Foreign Vulnerabilities, Domestic Risks: The Global Drivers of GDP-at-Risk

Abstract

We study how foreign financial developments influence the conditional distribution of domestic GDP growth. We propose a method to account for foreign vulnerabilities using bilateral-exposure weights when assessing downside macroeconomic risks within quantile regressions. For an advanced-economy panel, we show that tighter foreign financial conditions and faster foreign credit-to-GDP growth are associated with a more severe left-tail of domestic GDP growth, even controlling for domestic indicators. Incorporating foreign variables improves estimates of domestic GDP-at-Risk, both in and out of sample. Decomposing GDP-at-Risk into domestic and foreign origins, we show that foreign shocks are a key driver of domestic macroeconomic tail risks.

Appendices

Appendix 1: Data Sources

Table 7 presents a full list of data sources used in this paper—both in the main body and the appendices.

Table 7 List of data sources

Table 8 presents the bivariate correlations between domestic and foreign-weighted FCI and credit-to-GDP for each country over the sample of the baseline specification (1981Q1–2016Q3). To support this, in Figs. 4 and 5, we plot country-level time series of the two main explanatory variables used in our baseline specification: the FCI and the 3-year change in credit-to-GDP. The figures depict the standardised values of the series.

Table 8 Correlation between domestic indicator and foreign-weighted indicator for each country

Fig. 4

Country-level time series of FCI used in baseline specification. Note: Standardized country-specific time series of FCI used in baseline specification over the period 1981Q1:2016Q3

Fig. 5

Country-level time series of 3-year change in credit-to-GDP used in baseline specification. Note: Standardized country-specific time series of 3-year change in credit-to-GDP used in baseline specification over the period 1981Q1:2016Q3

Appendix 2: Additional Results and Robustness Analysis

1.1 Additional Results from the Baseline Empirical Model

In this Appendix sub-section, we report additional results from our baseline empirical model described in Sect. 3.1.

Coefficient Estimates for Macroeconomic Controls Across Horizons

Figure 6 presents coefficient estimates for the macroeconomic control variables—domestic and foreign-weighted quarterly real GDP growth—at the $\tau =0.05$th quantile across horizons in our specific model described in Sect. 3. Both domestic and foreign-weighted real GDP growth are associated with higher estimates of the 5th percentile of real GDP growth.

Fig. 6

Association between indicators and the 5th percentile of GDP growth across horizons. Note: Estimated association between one standard deviation change in each indicator at time t with 5th percentile of average annual real GDP growth at each quarterly horizon. Red dashed lines denote 90% coefficient bands from the domestic-only model, that excludes foreign covariates. Solid blue lines denote coefficient estimates from model that includes foreign covariates. Light (dark) blue-shaded areas represent 90% (68%) confidence bands from block bootstrap procedure. (Color figure online)

Coefficient Estimates Across Quantiles

Figure 7 compares coefficient estimates from our baseline foreign-augmented model at the 5th and 50th percentiles. The coefficient estimates for FCI and credit highlight notable differences over the distribution. The near-term impacts of tighter financial conditions are more negative at the 5th percentile than at the median, while the inter-temporal reversal is also specific to the left tail. For foreign-weighted credit, coefficient estimates are negative at all horizons for the 5th percentile. But faster foreign credit growth is associated with higher median GDP growth in the near-term.

Fig. 7

Association between indicators and GDP growth across horizons at the 5th and 50th percentiles. Note: Solid blue lines denote estimated association between one standard deviation change in each indicator at time t with 5th percentile of average annual real GDP growth at each quarterly horizon. Light (dark) blue-shaded areas represent 90% (68%) confidence bands around these estimates from block bootstrap procedure. Black dashed lines denote corresponding coefficient estimates at the 50th percentile (i.e., median). (Color figure online)

1.2 Robustness: Coefficient Estimates

In this Appendix sub-section, we report key robustness exercises around the coefficient estimates in our baseline specification. Table 9 summarizes the results from these exercises, illustrating that our headline results are robust to a range of alternative model specifications. Across all specifications, the estimated coefficient on foreign-weighted credit-to-GDP at the 5th percentile for medium-term horizons is significantly negative at the 5% level at least. These coefficients, and those on the foreign FCI, are typically more negative than coefficients estimates for the median, indicating the influence of these foreign variables on the left tail of the conditional GDP growth distribution in particular. We discuss each of the robustness exercises in more detail below.

Table 9 Coefficient estimates from robustness exercises

Foreign-Weighting Scheme

In our baseline specification, we use trade weights to capture countries’ bilateral exposures. These weights have the advantage of running back to 1980, enabling us to use time-varying weights. However, we find similar results when we use bilateral financial weights using BIS International Banking Statistics that capture banks’ exposures to the rest of the world (Panel A).³³

Alternate Financial Conditions

Panel B presents results from a specification using a measure of within-quarter realized equity market volatility, used by Aikman et al. (2019), as an alternative to the FCI used in the baseline. This equity-market volatility series is available for 13 countries, relative to 10 in our baseline panel, and it extends to 2018Q4, relative to 2016Q3 in our baseline sample.

Foreign Country Set

In Panel C, we present results from a specification where we extend the set of countries used to define foreign-weighted covariates. We increase our foreign country set ($N^*$) to 16, by including 6 emerging market economies (China, Korea, Indonesia, Mexico, Turkey and Hong Kong) in addition to the 10 advanced economies used in our baseline specification. We maintain our domestic variable set (N) at 10. We shorten the sample for this specification due to limited data availability in some emerging market economies. The results from this model are very similar to our baseline results, although we find slightly larger effects of foreign variables on domestic GDP-at-Risk when we extend the foreign country set.

Pre-GFC Sample

To assess the extent to which the GFC drives our results, Panel D reports coefficients from a sample estimated on pre-GFC data, from 1981Q1 to 2005Q4. As in the full sample, we find that foreign-weighted vulnerabilities exert a significant influence on the left tail of GDP growth, with foreign credit weighing more on the 5th percentile in the medium term than the median out to $h=12$. In addition, pre-GFC coefficient estimates for foreign-weighted credit-to-GDP, in particular, are similar in magnitude to full-sample estimates at most horizons, suggesting that the GFC period is not driving our results.

Domestic Covariates

Panel E presents results from a specification with additional domestic covariates. Here, we include domestic 3-year house price growth, the capital ratio (a measure of overall banking system resilience), the 1-year change in headline central bank policy rates and 1-year inflation in our domestic covariate set—as in Aikman et al. (2019). This allows us to test whether foreign variables provide additional explanatory power, even after accounting for a much wider range of potential domestic covariates. Despite the addition of more domestic covariates, estimated coefficients on the foreign variables continue to remain significant and of similar magnitude to the baseline.

US-Only Foreign Variables

In Sect. 2, we noted that our proposal nests one in which only US variables are used in the foreign variable set. When estimating this, we continue to find similar results: US financial market volatility weighs on domestic GDP-at-Risk in the near term, while US credit-to-GDP growth has a significant association with medium-term tails risks (Panel F). However, the magnitude of estimated coefficients is somewhat smaller. For example, at $h=8$, the coefficient on US credit-to-GDP growth is $-0.292$ (insignificant), versus $-0.691$ (significant at the 10% level) in the baseline. While this indicates that the US plays an important role in driving domestic tail risks, there are advantages to using a wider set of countries when constructing the foreign-weighted variables to account for a broader set of cross-border transmission channels and shocks—including the build-up of regional risks.

1.3 Model Fit Over Time

Figure 8 presents estimates of the average tick loss at the 5th percentile across countries over time for both the domestic-only and foreign-augmented model at various horizons. This gives an indication of when exactly incorporating foreign information into the model serves to improve estimation of GDP-at-Risk. A lower tick loss implies an improvement in fit—and so time periods where the blue foreign-augmented line lies below the red domestic-only line highlight occasions when foreign information improves the estimation of GDP-at-Risk. In general, these charts highlight the pay-off from including foreign information is highest around crisis episodes, consistent with a focus on the 5th percentile of GDP growth. For example, at the 1-quarter horizon, the blue line lies clearly below the red line around the early 1990s—a period of recession for the majority of advanced economies in our panel—and again around the GFC. The improvement in fit around the GFC is also visible for the 4- and 8-quarter horizon.

Fig. 8

Estimated tick loss at 5th percentile ($TL_t^h(0.05)$) over time. Note: Estimated average tick loss at the 5th percentile across countries over time and across horizons. The red line denotes estimates from the domestic-only specification and the blue line estimates from the foreign-augmented model. (Color figure online)

1.4 Country Heterogeneity: Coefficient Estimates from Interaction Regression

Table 10 presents key results for a specification that includes an interaction term between foreign variables and a country’s level of openness. Panel A shows estimated coefficients at the 5th percentile for the foreign variables and interaction terms, as well as their statistical significance. The interaction terms are generally insignificant across variables and horizons, only occasionally significant at the 32% level at most (e.g., the interaction term on foreign-weighted FCI at the 1-quarter horizon). This suggests that heterogeneity in country spillovers driven by differences in levels of observed openness is not a significant feature of our data.

To aid the economic interpretation of these results, Panel B shows the association between each foreign variable and GDP-at-Risk for different levels of openness. The first three rows correspond to the estimated association for a country with an average level of trade-to-GDP (around 54% in our sample), while the bottom three rows correspond to the estimated association for a country with level of trade-to-GDP one standard deviation above the average (around 74%). This demonstrates that, for example, at peak (at $h=1$), a one-standard deviation rise in a country’s openness increases the effect of foreign FCI on GDP-at-Risk by around a third (from $-1.2$pp to $-1.6$pp for a one standard deviation rise in foreign-weighted FCI). Similarly, at peak ($h=8$), a one standard deviation rise in a country’s openness increases the effect of foreign credit on GDP-at-risk by around a quarter (from $-0.6$pp to $-0.8$pp for a one standard deviation rise in foreign-weighted credit).

Table 10 Interaction coefficient estimates at 5th percentile from interaction regression (5)

1.5 Country Heterogeneity: Pooled Country-Specific Results

Figure 9 plots a comparison of our baseline coefficient estimates for foreign-weighted FCI and credit-to-GDP growth from a panel model with the mean and median of coefficient estimates from individual country regressions. The results indicate that the estimated pooled mean and median estimates are similar to those from the panel model.

Fig. 9

Average association between indicators and the 5th percentile of GDP growth across horizons from country-specific regressions. Note: Estimated association between one standard deviation change in each indicator at time t with 5th percentile of annual average real GDP growth at each quarterly horizon. Black line denotes mean coefficient estimate when pooling individual-country estimates. Black crosses represent the median. Blue line denotes point estimates from our baseline panel model. Light (dark) blue-shaded areas represent 90% (68%) confidence bands from block bootstrap procedure for the corresponding coefficient estimate over the full 1981Q1–2018Q4 sample. (Color figure online)

1.6 Robustness: In-Sample Model Fit

Table 11 reports $R_h^1(\tau )$ statistics for two of the robustness exercises, namely: calculating the statistics from the baseline foreign-augmented model, versus a restricted domestic-only model, using only the fitted values outside of the 2006–2008 period to ensure the GFC is not the sole driver of results; and assessing the fit of a foreign-augmented model with additional domestic covariates (as per Aikman et al. 2019), versus a restricted model with only these domestic variables. In both cases, we find that the addition of foreign-weighted covariates continues to result in a substantial increase in fit, especially at the 5th percentile, as in the baseline presented in the main body of the paper.

Table 11 $R_h^1(\tau )$ across horizons and quantiles for robustness exercises

1.7 Time Variation in In-Sample Moments

Figures 10 and 11 present estimated changes in in-sample moments for each country prior to the GFC at the 1- and 4-quarter horizon, respectively.

Fig. 10

Estimated change in 1-quarter-ahead GDP moments: 1997Q1 to 2006Q1. Note: Estimated change in the moments of 1-quarter-ahead annual average real GDP growth between 1997Q1 and 2006Q1 across countries. Blue bars represent estimates from model that includes foreign covariates. Red dots represent estimates from model that excludes foreign covariates. (Color figure online)

Fig. 11

Estimated change in 4-quarter-ahead GDP moments: 1997Q1 to 2006Q1. Note: Estimated change in the moments of 4-quarter-ahead annual average real GDP growth between 1997Q1 and 2006Q1 across countries. Blue bars represent estimates from model that includes foreign covariates. Red dots represent estimates from model that excludes foreign covariates. (Color figure online)

1.8 Out-of-Sample Coefficient Stability

Figure 12 plots real-time coefficient estimates for domestic and foreign-weighted variables in the foreign-augmented model.

Fig. 12

Real-time estimates of the association between domestic and foreign-weighted indicators and the 5th (50th) percentile of GDP growth Note: Estimated real-time association between one standard deviation change in each indicator at each forecast date and 5th percentile (blue line) and median (black dashed line) of annual average real GDP growth at 1-quarter horizon for domestic and foreign-weighted financial market volatility and $h=8$-quarter horizon for domestic and foreign-weighted credit-to-GDP. Light (dark) blue-shaded areas represent 95% (68%) confidence bands from block bootstrap procedure for the corresponding 5th percentile coefficient estimate over the full 1981Q1–2018Q4 sample. (Color figure online)

1.9 Out-of-Sample Model Fit Over Time

Figure 13 plots out-of-sample estimates of the average tick loss at the 5th percentile across countries over time.

Fig. 13

Estimated out-of-sample tick loss at 5th percentile ($TL_t^h(\tau )$) over time. Note: Estimated average tick loss at the 5th percentile across countries over time and across horizons. The red line denotes estimates from the domestic-only specification and the blue line estimates from the foreign-augmented model. (Color figure online)

1.10 Out-of-Sample PITs

Figures 14 and 15 report the 1- and 4-quarter-ahead PITs for the 10 countries in turn, supporting the discussion in Sect. 3.3.2.

Fig. 14

Out-of-sample PITs: one-quarter ahead. Note: Empirical cumulative distribution of the probability integral transform (PIT) of out-of-sample estimates at the 1-quarter-ahead horizon. Blue line shows the estimates from the foreign-augmented model, red line shows the estimates from the restricted domestic-only model, and green line shows estimates from GDP-only model. Dashed lines denote 95% confidence intervals, obtained using the method of Rossi and Sekhposyan (2019). (Color figure online)

Fig. 15

Out-of-sample PITs: 1-year ahead. Note: Empirical cumulative distribution of the probability integral transform (PIT) of out-of-sample estimates at the 1-year-ahead horizon. Blue line shows the estimates from the foreign-augmented model, red line shows the estimates from the restricted domestic-only model, and green line shows estimates from GDP-only model. Dashed lines denote 95% confidence intervals, obtained using the method of Rossi and Sekhposyan (2019). (Color figure online)

1.11 Time Variation in Out-of-Sample Moments

Figures 16 and 17 present estimated changes in moments across countries prior to the GFC, estimated out-of-sample.

Fig. 16

Estimated change in 1-quarter-ahead GDP moments: 1997Q1 to 2006Q1. Note: Estimated change in the moments of 1-quarter-ahead annual average real GDP growth between 1997Q1 and 2006Q1 across countries. Blue bars represent estimates from model that includes foreign covariates. Red dots represent estimates from model that excludes foreign covariates. (Color figure online)

Fig. 17

Estimated change in 4-quarter-ahead GDP moments: 1997Q1 to 2006Q1. Note: Estimated change in the moments of 4-quarter-ahead annual average real GDP growth between 1997Q1 and 2006Q1 across countries. Blue bars represent estimates from model that includes foreign covariates. Red dots represent estimates from model that excludes foreign covariates. (Color figure online)

Appendix 3: Structural Contribution of Foreign Drivers

1.1 Structural Coefficient Estimates

In this sub-section, we report coefficient estimates at the 5th percentile for our alternate structural model described in Section 4 (Fig. 18) the coefficient estimates are similar to those in Fig. 1, although the estimates of the impact of foreign credit-to-GDP and the foreign FCI on domestic GDP-at-Risk are now larger in magnitude. For example, in this specification, at peak, a one standard deviation increase in the foreign-weighted FCI is linked with a 1.5pp fall in the 5th percentile of GDP growth compared to a 1.1pp fall in Fig. 1. This is because the first-stage orthogonalization allows us to capture the contemporaneous impact of foreign variables on domestic covariates—e.g., capturing the fact that a sharp tightening in global financial conditions can spill over contemporaneously to domestic financial conditions (and thereby worsen domestic GDP-at-Risk via this tightening in domestic conditions).

1.2 Two-Step Orthogonalization: Equivalence with Factor Model

As discussed in Sect. 4, the orthogonalization procedure applied to distinguish foreign shocks from domestic ones is commonplace in the empirical international macroeconomics literature (e.g., Dedola et al. 2017; Cesa-Bianchi and Sokol 2022). It corresponds to a small-open economy assumption in which foreign events can contemporaneously influence domestic outcomes, but not vice versa.

In principle, an alternative proposal could be to decompose the kth domestic predictor for country i, $x_{i,t}^{(k)}$, using a factor model of the form:

$$\begin{aligned} x_{i,t}^{(k)} = \lambda _i f_t^{(k)} + \eta _{i,t}^{(k)} \end{aligned}$$

(10)

where $f_t^{(k)}$ represents a global factor and $\lambda _i$ is the country-specific loading on it.

However, we can show that our foreign-weighted variable $x_{i,t}^{*(k)}$ is observationally equivalent to the factor $f_t^{(k)}$ up to a scalar, so demonstrating the equivalence between our two-step procedure and the factor model. This result is not novel to our work. Cesa-Bianchi et al. (2019b) show this in a GVAR setting. We show how this equivalence extends to the quantile regression setting.

The logic underpinning the observational equivalence is as follows. First, recall the definition of the kth foreign-weighted predictor:

$$\begin{aligned} x_{i,t}^{*(k)} = \sum _{j=1}^{N} \omega _{i,j,t} x_{j,t}^{(k)} \end{aligned}$$

(11)

and suppose that the kth predictor for country i has the factor structure in Eq. (10).

Fig. 18

Association between orthogonalized vulnerability indicators and GDP growth across horizons at the 5th percentile. Note: Solid blue lines denote estimated association between one standard deviation change in each indicator at time t with 5th percentile of average annual real GDP growth at each quarterly horizon. Light (dark) blue-shaded areas represent 90% (68%) confidence bands around these estimates from block bootstrap procedure. (Color figure online)

Substituting the factor-model definition (10) into (11) yields:

$$\begin{aligned} x_{i,t}^{*(k)} = f_t^{(k)} \sum _{j=1}^N \omega _{i,j,t} \lambda _j^{(k)} + {\overline{\eta }}_{\omega ,t}^{(k)} \end{aligned}$$

where ${\overline{\eta }}_{\omega ,t}^{(k)} \equiv \sum _{j=1}^N \omega _{i,j,t} \eta _{j,t}^{(k)}$.

Assuming that the loadings $\lambda _i^{(k)}$ are distributed independently across i and from the common shock $f_t^{(k)}$ for all i and t, with non-zero mean $\lambda ^{(k)}$ and satisfy the following conditions:

$$\begin{aligned} \lambda ^{(k)} = \sum _{j=1}^N \omega _{i,j,t} \lambda _j^{(k)} \ne 0 \quad \text {and} \quad \sum _{j=1}^N {\lambda _j^{(k)}}^2 = {\mathcal {O}}(N) \end{aligned}$$

then the model can be written as:

$$\begin{aligned} x_{i,t}^{*(k)} = \lambda ^{(k)} f_t^{(k)} + {\overline{\eta }}_{\omega ,t}^{(k)} \end{aligned}$$

Under the following two further assumptions:

• that the weights $\omega _{i,j,t}$ for $i=1,\ldots ,N$ are such that $\sum _{j=1}^N \omega _{i,j,t}=1$ and satisfy granularity conditions, which requires individual countries’ contributions to the foreign-weighted variable to be of order 1/N, i.e., that $||\textbf{w}_{i,t}||={\mathcal {O}}(N^{-1})$ and $\frac{\omega _{i,j,t}}{||\textbf{w}_{i,t}||}={\mathcal {O}}(N^{-1/2})$; and

• that country-specific shocks $\eta _{i,t}^{(k)}$ have zero means, finite variances and are serially uncorrelated, and denoting the covariance matrix of the $N \times 1$ vector $\varvec{\eta }_t^{(k)} = [\eta _{1,t}^{(k)},\ldots ,\eta _{N,t}^{(k)}]'$ by $\varvec{\Sigma }_{\eta \eta } = \text {var} (\varvec{\eta }_t^{(k)})$ with $\varrho _{\max } (\varvec{\Sigma }_{\eta \eta })= {\mathcal {O}}(1)$;

then it follows that $\text {var}({\overline{\eta }}_{\omega ,t}^{(k)}) = {\mathcal {O}}(\textbf{w}_{i,t}' \textbf{w}_{i,t})={\mathcal {O}}(N^{-1})$ and hence ${\overline{\eta }}_{\omega ,t}^{(k)} = {\mathcal {O}}_p (N^{-1/2})$, allowing us to recover $f_t^{(k)}$ from $x_{i,t}^{*(k)}$ up to a scalar $\lambda ^{(k)}$ using:

$$\begin{aligned} f_t^{(k)} = \dfrac{1}{\lambda ^{(k)}} x_{i,t}^{*(k)} + {\mathcal {O}}(N^{-1/2}) \end{aligned}$$

thus proving the observational equivalence.

1.3 Towards a Structural Decomposition

In this sub-section, we report exemplar decompositions from our orthogonalization procedure.

Figure 19 shows the orthogonalized decomposition for the estimated 5th percentile of 3-year-ahead UK real GDP growth. The orthogonalized decomposition suggests that the estimated fall in UK 3-year GDP-at-Risk in the run-up to the 1990–1991 recession was predominantly driven by domestic drivers (red bars). Foreign drivers (blue bars) played a limited role. Following this recession, these factors reversed with the estimated rise in the 5th percentile of UK 3-year GDP growth supported by both domestic and foreign factors.

Tail risks built up substantially over the 2000s though, driven almost entirely by a build-up in foreign-weighted credit-to-GDP. This accords with the well-established view that the GFC had global origins, driven by worldwide trends in an increasingly interconnected international financial system.

Fig. 19

Estimated orthogonalized decomposition of UK GDP-at-Risk at the 3-year horizon. Note: Solid black line denotes estimated 5th percentile of annual average 3-year-ahead GDP growth at each point in time. The bars show the contribution of domestic and foreign-weighted indicators to that total from estimates of Eq. (8)

Fig. 20

Estimated orthogonalized decomposition of German GDP-at-Risk at the 3-year horizon. Note: Solid black line denotes estimated 5th percentile of annual average 3-year-ahead GDP growth at each point in time. The bars show the contribution of domestic and foreign-weighted indicators to that total from estimates of Eq. (8)

Since the GFC, these drivers of tail risks have again reversed, likely tempered by enhanced macroprudential policy toolkits and global monitoring of the financial system.

Figure 20 presents the comparable decomposition for German 3-year GDP-at-Risk. The relative evolution of domestic and foreign shocks in the run-up to the GFC is particularly notable for Germany. Domestic factors are associated with improvements in the left tail of the GDP growth distribution from 2004 to 2008. In contrast, foreign-weighted indicators are associated with a worsening in tail risk over the same period. In sum, these foreign factors dominate and contribute to an overall fall in fitted GDP-at-Risk over the period, exemplifying the importance of accounting for global influences when monitoring macro-financial risks.

Robustness

We also present details of the additional robustness exercises we run to complement the structural decompositions in Sect. 4. Specifically, we estimate structural decompositions from two model variants, in addition to the baseline model.

First, we re-estimate our baseline model, weighting foreign variables using bilateral financial linkages measured using BIS International Banking Statistics.

Second, we estimate an extended model, akin to that in Aikman et al. (2019). Here, the domestic variable set includes 3-year house price growth, the current account, bank capital ratios, 1-year CPI inflation and the 1-year change in central bank policy rates, in addition to our baseline domestic indicators (3-year change in credit-to-GDP growth and lagged quarterly real GDP growth).

The estimated share of variation in fitted values attributable to foreign shocks $ForShare_i^h(\tau )$, defined in Eq. (9), at $h=1,4,12$ and $\tau =0.05,0.5$ from these two models, alongside the baseline, are presented in Table 12.

In all three models, a substantial share of variation in estimated percentiles of GDP growth is attributable to foreign shocks. Moreover, foreign factors generally exert a larger influence on fitted values at the left tail of the GDP distribution, i.e., the 5th percentile, than at the median, corroborating the results in Table 6. Although the foreign share is lowest for the extended model, this is unsurprising given that it includes more domestic covariates than the baseline or its financially-weighted variant. Even so, the results in Table 12 indicate that, across models, between 39 and 56% of variation in the 5th percentile of 3-year GDP growth is attributable to foreign shocks.

Table 12 Share of variation in fitted values ($\%$) attributes to foreign shocks across horizons