This Selected Issues paper for Canada presents comprehensive and broad-based analysis of the role of domestic and external shocks. Canada’s economic history illustrates the important role played by external as well as domestic macroeconomic disturbances. Canada’s economy slowed in 2001 because of the global slowdown, although by less than in many other countries. In 2003, the recovery has been interrupted by a series of shocks that moderated growth. Fluctuations in Canadian real GDP are explained by external and domestic cycles.

Abstract

This Selected Issues paper for Canada presents comprehensive and broad-based analysis of the role of domestic and external shocks. Canada’s economic history illustrates the important role played by external as well as domestic macroeconomic disturbances. Canada’s economy slowed in 2001 because of the global slowdown, although by less than in many other countries. In 2003, the recovery has been interrupted by a series of shocks that moderated growth. Fluctuations in Canadian real GDP are explained by external and domestic cycles.

PART I: REAL SECTOR ISSUES

I. Factoring In Canadian Cycles1

1. Canada’s recent economic history illustrates the important role played by external as well as domestic macroeconomic disturbances. Canada’s economy slowed in 2001 because of the global slowdown, although by less than in many other countries. In 2003, the recovery was interrupted by a series of shocks that moderated growth (on the external side, an appreciation of the Canadian dollar and a case of mad cow disease that constrained agricultural exports, on the domestic side a SARS outbreak and forest fires). Growth rebounded in 2004, partly a result of strong global commodity demand, but further recent appreciation of the Canadian dollar has led to concerns about prospects for 2005.

2. While previous studies have documented the importance of U.S. real shocks on Canadian business cycles, further work is needed to analyze the economy-wide effects of external shocks. For instance, IMF (2004) concluded that the synchronization of real output, consumption and investment fluctuations between Canada and the United States has increased in the last two decades. Other work using vector autoregression (VAR) techniques on a small set of Canadian and foreign variables has also concluded that developments in the United States have strong influences on real activity and nominal variables in Canada (Schmitt-Grohé, 1998; Cushman and Zha, 1996; Burbidge and Harrison, 1985). These findings naturally lead to a question about the transmission channels through which U.S. and other external shocks are impacting on the Canadian economy. Empirical analysis focusing on this question is presented in this paper, using recent developments in dynamic factor models for a comprehensive and broad-based analysis of the role of domestic and external shocks in Canada.

3. Compared to VARs, dynamic factor analysis has a number of advantages:

  • A wider set of series can be analyzed. The number of variables that can be included in a VAR is limited by the need to include lagged values of all series in the estimation. Factor analysis, in contrast, allows a wider range of series to be analyzed, allowing for a more comprehensive analysis of economic fluctuations.

  • The number of shocks is determined by the data. In VAR models, the number of disturbances is by definition equal to the number of series in the estimation. In factor analysis, the number of shocks is determined statistically. In addition, the precision with which factors are estimated can be used to assess their relative importance over time.

  • Factor analysis provides more information on the disturbances. Factor analysis and VARs use similar techniques to identify shocks. In contrast to VAR estimation, however, convergence diagnostics in the estimation of factor models can be used to check if the identifying restrictions are valid.2

  • Factor models provide relatively efficient forecasts. The internal dynamics of thefactors and their effects across series can be used to project likely future developments in the economy. By summarizing the information contained in a large number of series, forecasts based on dynamic factor models can outperform those obtained from VARs.3

A. Factor Analysis

4. In contrast to recent work on the international transmission of shocks, this study analyzes the effects of multiple shocks with a flexible specification of dynamics.4 Extending the earlier work of Gregory, Head, and Raynauld (GHR, 1997) and Kose, Otrok, and Whiteman (KOW, 2003), this paper uses dynamic factors to examine multiple domestic and external shocks affecting the Canadian economy. Moreover, a flexible specification of dynamics allows the factors to affect series contemporaneously and with one lag. Therefore, the analysis can account for spillover effects.5

5. The factor model used here assumes that each series can be described using a small number of factors with series-specific dynamics plus an error term. For example, consider the case of two U.S. and two Canadian series labeled yUS1, yUS2, yCN1 and yCN2. Assume these series are driven by two external and two domestic factors labeled f E1, fE2, fD1 and fD2, that affect the series both contemporaneously and with one lag.6 Then the model is:

[yUS1(t)yUS2(t)yCN1(t)yCN2(t)]=A0[fE1(t)fE2(t)fD1(t)fD2(t)]+A1[fE1(t1)fE2(t1)fD1(t1)fD2(t1)]+[ηUS1(t)ηUS2(t)ηCN1(t)ηCN2(t)]

where η(t) is a series-specific error and the matrices of coefficients are given by

As=[αsUS1,E1αsUS1,E2βsUS1,D1βsUS1,D2αsUS2,E1αsUS2,E2βsUS2,D1βsUS2,D2αsCN1,E1αsCN1,E2βsCN1,D1βsCN1,D2αsCN2,E1αsCN2,E2βsCN2,D1βsCN2,D2] fors=0,1

6. Factors and coefficients are provided as output of the estimation process, based on a number of identifying restrictions. Factors are identified by assuming that they are orthogonal both to each other and to the series-specific error terms, and by exclusion restrictions similar to those used in VARs. For example, this paper assumes that Canada is a small open economy, so that external factors affect economic variables in both the United States and Canada, and domestic factors affect only Canadian series. In the example above, this implies βsUS,D1 and βsUS,D2=0 for the U.S. series both in the contemporaneous and lagged coefficients (s=0,1). In addition, the first external factor is assumed to affect the first U.S. series contemporaneously, whereas the second external factor only impacts with a lag (i.e., β0US1,E2=0). A similar assumption applies with respect to how the domestic factors affect the two Canadian variables.

B. Results

7. To provide a comprehensive description of economic interactions within and across the United States and Canada, a large number of variables is employed in the analysis. The estimation uses a panel of 44 quarterly series from early 1984 to early 2004, comprising world prices for oil and other commodities, 18 U.S. real and nominal series, and 24 real and nominal Canadian variables.7 All series except interest rates are included in terms of their logarithms. Real variables are detrended by calculating deviations from a Hodrick-Prescott trend (with the standard smoothing factor of 1,600), while prices and monetary aggregates are measured as rates of change (i.e. the change in the logarithm). Further details and sources for the dataset and detrending methods are provided in the Appendix.8

8. Bayesian analysis resulted in a preferred model including factors that broadly reflect international oil prices, the U.S. cycle, the exchange rate, the non-oil producer and commodity prices, and a Canadian cycle. This model—involving two external and two “domestic” factors (one of which is associated with the exchange rate, non-oil commodity prices, and producer prices)—resulted in the largest Bayes’ Factor out of a wide range of estimated models.9 The results also indicate that the factors follow an autoregressive process with three lags, implying potentially quite complex dynamics, and that the factors affect the series contemporaneously and with a one-quarter lag.10

9. The factors are estimated with fairly narrow error bands, although a widening of the bands over time suggests that the Canadian cycle may be playing a diminishing role (Figure 1). Decompositions that analyze the relative contribution of each factor to fluctuations in individual series, as well as examination of plots of the factors, suggest that external and exchange rate disturbances play a significant role in explaining Canadian fluctuations (Tables 1 and 2). That said, the explanatory power of each factor varies substantially across variables, and to some extent also over time. The discussion below provides an overview.

Figure 1.
Figure 1.

Factors and Posterior Deciles

(thin lines show tenth and ninetieth percentiles)

Citation: IMF Staff Country Reports 2005, 116; 10.5089/9781451806984.002.A001

Source: Fund staff calculations.
Table 1.

Variance Decompositions for the United States from a Factor Model with Two External and Two Domestic Factors

article image
Source: Fund staff calculations.

D = first difference, LD = log of first difference, DHP = deviation from HP trend, LDHP = log of deviation from HP trend

Table 2.

Variance Decompositions for Canada from a Factor Model with Two External and Two Domestic Factors

article image
Source: Fund staff calculations.

D = first difference, LD = log of first difference, DHP = deviation from HP trend, LDHP = log of deviation from HP trend.

10. The first factor can be interpreted as fluctuations in the world price of oil in U.S. dollars and in U.S. producer prices of intermediate inputs (Figure 2). It accounts for 65 percent and 82 percent of their respective variances and tracks these series closely. In the United States, this “oil” factor explains much of the variation in prices and the federal funds rate. In Canada, it accounts for a large amount of the variation in export and energy prices, some 10 percent of fluctuations in the headline CPI, but a smaller proportion of fluctuations in core CPI inflation, Canadian interest rates, and non-energy commodity prices.11 Consistent with post-1985 results reported in Kose et al. (2004), there is little interaction between oil prices and real variables.

Figure 2.
Figure 2.

“Oil” Factor and Comovements in Selected Series 1/

Citation: IMF Staff Country Reports 2005, 116; 10.5089/9781451806984.002.A001

Source: Fund staff calculations.1/ Each series is divided by its standard deviation and its mean removed. Vertical axes are therefore measured in standard deviations.

11. The second external factor, which tracks the U.S. cycle, accounts for almost 60 percent of the deviations of U.S. real GDP from trend (Figure 3). It captures the recessions (and subsequent recoveries) of 1990 and 2001, as well as the slowdown in 1995 and can explain around half of the changes in the federal funds rate, particularly since 1987 (as can be seen from Figure 3, the federal funds rate tends to lead the cycle). The factor also explains about half of the movements in U.S. imports and one quarter of consumption movements.

Figure 3.
Figure 3.

“Real” Foreign Factor and Comovements in Selected Series 1/

Citation: IMF Staff Country Reports 2005, 116; 10.5089/9781451806984.002.A001

Source: Fund staff calculations.1/ Each series is divided by its standard deviation and its mean removed. Vertical axes are therefore measured in standard deviations.

12. This “U.S. cycle” factor has a large influence on Canadian real GDP and industrial production, explaining around half their variance. The link with downturns in Canadian real GDP is particularly striking, whereas the synchronization of recoveries is less close—indeed, this factor often leads Canada’s upturns. Interestingly, the factor suggests that the 2001 downturn in Canadian real GDP was less than would have been expected given the U.S. slowdown. More recently, however, the recovery of Canadian real GDP has lagged behind the “U.S. cycle” factor.

13. The results emphasize the role of trade linkages for the transmission of U.S. cyclical shocks. The importance of trade linkages in explaining the synchronization of fluctuations between the United States and Canada is clear from the fact that the “U.S. cycle” factor explains about half of the variation in Canadian exports and imports. This relationship appears to have increased in the 1990s, plausibly reflecting greater economic integration over this period.

14. The “U.S cycle” factor also explains a significant proportion of fluctuations in Canada’s bank rate, particularly since the mid-1990s, but reveals limited links between capacity and inflation. It accounts for about one-third of the variation in Canada’s bank rate, a relationship that seemed to strengthen in the 1990s. However, these two series behave quite differently in 1991—at the inception of the Bank of Canada’s inflation targeting regime—and, to a lesser extent, more recently in 2002-2003. Despite the factor’s important role for the Canadian real economy, its impact on inflation is quite limited, echoing the conclusions from other studies that have encountered difficulties in establishing a stable relationship between capacity measures and inflation.12

15. The third factor closely tracks movements in Canada’s exchange rate and non-oil producer and commodity prices (Figure 4). As it might be expected, this factor is closely associated with movements in import prices and, to a lesser degree, export prices. However, the influence on fluctuations in headline and core CPI is limited, suggesting that pass-through from import prices subsides as goods move down the production chain. This “exchange-rate” factor also displays some comovements with Canada’s bank rate in the 1980s and mid–1990s, excluding the 1990-91 period when inflation targeting was adopted. Nonetheless, this relationship seems to weaken considerably after 1998, around the time that the Bank of Canada abandoned the Monetary Conditions Index (MCI) as an indicator of monetary policy.

Figure 4.
Figure 4.

"Exchange Rate" Domestic Factor and Comovements in Selected Series 1/

Citation: IMF Staff Country Reports 2005, 116; 10.5089/9781451806984.002.A001

Source: Fund staff calculations.1/ Each series is divided by its standard deviation and its mean removed. Vertical axes are therefore measured in standard deviations.

16. The last factor corresponds to domestic disturbances responsible for Canada’s cycle (Figure 5). The factor explains around half of fluctuations in Canadian real GDP and about one third of movements in industrial production.13 A close link existed between this factor and fluctuations in Canada’s real GDP through the mid-1990s. Subsequently, however, the two series became less correlated, similar to other variables that were well explained by this factor, such as industrial production, labor productivity, and hours worked.14 This shift is also reflected in the precision with which this factor is estimated, evident from the widening error bands reported in Figure 1. Finally, the “U.S. cycle” factor appears to somewhat lead this “domestic cycle” factor. The correlation coefficients of the first and second lag of the U.S. factor with the Canadian factor are 0.17 and 0.34, respectively. This could indicate that the impact of U.S. fluctuations may be underestimated even under this flexible dynamic specification.

Figure 5.
Figure 5.

“Real” Domestic Factor and Comovements in Selected Series

Citation: IMF Staff Country Reports 2005, 116; 10.5089/9781451806984.002.A001

Source: Fund staff calculations.1/ Each series is divided by its standard deviation and its mean removed. Vertical axes are therefore measured in standard deviations.

C. Robustness Checks

17. The results appear generally robust to changes in the way the data were measured. This was examined by re-estimating the model with real variables measured as rates of change, rather than deviations from trend. Statistical methods indicated that the same model structure—four factors with extremely similar features—remained valid. More generally, the results were extremely similar to the benchmark case with the following exceptions:

  • The “oil” factor now explains a greater share of consumption. This is particularly true for the United States.

  • The spillovers from the U.S. cycle to Canadian real GDP and industrial productionare lower.15 One possible explanation for this is that first differencing makes it more difficult to identify spillovers, as there is a greater degree of noise in the data.

18. Estimating the model with and without lags reveals the importance of spillover effects from external shocks. The model was re-estimated excluding the lags in the impact of factors on individual series to explore the importance of this assumption on the results. Comparing the variance decompositions obtained with and without a lag indicates the following qualitative differences:

  • The share of the variance explained by the U.S. real factor in the United States fallswhen the lag is excluded. This is particularly true for “sluggish” variables such as the unemployment rate and investment.

  • Without lags, the proportion of the variation in Canadian real GDP (as well asindustrial production and unit labor costs) attributed to the U.S. cycle falls.16 This indicates that lags matter in the effects of U.S. activity on the Canadian economy.

D. Conclusions

19. The results from the estimation suggest that:

  • Four factors can explain a large amount of the fluctuations across a wide range of macroeconomic series in Canada and the United States. For instance, they account for roughly 95 percent of the variance in Canadian real GDP and industrial production. The factors seem to correspond to world oil price shocks, the U.S. cycle, an exchange rate and non-oil price shock, and a Canadian cyclical factor.

  • The fraction of the variance accounted for by factor varies substantially across series. Fluctuations in Canadian real GDP are about equally explained by external and domestic cycles, while for other real series, inflation, and policy interest rates, the role of external factors is even larger. Furthermore, our analysis provides evidence that the importance of the “Canadian” cyclical factor declined during the 1990s.

  • These results appear relatively robust to alternative methods of detrending the data. In addition, allowing for differences in the speed at which factors affect specific series is important for distinguishing spillover effects.

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Appendix: I

Appendix Table 1.

United States Data Sources, Descriptions, and Transformations

article image

Abbreviations: D (Difference); LD (Log-Differences); DHP (Deviations from HP Trend); LDHP (Log-Deviations from HP Trend).

Abbreviations: SA (Seasonally Adjusted); SAAR (Seasonally Adjusted Annualized Rates or Levels); NSA (Not Seasonally Adjusted); % (Percentage rate).

Appendix Table 2.

Canada Data Sources, Descriptions, and Transformations

article image

Abbreviations: D (Difference); LD (Log-Differences); DHP (Deviations from HP Trend); LDHP (Log-Deviations from HP Trend).

Abbreviations: SA (Seasonally Adjusted); SAAR (Seasonally Adjusted Annualized Rates or Levels); NSA (Not Seasonally Adjusted); % (Percentage rate).

1

Prepared by Alejandro Justiniano.

2

Convergence diagnostics in the estimation can indicate problems with the identifying assumptions. Note that it is also possible to test restrictions in over-identified VARs.

3

Indeed, recent academic research suggests that factor models provide gains in the accuracy of forecasts of the data they describe, relative to small scale VARs and other methods. See for instance Stock and Watson (2002).

4

Much recent work in this field uses principal components to analyze the transmission of shocks across real GDP series. See, for instance, Bowden and Martin (1996), Lumsdaine and Prasad (2003), Melek-Mansur (1999), and Helbling and Bayoumi (2003). This partly reflects recent advances in estimation techniques (Stock and Watson 1998, Forni et al., 2001, and Kim and Nelson, 1999).

5

The specification of dynamics is, consequently, similar to the one preferred by Kaufman (2000) for the analysis of European business cycles.

6

Of course, the simplicity of this example does not highlight one of the greatest advantages of factor models: working with several (possibly hundreds of) series driven by a few common shocks.

7

This implies that the models and matrices described on the previous page would each consist of 44 rows. The U.S. and Canadian series comprise main national accounts aggregates (real GDP, consumption, investment, government consumption, exports, and imports), other measures of real activity (industrial production, unemployment, hours worked, labor productivity), prices at different stages of production, interest rates, other financial aggregates, and, in the case of Canada, real exchange rates, prices of exports and imports, and price indices for oil and non-oil commodities.

8

For the estimation, the data were also standardized, as it is customary in factor analysis, to prevent giving undue weight to the most volatile components in the data.

9

In the Bayesian setting adopted here, the Bayes’ Factor (i.e., the ratio of the posterior model probabilities) corresponds to the ratio of marginal likelihoods. See Kass and Raftery (1995) for an overview of Bayes’ factors; Geweke (1999) for the method used here to compute the marginal density; and Lopes and West (2004) and Justiniano (2004) for a discussion of these techniques in factor analysis.

10

Formal statistical methods did not validate additional lags.

11

The more limited impact on Canadian inflation compared to its U.S. counterpart presumably reflects the fact that oil prices are measured in the U.S. currency and hence change U.S. relative prices more directly.

12

Demers (2003) documents the instability of the Phillips Curve in Canada and finds that measures of cyclical activity are not linked to the evolution of inflation in most of our sample. Similar observations are discussed in Box 2 of the accompanying Staff Report.

13

The four factors explain close to 95 percent of the variation in Canadian real GDP and industrial production, with the U.S. and Canadian cycles explaining almost 90 percent of the variance.

14

As with the “US cycle” factor, this domestic real factor has very limited effects on CPI inflation. Indeed, it explains less than 5 percent of the variance of inflation.

15

Variance shares for Canadian real GDP and industrial production explained by the external real factor are 15 and 22 percent respectively. Curiously, the lower variance shares for Canada’s real GDP cannot be attributed to difficulties in explaining the volatility of Canadian trade volumes. Indeed, for real exports the proportion of the variance accounted for by the factor is higher in growth rates (56 compared to 46 percent).

16

In contrast, variance shares remain largely unchanged for Canadian exports, labor productivity and capacity utilization rate.

Canada: Selected Issues
Author: International Monetary Fund