Hierarchical predictive coding (hPC) is one of the major theories of sensory processing and cortical computation. It provides a comprehensive explanation of the role of top-down connections in cortex, by proposing how they can guide sensory processing, and has inspired many experimental studies, ranging from electrophysiological studies of individual neurons to high-level studies of cognitive computation. Still, after twenty years of research, important questions remain open: Experimental evidence for error units, which are central to the theory, is inconclusive, and little theoretical work exists that demonstrates how hPC and learning can be implemented in biologically plausible neural circuits. At the same time, recent work showed how spiking neurons can very efficiently encode information, by relying on the principles of tight excitation-inhibition (EI) balance and plastic lateral inhibition. We propose to combine these two branches of research, and show that a functionally equivalent formulation of hPC is possible without error units, using an architecture that exploits a tight EI balance on neural dendrites. This interpretation of hPC naturally leads to a biologically plausible implementation of hPC with spiking neurons, and provides promising alternative explanations for existing empirical results on predictive coding, as well as cortical connectivity and dynamics. Most centrally, we propose a purpose for the localized voltage (and inhibition) dependence of synaptic plasticity, and we demonstrate how mismatch responses to unexpected optic flow arise in a model of V1 that only contains prediction neurons. Our results promote a theory of cortical computation, where errors are computed not in distinct neural populations, but in separate dendritic compartments.