Research and Reviews 1999

Special Circular 168-99

Forecasting Herd Structure, Milk Production and Their Variances for Production Risk Management

N. R. St-Pierre^1*, C. S. Thraen^**, and L. R. Jones^22
*The Ohio State University Department of Animal Sciences
^**The Ohio State University Department of Agricultural, Environmental and Development Economics
²²FARME Institute, Inc., Homer, N.Y.

Abstract

Substantial increases in milk price volatility have resulted from changes in federal dairy policies. For a dairy farm, however, monthly gross milk receipts are a function of unit price and quantity produced. Both can vary substantially over time. Therefore, to be effective, risk-management strategies must address milk and input price volatility (price-risk management) and fluctuations in milk production per cow and cow numbers (production-risk management). Herd milk production through time can be modeled as a discrete stochastic process using finite Markov chains. Cows at time t = 0 are assigned to homogeneous production cells in four-dimensional arrays with coordinates determined by parity (PAR = 1,2,3), week in milk (WIM = 1,…52), pregnancy status (PREG = 0,1), and week pregnant (WP = 1,…42). The processes of aging, pregnancy, involuntary cull, voluntary cull, abortion, dry-off, and freshening from week i-1 to week i are accounted for using non-stationary transition probabilities. Bayesian estimates of transition probabilities are derived from historical herd data, assuming that individual outcomes are from Bernoulli distributions. The values of parameters uh for the Benoulli distributions are unknown but have prior distributions that follow beta distributions with parameters ah and bh estimated from historical data. Herd observations are then used to generate posterior distributions of uh, also from beta distributions. Projecting from one week to the next is accomplished by moving animals from one production cell to the next based on the transitional probability assigned to that path. Summing production estimates and variances of all independent cells provides for an expected herd production with an associated variance. As expected, the forecast variance increases with time, reflecting increased uncertainty of distant projections. Model validation presents an interesting problem because future observations used for validation are under human control and not independent of the forecast.

¹ For more information, contact at: The Ohio State University, 221 Animal Science Building, 2029 Fyffe Road, Columbus, OH 43210, 614-292-6507, Fax 614-292-1515, e-mail: st-pierre.8@osu.edu