Re: st: Simple question about interpreting an econometric model

[David Hoaglin <dchoaglin@gmail.com>]

Hi, Nick.

The coefficient b1 comes from fitting the model to data that include
all values of X1, so its interpretation must include the fact that it
reflects change in Y as X1 changes, adjusting for the contributions of
the other predictors in the model (X1*X1down, X1*X1down*X2, and
X1*X1down*X3).

Also, because X1 is involved in those interactions with X2 and X3
(when X1 < 0), it is a good idea to examine the predicted values of Y
at various combinations of X1, X2, and X3 (a grid?), not just at the
combination average(X2) and average(X3).  The presence of interactions
makes interpretations more complicated.  Maybe less so if X2 and X3
are indicator variables, rather than "continuous."

And when X1 > 0, you should check on the range of values of X1 that
your data cover when you set X2 = average(X2) and X3 = average(X3), so
as to avoid extrapolating (too far).

Regards,

David Hoaglin

On Fri, Dec 23, 2011 at 8:21 AM, Nick Kohn <coffeemug.nick@gmail.com> wrote:
> 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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