Log transformation of the dependent variable in a first-differences model

[Cla Tuor]

Hello all,

I am estimating a first differences model of the following form ΔY_it = ß₀ + ß₁ΔX_it + ɛ_it.

In one of the regressions estimated, the dependent variable is wages. As I am more interested in the percentage change than the level change, I want to use the logarithm for the dependent variable.

Do I have to use log(wage_it+1 - wage_it) or log(wage_it+1) - log(wage_it) as my dependent variable?

Thank you!

[Clyde Schechter]

As you might recall from high school algebra, log(wage_it+1) - log(wage_it) = log(wage_it+1/wage_it). So if you are interested in relative change, this is the way to go.