A Model of the Canadian Beef and Dairy Cattle Industry Based on Markov Chain Techniques

Abstract

<p>Like any livestock supply, the supply of Canadian beef and dairy cattle is characterized by a cyclical pattern in terms of the number of cattle on farm, the number of cattle slaughtered, the price of cattle, and the income of the beef and dairy cattle producers. In this study, we try to investigate the causes of such cyclical movements. To achieve this objective, semi-annual flow matrices are constructed for both Western and Eastern Canada for the period 1958 to 1972. The flow matrices are constructed according to the biological sequences of beef and dairy cattle. (Due to the limitation of the available data series, beef and dairy cattle are, in some instances, treated as homogeneous. Distinctions between the two types of cattle are made within the flow matrices whenever possible.) The flow matrices allow us to trace the movement of cattle from one age category to another. The age categories are not published according to the actual ages of the cattle, but rather under the categories of calves (under 1 year of age), yearling heifers (female cattle 1 year and older, but which have not given birth to calves), steers (castrated males), cows (female cattle that have already given birth to calves), and bulls (male cattle 1 year old or older).</p> <p>Using the flow matrices, transition matrices are formed. The transition probability matrices are constructed by dividing each row element in the matrix by its corresponding row total. These probabilities are treated as dependent variables to be explained by a set of relevant economic variables.</p> <p>Consistent with the evidence, fertility rates of cows in both regions are assumed constant, and based on these rates the number of calves born in each region is projected. Import functions of beef and dairy cattle are estimated. The introduction of the new-born calves and the estimated importation of cattle make the entire matrix endogenous. This enables us to predict the behaviour of the beef and dairy cattle industry in the long run.</p> <p>Finally, simulations are carried out using the transition probability matrices. In particular, attempts are made to simulate the consequences of changes in some of the important exogenous variables, for instance, the price of choice steers and personal disposable income.</p>