Are Banks Too Big to Fail or Too Big to Save?

In the empirical work so far, we have set the threshold level for the liabilities-to-GDP ratio used to define the Big variable somewhat arbitrarily equal to 0.5. Alternatively, Table 10 presents regressions analogous to the market-to-book and CDS regressions 3 and 8 of Panel B of Table 8 where we choose different thresholds to define the Big variable. Specifically, columns 1 and 5 of Table 10 present regressions of the market-to-book ratio and the CDS spread where the threshold value for the liabilities-to-GDP ratio in the definition of Big is 0.1, while in regressions 2 and 6 the threshold is 0.25 and in regressions 4 and 8 it is 1.0. For comparison, columns 3 and 7 copy regressions 4 and 9 of Panel B of Table 8. Looking across columns 1-4, we see that the Big variable obtains a significant negative coefficient, and its interaction with bank risk a significant negative coefficient, for thresholds in the definition of Big equal to 0.25 and 0.5. Apparently, the additional contribution of risk to bank valuation for large banks is only material for reasonably high thresholds for the liabilities-to-GDP ratio in the definition of Big. The Big variable and its interaction with bank stock risk fail to be estimated with a significant coefficient for a threshold level of 1.0, because either there are off-setting TBTF and TBTS effects or there are simply too few banks with liabilities exceeding GDP to estimate the coefficient for this interaction variable with precision.  

Table 10.  The impact of systemic bank size as measured by different thresholds for the liabilities-to-GDP ratio 

The dependent variable is the market-to-book ratio in columns 1 to 4 and the CDS spread in columns 5 to 8. Market-to-book is the market value of common equity divided by the book value of common equity. CDS is the annual average of daily credit default spreads on a 5-year contract. Assets is natural logarithm of total assets in constant 2000 US dollars. Pre-tax profits is pre-tax profits divided by total assets. Earning assets is earning assets divided by total assets. Leverage is liabilities divided by total assets.  GDP per capita is GDP per capita in constant 2000 dollars. Past crisis is dummy variable that is one if country is not currently experiencing a banking crisis but has experienced a banking crisis before and zero otherwise. Past fiscal cost is fiscal cost of resolving most recent but not current banking crisis divided by GDP. Public debt is central government debt divided by GDP. Fiscal balance is ratio of central government revenues minus expenses and minus depreciation of capital to GDP. Bank stock risk is annualized standard deviation of weekly dividend-inclusive bank stock returns. Big is a dummy variable that equals one if ratio of bank liabilities to GDP exceeds a threshold set equal to 0.1 in columns 1 and 5, to 0.25 in columns 2 and 6, to 0.5 in columns 3 and 7, and to 1.0 in columns 4 and 8. All regressions are estimated with year and country fixed effects and clustering at the bank level. *, ** and *** denote significance at 10%, 5% and 1% respectively. 

The CDS spread is the dependent variable in regressions 5 to 8 of Table 10 for varying thresholds in the definition of the Big variable. The Big variable obtains a significant positive coefficient, and its interaction with bank risk obtains a significant negative coefficient, for all four thresholds in the definition of Big. This suggests a strong TBTF effect relative to the TBTS effect for systemically large banks for varying definitions of systemic size. The estimated coefficients in regressions 5-8 monotonically increase from -0.021 with a threshold for Big of 0.10 in regression 5 to -0.012 with a threshold for Big of 1.0 in regression 8. This implies that the very largest banks see their CDS spreads decline less with additional risk than banks that are somewhat smaller. 

Table 11 represents several additional robustness checks. First, we recognize that a country's ability of bail out its biggest banks may depend on its public debt relative to its borrowing capacity rather than simply on its actual public debt ratio. To deal with this, we construct a country's public indebtedness relative to its borrowing capacity as the residual from a regression of the pubic debt ratio on per capita GDP, as richer countries can and in fact tend to borrow more. Then we re-estimate the market-to-book and CDS regressions 3 and 8 of Panel B of Table 8 after replacing the public debt ratio by this residual public debt ratio, and present the results in columns 1 and 2 of Table 11. The residual public debt variable is seen to be negatively and significantly reflected in bank valuation, while the Big0.5 variable now obtains a coefficient of -0.380 that is significant at the 5 percent level. 

Table 11.  Alternative specifications with respect to public debt and bank risk variables 

The dependent variable is the market-to-book ratio in columns 1,3 and 5, and it is the CDS spread in columns 2,4 and $6 .$ Market-to-book is the market value of common equity divided by the book value of common equity. CDS is the annual average of daily credit default spreads on a 5 -year contract. Assets is natural logarithm of total assets in constant 2000 US dollars. Pre-tax profits is pre-tax profits divided by total assets. Earning assets is earning assets divided by total assets. Leverage is liabilities divided by total assets. GDP per capita is GDP per capita in constant 2000 dollars. Past crisis is dummy variable that is one if country is not currently experiencing a banking crisis but has experienced a banking crisis before and zero otherwise. Past fiscal cost is fiscal cost of resolving most recent but not current banking crisis divided by GDP. Public debt is central government debt divided by GDP. Public debt (t-1) is the lagged value of Public debt. Bank stock risk is annualized standard deviation of weekly dividend-inclusive bank stock returns. Residual public debt is residual of regression of public debt on per GDP per  capita. Z-score is index of bank solvency constructed as $\frac{R O A+C A R}{\operatorname{SROA}}$ where ROA is return on assets, CAR represents capital assets ratio and SROA stands for standard deviation of return on assets. Big0.5 is a dummy variable that equals one if ratio of bank liabilities to GDP exceeds $0.5$ and zero otherwise. All regressions are estimated with year and country fixed effects and clustering at the bank level. ^{*},{ }^{* *} and ^{* * *} denote significance at 10 \%, 5 \% and 1 \%, respectively.

Next, it can be the case that the public debt is endogenous to the state of the banking system, as declines of bank share prices and increases in CDS spreads may prompt a bank bailout, which can raise public indebtedness. To deal with this, we replace the public debt ratio by its lagged value in regressions 3 and 8 of Panel B of Table 8, with the results in columns 3 and 4 in Table 11. The lagged public debt ratio is now estimated with a negative and significant coefficient in the market-to-book regression in column 3, confirming a capitalization of the public debt into lower bank share pricing consistent with a TBTS effect. Finally, in columns 5 and 6 of the table we replace the stock market variability variable by the bank's Z-score in the benchmark market-to-book and CDS specifications. This measure of bank risk derived from accounting information is negatively related the market-to-book ratio and the CDS spread (consistent with the positive relationships between bank stock risk and these two variables), but these relationships are not statistically significant. 

Table 11.  Alternative specifications with respect to public debt and bank risk variables, cont’d: