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The estimation of large social account matrices (Inglês)

Formalization and extension of a recent proposal for adjusting initial unbalanced estimates of components of a matrix allows them to satisfy accounting requirements imposed by tabular form in an optimal manner. The proposal, which is based on linear combinations of initial unbiased estimates, has many potential applications in national income accounting, input-output construction, and demography, among other fields. Given that the adjustment procedure simply represents the first-order conditions resulting from the minimization of a quadratic loss function, it is possible to develop alternative procedures for minimizing the constrained loss function. These procedures, based on the conjugate gradient algorithm, prove to be much more efficient than the traditional solution, both in terms of the time taken and storage requirements, and the optimal adjustment of very large social account matrices becomes quite feasible. Application of these techniques to a social account matrix constructed for the Muda River District in West Malaysia indicate the feasibility and usefulness of the method. Statistical data are included.

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