# Interpretation coefficient for log ratio as dependent variable and independent variable is 0-1 (percentage) [duplicate]

I'm struggling to follow the interpretation of the log coefficients. Union density represents the share of unionized households it is scaled between 0-1. The coefficient for union density is in my case -2.189 for the log(90/10) as a dependent variable. I would interpret the coefficient as follow: A 10 percentage point increase in union density decreases the 90/10 percentile income ratio by 0.2189 percent. I just multiplied the coefficient with 0.1 since there is an increase of ten percentage points in union density. However, the authors of my paper write that a 10 percentage point increase in union density decreases the 90/10 income ratio by 2-1.7%. How do they get those numbers? The table and interpretation can be found on page 1364 and 1365 of Unions and Inequality over the Twentieth Century: New Evidence from Survey Data
I'm truly grateful for any help!!! I have to present this paper on the 21 of June. :)

• Welcome to CV, Emil. Could you please explain what "2-1.7%" means?? We have many posts about interpreting slopes in log-log regressions: please check them out. The duplicate is the first relevant hit; the second duplicate explains the connection with percentage changes.
– whuber
Jun 13 at 17:59