U.S. Banking in the Post-Crisis Era: New Results from New Methods

Gorton (2018) refers to the financial crisis of 2007–2008, while Bolt et al. (2012) and others refer to the crisis of 2008. The National Bureau of Economic Research lists the corresponding peak-to-trough business cycle contraction as fourth-quarter 2007 through second-quarter 2009. Many of the effects of the recent financial crisis lasted beyond 2009.

See Hördahl and King (2008), Bernanke (2018) and Gorton (2018) for additional discussion. See also the comprehensive timeline of the financial crisis provided by the Federal Reserve Bank of St. Louis at https://​www.​stlouisfed.​org/​financial-crisis/​full-timeline.

Total loans and leases, net of unearned income for U.S. commercial banks reached a peak of 6.807 trillion dollars in 2008Q3, fell to 6.415 trillion dollars by 2009Q4, and did not reach the level of 2008Q3 until 2012Q4. All real estate loans reached a peak of 3.835 trillion in July 2009, fell to 3.491 trillion in September 2011, and did not reach the July 2009 level until November 2015. Commercial real estate loans reached a peak of 1.730 trillion in December 2008, fell to 1.419 trillion in January 2012, and did not reach the level of December 2008 again until September 2015. The levels of loans outstanding reflect in large part past loan-making activity; i.e., there is a good deal of inertia reflected in the values given here. The decline in values of loans originating during the financial crisis is likely far larger than the levels of loans outstanding, but is harder to measure.

Carry trades are those trades with an initial return or “carry,” but with large tail risks involving losses in the future which have low probability but which are perhaps catastrophically large.

An unintended consequence of burdensome capital requirements may be to induce movement of financial intermediation out of regulated entities into weakly or unregulated entities. This in large part gave rise to shadow banking that existed by 2007.

Patel (2014) reports that JP Morgan Chase & Co.’s chief executive officer, Jamie Dimon, stated in mid-2014 that JP Morgan would hire 13,000 new staff in compliance, audit, and other areas by year-end, increasing the bank’s risk control staff by 30%. The number of audit staff at Bank of America Corp. roughly doubled from mid-2011 to mid-2014. Between the end of 2011 and mid-2014, Citigroup Inc. increased its staff working on regulatory and compliance issues by 33% for a total of about 30,000 employees, representing 12.3% of Citi’s 244,000 total employees at the end of second-quarter 2014. Patel (2014) observes that these increases represent “the new normal for banks as they grapple with a host of new regulations and capital requirements in the wake of the financial crisis, according to analysts.”

Assumption 28 is slightly stronger, but much simpler than assumptions AII–AIII in Park et al. (2000).

Additional assumptions are needed for CRS efficiency estimators. See Kneip et al. (2015) for additional discussion.

In other words, standard CLT results hold in the FDH case if and only if p = 1 and output is fixed and constant, or q = 1 and input is fixed and constant.

Conceivably one could estimate the shadow price of equity capital, but for inefficient firms this is problematic since the estimated shadow price would depend on the particular direction in which an inefficient firm is projected onto the estimated frontier.

Note that equity capital can arguably be viewed as a free source of financial capital for banks. In each year 2006, 2008, …, 2016, the median value of X ₄∕X ₁ varies between 0.1005 and 0.1144, while the first quartiles range between 0.0802 and 0.0977 and the third quartiles range between 0.1229 and 0.1362. Hence equity capital typically amounts to around 10–11% of the financial capital of banks in the sample. One should perhaps not expect large differences between results from the two different specifications.

The situation becomes even worse if equity capital is included. Then the effective parametric samples sizes for the FDH, VRS, and CRS estimators are 3, 36, and 66 (respectively) for n = 533. Of course, the notion of effective parametric sample size defined by Wilson (2018) presupposes that one has a correctly specified parametric model. As Robinson (1988) notes, the root-n parametric convergence rate means that estimators converge quickly to the wrong thing in a mis-specified model, leading the author to refer to root-n inconsistency.

Consequently, the statistic I use for the input orientation is the negative of the statistic appearing in equation (18) of Kneip et al. (2016).

Since standard CLT results apply here, one can use sample covariance to account for dependence across periods among observations for banks observed in both periods. There is, however, some subtlety. Details are given in Appendix.

What has come to be known as the Shannon number, i.e., 10¹²⁰, is a conservative lower bound on the game-tree complexity of chess calculated by Shannon (1950).

A number of papers in the banking literature have regressed DEA efficiency estimates on some explanatory variables including categorical variables to capture differences in regulatory environments across countries. As far as I know, none of these tests the separability condition discussed by Simar and Wilson (2007, 2011b). Here, banks face the same regulatory environment at a given point in time, but the regulatory environment changes with passage of the Dodd-Frank Act in 2010. Rejection of separability with respect to time amounts to a rejection with respect to the different regulatory regimes before and after 2010. Hence my results cast some doubt on results from cross-country analyses that attempt to control for differing regulatory regimes across countries in second-stage regressions.