A Cox Parametric Bootstrap Test of the von Liebig Hypotheses

Abstract

"This study uses a Cox parametric bootstrap test to select between two specifications of the von Liebig hypothesis, a switching regression (SR) model, and a linear response function with a stochastic plateau. Specifying the production function as a linear response function with a stochastic plateau yields a superior approximation of the data for livestock gain as a function of forage allowance than the SR approach." Copyright 2007 Canadian Agricultural Economics Society.

Dynamic Optimization of Nitrogen in Plateau Cotton Yield Functions with Nitrogen Carryover Considerations

“…The calculated likelihood ratio test statistic was 30.8 with a critical chi-square value of 6.63, providing evidence that the stochastic plateau model fit the cotton yield data relatively better than its deterministic counterpart. These results agreed with previous studies (Boyer et al 2012(Boyer et al , 2013Harmon et al 2016;Kaitibie et al, 2007).…”

“…The study also developed a direct formula to estimate optimal fertilizer rates that maximize expected returns. The LRSP function has been used extensively to model crop yields to fertilizers in cotton, wheat, forage, corn, potatoes, and sorghum (Asci, Borisova, and VanSickle, 2015;Biermacher et al, 2009;Boyer et al, 2013Boyer et al, , 2015Brorsen and Richter, 2012;Harmon et al, 2016;Kaitibie et al, 2003Kaitibie et al, , 2007Tumusiime et al, 2011;Zhou et al, 2015).…”

The economic potential of precision nitrogen application with wheat based on plant sensing

“…The stochastic plateau function of Tembo et al (2008) was developed specifically to match the production function assumed by Raun et al (2002) and has been used successfully by Kaitibie et al (2003, 2007) Therefore, we use Tembo et al's linear response stochastic plateau function to represent wheat response to nitrogen: where y it is the wheat yield in kg per ha on grid i in year t ; N P it is the level of pre‐plant nitrogen; N T it is the level of topdress nitrogen; ORI S it ( N P it ) represents an optical reflectance index taken in the late winter on grid i in year t ; μ m is the average plateau yield, β 0 , β 1 , and β 2 are the parameters to be estimated; v t represents the plateau year random effect; u t is a year random effect that shifts the intercept, and ɛ it is an i.i.d. normal error term.…”

Forage Response to Swine Effluent: A Cox Nonnested Test of Alternative Functional Forms Using a Fast Double Bootstrap

“…The von Liebig function is an alternative to polynomial functions (Kaitibie et al, 2007). With von Liebig functional forms, a plateau exists in which crop yield does not increase with addition of nonlimiting production inputs (Ackello-Oguto, Paris, and Williams, 1985).…”

“…We extend this previous literature by using the fast double bootstrap (Davidson andMacKinnon, 2001, 2007), which is an alternative to the double bootstrap that considers the extra variability from estimated parameters and is much less computationally intensive than the double bootstrap. Kaitibie et al (2007) conducted a single bootstrap Cox test of alternative functional forms in a study of the effects of forage stocking density on average daily gain. The fast double bootstrap approach that we used has correct asymptotic size whereas the single bootstrap approach used by Kaitibie et al (2007) does not.…”