## Wednesday, November 6, 2013

### Three ideas

There are a three major ideas in information transfer economics:
(1) It creates a framework of supply and demand in which to build models to test against empirical data. You identify the demand (D), the supply (S) and the price (P) detecting signals of one to the other. I've written this Price:Demand→Supply which means that P = (1/κ) (D/S) in its simplest form. I'll call this equation the "first law" of information transfer economics (κ is just a parameter). On this blog, I've used P:NGDP→MB,  P:NGDP→LS, P:NGDP→U, r:NGDP→MB and r:NGDP→AS (where NGDP stands in for aggregate demand, MB is the monetary base, LS is the labor supply aka the total number of people employed), U is the total number of people unemployed, an AS is a generic aggregate supply. P, the price level (CPI) and r, the interest rate (short term) have acted as "prices". I've used this type of model to e.g. determine interest rates, study sticky wages, recover Okun's law and understand the Phillips curve.
(2) The framework allows you to create more complicated models of interacting markets using the same price signal like the IS-LM model (which uses r:NGDP→MB and r:NGDP→AS) and a labor-money model I called LS-MS for labor supply-money supply (which uses P:NGDP→MB and  P:NGDP→LS). In these cases I've used the "second law" of information transfer economics P = (1/κ) (dD/dS) in conjunction with the first law which has different solutions depending on whether you consider the variables D and S to be "exogenous" (set outside the model) or "endogenous" (set inside the model). Heuristically, these are D ~ S^(1/κ), D ~ exp S and D ~ log S. The first is related to the quantity theory of money, the second describes e.g. accelerating inflation and the third is used to describe supply and demand curves, either microeconomic or macroeconomic (e.g. IS-LM).

The first two ideas are really not much more than a series of proportionalities that allow you to say NGDP ~ MB (i.e. the quantity theory of money) or an increase in the money supply ceteris paribus lowers the interest rate (IS-LM model). Of course it also allows you to set up proportionalities you might not though of otherwise (P ~ NGDP/U). And it is pretty cool that these two laws follow from some basic arguments using information theory (hence the information transfer in information transfer economics).

However, there is a third idea that uses more information theory, relates specifically to one market (P:NGDP→MB) and produces weird conclusions (from the standpoint of conventional economics). The parameter κ is called the information transfer index and is used to measure the different information content in the definition of the "bits" that measure the information coming from D and going to S.
(3) The effect of the "unit of account" function of money (defining the dollar, yen, pound, etc.) can be combined with the "medium of exchange" function of money (how the market values the components of the aggregate demand) can be included in the market P:NGDP→MB by allowing κ to be a function of NGDP and MB. In terms of information theory, the monetary base defines the unit "bit" [1] and determines how many "bits" are being moved around in the economy. In this manner it becomes easy to see how there are two competing effects. More bits (dollars) allow for more information (bigger economy), but more bits (dollars) means each bit (dollar) carries less information (purchases fewer goods). I generically refer to this as the unit of account effect and it can lead to what I call an "information trap".
This third idea is a different unification of monetarist and Keynesian views of macroeconomics than the more traditional new Keynesian models. There are excellent returns to increasing the monetary base when it is small compared to the economy -- essentially allowing more bits to capture more information in the aggregate demand, the low hanging fruit of expanding your economy. This is when quantity theories of money work best to describe your economy. The gains slow down eventually and at some point you've captured all the information you can. At this point, interest rate theories based on the first and second laws above have better luck. Also at this point monetary expansion will fail to significantly increase NGDP or the price level -- sound familiar? This is the basic idea behind the liquidity trap (including the related zero lower bound) or the expectations trap (where the central bank must credibly promise to be irresponsible). However in the case of the information transfer this has nothing to do with zero bounds on interest rates or expectations. Your economy simply ran out of low hanging fruit that could be grabbed with monetary policy which is why I refer to it as an "information trap". This situation describes the US, the EU and Japan particularly well. Since it is not based on the zero lower bound, you can be in the trap at positive interest rates (like the EU). Additionally it shows how monetary expansions in Australia (see here also) and Canada could offset the shock of the financial crisis (those countries haven't consumed the low hanging fruit yet), but do far less in e.g. the US.

In the blog, when I've referred to "the" information transfer model I'm usually referring to the third idea. However, I work with all three from post to post and they form the basis of information transfer economics [2].
[1] I'm using "bit" here in a more generic way than the technical 1's and 0's; they can be "nibbles" aka hexadecimal values 0-9 + A-F or "bytes" aka ASCII characters. Actually the recent US economy appears to be operating in approximately base 283 (and climbing).
[2] I also use a lot of data from the FRED database as well as other sources. If you have a question about the data or I forgot to link to it, just ask and I can provide it.

#### 1 comment:

1. There is a typo in the "second law" in item #2: there should be no (1/κ) in the equation. It is just P = dD/dS.