Estimating a social accounting matrix using entropy difference 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) for a recent year is a difficult and a challenging problem. Typically, input-output data are collected at long intervals (usually five years or more), while national income and product data are available annually, but with a lag. Supporting data also come from a variety of sources; e.g., censuses of manufacturing, labor surveys, agricultural data, government accounts, international trade accounts, and household surveys. The traditional RAS approach requires that we start with a consistent SAM for a particular period and “update” it for a later period given new information on row and column sums. This paper extends the RAS method by proposing a flexible entropy difference 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 can be viewed as a special case of the general SAM estimation problem. The paper presents the structure of a SAM and a mathematical description of the estimation problem. It then describes the classical RAS procedure and the entropy difference approach. An example of the entropy difference approach applied to the case of Mozambique is presented. In addition, an appendix includes a listing of the computer code in the GAMS language used in the procedure.