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st: Comparing interaction (moderating) coefficient across models

From   Glenn Hoetker <>
To   "<>" <>
Subject   st: Comparing interaction (moderating) coefficient across models
Date   Thu, 8 Nov 2012 17:06:33 +0000

Greetings and thank you for considering the problem I pose below.  Any leads on underlying econometrics, as well as implementation in Stata, would be very appreciated.

I have the following model

Y1 = a0 + a1X1 + a2X2 + a3(X1*X2) + e

Y2 = b0 + b1X1 + b2X2 + b3(X1*X2) + e

My interest is in testing whether the moderating effect of X1 on X2 is greater for Y1 than for H2, that is,  is a3 > b3?  The relative impacts of X1 and X2 on Y1 and Y2 are not of interest to me.  I have panel data on 30+ countries for both equations, so the sample is the same for each.

My problem is that Y1 and Y2 are measured on fundamentally different scales.  Y1 is an count of firm creation and Y2 is a scale from a survey of managers by another organization.

How would one best proceed to conduct this test?  Are there any problems hiding in the shadows that I should be aware of?

Thank you for any help and guidance.

Glenn Hoetker
Dean's Council Distinguished Scholar and Associate Professor
Department of Management, W.P. Carey School of Business
Affiliate Professor, Sandra Day O'Connor College of Law
Senior Sustainability Scholar, Global Institute of Sustainability
Faculty Fellow,  Center for Law, Science & Innovation
Arizona State University
Tel: 480-965-4566

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