# Is this interpretation of a log-level model with dummy variable correct?

$$Logearnings_i$$ = 5.99 +0.383*$$gender_i$$ +$$u_i$$

This is a least squares regression model.

$$Logearnings_i$$ is the reported weekly earnings for individual i.

$$gender_i$$ is a dummy variable = 1 for females and 0 for males.

I'm asked to interpret the coefficient of the variable on gender.

My answer and thoughts:

• This is a log level model, so we would normally interpret the coefficient as one unit increase in the independent variable results in a 100 multiplied by the coefficient change in the dependent variable.

• However, we have a dummy variable, so my first-guess interpretation is, if the person is female (gender=1), then their reported weekly earnings are (38.3% = 0.383*100) higher than the self reported earnings of males (gender=0).

• However, because the more accurate method of calculating would be to take the exponent, so $$e^(0.383)$$ = 1.4666, so if the person is female (gender=1), then their reported weekly earnings are 46.6% higher than the self reported earnings of males (gender=0).

• You are adding 0.383 to the log of earnings not multiplying earnings by 0.383. Jan 26, 2021 at 17:29
• Your question is addressed in the second part of my answer here. Mar 6, 2021 at 2:31