the expected sign, they are not significant. This result is consistent with the study by
Selden and Song (1994). Generally speaking the values of upper turning points obtained
from the cubic function are slightly higher than the turning points identified by the
quadratic functional form for N. The significance of the cubic social capital variable
indicates that we cannot reject the cubic functional form in the nitrogen-social capital
relationship in all fixed and random effect models.
In the one way random effects formulation for the phosphorus equation, we found
a similar pattern as observed for the nitrogen-social capital relationship. The coefficients
were not, however, statistically significant. The estimated turning point generated by the
P equation is lower than the N equation. Estimated coefficients for the DO equation have
the expected sign for social capital variable only in the quadratic equation
The results from two-way random effect models for nitrogen, phosphorus and DO
are very similar to the one-way random effects models. In both models, coefficients
associated with phosphorus and DO equations were found to be insignificant.
The turning points for all three pollutants in two functional forms and four
different models indicated that for all pollutants except dissolve oxygen in one way fixed
effect model, it is around 0.5. This value indicates that all of the parishes are now
reducing pollution because of societal concern about water pollution.
Lack of significance of estimated parameters questions the validity of cubic or
quadratic functional forms in the parametric approach, especially in the case of
phosphorus and DO pollutants. It also indicates a need to estimate the social capital-
pollution relationship using a more flexible approach. Therefore, our strategy is to
further the analysis using a spatial panel fixed effect approach.
16
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