A comparison of alternative production function models using non-nested hypothesis tests

Abstract

The selection of an appropriate mathematical form for a production process is critical in applied research. The practical problem is that little is known, a priori, about the process which generated the sample data. Often, the researcher is faced with several alternative or competing specifications which purport to explain the same phenomena. The purpose of model selection tests is to "best" describe the production process under consideration. If the models belong to the same parametric family, the problem is one to which standard hypothesis testing procedures may be applied. When the models belong to different parametric families, additional methods for testing model specification, based on the fundamental work of Cox, can be used. These tests are referred to as non-nested hypothesis tests. In this study, five production function models have been chosen to represent crop response to fertilizer inputs. They are the quadratic, transcendental, translog, Spillman and von Liebig functions. Non-nested hypothesis tests are carried out to determine which of the competing models best describes the production process which generated the sample data. The results of the tests indicate that the translog is the superior specification. In particular, the results support input substitution and a plateau response with respect to phosphorous. With regard to nitrogen, the results indicate that the response surface increases at a decreasing rate for low levels of the input and decreases at an increasing rate at higher levels.