## Monday, May 20, 2013

### Money is an amoral tool and other observations

If this information transfer model of economics is correct and can be extrapolated to macroeconomics then it is interesting (to me at least) to think about the consequences:
• Money as such (including short term treasuries or other things measured in monetary aggregates) can be thought of as something closer to bandwidth that doesn't have as many moral implications including those around thriftiness, poverty, entrepreneurship or "hard money" as it is imbued with by e.g. advocates of the gold standard. Money is an amoral tool that allows information to get from one place to another. Given that, there is still a strain of thought in computer programming that sees using more than the bare minimum of resources as something of a moral transgression.
• Looking at the Shannon-Hartley theorem, in order to allow more information to be transferred (economic growth), you must increase the "bandwidth" (money supply). This is a necessary, but not sufficient condition. In the case of a noisy channel, increasing the "SNR" or improving your coding will also allow more information transfer (the latter will increase the time it takes to transfer the same information). As will making the information transfer more "ideal" (i.e. $I_{Q^d} = I_{Q^s}$). Of these latter three, only the third (ideal information transfer) has an obvious analog of making markets more transparent.
• As an aside on the the last point: a real number with random fluctuations on the order of a percent (20 dB SNR) has a limited channel capacity to transfer information. Assuming a single precision number and a best case micro-second scale for HFT, we can put a limit of $C = B \log_{2} (1 + SNR) \simeq 200 \text{ Mbps}$ that can be transferred through a single price market mechanism.
• Assigning properties of the macro theory to the micro theory is nonsensical; diminishing marginal utility is not a quality of an economic agent, but rather a quality of an ensemble of such agents. When moving along the demand curve, the price one is willing to pay appears to fall. Translating this to the thermodynamic analogy the ridiculousness becomes obvious: it says "when undergoing an isothermal expansion, the pressure an atom is willing to exert falls because of the diminishing marginal utility of extra volume". Diminishing marginal utility for goods is actually a sign choice and is due to choosing demand as the information source rather than destination.
• Money illusion appears to be directly related to the assumption that economic agents use the current price as a lower bound on the supply curve for non-ideal information transfer and hence a lower bound on the ideal information transfer price. First, it leads to sticky prices. And second, such a lower bound cannot be logically combined with an expectation of future inflation (else that future price, which should still be bounded by the ideal supply curve, could be deflated back to become the basis of a new estimate of the lower bound for the current price). This mechanism does not work as well if inflation is high: in such cases there is a deterministic element such that if the Fed says inflation will be $x$ regardless of economic conditions, you best plan on $x$.
• The IS-LM model can also be seen as a supply and demand system and can therefore be described in the same way as AS-AD. The IS market transfers information to the LM market via the interest rate. However, this market will fail to transfer information if it encounters the zero lower bound -- in the thermodynamic analogy, this is akin to attempting to describe a system with zero pressure (and contradicts the assumptions made that e.g. the price is non-zero). There are some attempts to work around this failure, such as using inflation targeting to make the zero lower bound on the nominal interest rate into a lower bound at (minus) the inflation rate for the real interest rate, but that again runs into problems since the inflation rate is generally not expected to be large compared to the nominal interest rate.
• One can cast elements of current economic debate in this framework: the interest rate operated as the primary information transfer mechanism from aggregate demand to aggregate supply (in this case, a proxy for AD and AS in the IS and LM markets, respectively) for many years in the US (since, say, the 1980s). Not only did this start far from the zero lower bound, over time it appears to have approached ideal information transfer such that uncertainty was small compared to the levels (the great moderation). As we approached the zero lower bound, the information transfer mechanism began to fail. The information from the aggregate demand was not reaching the aggregate supply and there was a drop in aggregate demand, causing a recession. Different solutions have been proposed. One is to assume that once the price goes to zero, the government as a large piece of aggregate demand can start buying goods and services (or give money to people who will buy goods and services) without regard to a market mechanism -- in a sense assuming aggregate demand will return to its previous level eventually -- until the IS/LM market is functioning again (interest rates rise, or inflation causes the nominal interest rate to rise). This is Keynesianism. A second is to try and create inflation via some existing market mechanism (inflation expectations/inflation target, monetary base expansion/QE) in order for the real interest rate to go below the zero lower bound and either allow the IS-LM framework/interest rate price mechanism to function again (I assume). This encompasses a set of monetarist views. A third is to create a new price in a new market that will function when the IS-LM model fails (and/or replace it). This view includes switching to NGDP level targeting using an NGDP futures market. There are also combination views. [Note: I chose these example links somewhat arbitrarily. They aren't the best exhibitions of the ideas, but rather the first relevant things that came up after some Google searches ...]
• A note on the previous point: one problem with creating new markets or using different channels is that the information transfer is likely highly non-ideal in the beginning. It is a bit like being unable to talk on your cell phone because your voice plan got too expensive and deciding to revert to text messages at a time in the past when text messages hadn't been used all that much. You are still trying to communicate the same information, but now you are limited to 140 characters (well, when texts were new they were ...). All kinds of emoticons and abbreviations were invented and became part of the culture to overcome these limitations and try and restore the information transfer capability of speech (yes, emoticons came way earlier, but you get the idea). In a similar sense, a whole language was developed around the interest rate targeting mechanism of the Fed. A new channel is going to take some time to start transferring as much information as the interest rate in the IS-LM framework. One way to visualize this is as two different lower bounds on the ideal price (see figure below). The darker region represents the lower bound from, say, the interest rate market and the lighter region represents the lower bound from the inflation expectations market (the top red curve is the ideal information transfer supply curve in this picture).

1. The bullet on money illusion should say "extrapolated back" instead of "deflated back" (which would just give you the original point again). It assumes no change in the fundamentals of S&D and so the inflated observed price should still be below the current ideal supply curve. Selling at your original price estimate would be too low (so your current price should have already priced in the inflation you were expecting) and buying at your original price estimate would be a deal (so you'd want to keep your price where it is). Inflation would occur as a periodic re-evaluation of the lower bound accompanied by a re-scaling of the price (to maintain the information gap between the ideal and observed supply curves).

2. Regarding the macro implications on the micro theory, take the example of Veblen (luxury/status) goods. While some people might be more likely to purchase a BMW at a higher price, their total income is limited and the net effect of an increase in price of BMWs is either reduction in other areas of consumption or a loss in total BMW sales due to a smaller population able to afford one (both of which lower aggregate demand). The macro effect still follows supply and demand (higher price leads to lower aggregate demand), hence we have lost some of the details at the micro scale in the transition to the macro scale.

3. The last picture and description is somewhat confusing since the "price" axis should represent two different prices (e.g. any two of the interest rate, the inflation rate or the price level).

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5. Interestingly the quantity theory of money has a money "velocity" that has units of $\text{s}^{-1} = \text{Hz}$.

http://en.wikipedia.org/wiki/Quantity_theory_of_money