This research provides one of the first empirical estimates of a data-based dynamic factor demand model for American and Canadian agriculture. Models such as these deserve more widespread use in the empirical analysis of agriculture. These models have the advantage that they do not impose inappropriate dynamics on the data. Rather they permit the data to select the appropriate dynamics. We use a model originally developed by Anderson and Blundell. This model is a general first-order dynamic model which contains as testable hypothesis several simpler models. This model permits us to estimate the long-run agricultural production structure as a subset of the dynamic parameter estimates. We will test this long-run structure for symmetry, homotheticity and neutral technical change. The estimated models may be used to test for three alternative dynamic structures. In the limit, dynamics may not be needed and we can test for the static long-run equilibrium model. Two intermediate cases are the autoregressive and the partial adjustment models which are simpler than the general model but still include dynamics. Our results suggest that the long-run equilibrium model is unsatisfactory in both countries. A dynamic model is needed. In both countries, the two more restricted dynamic models are rejected. The general dynamic model is required. In Canada, the long-run equilibrium structure is homothetic with neutral technical change. In the United States, homotheticity is also accepted but neutral technical change is rejected.