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This paper demonstrates that an estimated, structural, small open-economy model of the Canadian economy cannot account for the substantial influence of foreign-sourced disturbances identified in numerous reduced-form studies. The benchmark model assumes uncorrelated shocks across countries and implies that U.S. shocks account for less than 3% of the variability observed in several Canadian series, at all forecast horizons. Accordingly, model-implied cross-correlation functions between Canada and U.S. are essentially zero. Both findings are at odds with the data. A specification that assumes correlated cross-country shocks partially resolves this discrepancy, but still falls well short of matching reduced-form evidence. One central difficulty resides in the model's inability to account for comovement without generating counter factual implications for the real exchange rate, the terms of trade and Canadian inflation.

This paper investigates whether an estimated microfounded semi-small open-economy model can reproduce the observed comovement in international business cycles. Focusing on Canada as the semi-small open economy, the starting point for the analysis is the large body of empirical work that identifies a significant influence of U.S. shocks on Canadian economic fluctuations. There has been ample theoretical work seeking to replicate the observed comovement in economic activity across countries. Until recently, the empirical validation of these models largely relied on calibrations aimed at matching selected moments in the data—see the contributions of Backus et al., 1992, Backus et al., 1995, Stockman and Tesar, 1995 and Baxter, 1995 for a review. The new open-economy macroeconomics (NOEM) has since produced significant theoretical advancements in international macroeconomic modeling. Given the empirical success of closed-economy models built on similar foundations, it is not surprising that there is a growing literature estimating NOEM models. These include amongst others: Ambler et al., 2004, Bergin, 2003, Bergin, in press, Del Negro, in press, Ghironi, 2000 and Justiniano and Preston, 2008b, Lubik and Schorfheide (2005, Lubik and Schorfheide, 2005, Lubik and Schorfheide, 2007, Lubik and Teo, in press and Rabanal and Tuesta, in press. To our knowledge, the ability of these NOEM models to explain the observed comovement in economic fluctuations has not been previously systematically analyzed in this empirical literature. This paper fills this gap by evaluating a workhorse semi-small NOEM model in this particular dimension. The focal point is the model's ability to replicate the fraction of the variance in Canadian macroeconomic series attributed to U.S. shocks. We also contrast the cross-country correlation functions in the model and data, particularly for output. The analysis is pursued using generalizations of the semi-small open-economy framework proposed by Gali and Monacelli (2005).1 Following Monacelli (2005), we allow for deviations from the law of one price. In addition, we consider incomplete asset markets, a large set of disturbances, and incorporate other real and nominal rigidities (e.g., wage stickiness, indexation and habits) which have been found crucial in fitting closed-economy models as documented by Christiano et al., 2005 and Smets and Wouters, 2007. The model is estimated using Bayesian methods with data for Canada and the United States. Our baseline specification assumes that shocks across these two countries are independent. This contrasts with much of the international real business cycle literature which often assumes correlated cross-country technology shocks, but is consistent with all of the empirical NOEM studies cited above.2 Under independent shocks, the channels of transmission embedded in the model (e.g. risk sharing and expenditure switching effects) must account for the cross-country comovement in aggregate fluctuations. The main contribution of this paper is to document that the baseline specification fails to account for the influence of foreign shocks. A structural variance decomposition reveals that all U.S. shocks combined cannot explain more than 3% of the variability in Canadian output, interest rates or inflation. Furthermore, model-implied cross-correlation functions between these two countries are estimated to be essentially zero. Both findings are in stark contrast with reduced-form empirical evidence in the same data. These results are shown to be robust across alternative specifications, priors and detrending methods. Model parameters chosen based on previous calibrated studies can deliver both large shares of domestic variance being attributed to U.S. shocks and substantial cross-country correlation in some series. Therefore, our findings indicate that the inability to reproduce some international correlations—known as the quantity anomaly in the case of output (see Baxter and Crucini, 1995)—is exacerbated in estimated models. The results also suggest the need to be cautious in assuming that the empirical success of closed economy models built on similar microfoundations will readily translate to an open economy setting. A second contribution of this paper is to document that the international comovement problem can only be partially resolved by introducing disturbances that are correlated across countries. To do this, each Canadian structural shock is written as the sum of two orthogonal components: a disturbance common to the same type of shock in the U.S. block, and a country-specific disturbance. This decomposition can be viewed as a rough approximation to reduced-form dynamic factor models that have been used for business cycle analysis.3 When all U.S. shocks are common to the domestic block the DSGE model gets closer to matching the reduced-form variance decomposition. However, there are at least three reasons for not viewing this specification as a panacea for the model's inability to replicate the observed influence of foreign disturbances. First, at medium to long horizons the fraction of output variation explained by U.S. disturbances is still below the reduced-form evidence. Second, this specification engenders an extreme version of the exchange rate disconnect puzzle—see Devereux and Engel (2002). Third, some of the induced correlations are difficult to rationalize on structural grounds. A third contribution of our analysis is to elucidate reasons for the model's failure in this crucial dimension. The inability to match the comovement in the data gets reflected in cross-correlation amongst supposedly orthogonal innovations in our baseline model. These correlations point to a complex pattern of covariation, beyond pairing the same type of disturbance across countries, explaining the limited success of the common shocks models. More promising guidance for future research is given by the observation that while U.S. shocks can a priori match some bivariate cross-country correlations, they also have strong counter factual predictions, particularly involving the real exchange rate, the terms of trade and domestic inflation. This tension helps understand, at least in part, why the estimated model shuts down international linkages and indicates ample scope to improve the transmission mechanism of foreign disturbances in this class of models. This paper broadly relates to the international business cycle literature and recent empirical work with NOEM models. More closely related is Adolfson et al. (2007) who present a state-of-the-art model, more richly specified than the one considered here. While their model performs very well in several dimensions, an earlier version, Adolfson et al. (2005), reported variance decompositions revealing little transmission of foreign-sourced disturbances from the European Union to Sweden—a property that is not remarked upon. Similar observations apply to an extension of this framework by Christiano et al., in press and de Walque et al., in press in a two-country model for the U.S. and the Euro Area. We also build on Schmitt-Grohe (1998) who evaluates whether a calibrated small open-economy real business cycle model can replicate impulse responses to a single foreign output shock, extracted from a bivariate U.S.–Canada vector autoregression.4 Our results suggest that in estimation the failure to capture international linkages may be worse than when the model is calibrated.

This paper shows that an empirical semi-small open-economy model fails to account for one important dimension of Canadian data: the influence of U.S. disturbances. We initially assume uncorrelated shocks across countries, as it is done in almost all the empirical literature with this class of models. Variance decompositions reveal that the fraction of variation in Canadian series attributed to all shocks originating in the U.S. economy is negligible at all forecast horizons. Accordingly, the cross-country correlation functions implied by the model are close to zero. These findings contrast sharply with earlier work documenting strong linkages between these two countries and reduced-form evidence presented here. Alternative specifications with common shocks can only partially resolve this problem. A model in which all U.S. shocks have a common component with the corresponding Canadian disturbance begins to reconcile the influence of foreign shocks in the model and the data. However, the variance shares explained by all U.S. disturbances still fall short of those observed in the data at medium and long horizons. While the empirical evidence is consistent with both common shocks and spillovers, there remains the question of what economic effects do these common shocks capture in the model. In particular, whether they correspond to purely exogenous disturbances or are instead simply capturing model misspecification. Finally, any gains with common shocks come at the expense of fully detaching fluctuations in the exchange rate and the terms of trade from the foreign block. Analyzing the prior implications for the transmission of U.S. shocks indicates a role for exchange rate disconnect in the model's failure. In particular, we uncover a number of prior counter factual correlations between U.S. and Canadian series, particularly involving inflation, the real exchange rate and the terms of trade. Overall our findings suggest that additional work on the international transmission mechanisms of various shocks could improve the empirical performance of these models in this crucial dimension. An interesting exercise in this vein would be to alter the supply side of the model to account for cross-country linkages at multiple stages of production as in Huang and Liu, 2007 and Burstein et al., in press. Alternatively, expanding on international financial linkages and the role of asset prices might help explain the importance of U.S. disturbances abroad, as made evident by the current financial crisis.