This article studies the effects of endogenous participation of marginally attached workers on wage dynamics and hence on the unemployment fluctuations in a stylized search theoretic model. It shows that endogenous participation of these workers induces a countercyclical component in the wage equation under Nash bargaining. As a result, the elasticity of wage with respect to productivity becomes smaller and hence the model can generate larger unemployment fluctuations, compared to the textbook model. With careful calibration, I show that the model well captures the wage dynamics and can explain the unemployment and job openings volatility reasonably well.
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Lifang Xu (2024) studied this question.