Uncertainty treatment in input-output analysis

elation to one or all of the tools used (e.g. ten Raa and Steel, 1994; Kop Jansen, 1994;
Jackson, 1986) will not be further discussed here.
Quandt (1959) investigated the probabilistic properties of the solution (gross outputs) of
a Leontief system by means of a large number of sampling experiments, claiming that
„[i]n certain special cases it may be possible analytically to derive the distribution of the
solution, but in general this does not appear to be possible‟ (p.296). For this purpose, a
three-sector example is considered. Errors in input coefficients are assumed to be
independent, and 11 different three-valued discrete distributions for errors are
examined. Comparing the moments of 100 samples of random input matrices and the
relevant solutions using Spearman‟s rank correlation test, the author finds that „the
skewness of the original distribution tends to be transmitted to the distribution of the
solution‟ (p.300). Quandt then fits lognormal distributions to each of the eleven
frequency distributions by methods of moments, compares the fitted distributions with
the observed ones using a Chi-squared criterion, and concludes that „the lognormal
distribution provides a fairly adequate description of the distribution of the solution,
irrespective of the distribution of the original errors‟ (p.304). The practical implication of
this finding, according to Quandt, is that one can use the critical values of the
lognormal distribution to establish confidence intervals for the estimated gross outputs.
A number of simulation studies examined the impact of errors in the structural
parameters of regional IO analyses with the aim of guiding practitioners on optimal
allocation of scarce resources for building regional IO tables. For example, Stevens
and Trainer (1980), and Park, Mohtadi and Kurbursi (PMK, 1981) carry out simulations
by introducing multiplicative errors to the components (except final demand) of the true
regional IO model and compare the simulated IO multipliers with the true ones. 20 Errors
are normally distributed draws with mean 1.0 and standard deviation of one-half of the
percentage errors of 10, 20, 30 or 40 percent of the original coefficients and are
multiplied by the original IO coefficients in order to obtain new coefficients. Whereas in
the first study true IO matrices were hypothetically generated, PMK (1981) used the
Utah 1963 IO table as the true table. One of the main conclusions of these studies was
that errors in regional purchase coefficients (RPCs - elements of the diagonal matrix
in a regional IO model of
) contribute far more to inaccuracies in
calculated outputs and multipliers than errors in the technical coefficients matrix .
20 Park, Mohtadi and Kubursi (1981) provide also analytical results, following Park (1973). However, their
complicated form did not allow making statements on the relative importance of the different types of
errors, hence the authors perform simulations.
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