We develop a novel method of introducing real wage rigidity into an otherwise standard search and matching model. Wages are constantly renegotiated through Nash wage bargaining, however negotiations are based on imperfect information regarding the productivity level and consequently marginal productivity. The imperfect information mechanism is modeled by means of a Kalman filter. As a consequence, after a positive technology shock some of the increase in productivity is attributed to information noise, resulting in a smaller rise in the real wage. This in turn prompts firms to post more vacancies and increase capital investment. Overall, we show that the real wage rigidity mechanism substantially amplifies the model's internal propagation mechanism.