We present 16 GHz (1.9 cm) deep radio continuum observations made with the Arcminute Microkelvin Imager (AMI) of a sample of low-mass young stars driving jets. We combine these new data with archival information from an extensive literature search to examine spectral energy distributions (SEDs) for each source and calculate both the radio and sub-mm spectral indices in two different scenarios: (1) fixing the dust temperature (Td) according to evolutionary class; and (2) allowing Td to vary. We use the results of this analysis to place constraints on the physical mechanisms responsible for the radio emission. From AMI data alone, as well as from model fitting to the full SED in both scenarios, we find that 80 per cent of the objects in this sample have spectral indices consistent with free–free emission. We find an average spectral index in both Td scenarios, consistent with free–free emission. We examine correlations of the radio luminosity with bolometric luminosity, envelope mass and outflow force, and find that these data are consistent with the strong correlation with envelope mass seen in lower luminosity samples. We examine the errors associated with determining the radio luminosity and find that the dominant source of error is the uncertainty on the opacity index, β. We examine the SEDs for variability in these young objects, and find evidence for possible radio flare events in the histories of L1551 IRS 5 and Serpens SMM 1.