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Principal Components Analysis Applied to the Investigation of BANK Failures in the United States

The methodological approach used is based on a *logit* model that can identify two sub-groups of existing banks at the temporal moment t: (i) entities that will go bankrupt at time t+1, and (ii) entities that will survive at time t+1.

The Texas ratio variable is incorporated into the initially proposed logit model and at the same time requires the inclusion of the maximum number of CAMEL variables from all groups. The intention is to specify an initial model that is stable enough to prevent future bankruptcies one year in advance. The year 2007 is used as a starting point to predict bank bankruptcy patterns for 2008. The robustness of the model is corroborated through an analysis of prediction levels of bank failures in the United States from 2009-2012.

Overall, the results of this study suggest that using the statistical technique of principal components can prove successful as an effective intermediate instrument in the quantitative analysis of bank failures by revealing a persistent and significant degree of multicollinearity that affects many financial and accounting ratios commonly considered when studying and rating bank entities.

More specifically, we stress the relevance of performing early studies to determine whether the degree of correlation is significant enough to justify the use of PCA (through an analysis involving the determinant of a correlation matrix, Bartlett’s test of sphericity, and the KMO indicator among other techniques). This rigorous study considers the inclusion of factorials and of not selecting them in cases in which they are rejected by the above tests. The existence of econometric studies that have developed PCA techniques based on these indicators without prior testing is noteworthy.

As for our overall analysis of the results, we highlight the particularly accurate classifications of bankrupt entities found (after incorporating the significant principal components). We obtained bankrupt entity prediction levels of higher than 90% for all years of the recent financial crisis (2008-2012).