It is well established that job displacement causes large and persistent earnings losses, but their sources remain debated. A leading explanation ties the losses to workers' industry-specific human capital, yet direct evidence remains scarce. I develop a method for estimating the demand for workers' industry-specific skills, and show that the cost of specialization depends on industry conditions: within shrinking industries, laid-off workers who held highly industry-specific occupations suffer earnings losses 80\% greater than those of comparable workers in less specialized occupations. In growing industries, specialization is not costly. To measure specialization, I proxy a worker's skills by her occupation and define its industry-specificity as the share of that occupation employed in her industry; the demand for these specialized skills is proxied by the industry growth rate. These greater earnings losses are driven by a persistent employment effect: specialized workers are more than twice as likely to exit the labor market after displacement. The greater losses remain when comparing workers laid off from the same firm, and are not explained by the loss of firm wage premiums.
We study the spillover effects of Chile's minimum monthly earnings (ME) rule, a minimum wage policy updated annually. We exploit an unexpected delay in the ME schedule to estimate instantaneous spillovers, fading out at 60\% above the ME. These raises are observed in firms with and without ME workers alike. The evidence suggests two complementary mechanisms: relative-pay concerns lead firms, especially large ones, to give raises above the ME to preserve their internal wage structure; and labor market competition leads all firms to give raises as well. An interview with an HR manager at a large retailer supports both mechanisms.