Should We Take Estimates of the Optimal Level of Bank Capital Ratios Seriously or Not

The Bank Policy Institute is committed to using data and sound economic analysis to promote bank regulations that improve social welfare.  So too, we believe, are official sector economists and academic economists.  At its best, economic analysis can promote a disciplined and fact-based discussion of the advantages and disadvantages of a regulation and its calibration.  At its worst, economic analysis can provide a veneer of science for promoting a predetermined conclusion.  We all strive to stay on the best rather than the worst end of that spectrum, but economics is an imprecise science, and everyone has strong preconceived notions about correct bank regulations, so the struggle is never-ending.

An important component of the economic analysis that went into calibrating the Basel III international standard for capital regulation, and the U.S. implementation of that standard, was a 2010 study by economists working for the Basel Committee for Banking Supervision (BCBS) “An assessment of the long-term economic impact of stronger capital and liquidity requirements,” generally referred to as “the LEI study.”  The LEI study estimated the socially optimal level of a key bank capital requirement by determining where the marginal benefit of raising the requirement further equaled the marginal cost.  For increases in capital up to the optimal level, the gain in benefit exceeds the increase in cost, raising social welfare; for increases beyond optimal, the added cost exceeds the added benefit, reducing total social welfare.

Obviously critical to the analysis are the estimates of social benefit and the cost of bank capital.  Drawing on an extensive set of economic studies, the analysis estimated the social benefit of higher capital requirements as the resulting reduction in the annual probability of a financial crisis times the present value of lost GDP if a financial crisis were to occur.  The analysis estimated the social cost of higher capital requirements as the reduction in GDP resulting from higher interest rates on bank business loans.  The GDP reduction resulting from higher loan rates was calculated using several standard models of the macroeconomy.

It is difficult to overstate the continuing importance of the LEI analysis.  Multiple consequential studies have since used the LEI approach, although with slight variations, including studies by the Bank of England (twice (2011 and 2015)), Federal Reserve Board, IMF, and Bank for International Settlements.  The results of the LEI study, and subsequent similar studies, were used to help calibrate the level of the Basel III minimum capital requirements, the Global Systemically Important Bank (GSIB) capital surcharge, the Total Loss Absorbing Capacity (TLAC) requirement, and the Net Stable Funding Ratio requirement. Just two weeks ago, the Financial Stability (FSB) Board released an estimate of the social costs and benefits of post-crisis regulations intended to eliminate “Too Big to Fail” based on analysis that used the approach in the LEI study.

Nevertheless, at BPI, we have long struggled to take studies using the LEI approach seriously.  The estimate of the optimal level of capital depends critically on many assumptions that the researchers for each paper have to make, such as the amount by which bank funding costs fall when capital requirements increase, the extent to which banks pass on higher costs of capital requirements to customers, the lack of shifting of lending activity and risk into shadow banks, whether crisis have permanent or transitory effects, and the discount factor used to translate future expected costs and benefits into present values, just to name a few.  As a result, the results of these studies vary widely, reflecting in part differences in the specific assumptions made by the authors.

Moreover, the estimates of optimal capital requirements associated with any particular set of assumptions are statistically imprecise.  The 80 percent confidence interval of the Tier 1 capital ratio estimated by the Bank of England 2015 study, for example, ranged from 7 ½ percent to 16 percent and could justify an increase or decrease in capital requirements (see Chart 8 on p. 23).  This latter point about statistical precision is important to keep in mind because the studies, and those citing the studies (as can be seen in the quotes below), often present the range of point estimates provided under different assumptions, or the range of point estimates across studies, or both, as if those ranges provide a statistical confidence interval.  In fact, because each point estimate is highly imprecise, ranges of point estimates materially understate the range of uncertainty at normal levels of statistical significance.

Perhaps most importantly, the official sector has sent mixed signals about how seriously it takes the results.  For example, the Federal Reserve pointed to the LEI study as evidence that the Net Stable Funding Ratio requirement (an additional liquidity requirement that the Fed has proposed) has benefits that exceed its costs.  But the Fed misread the study.  At current capital levels, the LEI study actually found that the costs of the NSFR exceed its benefits by nearly $1 trillion.  When we pointed this out to the Fed, we were told “no one really takes those studies seriously.”

Another reason LEI-based estimates are hard to take seriously is that they seem to always call for capital ratios that are higher than wherever ratios happen to be currently, but not by so much as to seem preposterous.  The LEI estimates the optimal capital ratio measured using a pre-Basel III definition to be 13 percent (equivalent to 10 percent using the main current measure, as explained below), twice the average level before the crisis.  The Bank of England (2015) study concludes that “…there should be positive net benefits from increasing the minimum Tier 1 capital requirements of U.K. bank to 10 – 14 percent…”. The 2011 Bank of England study initially notes that a set of reasonable assumptions suggest optimal capital ratios should be 50 percent, but then adjusts the assumptions to deliver an estimated range for Tier 1 capital of 16 to 20 percent and concludes “Basel III sets levels well below what the results suggest is optimal.” The 2017 study by economists at the Federal Reserve Board estimated the optimal Tier 1 capital level to be between 13 and over 25 percent compared with the average actual ratio for U.S. bank holding companies, which they state is 12.5 percent.[1]

At the same time, in addition to feeding into the calibrations of all the main components of the bank capital regime, the studies are often cited by influential current and former Federal Reserve officials as evidence that capital requirements are either OK or too low but not too high.  For example, in his “Departing Thoughts” speech in 2017, former Federal Reserve Governor Daniel Tarullo stated

A recent study by three Federal Reserve Board researchers concludes that the tier 1 capital requirement that best achieves this balance is somewhere in the range of 13 percent to 26 percent, depending on reasonable choices made on some key assumptions. By this assessment, current requirements for the largest U.S. firms are toward the lower end of this range, even when one takes account of the de facto capital buffers imposed on most firms in connection with the stress test.

Nellie Liang, former head of the Financial Stability Division at the Federal Reserve Board and now a senior fellow at the Brookings Institution reviewed the range of estimates under different assumptions for the LEI, Bank of England, and Federal Reserve Board estimates of optimal capital, and used those estimates to inform her opinions on changes to regulations proposed by the Treasury Department.  In particular, she stated in a 2017 speech:

The Treasury also proposes changes that would effectively reduce capital requirements and supervision of the largest, most complex firms. In my view, these changes would increase risks to financial stability, and go too far. As discussed earlier, current bank capital requirements are near the low end of the range of estimates for optimal bank capital ratios.

And in a written answer to a Congressional question following testimony before the House on June 22, 2017, then-Fed Governor Jay Powell stated:

There is a growing body of research regarding the costs and benefits of bank capital that addresses the impact of capital standards on economic growth…While the optimal level of capital varies between studies, the basic framework is the same.

A variety of assumptions are required of all studies in the literature, and changes to the assumptions could result in either higher or lower levels of optimal bank capital. The current calibration of our risk-based capital requirements for U.S. banks is roughly in line with the optimal level of capital found under a wide range of these studies.

And these citations have second round effects.  For example, in an influential paper on bank capital regulation published in 2017, Jeremy Stein, former Fed Governor, and coauthors cited Tarullo citing the LEI-type analysis:

Here we are in close agreement with Tarullo (2017), who writes: “This assessment . . . suggests strongly that a reduction in risk-based capital requirements for the U.S. G-SIBs would be ill-advised. In fact, one might conclude that a modest increase in these requirements—putting us a bit further from the bottom of the range—might be indicated.” (p. 481)

It’s is tempting to conclude, therefore, that the LEI-type studies are taken seriously only in so far as they support the proposition that capital requirements should be increased, or at least not decreased, which always tends to be the case because the LEI construct allows the dials to unconsciously or consciously be set to deliver that result.

In any case, because the analyses appear to be influencing banking agency policymakers and are being used to support regulatory rulemakings and defend regulatory actions to Congress, we somewhat reluctantly feel obliged to engage them on their own terms.


With that lengthy prologue, we turn to the main point of this note.  The LEI analysis makes two fundamental and material mistakes and fixing those two mistakes changes the estimated level of optimal capital noticeably.

The first mistake is that the approach does not account for the reduction in expected private bankruptcy costs that occurs when capital ratios are increased.  Recall that the only benefit attributed to higher capital levels is the reduced annual probability, and therefore expected costs, of a future financial crisis.  This focus on external costs may seem to make sense because those costs will not be taken into account by the bank owners in choosing the level of capital.  By contrast, the loss in value that occurs when a bank goes bankrupt will mostly be taken into account by bank creditors and therefore bank owners.

However, that logic is incorrect.  Even though bankruptcy costs may not be externalities, they are nevertheless real costs whose reduction benefits society.  If that were not the case, then if the level of bank capital were irrelevant for the probability of a financial crisis, the socially optimal level of capital would be zero (or actually, negative infinity).  Banks would go bankrupt all the time, and costs from those bankruptcies would be astronomical.  Another way to look at it is that the private bankruptcy costs determine the capital ratios banks will choose to maintain on their own while inclusion of the external costs will provide the higher socially optimal levels for those ratios, but both types of costs need to be included or the procedure will be biased low.

Indeed, bankruptcy costs and lost franchise values are important drivers of current public policy to address the economic fallout from efforts to contain the coronavirus pandemic.  It is irrelevant that those costs will be borne by investors in the companies that fail, they are real costs, and reducing them is a legitimate object of public policy.

  • Considering the costs of individual bank bankruptcy in addition to the systemic spillover costs will raise the estimated optimal level of capital.

The second mistake is that the analysis fails to recognize that banks not only produce credit but also deposits and other money-like liabilities, and people value the money-like services provided by those bank liabilities.  The provision of money-like liabilities, in fact, is so important that it is the only socially beneficial output of banks considered when solving for optimal capital regulation in the Stein et al (2017) paper mentioned above.[2]

  • Considering the social benefits of money-like bank liabilities will lower the estimated optimal level of capital.

To estimate the individual and combined impact of correcting these mistakes, we first reproduce the analysis in the most recent study we know of using the LEI-approach, the technical appendix to a report of an FSB working group on Too-Big-to-Fail (TBTF) reforms published for comment on June 28, 2020.

The LEI (2010) study’s estimates of costs and benefits were necessarily calculated in terms of a pre-Basel III capital measure – the Tangible Common Equity (TCE) ratio – calculated using pre-Basel III definitions of equity and asset risk weights.  The FSB working group converted the LEI estimates of costs and benefits into the most important current capital metric – the Common Equity Tier 1 (CET1) ratio – using a conversion factor of 0.78 estimated by Fender and Lewrick (2016), the BIS study of optimal capital mentioned above.  For example, the FSB working group assumes that the costs and benefits of a 7.8 percent CET1 ratio are equal to the costs and benefits the LEI study reports for a 10 percent TCE ratio.  The FSB working group used the LEI estimate of the present value GDP cost of a financial crisis of 63 percent and the annual GDP cost of each half percentage point increase in the CET1 ratio resulting from a reduced supply of bank credit of 0.06 percent.[3]

Table 1 reports the results.  As can be seen by comparing the marginal benefit of each half percentage point increase in capital requirements to the marginal costs, social benefits are maximized for a CET1 ratio of 10 percent.  By way of comparison, the average CET1 ratio of U.S. bank holding companies is 12.1 percent as of 2020Q1.  The estimated optimal level of capital of 10 percent may seem low, but it is simply the LEI estimate that the optimal TCE ratio is 13 percent expressed in terms of the CET1 ratio.[4]

At this point, an astute reader will no doubt observe that the FSB working group evidently violated the rule that official sector studies invariably conclude that capital requirements should be a bit higher than wherever they happen currently to be.  The working group, however, only used the LEI/Fender-Lewrick analysis to calculate the total costs and total benefits of increasing capital levels from 7 percent to 7.59 percent, an increase that it equated with the combined impact of the reforms aimed at eliminating TBTF that the group studied.[5] [6] The working group did not offer a view on the optimal level of capital.

As discussed above, however, these estimates only account for the benefit from higher capital levels resulting from a reduced probability of a financial crisis.  In addition, higher capital ratios reduce the probability of failure for each individual bank in normal times as well as crisis times, reducing the expected bankruptcy costs borne by society.  To calculate those benefits, we calculate the annual probability of failure for a bank associated with any given level of capital using the formula developed in the Federal Reserve’s GSIB buffer calibration whitepaper.[7]  To measure bankruptcy costs, we need an estimate of the value lost when a bank fails.  In an FDIC working paper, Bennett and Unal (2014) calculate that between 1986 and 2007, the FDIC’s average loss on assets when a bank fails was 23.4 percent, 16.1 percent when weighted by assets.  We split the difference and assume that a bank failure destroys value equal to 20 percent of bank assets.  As can be seen in Table 2, the marginal benefit from reducing bankruptcy costs is about half the marginal benefit of reducing the probability of a financial crisis.  The estimate of the optimal CET 1 ratio is where marginal benefit equals marginal cost.  As can be seen, the optimal CET1 ratio rises from the LEI study’s estimate of 10 percent to 11 percent when the added benefit from the reduction in private bankruptcy costs is considered.[8]

The LEI also omits the cost of higher capital ratios that occurs from the reduction in the amount of bank deposits and other money-like liabilities, and the associated loss of social value of those liabilities.  Stein et al (2017) estimate the annual value of bank money-like liabilities to be equal to 2 percent of the liabilities.  As they do in their analysis, we assume that an increase in capital results in an equivalent reduction in money-like liabilities.  Total risk-weighted assets for U.S. bank holding companies equals 66 percent of nominal GDP, so one-half percent of RWA (the increment to the CET1 ratio) equals 0.33 percent of GDP, and 2 percent (the social value of deposits) of that equals 1 basis points.  As can be seen in Table 3, when the social cost of lost money-like liabilities is included along with the cost from reduced bank lending as a cost of higher capital ratios, the optimal CET1 ratio (where marginal benefit equals marginal cost) falls to 9.5 percent.

Exhibit 1 shows the results when the benefits of reduced bankruptcy cost and the cost of lost money-like bank liabilities are both included in the LEI analysis.  The estimate of the optimal level of the CET1 ratio occurs where the marginal cost of raising the ratio by one half percentage point equals the marginal benefit.  The original LEI estimate of the marginal benefit is the blue line and the estimate of the marginal cost is the red line.  As can be seen, the lines cross at 10 percent.  The silver line adds the benefit of reduced bankruptcy costs and the yellow line adds the cost of lost deposits and other money-like bank liabilities.  Those adjusted cost and benefit lines cross at 10.5 percent, 0.5 percent point higher than the LEI (2010)/FSB (2020) estimate, but still well below the average CET1 ratio of U.S. bank holding companies of 12.1 percent.

Exhibit 1


The point here is not that once an LEI-type analysis is adjusted to take into account private bankruptcy costs and the value of money-like bank liabilities its estimates should be used to inform actual policy.  Rather, the point is to illustrate the arbitrariness of the approach in that it omits two important determinants of the cost and benefit of capital requirements.  And, as discussed above, the analysis floats on a raft of assumptions that can be, and are, adjusted to deliver desired results.

Nevertheless, the analyses appears to at least sometimes be taken seriously by policymakers when making actual decisions about real policy.  Specifically, there is a view among some current and former policymakers that capital requirements in the United States are on the low end of the range of what is optimal.  Based on that view, any regulatory changes that lower capital requirements likely reduce social welfare.

To be consistent, current and former policymakers should, therefore, take seriously the finding reported above: after adjusting the LEI approach, the optimal level of banks’ CET1 ratios is 10.5 percent, and U.S. bank holding companies have a bit too much capital.  And if they reject the adjustments we propose, then the optimal level is even lower – 10 percent (the original estimate of the LEI study).

Conversely, if “nobody takes seriously” the findings of these models, and therefore the finding that bank capital requirements are a bit too high, then the Fed should not cite the results of the analyses when answering Congressional questions or as evidence that the cost of a new rule exceeds its benefit.

BPI is eager to engage in a constructive dialogue about the optimal level of bank capital, but we need to know.  Should we take the LEI-type estimates seriously or not?


Disclaimer: The views expressed do not necessarily reflect those of the Bank Policy Institute’s member banks, and are not intended to be, and should not be construed as, legal advice of any kind.

[1] The assertion that the Tier 1 capital level of U.S. banks is 12.5 percent incorrect.  The paper was published on March 31, 2017.  According to the New York Fed, the average Tier 1 capital ratio of U.S. banks as of 2017Q1 was 13.9 percent and had been above 12.5 percent since 2010Q3.

[2] It is worth noting when considering the role of bankruptcy costs that Stein et al assume banks are able to pay less on their liabilities because of those benefits, and therefore that the benefits are internalized by the bank, but they do not, therefore, think the benefits should be ignored.

[3] Fender and Lewrick (2016) argue that a better estimate of the present value of the cost of a financial crisis is 100 percent of GDP, but the FSB working group uses the LEI estimate of 63 percent.

[4] If we use the Fender and Lewrick estimate that the present value of the cost of a financial crisis is 100 percent of GDP, the estimated optimal level of the CET1 ratio is 11.5 percent.

[5] Fender and Lewrick (2016) also do not report the optimal level of capital implied by their calculation, although it can be inferred from Graph 2 in the paper, which plots the expected net benefits of different levels of capital.

[6] See the BPI blog post reviewing the FSB TBTF report available here for further discussion.

[7] The formula equals e ((f+4.36-k)/2.18)  where k is the bank’s CET1 ratio and f is the ratio at which the bank cannot continue to function.  We assume f equals 4.5 percent, the minimum required level of capital under Basel III and in the United States.

[8] This estimate of the increase is likely an upper bound because liquidation costs have been reduced by the revolution in bank resolution that occurred pursuant to Titles I and II of the Dodd-Frank Act, and in particular the issuance of trillions in bail-in debt to facilitate a more orderly single-point-of-entry bankruptcy or resolution.