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While the world real interest rate is potentially an important mechanism for transmitting international shocks to small open economies, much of the recent quantitative research that studies this mechanism concludes that it has little effect on output, investment, and net exports. We re-examine the importance of world real interest rate shocks using an approach that reverses the standard real business cycle methodology. We begin with a small open economy business cycle model. But, rather than specifying the stochastic processes for the shocks and then solving and simulating the model to evaluate how well these shocks explain business cycles, we use the model to back out the shocks that are consistent with the model's observable endogenous variables. Then we use variance decompositions to examine the importance of each shock. We apply this methodology to Canada and find that world real interest rate shocks can play an important role in explaining the cyclical variation in a small open economy. In particular, they can explain up to one-third of the fluctuations in output and more than half of the fluctuations in net exports and net foreign assets.

In theory, the world real interest rate is an important mechanism by which foreign shocks are transmitted to small open economies. Changes in the world real interest rate can affect behavior along many margins: they affect households by generating intertemporal substitution, wealth, and portfolio allocation effects, and they affect firms by altering incentives for domestic investment. It is surprising, then, that much of the recent quantitative research on the effects of world real interest rates find that they are not important in explaining the dynamics of small open economies. This literature (see for example, Mendoza, 1991, Correia et al., 1992 and Correia et al., 1995; Schmitt-Grohe, 1998) finds that world real interest rate shocks have small effects on output, consumption, and labor hours — and in some cases — even on investment, net exports, and net foreign assets. In obtaining these findings, the authors mentioned above follow the standard international real business cycle approach. They build a dynamic stochastic model of a small open economy. Then they parameterize the model, including the processes for the stochastic shocks — one of which is the world real interest rate. Finally, they solve the model and/or conduct impulse responses to quantitatively evaluate the role of interest rate shocks. There are, however, three difficulties with this standard approach. First, there is no consensus on a good proxy for the ex ante world real interest rate, which is, of course, unobservable.1 A wide variety of nominal interest rates, price indices, and inflation expectations have been used to construct measures of world real interest rates. For example, the 3-month U.S. T-Bill rate, the rate of return on the S&P 500, the LIBOR rate, as well as a weighted average of several countries’ T-Bill rates, have been employed as nominal interest rates.2 These different measures are not necessarily highly correlated with each other, as Table 1 shows for four ex ante real interest rates constructed from the same price index and inflation expectations, but with different nominal interest rates. Half of the correlations are less than 0.25. Second, as discussed extensively in Ingram et al. (IKS) (1994a,b 1997) models in which the number of unobservable exogenous shocks is less than the number of observable endogenous variables imply that some of the observable variables are related deterministically. This feature exists in many small open economy models, and is fundamentally inconsistent with the data. The models are singular, which implies that it is not possible to back out a unique realization of unobservable exogenous shocks. In such models, there are an infinity of ways in which the importance of shocks — even orthogonal shocks — in driving business cycles can be calculated. Finally, in any model with multiple shocks, it is possible to determine the impact of any single shock only by imposing often-arbitrary identification restrictions. For example, one often-imposed restriction in models of small open economies is that domestic shocks are uncorrelated with the world interest rate. Baxter and Crucini (1993, p. 432) find that this assumption is `empirically indefensible'. At best, then, only a range of estimates — corresponding to different identification orderings of the shocks — can be obtained on the importance of world interest rate shocks. Table 1. Properties of the real interest rate measures (contemporaneous correlations)a Int. rate rUSA rW rSP rL rUSA 1 rW 0.85 1 rSP 0.12 0.23 1 rL 0.95 0.76 0.01 1 a USA: U.S. T-Bill rate; W: weighted average rate of developed economies; SP: S&P 500 return; L: LIBOR rate. The T-Bill rate, the weighted rate, and the LIBOR rate are constructed using the IMF's International Financial Statistics (IFS). The S&P 500 return index is taken from the Ibbotson Associates Database. In constructing our ex ante real interest rates, we assume that inflation follows a random walk. We use changes in the U.S. Consumer Price Index (CPI) as our measure of inflation. The data are quarterly from 1963:1 to 1994:4. Table options The purpose of this paper is to pursue an alternative quantitative methodology to assess the importance of world real interest rates on small open economies. We continue to employ a standard dynamic stochastic small open economy model, (augmented to include preference and depreciation shocks). However, rather than parameterizing a shock process and using the model to solve for the endogenous variables, we let the model and the endogenous variables tell us the exogenous shocks — including the world real interest rate — that are consistent with the model. Specifically, we use the model's Euler equations, data on the model's endogenous variables, as well as estimated decision rules for the capital stock and net foreign assets, to recover the exogenous shocks implied by the model and the data.3 Then, to compute the importance of these backed-out shocks in driving business cycles, we perform variance decompositions. By altering the ordering of the shocks, we generate a range of estimates on the importance of each of the shocks. To a large extent, then, our methodology reverses the standard approach. Moreover, our approach deals with all three difficulties highlighted above. First, we avoid the problems associated with calculating the appropriate world real interest rate; our backed-out interest rate measures are consistent with the model and the data. Second, because our model is nonsingular, we can evaluate the importance of the world real interest rate in business cycles without violating any relationships implied by the model. Third, by using shocks that are consistent with the model and by examining all possible orderings of shocks we do not need to take a particular stand on the relationship between them nor on their orthogonality. We apply our methodology to quarterly Canadian data from 1961:1 to 1996:4. Our backed-out world real interest rate measure is quite different from proxies constructed from the data. Our variance decompositions indicate that world real interest rate shocks can play a significant role in explaining Canadian business cycle fluctuations. If world interest rates shocks are ordered first, they explain 33% of Canada's output variation. They can also account for a significant fraction of variation in Canada's external balances: up to 62% (57%) of the variation in net exports (net foreign assets) is explained by these shocks. These quantitative findings contrast sharply with the results of Mendoza (1991) and Schmitt-Grohe (1998). However, their results are qualitatively similar to our findings, and they are quantitatively similar to the variance decomposition results we obtain when real interest rates are ordered last. The rest of this paper is organized as follows. In Section 2, we present our dynamic stochastic small open economy model. In Section 3, we calibrate the model to Canada and present our methodology on recovering the exogenous shocks. Our results are presented in Section 4, and Section 5 concludes.

Most models of small open economies posit several channels by which world shocks are transmitted to the small economy. Of these channels, the interest rate channel is often given special prominence. Hence, it is surprising that several recent quantitative analyses applying the standard real business cycle approach have found that fluctuations in world interest rates have little effect on domestic investment, output, net exports, and net foreign assets. In this paper we employ an alternative approach to quantitatively address the importance of interest rate shocks in a small open economy. The key point of departure is that we use the model and data on the endogenous variables to back out the exogenous shocks that are consistent with the model, while the standard approach posits statistical processes for the exogenous shocks (based on proxies of these shocks) and feeds these processes through the model to generate the endogenous variables that are consistent with the model. We view our approach as addressing difficulties in the standard approach arising from the question of the appropriate proxy for world real interest rates and from the singularity of the models typically employed. A second feature of our framework is that we deal with the fact that the exogenous shocks are correlated by performing variance decompositions for all possible orderings of the shocks. We apply our approach to Canada, a country that has been studied quite thoroughly via the standard approach. Our findings indicate that world interest rate shocks can have large effects, particularly on net exports and net foreign assets, but also on output. Our sensitivity analysis indicates that both features of our methodology — the backed-out shocks and the multiple-ordering variance decompositions — are driving our findings. We conclude that the world real interest rate can be an important transmission mechanism of world business cycles to small open economies. Nevertheless, the results of the other recent research are qualitatively similar to our results, and quantitatively similar to the lower bound of our variance decompositions, occurring when the world real interest rate is ordered last. In our model, we do not include fiscal and monetary policy shocks, which are important in understanding business cycle dynamics in open economies. It would be useful to apply this methodology to examine the role of these shocks in a more complex small open economy model.