Guarding giants: resource commons quality and informal property rights in big-wave surfing

Abstract

This study extends prior empirical research on issues associated with the common-pool resource represented by surf breaks (i.e., surfing locations) by (1) creating an alternative, perhaps more objective metric, based on a logistic transformation of pairwise comparisons of the results of big-wave surfing competitions, of surf break quality, (2) applying the alternative surf break quality metric to “big-wave” surf breaks and (3) varying the test area by examining big-wave surf breaks worldwide. The results presented here are perhaps even more compelling than those from prior research—indicating that a marginal increase in surf break quality leads to a relatively large increase—in this case more than 30% points—in the probability of observing fierce localism at surf breaks. The finding here of a larger marginal effect of surf break quality on localism in big-wave surfing than in traditional surfing supports the idea that big-wave surfing and traditional surfing represent distinct markets, characterized by different technologies and inherent dangers, such that localism at big-wave surf breaks exceeds that at traditional surf breaks in terms of ferocity, ceteris paribus. Although this study focuses specifically on the relationship between surf break quality and localism, our research highlights the importance of informal property rights protection of common-pool resources.

1 Introduction

Early in his seminal theoretical study of property rights formation, Demsetz (1967: 347) notes that property rights derive their significance from the fact that they help us form those expectations which we can reasonably hold in our dealings with others and that “[t]hese expectations find expression in the laws, customs, and mores of a society.” Demsetz’s (1967) central argument is built around the use of a resource lacking well-defined property rights, wherein he concludes, as Kaffine (2009) indicates, that property rights will be endogenously created by users when the benefits of developing and enforcing property rights exceed the costs. Demsetz’s (1967) conclusion complements conceptual arguments made by Gordon (1954), Scott (1955), Coase (1960), Ostrom (1990) and Cole (2002) regarding the improvement made to resources by private or commonly enforced property rights by providing a positive association between resource quality and strong property rights protection. This association holds whether resource quality is high as a result of investments that are encouraged by strong property rights or whether strong property rights exist because users are able to recognize the high quality of the resource (Kaffine 2009).

Kaffine (2009) and Mixon (2014) provide an interesting set of complementary empirical examinations of the seminal work of Demsetz (1967) and others through their analyses of California surf gangs’ attempts to exclude nonlocal surfers from enjoying local surf breaks. Both studies find, ceteris paribus, that surf gangs exert greater effort enforcing exclusions to the local surf break as the quality of the local surf break increases. Notwithstanding these recent studies, the relative paucity of empirical examination of the basic tenets of the article by Demsetz (1967) suggests that additional exploration into the role that resource quality plays in property rights formation in the use of a resource, and particularly so regarding surf breaks of various quality, provides a contribution to the empirical literature on the commons. With that aim, this study extends previous research by Kaffine (2009) and Mixon (2014) on informal property rights at surf breaks by (1) creating an alternative, objective metric of surf break quality, based on a logistic transformation of pairwise comparisons of the results of big-wave surfing competitions and (2) applying the alternative surf break quality metric to “big-wave” surf breaks worldwide, such as those profiled by Peralta and George (2004). Given the differences between the “technologies” associated with the type of traditional surfing analyzed in Kaffine (2009) and Mixon (2014) and the big-wave surfing, characterized by waves measuring 20 or more feet in height, investigated here, one might expect to observe differences in the degree of informal property rights protection by local surfers across the two types of resources. Empirical analyses presented in this study will uncover such differences. Before delving into the empirical analysis, the following section of this study provides a brief overview of localism in surfing, with particular reference to big-wave surf breaks.

2 Surf gangs and the tragedy of the surfing commons: a brief overview

In his presentation of the problem of common-property resources, Kaffine (2009) details two different solutions, both of which link resource quality to property rights delineation. The more well known of the two, developed mainly by Gordon (1954), Scott (1955), Coase (1960), Hardin (1968), Ostrom (1990) and Cole (2002), establishes that absent well-defined property rights, resources often suffer from overexploitation—the “tragedy of the commons.” The implied solution to the problem lies in the development of private property rights or, instead, with the development of rules of use. Once implemented, this solution ends overexploitation and congestion, preserves rents and increases resource quality (Kaffine 2009). A second solution to the tragedy of the commons, rooted in later work by Demsetz (1967), Umbeck (1981) and Libecap (1989), suggests that property rights will be endogenously created by resource users when the benefits of developing and enforcing property rights exceed the costs.¹ One implication of this solution is that the probability of the endogenous creation of property rights is an increasing function of the quality of the common-pool resource. In the end, both solutions imply that the probability of the establishment of property rights is an increasing function of the quality of the common-pool resource.²

In answering questions regarding (1) the strength of informal property rights and resource quality, (2) the benefits to owners from an increase in resource quality and (3) the implications for empirical research if resource quality is endogenous to property rights, Kaffine’s (2009: 728) study of California’s surf gangs “. . . builds on the common-property literature by considering the strength of user-enforced informal property rights in an equilibrium setting, where welfare-maximizing locals and open-access nonlocals derive benefits from a resource [e.g., a surf break] of exogenous quality but suffer costs either from exerting exclusionary effort or from being on the receiving end of exclusionary effort.” Kaffine (2009) assumes that local surfers solve the collective action problem either formally or informally and decide how much effort should be expended to prevent nonlocal surfers from enjoying the local surf break.³ Using cross-sectional data on 86 surf breaks along the southern California coast, Kaffine (2009) finds a positive and statistically significant relationship between surf break quality, measured along an index from low to high quality, as judged by expert surfers, and informal property rights, specifically noting that a 10% increase in surf break quality leads to a seven to 17% increase in the strength of surf break property rights.

More recently, Mixon (2014) extends Kaffine’s (2009) study by (1) expanding the sample to include all of the state’s surf breaks (i.e., southern, central and northern California), (2) exploring additional features of surf break quality, (3) redefining “access” to the surf breaks by would-be users and (4) re-examining the linearity assumption in prior empirical modeling. In doing so, Mixon (2014) finds that previously unmeasured features of surf breaks, such as water current strength and geographic location, are important determinants of the degree of informal property rights that are established by local surfers, as is difficulty in accessing the break, a result not found in Kaffine’s (2009) empirical tests. As in Kaffine (2009), Mixon (2014) finds that the variable of interest, surf break quality, is positively related to the degree of localism present across California’s surf breaks. More specifically, Mixon (2014) finds that, beginning with a near top-notch surf break, a marginal increase in surf break quality leads to an increase in the probability of observing near-fiercest and fiercest informal property rights protections by local surfers of 28 and 23% points, respectively. These results are, like those in Kaffine (2009), quite compelling.

The following section of this study provides a discussion of the differences between big-wave surfing and traditional surfing, with particular attention to different “technologies” associated with the former, as well as its inherent danger.⁴ Next, we provide a brief presentation of localism in big-wave surfing in Sect. 4, while Sect. 5 provides the statistical framework for the construction of our alternative metric of surf break quality. The empirical model is also introduced in this section. Finally, Sect. 6 presents the results of our econometric tests, along with implications. The study concludes with some brief remarks in Sect. 7.

3 Is big-wave surfing a distinct market?

The question as to whether big-wave surfing represents a market that is distinct from traditional surfing revolves largely around the distinct technologies associated with the former activity, as well as differences in its more specialized techniques and its inherent danger.⁵ For example, big-wave surfing underwent a major evolution in the early 1990s when prominent big-wave surfers Laird Hamilton, Darrick Doerner and Buzzy Kerbox introduced the crossover sport of tow-in surfing (Struck 2013).⁶ According to Hamilton, the difference with tow-in surfing “speaks to having the right equipment and tools,” where “[b]eing versatile gives [a big-wave surfer] options (Struck 2013).” Big-wave surfing often involves being towed into very large surf breaks by a jet ski capable of traveling up to 70 miles per hour, which provides the necessary speed for accessing the breaks. Tow-in surfers also employ shorter surfboards, which provide added speed and greater maneuverability in wave faces exceeding 20 feet (Struck 2013).⁷

The dangers inherent in big-wave surfing also distinguish it from traditional surfing. Wipeouts in big-wave surfing can push surfers down as far as 50 feet below the surface, wherein they face disorientation that slows reaction time.⁸ In some cases, surfers have fewer than 20 s to get to the surface before the next wave arrives.⁹ One of the greatest dangers is the risk of being underwater by two or more consecutive waves, while surviving a three-wave hold-down is extremely difficult.¹⁰ Strong currents and water action at depths beyond 20 feet can also slam a surfer into a reef or the ocean floor, which can result in severe injuries or death.¹¹

The types of hazards mentioned above have killed several big-wave surfers. Some of the most notable are Mark Foo, who died surfing Mavericks in 1994, Donnie Solomon, who died in 1995 at Waimea Bay, Todd Chesser who died at Alligator Rock in Hawai’i in 1997, Malik Joyeux who died surfing on Oahu in 2005, Peter Davi, who died at Ghost Tree in 2007, Sion Milosky, who died surfing Mavericks in March 2011, and Kirk Passmore, who died at Alligator Rock in 2014.¹² Still, given the number of surfers (or wave-hours surfed) at big-wave venues, the big-wave surfing fatality rate is perhaps relatively low. This is likely due to the aforementioned human capital developments related to water skills in difficult surf conditions. It is also due to some of the aforementioned technology differences between big-wave and traditional surfing. As an additional example, one point of contention among big-wave surfers is the necessity of a surfboard leash, which, in the case of big-wave surfing, can often catch and hold big-wave surfers underwater, thus diminishing their opportunity to reach the surface (Struck 2013). In traditional surfing, surfers typically depend on the leash. Tow-in surfers have developed surfboards that include foot holds, similar to those on windsurfs, to provide security to the surfer (Struck 2013). These types of technological advancements are referenced by Hamilton, who notes that it is generally illegal to use jet skis at Mavericks, thus making it essentially a paddle-in only surf break, in concluding “. . . but then guys are dying out there [at Mavericks] too.”¹³

The differences between big wave and traditional surfing described above may have implications with regard to the degree localism associated with each form of the general sport. Laird provides some indication of such a possibility in his description of conditions either requiring tow-in technologies or allowing for paddle-in approaches. As he points out, some big-wave surf breaks exhibit what amounts to a gray area between when towing is optimum and when paddling is still possible, while other big-wave surf breaks, such as Teahupoo in Tahiti, exhibit a clear line in the sense that a wave face there of 15 feet or more precludes a paddle-in approach (Struck 2013).¹⁴ A tow-in only environment can easily become chaotic, according to Laird, as personal water craft and tow-in surfers continually crisscross the surf break at very high speeds. Moreover, tow-in only environments diminish the structure of the pecking order, which in a paddle-in only environment is determined by differences paddling skill, which are usually directly correlated with surfing skill (Struck 2013). In tow-in environments, jet skis equalize the surfers, thus blurring the pecking order in a sport where structure is paramount.

Lastly, where both towing and paddling are possible, different forms of danger are present. In these environments, not only are there different types of hazards associated with varying types of surfing traffic, a degree of individualism can develop that inhibits the camaraderie usually associated with big-wave surfing in paddle-in only environments (Struck 2013). As a result, safety becomes a considerable issue. What follows is a brief presentation of localism in big-wave surfing.

4 Localism and big-wave surfing

Kaffine (2009) and Mixon (2014) both employ Surfline.com’s Surfology glossary to define surfing “locals” as long-time regulars at a particular surf spot whose habitual surfing has endowed them with local knowledge and experience.¹⁵ Relying, in part, on the exposition of local norms among surfers given by Nazer (2004), Kaffine (2009: 730) indicates that the process of becoming a local varies from break to break but typically involves regularly surfing a site and showing deference (i.e., “paying one’s dues”) to the established locals. Next, and following Surfology, these studies add that locals are often very protective of their surf spot, particularly at the “lineup,” which is the area in water where surfers wait for waves, making it the point at which the common-pool resource, or surf break, is accessed by potential users.

In qualifying the types of protectiveness exhibited by local surfers against nonlocals, Kaffine (2009: 729) describes a type of localism continuum where hostility directed at nonlocals by local surfers may take the form of aggressive maneuvers on the waves, verbal abuse, or even physical confrontation. For example, in describing the “local vibe” around the Todos Santos big-wave surf break, located in the northern Baja area of Mexico, also known as “Killers,” Surfline.com offers a relatively mild summary:

Obviously, the guys who have been coming for a long time get first dibs. But if your skill level is there, everyone watches out for each other.

However, in describing the big-wave Puerto Escondido surf break off of Mexico’s southern coast, Surfline.com offers more forceful advice to nonlocals:

Puerto Escondido has some pretty intense crowds, complete with their own homegrown locals who rival the guys on O’ahu’s North Shore, so mind your Ps and Qs in the water, and be humble.

These vignettes provide a clear indication of the variation in how fiercely local surfers work to protect their “ownership” of a common-pool big-wave surf break.

Kaffine’s (2009) formal model considers a fixed number of identical local surfers of a surf break who collectively decide upon the optimal level of localism, or informal property rights protection, to apply against nonlocals in the vicinity of the break. Following Kaffine (2009), the nonlocals may be large in number, and they will traffic a big-wave surf break, such as Puerto Escondido, if the value to them of doing so exceeds that of the next-best big-wave surf break alternative. A big-wave surf break is considered to be of exogenous quality, yet the benefits of surfing a big-wave break increase with surf break quality and decrease with surf break congestion.¹⁶ Here, as in Kaffine (2009) and Mixon (2014), localism or informal property rights protection is costly, and the expected number of nonlocals at a big-wave surf break is a function of localism, break quality, and congestion.¹⁷ Also, as in the prior studies, the relationship of interest is that between the optimal strength of localism or property rights protection and big-wave surf break quality. This relationship is explored empirically in the following section of the study, beginning with the construction of an alternative, objective metric of surf break quality.

5 Big-wave surf breaks and localism: a statistical framework

The development of a new big-wave surf break quality metric follows the general statistical framework in Beard and Caudill (2009), though the present analysis is of individual big-wave surf breaks rather than collegiate football teams. It is assumed that each big-wave surf break is of some quality, given by quality rating $r_{i}$. For a given big-wave surf break, i, the quality rating is a function of the probability that big-wave surf break i outperforms big-wave surf break j in determining the top performers in Billabong’s XXL Global Big Wave Awards contests.¹⁸ These contests are continuous or open-ended in the sense that the big-wave surfers’ performances on the world’s big-wave surf breaks over the course of a year are videotaped and photographed so that they can be scored by a panel of experts (on behalf of Billabong). The annual winners of what has come to be called “the Oscars of big-wave surfing” receive prizes ranging from $5000 to $50,000, and totaling $85,000. In all, over $130,000 in prizes are awarded at the conclusion of the contest year. Thus, in establishing the quality ratings for the international big-wave surf breaks examined in this study, we view the breaks themselves as quasi-participants in Billabong’s annual big-wave surfing contests. Attesting to this view is the fact that the number of unique contest-winning surfers and the number of unique contest-winning big-wave surf breaks have been similar in recent periods.¹⁹

Returning to the statistical framework, the probability that big-wave surf break i outperforms big-wave surf break j in determining the annual winners and other finalists of Billabong’s XXL Global Big Wave Awards contests is given by,

$$\begin{aligned} P_{ij} =\frac{r_i }{r_i +r_j }. \end{aligned}$$

(1)

As in Zermelo (1929), the log-likelihood function is a product of probabilities like the one given in (1), or,

$$\begin{aligned} \log L=\sum _{i=1}^n {\sum _{j=1}^n {w_{ij} \log P_{ij}}}, \end{aligned}$$

(2)

where $w_{ij}$ is a variable equal to the number of times big-wave surf break i outperforms big-wave surf break j, and n is the number of big-wave surf breaks worldwide. In many cases, the variable w takes the value of zero (i.e., where big-wave surf break i never outperformed big-wave surf break j), though there are also many cases where its value exceeds zero.

A normalization is imposed on the model in order to confine the quality numbers, r, to the unit interval. In particular, we use the logistic transformation for r, or,

$$\begin{aligned} r_i =\frac{\exp (\theta _i )}{1+\exp (\theta _i )}. \end{aligned}$$

(3)

The likelihood function above must be maximized over the n-dimensional parameter vector, $\theta$. Maximization is accomplished using the algorithm of Berndt et al. (1974), which has the advantage of requiring only the first derivatives of the likelihood function. To illustrate the algorithm in Berndt et al. (1974), the parameter vector is denoted by column vector $\theta$. Given starting values for these parameters, the algorithm in Berndt et al. (1974) updates the parameter vector, as presented in Maddala (1977: 179), Greene (1993: 348) and Cameron and Trivedi (2005: 343), by,

$$\begin{aligned} \theta _{t+1} =\theta _t +\left[ {\sum _{i=1}^n {\frac{\partial \log L_i (\theta _t )}{\partial \theta }} \frac{\partial \log L_i (\theta _t )^{\prime }}{\partial \theta }} \right] ^{-1}\frac{\partial \log L_i (\theta _t )}{\partial \theta }\quad . \end{aligned}$$

(4)

As starting values, we used the logarithm of the odds of winning percentages for each big-wave surf break. Application of the logistic transformation resulted in starting quality ratings, $r_{i}$ (hereafter $r\hbox {Quality}_{i}$) equal to a big-wave surf break’s winning percentage. Once the parameter values have converged, the estimated covariance matrix is given by,

$$\begin{aligned} {\hbox {Cov}}(\theta )=\left[ {\sum _{i=1}^n {\frac{\partial \log L_i }{\partial \theta }\frac{\partial \log L_i ^{\prime }}{\partial \theta }} } \right] ^{-1}, \end{aligned}$$

(5)

evaluated at the converged values of the parameter vector.

The logistic transformation of pairwise comparisons technique employed in this study produces the ranking of the top 15 big-wave surf breaks presented in Table 1, which also includes descriptions of each big-wave surf break. As indicated there, the highest quality surf breaks worldwide, as determined by $r\hbox {Quality}$, are (1) Peahi/“Jaws” [USA], (2) Mavericks [USA], (3) Teahupoo [Tahiti], (4) Shipstern Bluff [Tasmania], and (5) Mulaghmore Head [Ireland]. The rQuality ratings for these top five surf breaks range from 0.361 to 0.987. Consideration of all of the 31 big-wave surf breaks worldwide produces the transformation curve shown in Fig. 1. There, the big-wave surf breaks located in California and Hawai’i are highlighted, three of which are examined in Mixon (2014).

Interestingly, where the common coverage occurs, the correlation coefficient estimate for $r\hbox {Quality}$ and Surfline.com Quality, the measure of surf break (common-pool resource) quality used in Kaffine (2009) and Mixon (2014), for the big-wave surf breaks studied here is both positive and significant. The magnitude of the correlation coefficient, +0.455, however, leaves room for $r\hbox {Quality}$ to perhaps offer an alternative to the Surfline.com quality measure used in Kaffine (2009) and Mixon (2014). This exploration is undertaken by way of the econometric model specified below.

Table 1 Top 15 big-wave surf breaks worldwide

The regression model used in this study to examine the relationship between big-wave surf break quality (i.e., $r\hbox {Quality}$) and localism is similar to that in Kaffine (2009), given below as,

$$\begin{aligned} \hbox {Localism}_{i} = {\beta }_{0} + \beta _{1}r\hbox {Quality}_{i} + \delta {{\varvec{X}}}_{i}+ {\varepsilon }_{i}, \end{aligned}$$

(6)

Fig. 1

Big-wave surf break quality captured through logistic transformation

wherein $\hbox {Localism}_{i}$ represents the intensity of property rights protection by locals at big-wave surf break i, $r\hbox {Quality}_{i}$ is the quality of big-wave surf break i, obtained from the logistic transformation process in the preceding section, and ${{\varvec{X}}}_{i}$ represents control variables capturing big-wave surf break congestion $(\hbox {Congestion}_{i})$, water quality ($\hbox {Dirty}_{i}$), paddle-out difficulty $(\hbox {Work}_{i})$ and access ($\hbox {Access}_{i}$). The variables $\hbox {Localism}_{i}, \hbox {Congestion}_{i}, \hbox {Dirty}_{i}$, and $\hbox {Work}_{i}$ are, following Kaffine (2009) and Mixon (2014), gathered from Surfline.com, which compiles information on surf breaks from expert surfers who are familiar with the local environment. The dependent variable in (6), $\hbox {Localism}_{i}$, is scored along an index ranging from 1 (least intense local protection) to 5 (most intense local protection). The first regressor in ${{\varvec{X}}}_{i}, \hbox {Congestion}_{i}$, is scored along an index ranging from 0 (least congested) to 10 (most congested), while the latter two are scored along indexes ranging from 1 (cleanest and least difficult to paddle, respectively) to 10 (dirtiest and most difficult to paddle, respectively).²⁰ Also following Mixon (2014), $\hbox {Access}_{i}$ is an index ranging from 1 (most accessible) to 3 (least accessible) that is based on the availability of parking near the break and the difficulty surfers face in getting to the beach.²¹

Of primary interest is the estimate of the coefficient $\beta _{1}$, which represents the impact of exogenous wave quality on localism. As pointed out by Kaffine (2009: 738), a positive (negative) result for $\beta _{1}$ in Eq. (1) would suggest that locals (nonlocals) derive greater benefits from increasing surf break quality, while a null result would suggest that locals and nonlocals benefit in a similar fashion from increasing surf break quality. As stated earlier, both Kaffine (2009) and Mixon (2014) find a positive result for $\beta _{1}$. However, empirical specifications in these studies employ surf break quality index scores—ranging from 1 (lowest quality) to 10 (highest quality)—that are developed through surveys of surfers with substantial knowledge of an area’s surf breaks, and obtained from Surfline.com’s individual travel reports, instead of the $r\hbox {Quality}_{\mathrm{i}}$ (logistic) transformation score generated in this study.

6 Localism and big-wave surfing: econometric results

Summary statistics for the big-wave surf breaks analyzed in this study are provided in Table 2. There, we note that the typical level of localism across the big-wave surf breaks worldwide is 2.95, on a range from 1 to 5. Table 2 also indicates that the average $r\hbox {Quality}$ score is 0.198 and ranges from a low of 0.040 to a high 0.987.

Table 2 Summary statistics

Results from OLS estimation of (6) are reported in the first portion of Table 3. The localism model applied to big-wave surf breaks worldwide that is specified in (6) yields an $R^{2}$ of 0.55. The results in Table 3 also indicate that $r\hbox {Quality}$ is both positively related to Localism and statistically significant, a result that supports those reported in the Kaffine (2009) and Mixon (2014) studies employing Surfline.com’s index scores of surf break quality. Also mirroring the OLS estimations in Kaffine (2009) and Mixon (2014), Congestion is both positively and significantly related to Localism. As in Kaffine (2009), Dirty is positively related to Localism; unlike in Kaffine (2009), this variable is statistically significant in the present study, indicating that localism at big-wave surf breaks is, unexpectedly, more prominent where water quality is relatively low.²²

Table 3 Initial econometric estimations

Next, and unlike in Kaffine (2009), Work is positively related to Localism, but insignificant in the present study.²³ The use of tow-in technology in the big-wave surfing case serves to reduce the level of effort required to reach the lineup, whereas the level of effort required to reach the big-wave lineup in paddle-in only environments is generally high across the board, thus reducing the effectiveness of this particular variable in the regression.

Lastly, whereas Kaffine (2009) and Mixon (2014) both find positive yet insignificant results for Access in the case of California’s surf breaks, the OLS results listed in Table 3 indicate that, in the case of big-wave surf breaks worldwide, Access is negatively related to Localism and statistically significant. Recalling that a greater value for Access means that a big-wave surf break is less accessible, this result supports the idea that the remoteness of surf breaks may affect localism by generating greater access costs to the potential users of a big-wave surf break.²⁴ Of course, a good example of this situation in the big-wave surfing genre is Cortes Bank, which is located 100 miles off the San Diego coast in California (see Table 1).

One issue with the results discussed above is that OLS estimation of (6) imposes a linear restriction on the measures of localism; Kaffine (2009) and Mixon (2014) address this issue by estimating (6) using an ordered logit model.²⁵ The ordered logit model is built around the same latent regression (i.e., $y^* = {{\mathbf{x}}^\prime }\beta + \varepsilon$) as the binomial logit model, wherein what is observed (y) in the ordered case is,

$$\begin{aligned} \begin{array}{ll} y = 0&{} \hbox {if } y^*\le 0,\\ y = 1&{} \hbox {if } 0 \le y^* \le \mu _{1},\\ y = 2&{} \hbox {if } \mu _{1} \le y^* \le \mu _{2},\\ .&{}\\ .&{}\\ .&{}\\ y=J &{}\quad \hbox {if } \mu _{J - 1} \quad \le \quad y^*,\\ \end{array} \end{aligned}$$

(7)

which is a form of censoring (Greene 2003: 736). In (7), the $\mu$s are unknown parameters to be estimated with $\beta$, and the mean and variance of $\varepsilon$ from the estimation are normalized to 0 and 1, respectively (Greene 2003: 736–737). This process produces probabilities,

$$\begin{aligned} \begin{array}{l} \hbox {Prob}( y = 0{\vert }{} \mathbf{x}) = \varPhi (-\mathbf{x }^\prime \beta ),\\ \hbox {Prob}( y = 1{\vert }{} \mathbf{x}) = \varPhi (\mu _{1 } - \mathbf{x}^\prime {\beta }) - (-\mathbf{x}^\prime \beta ),\\ \hbox {Prob}( y = 2{\vert }{} \mathbf{x}) = \varPhi (\mu _{2 } - \mathbf{x}^\prime \beta ) - ( \mu _{1 } - {\mathbf{x}}^\prime \beta ),\\ .\\ .\\ .\\ \hbox {Prob}( y=J {\vert }{} \mathbf{x}) = 1 - \varPhi (\mu _{J - 1} - \mathbf{x}^\prime \beta ),\\ \end{array} \end{aligned}$$

(8)

such that $0<\mu _{1}<\mu _{1}<\cdots <\mu _{J - 1}$ (Greene 2003: 737).

Results from ordered logit estimation of the model are included in the second portion of Table 3. The localism model applied to big-wave surf breaks worldwide that is specified in (6) yields an Estrella $R^{2}$ of 0.65 (Estrella 1998). The ordered logit results in Table 3 also indicate that $r\hbox {Quality}$ is both positively related to Localism and statistically significant, a result that again supports those reported in the Kaffine (2009) and Mixon (2014) studies employing Surfline.com’s index scores of surf break quality. Again, mirroring the ordered logit estimations in Kaffine (2009) and Mixon (2014), Congestion is both positively and significantly related to Localism.

The conclusions reached regarding both Dirty and Work are similar to those drawn from OLS estimations. As in Kaffine (2009), Dirty is positively related to Localism; unlike in Kaffine (2009), this variable is statistically significant in the present study, indicating that localism at big-wave surf breaks is, unexpectedly, more prominent where water quality is relatively low.²⁶ Also, and unlike in Kaffine (2009), Work is positively related to Localism, but insignificant in the ordered logit estimations given in Table 3. This again supports the idea that the use of tow-in technology in the big-wave surfing case serves to reduce the level of effort required to reach the lineup, whereas the level of effort required to reach the big-wave lineup in paddle-in only environments is generally high across the board, thus reducing the effectiveness of this particular variable in the regression. Lastly, and in the case of Access, the comparisons between the big-wave surf break models here and those in Kaffine (2009) and Mixon (2014) are a bit different. More specifically, estimation by OLS and ordered logit yield insignificant results in Kaffine (2009), while OLS estimation in Mixon (2014) yields an insignificant result for Access, and ordered logit estimation results in that study suggest that Access is both positively and significantly related to localism along California’s surf breaks. On the other hand, the ordered logit results presented here indicate that localism is less intense at big-wave surf breaks that are more difficult to access. This supports the idea stated above that the remoteness of surf breaks may affect localism by generating greater access costs to the potential users of a big-wave surf break.²⁷

Lastly, additional dummy variables capturing fixed effects by continent are included in the ordered logit specifications (see Table  3) in order to control for potentially unobservable differences in formal and informal institutions related to localism in surfing that lead to spurious correlations, such as might exist, for example, if the underlying physical conditions that give rise to great waves are correlated with countries that are more permissive of localism. In this case, we include three dummy variables—Australia, Europe, and NoAmerica—which are equal to 1 for big-wave surf breaks located on the named continents, and 0 otherwise. As the results in Table 3 indicate, although each of these logit coefficients is positively signed, none is statistically significant.

Table 4 Marginal probability estimates

As in Mixon (2014), marginal effects for the various regressors are presented in this study. As listed in Table 4, the marginal probability estimates for $r\hbox {Quality}$ are compelling. More specifically, a marginal increase in a big-wave surf break’s quality increases, by 34% points, the probability of observing local surfers employing the fiercest forms of informal property rights protections (i.e., Localism = 5). This result compares to the 23% point-increase found in Mixon (2014) for the traditional surfing genre. This particular result supports the idea that big-wave surfing and traditional surfing represent distinct markets, marked by different technologies and inherent dangers, such that localism at big-wave surf breaks exceeds that at traditional surf breaks in terms of ferocity, ceteris paribus. Lastly, the results in Table 4 also indicate that a marginal increase in the difficulty of accessing big-wave surf break decreases, by 4.4% points, the probability of observing local surfers employing the fiercest forms of informal property rights protections (i.e., Localism = 5).

Following Mixon (2014), we also address a statistical restriction in Kaffine (2009) regarding the use of index variables on the right-hand side of the model. In this case, dummy variables are substituted for Congestion, Dirty, Work and Access. In the cases of Congestion and Dirty, ConDum and DirtDum are dummy variables equal to 1, where Congestion and Dirty are, respectively, greater than 3 and 1, and 0 otherwise. In substituting for Work and Access, WorkDum and AccessDum are dummy variables equal to 1 where Work and Access are, respectively, greater than 8 and 3, and 0 otherwise. Thus, these dummy variables are generally equal to 1 where the index values exceed their respective means, and 0 otherwise.²⁸

Table 5 Additional econometric estimations

Results from this new empirical specification, again using the ordered logit approach, are presented in the first portion of Table  5. With exception of the Estrella $R^{2}$ of 0.49 in this case, the new results are essentially identical to their Table 3 counterparts. Specifically, the variable of interest, $r\hbox {Quality}$, remains positively and significantly related to the degree of localism at big-wave surf spots worldwide. The same is true for the dummy variable substitutions relating to surf break congestion (i.e., ConDum) and surf break water quality (i.e., DirtDum). Lastly, the difficulty in accessing the surf break, measured by AccessDum in this instance, remains negatively related to the degree of localism at big-wave surf breaks. Most of these results also hold when the continental dummy variable series is added to the specification. In this case, however, both Australia and NoAmerica are positive and significant, suggesting that there are institutional differences, vis-à-vis other continents, related to localism and big-wave surfing along coastlines on these two continents. Interestingly, the two parameters for Australia and NoAmerica are almost identical, suggesting that the formal/informal institutions governing localism on these two continents are perhaps quite similar.

As a final extension, we use MM estimation, which provides a combination of high breakdown value estimation and efficient estimation (Yohai 1987), in order to account for the high leverage points (i.e., breaks with quality well above the mean) present in our big-wave surf breaks sample (Rousseeuw 1984). Results from MM estimation are presented in the second portion of Table 5. As in the first ordered logit specification in Table 5, the variable of interest, $r\hbox {Quality}$, remains positively and significantly related to the degree of localism at big-wave surf spots worldwide. The same is true for the variables relating to surf break congestion (i.e., ConDum) and surf break water quality (i.e., DirtDum). The result for AccessDum also mirrors its ordered logit counterpart.

Lastly, the second set of MM estimates presented in Table 2 also mirrors its ordered logit counterpart. With the positive and significant estimate attached to $r\hbox {Quality}$, the results once again suggest that surf break quality is positively related to the likelihood of the fiercest degree of localism in big-wave surfing. Similarly as before, the insignificance of WorkDum supports the idea that the use of tow-in technology in the big-wave surfing case serves to reduce the level of effort required to reach the lineup, whereas the level of effort required to reach the big-wave lineup in paddle-in only environments is generally high across the board, thus reducing the effectiveness of this particular variable in the regression. Finally, the second set of MM estimates also indicates that there are institutional differences, vis-à-vis other continents, related to localism and big-wave surfing along coastlines of Australia and North America.

7 Concluding comments

Using data on big-wave surf breaks around the globe and a logistic transformation process applied to surfing competition outcomes in order to measure surf break quality, both of which represent new extensions of the published literature in this genre, this study finds that informal property rights are more likely to develop around the highest quality big-wave surfing spots than around those of lower quality. In fact, ordered logit estimations discussed in this study suggest that a marginal increase in big-wave surf break quality increases the probability of observing the most fiercely protective big-wave surf gang activity by more than 30% points, ceteris paribus. Thus, the findings presented here support the analytical model developed in Kaffine (2009) by suggesting that the gains to local surfers from preventing access to high-quality big-wave surf breaks by nonlocal surfers are larger than the costs of such prevention, and as such, local surfers collectively establish strong informal property rights protection of the big-wave surf break resource. Secondarily, the finding that the marginal effect of surf break quality on localism exceeds 30% points, being larger than that found in Mixon (2014) for traditional surfing, supports the idea that big-wave surfing and traditional surfing represent distinct markets, marked by different technologies and inherent dangers, such that localism at big-wave surf breaks exceeds that at traditional surf breaks in terms of ferocity, ceteris paribus. Finally, although this study focuses on the relationship between surf break quality and localism, its findings offer greater understanding of the general importance of informal property rights protection of common-pool resources, particularly with regard to the argument that endogeneity of property rights formation is important in assessing the impact of alternative property right regimes on resource quality.