MMT is not universally accepted. Plenty of economists reject it completely.
That is correct.
It is rejected by most orthodox (mainstream) economic schools of thought such as the neo-liberal, monetarist, new classical schools as well as other heterodox schools such as the Austrians, though the latter would accept the basic tenets I would argue. It has its roots in earlier theories such as Chartalism, Aba Lerner's work as well as others. In other words it's not new but it's been tweaked to recognise how modern sovereign nations fund their spending.
The important thing is not what the twats over on Sky News, The Sydney Morning Herald or the Treasury Department think, they're stuck in an old mindset, rather what you think and whether you can defend your understanding of it or not.
So have a go and throw up your criticisms of it and we'll see whether they can stand or if they'll waver and collapse. You can start a new thread if you like on MMT, @betterinvestmentthanshare's is keen for someone to do it.
