On taking the people out of economics

I have recently returned from business travel and haven't had much time until now to properly respond to this riposte from Mike at his blog Free Radical and the comments below from myself and Tom Brown. This post originated as a response in the comments at the blog, but has since became so unwieldy that I decided to post it here.

In general, I am am aware that the ideas I am presenting on this blog are outside the mainstream and may well be totally wrong (or worse, trivially obvious) when translated into more traditional economics language. That's why I try to make contact with more traditional economics as much as possible. Some examples: the quantity theory of money, the IS-LM model, some other pieces of Keynes' General Theory, equilibrium in a two-good market, and the behavior of interest rates with monetary policy.

In the following, I cut some quotes from the comments on Mike's post and respond to them below (so please excuse the lack of narrative flow). Most of the points Mike makes are valid criticisms of the theory (or are simply differences of opinion), so I'll mostly focus on answering explicit or implicit questions in the comments and the things that I disagree with.

Mike said: "If [the information transfer model] functional form doesn’t come from the data, I can’t tell where it comes from since, seemingly by his own description, it doesn’t come from some kind of logical analysis of human decision making."

It follows from information theory. The foundational hypothesis is that human decisions are demand information communicated through a channel (monitored by the price mechanism) to the supply. But like information theory, the meaning of the information in the channel is largely irrelevant, only the amount matters. The price moves to bring the information coming from the demand and the information received by the supply into equilibrium under ideal circumstances. Additionally, the total information flowing through a particular market is proportional to the size of that market. In most cases, I assume that the information flowing through a market is equal to the maximum amount of information that can flow through that market. That seems to work remarkably well. Human decisions do appear to have influence -- most of the time reducing the amount of information flowing through a market.

Mike: [questioning whether “dD/dS” is meaningful]

The mathematical object dD/dS is like an exchange rate of demand for supply and is equal (in the model) to the price of that specific good demanded/supplied. It is the infinitesimal change in demand that comes with an infinitesimal change in supply. A really good analogy is that it's a definition of the force due to the invisible hand. Demand must in general be allowed to change with changing supply so any theory of economics that involves supply and demand should state some relationship that includes dD/dS. It may be couched in terms of money -- so that we'd see dS/dm and dD/dm, which come together via (dD/dm) x (dm/dS) = dD/dS.

Mike: "if you have one model with a lot of “shortcuts” built mainly on statistical observations ... "

The information transfer model isn't built on statistical observations. It's built on information theory, and the information theory is consistent with statistical observations. It's more of a standard "posit some axioms and see what results" kind of approach (things are never that simple in practice, but that's kind of what I'm going for). Newton posited some axioms about force and momentum conservation. The predictions from that theory appeared to "explain" statistical observations.

Mike: " ... relationships with no logical justification related to individual decision making ..."

The idea is that humans can't violate information theory regardless of what they decide. Now that idea might not be useful (from looking at the data, it has some success but applicability limited to broad trends), but it can't be wrong -- e.g. humans cannot send more information through a channel than its capacity no matter how hard they try. Information theory represents a boundary of any possible economic theory. Boundaries are only useful if the system pushes up against them, though. Knowing the total available wind power available on Earth for extraction by windmills is a fairly useless number because neither wind power nor human power consumption are anywhere near that limit. Economic systems appear to be operating fairly close to their information processing limits and those limits are independent of the information being processed (e.g. human decisions).

Mike: " ... There is no logical reason why it makes sense for gravity to exist. It just does. It can only be identified through observation."

If you observe the effects of special relativity (a specific symmetry of the universe), then gravity (general relativity) has to exist unless you can produce a good reason it shouldn't exist. I only metion this because it carries over into the discussion here: if you observe long run neutrality of money (an approximate "symmetry" of economics), then functions of the supply and demand functions must obey homogeneity of degree zero -- if D → α D and S → α S, then f(αS,αD)  → α^0 f(S, D) -- which means that the simplest relationship between supply and demand you can write down is (1) dD/dS = c D/S. In the information transfer model, this equation gives you supply and demand curves (alternately holding S and D constant). If this equation (1) isn't true of your micro theory based on human decision-making, then your human theory is going to violate long run neutrality. What is interesting is that the information transfer model gives us long run neutrality as a symmetry without a lot of effort.

Another related point: people frequently say things like such and such result proves Newton was wrong about gravity and Einstein was right. Any theory of gravity must reduce to Newton's theory in some limit because it can't violate some basic mathematics of three dimensional space (and of course, Einstein's theory does). In this same way, any economic theory that at least approximately has long run neutrality must be approximated by the information transfer model -- and that is independent of human decision making. It is possible long run neutrality isn't even approximately true and the reason could well be due to human decision-making (or it could be true because of human-decision making). However, those are empirical points that don't come down to whether or not you think human decision-making is relevant to economics. Either there is an approximate long run neutrality of money or there isn't.

Mike: "For instance inflation runs at 5% forever but people continue to expect it to run at 1%. This is precisely that kind of thing is easy to overlook if you aren’t paying any attention to what makes sense for people to do and that’s what happened with early versions of the Phillips curve and that is why we now have rational expectations."

Yes, I completely agree that observing the Phillips curve and using the regularity as a basis for a theory is not always good methodology (it can be an interesting thing to try, but then your theory becomes vulnerable to whatever unknown effects you aren't modeling, not even restricted to changes in human behavior). However in the information transfer model, we start with ideas that must be true regardless of what human behavior is. Information transmitted through the price mechanism cannot be less than the information received at the other end, for example. If information in equals information out (the assumption in the information transfer model), you can say more -- especially about changes in the information on one side of the transaction vs the other. This approach doesn't have to result in anything useful (in physics, the information approach results in a rather simplified view of the expansion of the universe that doesn't say much more than "the universe can be expanding"); it is a happy accident if it does (in physics, the approach can be used to derive the ideal gas law). In economics, it seems to have some useful results.

Mike: "I’m not exactly sure what you mean by “analog.” Maybe a single molecule can’t “evaporate” but there is still something happening on the molecular level regarding the behavior of molecules relative to each other or something like that which you wouldn’t notice if you had no concept of a molecule to work with."

Entropic forces do not exist (have no analog) at the micro level (they are weakly emergent per Tom Brown's comment).  At the molecular level there is nothing happening that isn't captured at the macro level by the boiling point and heat of vaporization for a general fluid. Most of the laws of thermodynamics were worked out (correctly!) before anyone knew of the existence of atoms. Atomic theory allows you to predict the numbers (boiling points, heat of vaporization). In this sense, microeconomics and human behavior should allow you to e.g. predict the coefficients in the information transfer model and the deviations from it.

Mike: "I can’t remember who ([Tom Brown] or Jason) said it or where and I think I already said this once before but demand does exist at the individual level."

It was me. I was saying demand curves for single markets don't exist at the individual level, at least not in any way that could be captured mathematically. Nor does "aggregate demand". I'm not challenging the idea that an individual person will want to purchase something they want, though. They just won't necessarily have a smooth curve vs price that is independent of other goods. In a sense, a statement of demand for an individual is something like this:

I'd buy an android tablet if one is available soon between 100 and 200 dollars, or an iPad if the price drops to 350 dollars**. Maybe my wife will buy me an iPad for my birthday, so I'll stop shopping around when my birthday gets closer. I don't need more than one tablet, so regardless of price, I won't buy more than one.

This is just one piece of the information that is being transferred to the tablet supply when this person buys a Nexus tablet on sale for 200 dollars the next day. It strongly depends on more than a single good (iPad, Nexus tablet), has a non-linear dependence on price (constant between 100 and 200, but also totally different for an iPad), the preferences of other economic agents (his wife), and time (the birthday). If you aggregate every such desire in the information transfer model, you get something like a demand curve (the total quantity demanded vs price) even though most individuals will buy only one tablet (this is not critical and doesn't apply to all goods, but is at least one way demand curves don't really exist for individuals). The reason you can aggregate these desires in the information transfer model is because you really don't care about the content of the desire -- you just know it exists.

This is my opinion, but I'd say any micro theory that purports to model the content of that indented block of text above is, in a word, hubristic. (Maybe the ITM is just a different kind of hubris.) It's even more difficult than it seems because humans exhibit many cognitive behaviors that would render that block of text totally irrelevant. The preference may change in an Apple store (framing effects) or may not even represent an accurate description of the preference at the time (affective forecasting and rationalization). And even if you were successful, the details of the human model can't have any impact at the macro level if macro can be reduced to a small set of variables like the price level, NGDP, monetary base, etc (an kN dimensional space of N heterogeneous agents with k attributes cannot be collapsed into an M-dimensional space of M macro variables with M << kN unless human behavior doesn't matter except as small collection of parameter values). If macro is tractable as a finite dimensional model, then individual behavior can't matter as anything more than a coefficient.

Mike: "The only way to be able to predict [changes in economic relationships] is to try to identify that structure which is based on human decision making."

This may be more of a yin-yang or figure-ground thing. I'd say the only way to know how to incorporate human decision-making in economics is to first understand what is independent of human decision-making (or another way: what is true regardless of human decision-making). Maybe that isn't the best approach, but I'm giving it a try.

...

Tom Brown did a great job giving an accurate account from a different perspective of what I've been saying; if you don't want to take my word for it, Tom's account is great. Therefore I have only a couple of things to say about his comments (and an answer to a question):

Tom: "“If [microfoundations survive aggregation to into a macroeconomic model as anything other than a coefficient], the resulting model is likely intractable.” ... I take the idea to be one of his hypotheses, not necessarily a statement of absolute fact."

I'd liken it more to intuition (based on my experience with complex systems), but I guess statements of intuition are essentially hypotheses. And actually, I was quoting something I said that a commenter had an issue with.

Tom: "I wonder if Jason would describe his theory as looking at macro as a weakly emergent phenomena, rather than a strongly emergent one?"

Yes, weakly emergent is a good description. It should be possible to compute the macro theory from the micro theory, but the behavior of the macro theory doesn't necessarily follow directly from the micro theory.

** I don't write dollar signs because they mess up the LaTeX stuff on the blog via mathjax.

Testing an animation

I never quite got around to putting up my youtube video about information transfer economics, but I'm going to test the gif capability of blogger with a piece of it. Here is a animation of how the "unit of account (information)" and "medium of (information) exchange" relate:

One thing that is not quite correct: at constant N, increasing M should keep the height of the the stack the same by adding more units to it (making them shrink). Otherwise, this is a pretty good picture to have in your head.

In which I agree with John Cochrane

When I first read what John Cochrane said about interest rates, it was in a quote at Noahpinion:

[S]tandard theory makes a pretty clear prediction about [QE's] effects [on interest rates]: zero. OK, then we dream up "frictions," and "segmentation," and "price pressure" or other stories.

I thought this was ridiculous; anyone can see that the 3 month interest rate dropped precipitously (to the zero lower bound) at the onset of QE:

Maybe he was talking about real interest rates or some other measure. I checked the original post and sure enough Cochrane was talking about long term interest rates like the 10-year treasury. And that's something I agree with. The 10-year rate appears to be controlled by the currency component of the monetary base ("M0"). QE, which involved asset purchases, has full monetary base MB -- including reserves -- rising to over 4 trillion dollars. The full monetary base appears to control short term interest rates.

Let's say we have two markets rl:NGDP→M0 and rs:NGDP→MB with the same information transfer index (κ) where rl is the long run interest rate (10 year treasury rate) and rs is the short run interest rate (3 month rate). I fit κ to the 10 year treasury rate rl:NGDP→M0 and then looked at how well the MB data fit the 3-month rate in the same function:

The M0 model result is the darker blue line, while the MB result is the lighter blue one. The 10 year rate is darker green, while the 3-month rate is lighter green. The fit for both uses the function 

log r = c log NGDP/(κ Mx)

with κ = 10.4 and c = 2.8, and Mx being either the currency component ("M0") or currency + reserves (MB).

Now if the Treasury were to print more currency (or the Fed somehow caused banks to request more currency which would then grant Fed grants), then that would bring down long term interest rates. At least it would in today's economy with the "liquidity effect" dominating because log M0/log NGDP is close to ~ 1. If we were back in the 1970s, the extra currency would cause rates to rise via the inflation/income effect (log M0/log NGDP was closer to 0.5). See here for more details.

While I agree that QE has no impact on  long term interest rates, I don't agree with the just-so argument behind it. This has nothing to do with Wallace neutrality or Modigliani-Miller. It has to do with the information exchanged in the treasury markets in an economy and monetary base of a given size. The result requires ideal information transfer (information transmitted from the demand is equal to the information received by the supply), which is the information theory equivalent of "complete frictionless markets", but it is independent of government policy (except inasmuch as it affects NGDP, the monetary base or level of currency). The fluctuations around the theory likely come from non-deal information transfer and could be anything -- and likely stems from (irrational) human behavior.

Against human-centric macroeconomics

"Gravity might not be explainable in terms of any broader, more general phenomenon. But we know for a fact that macroeconomics is the result of a whole bunch of little economic decisions by individuals and companies."

Noah Smith

Do we really know this? For a fact? To be specific, I'm not questioning the idea that an economy is made up of humans making decisions with money (of course it is) -- I'm questioning the idea that observed macroeconomic relationships (price level and money supply, RGDP and employment) are the result of humans making decisions with money. This blog posits that macroeconomics is just about the large quantity of things (money, people in the labor force, goods and services) and human thought has a peripheral role. In that list we don't care what goods or money think, so why are humans so special?

I also have another question: is the idea of including human decision-making in economics a byproduct of our own human sense of agency rather than, say, solid reasoning or empirical justification? I think the answer is yes, it's a byproduct. Modern economics grew out of ethical philosophy and morality (it's all over everything: utilitarianism, the "Puritan work ethic" and macroeconomic "austerity", Adam Smith's The Moral Theory of Sentiments, the perceived morality of debt) and has therefore always been about human thought. It didn't grow out of natural philosophy (or science as it is known today) or accounting where it might have arisen from observation ("I noticed that everything seems to get more expensive on our books with each passing year, but also prices don't rise when business isn't good and we aren't hiring more people.").

In one of my early posts, I mention that my approach to economics has been that of an alien observer who has good enough instruments to see how nighttime lights are increasing and CO2 is increasing on Earth, land is cleared and posits the idea of a "civilization" on Earth that operates under a theory of "economics" ... analogous to Boltzmann positing atoms operating under a theory of statistical mechanics.

Macroeconomics does not take this approach, but instead started at the very beginning assuming that human behavior was important. Modern economics has some of its origins in physiocracy, and in that economic theory sits the 17th century analog of expectations (quoting from wikipedia, emphasis mine):

Pierre Le Pesant ... advocated less government interference in the grain market, as any such interference would generate "anticipations" which would prevent the policy from working. For instance, if the government bought corn abroad, some people would speculate that there is likely to be a shortage and would buy more corn, leading to higher prices and more of a shortage.

and incentives:

Le Pesant asserted that wealth came from self-interest and markets are connected by money flows (i.e. an expense for the buyer is revenue for the producer). Thus he realized that lowering prices in times of shortage – common at the time – is dangerous economically as it acted as a disincentive to production.

All that can be said (from the information-theoretic point of view) is that a price control changes the information transfer capacity of a particular channel detected by that price (relative to other channels). An incentive (i.e. the knowledge people are willing to pay way more for your goods and/or services than it costs to produce them) is just one piece of information transferred from demand to supply. So is irrational fear. So are speculative hedges ("I may pay top dollar for your goods now, but by the time you build the capacity, I won't"). So is random lack of knowledge ("I guess bacon just costs 50 dollars per pound"). The correctness (or content) of these ideas are not (to first order) important. This was part of the revolution of information theory (see the overview at that link) -- the human meaning of the message is irrelevant. It may be that human thought is very important to a description deviations from the underlying trend:

But in not looking at a human-independent baseline, we don't really know what the real economic fluctuations are (see here and here). Have we been led astray because we as humans were too close to the problem?

Tom Brown asks in a comment (that I can't seem to find right now, update: Tom found it, thanks!) if the information transfer model would apply to non-human economies. I don't know the answer to that. However, macroeconomics as conducted today has an answer: no, it doesn't apply. There are no economic laws that are independent of human thought. Even supply curves depend on expectations of future prices and demand curves depend on consumers' tastes and preferences (and diminishing marginal utility). Recessions might not happen among Klingons and the Ferengi Phillips curve might be perfectly stable. It would be an act of hubris to think an alien civilization thinks the same way we do ... e.g. would risk premia be the same? Some economists do this already with different human cultures, and I touched on it in an earlier post. Maybe this is the correct approach. If it is, then economists should completely abandon any pretense to universality and instead become a sub-discipline of history (the chapter on the period when economists thought universal laws existed would be entertaining).

I believe there is at least a major component that is independent of human behavior, not only because of the successes of the information transfer model but because one of the most successful economic predictions ever assumed that human behavior, on average, summed up to noise:

Suppose that there are a whole ton of different behavioral biases, and that these vary across time, across people, and across situations so much that even with a billion lab experiments we couldn't find them all. Only once in a while will the forces be aligned to make one behavioral bias dominate; most of the time, the net effect of all the biases will be unpredictable by the outside observer. When you have an unpredictable mishmash like that, you have to model it as a stochastic process. In other words, if it's too complicated to explain deterministically, then you treat it as randomness.

So what if psychology usually just ends up injecting randomness into our decisions?

That was from Noah Smith again. It is exactly the theory behind information transfer economics.

PS (added 8/4/2014, 9:28pm MDT): The thrust of this post is opposition to human-centric macro, and not saying human behavior has no role whatsoever (the third sentence says "of course" an economy is made of people, the graph in the middle is quite literally me calculating the impact of expectations, and I kept the piece of the quote of Noah's post that says "once in a while will the forces be aligned to make one behavioral bias dominate").

Monetary regime change

I'd previously noticed that monetary policy can undergo a "phase transition" (or regime change) where the information transfer model changes from one set of fit parameters (or even particular solution to the differential equation) to another. Both cases I've seen (US and UK) involved a period with pegged interest rates during WWII (see the previous links for the US and see this link for the UK). Working with Swiss data I recently found going back to the 1980s from my last post, I noticed another case:

This new case didn't involve a wartime economy or pegged interest rates (however, Switzerland may have imported interest rates through this mechanism, obscuring any information there). Switzerland changed their monetary target from a 1-year monetary base target to a 5-year target in 1990, and then transitioned to a completely new target that involved base growth, interest rates and price stability (inflation) more reminiscent of the US dual mandate (except without employment) that became official in 1999.

In this transition, Switzerland rapidly changed from an almost perfect "quantity theory of money" economy to an almost perfect "liquidity trap economy":

The Swiss economy also rapidly transitioned from relatively high NGDP growth to more modest growth (the smooth black line is LOESS curve):

It is a good sign that these two calculations are consistent with each other at the transition.

So now we have three examples of monetary phase transitions/regime changes. Two (US and UK) are likely due to the wartime pegging of interest rates and in the US may have been accompanied by a bout of hyperinflation. The third (Switzerland) is a more ordinary change in the monetary policy target (it may have been accompanied by a brief bout of hyperinflation as you can see in the first graph, but the period is too short to be conclusive [1]).

In Switzerland, the information transfer index was slightly below 0.5 before the 1990s -- that would cause the price level to increase more rapidly than the monetary base. Because of that, the SNB would see their monetary base target was producing too much inflation and therefore they would think they needed to change to a different target. In the monetary economics paradigm, it probably would have been thought that "expected" inflation was at a higher level than the concrete steps the SNB was taking, so they had to influence expectations. That's why the SNB changed from a 1-year to a 5-year base growth guidance.

[1] I have no doubt the hyperinflation solution would fit to the period 1990-1995, it just wouldn't be very illuminating. In the US, the solution operates over almost 20 years from 1940 to 1960; 5 years in Switzerland is just not long enough to be conclusive.

"Lowflation" is a meaningful concept

Scott Sumner is upset about using inflation to describe economies. He says that inflation doesn't describe shocks and that NGDP (of course) is a better measure. He then gives Portugal and Switzerland as an example where inflation isn't very indicative.

I thought this would be a good place to use my more precise definition of nominal shocks that takes into account monetary and fiscal impacts to NGDP. Taking this on included a pretty interesting challenge for the information transfer model: how do you describe Portugal?

In the information transfer model, one needs NGDP, CPI and currency data (M0) for the economy in question. Portugal doesn't have the last one, at least not on its own. So I posited that Portugal's M0 was αM0 for the Eurozone (i.e. Portugal has a fixed fraction of the Euro currency) where α was a free parameter. The best fit gave α = 0.052, which was sensible: Portugal is about 5% of the Eurozone economy. So here are the fits to the price level for the EU, Portugal and Switzerland from 2007-2014:

The nominal shocks follow from the price level (see the procedure outlined at the bottom of this post) by taking out the effect of the expansion of the monetary base and looking at the remainder -- this remainder is the nominal shock. Here are the nominal shocks for Switzerland and Portugal:

You can see the great recession shock at the end of 2008 and the subsequent shock to Portugal due to the post-crisis austerity measures. Since these three regions are all experiencing "lowflation", these shocks turn out to be roughly correlated with changes in NGDP. Here for example is the EU (change in NGDP is the dotted line, and the solid line is from the previous graph):

The pictures for Portugal and Switzerland are similar (I didn't want to put too many graphs in this one post). So Sumner is right: NGDP changes are a pretty good indicator. At least when inflation is low ... here is the same graph for the US going back to the 1980s:

As inflation increases, the actual nominal shocks (solid) and changes in NGDP (dotted) diverge. One benefit of the information transfer model nominal shocks is that going through zero is generally associated with a recession. Additionally, negative shocks are associated with an accelerating unemployment rate:

In particular note that the small negative shocks in the mid-to-late 1980s and after the 1991 recession (neither of which are associated with a recession) appear to arrest the fall in the unemployment rate. Although it is correlated, the change in NGDP doesn't have this meaningful zero-crossing quality.

The take-away is this: when you have "lowflation", you can say ΔNGDP ≈ nominal shocks, making NGDP a decent metric. However there is more information you can extract using the information transfer model definition of nominal shocks, and that definition is based in part on the price level.

Additionally, "lowflation" is also a good indicator of how monetary policy will affect interest rates. When an economy has low inflation, monetary expansion makes interest rates fall (the liquidity effect dominates). When inflation is high, monetary expansion makes interest rates rise (the income/inflation effect dominates).

You can't get everything from NGDP.

When will information theory influence economics?

Easy. By the end of 2015.

That's a joke; I'm celebrating the highest monthly pageview total I've gotten so far (still pretty small -- big blogs get as many per day), so I decided to project when my pageviews would reach the level of Scott Sumner's blog themoneyillusion.com. Since Sumner managed to influence the the post-financial crisis debate and even got Ben Bernanke talking about NGDP targeting, I thought that would be a good guide to the required number of pageviews per month**. I wasn't able to get a firm number, but on a log scale it doesn't matter so much. Luckily, my pageviews are pretty log-linear, so the extrapolation is easy:

Special thanks to Tom Brown for his advocacy and linking back to me here. Thanks also to the Feedly readers, Twitter followers and Google+ followers for your regular check-ins. (Sorry to the Feedly readers for the math being messed up and the pictures always coming out huge, messing up the flow of the text.)

** It doesn't really matter the quality of the arguments, just the number of people who see them, right? (Again, joking.)

Zen kōan inflation targeting

Tyler Cowen suggests the rather silly "target 4% to achieve 2% inflation" monetary policy for the ECB. I'm not sure if he actually meant it as a joke or not, but it certainly illustrates the utter ridiculousness of model-independent expectations that aren't the constrained "rational expectations" typically used in economic models.

Rational expectations are perfectly fine: you have an underlying model and the economic agents expect e.g. the level of inflation predicted by the model. In some sense, rational expectations make the economic agents superfluous. If the agents are just going to parrot back the expected values of model random variables, why not just say they aren't there. A better word for "rational" expectations would be model-dependent expectations, which I contrast with model-independent (MI) expectations above. These MI expectations are those typically invoked by e.g. Scott Sumner and Nick Rowe.

Cowen suggests that the ECB could target 2x% in order to achieve x% inflation relying on MI expectations. With MI expectations however, if the ECB doesn't keep this a secret, the agents will learn 2x really means x, and then the 4% inflation target will really be a 1% inflation target since 4% means the ECB is aiming for 2% so will only achieve 1%. Okay, then.

But here's where it really gets silly. If you see the ECB's current 2% target as not credible, then aiming for 4% and resulting in 2% manufactures a credible 2% inflation target out of an incredible one by renaming "two" as "four". Incredible!

Another solution, proposed by Scott Sumner, is that the ECB doesn't actually want 2% inflation, even though it says it does, but rather the ECB communicates its inflation targets by talking about unemployment and competitiveness. Yes, the official inflation target is 2%, but that is irrelevant: the actual inflation target is 1% because that is what makes the PIIGS competitive.

[*slice*]

Yes, that was Occam's razor.

Sure, countries seem to be able to achieve their inflation targets most of the time (in fact, the quantity theory of money works for a lot of cases), but now we have a series of countries that seem to be undershooting them a bit: Japan, US, EU, Canada ... etc. Maybe there is a maximum achievable inflation rate i* for an economy? For countries with inflation targets below this maximum, inflation targeting works: the central bank says 2%, it gets 2%. For countries with inflation targets above this level, all you get is the maximum i*.

The information transfer model produces this result. At every point on the price level surface (see e.g. here, or at the top right of this blog if you're not viewing it on a mobile device), there is a maximum gradient (inflation rate). This is the inflation limit at that point. During the 1960s in the US, this maximum inflation rate was 10% or more.

EU i* is predicted to be low by this model (almost zero) -- below their target of 2%. For the US, i* is just below 2%.

Where does this maximum come from? Money has two purposes: it is the medium of exchange, allowing transactions to occur and it is the unit of account, Fisher's measuring stick. In the information transfer model, money allows people to exchange information and measure the units of the information. As you increase the amount of money, the relative impact of these different capacities changes. You can imagine the unit of account as a box that gets smaller as more money is added to the system, while the medium of exchange is the number of boxes. The height of that stack is proportional to the price level. And it looks something like this:

Japan is on the right side of this diagram, while, say, China in on the left. The maximum inflation rate i* is the slope, higher on the left and lower on the right.

This is Cowen's "most economical model".

The economic future of China is so bright (I gotta wear shades)

Another request from Jon Prince in comments, this time for a projection of the future of China's economy with the information transfer model. His particular questions were about whether China's growth rate was sustainable and how long before the Chinese economy reaches information trap/liquidity trap conditions. I don't have data on interest rates for Chinese government debt, so this prediction it will only be based on the slowing of NGDP and the price level with respect to currency growth.

This will be based on the model in this post and starts with an extrapolation of NGDP and currency (M0):

This path results in the following predictions for RGDP growth, inflation, NGDP growth and the price level:

Although there is a slow fall in growth, these graphs show above 8% RGDP growth (and above 10% NGDP growth) through 2020. There will still be some fairly large fluctuations around these predictions, though. Overall, this is a pretty good position for an economy and I don't see any liquidity traps in China's near future. China's very mild economic deceleration will probably be attributed to many things in the mainstream economic media: slowing growth as the economy runs out of catch-up growth opportunities, moving of low cost manufacturing to poorer countries, economic inequality, etc. The real reason is that it's just a manifestation of a universal behavior of large economies -- at least if the information transfer model is right.

Prediction update: not bad for five parameters

I made some predictions back in March about the path of the US economy, so with the release of unemployment data today, I thought I'd update the plots from that post to see how the information transfer model is doing. Overall, it's doing just fine.

This first graph wasn't a prediction of the model, but instead the projected path of NGDP and money that forms the basis of the inflation, RGDP and interest rate predictions. It turns out the economy has followed these reasonably well:

That means the predictions of the model should still apply. However, it appears now that there was a fairly large NGDP shock coming from the sequester:

This is contra Sumner's view that NGDP actually did better in 2013 than 2012, and shows the importance of having a model. NGDP can have the same path for both Sumner and myself, but he sees growth (despite the data) and I show a large shock following the sequester.

Here is year over year (YoY) inflation:

A bit high, but well within the normal fluctuations for YoY inflation. Inflation and NGDP come together to give us YoY RGDP growth:

Here are the interest rates:

10 year rates are a bit above the expected value (I used the "upper bound' version of the interest rate model in the prediction).

And finally, we come to the unemployment rate. The information transfer model only says that the blue rectangular area is the economy's "natural rate", so the predicted curve is only a quadratic extrapolation. The prediction is that unemployment will start to flatten out when the prediction reaches the blue band (i.e we should start to see "positive curvature")

Overall, the model seems to be working just fine.

PS: There are actually seven parameters M0, γ, α, κi, c (interest rate), κL, and κU, but the normalization of the price level is arbitrary (α could be redefined to be 1 by picking a different year as the base of the price level -- and it actually drops out of all the predictions above) and κL and κU only appear as the ratio u* = κL/κU. Therefore there are only five meaningful parameters: M0, γ, κi, c, and u*.