Samuelson´s full duality and the use of directed acyclical graphs

To date, mixed demand systems have been all but ignored in empirical work. A possible reason for the scarcity of such applications is that one needs to know a priori which prices and quantities are endogenous in the mixed demand system. By using a directed acyclical graph (DAG), causal relationships among price and quantity variables are identified giving rise to a causally identified mixed demand system. A statistical comparison is made of the traditional Rotterdam model, a synthetic demand system, which subsumes the traditional Rotterdam model, and a Rotterdam mixed demand system identified through the use of a DAG. In this analysis, the respective demand systems consist of five products: steak, ground beef, beef roasts, pork, and chicken.