AGGREGATION IN LOGARITHMIC MODELS: SOME EXPERIMENTS WITH UK EXPORTS*
| Date | 01 February 1980 |
| Author | L. ALAN WINTERS |
| Published date | 01 February 1980 |
| DOI | http://doi.org/10.1111/j.1468-0084.1980.mp42001003.x |
AGGREGATION IN LOGARITHMIC MODELS: SOME
EXPERIMENTS WITH UK EXPORTS*
By L. ALAN WINTERS
Possibly the greatest frustration felt by the applied economist is the gulf
between the data he needs to test his hypotheses and what is available. This takes
many forms but among the most common is the need to estimate relationships
referring to individuals or single goods or markets on data that refer to large
aggregations of units. This is troublesome in any circumstances, but when the
postulated behavioural relationships are multiplicative in their arguments it is
potentially devastating, for if, as is usually the case, the aggregate data are the sums
of their elements, multiplicative relationships that are true at the individual level
will virtually never be precisely so at the aggregate level. And even if the
multiplicative relationship has been introduced as a useful approximation rather
than for a priori theoretical reasons the situation is not much better, for it will
strictly apply only to data at one level of aggregation (if any) and the researcher has
no way of knowing which. This is precisely the situation that research into exports
has reached: the multiplicative, or log-linear, function seems plausible and
convenient, but since no-one knows whether it applies to total exports or to exports
at, say, the eight-digit level, it is applied with equal abandon at any level of
aggregation. Using British exports as an example, this paper considers experimen-
tally the consequences of such linear aggregation in the context of log-linear models.
Linear aggregation in linear models is fairly well understoodstarting from
Theil's pathbreaking work (Theil, 1954) results have been generated by Boot and
de Wit (1960), Aigner and Goldfeld (1974) and Sasaki (1978) among others. Linear
aggregation in logarithmic models, on the other hand, has received little attention.
Gupta (1969) made progress by converting the logarithmic model into percentage
first differences and applying Theil's linear results, but the only systematic
investigation of the levels equation was by Barker (1970) and (1974). We have
shown elsewhere that these two approaches are closely related and have suggested
that Barker's approach is unlikely to be as fruitful analytically as Theil's, see
Winters (1979). If this contention is correct we can only explore this question
empirically, and that is the object of the present paper. It seeks to repeat Barker's
experiments in a different context and also to extend them in several directions.
Obviously our experimental results are specific to this particular context, but as
well as providing one observation on the effects of aggregation, this study also
explores certain methodological problems pertinent to the study of these effects.
The remainder of the paper comprises a section on the methodological aspects
of studying aggregation, a brief section on the model of exports used here and a
summary of the main empirical results. Fuller details of the aggregation results are
available from the author, in Winters (1979), while details of the model and the
* An earlier version of this paper was presented to the Seventh InputOutput Conference, Innsbruck,
Austria, April 9thl3th 1979. The author would like to thank his colleagues on the Cambridge Growth
Project and the editors of this journal for their help in revising it.
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