Diagnostic Testing and Sensitivity Analysis in the Construction of Social Accounting Matrices

This paper examines the issue of testing for initial estimate bias in the construction of a social accounting matrix (SAM). The issue arises because the statistician may have inadvertently provided incorrect initial estimates through simple human error, under‐reporting, miscategorization or for any of a host of possible reasons. Baxter has made a start on the subject, using only the Mahalanobis distance (or Wald test) as the basis for inference. The tests available fall into the standard likelihood ratio–Lagrange multiplier–Wald categorization and, as expected, display good power in identifying a biased cell estimate. However, the problem is much more complicated than raised by Baxter and the present paper only addresses some of the complications. How can tests be used to identify biased initial estimates? What happens to the tests as the size of an SAM increases? Which of the three tests is to be preferred? The simplest procedure, that of comparing the balanced with the unbalanced initial estimate within the context of the variance assigned to the initial estimate, is shown to be a likelihood ratio test. The performance of the tests does not appear to diminish as the size of the SAM increases, probably because the number of random terms introduced increases at a faster rate than the number of restrictions (the size of the SAM). The Wald and Lagrange multiplier tests of a cell require a joint test of a row and column restriction simultaneously; however, Monte Carlo experiments suggest the counter‐intuitive result that the difference (likelihood ratio) test based on the restricted and unrestricted estimate of a cell may be superior to either. The methods developed here have relevance to other areas of data construction, such as national accounting or the reconciliation of international trade statistics.