Demand Equations with some Nonstationary Variables: The Demand for Farmed and Wild Salmon in Japan

There seems to be substantial evidence in favor of treating price series as nonstationary. There are also strong arguments for treating expenditure shares as stationary. With this structure in the data, it is generally not valid to estimate share equations, which most commonly-used demand systems are formulated in, as there will not be a long-run relationship between data series that are integrated of different orders. We show that one can estimate a demand system using traditional tools if the shares are stationary and prices are nonstationary but cointegrated. Futhermore, with nonstationary prices, one can use the Generalized Composite Commodity Theorem to test the validity of grouping goods into an aggregate, while using only the data on the disaggregated goods. This is in contrast to the normal assumptions of weak separability, which is typically not tested because one needs additional data. We use these tools to investigate the extent of competition in the Japanese import market between wild-caught North American salmon and farmed salmon and trout.