The empirical migration literature has often identified the labor market effects of immigration using variation of immigration concentration across regions or sectors. However, this approach overlooks macroeconomic effects which occur in all regions and sectors. Instead, we estimate the relative contributions of competing macroeconomic and sectoral demand, supply and immigration effects, by applying a VAR approach to UK labor market variables for 35 different sectors from 2001-2019. We find that, while immigration is in part endogenously determined by supply and demand, most of the evolution in aggregate migration share over the sample period is driven by the identified exogenous aggregate migration process. This then plays a significant negative role in the determination of native aggregate wage growth. Historical decompositions, which decompose both the error terms and, novelly, the constant terms into their structural parts, reveal that other aggregate processes have offsetting effects which account for the weak observed association between wages and immigration observed in the data. We also find substantial heterogeneity in the responses of wages and hours to sector specific shocks.