RDP 2010-02: Learning in an Estimated Small Open Economy Model 1. Introduction

Forward-looking expectations are fundamental to the monetary policy transmission mechanism in modern macroeconomic models. The hypothesis of rational expectations is the standard paradigm for the formation of expectations in these models.^[1] Rational expectations assumes that agents – firms, households and policy-makers – have complete knowledge of the economy including its precise structure (the model and its parameters). In reality, however, economic and policy decisions are made under incomplete knowledge about the economy. This paper studies situations where economic agents have less precise knowledge than is presumed by rational expectations. It is assumed that economic agents engage in learning as they try to improve their understanding of the economy and make forecasts upon which they base their decisions.

Rational expectations models, in which agents are completely forward-looking, can sometimes exhibit unrealistic dynamic properties; in particular, households and firms will adjust their behaviour immediately in response to future anticipated events. In reality the economy does not ‘jump’ about in this fashion. So in order to match the empirical features of the data, models require mechanical sources of persistence, such as habit formation in consumption and indexation to past prices. These features partly reflect the fact that it is often costly for households and firms to change their behaviour rapidly, but it can also be argued that such modelling techniques lack a firm theoretical grounding. A plausible alternative is that agents are not as well informed as rational expectations assumes. Instead, they have to form expectations on the basis of limited information. One possibility is that agents behave as if they use an econometric learning algorithm to form their expectations.^[2] Intuitively, when agents are uncertain about their economic environment, exogenous shocks lead to revisions of beliefs over time, which may draw out the effects of a shock.

Recently, a number of papers have attempted to quantify whether learning is important empirically using closed economy models. Milani (2007) finds that learning generates persistence that can be a substitute for the inertia generated by indexation and habit formation in an equivalent rational expectations model. Using a larger new Keynesian model with a similar learning mechanism, Slobodyan and Wouters (2009) find that learning fits the data equally well or better than rational expectations. However, they argue that learning complements the canonical model but does not provide a substitute source of persistence. They suggest that Milani's (2007) result is a product of using a model that has a much poorer fit under rational expectations. Murray (2008) takes this a step further to conclude that learning actually makes the model worse in terms of forecastability. He estimates a new Keynesian model that falls somewhere between Milani (2007) and Slobodyan and Wouters (2009) in terms of its size, and finds that learning accounts for some, but not all, persistence. However, unlike Slobodyan and Wouters (2009), he finds that impulse responses are different for the two expectation assumptions.

We extend this line of research by considering the effect of learning in an open economy model. A variable of particular interest is the real exchange rate. Evidence from vector autoregression (VAR) models suggests that the response of the real exchange rate to an unexpected change in monetary policy is delayed with a peak effect after about one year (Eichenbaum and Evans 1995; Faust and Rogers 2003). This stands in contrast to standard structural general equilibrium models for which the peak effect typically occurs within the quarter, followed by relatively rapid reversion to the mean, consistent with the theory of exchange rate overshooting (Dornbusch 1976). One commonly applied method of generating more persistence to match the observed exchange rate behaviour is to assume that financial markets are imperfectly integrated. This implies that the exchange rate is subject to a stochastic ‘risk-premium’ shock – which is added to the uncovered interest rate parity (UIP) condition (see, for instance, Benigno 2009). This potentially very persistent shock weakens the link between the exchange rate and its fundamental determinants.

An alternative method of matching the behaviour of the real exchange rate, while satisfying the UIP condition, may be provided by learning. The idea here is that the process of learning can slow down the adjustment of the real exchange rate to economic shocks.

To examine the implications of learning, we estimate a small open economy model for Australia. We examine the effect of the expectations assumption by comparing a model with constant-gain learning^[3] to one with the standard rational expectations assumption. While we find that learning can replace some of the structural inertia in the model, it strengthens the role of habit formation somewhat. The impulse response functions in the learning model exhibit more persistence than those of the rational expectations model. At least part of this is due to learning rather than a shift in some of the estimated parameters. There is also some evidence that the learning model is preferred by the data. Further, we show that there has been a downward shift in the constant-gain learning parameter after the introduction of inflation targeting – that is, agents use a longer run of data when forming expectations – consistent with greater macroeconomic stability, particularly of inflation and interest rates.

The remainder of the paper is structured as follows. Section 2 outlines the key features of the model. Section 3 describes the solution of the model under rational expectations and learning as well as the estimation technique. Section 4 presents the estimation results for the different versions of the model and examines the impulse response functions of key variables to a monetary policy shock and a productivity shock. Section 5 extends the sample period and allows for a break in the speed of learning. Section 6 concludes.

Footnotes

For example, see Edge, Kiley and Laforte (2007) for the United States, Adolfson et al (2007) for Sweden, Christoffel, Coenen and Warne (2008) for the euro area and Jääskelä and Nimark (2008) for Australia. [1]

For a textbook treatment see Evans and Honkapohja (2001) and for a recent survey of articles see Evans and Honkapohja (2007) and Sargent, Williams and Zha (2006). [2]

Constant-gain learning does not weigh all earlier observations equally but discounts past data. This makes sense if the economy is subject to structural change over time. [3]