Solved – Log transformed dependent variable with interaction terms

interactionregression

I have three questions regarding a regression equation where the dependent is log transformed, a dummy $D$ is interacted with yer dummies, and other independent variables are present on the right hand side: $\newcommand{\year}{{\rm year}}$

$${\rm ln}(Y) = \alpha + \beta_{0}.D + \beta_{1}.\year1990 + \beta_{2}.\year1995 + \beta_{3}.\year2000 + \beta_{4}.D.\year1990 + \beta_{5}.D.\year1995 + \beta_{6}.D.\year2000 + \beta_{7}.X + {\rm error}$$

  1. How can I get the average effect of $D$ from this regression?
  2. Am I right to think that the coefficient of dummy + coefficient of dummy year interaction (say for 2000) gives the percent difference relative to the same coefficients for the year dummy omitted omitted due to collinearity?
  3. What would be the most meaningful interpretation of this regression?

Best Answer

1) The average impact of D on Y is \begin{equation} \beta_{0} +mean(0,\beta_{4},\beta_{5},\beta_{6})\end{equation}

You might want to weight the mean by the frequency with which the years appear in your dataset

2) $ \beta_{0}$ is the impact of D on $Ln(Y)$ in the omitted year. Therefore, $ \beta_{6}$ On it's own is the relative percentage impact D being 1 has on Y, when compared to the omitted year. I.e. if $ \beta_{6}$ =0.1. Then D being equal to 1 had 10 (exp(0.1)*100) percentage point greater impact on Y in 2000.

3)It depends on what your coefficients are and what D and Y stand for!

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