Richard Bookstaber is a PhD economist experienced in both the financial industry and government policy-making. For such a person to write this book is doubly courageous. First, he is challenging his colleagues, claiming that the orthodoxy of neoclassical economics cannot understand, let alone predict or correct, financial crises. Second, his alternative, agent-based modeling, is a sophisticated branch of computer science (CS), which he runs the risk of misrepresenting.

As a cogent challenge to the neoclassical consensus and an explanation of why agent-based models are necessary, the volume is brilliant. In highly readable prose, Bookstaber identifies the “four horsemen of the econopalypse,” basic insights of complexity science that govern economic crises. The introductory section of the book outlines these insights, which Section 2 develops in detail. “Emergent behavior” is the characteristic of a system whose overall behavior cannot be predicted from the individual components, but emerges from their interaction. “Non-ergodicity” is a system’s dependence on its past history, making it difficult to gather meaningful statistics that can be reused in other settings. “Radical uncertainty” captures the open nature of the real world: surprises happen, and by definition, we cannot anticipate them. “Computational irreducibility” means that there is no quicker way to tell what a system will do than to let it run. Analytically tractable closed-form mathematical summaries of its behavior do not exist.

Bookstaber abandons neoclassical analysis in favor of agent-based models. Such models represent each player in the economy (producers and consumers of goods, financial institutions, government agencies) with a computer agent whose code embodies not an idealistic representation of perfect rationality, but rules of thumb based on observation of what the corresponding real-world actor does. Section 3 shows how the four features of Section 2 manifest themselves in the economy and introduces the vision of an agent-based model, while Section 4 outlines such a model and uses it to elucidate the crash of October 19, 1987, the flash crash of May 6, 2010, and the global meltdown of 2008. An agent-based model cannot predict such events, but it does provide a sandbox to explore a broad range of possible futures and experiment on the possible impacts of alternative responses to events.

The bottom line is that economists must abandon the idea of a rigorous theory yielding crisp predictions. The four horsemen do not allow us to derive a number in answer to our questions. They do let us engage alternative narratives in decision-making.

It remains to be seen how academic economists will receive Bookstaber’s criticisms, but the cogency of his arguments, together with the failure of the current orthodoxy in the face of modern financial crises, deserves the close attention of practitioners in the trenches of investment banks and regulatory agencies. The book must be judged a success in engaging its first challenge of showing the inadequacy of the accepted approach and charting a path forward using agent-based models.

The book is less successful with the second challenge. Bookstaber repeatedly contrasts mathematical systems based on axioms with systems involving humans with their subjective feelings, and traces his four horsemen to the intimate engagement of people with the system. He attributes computational irreducibility to “the sickening feeling in a panicky investor’s stomach” (p. 19), and argues that there would be no need of an agent-based model to manage a system without humans, such as a system of self-driving cars (p. 189). In fact, all four horsemen appear in formal, axiomatic systems. The heart of the problem is not humans, but nonlinearity. An agent-based model is a computer program, which is a formally defined mathematical artifact. And agent-based models are very much necessary (and widely used) to study the performance of systems of multiple interacting robots. The appropriate contrast is not between mathematics and people, but between systems that can be characterized by a closed-form equation, and those that can only be characterized by an algorithm. Neoclassical economics seeks analytic solutions to equations. Agent-based modeling runs the algorithm, defined in terms of heuristics, to see what it does.

Bookstaber’s claim that people cannot be captured mathematically reflects the growing dissatisfaction among economists with the idealization of a rational actor, marked as early as 2002 by the award of the Nobel Prize in Economics to a psychologist, Daniel Kahneman, for documenting the “irrationality” of many human decisions [1]. But more recent work [2] suggests that the phenomena observed by Kahneman and Tversky reflect not a lack of rationality, but a different kind of rationality with its own axiomatic structure. The problem with neoclassical economics is not that it is mathematical, but that it is based on the wrong mathematics.

Readers of Computing Reviews, coming from the CS community, might dismiss the book because of these imprecisions, but that would miss the point. Here we have an expert in economics arguing cogently (and correctly) that his discipline needs an advanced technology. Most technologists know the frustration of trying to push their technologies out to users. Now a user is vigorously pulling our technology into his problems. His effort is courageous and, in terms of the substance of his argument, successful, and rewarding to those of us who have developed the technology that he is advocating.

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