Hi Statalist,

I am having trouble interpreting my regression that includes an interaction term with a logged variable, looking at the impact of county house price changes on county divorce rates. Divorce rates are level variable, whilst house prices are logged. The dummy variable D1 takes the value 1 if the county has an above-median unemployment rate.

Divorce rate=α+β1D1+β2ln(House prices)+δ1(ln(house prices)∗D1)

I am struggling to interpret δ1

If β2 = 1.1 and δ1= -0.5, I can come up with two interpretations:

1. For a 10% increase in house prices, when D1=1, divorce rates would increase by (e^(1.1-0.5)-1)/10 = 0.0822
2. For a 10% increase in house prices, when D1=0, divorce rates would increase by (e^(1.1)-1)/10 = 0.2

So clearly there is a difference in increase of 0.2-0.0822 = 0.1178. However, I thought that δ1 was supposed to be the additional increase? But -0.5 doesn't reconcile the difference in divorce rates and neither does (e^(-0.5)-1)/10 = -0.039

For this reason I am struggling to interpret δ1=-0.5 in my regression results. Any help would be much appreciated.