Tuesday, September 2, 2014

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.

16 comments:

  1. Thanks for this and your earlier reply to my previous comment.

    “I assume I(D) = I(S) so the direction of flow doesn't really matter”

    I think that this is the main point here and that I(D) = I(S) is the best assumption at the macro level. However, just to close off the discussion, I’d like to make a few further points.

    When you talk about “demand” you need to be clear exactly what you mean. When you look at GDP data you are looking at a summary of what actually happened in the past. In that case:

    Actual GDP = actual sales = actual purchases = actual demand = actual supply.

    The main information loss in the entire economic system is between what actually happened in the economy and what is reported in government statistics. You don’t have any visibility of the supplier’s forward looking view of demand, or what was supplied, or what the market demanded, or how customers and suppliers interacted to produce the GDP figure.

    For example, imagine that we are dealing with the manufacturing and sales of a consumer product. If actual sales in GDP statistics were $900,000, you don’t know whether that was 100,000 units at $9 or 90,000 units at $10. Maybe the supplier tried to sell 100,000 units at $10 but sold only 50,000 units and then reduced the price to $8 and sold another 50,000.

    Alternatively (and ignoring price), maybe the supplier estimated demand at 100,000 but could only sell 90,000. As you said previously “suppliers can never sell more goods than people wish to buy … that is my intuition behind I(D) >= I(S)”. However, equally the supplier could have estimated demand at 90,000 but demand was actually 100,000. This would also result in 90,000 sales as people can never buy more goods than suppliers try to sell.

    The main point here is that the market rewards suppliers who are good at estimating / meeting demand so suppliers have evolved many techniques for making this happen. For example:

    Forecast demand based on historical patterns including seasonality, and other external forecasts (which will vary from industry to industry)
    Agree contracts with customers to guarantee sales
    Implement just in time manufacturing where goods are manufactured only when orders are made (and deposits paid) e.g. cars, furniture
    Move manufacturing to retail outlets to optimize ability to respond to changes in demand on a minute by minute basis e.g. fresh bread at supermarkets
    Adjust prices to dispose of surplus supply e.g. clothes at end of season
    Include costs of waste in price. Suppose you manufacture 100 units and need a price of $9 to meet your profit targets i.e. sales of $900. However, demand fluctuates so much that, on average you waste 10 units and sell only 90. In that case you will raise the price to $10 to ensure that you still make $900. If the market won’t allow this then you will stop making the product
    Hold excess stock and include the extra costs of the stock holding in the price. Again, if the market won’t allow this then you will stop making the product
    Increase advertising when demand is lower than supply
    Use customer loyalty schemes / discounts to encourage repeat business
    Etc.

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    1. I agree with most of what you are saying here, but I would like to emphasize that under- or over-estimating demand represents information loss. (This information loss is based on the number of bits you lose in a communication channel if you've mischaracterized the symbol distribution).

      And yes NGDP = AD and AS ... It's at equilibrium in an AD/AS diagram or in the information theory view, I(AD) = I(AS).

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  2. “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”.

    Yes, but the supermarket knows a lot about the demand for bacon so it knows approximately how much to order and it knows what price is needed for profitability and it has many of the above management techniques. On the other hand, you have no leverage on the either price or volume. The supermarket will offer you bacon at a price which you can either take or leave. If the supermarket runs out of bacon then you won’t get any. The supermarket will even know the price of bacon at its rivals’ supermarkets which you won’t know either if you make no effort to find out, so the supermarket can exploit that fact to your disadvantage.

    “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”

    No that’s wrong. You are confusing the advertising itself and the commercial impact of the advertising. Suppliers advertise in order to increase sales volumes and/or prices over what they would otherwise be. Suppliers measure both sales and prices so they can estimate the impact of each advertising campaign. This information is invisible to individual customers and also to economists studying the macro-economy but that only goes to show further that suppliers have information sources and knowledge which are not available to others.


    I don’t understand enough about your technique to know what is or is not important. However, all of what I’ve discussed is relevant at a micro level but is mostly invisible at a macro level. At a macro level, other than the information loss issues I mentioned at the start, I’d say that the main information issue is not about information loss. Rather, it’s the reverse. Forecast demand information flows very efficiently.

    I do agree that (many) suppliers have to make forecasts of demand in advance of that demand appearing in the market. Also, the demand forecast then dictates everything else the supplier does including investment and supply plans.

    Recessions occur when suppliers detect (efficiently) that their customers are planning to cut back on their purchases. The suppliers then plan to cut back on their own purchases. The suppliers of the suppliers, in turn, then detect the planned supplier cut backs and cut back on their own plans. The cut backs then flow through the economy like a wave and cause job losses.

    I’d say that the challenge for macro forecasting is to detect these waves as they emerge but, as they can start anywhere in the depths of the economy and for many reasons, I’m dubious that it’s possible to do this. You use an analogy with gas particles. I think a better analogy would be with rocks / earthquakes or snow / avalanches or healthy people / disease epidemics. It feels to me that economists (and you) can probably detect trends i.e. the equivalent of the normal behavior of the rocks / snow / healthy people but not the exceptions i.e. earthquakes / avalanches / epidemics. Unfortunately, it’s the latter that the rest of us are interested in.

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    1. My statement was that literally advertising is not sent as a stream of price fluctuations (suppliers do have sales and such, but do not bring attention to a new product by alternatively pricing it at 5€ and 40€ each week for a year until people notice).

      Also -- I don't think the cause of recessions has been figured out yet. This one seems to be pretty clearly a fall in aggregate demand (that's not a cause, just a mechanism ... What caused AD to fall? I dunno).

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    2. Jason, I also have a question about advertising. I understand your comment here, but when you write (in regards to advertising):

      "advertising does not represent information flowing from I(S) to I(D) or vice versa"

      I understand that suppliers don't try to draw attention to a new product by altering its price in the manner you describe, but putting aside price altogether, I don't see how you rule out information flow from S to D: it seems to me that advertising is definitely information flowing from S to D. But that's not what you wrote, is it? You wrote that information from I(S) to I(D) is ruled out (via advertising). What's the distinction?

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    3. Is there a possibility of analyzing systems with information flow in both directions (perhaps with different detectors in each direction)?

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    4. Again, advertising is meaningful knowledge and not what we are talking about when we talk about information theory. Information is maximized in a random string of letters.

      Imagine the price system isn't working well. Do you think people will be getting great prices for their goods or terrible ones?

      Again, it doesn't matter in information equilibrium.

      I'd also point to evidence from interest rates. In short term rates, the price falls well below the info eq price.

      You also can't sell more widgets than people are willing to buy. You can have too many or too few widgets in supply, though. And in info theory, you're just matching up probability distributions. Not sending meaningful knowledge.

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    5. You'd just flip the differential equation, it actually gives the same result though unless you're talking about non ideal info transfer.

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    6. It seems like you could add a dimension or two to your P and Q density functions if you wanted to: one for time of the year (and perhaps another for day of the week). Or does that not make sense for Some reason?

      I'm just thinking of a supplier planning on Halloween. Or better still a Halloween on a Friday night vs a Wednesday night.

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    7. It's really a complicated multi-dimensional distribution where we don't even know the number of dimensions involved ... I actually wrote about that here:

      http://informationtransfereconomics.blogspot.com/2015/03/the-price-system-as-communication.html

      The way traditional economics has set up the price system as communicating information is fundamentally problematic.

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    8. Doesn't advertising shift both the demand and supply schedules upwards? The advertiser hopes that the demand schedule rises at a faster rate than the supply schedule.

      Henry

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    9. Hi Henry,

      I believe it operates by shifting demand up and either 1. supply follows in general equilibrium or 2. the price goes up in partial equilibrium or 3. both (depending on the value of k) in general equilibrium.

      But it is genuinely changing the distribution, not discovering the distribution (the information) via the price mechanism.

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    10. Jason,

      I was thinking more in terms of the mundane economic paradigm not your IE paradigm. (I have a great deal of trouble getting my head around where you are coming from.)

      Advertising aims to increase sales at every price -> shifts demand schedule upwards.

      Advertising is an additional cost -> shifts supply schedule upwards.


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  3. Some musings. :)

    "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."

    I think that typical economic thinking is the opposite. It is goods and services that are scarce, human demand that is potentially infinite. (IMX economists often conflate desire and demand.) The definition of an economic good is one that is scarce.

    That fits with a Malthusian worldview. Resources are scarce, humans consume as much as they can of them. The economics of the Petri dish. That may indeed be the long run fate of humans.

    However, modern advanced economies have the opposite problem, not one of scarcity but one of superfluity. (Thanks, perhaps to the Industrial Revolution.) They are Dickensian, with penury in the midst of prosperity. The US has, I have read, five times as many empty houses as homeless families; the ratio in Europe is 2:1. Advertising may be a symptom of superfluity.

    I wonder if the information flow is from demand to supply in Dickensian economies, but from supply to demand in Malthusian economies. Nowadays most Malthusian economies are in Africa, I suppose. Zimbabwe might be a good example, with its hyperinflation an example of Malthusian dynamics.

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    1. "I think that typical economic thinking is the opposite."

      That is an interesting observation. I will have to muse about that.

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