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 in itial estimates through simple human error, underreporting, miscategor ization or for any of a host of possible reasons. Baxter has made a st art on the subject, using only the Mahalanobis distance (or Wald test) as the basis for inference. The tests available fall into the standar d likelihood ratio-Lagrange multiplier-Wald categorization and, as exp ected, display good power in identifying a biased cell estimate. Howev er, 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 tes ts 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 as signed 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 int roduced increases at a faster rate than the number of restrictions (th e size of the SAM). The Wald and Lagrange multiplier tests of a cell r equire a joint test of a row and column restriction simultaneously; ho wever, Monte Carlo experiments suggest the counter-intuitive result th at 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, su ch as national accounting or the reconciliation of international trade statistics.