Econometrica: Jul, 1989, Volume 57, Issue 4
Econometric Analysis of Aggregation in the Context of Linear Prediction Models
M. H. Pesaran, M. S. Kumar, R. G. Pierse
This paper deals with the problem of aggregation where the focus of the analysis is whether to predict aggregate variables using macro or micro equations. The Grunfeld-Griliches prediction criterion for choosing between aggregate and disaggregate equations is generalized to allow for contemporaneous covariances between the disturbances of micro equations and the possibility of different parametric restrictions on the equations of the disaggregate model. A new test is proposed of the hypothesis of `perfect aggregation' which tests the validity of aggregation either through coefficient equality or through the stability over time of the composition of the regressors across the micro units. The tools developed in the paper are then applied to employment demand functions for the UK economy disaggregated by 40 industries. Firstly a set of unrestricted log-linear dynamic specifications are estimated for the disaggregate equations and then linear parameter restrictions are imposed as appropriate. Corresponding unrestricted and restricted aggregate equations are estimated. Two different levels of aggregation are considered: aggregation over the 23 manufacturing industries and aggregation over all 40 industries of the economy. In both cases the hypothesis of perfect aggregation is firmly rejected. For the manufacturing industries the prediction criterion marginally favors the aggregate equation but over all industries the disaggregated equations are strongly preferred.