15 to lower their costs, at least until the loans turned bad. And this is the problem, of course: the system would be very unstable and ultimately would likely end in a crisis situation.

A key variable used to measure financial stability is the z-score, a variable that explicitly compares buffers (capitalization and returns) with the potential for risk (volatility of returns). The z-score has gained traction as a measure of individual financial institutions‘ soundness (e.g., Boyd and Runkle 1993; Demirgüç-Kunt, Detragiache, and Tressel 2008; Čihák and Hesse 2010). The z-score is defined as z≡( _k_ + _μ_ )/ _σ_ , where _k_ is equity capital as percent of assets, _μ_ is return as percent of assets, and _σ_ is standard deviation of return on assets as a proxy for return volatility. The popularity of the z-score stems from the fact that it is inversely related to the probability of a financial institution‘s insolvency, i.e. the probability that the value of its assets becomes lower _k_ than the value of its debt. The probability of default is given by _p_ (   _k_ )   (  ) _d_  . If μ is   _z_ normally distributed, then _p_ (   _k_ )   _N_ (01,) _d_  , where _z_ is the z-score. In other words, if   returns are normally distributed, the z-score measures the number of standard deviations a return realization has to fall in order to deplete equity. Even if μ is not normally distributed, _z_ is the lower bound on the probability of default (by Tchebycheff inequality). A higher z-score therefore implies a lower probability of insolvency.

The z-scores have several limitations, as well as advantages. Perhaps the most important limitation is that the z-scores are based purely on accounting data. They are thus only as good as the underlying accounting and auditing framework. If financial institutions are able to smooth out the reported data, the z-score may provide an overly positive assessment of the financial institutions‘ stability. Also, the z-score looks at each financial institution separately, potentially overlooking the risk that a default in one financial institution may cause loss to other financial institutions in the system. An advantage of the z-score is that it can be also used for institutions for which more sophisticated, market based data are not available. Also, the z-scores allow comparing the risk of default in different groups of institutions, which may differ in their ownership or objectives, but face the risk of insolvency.

For other indicators, such as the regulatory capital to risk-weighted assets and nonperforming loans to total gross loans, the Global Financial Development Database cross-refers to financial soundness indicator database available on IMF‘s website (fsi.imf.org). Variables such as the nonperforming loan ratios may be better known than the z-score, but they are also known to be lagging indicators of soundness (e.g., Čihák and Schaeck 2010).

One alternative indicator of financial instability is ―excessive‖ credit growth, with the emphasis on _excessive_ . A well-developing financial sector is likely to report expansion in credit growth. Without credit growth, financial sectors would lack in depth or would not be able to provide good access to financial services. Credit growth is important, and indeed may be necessary even