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 ( T _ { d } ) according to evolutionary class ; ( 2 ) allowing T _ { d } 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 T _ { d } 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 , \beta . 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 .