Preserving the symmetry of estimated commuter travel elasticities

Abstract

Travel price and time elasticities are increasingly being derived from discrete choice models of the multinomial or nested logit form. These elasticities are then applied to obtain predictions of changes in travel demand consequent on a policy change in prices and travel times. The majority of the choice elasticities are estimated within the behavioural setting of modal choice, holding total travel fixed. A few mode choice models have recently relaxed the multinomial logit model assumption of equal variance in all the random components of the indirect utility function to permit unconstrained variances across all alternatives (subject to identification for one alternative). This enables the derivation of behaviourally meaningful and unique cross choice elasticities for each pair of alternatives. Under constant variance, only the direct choice elasticities have behavioural meaning. While this is an important advance in discrete choice modelling, the derivation of share elasticities is conditional on a fixed total demand, and the procedure cannot be relied on to carry through two important properties of the model into the demand elasticity matrix—namely symmetry and zero share weighted column sums. This paper takes a set of empirically derived choice elasticities and presents a second stage procedure to adjust these elasticities to arrive at an internally consistent matrix of demand elasticities. We draw on a recent data set collected in Sydney which utilises revealed preference and stated choice data to estimate a joint model of ticket choice conditional on mode and choice of mode for commuter travel.