18 thoughts on “Financial market equilibrium with bounded awareness

  1. Are the brackets in the correct place in this sentence?

    “If the investor considers only the (boom) slump state, she will regard the equity (bond) asset as dominant, and invest only in that asset.”

    I assume the sentence is intended to do the work of these two sentences.

    (A) If the investor considers only the boom state, she will regard the equity asset as dominant,and invest only in that asset.

    (B) f the investor considers only slump state, she will regard the bond asset as dominant,and invest only in that asset.

    More broadly, I might provide some philosophical ruminations once I have absorbed the paper. My comprehension of the paper will be very significantly incomplete and imperfect. Under those conditions could I ask any questions of value or provide any insights of value? This is a question which might not be completely unconnected to the essential subject matter of the paper. People suffer from bounded (and limited?) awareness and rationality not only with respect to markets but also with respect to theories about markets.

  2. J.Q.,

    In the spirit of full disclosure and an avoidance of false pretenses to competence, I have to state I don’t comprehend your paper. So, what the heck am I doing in commenting?

    The creed of the militant agnostic is generally given in strong form as “I don’t know, and you don’t know either.” In this particular case, I cannot reasonably state such a creed in the strong form. You might know. I have to state a weak form: “I don’t know and I don’t know if you know.” What you potentially “know” in this context requires defining. I am assuming that if you “know” then you know things like;

    (a) What kind of model your model is.
    (b) Whether or not your assumptions are robust (not fallacious or over-simplifying).
    (c) Whether your model could conceivably be tested in the real world for descriptive validity.
    (d) Whether your model (or conclusions from it) could conceivably be applied in the real world for prescriptive (public policy) effect.

    Of course, it has to be said that you might not be all the way to point (d) in this research program.

    In relation to point (a), I found this paper interesting:

    “Chameleons: The Misuse of Theoretical Models in Finance and Economics” – Paul Pfleiderer.


    This is NOT to imply that your paper is a “chameleon” in any of the senses that Pfleiderer develops the term.

    I substantially (though not completely) understand Pfleiderer’s paper after one close reading of it. I would be intrigued as to your thoughts on his paper and its implications, if any, for your paper and for economic modelling in general. It’s intriguing to me (though perhaps not to you) that I cannot understand your paper but I can “meta-understand” its position in a (potential) debate about the shape-shifting and nested nature of economic (or political economy) debates.

    After all, how does the intelligent layperson (one hopes) find the “Truth”, or an approximation thereof, in economic debates when he/she lacks intricate specialist knowledge? Truth in this case has to be, one would think, truth as correspondence: as a workable homomorphic correspondence between the model and the reality modelled.

  3. I did read the paper Financial market equilibrium with bounded awareness by Guerdjikova and Quiggin, Sept 2020 – it was a long night!

    To state the obvious first, the paper involves a lot of technical work and I say this even though I have some experience with increasingly complex notation due to the partitioning of the set of agents with their characteristica defined on partitions of Euclidean state contingent commodity spaces and product Eulidean spaces to allow for one type of agent that can trade and producein more than one local ‘market’. [1] I admire people who have the patients and the skills to work out the many special cases (if then propositions) as is done in the paper in question.

    In comparison to Radner’s work on equilibrium of prices and price expectations in a sequence of markets, which makes the essence of financial markets – securities – explicit (ie trade in contracts and commodities), the heading of the paper is, IMO, an overstatement of the model. In my reading of the paper, the model contains the simplest possible model of an economy (1 consumption good). What it is, is not made explicit, except that it is the argument in ‘standard’ expected utility functions, which is real valued. The endowment is presumably the same good (as per equilibrium condition) and the reference to ‘commodities’ in the paper, is technically legitimate but not helpful to the reader. The market opens only once, where the agents can exchange state dependent endowment streams. So, the prices are not prices of securities (as in Radner) or as a practising finance person might presume, but Arrow type prices of state contingent commodities. For post Radner models, see Darrell Duffie, Security Markets, Stochastic Models, Academic Press, 1988.

    The special feature of the model is its treatment of ‘bounded rationality’ regarding the state dependent choice sets of subsets of the total set of agents in the economy. This of course can also be done in a mathematically simpler form, namely working with appropriately partitioned Euclidean state contingent commodity spaces on which agents’ endowments and preferences of state dependent commodities are defined. Depending on the assumptions on the preferences, real valued utility functions can be derived.

    However, there is a benefit flowing from the mathematics used in the paper. The filtrations on the ‘true’ state space, ordered by coarseness, allow specific results regarding which exchanges of state dependent ‘goods’ (commodities) are possible. The insight being, some intertemporal exchanges do not take place, not because of external restrictions but because of ‘bounded rationality’, due to agents’ limited and differential awareness of the entire state space. A step closer to reality, I would say.

    Furthermore, the application of the mathematics by the authors results in clear distinctions between ‘full awareness’, ‘bounded awareness’ and beliefs (risk assessment) and the analysis of these on state contingent prices of the good and on the intertemporal allocations. [I enjoyed reading this part of the paper and I learned about the Kullback-Leibler distance measure!].

    I can’t see the assumption of an identical discount rate to be a problem (unless there is at least one agent whose life expectancy is finite, she says tongue in cheek!)

    A comment on ‘incompleteness of the market’. The market is complete in the sense of Arrow. I presume it wasn’t quite straight forward to get the conditions under which an equilibrium price can be proven to exist, given the structure of the model. I no longer subscribe to Econometrica and therefore can’t quickly access the 2019a and 2019b papers by the authors.

    But the completeness of the market is established only in relation to the state space for a single good. Clearly this single good is a tradeable thing. This fits Finance (and Financial Accounting). However, the paper contains the term ‘Ecological Rationality’ (as used by a referenced author). This term refers to the ‘human ecology’ (eg the evolution of heuristics) and not to the ecology as understood by natural scientists and as indicated in economics by the term ‘sustainability’.

    When considering ecology as understood by natural scientists then one is looking at a different state space then that used in the model. This space would have to allow for physical aspects that are essential for human survival (including the one good) but that are not tradeable by their nature, eg CO2 emissions and global warming. The state space in the paper would be a proper subspace of the state space that represent the natural ecology. Incompleteness follows.

    I allow myself one criticism of the paper. There are a few instances where arguments are presented that go beyond the scope of the model. For example, there is a reference to observations on unemployment and GDP growth. While it is the case that some traders of financial securities do condition their expectations on such information, such behaviour cannot occur in the model (a financial security market would be required and a signal space and at least 2 ‘goods’)

    I allow myself a side remark. For younger and less well established and respected economists like JQ, the paper may be viewed as an insurance against attacks by ‘free market apostles’ shouting ‘socialist’.

    [1] PhD thesis, 1989, which contains the model: Partially segmented markets with multinational producers

  4. The parentheses were Iko’s issue, not mine. Still, you invited my ruminations, so here goes.

    I wonder if you could also tackle bounded rationality from an institutional perspective. Economic transactions are governed by contracts of various types, using an expansive definition that includes forms of association and inheritance. The universe of possible contracts is potentially infinite, but in practice is limited to variations on a few standard types (land ownership, mortgages and rentals, bills of exchange, shares and bonds, employment, insurance, wills, etc.) Why?

    – There is no such thing as a perfectly unambiguous contract. Courts are continually redefining their meaning at the margin, and reading new implied terms into them. A contract type represents a large investment of social capital. New types emerge rarely: the PPA for electrical generation and the financial derivatives of the GFC are recent examples, with opposite signs for social utility. It’s very risky to sign an untested pioneering contract. The set of unused possible contracts includes lots of silly ones (say a bet combining the future price of soybeans with Trump’s winning Florida). It probably also includes useful (Pareto-improving) contracts.

    – Similarly, contracts are not perfectly understandable. This is not just a matter of the 200 pages of fine print but of future court interpretations. Agents also misconstrue the risks, as we saw with derivatives in the GFC and the blockchain fantasy.

    – Law also constrains the tradeability of contracts. An employment contract can’t be traded on human rights grounds. Nor can a will (I think).

    I don’t see how to formalise this line of enquiry, still less form an opinion how much I constrains the maximisation of social utility. But I suspect there is something in it.

  5. Are employment contracts tradeable? Suppose employer A offers a pay-out of $X to terminate an employment contract with employee B, I would say this is a trade if the employee accepts. Similarly, if employer A offers a pay-out of $Y and a gag contract [1] to employee B to settle out of court a case concerning the employment contract, then this is a trade. In both cases the employment contract is ‘redeemed’ in exchange for something else. (If one were to substitute bundles of commodities for the Dollar amounts, then this trade would fit into the Radner model, with a little more work to make it ‘formal’.) But employment contracts are not tradeable on an what is called an ‘open market’.

    As for limited and differential awareness (ie the crucial concept in the paper by G&Q, Sep 2020), I would say if employee B is a lawyer with expertise in employment law then he/she will have a finer filtration of the relevant sub-space of possible outcomes than employee B’, a person who cannot make any sense out of employment laws. If B’ is wealthy enough to exchange some of his/her wealth to buy a QC’s advice then B’ can potentially make a decision on the same ‘consumption set’ as B. I say potentially because the QC’s advice is not always independent of the content of the brief, which depends on B’s descriptions of the situation and the ‘true’ content of the QC’s advice may be filtered by B’s reading of it. Now, if there is no ‘true’ content in the advice, not even in a probabilistic sense (because ‘the Court is fickle’ – that is “Courts are continually redefining their meaning at the margin”) then there is some systemic risk. In some countries (eg Germany) individuals can buy legal insurance.
    [1] This type of contract is fascinating in so far as in so many words the contract specifies that it does not exist. Why are such contracts legal?

    Are wills tradeable contracts? Under some conditions it is conceivable and that which is conceivable tends to happen. Obviously, one condition would be the person who has written the will has died and it is established that the will in question is the last one. Another condition would be that the will contains something that is tradeable. A helpful condition would be that the beneficiary cannot think of anybody who would try to challenge the will. Suppose the beneficiary has $200,000 debt with a bank and is in arrears with repayments. The beneficiary will inherit real estate in Sydney with an estimated minimum value of $1mill. The beneficiary goes to the bank and uses the will as a state contingent security to ask for an extension of the loan for how ever long it takes to get probate. If the bank accepts then this is a trade involving a will. It would not be an ‘open market trade’.

  6. IIRC the Prodigal Son, broke but standing to inherit half his father’s assets, can’t sell his interest in the inheritance to Dives, on grounds of public policy. The Prodigal Son is inhibited by filial sentiment from accelerating the inheritance. This restraint does not apply to Dives. It’s a bad idea to muktiply incentives to murder.

  7. PS to my last sentence: it’s a commonplace that George Washington nobly freed his slaves in his will, unlike Jefferson. This is a half-truth. In fact his will freed the slaves on Martha’s death, not his own. In self-preservation, widow Martha freed them fairly quickly while she was still alive.

  8. Until probate is granted all assets are frozen, while interest can accrue the bank can’t take action on the loan.

  9. Does this relate to opportunity cost? I have a struggle with the idea of quantifying opportunity costs, since to my mind they are dependent on each person’s knowledge of the feasible opportunities. A minor input (‘hey, that choice is much easier/harder than you are assuming’) can make a major change.

  10. Thanks for lots of interesting comments

    @James Your last comment seems to imply both that George survived Martha and that Martha survived George. Can you clarify?

    @Ernestine Thanks for these thoughtful comments. Some of the points you mention relate to harmless simplifications. For example, we could allow for many goods rather than one, but it would add a lot more subscripts, without changing anything important. On the other hand, the assumption that markets open only once is important – once you allow for retrading, things get very complicated and difficult. We are still working on that.

    @Peter T Everything relates to opportunity cost :-), though it isn’t spelt out here. The rate of interest on bonds determines the opportunity cost of future consumption in terms of foregone present consumption. The state claim prices implicit in security prices determine the opportunity cost of consuming on one state of nature in terms of foregone consumption in other states.

  11. I remain sceptical or agnostic about mathematico-deductivist economic modelling. I am in reasonable company I think. I’m not a mathematician but I can quote mathematicians of this view. Wassily Leontief comes to mind. Leontief criticized “preoccupation with imaginary, hypothetical, rather than with observable reality”.

    My open scepticism about mathematico-deductivist economic modelling as a tool for understanding the real political economy system is not disrespect to J.Q. (in case it comes across like that). On the outsourcing thread, for example, I praise a significant portion of J.Q.’s career output.

    Can a non-mathematician critique complex mathematical models? No, not in their own terms. However, the empirical evidence for or against a mathematical model set (discipline area) can be assessed by a basically science-literate person. I am neither an aeronautical physicist nor am I an atmospheric physicist. I cannot critique their mathematical models. Yet, I can see that planes fly and that modern climate models also “fly” while still being granular and imperfect. In the second case, “fly” means that word summaries, diagrams and basic formulae of climate models make scientific explanatory sense (cause and effect sense) to a science-literate person and the models also make predictions which are being borne out empirically by real-world developments.

    It’s difficult, for me at least, to see that mathematico-deductivist economic models fly outside of the theoretical spaces in which they are constructed. That is, it is difficult to see that they fly in real spaces (real space-time to be precise). That’s fine up to a point. Theory, be it sociological or scientific, is the next step after inductive and adbductive reasoning from empirical hints and instances. Eventually the theory must be taken back to the empirical realm for testing.

    Much of “conventional” economics seems to me to be unclear about whether it is descriptive or a prescriptive discipline. I’m not alone in thinking this. These debates are now generations old and objective conclusions are not just rare but seemingly non-existent. The state of micro and macro in “conventional” economics seems as deplorable as ever.

    “Of several major theoretical problems, the most basic is that economic theory reasons deductively, from axioms. An axiom, said the English economist Peter Wiles, is “only a premise one is not allowed to question, dressed up as something grand.” … By reasoning deductively from axioms, economics confuses the normative with the descriptive.” – Robert Kuttner.

    I’d like to unpack further the normative-descriptive conundrum at the heart of economics but it’s probably not worthwhile if I can’t spark a genuine debate here or in a sandpit. J.Q, and his colleague are conducting a detailed “box-search” or grid-search, to use that analogy, in a particular theoretical arena for particular answers. What I am intrigued to know among other things is what heuristic or meta-search theory, based on which ontological theory [1], has been used to determine that that arena is the place to search in detail? That is just a side question really. My central question is this. Does economics need to go back to basic ontology (in philosophical and scientific terms) in an attempt to correct and properly found its ontology of economic objects and processes? I contend it does need to do this. If you can’t get the base ontology right (what really exists at the most basic observable levels) then you cannot get anything else right. Medicine, for example, could make no real progress until it abandoned the humors theory for the germ theory. Progress in medical science to date of course goes much further than crude germ theory. Economic theory has been going around in circles since the Cambridge capital controversy [1] at least.

    Note 1- “The Cambridge controversies were not a tempest in a teapot. We agree with Bliss’s conclusion in viewing “the theory of capital not as some quite separate section of economic theory, only tenuously related to the rest, but…as an extension of equilibrium theory and production theory to take into account the role of time.” Major issues—explaining (and justifying) the return to capital, visions of accumulation, limitations of equilibrium tools—were and are at stake. While many of the key Cambridge, England, combatants stopped asking questions because they died, the questions have not been resolved, only buried. When economists decide to delve again, we predict controversies over these questions will be revisited, just as they were time and again in the 80 years prior to the Cambridge controversies. – Whatever Happened to the Cambridge Capital Theory Controversies? – Avi J. Cohen and G. C. Harcoourt, 2003.

  12. JQ’s post made me re-read what I had written (because a miscommunication seems to have happened).

    “But the completeness of the market is established only in relation to the state space for a single good.”
    This statement is true. However, it obscures from my “one criticism” (which relates only to verbal statements in the paper rather than the formal model). So, let me re-write it:

    But the completeness of the market is established only in relation to tradeable commodities (at least one good which is time and and state dependent).

    This shifts the emphasis from the single good to the word ‘tradeable’. It is exactly the property of ‘tradeable’, which I need in the subsequent paragraph.

  13. I don’t see the ambiguity. George died first, his slaves passed to his widow Martha (who owned more in her own right). Much more on Washington’s slaves here: https://www.history.com/news/did-george-washington-really-free-mount-vernons-slaves

    “Though the will contained the unheard-of order to free his enslaved workers, it stipulated that they remain with Martha for the rest of her life. […] After at least one fire and a rumor that an enslaved person wanted to poison her, she freed the rest of George’s enslaved workers about a year after his death. It was just too risky to keep “restive” enslaved people who longed for freedom among those she had inherited, she implied to friends like Abigail Adams.”

    Advert for my Cunning Plan to bring back the portrait of Washington’s enslaved cook Hercules to the White House: https://www.samefacts.com/george-washingtons-cook/

  14. Any advance on the tontine as the weirdest contract type that has actually been used at any scale? It’s hard to see the welfare point; but the contract lends itself to formal actuarial analysis, as the risks can be re\d off mortality tables.

  15. Everything relates to opportunity cost 🙂

    Humphrey Appleby: Everything is connected to everything else. Who said that?
    Bernard Woolley: The Cabinet Secretary?
    Humphrey Appleby: Close. It was Lenin.

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