This paper develops and estimates a dynamic general equilibrium model that realistically accounts for an input-output linkage between firms operating at different stages of processing. Firms face technological change which is specific to their processing stage and charge new prices according to stage-specific Calvo-probabilities. Only a fixed fraction of households have an opportunity to adjust nominal wages to new information each period. Intermediate-stage technology shocks account for the bulk of output variability at business cycle frequencies, while final-stage technology shocks do not explain much. Although technology shocks drive the business cycle, the model predicts weakly procyclical real wages, and a near-zero correlation between return to working and hours worked. Furthermore, the model has rich implications for the dynamics of business cycles.