A Meta-Analysis of Recreational Fishing Values

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What Determines Willingness to Pay per Fish? A Meta-Analysis of Recreational Fishing Values

ROBERT J. JOHNSTON University of Connecticut MATTHEW H. RANSON ELENA Y. BESEDIN Abt Associates Inc. ERIK C. HELM NOAA/National Marine Fisheries Service

Abstract The use of estimated willingness to pay (WTP) to evaluate welfare associated with changes in the quality of recreational fishing presumes that WTP reflects variations in resource and policy attributes, and is not inappropri- ately influenced by attributes of applied non-market study methodology. This paper describes a meta-analysis conducted to identify systematic patterns in marginal WTP per fish among recreational anglers. Results establish the presence of systematic WTP variation associated with resource, context, and angler attributes, yet also indicate that WTP is subject to systematic variation associated with study methodology. While results are promising with regard to the ability of non-market research to provide insight regarding WTP for recreational fishery resources, they also suggest that researchers should consider the potential for methodological effects when conducting applied welfare analysis.

Key words Meta-analysis, recreational fishing, valuation methodology, willingness to pay, benefit transfer.

JEL Classification Codes Q2, Q22, Q26.

Introduction

Benefit cost analyses of programs affecting fresh and saltwater resources often in- corporate assessments of willingness to pay (WTP) for changes in the quality of recreational fishing sites (e.g., US EPA 2000, 2003, 2004). The use of WTP estimates for welfare assessment in these cases presumes that such measures provide

Robert J. Johnston is an assistant professor in the Department of Agricultural and Resource Economics, University of Connecticut Avery Point Campus, 1080 Shennecossett Rd., Groton, CT 06340, email: [email protected]. Matthew H. Ranson is an analyst with Abt Associates Inc., 4800 Montgom- ery Lane, Suite 600, Bethesda, MD 20814, email: [email protected]. Elena Y. Besedin is an as- sociate and project manager with Abt Associates Inc., 55 Wheeler Street, Cambridge, MA 02138, email: [email protected]. Erik C. Helm is an economist with the National Marine Fisheries Service, NOAA, 1315 East West Highway, Silver Spring, MD 20910, email: [email protected]. This research was partially supported by U.S. EPA Contract No. 68-C-99-239 and by Connecticut Sea Grant. Opinions belong solely to the authors and do not necessarily reflect the views or policies of U.S. EPA or Connecticut Sea Grant, or imply endorsement by the funding agencies.

1 2 Johnston, Ranson, Besedin, and Helm useful insights into true underlying WTP, notwithstanding potential biases associated with the use of various methods of nonmarket valuation (cf. Freeman 2003). More specifically, it is presumed that estimated WTP for recreational fishing varies systematically according to such elements as resource type, policy context, angler characteristics, and scope (e.g., Smith and Osborne 1996; Johnston, Besedin, and Wardwell 2003), and that such desirable variation is not overshadowed by systematic yet sometimes undesirable variation associated with applied research methods (Markowski et al. 2002). Aside from direct implications for the validity of WTP estimates, the source of potential variation in WTP for recreational fishing has important implications for benefit transfer. Benefit transfer may be characterized as the “practice of taking and adapting value estimates from past research … and using them … to assess the value of a similar, but separate, change in a different resource” (Smith, Van Houtven, and Pattanayak 2002, p. 134). Such methods are frequently encountered in benefit cost analyses of government programs (Bergstrom and De Civita 1999; Desvousges, Johnson, and Banzhaf 1998). This ubiquity notwithstanding, if welfare measures cannot be shown to vary systematically according to key attributes distinguishing study and policy sites, the validity of benefit transfer becomes questionable. The validity of benefit transfer may also be called into question if a large proportion of WTP variation is associated with study methodology or otherwise unexplained study-level effects, rather than identifiable attributes of resources, affected popula- tions, or policy contexts (Johnston et al. 2005). The use of estimated WTP to evaluate welfare associated with changes in the quality of recreational fishing, then, presumes that WTP reflects variations in resource and policy attributes, and is not strongly influenced by methodological attributes. Nonetheless, evidence from studies addressing non-fish resources suggests that estimates of both revealed and stated WTP are subject to influence from methodological attributes (e.g., Boyle, Poe, and Bergstrom 1994; Poe, Boyle, and Bergstrom 2001; Bateman and Jones 2003; Smith and Kaoru 1990; Smith and Osborne 1996; Johnston, Besedin, and Wardwell 2003; Brouwer et al. 1999; Rosenberger and Loomis 2000b). As noted by Markowski et al. (2002), this often implies the presence of “experimentally-induced biases in welfare estimates.” While the potential for such biases is frequently associated with stated preference methods, there is also evidence that methodological attributes of revealed preference methods may influence WTP (Markowski et al. 2002; Walsh, Johnson, and McKean 1992; Rosenberger and Loomis 2000b). Meta-analysis has been drawing increased attention as a means to assess causes of systematic variation in WTP, and thereby assess the validity of WTP estimates for policy applications, including benefit transfer. Recent applications of meta-analysis to assess systematic variation in WTP include, among others, Johnston, Besedin, and Wardell’s (2003) assessment of patterns in use and nonuse values for water quality improvements and Smith and Osborne’s (1996) examination of scope-sensitivity in stated WTP for air quality improvements. Despite these and other recent works, however, applications of meta-analysis in resource and environmental economics remain relatively uncommon. Moreover, notwithstanding unpublished work by Markowski et al. (2002) and Sturtevant, Johnson, and Desvousges (1998), the authors are aware of no large-scale, published meta-analyses that focus solely on WTP for recreational fishing. This paper describes a meta-analysis conducted to identify systematic patterns in WTP for recreational fishing, emphasizing implications for policy analysis. The purpose of the analysis is to assess whether variation in WTP for increased recreational catch may be explained sufficiently by systematic variation in resource, context, and angler attributes to justify the use of such measures for policy analysis, Meta-Analysis of Recreational Fishing Values 3 or whether WTP variation is dominated by methodological or unexplained study- level factors. Based on model results, we discuss practical implications for welfare evaluation and benefit transfer in policy contexts involving recreational fisheries.

Data and Conceptual Approach

Theory indicates that WTP for changes in the quality of recreational fishing sites should vary systematically according to variables characterizing resource, context, and angler attributes. Indeed, lack of responsiveness to such variables may be seen as an indication that WTP estimates are invalid or biased. In the current meta-data, these variables characterize such factors as: species targeted, geographic region, water body type, catch rates, angler demographics, and fishing method. In contrast, theory typically indicates that WTP should not vary according to methodological attributes—with the exception of those that would cause different components or types of WTP to be estimated (e.g., use WTP only versus a combination of use and nonuse WTP; stated WTP estimated under different information sets) (Johnston, Besedin, and Wardwell 2003). This is the rationale for the meta-analysis presented here: that assessment of the systematic influence of resource, context, and angler attributes on WTP—compared to systematic influences of study methodology—may provide insight into the validity of WTP estimates. Because policy analyses often call for welfare estimates denominated in per fish units (e.g., US EPA 2004), the model presented here estimates effects of independent variables on estimated WTP per angler for the catch of one additional fish—an additional departure from prior work (e.g. , Markowski et al. 2002). The data are drawn from non-market valuation studies that estimate the marginal value (or WTP) that anglers place on catching an additional fish or allow such a value to be calculated. An in-depth search of the economic literature revealed over 450 journal articles, academic working papers, reports, books, and dissertations that were potentially relevant for this analysis.1 Of these, 48 studies were considered suitable for inclusion in the meta-data. Specific criteria for inclusion were: (i) a requirement that the study estimate the marginal value that recreational anglers place on catching an additional fish (WTP) or provide sufficient information to allow such a value to be calculated; (ii) a limitation to studies conducted in the U.S. or Canada; (iii) a requirement that the study apply primary research methods widely supported by the economics literature; and (iv) a requirement that the study provide sufficient information on resource, angler, context, and study attributes to warrant inclusion. The resulting meta-data comprise 391 observations from 48 unique studies conducted between 1977 and 2001. All included studies apply generally accepted valuation methods, such as contingent valuation, travel cost models, or random utility models to assess WTP for increased recreational catch. As noted above, studies were excluded if they were not grounded in recognized concepts of economic

1 Sources reviewed included: (a) US EPA research and bibliographies dealing with recreational fishing benefits; (b) resource and environmental economics journals (e.g., Land Economics, Journal of Agricul- tural and Resource Economics, Journal of Environmental Economics and Management, Water Resources Research, etc.); (c) reference and abstract databases (e.g., Environmental Valuation Resource Inventory (EVRI), the Fish and Wildlife Service’s Database of Sportfishing Values); (d) academic search engines (e.g., EconLit, ISI Web of Science, Index of Digital Dissertations); (e) homepages of authors known to have published valuation studies of recreational fishing; (f) web sites of agricultural and resource economics departments at colleges and universities; and (g) web sites of organizations known to publish environmental and resource economics valuation research (e.g. , Resources for the Future (RFF), Na- tional Center for Environmental Economics (NCEE), National Oceanic and Atmospheric Administration (NOAA), Library of Congress’ Congressional Research Service). 4 Johnston, Ranson, Besedin, and Helm theory, or if applied methods did not conform to generally accepted practice. The 48 studies include 24 journal articles, 15 reports, five Ph.D. dissertations, three academic papers, and one book. The number of observations (391) exceeds the number of studies (48) because studies typically provide more than one estimate of WTP. Multiple WTP estimates from a single study are available due to in-study variations in such factors as baseline catch rate, the species being valued, locations where fish are caught, fishing method (e.g., boat versus shore), and valuation methodology applied. Table 1 summarizes principal study characteristics for those studies included in the metadata. Two hundred and nine observations are derived from random utility (RUM) or discrete choice models, 59 observations are derived from individual or multiple-site travel cost models, and 122 observations are derived from stated preference methods. Response rates from individual studies range from 38% to 99%, with sample sizes from 72 to 36,802. Marginal WTP per fish was provided by the authors for 298 of the 391 observations; for the remaining 93 observations, WTP per fish was calculated based on data provided by the original study. All per-fish WTP values were converted to June 2003 dollars. Resulting real WTP per fish over the sample ranged from $0.048 to $612.79, with a mean of $16.82.2 Independent variables included in the meta-analysis are derived from a list of attributes with potential influence on WTP per fish, based on theory and prior findings in the empirical literature. These variables are divided into two general categories. These include: (i) resource, context, and angler attributes; and (ii) study methodology attributes. Table 2 characterizes the full set of independent variables included in one or more estimated models. Although the interpretation and calculation of most variables is relatively straightforward, the specification of a small number of variables warrants additional explanation. These include the dependent variable, which characterizes marginal WTP per fish. The majority of studies provide estimates of marginal WTP per fish. However, approximately one-quarter of the observations (93) do not provide this information directly. In these cases, WTP per fish was calculated using one of two approaches. Where possible, regression coefficients provided in the original studies were used to calculate marginal WTP per fish directly.3 In 52 cases where WTP per fish could not be calculated from regression coefficients, either because the regression equa- tion was non-linear or because the study estimated WTP for a specified percentage change in catch rates, linear extrapolation was used to approximate marginal WTP.4 Angler income (inc_thou) was calculated using a combination of data provided by original studies and income averages from the U.S. Census. Of the 391 observations in the data, 203 provide information on angler income. For the remaining 188 observations, angler income is imputed based on U.S. Census averages for the specific region(s) addressed by the source study (e.g., county, state, group of states). While such in-filling is an unavoidable consequence of missing income data in source studies, it may generate errors-in-variables if angler income differs from population averages. To address this possibility, different specifications of income were tested in preliminary models, including the use of distinct variables for income provided by source studies

2 If two outlier observations corresponding to Morey, Shaw, and Rowe (1993) are excluded, WTP for catching an additional fish ranged from $0.048 to $327.29, with a mean of $14.33. 3 For example, in studies applying random utility models (RUM), angler WTP for catching an additional fish may be calculated as a ratio of the first derivative of the estimated utility function with respect to the travel cost and the first derivative with respect to catch rate. This is interpreted as the change in travel cost that is just sufficient to return a representative angler to a baseline level of utility, subsequent to a one-fish increase in catch rate that causes an increase in utility above the baseline. 4 In most cases, this involved calculating average WTP per fish for a specified increase in catch rates. For example, if a study reported that the average angler is willing to pay $10 per trip to catch an additional two fish per trip, then we calculated average marginal WTP per fish as $10 divided by two fish, or $5 per fish. Meta-Analysis of Recreational Fishing Values 5 6 Johnston, Ranson, Besedin, and Helm Meta-Analysis of Recreational Fishing Values 7 8 Johnston, Ranson, Besedin, and Helm Meta-Analysis of Recreational Fishing Values 9 10 Johnston, Ranson, Besedin, and Helm Meta-Analysis of Recreational Fishing Values 11

Table 2 Meta-Analysis Variables and Descriptive Statistics

Units Mean Variable a Description (Range) (Std. Dev.) log_WTP Natural log of the marginal value per Natural log of dollars 1.8419 fish. (–3.0260 to 6.4180) (1.3165) SP_conjoint Binary (dummy) variable indicating Binary variable 0.0435 that the study used conjoint or choice- (0 to 1) (0.2042) experiment stated preference methodology. SP_dichot Binary (dummy) variable indicating Binary variable 0.1739 that the study used stated preference (0 to 1) (0.3795) methodology with a dichotomous choice elicitation format. TC_individual Binary (dummy) variable indicating Binary variable 0.1074 that the study used a travel cost model (0 to 1) (0.3100) based on the number of trips taken by individual respondents to recreational sites. TC_zonal Binary (dummy) variable indicating that Binary variable 0.0409 the study used a zonal travel cost model (0 to 1) (0.1984) based on the aggregate number of trips taken to recreational sites by visitors who live within specified distance ranges. RUM_nest Binary (dummy) variable indicating Binary variable 0.2353 that the study used a nested random (0 to 1) (0.4247) utility model. RUM_nonnest Binary (dummy) variable indicating Binary variable 0.3043 that the study used a non-nested (0 to 1) (0.4607) random utility model. SP_year If the study used stated preference Year index 4.6036 methodology, this variable represents (0 to 25) (7.3592) the year in which the study was conducted, converted to an index by subtracting 1976; otherwise, this variable is set to zero. TC_year If the study used travel cost methodology, Year index 0.7315 this variable represents the year in which (0 to 18) (2.1914) the study was conducted, converted to an index by subtracting 1976; otherwise, this variable is set to zero. RUM_year If the study used RUM methodology, Year index 9.3734 this variable represents the year in which (0 to 25) (9.7162) the study was conducted, converted to an index by subtracting 1976; otherwise, this variable is set to zero. sp_mail Binary (dummy) variable indicating that Binary variable 0.0512 the study was a stated preference study (0 to 1) (0.2206) administered by mail. sp_phone Binary (dummy) variable indicating Binary variable 0.1304 that the study was a stated preference (0 to 1) (0.3372) study administered by phone. 12 Johnston, Ranson, Besedin, and Helm

Table 2 continued Meta-Analysis Variables and Descriptive Statistics

Units Mean Variable a Description (Range) (Std. Dev.) high_resp_rate Binary (dummy) variable indicating Binary variable 0.3581 that the sample response rate was (0 to 1) (0.4800) greater than 50%. inc_thou Household income of survey respondents 1,000s of June 46.7008 in thousands of dollars. If the study does 2003 dollars (10.2017) not list income values, inc_thou was (21.990 to 70.610) imputed from Census data. age42_down Binary (dummy) variable indicating Binary variable 0.0972 that the mean age of sample respondents (0 to 1) (0.2966) was less than 43. If the mean sample age was greater than or equal to 43, or was not reported, this variable was set equal to zero. age43_up Binary (dummy) variable indicating Binary variable 0.2711 that the mean age of sample respondents (0 to 1) (0.4451) was 43 or greater. If the mean sample age was less than 43, or was not reported, this variable was set equal to zero. trips19_down Binary (dummy) variable indicating that Binary variable 0.1100 the mean number of fishing trips taken (0 to 1) (0.3133) each year by sample respondents was less than 20. If the mean number of trips was not reported, this variable was set equal to zero. trips20_up Binary (dummy) variable indicating Binary variable 0.3350 that the mean number of fishing trips (0 to 1) (0.4726) taken each year by sample respondents was 20 or greater. If the mean number of trips was not reported, this variable was set equal to zero. nonlocal c Binary (dummy) variable indicating Binary variable 0.0051 that no respondents in the sample were (0 to 1) (0.0714) local residents. big_game_pac c Binary (dummy) variable indicating Binary variable 0.0077 that the target species was big game in the (0 to 1) (0.0874) California or Pacific Northwest regions. big_game_natl Binary (dummy) variable indicating Binary variable 0.0486 that the target species was big game in the (0 to 1) (0.2153) North Atlantic or Mid-Atlantic regions. big_game_satl Binary (dummy) variable indicating Binary variable 0.0205 that the target species was big game in the (0 to 1) (0.1418) South Atlantic or Gulf of Mexico regions. small_game_pac Binary (dummy) variable indicating Binary variable 0.0281 that the target species was small game in (0 to 1) (0.1656) the California or Pacific Northwest regions. Meta-Analysis of Recreational Fishing Values 13

Table 2 continued Meta-Analysis Variables and Descriptive Statistics

Units Mean Variable a Description (Range) (Std. Dev.) small_game_atl Binary (dummy) variable indicating Binary variable 0.1611 that the target species was small game (0 to 1) (0.3681) in the North Atlantic, Mid-Atlantic, South Atlantic, or Gulf of Mexico regions. flatfish_pac Binary (dummy) variable indicating Binary variable 0.0179 that the target species was flatfish in the (0 to 1) (0.1328) California or Pacific Northwest regions. flatfish_atl Binary (dummy) variable indicating Binary variable 0.0997 that the target species was flatfish in (0 to 1) (0.3000) the North Atlantic, Mid-Atlantic, South Atlantic, or Gulf of Mexico regions. other_sw Binary (dummy) variable indicating Binary variable 0.2276 that the target species was bottom fish (0 to 1) (0.4198) or other saltwater species. musky c Binary (dummy) variable indicating Binary variable 0.0026 that the target species was muskellunge. (0 to 1) (0.0506) pike_walleye Binary (dummy) variable indicating Binary variable 0.0307 that the target species was northern (0 to 1) (0.1727) pike or walleye. bass_fw Binary (dummy) variable indicating Binary variable 0.0358 that the target species was largemouth (0 to 1) (0.1860) bass or smallmouth bass. trout_GL Binary (dummy) variable indicating Binary variable 0.0128 that the target species was trout in (0 to 1) (0.1125) the Great Lakes region. trout_nonGL Binary (dummy) variable indicating Binary variable 0.1253 that the target species was trout in (0 to 1) (0.3315) states outside the Great Lakes region. salmon_pacific Binary (dummy) variable indicating Binary variable 0.0844 that the target species was salmon on (0 to 1) (0.2783) the Pacific coast. salmon_atl_Moreyc Binary (dummy) variable indicating Binary variable 0.0051 that the target species was salmon on (0 to 1) (0.0714) the Atlantic coast. salmon_GL Binary (dummy) variable indicating Binary variable 0.0230 that the target species was salmon in (0 to 1) (0.1502) the Great Lakes. steelhead_pac Binary (dummy) variable indicating Binary variable 0.0358 that the target species was steelhead (0 to 1) (0.1860) on the Pacific coast. steelhead_GL c Binary (dummy) variable indicating Binary variable 0.0051 that the target species was steelhead (0 to 1) (0.0714) in the Great Lakes. 14 Johnston, Ranson, Besedin, and Helm

Table 2 continued Meta-Analysis Variables and Descriptive Statistics

Units Mean Variable a Description (Range) (Std. Dev.) cr_nonyear For studies that present catch rate on Fish per day 2.1038b a per-hour, per-day, or per-trip basis, (0 to 14.0000) (2.0403) this variable represents the baseline catch rate for the target species, expressed in fish per day or fish per trip; otherwise, this variable is set to zero. See text for calculation details. cr_year For studies that present catch rate on Fish per year 41.2277b a per-year basis, this variable represents (0 to 67.3800) (24.7833) the baseline catch rate for the target species, expressed in fish per year; otherwise, this variable is set to zero. catch_year Binary (dummy) variable indicating Binary variables 0.0716 that the study expressed catch rates (0 to 1) (0.2582) on a per-year basis. spec_cr Binary (dummy) variable indicating Binary variable 0.8440 that the study presents information (0 to 1) (0.3633) on the baseline catch rate. shore Binary (dummy) variable indicating Binary variable 0.1458 that all respondents in the sample (0 to 1) (0.3633) fished from shore. a The default variable values are: • A zero value for all of the study methodology variables (SP_conjoint, SP_dichot, TC_individual, TC_zonal, RUM_nested, and RUM_nonnested) indicates that the study used a stated preference methodology with an open-ended, iterative bidding, or payment card elicitation format. • A zero value for sp_mail and sp_phone indicates that a survey was administered by phone or in person. • A zero value for nonlocal indicates that the survey included local anglers or a mix of local and nonlocal anglers. • A zero value for all of the species/region variables indicates that the target species was panfish caught nationwide. • A zero value for shore indicates that survey respondents fished from boats or from both the shore and boats. b These values represent mean values and standard deviations only for those observations in which the variable value was specified (i.e., zero values are suppressed for the purposes of calculating the mean and standard deviation only). c An important qualification applies to the variables nonlocal, salmon_atlantic_Morey, big_game_pac, steelhead_GL, and musky . These variables were judged to represent unique categories of angler and species characteristics, and as such were included in the model. However, none of these variables represent more than three observations in the meta-data. Hence, results associated with these variables should be interpreted with caution, given that they might also capture study-level effects. Meta-Analysis of Recreational Fishing Values 15 and income imputed from Census data. None of the tested specifications outperformed the single, consolidated income variable (inc_thou) reported in table 2. Other variables that warrant further explanation include those characterizing targeted fish species. Original studies in the meta-data address a substantial variety of species, many of which are similar (e.g., different species of Pacific salmon). To re- duce the number of occasions in which a species-specific dummy variable distinguished only a single study, species were assigned to aggregate species groups. These assignments were based on the angling, biological, and regional characteristics of each species. The assigned groups include four saltwater groups (big game, small game, flatfish, and other saltwater fish), two anadromous groups (salmon and steelhead trout), and five freshwater groups (panfish, bass, walleye/pike, muskellunge, and trout). Species groups that could be harvested in a variety of geographic areas were further subdivided on the basis of regional differences, using multiplicative interactions between species group and region. Table 3 shows the species assigned to each aggregate species group.

Table 3 Aggregate Species Groups in the Meta-Analysis

Number of Group Name Observations Species Includeda,b

Big game 30 billfish family, dogfish, rays, sharks, skates, sturgeon, swordfish, tarpon family, tuna, other big game Small game 74 barracuda, bluefish, bonito, cobia, Dolly Varden, dolphinfish, jacks, mackerel, red drum, seatrout, striped bass, weakfish, other small game Flatfish 46 halibut, sanddab, summer flounder, winter flounder, other flatfish Other saltwater 89 banded drum, black drum, chubbyu, cod family, cow cod, croaker, grouper, grunion, grunt, high-hat, kingfish, lingcod, other drum, perch, porgy, rockfish, sablefish, sand drum, sculpin, sea bass, smelt, snapper, spot, spotted drum, star drum, white sea bass, wreckfish, other bottom species, other coastal pelagics, “no target” saltwater species Salmon 44 Atlantic salmon, chinook salmon, coho salmon, other salmon Steelhead 16 steelhead trout, rainbow trout (in Great Lakes only)b Muskellunge 1 muskellunge Walleye/pike 12 northern pike, walleye Bass 14 largemouth bass, smallmouth bass Panfish 11 catfish, carp, yellow perch, other panfish, “general” and “no target” freshwater species Trout 54 brown trout, lake trout, rainbow trout, other trout a Some studies evaluated WTP for groups of species that did not fit cleanly into one of the aggregate species groups. In those cases, the groups of species from the study were assigned to the aggregate species group with which they shared the most species. b Rainbow trout in the Great Lakes were classified as steelhead trout because they share similar physical characteristics and life cycles with true anadromous steelhead. Although they have different common names, rainbow trout and steelhead both belong to the species Oncorhynchus mykiss. 16 Johnston, Ranson, Besedin, and Helm

In some cases, the original studies estimated WTP for aggregates of fairly di- verse species. In such cases, group assignments for the meta-data were made based on characteristics of the preponderance of species. For example, Schuhmann’s (1996) estimate of WTP to catch an additional billfish, swordfish, tarpon, shark, skate, ray, or dogfish was assigned to the big game category. This category was assigned because the majority of species in the original group are considered big game, despite the fact that some of these species (e.g., skate) would not be placed into the same category if considered individually. To further illustrate the types of methodologies applied to species group, table 4 illustrates a cross-tabulation of species/methodology combinations represented by at least one observation in the meta-data. A final set of variables that warrants additional explanation includes those characterizing average baseline catch rates (i.e., prior to improvements). Studies in the meta-data expressed catch rates using four different measurement conventions: fish/ hour, fish/day, fish/trip, and fish/year. Rather than include four distinct catch rate variables, we combine per-hour, per-day, and per-trip catch rates into a normalized variable denoted cr_nonyear, which transforms catch rates to per-day units.5 Per-year catch rates were specified as a separate variable, cr_year, with an additional dummy variable identifying those studies in which catch rates were so specified (catch_year). Finally, spec_cr indicates whether catch rates were provided by the original study (84% of the observations in the meta-data specify baseline catch rates).

The Empirical Model

Past meta-analyses have incorporated a range of statistical methods, with none uni- versally accepted as superior. Moreover, the literature provides mixed guidance on several specification and estimation issues (Poole and Greenland 1999; Johnston, Besedin, and Wardwell 2003; Johnston et al. 2005). Despite the variation in statistical approaches to meta-analysis, the literature has reached consensus on many issues. For example, there is general consensus that meta-models must somehow address potential correlation among observations provided by like authors or studies and the associated potential for heteroskedasticity (Bateman and Jones 2003; Rosenberger and Loomis 2000a,b). The present analysis follows recent work of Bateman and Jones (2003) and Johnston, Besedin, and Wardwell (2003) and applies a random effects model. As meta-data are often comprised of multiple observations per study, there is a possibility of correlated errors among observations that share survey data or author. To account for this potential correlation, random effects models divide the residual variance of estimates into two or more parts: a random error that is independently and identically distributed across all studies and for each observation, and one or more random effects that represent systematic variation related to studies, authors, or both. Most often, random effects models are estimated as a two-level hierarchy. Here, level one corresponds to individual estimates of WTP per fish (individual observations), and level two corresponds to individual studies or valuation surveys.6

5 For example, per-hour catch rates were converted to per-day catch rates by multiplying by the number of hours fished per day, as provided in the study. In cases where the study did not provide information on fishing day length, a four-hour fishing day was assumed. 6 Some individually published studies included in the meta-data rely on common valuation surveys (i.e., primary data). Where this occurs, the level-two effect is specified at the level of the valuation survey. For example, both Hicks et al. (1999) and U.S. EPA (2004) used data from the 1994 Marine Recre- ational Fisheries Statistics Survey. Meta-Analysis of Recreational Fishing Values 17 18 Johnston, Ranson, Besedin, and Helm

The model is estimated using maximum likelihood assuming that random effects are distributed multivariate normal, with robust variance estimation to account for potential heteroskedasticity across studies (Smith and Osborne 1996). Trials with functional forms led to the selection of a semi-log model, in which the natural log of WTP per fish is regressed against linear explanatory variables. The semi-log functional form was also chosen based on its ability to capture curvature in the valuation function, because it allows independent variables to influence WTP in a multiplicative rather than additive manner, and based on its common use in past meta-analyses (e.g., Smith and Osborne 1996; Johnston, Besedin, and Wardwell 2003). The issue of weighting (i.e., of observations within the statistical model) is one that has generated some controversy within the meta-analysis literature (for compet- ing perspectives, see Markowski et al. 2002 and Bateman and Jones 2003). The literature provides numerous examples of both weighted and unweighted models (e.g., Poe, Boyle, and Bergstrom 2001; Johnston, Besedin, and Wardwell 2003; Markowski et al. 2002; Rosenberger and Loomis 2000a,b). Weighted specifications prevent studies that provide multiple observations from unduly influencing model estimation, but also imply that such studies are no more informative, overall, than others (Bateman and Jones 2003). While this may be true when measuring the effects of variables with little intra-study variation (e.g., study methodology), it may not be true for variables with high levels of intra-study variation (e.g., species targeted). Given the lack of clear precedent in the literature, we illustrate results for both weighted and unweighted model specifications. Following common practice (e.g., Poe, Boyle, and Bergstrom 2001; Mrozek and Taylor 2002), the weighted model is specified such that each study is given identical weight in the analysis (i.e., weights on multiple observations within individual studies sum to one).

Model Results and Discussion

Statistical results are found in table 5. Model one is an unrestricted model, including the full set of variables listed in table 2. Model two is a restricted model, distinguished from model one by the omission of variables characterizing resource, context, and angler attributes (i.e., only methodological variables remain). Model three is a restricted model, from which all variables characterizing study methodology have been omitted. Model four is an unrestricted weighted model, with variables identical to those in model one. Likelihood ratio tests indicate that models one, three, and four (unrestricted and methodology-omitted models) are statistically significant at p < 0.01 (c 2 = 231.8, 185.0, and 192.5 with df = 41, 29, and 41, re- spectively). Model two (the methodology-only model) may be shown to be significant only at p = 0.1098 (c 2 = 18.2; df = 12). Based on the last of these results, one might conclude that methodological variables do not have a significant influence on WTP. However, this conclusion is not supported by tests of restrictions implicit in models two and three. Likelihood ratio tests reject the null hypothesis of zero joint influence of omitted variables in both cases, compared to model one. For model two, the restrictions are significant at better than p < 0.01 (c2 = 213.6; df = 29), indicating that the omission of resource, context, and angler characteristics has a significant impact on the model. For model three, the restrictions are also significant at better than p < 0.01 (c 2 = 46.8; df = 12), indicating that the omission of methodological variables has a significant impact on the model. Another perspective on the explanatory power of variable groups may be obtained by considering R2 values for models one, two, and three—where these values are obtained through ordinary least squares (OLS) estimation of the reported model Meta-Analysis of Recreational Fishing Values 19

Table 5 Meta-Analysis Regression Results: Random Effects Models

Intercept –1.4568 1.6123** 0.04085 –3.8189*** (1.0284) (0.7745) (0.9742) (0.9912) SP_conjoint –1.1672*** –0.03493 –0.8537 (0.3973) (0.7230) (0.5269) SP_dichot –0.9958*** –0.7178 0.3870 (0.2455) (0.5409) (0.4264) TC_individual 1.1091* 0.5990 3.1006*** (0.5960) (0.9212) (0.8116) TC_zonal 2.0480*** 1.3114 3.0369*** (0.6444) (1.2634) (0.6661) RUM_nest 1.3324** 2.2313** 3.7505*** (0.6377) (0.9910) (0.8089) RUM_nonnest 1.7892*** 1.4738 3.9482*** (0.6131) (0.9341) (0.7337) SP_year 0.08754*** 0.04569 0.1752*** (0.02588) (0.0396) (0.03473) TC_year –0.03965 0.02859 –0.00208 (0.03187) (0.04118) (0.05586) RUM_year –0.00291 –0.04726 –0.04176 (0.01948) (0.03479) (0.03191) SP_mail 0.5440 0.1023 0.1831 (0.4608) (0.5822) (0.3739) SP_phone 1.0859*** 0.2064 0.8595 (0.4098) (0.6195) (0.5892) high_resp_rate –0.6539** –0.5569*** –0.7627** (0.2779) (0.1663) (0.3367) inc_thou 0.003872 0.001915 0.02889** (0.01398) (0.01938) (0.01208) age42_down 0.9206*** 0.4534** 0.6310*** (0.2612) (0.2088) (0.2035) age43_up 1.2221*** 0.5261* 0.2447 (0.2369) (0.2779) (0.3277) trips19_down 0.8392*** 0.8894*** 1.5805*** (0.2230) (0.3427) (0.2520) trips20_up –1.0112** –0.3800 0.04328 (0.4381) (0.3104) (0.3680) nonlocal 3.2355*** 3.1453*** 2.6640*** (0.4666) (0.5305) (0.2170) big_game_pac 2.2530*** 2.9563*** 1.5199*** (0.4048) (0.4711) (0.3904) big_game_natl 1.5323*** 1.8854*** 0.8483** (0.4544) (0.5318) (0.3832) big_game_satl 2.3821*** 2.7475*** 1.9376*** (0.5356) (0.5332) (0.4882) small_game_pac 1.6227*** 2.1570*** 0.6228 (0.3488) (0.3889) (0.4493) small_game_atl 1.4099** 1.7489*** 0.9024 (0.7094) (0.5974) (0.5608) flatfish_pac 1.8909*** 2.4470*** 1.4501*** (0.4826) (0.4990) (0.4213) 20 Johnston, Ranson, Besedin, and Helm

Table 5 continued Meta-Analysis Regression Results: Random Effects Models

Model Two Model Three Model Four Model One (Methodology (Methodology (Weighted, (Unrestricted) Only) Omitted) Unrestricted) Parameterb Parameterb Parameterb Parameterb Variable (Std. Err.) (Std. Err.) (Std. Err.) (Std. Err.) flatfish_atl 1.3797*** 1.7201*** 0.7966** (0.3373) (0.4120) (0.3658) other_sw 0.7339* 1.1948*** 0.09879 (0.3902) (0.3879) (0.3614) musky 3.8671*** 3.7641*** 3.5316*** (0.3507) (0.4158) (0.2521) pike_walleye 1.0412*** 1.2048*** 1.1195 *** (0.3469) (0.3570) (0.2580) bass_fw 1.7780*** 1.6341*** 1.6013*** (0.4301) (0.4659) (0.4539) trout_GL 1.8723*** 2.0433*** 1.6933*** (0.2620) (0.3839) (0.2150) trout_nonGL 0.8632*** 0.7717** 0.2789 (0.3034) (0.3736) (0.2297) salmon_pacific 2.3570*** 2.8701*** 1.9706*** (0.4205) (0.4586) (0.4378) salmon_atl_Morey 5.2689*** 5.0829*** 3.6523*** (0.4100) (0.5564) (0.5377) salmon_GL 2.2135*** 2.2595*** 2.2100*** (0.2722) (0.3381) (0.2285) steelhead_pac 2.1904*** 3.2321*** 2.4803*** (0.5635) (0.5407) (0.5259) steelhead_GL 2.3393*** 2.2683*** 2.2928*** (0.2198) (0.2956) (0.1926) cr_nonyear –0.08135 –0.06364 –0.0955* (0.06810) (0.07762) (0.05004) cr_year –0.05208*** –0.02812*** –0.09036*** (0.01451) (0.009219) (0.01676) catch_year 1.2693*** 0.2846 1.4785*** (0.4888) (0.3213) (0.4304) spec_cr 0.6862*** 0.07473 0.6920** (0.2323) (0.1887) (0.2793) shore –0.1129 0.03924 –0.2816 (0.1299) (0.1690) (0.2178) –2 LnL c 2 (df) 231.8 *** 18.2 185.0 *** 326.3 *** (41) (12) (29) (41) –2 LnL c 2 for restrictions (df) — 213.6 *** 46.8 *** — (29) (12) LR c 2 for test of random effects 0.00 101.42*** 35.94 *** 106.40*** 2 –19 s u 1.25 ´ 10 1.0925 0.3063 0.4707 R2(OLS) a 0.6187 0.1479 0.5287 0.7997 N 391 391 391 391 aBecause maximum likelihood estimation of the random effects model does not generate a standard R2 value, the reported R2 values for each model are calculated based on OLS estimation. b *** denotes significance at p < 0.01. ** denotes significance at p < 0.05. * denotes significance at p < 0.10. Meta-Analysis of Recreational Fishing Values 21 specifications. As noted in table 4, OLS values are reported because maximum likelihood random effects models do not generate standard R2 estimates. Here, an estimated R2 of 0.62 for the unrestricted model specification compares to 0.15 for the methodology-only specification and 0.53 for the no-methodology specification. Given that these values are associated with preliminary OLS estimates, they should be interpreted with appropriate caution. Nonetheless, they suggest that methodology variables account for a relatively small proportion of the variance in WTP, compared to that associated with resource, context, and angler characteristics. These results mirror patterns indicated by the likelihood ratio tests (e.g., c 2 values) reported above. After accounting for systematic variation in WTP associated with model variables, the significance of study-level random effects also varies across models. Random effects are significant at p < 0.01 in the two restricted models (models two and three). This finding is not particularly surprising given the large number of omitted variables in these model specifications, whose effects might be captured by random effects correlated with the omitted variables. Random effects are also statistically significant in the weighted unrestricted model (model four). However, random effects cannot be shown to be statistically significant in the unweighted un- 2 restricted model (s u approximates zero in this model). This finding is similar to that of Johnston, Besedin, and Wardwell (2003), and suggests that once one accounts for variation in observable resource, context, and study attributes—at least in the unweighted, unrestricted specification—no additional systematic variation in WTP may be ascribed to study-level effects. Given results of likelihood ratio tests noted above, we base subsequent discussion and analysis on the unrestricted model specifications (unweighted and weighted). Contrasting these models, we find similar, but not identical, results.7 Where results are similar across the two models, the discussion follows Bateman and Jones (2003) and emphasizes unweighted model results. However, we also emphasize those instances in which results differ substantially across the two specifications. Readers interested in a more detailed discussion of the potential impacts of weighting in meta-analysis are referred to Markowski et al. (2002).

Influence of Study Methodology

While likelihood ratio tests indicate a statistically significant impact of methodological variables on WTP per fish, they also indicate that the joint explanatory power of these variables is lower that that of variables characterizing resource, context, and angler attributes. This somewhat positive sign notwithstanding, study methodology clearly influences WTP per fish. It is worthy of note that the statistical significance of methodological effects only emerges once one appropriately accounts for WTP variation associated with resource, context, and angler characteristics. (Recall, the model incorporating only methodological variables cannot be shown to be statistically significant at p < 0.10.) This finding indicates correlation between variables characterizing methodological and non-methodological attributes, and that omitted variables of either category may bias parameter estimates for remaining variables. Hence, not only are methodological variables statistically significant, but their omission may bias parameter

7 In general, the significance of individual parameter estimates is somewhat improved in the unweighted specification, with 35 out of 41 non-intercept parameters significant at p < 0.10 or better. In the weighted specification, only 28 of 41 non-intercept parameters are significant at this level. However, the OLS R2 value is much improved in a weighted specification (i.e., 0.80 versus 0.62). 22 Johnston, Ranson, Besedin, and Helm estimates for non-methodological variables. While one might argue that the influence of omitted methodological variables could be subsumed under random effects specified at higher levels in the model, past empirical tests have suggested that omitted variables bias is not eliminated by such modeling approaches (Johnston et al. 2005). Model results suggest a wide range of methodological variables with systematic effects on WTP. For example, results suggest that lower WTP estimates are associated with stated preference methods, compared to revealed preference approaches. Holding all else constant, this finding holds for all variants of stated and revealed preference approaches, as revealed by coefficient estimates for SP_conjoint, SP_dichot, TC_individual, TC_zonal, RUM_nest, and RUM_nonnest. While perhaps counter to common intuition, this finding is consistent with past findings of Cameron (1992), Carson et al. (1996), Rosenberger and Loomis (2000b), and others. This conclusion must be qualified, however, given the additional effects of variables characterizing stated preference implementation. For example, positive and significant coefficient estimates associated with SP_phone and SP_year suggest that higher WTP estimates are associated with telephone survey instruments (compared to in-person instruments) and more recent surveys. Thus, for studies based on recent telephone surveys, stated preference WTP estimates might be expected to exceed those from at least some revealed preference methods. The positive influence of SP_year on WTP per fish is of particular note. This finding is consistent with the hypothesis that real WTP increases over time due to changes in angler experiences, preferences, or purchasing power (Rosenberger and Loomis 2000b). However, it contradicts the expectation that advances in stated preference survey design over time have led to more conservative WTP estimates (Johnston, Besedin, and Wardwell 2003). Other findings are mixed with regard to correspondence with expectations and prior literature. For example, as noted above, telephone surveys (SP_phone) are associated with increased WTP estimates. The coefficient associated with SP_mail is also positive, but not statistically significant. These results correspond with the ar- guments of Arrow et al. (1993) regarding the ability of in-person surveys (the default case in the meta-analysis) to ameliorate WTP-inflating survey biases, but contradict prior meta-analysis findings (e.g., Johnston et al. 2005). The model also finds statistically significant reductions in WTP associated with dichotomous choice (SP_dichot) and choice experiment or conjoint surveys (SP_conjoint), compared to the default of open-ended surveys (including payment cards and iterative bidding). These results challenge prior findings that discrete choice methods may be associated with higher WTP estimates (Boyle et al. 1996; Ready, Buzby, and Hu 1996). As a final note, however, we emphasize that results for these three variables (SP_phone, SP_dichot, SP_conjoint) are not robust across all model specifications. While all are significant at p < 0.01 in the unweighted model, none are statistically significant in the weighted model. Given the lack of robustness across models, these findings should be treated with appropriate caution. Results also suggest that studies with higher response rates (for both stated and revealed methods) are associated with reduced estimates of WTP per fish. This finding is robust across models, and is consistent with prior findings of Johnston et al. (2005) regarding WTP for water quality improvements. It is also an expected result associated with a reduction in avidity bias. More specifically, low response rates might be associated with a systematic under-representation of less avid anglers with lower WTP values, who may be less willing to respond to surveys. While results show that a range of methodological attributes influence WTP per fish, some variables characterizing methodological attributes were clearly (statistically) insignificant in all model specifications, and were therefore excluded from Meta-Analysis of Recreational Fishing Values 23 illustrated models (table 5). These include binary variables identifying observations derived from peer-reviewed sources and observations for which WTP per fish was reported by the original source study (as opposed to cases in which WTP was calculated based on reported empirical results, as described above).

Influence of Angler Characteristics

Six variables characterize angler demographic and economic attributes. Five of these are statistically significant at p < 0.05 in the unweighted model; four are significant in the weighted model. Parameter estimates for significant variables are of expected signs, where prior expectations exist. While some differences exist between the unweighted and weighted specifications, most results regarding angler attributes are robust across the two models. For example, the parameter estimate for nonlocal is positive and significant in both models, indicating that anglers who travel out of state to fish may be willing to pay more to catch additional fish than those who fish in local areas. Similarly intuitive results are associated with variables characterizing the average number of trips taken by sampled anglers. The variable trips19_down identifies studies in which the mean number of trips by sampled anglers was less than 20, compared to the default of studies in which the average number of trips is unspecified. This variable—identifying cases in which anglers took relatively few trips—is associated with an increase in estimated WTP per fish. The matching variable trips20_up identifies studies in which mean number of trips by sampled anglers was 20 or more, and is associated with a statistically significant decrease in estimated WTP per fish (although this effect is only significant in the unweighted model.) These are expected results, associated with diminishing marginal utility of recreational fishing (e.g., as the number of trips increases, WTP per fish, per trip declines). Other statistically significant effects are associated with the average age of sampled anglers and angler income. While the signs of the associated parameter estimates appear robust, significance levels vary somewhat between the weighted and unweighted models.

Influence of Resource and Context Attributes

The model includes 18 binary variables that characterize target species and geo- graphical region, contrasted to the default of panfish harvested nationwide. All of these variables are statistically significant at p < 0.10 in the unweighted model; 14 are significant in the weighted model. These results suggest that WTP per fish is clearly related to the type of species targeted. Moreover, model results appear to be consistent with common intuition regarding the highest versus lowest valued recreational fish. For example, results suggest that higher WTP estimates are associated with anadromous species (i.e., salmon and steelhead), big game fish (particularly in the South Atlantic and Pacific), and muskellunge.8 Moderate values are associated with species groups such as small saltwater game fish and saltwater flatfish. Lower WTP estimates are associated with species groups such as panfish, trout (particularly in outside of the Great Lakes region, not including steelhead), and “other” saltwater species. To demonstrate the types of patterns revealed by the model, figure 1 illustrates

8 Although the estimated WTP for catching an additional muskellunge seems to be plausible, it should be interpreted with caution because meta-data included only one observation for this species. 24 Johnston, Ranson, Besedin, and Helm parameter estimates associated with a selected set of species/region groups, drawn from the unweighted model specification. As shown by figure 1, model results follow expected and intuitive patterns. For example, parameter estimates for small game in the Atlantic (small_game_atl) and Pacific (small_game_pac) are quite similar—an intuitive result suggesting a high degree of homogeneity in preferences for saltwater small game fishing nationwide. Similarly, WTP for an additional salmon or steelhead is remarkably stable across regions and subspecies, with parameter estimates ranging from 2.19 to 2.36. The sole exception is the parameter estimate for salmon_atlantic_Morey (5.27)—a parameter estimate associated with a single study of the highly valued Atlantic salmon sport fishery (Morey, Rowe, and Watson 1993). This result notwithstanding, the analysis reveals clear similarity in the marginal values associated with fishing for anadromous species nationwide. These and other model findings suggest that similar species tend to generate similar per fish WTP estimates, although variations exist across regions for certain types of species. For example, there is somewhat more divergence between parameter estimates for mid- size, common freshwater sport fish (bass_fw, pike_walleye; figure 1). A final set of variables characterizes other attributes of fishing, including the catch rate. Negative parameter estimates for cr_nonyear and cr_year indicate that WTP per fish decreases as the baseline catch rate increases. This result is consistent with both economic theory and expectations. In the unweighted model, only cr_year is statistically significant (p < 0.01); cr_nonyear is not statistically significant. Both catch rate variables are statistically significant at p < 0.10 in the weighted model, and are of the expected negative sign.

Figure 1. Parameter Estimates for Selected Species Groups Meta-Analysis of Recreational Fishing Values 25

Implications for Welfare Estimation: An Illustration

Findings suggest a range of systematic patterns influencing WTP per fish among recreational anglers, with results showing systematic and intuitive relationships between WTP and a wide range of variables characterizing anglers, species and geographic region, and other fishing attributes. Results also suggest that WTP is systematically influenced by methodological variables and may be influenced by un- observable attributes of survey datasets (as indicated by the statistical significance of random effects in one of the two unrestricted models). These results present a mixed message with regard to researchers’ ability to provide valid estimates of WTP per fish. Practical implications for welfare evaluation, however, depend on the relative magnitude of effects associated with methodological attributes or other study-specific attributes. In some cases, changes in methodological approaches may lead to large differences in WTP per fish that may overwhelm differences related to species, resource or angler attributes. In other cases, estimates of WTP may be relatively robust to changes in methodology. To illustrate the potential magnitude of methodological effects on WTP, we use model results to forecast marginal WTP per fish for four species groups (trout_nonGL, other_sw, small_game_atl, flatfish_atl), under varying assumptions regarding study methodology (figure 2). These species groups were chosen because they are associated with a large number of distinct valuation methods in the meta- data (table 4), such that all combinations of species and methodology illustrated in figure 2 represent in-sample pairs. That is, within the meta-data, all four species are associated with at least one nested RUM study, dichotomous choice stated preference study, and individual travel cost study (table 4). For each of the four species groups, WTP is forecast under five methodological specifications. With the exception of the last specification (5), all forecasts are based on unweighted model results. The methodological specifications include: (i) nested RUM; (ii) dichotomous choice stated preference model, in-person survey in- strument; (iii) individual travel cost model; (iv) mean values for all methodological variables, and; (v) mean values for all methodological variables (weighted model). In all cases, WTP is forecast assuming that angler characteristics are set equal to mean sample values (table 2). Catch rates are assumed to be specified per day, at the mean sample value of 2.10 for cr_nonyear. Finally, because there is correlation between study methodology and the year in which studies were conducted, variables indicating study year (SP_year, TC_year, and RUM_year) are set equal to mean values for each valuation methodology. Figure 2 illustrates resulting WTP forecasts.9 As shown by this illustration, study methodology may have substantial effects on WTP. Across the four species groups—and given other assumptions noted above—model results predict a 172% increase in WTP associated with the use of nested RUM and an 83% increase in WTP associated with the use of individual travel cost methods, compared to WTP associated with dichotomous choice stated preference methods. Nested RUM WTP forecasts exceed individual travel cost forecasts by 49%.10 The least conservative (highest) WTP estimates are associated with the assignment of mean values for all methodological variables.

9 2 Following Bockstael and Strand (1987), sˆ e 2 is incorporated into the sum of variable effects when estimating WTP, to account for regression error in WTP estimates. 10 Given the multiplicative functional form underlying the semi-log statistical model, and the assumptions underlying WTP forecasts, the predicted percentage difference in WTP across methodologies re- mains constant across species groups. 26 Johnston, Ranson, Besedin, and Helm

This variation in cardinal WTP magnitude may also affect the ordinal ranking of WTP for different species groups. For example, species group coefficients alone suggest that WTP per fish for Atlantic small game exceeds that for non-Great Lakes trout, holding all else equal (table 5). However, the illustrated forecast of WTP for Atlantic small game assuming dichotomous choice stated preference methodology ($3.37) is lower than the forecast for non-Great Lakes trout assuming individual travel cost methodology ($5.31) (figure 2). The ordinal rankings of WTP associated with certain other species groups are more robust to methodological variation. Nonetheless, such results suggest that pairwise or small-sample comparisons of WTP across studies using different methodological approaches may result in mis- leading conclusions regarding the relative magnitude(s) of WTP per fish. Further complicating WTP effects associated with study methodology is the potential impact of variables characterizing other aspects of research design and implementation. These include, for example, survey administration method, study year, and response rate. As an example of such effects, figure 3 reprises the WTP illustration shown in figure 2, but with study year variables (SP_year, TC_year, and RUM_year) set to 2000 instead of mean values. Results again show considerable divergence in WTP per fish across methodologies. Given the prior results of figure 2, this is not particularly surprising. However, a more fundamental issue is revealed by a comparison of figures 2 and 3. Compared to figure 2, figure 3 illustrates a different ordering of WTP magnitude, with regard to study methodology. For example, for any given species group, figure 2 indicates that WTP associated with individual travel cost studies exceeds that associated with dichotomous choice stated preference methods, assuming mean study year values. In contrast, figure 3 indicates that WTP associated with individual travel cost studies is lower than that associated with dichotomous choice stated preference approaches, assuming a study year of 2000. Hence, conclusions regarding the influence of methodology on WTP estimates may depend on details of study implementation, including the year in which a study was conducted.

Figure 2. Per Fish WTP as a Function of Research Methodology: An Illustration Assuming Mean Year for Included Study Methodologies Meta-Analysis of Recreational Fishing Values 27

Figure 3. Per Fish WTP as a Function of Research Methodology: An Illustration Assuming Equivalent Study Years (2000)

Such results suggest that careful consideration be given to the assumptions used in applying meta-analysis models to forecast WTP. More fundamentally, however, results highlight the potential difficulty in establishing invariant patterns in WTP associated with particular types of methodology (e.g., RUM, dichotomous choice stated preference methods). Here, such conclusions vary depending on assumed values of other study attributes. Simply put, effects of methodology on estimated WTP—in this case WTP per fish among recreational anglers—may not follow uni- versal, easily identifiable patterns.

Conclusion

Empirical results of the meta-analysis suggest two broad findings. First, WTP per fish is systematically sensitive to variation in resource, context, and angler attributes. These effects are largely intuitive and match those expected based on prior empirical assessments of recreational fishing. Such findings mirror those found in meta-analysis of WTP for improvements in other aquatic and non-aquatic resources (e.g., Johnston, Besedin, and Wardwell 2003; Poe, Boyle, and Bergstrom 2001; Smith and Osborne 1996), and suggest that non-market valuation can provide mean- ingful insight into WTP for improvements in recreational catch. The second broad finding is that WTP per fish varies systematically according to methodological attributes. From a statistical perspective, methodological effects account for a relatively small proportion of the total variation in WTP estimates across studies. Nonetheless, from the perspective of estimated impacts on WTP magnitude, joint effects of methodological variation can be greater or less than effects related to species, context, and angler attributes. Study results also suggest that significant differences in WTP may be associated with less commonly discussed methodological attributes, such as response rate and study year. Hence, even subtle methodological distinctions between studies may influence WTP estimates. 28 Johnston, Ranson, Besedin, and Helm

Model results highlight the many systematic and intuitive relationships that influence WTP per fish among recreational anglers, but also show the potentially significant impacts of research methodology. The effects of methodological variation may be particularly germane for small-sample comparisons of WTP generated by valuation studies that apply fundamentally distinct methods (e.g., stated versus revealed preference models) or for benefit transfer applications (cf. Johnston et al. 2005). Hence, while results are promising with regard to the ability of non-market research to provide insight regarding WTP for recreational fishery resources, results also suggest that researchers should consider the potential for methodological effects when conducting applied welfare analysis.

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