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st: Interpretation of interaction term in log linear (non linear) model


From   Suryadipta Roy <sroy2138@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interpretation of interaction term in log linear (non linear) model
Date   Sat, 8 Jun 2013 12:12:04 -0400

Dear Statalisters,

I was wondering if some one would be kind enough to clarify if I am on
the right track in clarifying the coefficient of the interaction term
when the dependent variable is in logarithm. The estimated model is of
the form: log(Trade) = constant + 0.15dummy - 0.15x1 + 0.12dummy*x1,
where dummy is (0,1) categorical variable, x1 is a continuous variable
(standardized 0 - 1), and dummy*x1 is the interaction term. The result
has been obtained from a fixed effects panel regression using -areg-
with robust standard error option, and all the variables are
statistically significant. Based on readings of Maarten's Stata tip
87: Interpretation of interactions in non-linear model, several
Statalist postings, and the following link
http://www.stanford.edu/~mrosenfe/soc_388_notes/soc_388_2002/Interpreting%20the%20coefficients%20of%20loglinear%20models.pdf
, I wanted to make sure if any of the following interpretation of the
above result is correct:

1. The coefficient of "dummy" indicates that this category (dummy
variable = 1) has 16% (= exp(0.15) - 1) more of "Trade" compared to
the base category (dummy variable = 0).
2. The effect of being in this category on "Trade" increases when the
value of x1 increases. For every standard deviation increase in x1,
the effect of "dummy" increases by about 13% (exp(0.12) - 1), OR there
is a statistically significant 13% increase in "Trade" to countries
having more of x1 relative to countries that have one standard
deviation lower value of x1, OR the effect of being in the "dummy = 1"
category in a country with one standard deviation more of x1 than
average is exp(0.12)*exp(0.15) = 1.31, which means that "dummy=1"
category has about 31% more "Trade" than "dummy=0" category.

Following suggestions elsewhere in the Statalist, I have pursued other
non-linear estimation strategies (and have asked questions to that
effect earlier), but there is a tradition in this literature to use
log-linear models. Any suggestion is greatly appreciated.

Sincerely,
Suryadipta Roy.
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