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$Logearnings_i$ = 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).

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

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