A surplus production model with latent truncation and species targeting, with an application to Papua New Guinean fisheries

Fisheries Research 95 (2009) 296–308

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A surplus production model with latent truncation and species targeting, with an application to Papua New Guinean fisheries Stefano Mainardi Department of Informatics and Econometrics, Card. S. Wyszy´ nski University, ul. Dewajtis 5, 01815 Warsaw, Poland

a r t i c l e

i n f o

Article history: Received 17 March 2008 Received in revised form 24 September 2008 Accepted 25 September 2008 JEL classification: C24 C39 Q22 Keywords: Surplus production models Multi-species fisheries Incidental truncation Seemingly unrelated regressions PNG

a b s t r a c t This paper first reviews traditional bio-economic models of catch–effort equilibrium and later contributions based on augmented and revised specifications. To overcome some of the pitfalls in fisheries analysis, an approach is formulated which accounts for latent truncation in the fishing fleet, species targeting and non-linear long-term relationships among catch, effort and biomass. The procedure is applied to purse seine and longline offshore marine fisheries in Papua New Guinea, where tuna and other fish resources are believed to be under-exploited on the whole, but selective overfishing is reported to take place. Statistical evidence of incidental truncation is weak, with results being sensitive to the selection of variables. Based on regression diagnostics and expected signs/statistical significance of parameter estimates, nonlinear surplus production specifications prove to be more suited than original and unrestricted versions of the conventional approach for modelling the dominant (purse seine) fishery in PNG over the period 1979–2007, with both main and secondary target fishing being found not to exceed the maximum sustainable yield. In either case, policy implications of these results should be pondered against underreporting of official fish catches. © 2008 Elsevier B.V. All rights reserved.

1. Introduction In several developing countries, marine fishery authorities have been concerned with strengthening the relative position of the local fishing industry, reducing poverty in coastal communities, maintaining or restoring sustainable fish harvesting, and matching an increasing demand for fish products. Discordant assessments on the current state of fisheries complicate the debate as to which of these, sometimes conflicting objectives should be prioritised. Some policy-makers highlight the need to upgrade fishing port and fish landing infrastructures, regarded as undersized relative to fishing potential and too concentrated around major urban areas. Others argue that actual depletion and over-exploitation of a fishery is belied by underreported catch data. Conventional surplus production models are used to estimate the maximum sustainable average annual catch that can be removed from a fish stock without impinging upon the long-term sustainability of the fishery (i.e. the maximum sustainable yield, henceforth MSY: this definition is based on ecological principles which do not account for stochastic variability in the marine environment, and do not pay

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specific attention to stock abundance thresholds and depensation). In recent model refinements, stochastic variability is incorporated by including randomly varying elements in the fish population dynamics, in the form of stochastic components of carrying capacity or additive/multiplicative white noise (Quinn and Collie, 2005; Pitchford et al., 2007), but conventional models continue to be widely applied for fisheries management because of their simplicity. However, these models have been criticised for relying on too restrictive assumptions. Theoretical reassessments have spurred an interest towards model reformulations, but some concerns remain insufficiently addressed. The seminal contributions to bio-economic surplus production modelling of fisheries by Schaefer (1957) and Fox (1970), assume specific biological, economic and technological features of a fishery: (i) uniform distribution of the fish population and constant short-run catch per unit of effort (CPUE), in the presence of a given stock level and a constant catchability coefficient, (ii) uniform fishing effort in space and time, without accounting for the effects of varying fleet capacities, fishing gear and technology on its aggregate measures (reflecting a combination of capital, labour and energy inputs invested in fishing), (iii) uniform catch, with no distinction in terms of composition of multi-species catch or by-catch (with the latter defined as part of the catch incidentally taken in addition to the target species), (iv) rate of growth of the fish biomass

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based on an estimated fish population dynamics, resulting from a biological process of density dependence and a constant per-capita reproduction potential, (v) unique sustainable fishery equilibrium, where fishing effort is at a level consistent with long-term fishery sustainability, and (vi), in the absence of fishing, unique population path convergence to a stable equilibrium state of pristine biomass, corresponding to the ecological carrying capacity. As implicit in (ii), vessels are assumed to be equally representative of fishing effort, with no sample selection bias in any period of time. In empirical terms, assumption (iii) implies that multi-species fish catch can be regarded as non-separable according to type of gear and fishing zones, that is purely joint in production (or entirely disjoint in studies focusing on one species). In practice, fishing represents an in-between case of largely joint production activity, with a discretionary element in composition of output mix (Pascoe et al., 2007). This supports the rationale for model revisions, as proposed in this analysis. The paper is organised as follows. In the next section, two traditional surplus production models are first compared, followed by a review of revised assumptions and specifications, especially concerning the first four points (i–iv) (issues concerning wildlife and multi-species fisheries related to (v) and (vi) above are focused on by other studies: Kremer and Morcom, 2000; Hommes and Rosser, 2001; Bulte, 2003). Building upon literature contributions which highlight several drawbacks in the conventional approach, attention is particularly addressed here to problems of non-random sampling, fish species targeting/target switches, and non-constant marginal returns of a fishery, relative to fish biomass and fishing effort. Section 3 brings forward a three-stage estimation procedure aimed at jointly modelling these issues (supplementing this section, the Appendix briefly reviews possible directions for an extension of the model, data constraints and estimation problems, and technical aspects of the econometric methods). In Section 4, this procedure is applied to commercial multi-species marine captures by purse seine and longline in Papua New Guinea (henceforth PNG), over the period 1979–2007. The analysis of results is preceded by a discussion of key features of PNG fisheries, data sources and variables, and econometric estimates are compared with those of conventional surplus production models. Conclusions are drawn in Section 5. 2. Surplus production models: approaches and empirical problems 2.1. Conventional models Given the assumptions listed above and a reference unit of time with fish catch Q (in weight or yield), catchability constant c, fishing effort E, and fish biomass B, a commonly adopted production function is the following: Q = cE ϕ B

(1)

where a simplifying restriction ϕ =  = 1 is imposed by both Schaefer (1957) and Fox (1970). As expressed in the equation of motion (2), the Schaefer model assumes that the growth of the fish population is the net outcome of a logistic natural growth of the biomass (g(B), which depends on an intrinsic growth rate ı and the ecological carrying capacity K) and fish harvesting (Q). Based on B in optimum sustainable fishery equilibrium (with the first derivative of the function with respect to time dB/dt = 0) and replacing it in (1) (with unit parameter restrictions), Eq. (3) is derived. dB/dt = g(B) − Q = ıB[1 − (B/K)] − cEB Q = ˛E − ˇE

2

(2) 2

(with ˛ = cK and ˇ = c K/ı)

(3)

297

By differentiating Eq. (3) with respect to E and using the result for Q, the MSY-related effort and the MSY are given by EMSY = ˛/2ˇ and QMSY = ˛2 /4ˇ, respectively (subject to inequality constraints 0 < E ≤ ˛/ˇ, with E = ˛/ˇ implying zero value of the CPUE, and U = Q/E = ˛ − ˇE). The Fox model assumes a Gompertz natural growth trajectory of the fish stock in terms of population dynamics (Eq. (4)). Following the same approach as above, Eq. (5) is obtained, which can be linearised in terms of log-transformed CPUE (Eq. (6)). dB/dt = g(B) − Q = ıB ln(K/B) − cEB

(4)

Q = cKEe−(c/ı)E

(5)

ln U =  − E

(with  = ln(cK) and  = c/ı)

(6)

The MSY-related effort and the MSY are given by EMSY = 1/ and QMSY = e(␪−1) /, respectively. Given their different functional properties, if one assumes that e.g. the Gompertz distribution is a more adequate depiction of reality and therefore the Fox model specification (6) correctly estimates the MSY, the Schaefer Eq. (3) would systematically overestimate the MSY, and underestimate the MSYrelated fishing effort (Sparre and Venema, 1998). 2.2. Revisions and empirical problems The assumption under point (i) above has been questioned by Coppola and Pascoe (1998). Given a fixed level of biomass, capital and technology, and imperfect a priori knowledge by fishers of marine resource location, a production function should account for diminishing marginal returns of the fishery unless the fish habitat location is very dispersed. As in mineral resource extraction in the presence of varying ore grades, sea-bed areas of relatively higher abundance are bound to be harvested first, followed by the search for progressively less resource-abundant areas. Therefore in Coppola and Pascoe (1998), Eq. (1) is replaced by a Spillman-Mitscherlich production function, which incorporates a non-constant parameter E varying inversely to the level of effort (for a review of these functions, see Humphrey, 1997): Q = B(1 − E )

(with 0 <  < 1 and rescaled E ≥ 0)

(7)

which assumes that fish resources are fully accessible by fishing vessels, without technological and regulatory hindrances. An alternative view attributes the distribution of fishing vessels to differences in regulations among sea areas, rather than to the relative abundance of fish. Indeed, increasing efficiency in search and fishing technologies has allowed some fisheries to become increasingly independent of fish stock density, thus causing a quick degradation of the marine environment (Birkeland and Dayton, 2005; Wilson, 2006). A drawback of Coppola and Pascoe’s approach lies in data requirements for non-linear least squares estimation of the parameters (Greene, 2003: pp. 162–190). Relative to points (ii) and (iii), in traditional surplus production models both fishing effort and catch are usually specified as uniform aggregates. The number of days at sea (as a proxy for fishing effort) can be standardised, so as to account for different fleet capacities. Similarly, different gear categories (sets for purse seine, hauls for hand-line fishery, etc.) can be standardised and aggregated in relative effort units (Yew and Heaps, 1996). At a given fishing efficiency and geographical location, an increasing CPUE is usually regarded as an indicator of good standing biomass, while a steady decline in CPUE coupled with increasing fishing effort is likely to be a symptom of overfishing. However, the reliability of the CPUE as an index of marine resource abundance is improved if the actual amount of catch per unit of fishing gear (nominal CPUE) is adjusted to account for changes in gear efficiency and other

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factors unrelated to stock abundance (effective CPUE; FAO, 1999: Annex 5; Quirijns et al., 2008). Alternatively, a suitable measure of effort can differ depending on type of gear and vessel (Sparre and Venema, 1998: p. 22). Even if different features are included in a composite index (e.g. engine horsepower of vessel times the hours spent fishing), fishing effort is difficult to measure consistently, due to changing interaction and substitution among various units of effort, and the impossibility of choosing a proxy variable which is a priori proportional to fishing mortality (similarly, for stock assessment purposes, different measures of fishing effort can be appropriate, depending on relationships between packing density, school sizes and stock abundance: FAO, 1999, Annex 2). Given a limited or slow substitutability of capital and labour in vessels built with a specific on-board gear, a two-stage approach can first model effort as a function of cross-vessel inputs, followed by a second regression explaining fish catches in terms of estimated effort (FØI, 2003). Besides fishing effort, a linear trend variable can be used to account for technology or unspecified factors which are not captured by original surplus production specifications (Priyono, 2003: p. 509). In the presence of relatively higher-frequency observations, a dynamic Schaefer model can incorporate lagged endogenous catch, as a proxy for agents’ expectations (for a study on monthly catches by the Danish demersal trawl fleet in the North Sea, see FØI, 2003). If the uniform catch assumption (iii) is relaxed, MSY estimates are likely to be sensitive to the choice of aggregate multi-species versus individual species catches. If a quantity aggregate measure is relied on without additional information on catch composition by species, a vessel catching a large quantity of low value fish turns out to be spuriously more efficient than a vessel with a smaller quantity of high value fish. In turn, an aggregate value of a multi-species catch as output measure (as used by some studies based on stochastic frontier models, e.g. Sesabo and Tol, 2007) does not allow a distinction between allocative and technical efficiency, unless dual functions (including costs) are used. Since most fishing gear is not highly species-selective and price expectations are often inaccurate, both biases should partly level out if sufficient time and vessel aggregation is used (e.g. annual data; Pascoe and Mardle, 2003). Estimates will also vary according to whether account is taken of ecological responses of one species to another, changing abiotic factors in the marine environment, and changing cohort composition within individual fish species. At a disaggregate level, apparent favourable fishing conditions for a target fish species may be due to migratory pressures by predators and climatic events inducing a local fish prey population to concentrate into restricted fishing areas, with consequent risk of local depensatory effects for the species concerned (i.e. crossing of minimum population size below sustainable reproduction levels). At a relatively wider spatial level, marine ecosystems with severe loss of biodiversity are likely to be relatively more vulnerable to internal and external perturbations, with weaker compensatory dynamics in the system (Wilson, 2006). For highly migratory species, account should be taken of catches in neighbouring fishing areas and fish migration patterns across these areas. Unlike other tuna sub-species, the skipjack tuna is regarded as an example of viscosity, that is low interchange between broad fishing areas, with only small population groups undertaking large-scale migrations. Other pelagic fish, such as sardine, anchovy and yellowfin tuna, tend to swim in high-density schools, with different species often sharing the same sea area and competing for food (Basch et al., 2003). Different gears can have different longterm effects on the biomass, average fish body size and fecundity for individual sub-species. In overlapping fishing grounds in the Pacific Ocean, modal sizes of yellowfin tuna caught by longlines are found to exceed by 30–100% those of yellowfin catches by purse seines (Ortega-García, 1996). Purse seine catches in recent

years are considered to have affected the population dynamics of bigeye and yellowfin tunas, as discussed in Section 4 relative to PNG. Longline fishing gear is in turn regarded to have selectively removed the largest and oldest individuals, thus being responsible for reduced biomass of large-sized tunas. In principle, the latter is often regarded to be a problem of relatively less concern for sustainable fishery management, since large-sized tunas represent less than 5% of total Pacific tuna stock (Sibert et al., 2006). However, selective fishing of older and larger individuals may seriously disrupt the capacity of a fishery to recover from overfishing, due to the higher survival rate of their larvae (with spawning in the presence of greater metabolic reserves) and adult-led group behaviour in many fish species. Regarding assumption (iv), the fish biomass dynamics can be reconsidered in the light of revisions of other basic assumptions reviewed above. Fishery location, survival rates and the growth rate of a fish population can be influenced by environmental determinants and measures of fishery management. The former determinants include climatic factors, such as monsoon-related ˜ and changing depth of the therseasons, years affected by El Nino mocline, loss in resilience and hysteresis effects due to pollution, and interactions with the marine environment (coral reefs, mangroves) (Basch et al., 2003). Opposite to the resilience of small pelagic species, the slow growth rate and late age of first maturity of deep-water demersal fish, including some tuna sub-species, increases its vulnerability to overexploitation (FAO, 2007: p. 11). Through multi-year fishing restrictions or periodic closures (some of them based on decisions influenced by traditional ecological knowledge and specific events of social nature), rotational harvesting (pulse fishing) allows the biomass to rebuild (Cinner et al., 2006; Valderrama and Anderson, 2007). While these measures can be effective if the target species has low mobility and natural mortality, and can also benefit short-lived species in terms of biomass and average size compared with open access (Cinner et al., 2006), they may encourage shifts in fishermen’s strategies. Reduced quota and regulated sea-zone catches can be compensated by increased fishing efforts in unregulated fishing grounds, with target species replacement of often larger overexploited species with smaller short-lived fish groups (Asche et al., 2007; Danzell and Pauly, 1989). 3. Incidental truncation, multi-species targeting and non-linearity With the view to redressing deficiencies in conventional fisheries analysis examined above, this paper proposes a revised surplus production approach, based on a three-stage procedure. This procedure is especially suited to analyse a multi-species fishery characterised by gear- and time-varying species targeting, and consists of the following steps (rationale and functional specifications are discussed underneath in this section and in Appendix B): (1) A two-equation model of incidental truncation in the fishery, to test for unobserved sample selection. If statistically significant, the selectivity variable estimated from the output equation (Eq. (8) below) feeds as a control variable in step 2. (2) A simultaneous equation model of seemingly unrelated regressions (SURE), which accounts for correlation between target and non-target, or secondary target, species catches, thus ensuring asymptotic efficiency in the estimates. (3) Non-linear surplus production modelling, specified in terms of non-linear SURE (NLSURE) or single equation for the predominant fishery (or aggregate catch and effort measures of a multi-gear/species fishery, based on estimates from step 2),

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with non-linearity induced by non-constant marginal returns and target switching in fishing activities. 3.1. Fishing fleet with latent truncation Sample selection bias can occur due to the impact of different fishing regimes on observed and unobserved (latent) fishing vessels, with changes within and between the two groups occurring in time and space. Low levels of administrative control are typically followed by more restrictive regulations, coupled with changing features of fishing gears and other responses by fishermen (the case of PNG is outlined in the next section). Due to higher access fees for a restricted fishing zone, fishermen may partly shift to less productive fishing grounds and/or decide to concentrate more on high-value non-target species, or just exit the sector altogether, thus becoming partly or fully unobservable based on information of marine captures registered in the area. The implementation of satellite radar-monitored marine protected areas in high-seas enclaves between geographically adjacent fishing zones (e.g. exclusive economic zones, defined in Section 4) can have opposite effects. No choice is independent of the other, and selection decisions are influenced by institutional and related factors, including state of infrastructure development, vessel ownership, and scope for alternative uses of inputs (Yew and Heaps (1996) consider the opportunity cost of fishing relative to employment in sectors other than fisheries; an analysis of site-, householdand individual-related factors influencing quitting versus staying decisions in artisanal fisheries is provided by Cinner et al. (2008)). The model is specified for officially reported fish catch Q and a latent variable Z*, which represents the compliance by fishing vessels with local reporting of fish catches. While values of Z* are not observed, these values can be distinguished dichotomously based on a binary variable Z (=1 if Z* > 0, =0 if Z* ≤ 0), which reflects the selection decision, that is the actual participation of fishing vessels in registered fish catches (as opposed to illegal or unreported fishing). The exogenous variable vector X includes indicators of fishing gear and effort, while the variables in vector W represent determinants of latent truncation. Regarding the latter, the selection mechanism producing the observations in the sample of fishing vessels can be specified in terms of original or suitably transformed regressors from the outcome equation (i.e. taken from X in Eq. (8)) and other variables, so as to account for gear-related, climatic and institutional factors which help distinguish the observed from the non-directly observable (latent) group. Q = Xˇ + ε 

Z∗ = W ˛ + 

(8) (9)

Determinants of membership in the selected or observed sample of fishing vessels are likely to be correlated with those explaining the outcome, with inconsistent OLS parameter estimates for Eq. (8). For instance, eligibility for fishing license renewals is most often positively correlated with catch efficiency, thus possibly causing truncation from below in the observed CPUE (hence, the truncated mean is ‘pushed’ in the direction of the correlation, and vice versa in the opposite case; Greene, 2003: p. 782). Vessels outside the process generating the membership are not observed (as the case of PNG fisheries focused on in the next section), so that observations are available only for Z = 1. This renders the Heckman procedure of bias correction unfeasible (Heckman, 1979; Maddala, 1986). Provided that the error terms are jointly normal with zero mean and non-zero cross-section correlation (ε = / 0) and a priori fixing  = 1, a maximum likelihood procedure for consistent parameter estimates is formulated by Bloom and Killingsworth (1985).

299

3.2. SURE for multi-gear/multi-species fisheries As for SURE equations, a double-log specification yields estimates of catch–effort elasticity by fish catch and gear type. The use of these results can be twofold, depending on main features of fisheries and data availability. In the presence of balanced shares of fleets with different gears, this helps estimating composite gearadjusted measures of fishing effort, by providing estimates of the relative weights to be assigned to different fishing gears and/or varying efficiency levels of a specific gear in targeting different fish species bundles. If several gear types, fleets and fish targets are examined, this approach is more practical and statistically efficient than reliance on separate Gulland regressions, which disregard contemporaneous residual correlation across equations in a multigear/species fishery (Gulland, 1956). Alternatively, if the fishery is dominated by one fishing gear fleet, SURE estimation allows a better understanding of feedback effects with other fishing vessels, and can help in the selection of proxies of fishing effort and possible control variables for non-linear surplus production models (which otherwise, especially in the presence of many explanatory variables, require large samples for maximum likelihood convergence). Finally, in either case, if detailed information is available on factors such as location of fishing grounds, experience of the crew, and seasonal patterns of fishing, SURE crossequation residuals can highlight common unobserved components in multi-species and multi-gear fisheries, which can be useful in raising new hypotheses and stimulating the analysis in further directions. 3.3. Non-linear bio-economic modelling A production function for a fishery can be modelled as the product of two components, which reflect partly offsetting catch effects of catchability, fishing effort and biomass, as interacting factors. A component H depends non-linearly on fishing effort, so as to account for increasing followed by decreasing marginal returns of fishing effort. In a multi-species fishery, at a given level of biomass, decreasing returns can induce switches in fish catch targeting, due to lower biomass density in an overly exploited target fish population relative to non-target species. In the second component (V), the unit elasticity assumption in the Schaefer–Fox production function is removed by assuming a less-than-unit parameter  for fish biomass, i.e. decreasing marginal returns of the fishery (0 <  <1) or even absolutely diminishing returns beyond the MSY ( < 0). Reflecting an implicit long-term biomass-effort feedback (not directly modelled here) and subject to other possible factors influencing the state of marine resources in a long time horizon, this parameter will vary negatively with effort, with  →  min for E → ∞, thus implying downward shifts in catchability with high rates of fishery exploitation. Effort-biomass feedbacks make ceteris paribus conditions (for instance, changes in fishing effort with constant levels of catchability and/or biomass, or vice versa) less tenable than in the case of conventional factors of production. Moreover, to be closer to theoretical underpinnings of the MSY and its implications for effort–catch relationship (e.g. effort measured by number of fishing vessels versus returns to fishing effort, as in Harris, 2002: pp. 78–81), fishing effort and fish biomass in the two component functions of Eq. (10) could be reversed. However, Eq. (10), given by the product of H and V, does not distort the combined impact on fish catch, and is preferred here in view of mathematical tractability and empirical testing. Since the sustainability of a fishery is usually analysed over periods between 10 and 30 years (e.g. 17 years in Mkenda and Folmer, 2001),  can be assumed to be a near-constant parameter whose value indicates the state of a fishery within a

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sample period. Hence, the production function (1) is re-specified as follows: Q = VH = (B) exp[ − (E)−n ]

(10)

While it resembles conventional models in terms of parameters and variables, Eq. (10) implies more complex behavioural responses in the fishery. At a given biomass, with E = 0, n > 0 and  > 0, H → 0 (e−∞ ), from where H traces an upward S-shaped pattern up to an asymptotic saturation level e (for E → ∞). Fish natural growth (g(B) in (2) and (4)) can be rearranged in terms of time-dependent logistic and Gompertz distributions, respectively. For the logistic distribution, B(t) = K/[1 + ˇe−␦t ], which yields a log-reciprocal surplus production model with (log)linear and non-linear time trends, expressed in Eq. (11), where ˛1 = (1 − ω) + ω ln(ıˇK), ω = /( − 1),  1 = (1 − ␻) and  2 = −ıω. Likewise, for the Gompertz distribution B(t) = K exp[−ˇe(−␦t) ], thus yielding the surplus production specification (12) with no non-linear time trend (and ˛2 = (1 − ω) + ω ln (ıˇ), while ω,  1 and  2 are defined as above). ln Q = ˛1 − (1 − ω)(/E n ) − (ıω)t − ω[ln(1 + ˇe−ıt )] = ˛1 − 1 /E n + 2 t − ω[g(t)]

ln Q = ˛2 − (1 − ω)(/E n ) − (ıω)t = ˛2 − 1 /E n + 2 t

(11)

(12)

Unlike conventional models, the MSY is not identifiable directly in terms of fishing effort (given n > 0 and ω = / 1 in (11) and (12), d ln Q/dE = 0 only with  = 0), but its approximate location can be inferred from signs and statistical significance of estimated parameters. The trends will be (i) upward-sloping if the MSY has not been reached (if ω < 0, i.e. 0 <  < 1), (ii) downward-sloping if the fishery operates beyond the MSY ( < 0), or (iii) (by definition of time-invariant optimum sustainable fishery equilibrium) not statistically different from zero if most fishing occurs around the MSY (i.e.  ∼ = 0). Moving from (i) to (ii), that is passing from sustainable to unsustainable states of a fishery,  1 will shift from higher to lower values than , which implies declining catch–effort elasticity for given levels of fish catch (in models (11) and (12), this elasticity is equal to  1 /Q; Gujarati, 1992: p. 241). Beyond theoretical distinctions, close attention should also be paid to interpreting econometric estimates. In the absence of negative trend parameters, if 0 <  < 1 and  1 ∼ = 0, the fishing effort variable may be negatively related to catch, but overshadowed (in terms of multicollinearity effects, with 1/En and t being positively correlated) by enduring catch increases. This is likely to originate from combined effects of biomass variations (other than those traced by the natural growth paths initially hypothesised), undetected efficiency improvements (which should be filtered out prior to surplus production modelling: see Appendix A) and excessive fishing, and implies conditions similar to those of case (iii) outlined above. Model specification (11) is to be preferred to (12) if one cannot reject a zero parameter restriction for a non-linear trend variable. The latter may be given by t2 or t-0.5 , as a proxy for the non-linear trend component in (11) (for a similar approach in a different context, see Franses, 1994). Relative to surplus production Eqs. (3) and (6), Eqs. (11) and (12) are non-nested. However, the production function (1) (Q = cEϕ B ) can assume parameter boundaries 0 < ϕ ≤ 1 and 0 <  <1, thus partly encompassing unrestricted versions of Schaefer and Fox models (partly since  = / 1). Optimum sustainable equilibrium conditions can be obtained by following the same approach as for (11) and (12). This yields equation specifications which, compared with (11) and (12), differ in terms of parameter equality restrictions (for the Gompertz,  2 = −ıω, but

constant term and parameter associated to fishing effort become (keeping the same symbols): ˛ = ln c + ωln(ıˇ) and  1 = ϕ(1 − ω), with ω = /( − 1) as above) and mathematical form for fishing effort (the reciprocal term is replaced with the log-transformed variable ln E). Hence, Eq. (10) can be tested against Eq. (1) with a Box–Cox regression for selection of functional specification, including log-reciprocal versus double-log forms, i.e. specifications (11) and (12) versus unrestricted conventional models (among reviews of this procedure, see Dougherty, 1992 and Neter et al., 1996), or by direct comparison of regression diagnostic statistics and tests for non-nested models (Charemza and Deadman, 1993: chapter 8).

4. An application to PNG offshore marine fisheries Unlike countries with a longer history of extensive commercial fishing activities, PNG as a whole is not regarded as a case of severe overexploitation of offshore marine resources. Yet, a number of aspects highlight a need for assessments at various levels. The sea areas surrounding eastern Indonesia and PNG, located between the islands of Sulawesi and New Guinea, are considered to contain one of the highest levels of marine biodiversity in the world (Kramer et al., 2002). Although in recent years increasing costs of fishing materials and fuels are considered to have reduced reliance on fishing in coastal communities, some of these communities are highly dependent on small-scale and subsistence fish harvesting, with small-scale fish catches estimated to cover 35% of protein intake for parts of PNG’s population (FAO Fishery Country Profile, www.fao.org/fishery/countrysector). On one hand, fishing in coral reef waters and remote coastal areas remains under-exploited and poorly developed, and is estimated to lag far behind the MSY (Cinner and McClanahan, 2006; MRAG, 2005; OEC, 2000: p. 20). On the other hand, some coastal areas, especially in the vicinity of main markets, have been experiencing environmental degradation and overfishing, which have been exacerbated by enduring conflicts in the transition from highly fragmented (common in PNG) customary and communal land and marine tenure to more defined property rights, increasing transgressions of temporary fishing closures, and cash inflows from mining partly invested in fishing activities (Foale and Manele, 2004; Macintyre and Foale, 2007; Turner et al., 2007). In the presence of sparsely populated coastal regions and a claimed exclusive economic zone (EEZ, defined as landsurrounding sea areas up to 200 nautical miles (i.e. nearly 370 km) wide from the shore and under national jurisdiction: 1982 UN Convention of the Law of the Sea) which is more than three times larger than its land area (World Resources Institute Earthtrends, www.earthtrends.wri.org), the extensive fishing ground makes surveillance and regulation enforcement particularly difficult for PNG fishery authorities. Offshore marine fisheries can offer a potential outlet to reduce pressure on coral reef fisheries. As such, both fisheries should be the object of in-depth analysis, aimed at better understanding prospects for sustainable management. The remaining part of this section first highlights some key features of the offshore sector in PNG, by focusing on specific institutional, environmental, technological and demand–market factors which, within the general framework outlined in Section 3, are likely to influence both the composition of the fishing fleet and its marine catches in the PNG EEZ. Following some remarks on data sources and variables and preliminary statistical analysis, the three-stage surplus production modelling approach is applied to tuna fisheries, so as to assess the relevance of these factors and compare model respecifications (11) and (12) with conventional surplus production equations in terms of regression diagnostic statistics.

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4.1. Fishing fleets, gears and fish captures Based on fish catch landings from the EEZ, PNG fisheries have undergone periods of high exploitation followed by years of relatively lower intensity of fishing. This pattern is partly influenced in a spurious way by institutional factors. Completion of logbooks for catch registries became mandatory only in 1997, and large fish catch amounts in previous years are presumed to have been landed outside PNG, thus remaining unreported and untaxed (OEC, 2000: p. 19). In the offshore marine fisheries in the PNG EEZ, where tunas tend to cover 80–90% of fish captures, more than two thirds of licensed tuna vessels are foreign-controlled. Since the mid-1990s, PNG government efforts have been directed towards fostering participation by local companies, and also limiting the number of fishing boats so as to maintain sustainable levels of harvesting. In 1995, the government ceased issuing foreign long-lining licenses. Since the late 1990s, to avoid local charter arrangements by foreign operators, new licenses have been reserved to bona fide domestic entrants. ˜ events, PNG marine fisheries are strongly influenced by El Nino which is regarded to substantially affect year-to-year variations in resource abundance. Despite the warm current of nutrient-poor ˜ does not appear to always inhibit the fish tropical water, El Nino population dynamics: this is registered for albacore among other marine species, but an opposite enhancing effect seems to have been associated with yellowfin (PFRP, 1998: p. 7). These changes may induce in turn a relatively higher presence of full-time fishing vessels in some years, as opposed to part-time or occasional boats, with part-time fishers being more open to eventually retiring or temporarily shifting to alternative occupations. As a possible case of latent changes in the fishing fleet, this can be a source of sample selection bias, due to different characteristics of fishermen in these categories (Hannesson, 1989: p. 52; Hanna et al., 2006: p. 16; three categories of fishermen are generally distinguished, with FAO criteria based on the relative contribution of fisheries to their livelihood and/or share of working time devoted to fishing: full-time, i.e. at least 90% of livelihood from fisheries or time spent in that occupation, seasonal or part-time (30–89%), and occasional (less than 30%): see FAO, 1999a). In the absence of an effective enforcement of government fisheries regulations, for a number of species commercial fishery has registered reduced harvests and over-exploitation, often in the vicinity of main markets. However, on the whole the stock status of tuna in the PNG EEZ is regarded as healthy, except for bigeye which is presumed to be overfished. This reflects the general trends of tunas in the Western Pacific Ocean, with bigeye believed to be overexploited, skipjack and albacore under-exploited, and yellowfin being possibly close to full exploitation (Lungren et al., 2006). MSY estimates of PNG tuna resources are subject to wide margins of variation, from marginally higher to possibly three times higher than current catch levels (OEC, 2000: 20; MRAG, 2005). Purse seiner and longliner operations are restricted to grounds beyond 6 miles from the coastal shores (NFA, 2003a). Discrepancies are found between logbook catch registries and export of derived fished products, with an apparent underreporting of 4% by purse seiners, and up to 30% by longliners (this problem is common in fisheries analysis: see Appendix A). The latter percent figure concerns to a large extent sharks, whose unreported annual catches from longline fishing may amount to more than 6000 tonnes, that is much higher than official catches of less than or barely exceeding 1000 tonnes reported in recent years (MRAG, 2005). Since the adoption of the tuna fishery management plan in 1999, the total allowable catch limit of 338,000 tonnes for purse seine vessels was exceeded in 2003 and 2006. By contrast, annual tuna catches for longline vessels, which largely share the same fishing areas, have

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remained at levels which are less than half of the respective total allowable catch limit, fixed at 10,000 tonnes per year (NFA, 1999). The increasing share of purse seines in total EEZ fish catches, from slightly less than 70% in the early 1980s to 98% in the period 2005–2007, is largely due to expanding activities of foreign vessels, with the remaining percentage shares represented by longliners (NFA database; PFRP, 1998). Relative to varying catch composition over time, increasing demand for shark-fin and shark-meat from Asia and improved storage facilities in the late 1990s encouraged some longliners to diversify towards deliberate targeting of sharks, thus shifting from sharks by-catch to shark catch shares exceeding 10% of total catches. More recently, PNG fishery authorities have established an annual total allowable catch limit of 2000 tonnes for sharks and a phasing down of the sharks fishery, with prohibition of new entrants and removal of two longline vessels in 2003 (NFA, 2003b). A further explanation of the above trends in fishing fleets refers to the evolution of fishing gears and its consequences for fish targeting. Fish aggregating devices (FADs) were introduced in the 1980s by purse seine vessels from the Philippines operating in PNG EEZ, and have become relatively more common in the 1990s due to higher fish catch success rate. These devices are considered to increase also the targeting capacity, by allowing higher catches of juvenile bigeye (which is typically fished by purse seines, along with skipjack and young yellowfin). While both yellowfin and bigeye are most highly priced among tunas, the premium relative to less priced tunas is only marginal for juvenile fish catches (relative to skipjack tuna price, a 6% gap of price/kg for juvenile yellowfin contrasts with a more than 250% price jump for adult yellowfin; PFRP, 1998: p. 4). Longline fishing vessels tend to concentrate on deep-water species, mainly including adult bigeye, yellowfin and albacore (as discussed in the previous section). As a consequence of possibly excessive captures of juvenile high-value sub-species, the sustainability and overall net economic benefit for the fishery may be compromised, mainly to the detriment of longliners. With improved species targeting allowed by modern fishing gear, the allocation of tuna catch could be managed towards greater long-term sustainability (especially if adequate monitoring is also undertaken for larger size tunas, as considered in Section 2) and economic returns if purse seiners were to partly replace high-value juvenile tuna sub-species with skipjack, which is considered to be not affected by overexploitation. In contrast with trends registered for other tuna sub-species (bigeye, yellowfin), skipjack biomass estimates indicate a net increase in resource stock in the western Pacific Ocean over the last 50 years, which may be related to biomass reductions of large predators, including larger tunas (Sibert et al., 2006). The potential damage to the longline fishery is aggravated by reduced access of these vessels to some fishing grounds, where mooring ropes of inactive FADs are believed to discourage longline fishing (FADs are either anchored in the fishing ground or drifting with call-up buoys or sensors, and some FADs in disuse with broken-off float sections have anchor ropes in the sea, which can tangle with longline gear; Kumoru (2002)). To counter these effects, ad hoc rules have been introduced in the last few years, including maximum numbers of allowable anchored FADs per licensed purse seine vessel (NFA, 2002). 4.2. Data sources, variables and preliminary statistical analysis The analysis is based on National Fisheries Authority (NFA) annual data of purse seine and longline (mainly tuna) fish catches in the PNG EEZ, over the period 1979–2007, and the respective fishing effort measured in terms of number of vessels, sets and fishing days (www.fisheries.gov.pg). Abnormal climatic events are proxied by a dummy for years affected by episodes of marked seasonal oscilla-

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Table 1 List of variables. Variables

Description

Operational set up of data or dummies

Model

Dependent variables lncatch

Fish catch in tonnes

Panel batches: [m1] skipjack by purse seine, [by1] bigeye, yellowfin and other species by purse seine, [m2] bigeye, yellowfin and albacore by longline, [by2] blue marlin, sharks and other species by longline As a predictor variable for regression tree analysis: [m1 + by1] purse seiners, [m2 + by2] longliners Panel batches: [m1] purse seiners, [m2] longliners Time series only: purse seiners [m1] Panel batches: [by1] purse seiners, [by2] longliners Time series only: purse seiners [by1]

Incidental truncation

Purse seines: % species other than tunas; longlines: % blue marlin, sharks and species other than bigeye, yellowfin and albacore tunas (scale: 0-100) Number of days absent from port spent fishing within the EEZ (excluding time spent without fishing due to breakdown or bad weather) ln(days/ves) Number of times the gear has been set or shot (purse seine) or hooks recovered (longline) (whether or not a catch is made) lnset·pseine

Regression tree

1/sets (purse seiners) Number of purse seiners or longliners fishing in the EEZ lnves for panel observations [m1] and [m2]; 0 otherwise 1/ves (purse seiners) Regressor for longline main catches in years with mandatory logbook registries; 0 otherwise 1 by-catch >20% of total catch; 0 otherwise (20% threshold based on regression tree analysis) 1 mandatory, i.e. from 1997 onwards; 0 otherwise 1 year recorded with ENSO events; 0 otherwise 1 vessels with purse-seine fishing gear; 0 long-liners

Surplus production Incidental truncation and surplus production

lnmaincatch

Main target catch

lnbycocatch

By-catch and catch of minor target species

Explanatory and dummy variables bycatchr

By-catch rate

lnday

Number of fishing days

lndayves lnset

Number of fishing days per vessel Number of sets

lnsetpse

Set slope dummy for purse seine vessels Reciprocal number of sets Number of vessels

setrev lnves lnvesmc

dumbyc

Vessel slope dummy for main target catch Reciprocal number of vessels One-year lagged purse seine catches of (largely juvenile) bigeye and yellowfin tuna High by-catch ratesa

dumlogreg

Mandatory logbook registries

enso

˜ Southern Oscillation events El Nino

pseine

Purse seine dummy

vesrev lnjuvbeyft

SURE Surplus production SURE Surplus production

Regression tree

Incidental truncation SURE and surplus production

SURE

Incidental truncation Surplus production SURE

Incidental truncation

Incidental truncationb Incidental truncation and SURE Incidental truncation and SURE

a

Fish species regarded as non-target by most fishing vessels in the PNG EEZ (blue marlin, sharks, and other species, excl. skipjack, bigeye, yellowfin and albacore). Outcome variable in regression tree analysis. Symbols preceded by ln: log-transformed variables, dln: differenced logarithms. Sources: PNG National Fisheries Authority (www.fisheries.gov.pg); for enso: en.wikipedia.org. b

tions in air pressure differences and water temperature anomalies in the tropical Pacific Ocean (Table 1: enso), or alternatively by the NASA index of global land-ocean temperature anomaly (UNEP GeoData, geodata.grid.unep.ch; regression estimates when the latter proxy is used are similar to those based on the dummy enso, and are not reported). Fish catches have been aggregated by taking account of main target versus less relevant target fish or by-catches, with fish species bundles varying for the two fishing gear fleets (Table 1). For purse seines, bigeye and yellowfin have been regarded as minor target catches (with joint catches corresponding to 36% of skipjack caught by this gear on average over the sample period), but they do not form part of by-catches (Table 1: bycatchr). If NFA logbook-reported catches are compared with FAO estimates, as a different source of marine capture data by fish species

for PNG (covering the period 1994–2005 on broad fishing areas, whose boundaries are not strictly comparable with those of the EEZs, lying within or outside the latter), the two series markedly differ from each other. EEZ-related catches are twice as high for major tuna sub-species (skipjack, yellowfin) and tuna fishing as a whole, while gaps between EEZ and FAO estimates are reversed for subspecies with minor shares in total tuna catches (bigeye, albacore) (Table 2). However, similar time series dynamics between the two sources concern most tuna sub-species, as highlighted by correlation coefficients on log-differenced annual catch figures (Table 2: r(NFA-FAO), PNG EEZ versus PNG Seas). Compared to adjacent fishing grounds, registered tuna catches in the PNG EEZ fall short of the respective figures in adjacent eastern Indonesian seas, by amounting to nearly 70% of the latter. Except for albacore (for which fishing

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Table 2 Tuna catches in the PNG EEZ: sub-species composition, relative importance and variations vis-à-vis respective catches in eastern Indonesia (1994–2005). Tuna species

Skipjack (Katsuwonus pelamis) Bigeye (Thunnus obesus) Yellowfin (Thunnus albacares) Albacore (Thunnus alalunga) Total tuna

Average annual catch (thousands tonnes)

138.8 1.0 40.9 0.4 181.1

Correlation coefficients and ratios (log-differenced annual catches) PNG EEZ vs. PNG Seas

PNG EEZ/seas vs. eastern Indonesian seas

r(NFA-FAO)

Ratio (NFA-FAO)

r(NFA-FAO)

r(FAO-FAO)

Ratio (NFA-FAO)

0.53 0.6* 0.86** 0.84** 0.6*

2.2 0.4 2.4 0.9 2.2

−0.14 −0.32 0.12 0.6* −0.1

0.23 −0.18 0.06 0.7* 0.14

0.85 0.1 0.5 0.2 0.7

Sources: estimates based on PNG NFA data (www.fisheries.gov.pg) and FAO FishStat Plus (www.fao.org/fishery/statistics), for PNG fishing zones and Indonesian seas adjacent to PNG (Indonesian estimates refer to western Pacific Ocean, except for albacore: eastern Indian Ocean). * Statistical significance of correlation coefficient p < 0.10. ** Statistical significance of correlation coefficient p < 0.01.

in PNG is relatively more common in the Coral Sea area, that is not far from southern West Papua waters), no significant positive or negative co-movements are observable between the two fishing areas based on correlation coefficients (Table 2). By comparison, figures for other adjacent fishing zones tend to be substantially lower than eastern Indonesia (for instance, Fiji registers an average of less than 5% of PNG EEZ tuna catches over the same period) and follow erratic patterns in some cases (skipjack catches in the Solomon Islands; FishStat Plus: www.fao.org/fishery/statistics). For this reason and the geographical proximity, potential migratory effects or possible environmental factors simultaneously affecting adjacent fishing zones (discussed in Section 2) have been tested here limited to the West Papua Sea. To this purpose, a regression equation for main target catches in the PNG EEZ can be specified as model [4] in Table 3, with the inclusion as an additional explanatory variable of log-transformed West Papua tuna catches grouped in the same way as the dependent variable (skipjack vs. bigeye, yellowfin and albacore). OLS regressions estimates (not reported) show no influence of tuna catches in adjacent eastern Indonesian seas. Among possible indicators of latent sample truncation, in this analysis the use of a categorical variable distinguishing fishing fleets/years with high versus low by-catch rates has been preferred to officially reported fish by-catch rates, due to the presence of clustered observations and the likely low degree of precision in reports for these fish catches. In order to identify a categorical variable reflecting the extent to which different levels of recorded by-catch rates contribute to ‘characterise’ periods with/without mandatory logbook registries in the PNG EEZ, so as to split the panel sample (58 observations by year and fishing gear) into a number of mutually exclusive homogeneous sub-groups, regression tree analysis can be useful. This statistical technique is non-parametric (with goodness-of-fit based on a Gini measure of impurity of nodes: www.statsoft.com/textbook), and helps highlight interactions among a number of predictor variables and between the latter and an outcome variable, in the presence of unstructured problems and no distributional assumptions (Yohannes and Hoddinott, 1999). Binary recursive partitioning on the dummy dumlogreg (see Table 1) for vessels fishing in the PNG EEZ point to by-catch rates (bycatchr: including blue marlin, as a billfish with relatively small and erratic year-to-year catches) and level of annual catches (lncatch), as by far the most relevant classification criteria of years/gear fleets under different fishery regulatory frameworks, with a nearly 93% predictive accuracy (in regression tree results illustrated by Fig. 1, the importance of predictors ranked on a zeroone scale, is: bycatchr 1, lncatch 0.9, lnves 0.72, lnday 0.69). These results are robust to varying sets of predictor variables and the use of non-equal weights, i.e. asymmetrical costs, for mispredictions (not reported here), and identify observations which are more likely to represent less regulated years (bottom-left quadrant of

Fig. 1. Fishery regulation (years/gear fleets with/without mandatory logbook registries) vs. fish catch and by-catch rates: recursive partitioning in tree regression, Outcome variable: dumlogreg. Predictor variables: lncatch, lnday, lnves, bycatchr (list of variables in Table 1).

Fig. 1). These observations correspond to annual catches of less than 127 thousand tonnes (i.e. lncatch < 11.753, which is the bifurcation threshold estimated at the root node, with some purse seine catches exceeding this value in years of compulsory logbooks), and by-catch rates lower than 20% (based on the second partitioning in the regression tree). The latter has been chosen as a threshold suited to distinguish high from low by-catch rates in the econometric analysis (Table 1: dummy variable dumbyc). 4.3. Econometric results For the first stage, observations are arranged in a time-series cross-section panel, based on fishing gear and relevance of the fish catch, i.e. main target versus minor target (co-catch) and by-catch. Log-transformed fish catches are modelled as a function of fishing effort, which is defined in terms of size of the fleet and intensity of use, with the latter being proxied by fishing days per vessel (Table 1: lndayves). Although the latter variable is not typically considered in surplus production models, in this stage of the analysis it can help understand to what extent fishing by a more numerous fleet, due to among others favourable weather conditions in some years, may have been also fostered by higher time spent in this activity by each vessel. Annual rates of change in fleet sizes, rules on fish catch reporting and their interactions with by-catch rates, and possible fleet composition changes induced by disrupting climatic events, are accounted for by four variables in the truncated selection equation (Table 3: model [2]). Alternatively, the fleet dynamics is used as an explanatory variable in the outcome equation, and fishing days per vessel can contribute to explain the truncated selection

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Table 3 Incidental truncation and SURE regression estimates: PNG purse seine and longline catches, 1979–2007. Method [model] OLS [1]

Maximum likelihood [2]

Dependent variable

Constant pseine lnves lnvesmc lndayves dlnves lnset lnsetpse lnjuvbeyft

lncatch Estimates

t-statistics

−2.94 3.29 1.01 0.35 1.19

−4.14 18.2* 8.58* 8.97* 6.29*

N

*

Estimates −2.31 3.53 1.16 0.34 0.82

lnmaincatch t-statistics −2.79 13.9* 7.75* 6.16* 2.82* *

Estimates 0.92 3.39 1.14 0.33 −0.18

Constant dumlogreg enso dumbyc dlnves lndayves ε ε ε ε(29) DW 2 Ps.R2 [Radj ]

SURE (FGLS) [4] [3]

0.61 −0.51

1.24 0.523 [0.92]

(Truncated) Selection equation 0.3 10.5 1.76*** −0.3 −0.58 −1.22 0.34 0.3 −2.66 −0.6 1.54 0.6 −2.42 0.77 4.68* 0.95 0.49 0.74 0.79 0.31 3.04* 0.37 −0.56 −3.86* −0.44 0.545 105 (116)

0.546

t-statistics **

2.24 16.1* 8.44* 6.91*

Estimates 1.57 2.58 1.64

lnbycocatch t-statistics *

5.77 16.7* 21.9*

Estimates

t-statistics

−4.52 6.83

−5.66* 5.08*

1.28 −0.35

12.2* −2.11**

0.76 −0.37

3.23* −1.81***

−0.94

0.02

0.9

−0.01 0.05

−0.1 0.4

−1.68*** 3.81* 2.86* 3.41* −2.58* 1.49 0.77

2.23 0.57

55 (58)

␧ , ␧(29) : Autoregressive parameters of residuals in auxiliary regression test for residual correlation (lag of order 1 and 29, for serial autocorrelation and contemporaneous cross-equation correlation, respectively). Pseudo R2 (McFadden likelihood ratio index): 1 − [lnL/LnL0 ]. N sample size (in italics: including missing observations). * Statistical significance (t-statistics): p < 0.01. ** p < 0.05. *** p < 0.10 (otherwise: p > 0.10).

mechanism (Table 3: model [3]): the introduction of compulsory logbook registries may encourage many fishing vessels to operate more openly, thus increasing the time officially spent in this activity. Indeed, compared to respective average numbers of fishing days in the sample period preceding the introduction of compulsory logbooks, fishing days per vessel in the period 1997–2007 were 15% higher for purse seiners, and more than twice as high for longliners. This has no systematic relationship with fleet sizes: between the two sub-periods, purse seine vessels more than double on average, while the number of longliners shrinks by one third (PNG NFA data). As commented above, observations are available only for Z = 1 (i.e. for vessels officially reporting fish catches Q) and logbook registries have become compulsory for PNG commercial fisheries only since the late 1990s. This entails a relatively high risk of catch underreporting over most of the panel sample analysed, with negative parameter signs expected for the dummy dumlogreg and average fishing days per vessel as possible determinants of a zero-truncated selection bias. After accounting for regulatory measures and the fishing fleet dynamics over time (dlnves), high catch rates of nontarget species are presumed to have remained unreported to a relatively greater extent in official fishery statistics (Section 4.1), thus implying an expected negative parameter sign also for the ˜ events conproxy of high by-catch rates (dumbyc). As for El Nino sidered in Section 4.1, years with disrupting climatic conditions are likely to influence fishers’ decisions towards increasing fishing efforts or, conversely, in the direction of devoting more time to supplementary occupations. Similarly to results of cross-vessel stochastic frontier studies for other countries (Appendix A), maximum likelihood parame-

ter estimates of the outcome equation (Table 3: models [2] and [3]) highlight the relatively higher gear-efficiency of purse seiners (as usually larger and technologically more advanced than longline vessels), with a positive parameter value associated with this gearrelated dummy. Possibly related to this point, the effort-elasticity of main target catches is estimated to be nearly 30% higher relative to the overall fishing activity of the two commercial fisheries jointly considered, including by-catches and minor target species (Table 3: lnvesmc vs. lnves). This may be the consequence of a more limited capacity or willingness of concentrating on target species, when the scale of fishing operations is constrained by small fleet sizes. Maximum likelihood parameter estimates of the outcome equation do not remarkably differ from OLS estimates with no modelling of latent truncation (Table 3: model [1] vs. [2]). Moderate statistical evidence of a significant difference between estimates, at a 10% level based on a t-test (and only in one direction, i.e. based on the OLS standard error), is only found for the parameter associated with log-transformed fishing days per vessel (Table 3: lndayves). The use of this variable in both outcome and selection equation yields statistically insignificant estimates, and the same applies for other independent variables which are of potential interest for both equations. This is likely to be partly induced by small sample size. On the whole, statistical evidence of incidental truncation is weak for the case analysed here. In selection equations in models [2] and [3] (Table 3), signs of estimated parameters do not contradict the hypotheses underlying the selection mechanism, exposed above. However, while for fishing days per vessel the estimated parameter is statistically significant at a 10% level (model [3]), in model [2] neither the parameter estimates of this equation, nor the cross-equation residual correlation coefficient between estimated

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305

Table 4 Log-reciprocal versus Fox surplus production model: PNG purse seine catches, 1979–2007. Model

Fox [5]

UR Fox [6]

Dependent variable

ln Um

lnmaincatch

Constant ves lnves(v)/lnset(s) vesrev(v)/setrev(s) t t−0.5

6.15 (32.6)* 0.01 (4.17)*

4.86 (7.16)*

DW 2 Radj

1.4 0.39

LR logistic [7a]

LR logistic [7b]

LR Gompertz [8]

UR Fox [9]

LR logistic [10]

LR Gompertz [11]

9.15 (11.5)*

9.01 (44.9)*

lnbycocatch 9.1 (14.6)*

9.01 (11.9)*

10.6 (39.8)*

0.02 (1.27)

−53.05(v) (−5.49)* 0.1 (5.77)* 4.64 (2.66)*

−332.8(s) (−4.43)* 0.11 (5.12)* 1.81 (1.17)

−29.4(v) (−6.89)* 0.07 (5.28)*

0.01 (1.13)

−238.01(s) (−2.99)* 0.07 (3.03)* −0.3 (−0.2)

−251.01(s) (−6.47)* 0.07 (6.54)*

1.6 0.87

2.07 0.9

1.18 0.87

1.3 0.87

2.06 0.94

1.72 0.83

1.75 0.83

1.4(v) (6.61)*

1.91 (3.6)* 0.97(s) (12.4)*

UR Fox: unrestricted Fox model (without unit parameter restrictions in the production function). Um : CPUE (ratio of main target catch to fishing effort, measured by number 2 ) for regression [5]. of vessels). t-statistics in parentheses. R2 (instead of Radj *

Statistical significance: p < 0.01 (in all other cases: p > 0.10).

residuals of the outcome equation and the truncated selection equation (ε , with ε and  defined as in the general specifications (8) and (9) in Section 3) turn out to be statistically significant. Positive first-order residual correlation cannot be rejected in both OLS and incidental truncation regression models (against the assumption of serially independent errors in incidental truncation models), while negative cross-panel simultaneous residual correlation is suggested by auxiliary regressions on estimated residuals from output regressions, for models [2] and [3]. However, Bloom and Killingsworth’s maximum likelihood estimation method has no ad hoc adjustment to account for panel data. Moreover, in this case, the sample is limited to four batches and is unbalanced, with missing observations for 1988 and 1989 relative to the longline fishing fleet. The introduction of a lagged endogenous variable leads to problems of maximum likelihood estimation convergence, with an overparameterised model (although this model is under-parameterised relative to a generalised differenced specification suited to correct first-order autocorrelation: Maddala, 1986, p. 1663). Correlation analysis on individual fish catches (not shown) and SURE regression estimates (Table 3: model [4]) indicate a relatively high responsiveness of main target catches to fleet sizes, and secondary target and by-catches to fishing sets/days (with the variables lnset and lnday being highly correlated), particularly for longline fishing boats. As indicated by first-stage regressions, SURE regression results highlight a gap in catchability between the two fishing gear fleets: other conditions being equal, purse seiners achieve higher catch levels for both main and secondary target caches (model [4]: pseine). On the other hand, the relatively higher fishing sets-elasticity of secondary target catches and by-catches for longliners may be interpreted as an indication of relatively higher gains in gear efficiency by these vessels at increasing levels of effort measured in terms of fishing sets (model [4]: lnsetpse vs. lnset). The latter does not hold for main target catches (given an estimated parameter of the respective slope dummy lnvespse not statistically different from zero: results not reported). The hypothesis (Section 4.1) of possible negative effects of increased purse seine catches of juvenile yellowfin and bigeye tunas in recent years on longline operators’ target tuna catches (including these two sub-species and albacore: see definition of lnmaincatch in Table 1) has been tested with one year-lagged catches, so as to account for an 18-month lag between juvenile and adult individuals for these tuna sub-species. This hypothesis is not substantiated by the regression parameter estimate (model [4]: lnjuvbeyft). While the implementation of mandatory logbooks and, to a lesser degree and with opposite effects, abnormal climatic events are found to have influenced registered secondary target catches and bycatches, at the aggregate annual level examined this does not

appear to have remarkably affected main target catches (dumlogre, enso). Relative to the third stage and in view of the strong predominance of the purse seine fishery, surplus production models have been applied to this fishery, so as to compare the Fox model with/without trend (and, if applicable, the unrestricted Schaefer variant: see Section 3.3) with log-reciprocal specifications (11) and (12). Due to sample size limitations, non-linear regression procedures accounting for simultaneous residual correlation and functional form selection (without a priori parameter restrictions), that is NLSURE and Box–Cox regression, do not provide reliable and statistically significant results (results not shown). Hence, for simplicity, it has been assumed here that n = 1, and the non-linear trend term in (12) has been tested with t2 or t-0.5 (Section 3.1; Table 4

Fig. 2. Catch vs. fishing effort in the PNG purse seine fishery: scatter plots for primary and secondary target species (1979–2007). (a) Main target (skipjack, tonnes in natural logarithms) vs. fishing vessels. (b) Secondary target and by-catches (other species, tonnes in natural logarithms) vs. fishing sets.

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reports results for the latter term). In line with SURE results, the number of fishing vessels is found to be a relatively more suitable proxy of effort for main target catches than fishing sets (suggested among others by residual autocorrelation in model [7b] in Table 4), while the opposite turns out to be the case for minor target- and by-catches. Regression diagnostics of alternative specifications within each approach (original and unrestricted surplus production models and non-linear models) and estimated parameter signs in OLS regressions indicate log-reciprocal specifications as relatively more suited for modelling the PNG purse seine fishery over the sample period. In the case of secondary target catches and by-catches, the Fox model, with number of sets used as a proxy for fishing effort in the CPUE, yields statistically insignificant estimates (not reported), while for main target catches the CPUE parameter has its sign reversed relative to model assumptions (this result also concerns the Schaefer specification) and the Durbin–Watson statistic is inconclusive (Table 4: model [5]). In the unrestricted version of the Fox model, log-linear trend parameter estimates are statistically insignificant, which highlights model misspecification for the fishery analysed (models [6] and [9]). As for non-linear specifications (11) and (12) in Section 3.1, the logistic distribution is found to be more appropriate for main target catches (Table 4: model [7a] vs. its Gompertz analogue [8], for which the DW test cannot reject the null hypothesis of positive residual autocorrelation). In turn, the Gompertz distribution appears to be more appropriate for secondary target and by-catches (model [11] vs. [10], since the non-linear trend component in [10] is not statistically significantly different from zero). On the whole, signs and statistical significance of estimated parameters indicate that the MSY has never been exceeded by the fishery in the period analysed (as one can visualise to some extent in Fig. 2).

5. Conclusion Besides contending views on the design and effectiveness of alternative fishery management measures, discordance persists among marine resource analysts and national fishery authorities about the choice of suitable model specifications and variables for the estimation of maximum sustainable yields. Traditional surplus production models are based on very restrictive assumptions, and are not suited to analyse multi-species fisheries. A number of revisions and methodological refinements have been formulated in recent years, but several aspects remain insufficiently investigated. Among others, marine fisheries are often analysed individually, without examining the interactions between commercial fishing fleets, and of the industrial fishery sector as a whole with onshore fishing. Yet, studies with this wider focus could provide useful tools for the design of fisheries management, and serve a broader purpose. In this analysis, a three-stage modelling approach is proposed, aimed at testing for the presence of latent truncation in the fishing fleet, observable and unobservable feedbacks between primary and secondary target catches (and by-catches) across different fishing gear vessels, and non-linear patterns in the bio-economic framework underlying MSY estimation due to non-constant marginal returns and switches in species targeting in the fishery. This approach is applied to commercial tuna fisheries in the Papua New Guinean EEZ. These fisheries are believed to be under-exploited as a whole, but selective fishing may have led in recent years to possible over or full exploitation in specific high-priced species, such as bigeye and yellowfin. In order to improve fisheries management of tuna sub-species close to over-exploitation, a differential royalty on purse seine tuna catches may stimulate the replacement by purse seiners of bigeye and yellowfin with skipjack tunas in the compo-

sition of their target fish catches. If these fishing vessels prove to have only limited capacity for selective targeting, an increase in the level of the access fee can be preferred as a fishery management measure (PFRP, 1998: p. 3). More broadly, due to their rich endowment in marine biodiversity, the sea areas surrounding PNG and the eastern Indonesia need close monitoring also in view of more general environmental concerns. Statistical evidence of incidental truncation in PNG commercial fisheries is weak, and results are sensitive to the selection of variables. Selective species targeting, catch efficiency, reporting rules and climatic conditions, are all factors undergoing changes over time, which influence fishing decisions. These changes are not easily identifiable, particularly at an aggregate temporal and spatial level of annual gear fleet-level data, used in latent truncation regressions for the first stage of the modelling approach. Since the analysis assumes that not all vessels are equally representative of fishing effort and fishing activities by some vessels remain largely underreported, additional, more detailed information would be necessary. Similarly, SURE equation results from the second stage do not support the hypothesis that captures of largely juvenile bigeye and yellofin by purse seine in recent years have impacted negatively on target tuna longline catches, but more disaggregate data would be helpful in providing additional evidence. Incidental truncation and SURE models reveal substantial differences between the two fishing gears and fish target groups in terms of gaps in catchability and catch–effort elasticity, accounted for by intercept and slope dummies. Relative to longline marine catches over the period 1979–2007, non-linear surplus production models are found to trace long-term relationships among catch, effort and biomass in a more flexible and statistically congruent way than original and unrestricted versions of the conventional approach. For the latter, regression results are either statistically insignificant or do not comply with expected signs for all estimated parameters. Given these results, both primary and secondary target fishing appear not to exceed the MSY in the period analysed, but these indications should be assessed without disregarding underreporting in registered fish catches. Acknowledgement This research was partly undertaken while the author was at the Papua New Guinea University of Technology. The author is grateful to two anonymous referees for helpful comments and suggestions. The usual disclaimer applies. Appendix A. Possible extension and limits of the analysis With disaggregate statistical information on fishing vessels, an additional stage (between step 1 applied to fishing vessel-level survey information, and step 2 in the procedure exposed in Section 3) can include a stochastic cost frontier model (as in Rahman, 2002). This would be aimed at estimating cross-vessel technical efficiency and capacity utilisation while accounting for incidental truncation in the observed fishing fleet. Applications of stochastic frontier modelling to fish-harvesting are reviewed by Basch et al. (2003), Pascoe and Mardle (2003), and Sesabo and Tol (2007). Fishery indicators are explicitly used as explanatory variables for production and efficiency, and latent-class regression is used to account for heterogeneous technology within a fishery. Scale of fishing operation and other vessel-type attributes, distance to the fishing ground, and level of market integration, are often found to be relevant determinants of cross-vessel gaps in output (volume or value of catches: see Section 2.2) and/or catch efficiency. In multispecies fisheries, larger vessels show a relatively higher elasticity

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of substitution between different target species, possibly due to greater mobility across fishing grounds (Pascoe et al., 2007). Econometric results often lend support to a translog specification, with unrestricted elasticity parameters of substitution between inputs (and between outputs in multi-species fisheries), as opposed to nested specifications (e.g. see Basch et al., 2003 and Sesabo and Tol, 2007). In principle, large panel cross-vessel data offer the advantage of allowing inference of a biomass stock index, based on harvest estimates. However, since catchability depends on resource stock as well as gear- and area-specific variables within each period, this does not guarantee unbiased estimates of biological dynamics visà-vis time-varying gear efficiency. The estimation of a stochastic frontier using fleet aggregate, instead of vessel, data can be questioned since it would imply that in some years the fleet was less efficient than in others: even if theoretically realistic, this contradicts the assumption of no underlying behavioural change at an aggregate fleet level (FØI, 2003, op. cit.: p. 20). A counterargument points to the truncated non-homogeneous nature of fleet data, with boats leaving the fishery in earlier years of a sample period likely to have been decommissioned due to loss of seaworthiness, and new boats entering in later years exercising the opposite effect on average fleet efficiency and capacity to influence the catch composition (Pascoe et al., 2007). In the absence of additional information such as fish price trends, both surplus production models and stochastic frontier models can be subject to heterogeneity and endogeneity biases. Heterogeneity arises from inability to clearly distinguish between fishermen’s independent choices and relative stock abundance as main determinants of changing catch composition. Regarding endogeneity, the expected value per unit of effort is likely to influence fishermen’s decisions to spend time at sea. This may introduce simultaneity in a regression of catch versus days at sea, to a limited extent due to the stochastic nature of catch (Pascue-Mardle, 2003). In this respect, fisheries data are typically associated with inaccuracies and inconsistencies. Registered catches at ports do not necessarily represent actual catches, due to possible significant amounts of unrecorded catches, such as by-catches discarded or distributed to crewmembers as partial payment and offloading catch to other vessels. Global fish discards are believed to amount to nearly one twelfth of global registered marine capture fisheries, but discard rates are likely to be substantially higher for industrial fisheries in many countries (Kelleher, 2005; Wernerheim and Haedrich, 2007: p. 75). In the presence of illegal access by commercial fleets to over-exploited coastal areas, the officially reported origin of catches reflects only to some extent its true location. If fish catch monitoring and reporting is port-based, discarding and illegal landings may increase with tighter fishing restrictions (Pascoe et al., 2007). On the opposite side, over-reporting may be induced by attempts by fishermen to pre-empt further quota restrictions and season closures by local authorities, in the presence of perceived declines in fishery resources (Wernerheim and Haedrich, 2007).

Appendix B. Methodological note B.1. Incidental truncation In Eqs. (8) and (9), suppose that ε and  follow a bivariate normal distribution, with zero means and covariance  ε = / 0 (i.e. assuming  = 1, and with  being the correlation coefficient of ε and ) (Mood et al., 1974: 165). Under this joint normality hypothesis and standardisation, the conditional distribution of ε given  > − W ˛ (Z* > 0, i.e. the vessels are observed) is normal with mean ( ␧ ) (Mood et al., 1974: pp. 167–168). Another useful property is that the

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c-(lower)bounded conditional probability of a standardised normal variable (as in this case  ∼ N(0,1)) is equal to the inverse Mill’s ratio (defined as ‘selectivity variable’  by contributions to sample selection modelling), that is the ratio of its standard normal density ϕ(c) to the complementary cumulative distribution function 1 − ˚(c), i.e. ˚(−c) (Heckman, 1979; Wooldridge, 2002: 521–522; Greene, 2003: 780–787). Hence, given 1 − ˚(−W ˛) = ˚(W ˛), Eq. (8) can be re-specified as follows: Q |Z ∗ > 0 = E[Q |Z ∗ > 0] + = X  ˇ + E(ε| > −W  ˛) + = X  ˇ + ( ε ) + = X  ˇ + ( ε )[ϕ(−W  ˛)/˚(W  ˛)] + = X  ˇ + ( ε ) +

(13)

where residuals have mean zero and are independent of ε. The hypothesis of selectivity bias is rejected if  ε = 0. If observations are available only for Z = 1 (as hypothesized in Section 3 and illustrated in Section 4 by PNG fisheries), a Maclaurin expansion of the truncated regression function (13) can be estimated by maximum likelihood (Bloom and Killingsworth, 1985). B.2. Seemingly unrelated regressions Multi-species fishery output can be expressed as a (non-)linear system of regressions, with a vector Q of variables representing catches of different fish species bundles (e.g. main target catches Qm and by-catches Qb ), and a matrix X of explanatory variables. Since the fishery consists of largely joint production activity, the endogenous variables bear a close conceptual relationship to each other. Some explanatory variables are likely to be common to different equations in the system, and some equations may include among regressors endogenous variables from other equation(s) (in the latter case, the model becomes a simultaneous equation system, which requires full information methods of estimation, such as 3SLS: see Stewart, 1991, chapter 8). In matrix form, the system can be expressed as: Q = f (X, ˇ) + ε

(14) E(εε ) = ˙.

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