Sand dredging and environmental efficiency of artisanal fishermen in Lagos state, Nigeria

Abstract

Environmentally detrimental input (water turbidity) and conventional production inputs were considered within the framework of stochastic frontier analysis to estimate technical and environmental efficiencies of fishermen in sand dredging and non-dredging areas. Environmental efficiency was low among fishermen in the sand dredging areas. Educational status and experience in fishing and sand dredging were the factors influencing environmental efficiency in the sand dredging areas. Average quantity of fish caught per labour- hour was higher among fishermen in the non-dredging areas. Fishermen in the fishing community around the dredging areas travelled long distance in order to reduce the negative effect of sand dredging on their fishing activity. The study affirmed large household size among fishermen. The need to regulate the activities of sand dredgers by restricting license for sand dredging to non-fishing communities as well as intensifying family planning campaign in fishing communities to reduce the negative effect of high household size on fishing is imperative for the sustainability of artisanal fishing.

Appendices

Appendix 1

Sample size

The sample size (453.6 ≅ 450) used for the study is obtained using International Fund for Agricultural Development (IFAD) procedure based on the formula below. The final sample size made allowances for design effect (1.5) and contingency (5 %). The allowance for design effect is expected to correct for the difference in design while the allowance for contingency accounts for contingencies such as non-response or recording error.

$$ n=\frac{t^2p\left(1-p\right)}{m^2} $$

(3)

where:

• n = the sample size

• t = the confidence level at 95 % (1.96)

• p = the estimated percentage of artisanal fishermen out of the fishermen population in Lagos state (75 %)

• m = the margin of error (5 % or 0.05)

Appendix 2

Table 8 Descriptive statistics for the traditional and detrimental inputs

Appendix 3: Methodological framework of environmental efficiency

The environmental efficiency (EE) that this study estimates is different from conventional technical efficiency (TE). Environmental efficiency is defined as the ratio of minimum feasible to the observed use of an environmentally unfavourable input (water turbidity), based on observed levels of output and the traditional production inputs. The environmental efficiency is calculated from TE with the classical stochastic frontier approach (SFA). Determination of environmental efficiency follows the Reinhard (1999) two-step approach. Environmental efficiency is first calculated from TE using SFA. This is followed by regressing environmental efficiency on variables that are not used in the estimation of technical efficiency. Following Reinhard et al. (2000), the non-radial environmental efficiency can formally be defined as

$$ {\mathrm{EE}}_i\left(x,y\right)=\left[ \min \theta :\;F\left({X}_i,\;\theta {Z}_i\right)\ge {y}_i\right] $$

(4)

where:

• y _i is the quantity of fish caught per day, using

• X _i of the conventional inputs and

• Z _i the environmentally detrimental input.

• F(.) is the best practice frontier with X and Z.

Technical efficiency was measured using an output-expanding orientation, as the ratio of observed to maximum feasible output, conditional on technology and observed input usage. This is defined as

$$ \mathrm{T}\mathrm{E}={\left[ \max \left\{\varphi :\;\varphi Y\le F\left.\Big(X,\;Z\right\}\right.\right]}^{-1} $$

(5)

In SFA (Aigner et al. 1977; Meeusen and van den Broeck 1977), inefficiency is modelled by an additional error term with a two-parameter (truncated normal) distribution introduced by Stevenson (1980). A stochastic production frontier is defined by

$$ {Y}_{it}=f\left({X}_{it},\;{Z}_{it},\;\beta,\;\gamma, \zeta \right) \exp {\varepsilon}_{it} $$

(6)

where all fishermen are indexed with a subscript i and the period of data collection indexed with a subscript t; Y _it denotes the quantity of fish caught per day; X _it is a vector of normal inputs (with X _it1 is the labour hour, X _it2 the capital (the depreciation value of fixed input), X _it3 the variable input (bait), Z _it a vector of environmentally detrimental input (with Z _it1 the water turbidity)); β, γ and ζ are the parameters to be estimated; V _it is a symmetric random error term, independently and identically distributed as N(0, σ ² _v ), intended to capture the influence of exogenous events beyond the control of fishermen; ε _it is a composite error term; and U _i is a non-negative random error term, independently and identically distributed as N ⁺(μ, σ ² _u ).

$$ {\varepsilon}_{it}={V}_{it}-{U}_i $$

(7)

The stochastic version of the output-oriented technical efficiency measure (Eq. (5)) is given by the expression:

$$ {\mathrm{TE}}_{it}=\frac{Y_{it}}{Y_{it}=f\left({X}_{it},\;{Z}_{it},\;\beta,\;\gamma, \zeta \right) \exp \left({V}_{it}\right)}= \exp \left(-Ui\right) $$

(8)

Since U _i  ≥ 0, 0 ≤ exp(U _i ) ≤ 1. In order to implement Eq. (8), technical inefficiency must be separated from statistical noise in the composed error term (V _it  − U _i ). Battese and Coelli (1988, 1992) have proposed the technical efficiency estimator as

$$ {\mathrm{TE}}_{it}=E\left[\left. \exp \left\{-\left.{U}_i\right\}\right.\right|\left({V}_{it}-{U}_i\right)\right] $$

(9)

Within the framework developed by Reinhard (1999), TE is calculated using a standard translog production function as shown in Eq. (10) (Christensen et al. 1971).²

One of the main advantages of translog production function is that, unlike in the case of the Cobb–Douglas production function, it does not assume rigid premises such as perfect or “smooth” substitution between production factors or perfect competition on the production factor market (Klacek et al. 2007). Translog production function can be used for the second-order approximation of a linear homogenous production, the estimation of the Allen elasticities of substitution, the estimation of the production frontier or the measurement of the total factor productivity dynamics (Pavelescu 2011).

$$ \begin{array}{c}\hfill \ln \left({Y}_{i,t}\right)={\beta}_0+{\displaystyle \sum_{j=1}^m{\beta}_j} \ln \left({X}_{i,j,t}\right)+{\beta}_z \ln \left({Z}_{i,t}\right)+\frac{1}{2}{\displaystyle \sum_{j=1}^m{\displaystyle \sum_{k=1}^m{\beta}_{jk} \ln \left({X}_{ji,t}\right)}} \ln \left({X}_{ki,t}\right)\hfill \\ {}\hfill +\frac{1}{2}{\displaystyle \sum_{j=1}^m{\beta}_{jz}} \ln \left({X}_{ji,t}\right) \ln \left({Z}_{i,t}\right)+\frac{1}{2}{\beta}_{zz} \ln {\left({Z}_{i,t}\right)}^2-{U}_{i,t}+{V}_{i,t}\hfill \end{array} $$

(10)

where i = 1,…, n is the total sampled fishermen and t = 1,…, T is the number of periods; j, k = 1, 2,…, m are the applied traditional inputs; ln(Y _i,t ) is the logarithm of the quantity of the fish caught by fisherman i; ln(X _ij,t ) is the logarithm of the jth traditional input applied by the ith individual fisherman; ln(Z _i,t ) is the logarithm of the environmental detrimental input applied by the ith individual; and β _j , β _z , β _jk , β _jz and β _zz are the parameters to be estimated.³ The logarithm of the output of a technically efficient fisherman Y ^F _i,t with X _i,t and Z _i,t can be obtained by setting U _i,t  = 0 in Eq. (10). However, the logarithm of the output of an environmentally efficient fisherman Y _i,t with X _i,t and Z _i,t is obtained by replacing Z _i,t by Z ^F _i,t where Z ^F _i,t  = EE _i,t  × Z _i,t and setting U _i,t  = 0 in Eq. (10) as follows:

$$ \begin{array}{c}\hfill \ln \left({Y}_{i,t}\right)={\beta}_0+{\displaystyle \sum_{j=1}^m{\beta}_j} \ln \left({X}_{i,j,t}\right)+{\beta}_z \ln \left({Z}_{i,t}\right)+\frac{1}{2}{\displaystyle \sum_{j=1}^m{\displaystyle \sum_{k=1}^m{\beta}_{jk} \ln \left({X}_{ji,t}\right)}} \ln \left({X}_{ki,t}\right)\hfill \\ {}\hfill +\frac{1}{2}{\displaystyle \sum_{j=1}^m{\beta}_{jz}} \ln \left({X}_{ji,t}\right) \ln \left({Z}_{i,t}\right)+\frac{1}{2}{\beta}_{zz} \ln {\left({Z}_{i,t}\right)}^2+{V}_{i,t}\hfill \end{array} $$

(11)

The logarithm of EE (lnEE _i,t  = lnZ _i,t ) can now be calculated by setting Eqs. (10) and (11) equal as follows:

$$ \frac{1}{2}{\beta}_{zz}{\left( \ln {\mathrm{EE}}_{i,t}\right)}^2+\left( \ln {\mathrm{EE}}_{i,t}\right)\left[{\beta}_z+{\displaystyle \sum_{j=1}^m{\beta}_{jz} \ln {X}_{ij,t}+{\beta}_{zz} \ln {Z}_{i,t}}\right]+{U}_{i,t}=0 $$

(12)

By solving Eq. (12), lnEE _i,t is obtained as shown below:

(13)

As mentioned by Reinhard (1999), the output-oriented efficiency was estimated econometrically whereas environmental efficiency (Eq. (8)) was calculated from parameter estimates (β _z and β _zz ) and the estimated error component (U _i,t ). Since a technically efficient fisherman (U _i,t   = 0) is not necessarily environmentally efficient (lnEE _i,t  = 0). The sign $+\sqrt{}$ is ideal.⁴