The NCR aquaculture industry

The NCR spans from the Great Lakes Region to the Great Plains, has plentiful water resources, and experiences a seasonally cold climate. The region produces a wide variety of seafood species (Batterson, Reference Batterson, Taylor, Lynch and Leonard2013) with strength in the food fish production of trout, yellow perch, and sport fish production of largemouth bass, which is also sold as food fish, and walleye (Table 1). Other species produced in the region include catfish, tilapia, carp, hybrid striped bass, crawfish, shrimp (saltwater), prawns (freshwater), ornamental fish, and baitfish. Most NCR trout farms are in Wisconsin, Michigan, and Nebraska, but trout farms can be found in all other NCR states except North Dakota. Yellow perch production is strong in Ohio and Wisconsin, but it is also produced in Michigan and Minnesota.

Table 1.

Total number of farms and sales reported by NCR Aquaculture^a

^a Source: 2018 USDA Aquaculture Census.

Rainbow trout (Oncorhynchus. Mykiss), though nonnative, is an important species in the NCR. It is a typical cold-water fish that thrives in the climatic conditions of the Great Lakes region (Kinnunen, Reference Kinnunen2000; Hinshaw et al., Reference Hinshaw, Fornshell and Kinnunen.2004). In 2005, the NCR accounted for 28% of all U.S. trout farms and 9% of national sales (USDA, 2006), but regional production contracted modestly to 23% of total farms and 7% of national sales in 2018 (USDA, 2019) and nationally, trout generated $12.4 million dollars in exports in 2018 (USDA ERS, 2019). Presently, the NCR produces less than 8% of total domestic trout value (USDA ERS, 2019) but boasts 90.2% of U.S. walleye (Sander vitreus) production and 81.3% of U.S. yellow perch (Perca flavescens) production (USDA, 2019). Once abundant in the Great Lakes, commercial fisheries serviced the large domestic demand for yellow perch and walleye, solidifying the two species in the gastronomic traditions of the region (Riepe, Reference Riepe1999; Malison, Reference Malison2003; Summerfelt et al., Reference Summerfelt, Clayton, Johnson and Kinnunen.2010).

Walleye is regionally important as both a sport fish and a food fish; increasingly becoming a food fish in recent decades. In the late 1990s, recreational sport fishing crowded out the commercial walleye catch in the United States (Riepe, Reference Riepe1999). Today, only Native American commercial fishers may harvest walleye in the U.S. waters of Lakes Huron, Michigan, and Superior: no harvesting is allowed for state-licensed commercial fisheries. Due to these regulations, domestic walleye landings cannot satisfy domestic walleye demand. The domestic walleye catch pales in comparison to the Canadian catch. In 2020, imported Canadian walleye accounted for 1,300 metric tons, equivalent to nearly 3 million lbs. and $17 million U.S. dollars (USDA FAS, 2021). Walleye’s biological characteristics make it a good fit for aquacultural production, while its excellent flesh quality and palatability make it a popular food fish (Kinnunen, Reference Kinnunen and Summerfelt1996; Summerfelt et al. Reference Summerfelt, Clayton, Johnson and Kinnunen.2010). With a relatively high market value, walleye is considered an opportunity for the NCR aquaculture industry’s growth and development (Summerfelt et al. Reference Summerfelt, Clayton, Johnson and Kinnunen.2010). As such, walleye received the NCR priority species designation for financial support and research funding through the 1990s (Riepe, Reference Riepe1999).

Yellow perch is another historically important species in the Great Lakes region, and it also bears the NCR priority species designation. Like walleye, yellow perch is particularly adapted to the seasonal cycle of the lower NCR temperate systems (Hokanson, Reference Hokanson1977; Linkenheld, Reference Linkenheld2019) making it an ideal candidate for aquacultural development in the region. During the twentieth century, the international supply of yellow perch came from capture fisheries in the Great Lakes region of the United States and Canada (Malison, Reference Malison2003). Wild catch exceeded 33 million lbs. annually in the 1950s and 1960s but fell significantly to 11–18 million lbs. by the end of the century (Malison, Reference Malison2003). With its natural population in decline since the 1980s, aquaculture and the Canadian Lake Erie commercial fishery currently service U.S yellow perch demand. Canadian imports alone accounted for 155 metric tons in 2020, the equivalent to $4.2 million dollars (USDA FAS, 2021). On a smaller scale, there is a limited U.S. state-licensed commercial fishery for yellow perch in Lake Huron’s Saginaw Bay and Lake Michigan’s Green Bay in addition to Native American commercial fisheries in Michigan.

U.S. consumer preferences for fish

U.S. per capita seafood consumption grew 10.3% between 2009 and 2019 (National Marine Fisheries Service, 2021). Most of this growth can be attributed to an increase in the consumption of fresh and frozen seafood, while per capita consumption of canned and cured seafood products held constant (National Marine Fisheries Service, 2021). With increasing frequency, consumers choose seafood to meet their dietary needs based on the abundance of omega-3 fatty acids, low fat content, and high protein content it affords (Averbook, Reference Averbook2018; de Boer et al., Reference de Boer, Schösler and Aiking.2020; Runge et al., Reference Runge, Shaw, Witzling, Hartleb, Yang and Peroff.2021).

Consumer preferences and consumption trends ultimately reflect individual definitions of quality, which in turn is a multidimensional attribute constructed from perceptions of a combination of traits (Wirth et al., Reference Wirth, Stanton and Wiley.2011). As a result, retail seafood products may be thought of as “bundles of characteristics” composed of many search, experience, and credence attributes (Ward et al., Reference Ward, Lusk and Dutton.2008; Ahmad and Anders, Reference Ahmad and Anders.2012; Alfnes, et al., Reference Alfnes, Chen and Rickertsen.2018). Consumers can readily observe “search” attributes, like prices, at the time of sale. In contrast,“experience” attributes require an interaction, such as eating, to discern. “Credence” attributes are most difficult to verify, even after handling or consumption, and are imparted through labels. In the case of seafood, search attributes include species, price, and form of the product (such as fresh or frozen). The latter, if taken as a search attribute, subdivides into a range of possible attributes such as convenience and flavor. Nevertheless, choices between fresh and frozen can be associated with individuals’ previously experienced taste, blurring the lines that separate this classification of attributes. However, flash-freezing technology has improved the quality of frozen fish in comparison to fresh fish, rendering attributes such as fresh (not previously frozen) and frozen imperceptible and therefore credence attributes. In blind taste tests, consumers prefer flash-frozen samples to never-frozen-fresh samples (Kinnunen and Pisitis, Reference Kinnunen and Pistis.2007; Cox et al., Reference Cox, Colonna, Norton, Mackey, Behnken, Cobb, Lovewell, Rasor, Pelissier, Oborne and Bowman.2017).

At present, whether fish is sold fresh or frozen plays an important role in framing consumer fish choices. Consumers face many forms of fish products at seafood retail counters and freezer cases from live, undressed whole to processed frozen fillets. National scanner data show most seafood expenditures go to frozen products with just 18% spent on fresh seafood products (Gorstein and Larkin, Reference Gorstein and Larkin.2014). Fresh fish is considered least affordable based on consumer perceptions, and cost is the most influential attribute for consumer purchasing decisions (42% of respondents), followed closely by taste (41%) and healthfulness (30%) (Averbook, Reference Averbook2018). In some instances, the preference for fresh seafood over frozen is specific to a geographical region or species (Foltz et al., Reference Foltz, Dasgupta and Devadoss.1999). For example, when U.S. consumers were presented with fresh tilapia versus previously frozen tilapia, consumers in Colorado exhibited a $2.67/lb. lower WTP, while consumers in Florida showed a $4.47/lb. WTP premium; consumers were indifferent about the form of salmon and tuna (Meas and Hu, Reference Meas and Hu.2014). More recently, consumers report purchasing equal shares of fresh fish and frozen fish and viewing frozen foods as equally nutritious to their counterparts (Averbook, Reference Averbook2018). Our choice experiment presents the form of fish at retail, a search attribute, as either fresh fillets or frozen fillets.

Similarly, whether fish was wild-caught or farm-raised can be considered a credence attribute because it cannot be consistently perceived or identified by consumers in the absence of a label (Sogn-Grundvag et al., Reference Sogn-Grundvåg, Larsen and Young.2014). WTP estimates for wild-caught fish are neither widespread nor uniform in the literature, and evidence shows geographic heterogeneity in preferences for production method (Jaffry et al., Reference Jaffry, Pickering, Ghulam, Whitmarsh and Wattage.2004; Davidson et al., Reference Davidson, Pan, Hu and Poerwanto.2012; Roheim et al., Reference Roheim, Sudhakaran and Durham.2012; Uchida et al. Reference Uchida, Onozaka, Morita and Managi.2014; Rickertsen et al., Reference Rickertsen, Alfnes, Combris, Enderli, Issanchou and Shogren.2016). Nationwide, consumer surveys show that 36% of consumers report searching for wild-caught fish while only 14% report seeking out farm-raised fish, but the equal shares of regular buyers of seafood buy farm-raised and wild-caught fish (Kraushaar, Reference Kraushaar2014; Averbook, Reference Averbook2018). For example, Hawaiian consumers are willing to pay a premium for wild-caught fish (Davidson et al., Reference Davidson, Pan, Hu and Poerwanto.2012). A 2012 study of consumers in Colorado and Florida found no positive WTP for wild-caught salmon or tuna relative to farm-raised, a $2.98/lb. discount for wild-caught or farm-raised Salmon, and a $6.69/lb. discount for wild-caught tuna (Meas and Hu, Reference Meas and Hu.2014). Other studies have focused on those in Europe and China, where per capita seafood consumption is much higher (Menozzi et al., Reference Menozzi, Nguyen, Sogari, Taskov, Lucas, Castro-Rial and Mora.2020; Zheng et al., Reference Zheng, Wang and Shogren.2021). The number of studies estimating WTP for wild-caught or farm-raised fish, especially those of U.S.-based consumers, are few but indicate a positive WTP for wild-caught fish that may vary across species (Maesano et al., Reference Maesano, Di Vita, Chinnici, Pappalardo and D’Amico.2020) or seafood product (Brayden et al., Reference Brayden, Noblet, Evans and Rickard.2018).

Consumers sometimes associate health and environmental impacts with the two forms of production. In part, wild-caught preferences can be attributed to the perception of wild-caught fish as more “natural” and better quality, consumer apprehension regarding the environmental impact of aquaculture farms, and lack of trust in farm production systems (Whitmarsh and Palmieri, Reference Whitmarsh and Palmieri.2011; Claret et al., Reference Claret, Guerrero, Ginés, Grau, Hernández, Aguirre, Peleteiro, Fernández-Pato and Rodríguez-Rodríguez.2014; Runge et al., Reference Runge, Shaw, Witzling, Hartleb, Yang and Peroff.2021). In contrast, the Aquaculture Stewardship Council (ASC) reports more than half of seafood consumers are indifferent between wild-caught and farm-raised fish, if production is environmentally and socially responsible (Holland, Reference Holland2020). Moreover, 69% of the ASC report respondents stated they bought both farmed and wild-caught products or did not know which production method was used. This international survey reported respondent consensus prioritizing responsibly produced food. Further, 29% of respondents believed purchasing farm-raised fish provides positive ecological impacts by preserving wild stocks, and 40% agreed that significantly more farm-raised seafood should be consumed globally. In the United States, consumers report growing trust in fish farmers and government regulatory agencies and understand that aquaculture reduces pressure on wild stocks (Runge et al., Reference Runge, Shaw, Witzling, Hartleb, Yang and Peroff.2021). Aquaculture standards and fishery management practices improved steadily over the last decade, which has catalyzed a worldwide movement to demystify the “wild versus farmed” debate to benefit both capture fisheries and aquaculture industries (Hill, Reference Hill2020).

Given the prominence of trout as a farmed commodity domestically, the familiarity of NCR residents with walleye as a sport fish, and evidence of consumer nonattendance toward wild-caught fish, one would expect our estimates to vary compared to the localized studies of the extant literature. The two production alternatives presented to consumers are wild-caught or farm-raised. Ultimately, the ability of NCR and U.S. aquaculture to serve domestic demand rests on the willingness of consumers to purchase farm-raised products. A strong preference for wild-caught fish would imply further reliance on landings from Canada.

Another example of a credence attribute is “locally sourced,” which is often sought due to concerns about health, nutrition, and food safety (Wirth et al., Reference Wirth, Stanton and Wiley.2011). Fish products sold in the United States must bear a country-of-origin label (COOL), but these labels do not necessarily convey state or region of production in the United States (Mandatory Country of Origin Labeling of Beef, Pork, Lamb, Chicken, Goat Meat, Wild and Farm-Raised Fish and Shellfish, Perishable Agricultural Commodities, Peanuts, Pecans, Ginseng, and Macadamia Nuts, 2013). Labels indicating the fish geographic origin or source are known to affect consumer seafood preferences (Brayden et al., Reference Brayden, Noblet, Evans and Rickard.2018). Some studies show consumers find it only “somewhat” important to purchase locally produced or farm-raised fish (Gvillo et al., Reference Gvillo, Quagrainie, Olynk and Dennis.2013; Runge et al., Reference Runge, Shaw, Witzling, Hartleb, Yang and Peroff.2021), indicating the term “locavore” has yet to cross over from beyond terrestrial food products to seafood. More recently, supply chain disruptions during the COVID-19 pandemic were especially severe for meat products and seafood (Arita et al., Reference Arita, Grant, Sydow and Beckman.2021), expanding the benefits of local production beyond healthy and food safety concerns to food security. Stated preferences for locally sourced food fish have been previously reported in Europe (Altintzoglou et al., Reference Altintzoglou, Verbeke, Vanhonacker and Luten.2010; Risius et al., Reference Risius, Janssen and Hamm.2017) and have been elicited more recently in the United States (Runge et al., Reference Runge, Shaw, Witzling, Hartleb, Yang and Peroff.2021). A survey of Wisconsin-based seafood consumers identified preferences for fish sourced locally or in the United States relative to imported alternatives (Shaw et al., Reference Shaw, Runge, Yang, Witzling, Hartleb and Peroff.2019; Runge et al., Reference Runge, Shaw, Witzling, Hartleb, Yang and Peroff.2021). While certain regions in the United States hold strong historical affinities for certain seafood species, evolving attitudes regarding the health and welfare of seafood have changed the landscape nationally. We capture the consumer WTP for NCR state-sourced fish compared with non-NCR-sourced fish through our choice experiment design. Within the NCR, the NCR-sourced designation serves as a proxy for local production or landing.

As the lines between search, experience, and credence attributes change for fish and seafood due to farm production and preservation technology improvements, the consumer preferences for these attributes should also adjust. This paper estimates consumers’ WTP for fish search attributes including species and fresh versus frozen fillets, as well as wild-caught versus farmed. We produce national and NCR-specific WTP estimates using a hypothetical choice experiment of trout, walleye, and yellow perch to identify whether these attributes attract premia.

Consumer survey

Data

We collected the data for this analysis by constructing and distributing an online survey instrument using Qualtrics^XM in the fall of 2020. The survey featured screening questions, a consequentiality statement (Zheng et al., Reference Zheng, Wang and Shogren.2021), an image illustrating the geography and states of the NCR, a DCE, and a demographics section. Qualtrics recruited adult respondents from across the United States through email and provided them with compensation for participation. The choice experiment designed for this study, described below, asked respondents to consider a hypothetical purchasing scenario typical of a fish retailer. This required us to include respondents who prepared and ate fish at home and screen out those who only dined on fish away from home. Further, our targeting of fish consumers, as opposed to seafood consumers, removes those who reported eating only crustaceans and/or mollusks from the sample.

A pilot study of 106 respondents preceded the full survey release to provide a quality check on the suitability of the questions, survey flow, and display logic. After full distribution, we discarded any respondents who fell outside the sampling frame, did not complete the survey, failed a speed test, or submitted multiple survey responses from the final sample.

After screening and quality control, the final sample consisted of 876 respondents. Summary statistics for the demographics of the respondents are presented in Table 2. According to the 2019 American Community Survey (U.S. Census Bureau, 2020), one in five Americans lives in the NCR and our sample is proportionate in composition. Our sample skews slightly more female, younger, and lower on the income spectrum than is nationally representative.

Table 2.

Summary of consumer demographics (N = 876)

^a Source: American Community Survey 2019 1-Year Estimates.

^b Due to differences in the classification of race and ethnicity, the national race statistics do not sum to one and “Hispanic” overlaps with other categories.

Discrete choice experiment

In the DCE portion of our survey, respondents faced several hypothetical purchasing choice scenarios (Appendix Figure 1). Each choice scenario presented attributes across alternatives to force respondents to make trade-offs between species and attributes. Each choice scenario included three labeled alternatives (trout, yellow perch, and walleye) and a no-buy option to simulate a real purchasing situation (Lusk and Schroeder, Reference Lusk and Schroeder.2004; Scarpa et al., Reference Scarpa, Ferrini, Willis., Scarpa and Alberini2005). Each alternative was accompanied by a picture of species-specific fillets. Attributes varied over the alternatives according to levels presented in Table 3. Prices ranged from $9 to $16 in dollar increments for each alternative, producing eight price levels. ^{Footnote 3} We chose price levels conservatively to avoid biasing WTP results up due to large magnitude price vectors (Glenk et al., Reference Glenk, Meyerhoff, Akaichi and Martin-Ortega.2019). The two production methods considered were farm-raised and wild-caught. Each alternative was labeled as “NCR sourced” or “Not NCR sourced” to differentiate fish originating inside or outside the region. This grouping of non-NCR but U.S.-sourced fish with imported fish is like the categorization used in the analysis of Brayden et al. (Reference Brayden, Noblet, Evans and Rickard.2018). Each alternative bore a “Fresh Fillets” or “Frozen Fillets” label to reflect the availability of different forms at retail.

Table 3.

Choice experiment attributes and levels

We constructed the experimental design for this study using NGene software. The combination of four labeled alternatives, eight prices, two regions of origin, two production methods, and two product forms yielded an untenable number of choice tasks under a full factorial design: 262,144 (8³ × 2³ × 2³ × 2³) different choice tasks. To address this dimensionality, we employ a simultaneous orthogonal factorial design ^{Footnote 4} and subdivide the resulting 24 choice scenarios into 4 blocks. Each respondent faced just six choice scenarios randomly assigned from the four blocks to combat respondent fatigue ^{Footnote 5} (Hanley et al., Reference Hanley, Wright and Koop.2002). This design achieved orthogonality within and across the attribute levels of alternatives to ensure pairs of attributes are uncorrelated while every pair of attributes occurred equally often to attain balance. The full design, an example of a choice scenario presented to respondents, and ex ante multinomial logit efficiency measures are found in the appendix.

Conceptual framework

Our conceptual framework follows McFadden’s random utility model (RUM) (McFadden, Reference McFadden and Zarembka1974). The utility of consumer n for fish alternative j can be decomposed into two components: observed component ${V_{nj}}$ and unobserved component ${\varepsilon _{nj}}$ :

(1) $${U_{nj}} = {V_{nj}} + {\varepsilon _{nj}}$$

This model forms the foundation of multinomial logit model assuming the unobserved utility component is identically and independently (i.i.d.) distributed following an extreme value type 1 distribution. Under this assumption, the probability of consumer n choosing fish alternative j is

(2) $${P_{nj}} = Prob\left[ {{V_{nj}} + {\varepsilon _{nj}} \gt \;{V_{ni}} + {\varepsilon _{ni}}} \right]\;\forall \;i \ne j{\rm{\;}}$$

(3) $$ = Prob\left[ {{\varepsilon _{nj}} \gt \;{V_{ni}} - {V_{nj}} + {\varepsilon _{ni}}} \right]\;\forall \;i \ne j$$

which is to say that the unobserved component of utility for every unchosen fish alternative i must be smaller than the differences between the observed component n and observed component for fish alternative i plus the unobserved component of fish alternative j.

Under the assumption of independence between unobserved utility components, we can multiply the probability for all i ≠ j to obtain the probability of individual n choosing alternative i and integrate the conditional probability over all possible ${\varepsilon _{nj}}$ values to obtain the closed-form equation:

(4) $${P_{nj}} = \;{{\exp \left( {\beta '{x_{nj}}} \right)} \over {{\sum _i}\exp \left( {\beta '{x_{ni}}} \right)}}\;.$$

The multinomial logit has several limitations due to the strong assumptions required to obtain equation (4) (Henscher et al., Reference Hensher, Rose and Greene.2005). These include an inability to model random taste variation, the imposition of irrelevance of independent alternatives (IIA) property, and state independence. These challenges can be addressed with more flexible models like universal logit models, heteroskedastic extreme value models, random parameter logit (RPL) models, and error components models (ECM) (Lusk and Schroeder, Reference Lusk and Schroeder.2004; Scarpa et al., Reference Scarpa, Ferrini, Willis., Scarpa and Alberini2005; Scarpa et al., Reference Scarpa, Campbell and Hutchinson.2007).

In particular, ECMs provide desirable innovations because they can include random parameters as well as correlation between alternatives and the random parameters (Train, Reference Train2003). A random parameter logit with error component model (RPLEC) decomposes equation (1) into three components:

(5) $${U_{nj}} = \alpha ^\prime{x_{nj}} + \;{\mu _n}^\prime{z_{nj}} + {\varepsilon _{nj}}$$

where x _nj and z _nj are observed attribute vectors for fish alternative j, α represents fixed coefficients, μ represents random coefficients with zero means, and ${\varepsilon _{nj}}$ is the i.i.d. extreme value type 1 unobserved portion of utility. The random part of the utility specification is thus ${\eta _{nj}} = \;\;\mu _n^\prime{z_{nj}} + {\varepsilon _{nj}}$ , and this portion can exhibit correlation over alternatives for individual n. In the case of nonzero error components, consider individual i facing alternative i and alternative j:

(6) $${\rm{Cov}}\left( {{\eta _{ni}},\;{\eta _{nk}}} \right) = {\rm{\;E}}\left( {\;\mu _n^\prime{z_{ni}} + {\varepsilon _{ni}}} \right)\left( {\;\mu _n^\prime{z_{nk}} + {\varepsilon _{nk}}} \right) = z_{ni}^\prime{\rm{W}}{z_{nj}}{\rm{\;}}$$

where W is the covariance of μ _n. Through these error component terms, utilities U _ni and U _nk are correlated so the utility of individual n is correlated across alternatives. In the hypothetical choice experiment context of this paper, we prefer error component random parameters logit models to handle heteroskedasticity emerging from correlation between the labeled fish species alternatives. We expect respondents to experience our hypothetical labeled fish alternatives differently than the no-buy option as respondents can only experience the no-buy option in reality (Scarpa et al., Reference Scarpa, Ferrini, Willis., Scarpa and Alberini2005, Reference Scarpa, Campbell and Hutchinson.2007).

Empirical estimation

We choose a panel logit specification with random parameters and error component to relax the strict assumptions of i.i.d. errors and account for correlation between choices and alternatives. This allows the choice model to exhibit more realistic substitution patterns, correlation between the utilities of the fish species, and correlation across the utilities associated with specific respondents. The random parameters and latent random effects may covary between the labeled alternatives but not between labeled alternatives and the no-buy option. This is modeled as:

(7) $${{U_{njt}} = {\alpha _{nj}} + \;{\beta _1}Pric{e_{njt}} + {\beta _{n2}}NCRSource{d_{njt}} + \;\beta {n_3}WildCaugh{t_{njt}} + \beta {n_4}Fres{h_{njt}} + {\eta _{nj}} + \;{\varepsilon _{njt}}}$$

where j = trout, yellow perch, and walleye; α _j is the alternative specific constant relative to the “no buy” option; Price _njt is the continuous price of alternative j for consumer n; NCRSourced _njt is an indicator variable taking a value of 1 for NCR state origin; WildCaught _njt is an indicator variable taking a value of 1 when alternative j is labeled wild-caught; and Fresh _njt is an indicator variable taking a value of 1 when alternative j is labeled fresh. Each non-price attribute enters as a random variable ${\beta _{njt}} = \overline {{\beta _j}} + \;{\sigma _j}{\tilde \beta _{nj}}$ with population mean ${\bar \beta _j},$ standard deviation ${\sigma _j},\;$ and individual-specific independently and identically distributed standard normal disturbance ${\tilde \beta _{nj}}$ (Revelt and Train, Reference Revelt and Train.1998). Both correlation across utilities and heterogeneous alternative specific constant parameter can introduce stochasticity into the model and prevent a closed-form solution for the log-likelihood of the choice probability (Train, 2009). Due to this computational necessity, we employed a simulated maximum likelihood estimation strategy to perform integration and estimate probabilities. We used NLogit (Version 6.0, Econometric Software Inc.) to perform all estimation and simulation.

The estimates obtained from equation 7 can be used to estimate total and marginal WTP for fish attributes and alternatives. The total WTP for an attribute represents the amount an individual would pay to obtain attribute j relative to forgoing purchase. When the attribute in question is species, alternative specific constants are used to estimate the total WTP relative to the no-buy option (Lusk and Schroeder, Reference Lusk and Schroeder.2004). To obtain the total WTP for alternative j, we estimate

(8) $$WTP = - {{{\beta _j}} \over {{\beta _{price}}}}$$

where $WT{P_j}$ is the willingness to pay for the ${j^{th}}\;$ attribute, ${\beta _j}$ is the coefficient associated with the ${j^{th}}$ attribute, and ${\beta _{price}}$ is the price coefficient. In the context of this study, the WTP measures for the dummy variables $WildCaught$ , $Fresh$ , and $NCRSourced$ are relative to the base level, or converse label. They are thus interpreted as farm-raised to wild-caught, frozen fillets to fresh fillets, or not NCR-sourced to NCR-sourced. Further, all the species-specific WTP estimates are relative to the no-buy option as we normalize the utility of no-buy option to zero.

We model each of the random attribute parameters using a normal distribution ${\beta _{nj}}\;\sim \;N\;\left( {\widehat {{\beta _j}}\;,{\sigma _j}} \right).$ As such, the WTP estimates for attributes (and alternatives) also follow normal distributions. Since this study seeks to identify the WTP estimates for attributes and species pertinent to NCR aquacultural production, the distributions provide illustrations of consumer valuation beyond mean WTP estimates. We use Krinsky and Robb’s bootstrapping approach (Krinsky and Robb, Reference Krinsky and Robb.1986; Lusk and Schroder, Reference Lusk and Schroeder.2004; Hensher et al., Reference Hensher, Rose and Greene.2005) with 1,000 simulated draws to obtain the parameters of these distributions.