Uncertainty treatment in input-output analysis

3. ECONOMETRIC AND OTHER (NON-BAYESIAN) STATISTICAL
APPROACHES
Attempts to account for uncertainties in IO data, in particular, those assuming random
measurement errors, led to a large literature on statistical estimation of the parameters
of the IO model as opposed to their mere computations. The very first studies
attempted to estimate IO coefficients from the following set of n simultaneous
equations
, (2)
i.e. a disturbance term is added to the open Leontief model. If long enough time
series on x and f are available, input coefficients could be estimated from (2). Such
time series approach has been pursued by e.g. Stone (1955), Briggs (1957) and Klein
(1974, pp.341-342). In particular, Briggs (1957) discussed the issue of efficient
estimation of IO coefficients focusing on ordinary least squares (OLS) and maximum
likelihood estimation techniques.
However, Gerking (1976a) points to two problems with the time series approach. First,
sufficiently long time series is required to estimate n 2 parameters in (2) by means of
regression. Briggs (1957) had to implement his estimations at a high level of
aggregation, because his time series consisted of only 6 observations (in fact, these
were post-war British national accounts data used in Stone, 1955). Secondly, and of
equal importance, Gerking noted that even with the availability of a long enough data
series, „such problems as structural change and variations in product mix may render
these estimates meaningless‟ (Gerking, 1976a, p.276). The estimation of technical
coefficients together with their standard errors from a set of cross-sectional data (i.e.
cross-sectional approach) was first proposed by Gerking (1976a, 1976b). Primary data
for building IO tables are obtained from representative firms/establishments in all
sectors of an economy and, in general, can include information on firms‟ purchases
only, sales only or both purchases and sales. Apparently, conducting the last type of
survey provides more information, but is more expensive. The estimates of IO
coefficients and flows derived from purchases (resp. sales) only data are referred to as
„columns only‟ (resp. „rows only‟) estimates, in analogy to the structure of IO
transactions table. Gerking (1976a) discusses the estimation procedure of „columns
only‟ estimates, while both types of estimates and their optimal combination in the
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