Cross-sectional aggregation of non-linear models

This paper considers the problem of cross-sectional aggregation when the underlying micro behavioural relations are characterized by general non-linear specifications. It focuses on forecasting the aggregates, and shows how an optimal aggregate model can be derived by minimizing the mean squared prediction errors conditional on the aggregate information. The paper also derives model selection criteria for distinguishing between aggregate and disaggregate models when the primary object of the analysis is forecasting the aggregates, and establishes the consistency of the model selection criteria in large samples. In the case of standard non-linear micro relations with additive errors it also provides suitable small sample corrections. For more general non-linear specifications we consider bootstrap techniques to correct for small sample bias of the proposed model selection criteria. Some of the ideas in the paper are illustrated using log-linear micro relations, often employed in applied research. The paper also contains an empirical application where log-linear production functions are estimated for the UK economy disaggregated by eight industrial sectors and at the aggregate level over the period 1954–1995.