The search and matching model of the labor market has become the workhorse for analyzing unemployment dynamics and the business cycle transmission mechanism. However, many quantitative studies of the search and matching framework argue that it is unable to replicate key labor market facts. These studies typically rely on a wide range of calibrated parameter values for which independent information is difficult to obtain. In this article, I specify and estimate a simple version of the search and matching framework using Bayesian methods. I show that the model has extremely weak internal propagation and that labor dynamics are explained almost exclusively by shocks that are residuals in the respective equations. Moreover, the structural parameter estimates appear to be only weakly identified and can change considerably across minor specification changes. This suggests that the search and matching model may not be a good framework for explaining business cycle fluctuations in the labor market.