Abstract
Using a Social Accounting Matrix (SAM) to forecast the effect of exogenous shocks on the economy should be based on incorporate and error-free information that requires to update data in the SAM cells. Many techniques are available for updating a SAM. Here we use an approach based on the fuzzy set theory. Essentially, we restrict estimates of a matrix of direct input-output coefficients, the core of a matrix of SAM direct coefficients, to just seven possible size categories when they are updates. These rough categorical estimates are transformed to some quantitate functions with domain that reflects of coefficient sizes. These resulting model functions are interpreted as quasi probability density functions so a quasi-stochastic programing problem is used to estimate fuzzy impacts. The fuzzy results are compared to “true” ones, estimated via a classically created SAM, by calculating the estimation error. Finally, we explore factors of the error sensitivity. In an empirical exercise, we use a 57-industry 2010 SAM for New Jersey and develop a SAM model with fuzzy direct input-output coefficients. Based on this model we forecast effect from relative and absolute changes for three groups of exogenous factors: the elements of the final demand, the institutional incomes and value added. We next extend the initial model by also fuzzifying other structural components of SAM: the matrix of value-added by industry coefficients and the matrix of institutional expenditures by industry coefficients and estimate the same effects. The fuzzy forecasts for the initial and “new” SAM model with fuzzy parameters are compared to results estimated when using a classical approach. In all cases we obtain the small estimation error that makes it possible to consider a fuzzy approach as an efficient way for forecasting effects of exogenous shocks on the economy using inaccurate and incomplete SAM data