Imposing Symmetry On A Complete Matrix Of 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 strong assumption of constant variance in the random components of the indirect utility function to enable the derivation of behaviourally meaningful cross choice elasticities. Under constant variance, only the direct choice elasticities have behavioural meaning. While this advance in discrete choice modelling is to be applauded, the procedures used derive share elasticities conditional on a fixed total demand, and in addition make no corrections for two important conditions required to ‘convert’ the choice elasticity matrix into a demand elasticity matrix - namely symmetry and share weighted column sums. This paper takes a set of empirical choice elasticities and shows the procedures required to adjust these elasticities to arrive at a 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

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