Accounting for the business cycle reduces the estimated losses from systemic banking crises

Abstract

We re-estimate the effects of systemic banking crises in industrialised countries reported by Cerra and Saxena (Am Econ Rev 98(1):439–457, 2008) with a model that includes transitory business cycle shocks. We use the correlation between countries’ business cycles to identify temporary business cycle shocks, which helps prevent these transitory shocks being incorrectly explained by the crisis dummy. Doing so results in estimated permanent losses from systemic banking crises of 4% rather than the 6% reported in the original article. In contrast, accounting for the business cycle has no effect on the estimated losses from currency and debt crises. These typically occur when the crisis country becomes sufficiently uncorrelated with the country to which it has tied itself, so accounting for the cross-correlation in business cycles does not improve the counterfactual of what would have happened without a crisis.

Appendix A

In this Appendix, we provide a brief overview of various alternative model specifications we have explored in an attempt to gauge the robustness of our estimates in Sects. 3 and 4 . Table 2 provides an overview. This table indicates that our results are robust to alternative model specifications.

Table 2 Model selection

The estimates shown in the first row of the table are for a restricted version of the CSM in which all countries are assumed to have the same value of the variance $\sigma _{\xi }=\sigma _{\xi ,i}$, $i=,\ldots ,N$. According to the AICc this restricted model does not fit the data as well as the standard CSM listed in the second row, as lower values for AICc indicate a better fit. We note, however, that the estimated maximum and final drop due to a systemic banking crisis are essentially same.

For the remainder of the models listed in the table, the specification of the covariance matrix $\varSigma _{\xi }$ is the same diagonal specification used in the CSM in the second row. These models all represent variants of the CSM with cycle. The second column in the table indicates the number of nonzero elements in the diagonal matrix D of the Cholesky decomposition of $\varSigma _{\zeta }$, the covariance matrix of the cycle innovation $\zeta$. This number is also equal to the rank of $\varSigma _{\zeta }$. When the rank is one, the weight corresponds to the USA. When it is two, it corresponds to the USA and Japan, with the USA first. The order by a rank of three is USA, Japan and Germany, respectively. In other words we assign the weights to the largest industrialised economies. The table shows that we obtain the best fit for a rank of two, but the results for ranks of three or more also produce similar maximum and final drops.¹⁶

We also experiment with various autoregressive (AR) lengths for the growth rate component, $\beta _{i,t}$, and find that an AR(4) model produces the best fit. Similarly by varying the number of lags, s, of the dummy variable, $D _{i,t-s}$, we find that we obtain an optimal fit with $s=2$. In all cases the maximum and final drops estimated for these models are of a similar magnitude and all permanent drops in the level of output are significant at well under the $p=0.001$ level.

Based on a similar model selection exercise, we obtain optimal models based on the crisis dummies produced by Laeven and Valencia for the larger panel of 31 countries discussed in Sect. 6. In Table 3, we report only the final model specifications used in the paper to avoid presenting too many models. We obtained models with an optimal fit according to the AICc criterion using a business cycle component with covariance matrix $\varSigma _{\zeta }$ of rank 3. All the models assume a diagonal covariance matrix $\varSigma _{\xi }$ of full rank. The number of lags for the banking crisis dummies is $s=5$, while for both the currency crisis and debt crisis dummies $s=1$. In the table, we also include the estimates for the same model specifications using the dummies produced by Reinhart and Rogoff. We denote those models we estimate with the crisis dummies produced by Laeven and Valencia by L&V, and those produced by Reinhart and Rogoff by R&R. Finally, we note that the models we use in Sect. 5 also employ the same specifications shown in Table 3 for the Reinhart and Rogoff dummy variables.

Table 3 Model selection