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In previous work we showed that a model that integrates job assignment, human-capital acquisition, and learning can explain several empirical findings concerning wage and promotion dynamics inside firms. In this paper we extend that model in two ways. First, we incorporate schooling into the model and derive a number of testable implications that we then compare with the available empirical evidence. Second, and more important, we show that introducing "task-specific" human capital allows us to produce cohort effects (i.e., the finding that a cohort that enters a firm at a low wage will continue to earn below-average wages years later). We argue that task-specific human capital is a realistic concept and may have many important implications. We also discuss limitations of our (extended) approach.

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