We present a hierarchical (i.e., empirical) Bayesian framework for testing hypotheses about synaptic neurotransmission, based on the integration of ultra-high field magnetic resonance spectroscopy (7T-MRS) and magnetoencephalography. A first level dynamic causal modelling of cortical microcircuits is used to infer the connectivity parameters of a generative model of neurophysiological observations. At the second level, 7T- magnetic resonance spectroscopy (MRS) estimates of regional neurotransmitter concentration supply empirical priors on synaptic connectivity. We compare the evidence for alternative empirical priors, defined by monotonic functions of spectroscopic estimates, on subsets of synaptic connections. For efficiency and reproducibility, we used Bayesian model reduction, parametric empirical Bayes and variational Bayesian inversion. In particular, we used Bayesian model reduction to compare models of how spectroscopic neurotransmitter measures inform estimates of synaptic connectivity. This identifies the synaptic connections that are influenced by neurotransmitter levels, as measured by 7T-MRS . We demonstrate the method using resting-state magnetoencephalography (i.e., task-free recording) and 7T-MRS data from healthy adults. We validate the analysis by split-sampling of the magnetoencephalography dataset. Our results confirm the hypotheses that GABA concentration influences local recurrent inhibitory intrinsic connectivity in deep and superficial cortical layers, while glutamate influences the excitatory connections between superficial and deep layers and connections from superficial to inhibitory interneurons. The method is suitable for applications with magnetoencephalography or electroencephalography, and is well-suited to evince the mechanisms of neurological and psychiatric disorders, including responses to psychopharmacological interventions.