A Markov chain measure of systemic banking crisis frequency

ABSTRACT

This study nests historical evidence for credit growth-fuelled financial instability in a two-state nonhomogeneous Markov chain with logistic crisis incidence. A long-run frequency measure is defined and calibrated for 17 advanced economies from 1870 to 2016. It is found that historical (implied) crisis frequencies display a V (J) pattern over time. A key implication is that policies strengthening capital adequacy contribute more to systemic stability than expanding deposit insurance or curbing sustained credit booms.

KEYWORDS:

• Credit cycle
• systemic banking crises
• Markov chain

JEL CLASSIFICATION:

• C15
• E30
• E58
• G01

Acknowledgments

This study is dedicated to Anton Webern. I am grateful to Solomos Solomou and an anonymous referee for their comments and to Pembroke Fellows’ Research Fund for financial support.

Disclosure statement

The author reported no potential conflict of interest.

Notes

¹ To determine historical crisis frequency (share of years in a crisis), researchers have focused on binary crisis indicators based on financial events, including bank runs and official interventions (Bordo et al. (2001), Reinhart and Rogoff (2009)), events of systemic importance (Jordà, Schularick, and Taylor (2017a), Taylor (2015)) and fluctuations in bank share prices (Baron, Verner, and Xiong (2019)). Bordo and Meissner (2016) contrast the alternative long-run perspectives. The duration of banking crises since 1970 has been rigorously documented by Laeven and Valencia (2013, 2018). Recently, Romer and Romer (2017) have proposed a narrative-based, nonbinary financial distress index.

² Aldasoro, Borio, and Drehmann (2018) review the EWI literature, including indicators of household and cross-border debt build-up. Simorangkir (2012) finds a univariate model of Markov switching bank deposit growth serves as an effective EWI for Indonesia.

³ Extensive theoretical and empirical research suggests that higher bank equity capital counters the risk-taking incentives created by limited liability; in addition to Admati and Hellwig (2013), see Merton (1974), Collard et al. (2017) and Hanson, Kashyap, and Stein (2011).

⁴ ${\bar{Z}}_T=\frac{1}{T}{\sum }_{t=1}^T{Z}_t$ and ${\bar{Z}}_T\sim N\left({\pi }_1,\frac{1}{T}\frac{pq(2-p-q)}{{(p+q)}^3}\right)$ by a central limit theorem for non-i.i.d. variables (Kelbert and Suhov (2008)). Convergence follows $M{}^T=\left(\begin{array}{cc}{\pi }_0& {\pi }_1\\ {\pi }_0& {\pi }_1\end{array}\right)+\frac{{\lambda }^T}{p+q}\cdot \left(\begin{array}{cc}p& -p\\ -q& q\end{array}\right)$, where $\lambda =1-p-q<1$ is the real-valued eigenvalue.

⁵ By controlling the steepness of the logistic function, $h_1$ determines the sensitivity of the probability of switching state to the fundamental. This is a simple version of Benigno et al.’s (2020) medium-scale structural model; these authors also endogenize the crisis exit rate.

⁶ Allowing feedback from the target variables to credit growth does not affect the main insight. I adopt these authors’ baseline parameter values ${\rho }_L=0.80$, $h_0=-3.396$, $h_1=1.88$ (${\sigma }_h=1.14$) for ADV and estimate the AR(1) persistence coefficient for the U.S.

⁷ The certainty-equivalent crisis incidence rate, $\underset{\_}{p}$, ranges from $3.5$% to $3.8$% annually; Schularick and Taylor's (2012) annual unconditional crisis likelihood is nearly $4$%.

⁸ Baron, Verner, and Xiong (2019) report higher historical frequencies because their bank equity-based crisis identification reveals more ‘quiet’ episodes. Similarly, da Rocha and Solomou (2015) find that nonsystemic crises had a long-lasting impact on inter-war industrial production.

⁹ To gauge the robustness of post-1970 ADV (pre-war US)-implied frequencies to the Global Financial Crisis and Great Recession (Great Depression) outliers – lasting 5 or more years for many economies – in column 3 I also report ${\pi }_1(\underset{\_}{p})$ and ${\pi }_1^{\mathrm{\infty }}$ for median duration. The mean–median gaps are comparable to Reinhart and Rogoff’s (2014) peak-to-trough measure. Crisis frequencies fall by $1.5$-$2$%, but the J shape remains as the 1947–2008 decline appears less pronounced.

¹⁰ Reinhart and Rogoff’s (2014) study of $63$ financial crises in advanced economies (1857–2013) reports a mean (median) duration of 2.9 (2) years for peak-to-trough contractions of per-capita GDP. Romer and Romer’s (2017) real-time narrative index for OECD countries (1967–2012) also reveals wide dispersion in recovery times.