IDENTIFICATION OF ACTIVITY EFFECTS, TRENDS AND CYCLES IN IMPORT DEMAND

Date01 February 1979
DOIhttp://doi.org/10.1111/j.1468-0084.1979.mp41001005.x
Published date01 February 1979
IDENTIFICATION OF ACTIVITY EFFECTS, TRENDS
AND CYCLES IN IMPORT DEMAND
By TERRY BARKER
I. INTRODUCTION
Activity effects, time trends and cyclical variables, together or in combination,
are usually included in import demand functions. Although most of the published
econometric work finds that activity effects or time trends are important, there is
a divergence of results on the effects of cyclical variables. Marston (1971), Gregory
(1971), Rees and Layard (1971) and Hughes and Thirlwall (1977) find significant
and important positive cyclical effects; Barker (1970, 1977) and Hibberd and
Wren-Lewis (1978) find that cyclical influences (pressure of demand, utilisation
of capacity or stockbuilding) are insignificant, unstable or of the wrong sign except
for a few specific products.
However there is a problem of identification in the estimation of these functions
which has not been fully recognized. Any two of the three variables (activity,
trend and cycle) may imply the third. It is the conclusion of this paper that the
issue of which to include cannot be decided empirically. The interpretation and
restriction of coefficients should be done explicitly on the basis of economic theory;
and the restrictions should then be tested against the data.
The next section of this paper illustrates the problem by an algebraic example
showing, for a simple linear import function, how activity effects, time trends and
cyclical effects cannot be identified. Section III re-interprets some previous work
estimating import functions to show how the omission or restriction of one of the
three variables can lead to apparently significant results, for example significantly
positive time trends and capacity utilization effects. Section IV presents some
estimates for the British economy supporting the interpretation of previous
results and showing the quantitative importance of the problem for the estimated
coefficients. The conclusions are given in Section V.
II. THE IDENTIFICATION PROBLEM: AN ALGEBRAIC EXAMPLE
For the sake of argument, take the simple linear model:
m=a0+a1y+u2c+cz3t (1)
where in is the total imports of a commodity
yis real income
cis the capacity variable
tis a time trend
and a0 to a3 are parameters.
Now assume that the capacity variable is equal to the deviation of income from
its trend c = (y - (2)
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