Uncertainty treatment in input–output analysis

An input-output coefficient may vary between observations because of objective or subjective differences, such as spatial differentiation and measurement errors, respectively. The literature is organized by methodology. The first methodology is deterministic error analysis. Upper and lower bounds on exogenous variables (input-output coefficients and final demand) transmit into upper and lower bounds on endogenous variables (output). The analysis is not straightforward because Leontief inversion is a non-linear operation. The second methodology is the econometric estimation of input-output coefficients using establishment data. The third methodology returns to the transmission of errors but now takes into account the canceling out of random errors, yielding sharper results. The expected value of the Leontief inverse is compared to the standard Leontief inverse of the expected input-output coefficients matrix. Systematic establishment differences are the subject of the fourth methodology, the full probability density function approach, which is essentially an aggregation procedure. The next two methodologies are new and promising. Monte Carlo simulations are extended to equilibrium analysis and Bayesian and entropy approaches address data treatment such as balancing.