# oaxaca decomposition: how to treat error term and do intercrossing intercepts matter

I am just wondering if I can decompose a difference in earnings let's say between year 1999 and 2002 into the difference due to a higher education level of labour market participants and due to higher wage premium they get for their education in 2002 using Oaxaca decomposition.

According to my simple regression model: log (w) = α + β*number of years of education + ε there are different education premia:

1999 β  = 0.0849657
2002 β  = 0.1041767

mean Wages in 1999:1.625728
mean Wages in 2002:1.632374

mean log wages 1999:1.617639
mean log wages 2002:0.2387489

mean years of schooling 1999: 11.78819
mean years of schooling 2002: 11.98008


I understand it is the log wage difference that matters here:

If I subtract the regression equation of 1999 from the one of 2002 & I transform the equations I arrive at:

The difference due to observable characteristics (different means in the years of schooling) reads as:

β2002 (s ̅2002 - s ̅1999) = log(w ̅2002) - log(w ̅1999) - (α2002 - α1999) - s ̅1999 (β2002 - β1999) - (ε2002 -  ε1999)


The difference in coefficients is:

α2002 - α1999+  s ̅1999 (β2002 - β1999 ) = log(w ̅2002) - log(w ̅1999) - β2002 (s ̅2002 - s ̅1999) - ( ε2002 -  ε1999 )


My model explains below 20% of the variance. Am I right to understand there is no way to calculate the difference due to the changing coefficients? Is there any way to transform the equation further?

Additionally, I am wondering if the intercept of year 2002 (blue part of the graph) that is below the one from year 1999 (orange part of the graph) matters for the calculations...