Fisheries Economics

3.2.6. Interpreting the results

First the zero order correlation matrix should be estimated. This will indicate presence of multi-collinearity, if any, among the variables. If multi-collinearity exists between any two variables, then, the production function should be re-estimated repeatedly by dropping one of the correlated variables. If there is any improvement in the values of partial regression co-efficients or R-square value, then, that function should be taken for interpretation; otherwise, the same function could be retained. Let us consider the result of a production function estimated by Jayaraman (1996) for carp culture in Thanjavur district in Tamil Nadu.

The equation shows that only two variables had coefficients with the unexpected negative sign but they were not statistically significant and hence could be accepted. The R-square value is 0.5528 which means that the estimated equation could explain only 55 % of variations in the yield of farmed carps. However, it is statistically highly significant and the equation is valid for interpretation and drawing inferences. Among the partial regression co-efficients, only those for cattle manure and groundnut oilcake were statistically significant and had positive signs. Therefore, at mean level, these are the inputs that could increase the yield of farmed carps and the marginal productivities of all other inputs were not statistically different from zero.

The results imply that a hundred percent increase in the use of groundnut oilcake and stocking density of the carps would enhance the yield by 70.37 % and 2.55 % respectively. Yield responded to the cattle manure applied at 21 % level of significance only suggesting its use at sub-optimal level. The intercept (regression constant) term is positive and statistically highly significant revealing that the effect of the omitted variables was not small and consistent with the value of R-square obtained. One of the omitted variables is the managerial skill of the fish farmer. Although this variable could have a significant influence in the yield of farmed carps, its quantification is difficult. Hence, it is common to observe most of the production function analyses excluding this variable on the assumption that there were no significant differences in the managerial skill of the fish farmers considered in the analysis. However, this problem could be overcome to some extent by estimating frontier production functions and other analytical methods. The other variables could be disease incidence, rainfall, drought, climate, etc.

Thus, this production function shows that the farmer could enhance yield by appropriately increasing the use groundnut oil cake and stocking density. Remember that the analysis considers yield enhancement only. If the fish farmer is interested in income or profit enhancement, then we need data on prices, consumer preferences and demand, prices and supply of substitute products, etc. Also, we should analyse the economic efficiency of the fish farms using frontier functions for this purpose. We shall deal with the aspect elsewhere.