Levels or Differences in Meat Demand Specification

We estimated a wholesale demand system for beef, pork, lamb, chicken, and turkey using quarterly U.S. data and a dynamic, CBS system (Keller and Van Driel). The CBS system is a differential system, which means that it might be more appropriately applied in those situations where the data have unit roots. If there are unit roots, differencing the data can improve the properties of the estimates. If the data do not have unit roots, differencing the data might harm the properties of the estimates. We tested the specification of the model's error terms using state-space techniques. State-space units allow one to deal with roots on the unit circle without filtering the data (See Durbin and Koopman). The demand system has only four independent error terms. The state-space model we used could have decomposed these four independent error terms into four errors with unit roots and four with 0 roots. Adding state-space features to the model greatly improved its performance as measured by the likelihood ratio statistics. The estimates imply that the raw demand data have two unit roots and three 0 roots. Our mixed approach improves the properties of the estimates.