Estimation of von Liebig Response Functions

Abstract

Two distinct but related approaches for the estimation of von Liebig response functions are presented. The first approach is based upon a two‐phase, ordinary least squares procedure combined with bootstrapping for computing the standard errors of the estimates. The second approach generates maximum likelihood estimates of the parameters and can be implemented according to two different parameterizations of the model. Application of the procedures to a sample of experimental data suggests a satisfactory degree of conformity of the results. A test of normality of the disturbance term based upon the estimated residuals failed to reject the null hypothesis, further supporting the maximum likelihood approach.

Social contracts, markets and efficiency: Groundwater irrigation in North India

“…7 We also considered the von Liebig production function that often works well in plant experiments (e.g. Paris and Knapp, 1989). However, the von Liebig implies a cost function linear in input prices.…”

A Cox Parametric Bootstrap Test of the von Liebig Hypotheses

“…Previous research aimed at specifying production functions that characterize the von Liebig hypotheses have been undertaken (e.g., Paris and Knapp 1989; Berck and Helfand 1990; Paris 1992; Chambers and Lichtenberg 1996; Berck et al 2000). While most of these studies suggest that production functions that derive from the von Liebig hypothesis are mostly superior to other specifications, many do not account for the stochastic nature of the response function and the plateau.…”

“…Two issues that have been debated about the specification of the von Liebig hypothesis are the analytical form of the yield function and the statistical specification of experimental errors (Paris 1992). For instance, following Paris and Knapp's (1989) definition of an empirically tractable version of the von Liebig production function, we present a multivariate linear response plateau with cross‐section time series data implications as where y j t is animal gain in the j th pasture in time t , f i (·) is a linear response function for the i th input, x is the input, β is the coefficient, P is the plateau, and u jt represents the random error term associated with the j th pasture in time t . This basic formulation by Paris and Knapp (1989) was static, and it was applied to the famous Heady and Pesek (1954) data.…”

“…For instance, following Paris and Knapp's (1989) definition of an empirically tractable version of the von Liebig production function, we present a multivariate linear response plateau with cross‐section time series data implications as where y j t is animal gain in the j th pasture in time t , f i (·) is a linear response function for the i th input, x is the input, β is the coefficient, P is the plateau, and u jt represents the random error term associated with the j th pasture in time t . This basic formulation by Paris and Knapp (1989) was static, and it was applied to the famous Heady and Pesek (1954) data. To make the model empirically tractable, the response functions and the plateau have a common error term, which is indicative of the assumption that similar exogenous and uncontrollable factors affect the response processes for all inputs.…”

Payments for environmental services in upper-catchments of Vietnam: will it help the poorest?

“…This production function ensures that marginal productivities of fertility and labour inputs are decreasing, and can be considered to be a continuous version of the von-Liebig production function (Paris and Knapp 1989;Paris 1992). …”