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Derivational robustness, credible substitute systems and mathematical economic models: the case of stability analysis in Walrasian general equilibrium theory

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Abstract

This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers who have offered a general epistemic justification of such practices.

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Notes

  1. There is not complete agreement on how exactly the terms “idealization” and “isolation” should be used in these discussions. See Morgan (2012, pp. 137, 158) and Morgan and Knuuttila (2012, p. 51) on this issue.

  2. Influential defenders of the isolationist account in the recent literature on economic models include Nancy Cartwight (e.g., 1991) and Uskali Mäki (e.g., 1994, 2009a).

  3. A substitute system is Mäki’s term for a model that is “a freely floating subject of inquiry, unconstrained by any real concern as to how it might be connected to real world facts” and they are “strong failures of representation” (Mäki 2009b, p. 36). For Mäki the alternative to a substitute system is a surrogate system that adequately represents (or at least is intended to represent) the relevant target, but many would argue there is a third alternative – I will use the term credible-substitute models—that do tell us something about certain aspects of the economic world. We learn from them, make inferences with them, and assess credibility-increasing and credibility-decreasing moves within them, while they still tell us less about real economies than fully representational models.

  4. The word “competing” needs to be clarified here. Most who support some version of a fictionalist account would agree that certain economic models do satisfy the requirements of the isolationist account. The problem is that many do not, and these models are often the most influential work economists produce. The problem is not that the isolationist view is incorrect, it is simply that it is not applicable to important theoretical modeling in economics, some of which, the defenders of fictionalist views assert, can also be justified. In other words, isolation may be sufficient for the success of models, but it is not necessary (Grüne-Yanoff 2011; Knuuttila 2009, 2011). Perhaps the best way to think about the issue is to draw an analogy with a much earlier debate in the philosophy of science. Ian Hacking once said that Popper took the positivist dichotomy of science vs. metaphysics/muck and converted it into the three-way distinction of science vs. metaphysics vs. muck (Hacking 1979, pp. 384–385). Similarly, we could replace the isolationist dichotomy of surrogate vs. substitute/muck with an alternative three-way distinction of surrogate vs. credible substitute vs. muck.

  5. The fictionalist view is sometimes called constructionist, but I will employ only the former term to avoid confusion with constructionist views within the sociology of science.

  6. Contributions to this literature include: Cartwright 2009; de Rodríguez and Zamora Bonilla 2009; Grüne-Yanoff 2009a, 2009b, 2011, 2013; Knuuttila 2005, 2009, 2011; Kuorikoski and Lehtinen 2009; Mäki 2009b, 2013; Morgan and Knuuttila 2012; Sugden 2000, 2009; and Weisberg 2007, 2013.

  7. This is a modified version of the characterization of robustness in Odenbaugh and Alexandrova, (2011, p. 764).

  8. The recent literature supporting various types of robustness analysis in economics includes: Guala and Salanti 2003; Kuorikoski and Lehtinen 2009; Kuorikoski et al. 2010, 2012; Lehtinen and Kuorikoski 2007; Lehtinen and Marchionni 2011; Weisberg 2013; and Woodward 2006. For critical remarks on robustness analysis see Cartwright (1991, 2007, 2009), Odenbaugh and Alexandrova (2011), and Reiss (2012). It should be noted that robustness analysis is also an important topic in the philosophy of biology (particularly in systems biology and ecology) and many of the papers discussing robustness in economics also consider biology. I will only be concerned with economics.

  9. “By a model ‘result’ we mean any proposition derivable from a model that is thought to be epistemically or cognitively important in the appropriate scientific community” (Kuorikoski et al. 2010, p. 545).

  10. The assumptions of a perfectly competitive economy also demonstrate how difficult it is to classify the various types of assumptions used in economic models (i.e., how a single assumption can play multiple roles). The key assumption of price-taking behavior is a substantive assumption about the behavior of the agents in the model (and is approximated by some real world agents), yet it is also a very effective tractability assumption since taking prices as parameters greatly simplifies the application of differential calculus to such models.

  11. Attention was given to perfect competition in the work on idealization in economics published in the 1980s and 1990s (e.g., Hamminga 1983 and various papers in Hamminga and De Marchi 1994), but it has received much less attention in the recent literature. Mäki (2001) discusses perfect competition, but from the viewpoint of three economists who criticize it.

  12. McKenzie (2002) provides a fairly recent survey of this type of general equilibrium theory, Quirk and Saposnik (1968) is a text from the period that emphasized stability, and Hahn (1982) provides a useful survey. See Ingrao and Israel (1990) for historical discussion.

  13. For our purposes we can assume p* > 0.

  14. Other specifications were used in the literature such as dpi/dt = kiZi(p) with ki > 0 and dpi/dt = Hi[Zi(p)] with Hi’ > 0, but these differences can be neglected here. These, like (T), are systems of ordinary differential equations where prices change in the direction of excess demand.

  15. Takayama’s symbolism was changed to be consistent with the symbolism used in this paper.

  16. I note in passing that these concerns did motivate economists to try to develop models without some of the undesirable features of (T) – in particular to allow for disequilibrium trading—but the research project was never very successful: see chapter thirteen of Arrow and Hahn (1971) for a survey of the results at that time.

  17. This belief can be thought of as what Mäki calls the ontological way the world works (www) constraint on scientific theorizing. Various scientific communities (and research programs within those communities) have commitments to particular “causal processes that constitute the ways the world works” (Mäki 2001, p. 371) and for most economists that commitment was (and is) to the rational actions of individual agents, not central planners or mechanisms that represent the behavior of a central planner, as the ultimate cause of market phenomena.

  18. See Hands and Mirowski (1998) and the references therein for a discussion of these various testing efforts.

  19. One might think about this as an example of the hierarchy of models (Suppes 1962, 1967), but I will not pursue this idea here.

  20. There is also an argument that robustness analysis in general is only relevant to directional changes, but commitment to this view is not necessary for the argument offered here.

  21. Being a Giffen good means that the good is inferior (consumption decreases with increases in income) and given the budget constraint associated with the standard utility-maximization problem, not all goods can be inferior.

  22. Kuorikoski, Lehtinen and Marchionni do recognize that an assumptions that have dual roles—“a single explicitly stated modelling assumption may simultaneously encode a tractability assumption as well as a substantial assumption” (2010, p. 548)—but do not have a separate category for such assumptions or explicitly define the property of having an economic interpretation.

  23. “There seem to be no examples in the literature of utility and production functions which yield diagonal dominance other than of course the GS case” (Hahn 1982, p. 759)

  24. The most important papers were Debreu (1974), Mantel (1974), and Sonnenschein (1972, 1973). See Shafer and Sonnenschein (1982) for a survey, and Hands (2012), Ingrao and Israel (1990), and Rizvi (2006) for historical discussions.

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  1. Department of Economics, University of Puget Sound, Tacoma, WA, 98416, USA

    D. Wade Hands

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Correspondence to D. Wade Hands.

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Helpful comments on earlier drafts were received from Aki Lehtinen, Caterina Marchionni, and two anonymous referees.

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Hands, D.W. Derivational robustness, credible substitute systems and mathematical economic models: the case of stability analysis in Walrasian general equilibrium theory. Euro Jnl Phil Sci 6, 31–53 (2016). https://doi.org/10.1007/s13194-015-0130-0

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