In a reasonably calibrated Mortensen and Pissarides matching model, shocks to average labor productivity can account for a small portion of the fluctuations in unemployment and vacancies (Shimer (2005)). I add heterogeneity in jobs (matches) with respect to the time the job is created in the form of different embodied technology levels. I also introduce specific capital that, once adapted for a match, has less value in another match. I show that the augmented model can account for fluctuations in unemployment and vacancies, and that specific capital is important to decreasing the volatility of the destruction rate of existing matches.