Interpretation of a log-linear (percentage) model

[Konstantina Boutsioukou]

Hi everyone! I am running an OLS model exploring the relationship between the reported likelihood of a student going to university (independent variable ranging from 0%-100%) and the log expected earnings at age 30 (dependent variable). The coefficient for the reported likelihood of a student going to university is 0.002 and i have interpreted this as follows: a percentage point increase in the reported likelihood of a student to pursue tertiary education is associated with a 0.002% increase in earnings expectations. Is this correct or the coefficient should be multiplied by 100, thus becoming 0.2%. Many thanks in advance for any contribution.

[Ken Chui]

It's possible to work this out; may help with remembering the process.

Let the chance of going to university be "a" percent:

ln(earning) = b0 + 0.002(a) --- (i)

With one percent point increase, we'll have a new earning which we call it earning':

ln(earning') = b0 + 0.002(a + 1) --- (ii)

Formula (ii) - (i):

ln(earning') - ln(earning) = 0.002

ln(earning'/earning) = 0.002

earning'/earning = exp(0.002) = 1.002

The ratio of earning with (a + 1) percent versus that of (a) percent is 1.002 times, which is an increase of 0.2%.

[Konstantina Boutsioukou]

Dear Ken,

Thank you so much for your answer.