| dc.description.abstract | The study is motivated by the rapidly escalating energy prices, the accumulation of the major nutrients in many prime agricultural soils and the need to recognize the dynamic nature of the crop fertilization pro blem. The major objective of the study is to statistically test the appropriateness of alternative specifications of the relationship between crop response and factors of production. The hypothesis of nutrient non substitutability is given special attention.
A model of corn response is formulated as a simultaneous equations system with response, soil phosphorus and soil potassium as the endogenous variables. The system is assumed to be recursive and the equations are therefore estimated separately as opposed to applying simultaneous equa- tions techniques.
The equations estimating the soil level of the two nutrients are referred to as the carryover functions and are given a distributed lag model interpretation after introducing lagged values of the endogenous variables as exogenous variables.
The appropriateness of two kinds of specification of corn response
functions is examined. The first kind is a polynomial approximation which has frequently been applied by many agricultural economists and
soil scientists and by now considered as the conventional form for depic- ting crop response surfaces. The second kind is a nutrient non-substitu- tion formulation.
The non-substitution model generalizes Liebig's "law of the minimum."
It gives the expected corn yield (in the two nutrient case examined in
the study) as A Min [fp(PT), fk(KT)] where A is the estimated yield maximum and the arguments in fp(o) and fk(o) representing estimated total availability of phosphorus (P) and potassium (K), respectivelyo The indi vidual-response functions fp(o) and fk(o) are approximated by linear splines and estimated by applying a nonlinear mathematical programming technique to a nonlinearly constrained problem. The estimation proce- dure, unlike those used hitherto in fitting the IIlawof the minimum,1I requires no prior sorting out of data in order to separate those for which either P or K is limiting growth.
Two polynomial formulations are estimated: the square root and the quadratic forms. Both indicate a general lack of response to P thus pointing to an oversupply of this nutrient in the experimental plots. These results are verified by those of the non-substitution model which indicates that the maximum corn yield could be obtained by total nutrient supplies no more than 165 kg/ha for both P and K.
Three non-nested hypothesis testing procedures are employed in
testing the nutrient non-substitution hypothesis. The statistics used
are Cox-Pesaran Statistic, C-statistic and linearized Cox-Pesaran statis- tic. The three test statistics give consistent results for small samples. For larger samples, the C-statistic gives results conflicting with those
of the Cox-Pesaran statistic. The linearized Cox-Pexaran statistic is not found to be useful.
On the basis of the Cox-Pesaran statistic, it is concluded that the two polynomial forms cannot be supported against the nutrient non-substi- tution hypothesis given the data analyzed in the study. The nutrient
non-substitution model is therefore proposed as a generalized tool which
is not only biologically more appealing but is also statistically more
appropriate than the conventional approximations currently employed
in crop response analysis. | en |
