A question about physics-types models for flows in economics

Phillip Middleton writes:

I’ve been attempting to generate a set of visually (animated in fact) mappable models which represent measurable forces that demonstrate effects on localized economic (census block level) outcomes, which in turn affect and are affected by regional education dynamics, brick/mortar business development, etc… This is coming out of some reading and observation of mine that such forces appear interestingly to resemble fluid-like behavior.

Who might you know who seems fairly keen in geospatial/geotemporal economics? While my model perspective is currently quite bayesian, and mode of interpretation physical (fluids, non-linear dynamical systems, etc), I have yet to make any reasonably solid links between the two (i.e. solidly connecting the modeled factors fairly predictive and explanatory nature over space-time), and the seemingly fluid nature of their occurrence (i.e. think ideas like ‘ebb’ ‘flow’, ‘ripples’, vortices (and other decaying phenomena, sinks, etc). Think I’m hitting a brick wall and need a bit of external thought, or a scotch-laden reboot.

He continues:

This entire ‘thing’ i’ve been chasing came out of a picture I was drawing when imagining the free-market as a bathtub. Each spigot is an economic output, and the drain an input for one entity (no matter the scale). The ‘water table’ of the tub is simply the summary state of this economic system, measurable in currency, to the entities who share in that system. Obviously, spigots and drains can vary in size (spending vs hoarding at any level for example). Big drains and small spigots can lower the water table – less capacity of the system available left for which the rest can compete –> problem (cost vs living std gap, etc etc blah blah). Nothing new here – perhaps not even my imagery.

I don’t know anything about this but maybe some of you do?

46 thoughts on “A question about physics-types models for flows in economics

  1. Being a mainstream economist I am skeptical that there is much to gain from adopting modelling techniques wholesale from physics. But I do want to point out that the hydraulic model has been attempted (and built)! It is known as the Phillips Machine, when I worked at VU University Amsterdam, we had one (out of, I think, 10 that were built). Impressive machinere, but naive economics.

    They are just historical curiosities now, and I don’t think they were ever taken very seriously. But a lot of care went into building them. There is a demonstration here: https://youtu.be/k_-uGHWz_k0 , and documentation can be found in Phillips’ 1950 paper, “Mechanical Models in Economic Dynamics,” Economica 17(67), 283-305;

  2. This reminds me of:

    Brian Hayes write-up on control theory in economics, see:

    Krugman’s work on economic geography theory, see:

    and more on this using group theory, symmetry breaking (spreading) in:
    Bifurcation Theory for Hexagonal Agglomeration in Economic Geography

  3. Economist here, it’s always a pleasure to meet open-minded fellows with an interest in the cross disciplinary exchange of ideas and a desire to circumvent narrow subject boundaries.

    Unfortunately I can’t help with your specific question, but I do wonder whether you would be willing to help me instead, since I have a query in the oppose direction. I was sitting on the bus last week and saw someone reading a Brian Greene book abut string theory and it got me thinking – my field of microeconomics now has a well developed theoretical framework for modelling the market for household items such as strings, and this might be applicable to high energy physics. Specifically, we could model high energy strings as a durable consumer good and treat their vibrations in high dimensional space as being equivalent to fluctuations in the market price of strings. If we then postulate that gravity particles exist and treat these as being rational agents whose interactions can be described with agent based models, then it may be possible to come up with a microfounded general equilibrium theory of physics which can finally unify quantum physics and gravitation

    I don’t have any formal training in physics and indeed have never taken even an undergraduate level class in the subject, but I did study AP physics in high school and feel that my ideas may be important to the physics community

    • Steven:

      I get that you’re being sarcastic and that you’re annoyed at physicist types who think they can step into social science and solve all our problems. I hate that too! I’m so sick of those news stories of the form, some-guy-on-arxiv-used-the-principles-of-fluid-dynamics-to-explain-political-polarization. But, in defense of Phillip Middleton here: he doesn’t seem to be claiming to come up with a major contribution to economics. He expresses interest in visualizing and understanding—and it could well be the case that a physics-based model could be useful in such visualizations. There is, for example, a “gravity” model of international trade, and everybody knows it’s just an analogy.

      • I agree with what Andrew said, it’s silly to object to creating a visualization that displays economic flows in terms of physical flows, if such a visualization will help people understand what’s going on (even if the model is imperfect).

        But I also think Steven’s sarcasm, though amusing, is misplaced, assuming he really means it. What physicists bring to the economics table isn’t physical understanding, which isn’t useful in that arena at all, it’s mathematical methods. That’s also why they have things to offer in statistics (Didn’t Hamiltonian Monte Carlo, used in Stan, come from physics, for example? I think so, but I’m not sure. But I do know that Stan is named after Stanislaw Ulam, the mathematical physicist who invented Monte Carlo sampling among other things).

      • Wow. I hadn’t a clue that I would be generating such rich vitriol. But in a way I *do* understand it, as much as I don’t understand the need for backhanded ad hominem remarks :).

        A number of physics-folk moved into econ in the 80s and generated a plethora of mistakes. Namely, the long term of their work (we’re talking about physicists become quants) wasn’t generally considered – and the long-term risk and subsequent ethic of their work wasn’t what they were tasked to deal with (at least by their bosses) anyway. And there were plenty of things they didn’t sufficiently either – namely social behavior. And there were consequences to this. And true, some researchers since think they have found eureka moments that aren’t terribly sound (but I wouldn’t level this merely against physicists). So yeah, I see from where some of the annoyances come.

        But I think it is a common error to think that physics is ‘all about’ particles, black holes, and space rockets. Sure, those are research subdomains, but really it’s simply a very general perspective of trying to understand ‘how things are and how they work’ using scientific thought and action – be it a quark or a quack. I don’t see a legitimate reason to raise rigid boundaries around research disciplines.

      • Moving on – Andrew is correct. I’m not attempting to generate any grand unified theory or theoretical insight. My interest is purely to examine localized (to the degree possible) geotemporal economic (and related) effects.

        Some example applications:

        * What does a middle-class to poor transition in a neighborhood *look* like as a process given the forces/actors in this change (we know the effects, but by then it’s often too late to amend)?

        * What about just the opposite transition (i.e. gentrification as a process)?

        * Societal and economic transitions can generate both physical (people move out/in neighborhoods. But to where and how far?) and social (i.e. socioeconomic mobility induced by things like housing value changes, job creation, infrastructure, and localized income changes) movement across geographies and classes respectively. But can we visualize these things relatively accurately?

        Overall, I think socioeconomic processes can be represented from a dynamic, visual, and ‘temporally aware’ angle (which is why ‘animated’).

        When I mentioned ‘fluid’ – of course I don’t characterize social/economic behavior purely in that sense (economic systems in modern day hardly reach equilibrium, at any scale – as much as they may try). I’m only using ‘fluid’ as an analogy. Socio-economic systems are of course far more behaviorally dynamic, and depending on the level of behavior observed, rather chaotic.

        So my computational approach in this little sojourn thus far has been both statistical and numeric. Statistical from a geospatial inference perspective, and numeric (non-linear dynamical systems, stochastic processes, blah blah) to visualize the ‘mechanics’ of these processes (sans behavioral interpretation). My ideal goal, if it is even reasonable to do so, is bridge the gap between the numeric methods and output to statistical inference/interpretation.

        No I’m not an economist. At most, I minored in economics (econometrics) and sociology. My primary background (in work/education) is in stats and physics, with current interest in local economic behavior (and its regional impact on education). I admit, any or all of this may be completely naive. But I neither see how that discredits me from examining economic systems analogously as physical constructs nor how the idea itself should be so hastily torched. To me, the only way to find out is by doing the work – then shoot the rifle bullets at it to see if it holds any water.

        • What if you focus on the visualization itself? Visualization is then agnostic to physics etc. Flows are just flows; an economist might think more about flows of people or money whereas a physicist about say plasmas or electrons.

          What if you focus on visualizing flows but use existing models & data? For example, take mobility. There’s already rich county level data available about demographics, income etc. And models to predict employment etc. And statistical procedures to impute some missing values. And GIS procedures to model the geospatial variation.

          Why not use all that to generate a visualization?

        • Right, i agree, and the visual work is my current effort.

          Now I wouldnt say in this case that ‘flows are just flows’. Not with any precision anyway. As with any dynamical system, things get really messy (think ‘choppy waters’, decomposing vortices, etc). No less so in economics, which is why i leave that for the experts to help guide and interpret.

          I have collected alot of general geodemographic data (roughly 8000+ variables worth), but the time domain is quite sparse. Gov’t GIS is relatively easy to come by for the geographic region of interest, and is updated weekly. Traffic data has also been helpful, as has housing data (i lack more specific house and apt rental dara, so big gap there). Mobile data would be terribly useful to fiLl in a number of geotemporal gaps (and certainly aid in variation of imputed values), but that is an entirely different (and proprietary) hurdle.

        • Do you have any visualization ready? Even the data you mention seems huge & rich enough to get some visualization to get a taste of things. Why not start simple?

          If you say you are generating a novel visualization I think you will generate a lot less friction than by claiming to apply Physics methods to Econ Modelling. :)

        • What I have currently is a very rough 2D surface animation yet to be applied accurately as a layer to a map (I have a number of self-induced geocoding errors to deal with at the moment). In recent iterations – I’ve somehow managed to make it quite jittery. So definitely NOT ready :)

          I don’t believe I ever made any claims as you suggest at all. At this point, I’m mostly asking questions and making quite transparent statements of what I do (or think I do) and do not understand (the latter of which is quite plentiful :)). If friction is generated in that regard, that’s not something I can, nor do I intend, to help.

    • Steven:

      I was going to make a quip that you say metachrysis (bad metaphor) and I say metafor but in trying to find the correct spelling I goggled and found a similar post be me in 1996 with apparently with Radford (maybe only of interest to regular comment readers.)

      I guess this stuff never goes way.

      Keith O’Rourke

      >Article 8643 of 8647 (sci.stat.math) (32 lines) Mon Mar 11 15:31:27 1996

      >Subject: Re: Fuzzy logic compared to probability
      >From: rad…@cs.toronto.edu (Radford Neal)

      >There might, however, be an objective summary of the data, such
      >as the likelihood function.
      Only if the assumed probability model is exactly correct …

      But more importantly why do we need (these days) a summary other
      than the data themselves or a large random sub-sample???

      >This is an advantage! It means that you actually know what the
      >indications of uncertainty (probabilities) for the universals mean,
      >by analogy with what probabilities for particulars mean.
      But analogies can sometimes be very dis-advantageous.
      (There is a word for a bad metaphor – metachrysis (not in my dictionary)
      especially to denote this danger)

      Keith O’Rourke
      The Toronto Hosp.

  4. You got my interest with the “scotch-laden reboot” : – )

    I have a physics background (PhD with h-index 15, > 1000 citations), looking at time/space non-linear physical models for flood / environmental pollution for my own interest, access to a theoretical physics professor specializing in glass /fluid systems for hard math

    knowing and understanding “von Thuenen, der isolirte Staat” (Geospatial economics 200 years ago), always willing to bitch about Mr Krugman having not really contributed anything : – )

    Showing that the Gallup “The measuring stick” http://static1.1.sqspcdn.com/static/f/552212/8291575/1282829576767/firstbreakalltherules.pdf?token=9a1OwqfSpn0KMUDtaUqJJP%2Bwg6M%3D was just about talking up NOISE

    how about we have a nice little chat? How should I contact you?

  5. Goods, and even money, even electronic money, are physical objects. So they physically flow. Ergo, it’s possible to visualize their spatial flow.

    The basic physics of fluids says that flow comes from changes in velocity, which come from forces which are more or less understood. I think with economics, the question is can you come up with relatively simple laws that govern economic flows. if you can, then you can predict economic flow, if you can’t, then you can only observe and visualize them.

    What is the goal of this research? To come up with descriptions of forces from observed phenomena, or to figure out ways to visualize what is happening in the economy?

    • So I have several, some shorter, others – well who knows:
      * Visualization, is the shorter term goal. As a computational exercise (and given what I’m limited to use) I’m employing numeric methods

      * Longer term: describe the origins, mechanics, and interactions of various forces is more challenging as statistical analysis, rather than numerical method, suits the explanatory process. Ideally I’d like to be able to soundly translate one to the other rather than do each independently.

      * Prediction of various economic changes geospatially/geotemporally (and be able to ‘see’ it play out) – also numeric.

      • So what aspect of the economy are you trying to visualize? Is there a smaller, more specific problem? Or will this be a grand, overarching visualization of the “entire” economy?

        • No. As far as an ‘entire’ economy, that is an abstraction which I truly don’t understand enough to make any sound judgments in construction without outside advice. I’m currently focusing on flux in residential income (with particular interest in estimating mobile income), tenant migration/transience, and brick/mortar business longevity and migration – in that order. One at a time for now.

        • No grandiose models. I’m taking my first stab at dynamics in residential (census block level) income, with interest in estimating dynamics in mobile income, and get thorough feedback before I go any further.

          Now, my original aim *was* to examine regional small brick/mortar business dynamics (growth, decline, and movement), and then examine their effects on regional residential income. That was a more focused topic, but probably far too narrow. Plus, getting sufficient data particularly from non-franchise businesses proved more of a challenge than I anticipated. To keep moving fwd, I decided to work on the surface animations on resdential income first while collecting data on the latter.

      • One thing I think may be of interest is a concept that I’ve been sort of sitting on related to non-local dynamical systems. In particular, when you look at long timescale economic changes, there’s a lot of influence on the local decisions that comes from information “far away” from the local region. For example, although you might be able to predict a decline in a local neighborhood’s economic condition from the nearby surroundings (say a creep outward of a region as people move away from blight, on a length scale of city blocks say) there’s also going to be “long range” effects at different spatial scales, say at the length scales of the diameter of the city, the diameter of the metropolitan region, and even distinct effects from say neighboring states (draining off talent into a newly growing city) or federal government level (redistributing money via taxes on certain industries etc).

        The point is, if you want to write a differential equation for how a local small region’s economy changes, it won’t be a simple PDE (ie. mostly local effects) it will have to be some kind of integro-differential equation in which the integrated effects of all the various far off regions are considered in addition to local effects that might be approximated in terms of a spatial derivative.

  6. I’m starting to build similar models for my dissertation on Global Cities Theory. Try looking up the Sante Fe institute, they have a few economist publishing interesting research that may help. Also the book Sociodynamics by Weidlich ties some theory to these types of models. Jon Butner is applying non-linear dynamical models to psychological phenomena if you want to see how other social scientists are using and explaining models not normal found in their discipline.

    • Thanks John. I’ve been reading Weidlich’s work/text for the past month or so, but not familiar with Butner. This has brought up any number of additional questions to mind….. I need a larger notepad :)

  7. I seem to recall that the British Treasury (or at least the British something or other) at one point, presumably in the fifties or early sixties, had a literally hydraulic model of the economy. I suppose that in more highfalutin language it would have been called an analogue computer, but I have the distinct impression that it was a gadget into which you poured water at the top and economic predictions flowed out at the bottom. Does anyone know anything more about this? Or am I misremembering.

  8. Phillip’s question is nontrivial and is deserving of serious consideration, not ridicule. At last week’s (May 4-5, 2015) Systemic Risk seminar at Columbia, Ulam van Lelyveld presented a dynamic visualization of the interconnectedness of assets and exposures for all Dutch banks from 1990-2014 in the form of a “movie” of the evolution of the banks’ network(s). It was a stunning achievement. Van Lelyveld works for the Dutch Central Bank with the goal of developing orthodox metrics (i.e., from within the BIS II and BIS III frameworks) of global or systemic risk. His approach represents a mashup of economics, financial mathematics, physics and complexity science, to name a few of the fields integrated. He should be on your short list for further research and contact.

    The link to this POne paper on the dynamics of economic complexity attempts a similar visualization only in 2-D space.


  9. A starting point would be to look at what was done in the early days of macroeconomics, beginning with Irving Fisher in 1891 and others later on.


    Re: Steven’s quip, I understand that this is about visualizing concepts, and not claiming new theoretical insights, but keep in mind that economists have been for decades swamped with suggestions from well-meaning natural and physical scientists who don’t have a clue about the field yet are convinced they have brilliant insights to contribute. Preston McAfee, writing about his editorial experience at the helm of the top journal in economics, said “There are thousands of people who believe they have a Great Economic Idea that economists desperately need to know. Let us agree to call these people “kooks” for want of a better term. Pretty much 100% of kooks are theorists; you won’t meet a, say, physicist or physician with a Great Economic Idea that involved running regressions or doing lab experiments, although occasionally there is a table illustrating a correlation between some economic variable like lawyers or fluoridated water and per capita GDP.”

    • I have no illusions of a Great Economic Idea. That’s not my purpose at all. My intent is merely the test of a scientific interest in an idea – right, wrong, or indifferent. Yet, whether or not the quip was righteous (my distaste for ad hominem argument aside), I understand the annoyance from a historical viewpoint.

      • Here is another good lead that may be of interest to you: Daron Acemoglu and co-authors develop a network approach for the macroeconomy, still very much in its infancy, but could give you an idea of what economists are doing in this area


        I don’t think you should take criticism personally, I don’t think it was ad hominem, though it was certainly unkind. But ask yourself: if an economist proposed to test key ideas of physics using economic concepts, wouldn’t you laugh him out of the room? Honestly? There are sometimes truly brilliant minds whose thinking transcends disciplinary boundaries–say, John Von Neumann (who allegedly once walked past an open classroom where a talk was given, spotted a mistake made by the speaker on the blackboard, proceeded to correct it, and kept on walking). But most of us cannot hope to make meaningful contributions to more than one field without having a co-author in said field.

  10. When people bitch about physicists invading economists territory,

    you should keep in mind, that

    A) those are pretty often people coming from a very theoretical background, like many at the Santa Fe Institute
    B) people, who just did a theoretical bachelor or master, like a certain Noah Smith, and WHO NEVER practiced Physics / Engineering in the real world.

    What (some) experienced real world / applied / experimental physisicsts can bring to the table, is an eye for statistical noise, a robust aversion against overfitting (too many meaningless parameters and variables), and a penchant for what a crucial (potentially deadly) question for a certain model would be


    Hans Rosling’s 200 Countries, 200 Years, 4 Minutes – The Joy of Stats – BBC Four


    nice colourful, animated, multidimensional graphics, most people get impressed with (TED talks, state department, Google money spenders, etc.)

    But I looked at it the first time, and said, something is wrong with it. I looked at it the second time, and I knew what it was.

    Does any of you see / know it ?

      • when take a conscious look at the lower left side,
        you will see that there is no noise on many of the data for many years.

        Downloading the data and extracting (with some difficulties) the data gives you more like 50 years 50 countries data.
        Often justa wild guess from somewhere repeated many times.

        What you can do with that is easily generating colourful dynamic plots of pseudo dependencies, because nearly all these data are massively co-correlated over time. It luress people to “false insights” which is worse than saying ” we dont know”.

        What it also hampers is trying some fit, especially non-linear or to more variables.

    • I’ll tell you that I was showing that graph in my class last week just as an example of scatter plots and the idea of correlation, and I said what happens if you change life expectancy to linear instead of log?

    • I’m sorry, genauer, but you don’t understand what people are complaining about. For example, Noah Smith isn’t an example, because he does indeed have training in economics (i.e., a PhD in it, although that hasn’t seemed to help him any). The complaints are about garbage research that happens to be done by physicists and is thus picked up in the popular press as being revolutionary, despite physicists’ total lack of knowledge about the field, e.g., http://www.nature.com/news/physicists-make-weather-forecasts-for-economies-1.16963 or http://www.nature.com/nature/journal/v497/n7447/full/nature12047.html. Or, physicists who just lay their opinions down with no backing, like this definitely-not-true story: http://physics.ucsd.edu/do-the-math/2012/04/economist-meets-physicist/.

      “What (some) experienced real world / applied / experimental physisicsts can bring to the table, is an eye for statistical noise, a robust aversion against overfitting (too many meaningless parameters and variables), and a penchant for what a crucial (potentially deadly) question for a certain model would be”

      I honestly have no idea what this means.

    • “What (some) experienced real world / applied / experimental physisicsts can bring to the table, is an eye for statistical noise, a robust aversion against overfitting (too many meaningless parameters and variables), and a penchant for what a crucial (potentially deadly) question for a certain model would be”

      Any good quantitative researcher should have these traits. And indeed we teach all of this in all econometrics courses (except for “question”, which is more of a PhD topic, covered throughout any good PhD program).

      I’ve participated in several pluri-disciplinary research projects, and sadly, in my experience the value-added is negative.

  11. Jack,

    that some artifically organized academic mulit-disciplinary often does not work, comes at no surprise.

    ZC, that some others make bold statements with little detailed knowledge, is not my fault, and is precisely what we critizise about american economists dishing out unrequested advice to Europe.

    I did my required (and critical) reading on economics, textbooks, special topics, and papers.

    I did explain to Mr. Noah Smith, why Krugmans 1991 paper to geo spatial is crap.

    But maybe you or somebody else here likes to tell me just one PAPER of Krugman (preferable the 1991, which was named to have contributed to his nobel prize), that he considers to be good, explains in a few sentences, why he thinks so, and is then willing to defend it against my counter argument.

    I believe that could lead to some valuable insights, from a real world physicist like me : – )

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