$Logearnings_i$ = 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).
