Estimating a social accounting matrix using cross entropy methods

There is a continuing need to use recent and consistent multisectoral economic data to support policy analysis and the development of economywide models. Updating and estimating input-output tables and social accounting matrices (SAMs), which provides the underlying data framework for this type of model and analysis, for a recent year is a difficult and a challenging problem. The traditional RAS approach requires that we start with a consistent SAM for a particular year and “update” it for a later year given new information on row and column sums. This paper extends the RAS method by proposing a flexible “cross entropy” approach to estimating a consistent SAM starting from inconsistent data estimated with error, a common experience in many countries. The method is flexible and powerful when dealing with scattered and inconsistent data. It allows incorporating errors in variables, inequality constraints, and prior knowledge about any part of the SAM (not just row and column sums). Since the input-output accounts are contained within the SAM framework, updating an input-output table is a special case of the general SAM estimation problem. The paper describes the RAS procedure and “cross entropy” method, and compares the underlying “information theory” and classical statistical approaches to parameter estimation. An example is presented applying the cross entropy approach to data from Mozambique. An appendix includes a listing of the computer code in the GAMS language used in the procedure.