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Article Excerpt
RECENT WORKS IN monetary policy and learning have suggested that private sector's expectations should be taken into account in the policy rule implemented by the central bank (CB), as this practice could improve the ability of the policymaker to stabilize the economy, especially when agents are learning. In particular, it has been shown that an expectations based policy in a New Keynesian framework is able to ensure that the economy has a unique stable equilibrium and that the equilibrium is learnable by agents (Evans and Honkapohja 2003, 2006).
Unfortunately, no such a variable as "private sector's expectations" exists in reality, as expectations can vary quite significantly across economic agents. For example, the Barclays Basix survey in the United Kingdom, a now discontinued series, used to show a systematic positive bias in general public expectations on inflation, bias that was instead absent in the expectations of other groups surveyed, such as finance directors, investment analyst and business economists. The aim of this paper is to start studying the implications of this heterogeneity of expectations and learning dynamics for monetary policy.
In order to form their expectations on key macroeconomic variables, agents need a representation of the economy, i.e., a model, also called perceived law of motion (PLM). In this respect they face the same problem of an econometrician having to select the right-hand-side variables in his regression. We can reasonably argue that agents will not scan the whole (possibly infinite) set of potentially relevant variables but will start with a restricted set of indicators and will then change their choice only if the previous one has been rejected by data. (1, 2)
In this respect, an interesting equilibrium concept is the restricted perceptions equilibrium (RPE), in which agents are in fact underparameterizing their model but might not discover it because their forecast errors are orthogonal to the variables included in their information set. (3) An application of this equilibrium concept to a New Keynesian monetary model has been studied by Berardi and Duffy (2007), where the misspecification in the agents' model is linked to the degree of transparency of the CB.
In this paper we introduce the possibility of different agents choosing different models, and in particular we consider the case in which the population is split in two groups: type 1 agents use a correct model of the economy in their learning process, while type 2 agents are instead constrained to use an underparameterized model (in particular, one that neglects lagged values of the endogenous variables). We can think of these two groups of agents as representing informed and uninformed agents, the former in particular aware of the existence of a CB and of its role in the economy, while the latter neglectful of it. (4)
Heterogeneity between the two learning processes arises because of asymmetric information among agents: while one group knows what kind of policy the CB is implementing and what are the consequences of that policy in terms of the dynamics of the system, the other group does not have (or disregards) this piece of information and thus neglects those variables (here, lagged output) that affect the current state of the economy only because of CB's policy. The rationale for this is that there might be limits in CB's ability to communicate clearly its policy to the public, so that part of the private sector might remain unaware of some details of the policy. Alternatively, part of the private sector could disregard the CB's claim to be acting under commitment because aware of the time inconsistency problem and of the temptation for a CB to surprise the public by announcing a commitment policy but then acting under discretion.
Given the constraints on their learning scheme, type 2 agents can not possibly learn the true data-generating process for the system, and the economy can not converge towards a rational expectations equilibrium (REE). Nevertheless, we show that the economy can still converge to an equilibrium in which beliefs of all agents, informed and uninformed, are confirmed by data, in the weaker sense of forecast errors being uncorrelated with regressors in the PLMs. This is an important result because if parameter estimates were not to converge, agents would probably dismiss their current model and try a different one. Instead, if their estimates converge, it is possible that agents will not try and use a different model, and therefore the economy can get stuck in an equilibrium different form the REE.
While the two types of expectations that coexist in equilibrium differ in their degree of accuracy, they both satisfy a consistency condition that makes them an equilibrium point for the relative learning scheme. We call this equilibrium an Heterogeneous Expectations Equilibrium (HEE), where one group of agents holds rational expectations while the other has expectations that are rational only in a limited sense, in that they are the best forecasts agents can make given the misspecified model they are using. We provide conditions for the existence and learnability (E-stability) (5) of such an equilibrium in a basic New Keynesian monetary model under different policy specifications, and then compare the properties of different equilibria in terms of output gap and inflation volatility. In particular, we want to investigate what happens if the CB does not realize that there exists heterogeneity in private sector's expectations and uses only one type of expectations when deciding its policy rule.
The main result of the paper is that heterogeneity in expectations can play an important role and that the CB should be aware of this fact when deciding its policy action: in particular, our analysis shows that the CB in its policy rule should use the most accurate type of expectations available to the private sector.
The structure of the paper is as follows. Section 1 presents the literature this paper builds on; Section 2 develops the model, finds the HEE under different policy specifications, and compares them; Section 3 concludes.
1. SOME BACKGROUND THEORY
1.1 Expectations and Monetary Policy
When the CB sets its policy instrument, the short term interest rate, it usually takes into account various indicators. Among them, it has been suggested, there should be private expectations about future output and inflation, especially when agents are not fully rational. By responding to private sector's expectations, in fact, the CB can induce an otherwise unstable REE to be E-stable, i.e., learnable Evans and Honkapohja (2003, 2006). For the learning process to converge to the REE, of course, private agents must use a correctly specified PLM in their learning algorithm. Berardi and Duffy (2007) show that when the PLM employed by agents is underparameterized and neglects the dependency of the endogenous variables on lagged output, the economy can still converge to an RPE that is stable under least squares learning (E-stable).
These results rely on the existence of common expectations among private agents and on the ability of the CB to observe the value of those expectations. In reality, though, we observe a wide spectrum of expectations/forecasts across...
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