This wage can then be regressed on a number of (mean) characteristics of the workers and the local sector. More specially, we can estimate the following first-step regression:

(12)         ln wast= Wast + rs + b*Xast + εast

In this equation, r is a sector dummy, and Xast is a set of characteristics for  sector s in area a and year t and the workers employed therein. To capture sector effects, we use in Xast the (log) share of local employment in sector s and the (log) number of local establishments in this sector. Also in Xast, the mean individual characteristics are the age, its square, and the shares of employment in each of six skill groups. In equation (12), the coefficient of interest is Wast, a fixed effect for each employment area and year. When at estimating equation (12), all local sector and mean individual characteristics are centered, and the observations are weighted by the number of workers in each cell to avoid heteroscedasticity.

   The coefficients Wast can, in a second step, be regressed on local employment density and other local characteristics.