In aggregate U.S. data, exogenous shocks to labor productivity induce highly persistent and hump-shaped responses to both the vacancy-unemployment ratio and employment. We show that the standard version of the Mortensen-Pissarides matching model fails to replicate this dynamic pattern due to the rapid responses of vacancies. We extend the model by introducing a sunk cost for creating new job positions, motivated by the well-known fact that worker turnover exceeds job turnover. In the matching model with sunk costs, vacancies react sluggishly to shocks, leading to highly realistic dynamics.