Agents, Equations and Economics

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Critiques of Neoclassical Economics extend, unsurprisingly, to its mathematical structure.  The discussion has largely focused on General Equilibrium Theory (GET), a set of differential equations developed by Léon Walras over a century ago.  Internally consistent, but highly unrealistic, GET lacks predictive power, and has been a historical failure.  As an alternative, this article proposes a methodology largely developed by Gräbner et al. (2019), in which Agent-Based Models (ABMs) are correlated with existing Equation-Based Models (EBMs) as a means of developing a more powerful formalism.  The approach is illustrated by application to the Arrow-Debreu (AD) model of Neoclassical theory, and the Kuznets Curve of Developmental Economics.  Broader implications for the social and natural sciences are briefly considered.

Posted for comments on 6 Oct 2020, 3:54 pm.

Comments (3)

  • Claudius Gräbner-Radkowitsch says:

    This is an interesting essay on the methodological problems of neoclassical economics and potential avenues for a more pluralist approach to social sciences, and economics in particular. I enjoyed reading the short essay and I see a potential contribution to this journal, yet I also believe that some fundamental revisions are necessary. Below I list the points that I found most problematic, and I make some suggestions of how they might be addressed. I hope these comments will be useful to the authors when revising his work. Several of the issues I mentioned require some extra space, but since the paper is extremely short at the moment, I believe that this would rather contribute to its quality.

    Major issues to be addressed

    I would not use the distinction between agent-based and equation-based models. Rather, I suggest using the distinction proposed by Weisberg (2013) between computational and mathematical models.
    The reason is that while both not 100% correct from a puristic viewpoint (as also acknowledged by the authors), Weisberg’s distinction is more closely aligned with the relevant philosophical literature, and he discusses the kinds of models in more depth.

    I am not convinced that the Gräbner et al. methodology really operates at the same level as GET?
    It seems to me that the proposal of Gräbner et al. is more like a general methodological approach that tries to bring together strengths and weaknesses of computational and mathematical models.
    It is, in this case, more general than GET, which is a very particular theory. I would rather argue that the approach of Gräbner et al. helps clarifying the limits of what GET can represent and explain.

    Moreover, the approach of Gräbner et al. is a pragmatic one that tries to communicate with the EBM mainstream, but also to formally illustrate what it could gain from adopting a more pluralist attitude towards methodologies. The benefit from this pluralism stems from the fact that models have different strengths and weaknesses. ABM and EBM are complementary in this sense, since the former can be more complex and realistic, but the latter is more transparent and easier to verify. I suggest that the author has a look at Gräbner (2018) and the references therein, especially the section on trade-offs in modelling. It is also important, in my view, to refer to this trade-off at the end of section 2.

    At the beginning of section 2 the author claims that the dictum of Friedman according to which wrong assumptions may yield better theories is, in my view, inconsistent with the practice of neoclassical economics. Many scholars at least claim to build models with more and more realistic assumptions – although they stick to the central concepts of ‘utility maximisation’ and ‘equilibrium’. Nevertheless, more realistic assumptions are generally considered something positive. Maybe the author can comment on this. Personally, I feel that neoclassical economics is defined more by its methodological commitments to the maximization-cum-equilibrium approach, rather that to an commitment to instrumentalism a la Friedman.

    The link to Gerard Debreu at the top of page two is not clear to me. Debreu is making an argument about how models are linked to their targets, not about the relevance of their assumptions. At least this was my reading. Maybe the author can modify his exposition or explain it in a bit more detail?

    I think the exposition of the Kuznets example on pages 4ff requires careful revision:
    First, the author refers to an x-axis and a y-axis, but the figure is missing. It should be added to the article and the reference to it should be clarified.
    Second, I would put the sentence in brackets, starting with “(In an important variation…” Into a footnote.
    Third, the EBM under question was not developed by Gräbner et al., but by Acemoglu and Robinson (2002). Gräbner et al. then added dynamic features and assortative matching to this original model, developing it into an ABM.
    Fourth, a central contribution of the Gräbner et al. paper was that it facilitates an empirical test of the Kuznets hypothesis since it contains a clear hypothesis with regard to its timing. I suggest looking into this in the paper more clearly. I also want to add that the contribution was not meant as a defence of the Kuznets curve, but as an illustration of how the principle of ‘sequential modelling” might work. In the end, the paper is a strong argument for methodological pluralism.

    Minor inconsistencies, ambiguities or mistakes that should be resolved

    At least to my knowledge, General Equilibrium Theory is not (necessarily) built on differential equations. As far as I know, Arrow and Debreu (1954), for instance, do not use differential equations.

    While I share the author’s critical attitude towards neoclassical economics, I also believe one should treat the research project fair. This includes to acknowledge that neoclassical (or ‘mainstream’) models now frequently include imperfect competition and unemployment, or, more broadly, inefficient equilibria. This is most obvious in the case of macroeconomics, where the dominant Dynamic Stochastic General Equilibrium (DSGE) models have these features, despite being general equilibrium models (see Christiano et al. (2018) for a defence of these models; while I do not think their defence is successful, it clarifies many misunderstandings about what these modes are capable of). So, my recommendation for the present article would be to remove wrong accusations, such as in the second sentence in the introduction, and to stick to the central argument that general equilibrium models have serious deficits.

    In the introduction the author writes that neoclassical models “did not anticipate economic shocks”. I suppose it would be clearer to speak of “economic crisis” since “shocks” in these models often refer to “technological” or “monetary policy” shocks, which are by definition exogenous and do not seem to be what the author is referring to.

    On page 2, the authors writes “The rationale is twofold”. But I was not able to finde the second point mentioned. Also, I did not fully understand the reference to the Church-Turing Thesis. Maybe the author could elaborate on this issue in a little more depth?

    On page 2, I suggest adding a footnote explaining the von Neumann bottleneck problem.

    In the last paragraph in the introduction the author claims that realist approaches “provide greater information regarding the systems under study” and, thereby, “yield higher predictive power”. While the first point should be clarified a bit more (information in which sense?), the second point is not correct, or at least imprecise. See the elaborations on trade-offs in modelling in Gräbner (2018) mentioned above.

    Page 3: I think it would be useful to explain what Friedman means with invariant relations.

    P. 5: I would not say that EBM can be correlated with ABM, but that EBM could be complemented and developed into ABM during the course of sequential modelling.

    I would suggest that the author has a look at the following two papers, which might be of interest for his undertaking: Boldyrev and Ushakov (2018), which contains a lot of historical information of GET in the post-war period, and Törnberg and Uitermark (2021), which contains a (different) heterodox reading of computational modelling.

    Finally, the paper should undergo a careful spell check since it contains numerous typos.


    Acemoglu, D., & Robinson, J. A. (2002). The Political Economy of the Kuznets Curve. Review of Development Economics, 6(2), 183–203.

    Boldyrev, I., & Ushakov, A. (2016). Adjusting the model to adjust the world: constructive mechanisms in postwar general equilibrium theory. Journal of Economic Methodology, 23(1), 38–56.

    Christiano, L. J., Eichenbaum, M. S., & Trabandt, M. (2018). On DSGE Models. Journal of Economic Perspectives, 32(3), 113–140.

    Gräbner, C. (2018). How to Relate Models to Reality? An Epistemological Framework for the Validation and Verification of Computational Models. Journal of Artificial Societies and Simulation, 21(3).

    Törnberg, P., & Uitermark, J. (2021). For a heterodox computational social science. Big Data & Society, 8(2), 205395172110477.

    Weisberg, M. (2013): Simulation and Similarity. New York: Oxford University Press.


    I hope these comments are useful to the author when revising this interesting manuscript!

  • Simon D Angus (Monash University) says:

    This is another helpful contribution to the discourse on Economics methodologies and the inherent complexity of the phenomenon under study. That said, I feel that this essay will benefit from both a fairer treatment of the methodological options on the table, and by interacting with literature which has made similar points before in a variety of ways. In my comments below I aim to provide suggestions on both of these points.

    The main thrust of the paper — that neo-classical/GET economics has ‘failed’, and that agent-based-models (ABMs) should provide an alternative, needs some refinement in my opinion.

    Let us agree that economic systems are complex (adaptive) systems. The question then becomes, what is the appropriate formalism to represent their dynamics, at the scale of inquiry, and for the research question at hand? We have at our disposal a range of tools, from mean-field approaches (e.g. GET) to systems-dynamics approaches (e.g. CGE models), through to meso- or micro- based agent models (e.g. ABMs). To this spectrum, Wallace argues we should consider the GET (and even CGE?) end worthy to be discarded, and instead, shift only to the ABM end. With such a perspective, the diagnosis of the problem, and the remedy, can be seen as overly severe. Or at least, one would need very convincing evidence to proceed with such a limited toolset.

    Yet, if we look to other fields who have grappled with complex phenomena, we do not see the abandonment of mean-field approaches. Ecological sciences, as Wallace notes, have embraced a ‘both/and’ approach, using both coupled dynamical systems to get at mean-field predator-prey dynamics, and ABMs to get at more complex second-order effects in larger food-webs. Epidemiology has continued (and especially so, during the COVID-19 era) to provide insights with models ranging from entirely standard few-type SIR systems models, through to many-type block-models, through to ABMs. Each has given helpful insights and predictions at different levels of infectiousness and different scale contexts. Physics persists with mean-field gas models through to dynamical systems, and then computational fluid or kinetic models. .. We could go on.

    In the Economic sciences, yes, there are notable ‘failures’ of one framework or another to make accurate predictions (or testable predictions at all), but many contexts, and scales, still have a strong place for a mean-field, general equilibrium formalism. I would point to the theory of games as a strong example of the kind of systems I have in mind. On the one hand, from spectrum auctions, through to rock-paper-scissors, the rational formalism of game theory provides strongly grounded, and accurate models of behaviour. On the other, in large, statistical or small-world networks, ABMs or numerical simulation of quasi-agent models are increasingly being used to understand lab and field experimental results, to model games on networks, or games which build networks themselves.

    My point is that the substitutionary thesis of the paper, I believe, is not warranted either from the experience of other sciences, or within branches of economics itself. I would thus urge Wallace to consider a far more complementary tone in this work, and consider a future in which our formalism is matched well to the problem at hand. With my own students who often come excitedly to propose an ‘ABM approach’, my first question is always, ‘why do you think an ABM is appropriate for this problem, at this scale?’ As a practitioner, if one can avoid implementing (and defending all model choices therein) an ABM, so much the better!

    My second main suggestion is that Wallace incorporate literature which has made, or is making, something of the same critique before. Here, the options are rather abundant, and Wallace would do well to consider how to integrate these voices, and determine the unique contribution of the present work, given that context. Here is just a quick, but no means comprehensive flight in this literature:
    – Arthur (2021) – Economics in Nouns and Verbs
    – Arthur (2021) – Foundations of complexity economics
    – Arthur (2010) – Complexity, the Santa Fe approach, and non-equilibrium economics
    – Dosi et al. (2020) – ‘Rational heuristics? Expectations and behaviors in evolving economies with heterogeneous interacting agents’
    – Dosi et al. (2010) – Schumpeter meeting Keynes: A policy-friendly model of endogenous growth and business cycles
    – Farmer et al. (2015) – A Third Wave in the Economics of Climate Change
    – Farmer (2012) – Economics needs to treat the economy as a complex system

  • Ron Wallace says:

    I appreciate this detailed and valuable commentary.
    I will be reviewing the resources you provided and making necessary changes.
    Ron Wallace

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