Testing a von Liebig Crop Response Function against Polynomial Specifications

Abstract

Crop responses to fertilizers traditionally have been specified as polynomial functions. Recently, criticisms were raised against such specifications because they force substitution between nutrients and overestimate the optimal fertilizer quantity. With those criticisms, an alternative crop response function was presented in the form of a minimum function which equates the realized output to the production potential associated with a limiting input. In this paper a nonnested test is performed to discriminate between the two rival specifications. The results ofthis test reject the hypothesis that a crop response is of the polynomial type, while they do not reject the hypothesis that it is of the minimum and plateau type.The question of how to generate an adequate food supply remains a pressing concern in developed and developing countries. As a consequence, appropriate fertilization technologies are important cornerstones of any sensible food policy.For the last three decades, the majority of agricultural economists has suggested the use of polynomial functions (quadratic and square root) for representing crop responses to fertilizer nutrients (for example, Baum, Heady, and Blackmore; Hexem and Heady; Woodworth). Proponents of polynomials argued that since the exact mathematical nature of crop response is unknown, approximation by polynomials is preferable in view of their computational simplicity and high fit. During the last decade, however, researchers have pointed out the inappropriateness of polynomial crop response functions (Anderson and Nelson, Lanzer and Paris). These relations consistently overestimate the maximum yield and the optimal fertilizer recommendations; they introduce the appearance of a nonexistent biological substitution between nutrients and, finally, their parameters do not possess agronomic interpretations easily discernible.Among these undesirable properties, the most crucial one is the excessive use of fertilizers derived from recommendations based on polynomials. Such a waste of scarce resources unnecessarily pollutes the environment and is intolerable for developing countries attempting to attain food self-sufficiency by boosting crop production through an increasing use of fertilizers.With the criticisms, a new family of crop response functions was introduced. It is inspired by basic agronomic principles and was called the von Liebig family of response functions in honor of the German chemist who first formulated those principles. Contrary to the polynomial response, a von Liebig function does not allow for nutrient substitution (although it admits interaction) and implies a response surface with a plateau maximum. An empirical study of crop response using a von Liebig specification was presented by Lanzer and Paris. Many of the criticisms of the polynomial response were detailed in that paper. However, no formal statistical test between the two rival specifications was given. This paper will provide such a rigorous test using a new set of data.' The evidence shows that the von Liebi...

The Application of Robust Regression to a Production Function Comparison~!2008-08-21~!2008-11-10~!2008-11-28~!

“…This extends the literature on the comparison of different functional forms [e.g. [1][2][3][4][5] by taking the effect of outliers for the estimation and evaluation of crop production functions into account.…”

“…About 25% of the observations that are identified by the RLS method as outlier or are given very small weights in the IRLS method, can be attributed to this particular year 1 . It is characterized by high temperatures and low precipitation in the relevant seeding-to-harvest period that caused particularly low corn yields in all Europe [30].…”

“…These functional forms are frequently used in the literature and proved to accurately capture the underlying relationships [1,[4][5][6][7][8][9][10][11][12].…”

“…The quadratic form, shown in equation (1), consists of an additive composition of the input factors, their squared values, and an additional interaction term. The latter elucidates whether the input factors are independent of each other or not.…”

Ability of Mitscherlich-Spillman Model to Estimate Critical Soil Phosphate Levels

“…Beginning in 1909, the works of Mitscherlich [7] and independently from 1923 works of Spillman [8] offered a model (productivity functions of Mitscherlich-Spillman PFMS) based on the inverse exponent, which has also a plateau as productivity function of Liebig, but it has damped response within the break point. Further development of theoretical concepts of the FP was made by Baule in 1918 (multifactor model of Mitscherlich-Baule [9]), Bray since 1944 (the concept of influence of mobility of food compounds on PF [10][11][12], Von Boguslawski E., & B. Schneider, refinement of Mitscherlich model [13][14][15][16] and many other researchers [2][3][4][17][18][19][20][21][22][23][24][25][26][27][28][29]. It is necessary to recognize the technical complexity of calibration of PFMS, especially for two or more variables.…”