500 € ... sounds like a lot of money

Tom Brown asked if currency denominations had any impact on the price level in a comment here., and sent me to JP Koning's blog post about the macroeconomic impact of 500 € notes. What caught my eye was the shape of the 500 € note's contribution to M0. See, for awhile now (e.g. here), the shape of M0 has been a serious impediment to a good fit of the information transfer model to the EU price level. I always thought it had to do with the introduction of the Euro. The currencies of countries such as Italy's Lira continued to circulate for some time after the Euro notes were available -- I remember some prices were still in Lira when I was there in 2002 -- and I thought that the Euro M0 wasn't capturing that.

Here is the fit to the price level and inflation rate using M0 (including 500 € notes):

Not only is inflation too high at the introduction of the Euro, but it is way too low as you approach the present day. Here is a graph of M0 with and without the 500 € notes -- already you can see some of the variation disappear:

 

And sure enough, the fit is much improved if we leave them out:

There is still some impact at the introduction of the Euro, but overall, this is a much better fit -- in particular it gets present-day inflation about right.

Koning points out that the 500 € notes don't really circulate the way other denominations do (he cites that 9 of 10 notes are used for illegal purposes). Koning also points out that the existence of 500 € notes may impact effective short term interest rates (a negative IOR makes holding these zero-interest Euro notes a more attactive option) -- I plan on looking at the effect on interest rates in the future.

So how do we know whether or not to include a particular denomination? Well, only in the case of the 500 € note does it seem particularly obvious (empirically): it is particularly large with a particularly large volume. In other cases, it's probably not going to be very obvious. The question of what is considered "money" is of great interest -- maybe there are more examples out there.

If anyone would like to help me conduct an experiment -- please send me a few of these notes and I will keep them out of EU circulation and look at the impact on the price level. I will then travel to the EU (e.g. Paris) and personally put them back in circulation a few months later.

PS, the title reference ...

Update 9/9/2014: Fixed graph titles.

The emerging story of the Great Recession?

This is a synthesis of a few posts that seem to be converging on a coherent story of the Great Recession.

The Fed caused the Great Recession 

The Fed both reduced the monetary base (M0 and MB) and raised interest rates (also dependent on MB and M0) starting after 2005 relative to a log linear path of monetary policy from the early 2000s. These effects combine to account for the entire shock that caused the Great Recession, but come from two different views of monetary policy: an interest rate/ISLM view and a quantity theory view.

Can information theory predict recessions?

This post posits the idea that a deviation from a long term path of NGDP vs M0 is an indicator of a recession. What pushes the economy away from the path is an open question.

Was the Fed's quantitative easing serious overkill?

This post tries to see the relationship between MB (which governs short term interest rates) and M0 (which governs inflation). It shows that QE might have been larger than necessary and that base reserves only seemed to impact currency (M0) -- and therefore inflation -- during QE1.

The first task is to add the monetary base (including reserves) to the graph in the second post above (as was first done here)  giving us the left-hand picture below and zoom in on the 1980s and 1990 recessions, giving us the right-hand picture:

 

In the right-hand graph we can see the NGDP-MB line (dotted blue line) push up closer to the NGDP-M0 trend line (black) during the 1983 and 1990 recession (but there's no recession in the mid-1980s). The NGDP-M0 data line (solid blue) is "repelled' by the NGDP-MB line; the primary reason is reserve requirements (MB - M0 are the central bank reserves).

If these two lines move near or cross each other, according to the interest rate model, the yield curve would invert (short rates determined by MB would be higher than long rates determined by M0). Since the interest rates are stochastic paths following these theoretical trends, we can only say the probability of an inverted yield curve increases as the NGDP-M0 and NGDP-MB paths approach each other.

Interestingly, an inverted yield curve is, according to Wikipedia, is considered by the New York Fed to be "a valuable forecasting tool in predicting recessions two to six quarters ahead." This interpretation of the data gives a foundation for that metric. It looks like the Fed steers the path of NGDP-M0 by adjusting short term interest rates (which depend on MB), pushing the NGDP-MB curve towards or away from it (with a buffer defined by central bank reserves).

 

How does the Great Recession look in this regard? Pretty shocking:

The Fed begins to effectively raise interest rates (or, from the monetarist view, contract the monetary base relative to its previous trend) in the mid-2000s, steering the NGDP-M0 line representing the economy (solid blue) right over the NGDP-M0 trend line (black). NGDP dramatically collapsed back to the trend in 2008.

 

After the recession began, the Fed quickly expanded the monetary base (QE1) to allow the economy to fall back to the trend line. But did the Fed need to expand as much as it did? If we take the 2000-2008 average monetary base reserves as a baseline, then the Fed only needed to expand to the purple point to achieve the same relative paths of NGDP-M0 and NGDP-MB with the same average monetary base reserves. The path is shown as a dashed purple line. In the following two graphs, I show what this means in terms of interest rates (only dropping from 4% to 2%) and QE (only about 200 billion dollars) -- the counterfactual is shown in dashed purple:

I think this picture of the economy is a nice synthesis of a couple of views (in terms of the money supply and in terms of interest rates) and seems to explain not only the broad trends of NGDP, but also the major shocks -- even down to a level of detail where I could (probably with a great deal of hubris) say how much QE should have happened.

This picture also explains why interest rates are not necessarily a good indicator of monetary policy. One, the fluctuations in the interest rate data mean the monetary base and currency are better indicators of where the trends should be. And two, the trend of NGDP-M0 moves relative to lines of constant interest rate (see here), meaning that "high" and "low" interest rates are relative terms (i.e. the trend of interest rates rises and falls).

However, we're also left with an issue. If recessions are like avalanches, steering the economy with monetary policy seems to be like pouring more snow on the mountain until an avalanche happens. The problem with that is that you increase the size of the potential recession. The Fed kept trying to cool the economy since the mid-2000s, but there's no telling how much snow will build up before the avalanche kicks in (i.e. how bad the recession will be).

The one thing this story doesn't explain is the prolonged period where the path of NGDP-M0 was persistently below the trend line after the 1990 recession (which is remarkably coincident with the Greenspan Fed). What held the economy below the trend for 10 or more years?

There are still some holes in this emerging story. However, I think it's a remarkably coherent story -- and it points to tight monetary policy as the leading cause of the Great Recession.

Update on Japanese inflation

Here area couple more points to add to the graph from this post; we're still above the predicted price level but it seems right on for averaging 0% inflation and the VAT increase is looking more and more like a temporary jump:

I'd like to emphasize that the model fit stops in 2013 -- data from before 2013 were used to fix the parameters of the model, and the subsequent results are "out of sample" (but given the latest NGDP and monetary base/currency numbers).

The result is hovering at the bleeding edge of the error band and there are several possibilities for the discrepancy. One is that there will be upward revisions in NGDP (or downward revisions in the price level. Another possibility is that the data is experiencing another of its occasional excursions from the model (that might be based on human behavior, for example). If we zoom out a bit, we can see the last period like this in 2008:

How about if we concentrate on the trend alone? I performed the smoothing I did in this post and the result is pretty much spot on (assuming the VAT was a one-time event):

Actually the temporary nature of the VAT increase becomes even more apparent if we look at the inflation rate (this time there is no red counterfactual no-VAT scenario):

This goes right through the data with the VAT increase appearing as a spike.

Overall, there doesn't yet appear to be any reason to abandon the information transfer model.

Update/correction 9/30/2014:

The first graph was a bit messed up. I correct a couple of the graphs and add data points here:

http://informationtransfereconomics.blogspot.com/2014/09/inflation-in-japan-updatecorrection.html

300

300 posts! I thought I'd celebrate with a list of the top 3 posts since the blog started back in April of 2013.

1. How money transfers information 

This is still one of my favorite posts to introduce people the information transfer model. It's likely here because I link to it so frequently.

2. If physics blogs were like economics blogs 

This post was my crossover hit! It was a comedy piece inspired by what happened to my inbox after subscribing to the comments at this post by John Quiggin. A large fraction of the hits came from the post being tweeted by Unlearning Economics (who is giving up the blog for greener pastures and post-graduate studies -- and was a good sport). 

3. Models matter 

So many of my posts begin with a reference to Scott Sumner and some claim he's making. This post discusses how the interpretations of economic data are model dependent. Of course the latest inflation data is consistent with your model and inconsistent with your interpretation of another model -- why wouldn't it be?

Feynman gets one wrong?

Imagine how much harder physics would be if electrons had feelings!

 – Richard Feynman, speaking at a Caltech graduation ceremony.

I found this quote in "WARNING: Physics Envy May Be Hazardous To Your Wealth!" by Andrew Lo and Mark Mueller. I took it as a challenge. Let's switch from electrons to molecules for first brush analysis using statistical mechanics.

There are approximately 6 x 10^23 molecules in 18 grams of water. Wikipedia lists approximately 70 human emotions substantial enough to receive their own listing in the side bar. Call it 100 as an order of magnitude estimate and say the emotion of a given molecule represents a vector in a 100 dimensional vector space. Unless the molecules were highly correlated in their emotions, there would still be 6 x 10^21 ± 8 x 10^10 molecules of each emotion (a variance of 0.000000001%) and the average emotion would be fairly neutral to a high degree of certainty [1].

Now, sure, that error represents a ten-fold increase in the expected variance of ensemble averages of emotionless water molecules. But we really don't measure many thermodynamic quantities to that level of accuracy (except maybe the cosmic microwave background radiation). Essentially, physics would be the same if molecules had feelings unless they also had ways to coordinate their emotions -- and a society that has correlated emotions usually doesn't have functioning markets because they're at war or there's an economic depression [2].

This is why I am skeptical that including human behavior in macroeconomics would be fruitful.

Footnotes:

[1] Applying this calculation to e.g. the US labor force (130 million people) results in an error of 0.09% -- a tenfold increase over the emotionless error of 0.009%.

[2] This raises an interesting question: Do correlated emotions ruin the ability of markets to function?

What would happen if the Fed unwound the QE?

What would have happened if the Fed unwound its quantitative easing program at the beginning of 2014?

Not much.

Well, the stock market would probably panic, overreact and fall a few hundred or thousand points. Republicans would probably call for Obama's impeachment (even though many of them believe that QE is hurting the economy).

But after things settled down, we'd be left with a world with an effective Fed funds rate of about 2%, rather than the current 0.09%. The rise in rates would have no direct effect on output (the market crash might impact output, but that would be because of market failure, not fundamentals).

Here is the counterfactual path of the effective Fed funds rate (based on this model) after reducing base reserves to their average level between 2001 and 2008:

Zooming in on the interesting bit (on a linear scale):

What do exchange rates measure?

Scott Sumner says that because the ECB lowered interest rates and reduced IOR -- and since the Euro fell on that news -- the ECB (i.e. monetary policy) is capable of producing inflation and that the zero lower bound/liquidity trap is incorrect.

That sure sounds like a coherent theory, but is it the only one? And what does a falling price of a Euro in terms of e.g. dollars mean? This sounds like a perfect opportunity to take on exchange rates with the information transfer model.

I first looked at a naive model where the exchange rate is based on the ratio [1] of the supply of each currency and got a not entirely terrible fit (exchange rate data is in orange and the ratio is in blue):

However this model only works with the supply of Euros in the numerator! This is weird because it means if the supply of Euros goes up, the dollar price of a Euro also goes up. Or in terms of macro, if the exchange rate (dollar price of a euro) goes up it means the supply of base money Euros increased implying inflation. That would mean (when Sumner reasons from a price change above) that if the exchange rate falls on an ECB announcement (meaning Fed policy can be taken as constant) we should expect a fall in the supply of base Euros and deflation -- on news of expansionary monetary policy, no less!

How do we make sense of this? The dollar price of Euro goes up when there are more Euros -- that must mean demand for Euros has gone up. That's the key insight here. Let's start from the basic information transfer model:

$$
\frac{dD_{EU}}{dM0_{EU}} = P_{EU} = k_{EU} \frac{D_{EU}}{M0_{EU}}
$$

where $D_{EU}$ is the demand for Euros, $M0_{EU}$ is the amount of Euro currency in circulation and $P_{EU}$ is the "price" of a Euro (the Platonic ideal price that we'll later compare to another price to determine an exchange rate). We can solve this differential equation to obtain:

$$
D_{EU} \sim {M0_{EU}}^{k_{EU}}
$$

and

$$
P_{EU} \sim k_{EU} {M0_{EU}}^{k_{EU}-1}
$$

We can solve the analogous model for the dollar demand and obtain:

$$
P_{US} \sim k_{US} {M0_{US}}^{k_{US}-1}
$$

The exchange rate is then the ratio of these prices

$$
X_{EU,US} = \frac{P_{EU}}{P_{US}} = \alpha \frac{{M0_{EU}}^{k_{EU}-1}}{{M0_{US}}^{k_{US}-1}}
$$

where $\alpha$ is a constant fit to the data like $k_{EU}$ and $k_{US}$. This now makes sense of exhange rate price movements -- if the dollar price (exchange rate) of a Euro goes up it means that the price (value) $P_{EU}$ of a Euro has gone up (supply has decreased or demand has increased) or the price (value) of a dollar $P_{US}$ has gone down (supply has increased or demand has decreased).

In addition to making sense, it also fits the data pretty well (with nice Gaussian residuals):

And not just for the Euro -- here is the Yen-Dollar exchange rate:

The other key takeaway from this analysis is that exchange rate moves are not always relevant to inflation. Since $X$ is a function of $M0$ [2] and moves in $M0$ do not always lead to inflation (especially in a liquidity trap/information trap), moves in $X$ do not indicate monetary policy effectiveness or inflation. Long term interest rates will probably fall in the Eurozone, which may help the fiscal situations of several member states, but there does not appear to be any monetary impact from the ECB's announcement.

Another way to say this is that printing money will impact exchange rates, but may not impact inflation if you are in a liquidity trap. One could say that exchange rates and inflation decouple in a liquidity trap.

It's also important to note that the fluctuations in the exchange rates are large, so any particular move is unlikely to be very informative ... never reason from a price change.

Footnotes:

[1] We could imagine this as a purely exogenous information transfer model where P = k D/S (where P is the price or exchange rate, D is the demand and S is the supply).

[2] The other measures of money are also decent models, for example, here are the M2 versions:

But I've shown before that log M2 ~ k log M0 so this doesn't actually add information (we can just re-write the M2 versions of the equations in terms of M0).

Annihilation and sterilization

The always excellent David Glasner has a couple of posts up [1], [2] about the gold standard. One thing he mentions is David Hume's thought experiment:

"The [automatic] adjustment process, which came to be known as the price-specie flow mechanism (PSFM), is widely considered one of Hume's greatest contributions to economics and to monetary theory. Applying the simple quantity theory of money, Hume argued that the loss of 80% of Britain's gold stock would mean that prices and wages in Britain would fall by 80%. "

I thought I would see what happens in the information transfer model, replacing 18th century Britain with 21st century United States and gold with fiat currency. In the information transfer model a gold standard currency would operate in the same way as a fiat currency at least in its effect on the price level (if a dollar was replaced by a commodity coin worth a dollar, the value of the currency stock at approximately one trillion dollars today would be a minor perturbation to NGDP and changes in its market price would be even smaller).

Hume apparently did not appreciate the nuance of perturbative analysis in his thought experiment where 4/5 of the gold supply in Britain was annihilated. I only annihilate 1/5 of the currency supply in the following graph:

We see that in general, the price level drops but not necessarily by 20% -- the result depends on the information transfer index (which was different in different years in the US). For an IT index ~ 1 like in 2014, the fall is much smaller than for an IT index nearer ~1/2 like in the 1970s (where the change in currency is approximately equal to the change in the price level).

Glasner also refers to Milton Friedman's claim of gold "sterilization"  (the money stock not rising as much as 'it should' as gold flows into a country) and Hayek's claim that it wasn't happening in France. Here's Glasner:

"What Friedman meant by sterilization is that the incremental gold reserves flowing into the Fed did not lead to a commensurate increase in the stock of money held by the public, the failure of the stock of money to increase commensurately with an inflow of gold being the standard understanding of sterilization in the context of the gold standard."

"Of course 'commensurateness' is in the eye of the beholder. Because Friedman felt that, given the size of the gold inflow, the US money stock did not increase 'enough,' he argued that the gold standard in the 1920s did not function as a 'real' gold standard would have functioned."

And again:

"Thus, in his 1932 defense of the insane Bank of France, Hayek pointed out that the domestic quantity of money had in fact increased in France along with French gold holdings. To Hayek, this meant that the Bank of France was not sterilizing the gold inflow. Friedman would have said that, given the gold inflow, the French money stock ought to have increased by a far larger amount than it actually did."

The issue here appears to be that there was no agreed upon fixed relationship between the money stock and gold, with the stock rising in a less than one-to-one correspondance. How does this look in light of the information transfer model example above? I won't be looking at the money stock (monetary aggregates such as M1 or M2), but rather the price level, however the argument still holds since both Friedman and Hayek both believed in some variant of a quantity theory of money such that in the long run e.g. P ~ M1.

Here is the graph of the effect of a 20% increase in the currency (i.e. gold) on the price level:

Again, we see that the change in the price level is somewhat less than 20% -- this difference is effectively the "sterilization" early 20th century monetary economists referred to.

One interesting thing is that this seems to provide evidence that the information transfer index was close to ~ 1 in the 1920s and 1930s: France and the US increasing their gold supplies didn't cause the price level to shoot up as much as the gold supplies increased (nor the same amount of deflation in other countries as the fraction of gold supplies decreased). Everyone seemed to be in liquidity trap conditions that set up the Great Depression and the apparent fecklessness of monetary policy. I say apparent because, in fact, monetary policy couldn't stop the deflation happening because of the fall in NGDP (or RGDP).

Update: 1/14/2015. In my trip to Scotland, I stopped by Hume's tomb ...

Insights from non-ideal information transfer in physical processes

In addition to the discussions about the source of information in a transfer process, Peter Fielitz provided a great insight into how non-ideal information transfer manifests itself through an analogy with a real gas (as opposed to an ideal gas). In the graph below, I plot a schematic path followed by a real gas in an isothermal compression/expansion on a p-V diagram in blue:

The ideal gas behavior p = (2/f) (E/V) is given by the dashed line; this is the expected path followed with ideal information transfer, I(E) = I(V). We see the pressure is p ≤ (2/f) (E/V) if we are at the blue point near the gas-liquid transition.

There are a couple of interesting analogies [1] to be gleaned from this:

• Peter pointed out that as V→∞, the information transfer becomes ideal and  I(V) ≈ I(E). We would imagine that given approximately constant demand D, information transfer in an economic process if not already ideal would become ideal as the supply S becomes sufficiently large. This is an interesting result because it implies that sufficiently large markets should behave like an ideal information transfer process.
• The reason that the blue curve deviates from the dashed curve is primarily attractive forces between molecules (which eventually cause the gas to condense into a liquid). This would be analogous to the details of a micro-economic theory ("microfoundations", e.g. agent based models, DSGE models) causing the market to deviate from ideal information transfer, resulting in I(S) < I(D). Coupled with the previous point, we could expect the effect of the microfoundations to vanish in a sufficiently large economy (S→∞) as we approach I(S) ≈ I(D).

[1] We must always remember to keep Samuelson in the back of our minds when looking at analogies between physics and economics:

There is really nothing more pathetic than to have an economist or a retired engineer try to force analogies between the concepts of physics and the concepts of economics. How many dreary papers have I had to referee in which the author is looking for something that corresponds to entropy or to one or another form of energy.

Or:

The formal mathematical analogy between classical thermodynamics and mathematical economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes -- such as entropy or energy -- in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should 'utility' be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?

Which way does the information flow?

I've been asked how I know information flows from the demand to the supply several times, most recently by commenter Jamie and David Glasner. The easiest answer is that I don't really know, but just assumed that for now. However there are some plausible arguments that I will try to clearly present here. For concreteness, let's call I(D) the information sent (or received) by "the demand" and I(S) the information received (or sent) by "the supply".

This is going to be both technical and philosophical, but first let me start off with three points:

1. The direction of information flow is largely irrelevant to most of the results of the information transfer model I've presented on this blog because I nearly always take I(D) = I(S); in that case the direction of information flow essentially comes down to a sign convention in which solutions of the differential equation to choose to reproduce supply and demand diagrams.
2. "Information" in the information transfer framework is not specific insider knowledge about corporate earnings, understanding of the IS-LM model, political intuition, theories of inflation or really anything people colloquially equate with the word information. Actually, information in information theory generally represents a lack of knowledge (a random sequence of numbers has more information than a predictable one). The entirety of I(D) would consist of a list of numbers of widgets purchased at various prices by different individuals. Now it is true that e.g. consumers' theories about inflation might determine the numbers of widgets they might buy at various prices, but as far as the market is concerned (and the information transfer framework), those theories are irrelevant once you have that list of numbers of widgets purchased at various prices. This also helps us understand point three ...
3. The selection of I(D) or I(S) as the information source is not ideological. Nor does it mean that corporations are "dumber" than consumers or vice versa.

Now for cases where I(S) < I(D) -- or I(D) < I(S) -- it does make a difference which one is the information source; let me present a couple of arguments for how one should be able to tell the difference.

Argument from abstract physical processes

This argument is based on email discussions with Peter Fielitz and can be found in his paper with Guenter Borchardt [1]. What follows is my version of his argument and any errors are mine. The idea is that if a process variable (our D or S above) could theoretically generate an infinite amount of information, then it cannot be an information source -- the amount of information transferred must be finite, i.e. I(source) < ∞.

This seems to point towards demand being the information source since one could (theoretically) produce an infinite supply of widgets (or an effectively infinite supply of widgets relative to the number of consumers -- so many that no more will be bought or the price goes to zero), but a market with an infinite quantity demanded relative to the number of consumers is non-sensical.

Peter gives an analogy with an ideal gas where the internal energy E maps to the demand D and the volume V maps to the supply S. We could set up an experiment where V is effectively infinite (relative to the number of particles) but an experiment where E is infinite relative to the number of particles is non-sensical.

Peter also allows that if one changes the conditions (e.g. keeping one variable constant), it might change the status of which process variable is the source or the destination.

Argument from information loss

Peter Fielitz also had an interesting observation in our email exchange. Using the ideal gas analogy where E maps to D and V maps to S, he pointed out that the internal energy of an ideal gas is hard to measure directly. However one can achieve a very accurate estimate by measuring the pressure and volume and using the ideal gas law E ~ pV.

Now demand is hard to measure directly, but if one uses the analog of the ideal gas law D ~ PS where P is the market price, one should be able to get an accurate estimate of the demand. This is especially interesting because this is exactly how the government tries to measure aggregate demand (AD) or NGDP. Either the statisticians tally up how much everyone made from selling all their goods (income method) or tally up how much all the goods were purchased for (expenditure method), but the result in both cases is an estimate of aggregate demand.

This analogy also points to demand being the information source so that I(S) ≤ I(D): that tally based on aggregate supply AS at best will give us aggregate demand. The estimate of NGDP is either below the true NGDP (in which case it is missing information or wrong) or it is above the true NGDP (in which case it is wrong). Overestimates of NGDP are always wrong; underestimates are either missing information (but can be wrong, too). Even the best estimate from the market will result in NGDP below potential NGDP.

This was part of my original intuition behind why demand is typically the information source in trying to describe economic data -- the total sum of widgets sold (along with their prices) is at best a lower bound for the maximum possible number of widgets sold at various prices.

Let's imagine the demand as a probability distribution P(i, j, k) where i represents a given consumer, j represents a given number of widgets and k represents a given price, and Q(i, j, k) is the probability distribution of desired sales. You could imagine P as the number of people that will buy widgets (at a given price point) in Seattle vs Tacoma and Q as how many widgets at what prices suppliers put in stores in Seattle vs Tacoma.

It seems fairly obvious to me that the market mechanism is trying to figure out P and suppliers with incorrect Q's will lose money (or not make as much) relative to those with correct Q's. I personally don't care how many pounds of bacon the bacon industry is trying to sell in which markets (i.e. Q) -- and I am spending zero effort to find out.

As pointed out by commenter Jamie, firms will produce advertising to influence P. However advertising does not travel through the price mechanism, but rather through human communication systems -- advertising does not represent information flowing from I(S) to I(D) or vice versa. Additionally, firms will spend money on market research in order to figure out P -- they are essentially bypassing the market estimate Q. This could represent an individual firm's lack of information about P (because they have competition and so don't know the entire market estimate Q) or the fact that the full market estimate Q is also imperfect ... giving further evidence that that I(S|Q) ≤ I(D|P). [The notation I(x|y) means the information in the process variable x given the probability distribution y.]

The probability distribution Q as an incorrect estimate of the distribution P represents information loss calculated via the Kullback-Leibler divergence D(P||Q). Now in general 0 ≤ D(P||Q), so an incorrect estimate Q of the distribution P always represents information loss. This is relevant to e.g. this post on Walras' law where information loss could represent excess demand or excess supply at a given price -- the distribution in either case is wrong, and only when there is no excess supply or demand is P = Q.

In this view, the market appears to be a mechanism that attempts to find the best available Q to minimize D(P||Q) given potential constraints, but since D is semi-definite, we generally have I(S|Q) ≤ I(D|P).

Summary

While it's not set in stone (feel free to point out errors in comments!), I think these are some pretty plausible arguments for why we can assume information flows from demand to supply.

The other thing to keep in mind is that for most of this blog, remember point 1 at the top of this post: I assume I(D) = I(S) so the direction of flow doesn't really matter.

[1] P. Fielitz and G. Borchardt, Physics Essays 24 (2011) 350.