A central question in immigration policy is how mobility restrictions affect the wages of temporary foreign workers (TFWs). We study the labor market return to TFWs gaining permanent residency (PR), which loosens mobility restrictions. Using administrative data linking matched employer-employee data in Canada to temporary and permanent visa records from 2004–2014 along with an event-study design, we find that gaining PR leads to a sharp, immediate, and persistent increase in the job switching rate of 21.7 percentage points and an increase in earnings of 3.2 percent three years after PR. These gains are driven primarily by reallocation across firms: workers move to higher-paying firms, and our estimates are consistent with no within-firm effects. To guide and interpret our reduced-form results, we develop a search-and-matching model featuring heterogeneous workers and firms. Permanent residents and native-born workers search for jobs in the same labor market and engage in on-the-job search, while TFWs search separately within a segmented labor market and do not receive outside wage offers. We calibrate the model to match our reduced-form results, and we use it to simulate the long-run effects of PR and consider two counterfactual policies: (1) increasing the cost to firms of posting a TFW vacancy and (2) allowing TFWs to switch employers freely under "open" visas. We evaluate how these policies affect output, wages, profits, and overall social welfare.

Heterogeneity robust difference-in-differences methods typically require control units that remain untreated throughout the entire post-treatment window. This prevents the identification of long-run effects when researchers observe fewer pre-treatment periods than post-treatment periods. We show that cohort-stacked estimators identify long-run effects by chaining together successive not-yet-treated controls. This approach uses overlapping cohorts to extend identification under standard common trends assumptions. We apply this to the earnings effects of parenthood. In a setting where direct methods identify effects only four years post-birth, chaining extends identification to eight years.