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st: How to Reconcile R2 with Economic Significance


From   Erasmo Giambona <e.giambona@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: How to Reconcile R2 with Economic Significance
Date   Wed, 29 Jul 2009 16:08:34 +0200

Dear Statalist,

I am trying to understand how to reconcile statistical and economc significance.

Consider a simple model: y = a + b1x1 + b2x2 +e, fitted for panel data
and estimated via OLS. Suppose the t-values are respectively 10 and 2
for x1 and x2, implying that x1 contributes more to the R2 for the
model. Suppose also that a 1 standard deviation increase in x1 cause y
to increase by 2% from its mean while a 1 standard deviation increase
in x2 causes y to increase by 25% from its mean. Now, a simple
interpretation of a model R2 is that it is a proportion in the
variability of y that is accounted for by the model. Accordingly,
because of its t-value (and its effect on the R2), x1 would seem to be
one of the key drivers of this variabillity in y. However, from an
economic point of view, x1 seems to have a very marginal abillity in
explaining this variation in y (while x2 seems to be very important).

Statistical and economic significance would seem to lead to seemingly
"contradicting" results. Can someone provide some suggestions that
could help me reconciling statistical and economic significance?

Thanks,

Erasmo
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