As in the data, the price of risk in our model sharply increases in recessions. The benefit from hiring new workers therefore greatly declines, leading to a large decrease in job vacancies and an increase in unemployment of the same magnitude as in the data.
Yes, nominal wages are sticky but this is the other and all-important side of the hiring equation.
That is from a new and important NBER working paper by Patrick J. Kehoe, Pierlauro Lopez, Virgiliu Midrigan, and Elena Pastorino. There is much more to their general model than that single sentence would indicate.