Deep learning in artificial intelligence (AI) has demonstrated that learning hierarchical representations is a good approach for generating useful sensorimotor behaviors. However, the key to effective hierarchical learning is a mechanism for ""credit assignment"", i.e. a means for determining which neurons and synapses in the hierarchy are ultimately responsible for behaviors/errors. In AI, credit assignment is accomplished with the backpropagation of error algorithm, but backpropagation of error is biologically infeasible, requiring distinct feedforward and feedback phases or pathways. Moreover, backpropagation applied to standard neural network architectures does not actually deliver the flexibility that characterizes animal learning. Here, we present a computational model for hierarchical credit assignment motivated by neocortical microcircuits. Thanks to the unique physiology of apical dendrites in pyramidal neurons, bottom-up and top-down signals can be multiplexed in ensembles of pyramidal neurons using spikes versus high-frequency bursts, respectively. We demonstrate that with the help of apical dendrite targeting inhibition, akin to somatostatin positive interneurons, recursive credit assignment is possible without distinct phases or pathways for feedforward and feedback signals. Moreover, by using ensembles of pyramidal neurons to encode these signals, dynamic routing of information is possible, which could help to generate more flexible representations for continual learning. Altogether, our work provides a model of hierarchical learning that is motivated by the structure of neocortical microcircuits. It also provides specific experimental predictions about which components of the neocortical microcircuit may be involved in credit assignment calculations in the real brain.