This paper is a quantitative, equilibrium study of the insurance role of severance pay when workers face displacement risk and markets are incomplete. A key feature of our model is that, in line with an established empirical literature, job displacement entails a persistent fall in earnings upon reemployment due to the loss of job-specific human capital. The model is solved numerically and calibrated to the US economy. In contrast to previous studies that have analyzed severance payments in the absence of persistent earning losses, we find that the welfare gains from the insurance against job displacement afforded by severance pay are sizable. These gains are higher if, as in most OECD countries, severance pay increases with tenure. The result is a consequence of the higher persistence of earnings losses for workers with a larger stock of job-specific human capital at the time of displacement.