Implementing an Almost Ideal Demand System of mobility expenditure in Stan

Abstract

The Almost Ideal Demand System (AIDS) by Deaton is widely used in economics to estimate systems of demand functions. The model predicts (across households and/or over time) how consumers change their demand in response to price and/or income changes. This is why the AIDS is often used to investigate the welfare implications of, for example, taxes or subsidies, or price changes. Reasons for the AIDS's popularity in econometrics is inter alia its flexibility as it gives an arbitrary first-order approximation to any demand system. In the majority of applications, the AIDS is estimated using frequentist methods. A few applications use Bayesian methods, but as of yet these studies employ Gibbs Sampling in their estimation. Taking advantage of the efficiency gains that arise from using Hamiltonian Monte Carlo to estimate the model, this work estimates an AIDS using Stan. Data on expenditures for three transport modes, car, train and bus/taxi, by different groups of households in Germany are used. The objective is to investigate substitute and complementary relationships between transport modes so as to better understand the impact of recent increases in energy costs on transport demand. The poster explains model specification including parameter restrictions, estimation in Stan, as well as the computation of the price and expenditure elasticities. Interesting issues arise in relation to 1) the prior specification in the light of the parameter restrictions required by economic theory, which leave only a subset of parameters free to be estimated, and 2) the imposition of curvature (i.e. a downward sloping demand function) which requires the computation of Eigenvalues of the matrix of second order derivatives and some kind of rejection step.