Minimum wage in a multi-tier search and wage-posting model with cross-market substitutions

While minimum wage policy is widely adopted in the real world, can it effectively raise the average wage of lower paid jobs without having large detrimental consequences for employment? The empirical literature fails to establish robust findings. We develop a general-equilibrium search and wage-posting framework with heterogeneous workers and tasks matching in multi-tier labor markets: abstract, routine high-skilled, routine middle-skilled, manual middle-skilled and manual low-skilled.