Chapter

I Factoring in Canadian Cycles

Author(s):
Vladimir Klyuev, Martin Mühleisen, and Tamim Bayoumi
Published Date:
October 2007
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Author(s)
Alejandro Justiniano

Canada’s recent economic history illustrates the important role of external as well as domestic macroeconomic disturbances. Canada’s economy slowed in 2001, in the wake 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: externally, there was an appreciation of the Canadian dollar and a case of mad cow disease that constrained agricultural exports; domestically, there were an outbreak of SARS (severe acute respiratory syndrome) and some forest fires. Growth rebounded in 2004, partly as a result of strong global commodity demand, but appreciation of the Canadian dollar led to concerns about the prospects for 2005.

Previous studies have documented the importance of U.S. real shocks on Canadian business cycles. For instance, IMF (2004a) concluded that the synchronization of real output, consumption, and investment fluctuations between Canada and the United States has increased over the last two decades. Other work using vector autoregression (VAR) techniques on a small set of Canadian and foreign variables also has concluded that developments in the United States strongly influence real activity and nominal variables in Canada (Schmitt-Grohé, 1998; Cushman and Zha, 1997; Burbidge and Harrison, 1985). These findings naturally lead to questions about the transmission channels through which U.S. and other external shocks impact the Canadian economy. This section uses recent developments in dynamic factor models to undertake a comprehensive and broad-based analysis of the role of domestic and external shocks in the Canadian economy.

Dynamic Factor Analysis

Dynamic factor analysis has a number of advantages over the use of VARs:

  • 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.
  • Factor analysis provides more information on the disturbances. Factor analysis and VARs use similar techniques to identify shocks. However, in contrast to the estimation of exactly identified VARs, convergence diagnostics in the estimation of factor models can be used to check if the identifying restrictions are valid.1
  • Factor models provide relatively efficient forecasts. The internal dynamics of the factors 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.2

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.3 Extending the earlier work of Gregory, Head, and Raynauld (1997) and Kose, Otrok, and Whiteman (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.4

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 fE1, fE2, fD1 and fD2, that affect the series both contemporaneously and with one lag.5 Then the model is

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

Factors and coefficients are provided as outputs of the estimation process, based on a few 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 analysis 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 the Canadian series. In the example above, this implies that 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 (β0US1,E2=0). A similar assumption applies to the way domestic factors affect the two Canadian variables.

Canadian–U.S. Economic Interactions

To provide a comprehensive description of economic interactions within and across the United States and Canada, a large number of variables are employed in the analysis. Specifically, 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.6 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 (that is, the change in the logarithm). Further details and sources for the dataset and detrending methods are provided in Boxes 1.1 and 1.2.7

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.8 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.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 (see Justiniano, 2005, Figure I.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 1.1 and 1.2). 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 1.1.“Oil Factor” and Comovements in Selected Series

(Standard deviations)

Source: IMF staff calculations.

Note: Each series is divided by its standard deviation and its mean is removed. Vertical axes are therefore measured in standard deviations.

Table 1.1.Variance Decompositions for the United States from a Factor Model
SeriesTransformationExternal

Factor 1,

Median
External

Factor 2,

Median
U.S. producer price index intermediate goodsLD0.820.01
U.S. industrial production indexLDHP0.030.65
U.S. unemployment rateDHP0.020.26
U.S. shares price index (nominal)LD0.070.04
U.S. GDPLDHP0.010.58
U.S. consumptionLDHP0.030.25
U.S. investmentLDHP0.010.23
U.S. governmentLDHP0.040.05
U.S. exports (goods)LDHP0.010.14
U.S. imports (goods)LDHP0.010.51
U.S. hoursLDHP0.070.33
U.S. labor productivityLDHP0.020.32
U.S. capacity utilization rateDHP0.030.71
U.S. CPI (all goods)LD0.480.03
U.S. producer price index, finished goodsLD0.680.08
U.S. unit labor costsLD0.050.10
U.S. federal funds rateD0.150.45
U.S. M2LD0.080.06
World price of oil (non-OPEC countries)LD0.650.03
World commodity price indexLD0.170.11
Source: IMF staff calculations.Notes: CPI = consumer price index; D = first difference; LD = log of first difference; DHP = deviation from Hodrick-Prescott (HP) trend; LDHP = log of deviation from HP trend; OPEC = Organization of Petroleum Exporting Countries.
Source: IMF staff calculations.Notes: CPI = consumer price index; D = first difference; LD = log of first difference; DHP = deviation from Hodrick-Prescott (HP) trend; LDHP = log of deviation from HP trend; OPEC = Organization of Petroleum Exporting Countries.
Table 1.2.Variance Decompositions for Canada from a Factor Model
SeriesTransformationExternal

Factor 1,

Median
External

Factor 2,

Median
Domestic

Factor 1,

Median
Domestic

Factor 2,

Median
Canadian real exchange rateLD0.020.030.530.01
Canadian GDPLDHP0.030.420.010.47
Canadian industrial production indexLDHP0.030.480.010.38
Canadian nominal exchange rateLD0.040.040.760.01
Canadian labor productivityLDHP0.020.120.010.43
Canadian consumptionLDHP0.070.190.050.16
Canadian governmentLDHP0.010.070.010.05
Canadian investmentLDHP0.010.100.020.02
Canadian exports (goods)LDHP0.020.440.010.02
Canadian imports (goods)LDHP0.010.490.020.07
Canadian hoursLDHP0.050.250.020.25
Canadian capacity utilization rateDHP0.020.480.010.02
Canadian unemployment rateDHP0.010.260.010.01
Canadian unit labor costsLD0.060.530.010.02
Canadian M2LD0.020.050.020.03
Canadian bank rateD0.030.360.060.05
Canadian CPI (all goods)LD0.100.050.020.05
Canadian CPI (minus volatile components)LD0.020.040.020.02
Canadian producer price index, excluding oilLD0.030.150.260.02
Canadian commodity price index: energyLD0.680.030.010.02
Canadian commodity price index: nonenergyLD0.050.080.070.04
Canadian export pricesLD0.440.030.250.01
Canadian import pricesLD0.060.090.660.03
Canadian shares price index (nominal)LD0.020.030.150.04
Source: IMF staff calculations.Notes: CPI = consumer price index; D = first difference; LD = log of first difference; DHP = deviation from Hodrick-Prescott (HP) trend; LDHP = log of deviation from HP trend.
Source: IMF staff calculations.Notes: CPI = consumer price index; D = first difference; LD = log of first difference; DHP = deviation from Hodrick-Prescott (HP) trend; LDHP = log of deviation from HP trend.

The first external 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 1.1). It accounts for 65 percent and 82 percent of the respective variances and tracks these series closely. In the United States, this “oil factor” explains much of the variation in prices and in the federal funds rate. In Canada, it accounts for a large amount of the variation in export and energy prices and some 10 percent of fluctuations in the headline consumer price index (CPI), but a smaller proportion of fluctuations in core CPI inflation, Canadian interest rates, and nonenergy commodity prices.10 Consistent with post-1985 results reported in Kose, Otrok, and Whiteman (2003), there is little interaction between oil prices and real variables.

The second external factor, the “real foreign factor,” which tracks the U.S. cycle, accounts for almost 60 percent of the deviations of U.S. real GDP from trend (Figure 1.2). It captures the recessions (and subsequent recoveries) of 1990 and 2001, as well as the slowdown in 1995, and it can explain about half of the changes in the federal funds rate (which tends to lead the cycle), particularly since 1987. This real foreign factor also explains about half the movements in U.S. imports and one-quarter of consumption fluctuations.

Figure 1.2.“Real Foreign Factor” and Comovements in Selected Series

(Standard deviations)

Source: IMF staff calculations.

Note: Each series is divided by its standard deviation and its mean is removed. Vertical axes are therefore measured in standard deviations.

This real foreign factor has a large influence on Canadian real GDP and industrial production, explaining about 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 expected given the U.S. slowdown. More recently, however, the recovery of Canadian real GDP has lagged behind the real foreign factor.

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 real foreign factor explains about half of the variation in Canadian exports and imports. This relationship appears to have increased during the 1990s, plausibly reflecting greater economic integration over this period.

The real foreign factor also explains about one-third of the fluctuations in Canada’s bank rate, particularly since the mid-1990s. However, these two series behaved quite differently in 1991—the inception of the Bank of Canada’s IT regime—and, to a lesser extent, more recently in 2002–03. Despite the factor’s important role for the Canadian real economy, its impact on inflation is quite limited, however, echoing the conclusions from other studies that have encountered difficulties in establishing a stable relationship between capacity measures and inflation.11

The third factor, the “exchange rate factor,” closely tracks movements in Canada’s exchange rate and non-oil producer and commodity prices (Figure 1.3). As 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 IT was first adopted. Nonetheless, this relationship seems to weaken considerably after 1998, about the time that the Bank of Canada abandoned the Monetary Conditions Index as an indicator of monetary policy.

Figure 1.3.“Exchange Rate Factor” and Comovements in Selected Series

(Standard deviations)

Source: IMF staff calculations.

Note: Each series is divided by its standard deviation and its mean is removed. Vertical axes are therefore measured in standard deviations.

The last factor, the “real domestic factor,” corresponds to domestic disturbances responsible for Canada’s cycle (Figure 1.4). The factor explains about half the fluctuations in Canadian real GDP and about one-third of movements in industrial production.12 There was a close link between this factor and fluctuations in Canada’s real GDP through the mid-1990s. Subsequently, however, the two series became less correlated, as did other variables that were previously well explained by this factor such as industrial production, labor productivity, and hours worked.13 Finally, the real foreign factor appears to lead this domestic real factor somewhat. The correlation coefficients of the first and second lag of the real foreign factor with the real domestic 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 1.4.“Real Domestic Factor” and Comovements in Canadian GDP

(Standard deviations)

Source: IMF staff calculations.

Note: Each series is divided by its standard deviation and its mean is removed. Vertical axes are therefore measured in standard deviations.

Robustness Checks

The results appear generally robust to changes in the way the data are measured. This was examined by reestimating the model with real variables measured as rates of change, rather than as deviations from trend. Statistical methods indicate that the same model structure—four factors with extremely similar features—remain 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 production are lower.14 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.

Estimating the model with and without lags reveals the importance of spillover effects from external shocks. The model was reestimated excluding the lags in the impact of factors on individual series to explore the importance of this assumption to 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 foreign factor in the United States falls when 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 as industrial production and unit labor costs) attributed to the U.S. cycle falls.15 This indicates that lags matter in the effects of U.S. activity on the Canadian economy.

Box 1.1.United States: Data Sources, Descriptions, and Transformations

SeriesTransformationDescriptionSource
US capacity utilization rateDHP and DManufacturing survey: capacity utilization rate (SA, %)OECD
US consumptionLDHP and LDPrivate final consumption expenditure (SAAR, millions chained 2000 US$)OECD
US CPI (all goods)LDAll urban consumers, all itemsFederal Reserve Bank of St. Louis
US exports (goods)LDHP and LDExports of goods (SAAR, billions chained 2000 US$)OECD
US federal funds rateDEffective federal funds rates (averages of daily values)Federal Reserve Bank of St. Louis
US GDPLDHP and LDGross domestic product (SAAR, billions chained 2000 US$)OECD
US governmentLDHP and LDGovernment final consumption expenditure (SAAR, millions chained 2000 US$)OECD
US hoursLDHP and LDTotal private, quarterly averages (SA, hours)Bureau of Labor Statistics
US imports (goods)LDHP and LDImports of goods (SAAR, billions chained 2000 US$)OECD
US industrial production indexLDHP and LDIndustrial production index (SA, 1997 = 100)Federal Reserve Board
US investmentLDHP and LDGross fixed capital formation (SAAR, millions chained 2000 US$)OECD
US labor productivityLDHP and LDLabor productivity index of the total economyOECD
US M2LDMoney stock, M2Federal Reserve Board
US producer price index finished goodsLDPPI finished goods (SA, 1982 = 100)Bureau of Labor Statistics
US producer price index intermediate goodsLDPPI intermediate materials, supplies and components (SA, 1982 = 100)Bureau of Labor Statistics
US shares price index (nominal)LDStandard & Poor’s 500 Composite (1941–43 = 10)Wall Street Journal
US unemployment rateDHP and DStandardized unemployment rate (SA, %)OECD
US unit labor costsLDUnit labor cost, business sector (SA, 1992 = 100)Bureau of Labor Statistics
World commodity price indexLDSpot commodity price index: all commodities (1967 = 100)Commodity Research Bureau
World price of oil (non-OPEC countries)LDAverage crude oil spot price: total non-OPEC (US $/barrel)Department of Energy
Notes: CPI = consumer price index; PPI = producer price index; D = difference; LD = log differences; DHP = deviations from Hodrick-Prescott (HP) trend; LDHP = log-deviations from HP trend; SA = seasonally adjusted; SAAR = seasonally adjusted annualized rates or levels; OPEC = Organization of the Petroleum Exporting Countries; OECD = Organization for Economic Cooperation and Development.
Notes: CPI = consumer price index; PPI = producer price index; D = difference; LD = log differences; DHP = deviations from Hodrick-Prescott (HP) trend; LDHP = log-deviations from HP trend; SA = seasonally adjusted; SAAR = seasonally adjusted annualized rates or levels; OPEC = Organization of the Petroleum Exporting Countries; OECD = Organization for Economic Cooperation and Development.

Box 1.2.Canada: Data Sources, Descriptions, and Transformations

SeriesTransformationDescriptionSource
CDN bank rateDOfficial discount rate of the Bank of Canada (monthly average, %)Bank of Canada
CDN capacity utilization rateDHP and DManufacturing survey: capacity utilization rate (NSA, %)OECD
CDN commodity price index: energyLDCommodity price index, energy (1982–90 = 100)Bank of Canada
CDN commodity price index: non-energyLDCommodity price index, total excluding energy (1982–90 = 100)Bank of Canada
CDN consumptionLDHP and LDPrivate final consumption expenditure (millions chained 1997 Can$, SAAR)OECD
CDN CPI (all goods)LDCPI, all items (NSA, 1992 = 100)Statistics Canada
CDN CPI (minus volatile components)LDCPI, all items excluding 8 volatile components and indirect taxes (NSA, 1992 = 100)Bank of Canada
CDN export pricesLDExport price index (SA, 1992 = 100)Statistics Canada
CDN exports (goods)LDHP and LDExports of goods (SAAR, millions chained 1997 Can$, SAAR)OECD
CDN GDPLDHP and LDGross domestic product (millions chained 1997 Can$, SAAR)OECD
CDN governmentLDHP and LDGovernment final consumption expenditure (millions chained 1997 C$, SAAR)OECD
CDN hoursLDHP and LDActual hours worked during reference week, all sectors (SA, 1,000s of hours)Statistics Canada
CDN import pricesLDImport price index (SA, 1992 = 100)Statistics Canada
CDN imports (goods)LDHP and LDImports of goods (SAAR, millions chained 1997 Can$, SAAR)OECD
CDN industrial production indexLDHP and LDIndustrial production index (SA, 2000 = 100)OECD
CDN investmentLDHP and LDGross fixed capital formation (millions chained 1997 Can$, SAAR)OECD
CDN labor productivityLDHP and LDLabor productivity index of the total economyOECD
CDN M2LDM1 plus all checkable notices and personable term depositsBank of Canada
CDN nominal exchange rateLDU.S. dollar noon spot rate (Can$/US$)Bank of Canada
CDN producer price index excluding oilLDPPI, total excluding petroleum/coal products (NSA, 1997 = 100)Statistics Canada
CDN real exchange rateLDBroad real effective exchange rate index (2000 = 100)JPMorgan
CDN share price index (nominal)LDS&P/TSX: 60 index (1/29/1982 = 100)Bank of Canada
CDN unemployment rateDHP and DStandardized unemployment rate (SA, %)OECD
CDN unit labor costsLDUnit labor cost, manufacturing (SA, 2000 = 100)OECD
Notes: CPI = consumer price index; PPI = producer price index; D = difference; LD = log differences; DHP = deviations from Hodrick-Prescott (HP) trend; LDHP = log-deviations from HP trend; S&P = Standard and Poor’s; TSX = Toronto Stock Exchange; SA = seasonally adjusted; SAAR = seasonally adjusted annualized rates or levels; NSA = not seasonally adjusted; OECD = Organization for Economic Cooperation and Development.
Notes: CPI = consumer price index; PPI = producer price index; D = difference; LD = log differences; DHP = deviations from Hodrick-Prescott (HP) trend; LDHP = log-deviations from HP trend; S&P = Standard and Poor’s; TSX = Toronto Stock Exchange; SA = seasonally adjusted; SAAR = seasonally adjusted annualized rates or levels; NSA = not seasonally adjusted; OECD = Organization for Economic Cooperation and Development.

Conclusions

The results of this analysis suggest the following:

  • Four factors 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. These factors seem to correspond to world oil price shocks, the U.S. cycle, an exchange rate and non-oil price shock, and a domestic 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 the role of external factors is even larger for other real series and for policy interest rates. Furthermore, the analysis indicates that the importance of the real domestic 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.
1Convergence diagnostics in the estimation can indicate problems with the identifying assumptions. Note that it is also possible to test restrictions in overidentified VARs.
2Indeed, 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).
3Much 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 Mansour (1999); and Helbling and Bayoumi (2003). This partly reflects recent advances in estimation techniques (Stock and Watson, 1998; Forni and others, 2001; and Kim and Nelson, 1999).
4The specification of dynamics is, consequently, similar to the one preferred by Kaufmann (2000) for the analysis of European business cycles.
5Of 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.
6This implies that the models and matrices described on the previous page would each consist of 44 rows. The U.S. and Canadian series include 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.
7For the estimation, the data were also standardized, as is customary in factor analysis, to prevent giving undue weight to the most volatile components in the data.
8In the Bayesian setting adopted here, the Bayes Factor (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.
9Formal statistical methods did not validate additional lags.
10The 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 affect U.S. relative prices more directly.
11Demers (2003) documents the instability of the Phillips Curve (inflation versus unemployment) in Canada and finds that measures of cyclical activity are not linked to the evolution of inflation during most of our sample period. Similar observations are discussed in Box 2 in IMF (2004a).
12The 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.
13As with the real foreign factor, this real domestic factor has very limited effects on CPI inflation. Indeed, it explains less than 5 percent of the variance in inflation. This shift is also reflected in the precision with which this factor is estimated, evident from widening error bands reported in Justiniano (2005, Figure I.1).
14Variance shares for Canadian real GDP and industrial production explained by the real foreign 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 percent, compared to 46 percent).
15In contrast, variance shares remain largely unchanged for Canadian exports, labor productivity, and the capacity utilization rate.

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