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st: Simple question about interpreting an econometric model


From   Nick Kohn <coffeemug.nick@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Simple question about interpreting an econometric model
Date   Fri, 23 Dec 2011 14:21:45 +0100

Hi,

My specification is as follows:

Y = b1*X1 + b2*X1*X1down + b3*X1*X1down*X2 + b3*X1*X1down*X3

X1down is an indicator variable that is = 0 when X1 > 0

Thus, the sensitivity of Y to X1 when X1 > 0 is b1, and the
sensitivity of Y to X1 when X1 < 0 is b1+b2 + b3 * X2 + b4 * X3

I'm looking at how X2 and X3 affect this sensitivity when X1 < 0

Now, my problem is that I'm getting a bit confused when I want to
interpret the coefficients.

Can you please tell me whether the following statement is correct:
"The sensitivity when X1 > 0 in a firm with AVERAGE VALUES OF X2 and
X3 is b1, and the sensitivity when X1 < 0 is  b1 + b2 + b3 *
average(X2) + b4 * average(X3)"

I need to compare them, and I cannot change my specification at this
point. My biggest uncertainty is about the capitalized part statement
above, because if it is correct, I can compare the sensitivities by
plugging in the average values of X2 and X3 into the last part of the
statement.

Thanks!
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