We address the main question in the paper here by decomposing and quantifying which time-varying risk—in domestic demand or supply conditions, in domestic monetary or fiscal policy, or, in international economic and policy spillovers factors—matter for a small open economy.
To this end, historical decompositions of real GDP growth are constructed as follows: First, using the draws from the posterior distribution the model parameters, we obtain a simulated sample {u˜t}Tt=2 of (compound) structural shocks—defined in (5.30) and (5.32)—which contains i.i.d. and stochastic-volatility components, for each type of shocki∈I.
Second, we simulate the path of real GDP growth, using the Wold representation of the VAR representation of the theoretical model; i.e., given yo1, and {u˜
t} T t=2, we have: yot(i) =Ho " (Aθ) t−1 y1+ t−2 X j=0 (Aθ) j BθSiu˜t−j # , ∀t >1
where Si selects a particular structural shock u˜i,t−j ∈u˜t−j.
Third, we construct historical decomposition statistics, {HDn,t(i) :i∈I} T
t=2, which account for the contribution to each date-t observable variable, yn,t, by the cumulativeo
effect of the structural shock i, i.e., u˜i, from the beginning of the sample period until
date t. The accounting formula for this is: HDn,t(i) := yon,t(i) P i∈I yon,t(i) . (5.34)
Note that we define this statistic in terms of absolute sizes or magnitudes of contribu- tions, since we are not per se interested in the directions or net effects of these shocks.
A rough cut. We plot the historical decomposition statistics defined by (5.34) for each combined structural shock u˜i, i ∈ I, in Figure 5.3. (Note that this is a coarser
analysis for now as each combined shock contains variations from an i.i.d. shocks component and an stochastic-volatility shock component.) Each shock i has a unique
color-coded patch in the figure. From Figure 5.3, we can deduce that domestic shocks have contributed to majority of the output fluctuations over the sample period. On average, international spillovers have contributed to around five percent of domestic real GDP fluctuations, with the majority of contributions stemming from foreign output shocks. In contrast, domestic policy shocks have contributed around 90 percent of all output fluctuations with monetary policy having particularly pronounced impacts in the mid-1980s. Interestingly, the contribution of the shocks seems to reach a stable share after the introduction of inflation targeting in 1991.
1980 1985 1990 1995 2000 2005 2010 2015 0 0.2 0.4 0.6 0.8 1 Technology Shock Domestic Monetary Policy Labour Tax Shock
Foreign Monetary Policy Shock Foreign Output Shock
Foreign Inflation Shock
Figure 5.3: Historical decomposition by combined structural shocks (u˜)
A finer cut. To analyze the relative contribution of uncertainty shocks, we further decompose the contribution of the two stochastic elements of the structural shocks
˜
ut—i.e., changes in the i.i.d. innovations (εt) versus changes in the riskiness of struc-
tural shocks (Σt). More precisely, givenu˜i,t fromu˜t, we can square the definition (5.30) and take logarithms on both sides to obtain:
We can then define the (absolute) proportion of log(˜u2i,t) explained by the stochastic volatility component as:
ξi,t =
|log(σ2i,t)|
|log(˜u2
i,t)|
. (5.36)
What this refined measure tell us is as follows: A larger magnitude of ξi,t implies that the distributional riskiness of a particular shock i is more important in accounting for
the variations in the compound structural shock i, i.e., u˜i,t. (The complement of this statistic, which accounts for the share of the i.i.d. component, can be readily deduced as well.)
We present a refinement of the statistics (5.34) using (5.36), and its complement, for each shockiacross the sample periodst, in Figure 5.4. Figure 5.4 is basically Figure 5.3
decomposed further using the formula (5.36). Recall from Figure 5.3, we learned that monetary- and fiscal-policy shocks account for most of the variations in the Canadian data’s real GDP growth. Now, in Figure 5.4 we further deduce that these policy shocks are largely accounted for by their respective i.i.d. components, εR,t and ετW,t.
However, there is also non-negligible contributions to real GDP growth by fiscal and monetary policy-shock uncertainties.
1980 1985 1990 1995 2000 2005 2010 2015 0 0.2 0.4 0.6 0.8 1 Technology Shock Technology Uncertainty Domestic Monetary Policy
Domestic Monetary Policy Uncertainty Labour Tax Shock
Labour Tax Uncertainty Foreign Monetary Policy Shock Foreign Monetary Policy Uncertainty Foreign Output Shock
Foreign Output Uncertainty Foreign Inflation Shock Foreign Inflation Uncertainty
Figure 5.4: Historical decomposition by uncertainty shocks (σi,t)
In Figure 5.5 we plot the contributions of the stochastic volatility to variations in Canadian real GDP directly. The contribution of uncertainty shocks, averaged over the
data sample, is around 17 percent, with fiscal- and monetary-policy-shock uncertainty explaining most of the effects. This result is much larger than closed-economy studies on the US economy. For instance Mumtaz and Zanetti (2013) find that monetary-policy- shock uncertainty has a negligible effect on US real GDP (approximately 0.15 percent). A similar result which also encompasses the effects of fiscal-policy-shock uncertainty is found by Born and Pfeifer (2014). Interestingly, when exploring a zero lower bound environment, Fernández-Villaverde et al. (2015) find that fiscal uncertainty shocks may decrease real GDP by around 1.5 percent.
1980 1985 1990 1995 2000 2005 2010 2015 0 0.2 0.4 0.6 0.8 1 Technology Uncertainty
Domestic Monetary Policy Uncertainty Labour Tax Uncertainty
Foreign Monetary Policy Uncertainty Foreign Output Uncertainty
Foreign Inflation Uncertainty
Figure 5.5: Historical decomposition by IID (i,t) and uncertainty shocks (σi,t)
In summary, our results suggest that the historical movements in Canadian real GDP is due largely to domestic fiscal- and monetary-policy shocks, and, due to non- negligible time variations in the riskiness of these policy shocks.
5.7
Conclusion
In this paper, our main goal was to understand which of unexpected variations in international economic uncertainty, or domestic economic and policy uncertainties, are the more dominant drivers of a small open economy’s business cycle.
To answer this question, we extended a version of a well-known small-open-economy DSGE model to allow for the volatilities of the structural disturbances to change over time. Using this model structure as a yardstick for interpretation and quantification,
we identified and accounted for both domestic versus international, and, market-driven versus policy-driven, sources of uncertainty shocks.
First, we identify considerable time-varying volatilities in both domestic and foreign shock processes. Specifically, we find that there has been a broad decline in economic and policy shock uncertainty for both the Canadian (domestic) and our representation of the U.S. (foreign) economy. However, there has been a noticeable increase in our identified monetary- and fiscal-policy shocks’ uncertainties leading up to and after the Great Recession period.
Finally, in contrast to the closed-economy literature on the US economy, we found that uncertainty accounts for a significant proportion of output fluctuations (around 17 percent). The primary contributors are domestic fiscal- and monetary-policy-shock uncertainty (around 8 percent each), with international uncertainty spillovers having a negligible effect (less than one percent). While the former result is new, the latter result is complementary to the existing DSGE literature examining the Canada/US relationship.