RDP 2007-06: The Butterfly Effect of Small Open Economies 1. Introduction

The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. Stewart 1990, p 141

A general agreement in the modern literature on monetary economics is that monetary policy should obey the Taylor principle: that the nominal short-term interest rate should rise eventually more than one-for-one with the rate of inflation. There is evidence that the success of monetary policy over the past two decades, compared to the problems in the 1970s, can be explained by reference to the Taylor principle.^[1] In most sticky-price models, this principle ensures that beliefs themselves do not turn into independent sources of fluctuations.

In these models, a central bank that fails to satisfy the Taylor principle is unable to ensure a unique rational expectations equilibrium (REE) for the economy.^[2] Such monetary policies lead to indeterminacy of the equilibrium: an economy for which many different outcomes are possible given the same fundamental situation. This problem of non-uniqueness has attracted considerable attention in the literature.^[3]

With a new Keynesian closed economy model, in which violations of the Taylor principle lead to multiple equilibria, Lubik and Schorfheide (2004) show that passive monetary policy better accounts for the dynamics of inflation and output in the United States prior to 1979. To the extent that indeterminacy – in a closed economy – is the result of an improper policy, determinacy could easily be restored by changing policy settings appropriately. As emphasised by Bullard and Singh (2006), however, good monetary policy can be insufficient to ensure determinacy of the REE in an open economy. Thus, an open economy may be exposed to non-fundamental fluctuations that ‘originate abroad’.

In general, indeterminacy of the REE can manifest itself in two non-exclusive ways. Non-fundamental disturbances may become additional sources of economic fluctuations and fundamental shocks may propagate differently. One of our goals is to study the implications of foreign-induced indeterminacy for the conduct of monetary policy in a small open economy. In particular, with a sticky-price small open economy model we address the following questions. How does the small economy respond to non-fundamental disturbances? Can monetary policy insulate, to some extent, the small economy from non-fundamental disturbances? To the best of our knowledge, no study has examined the implications of foreign indeterminacy for monetary policy in a small open economy. There is literature studying specific conditions for determinacy and indeterminacy in open economy models.^[4] Our focus here is different. We study the dynamic behaviour of the economy and optimal policy responses under ‘inherited’ indeterminacy.

Surprisingly, however, our main finding is this: if the large economy fails to achieve a unique equilibrium, shocks to the small economy affect the large one. In other words, ‘loose’ expectations abroad create a channel through which shocks that originate in the small economy influence the large economy. We call this channel the ‘butterfly effect’. In this way, the theory gives a structural and elegant interpretation of sunspot shocks for the large economy.

Another of our goals is to examine methodological aspects of solving small open economy models under rational expectations. As we discuss at length below, the ‘butterfly effect’ can be viewed as a result of an implicit assumption: expectations (in the small and large economy) are formed rationally with access to full information. Only if the equilibrium of the large economy is unique, is the small economy truly ‘small’. Therefore, ‘smallness’ is a property of the unique REE of the large economy. It is not our goal here, however, to assess the empirical relevance of this mechanism.

The rest of the paper is structured as follows. Section 2 describes the model. Section 3 discusses indeterminacy. Section 4 presents our main findings and Section 5 concludes.

Footnotes

See, for example, Clarida, Galí and Gertler (2000), Mankiw (2002), Bernanke (2004) and Lubik and Schorfheide (2004). [1]

See Woodford (2003) for a detailed description of the relationship between the Taylor principle and uniqueness of the REE. See also Benhabib, Schmitt-Grohe and Uribe (2001) for an example of a model in which the Taylor principle is not necessary for determinacy of the equilibrium. [2]

We cannot possibly do justice to the literature. Instead, we point the interested reader to Sargent and Wallace (1973), Taylor (1977), Barro (1981), Pesaran (1987), Bernanke and Woodford (1997), Farmer (1999), and the references therein. Although these studies differ along various dimensions, they refer to indeterminacy of the REE. It is important to keep in mind as McCallum (1983) argues, however, that the non-uniqueness problem is a more general feature of dynamic models that involve expectations, and not a particular one attributable to the rational expectations hypothesis. [3]

Benigno and Benigno (2006) and Benigno, Benigno and Ghironi (2007) study how the indeterminacy regions of the parameter space vary with regard to different types of monetary policy rules in a dynamic general equilibrium model with two similar countries. De Fiore and Liu (2000) and Zanna (2003) study how determinacy of the equilibrium depends on the degree of openness of a small economy, among other things. [4]