Economics, Equilibrium Methods, and Multi-Scale Modeling

Abstract

In this paper, I draw a parallel between the stability of physical systems and that of economic ones, such as the US financial system. I argue that the use of equilibrium assumptions is central to the analysis of dynamic behavior for both kinds of systems, and that we ought to interpret such idealizing strategies as footholds for causal exploration and explanation. Our considerations suggest multi-scale modeling as a natural home for such reasoning strategies, which can provide a backdrop for the assessment and (hopefully) prevention of financial crises. Equilibrium assumptions are critical elements of the epistemic scaffolding that make up multi-scale models, which we should understand as a means of constructing explanations of dynamic behavior.

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Notes

  1. 1.

    The other option would have been to invest in US treasury bonds, but investors wanted high-return low-risk investments and Greenspan wasn’t keen on raising the federal interest rate at that time.

  2. 2.

    For more details, see Davidson and Blumberg (2008).

  3. 3.

    See Hamilton (2009) for a summary of tranches.

  4. 4.

    For a discussion of risk distribution and absorption, see DiMartino and Duca (2007).

  5. 5.

    In the US economy, government sponsored enterprises (GSEs) are the largest of these institutions that sets the underwriting standards. Stable economies in Europe have a high market concentration of securitizers—that is, a small number of firms control the industry overall—and fairly rigid underwriting practices. That means these institutions were less able to offer things like subprime mortgages.

  6. 6.

    There are some, however, who don’t think this—Earman et al. (2002) think that differential equations that describe system evolution are themselves not laws. On the other hand, they also admit of classical thermodynamics as delivering real laws, because they claim that thermodynamics reduces to statistical mechanics.

  7. 7.

    Extensive literature on the status of ceteris paribus laws is testament to this (see Earman and Roberts 1999; Fodor 1974; Fodor 1991; Pietroski and Rey 1995; Schurz 2001; Woodward 2003 for a non-exhaustive discussion). In fact, the more general field of literature simply devoted to asking the question of whether or not there are social science laws is enough to indicate that there seems to be a well-accepted demarcation between laws of physics and other fields.

  8. 8.

    This makes our analysis convenient, because it requires using fewer state variables to describe our system when it’s at equilibrium.

  9. 9.

    More specifically, we would require the processes to approximate quasi-static loci—the pathway on the surface of a hyper-surface representing the fundamental equation that describes the system in configuration space (Callen 1960, 59).

  10. 10.

    This implies that a system will undergo changes, and thus spend time out of equilibrium, which classical thermodynamics cannot handle with its own resources. In particular, in classical thermodynamics all the equations we see are state equations. For example, one familiar state equation is the following: PV = nRT, the ideal gas law. In order to specify the state variables that characterize the system in question, it’s presupposed that the system is at equilibrium. We simply do not have the vocabulary in classical thermodynamics to talk about a system that is out of equilibrium, though other extensions—such as disequilibrium thermodynamics—attempt to do so.

  11. 11.

    That is, there is a robust formal analogy—though not necessarily a substantive one—between the two fields in terms of how they employ equilibrium analysis.

    There is really nothing more pathetic than to have an economist or a retired engineer try to force analogies between the concepts of physics and the concepts of economics…However, if you look upon the monopolistic firm hiring ninety-nine inputs as an example of a maximum system, you can connect up its structural relations with those that prevail for an entropy-maximizing thermodynamic system. Pressure and volume, and for that matter absolute temperature and entropy, have to each other the same conjugate or dualistic relation that the wage rate has to labor… (Samuelson 1970).

  12. 12.

    See Jhun (2018) for a lengthier defense of this claim. One could understand this interpretation of equilibrium idealization as providing a methodological backdrop to Cartwright’s (1989) account of causal capacities and the nomological machines (1999, 2007) that isolate them.

  13. 13.

    Whether mechanistic perspectives escape this is hard to say, and depends on the particular view in question. Certainly, views that do not distinguish between mechanistic, organized behavior and merely aggregative behavior will fail to do so. See Machamer et al (2000), Bechtel and Abrahamson (2005), Craver (2007) and Kaplan and Craver (2011). The danger, even with mechanistic perspectives, is failing to take seriously inter-level relations.

  14. 14.

    See Butterfield and Bouatta (2011) for this view, and Batterman (2013) for an argument against. For discussion of multi-scale systems and modeling, see also Bokulich and Oreskes (2017), Bursten (2016), and Batterman and Rice (2014). Green (2013) and Winsberg (2006).

  15. 15.

    We can think of the “dominant behavior” of the scale, says Wilson as that manifested by: “central physical processes normally witnessed at [a system’s] characteristic scale length” (19).

  16. 16.

    For the aggregate function to depend only on societal income and the price (in addition other usual restrictions, e.g. that demand curves all be independent) the preferences of the individual need to be identical and quasi-homothetic. Then there’s the further problem of whether equilibria can be unique. In a two-agent, two-commodity exchange economy, if agents view commodities either as perfect substitutes or as perfect complements, there is no unique equilibrium. Rather there is a continuum of equilibria.

  17. 17.

    The only things that do seem to carry over is homogeneity of degree zero, continuity, and obeying Walras’ Law (excess market demand/supply is zero) and boundary behavior when prices approach zero.

  18. 18.

    Efforts in this direction do not, thus far, seem especially successful or satisfying. Grandmont (1992) and Hildenbrand (1994) are two well-known attempts that recognize the role of meso-scale details, in particular population heterogeneity, in achieving stable equilibrium.

  19. 19.

    One might worry that physics and economics are disanalogous because the latter includes self-conscious agents. For instance, as per the Lucas Critique, the economy is receptive to the policies it sets for itself and will adjust accordingly. While we agree that this is, indeed, a problem for economists, it is not troublesome for our methodological point. Suppose we agree that even in principle, most physical systems of interest could not be explained bottom–up. Properties such as elasticity require structural features that simply cannot be seen at the microscale, despite depending on there being one. But so long as goings-on at the microscale can be thought of as responsive to (even if not adaptive in the same kind of way) other scale goings-on, then it seems like the moral still stands: that equilibrium reasoning helps us identify relevant scales when it comes to the purposes of modeling because it tells us something about what kinds of behaviors we do (or don’t) expect to see, and that multi-scale modeling is a route to integrate different scales together (which may exhibit different dominant behaviors). In fact, this may very well be a promising way of addressing the Lucas Critique. We thank an anonymous referee for pressing on this point.

  20. 20.

    As a disclaimer that not all physical phenomena that we usually associate as lagging behavior, off-equilibrium behavior, and the like, need be due to be frictional forces strictly speaking. For example, one might expect lags to occur when two bodies exert force against one another without sliding (think normal force). This derives from the gravitational force multiplied by the mass of the object itself. These may not be frictional forces, but different kinds of interactions. Thus we ought to be cautious in drawing any substantive analogies in economics to one of “friction” in physics.

  21. 21.

    In engineering this is what they call “metastable” rather than just merely stable.

  22. 22.

    Note that there is no such thing as the meso-scale, so there may be many structures spread over several scales.

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Jhun, J. Economics, Equilibrium Methods, and Multi-Scale Modeling. Erkenn (2019). https://doi.org/10.1007/s10670-019-00113-6

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