Testing for Aggregation Bias in Linear Models

Direct tests of aggregation bias are developed to test the theory that all the disaggregated coefficients are equal. The problem of aggregation bias is defined in terms of the deviations of macro parameters from the averages of the corresponding micro parameters. Tests are applied to the annual estimates of aggregate and disaggregate employment demand functions for the UK economy presented by Pesaran, Pierse, and Kumar (1989). The data used cover the whole private sector, except for the mineral oil and natural gas sector. Estimates of the disaggregate labor demand relationships show considerable variation across sectors; thus, important information may be lost in working with aggregate figures. Significant aggregation biases are found in the estimates of a variety of measures of the responsiveness of employment to real wage and output changes based on the aggregate and disaggregate employment equations.