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On Complex Economic Dynamics: Agent-Based Computational Modeling and Beyond Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Rational Versus Adaptive Expectations in an Agent-Based Model of a Barter Economy

Author : Shyam Gouri Suresh

Published in: Complex Systems Modeling and Simulation in Economics and Finance

Publisher: Springer International Publishing

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Abstract

To study the differences between rational and adaptive expectations, I construct an agent-based model of a simple barter economy with stochastic productivity levels. Each agent produces a certain variety of a good but can only consume a different variety that he or she receives through barter with another randomly paired agent. The model is constructed bottom-up (i.e., without a Walrasian auctioneer or price-based coordinating mechanism) through the simulation of purposeful interacting agents. The benchmark version of the model simulates homogeneous agents with rational expectations. Next, the benchmark model is modified by relaxing homogeneity and implementing two alternative versions of adaptive expectations in place of rational expectations. These modifications lead to greater path dependence and the occurrence of inefficient outcomes (in the form of suboptimal over- and underproduction) that differ significantly from the benchmark results. Further, the rational expectations approach is shown to be qualitatively and quantitatively distinct from adaptive expectations in important ways.

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Footnotes
1
Results are somewhat quantitatively sensitive to the chosen parameters but the broader implications do not change. This will be discussed further in the next section.
 
2
In addition, the RBC model described in [20] features capital in the production function as well as the associated consumption-investment trade-off. Adding capital to the model in this paper would not affect its central findings but would complicate the analysis considerably since agents would need to base their own decisions not just on their expectations of others’ stochastic productivity levels and labor allocation decisions but also on their expectations of others’ capital holdings. This increase in dimensionality renders the problem computationally impractical if REH is assumed along with heterogeneous shocks and a finite number (i.e., not a continuum) of distinct individuals.
 
3
In theory, non-Pareto optimal outcomes are possible with REH here. For instance, it would be rational for all agents to expend low effort regardless of productivity levels with the expectation that everyone else too expends low effort in every state.
 
4
A two-agent version was also analyzed but this version is qualitatively different since it does not include the randomness associated with the pairing for the barter process. Results for this version are available upon request.
 
5
An implicit assumption here is that all agents are distinctly identifiable. If such distinctions are assumed away, then the most parsimonious description for the current state involves one unit of information for the agent’s own current period shock (which can take on one of the two values), one unit of information for the number of red producers who received high productivity levels in the last period (which can take on three values—none, one, and both) and one unit of information for the number of blue producers who received high productivity levels in the last period (which can also take on three values). Thus if, we assume away distinctiveness, an agent can find himself in any one of 2 × 3 × 3 = 18 different states.
 
6
Technically, since distinctiveness is unnecessary if SREE is assumed, the more parsimonious method mentioned in footnote 5 can be adopted resulting in the need to explore only 29 or 512 strategies. As one of the exercises in this paper allowed for a sampling of asymmetric strategies, all 65,535 possibilities were treated as distinct for comparability.
 
7
The number of SREEs obtained was robust to small changes in parameter values. However, the number of SREEs obtained was affected by large changes in parameter values and even dropped to as low as one (e.g., when the low productivity level was a near certainty, the only SREE was to always provide low effort).
 
8
In the 2 agent version of the model, 16 REEs were found of which 8 were also SREEs.
 
9
Detailed results for all SREE strategies are available from the author upon request.
 
10
It can be shown mathematically that regardless of how many agents are included in the model, both of these contrasting strategies (i.e., 1. always choosing low and 2. choosing low only when individual productivity level is low) will be equilibria for the chosen values of α and Π in this model.
 
11
The concept of equilibrium here is the one adopted by Page [19] and is completely unrelated to economic equilibrium or market clearing.
 
12
I would like to thank an anonymous referee for highlighting this point.
 
13
For all figures, the initial (zeroth) period is dropped from consideration.
 
14
It can be shown, for instance, that if all agents were to receive a low productivity level in any period (a scenario with an extremely low but still nonzero probability in a model with many agents) then everyone would switch to the low strategy in the next period.
 
15
Intuitively, with more memory, AE–I and AE–P may sustain the high effort equilibrium for longer because individuals would take into consideration more periods with high outputs while making decisions in subsequent periods. For instance, even in the period right after an economy-wide recession, if agents possessed longer memories, they could revert to expending high effort the next period if their own individual stochastic productivity level was high.
 
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Metadata
Title
Rational Versus Adaptive Expectations in an Agent-Based Model of a Barter Economy
Author
Shyam Gouri Suresh
Copyright Year
2018
Book
Complex Systems Modeling and Simulation in Economics and Finance

Print ISBN: 978-3-319-99622-6

Electronic ISBN: 978-3-319-99624-0

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-99624-0_7