Yield curve and financial crisis prediction: evidence from a machine learning approach

Based on analysis presented by Bank of England, January, 2020

Machine learning models mostly outperform logistic regression in out?of?sample predictions and forecasting. Identification of economic drivers via machine learning models using a novel framework based on Shapley values, uncovering non?linear relationships between the predictors and crisis risk. The most important predictors are credit growth and the slope of the yield curve, both domestically and globally. A flat or inverted yield curve is of most concern when nominal interest rates are low and credit growth is high.

Financial crises have huge economic and social costs (Hoggarth et al., 2002; Ollivaud and Turner, 2015; Laeven and Valencia, 2018; Aikman et al., 2018). Spotting their warning signs sufficiently early is therefore of great importance for policy makers. Doing so can facilitate the timely activation of countercyclical macroprudential policies, and reduce the likelihood and severity of financial crises in the face of rising risks (Giese et al., 2013; Cerutti et al., 2017; Akinci and Olmstead-Rumsey, 2018).

This paper is the first to provide a rigorous inference analysis of how black box machine learning models predict financial crises by decomposing their predictions into the contributions of individual variables using the Shapley value framework (Strumbelj and Kononenko, 2010; Joseph, 2019). This approach allows both to identify the key economic drivers of the models presented in this paper and to test those statistically. It also helps to tackle a key challenge faced by policy makers in using machine learning models to inform their decisions, because it provides narratives which can be used to justify policy actions which may be partially based on such models.

The paper aims to identify robust predictors for financial crises one to two years in advance.

This gives time to implement policies that can potentially avert a crisis altogether or dampen its negative consequences. In this research, the authors find that, with the exception of individual decision trees, all machine learning models outperform the logistic regression. Among other findings, the best-performing machine learning model, extremely randomised trees, also correctly predicts the global financial crisis of 2007–2008, giving differentiated signals between countries that reflect different economic realities and outcomes. Investigating the drivers of the models, it was found out that credit growth and the slope of the yield curve are the most important predictors for financial crises across a diverse set of models. While the importance of domestic credit growth is well known in the literature (Borio and Lowe (2002); Drehmann et al. (2011); Schularick and Taylor (2012); Aikmanet al. (2013); Jordà et al. (2013, 2015b); Giese et al. (2014)), the role of the yield curve has been far less explored.

From the results presented in this paper, it is clear that the flatter or more inverted the yield curve is, the higher the chance of a crisis. This could reflect the search for yield and increased risk-taking that can often be observed prior to financial crises. Both credit growth and the yield curve slope are also highly important predictors at the global level, with one major difference. The global slope provides a robust signal over the entire period from the 1870s until the present, while global credit is a key predictor of the global financial crisis of 2007–2008 but less important for the prediction of other crises. The results presented in this research also indicate that stock prices, money and the current account have lower overall predictive power when controlling for other factors. 

The models here uncover relatively simple and intuitive nonlinear relationships and interactions for the selected key indicators. For example, crisis probability increases materially at high levels of global credit growth but this variable has nearly no effect at low or medium levels. Similarly, interactions seem to be important—particularly between global and domestic variables. For example, many crises fall into an environment of strong domestic credit growth and a globally flat or inverted yield curve. It is also found, that a flat or inverted yield curve is more concerning when nominal yields are at low levels.

Beyond domestic credit growth, several studies have identified the importance of global credit growth. Financial crises often occur on an international scale and may reflect global financial cycles (Rey, 2015), or be driven by cross-country spillovers rather than only domestic imbalances. For example, Cesa-Bianchi et al. (2019) find an increasing correlation of credit growth across countries over time and show that global credit growth is an even stronger predictor for financial crises than domestic credit. Similarly, Alessi and Detken (2011) and Duca and Peltonen (2013) show that the global credit gap is an effective early warning signal. Rising asset prices—including equity and house prices—are also often associated with pre-crisis periods (Aliber and Kindleberger, 2015; Reinhart and Rogoff, 2008). In particular, rapid rises of asset prices could indicate the formation of a bubble. The slope of the yield curve, i.e. the difference between the long and short-term interest rate, is often seen as a strong predictor of an impending economic recession (Estrella and Hardouvelis, 1991; Wright, 2006), especially of a longer horizon of 12–18 months (Rudebusch and Williams, 2009; Liu and Moench, 2016; Croushore and Marsten, 2016). But while some early warning models for financial crises have identified the slope of the yield curve as an important predictor of financial crises (Babeck`y et al., 2014; Joyet al., 2017; Vermeulen et al., 2015), they have not explored the drivers of its predictive power in detail.

The yield curve reflects expectations of the future path of short-term interest rates, as well as a risk premium (i.e. the term premium) for holding an asset for a longer duration. In normal times, the slope is positive, which means that long-term interest rates are higher than short-term rates. But there are two distinct reasons why a flat or negative sloping yield curve might be predictive of financial crises, separate from the possible signal on the macroeconomic outlook.

First, for a given macroeconomic environment, a flatter yield curve tends to be associated with lower net interest margins and weaker banking sector profitability (Adrianet al., 2010; Borio et al., 2017). This may potentially directly affect the resilience of the banking sector. It could also lead to a contraction in credit supply with implications for real economic activity. If these effects are severe enough, the slope of the yield curve might be a useful predictor for financial crises. Second, a flat or inverted yield curve may often be associated with low term premia. In such an environment, investors might have to search for riskier investment, rather than longer maturity, to achieve higher absolute returns, and they may not be properly compensated for their increased risk exposure. For example, Coleman et al. (2008) find that house prices in the United States rose with the flattening of the yield curve prior to the global crisis of 2007–2008. They suggest (p. 286), that “the hunger for spread during this period of a flat yield curve could have been fuelling sub-prime and other alternative mortgage activity”. Such a system-wide build-up of under-priced risk leaves the financial system highly exposed to a sharp correction which may result in a crisis. In this regard, the levels of short and long-term interest rates may also be important. For instance, low nominal interest rates may also drive excessive risk taking in the financial system as banks and other intermediaries search for yield (Taylor, 2009; Adrian and Shin, 2010; Borio and Zhu, 2012).

The debt service ratio has also been identified as a good early warning indicator (Drehmann and Juselius, 2014). It measures interest payments relative to income. This can provide a gauge of how overextended borrowers are: the higher the debt service ratio, the more vulnerable borrowers are to falls in their incomes or increases in the interest rate. Overextension in borrowing could result in an increased rate of defaults, a loss in consumption smoothing capabilities, or a lack of new investment. The downside of the simplistic debt service ratio measure (credit × long-term interest rate over GDP), which is driven by data availability, is that it does not capture short-term lending rates, capital repayments, or the maturity structure of the debt, all of which may also be important.

Current account imbalances have often been found to be a strong driver of crises due to capital inflows pushing down interest rates and thus encouraging excessive risk-taking behaviour potentially financed by flightly funding (Reinhart and Rogoff, 2008; Bernanke, 2009; King, 2010).

This paper shows that machine learning models outperform logistic regression in predicting financial crises on a macroeconomic dataset covering 17 countries between 1870 and 2016 in both out-of-sample cross-validation and recursive forecasting. The consistently most accurate models are decision-tree based ensembles, such as extremely randomised trees and random forests. The gains in predictive accuracy justify the use of initially more opaque machine learning models. To understand their predictions, a novel Shapley value framework was applied, which allows to examine the contributions of individual predictors economically and statistically.

All models consistently identify similar predictors for financial crises, although there are some variations across time reflecting changes in the nature of the global monetary and financial system over the past 150 years. These key early warning signs include: (i) prolonged high growth in domestic credit relative to GDP; (ii) a flat or inverted yield curve especially when nominal yields are low, and (iii) a shared global narrative in both of these dimensions as indicated by the importance of global variables. While the crucial role of credit is an established result in the literature, the predictive power of the yield curve has obtained far less attention as an early warning indicator. Indeed, the global yield curve slope is a robust crisis indicator throughout the sample period. This contrasts with global credit, which proves a strong indicator only for the recent global financial crisis.

There were also found nonlinearities and interactions identified by the machine learning models. Global credit shows a particularly strong nonlinearity—only very high global credit growth beyond a certain point influences the prediction of the models. Interactions are particularly strong between global and domestic indicators. For instance, a globally flat or inverted yield curve coupled with strong domestic credit growth may highlight a significant crisis risk. Overall, the findings suggest a combination of low risk perception, search-for-yield behaviour and strong credit growth in the years preceding a crisis.

The results may help policy makers to identify the risk of financial crises in advance and potentially act on these signals. The ability to do so is crucial given the enormous economic, political, and social consequences that financial crises entail. With more accurate predictive models and reliable indicators complementing softer information and judgement, policy makers can pre-emptively adjust macroprudential measures such as countercyclical capital buffers (BCBS, 2010). Such action may help to avoid or at least reduce the consequences of financial crises.

Detailed description of the models is presented further in the report under the following link:

https://www.bankofengland.co.uk/-/media/boe/files/working-paper/2020/credit-growth-the-yield-curve-and-financial-crisis-prediction-evidence-from-a-machine-learning.pdf?la=en&hash=F37E72F9D003C4D3FE66AA4F1A70CDC2EC4C3A0D

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