PRACTITIONERS CORNER: A Note on the Use of Logged Variables in Interaction Terms: Why Units Matter†
| Author | Anders Ågren,Bo Jonsson |
| Published date | 01 November 1992 |
| DOI | http://doi.org/10.1111/j.1468-0084.1992.mp54004009.x |
| Date | 01 November 1992 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 54,4(1992)
030 5-9049 $3.00
PRACTITIONERS CORNER
A Note on the Use of Logged Variables in Interaction
Terms: Why Units Mattert
Anders Agren and Bo Jonsson
I. INTRODUCTION
In a regression model which is linear in both variables and parameters infer-
ence from the estimated model is not affected by a change of scale in the
variables. But if the model contains logged variables in interaction terms care
must be taken since the results sometimes depend on the unit chosen. This
was pointed out be Giordano and Veall (1989) in the case of testing for stabil-
ity by using the dummy variable approach. They showed that if the intercept
dummy is not included in the model the resulting estimates will be scale
dependent.
In this note we will show how units matter in two other situations. The first
one is when for a loglinear model we assume that the coefficient of the logged
variable depends on another variable. This results in a situation which is simi-
lar to the one studied by Giordano and Veall and inferences based on the esti-
mated model will be scale dependent and possibly completely misleading.
Secondly, in testing for cointegration one usually starts with testing for unit
roots in each one of the included variables to determine the order of integra-
tion. We will show that for an interaction variable where at least one factor is
logged the usual unit root tests can not be applied.
II. THE CASE WITH VARYING COEFFICIENTS
Let us consider the following model with two explanatory variables and an
interaction term
logy = a + ß1 logx + ß2z + ß3(log x)z + e (1)
fThis research had been supported by the Swedish Council for Research in the Humanities
and Social Sciences and by the National Institute of Economic Research.
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