Estimating concave substitution possibilities with non-stationary data using the dynamic linear logit demand model

Measuring substitution possibilities is crucial for estimating the costs and benefits of climate, trade, banking, and many other policy issues. This paper addresses two problems encountered when modeling substitution: spurious correlations arising from data with trends and violations of the law of demand. This paper shows how the dynamic linear logit model addresses these two problems. First, the model allows adjustment in quantities and, thereby, avoids spurious correlations arising from data with significant trends. Secondly, the linear nature of the substitution elasticities facilitates parameter restrictions to ensure that substitution estimates are consistent with the law of demand and the mathematical conditions consistent with cost minimizing behavior by producers. These features are illustrated by estimating the dynamic linear logit model for energy demand in the U.S. industrial sector. The empirical results demonstrate that the dynamic linear logit model is well suited for data with common trends and for ensuring robust and intuitively appealing estimates of demand elasticities and associated substitution possibilities.