PRACTITIONERS CORNER: A Note on Log‐Log Regressions with Dummy Variables: Why Units Matter*
| DOI | http://doi.org/10.1111/j.1468-0084.1989.mp51001008.x |
| Published date | 01 February 1989 |
| Date | 01 February 1989 |
| Author | Rosanna Giordano,Michael R. Veall |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 51, 1(1989)
0305-9049 $3.00
A Note on Log-Log Regressions with Dummy
Variables: Why Units Matter*
Rosanna Giordano and Michael R. Veall
I. THE PROBLEM
The point of this note is trivial. Nonetheless, when the issue came up in
application, it puzzled a number of econometricians (including us) for an
embarassingly long time.
Most econometricians learn as undergraduates that the slope coefficients
of loglog regressions are estimated elasticities and will be invariant to the
choice of units of measurement for the explanatory variables. However, as a
simplified example, consider a regression equation for a segment of the
demand for customer-dialled long distance telephone services in Canada,
1975, quarter ito 1985, quarter 4:1
log(R,/P1) = 40.51 -0.58 log(P1/CPI1) + 1.64 D1log(P1/CPI1)
+xá+residual (1)
where log denotes natural logarithm and denotes OLS estimate, R1 is
revenue for a particular market segment, P, is a chained Laspeyres price
index for that segment and D1 is a dummy variable and equals 0 up to and
including the fourth quarter of 1983 and 1 afterwards. The x â represents
other variables in the regression (such as real income) whose coefficients are
not reported for brevity. CPI1 is the Consumer Price Index, 1981 = 100.
If the units of CPI1 are changed from 1981 = 100 to 1981 = 1, with no
other changes, the results change to:
log(R1/P1) = -40.32 0.50 log(P1/CPI1) -0.02 D1log(P1/CPI1)
+x/+resjdual (2)
Notice, for example, that from (1) to (2) the estimated own-price elasticity has
changed from 0.58 to 0.50 for prior to 1984 and from
*Any views expressed are those of the authors and are not necessarily those of Telecom
Canada. The latter author thanks the Natural Sciences and Engineering Council of Canada for
research support.
'The model is not a Telecom Canada working model. It was developed to illustrate the slope
dummy problem in a log-log regression model. No inferences should be made with respect to
the price elasticities reported.
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