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In this chapter we develop a prototype bottom-up macroeconomic (BAM) model,40 which epitomizes the key features at the root of a series of computational investigations of macroeconomic processes conceived as complex adaptive systems (CATS), as recently performed by our research group. Other exemplifications of the CATS approach can be found in (2005), (2007) and (2007).
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A streamlined version of the present model and a succinct discussion of its features can be found in Delli Gatti et al. (2008).
Several interpretations of the acronym KISS circulate, most of them overlapping. The one we prefer is keep it simple, stupid!
Behavioral rules represent by construction the process of adaptation of the agent’s actions to changes of the environment. In a behavioral setting therefore expectations formation can be modeled quite straightforwardly as an adaptive scheme: Firms form expectations on future demand only on the basis of the past history of production (which is demand constrained). This adaptive mechanism is inefficient from a rational expectations (RE) viewpoint. In fact, if agents cast adaptive expectations, sooner or later they will incur in systematic errors. In a RE setting, on the contrary, agents are rational, i.e. they are able to elicit all the necessary information — not only the past history of the variable in question — and process it in such a way as to make only random errors which cancel out in the aggregate. Notice, however, that from the statistical point of view REs are conditional expectations of the system’s data generating process (DGP). As such they are inherently liable to errors. In any given situation, according to the RE theory agents endowed with rational expectations should not make mistakes on average, but in practice they do. In order for agents to assess whether their specification of the DGP’s conditional mean is right or not, the situation must be repeated over time in such a way as to allow agents to learn and update their expectation formation with the help of an “error correction” procedure. At the same time, however, the DGP is likely to change as well, frustrating agents’ efforts to be “rational”.
In simulations we set the duration of contracts θ to 8 periods, while the minimum wage is revised every 4 periods. If we assume that one simulation period corresponds to a quarter, this means that labour contracts last two years, while the minimum wage is revised annually.
In a monopolistic competition setting characterized by Bertrand competition, this would correspond to a Symmetric Bertrand-Nash Equilibrium.
For simplicity, we assume that firms do not attempt to raise funds by issuing new equities. This admittedly extreme assumption can be grounded in asymmetric information on the stock market. The manager of the equity issuing firm, in fact, can assess the fundamental value of the firm much better than the potential shareholder and this asymmetric information scenario is common knowledge. In this setting equity rationing can occur, i.e. the firm may eventually rule out the issuing of new equities because the shareholders would purchase the new shares only at too low a price.
To compute the average size of the incumbent firms we use the truncated mean at 10%. This means the lower and upper 5% of the firms’ population are ruled out.
Examples of degenerate dynamics we want to avoid are extremely volatile aggregate GDP dynamics, average rates of bankruptcy and unemployment over 50%, and average rates of annualized inflation outside the ±10000% range.
GB2, D and SM can be derived as the solution of a differential-equation Pearson system, with D and SM being three-parameter specializations of the GB2 distribution. The κ-Generalized distribution, on its part, is obtained from the entropy constrained maximization of a deformed exponential function.
- The BAM Model at Work
Domenico Delli Gatti
- Springer Milan
- Chapter 3
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