Friday, May 1, 2020

What's in a name?


That which we call a model by any other name would describe as well ... or not
Shakespeare, I think.

I'm in the process of trying to distract myself from obsessively modeling the COVID-19 outbreak, so I thought I'd write a bit about language in technical fields.

David Andolfatto didn't think this twitter thread was very illuminating, but at its heart is something that's a problem in economics in general — and not just macroeconomics. It's certainly a problem in economics communication, but I also believe it's a kind of a professional economics version of "grade inflation" where "hypotheses" are inflated into "theorems" and "ideas" [1] are inflated into "models".

Now every economist I've ever met or interacted with is super smart, so I don't mean "grade inflation" in the sense that economists aren't actually good enough. I mean it in the sense that I think economics as a field feels that it's made up of smart people so it should have a few "theorems" and "models" in the bag instead of only "hypotheses" and "ideas" — like how students who got into Harvard feel like they deserve A's because they got into Harvard. Economics has been around for centuries, so shouldn't there be some hard won truths worthy of the term "theorem"?

This was triggered by his claim that Ricardian equivalence is a theorem (made again here). And I guess it is — in economics. He actually asked what definitions were being used for "model" and "theorem" at one point, and I responded (in the manner of an undergrad starting a philosophy essay [2]):
the·o·rem 
a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths 
mod·​el 
a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs
I emphasized those last clauses with asterisks in the original tweet (bolded them here) because they are important aspects that economics seems to either leave off or claim very loosely. No other field (as far as I know) uses "model" and "theorem" as loosely as economics does.

The Pythagorean theorem is established from Euclid's axioms (including the parallels axiom, which is why it's only valid in Euclidean space) that include things like "all right angles are equal to each other". Ricardian equivalence (per e.g. Barro) instead based on axioms (assumptions) like "people will save in anticipation of a hypothetical future tax increase". This is not an accepted truth, therefore Ricardian equivalence so proven is not a theorem. It's a hypothesis.

You might argue that Ricardian equivalence as shown by Barro (1974) is a logical mathematical deduction from a series of axioms — just like the Pythagorean theorem — making it also a theorem. And I might be able to meet you halfway on that if Barro had just written e.g.:

$$
A_{1}^{y} + A_{0}^{o} = c_{0}^{o} + (1 - r) A_{1}^{o}
$$

and proceeded to make a bunch of mathematical manipulations and definitions — calling it "an algebraic theorem". But he didn't. He also wrote:
Using the letter $c$ to denote consumption, and assuming that consumption and receipt of interest income both occur at the start of the period, the budget equation for a member of generation 1, who is currently old, is [the equation above]. The total resources available are the assets held while young, $A_{1}^{y}$, plus the bequest from the previous generation, $A_{0}^{o}$. The total expenditure is consumption while old, $c_{1}^{o}$, plus the bequest provision, $A_{1}^{o}$, which goes to a member of generation 2, less interest earnings at rate $r$ on this asset holding.
It is this mapping from these real world concepts to the variable names that makes this a Ricardian Equivalence hypothesis, not a theorem, even if that equation was an accepted truth (it is not).

In the Pythagorean theorem, $a$, $b$, and $c$ aren't just nonspecific variables, but are lengths of the sides of a triangle in Euclidean space. I can't just call them apples, bananas, and cantaloupes and say I've derived a relationship between fruit such that apples² + bananas² = cantaloupes² called the Smith-Pythagoras Fruit Euclidean Metric Theorem.

There are real theorems that exist in the real world in the sense I am making — the CPT theorem comes to mind as well as the noisy channel coding theorem. That's what I mean by economists engaging in a little "grade inflation". I seriously doubt any theorems exist in social sciences at all.

The last clause is also important for the definition of "model" — a model describes the real world in some way. The Hodgkin-Huxley model of a neuron firing is an ideal example here. It's not perfect, but it's a) based on a system of postulates (in this case, an approximate electrical circuit equivalent), and b) presented as a mathematical description of a real entity.

Reproduced from Hodgkin and Huxley (1952)
The easiest way to do part b) is to compare with data but you can also compare with pseudo-data [3] or moments (while its performance is lackluster, a DSGE model meets this low bar of being a real "model" as I talk about here and here). *Ahem* — there's also this.

Moment matching itself gets the benefit of "grade inflation" in macro terminology. I'm not saying it's necessarily wrong or problematic — I'm saying a model that matches a few moments is too often inflated to being called "empirically accurate" when it really just means the model has "qualitatively similar statistics".

One of the problems with a lack of concern with describing a real state of affairs is that you can end up with what Paul Pfleiderer called chameleon models — models that are proffered for use in policy, but when someone questions the reality of the assumptions the proponent changes the representation (like a chameleon) to being more of a hypothesis or plausibility argument. You may think using a so-called "model" that isn't ready for prime time can be useful when policy makers need to make decisions, but Pfleiderer put it well in a chart:



But what about toy models? Don't we need those? Sure! But I'm going to say something you're probably going to disagree with — toy models should come after empirically successful theory. I am not referring to a model that matches data to 10-50% accuracy or even just gets the direction of effects right as a toy model — that's a qualitative model. A toy model is something different.

I didn't realize it until writing this, but apparently "toy model" on Wikipedia is a physics-only term. The first line is pretty good:
In the modeling of physics, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely.
In grad school, the first discussion of renormalization in my quantum field theory class used a scalar (spin-0) field. At the time, there were no empirically known "fundamental" scalar fields (the Higgs boson was still theoretical) and the only empirically successful uses of renormalization were QED and QCD — both theories with spin-1 gauge bosons (photons or gluons) and spin-½ fermions (electrons or quarks). Those details complicate renormalization (e.g. you need a whole different quantization process to handle non-Abelian QCD). The scalar field theory was a toy model of renormalization of QED — used in a class to teach renormalization to students about to learn QED that had already been shown to be empirically accurate to 10s of decimal places.

The scalar field theory would be horribly inaccurate if you tried to use it to describe the interactions of electrons and photons.

The problem is not that many economic "toy models" are horribly inaccurate, but rather that they don't derive from even qualitatively accurate non-toy models. Often it seems no one even bothers to compare the models (toy or not) to data. It's like that amazing car your friend has been working on for years but never seems to drive — does it run? Does he even know how to fix it?

At this stage, I'm often subjected to all kinds of defenses — economics is social science, economics is too complex, there's too much uncertainty. The first and last of those would be arguments against using mathematical models or deriving theorems at all, which a fortiori makes my point that the words "model" and "theorem" are inflated from their common definition in most technical fields.

David's defense is (as many economists have said) that models and theorems "organize [his] thinking". In the past, my snarky comment on this has been that economists must have really disorganized minds if they need to be organizing their thinking all the time with models. Zing!

But the thing is we have a word for organized thought — idea [4]:
i·de·a 
a formulated thought or opinion
But what's in a name? Does it matter if economists call Ricardian equivalence a theorem, a hypothesis, or an idea? Yes — because most human's exposure to a "theorem" (if any) is the Pythagorean Theorem. People will think that the same import applies to Ricardian Equivalence, but that is false equivalence.

Ricardian Equivalence is nowhere near as useful as the Pythagorean Theorem, to say nothing about how true it is. Ricardian Equivalence may be true in Barro's model — one that has never been compared to actual data or shown to represent any entity or state of affairs. In contrast, you could right now with a ruler, paper, and pencil draw a right triangle with sides of length 3, 4, and 5 inches [5].

I hear the final defense now: But fields should be allowed their own jargon — and not policed by other fields! Who are you fooling? 

Well, it turns out economists are fooling people — scientists who take the pronouncements of economics at face value. I write about this in my book (using two examples of E. coli and capuchin monkeys):


We have trusting scientists going along with rational agent descriptions put out there by economists when these rational agent descriptions have little to no empirical evidence in their favor — and even fewer accurate descriptions of a genuine state of affairs. In fact, economics might do well to borrow the evolutionary idea of an ecosystem being the emergent result of agents randomly exploring the state space.

...

PS

My "to be fair" items so that I'm not just "calling out economics" are "information" in information theory and "theory" in physics. The former is really unhelpful — I know it's information entropy, but people who know that often shorten it to just information and people who don't think information is like knowledge despite the fact that information entropy is maximized for e.g. random strings.

In physics, any quantum field theory Lagrangian is called a "theory" even if it doesn't describe anything in the real world. It is true that the completely made up ones don't get names like quantum electrodynamics but rather "φ⁴  theory". If it were economics, that scalar field φ would get a name like "savings" or "consumption".

...

Footnotes:

[1] I had a hard time coming up with the word here — my first choice was actually "scratch work". Also "concepts" or "musings".

[2] ... at 2am in a 24 hour coffee shop on the Drag in Austin.

[3] "Lattice data" (for QCD) or data generated with VAR models (in the case of DGSE) are examples of pseudo-data.

[4] Per [1], this is also why I thought "concept" would work here:
con·cept

something conceived in the mind
[5] This is actually how ancient Egyptians used to measure right angles — by creating 3-4-5 unit triangles [pdf].

11 comments:

  1. That's a good analysis of some of the biggest problems with economics. I've always found it strange that so many economics "theorems" don't make sense from an accounting point of view. It's easy to diss accounting since so many of its rules are arbitrary, but I learned running a soft drink cooperative some decades back - we had to deal with an inventory of deposit back bottles - that there is a core of truth. When an economics theory violates an accounting conservation law, something is awry. I find that accounting is, at heart, a lot like free body diagrams in physics. A lot of stuff may be happening all over the place, but the accounting forces act locally.

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    1. You might enjoy this post on conservation laws and accounting identities.

      https://informationtransfereconomics.blogspot.com/2019/05/accounting-identities-and-conservation.html

      I would disagree on the existence of "accounting forces" — what you are more likely seeing is the (entropic) forces of human behavior exploring the realm of opportunities. If we set up (define) our accounting units to closely approximate those realms, then yes accounting can work as a shortcut. This appears to work for e.g. national income accounting and the government sector G. However if those accounting definitions are a structure we humans imposed on the world with no basis in the underlying categories, there's no need for them to be enforced except in the most trivial way. Sure, X = Y + Z, but if Y goes up and Z can go up, down or stay the same so that X could go up, down, or stay the same as well.

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  2. I’m a new reader of your blog and I’m impressed how interestingly the complex question is described, how easy the information is. Thank you, your work is priceless!

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  3. Should we blame the economists more, or the paucity of data?

    It seems to me that, for example, that in a developed economy with no debt crises, the nominal interest rate should equal expected NGDP growth rate, in monetary equilibrium. This was an assumption in von Neumann's general equilibrium model, though I think he only referenced real variables in that model. So, the real equilibrium interest rate should equal real GDP growth, in that case.

    While this seems a reasonable hypothesis, finding convincing support for it is difficult. Data seems pretty consistent with it, but there's not that much modern macro data. It remains a hypothesis, and perhaps a weak one, even though it may ulimately prove to be a model, and even a theorem.

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    1. It's possible that's a valid model, but if it's hard to show in the data then it could well be valid but not useful. To take it to an extreme, string theory might be a valid theory of quantum gravity but as it doesn't show up in the data it's not a useful theory.

      I wrote about this awhile ago here:

      https://informationtransfereconomics.blogspot.com/2016/07/ceteris-paribus-and-method-of-nascent.html

      But I don't think this particular hypothesis is likely to be a theorem — and that's because it has to do with time scales.

      A growth rate or an interest rate is measured in units of 1/time, and so it's inverse is a time scale: 2% is 50 years, 5% is 20 years, and 10% is 10 years. You can think of it as the scale over which fluctuations become small compared to the growth resulting from that rate.

      The hypothesis then becomes a comparison between two different time scales: nominal growth and nominal interest rate. But the latter has multiple time scales — which interest rate? Selecting a specific one chooses *another* time scale ... the 10-year rate is associated with two time scales right now 10 years and 150 years (0.66%). And to sweep it under the rug and say all the rates are the same is saying the yield curve is a meaningless metric. It's possible that it is, but that seems less likely.

      On the other hand, switching from quarterly growth to annualized is a constant factor (no time scale information).

      There might be an empirical relationship between interest rates and growth rates (I have an information equilibrium relationship that relates NGDP growth, the 10 year rate and currency base growth that has done fairly well over the past 5 years) — but that's likely to depend on the structure of the economy (how much of a nation's GDP is due to housing vs capital investment).

      Additionally, the structure of the 10-year interest rate and GDP growth are very different (both in fluctuations and temporally). I speculated that interest rates are more about capital formation here (based on a previous comment from you):

      https://informationtransfereconomics.blogspot.com/2019/12/money-velocity-interest-rates-and-robots.html

      ... but that would mean the relationship between GDP growth and interest rates would depend on the relative size of capital intensive manufacturing to e.g. services. And that's something that changes over time.

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    2. The way I see the proposed equilbrium relationship between interest rates and NGDP growth working would be that the one year Treasury rate, for example, should equal NGDP growth expectations going out one year.

      What complicates things is that interest rates, particularly Treasury rates, largely reflect market expectations for where the Fed will set rates in the future. It's not as if market forces are being revealed, for the most part.

      Also, I don't think anyone is really sure what the shape of a yield curve should be, in monetary equilibrium. Should it be positive, flat, or negative? If positive or negative, how much so? And what is the reason for the shape? Marginal utility? Temporal discounting? Something else?

      I tend to sympathize with your view that not all micro phenomena, such as risk aversion or temporal discounting, have to show up in macro data. It really may be that more or less "random" state space exploration within budget contraints results in the supply/demand relationships we see.

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  4. From Prof. R. A. Werner.
    'This “equilibrium” graph (Figure 3) and the ideas behind it have been re-iterated so many times in the past half-century that many observes assume they represent one of the few firmly proven facts in economics. Not at all. There is no empirical evidence whatsoever that demand equals supply in any market and that, indeed, markets work in the way this story narrates.
    We know this by simply paying attention to the details of the narrative presented. The innocuous assumptions briefly mentioned at the outset are in fact necessary joint conditions in order for the result of equilibrium to be obtained. There are at least eight of these result-critical necessary assumptions: Firstly, all market participants have to have “perfect information”, aware of all existing information (thus not needing lecture rooms, books, television or the internet to gather information in a time-consuming manner; there are no lawyers, consultants or estate agents in the economy). Secondly, there are markets trading everything (and their grandmother). Thirdly, all markets are characterized by millions of small firms that compete fiercely so that there are no profits at all in the corporate sector (and certainly there are no oligopolies or monopolies; computer software is produced by so many firms, one hardly knows what operating system to choose…). Fourthly, prices change all the time, even during the course of each day, to reflect changed circumstances (no labels are to be found on the wares offered in supermarkets as a result, except in LCD-form). Fifthly, there are no transaction costs (it costs no petrol to drive to the supermarket, stock brokers charge no commission, estate agents work for free – actually, don’t exist, due to perfect information!). Sixthly, everyone has an infinite amount of time and lives infinitely long lives. Seventhly, market participants are solely interested in increasing their own material benefit and do not care for others (so there are no babies, human reproduction has stopped – since babies have all died of neglect; this is where the eternal life of the grown-ups helps). Eighthly, nobody can be influenced by others in any way (so trillion-dollar advertising industry does not exist, just like the legal services and estate agent industries).
    It is only in this theoretical dreamworld defined by this conflagration of wholly unrealistic assumptions that markets can be expected to clear, delivering equilibrium and rendering prices the important variable in the economy – including the price of money as the key variable in the macroeconomy.

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    1. "There is no empirical evidence whatsoever that demand equals supply in any market and that, indeed, markets work in the way this story narrates."

      Hey, if you like that, you'll love the information equilibrium approach because it assumes "supply and demand" are never equal.

      Another assumption goes even further than rejecting "perfect information" and says we don't know what information agents have *at all*, nor how they act on that information.

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  5. This is the origin of the idea that interest rates are the key variable driving the economy: it is the price of money that determines economic outcomes, since quantities fall into place.
    But how likely are these assumptions that are needed for equilibrium to pertain? We know that none of them hold. Yet, if we generously assumed, for sake of argument (in good economists’ style), that the probability of each assumption holding true is 55% – i.e. the assumptions are more likely to be true than not – even then we find the mainstream result is elusive: Because all assumptions need to hold at the same time, the probability of obtaining equilibrium in that case is 0.55 to the power of 8 – i.e. less than 1%! In other words, neoclassical economics has demonstrated to us that the circumstances required for equilibrium to occur in any market are so unlikely that we can be sure there is no equilibrium anywhere. Thus we know that markets are rationed, and rationed markets are determined by quantities, not prices.
    On our planet earth – as opposed to the very different planet that economists seem to be on – all markets are rationed.

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  6. In rationed markets a simple rule applies: the short side principle. It says that whichever quantity of demand or supply is smaller (the ‘short side’) will be transacted (it is the only quantity that can be transacted). Meanwhile, the rest will remain unserved, and thus the short side wields power: the power to pick and choose with whom to do business. Examples abound. For instance, when applying for a job, there tend to be more applicants than jobs, resulting in a selection procedure that may involve a number of activities and demands that can only be described as being of a non-market nature (think about how Hollywood actresses are selected), but does not usually include the question: what is the lowest wage you are prepared to work for?
    Thus the theoretical dream world of “market equilibrium” allows economists to avoid talking about the reality of pervasive rationing, and with it, power being exerted by the short side in every market. Thus the entire power hiring starlets for Hollywood films, can exploit his power of being able to pick and choose with whom to do business, by extracting ‘non-market benefits’ of all kinds. The pretence of ‘equilibrium’ not only keeps this real power dimension hidden. It also helps to deflect the public discourse onto the politically more convenient alleged role of ‘prices’, such as the price of money, the interest rate. The emphasis on prices then also helps to justify the charging of usury (interest), which until about 300 years ago was illegal in most countries, including throughout Europe.
    However, this narrative has suffered an abductio ad absurdum by the long period of near zero interest rates, so that it became obvious that the true monetary policy action takes place in terms of quantities, not the interest rate.
    Thus it can be plainly seen today that the most important macroeconomic variable cannot be the price of money. Instead, it is its quantity. Is the quantity of money rationed by the demand or supply side? Asked differently, what is larger – the demand for money or its supply? Since money – and this includes bank money – is so useful, there is always some demand for it by someone. As a result, the short side is always the supply of money and credit. Banks ration credit even at the best of times in order to ensure that borrowers with sensible investment projects stay among the loan applicants – if rates are raised to equilibrate demand and supply, the resulting interest rate would be so high that only speculative projects would remain and banks’ loan portfolios would be too risky.
    The banks thus occupy a pivotal role in the economy as they undertake the task of creating and allocating the new purchasing power that is added to the money supply and they decide what projects will get this newly created funding, and what projects will have to be abandoned due to a ‘lack of money’.
    It is for this reason that we need the right type of banks that take the right decisions concerning the important question of how much money should be created, for what purpose and given into whose hands. These decisions will reshape the economic landscape within a short time period.
    Moreover, it is for this reason that central banks have always monitored bank credit creation and allocation closely and most have intervened directly – if often secretly or ‘informally’ – in order to manage or control bank credit creation. Guidance of bank credit is in fact the only monetary policy tool with a strong track record of preventing asset bubbles and thus avoiding the subsequent banking crises. But credit guidance has always been undertaken in secrecy by central banks, since awareness of its existence and effectiveness gives away the truth that the official central banking narrative is smokescreen.'
    https://professorwerner.org/shifting-from-central-planning-to-a-decentralised-economy-do-we-need-central-banks/

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