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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: interpreting cofficient on interaction of two logged variables |

Date |
Tue, 21 Aug 2012 16:24:56 -0400 |

Dear Anna, Others have commented on the mathematics of the log function. I assume that the interaction predictor is in that model for a good reason, either from the theory underlying the model or because you (or others) have found that it makes a useful contribution in actual sets of data. The justification for including the interaction term should come from one of these sources. After you have decided to transform x1 and x2 by taking their logarithms (for any of a variety of reasons), they are simply predictors in the model (that happen to be measured in the log scale). Their interaction represents (or summarizes) a nonlinearity in the relation of log(y) to log(x1) and log(x2). The slope of log(y) against log(x1) varies with the value of log(x2), and similarly for the slope of log(y) against log(x2). Viewed in another way, the model describes a particular type of quadratic surface in the variables log(x1) and log(x2). By replacing log(x1) and log(x2) by suitable linear combinations of those two variables, it should be possible to eliminate the interaction term, in trade for separate quadratic terms in log(x1) and log(x2), though that may not improve the interpretability of the model. David Hoaglin On Tue, Aug 21, 2012 at 8:40 AM, D'Souza, Anna - ERS <ADSOUZA@ers.usda.gov> wrote: > Hello, > > I am interested in estimating the following model: log y = b0 + b1 log x1 + b2 log x2 + b3 (log x1 * log x2) + e > > Question 1: Does anyone have a reference that describes the interaction of logged variables? I am looking for a justification as to why to use "log x1 * log x2" vs. log (x1 * x2). > > Question 2: What is the best way to calculate the (i) average marginal effect on x1, and (ii) the marginal effect of x1 evaluated at the mean of x2 in STATA? > > Thank you, > > Anna * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: interpreting cofficient on interaction of two logged variables***From:*"D'Souza, Anna - ERS" <ADSOUZA@ers.usda.gov>

**References**:**st: interpreting cofficient on interaction of two logged variables***From:*"D'Souza, Anna - ERS" <ADSOUZA@ers.usda.gov>

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