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The Blanket Shotgun Process

How does behaviour evolve over time? Imitation, Exploitation and Innovation
The Blanket Shotgun Process

In undergraduate economics I was introduced to equilibrium concepts, preferences in utility functions, and rational forward-looking expectations. Using mathematical tools, we could find solutions to well-defined questions (e.g. international trade through competitive advantage, game theoretic outcomes, prices of goods in clearing markets). In other words, we solved problems of allocation that deal with quantities. In graduate school this continued, though we introduced some frictions such as imperfect information, bounded rationality, and probabilistic uncertainty.

Yet this setup doesn't yield satisfactory, if any, answers to questions of formation in the economy. To quote W Brian Arthur, formation in the economy is about processes such as "economic development, discovering novel technologies, structural change, arrival of new institutions, temporary phenomena like bubbles, crashes...". To answer these questions we need theories of how behavior evolves over time.

Why? There are two aspects of our economy to consider here: (1) complexity, i.e. even perfect knowledge of individual behavior doesn't mean knowledge of macroeconomic outcomes (more is different), and (2) uncertainty, i.e. the absence of a trivial probabilistic mapping between the set of possible actions and the set of resulting states of the world. In such an environment rationality can only be bounded (Simon, 1955) and thus our behavior is procedural and adaptive.

There isn't a single best behavior over time. As the environment (such as societal norms and institutions or the state of the economy) changes, some heuristics might be more successful than others. For instance, high leverage ratios are great in booms and terrible in busts. We adapt our strategy to our environment we are in, even if we do not do so quickly. For example, in financial markets different investment strategies are successful at different moments (see this recent paper by Scholl, Calinescu, and Farmer).

This week, I take a look Seppecher, Salle, and Lang's paper Is the market really a good teacher? which applies blanket shotgun approach to firm's behavior with respect to how much debt they wish to take on. They show that in complex evolving economies - market processes do not lead to the selection of optimal behaviors because the characterization of successful behaviors itself constantly evolves as a result of the market conditions that the behaviors contribute to shaping

Evolving behavior

Why is modeling agent behavior so tough?

An ABM tends to have two important features: (1) Complexity, i.e. even perfect knowledge of individual behavior does not mean knowledge of macroeconomic outcomes (more is different), and (2) uncertainty, i.e. there is no trivial probabilistic mapping between the set of possible actions and the resulting states of the world. Therefore, Simon (1955) argues rationality can only be bounded, it is adaptive and procedural.

What does this imply? Rather than modeling a constant behavioral rule, we should pick an algorithm by which agents in the economy update their behavior. Rather than trying to find the optimum rule (e.g. maximum payoff), we focus on the best tradeoff between exploring new rules and exploiting currently functioning rules (multi-armed bandit problem of Holland). This notion has been explored extensively in the heterogeneous agent literature (see Brock and Hommes 1997 for a fixed set of heuristics and Anufriev et al. 2015 for an evolving set), and it isn't an easy task.

Social Learning and the Ecology of Competition

There are two strands of learning, or an ecology of competition (March, 1991) - agents adapt behavior both in response to the macro environment as well as based on interactions (interdependence) at the micro level.

Seppecher & Salle distinguish between learning at the individual and social level. Individual learning is a trial-and-error process of sequentially testing different strategies. Social learning is analogous to considering each agent as a strategy, and "adaptation intervenes at the population level".  In market economies this means "survival of the fittest".

Economists have used genetic algorithms to approximate such a process. However, this suffers from several limitations: (1) it is hard to interpret them, (2) they are developed in static problems and so they perform badly in changing environments, (3) economic literature has focused on the conditions under which these algorithms leading to coordination on the optimal state.

The Blanket Shotgun Process (BSP)

The BSP is a description of the co-evolution of market selection and behavioral adaptation through three operations:

  1. Natural Selection: positive profits are considered successful and survive (this is a satisfycing criterion - as opposed to the common maximal profits)
  2. Innovation: intervenes at any time, even in case of positive profits, through trial-and-error (Alchian's extreme hypothesis of random, blind and unintentional exploration - see persistent search in Winter 1971)
  3. Imitation: operating characteristics of successful firms are copied inexactly by non-successful firms

Two observations: Firstly, the imitation process is triggered only at default, i.e. by a market mechanism, making it endogenous rather than dependent on a fixed probability. Secondly, there is an almost 100% weighting on exploration vis-à-vis exploitation. There is a perpetual changing of the system due to the random innovations and hence the environment. This reinforces the adaptability of the system.


In the paper, Seppecher and Salle build on their JAMEL framework for ABMs (See 2015 paper), and incorporate the BSP in the choice of leverage strategies by the firm. The choice is motivated by the idea that the leverage choice has a tricky trade-off: continuous debt-financed increase in capacity vs. financial safety at low debt levels (insufficient capital due to low investment).

The results are intriguing but feel expected. Decentralized market selection (meeting only a subset of buyers/sellers) together with the BSP implies that firms are continuously and collectively adapting their leverage strategies. This comes at the price of wild fluctuations and deep downturns. There is a causal cycle too as there are alternating patterns. During a boom phase there is a rise in indebtedness, which feeds into goods demand. At some point it is unsustainable (financial fragility, increased interest rates, and excess production) leading to a very brutal deleveraging cycle due to to unavoidable insolvency and bankruptcy. At this point the cycle repeats, in a simple version of Minsky's financial instability hypothesis.

The key note is that there does not appear to be a statistical steady state, though this hasn't been explicitly investigated. Consequently, the economy, as modelled in this ABM, does not result in collective optimisation or convergence to an "optimal" equilibrium. Seppecher and Salle suggest that we should thus consider an evolutionary characterization of a crisis. Namely, the point where the evolution of the macroeconomic system becomes faster than the adaptation capabilities of the agents that populate it (e.g. run-away investment and indebtedness where demand cannot catch up).

Is this the way to go?

The results of the paper are not entirely new. Similar works on cyclical behavior based on evolutionary innovation/exploitation trade-offs exist. However, this is the first application within a macroeconomic ABM (at least that I know of).

There are two very cool aspects that I like about this particular modeling strategy:

  1. This model already endogenizes the tradeoff between exploitation vs. innovation (higher exploitation in downturns, higher innovation in booms), which is great.
  2. Innovation and change can happen at any particular moment for any firm, and transfer of exploitation is also a noisy experience. This very much captures the randomness of innovation that may occur at different stages of the firm. The persistent search of Winter (1971)

What I would love to see is the presence of some intentionality in the innovation investment or the like. I also do think that it is very important to explicitly pay attention to firm entry and exit. In this model the number of firms are constant and they are essentially "replaced" with an imitation technology. I would prefer if some firms can choose to try to exploit and innovate, and new firms enter on the basis of a "better technology" of some form. Alas, in this model Seppecher and Salle look at leverage ratios rather than different products. How would one model the differentiation in products and production technology in this manner? As well as, how do we model information flows within the economy for the purposes of imitation.

I think this type of behavioral modelling in ABM is the way forward, namely that the behavior of all the agents changes on the basis of their interactions and the changes in the environment itself. This endogenizes the behaviors of the agents. It focuses our attention on how agents might learn or make mistakes in learning rather finding the optimal parameter for a constant behavioral rule. Modelling the innovation/exploitation trade-off might also be an explanandum for the various behavioral biases that have been documented by behavioral economists in recent years (there are ~190 of them by now). It would leave behaviors to adapt and evolve endogenously. Therewith we reduce the parameter space (only initial conditions and random seed) such that we can (1) explicitly collect and use data as starting points, and (2) focus on the structural and institutional aspects of the economy together with policy-choices.

My biggest question is how would we know which is the right algorithm? And what is the distribution of innovations? (We will never know the latter). What Seppecher and Salle abstract from is intentional investment into innovation (as in e.g. the Keynes meets Schumpeter literature with the Island's growth model)

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