A Production Function Analysis of Seabass and Seabream Production in Greece

JOURNAL OF THE WORLD AQUACULTURE SOCIETY

Vol. 31, No. 3 September, 2000

A Production Function Analysis of Seabass and Seabream Production in Greece

GIANNIS KARAGIANNIS Institute of Agricultural Economics & Rural Sociology, National Agricultural Research

Foundation, Kifsias 1 8 4 ~ . I4562 Kifsia, Athens and Department of Economics, University of Crete, Greece

STELIOS D. KATRANIDIS Department of Economics, University of Macedonia, Egnatia 156,

54006 Thessaloniki, Greece

Abstract This paper analyzes the technical relationships involved in the production of seabass and

seabream in Greece. The empirical findings indicate that the marginal productivity of juveniles and fish feed exhibit the largest fluctuates among fish farms, while at the same time consist of the most important inputs in the production of seabass and seabream. In contrast, little variation was found with respect to the marginal productivity of labor among fish farms. Returns to scale were found to be decreasing for all fish farms included in the sample. Esti- mates of Allen-Uzawa partial elasticities of substitution indicated a strong complementary relation between juveniles and fish feed and labor along with a quite strong substitutability between fish feed and labor given the prevelance of use of mechanical feeders.

The evolution of the aquaculture industry in Greece followed behind that of other Eu- ropean countries. Until the end of the 1950s, aquaculture was based on an exten- sive production mode, with production tak- ing place mainly in rivers and lakes. In the beginning of the 196Os, intensive production of trout began, and production diver- sified into rearing carp, tilapia, eel and mul- let. The second turning point in the devel- opment of aquaculture industry in Greece took place in the middle of the 1980s. Over- all, production grew from 53 metric tons in 1985 to 17,500 metric tons in 1995 (Table 1). The growth of seabass Sparus aurarus and seabream Dicentrarchus labrax production since the middle of the 1980s was accompanied by a steady deterioration of freshwater fish production, primarily of trout and carp (Table 1). This may be ex- plained by two factors: first, the declining demand for freshwater species, due to food preferences in Greece for marine fish; and second, the climactic and physical conditions in Greece are more suitable for the production of marine than for freshwater

fish. This shift in product concentration be- came more significant in the first half of the 1990s with the complete dominance of the Greek aquaculture industry by the production of seabass and seabream. Greece’s market share grew from 25% in 1989 to 55% of the European market for seabass and seabream in 1995. A relatively large propor- tion (47% in 1995) of seabream is con- sumed domestically, while the majority (80% in 1995) of the seabass production is exported.

The number of seabass and seabream farms increased from two in 1985 to 160 in 1995 (Table 2). Even though the number of producing farms almost doubled in the first half of the 1990s, the number of farms en- tering the industry in the 1990s decreased compared to the second half of the 1980s. Firm size varies considerably; there are some small farms producing up to 50 metric tons per year, while others produce more than 200 metric tons. Almost all, however, use more or less the same type of technology as far as fish cages and growing herds are considered. On the other hand, the num-

0 Copyright by the World Aquaculturr Society 2000

297

298 KARAGIANNIS AND KATRANIDIS

TABLE 1 . Greek aquaculture production, 1980-1995 (Papaelias 1996; Kallifeidas 1997).

Seabass & Trout Eel Carp Seabream Mussel

Production (in metric tons) 1980 2,200 - 12 - 79

60 1981 2,250 - 34 130 1982 1,820 - 90 -

1983 2,150 1 140 1 200 1984 1,800 4 130 3 180 1985 1,780 5 160 53 115 1986 1,800 7 120 89 227 1987 1,900 12 254 105 380 1988 2,250 16 364 200 1 , 1 0 0 1989 2,000 47 326 500 1,500 1990 1,900 56 200 1,600 3,800 1991 2,415 58 159 2,459 7,580 1992 2,050 132 235 4,845 13,670 1993 1,885 337 240 9,500 16,700 1994 1,943 341 253 13,500 19,057 1995 2,455 234 211 17,553 21,214

-

ber of seabass and seabream hatcheries increased at much slower rates, due to a de- ficiency of technical expertise and very high establishment cost. As a result, the degree of vertical integration is still low in the sector. For small and medium-size enter- prises, it is usually difficult to build up their own hatcheries.

The objective of this paper is to analyze the technical relationships involved in the production of seabass and seabream in Greece. The empirical analysis is based on the econometric estimation of a translog production function for a sample of 40 fish farms in the industry. The estimated production function is used to measure marginal factor productivity, returns to scale, and (partial) elasticities of substitution among factor inputs. Measures of marginal factor productivity provide a means to de- termine the relative importance of factor inputs; returns to scale provide an indication of potential farm size expansion or contrac- tion; and elasticities of substitution portray the relative ease of using different input combinations to produce the same amount of output. Moreover, estimates of marginal factor productivity and returns to scale may

TABLE 2. Fish farms and fish hatcheries of seabass and seabream in Greece. 1985-1995 (Apostolopou- 10s et al. 1994: Kallifeidas 1997).

Fish farms Fish hatcheries

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995

2 9

17 27 62 86

114 139 145 164 160

1 1 1 5 9

1 1 16 22 22 25

provide some useful information about dif- ferences (if any) in input usage among fish farms with different sizes, and the possible constraints to expansion. In addition, information about the technical production relationships may provide insights to design adequate abatement mechanisms to restrict environmental impacts arising from ex- panding aquaculture production.

To the best of our knowledge this is the first attempt to analyze the technical relationships involved in the production of seabass and seabream in Greece as well as in other Mediterranean countries. However, several previous studies have used a production function analysis to study technical relationships in aquaculture (for a survey see Hatch and Tai 1997). For example, La- cewell et d. (1973), Lee (1983), and Nerrie et al. (1990) used a Cobb-Douglas production function to analyze the Texas catfish industry, milkfish farming in Taiwan, and the west-central Alabama catfish industry, respectively. Crawford (1976) used a quadratic production function to study the West Alabama catfish industry. Recently, Tvet- eras (1999) and Asche and Tveteras (1999) used a translog production function to analyze Norwegian salmon aquaculture. Pan- ayotou et al. (1982). Chong et al. (1982), Sharma and h u n g (1998), and Iinuma et al. (1999) employed a production function approach to measure technical inefficiency

ECONOMIC ANALYSIS OF SEABASS AND SEABREAM CULTURE IN GREECE 299

in catfish farming in Thailand, milkfish production in the Philippines, and carp aquaculture in Nepal and Peninsula Malaysia, respectively. On the other hand, some other authors (e.g., Salvanes 1989, 1993) used a cost function to model aquaculture industry.

Empirical Model It is assumed that seabass and seabream

production in Greece can be fully described by a well-defined production function Q = f(x), where Q is the annual output level (the sum of seabass and seabream produce) and x is a vector of input quantities, i.e., stocking rate (juveniles), fish feed and labor. This unknown production function should have positive but decreasing marginal products and it should be quasi-concave in x as long as the law of diminishing returns holds. For a given production function, producers seek to maximize the output produced for a given set of inputs and an exogenously determined set of prices of output and inputs. Thus, it is explicitly assumed that they op- erate at the efficient frontier of the production function. For the purposes of analysis, it is also assumed that the contribution, in logarithmic form, of each input is equal to the ratio of input cost and the value of total physical product. This is a consequence of optimization behavior (i.e., profit maximization) and of exogenous prices of output and inputs. It implicitly implies marginal cost pricing and that all inputs are paid at their marginal products.

For the purposes of this study, the true production function is approximated by a translog function, which represents a second-order Taylor series approximation of the true function around a point of approximation. This point is usually defined as the sample arithmetic mean or in the case of cross-section data as the representative fish farm. In either case, all variables are nor- malized to one at the point of approximation and the rest of the data points are adjusted accordingly. Then, translog may be viewed as a Taylor series approximation around the point (1,1, . . . ,1) or In( 1) = 0.

By this way, a number of calculations are simplified at the point of approximation. The functional form of the translog production function is specified as (Berndt and Christensen 1973):

n

In Q = a. + C ai lnx i i= I

where the parameter ct0 represents the state of technical knowledge and ai and aij are technologically determined parameters. Translog does not satisfy all production function properties globally. In particular, when at least one aij # 0 there are some input values such that neither monotonicity nor convexity of isoquants is satisfied. This follows from the quadratic nature of the translog function. There are however re- gions in input space where these conditions are satisfied either a fortiori or by restrictions on particular parameters. For the translog functions, it is important that these conditions are at least satisfied at the point of approximation.

A number of parameter restrictions are required for the translog function (1) to be a plausible representation of production technology at the point of approximation. First, symmetry restrictions, i.e., d21n Q/d In xid In xj = d2 In Qld In xj d In xi, are required, which in terms of parameter restrictions im- ply that aij = aji. Second, monotonicity requires the marginal product of each input to be positive; that is dQ/dxi > 0 for all i. The marginal product of the ith inputs indicates the additional amount of output that would be produced if the use of the ith input increases marginally and that of all other inputs remains unchanged. In the context of the translog function, the marginal product of the i* input may be obtained by multi- plying its output elasticity by its average product. That is,


6'Q d l n Q = (=)I(:)

m

= (ai + c aijln xj)(:) (2) j = 1

The output elasticity of the i* input indicates the percentage change in the output produced due to a percentage change in the use of the ith input, given that the use of all other inputs remains unchanged. From equation (2) it is clear that, at the point of approximation, the marginal product of each input equals to its output elasticity. Given that both Q and lnr, are positive, monotonicity depends on the sign of the terms in the first parenthesis. Thus, at the point of approximation, the condition of positive marginal products is ensured as long as a, > 0 for all inputs. Third, the condition of decreasing marginal factor productivity for each factor input is satisfied at the point of approximation as long as ai(ai - 1) < 0 for all inputs, which is always true if 0 < ai < 0 for all inputs. Finally, quasi-concavity of (1) requires the bordered Hessian matrix of the second-order deriva- tives to be positive semi-definite. All these parameter restrictions can be tested to eval- uate the performance of translog function in each study case.

The translog function is, however, flexi- ble in the sense that it does not impose any a priori restrictions on the values of marginal products, output elasticities, returns to scale and elasticities of substitution (Griffin et al. 1987). In contrast, all these measures are allowed to vary with input use and thus, differ across fish farms. In contrast, the commonly used Cobb-Douglas production function (e.g., Lacewell et al. 1973; Lee 1983; Nerrie et al. 1990) restricts these measures to be the same for all fish farms in the sample. In addition, the translog function allows for the possibility of com- plementarity between any pairs of inputs, while the Cobb-Douglas production function rules out this possibility because the partial elasticities of substitution between

all pairs of inputs are equal to one. More importantly, the translog function contains the Cobb-Douglas form as a special case. Imposing the following restrictions in the estimated parameters can test the hypothesis that Cobb-Douglas is an appropriate representation of production technology: aij = 0 for all i and j (Berndt and Christensen 1973).

By assuming profit maximization, exogenous prices of output and inputs, and dif- ferentiating equation (1) with respect to h i , the following set of factor share may be obtained:

aQxi ~3 In Q wixi M,=--=-- -- ' %xi Q a In xi pQ

= ai + 2 aijln xi (3)

where Mi is the factor share of the i* input defined as factor cost divided by total revenue, p refers to output price, and wi is the price of the i* input. Notice that these factor shares do not necessarily sum to one.

Returns to scale indicate the proportional increase in output produced from an equiproportional increase in all inputs. The degree of returns to scale is measured equiv- alently by either the sum of output elasticities or by the sum of factor shares (see equation (2)). For the translog production function, the degree of returns to scale E is:

Returns to scale are either increasing or decreasing according to whether E is greater or less than one. Increasing (decreasing) returns to scale implies that the proportional increase in output produced is greater (less) than the equiproportional increase in all inputs. If E = 1, production is characterized by constant returns to scale. Constant returns to scale is a testable hypothesis for the translog production function, which re-


quires the following set of restrictions on the estimated parameters (Berndt and Chris- tensen 1973):

m 2 ai = 1 and yij = 0 (5) i = l j = i

Rejection of the null hypothesis implies that returns to scale are either decreasing or increasing.

The elasticity of substitution measures the extent to which one input substitutes for another along an isoquant, as all other inputs remain unchanged. Following Berndt and Christensen (1973), the Allen-Urawa own- and cross-partial elasticities of substitution for the translog production function are given as:

UII = lGlll/lGl

ulJ = ~ G ~ ~ ~ / ~ G ~ for i # j (6)

where G is defined as

M 3 I 0 M , M2

M I all + M: - M i ail + M , M 3 M , a12 + M l M 2 + M : - M , a,) + M , M 3 M3 ail + M,M3 a,) + M , M 3 a3, + M i - M3

a,, + M , M ,

IGl is the determinant of G, ~ G l l ~ is the cofactor of the element a,, + MI2 - MI and IG,l is the cofactor of al, + MIMJ (i = 1 (stocking rate), 2 (fish feed), 3 (labor)). The Allen-Uzawa elasticities of substitution are used to classify inputs as substitutes or complements. If ulJ is positive, the inputs are substitutes for each other, while if it is negative, they are complements. A value of zero implies that inputs do not substitute for each other, while a value that approaches infinity indicates that inputs become perfect substitutes for each other. Moreover, if a, > 1 there is strong substitutability between these two inputs, while if 0 < aIJ < 1 there is weak substitutability.

Estimation Procedure and Data Estimates of the translog production

function parameters may be obtained by using stochastic versions of equations (1) and (3). i.e., by appending disturbance terms in

an additive way into equations (1) and (3), which are assumed to have zero mean and constant variance. These disturbance terms may be attributed to a variety of forces, in- cluding errors in profit maximizing behav- iour, inability of fish farms to maximize profit instantaneously, as well as in other exogenous forces, such as weather conditions. The disturbance terms across equations (1) and (3) are likely to be correlated, because random deviations from profit maximization should affect all input mar- kets and through them the total output produced. This suggests that obtaining estimates of the translog production function parameters by simply applying ordinary least square (OLS) into equation (1) will result in inefficient estimates. In addition, estimating (1) with a single-equation tech- nique, such as OLS, implicitly neglects the consequences of profit maximizing behavior.

The seemingly unrelated regression (SUR) procedure suggested by Zellner (1962) yields more efficient parameter estimates under these circumstances. This procedure requires the estimation of (1) and (3) as a system and the imposition of across-equation restrictions on the parameters appearing in more than one equation, in order to ensure profit maximization. However, to apply SUR on the system of equations (1) and (3) it should be ensured that the regressors, i.e., input quantities, are exogenous variables. As shown by Zellner et al. (1966) this occurs whenever producers maximize expected profits and input choice decisions are made prior to output decision. Then producers attempt to produce that amount of expected output that maximizes expected profit. This seems an appropriate assumption for aquaculture production as expected output is not known with certainty at the time input decisions are made.

The data required for estimating the system of equations (1) and (3) are: output quantities of seabass and seabream; quantities used of stocking rate, fish feed, and


TABLE 3. Summary statistics for a sample of 40Jish farms in Greece, 1994.

Sample Standard Minimum Maximum mean deviation

Seabass sales (million Drachmas) 20 1,468 177 123 Seabass production (metric tons) 10 562 91 58 Seabream sales (million Drachmas) 25 1,763 186 142 Seabream production (metric tons) 13 660 94 63 Seabass juveniles (thousands) 64 720 293 146 Seabass juveniles cost (million Drachmas) 50 2,509 349 26 1 Seabream juveniles (thousands) 7 79 30 15 Seabream juveniles cost (million Drachmas) 4.5 I25 26 18 Fish feed cost (million Drachmas) 85 2,770 414 238 Fish feed quantity used (metric tons) 17 555 83 47 Number of unskilled workers 2 97 12 8 Number of skilled workers 1 23 3 2 Labor cost (million Drachmas) 9 360 43 29

labor; total revenue of seabass and seabream production; and cost of stocking rate, fish feed, and labor. To avoid any problems associated with units of measurement, quantity data were converted to indices using the Divisia index, which is exact for the translog function (Diewert 1976). Divisia indices were also used to aggregate seabass and seabream production into a single output index, which is the dependent variable in equation (1) while the quantities of stocking rate, fish feed and labor are the independent variables. For all quantity indices, a representative firm was used as a base. Its choice was based on total sales and the smallest deviation from sample mean. The data related to total revenue, and cost of inputs were used to calculate factor shares for equation (3).

The data used in this study were collect- ed through questionnaires filed with the Greek Ministry of Agriculture, Department of Fishery, by 140 seabass and seabream farms in 1994. From these, 40 were selected randomly for the purposes of the present study. This sample corresponds to almost 25% of fish farms producing seabass and seabream in Greece in 1994. These 40 farms in the sample accounted for approx- imately 30% of the total national production in that year. For each fish farm there is available information about production of seabass and seabream, annual sales, outlays

on and quantities of stocking rate and fish feed, and the number of workers employed. There were no available data on capital and for this reason it is not included as an input variable in the production function. A summary of variables is given in Table 3.

Output, consisting of seabass and seabream production, is measured in metric tons, and total revenue is measured in million drachmas ($1 U.S. = 232 drachmas in 1994). Stocking rate, fish feed, and labor were the primary inputs. Stocking rate is measured by the number of juveniles used and the quantity of fish feed is measured in metric tons. The cost of stocking rate and of fish feed is measured in million drachmas. There is also information about the number of skilled and unskilled workers as well as the total annual labor cost. In order to construct a Divisia quantity index for labor, it was assumed that skilled labor was paid one and a half times more than unskilled labor; this ratio was based on skilled and unskilled labor salaries in food industry. By using this ratio the total number of workers was converted into equivalent unskilled employers.

Empirical Results The estimated parameters of the translog

production function for seabass and seabream production in Greece are reported on Table 4. The adjusted R2 was found to be


TABLE 4. Estimated parameters of a translog production function for seabass and seabream industry in Greece. Subscripts ( I ) refers to stocking rate, ( 2 ) to fish feed and (3) to labor. An asterisk denotes statistically insignijicant parameters at 95% confidence interval.

Parameter Estimated value t-statistic

-0.279 0.267 0.330 0.128 0.092 0.074

-0.021 -0.037

0.041 -0.040

-9.98 24.08 30.26 8.61 8.20 6.11

-0.23* -3.56

1.99 1.74*

0.68, indicating a good fitness for cross-section data. Most of the estimated parameters (eight out of ten) are statistically significant within a 95% confidence interval, and they also had the expected sign. At the point of approximation, marginal products are all positive and diminishing since all estimated ai parameters fall between zero and one. Also, at the point of approximation, the determinant of the boarded Hessian was found to be -0.0048, indicating that the under- lying production function is quasi-concave with respect to input quantities. Moreover, both the hypotheses of a Cobb-Douglas production function and of constant returns to scale are rejected on any significant level. The calculated x2 statistics were found to be 126.82 and 36.75, respectively.

Marginal factor productivities. Estimates

of marginal factor productivities and returns to scale are presented in Table 5. Marginal factor productivity is a partial measure of the contribution of each factor of production to the output level and indicates the additional amount of output that would be produced by increasing the use of one input by a certain amount and keeping that of all other inputs constant. According to our results, fish feed had the highest marginal factor productivity, followed by stocking rate, and then labor. On average, the marginal productivities of stocking rate, fish feed, and labor were 0.313, 0.259, and 0.131, respectively. This indicates that fish feed and stocking rate are the inputs (of those ana- lysed) with the greatest potential to increase yield in the production of seabass and seabream in Greece.

There is a positive relationship between farm size and the marginal productivity of fish feed and stocking rate. Farm sizes are classified according to total sales. Farms with sales 45-100 mil Drs are classified as small, those with sales between 1 0 0 and 500 mil Drs as medium, and with sales greater than 500 mil Drs as large. Our results indicate that the contribution of fish feed and stocking rate as production factors is greater for larger farms. The estimated figures for small and large farms are 0.325 and 0.302, and 0.278 and 0.246 for fish feed and stocking rate, respectively (Table 5) . The marginal productivity of labor seems to be independent of farm size. As it can be seen from the corresponding standard de-

TABLE 5. Estimates of marginal factor productivities and returns to scale for seabass and seabream production in Greece.

Stocking rate Fish feed Labor Returns to scale

Sample mean 0.259 0.313 0.131 0.703 Minimum 0.220 0.284 0.117 0.649 Maximum 0.331 0.349 0.144 0.791 Standard deviation 0.021 0.014 0.007 0.03 1 Sample mean for

Small-size fish farms 0.246 0.302 0.130 0.678 Medium-size fish farms 0.258 0.314 0.131 0.703 Large-size fish farms 0.278 0.325 0.132 0.733


TABLE 6. Esrimares of Allen-Uzawa partial elasticities of substitution for seabass and seabream industry in Greece.

Stocking rate Fish feed Labor

~~

Stocking rate -3.54 - 1.94 -2.25 Fish feed -3.36 2.62 Labor -6.41

viation, the marginal productivity of labor is quite similar across fish farms (Table 5 ) .

Returns to scale. Returns-to-scale, which measure output increases due to an equiproportional increase in all inputs, were found to be decreasing for all fish farms included in the sample, with an average magnitude of 0.703 (Table 6). This finding likely reflects biological constraints of seabass and seabream production, as well as the restricted amount of sea area that can used by farms. The latter is regulated in order to avoid environmental problems with the water quality of nearby beaches. On the other hand, it restricts potential expansion of diseases and thus reduces production un- certainty associated with environmental growing conditions. In either case, less variable inputs are used in the production pro- cess. Even though the magnitude of returns- to-scale exhibits little variation (ranging from 0.649 to 0.791), the results indicated that returns-to-scale are positively related to farm size.

Elasticities of substitution. The estimates of Allen-Uzawa partial elasticities of substitution, which show the easiness of factor substitution along a given isoquant, are reported in Table 6. Given the quasi-concavity of the estimated production function, all own-price Allen-Uzawa partial elasticities of substitution were negative. The estimated cross-price elasticities of substitution indicate that there is a strong complementary relationship between stocking rate and fish feed and labor. This indicates that an increase in stocking rate used requires an increased use of both fish feed and labor. In order to increase output, more juveniles

should be stocked and this requires an increased use of both fish feed and labor. Sec- ondly, labor and fish feed were found to be substitutes. This relationship likely reflects the increased use of demand feeders to pro- gressively replace feeding fish by hand. De- mand feeders reflect a labor-saving technology that results in higher feeding levels that require less labor. Thus, for any given output, the same amount of fish feed can be used with less labor.

Conclusions

This study provides a first attempt to analyze the technical relationships involved in production of seabass and seabream, the most rapidly growing aquaculture industry in Greece. By using a production function framework, estimates of marginal factor productivities, returns to scale, and elasticities of substitution were obtained. Empiri- cal results indicated that the marginal productivity of stocking rate and fish feed ex- hibited the largest fluctuation among fish farms, and are the most important inputs in seabass and seabream production. In contrast, little variation can be found with respect to labor marginal productivity among fish farms. Estimates of Allen-Uzawa partial elasticities of substitution indicated a strong complementary relation between stocking rate and fish feed and labor along with a strong substitutability between fish feed and labor.

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A Production Function Analysis of Seabass and Seabream Production in Greece