Uncertainty treatment in input-output analysis

Monetario Centroamericano' (see van Tongeren and Magnus, 2012, p.278). This
paper also presents for the first time an empirical application to a large dataset of
Guatemala (2500 variables). Thus, the Bayesian method, similar to the conventional
national accounting approaches, deals with 'reconciliation' or 'integration' of data, but
differs from the last in several respects. 'First, all conditions of conventional estimates
are formalized: identities are explicitly included and ratios are introduced as priors;
second, reliabilities of data and ratio values are reflected in well-defined prior variation
coefficients; third, the system is simultaneous rather than sequential; and finally,
updating the system when new information becomes available is easy and fast, and
does not require changes in the compilation method' (van Tongeren and Magnus,
2012, p.278). In addition, '[t]he method also facilitates the simultaneous use of indicator
ratios in compilation and analysis' (Magnus, van Tongeren and de Vos, 2000, p.347,
emphasis added). For IO analysis, the implication is that the estimated supply and use
tables from the Bayesian approach will have reliability intervals element-wise, and thus
can be readily used in subsequent analysis, e.g. sensitivity analysis. Or alternatively,
the method itself can be used, alone or in combination with existing ones, in order to
construct IO tables, again with uncertainty values attached to each element. Such an
attempt is already made by Lugovoy, Polbin and Potashnikov (2014) who update IO
tables for selected EU countries and SUTs for Russia using Bayesian methods. Their
experimental results and comparisons with other existing updating methods confirm the
usefulness of such approach.
The problem of balancing IO data from the Bayesian perspective is considered by
Rodrigues (2014). The author states that considering all available information in
dealing with the data balancing problem implies accounting explicitly for the first and
second moment constraints that include prior information about the values of the data
(best guess) and their uncertainties. Rodrigues (2014) then derives an analytical
solution of the data balancing problem by application of cross-entropy minimization
subject to the first and second moment constraints, and shows that the conventional
data balancing methods, such as generalized least squares, weighted least squares
and biproportional methods, are particular cases of the proposed method.
Rickman (2001) presents a Bayesian integrated IO and econometric model of the state
of Oklahoma. Comparing seven models in terms of their performance in forecasting
industry employment, the author, for example, concludes that '[o]n average, a Bayesian
model produced the lowest MAPE [mean absolute percentage error] across the thirty
employment sectors and five forecast horizons' (p.241).
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