# How to use elasticity coefficient obtained from a log-log model

Dear Colleagues,
I have a rather trivial but vexing problem... I am having trouble
trying to interpret the results from a log-log regression. The
equation was
Log(Y) ~ b0 + b1Log(X) + a1A1 + a2A2 + a3A3 ...

where the Ai are covariates and b1 is the coefficient of interest, and
came out to 0.54. All the data was measured monthly. I took the
coefficient b1 to mean that a 1% change in X would result in 0.54%
change in Y.

When I summarize the data X and Y by years, I see the following
pattern, where the columns are years 1-4.

X: 100.0, 105.0, 111.3, 113.5
Y: 80, 96.0, 111.4, 211.6

% change in X from year to year: 5%, 6%, 2%
% change in Y from year to year: 20%, 16%, 9%

For year 5 then, how would I use my coefficient b1 to predict the %
change in Y if X were to grow by a specific value, say 1% or -1%? Am
I wrong in taking the coefficient calculated on monthly data and
applying it to annual data?

Thanks.

RD
.

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