This paper studies the impact of immigration on the US macroeconomy. I identify structural vector autoregressions (SVARs) with time-varying parameters (TVPs) and stochastic volatility (SV) using a novel set of restrictions. The TVP-SV-SVARs are estimated on a quarterly sample including average labor productivity (ALP), hours worked, immigration, consumption, and term spread from 1953 to 2017. An immigration supply shock increases domestic ALP and hours worked over the business cycle horizons. Movements in immigration are explained by its own shock and to a lesser extent by the productivity and news shocks. IRFs driven by these shocks vary over the sample, especially around changes in immigration policy such as the Immigration Act of 1990. In contrast, the forecast error variance decompositions exhibit little change over the sample. Immigration plays an important role in the US macroeconomy.