We demonstrate the use of the small-sample econometrics principles and strategies to come up with reliable yield and acreage models for policy analyses. We focus on demonstrating the importance of proper representation of systematic and random components of the model for improving forecasting precision along with more reliable confidence intervals for the forecasts. A probability distribution function modeling approach, which has been shown to provide more reliable confidence intervals for the dependent variable forecasts than the standard models that assume error term normality, is used to estimate cotton supply response in the Southeastern United States.

Consider two independent Goldstein-Kac telegraph processes X1(t) and X2(t) on the real line ℝ. The processes Xk(t), k = 1, 2, describe stochastic motions at finite constant velocities c1 > 0 and c2 > 0 that start at the initial time instant t = 0 from the origin of ℝ and are controlled by two independent homogeneous Poisson processes of rates λ1 > 0 and λ2 > 0, respectively. We obtain a closed-form expression for the probability distribution function of the Euclidean distance ρ(t) = |X1(t) - X2(t)|, t > 0, between these processes at an arbitrary time instant t > 0. Some numerical results are also presented.