Can structural small open-economy models account for the influence of foreign disturbances?

https://doi.org/10.1016/j.jinteco.2010.01.001Get rights and content

Abstract

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.

Introduction

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, 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, Justiniano and Preston, 2008b, Lubik and Schorfheide (2005, Lubik and Schorfheide, 2005, Lubik and Schorfheide, 2007, Lubik and Teo, in press, 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, 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, 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.

Section snippets

Evidence on international linkages

A central empirical regularity that international business cycle models seek to explain is the observed cross-country comovement amongst economic variables. This section documents a number of statistics suggesting that comovement is a salient feature of U.S. and Canadian business cycles, understanding that earlier literature testifies to the generality of these insights in other economies. This close link is not surprising considering the U.S. accounts for 75% of Canada's average trade share.5

The model

Building on Gali and Monacelli, 2005, Monacelli, 2005, Justiniano and Preston, 2008b, the following section details a small open-economy model, allowing for habit formation, indexation of prices, labor market imperfections and incomplete markets. These papers extend the microfoundations described by Woodford (2003) for analyzing monetary policy in a closed-economy setting to an open-economy context.

Estimation and priors

Model parameters are estimated using Bayesian methods now used extensively in the empirical macroeconomics literature—see Schorfheide (2000) for a seminal reference and Justiniano and Preston (2006) for further details in the context of the model estimated here. We work with a log-linear approximation of the model in a neighborhood of a non-stochastic steady state. The observables used in estimation were described in Section 2.

The first column of Table 2 presents the priors for the

Accounting for the influence of foreign shocks

This section documents the central result of the paper: the baseline model with independent shocks is unable to account for international comovement. Two pieces of evidence are adduced. First, variance decompositions reveal that U.S. disturbances explain a negligible fraction of variation in the domestic economy. Second, model-implied cross-country correlations are very close to zero. Both findings are clearly at odds with the reduced-form evidence discussed in Section 2.

Robustness

The benchmark specification makes a range of assumptions, both on model structure and its match with data. Table 4 presents the estimated contribution of foreign disturbances to the variability of Canadian series for a number of alternative specifications. Further robustness checks are conducted in Justiniano and Preston (2006). To present a worst-case scenario against our findings, the numbers reported are for the horizon at which the share for output is greatest. A comparison with the first

Common shocks

The benchmark model assumes that all shocks in the U.S. and Canada are independent. However, the empirical evidence presented in Section 2 is consistent with both spillovers from U.S.-specific disturbances and the existence of common shocks affecting both countries. This section presents alternative model specifications that accommodate the latter. Such specifications are unusual in the new open-economy macroeconomics literature. Notable exceptions are Adolfson et al., 2007, de Walque et al.,

On the source of model failure

The results so far have documented an important model failure with little said about its determinants. This section provides several insights on model and data features which limit comovement. We first show that the unaccounted correlation seen in the data translates into correlated innovations—in violation of the maintained assumption of orthogonality. This information, together with insights into which U.S. disturbances are a priori responsible for comovement, guides a set of exercises

Conclusion

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

Acknowledgements

We are grateful to Gunter Coenen, Charles Engel, Jordi Gali, Paulo Giordani, Thomas Lubik, Adrian Pagan, Giorgio Primiceri and two anonymous referees for discussions and detailed comments. We also thank seminar participants at the Federal Reserve Bank of Atlanta, Federal Reserve Bank of Chicago, Board of Governors of the Federal Reserve, Federal Reserve Bank of Cleveland Conference on “DSGE and Factor Models”, Duke University conference on “Identification and estimation of structural models”,

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