Demographics and sectoral reallocations: A search theory with immobile workers

We propose a mechanism via which a decline in the share of young workers slows employment growth in expanding sectors, and exacerbates sectoral reallocation costs. To quantify this mechanism, we develop a search model with perpetual youth, three sectors and endogenous separations of worker-firm matches. Our model incorporates three important features: sector-specific human capital; sectoral preferences, which imply that only some workers are mobile across sectors; and a wage bargaining distortion, whereby unskilled workers' wages in shrinking sectors are determined by mobile workers. In our parameterized model, output losses after a sectoral reallocation shock are significant and rise substantially at low population growth rates. While this result is driven by the interactions between the three model features, the wage distortion for unskilled wages is responsible for amplifying the sectoral reallocation costs. The model generates a rise in unemployment and a fall in vacancies after a sectoral shock, counter to conventional wisdom.