Flexible Estimation of Demand Systems: A Copula Approach

摘要

In this paper we study the own-price elasticity for gasoline in demand systems involving three expenditure categories in the transportation sector in Canada: gasoline, local transportation, and intercity transportation for Canadian households from 1997 to 2009. In particular, we conduct a replication of Chang and Serletis, (The demand for gasoline: Evidence from household survey data, Journal of Applied Econometrics, 2014, 29, 291-343) hereafter CS, who-using TSP version 5.1-estimated Deaton and Muellbauer, 's Almost Ideal Demand System (AIDS) (American Economic Review, 1980, 70, 312-326), Banks et al., 's Quadratic AIDS (Review of Economics and Statistics, 1997, 79, 527-539), and Barnett, 's Minflex Laurent (ML) (Journal of Business and Economic Statistics, 1983, 1, 7-23) models to demand systems consisting of these three goods, analyzing and enforcing theoretical economic regularity-that is, the compliance of estimates with positivity, monotonicity, and curvature. Using the R statistical language instead, we found that our estimates are similar to those of CS using data for single-member households and married couples without children, but differ for households with one child. (All replicated estimation tables in CS, as well as our full implementation, are available as supplementary material in the online version of this paper.) However, using a more flexible copula model, a total of 168 possible specifications for each type of household and their resulting gasoline own-price elasticities are also estimated. We find that allowing for skewness in the marginal distributions of local transportation budget shares greatly improves the Bayesian information criterion (BIC) of our models.