In the surprisingly lengthy comments thread to Yes, banking really is that simple, I somehow get the impression that a lot of people think that there is one answer to the exclusion of all others. A bit like the argument between Intelligent Design and evolution. IMHO there is plenty of evidence for the latter, it can be observed and it stacks up in theory; the former is blind faith, but hey.
The point is that banks 'split the zero' and create debts/financial assets out of thin air.
This is fine if all banks are doing is acting as debt collectors for producers of new goods and services. So if I want to buy a new car from Ford, I could pay £20,000 cash or take out a personal loan of £20,000, in which case. Ford are given a credit with the bank (just the same as if they had paid in my £20,000 cash) and I am given a debit which I pay off over four years. This is not really any different to me buying the car from Ford and agreeing that I will pay them £5,000 a year for four years, with the bank factoring that debt, doing the administration and chasing etc.
The mischief we want to prevent is credit/land price/share price bubbles. The full reserve banking idea not only misses the point but contains a loophole a mile wide, so would achieve nothing unless you heap more and more rules on top.
Let's do the easiest one first, Modern Monetary Theory, which keeps cropping up, despite the fact that they have no strong opinions on bank reform one way or another. To my mind, the basic tenet is is a statement of the bleeding' obvious:
An ongoing tax obligation, in concert with private confidence and acceptance of the currency, maintains its value. Because the government can issue its own currency at will, MMT maintains that the level of taxation relative to government spending (the government's deficit spending or budget surplus) is in reality a policy tool that regulates inflation and unemployment, and not a means of funding the government's activities per se.
So you have to have some taxes, or else the currency is meaningless: you can consider rationing vouchers to be a kind of citizen's income (spending), but they only have value because you have to hand them over when you buy something that is rationed (pay a tax). The vouchers also have value, because different people have different preferences, so somebody who doesn't smoke can sell his tobacco vouchers to a smoker etc. If the government then goes a bit mad and prints more vouchers than food or petrol is available, they fall in value (= inflation). If the government abandons rationing (stops taxing) then the vouchers are just so much waste paper.
However, most MMTers don't commit themselves to what kind of tax is best, they seem to consider them as interchangeable. It is only if you apply logic that you can divine which kind of tax sits best with the theory.
Clearly, if the government wants to minimise unemployment, taxing employment (or 'wealth creation' or whatever you want to call it) is a no-no in good times or in bad. So minimising inflation must be key, in which case, look at what sort of inflation you are getting and then tax the thing whose price is being inflated.
There is no natural tendency of wages or prices in a free-trade economy without currency controls to increase in nominal terms; so most of the 'inflation' is in the price of land/location (and other monopoly rights). Seeing as the initial selling price of these was precisely zero, every single penny of land/location values is pure inflation, so it seems consistent with MMT to have taxes on land/location values.
Next, The Austrian School. Some of the underlying stuff is pretty waffly, but you can't really argue with the subjective theory of value, the concept of opportunity costs or consumer sovereignty.
The interesting bit is their views on the business cycle and bank regulation. They missed the point a bit here, very little bank lending is to business, the best source of finance is realised and reinvested profits. They seem to think that over-lending during credit bubbles all goes into business mal-investment and this leads to crashes. There is some element of this, but most of the over-lending just inflates the price of land, shares and other monopoly/non-productive assets/rights.
Mises said it is central banks which encourage over-lending (observably true) but Hayek countered that if left to their own devices, banks would behave just as badly (also observably true) and that therefore central bank control was necessary. We can complete the circle by pointing out that even if a central bank's initial clear instructions are to prevent credit bubbles, in the end they suffer regulatory capture and if not, politicians will ride the wave of Home-Owner-Ism and the central bank ends up encouraging banks to over-lend (with low interest rates, deposit protection guarantees, too big to fail mentality etc).
So again, if we had a tax system which kept land prices low, and either broke up or regulated monopolies (with a special tax or with price caps), much less lending would be diverted into these.
The Chicago School is worth a mention, if only to point out that a couple of them such as Frank Knight were shills for the landowners and oil and mining companies and tried to trash LVT by pretending that these things are 'capital' in the same way as machines or know-how. Milton Friedman on the other hand said that LVT was the least bad tax and supported simplification of the welfare system down to something akin to a Citizen's Dividend. He called it negative income tax, but it's the same thing, really.
Many MMTers seem to recommend policies which we could call "Keynesian". The general idea is that the government should spend counter-cyclically, so it runs deficits during a recession and surpluses when things are going well (although most people and politicians ignore the second bit). If you look at J M Keynes' theories in a bit more detail, they are in fact nonsense - stuff like the fiscal multiplier and so on. But the general idea is fair enough, the Hoover Dam is a concrete example.
But he misses the point - why not try and have a system which eliminates or at least minimises recessions in the first place? At least the Austrians went back a step and looked at ways of doing this rather than working out how to patch things up afterwards (the Austrians were very much in favour of small government and non-intervention).
Again, avoiding credit/land price/share price bubbles is key to this. There is no perfect correlation, but by and large, the bigger the land price boom in a country, the worse the ensuing recession. So the worst affected countries in Europe were Ireland, Spain, Greece, Iceland and the UK (the effects have been mitigated by keeping the land price bubble going at enormous cost to the taxpayer, chickens which will all come home to roost eventually). Germany, Austria and Switzerland had much less land price inflation and they suffered the least.
So taxes which depress the productive economy (VAT, income tax, NIC, corporation tax) should be kept to a minimum and as much tax as possible or necessary collected from land values - see Singapore and Hong Kong, who barely had a recession at all. Then you won't have such bad recessions and we won't need to try Keynesian patching up after the event, bearing in mind that a lot of the extra government spending is either on complete crap/white elephants or just goes into keeping the land price bubble going - Hoover Dam aside.
You'll see the general theme here.
All these schools of thought are just looking at different things, they are not mutually exclusive. The only economic theory, which works in practice and which sits comfortably with all of them is replacing as many taxes as possible with Land Value Tax, i.e. Georgism.
Henry George was suitably vague on how LVT receipts should be 'spent'. It's like MMT in reverse; the government should prevent land price inflation by taxing land values; how it is spent is a separate topic. So arguments about whether to replace Trident; give money to third world dictators; provide 'free' healthcare and education; who should get welfare and how much; are separate arguments. LVT would lead to a massive improvement (boost to the economy and more equality) if it were simply a replacement tax and what the government spends money on left entirely unchanged.
Until you realize that there is a virtuous circle. If spending is focussed more on things which help the economy and which boost the rental value of land; then the government makes a 'profit' just like any good landlord, which can be ploughed back in, and so on and so forth, until we reach a level where there is nothing more worth spending it on and the surplus is dished out as a Citizen's Dividend.
The notion of the Citizen's Dividend neatly closes the circle with the MMTers again, who seem to support the idea of the Job Guarantee. Apart from the administration involved, if we can reduce unemployment to its bare minimum by getting rid of taxes on employment, then trying reducing it further is a futile exercise and leads to malinvestment i.e. government sponsored job creation schemes. it is better to just give somebody £100 a week and gamble on him topping this up with a private sector job which creates extra wealth, however little, than giving him £100 a week to dig holes and somebody else £100 a week to fill them in again, leaving them no spare time to create real new wealth.