On the Statistical Estimation of Isoquants and Their Role in Livestock Production Decisions

Abstract

Animal production experiments permit limited control of experimental factors because the animals themselves partially determine total feed consumption per unit of time. Within practical limits, the variables that economists would like to have as controlled factors in the experiment are not subject to direct control, but instead, are controlled indirectly by other closely related variables. The problems involved are illustrated by a recent article of Sonka, Heady, and Dahm. In a swinefeeding experiment, percentage of protein in the ration was the only design variable, but economists would have liked to see corn and protein supplement as the controlled factors since they are the direct inputs for which there exist price quotations. Of course, other variables besides percentage of protein can be thought of as the single controlled factor; either percentage of the ration by weight which is corn or a standardized protein supplement would serve equally well. The important point to be recognized is that the controlled factors are different than the direct feed inputs and one less in number because the animals themselves control total feed consumption per unit time. In the swinefeeding experiment analyzed in Sonka, Heady, and Dahm, percentage of protein is the single factor instead of the pair of variables, corn and protein supplement consumption. Data from the swine-feeding experiment can be analyzed in two basic ways: (a) weight gain, corn consumption, and protein supplement consumption per unit of time are treated as multivariate responses to the single controlled factor, namely, percentage of protein in the ration; and (b) weight gain is divided into discrete intervals, and for each of these intervals, corn consumption, protein supplement consumption, and time required to achieve a specific gain are treated as multivariate responses to the single experimental factor. Following (Sonka, Heady, Dahm), we consider only the latter type of analysis which simplifies statistical estimation problems. Adopting most of the notation in Sonka, Heady, and Dahm, there are three equations of possible economic interest to be estimated from the experimental data: