The empirical migration literature often identifies the labor market effects of immigration using exogenous variation of migration concentration across sectors. However, this approach differences out macroeconomic effects which occur in all sectors. We apply macroeconomic time series methods to UK labor market data for 35 different sectors, to model, for the first time, immigration, native wages and hours worked, as responding to demand, supply and immigration shocks at both aggregate and sectoral levels. The labor market is modeled as being subject to multiple shocks at any one time. Using VAR, we find that migrant labor is, in part, endogenously determined by aggregate demand and supply along with an exogenous component. Using historical decompositions which decompose both the error terms and, novelly, the constant terms into their structural parts, we show that the ‘migration shock’ accounts for most of the change in migration share and has a significant negative effect on native wage growth, particularly in unskilled sectors. However other contemporaneous shocks have offsetting positive associations between immigration and native wages, whoe effects differ across sectors