An Agent-Based Simulation of the Stolper–Samuelson Effect

Abstract

We demonstrate that agent-based simulations can exhibit results in line with classic macroeconomic theory. In particular, we present an agent-based simulation of an Arrow–Debreu economy that accurately exhibits the Stolper–Samuelson effect as an emergent property. Absent of a Walrasian auctioneer or any other central coordination, we let firm and consumer agents of different types interact in an open, money-driven market. Exogenous preference shocks result in price and wage shifts that are in accordance with the general equilibrium solution, not only qualitatively but also quantitatively with high accuracy. Key to this achievement are three independent measures. First, we overcome the poor input synchronization of conventional price finding heuristics of firms in agent-based models by introducing sensor prices, a novel approach to price finding that decouples information exploitation from information exploration. Second, we improve accuracy and convergence by employing exponential search as exploration algorithm. Third, we normalize prices indirectly by fixing dividends, thereby stabilizing the system’s dynamics.

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Notes

  1. 1.

    Originally, the theorem was only shown to hold for two inputs and two outputs, with constant returns to scale and constant supply of inputs. While Jones and Scheinkman (1977) generalized it to larger number of inputs and outputs, the Stolper–Samuelson effect is not guaranteed to appear when returns to scale are not constant (Jones 1968) or supply of inputs is variable (Martin 1976), both of which is the case in our model. Nonetheless, the effect is present in the discussed settings thanks to their parametric symmetry.

  2. 2.

    With threshold \(\tau \), total dividends of n firms f with cash \(c_f\) each are \(d_{tot} = \sum _f (c_f - \tau ) = \sum _f c_f - n \tau \), which is constant.

  3. 3.

    A quick path to this insight is to imagine the consumer being endowed with one gold nugget of market price d instead of dividends d. This yields the same outcome, yet transforms d into a price that must be—like every price— proportional to the general price level.

  4. 4.

    To be precise, Riccetti et al. randomize the percentage approach, i.e. \(p_{t+1} = (1\pm s) p_t\) with s uniformely distributed, leading to a forth variant not discussed here.

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Acknowledgments

We would like to thank Johannes Brumm and Gregor Reich for their valuable inputs, Abraham Bernstein for pointing us to system dynamics, Krzysztof Kuchcinski and Radoslaw Szymanek for the JaCoP solver, and participants of CEF 2015 – most notably Ulrich Wolffgang – for their helpful comments.

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Correspondence to Luzius Meisser.

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Meisser, L., Kreuser, C.F. An Agent-Based Simulation of the Stolper–Samuelson Effect. Comput Econ 50, 533–547 (2017). https://doi.org/10.1007/s10614-016-9616-x

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Keywords

  • Computational economics
  • Agent-based economics
  • Price finding
  • Price normalization
  • Sensor prices
  • System dynamics