"We introduce a matching model that allows for classical and frictional unemployment. The labor market is dual featuring low-skilled and high-skilled workers and simple and complex jobs. Simple jobs pay a minimum wage, while wages in the complex jobs are determined by Nash bargaining. Opportunities for low-skilled workers are limited to simple jobs; while high-skilled unemployed can apply for both types of jobs, and thereby can accept to be downgraded. We analyze the outcomes of simple job subsidy policies assuming that government budget is balanced through taxes on occupied workers. We first give conditions for the existence and uniqueness of a steady-state equilibrium and we then analyze the effects of different fiscal instruments. We show that in this set-up, increasing simple job subsidies does not necessarily reduce low-skilled unemployment or unemployment spells. By introducing heterogeneous skills and possible downgrading of the high-skilled workers, we show that the effectiveness of such policies in reducing the classical unemployment is decreasing. In fact, any additional classical unemployed re-entering the job market is accompanied by an increasing number of high-skilled workers downgrading to low-skilled jobs. We calibrate the model on French labor market data. It is found that for five low-skilled workers leaving classical unemployment, two high-skilled workers are downgraded."

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