|It doesn't matter where or how the central bank injects liquidity. Image from wikimedia commons.|
A quick note on causality because it's come up in a variety of forms recently (I'll use the interest rate model for concreteness):
- Can you be sure that the relationship between interest rates and the monetary base will hold if the central bank does X?
- Does lowering interest rates cause the monetary base to rise or vice versa?
- You say that interest rates can be lowered by the central bank printing currency, but that's not how open market operations work in real life, so the central bank can't lower interest rates by printing currency.
The information transfer model is based on information theory, but also behaves like a kind of generalized thermodynamics. Let's say we have two variables: money m and interest rate r. The idea is that if you change one variable (r1 → r2), then the other variables respond (m1 → m2) not because they are "caused" to do so by "forces", but rather because it is overwhelmingly statistically probable that if r2 becomes true of the macrostate, then the microstates will be in a macrostate described by m2. This is the basic idea behind entropic forces. Money doesn't make its way from bank vaults into a person's hand because of changes in incentives or utility because you changed r and m (well, at least in this model ). It makes its way there because the state with the money in a person's hand is far more likely than the state with the money in the vault given the macroeconomic observation of the system in the state (r2, m2). It is not important how the money got there from a macroeconomic perspective.
Imagine bacon cooking in the kitchen. In the diffusion process, the smell fills the house. I do not need to know the actual trajectories of the molecules, or even how much kinteic energy they leave the bacon with. It doesn't matter if the bacon is cooked in the kitchen or in one of the bedrooms -- the smell will fill the whole house.
The thing that is important is that the economy is a large system. In that case, because of the law of large numbers, I can know that the result will converge to the mean and fluctuations around it will be small. Flipping a fair coin 5 times has a lot of uncertainty in the final outcome (4 heads, 1 tail? 2 heads, 3 tails? 5 tails?). Flipping a fair coin 5 million times does not (2.5 million ± 2200 heads).
The law of large numbers means we know that the final state (r2, m2) will be realized with high probability. But it actually doesn't have to be! It could end up as (r2, m1) or (r2, m3). That's why saying r1 → r2 causes m1 → m2 is problematic. The final state m2 is not a foregone conclusion -- there will be some statistical fluctuation around it.
The law of large numbers also lets us know that the reverse causality works. If m1 → m2 then we will have r1 → r2. That's because if the most probable macrostate (r2, m2) is consistent with r2 if we change r, then it is also the most probable macrostate with m2 if we change m. If m1 → m2 but r1 → r3, then (r3, m2) would be the most probable macrostate consistent with m2. This state would have to be more probable than (r2, m2) since it is the most probable macrostate consistent with m2. The only way this is logically consistent with is if r2 = r3. See this link for more on this subject.
So the answers are:
- If the model is correct, then yes.
- Yes. Both. Or neither. Doesn't matter.
- If the model is correct, the particulars of the process do not matter.
 This represents a huge break with traditional economics. It also makes traditional economics seem kind of silly if you try to use the language of utility in thermodynamics ... The pressure of an ideal gas falls because an atom has diminishing marginal utility of extra volume. Ha! This break is also interesting because it means that all the properties of supply and demand are emergent. Atoms don't have feelings about pressures and volumes and the idea gas law isn't even true for an individual atom. Bringing this insight back to economics: diminishing marginal utility is not a property of an individual economic agent, but rather an ensemble of agents. Supply and demand is not about incentives, but rather a property of ensembles of people performing market transactions.