Abstract
Financial stability indicators can be grouped into financial stress indicators that reflect heightened spreads and market volatility, and financial vulnerability indicators that reflect credit and asset price imbalances. Based on a panel of euro area countries, we show that both types of indicators contain information about growth-at-risk in the short-term. However, only vulnerability indicators contain information about growth-at-risk in the medium-term. Among various vulnerability indicators suggested in the literature, the Systemic Risk Indicator (SRI) proposed by Lang et al. (Anticipating the bust: a new cyclical systemic risk indicator to assess the likelihood and severity of financial crises, 2019) outperforms in terms of in-sample explanatory power and out-of-sample predictive ability for medium-term growth-at-risk in euro area countries. Shocks to the SRI induce a rich term structure for growth-at-risk, which is different to the one induced by financial conditions.
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Notes
For an overview of the literature, see the discussion further below.
We include DK, SE, and GB in the estimation sample as these countries have long time series available with relevant GDP tail risk events and are sufficiently similar to many euro area countries. For simplicity we will refer to euro area countries throughout the remainder of this paper.
Throughout the paper we use the 2-year change in the debt service ratio rather than the level, as this transformation yields better in-sample performance than the level of the debt service ratio and similar out-of-sample performance.
Credit gaps are computed as deviations from a recursive HP-filter with a smoothing parameter of 400,000. The SRI is constructed as a weighted average of six early warning indicators: (1) the two-year change in the bank credit-to-GDP ratio (with 36% weight); (2) the two-year growth rate of real total credit (5%); (3) the two-year change in the debt service ratio (5%); (4) the three-year change in the residential real estate price-to-income ratio (17%); (5) the three-year growth rate of real equity prices (17%); and (6) the current account-to-GDP ratio (20%). The financial cycle is constructed as a time-varying weighted average of the percentile ranks of four indicators: percentage change in total credit, percentage change in house prices, percentage change in equity prices and percentage point change in bond yields. The time-varying aggregation weights are based on the cross-correlations among the indicators.
Throughout the paper we use the 2-year change in the debt service ratio rather than the level, as this transformation yields better in-sample performance than the level of the debt service ratio and similar out-of-sample performance. To simplify terms, we will just refer to the debt service ratio when talking about the 2-year change of the debt service ratio.
Countries included in the out-of-sample exercise: BE, DE, DK, ES, FI, FR, GB, IE, IT, NL, SE.
The main exception is the out-of-sample performance for \(h=1\), where the DSR and the financial cycle are better. In addition, for \(h=16\) real credit growth does marginally better out-of-sample than the SRI, 18.4% improvement versus 17.2% improvement, but does worse in-sample, 2.5% improvement versus 4.4% improvement.
Mean empirical coverage measures the average proportion of times that the prediction falls within the true quantiles and is computed as in Brownlees and Souza (2021). The dynamic quantile test refers to the model adequacy test proposed by Engle and Manganelli (2004). We follow Brownlees and Souza (2021) and regress the hit sequence (i.e., the sequence of binary random variables that are equal to \(1-\tau \) when the t-th realization of the target variable is below its corresponding growth-at-risk prediction and \(-\tau \) otherwise) on a constant to check whether forecasts are unconditionally optimal in the sense of having correct unconditional coverage. The numbers denote the percentage of country series that pass the test at the 5% significance level. Improvement in log score denotes the percentage improvement in log score of a given model relative to the baseline model (Bernardo 1979; Vuong 1989; Gneiting and Raftery 2007). Improvement in weighted log scores is computed by weighting by the cumulative normal distribution function to give more weight to the low tail, as in Amisano and Giacomini (2007).
Our shortest prediction horizon corresponds to the annual GDP growth rate five quarters ahead. As financial stress indicators contain mainly information for very near-term horizons, e.g., 1–2 quarters ahead, this can partly explain why the CLIFS has lower information content at \(h=1\) than the SRI.
Numbers differ slightly to the ones reported in Sect. 3.2, due to different balancing of the sample across variables.
The fact that the QIRFs for different quantiles cross in some cases does not imply that the predicted quantiles from the model cross. The QIRFs simply reflect the estimated model coefficients at different horizons. In fact, predicted quantiles from the full model do not cross 99.75% of the time. This is also illustrated visually for the euro area in Fig. 24 and at country-level in Fig. 25 in the Appendix.
Recall that the left-hand side variable of our model is the 1-year ahead annual real GDP growth rate at different future horizons. Hence, horizons \(h=1\) and \(h=4\) correspond to the 5-quarter ahead and 8-quarter ahead annual real GDP growth rates.
For completeness, the QIRFs for the economic sentiment indicator can be found in Fig. 23 in the Appendix.
The short-term horizon refers to the model using \(h=1\), i.e., the 1-year ahead real GDP growth rate in the next quarter. Given publication lags of around 1 quarter for some of the explanatory variables, such a model specification seems appropriate for real-time monitoring of 1-year ahead growth-at-risk. The medium-term horizon refers to the model using \(h=8\), i.e., the 1-year ahead real GDP growth rate in 2 years time, or in other words the real GDP growth rate between year 2 and year 3 into the future.
Data availability to estimate the euro area aggregate model starts in 1988.
Due to short time series availability, the 2-year change in the debt service ratio and the economic sentiment indicator were not included in the evaluation exercise for the US.
Compared to the euro area SRI term structure when the SRI is negative, which is shown in Fig. 5 panel b, the reduction in tail risk in the short-term and the increase in downside risk over the medium-term are both somewhat less pronounced for the US.
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Appendices
Appendix A: Additional Figures
See Figs. 16, 17, 18, 19, 20, 21, 22, 23, 24 and 25.
In-sample tick loss for different models over time. Notes: The shaded area shows for each point in time the interquartile (IQ) range of the tick loss across all models displayed in Table 2. The red line shows the tick loss for the best performing model at horizon \(h=8\)
Relationship between the full-sample and “real-time” SRI. Notes: The “real-time” version of the SRI only uses data available up until 1995 for the indicator normalization (median and standard deviation) and for computing the optimal indicator weights
Improvements in tick loss for various models without country fixed effects. Notes: Improvement in tick loss is relative to the model that only conditions on current real GDP growth. Panel headings indicate the quantile of the model (\(\tau = 0.05, 0.1, 0.5\))
QIRFs for SRI (full model, no fixed effects)
QIRFs for Debt Service Ratio (full model, no fixed effects)
QIRFs for CLIFS (full model, no fixed effects)
QIRFs for ESI (full model, no fixed effects)
QIRFs for ESI (full model, fixed effects). Notes: The left panels shows the QIRF for the 5th percentile model with one and two standard error confidence intervals. The right panel shows the QIRFs for different quantiles
Evolution of predicted quantiles for the euro area over time
Visual check for instances of quantile crossing at country level
Appendix B: Additional Tables
See Tables 5, 6, 7, 8, 9 and 10.
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