In the last few decades there is a clear shift of employment shares from the manufacturing sector to the service sector in the US and in many industrialized countries. At the same time, the structure of residual wages changes considerably, within and across sectors. To understand the sources of sectoral reallocation and its relation to changes in sector-specific and economy wide wage distributions, we construct a non-stationary two-sector economy where workers search on the job. We first examine the dynamic equilibrium when the relative productivity between the two sectors follows a trend. We show that in equilibrium there are two endogenous sector-specific and non-degenerate distributions of residual wages that evolve non-trivially as relative productivities change over time. Then we calibrate the model to CPS data to address the following questions: (a) Can the changes in the relative productivity between the two sectors generate the observed changes in the relative wage between the two sectors as well as the shift in employment shares? (b) How do the changes in relative productivity affect residual wage inequality within each sector and between the two sectors? (c) How do the changes in relative productivity affect the transition rates of workers within each sector and between the two sectors? (d) Is there any need for policy to affect labor mobility between the two sectors in response to the change in relative productivity?
