On estimation of almost ideal demand system using moving blocks bootstrap and pairs bootstrap methods

This paper applies a bootstrap method to the Almost Ideal Demand System (AIDS) proposed by Deaton and Muellbauer (Am Econ Rev 70:312–326, 1980), where the moving blocks bootstrap (MBB) and pairs bootstrap (PB) methods are adopted taking into account serially correlated error terms and limited dependent variables (note that the dependent variables in the AIDS model lie on the interval between zero and one). We aim to obtain the empirical distribution of the expenditure and price elasticities. Note that, the expenditure and price elasticities are obtained using the parameter estimates included in the AIDS model. In the past, a few studies report both the elasticity estimates and their standard errors obtained from the Delta method, but most of studies show only the elasticity estimates (i.e., statistical tests have not been done in most of the past studies). Applying MBB and PB methods to the AIDS model and using Japanese monthly household expenditure data from January, 1975 to December, 2012, we show in this paper that a few elasticities are statistically insignificant. We also compare the standard errors based on the bootstrap method with those based on the Delta method. We obtain the results that the differences between the Delta method and the bootstrap method are not negligible. In addition, the validity of the linear approximated AIDS (LA–AIDS) model which is commonly used in empirical studies is examined. In consequence, we find that the LA–AIDS model shows a poor performance, compared with the AIDS model, because the LA–AIDS model yields inconsistency on the elasticity estimates.