Uncertainty treatment in input-output analysis

ordinal information is transformed into cardinal data by using a minimum number of
assumptions on the underlying probability distributions of the IO coefficients (e.g. in the
absence of additional information, the well-known principle of insufficient reason would
imply using uniform distribution), while a random number generator makes the core of
the stochastic method that is used to generate an empirical distribution of interest. The
authors conclude that „[t]he main advantage of ordinal input-output analysis is the
integration of input-output table construction and the determination of standard errors
into one framework‟ (p.416, emphasis added) and the last „can be used as a tool for
error measurement‟ (p.408).
The notion of a balanced growth path is of particular interest in the analysis of dynamic
IO models. Ćmiel and Gurgul (1996, 1997) introduce backward, forward and mixed
time lags into the IO dynamic model, and study some of their statistical properties.
Specifically, they focus on the random balanced growth factor within each setting,
which „enables [one] to take into account the uncertainty that is always present in
empirical investigations of real economic processes‟ (Ćmiel and Gurgul, 1996, p.138).
The authors derive distribution functions and approximate formulas for the stochastic
characteristics of the random balance growth factors for the so-called forward-lag-type,
backward-lag-type and mixed-lag-type IO models.
Other approaches attempt to account for inherent IO data uncertainties in their final
outcomes include such tools as interval arithmetic (see e.g. Jerrell, 1997; Barker and
Rocco S., 2011), fuzzy systems theory (see e.g. Beynon, Munday and Roberts, 2005;
Beynon and Munday, 2007, 2008; Díaz and Morillas, 2011), and grey systems theory
(see e.g. Wu and Chang, 2003; Li and Liu, 2008). Similarly, to measure global
robustness of the outcomes of empirical IO models with respect to errors in IO
coefficients, Wolff (2005) applies the theory of robust systems (or theory of norms) in
linear algebra. Presenting the main features of these techniques is apparently beyond
the scope of this chapter, and thus the interested reader is referred to the mentioned
references.
9. DISCUSSIONS AND CONCLUDING REMARKS
In this study, we have surveyed the major contributions to the field of stochastic inputoutput
(IO) analysis broadly defined. The literature was discussed rather extensively
according to the specific tools used in dealing with the inherent IO data uncertainty
problems. Within each such blocks a sort of history of thought approach has been
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