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The rational expectations equilibrium of a small open economy can be subject to indeterminacy if foreign monetary policy does not satisfy the Taylor principle. We study the implications of foreign induced indeterminacy in the two-country version of the sticky-price small open economy model. Our main finding is that ‘smallness’ is a property of the unique rational expectations equilibrium of the large economy, and not a general property of the small open economy model. If the large economy fails to anchor expectations, shocks to the small economy can affect the large one. This form of indeterminacy gives rise to a ‘butterfly effect’. Additional assumptions are required to preserve the ‘smallness’ of the small economy.

A general agreement in the modern literature on monetary economics is that monetary policy should obey the Taylor principle: that the nominal short-term rate of interest should rise eventually more than one-for-one with the rate of inflation. There is evidence that the successes 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; numerous authors long noticed, studied, and reacted in various ways to the multiplicity of solution paths in rational expectations models.3 With a closed economy new Keynesian model, in which violations of the Taylor principle lead to multiple equilibria, Lubik and Schorfheide (2004) show that prior to 1979 passive monetary policy better accounts for the dynamics of inflation and output in the U.S. economy. 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 emphasized by Bullard and Singh (2008), 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 business fluctuations and fundamental shocks may propagate differently. One of our goals is to study the implications of foreign induced indeterminacy for a small open economy. In particular, with a sticky-price small open economy model we address the following question. How does the small economy respond to non-fundamental disturbances? To the best of our knowledge, no study has examined the implications of foreign indeterminacy 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, with a sticky-price small open economy model, the dynamic behavior of the economy under ‘inherited’ indeterminacy. Our main finding, however, is this: if the large economy fails to achieve a unique equilibrium, shocks to the small economy may 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’.5 In this way, the theory gives a structural interpretation of sunspot shocks to the large economy. Another one 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 findings and Section 5 concludes.

This paper studies implications of indeterminacy of the rational expectations equilibrium for a small open economy. We find that ‘smallness’ is not a general property of this class of small open economy models, but instead, a property of the large economy's unique determination. This finding, we think, is methodologically important, since even if the ‘butterfly effect’ is to be considered a theoretical curiosity or an unacceptable prediction of economic theory, then such reactions require, at least, a reconsideration of the expectations formation process in open economy models. Acknowledgments We would like to thank an anonymous referee and the Editor Michel Juillard, whose suggestions have improved the paper. We also wish to thank Adam Cagliarini, Roger Farmer, Fabio Ghironi, Richard Harrison, Peter Ireland, Christopher Kent, Thomas Lubik, Federico Mandelman, Tommaso Monacelli, Kristoffer Nimark, Antti Ripatti as well as seminar participants at the Banco Central de la Republica Argentina, UNSW, Universidad Torcuato DiTella, and the Reserve Bank of Australia for valuable comments and discussions. The views expressed here are our own and should not be attributed to our colleagues at the Reserve Bank of Australia.