Friday, October 31, 2014

The trouble with Nick Rowe's expectations without concrete steps

I've been thinking about how expectations can set macroeconomic variables without "concrete steps", and in particular Nick Rowe's analogy with daylight savings time. I had some brief interaction with Nick in comments on my post here and this can be seen as an counterargument to this post by Nick.

Nick puts forward two analogies where we achieve a real macro outcome we don't know what the concrete steps are (or there aren't any concrete steps): driving on the right and daylight savings time. In these situations, the government sets an expectation and everyone complies. This motivates the same logic applying for NGDP (and elsewhere inflation) targeting.

The trouble I've been having with this argument comes down to the fact that we as individuals choose which side of the road to drive on or to set our clocks back. Individuals have the power to set their clocks to any time or drive on either side of the road, and individuals enact the concrete steps. Individuals can't turn a wheel or push a button to set inflation or NGDP.

If the central bank set an inflation target and everyone decided to set their prices to rise at 2% per year, then the above analogies seem appropriate. In some cases that could be true: cost of living adjustments, long term contracts, investment decisions, buying a house, etc. However, we as individuals (or even firms) don't make all the choices involved in setting inflation. Some goods actually decrease in price (here is the CPI for computers):


This would be akin to whole segments of the population setting their clocks back when everyone else sets them forward. Additionally, "hedonic" and "quality" adjustments adjustments are made to CPI [1]. The owner of a restaurant can't decide to have prices rise at 3% while having people enjoy the food 1% more. No one can make technology improve based on expectations alone (or can they?).

Unlike daylight savings time or driving on the right, the concrete steps required to enact the inflation or NGDP expectations set by central bank are out of the individual's hands. This is why I reside on the concrete steppes and believe that physical currency ("M0") sets inflation [2], with a changing, but concrete [3], definition of the unit of account.

Footnotes:

[1] PCE inflation measures are highly correlated with CPI and chained CPI, so it would be remarkable if they represented completely independent processes. Without loss of generality, let's stick to CPI inflation.

[2] Empirically, not ideologically -- if it was M1, MB, MZM or any other definition of money, that would be fine by me.

[3] It's very concrete -- the factor is given by the information transfer index and is explicitly κ = (log M0/c) / (log NGDP/c).

Thursday, October 23, 2014

Psychohistory? (Qu'est-ce que c'est)

I was reminded of Asimov's psychohistory after reading Igor Carron's post on a new book on signal processing. There were two main axioms (from Wikipedia):
  • that the population whose behaviour was modeled should be sufficiently large
  • that the population should remain in ignorance of the results of the application of psychohistorical analyses
The theory seems to axiomatically depend on expectations (in economics terms). Knowing the results, in Asimov's galaxy, can influence the outcomes -- hence the rationale for keeping the population in the dark. The information transfer framework mostly depends on the first axiom to produce models, and should produce the same results even if people know about the results of the models -- could it be considered a generalization of psychohistory?

However, Asimov seemed to believe correlations caused things to happen ('mass action'); in the information transfer framework, correlations cause things to fall apart.

Supply and demand for non-ideal information transfer (and other stuff)

Sorry about the lack of posts lately -- I've been busy with with work and on travel. I also discussed actual research money for the model through a (somewhat non-traditional for economics) funding agency and put the idea in front of two professional economists. Understandably, skepticism all around (I have an upcoming post on one of those interactions).

I am also working on a post that started out as a start towards fully incorporating the idea of expectations (as a source of information loss) in response to a piece by Nick Rowe, but Nick has another interesting one that I haven't fully digested yet. Still writing there.

So here's a quick post. Awhile back I did a post on the minimum wage; I used a least informative prior with the non-ideal information transfer to say that the observed price is somewhere in the lower triangle of a supply and demand diagram (see link at the beginning of this sentence for details) -- I don't know where. If we take each position in that lower triangle to be equally probable, then you can show that the centroid appears below the ideal price but at the same quantity supplied/demanded as the ideal equilibrium.

What happens to this point under shifts of the supply and demand curves? Well, it turns out, the non-ideal price follows along a non-ideal supply (or demand) curve that is parallel to the ideal curve. Here's a graph; the purple points represent the starting point and the point after the shift while the dashed purple curve represents the locus of points for different shifts:


Tuesday, October 14, 2014

Did the Fed cause the Great Recession in the Eurozone?

Scott Sumner's post on Euro-denial among the econ reminded me that I hadn't yet updated the Eurozone trend to account for the strange (and likely not relevant to inflation) impact of 500 € notes. Needless to say, I remain an ECB apologist. It still looks like the big shock of the recession was a result of being above trend:


The secondary shock in 2011 still looks like it came from being above trend as part of a rebound from the lows of 2010. If there is a shock happening now it may well result from external factors like Russia/Ukraine since the data appear fairly close to the trend line.

There was something interesting I saw, however. In this post, I showed that the deviation from the trend in the US in the lead-up to the Great Recession was due to monetary policy by plotting the monetary base on this same graph as M0 (currency). The dotted monetary base line appears to push the M0 curve above the trend and then falls away after the recession (graph reproduced from the linked post):


The monetary base controls the short term interest rates. When the two curves (M0 and MB) approach each other, yield curve inversion becomes more likely, which tends to be a precursor to a recession. The existence of minimum central bank reserves tends to keep the M0 line a constant distance to the left of the MB line. We can see the Fed raising short term interest rates in the mid-2000s and then rapidly lowering them as the Great Recession hits. However, after that, the MB line is so far from the M0 line, it has little to no effect on NGDP (a liquidity trap).

What does this curve look like for the ECB?


It looks like the monetary base has been too large since the inception of the Euro to have any impact on the NGDP-M0 path of the Eurozone economy. It is possible "tight money" (i.e. slow MB growth) pushed the M0 path above the trend in 2010-2011, like a miniature version of the US in 2008. Overall, though, it looks as if short term interest rates (monetary policy) haven't had any traction since 2002. Even with the base expansion, the ECB has mostly been spinning its wheels -- it's been in a liquidity trap this whole time.

Sumner puts the expert witness [3] on the stand:
But the ECB wasn’t even close to the zero bound in 2008.  I get that people don’t like NGDP growth as an indicator of monetary policy, and want “concrete steppes.”  Well the ECB raised rates in 2008. The ECB is standing over the body with a revolver in its hand. ... And then three years later they do it again.  Rates were already above the zero bound in early 2011, and then the ECB raised them again. Twice.  The ECB is now a serial killer.
The liquidity trap has little to do with the zero lower bound (although there is a sense in which they tend to occur together). Interest rates were already too low to move the economy in 2008 and continued to be low through 2011 (the MB curve was well to the right of the M0 curve).

The Eurozone has been like a rudderless ship since the Euro started -- it just so happens that the Great Recession is the only major shock they'd ever had to deal with and the fact that they can't do anything about it makes them look hapless. [1]

But that leaves a question: if the ECB didn't cause the path to rise above the trend (like in the US case), what did? Did the Eurozone import a financial boom from the US? Did the Fed cause the Euro crisis as well as the US recession? Was the ECB framed? [2]

Hmm...

[1] As an aside, I wonder if this explains the strange movements of the Euro monetary base during the Great Recession -- it's like the rudder inputs from a pilot who doesn't know he has lost the rudder, moving side to side, erratically.

[2] I thought about using the title "Has the Eurozone always been in the liquidity trap?" with a nod to The Shining, but Sumner's murder mystery was too much fun.

[3] The economists in denial, per Sumner's accusation.

Monday, October 13, 2014

Coordination costs money, causes recessions

Let me put forward a thesis of what causes recessions: coordination.

This is, in a sense, the converse of what David Glasner refers to in his recent and several of his prior posts. Glasner advocates a theory of coordination failure to explain what recessions are, how unemployment can rise above full employment and why wages are "sticky". I will get back to Glasner towards the end of this post.

I started to put together an initial version of my thesis in part III of this post; here I plan to further develop it with a toy model (although there is no real loss of generality here -- it just helps to be explicit).

In my response to one of Glasner's prior posts, I put forward the idea that wage stickiness is an entropic force. Coordinated changes to the distribution of wages costs "entropy", and this cost is experienced in the macroeconomy as the resistance of the wage distribution to change ("stickiness"). Let me return to the wage distribution in that post; we had four cases:



Starting from the top left and going clockwise we have (1) the original distribution(roughly coinciding with the theoretical curve in blue) , (2) the distribution re-arranged to over-represent nominal wage cuts (the vertical line represents zero growth), (3) the distribution re-arranged to over-represent zero nominal wage growth (as observed in data from the SF Fed), and finally (4) a distribution with 10% of the distribution thrown out of the labor force (i.e. unemployment).

Of course, dealing with a continuous normal distribution is hard, so I decided to take these scenarios on as uniform distributions:



The other benefit to using a uniform distribution is that we can directly relate it to the economic combinatorial problem where the number of states goes as $NGDP!$ (that's a factorial, not shouting NGDP) and "economic entropy" $S_{e}$ is:

$$
\text{(0) }S_{e} (NGDP) \simeq k_{e} \log \left( \frac{NGDP}{c_{0}}!\right)
$$

Let's call $(NGDP/c_{0})! \equiv n$ the number of states in the economy. The other key ingredient we need to use is the fact that total nominal wages (NW) are directly proportional to NGDP -- this allows us to make identical arguments and switch back and forth between NGDP and nominal wages. Now scenario 4 directly reduces NW -- we've thrown 10% (let's call that $m$) of the labor force out of the economy -- and is associated with a fall in $S_{e}$:

$$
\text{(1) }\Delta S_{e}(n, m)/ k_{e} =  \log (n - m) -  \log n = \log (1-m/n)
$$

It is not necessarily immediately obvious that the other changes are also associated with changes in $\Delta S_{e}$, but it turns out they are. In scenario 2, if we take the probability that a state is one of the over-represented states to be $p$ and the under-represented states to be $1 - p$, then going back to the definition of entropy in terms of the probability of states (which coincides with the Shannon entropy in information theory I touched on once before in this post), we can work out the change in entropy to be:

$$
\text{(2) }\Delta S_{e}(n, m, p)/ k_{e} =  p \log \frac{m}{p} +(1 - p) \log \frac{n - m}{1 - p} - \log n
$$

If we take $m = 0.1 n$ and $p = 0.3$, then  equation (1) gives us -0.105 and equation (2) gives us -0.154. If $p = 0.262$, then the entropy loss is the same for scenarios 2 and 4 (i.e. -0.105). That is to say that an over-representation of 10% of the wage growth (or here, wage cut) states by a bit more than a factor of 2 (e.g. doubling the number of people who take wage cuts relative to normal times) is an equivalent entropy loss to removing that 10% from the labor force.

We can also use equation (2) to give us an estimate of the entropy loss from "sticky wages" in scenario 3 -- zero nominal wage growth for some fraction of the population. In that case $m = 1$ (a single state, zero growth, is over-represented). If we have a lot of states and $n \gg 1$, we can approximate

$$
\text{(3) }\Delta S_{e}(n, p)/ k_{e} \simeq  - H(p) - p \log n \simeq - p \log n
$$

where $H$ is the binary entropy function with information measured in nats. The entropy loss in scenario 3 is approximately the fraction of entropy given by the probability of an individual in the labor force finding himself or herself in the zero nominal wage growth state. In the data from the SF Fed, 16% of individuals are in that state, so that would represent a loss of 16% of "entropy" ... assuming the initial distribution was uniform. Now it isn't a uniform distribution and what really matters is the change in the distribution relative to the distribution in normal times. Most people usually go for a long period of time -- maybe a year or so -- at the same wage/salary after they get a raise, for example. That would mean the zero growth state is probably over-represented in normal times regardless of the distribution, and we would be referring to over-representation above and beyond that level.

The key take-away, however, is that all three scenarios represent a loss of entropy. And for small changes in NGDP, we can use Stirling's approximation in equation (0) to show:

$$
\Delta S_{e} \simeq \frac{k_{e}}{c_{0}}\Delta NGDP
$$

Entropy loss is NGDP loss -- an economic shock. In each of the scenarios 2 and 3, the resulting distribution is more coordinated relative to the normal state in scenario 1. The uniform distribution (or Gaussian/normal distribution) represent minimally informative (maximum ignorance) distributions; another way, there is knowledge gained (ignorance lost) in the distributions of scenarios 2 and 3. Something is coordinating market outcomes to produce a distribution that otherwise would not exist. That something is human behavior.

A recession is a temporary human coordination of the market [2] (through some sort of market panic or possibly guided by an economic authority like the central bank) that results in a loss of NGDP. This is how we can have all the same stuff before and after a recession strikes, but somehow it's all worth a bit less in the aftermath. The temporary coordination results in a bit of scenario 4 (the economy shedding jobs) and scenario 3 (zero nominal wage growth/sticky wages).

Why not scenario 2 (nominal wage cuts)? This is the problem that Keynes tried to deal with via sticky wages and the liquidity trap and to suggest that it wouldn't happen was so implausible to neoclassical economics that they assumed it away. This is Glasner's coordination failure -- if we (or the market) implemented scenario 2 instead of scenario 4 (unemployment), we could keep everyone employed.

My guess is that scenarios 3 and 4 represent channels that are much more efficient than scenario 2. In order to achieve the same entropy loss as scenario 4, scenario 2 has to over-represent 10% of the wage states by more than a factor of 2 -- that means that on the order of 30% of the labor force has to get nominal wage cuts (rather than 10% of the labor force getting pink slips). Likewise, 10% of the labor force having zero wage growth can accommodate a shock of 5% of NGDP (using NGDP ~ 2.1 NW). Using scenarios 3 and 4 together can have more impact than scenario 2 and involve fewer people. This suggests the market could be using its own principle of least effort.

Interestingly, attempting to implement the nominal wage cut coordination it after the recession hits would involve adding NGDP comparable to the loss in NGDP from the sticky wages/unemployment coordination -- immediately bringing to mind fiscal stimulus sufficient to close the output gap as advocated by Keynesians.

Whether the coordination happens spontaneously due to announcements from the Fed or financial panics or is encouraged through government spending or monetary stimulus, it costs money in both senses of the word -- you lose money if coordination happens and you have to pay in order to get coordination.

Footnotes:

[1] Also note that for a system with constant volume and temperature, a change in entropy is a change in "free energy" -- a reduction in entropy consumes free energy, whereas an increase in entropy gives off free energy (this is how e.g. life typically works).

[2] Basically, because the market is made of people, we can violate the second law of thermodynamics (ΔS > 0) by coordinating ourselves in a way that atoms or particles can't. There is no second law of econo-dynamics because of human behavior -- which is unfortunate because otherwise (if human nature didn't matter) ΔS > 0 would imply ΔNGDP > 0 -- the economy would always grow (absent real shocks like natural disasters or resources running out).

Sunday, October 12, 2014

Can China successfully slow down?


I was asked a couple months ago whether China's growth was sustainable, and the answer was basically yes over the next several years:

http://informationtransfereconomics.blogspot.com/2014/08/the-economic-future-of-china-is-so.html

The data is very noisy, but a long run average of 8% RGDP growth seemed to fit the general trend.

This is also consistent with China's official target of 7.5% (at least given the noisy data). I learned that fact alongside the fact that China is deliberately trying to slow growth from this article by Ken Rogoff:

http://www.project-syndicate.org/commentary/questioning-chinese-economic-climate-by-kenneth-rogoff-2014-10

Rogoff says that Greenspan was able to accomplish this, but in the information transfer model, the economy was basically on a falling inflation path all along. Kind of like giving someone credit for the sun rising in the morning. (Does that mean Greenspan was basically like the god-kings of old, given credit for good harvests and the flooding of the Nile?)

Can China push itself off of the NGDP-M0 path (in the graph above)? I don't know, but it will be interesting to find out.

[I'm on travel, so sorry about the bad formatting and lack of graphs -- I'll fix it at some point. ... Fixed some of it 10/13/2014]

Saturday, October 11, 2014

Entropy, in three pieces

Entropy. Picture from askamathematician.com.

I. 

Noah Smith thinks that the Efficient Markets Hypothesis has something to do with information theory:
This is because the EMH doesn't emerge from any peculiarity of the way our market system is set up, or the way human beings behave. The EMH comes from something much deeper than that, something that probably has to do with information theory. It comes from the fact that when you exploit information to make a profit in a financial market, you decrease the amount that others can exploit that information. In other words, the financial value of information gets used up [emphasis in original].

One way to see biology is as a process by which living things intercept entropy (free energy) flows. An autotroph converts low entropy high energy photons into high entropy waste (heat, low energy photons); a heterotroph converts low entropy organisms into high entropy waste (heat, poop). Economic agents intercept entropy (information) flows: they convert low entropy money into high entropy goods and services. 
In living things, the free energy in the photons or sugars is converted into lower free energy products and the information in their original structure is lost. The information in the market (e.g. prices of goods) is converted in to quantities of goods where the prices they were bought at no longer matter (according to the EMH). This information is consumed by the market in the same way free energy is consumed by organisms [emphasis mine].
Actually, the main thrust of this blog is that supply and demand are a manifestation of information theory, and market forces are entropic forces. The EMH itself is the analog of the fundamental postulate of statistical mechanics.

II. 

Mark Buchanan defends his view that energy consumption rises with GDP, contra Paul Krugman who says it doesn't have to. Buchanan says that his view was that energy rising with GDP was not an inevitable law of nature, but rather pessimism about our ability to conserve energy (with which I agree). But Buchanan does seem to want to hold on to his point by citing a paper which shows that power use per capita is related via a power law to real GDP per capita. The paper makes the claim that it may not be a coincidence that the power law has an exponent of 0.76, close to the 3/4 power law relationship between mass and energy consumption for organisms. I have two issues with this. One, the units seem all wrong. the relationship for economies is in Watts per capita while GDP is in year-2000 dollars per capita per year -- GDP is not "mass" but rather a growth rate (mass would seem more likely proportional to the value of all goods and services in existence ... the computer I'm using right now still consumes a few hundred Watts of power, but no longer contributes to GDP as I already purchased it). Two, the financial sector is now 10% of US GDP but is a tiny fraction of total US power consumption while the transportation sector is about the same fraction of GDP but uses a large portion of the total energy.

I also think the calculation E ~ GDP is all wrong in general (the economy is not an engine), and showed in this post (in a footnote) that the fundamental physical (computational) limits of the economy as an information processing system required only about 1 red visible light photon per day to produce the entropy change going from 2013 to 2014. Here's more:
Based on this measure (comment) of the number of states in the economic system in the US the amount of energy that would need to be supplied to change the entropy of the US economy from 2013 to 2014 (at 290 K) comes out to be about 6 x 10^-17 Joules or about 400 eV, or about the energy equivalent of 1 red photon per day. 
Now our conversion factor from information to energy is not as good as Nature's kB = 1.38 x 10^-23 J/K -- in fact, given the US energy consumption of ~100 quadrillion BTUs, I'd estimate [the economic Boltzmann constant at] kE ~ 2.5 x 10^13 J/K, or off by a factor of 10^36 from the fundamental limit (kB). That leaves a lot of room for improvement! 
Now if kE doesn't change, you could make an argument that limits to energy consumption (and conservation) are limits to growth [that go as GDP log GDP]. However, in 1960, kE ~ 100 x 10^13, or about a factor of 40 higher (based on ~ 50 quadrillion BTU energy consumption). Assuming we could get another factor of 40, the nominal economy could grow by about 2.5 times and use the same amount of energy.
The survival of biological organisms depends on the consumption of free energy, which is a change in entropy (at constant temperature and pressure), not mechanical power (as is measured by the energy consumption statistics). It is also worth noting that dollars are units we as humans invented. They lack the fundamental heft of "mass" or "energy" (analogs of which would like exist on alien worlds). There is no reason why there should be a decades-long stable relationship between dollars and energy.

III.

David Glasner has another great post on coordination failures and "sticky prices" where he gives two sticky prices (the real wage and the real rate of interest) and two separate human-behavior mechanisms for why they do not fall far enough during a recession (no one worker accepting a lower wage can ameliorate the fact that wages are too high and entrepreneurial pessimism, respectively).

These mechanisms are only unified in the sense that they are coordination failures -- they involve completely different sets of human behaviors and expectations. They also strike me as just-so stories. Reading through Glasner's discussion, you ask yourself questions. If an employer only had a few employees, wouldn't the effect of the reduction in one employee's wages on the business's bottom line be comparable to the few percent slowdown that happens during a recession? If faced with a choice between a layoff or a wage cut, I think I would take the wage cut (I happen to like my job). Employers say they don't cut wages because it hurts morale. However, employers frequently reduce hours -- wouldn't that reduce morale as well? Why more in one case, but not the other? Also, wouldn't some entrepreneurial optimist clean up during a recession with all that free money?

That's why I'm glad Glasner doesn't put too much stock in the specific explanations, but instead says:
It is not obvious what sequence of transactions would result in an increase in output and employment when the real wage is above the equilibrium level. There are complex feedback effects from a change, so that the net effect of making those changes in a piecemeal fashion is unpredictable, even though there is a possible full-employment equilibrium ...
 ... [the explanations leave out] coordination problems that might arise in a multi-product, multi-factor, intertemporal model in which total output depends in a meaningful way on the meshing of the interdependent plans, independently formulated by decentralized decision-makers, contingent on possibly inconsistent expectations of the future.
I think at the heart of these coordination problems lies entropy. Sticky wages or prices are the result of an entropic force -- a (minimally informative, i.e. equilibrium) distribution of wages does not spontaneously arrange (coordinate) itself so that everyone is still employed at the new (lower) wage. Instead you likely get a break-down of the information transfer system of the market (I once looked at the possibility that the information received by the supply was less than the information source information in the demand and that the difference was about the same across employment and interest rate markets).

But one difference between my view and Glasner's is that there really isn't any coordination in the first place. People's plans are randomly sufficiently consistent (or not seriously inconsistent) with each other to keep the economy going most of the time -- the economy is in a random configuration that is consistent with NGDP. The problem seems to be that, occasionally, humans coordinate themselves (mass panic) and the coordination required to undo the damage done by that spontaneous coordination does not happen spontaneously (much like entropy doesn't spontaneously decrease). For example, Vulcans might not have recessions in their economy (were it to have money) because the coordination in the initial mass panic (or just mass pessimism) that triggers layoffs and the fall in NGDP would not occur. No coordination required to undo the (non-existent) damage.

You can imagine a mass panic due to someone yelling fire in a movie theater; the coordination required to undo the spontaneous coordination that happens when someone yells "fire" does not happen spontaneously. Sometimes humans can spontaneously coordinate to increase economic output -- unfortunately the examples seem to be wars and market bubbles.

If you yell "fire" at a bunch of methane molecules in air, they don't spontaneously change their velocity to avoid combustion. But if they did, that would be a spontaneous decrease in entropy as well as lower the free energy of the gas -- meaning the new equilibrium energy is lower. You can't get that free energy back unless you coordinate the methane molecules to return to their original distribution (you might have to coordinate some of the molecules in the air as well) -- which would cost about as much free energy as the original loss [1].

In economic terms, the spontaneous coordination in a recession costs GDP (economic entropy is a function of GDP) that doesn't come back without government coordination (monetary and/or fiscal) or a long wait for GDP growth.

Footnotes:

[1] I'm thinking there's a good analogy with fiscal stimulus and the output gap here.