Estimating a third-order translog demand system using Canadian micro-data

This paper presents a flexible functional form called third-order translog, which includes higher-order terms, to estimate systems of budget-share equations using Canadian crosssectional micro-data. We test the statistical significance of the third-order terms, and also test regularity conditions such as homogeneity and symmetry restrictions of the budgetshare systems. It is important to test these restrictions, since their rejection might imply that our data does not support the theory of utility maximization or the particular functional form used in the model is flawed. We find that the third-order terms are statistically significant which means that they are important determinant of consumer demand. But we reject the regularity conditions for most of the demographic groups. We also find that our model suffers from heteroscedastic errors and repeat the tests using “Heteroscedastic Consistent Covariance Matrix Estimator (HCCME).” The third-order terms are once again found to be significant but the regularity conditions fail to hold for all the demographic groups. The rejection of regularity conditions indicate a need for proper aggregation restrictions and determining the “neighborhood” of the observation space where the regularity conditions can hold.