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We study a simple monetary model in which a central bank faces a boundedly rational private sector and has the goal of stabilizing inflation. The system's dynamics is generated by the interaction of the expectations about inflation of the various agents involved. A modest degree of heterogeneity in such expectations is found to have interesting consequences, in particular when the central bank is uncertain about the relevant behavioral parameters. We find that a simple heuristic based on mean and variance of the distribution of behavioural parameters stabilizes the system for a wide parametric region.

In recent years the ability of central banks to control inflation by way of inflation targeting policies has generally increased and their credibility has improved accordingly. The issue of whether monetary authorities are also actually able (and therefore should commit themselves) to tackle full employment at the same time is controversial, however (see e.g. [9]). More recently the worldwide crises has also put forward the issue of the zero lower bound constraint on nominal interest rates reaching effectiveness, with implications on the range of policy instruments which remain viable for monetary policy (see [10]). In this paper, we study a simple model in which an inflation targeting monetary policy is carried out by a Central Bank (CB henceforth), using money supply as its sole instrument. We assume bounded rationality for both the monetary authority and the private sector. The model builds on Bischi and Marimon [1] who rank a number of different policies according to the size of the basin of attraction associated with meaningful steady state equilibria. Also, they posit bounded rationality for the private sector, which is in turn modelled as a representative agent but do not especially focus on the CB's forecasts of relevant variables. In contrast, here the CB is supposed to know the functional form underlying the private sector's inflation expectations but not its specific parameters. Besides, the private sector is assumed to be a collection of heterogeneously adaptive agents. This behavioural assumption is motivated by previous experimental evidence (see e.g. [7], [3] and [6]). The criterion of judging policies according to the probability of reaching the target is maintained, in the context of an exercise about parametric uncertainty for the CB. The authorities are assumed to have correct information about the sample moments of the distribution of behavioural parameters characterizing the private sector, while ignoring the fine detail of the actual realization of such parameters. The results are as follows: within the representative agent framework we show how local stability depends on the interaction between money demand elasticity to inflation, the inflation target and the parameters involved. We also document the relative ranking of this policy with various alternatives, given a criterion based on the probability of a stable outcome for the dynamics of inflation. With heterogeneous agents we study the effect of the number of different types of agents playing a role within the private sector and find a phenomenon of polarization: the larger such number the less uncertain becomes the issue of whether stability will prevail, with the actual answer depending on the money demand slope and the inflation target. In this context a significant role is played by the dispersion of the private sector's key parameters, which proxies the amount of behavioural heterogeneity. We describe a heuristic for the optimal choice of an adaptive parameter for the CB, in terms of the expected long-run outcome.

This paper studies a simple model in which a central bank and a boundedly rational private sector interact as the monetary authority pursuits a target for the level of inflation. The expectations about inflation of the various players involved drive the dynamics of the system. Introducing heterogeneity in such expectations is shown to have a significant impact, in particular when the central bank is uncertain about the relevant behavioural parameters. A heuristic for the central bank, based on the knowledge of mean and variance of the probability distribution of the adaptive parameters used within the private sector, is shown to be able to stabilize the system for a rather large parametric region. In contrast, a strategy based on the mean only, i.e. reducing the private sector to a representative agent, performs considerably worse. The analyses carried out in this paper might be developed along various direction. In particular it would be interesting to consider different kinds of agents using different rules, thus adding genuine behavioural heterogeneity to the model, beside the parametric heterogeneity of the adaptive agents considered here. It would also be possible to consider the effect of some asymmetry in the agent size, e.g. by allowing some agents to be especially influential by way of a nonvanishing weight even as n increases, thus studying the possible implications of some “guru” effect.