Turbulence and Unemployment in Matching Models

Ljungqvist and Sargent (1998, 2008) show that worse skill transition probabilities for workers who suffer involuntary layoffs (i.e., increases in turbulence) generate higher unemployment in a welfare state. den Haan, Haefke and Ramey (2005) challenge this finding by showing that if higher turbulence means that voluntary quits are also exposed to even a tiny risk of skill loss, then higher turbulence leads to lower unemployment within their matching model. We show (1) that there is no such brittleness of the positive turbulence-unemployment relationship in the matching model of Ljungqvist and Sargent (2007) even if we add such “quit turbulence†, and (2) that if den Haan et al. had calibrated their productivity distribution to fit observed unemployment patterns that they miss, then they too would have found a positive turbulence-unemployment relationship in their model. Thus, we trace den Haan et al.’s finding to their assuming a narrower productivity distribution than Ljungqvist and Sargent had. Because den Haan et al. assume a distribution with such narrow support that it implies small returns to reallocating labor, even a small mobility cost shuts down voluntary separations. But that means that the imposition of a small layoff cost in tranquil times has counterfactually large unemployment suppression effects. When the parameterization is adjusted to fit historical observations on unemployment and layoff costs, a positive relationship between turbulence and unemployment reemerges.