Those who want to get the major links to this topic need only go right here
to gather some links, and can get more if they get the links cited in those links.
But you, dear reader, aren't here for links. If that were the case, you'd be out golfing. No, you want to see Smiling Dave's humble take on this deep, tangled, intricate matter, and hope he will lay it all out for you in simple language. Fear not, intrepid seekers. Without further ado:
The essence of ABCT is the claim that booms and busts in modern times are caused by money printing by a central bank. [Indeed, even when central banks did not exist and booms and busts occurred, careful research will show that there was some other way the money supply increased, such as when the Spaniards brought in boat loads of gold from South America].
Now big picture, an increase in money supply means someone will be consuming more than he produced, as explained in this humble article [see second question]. Of course this will hurt the economy.
But Mises, and Hayek after him, fleshed out the details, wishing to explain specific patterns that seemed to occur again and again in booms and busts. They found that the key to understanding things down to the fine points is the lowering of the interest rate, which the central bank always seems to be doing when there is a boom and bust.
[EDIT: Just occurred to me that inflation of the money supply does indeed give someone the ability to be parasitic, but there is no guarantee that the parasite will malinvest. He may just consume randomly, or invest wisely.
So that Mises' making the interest rate key to a business cycle is very necessary.]
Obviously, to explain everything based on a low interest rate, one has to have a definition of "low". And their definition was "lower than it should be". Which of course requires a new definition of what an interest rate "should be". The easy way, that avoids all attacks from Sraffa and the blogger Lord Keynes and everyone else, is to say "whatever it would have been had the central bank not printed all that money". After all, central banks admit that they have the power to influence interest rates, and that their way of doing so is by printing money. [That's why he's called Helicopter Ben].
But Hayek had a certain fish to fry. [Edit: This has to be fact-checked]. He wanted, for reasons I have not investigated, the central banks to make sure they set the interest rate to the "real, genuine, authentic, natural" one, not one that is too low. Which means Hayek had to go out and find what the real interest rate is.
Nowadays, I think Austrians agree that we'd be better off without any central bank at all. We don't need a central bank to set any interest rate, not the real one and not the phony one. So that we have no need of finding out what the "real" rate is. Suffice to say that it is certainly higher than the one that comes into being after mountains of money printing, and that's enough to explain the ABCT.
In any case, Sraffa told Hayek that there are many different interest rates. Each commodity has a different rate of what it costs now and what it costs to buy a future crop of it, which is an interest rate. So that the central bank cannot set the "real" rate, because there isn't one. Each commodity has a different rate. It's like asking what is the real price of a car. Are you talking about a Jaguar or a jalopy?
Hayek wrote that he has no problem with that, since there is a tendency for all commodities to eventually converge to the same interest rate, and that number they all tend to is the magic number we are looking for, the real interest rate. Mises and Rothbard also made the same assumption as Hayek does, that there is indeed a magic number, albeit one that we may not be able to calculate in practice.
Bob Murphy writes that Hayek did not solve the problem with that explanation, and proposes his own solution. Given my level of understanding, I'll have to go tl;dr on his paper. Huisman also wrote a tl;dr article, apparently proposing 8 possible numbers.
Bottom line, there are two topics going on. First, there is a quest for the holy grail, the elusive magic number which is the real interest rate. Mises and Hayek and Murphy and Huisman and Sraffa and the blogger Lord Keynes are out there slugging it out, either claiming they found the magic number, or claiming it doesn't exist. The whole discussion is way over my head, at least when we get to the writings of the modern Austrians, Murphy and Huisman. But it is a technical topic of theoretical interest for specialists, and has nothing to do with refuting ABCT, as we have already shown and will shortly summarize again.
But Sraffa and LK then move on to a different, second, topic. They claim that if no magic number exists, then it is absurd to say that banks ever lend money at a rate lower than some non existent magic number.
They claim that the Austrians are saying that the winner of the World's Strongest Man contest declared on television is not the world's strongest man in fact, since the Incredible Hulk is stronger. And Sraffa and LK are refuting that by pointing out that there is no Incredible Hulk.
And that's where Sraffa and LK make their big mistake. They are saying that depending on the givens of a particular case, Jaguar or jalopy, you get a different number, and thus there is no one unique number at all. And my humble rebuttal is that there is a unique number, for a given particular situation. [Even though it may be impossible to actually calculate, it's there]. And that number is, given a specific banker and a specific given borrower on a given specific day and all the given specific details of a given specific loan, the rate that would have been set by that specific banker if there was no central bank printing money.
Now I know that some people won't be happy with an economics discussion unless they have some math jargon to chew on. So for them, here is that final paragraph, restated for their pleasure in cumbersome language:
Let A be a given borrower. Let B be a given Banker. Let C be a given loan made on date D with specific details of the loan denoted by E. Define X(A, B, C,D,E) as the interest rate that would have existed absent a central bank. Define Y(A,B,C,D,E) as the interest rate that actually happened, because the central bank printed tons of money. If, for a great many values of A,B,C,D, and E, we have Y<<X [meaning Y is much lower than X], then the conditions exist for a valid ABCT explanation.