Harvest per Trip 0.356 0.001 0.355 0.357 

Ekarate Expected Harvest per Trip 0.448 0.002 0.444 0.452 

pr_boater 

Private/Rental Mode Crossed with 

Boater 0.095 0.000 0.094 0.096 

north_shore North Crossed with Shore 0.114 0.000 0.114 0.115 

wave3 Intercepted in Wave 3 0.357 0.008 0.340 0.373 

wave4 Intercepted in Wave 4 0.524 0.009 0.507 0.541 

wave5 Intercepted in Wave 5 0.100 0.005 0.090 0.110 

5.2.4 Expected Keep Rates 

To conform to current theories on the calculation of welfare effects stemming from 

quality changes, expected keep rates, rather than actual keep rates, were used as the 

quality variable in the nested logit model. Typically, a poisson regression is used to 

estimate expected keep rates. However, if over-dispersion is found in the data the zero 

alter poission (ZAP) or the negative binomial models are more appropriate. In some 
51

cases, such as ours, the most appropriate model may be the zero inflated negative 

binomial (ZINB). Initial runs using a poisson indicated over-dispersion in the data so 

ZAP, negative binomial, and ZINB models were all estimated.7

 The negative binomial 

model performed far better than the ZAP. Next we performed Vuong test to compare the 

performance of the negative binomial with the ZINB. The Vuong test indicates the ZINB 

as the preferred model.8

 The specification of the negative binomial is: 

( )

i x

i

i

i i

i

i

x

x

x

⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎝

⎛

⎟ + ⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎝

⎛

⎟ +

⎠

⎞ ⎜

⎝

⎛ Γ+Γ

⎟

⎠

⎞ ⎜

⎝

⎛ +Γ

=

λ

α

λ

λ

α

α

α

α

α

11

1

1 1

1

)Pr(

1

 5.16) 

Whereλi = exp( ) ziβ , xi equals harvest of individual i on the intercepted trip, and zi

contains variables describing the site and the individual including a constant term, karate, 

ffdays2, hrsf, shore, pr, and wave3. In previous studies (Hicks et al 1999, and Haab et al 

2000), years of fishing experience was used to describe angler experience. This variable 

was not collected in the 2006 add-on, so 12 month fishing avidity was used as a proxy for 

fishing experience. 

In the ZINB, the negative binomial accounts for over-dispersion and the zero-inflated 

model augments the negative binomial by combining it with a point mass at zero. 

Cameron and Trivedi (1998,2005) overview these methods. In our application, the model 

utilizes a binary logit model to determine if the observed state is a zero or a count. In a 

generalization of this equation, the ZINB can be depicted as 

 ) ()1()()( 0 yIyf NB yf ZINB π +⋅= −π ⋅ 5.17) 

where y represents a count, π represents the probability of a zero count (estimated by a 

binary logit), ) ( 0 yI is an indicator representing a zero count, and ) NB ( yf represents the 

negative binomial model with count y. In our application, the binary logit model was 

estimated with the following regressors: constant, hrsf, pr, and wave3. 

Table 5.8 contains the parameter estimates from the negative binomial expected keep 

model. In the negative binomial model, all variables were significant at the 95% level 

except shore, which was significant at the 90% level. All parameter estimates are 

significantly different from zero with a chi-squared test statistic of 347.96. As discussed 

earlier, the value of alpha, the over-dispersion parameter is 0.776 and significant 

indicating that over-dispersion was indeed a problem in this data set. The Vuong test 

statistic is 3.07 and significant indicating a need to account for an excessive number of 

zeros during estimation. All parameters had a positive and significant impact on the 

expected keep rate except for shore and wave3. Historic catch rate had the largest impact 

 

7

 The test for overdispersion uses a likelihood ratio test where the null hypothesis assumes α = 0 . We 

rejected the null at the .001 significance level ( 101)1( 2

χ = ). 8

 The calculated Vuong test statistic was z = 3.07 with a pvalue of .0011. 
52 

on expected catch. As expected, hours fished also positively influenced expectations. 

The parameters from this model were used construct the expected keep rates for all 

potential choices in the model. 

Table 5.8. Zero Inflated Negative Binomial Expected Keep Rate Model Results 

Variable 

Parameter 

Estimate 

Standard 

Error T-ratio P-value 

constant -2.3033 0.2426 -9.49 0 

 Karate 1.4546 0.0363 4.35 0 

 Hrsf 0.1579 0.0049 6.34 0 

 ffdays2 0.0311 0.1099 4.29 0 

 Pr 0.4720 0.3856 -4.32 0 

 Shore -1.6656 0.1307 -1.94 0.053 

 wave3 -0.2534 0.2426 -9.49 0 

Inflate 

 Hrsf -0.3162 0.0922 -3.43 0.001 

 Pr 1.5817 0.5018 3.15 0.002 

 wave3 0.3682 0.3050 1.21 0.227 

constant -0.4661 0.6583 -0.71 0.479 

Alpha 0.7762 0.1844 

Log 

Likelihood -2,364.55 

5.2.5 Propensity Score Results 

In our application, the propensity score methods model observed differences in the 

selection process between the two different samples. This represents a “quasirandomizing” process, because the propensity score can only be used to balance 

differences between the two groups based on observed differences. Variable selection 

and model selection are vital components for any attempt to reduce differences between 

the two samples. 

We attempted several different methods for estimating the propensity score. The most 

commonly applied propensity score estimators use parametric models such as the linear 

logistic regression model. When specifying these parametric models, variable selection 

becomes vital. Millimet and Tchernis (2008) have a detailed discussion of variable 

selection in propensity score estimation. 

Our first attempts utilized the linear logistic regression model with variable selection 

algorithms developed by Dehejia and Wahba (2002) and Hirano and Imbens (2001). In 

our application, neither of these algorithms performed well due to the high number of 

dummy variables associated with mode, zone, and mode/zone interactions. 

Unfortunately, the MRFSS no longer collects information on quantitative variables such 

as angler experience. Qualitative variables provide less information for balancing 

differences between the samples. 

Once we determined that traditional parametric methods would not perform well, we 

decided to estimate the propensity score models using a flexible, nonparametric method 

called a generalized boosted model (GBM) (McCaffrey, Ridgeway, and Morral 2004). 

Unlike traditional parametric methods, GBM is not constrained by large numbers of 
53

covariates. In fact, GBM can estimate models with large numbers of covariates in a 

nonlinear fashion without being hampered by issues such as multi-collinearity. GBM 

combines numerous simple functions to estimate one large smooth function (Friedman, 

Hastie, and Tibshirani 2000). 

In our application, the GBM algorithm uses an iterative process to find a specification 

that maximizes a Bernoulli log-likelihood function. The first iteration begins by setting 

the log odds to a constant value (the average number of observations in the CHTS sample 

divided by the average number in the intercept sample, represented by ( )t

t

1− log ). The 

GBM algorithm then iteratively works to make small improvements to this baseline 

estimate. In each iteration, the algorithm works find an improvement that increases the 

expected log-likelihood such that 

))),,(ˆ (())),,(),,(ˆ (( nn + λ nn > nn szifLLEszihszifLLE 5.18) 

 

Each iteration contributes a small adjustment, ) ,,( szihλ nn which updates the current 

estimate of ),,( ˆ szif nnk such that 

),,(),,( ˆ ),,( ˆ 1 szihszifszif + nnk ← nnk + λ nnk 5.19) 

 

where k represents the current iteration, and k + 1 represents the updated estimate. With 

GBM, each adjustment is represented by the difference between the treatment indicator 

and the probability of treatment. The algorithm uses Classification and Regression Trees 

(CART), as developed by Breiman, Friedman, Olshen and Stone (1984), to estimate this 

difference. According to Friedman (2001), this difference, which can be interpreted as a 

type of residual, contains information pertaining to those values of ni , nz and s which fit 

the model poorly. CART evaluates this relationship using a piecewise constant function. 

GBM then uses a line search to find the coefficientλ with the greatest increase in the log 

likelihood. According to Ridgeway (2006), a bias/variance tradeoff exists where, with 

additional iteration, any reduction in bias comes at the expense of increasing variance. 

For the GBM package, we utilize the smallest average effect size difference across 

covariates between the treatment and comparison groups as our stopping rule (GBM 

2006). The standardized effect size is the difference between the treatment group mean 

values and the control group mean values divided by the treatment group standard 

deviation. For more information on boosting algorithms, see Friedman, Hastie, and 

Tibshirani (2000). 

In our GBM model, we allow for interactions between the three different variables types 

(site, mode, avidity) and we set the shrinkage coefficient to 0.0005. The shrinkage 

coefficient acts to constrain the size of the improvement possible in any given iteration. 

As a shrinkage coefficient decreases in size, it improves the accuracy of estimation, but 

necessitates many more iterations. Using these settings, the optimal mean effect size 

occurred after 23204 iterations. Tables 5.11 (unweighted), 5.9 (unweighted), 5.13 

(weighted), and 5.10 (weighted) depict the means, standard deviations, standard effect 

sizes, t-values, and pvalues for the variables used in the propensity score model. 
54 

Although we primarily use the standardized effect size to determine balance, we are also 

interested in decreasing t-statistics. According to Cohen (1988), a rule of thumb 

generally applies when using the standardized effect size, where 0.2 is a small value, 0.5 

is a medium sized value, and 0.8 is a large value. Our application resulted in a mean 

effect size of 0.0399, a decrease of roughly 79 percent from the baseline. This indicates 

that, on average, the absolute standard effect size is small after weighting. Using the 

estimated propensity scores, the maximum absolute effect size for a variable is .27 as 

compared to 1.95 in for the unweighted comparison. In a comparison of t-values, we find 

that the t-value for the site dummy variables (zone2) decreases from 81.35, a highly 

statistically significant value, to 0.797, a value which is not statistically significant. We 

also find that the t-value for 2 month avidity changes from -0.495 to 0.407, both 

statistically insignificant values. Last, the mode dummy variables (mode2) decreases 

from 840.76 to 13.47. This last t-statistic represents a statistically significant difference, 

but there was large decrease in the value. We will discuss limitations of this method 

more in the discussion section. 

Figure 5.6 shows the change in the absolute standard effect sizes for mode, zone, and 2 

month avidity. The blue lines depict a decrease in the absolute effect size before and 

after weighting and a red line depicts an increase. We find decreases in the absolute 

effect size for the mode and zone variable and a small increase for the 2 month avidity 

variable. 

Table 5.9. Means before Propensity Score Weighting 

 CHTS CHTS Intercept Intercept Standard 

variable Mean St Dev Mean St Dev Eff. Size t-value p-value 

ffdays2 5.818 7.467 5.897 7.463 -0.011 -0.495 0.621 

mode2:1 0.347 0.476 0.056 0.231 0.611 840.673 0 

mode2:2 0.11 0.313 0.412 0.492 -0.967 NA NA 

mode2:3 0.543 0.498 0.532 0.499 0.023 NA NA 

Table 5.10. Means after Propensity Score Weighting 

 CHTS CHTS Intercept Intercept Standard 

variable Mean St Dev Mean St Dev Eff. Size t-value p-value 

ffdays2 5.818 7.467 5.68 6.931 0.018 0.407 0.684 

mode2:1 0.347 0.476 0.23 0.421 0.245 13.471 0 

mode2:2 0.11 0.313 0.092 0.289 0.057 NA NA 

mode2:3 0.543 0.498 0.678 0.467 -0.27 NA NA 

GBM has the ability to measure the relative influence for a given variable in explaining 

the differences between the CHTS and the intercept sample. Freidman (2001) 

determined that a variable’s relative influence in a given iteration is the empirical 

improvement which results from partitioning the data at a given point using that variable. 

The TWANG package (Ridgeway et al 2006) allows us to determine the relative 

influence for a given model by using the average of these values over all iterations. This 

procedure indicates that the site represents 73.14%, fishing mode represents 21.23%, and 

2 month avidity represents 5.62% of the difference between the two samples. 
55

Table 5.11. Individual Site Choice Frequencies and Standard Effect Sizes between 

the CHTS Sample and the Intercept Sample before Propensity Score Weighting 

 CHTS CHTS Intercept Intercept Standard 

variable Mean St Dev Mean St Dev Eff. Size t-value p-value 

zone2:1 0.007 0.085 0.001 0.03 0.075 81.346 0 

zone2:2 0.007 0.084 0.009 0.092 -0.018 NA NA 

zone2:3 0.012 0.108 0.001 0.035 0.098 NA NA 

zone2:4 0.026 0.158 0.032 0.177 -0.044 NA NA 

zone2:5 0.013 0.114 0.032 0.177 -0.169 NA NA 

zone2:7 0.058 0.233 0.097 0.296 -0.167 NA NA 

zone2:17 0.03 0.17 0.001 0.03 0.17 NA NA 

zone2:18 0.034 0.182 0.003 0.058 0.17 NA NA 

zone2:19 0.033 0.179 0.012 0.109 0.119 NA NA 

zone2:22 0.105 0.306 0.002 0.046 0.335 NA NA 

zone2:24 0.043 0.202 0.023 0.149 0.099 NA NA 

zone2:25 0.014 0.117 0.01 0.102 0.03 NA NA 

zone2:26 0.013 0.113 0 0.017 0.111 NA NA 

zone2:27 0.026 0.158 0.001 0.025 0.158 NA NA 

zone2:30 0.022 0.146 0.005 0.072 0.114 NA NA 

zone2:32 0.023 0.15 0.001 0.025 0.15 NA NA 

zone2:33 0.022 0.148 0.091 0.287 -0.462 NA NA 

zone2:34 0.008 0.088 0.012 0.107 -0.044 NA NA 

zone2:35 0.005 0.069 0.004 0.063 0.011 NA NA 

zone2:36 0.042 0.201 0.044 0.206 -0.011 NA NA 

zone2:37 0.016 0.125 0.04 0.196 -0.193 NA NA 

zone2:38 0.013 0.115 0.007 0.082 0.057 NA NA 

zone2:39 0.017 0.129 0.025 0.156 -0.061 NA NA 

zone2:40 0.01 0.098 0.051 0.22 -0.42 NA NA 

zone2:42 0.005 0.072 0.023 0.15 -0.247 NA NA 

zone2:43 0.005 0.068 0.003 0.058 0.018 NA NA 

zone2:44 0.006 0.076 0.003 0.055 0.036 NA NA 

zone2:45 0.003 0.052 0 0.017 0.047 NA NA 

zone2:46 0.009 0.092 0.004 0.061 0.053 NA NA 

zone2:47 0.007 0.083 0.041 0.198 -0.413 NA NA 

zone2:48 0.026 0.158 0.032 0.176 -0.042 NA NA 

zone2:50 0.01 0.101 0.209 0.407 -1.956 NA NA 

zone2:51 0.014 0.119 0.001 0.03 0.113 NA NA 

zone2:52 0.013 0.112 0.001 0.03 0.105 NA NA 

zone2:53 0.022 0.146 0.005 0.07 0.116 NA NA 

zone2:55 0.036 0.187 0.101 0.301 -0.343 NA NA 

zone2:56 0.028 0.165 0.03 0.171 -0.014 NA NA 

zone2:57 0.026 0.161 0.014 0.117 0.079 NA NA 

zone2:58 0.036 0.187 0.004 0.061 0.175 NA NA 

zone2:59 0.023 0.15 0.012 0.107 0.076 NA NA 

zone2:60 0.009 0.095 0 0.017 0.093 NA NA 

zone2:61 0.01 0.099 0.001 0.025 0.094 NA NA 

zone2:62 0.1 0.3 0.001 0.025 0.331 NA NA 

zone2:63 0.014 0.117 0.012 0.11 0.014 NA NA 
56 

Table 5.12. Weighted Individual Site Choice Frequencies and Standard Effect Sizes 

between the CHTS Sample and the Intercept Sample after Propensity Score 

Weighting 

 CHTS CHTS Intercept Intercept Standard 

variable Mean St Dev Mean St Dev Eff. Size t-value p-value 

zone2:1 0.007 0.085 0.006 0.079 0.012 0.797 0.681 

zone2:2 0.007 0.084 0.007 0.081 0.005 NA NA 

zone2:3 0.012 0.108 0.007 0.082 0.047 NA NA 

zone2:4 0.026 0.158 0.027 0.162 -0.008 NA NA 

zone2:5 0.013 0.114 0.009 0.096 0.034 NA NA 

zone2:7 0.058 0.233 0.083 0.275 -0.107 NA NA 

zone2:17 0.03 0.17 0.032 0.177 -0.015 NA NA 

zone2:18 0.034 0.182 0.042 0.2 -0.042 NA NA 

zone2:19 0.033 0.179 0.032 0.177 0.006 NA NA 

zone2:22 0.105 0.306 0.105 0.306 0 NA NA 

zone2:24 0.043 0.202 0.056 0.229 -0.064 NA NA 

zone2:25 0.014 0.117 0.014 0.117 0.001 NA NA 

zone2:26 0.013 0.113 0.014 0.116 -0.007 NA NA 

zone2:27 0.026 0.158 0.02 0.14 0.035 NA NA 

zone2:30 0.022 0.146 0.02 0.14 0.012 NA NA 

zone2:32 0.023 0.15 0.018 0.134 0.033 NA NA 

zone2:33 0.022 0.148 0.022 0.148 0 NA NA 

zone2:34 0.008 0.088 0.008 0.091 -0.005 NA NA 

zone2:35 0.005 0.069 0.005 0.072 -0.006 NA NA 

zone2:36 0.042 0.201 0.052 0.221 -0.047 NA NA 

zone2:37 0.016 0.125 0.018 0.133 -0.017 NA NA 

zone2:38 0.013 0.115 0.013 0.111 0.007 NA NA 

zone2:39 0.017 0.129 0.024 0.153 -0.055 NA NA 

zone2:40 0.01 0.098 0.012 0.111 -0.027 NA NA 

zone2:42 0.005 0.072 0.005 0.073 -0.003 NA NA 

zone2:43 0.005 0.068 0.005 0.068 -0.002 NA NA 

zone2:44 0.006 0.076 0.004 0.06 0.03 NA NA 

zone2:45 0.003 0.052 0.002 0.05 0.006 NA NA 

zone2:46 0.009 0.092 0.008 0.087 0.011 NA NA 

zone2:47 0.007 0.083 0.009 0.096 -0.03 NA NA 

zone2:48 0.026 0.158 0.025 0.155 0.005 NA NA 

zone2:50 0.01 0.101 0.015 0.121 -0.043 NA NA 

zone2:51 0.014 0.119 0.016 0.124 -0.011 NA NA 

zone2:52 0.013 0.112 0.012 0.109 0.007 NA NA 

zone2:53 0.022 0.146 0.03 0.17 -0.054 NA NA 

zone2:55 0.036 0.187 0.041 0.198 -0.024 NA NA 

zone2:56 0.028 0.165 0.035 0.184 -0.044 NA NA 

zone2:57 0.026 0.161 0.025 0.156 0.01 NA NA 

zone2:58 0.036 0.187 0.041 0.197 -0.022 NA NA 

zone2:59 0.023 0.15 0.022 0.147 0.005 NA NA 

zone2:60 0.009 0.095 0.008 0.09 0.01 NA NA 

zone2:61 0.01 0.099 0.005 0.071 0.049 NA NA 

zone2:62 0.1 0.3 0.029 0.168 0.237 NA NA 

zone2:63 0.014 0.117 0.018 0.133 -0.036 NA NA 
57

5.2.6 Model Results 

The multinomial logit models were estimated in Stata using the clogit routine. Table 5.13 

5.2.6 Model Results 

The multinomial logit models were estimated in Stata using the clogit routine. Table 5.13 

contains the parameter estimates and model fit information. Our model specification 

includes site specific constants, mode specific constants, a travel cost measure, and an 

expected catch measure. In Table 5.13, we do not include the site specific constants due 

to the sheer number. Estimation results for the entire models can be found at the end of 

the report. Overall model fit was good with a Pseudo R-square value of roughly 0.60 for 

the unweighted models and between 0.56 and 0.57 for the weighted models. 

As expected, the travel cost coefficients are negative and significant in each model, 

suggesting that closer sites are preferred to more distant sites. Also as expected, the 

parameter on expected keep is positive and significant suggesting that sites with higher 

expected keep rates are preferred to sites with less expected keep. 

Table 5.14 contains the CV estimates for one summer flounder and one pound of summer 

flounder as calculated using the parameters in Table 5.13 for the unweighted model and 

Table 5.15 contains the CV estimates for the balanced WESMLE model. Confidence 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Absolute Std Difference

Unweighted Weighted

mode 

zone 

ffdays2 

Figure 5.6. Absolute Standard Effect Size: This plot depicts the absolute standard difference 

for variables in the CHTS and intercept samples before and after propensity score 

weighting 
58 

intervals were estimated using the method of Krinsky and Robb (1986). The marginal 

value of a summer flounder pound was calculated by dividing the CV for one fish by the 

average weight per fish of 2.77 pounds from the MRFSS web queries (NMFS 2008). 

Using the Northeast Fisheries Science Center length/weight/age conversion web site, this 

translates into a 17.5” summer flounder (NMFS 2008a). 

Table 5.13. Parameter Estimates and Model Fit for Conditional Logit Model 

 Unweighted Model Balanced WESMLE

 Coefficient Coefficient Coefficient Coefficient 

 Std Error Std Error Std Error Std Error 

 pr 2.1893 2.1883 1.3072 1.3057 

 0.0802 0.0802 0.1421 0.1420 

charter 1.9304 1.9294 0.2886* 0.2872* 

 0.0816 0.0815 0.1323 0.1321 

travelc -0.0701 -0.0818 

 0.0017 0.0045 

travel_opp -0.0392 -0.0453 

 0.0009 0.0024 

ecatch 0.1505 0.1527 0.1212* 0.1248* 

 0.0442 0.0440 0.0606 0.0596 

LL (Null) -16675.304 -16675.304 -41151.047 -41151.047 

LL 

(Model) -6702.9861 -6737.466 -17901.735 -18049.539 

Pseudo R2 0.598 0.596 0.565 0.5614 

All unmarked variables are statistically significant at .01 level 

* Statistically significant at the .05 level 

Table 5.14. Compensating Variation Estimates for the Current Keep Levels 

(Unweighted 2007 dollars) 

Model Compensating Variation Mean 

95% Lower 

Bound 

95% Upper 

Bound 

Opportunity One Summer Flounder $4.02 $3.97 $4.07 

Cost of 

Time 

Included One Pound of Summer Flounder $1.45 $1.43 $1.47 

Opportunity One Summer Flounder $2.21 $2.18 $2.36 

Cost of 

Time Not 

Included One Pound of Summer Flounder $0.80 $0.79 $0.81 

When the census opportunity cost of time calculations are included, CV estimates are 

45% higher for the unweighted estimates and 46% higher for the balanced WESMLE 

estimates. The Hicks et al (1999) and Haab et al (2000) methodologies only included 

opportunity cost of time when the respondent took time off work without pay to go 

fishing. Because very few people in previous surveys took time off work without pay to 

fish, the Haab et al (2000) and the Hicks et al (1999) methods would produce opportunity 

cost of time estimates that are lower than the census method used here. Since the time off 

work without pay question was not asked in the 2006 intercept survey, it is impossible to 

construct a similar measure for this study. Aggregating the per fish CV value across the 
59

current catch of summer flounder in 2006 (11.7 million pounds) the total value of the 

recreational summer flounder fishery was between $9.7 and $17.5 million in 2007 

dollars. Using the balanced WESMLE estimates, the aggregated CV value across the 

current catch of summer flounder in 2006 was between $6.4 and $12.0 million dollars in 

2007 dollars. 

Table 5.15. Compensating Variation Estimates for the Current Keep Levels 

(Weighted 2007 dollars) 

Model Compensating Variation Mean 

95% Lower 

Bound 

95% Upper 

Bound 

Opportunity One Summer Flounder $2.75 $0.18 $5.52 

Cost of 

Time 

Included One Pound of Summer Flounder $0.99 $0.06 $1.99 

Opportunity One Summer Flounder $1.48 $0.03 $3.04 

Cost of 

Time Not 

Included One Pound of Summer Flounder $0.53 $0.01 $1.10 

5.3 Recreational Valuation Discussion

This analysis shows that the recreational summer flounder fishery is a very valuable 

recreational fishery. It is likely that effort would increase with higher allocation to the 

recreational sector, but it is unknown how angler preferences for increased keep would 

change as allocations increased. As a result, it is impossible to trace a complete WTP 

schedule for this sector. 

Since there is evidence that sample selection bias exists in the MRFSS intercept sample, 

we should be somewhat wary of our reported results. The CHTS survey has the potential 

to address some of this bias, but in its present state, there are significant limitations. 

First, the CHTS only covers households in coastal counties. This is problematic in that it 

truncates the angler population according to political boundaries. Although this 

truncation is performed for pragmatic reasons (cost), it limits the effectiveness of using 

this sample in applications which address sample selection bias for RUMs. In addition to 

the sample truncation which occurs according to geographic boundaries, the CHTS also 

does not collect certain types of information which would be helpful in this process. For 

example, previous CHTS samples collected information on which species anglers 

targeted, 12 month avidity, and years of fishing experience. Because the CHTS does not 

include information on which species angler’s target, this analysis was forced to use data 

across all species targeted by recreational anglers. This disqualifies the use of these 

estimates because anglers likely targeted any number of other species with lower 

marginal WTP estimates. 

Also, the performance of weighting procedure depends on the existence of observed 

attributes which may explain differences in the sample selection process. Variables such 

as 12 month avidity give important information for developing propensity score based 

weights. In past years, when 12 month avidity was still collected on the CHTS, we 

found significant differences in 12 month avidity between the two samples (Steinback 

and Gentner 2001). Looking at two month avidity across these two samples now shows 
60 

no significant difference in avidity between the two samples. While there is no theoretical 

reason to include variables such as years of fishing experience, these variables may also 

improve balance between the samples. As a result, further analysis of allocations below 

will use only the unweighted results, recognizing that those estimates are likely upper 

bound estimates. 

In addition to issues associated with the development of weights, future applications 

should also focus on developing models which allow for relaxation of the IIA property. 

At this time, we are only aware of one paper which relaxes IIA while also addressing 

endogenous stratification. Bierlaire, Bolduc, and McFadden (2008) develop methods to 

utilize nested and cross-nested logit models while accounting for endogenous 

stratification. Their application, however, differs from ours in that it deals with much 

smaller choice sets and the sample selection process reflects a “pure” choice-based 

sampling process, since it assumes that within choice sampling occurs at random. We 

leave new methods to future studies. 

The results presented here also demonstrate that the WTP estimates are very sensitive to 

specification of expected catch rate models. The model estimated in the unweighted 

section utilized a different expected catch model than the estimates in the unweighted 

portion of the analysis. Both estimates will be compared in the allocation discussion in 

Chapter 6. 

Additionally, the results here show that WTP estimates are sensitive to inclusion of 

angler opportunity cost of time. While is it inappropriate to dismiss opportunity cost of 

time calculations, past NMFS calculations of opportunity cost of time were more 

conservative that the estimates of opportunity cost of time used here. Unfortunately data 

necessary to calculate opportunity cost of time in the standard NMFS fashion were not 

available for this analysis. As a result, recreational marginal WTP estimates used in the 

allocation analysis will include the opportunity cost of time as specified here. 

6.0 Allocation Discussion 

Figure 6.1 displays the commercial WTP schedule and the consumer plus the commercial 

WTP schedule both overlaid with upper and lower bound recreational WTP estimates9

. 

For the recreational WTP, the upper bound is the unweighted WTP estimate from Table 

5.5, including the error bars associated with that estimate. The lower bound recreational 

estimate is the weighted estimated from Table 5.15, including error bars. Both estimates 

of recreational WTP include the opportunity cost of time in the WTP calculation. The 

commercial WTP schedule represents the entire fleet using only data on the otter trawl 

gear type. It is likely, given the lower prices other gear types receive for their catch and 

given likely different fixed and trip cost structures, that this method introduces an upward 

bias in the commercial WTP estimates. Current commercial WTP for the current level of 

quota is $1.06/pound. 

The commercial plus consumer schedule was constructed by adding $0.15/pound across 

the entire commercial schedule. This method is unbiased at the current allocation, but 

 

9

 Marginal WTP on the commercial side is expressed as simulated market values for a pound of summer 

flounder quota. Consumer and private recreational WTP for a pound of summer flounder is expressed as 

compensating variation. 
61

produces an upward bias for increasing commercial allocation and a downward bias for 

allocations less than current commercial allocation. That is, if allocation were moved 

towards the recreational sector, the consumer WTP would be higher than $0.15/pound 

and if allocations were moved towards the commercial sector, the consumer WTP would 

be less than $0.15/pound. Looking closely at Figure 6.1, one notices that across high 

allocation values, the WTP function is actually upward sloping for across a narrow range 

of values implying upward sloping quota demand function. That is, it appears that there 

are two values for the dependent variable (WTP) for a single value of the independent 

variable (pounds of quota). This is explained above, but suffice it to say that caution is 

warranted when simulating values to far from the mean. 

While a full WTP schedule for the recreational sector cannot be calculated using the data 

available, the principle of diminishing marginal returns suggest that this function should 

be downward sloping, referring to the orientation in Figure 6.1. It is possible however 

the recreational function could be flat or have an upward slope across portions of the 

range (graph orientation). If effort and total catch increases such that there is no quality 

improvement for increasing allocations, the recreational function would be horizontal 

from the current allocation and for all increasing recreational allocations. Likewise, if 

reductions in quota caused no change in the quality of fishing through reductions in effort 

and total catch, the function would be horizontal across the entire range of allocations. 

However, if increasing recreational quota induced enough additional effort and catch to 

induce a decrease in catch rates, the function would have an upward slope. 

At the current allocation, the upper bound estimate on recreational WTP is $3.48/pound 

while the lower bound estimate is $0.99/pound, including the opportunity cost of time. 

Because data necessary for the construction of proper weights is no longer collected by 

the MRFSS, the lower bound estimate of $0.99 per pound under estimates the true value 

held by summer flounder anglers. The current data limitations required the weights to be 

constructed using trips for all fish species and are only calculated using coastal county 

residents. Both limitations have the effect of reducing recreational WTP below the actual 

value, although that actual value is unknown. The weighting strategy also adds 

significant uncertainty in the point estimate itself as reflected in the error bars that stretch 

from $0.06/pound to $1.99/pound. On the other hand, the unweighted estimates contain 

an upward bias because of the way sampling is conducted in the MRFSS intercept 

survey. Additionally, if substitute species were included, the actual WTP value would be 

lower. Including uncertainty in the point estimate, unweighted recreational WTP ranges 

from $3.44 to $3.51 per pound. Unfortunately, the true recreational WTP number is 

impossible to calculate given the current data, but it lies somewhere between the two 

estimates presented here. 

Additionally, for-hire fishing for summer flounder is valuable sector in the study area, 

particularly for summer flounder. Unfortunately, there is no existing cost and earnings 

data for the Atlantic for-hire fleet. Without cost and earnings data, it is impossible to 

estimate marginal WTP for this important sector and it has been left out of Figure 6.1. 

Often advocacy groups will make arguments for changes in allocations using economic 

impact estimates. While total output impacts are clearly inappropriate for making an 

allocation decision, income impacts have been used as a proxy for either consumer or 
62 

producers surplus (Kirkley et al 2000). It is widely acknowledged, however that income 

impacts overstate estimates of consumer or producer value (Edwards 1990). 

$2.45

$1.06

$3.48

$0.99

$1.21

-$0.50

$0.00

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

$3.50

$4.00

14.0015.5017.0015.5014.0012.5010.50

9.508.006.505.003.502.000.50

Millions of Pounds of Commercial Quota

Marginal WTP

Rec Unweighted Upper Rec Weighted Lower

Commercial WTP Commercial + Consumer

0% Recreational 100% Recreational

100% Commercial 0% Commercial Allocation

Figure 6.1. Marginal Willingness to Pay (compensating variation) Schedule for 

Recreational and Commercial Summer Flounder Fishermen (2007 dollars) 

Table 6.1 contains the income impact estimates for summer flounder fishing across all 

three fishing modes. Gentner and Steinback (2008) used the same 2006 MRFSS 

economic add-on data used here to estimate angler expenditures and economic impacts. 

For this report the same methodology was used to estimate summer flounder specific 

recreational trip expenditures by mode across all states included in the RUM model 

presented above. In 2006, summer flounder anglers spent $65.87/person/trip in the forhire modes, $33.31/person/trip in the private/rental mode, and $21.99/person/trip in the 

shore mode. Total expenditures across all modes were $234.1 million dollars with $16.4 

million, $190.8 million and $26.9 million spent in the for-hire, private/rental, and shore 

modes respectively. 
63

Income was calculated by taking the implied multiplier by expenditure category from 

Gentner and Steinback (2008) and applying the multiplier to the total expenditures. 

Overall, summer flounder angling generated $232.9 million in income impacts. To 

calculate marginal WTP values for this important sector, two approaches were taken 

(Table 6.2). First, total income impacts by sub-sector were divided by total summer 

flounder harvests across these sectors. Looking only at the for-hire businesses 

themselves, the upper bound estimate is $9.73/pound. This is the upper bound on the 

proxy measure as the summer flounder for-hire trips target multiple species. To calculate 

a lower bound, the income estimates by sub-sector were divided by all for-hire harvests 

of all species over the entire study area. Using this method, the estimate for for-hire 

business WTP for summer flounder is $0.52/pound. This is thought to be a lower bound 

as summer flounder trips typically harvest a narrower subset of all the species landed by 

for-hire boats in the study area. This proxy method does not allow the estimation of the 

entire WTP function. 

Table 6.1. Recreational Summer Flounder Trip Expenditures and Income Impacts 

(2007 dollars) 

Charter Mode Private Boat Mode Shore Mode 

Expenditure 

Category Total 

Expenditure 

Income 

Impacts 

Total 

Expenditure 

Income 

Impacts 

Total 

Expenditure 

Income 

Impacts 

PRIVATE 

TRANSPORTATION $2,344,484 $1,443,761 $45,456,670 $27,992,763 $9,233,975 $5,686,393 

AUTO RENTAL $972 $967 $0 $0 $49,490 $49,244 

GROCERY FOOD $1,322,249 $1,315,674 $21,087,062 $20,982,207 $3,660,433 $3,642,232 

RESTAURANT $674,601 $671,247 $8,344,780 $8,303,285 $2,657,737 $2,644,521 

LODGING $43,609 $43,392 $108,350 $107,811 $176,750 $175,871 

PUBLIC 

TRANSPORTATION $1,563 $1,555 $44,805 $44,582 $0 $0 

BOAT FUEL $0 $0 $65,381,829 $65,056,718 $0 $0 

BOAT RENTAL $0 $0 $1,145,892 $1,140,194 $0 $0 

GUIDE FEES $10,097,568 $10,047,358 $0 $0 $0 $0 

CREW TIPS $657,671 $654,400 $0 $0 $0 $0 

FISH PROCESSING $2,529 $2,517 $0 $0 $0 $0 

BAIT $98,598 $98,108 $24,935,848 $24,811,854 $4,761,019 $4,737,344 

ICE $116,920 $116,339 $5,077,567 $5,052,319 $609,203 $606,174 

FISHING TACKLE $615,337 $612,277 $11,487,408 $11,430,287 $4,257,243 $4,236,074 

TOURNAMENT 

FEES $348,489 $346,756 $88,597 $88,156 $0 $0 

PARKING $59,890 $59,592 $5,730,912 $5,702,415 $1,365,247 $1,358,458 

SOUVENIRS $27,447 $27,310 $164,393 $163,575 $35,556 $35,379 

TOTAL EXPENSE $16,417,408 $16,335,772 $190,763,571 $189,815,000 $26,898,299 $26,764,547 

TOTAL ALL 

MODES $234,079,278 $232,915,319 
64 

Table 6.2. Proxy For-Hire Mode Producer Surplus per Pound of Summer Flounder 

(2007 dollars) 

Proxy Producer Surplus per Pound 

Expenditure Category Income Impacts Boats Only Land 

Summer Flounder 

Summer Flounder 

Trips Land All 

For-Hire Landings 

PRIVATE TRANSPORTATION $2,344,484 $2.26 $0.12 

AUTO RENTAL EXPENSE $972 $0.00 $0.00 

GROCERY FOOD EXPENSE $1,322,249 $1.27 $0.07 

RESTAURANT FOOD EXPENSE $674,601 $0.65 $0.03 

LODGING EXPENSE $43,609 $0.04 $0.00 

PUBLIC TRANSPORTATION EXPENSE $1,563 $0.00 $0.00 

BOAT FUEL EXPENSE $0 $0.00 $0.00 

BOAT RENTAL EXPENSE $0 $0.00 $0.00 

GUIDE FEES EXPENSE $10,097,568 $9.73 $0.52 

CREW TIPS $657,671 $0.63 $0.03 

FISH PROCESSING EXPENSE $2,529 $0.00 $0.00 

BAIT EXPENSE $98,598 $0.10 $0.01 

ICE EXPENSE $116,920 $0.11 $0.01 

FISHING TACKLE EXPENSE $615,337 $0.59 $0.03 

TOURNAMENT FEES EXPENSE $348,489 $0.34 $0.02 

PARKING EXPENSE $59,890 $0.06 $0.00 

GIFTS & SOUVENIRS EXPENSE $27,447 $0.03 $0.00 

TOTAL EXPENSE $16,417,408 $15.82 $0.85 

The marginal WTP estimates presented here contain uncertainty on all fronts. First, 

confidence intervals for consumer, commercial, and for-hire proxy estimates were not 

calculated. While private recreational unweighted confidence intervals are fairly tight, 

bounds on the proxy estimates for for-hire recreational estimates were not calculated. It 

is recognized that using income impacts as a proxy for producer surplus overstate actual 

surplus, the lower bound estimates were calculated using an overly conservative estimate 

of harvest as their denominator. Additionally, the private recreational estimates contain 

an upward avidity and/or sample selection bias that could not be accurately accounted for 

using the current data. Also, recreational estimates do not include substitute species. 

Inclusion of substitute species will reduce the private recreational WTP estimates. 

Finally, private recreational estimates are sensitive to the specification of the expected 

catch rate models. Two different models were used here and the difference is significant. 

Furthermore, the stock of summer flounder is not included in either the commercial or 

recreational demand models. Therefore WTP is conditioned on the stock level across the 

years of data used; 2005-2007 for the commercial sector and 2006 for the recreational 

sector. If the stock level associated with maximum sustained or maximum economic 

yield is significantly higher (lower) than that of the data years used, the average welfare 

of each sector will change. Figure 2.2 shows the considerable fluctuation in landings 

across both sectors over a longer time series. 

Even with uncertainty on WTP estimates across all sectors, the allocation of summer 

flounder should move towards the recreational sector. Using the upper bound recreational 

estimate plus the upper bound estimate of WTP for just for-hire business of Table 6.2 of 
65

$9.73/pound at the current allocation suggest a move to a 100% recreational allocation. 

Adding the values for these two recreational sectors together results in a recreational 

WTP estimate of $13.21/pound. This conclusion would hold for every shape of a 

recreational WTP function except a sharply downward sloping recreational WTP 

function. That is, the sum of for-hire and private recreational WTP would have to fall 

below $2.45 at a 100% allocation. Without additional data, it is impossible to know the 

actual slope of this function. 

The conclusion reached when the lower bound private and lower bound for-hire estimates 

is similar. Adding these two values together, the lower bound for the current recreational 

WTP is $1.51/pound and the upper bound $13.21/pound. Again, the theory of 

diminishing marginal returns states that the function should be downward sloping and 

without additional data on angler preferences and for-hire business costs, it is impossible 

to determine the optimal allocation. However, both the lower and upper bound 

recreational WTP estimates are considerably higher ($0.31 and $12.00 per pound higher 

respectively) than the commercial plus consumer estimate of $1.21 per pound. This 

suggests that the allocation should move towards the recreational sector. 

Another way to look at the allocation issue is using total net benefits. The current total 

net benefit accruing to the commercial fleet is $10.9 million in 2007 dollars. Using the 

total 2006 harvest for summer flounder and the lower and upper bound estimates of 

recreational WTP, the current total benefits accruing to the recreational sector is between 

$12.0 to $42.0 million in 2007 dollars. Again the true total net benefit estimate is 

somewhere between the two figures. Because a total net benefit schedule for all 

allocations in the recreational sector cannot be developed for technical and data 

limitations, it is impossible to tell where the optimal allocation should be, however it does 

suggests the allocation should move towards the recreational sector. These total value 

estimates are based on a year when the recreational sector overshot its quota by a 

significant amount. 

This analysis does not explore potential spillover effects in either the recreational or 

commercial fisheries. The commercial fishery is a multispecies fishery. None of the gear 

types that harvest summer flounder target summer flounder individually. As a result, 

there would likely be significant commercial bycatch if the allocation was moved to 

100% recreational. Unfortunately, because of discard mortality under a 100% 

recreational allocation, there would likely still be significant commercial summer 

flounder mortality for this gear. Further studies would be needed develop an allowance 

for commercial bycatch in any significant shift of the allocation to the recreational sector. 

Additionally, technology tests conducted above indicate that production of summer 

flounder is non-joint in inputs. As a result, reductions in summer flounder allocations on 

the commercial side would increase the exploitation of the other species in this fishery. 

Finally, this study does not examine social impacts, fairness, or equity concerns. 

Changing allocations may change the type of jobs available in coastal communities and 

no attempt was made here to examine those potential changes. Changing allocations 

could change the structure and function of local economies and impact community well 

being. Economic impact analysis can be a good tool to examine the distributional 

impacts of allocation changes; however a full economic impact analysis was not 
66 

conducted. While the current economic impacts of the recreational fishery are detailed in 

Table 6.1, additional data would be needed to forecast the change in recreational effort 

stemming from changes in allocations. Calculating commercial economic impacts of the 

current summer flounder fishery was beyond the scope of this analysis. 
67

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73

Appendix 1: Model Estimation Results 

The 5 Equations to Estimate 

FLUKELB 

= 

F(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, 

a18, a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, 

a33, a34, a35, a36, a37, a38, a39, a40, a41, a42) 

baitlb = F(b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, 

b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, 

b32, b33, b34, b35, b36, b37, b38, b39, b40, b41, b42) 

shelllb = F(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, 

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, 

c33, c34, c35, c36, c37, c38, c39, c40, c41, c42) 

bottlb = F(d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11, d12, d13, d14, d15, d16, 

d17, d18, d19, d20, d21, d22, d23, d24, d25, d26, d27, d28, d29, d30, d31, 

d32, d33, d34, d35, d36, d37, d38, d39, d40, d41, d42) 

otherlb = F(e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15, e16, e17, 

e18, e19, e20, e21, e22, e23, e24, e25, e26, e27, e28, e29, e30, e31, e32, 

e33, e34, e35, e36, e37, e38, e39, e40, e41, e42) 

Observations will be weighted by tc 

NOTE: At FIML Iteration 0 CONVERGE=0.001 Criteria Met. 
74 

Minimization Summary 

Parameters Estimated 200 

Method Gauss 

Hessian GLS 

Covariance Estimator Cross 

Iterations 0 

Final Convergence Criteria 

R 0.000183 

PPC(c6) 0.099899 

Trace(S) 5.529E10 

Gradient norm 0.000014 

Log likelihood -1008728 

Nonlinear FIML Summary of Residual Errors 

Equation DF 

Model 

DF 

Error 

SSE MSE Root 

MSE 

RSquare Adj RSq 

FLUKELB 40 21806 3.008E14 1.379E10 117444 0.7598 0.7594 

baitlb 40 21806 2.681E14 1.23E10 110890 0.1581 0.1566 

shelllb 40 21806 1.382E14 6.3375E9 79608.6 0.1606 0.1591 

bottlb 40 21806 1.614E14 7.4019E9 86034.4 0.2440 0.2427 

otherlb 40 21806 3.394E14 1.557E10 124766 0.0859 0.0842 
75

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

a1 0.606795 0.00474 128.00 <.0001 Trip cost 

a2 -0.00002 1.482E-7 -164.37 <.0001 Trip cost squared 

a3 0.030578 0.00148 20.59 <.0001 Shellfish price 

a4 0.146146 0.00278 52.62 <.0001 Bait price 

a5 0.260425 0.00195 133.86 <.0001 Bottomfish price 

a6 0.040109 0.00262 15.33 <.0001 Other price 

a7 0.131472 0.00266 49.47 <.0001 January 

a8 0.160974 0.00280 57.56 <.0001 February 

a9 0.211679 0.00272 77.81 <.0001 March 

a10 -0.19188 0.00507 -37.83 <.0001 April 

a11 -0.20451 0.00707 -28.94 <.0001 May 

a12 -0.10671 0.0114 -9.37 <.0001 June 

a13 -0.115 0.0100 -11.47 <.0001 July 

a14 -0.18326 0.0240 -7.63 <.0001 August 

a15 -0.02347 0.0222 -1.06 0.2893 September 

a16 0.150098 0.0149 10.07 <.0001 October 

a17 0.005303 0.00518 1.02 0.3064 November 

a18 0.015071 0.00195 7.74 <.0001 2006 

a19 -0.1278 0.00219 -58.35 <.0001 2007 

a20 -0.5976 0.1755 -3.40 0.0007 Barnstable, MA 

a21 -0.50465 0.00606 -83.30 <.0001 Bristol, MA 

a22 -0.50097 8.4600 -0.06 0.9528 Dukes, MA 
76 

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

a23 -0.52311 1.5063 -0.35 0.7284 Nantucket, MA 

a24 -0.49161 0.0559 -8.80 <.0001 Suffolk, MA 

a25 -0.42264 0.0266 -15.89 <.0001 Worcester, MD 

a26 -0.69335 3.927E16 -0.00 1.0000 Hancock, ME 

a27 0.022978 0.00298 7.72 <.0001 Carteret, NC 

a28 0.097848 0.00309 31.65 <.0001 Dare, NC 

a29 0.057774 0.00293 19.75 <.0001 Hyde, NC 

a30 0.05839 0.00286 20.40 <.0001 Pamlico, NC 

a31 -0.17136 5.765E16 -0.00 1.0000 Atlantic, NJ 

a32 -0.22182 0.00718 -30.91 <.0001 Cape May, NJ 

a33 -0.40904 0.0276 -14.83 <.0001 Monmouth, NJ 

a34 -0.28188 0.0125 -22.61 <.0001 Ocean, NJ 

a35 -0.58417 2.4984 -0.23 0.8151 Kings, NY 

a36 -0.58357 0.1988 -2.94 0.0033 Nassau, NY 

a37 -0.49317 0.0311 -15.85 <.0001 New York, NY 

a38 -0.5545 0.00862 -64.34 <.0001 Suffolk, NY 

a39 -0.44578 0.0249 -17.90 <.0001 Newport, RI 

a40 -0.32647 0.00443 -73.75 <.0001 Washington, RI 

a41 0.074431 0.00335 22.20 <.0001 Accomack, VA 

a42 0.051687 0.0636 0.81 0.4164 Northhampton,VA 

b1 -0.44506 0.0125 -35.50 <.0001 Trip cost 

b2 -3.03E-6 3.197E-7 -9.49 <.0001 Trip cost squared 
77

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

b3 0.018823 0.00251 7.50 <.0001 Shellfish price 

b4 0.146146 0.00278 52.62 <.0001 Fluke price 

b5 0.03374 0.00263 12.83 <.0001 Bottomfish price 

b6 0.008325 0.00408 2.04 0.0416 Other price 

b7 0.097829 0.00888 11.01 <.0001 January 

b8 0.117101 0.00819 14.30 <.0001 February 

b9 0.130056 0.00781 16.66 <.0001 March 

b10 -0.01875 0.00834 -2.25 0.0247 April 

b11 -0.18139 0.0115 -15.84 <.0001 May 

b12 -0.14429 0.0130 -11.06 <.0001 June 

b13 -0.32948 0.0110 -29.88 <.0001 July 

b14 -0.47694 0.0183 -26.09 <.0001 August 

b15 -0.25446 0.0282 -9.02 <.0001 September 

b16 -0.07481 0.0268 -2.79 0.0053 October 

b17 0.055585 0.0115 4.82 <.0001 November 

b18 -0.01583 0.00478 -3.31 0.0009 2006 

b19 0.019175 0.00516 3.72 0.0002 2007 

b20 0.006146 0.1191 0.05 0.9588 Barnstable, MA 

b21 0.132865 0.00721 18.44 <.0001 Bristol, MA 

b22 0.099571 8.8394 0.01 0.9910 Dukes, MA 

b23 0.053652 0.9816 0.05 0.9564 Nantucket, MA 

b24 -0.02346 0.0367 -0.64 0.5225 Suffolk, MA 
78 

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

b25 0.018717 0.0635 0.29 0.7682 Worcester, MD 

b26 -0.08327 9.763E16 -0.00 1.0000 Hancock, ME 

b27 -0.04202 0.0109 -3.85 0.0001 Carteret, NC 

b28 -0.04533 0.0103 -4.38 <.0001 Dare, NC 

b29 -0.03068 0.0136 -2.26 0.0238 Hyde, NC 

b30 -0.0343 0.0119 -2.88 0.0040 Pamlico, NC 

b31 0.210426 1.122E18 0.00 1.0000 Atlantic, NJ 

b32 -0.00718 0.0256 -0.28 0.7794 Cape May, NJ 

b33 -0.00458 0.0464 -0.10 0.9214 Monmouth, NJ 

b34 -0.01279 0.0320 -0.40 0.6891 Ocean, NJ 

b35 0.115762 1.6726 0.07 0.9448 Kings, NY 

b36 -0.017 0.1251 -0.14 0.8919 Nassau, NY 

b37 0.019618 0.0736 0.27 0.7899 New York, NY 

b38 -0.05769 0.0226 -2.56 0.0106 Suffolk, NY 

b39 0.827602 0.00758 109.25 <.0001 Newport, RI 

b40 0.074029 0.00766 9.66 <.0001 Washington, RI 

b41 -0.03384 0.0148 -2.28 0.0226 Accomack, VA 

b42 0.01219 0.0498 0.24 0.8065 Northhampton,VA 

c1 0.037653 0.00599 6.28 <.0001 Trip cost 

c2 -5.53E-6 1.382E-7 -39.97 <.0001 Trip cost squared 

c3 0.018823 0.00251 7.50 <.0001 Bait price 

c4 0.030578 0.00148 20.59 <.0001 Fluke price 
79

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

c5 -0.0219 0.00130 -16.87 <.0001 Bottomfish price 

c6 0.001815 0.00166 1.10 0.2734 Other price 

c7 0.028104 0.00505 5.57 <.0001 January 

c8 0.032278 0.00452 7.15 <.0001 February 

c9 0.033332 0.00419 7.95 <.0001 March 

c10 0.089267 0.00418 21.37 <.0001 April 

c11 -0.0602 0.00790 -7.62 <.0001 May 

c12 -0.07272 0.0135 -5.39 <.0001 June 

c13 -0.08586 0.00850 -10.10 <.0001 July 

c14 -0.13983 0.0275 -5.08 <.0001 August 

c15 -0.08786 0.0209 -4.21 <.0001 September 

c16 -0.04082 0.0183 -2.23 0.0255 October 

c17 0.012731 0.00705 1.81 0.0709 November 

c18 -0.006 0.00263 -2.28 0.0225 2006 

c19 0.012563 0.00240 5.24 <.0001 2007 

c20 0.009917 0.1971 0.05 0.9599 Barnstable, MA 

c21 0.030536 0.00885 3.45 0.0006 Bristol, MA 

c22 0.024772 9.5935 0.00 0.9979 Dukes, MA 

c23 0.026087 1.5421 0.02 0.9865 Nantucket, MA 

c24 0.172124 0.00639 26.92 <.0001 Suffolk, MA 

c25 0.001982 0.0501 0.04 0.9684 Worcester, MD 

c26 0.008231 1.32E17 0.00 1.0000 Hancock, ME 
80 

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

c27 0.0027 0.00683 0.40 0.6927 Carteret, NC 

c28 -0.00061 0.00808 -0.08 0.9394 Dare, NC 

c29 -0.0063 0.00832 -0.76 0.4484 Hyde, NC 

c30 -0.00501 0.00745 -0.67 0.5014 Pamlico, NC 

c31 -0.00806 6.008E17 -0.00 1.0000 Atlantic, NJ 

c32 0.087259 0.00601 14.53 <.0001 Cape May, NJ 

c33 0.03567 0.0219 1.63 0.1026 Monmouth, NJ 

c34 0.022706 0.0113 2.01 0.0439 Ocean, NJ 

c35 0.044077 3.6738 0.01 0.9904 Kings, NY 

c36 0.033455 0.0969 0.35 0.7299 Nassau, NY 

c37 0.020328 0.0615 0.33 0.7410 New York, NY 

c38 0.012958 0.00877 1.48 0.1396 Suffolk, NY 

c39 0.307557 0.00556 55.34 <.0001 Newport, RI 

c40 0.193572 0.00452 42.83 <.0001 Washington, RI 

c41 -0.01817 0.00970 -1.87 0.0611 Accomack, VA 

c42 -0.04748 0.0665 -0.71 0.4750 Northhampton,VA 

d1 -0.10948 0.00459 -23.86 <.0001 Trip cost 

d2 -7.23E-6 1.531E-7 -47.24 <.0001 Trip cost squared 

d3 -0.0219 0.00130 -16.87 <.0001 Shellfish price 

d4 0.03374 0.00263 12.83 <.0001 Bait price 

d5 0.260425 0.00195 133.86 <.0001 Fluke price 

d6 0.065053 0.00208 31.30 <.0001 Other price 
81

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

d7 0.081627 0.00397 20.57 <.0001 January 

d8 0.049761 0.00387 12.85 <.0001 February 

d9 0.099907 0.00379 26.34 <.0001 March 

d10 0.050005 0.00400 12.50 <.0001 April 

d11 -0.03337 0.00700 -4.77 <.0001 May 

d12 -0.11853 0.0138 -8.59 <.0001 June 

d13 -0.13317 0.00937 -14.21 <.0001 July 

d14 -0.19932 0.0112 -17.72 <.0001 August 

d15 -0.11598 0.0182 -6.37 <.0001 September 

d16 -0.07851 0.0260 -3.02 0.0026 October 

d17 -0.04615 0.00691 -6.68 <.0001 November 

d18 -0.04845 0.00178 -27.19 <.0001 2006 

d19 -0.09676 0.00260 -37.27 <.0001 2007 

d20 -0.10674 0.1663 -0.64 0.5210 Barnstable, MA 

d21 -0.06499 0.00790 -8.22 <.0001 Bristol, MA 

d22 -0.08734 3.2037 -0.03 0.9783 Dukes, MA 

d23 -0.13857 0.8506 -0.16 0.8706 Nantucket, MA 

d24 -0.1047 0.0138 -7.58 <.0001 Suffolk, MA 

d25 -0.11409 0.0418 -2.73 0.0063 Worcester, MD 

d26 -0.16508 3.049E16 -0.00 1.0000 Hancock, ME 

d27 -0.01477 0.00319 -4.63 <.0001 Carteret, NC 

d28 0.001125 0.00331 0.34 0.7341 Dare, NC 
82 

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

d29 -0.01235 0.00315 -3.92 <.0001 Hyde, NC 

d30 -0.06864 0.00347 -19.76 <.0001 Pamlico, NC 

d31 -0.08027 2.999E17 -0.00 1.0000 Atlantic, NJ 

d32 -0.0381 0.00877 -4.35 <.0001 Cape May, NJ 

d33 -0.07258 0.0135 -5.38 <.0001 Monmouth, NJ 

d34 -0.00884 0.00994 -0.89 0.3742 Ocean, NJ 

d35 -0.11259 2.6121 -0.04 0.9656 Kings, NY 

d36 -0.04273 0.0544 -0.79 0.4320 Nassau, NY 

d37 -0.22999 0.0675 -3.41 0.0007 New York, NY 

d38 -0.12458 0.0133 -9.35 <.0001 Suffolk, NY 

d39 -0.04356 0.00719 -6.05 <.0001 Newport, RI 

d40 0.056146 0.00287 19.53 <.0001 Washington, RI 

d41 0.009314 0.00305 3.06 0.0022 Accomack, VA 

d42 -0.02213 0.0632 -0.35 0.7264 Northhampton,VA 

e1 -0.23916 0.00677 -35.30 <.0001 Trip cost 

e2 -4.46E-7 2.602E-7 -1.71 0.0866 Trip cost squared 

e3 0.001815 0.00166 1.10 0.2734 Shellfish price 

e4 0.008325 0.00408 2.04 0.0416 Bait price 

e5 0.065053 0.00208 31.30 <.0001 Bottomfish price 

e6 0.040109 0.00262 15.33 <.0001 Fluke price 

e7 -0.01498 0.00517 -2.90 0.0038 January 

e8 0.018399 0.00631 2.92 0.0035 February 
83

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

e9 0.043759 0.00466 9.40 <.0001 March 

e10 0.005475 0.00644 0.85 0.3952 April 

e11 -0.01309 0.0193 -0.68 0.4976 May 

e12 0.03273 0.0642 0.51 0.6103 June 

e13 0.012122 0.0282 0.43 0.6673 July 

e14 0.066595 0.0502 1.33 0.1846 August 

e15 0.106912 0.0202 5.29 <.0001 September 

e16 0.289763 0.0122 23.79 <.0001 October 

e17 0.062746 0.00894 7.02 <.0001 November 

e18 -0.00458 0.00408 -1.12 0.2611 2006 

e19 0.065444 0.00403 16.24 <.0001 2007 

e20 0.025129 0.2549 0.10 0.9215 Barnstable, MA 

e21 -0.02198 0.0237 -0.93 0.3529 Bristol, MA 

e22 0.039439 9.7616 0.00 0.9968 Dukes, MA 

e23 0.119831 1.0603 0.11 0.9100 Nantucket, MA 

e24 0.045496 0.0435 1.05 0.2960 Suffolk, MA 

e25 0.034552 0.1075 0.32 0.7480 Worcester, MD 

e26 0.008059 3.58E17 0.00 1.0000 Hancock, ME 

e27 0.000416 0.00889 0.05 0.9627 Carteret, NC 

e28 0.181269 0.00451 40.20 <.0001 Dare, NC 

e29 0.011869 0.00800 1.48 0.1379 Hyde, NC 

e30 0.020514 0.00635 3.23 0.0012 Pamlico, NC 
84 

Nonlinear FIML Parameter Estimates 

Parameter Estimate Approx Std Err t Value Approx

Pr > |t| 

Label 

e31 -0.05007 1.064E18 -0.00 1.0000 Atlantic, NJ 

e32 0.022965 0.0158 1.45 0.1461 Cape May, NJ 

e33 -0.0161 0.0985 -0.16 0.8701 Monmouth, NJ 

e34 -0.05755 0.0572 -1.01 0.3142 Ocean, NJ 

e35 -0.01267 2.5331 -0.01 0.9960 Kings, NY 

e36 -0.04861 0.2739 -0.18 0.8591 Nassau, NY 

e37 0.068423 0.1596 0.43 0.6682 New York, NY 

e38 -0.05634 0.0339 -1.66 0.0963 Suffolk, NY 

e39 0.010408 0.0921 0.11 0.9100 Newport, RI 

e40 0.013139 0.0113 1.17 0.2429 Washington, RI 

e41 0.006534 0.0123 0.53 0.5948 Accomack, VA 

e42 -0.02604 0.0563 -0.46 0.6439 Northhampton,VA 

Restrict0 1854.302 281.7 6.58 <.0001 a3 = c4 

Restrict1 266.5896 91.6066 2.91 0.0036 a4 = b4 

Restrict2 524.3278 200.8 2.61 0.0090 a5 = d5 

Restrict3 769.542 165.9 4.64 <.0001 a6 = e6 

Restrict4 2786.622 189.4 14.72 <.0001 b3 = c3 

Restrict5 1271.905 185.2 6.87 <.0001 b5 = d4 

Restrict6 989.5236 114.8 8.62 <.0001 b6 = e4 

Restrict7 1340.12 376.4 3.56 0.0004 c5 = d3 

Restrict8 -1973.56 260.1 -7.59 <.0001 c6 = e3 

Restrict9 -831.902 238.4 -3.49 0.0005 d6 = e5 
85

Test Results (pre symmetry restriction) 

Test Type Statistic Pr > ChiSq Label 

nonjointness Wald 91427 <.0001 a3, a4, a5, a6, b3, b4, b5, b6, c3, c4, c5 

, c6, d3 , d4 , d5 , d6, e3 , e4 , e5 , e6 

fluke nj Wald 19333 <.0001 a3 , a4 , a5 , a6 

bait nj Wald 14211 <.0001 b3 , b4 , b5 , b6 

shell nj Wald 774.54 <.0001 c3 , c4 , c5 , c6 

bottom nj Wald 47061 <.0001 d3 , d4 , d5 , d6 

other nj Wald 5350.5 <.0001 e3 , e4 , e5 , e6 

separability Wald 19418 <.0001 a1 , b1 , c1 , d1 , e1 

Heteroscedasticity Test 

Equation Test Statistic DF Pr > ChiSq Variables 

FLUKELB White's Test 14311 490 <.0001 Cross of all vars 

baitlb White's Test 6270 490 <.0001 Cross of all vars 

shelllb White's Test 11032 490 <.0001 Cross of all vars 

bottlb White's Test 9352 490 <.0001 Cross of all vars 

otherlb White's Test 8323 490 <.0001 Cross of all vars 
86 
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