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Economic Quarterly— Volume 105, Number 1— First Quarter 2019— Pages 1–40

US Bank Capital
Regulation: History and
Changes Since the Financial
Crisis
John Walter

L

egislators and supervisors (policymakers) impose minimum capital requirements on banks because they believe that, left to
themselves, banks tend to hold too little.1;2 Banks tend to hold
too little capital because while higher capital reduces the risk of failure,
it tends to be more costly than debt. And while bankers worry about
failure, they worry less than policymakers argue that they should, for
two reasons. First, a bank’s creditors (and especially insured depositors) do not penalize the bank for taking on risk, so banks, which can
pro…t from high-earning, risky assets, will tend to make excessively
The views in this article are those of the author and do not necessarily represent
the views of the Federal Reserve Bank of Richmond, the Federal Reserve Board of
Governors, or the Federal Reserve System. The author thanks Arantxa Jarque for
discussions that clari…ed many of the concepts reviewed in this article and Arantxa
Jarque, Justin Kirschner, Elliot Tobin, Nicholas Trachter, and John Weinberg for
helpful comments on an earlier draft.

1
Throughout this article, unless speci…cally noted, the term “bank” will be used as
shorthand to mean any insured depository institution (commercial banks, savings banks,
and savings and loan companies) as well as any company owning an insured depository
institution (bank holding company or savings and loan holding company). The article
does not address credit union capital requirements.
2
In June 2007, then-chair of the FDIC Sheila Bair explained the tendency of banks
to hold too little capital: “There are strong reasons for believing that banks left to their
own devices would maintain less capital – not more – than would be prudent. The fact
is, banks do bene…t from implicit and explicit government safety nets. Investing in a
bank is perceived as a safe bet. Without proper capital regulation, banks can operate
in the marketplace with little or no capital. And governments and deposit insurers end
up holding the bag, bearing much of the risk and cost of failure. History shows this
problem is very real . . . as we saw with the U.S. banking and S&L crisis in the late
1980s and 1990s. The …nal bill for inadequate capital regulation can be very heavy.
In short, regulators can’t leave capital decisions totally to the banks. We wouldn’t be
doing our jobs or serving the public interest if we did” (Bair 2007).

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Federal Reserve Bank of Richmond Economic Quarterly

risky investments. Second, a large bank’s failure is thought to have
the potential to impose widespread economic impacts, which the banks
themselves do not take into account when making decisions. But policymakers do care about these impacts; for one, they are likely to face
hostile political repercussions. As a result, policymakers are keen to
ensure that banks maintain at least certain minimum levels of capital
in order to reduce the danger of failure.
Higher capital reduces the risk of failure because it acts as a cushion
to absorb losses su¤ered by banks (and other types of …rms). Capital
is the di¤erence between the value of a bank’s assets and its liabilities.
If the organization encounters …nancial troubles that reduce the value
of its assets, for example, some of its loan customers default on their
loans, the bank can still repay its liabilities (meaning avoid insolvency
and continue operating) as long as the decline in asset values is smaller
than the amount of capital.3 Therefore, other things equal, the higher
the ratio of equity-to-assets, the less risky the bank. Beyond this losscushioning role, capital is also an alternative to deposits and debt,
providing another means of …nancing asset holdings.
A reason that capital is more expensive for banks than debt is
that interest payments on debt are tax deductible for banks (paid from
before-tax earnings), while dividends are paid from after-tax earnings
and are not tax deductible. Because debt is less expensive than capital,
banks will tend to prefer debt …nance to equity (capital) …nance. Other
corporations, not just banks, have this same preference, because the tax
advantage of debt applies to nonbank corporations. But debt’s advantage is o¤set to a degree by the fact that increases in leverage (i.e., the
debt-to-equity ratio) make a corporation more fragile. Consequently,
as a corporation increases its leverage, its creditors will worry that their
investments in the corporation will not be repaid and therefore will increase the interest rate they charge, driving nonbank corporations to
limit leverage.
In the case of banks, however, some of their creditors, such as depositors insured by the Federal Deposit Insurance Corporation (FDIC),
care little about the increased fragility high leverage can bring; depositors with balances of less than $250,000 are protected from any loss in
value of their deposits in the case of bank failure by an agency of the
federal government, the FDIC. Further, in past crises, some uninsured
bank creditors have been protected. Because of these forms of protec3
This point is somewhat abridged. Firms with positive capital might, nevertheless,
become unable to repay their liabilities because of liquidity weaknesses (for example,
when short-term liability holders demand repayment and the …rm is unable to sell—
liquidate— enough assets, or sell them quickly enough, to meet these demands).

Walter: US Bank Capital Regulation

3

tion, bank creditors do not penalize banks for increases in leverage to
the same extent that nonbank creditors do. At the same time, bank
owners (shareholders) can bene…t signi…cantly from risky investments,
given that, at least in good times, such investments produce higher
pro…ts than less-risky investments. And in bad times, the downside is
limited because owners’maximum loss is limited to their investment in
the bank’s equity, while the government and creditors bear the remainder of the bank’s losses (Grochulski and Slivinski 2009, p. 2). Because
of the concern that taxpayers will get stuck with bank losses (as occurred during the savings and loan crisis of the late 1980s and early
1990s), policymakers are keen to limit bank risk-taking and require
banks to meet minimum capital requirements.
Additionally, some policymakers argue that bank failures (and especially large bank failures) are likely to trigger economy-wide (systemic) calamities.4 Further, banks are unlikely to account for this risk
when deciding how much capital to hold given that most of the costs of
systemic problems are borne by others— i.e., are external to the bank.
Therefore, banks hold less capital than is ideal from a societal point
of view, providing one more justi…cation for minimum capital requirements.
But policymakers see a trade-o¤ between the dangers of low levels
of capital (high leverage) on one hand and certain economic bene…ts
of leverage on the other. As discussed by Van den Heuvel (2008, p.
298-99), there may be signi…cant bene…ts from allowing banks to fund
themselves with a signi…cant amount of debt and especially with deposits. Individuals and businesses derive signi…cant bene…ts from holding checkable deposits in banks. Such deposits provide an immediately
available means of payment, such that depositors can meet unexpected,
sudden demands for payment, such as an emergency medical or auto
repair bill. Further, deposits have a highly predictable value equal to
exactly what the investor initially deposited, plus interest. A deposit’s
value can never decline below this amount, at least as long as the bank
does not become insolvent (fail).
Nonbank investments, such as stock or bond investments, generally
do not o¤er this immediate payment and predictable value combination of features. Instead, nondeposit investments must …rst be sold
(and such sales can impose transactions costs), often for a price that
is di¢ cult to know with certainty in advance, and then deposited in a
bank account, which can then be used for payments. Therefore, the al4

For a discussion of the view that banks are more likely to produce systemic consequences than nonbank …rms, see Bullard (2008), section entitled “Why the Financial
System is Special.”

4

Federal Reserve Bank of Richmond Economic Quarterly

ternatives lack predictability and immediacy. These features of deposits
make them attractive to investors (depositors) and, as a result, banks
can pay a lower rate of interest for deposit funding than the nondeposit
funding o¤ered by nonbanks. At the same time, while holding a small
fraction of deposits as reserves (to meet the normally steady ‡ow of depositor withdrawals), banks can lend out the remainder of their deposit
funding to long-term borrowers (such as businesses needing long-term
funding and homebuyers), earning a spread for the bank while providing bene…ts to depositors and long-term loan customers. This blend of
gathering short-term deposit funding while making long-term investments is referred to as the process of maturity transformation.
While policymakers could reduce the danger of bank failure to almost zero by requiring banks to completely, or nearly completely, fund
themselves with equity, doing so would destroy the bene…ts of maturity
transformation. So policymakers must balance the failure-reduction
bene…ts of higher capital requirements with the cost of reducing valuable maturity transformation and the availability of bank-provided deposit services. As a result, capital requirements are set, now and in the
past, at something well below 100 percent.
US bank capital requirements were revised along a number of important dimensions following the 2007-08 …nancial crisis. The goal was
to shore up the banking system and reduce the likelihood of another
crisis. The changes include new measures of capital and increased minimum requirements.
Government-imposed capital requirements extend to at least the
mid-1800s, and requirements that banks maintain minimum capital-todeposits ratios are found in early twentieth century legislation. Capitalto-asset ratio minimums, not dissimilar from those in place today, were
present in pre-WWII regulations. Further, during the 1940s and 1950s,
supervisors experimented with some of the fundamental capital requirement features that returned in the late 1980s and early 1990s:
capital-to-risk-weighted-asset ratios and capital requirements covering
o¤-balance-sheet activities. Therefore, many of the features that we
view as fundamental to our modern capital requirement regimes were
…rst employed decades ago.
Bank capital requirements were strengthened signi…cantly starting
with international agreements in the late 1980s (Basel Accords) and
later were made more sophisticated and stronger, both before and after the 2007–08 …nancial crisis with updated versions (Basel II and
Basel III— see the Glossary for a listing of frequently occurring banking capital expressions and abbreviations) of the initial Basel Accord
(also known as Basel I). Postcrisis reforms included not only broad
increases in capital requirements and new measures of capital, but ad-

Walter: US Bank Capital Regulation

5

ditional, more detailed requirements for the largest and most systemically important institutions, including added surcharges and the use of
stress testing to evaluate large banking organization capital adequacy.
Since the …nancial crisis, banking companies have increased their capital holdings appreciably.
This article will discuss the history of requirements and the changes
made in response to the …nancial crisis.

1.

PRECRISIS HISTORY OF CAPITAL
REQUIREMENTS

Bank capital requirements have a long history in the US, going back to
the earliest days of federal bank regulation. Early requirements, from
the nineteenth century, were quite crude by today’s standards. Yet
by the early and mid-twentieth century many of the main features of
today’s capital requirements had shown up, though in some cases only
temporarily, such as minimum capital requirements based on a proportion of deposits or assets (1939), risk-weighted capital requirements
(mid-1940s), and the inclusion of o¤-balance-sheet activities in capital
measures (1956).
An early capital requirement can be found in the National Bank
Act of 1864. The focus of the 1864 capital provision of the act (Section
7) was on the amount of capital needed to form a national bank (a
bank with a charter from the federal government). Given that at formation a bank has few if any assets, this capital requirement was a set
dollar amount of capital in relation to the size of the city in which the
bank was formed rather than the capital-to-assets ratios that are more
familiar today. Speci…cally, Section 7 required that the founders of the
national bank had, at origin or within …ve months of the bank’s opening, $50,000 if the bank was headquartered in a city of fewer than 6,000
people, $100,000 for cities of fewer than 50,000 people, and $200,000
if the city’s population was more than 50,000.5 This formation capital
requirement had an ongoing component in that national banks were
also required to build and then hold an additional capital amount (a
“surplus” account) equal to 20 percent of their initial capital requirement, which was allowed to decline when the bank su¤ered losses, but
no dividends could be paid by the bank until the surplus was rebuilt
(similar to bu¤er requirements established after the 2007–08 …nancial
crisis). If the national bank su¤ered a loss greater than its retained
5
Dollar amounts from National Bank Act of 1864, Section 7. Five-month requirement from White (1983), p. 16.

6

Federal Reserve Bank of Richmond Economic Quarterly

earnings and the surplus account, the bank was closed by supervisors
(White 1983, p. 16-17).
An early example of a capital rule that was a function of the size of
the bank (like today’s capital requirements), and therefore increased in
some, perhaps rough, proportion to the losses a bank might ultimately
su¤er, was a 1909 California banking law applying to banks chartered
by that state. The California Bank Act of 1909 required state banks
to maintain capital amounting to at least 10 percent of their deposits
(California Superintendent of Banks 1909, p. 7-8, Section 19). In
the 1920s and 1930s, thirteen other states, including large states such
as New York, Michigan, and Texas, passed similar statutes for the
banks they chartered, typically requiring the maintenance of a capitalto-deposits ratio of 10 percent (Robinson 1941, p. 47-49).
Mitchell (1984, p. 19) notes that in 1914 the O¢ ce of the Comptroller of the Currency, the supervisor of national banks (meaning banks
chartered by the federal government rather than by a state government), required such banks to maintain a minimum equity-deposits
ratio of 10 percent. Following its 1933 creation, the FDIC required
banks that it supervised— state-chartered banks that were not members of the Federal Reserve System— to meet a minimum 10 percent
equity-to-deposits ratio (Robinson 1941, p. 45). By 1939, however, the
FDIC had shifted to requiring state nonmember banks to hold capital
equal to at least 10 percent of assets (Robinson 1941, p. 46). Mitchell
(1984, p. 19) conjectures that the reason for the shift from an equityto-deposits ratio to an equity-to-assets ratio was that the advent of
federal deposit insurance meant there was little need for capital to protect against deposit withdrawals; instead, capital was now intended
to act as a cushion for asset losses. Over the period in which the 10
percent capital-to-deposits ratio was important— 1920 until 1939— the
average capital-to-deposits ratio held by all US banks was 15.2 percent,
so this minimum capital requirement may not have been binding for a
large proportion of banks.
Following a signi…cant investment by banks in US Treasury securities during World War II, federal supervisors (the comptroller of the
currency, the FDIC, and the Federal Reserve) modi…ed the denominator of the required capital-assets ratio so that bank-held Treasury
securities— as well as cash holdings— were deducted from assets before
calculating the ratio (Alfriend 1988, p. 28; Mitchell 1984, p. 19). Treasury security holdings were essentially risk-free, so it made little sense
to require banks to hold capital against such holdings. This mid-1940s
change to a capital measure that deducted banks’holdings of Treasury
securities and cash from assets was an early, if short-lived, example of a
risk-weighted assets (RWA) capital measure that appeared, in a more

Walter: US Bank Capital Regulation

7

sophisticated manner, following changes to US capital requirements
that came out of Basel I in 1989.
In the mid-1940s, regulators viewed a 20 percent ratio of equity-toRWA su¢ cient, and in fact, in 1945 the average equity-to-RWA ratio
for all US commercial banks was 25 percent.6;7 The Federal Reserve’s
RWA-based capital requirement was made more sophisticated with a
change in 1952 that applied di¤erent capital requirements— with higher
capital for more risky assets— to various categories of assets. In 1956,
the Federal Reserve’s capital ratio was again modi…ed along several
dimensions, including the addition of capital for some o¤-balance-sheet
items (Mitchell 1984, p. 19; Alfriend 1988, p. 28, Wall 1985, p. 10).
Baer and McElravey (1992, footnote 2), however, argue that the Fed’s
RWA capital requirement was not “seriously enforced.”
While in the 1950s the federal banking supervisors (the Federal
Reserve, the FDIC, and the comptroller of the currency) maintained
similar capital requirements, in the 1960s and 1970s di¤erences between the various supervisors developed. For example, the comptroller
dropped its focus on RWAs in the 1960s, and the regulators disagreed
on how to measure capital. The Fed de…ned capital as equity plus reserves for loan losses, while the other two regulators counted certain
types of debt as capital (Alfriend 1988, p. 29).
As can be seen in Figure 1, the banking industry, in aggregate,
experienced a continuing downward trend in its equity-to-assets ratio.
Speci…cally, the ratio fell from 58.3 percent in 1843 to 5.5 percent in
1945.8 Afterward, this ratio increased in the late 1940s and 1950s,
peaked in 1963, and then declined fairly steadily until 1979.
In 1981, the federal agencies focused on increasing bank capital levels and did so in a coordinated way (Wall 1985, p. 5). This focus was
driven in part by declining capital ratios at the largest banking organizations in the face of growing international and domestic risks (Tarullo
2008, p. 36). All three federal agencies agreed on similar numerical
capital standards of 5 percent capital-to-assets (meaning total balance
sheet assets, not RWA assets) for large banks ($1 billion to $15 billion
in assets) and 6 percent for smaller (community) banks. Multinational
6

Mitchell (1984, p. 19) discusses the 20 percent RWA ratio requirement.
Treasury securities increased from 19 percent of bank assets in 1940
to 56 percent in 1945.
In 1945, aggregate commercial bank total assets
were $157.6 billion.
Cash and due from balances accounted for $34.3 billion of these assets, Treasuries were $88.9 billion, and total equity capital was
$8.6 billion.
From FDIC, Historical Statistics on Banking, Commercial Banks
https://www5.fdic.gov/hsob/SelectRpt.asp?EntryTyp=10&Header=1.
8
Figure 1 ratios are calculated by dividing the aggregate amount of total equity
for all banks by the aggregate amount of total assets.
7

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 US Bank Equity/Assets Ratio 1834-2017

Notes: Sources: 1834–1933 data from Bureau of the Census; 1934–2017 data from
Federal Deposit Insurance Corporation (2018).

banks (over $15 billion) faced a 5 percent minimum capital-to-asset
standard starting in 1983 (Alfriend 1988, p. 30).
In a February 1983 federal appeals court ruling, supervisors’ authority to enforce capital rules on banks was called into question when
that court argued, at least in this case, that capital weakness alone, as
measured by capital ratios, was not su¢ cient justi…cation to impose a
cease and desist order on a bank (First National Bank of Bellaire v.
Comptroller 1983, p. 8-9). In November 1983, Congress responded to
this court ruling by granting clear authority over bank capital levels to
the federal banking supervisors in the International Lending Supervision Act of 1983 (ILSA).9
9
That act accorded federal supervisors “the authority to establish . . . minimum
level[s] of capital for a banking institution” and authorized the supervisors (called “agencies” in the act) to “issue a directive to a banking institution that fails to maintain

Walter: US Bank Capital Regulation

9

While the federal supervisors gained clear enforcement authority for
capital requirements from the ILSA, the Federal Deposit Insurance Corporation Improvement Act of 1991 (FDICIA) went a step further. This
act established a “prompt corrective action”structure, setting tripwires
whereby supervisors are required to undertake, without delay, progressively more severe actions as a bank’s capital declines below “Adequately Capitalized” into progressively lower capital ratio categories:
“Undercapitalized,” “Signi…cantly Undercapitalized,” and “Critically
Undercapitalized”(see Figure 4 for the current minimum capital ratios
for each category). FDICIA mandates certain supervisory actions as a
bank’s capital declines into lower categories, including: heightened supervisory monitoring; restrictions on bonuses and raises to executives;
and any acquisitions or new branch formations require prior supervisory
approval. FDICIA also dictates that if a bank’s equity-to-assets ratio
of capital falls below 2 percent, supervisors must, within ninety days,
place the bank in receivership or conservatorship, with few exceptions.
(Spong 2000, p. 90-94; and Federal Deposit Insurance Corporation
Improvement Act 1991, Section 131(c)(3)(B)(i)).
Beyond its clear grant of authority over capital requirements to federal supervisors, the ILSA also contained language supporting ongoing
US participation in e¤orts to adopt international standards of bank
supervision, including more uniform international capital standards.10
E¤orts to increase the uniformity of bank supervision internationally, under the auspices of the Basel Committee, had begun in the mid1970s, well before ILSA’s enactment. Originally named the Committee
on Banking Regulations and Supervisory Practices, the Basel Committee was formed in 1974 by the heads of the central banks of the Group
of Ten countries. It now includes representatives from twenty-eight
countries and is typically referred to as the Basel Committee on Banking Supervision (BCBS). The creation of the committee was driven by
a number of disruptions in international …nancial markets caused by
failures of important internationally active banks, particularly the June
1974 failure of the West German bank Bankhaus Herstatt (Bank for International Settlements 2018, p. 1). The committee is headquartered at
capital at or above its required level. . . Such directive may require the banking institution to submit and adhere to a plan acceptable to the appropriate Federal banking
agency describing the means and timing by which the banking institution shall achieve
its required capital level” (Public Law 98-181, November 30, 1983, section 908).
10
Speci…cally, ILSA stated that the “Chairman of the Board of Governors of the
Federal Reserve System and the Secretary of the Treasury shall encourage governments,
central banks, and regulatory authorities of other major banking countries to work toward maintaining, and where appropriate, strengthening the capital bases of banking
institutions involved in international lending.” (Public Law 98-181, November 30, 1983,
section 908).

10

Federal Reserve Bank of Richmond Economic Quarterly

the Bank for International Settlements in Basel, Switzerland, and held
its …rst meeting in February 1975. The BCBS’s focus is most directly
on internationally active banks and their cross-border supervision.

2.

BASEL I REINTRODUCED RISK-WEIGHTED
ASSETS AND INCLUDED OFF-BALANCE-SHEET
EXPOSURES

One of the most signi…cant early decisions of the BCBS was a multinational agreement on minimum capital standards, the Basel Capital
Accord (later called Basel I)— published in …nal form in 1988. The
accord was motivated by the Latin American debt crisis of the early
and mid-1980s and the shrinking capital ratios of internationally active
banks. It called on accord participants to require banks in their countries to hold a minimum of 8 percent capital to RWA. Banks were to
meet this standard by the end of 1992 (Bank for International Settlements 2018, p. 3). Prior to the adoption of the accord, in 1986 US bank
supervisors had proposed, but not implemented, a return to the RWA
standards that also accounted for o¤-balance-sheet exposures. In 1987,
US and British authorities worked together on RWA and o¤-balancesheet-based capital standards (Alfriend 1988, p. 30).
RWA standards were seen as addressing a weakness in simple capitalto-assets standards: they were insensitive to asset riskiness. Bank A
with very safe assets (for example, mostly Treasury securities and loans
to only the most credit-worthy borrowers) and a 5 percent capital-toassets ratio is much less likely to face …nancial problems than Bank B
with the same 5 percent ratio but more risky assets (for example, mostly
loans made to developers of speculative properties); nevertheless, the
risky bank is allowed to hold the same amount of loss-cushioning capital
as the less risky bank under a non-RWA capital-to-assets standard.
The Basel RWA standard categorized assets into …ve groups (0,
10, 20, 50, and 100 percent risk weights) based upon riskiness of the
assets (Bank for International Settlements 1988, p. 8).11 For example,
cash and government debt securities were placed in the lowest risk
group, and unsecured loans made to commercial …rms were placed in
the highest risk group. The lowest risk asset group received a weight
of zero (meaning no capital need be held against these assets). The
two next riskiest groups received a 10 percent weight and a 20 percent
weight, in turn. With a 5 percent capital requirement for assets with a
11

As implemented in the US in 1992, the 10 percent risk category was not used.
See Board of Governors of the Federal Reserve System (1989, p. 4207-08, 4214); and
US Department of the Treasury (1989, p. 4180-81).

Walter: US Bank Capital Regulation

11

Figure 2 US Minimum Capital Requirement Ratios Before
Basel III

Notes: *In 1985, the Federal Reserve adopted a 6 percent minimum Total Capital
Leverage Ratio, meaning the ratio of total capital to total assets, for all banks and
BHCs it supervised (Alfriend 1988, p. 30). In addition to the Total Capital Leverage requirement, in 1985 there was also a 5.5 percent “primary capital” leverage
requirement. Primary capital was broader than Tier 1 capital under Basel I–III
(primary capital included reserves for loans losses, for example) but narrower than
the 1985 de…nition of total capital. **Tier 1 to quarterly average total assets.
Three percent for BHCs with a composite strength rating of 1, 4 percent otherwise. From Bank of New York Mellon Corporation (2007), p. 8; Basel II …nal
rule, p. 69302 (footnote 27); and Citigroup (2009), p. 43.

50 percent weight, banks were therefore required to hold capital equal
to 2.5 percent of these assets. The riskiest group of assets received a
100 percent weight, meaning banks were required to hold capital equal
to 5 percent of the amount of such assets.
The Basel Accord standards also required banks to hold capital
against o¤-balance-sheet (OBS) exposures. A line of credit is an example of such an exposure, whereby the bank commits to make a loan to
a business or to an individual, which can be drawn upon whenever the
business or individual chooses.
US supervisors published their …nal Basel I-based rules in January
1989. The rules included a two-year phase-in: December 1990 through
December 1992 (Board of Governors 1989, p. 4186-221; and US Trea-

12

Federal Reserve Bank of Richmond Economic Quarterly

sury Department 1989, p. 4168-84). As of December 31, 1992, all US
banks and bank holding companies (BHCs) were required to maintain a
minimum ratio of Tier 1 capital-to-RWA (including OBS) of 4 percent
and total capital-to-RWA of 8 percent (see Figure 2). Tier 1 capital,
the narrowest de…nition of capital at the time, was a new measure
based on an internationally agreed-upon Basel de…nition. It consisted
of common equity, certain perpetual preferred stock, and investments
by outsiders in the stock of the bank’s or BHC’s subsidiaries (“minority interests”). Total capital was made up of Tier 1 capital plus Tier 2
capital, which included a limited amount of the banking organization’s
reserves for loan losses, some additional preferred stock not allowed in
Tier 1, and certain debt instruments with equity-like features such as
unsecured perpetual debt.
Supervisors retained leverage ratio (non-RWA ratio) minimums in
addition to Basel I’s RWA standards (see Figure 2). They list two
justi…cations: 1) RWA measures address credit risk, “but there are a
number of other banking risks not addressed— e.g. interest rate risk,
operational risk and asset concentrations”; and 2) with zero risk weights
on some assets, banks could lever up considerably in a RWA-only capital regime (Board of Governors 1989, p. 4193; and US Treasury Department 1989, p. 4171).12
Comparing US capital requirements prior to Basel I with those
implemented by Basel I-based requirements is di¢ cult because Basel I
added RWA requirements and modi…ed the leverage ratio requirement.
Nevertheless, it seems clear that bank capital, at least as measured by
the simple equity/assets leverage ratio, began to increase as the US
Basel I requirements began to take e¤ect (Figure 1).

3.

BASEL II MODERNIZED RISK CATEGORIES
FOR THE LARGEST BANKS

While the Basel I RWA capital measure was a more risk-sensitive measure of capital than the simple equity-to-asset (leverage) measures that
predominated in the early 1980s, supervisors viewed the …ve (four in
the US) invariant (from bank to bank) risk categories as being too blunt
and replaced them, for the largest banks and BHCs, with “Basel II”
requirements in the mid-2000s. Basel II took greater account of differences in banking organization riskiness by including more detailed
risk measurements of assets and OBS exposures— the denominator of
12
Gambacorta and Karmakar (2016) explore the advantages and disadvantages of
leverage versus RWA-based capital ratios.

Walter: US Bank Capital Regulation

13

the required capital ratios. Basel II left the numerator unchanged from
Basel I.
As implemented by US banking supervisors, Basel II was meant to
improve on Basel I by requiring large, internationally active banking
organizations (banks or BHCs with assets over $250 billion or at least
$10 billion in foreign exposures) to provide data describing the characteristics of individual assets or groups of assets. These data were
fed into a formula, created by supervisors, which converted the data
into requisite capital holdings.13 The required data go beyond simple
amounts of various types of assets (and OBS exposures) and include information on the expected losses that might be generated by the assets,
as determined by the individual banking organization’s risk-estimating
models. Of course, supervisors were unwilling to simply take organizations’ word for the riskiness of assets, so Basel II also emphasized
supervisory examination of banking organizations’ risk-measurement
systems. Further, the US Basel II rules expanded large organizations’
public disclosures of risk measures in the hopes that market oversight
would encourage appropriate risk-taking. (Board of Governors 2007;
Bank for International Settlements 2018, p. 4-5; US Government Accountability O¢ ce 2014, p. 7-8).
Final Basel II capital rules for large US organizations were published by the federal supervisors on December 7, 2007, took e¤ect on
April 1, 2008, and would be phased in by organizations over a period
of years.14 Basel II, at least for some of the covered banks and BHCs,
was thought to have the potential to lower total capital holdings, which
was a concern for supervisors and other observers, so that the multiyear
phase-in period involved limits on the amount by which an organization’s capital could decline. Further, these organizations were required
to meet minimum leverage ratios and the minimum requirements, for
bank subsidiaries, established by FDICIA.
For banking organizations smaller than the $250 billion cuto¤ in
the US Basel II rule, the Basel I risk weights remained in place (called
standardized approach in contrast to the advanced approaches for banks
above the $250 billion cuto¤).15 The major di¤erence between the standardized and advanced approaches is that the standardized approach
13

The supervisor-created formula can be found at US Department of the Treasury
(2007), p. 69411.
14
The December 7, 2007, US Basel II rules can be found at US Department of the
Treasury (2007).
15
See for example, BB&T Corporation (2009), p. 78, and BB&T Corporation
(2010), p. 87, which note that in this standardized approach ($157 billion in assets as
of 2010) BHC’s RWAs are calculated by assigning each “asset class . . . a risk-weighting
of 0%, 20%, 50%, or 100% based on the underlying risk of the speci…c asset class,”
abiding by Basel I-based RWA calculation methods.

14

Federal Reserve Bank of Richmond Economic Quarterly

did not gather information from internal risk models, which meant that
smaller organizations were not required to create such models, unlike
the larger organizations.
As can be seen in Figure 2, Basel II did not change the minimum
capital ratios compared to Basel I. Its focus was on the method of calculating RWAs, the denominator of the nonleverage ratios in the …gure;
and in fact, changed RWA denominators only for the largest banking
organizations. Therefore, Basel II had a limited e¤ect on capital requirements for the broad swath of organizations. Only with changes
made following the …nancial crisis and the resulting Basel III shifts were
requirements altered in major ways for all organizations, compared with
Basel I.

4.

POSTCRISIS CAPITAL REQUIREMENTS

Following the …nancial crisis of 2007–08, global bank supervisors strengthened capital requirements by: 1) tightening the elements that count as
capital (the numerator of capital ratios); 2) revising the ways that bank
risks are measured (the denominator of capital ratios); and 3) requiring that higher ratios be met, at least when all bu¤ers and surcharges
are counted. The BCBS released new Basel capital standards, “Basel
III,”in December 2010 (Bank for International Settlements 2010). US
legislators included in the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 (DFA) requirements that US supervisors
tighten capital requirements, and in 2013, US supervisors developed
requirements that conformed with the Basel agreement standards as
well as those in the DFA. Figure 3 provides a summary, in table form,
of the major capital requirements in place after these changes.
The new US capital requirements apply to all banks— no matter
their asset size— and to BHCs with assets greater than $1 billion (US
Department of the Treasury and the Federal Reserve System 2013, p.
62151).16 BHCs smaller than $1 billion are not required to meet the
new capital standards, but their depository institution subsidiaries are.
The logic of focusing only on the depository institution subsidiaries of
small BHCs is that such BHCs are likely to have few, if any, activities
outside of their bank subsidiaries and therefore carry little risk other
than the ones found in these subsidiaries. Additionally, the relevant
federal banking regulations state that if a small BHC has a signi…cant
16
In April 2015, the Board of Governors announced that it was increasing the
BHC size cuto¤ (originally speci…ed in October 2013 in Regulation Q) from $500
million to $1 billion in response to legislation enacted in December 2014.
See:
https://www.federalreserve.gov/newsevents/pressreleases/bcreg20150409a.htm.

Walter: US Bank Capital Regulation

15

Figure 3 Summary of Main Basel III/DFA Capital
Requirements

Notes: In the > $250 B and GSIBs columns, T1 means Tier 1 capital, T2 is
Tier 2 capital, TE is total exposures, AT1 is additional Tier 1 capital (meaning
items that count as part of Tier 1 capital but not as part of the narrower CET1
capital), RWA means standardized approaches RWA, and AARWA is advanced
approaches RWA.

amount of activities outside the bank subsidiary (and therefore risks
outside of the bank), that BHC may become subject to BHC-level
capital requirements.17
One important principle underlying the 2013 US capital regulations
is that they should increase in complexity and detail as the size of the
institution increases (and similarly, require less complex analysis and
detail from smaller institutions). Two factors seem to motivate this
principle. First, the largest institutions face the most complex risks
(e.g., hedging, complicated derivatives exposures, and brisk trading
17
The regulations addressing small BHCs with signi…cant activities outside of the
bank subsidiary are found in two locations. First, the Federal Reserve’s Regulation
Q— adopted in July 2013 but updated through amendments since. The up-to-date version is Board of Governors (2018a), and the section relevant for small BHCs is Section
217.1(c)(ii). Further relevant discussion is also found in Board of Governors (2015a),
Section 1 of Appendix C to Part 225.

16

Federal Reserve Bank of Richmond Economic Quarterly

activities), and their requirements must be detailed and sophisticated
to account for as much of this risk as possible; smaller institutions’risks
are less di¢ cult to measure (generally, lending and securities holdings).
Second, the largest institutions engender the greatest moral hazard
risks, so they should face the most intense focus; small institutions
can fail without producing economy-wide concerns (and many small
banks were allowed to fail during the last crisis and during …nancial
di¢ culties in the 1980s and 1990s), while a number of large, troubled
…nancial institutions were propped up during the recent crisis. As a
result of this principle, the highest capital requirements, and the ones
requiring the most detailed input from the institutions themselves, are
those borne by the largest and most complex institutions; for example,
additional capital charges and reporting requirements are imposed on
the eight US Global Systemically Important Bank Holding Companies
(GSIBs), which are the largest and most complex US BHCs.18
Another feature of the new capital regulations is the broad application of capital bu¤ ers for banks and BHCs. Bu¤ers are required
amounts of capital above speci…ed minimum ratios. For example, as
will be discussed in more detail below, banks and BHCs must hold
common equity Tier 1 (CET1) capital at least equal to 4.5 percent
of their RWAs. But beyond this amount, they must also hold an additional capital conservation bu¤ er (CCB) amount of CET1 capital
equal to 2.5 percent of RWA. This bu¤er amount acts as a tripwire,
requiring mandatory banking organization action if the organization’s
capital lies between 7.0 percent of RWA (4.5 plus 2.5 percent) and 4.5
percent; the organization must begin to shrink its dividend payments
to shareholders and bonus payments to senior managers as the organization’s capital declines below 7.0 percent. Limiting dividend and
bonus payments will naturally tend to rebuild capital, given that earnings that are not paid out as dividends or bonuses become retained
earnings, adding to capital. These bu¤ers, which apply to banks and
BHCs, therefore, can be thought of as performing a role similar to the
one played by FDICIA’s prompt corrective action (PCA) requirements,
18
The principle that more stringent requirements should be imposed on the largest
and most systemically important institutions was a key feature of the Dodd-Frank Act
(for example, Section 165), which required “more stringent” supervisory standards for
the largest banking organizations. This same principle also underlies the October 31,
2018, Board of Governors proposals to “more closely match the regulations for large
banking organizations with their risk pro…les.” Board of Governors Chairman Jerome H.
Powell emphasized this strategy when explaining the proposals: “The proposals would
prescribe materially less stringent requirements on …rms with less risk, while maintaining
the most stringent requirements for …rms that pose the greatest risks to the …nancial
system and our economy” (Board of Governors of the Federal Reserve System 2018e).

Walter: US Bank Capital Regulation

17

which apply only to banks.19 The bu¤ers automatically force actions
that help to rebuild the capital strength of the BHC, just as the PCA
requirements compel supervisors to take actions to force a bank to limit
certain actions, and take other actions, with the intention of rebuilding
the bank’s capital strength.

5.

NEW CAPITAL RATIOS

A New, More Narrow Numerator
The 2013 capital regulation put in place a new, narrower measure of
capital, CET1 capital for banks (and for BHCs). CET1 includes common stock, retained earnings, and two more minor items of capital:
certain minority interests and certain accumulated other comprehensive income (AOCI). As discussed earlier, “minority interests” are investments by outsiders in the stock of the bank’s or BHC’s subsidiaries.
AOCI is “unrealized gains and losses on certain assets and liabilities
that have not been included in net income,” for example gains and
losses on available-for-sale assets (US Department of the Treasury and
the Federal Reserve System 2013, p. 62024). Previously, the narrowest
de…nition of capital was Tier 1 capital, which remains in place. Tier 1
capital is similar to CET1, but it adds certain types of preferred stock
that CET1 excludes.

New Denominators
The new US capital regulation also made changes to the denominator
of the capital ratio for banks. For advanced approaches institutions,
RWAs must be calculated in two ways, and the method that produces
the lower ratio must be compared to the minimum requirement to determine if the organization is meeting capital requirements. The two
methods are the standardized RWA calculation, whereby set weights
are multiplied by speci…ed categories of assets (such as: 0 percent for
cash and certain government-issued or government-guaranteed debt instruments; 20 percent for exposures to US depository institutions; 50
percent for certain residential mortgage debt securities; and 100 percent
for corporate debt and loans), and the advanced approaches RWA calculation.20 Under the new capital rules, the advanced approaches method
19
See Prompt Corrective Action provisions found in Section 38 (and especially subsection (b)) of FDICIA.
20
Standardized and advanced approaches RWA calculations are discussed at length
in the Federal Reserve’s Regulation Q (Board of Governors 2018a): for standardized
approach see Subpart D; for advanced approaches see Subparts E and F. The so-called

18

Federal Reserve Bank of Richmond Economic Quarterly

is largely the same as the method (discussed earlier) introduced in the
US in response to Basel II, and the standardized approach is similar to
that introduced in the US following the Basel I approach. However, the
standardized approach under the new (2013) capital rule contains many
more risk weight categories than the four categories found in the earlier
Basel I-based RWA approach (Davis Polk 2016). Banks that are not
advanced approaches banks, standardized approaches banks, measure
RWA using only the standardized method.
These new capital ratio requirements (the CET1 numerator and
the new advanced approaches and standardized denominators), once
in place, became the new prompt-corrective action (FDICIA) rules for
banks (see Federal Deposit Insurance Corporation Improvement Act
1991, Section 131(d)-(h), and Code of Federal Regulations 1998, (a)(c)). FDICIA authorized supervisors to establish the capital ratios,
and the levels of these ratios, to be used in the PCA enforcement
regime (greater strictures imposed as a bank’s capital declines from
“Adequately Capitalized” to “Undercapitalized” and so on). Banks
must meet or exceed all ratios speci…ed in a row in Figure 4. Beyond banks, BHCs also must meet all of the risk-weighted capital ratio
amounts in the “Adequately Capitalized”row of Figure 4 to be considered su¢ ciently capitalized under the 2013 capital regulation (Board
of Governors 2018a, Section 217.10(a)).
“Collins Amendment” to the DFA— Section 171— is responsible for the requirement that
advanced approaches institutions calculate these capital ratios by both the standardized
and advanced methods and then meet requirements under both (meaning whichever calculation method produces the lower ratio is the binding calculation).

Walter: US Bank Capital Regulation

19

Figure 4 Prompt Corrective Action Requirements for Banks

Notes: Source: Davis Polk (2015, p. 23) and Prompt Corrective Action regulation
found in Code of Federal Regulations (1998).

Notes: Source: Board of Governors (2018a), which provides extensive details on
these de…nitions.

20

Federal Reserve Bank of Richmond Economic Quarterly

Minimum Leverage Ratio for all Banks and
Bank Holding Companies
The next-to-the-last column in Figure 4 lists the leverage requirement
that must be met by all banks regardless of size. This leverage requirement is the ratio of Tier 1 capital to average total consolidated
assets (daily or weekly averages over the quarter, depending on the
size of the bank) (Federal Financial Institutions Examination Council 2018, p. RC-O-3; Board of Governors 2018a, section 217.10(a)(4)).
This same ratio applies to all US BHCs except those with less than $1
billion in assets.

Supplementary Leverage Ratio
Advanced approaches banks are also subject to the Supplementary
Leverage Ratio (SLR)— the last column in Figure 4 (see Board of Governors 2018a, section 217.10(c)(4)). This requirement took e¤ect on
January 1, 2018. The minimum for this ratio is 3 percent, lower than
the 4 percent requirement for the leverage ratio— applicable to all organizations. While the numerator of the supplementary ratio is the same
as the numerator for the simple leverage ratio (“All Banks”column)—
Tier 1 capital— the denominator of the SLR is much more comprehensive. While the leverage ratio includes only on-balance-sheet assets,
the SLR includes a broad compilation of o¤-balance-sheet exposures,
such as derivatives and credit commitments (Davis Polk 2015, p. 22).
This same ratio applies to all US advanced approaches BHCs as well.
GSIBs face a higher SLR requirement (5 percent) than other advanced
approaches …rms: the 3 percent ratio plus an added 2 percent “leverage
bu¤er” (Board of Governors 2018a, section 217.11(d); Citigroup 2017,
p. 36; Goldman Sachs Group 2017, p. 72).

6.

CAPITAL BUFFERS

Capital Conservation Bu er
Beyond the minimum capital requirements enumerated in Figure 4,
the supervisors also impose an additional requirement on all banks and
BHCs (except those BHCs with assets less than $1 billion): the capital
conservation bu¤er (CCB).21 This bu¤er acts as an early warning trigger device for any banking organization for which capital is declining.
As mentioned earlier, the CCB requirement forces banks and BHCs to
21
Note that while Figure 4 lists requirements for banks, the “Adequately Capitalized” row is also a minimum requirement for BHCs.

Walter: US Bank Capital Regulation

21

Figure 5 Payout Triggers for Capital Conservation Bu er
Requirement

Notes: Source: Davis Polk (2015, p. 28).

retain a higher and higher percentage of earnings (i.e., limit payouts
to shareholders and bonuses to senior managers to a greater degree) as
the organization’s bu¤er holdings decline below 2.5 percent. The payout maximum begins at 60 percent (see Figure 5), so that the entity
must retain 40 percent of its earnings, and declines to zero. The goal
is to return the bu¤er to 2.5 percent, at which time the institution no
longer faces a CCB-driven limit on its earnings payouts. The entity
must hold this bu¤er amount above and beyond its “adequately capitalized”ratios (see Figure 4) of total capital, Tier 1, and CET1; should
any of these ratios fall below the adequately capitalized ratio shown
in Figure 4, plus 2.5 percent, the limits are imposed. Entities are also
prohibited from paying bonuses without supervisory approval whenever
their bu¤er falls below 2.5 percent (Board of Governors 2018a, sections
217.10-217.11). The CCB was phased in over a three-year period from
January 2016 to January 2019 (Davis Polk 2015, p. 17, 19).

Countercyclical Bu er
Advanced approaches organizations are also subject to the Countercyclical Bu¤er (CCyB) (Board of Governors 2018a, section 217.11(b)).
As with the CCB, this bu¤er must be met or the organization will face
limits on distributions of earnings to shareholders and bonus payments
(Board of Governors 2016, p. 24). Unlike other capital requirements,
the CCyB requirement is meant to vary with the state of the overall
economy. It is set by supervisors and can range from zero to 2.5 percent
of RWA (Board of Governors 2018a, Section 217.11(b)(2)(iii)).
The decision by supervisors about where to set the CCyB amount
will depend on such factors as “macroeconomic, …nancial, and supervi-

22

Federal Reserve Bank of Richmond Economic Quarterly

sory information indicating an increase in systemic risk including, but
not limited to, the ratio of credit to gross domestic product, a variety
of asset prices, other factors indicative of relative credit and liquidity expansion or contraction, funding spreads, credit condition surveys,
indices based on credit default swap spreads, options implied volatility, and measures of systemic risk”(Board of Governors 2018a, section
217.11(b)(2)(iv)). The CCyB amount will be increased “during periods when systemic risk is increasing” and reduced “as vulnerabilities
diminish.” The idea is that the CCyB could “moderate ‡uctuations
in the supply of credit over time” (Board of Governors 2016, p. 4).
The CCyB was created to respond to a DFA requirement that a countercyclical bu¤er be put in place that “increases in times of economic
expansion and decreases in times of economic contraction” (DFA Section 616(a)). As of December 2018, supervisors were imposing a zero
CCyB bu¤er requirement.

7.

ADDED CAPITAL REQUIREMENTS FOR
GLOBAL SYSTEMICALLY IMPORTANT BANK
HOLDING COMPANIES

Because of the potential for widespread economic damage from the failure of the largest and most interconnected, internationally active banking organizations, such organizations— the GSIBs— are subject to additional capital requirements beyond those imposed on other advanced
approaches institutions.22
GSIBs are those BHCs that have been determined, based on a systemic importance scoring methodology developed by the BCBS, likely
to produce the greatest economic damage should they fail. In the US,
all advanced approaches BHCs are scored. The score is based on a set
of …nancial measures of on-balance-sheet and o¤-balance-sheet assets
and liabilities, as well as measures of …nancial transaction ‡ows, such
as payments transfers. The set includes size (“Total Exposures,”based
not only on total assets, but also on o¤-balance-sheet exposures such as
dollar amounts of derivatives, lines of credit, and loan commitments), a
measure of how connected the organization is to other …rms (“Interconnectedness”), and how di¢ cult its activities might be to replace were
it to fail (“Substitutability”), among others. Each measure is chosen
because it is thought to correlate with how much economic harm the
organization’s failure might impose, so that the higher an organization’s score, the higher its expected harm should the …rm fail. Any US
22
Jarque et al. (2018, p. 11-12) discuss the logic underlying the GSIB score and
the GSIB capital surcharge and provide detailed descriptions.

Walter: US Bank Capital Regulation

23

advanced approaches BHC with a measure above a designated score is
declared a GSIB and is subject to additional capital requirements.23

GSIB surcharge
One of the additional capital requirements imposed on GSIBs is the
GSIB surcharge. This surcharge, which is really just a bu¤er applicable
only to GSIBs, is calibrated so that it should just o¤set the additional
harm the failure of these large, interconnected …rms would impose,
compared to non-GSIB organizations. The idea is that the greater this
bu¤er requirement, the lower the failure probability of the GSIB. If
one thinks of the expected harm a GSIB might impose as a function
of the probability of its failure and the harm given its failure, by lowering the probability, the expected harm can be reduced to something
close to the same level as that of smaller, less interconnected non-GSIB
organizations.
The surcharge was phased in between January 2016 and December
2018. When fully phased in, for US GSIBs the surcharge should range
between 1.5 percent and 3.5 percent— common equity Tier 1 capital as a
percent of RWA.24 This requirement, like the capital conservation bu¤er
and the countercyclical capital bu¤er, is enforced by limiting payouts to
shareholders and senior managers (Board of Governors 2018a, section
217.11).

Total Loss-Absorbing Capacity
The other added requirement applicable to GSIBs is the Total LossAbsorbing Capacity (TLAC) requirement. In December 2016, the
Board of Governors adopted a …nal rule requiring that the eight US
GSIBs maintain a speci…ed minimum level of equity (as measured by
Tier 1 capital) plus loss-absorbing (long-term) debt, the combination
of which is called TLAC (Board of Governors 2017).25 The Board of
23
For descriptions of the US GSIB designation test and GSIB surcharge, see: Jarque et al. (2018); Board of Governors (2018a, Sections 217.400-217.406); Board of Governors (2015b); and Passmore and von Ha¤ten (2017). As of November 2017, when the
latest list of international GSIBs was announced by the Financial Stability Board (see
Financial Stability Board 2017), there were eight US GSIBs: Bank of America, Bank of
New York Mellon, Citigroup, Goldman Sachs, JPMorgan Chase, Morgan Stanley, State
Street, and Wells Fargo.
24
Based on the author’s review of 2017 annual reports or 10-K …lings of all eight
US GSIBs. These reports and …lings all contained forecasts of fully phased-in (2019)
GSIB surcharge ratios.
25
The rule requires the GSIB to meet this ratio requirement with externally derived debt and equity— meaning debt and equity raised from outside the organization.
The rule includes similar requirements for US-located, foreign-owned intermediate hold-

24

Federal Reserve Bank of Richmond Economic Quarterly

Governors’rule is similar to rules adopted in other countries through
auspices of the BCBS and the Financial Stability Board (FSB) and the
direction of the Group of 20 (G20) leaders (Board of Governors 2017,
p. 8).
Under the US rule, TLAC must be no less than 18 percent, plus
relevant bu¤ers (CCB, CCyB, and the GSIB surcharge), of RWA and
9.5 percent of total leverage exposure (meaning on-balance-sheet assets, plus o¤-balance-sheet exposures).26 Further, the rule requires the
GSIBs to maintain an amount of long-term debt equal to at least 6
percent, plus the …rm’s GSIB surcharge, of RWA and 4.5 percent of
total leverage exposure (see Figure 3). US GSIBs must meet the TLAC
rule by January 1, 2019 (Board of Governors 2017, section I(A)). For
all TLAC RWA-based ratios, GSIBs must calculate the ratio using
both the advanced approaches and standardized approaches methods
and use whichever ratio is lower to determine whether it has met the
requirement.
Equity, as has been discussed, is …rst to absorb …rm losses. If
losses are large enough to consume equity, then in a bankruptcy or
supervisory-required reorganization (such as a DFA Orderly Liquidation Authority reorganization) of a troubled GSIB, some or all of the
TLAC debt could be converted to equity, reducing the value of liabilities and returning the GSIB, or at least its important subsidiaries,
to solvency.27 In this way, important GSIB subsidiaries— such as the
bank, investment bank, and payments subsidiaries— could continue operating, minimizing the bankruptcy’s damage to the overall economy.28
Long-term debt is the focus of the debt portion of the TLAC requirement because of the idea that long-term creditors are in a better
position to have their debts converted to equity than short-term creditors. The TLAC requirement can only be met with debt that has a
maturity of at least one year— and debt with a maturity of between one
and two years counts toward the requirement only after a 50 percent
discount. The process of converting the debt to equity in the troubled
GSIB is likely to take some time (likely more than a few days), so that
only after such a period could the now-equity holder get repaid by selling companies with assets exceeding $50 billion. The TLAC rule is contained within
the Federal Reserve’s Regulation YY (subparts G and P are wholly devoted to TLAC;
sections 252.2 and 252.2 of Reg. YY contain short TLAC stipulations).
26
Board of Governors (2018a), section 252.63.
27
See Pellerin and Walter (2012) for a detailed comparison of bankruptcy versus
Orderly Liquidation.
28
In its “Approaches to Resolution” section, the Fed’s October 2015 then-proposed
TLAC rule provides a detailed explanation of how TLAC would be used in a GSIB
insolvency to preserve the health of important subsidiaries (Board of Governors 2015c,
p. 74928).

Walter: US Bank Capital Regulation

25

ing its equity shares in the securities market (perhaps for less than its
original investment). But short-term creditors of …nancial …rms, many
of which have overnight maturities, are thought of as dependent on
immediate repayment of their investment in …nancial …rms in order for
them to repay their own creditors on time. Should such creditors’repayments be held up for an extended period, their losses might spread
to other …nancial …rms, creating a system-wide problem (often called
“contagion”). It is this concern about short-term creditors’ need for
timely funds availability (which is the reason they make short-term investments even though such investments typically pay lower interest
rates) and contagion to other …rms that drives the requirement that
TLAC debt be long-term debt.

8.

STRESS TESTS

Current banking law requires the Federal Reserve, in coordination with
the other bank supervisors, to conduct annual stress tests of banking
companies larger than $250 billion and “periodic”stress tests of companies with assets between $100 billion and $250 billion.29 The required
tests are meant to evaluate a company’s capital under various economic
scenarios.
In its stress tests, the Federal Reserve employs three scenarios:
“baseline,” “adverse,” and “severely adverse.” Essentially, the stress
test requires covered BHCs to prove— via the test— that they could
su¤er a negative economic shock (of various levels of severity— the scenarios) and still maintain their required capital ratios. The baseline
scenario is centered on current forecasts (but does not represent the
Fed’s own forecasts) of the likely state of the economy over the next
several years and includes forecasts of various economic variables (such
as quarterly GDP growth, the unemployment rate, interest rates, and
house prices) in the US and internationally.
The adverse and severely adverse scenarios involve weaker economic
conditions (as measured by many of the same variables) than the base29
The initial stress test requirement was found in Section 165 of the Dodd-Frank
Act of 2010. The DFA required the Board of Governors, along with the other bank
supervisors, to conduct annual stress tests for BHCs with $50 billion or more in assets.
In May 2018, this requirement was modi…ed by the Economic Growth, Regulatory Relief,
and Consumer Protection Act (Public Law 115-174), raising the size cuto¤ for required
annual stress tests to $250 billion. Any US BHC that is declared a GSIB, regardless
of size, is subject to annual stress tests under the revised law. Currently (based on
March 31, 2018, …nancial reports), a $50 billion cuto¤ would have included forty-…ve
US BHCs, while the new $250 billion cuto¤ includes fourteen. The Federal Reserve’s
rules are found in Board of Governors (2011).

26

Federal Reserve Bank of Richmond Economic Quarterly

line scenario.30 For example, the 2018 severely adverse scenario examined the impact on BHC balance sheets of a recession that produces:
quarterly GDP growth rates that decline precipitously in the US to a
low of negative 8.9 percent; a signi…cant decline in GDP growth rates
in the euro area (down to negative 5.2 percent) and Japan (negative
11.4); a peak US unemployment rate of 10.0 percent; and a quarterly
US growth rate of disposable income falling as low as negative 5.1 percent. The idea is that if the BHC can endure the hypothesized adverse
and severely adverse scenarios and still meet its capital requirements,
then in an actual future recession the BHC will be able to continue to
provide necessary lending and payments services and not exacerbate
the already weak economic conditions by reducing its performance of
these functions. If the company is unable to absorb any losses produced by the scenarios and still meet requirements, its ability to pay
out dividends to shareholders is restricted (Board of Governors 2018b,
p. 9, 25).
Large banking organizations are subject to two types of stress tests:
the Dodd-Frank Act Supervisory Stress Test (DFAST) and the Comprehensive Capital Analysis and Review (CCAR). Both involve projections of losses produced by various hypothetical stress scenarios, as
described above. However, the DFAST and CCAR di¤er along one
dimension: how dividend payouts during the forecast period are calculated. Under the DFAST, the test assumes that the banking company
will pay out dividends at a rate equivalent to the …rm’s previous year’s
payout.
In contrast, the CCAR test involves individual banking …rms specifying their planned dividends over the test period (nine quarters). The
Federal Reserve requires …rms to limit their payouts below the level the
…rm had planned, and included in its dividend plan, if the CCAR stress
test indicates that its capital will fall below required minimums given
the planned payouts (Board of Governors 2018b, p. iii, 9-10).31 Following the stress test process, the Federal Reserve publicly announces
results.
30

A detailed description of the 2018 stress test scenarios can be found in documents
linked in Board of Governors (2018d).
31
In April 2018, the Board of Governors proposed, for comment, a change to its
CCAR process— replacing the CCAR procedure whereby the Fed will object to a banking …rm’s proposed dividend payout plans following its stress test if the Fed’s stress
test indicates that the payouts would leave the …rm with low capital ratios. Instead,
under the proposal, the Fed would run its stress test and a bu¤er would be added to
the …rm’s risk-weighted and leverage capital requirements equivalent to the amount by
which the …rm’s capital declines in the Fed’s stress test (Board of Governors 2018c, p.
2-3).

Walter: US Bank Capital Regulation
9.

27

RECENT INCREASES IN BANKING COMPANY
CAPITAL

Given the many revisions to the implementation of capital requirements made by supervisors in response to Basel II, Basel III, and the
DFA, it is somewhat di¢ cult to determine how much requirements have
changed, or even in what direction, over the past …fteen years. Comparing Figure 2 and Figure 4 might cause one to imagine that capital
requirements have increased some, but not precipitously, since Basel I
requirements were put in place in the early 1990s. Speci…cally, the minimum adequate level of total capital/RWA has been unchanged since
Basel I at 8 percent, while the Tier 1/RWA requirement was increased,
from 4 percent under the US Basel I and Basel II requirements (Figure
2) to 6 percent now (Figure 4, “Adequately Capitalized” row), under
the Basel III-based requirements. Once the various bu¤ers are added—
the CCB for all banking organizations and the GSIB surcharge for the
largest banks— however, it seems clear that capital requirements have
increased noticeably, at least since the …nancial crisis.
The data on actual banking organization capital holdings seem to
support the idea that requirements have increased— though, of course,
organization holdings can shift for reasons other than shifts in regulatory requirements. Since the 2007–08 …nancial crisis, banking organizations have boosted their capital ratios appreciably in comparison
to the lows experienced during the crisis and to the years immediately
prior to the crisis (see Figures 5 and 6).
Prior to the …nancial crisis, Figure 6 shows that, on average, for
US banking institutions (BHCs plus banks not owned by BHCs), CET1
capital relative to risk-weighted assets hovered around 8.4 percent.32
Beginning with the …rst quarter of 2007, the ratio began declining and
ultimately fell to a low of 6.1 percent in the …rst quarter of 2009. After
that, the ratio began to climb back to former levels and then well above.
While not charted here, the Tier 1-to-RWA and total-capital-to-RWA
ratios follow a comparable path.33
As the ratio in Figure 6 was declining during the …nancial crisis,
RWAs were increasing at a pace similar to their growth over the pre32

Note that while data on CET1 capital were not reported on bank …nancial reports until after the …nancial crisis, a similar capital measure, “Tier 1 Common Equity,”
(not to be confused with the somewhat broader measure, Tier 1 capital, which has been
collected since Basel I), was derived from data that were available on earlier …nancial
reports. See the notes on Figure 6 for further discussion.
33
See Federal Reserve Bank of New York (2018) for charts of Tier 1 and total
capital relative to RWA. For Figure 6, note that because of capital requirement rule
changes and reporting requirement changes, the de…nitions of the numerator and denominator changed somewhat over the charted period, leading to small breaks in the
series between 2014Q1 and 2015Q1.

28

Federal Reserve Bank of Richmond Economic Quarterly

vious …ve years. CET1 capital, however, ‡attened out starting in the
…rst quarter of 2007, declined for several quarters in 2008, ‡attened
again, and then began increasing in the third quarter of 2009. Therefore, the decline in the ratio, during the recession, was driven by both
an increase in the denominator (RWA) of the ratio and a decline in
the numerator (CET1 capital). The decline in CET1 was the result
of losses su¤ered (for one reason, because of a signi…cant increase in
loan loss provisions in 2008) during several quarters of the crisis, as
well as low but positive earnings in other quarters of the crisis. Quarterly losses reduce capital, and low earnings reduce retained earnings
(additions to capital). These reduced earnings and losses along with
increasing RWA led to a decline in the ratio of CET1 capital to RWA.
(Federal Reserve Bank of New York 2018; Excel data …le).
As earnings began to recover following the …nancial crisis, banking
companies began to retain more earnings (adding to capital). They
also received $313 billion in injections of capital from the government
and gathered capital from private investors.34 In total, between the
…rst quarter of 2009 and the second quarter of 2014 (when the CET1
ratio in Figure 6 plateaued), banking companies added $752 billion to
CET1 capital (Federal Reserve Bank of New York 2018; Excel data
…le). As a result, the CET1-to-RWA ratio increased signi…cantly between 2009 and 2014, as can be seen in Figure 6. At the same time,
new, higher capital requirements (once bu¤ers are accounted for) were
being implemented, encouraging additions to banking company capital
holdings.
The category containing the largest banks shown in Figure 7, BHCs
with assets over $500 billion (blue dashed line), as a group experienced
the most rapid decline in their capital ratio of the four categories during
the …nancial crisis. These large institutions also show the greatest
increase in their capital ratio. Indeed, while prior to the …nancial crisis
their capital ratio was considerably below the ratio for the smallest
institutions (banks and BHCs with assets less than $50 billion, the
dashed green line), the largest institutions now have a capital ratio
commensurate with that of the smallest.
Figure 7 shows the leverage ratio for the same institutions shown
in Figure 6. Speci…cally, the …gure charts Tier 1 capital as a percent
of average assets (assets measured at the beginning of the quarter plus
assets measured at the end of the quarter, divided by two). It in34
This …gure ($313 billion) is the sum of the following TARP capital injection
programs: Capital Purchase Program ($204.89 billion), Targeted Investment Program for
Citibank and Bank of America ($40.0 billion), and the American International Group
injection ($67.84 billion). See US Treasury Department (2018, p. 5.)

Walter: US Bank Capital Regulation

29

Figure 6 Common Equity Tier 1 Capital as a Percent of
Risk-Weighted Assets

Notes: This …gure charts Tier 1 Common Equity (as a percent of RWA) for the
quarters before banks and BHCs began reporting the new Basel III-based measure CET1 capital, and it charts CET1 capital (as a percent of RWA) for the
later quarters in which CET1 was reported in …nancial statements. Tier 1 Common Equity is derived from data available on bank and BHC …nancial statements
and is meant to be similar to CET1. Over a period of time, between 2014 and
2015, CET1 began to be reported by banks and BHCs, …rst for the largest banking organizations and later for smaller banking organizations. Between 2014 and
2015, breaks in the series are driven by this shift from the derived Tier 1 Common Equity measure to the reported CET1 measure. The …gure includes data for
BHCs and non-BHC banks.
Source: Federal Reserve Bank of New York (2018).

volves no risk-weighting of assets and also includes no o¤-balance-sheet
exposures in the denominator (in contrast, RWA, the denominator in
Figure 6, includes o¤-balance-sheet exposures). This chart looks similar to Figure 6 in that the largest size category of institutions shows
the deepest decline in their ratio during the …nancial crisis and the
largest improvement afterward. One di¤erence is that the largest institutions never reach the capital ratio of the smallest, indicating that
risk-weighting assets (relevant for Figure 6 but not Figure 7) augments
capital ratios more for large institutions than for small. Further, the
under $50 billion category shows a smaller decline in their leverage ratio
than their risk-weighted ratio (Figure 6) during the …nancial crisis.

30

Federal Reserve Bank of Richmond Economic Quarterly

Figure 7 Leverage Ratio: Tier 1 Capital as a percent of
Average Total Assets

Notes: The …gure includes data for BHCs and non-BHC banks.
Source: Federal Reserve Bank of New York (2018).

10.

CONCLUSION

Following the …nancial crisis of 2007–08, policymakers made signi…cant changes to bank and BHC capital requirements. Included were a
new, more narrow, measure of capital, CET1, and a change to the way
risk-weighted denominators are calculated for large banks and BHCs—
requiring them to calculate their ratios using the standardized measure
(similar to that introduced by Basel I) and the advanced approaches
method (as introduced by Basel II). Stress tests, bu¤ers, the TLAC
requirement, a GSIB surcharge, and a special leverage requirement
(supplementary leverage ratio) were also introduced in the postcrisis
period. The emphasis of many of the changes was to more e¤ectively
control the risk-taking incentives of large banking organizations, the
failure of which is considered the most worrisome for broad economic
health, and which the …nancial crisis demonstrated as the most likely
to receive government aid.
At the same time, policymakers were focusing on ensuring that the
regulatory burden of the new capital requirements is minimized for

Walter: US Bank Capital Regulation

31

smaller banking organizations, the failure of which in‡ict fewer costs
on the economy. Small banks and BHCs are also less likely to receive
government aid should they face failure. For example, this focus was an
important motivation for the Economic Growth, Regulatory Relief and
Consumer Protection Act, which increased the minimum size threshold
for stress tests, among other changes.
While capital requirements have become a major element of the
bank regulatory toolkit since the late 1980s and Basel I, we shouldn’t
be tempted to think that their genesis is with these modern changes.
Instead, the origins of modern capital requirements extend back much
further. Indeed, capital ratios were an important enough feature in
banking regulation near the beginning of the twentieth century that
they were included in the banking laws of a number of states. Likewise, supervisors understood the bene…ts of imposing risk-based capital
requirements and accounting for o¤-balance-sheet risks as early as the
1940s.
Though policymakers have increased capital requirements and banks
have increased their holdings since the …nancial crisis, the question of
the appropriate amount of capital remains highly controversial. Some
observers call for much higher capital requirements. For example, a
2017 proposal issued by the Federal Reserve Bank of Minneapolis calls
for a large increase in the minimum common-equity-to-RWA ratio to at
least 23.5 percent and of the leverage ratio to 15 percent (Federal Reserve Bank of Minneapolis 2017, p. 41). Others argue that raising the
requirements can have serious o¤setting costs that might exceed any
bene…ts (Levkov and Peterson 2014). Along these lines, in 2017 the
US House of Representatives passed the Financial Choice Act (which
did not pass in the Senate), including a provision calling for reduced
noncapital regulatory requirements for banks that maintain at least a
10 percent leverage ratio (equity/total leverage exposure). Therefore,
while supervisors have now mostly fully implemented Basel III and
Dodd-Frank capital requirements covering the spectrum of bank and
bank holding companies, the current requirements are unlikely to be
the last word.

32

Federal Reserve Bank of Richmond Economic Quarterly

APPENDIX
1.

GLOSSARY
Advanced Approaches Banks— Banks and BHCs with assets greater
than $250 billion, which must calculate capital using more detailed (advanced) methods
Basel I— The …rst multinational agreement on minimum capital
requirements (under the auspices of the BCBS), published in
…nal form in 1988
Basel II— The second major multinational agreement on capital
requirements as well as broader supervisory standards, published
in …nal form in 2007
Basel III— Third major international agreement, published in …nal form in 2010
BCBS— Basel Committee on Banking Supervision, a committee
of representatives of the largest countries, meant to increase uniformity of bank supervisory standards
BHC— Bank holding company, a corporation that owns, or has
a controlling interest in, one or more banks
Bu¤er— required amounts of capital, above speci…ed minimum
ratios, that must be met to avoid restrictions on dividend and
senior manager bonus payments
CCAR— Comprehensive Capital Analysis and Review, a stress
test of the largest banking institutions’ability to maintain strong
capital even when subject to a hypothetical adverse economic
(stress) scenario. The test is conducted by the Federal Reserve,
focused on a future dividend payout plan speci…ed by the institution
CCB— Capital Conservation Bu¤er, a 2.5 percent additional capital requirement that must be held by all banks and BHCs
CCyB— Countercyclical Bu¤er, applicable only to the largest institutions, this bu¤er is meant to vary with the state of the overall
economy and is increased when supervisors view systemic risks
as increasing
CET1 Capital— the most narrow measure of capital; made up
largely of common stock and retained earnings

Walter: US Bank Capital Regulation

33

DFA— Dodd-Frank Wall Street Reform and Consumer Protection Act, enacted in 2010, included wide-ranging changes to bank
regulation and supervision meant to reduce the chance of a repetition of the …nancial crisis of 2007-08
DFAST— Dodd-Frank Act Supervisory Stress Test, a stress test
of the largest banking institutions’ ability to maintain strong
capital even when subject to a hypothetical adverse economic
(stress) scenario. The test is conducted by the Federal Reserve,
focused on a future dividend payout plan determined by past
dividend payouts by the institution.
FDICIA— Federal Deposit Insurance Corporation Improvement
Act of 1991, enacted in the wake of the savings and loan crisis of
the late 1980s, required the supervisors to take prompt corrective
action when a bank’s capital begins to decline
GSIB— Global Systemically Important Bank Holding Company
(or Bank)
ILSA— International Lending Supervision Act of 1983, required
bank supervisors to establish minimum international lending standards and granted federal bank supervisors clear authority to
establish and enforce capital standards, and called on the Fed
and the Treasury to encourage other governments to strengthen
capital requirements for their country’s banks
OBS— O¤ Balance Sheet; …nancial exposures that do not currently show up as assets or liabilities of the bank but nevertheless could produce income or expenses (and in some cases, assets
or liabilities) in the future; examples are commitments to make
future loans or derivative instruments such as swaps and options
PCA— Prompt Corrective Action; a feature of the FDICIA requiring banking supervisors to take prompt action (within a speci…ed number of days) when a bank’s capital falls below required
levels
RWA— Risk-Weighted Assets; weighting assets by their riskiness
in the denominator of capital ratios
SLR— Supplementary Leverage Ratio, a measure of capital applicable to advanced approaches banks; the numerator is Tier 1
capital, and the denominator is on-balance-sheets assets plus a
broad compilation of o¤-balance-sheet assets

34

Federal Reserve Bank of Richmond Economic Quarterly
Standardized Approaches Banks— Banks and BHCs with assets
below $250 billion, which calculate capital using less-detailed
methods (compared with the advanced approaches banks)
TE— Total Exposures, a measure of bank and BHC size, including total assets as well as o¤-balance-sheet exposures such as
derivative and loan commitments
Tier 1 Capital— A narrow de…nition of capital made up largely
of common stock and retained earnings but also some preferred
stock (excluded from the even more narrow CET1 capital)
TLAC— Total Loss-Absorbing Capacity, applicable to GSIBs only;
a broad measure of “capital”including Tier 1 capital and certain
types of long-term debt (with maturities of at least two years,
and a portion of long-term debt with maturities of between one
year and two years)
Total Capital— A broad de…nition of capital equal to the sum of
Tier 1 capital and Tier 2 capital

Walter: US Bank Capital Regulation

35

REFERENCES
Alfriend, Malcolm C. 1988. “International Risk-Based Capital
Standard: History and Explanation.” Federal Reserve Bank of
Richmond Economic Review (November/December): 28–34.
Baer, Herbert, and John McElravey. 1992. “Capital Adequacy and
the Growth of U.S. Banks.” Federal Reserve Bank of Chicago
Working Paper 92-11 (June).
Bair, Sheila. 2007. “Remarks by Sheila Bair Chairman, U.S. Federal
Deposit Insurance Corporation, 2007 Risk Management and
Allocation Conference.” Paris, France, June 25, 2007.
Bank for International Settlements. 1988. “Basel Committee on
Banking Supervision: International Convergence of Capital
Measurement and Capital Standards.” (July 15).
Bank for International Settlements. 2010. “Press Release: Results of
the December 2010 meeting of the Basel Committee on Banking
Supervision.” (December 1).
Bank for International Settlements. 2018. “History of the Basel
Committee.” https://www.bis.org/bcbs/history.htm [April 14].
Bank of New York Mellon Corp. 2007. “Form 10-K 2007.”
https://otp.tools.investis.com/clients/us/bnymellon/SEC/secshow.aspx?FilingId=5764771&Cik=0001390777&Type=PDF&hasPdf=1
BB&T Corp. 2009. “Form 10-K 2009.”
http://app.quotemedia.com/data/downloadFiling?webmasterId=
101533&ref=6793101&type=PDF&symbol=BBT&companyName=BB%26T
+Corp.&formType=10-K&dateFiled=2010-02-26
BB&T Corp. 2010. “Form 10-K 2010.”
http://app.quotemedia.com/data/downloadFiling?webmasterId=
101533&ref=7438216&type=PDF&symbol=BBT&companyName=BB%26T
+Corp.&formType=10-K&dateFiled=2011-02-25
Board of Governors of the Federal Reserve System. 1989. “Risk-Based
Capital Guidelines, Final Rule.” Federal Register vol. 54, no. 17,
January 27: 4185.
Board of Governors of the Federal Reserve System. 2007. “Board
approves …nal rules to implement Basel II risk-based capital
framework.” Press Release (November 2).

36

Federal Reserve Bank of Richmond Economic Quarterly

Board of Governors of the Federal Reserve System. 2011. “Federal
Reserve Board issues …nal rule on annual capital plans, launches
2012 review.” Press Release (November 22).
Board of Governors of the Federal Reserve System. 2015a. “Appendix
C to Part 225— Small Bank Holding Company and Savings and
Loan Holding Company Policy Statement: Policy Statement on
Assessment of Financial and Managerial Factors.” 12 CFR Part
225.
Board of Governors of the Federal Reserve System. 2015b.
“Regulatory Capital Rules: Implementation of Risk-Based Capital
Surcharges for Global Systemically Important Bank Holding
Companies; Final Rule.” Federal Register vol. 80, no. 157, August
14: 49082.
Board of Governors of the Federal Reserve System. 2015c. “Total
Loss-Absorbing Capacity, Long-Term Debt, and Clean Holding
Company Requirements for Systemically Important US Bank
Holding Companies and Intermediate Holding Companies of
Systemically Important Foreign Banking Organizations;
Regulatory Capital Deduction for Investments in Certain
Unsecured Debt of Systemically Important U.S. Bank Holding
Companies.” Federal Register vol. 80, no. 229, November 30:
74926.
Board of Governors of the Federal Reserve System. 2015d.
“Calibrating the GSIB Surcharge.” White Paper (July 20).
Board of Governors of the Federal Reserve System. 2016. “Regulatory
Capital Rules: The Federal Reserve Board’s Framework for
Implementing the U.S. Basel III Countercyclical Capital Bu¤er.”
12 CFR Part 217, Appendix A.
Board of Governors of the Federal Reserve System. 2017. “Total
Loss-Absorbing Capacity, Long-Term Debt, and Clean Holding
Company Requirements for Systemically Important US Bank
Holding Companies and Intermediate Holding Companies of
Systemically Important Foreign Banking Organizations.” Federal
Register vol. 82, no. 14, January 24: 8266.
Board of Governors of the Federal Reserve System. 2018a. “Part
217— Capital Adequacy of Bank Holding Companies, Savings and
Loan Holding Companies, and State Member Banks (Regulation
Q).” 12 CFR Part 217.
Board of Governors of the Federal Reserve System. 2018b.
“Comprehensive Capital Analysis and Review 2018: Assessment
Framework and Results.” June 2018.

Walter: US Bank Capital Regulation

37

Board of Governors of the Federal Reserve System. 2018c. “Proposed
rule regarding the stress bu¤er requirements.” Press Release
(April 5).
Board of Governors of the Federal Reserve System. 2018d.
“Supervisory Scenarios for Annual Stress Tests Required under
the Dodd-Frank Act Stress Testing Rules and the Capital Plan
Rule - February 2018.”
https://www.federalreserve.gov/publications/2018-februarysupervisory-scenarios-for-annual-stress-tests.htm [February 13,
2018].
Board of Governors of the Federal Reserve System. 2018e. “Federal
Reserve Board invites public comment on framework that would
more closely match regulations for large banking organizations
with their risk pro…les.” Press Release (October 31).
Bullard, James. 2008. “Systemic Risk and the Macroeconomy: An
Attempt at Perspective.” Presentation at Indiana University,
Bloomington, Indiana, October 2.
Bureau of the Census. 1975. “Series X 580-587. All Banks–Number of
Banks and Principal Assets and Liabilities: 1834 to 1970.” In
Historical Statistics of the United States: Colonial Times to 1970,
Part 2, Washington, DC: Government Printing O¢ ce, 1019–20.
California Superintendent of Banks. 1909. California Bank Act.
Sacramento, California.
Citigroup Inc. 2009. “Form 10-K 2009.”
https://www.citigroup.com/citi/investor/data/k09c.pdf?ieNocache=156
Citigroup Inc. 2017. “Form 10-K 2017.”
https://www.citigroup.com/citi/investor/data/q1704c.pdf?ieNocache=883
Code of Federal Regulations. 1998. “Capital Measures and Capital
Category De…nitions.” 12 CFR 208.43, July 13.
Davis Polk. 2015. “U.S. Basel III Final Rule: Visual Memorandum.”
April 30.
Davis Polk. 2016. “U.S. Basel III Final Rule: Standardized Risk
Weights Tool.” http://usbaseliii.com/tool/index.html.
Davis Polk. 2017. “Federal Reserve’s Final Rule on Total
Loss-Absorbing Capacity and Eligible Long-Term Debt.” January
11.
Ennis, Huberto M., and David A. Price. 2011. “Basel III and the
Continuing Evolution of Bank Capital Regulation.” Federal
Reserve Bank of Richmond Economic Brief 11-06 (June).

38

Federal Reserve Bank of Richmond Economic Quarterly

Federal Deposit Insurance Corporation. 2018. “Commercial
Banks–Historical Statistics on Banking.” Tables CB09 and CB14,
https://www5.fdic.gov/hsob/SelectRpt.asp?EntryTyp=10&Header=1.
Federal Deposit Insurance Corporation Improvement Act (FDICIA).
1991. U.S. Public Law 102-242. 102nd Cong., 1st sess.
Federal Financial Institutions Examination Council. 2018.
“Instructions for Preparation of Consolidated Reports of
Condition and Income— FFIEC 031 and FFIEC 041.”
https://www.¢ ec.gov/pdf/FFIEC_forms/FFIEC031_FFIEC041_201812_i.pdf
[December 2018].
Federal Reserve Bank of Minneapolis. 2017. “The Minneapolis Plan
to End Too Big to Fail.” December.
Federal Reserve Bank of New York. 2018. “Quarterly Trends for
Consolidated US Banking Organizations.”
https://www.newyorkfed.org/research/banking_research/quarterly_trends.html.
Financial Stability Board. 2017. “2017 List of Global Systemically
Important Banks (G-SIBs).”
http://www.fsb.org/wp-content/uploads/P211117-1.pdf
[November 21].
First National Bank of Bellaire v. Comptroller of the Currency, 697
F.2d 674 (5th Cir. 1983).
Gambacorta, Leonardo, and Sudipto Karmakar. 2016. “Leverage and
Risk Weighted Capital Requirements.” Bank for International
Settlements Working Paper 586 (September).
Goldman Sachs Group. 2017. “Form 10-K 2017.”
https://www.goldmansachs.com/investorrelations/…nancials/current/10k/2017-10-k.pdf
Grochulski, Borys, and Stephen Slivinski. 2009. “Systemic Risk
Regulation and the ‘Too Big to Fail’Problem.” Federal Reserve
Bank of Richmond Economic Brief 09-07 (July).
International Lending Supervision Act. 1983. U.S. Public Law 98-181.
98th Cong., 1st sess.
Jarque, Arantxa, John Walter, and Jackson Evert. 2018. “On the
Measurement of Large Financial Firm Resolvability.” Federal
Reserve Bank of Richmond Working Paper 18-06 (February).
JPMorgan Chase and Company. 2018. “JPMorgan Chase & Co. 2017
Annual Report.” April.

Walter: US Bank Capital Regulation

39

Kashyap, Anil K., Jeremy C. Stein, and Samuel Hanson. 2010. “An
Analysis of the Impact of ‘Substantially Heightened’Capital
Requirements on Large Financial Institutions.” Working Paper
(May).
Levkov, Alexey, and Clark Peterson. 2014. “Too Much of a Good
Thing: The Implications of Higher Bank Capital Requirements.”
The Clearing House Banking Perspectives vol. 2, no. 4
(November): 36–44.
Mitchell, Karlyn. 1984. “Capital Adequacy at Commercial Banks.”
Federal Reserve Bank of Kansas City Economic Review
(September/October): 17–30.
Passmore, Wayne, and Alexander H. von Ha¤ten. 2017. “Are Basel’s
Capital Surcharges for Global Systemically Important Banks Too
Small?” Board of Governors Finance and Economics Discussion
Series 2017-021 (February).
Pellerin, Sabrina R., and John R. Walter. 2012. “Orderly Liquidation
Authority as an Alternative to Bankruptcy.” Federal Reserve
Bank of Richmond Economic Quarterly vol. 98, no. 1 (First
Quarter): 1–31.
Robinson, Kenneth J. 2013. “Savings and Loan Crisis.”
https://www.federalreservehistory.org/essays/savings_and_loan_crisis
[November 22].
Robinson, Roland I. 1941. “The Capital-Deposit Ratio in Banking
Supervision.” Journal of Political Economy vol. 49, no. 1
(February): 41–57.
Ryan, Sandra L. 1969. “History of Bank Capital Adequacy Analysis.”
Federal Deposit Insurance Corporation Working Paper 69-4.
Spong, Kenneth, 2000. Banking Regulation: Its Purposes,
Implementation and E¤ ects, Fifth Edition. Kansas City, Kansas:
Federal Reserve Bank of Kansas City.
Tarullo, Daniel K. 2008. Banking on Basel: The Future of
International Financial Regulation. Washington, DC: Peterson
Institute for International Economics.
U.S. Department of the Treasury. 1989. “Risk-Based Capital
Guidelines, Final Rule.” Federal Register vol. 54, no. 17, January
27: 4168.
U.S. Department of the Treasury. 2007. “Risk-Based Capital
Standards: Advanced Capital Adequacy Framework— Basel II:
Final Rule.” Federal Register vol. 72, no. 235, December 7: 69288.

40

Federal Reserve Bank of Richmond Economic Quarterly

U.S. Department of the Treasury, and the Federal Reserve System.
2013. “Regulatory Capital Rules: Regulatory Capital,
Implementation of Basel III, Capital Adequacy, Transition
Provisions, Prompt Corrective Action, Standardized Approach for
Risk-weighted Assets, Market Discipline and Disclosure
Requirements, Advanced Approaches Risk-Based Capital Rule,
and Market Risk Capital Rule.” Federal Register vol. 78, no. 198,
October 11: 62018.
U.S. Department of the Treasury. 2018. “Monthly Report to
Congress, July 2018, Troubled Asset Relief Program.” August 10.
U.S. Government Accountability O¢ ce. 2014. “Bank Capital
Reforms: Initial E¤ects of Basel III on Capital, Credit, and
International Competitiveness.” GAO-15-67 (November 20).
Van den Heuvel, Skander. 2008. “The Welfare Cost of Bank Capital
Requirements.” Journal of Monetary Economics 55 (2): 298–320.
Wall, Larry D. 1985. “Regulation of Banks’Equity Capital.” Federal
Reserve Bank of Atlanta Economic Review (November): 4–18.
White, Eugene Nelson. 1983. The Regulation and Reform of the
American Banking System, 1900–1929. Princeton, New Jersey:
Princeton University Press.

Economic Quarterly— Volume 105, Number 1— First Quarter 2019— Pages 41–54

How Likely Is the Zero
Lower Bound?
Thomas A. Lubik and Christian Matthes

D

uring the course of the Great Recession and for long after, the
Federal Reserve kept the main monetary policy rate at the
zero lower bound (ZLB).1,2 This policy was pursued in order
to …ght the deepest recession since the Great Depression and to support
the budding recovery. The Federal Reserve …nally abandoned its low
interest rate policy and exited from the ZLB in December 2015 as the
expansion gathered pace. It is now one of the longest on record in
US economic history. Y et, given the length of the expansion and its
recent strength, the level of the policy rate is arguably still low when
compared with the historical experience.3
We are grateful to Caroline Davis for outstanding research assistance and to Felix
Ackon, James Geary, John Jones, and John Weinberg, whose comments are greatly
appreciated. The views expressed in this paper are those of the authors and should
not be interpreted as those of the Federal Reserve Bank of Richmond or the Federal
Reserve System.
1
Strictly speaking, the Federal Reserve’s key policy rate, the federal funds rate, was
maintained in a range between zero and twenty-…ve basis points and never was actually
at zero. However, the interest rate on excess reserves that the Federal Reserve paid to
banks was set at zero. Other major central banks, such as the European Central Bank,
the Bank of Japan, and the Swedish Rijksbank set policy rates to zero or even negative
values. The label ZLB is thus shorthand for rates that are e¤ectively zero.
2
The ZLB is often taken to coincide with the ELB, or e¤ective lower bound, but
experience has shown that nominal policy rates can be negative for extended periods.
For instance, the European Central Bank and the Swedish Rijksbank have maintained
negative rates on excess deposits held willingly by banks in their reserve accounts. In
that sense, the ELB is below the ZLB, but there is no consensus in the economics
profession on how low nominal policy rates could go. For the purpose of this article,
we assume, however, that the ELB and the ZLB coincide, since the Federal Reserve is
unlikely to consider negative policy rates.
3
One explanation of why the nominal policy rate is low is that with in‡ation expectations anchored at the Federal Reserve’s target of 2 percent, the natural real rate
of interest is lower than in prior expansions. There is substantial evidence (e.g., Lubik
and Matthes 2015b; Laubach and Williams 2016) that the natural rate exhibits secular
decline over the last thirty years, which limits how high the equilibrium policy rate can
go.

42

Federal Reserve Bank of Richmond Economic Quarterly

Naturally, this raises the question of how likely it is that monetary policy will again be subject to the ZLB in the coming years.
More speci…cally, policymakers may wonder when the current expansion might end and whether they may have to pursue accommodative
policies, possibly in a preemptive manner. During contractions, the Fed
has traditionally lowered policy rates and kept them low to support the
recovery. However, when policy rates are already low during the expansionary phase, as is currently the case, this potentially limits the
ability of the Fed to provide accommodation because of the presence
of the ZLB. This might arguably put the Fed in a dilemma regarding
the pace of interest rate increases.
On the one hand, the Fed could raise rates faster than is usually
warranted in order to create more distance from the ZLB as insurance
against the possibility that it might have to lower rates signi…cantly to
stem against a contraction. On the other hand, the Fed could go slower
so as not to endanger a budding recovery and not face a contraction
at all. At the same time, the likelihood of ZLB episodes is also central
to debates about whether the Fed should replace its current 2 percent
in‡ation target with either a higher target or a di¤erent framework.
But all of these discussions center around the idea of insurance against
being too close to the ZLB.
In this article, we therefore investigate the likelihood that the economy may be subject to the ZLB again. In this sense, we provide a
quanti…cation of the insurance aspect against the ZLB in terms of a
forecast of that uncertainty. Speci…cally, we focus on the forecasting
framework surveyed by Lubik and Matthes (2015a), which was previously applied to estimation of the natural rate of interest (Lubik and
Matthes 2015b). We specify a time-varying parameter vector autoregressive model (TVP-VAR) for a set of key macroeconomic variables
and estimate the model on the available data. Interpreting the model
as an acceptable representation of the underlying structure of the economy and the e¤ects of monetary policy, we then simulate the estimated
TVP-VAR forward based on the estimated posterior distribution of its
parameters. This generates a distribution of trajectories for macroeconomic outcomes, including the path of the federal funds rate (FFR),
which we use as a monetary policy variable. From this distribution, we
can then compute the probability that the interest rate will be at the
ZLB in the future.
Our main result is that the probability of the ZLB is negligible over
the next two years. It is only during 2022 that the probability rises
above 5 percent. Depending on the speci…c interpretation of the ZLB
probability, whether it is date-speci…c or horizon-speci…c, the probability rises at most to 15 percent by the end of the 2020s. While these

Lubik and Matthes: How Likely Is the Zero Lower Bound?

43

numbers are not negligible, they do not appear large enough to cause
undue alarm. We also …nd that the ZLB probabilities have declined
over the last three quarters. Our main …ndings are based on data up to
and including the third quarter of 2013, which saw robust growth. The
same exercise with a sample ending in 2018Q1 yields longer-term ZLB
estimates of around 25 percent while still being negligible at a short
horizon. The strength of the recent data ‡ow thus makes the ZLB less
likely since the model incorporates the possibility of an ever-so-slight
trend GDP growth shift.
As a robustness check and an assessment of the overall validity of
our forecasting model, we also investigate how well the TVP-VAR has
performed in the past, speci…cally during the Great Recession. To do
so, we conduct a pseudo out-of-sample exercise where we carry out our
forecasting exercise while conditioning on the parameter estimates at
that point in time. The ZLB probabilities are computed in a like manner, that is, as if the subsequent data were unknown to the researcher.
We …nd that right at the onset of the downturn, the model predicts
the ZLB with a very high probability of 80 percent on account of the
dramatic decline in real GDP growth. Going further out, however, and
as the subsample expands, this probability drops to below 40 percent,
even as the policy rate remains at the ZLB and has been there for a
while.
This observation reveals a feature of the data that even a ‡exible nonlinear model such as the TVP-VAR has di¢ culty dealing with,
namely reversion to the mean. In other words, the Great Recession and
the subsequent ZLB period are such unusual events that the model has
a tendency to discount their impact going forward. At best, this feature
of the data is re‡ected in a wider distribution of the forward simulation that underlies the computation of the ZLB probabilities. In that
sense, a shift in the ZLB probabilities observed in 2018 can be seen as
evidence of an underlying trend shift.
Perhaps surprisingly, the question of how likely the ZLB is has not
attracted much attention in the empirical macroeconomics literature,
speci…cally the forecasting literature. While there is much research
on the e¤ects of the ZLB in traditional New Keynesian models, these
studies are not forecast-based but instead study the probability of being
at the ZLB generically. Perhaps closest to our exercise is Chung et al.
(2012), who use several forecasting models used in the policy process,
such as the Federal Reserve’s own large-scale macroeconometric model
FRB/US, two canonical New Keynesian dynamic stochastic general
equilibrium (DSGE) models, and also a TVP-VAR closely related to
ours. In a similar stochastic simulation exercise, they construct forecast
densities based on data up to and including 2007Q4. None of the

44

Federal Reserve Bank of Richmond Economic Quarterly

models, perhaps surprisingly least of all the TVP-VAR, include the
ZLB in their 95 percent coverage region, which echoes some of our
…ndings. However, they focus on this one base year only, whereas
we compute densities for forty quarters out and also conduct a model
validation exercise.
In a more recent study, Kiley and Roberts (2017) simulate both
the FRB/US policy model and a standard DSGE model often used in
the policy process with shocks drawn from estimated distributions over
the 2000–15 period. They …nd that the ZLB probabilities are small,
reaching at best 20 percent for levels of the natural rate at 3 percent,
which is consistent with the natural rate forecast embedded in our
model.4 In a pseudo out-of-sample exercise for 2013 that is similar to
ours, they also have the feature of mean reversion unless they strongly
force the policy rule to follow the ZLB.5
We proceed as follows. In the next section, we discuss our empirical
approach in more detail. We introduce our statistical forecasting model,
a TVP-VAR, and then describe two alternative measures of the ZLB
probabilities. Section 3 contains the results of the paper, including a
pseudo out-of-sample exercise to assess the quality of the forecasting
model. The …nal section concludes.

1.

METHODOLOGY

We estimate the probability that the federal funds rate will be at or
below the ZLB from a statistical model of the US economy. The …rst
step of our analysis is therefore to develop a model that captures the
behavior of key macroeconomic variables well, especially during previous ZLB episodes. Since an assessment of such probability involves a
forecast, a desirable property of the statistical model is a good forecasting performance. For this purpose we use a TVP-VAR, which has
become widely used for economic and policy analysis and is a ‡exible
framework to address the kinds of issues discussed in this article.6
The advantage of a TVP-VAR is that it is a largely atheoretic timeseries model, which absolves the researcher from taking a stand on the
4
See
Lubik
and
Matthes
(2015b)
and
updates
thereof
at:
https://www.richmondfed.org/research/data_analysis.
5
Jones (2017) …nds similar results in a fully estimated DSGE model that accounts
for possible trend breaks associated with the secular decline in the natural real rate of
interest. He is able to match the data with a forward guidance policy rule.
6
Doh and Connolly (2012) and Lubik and Matthes (2015a) provide an overview of
the methodology and a step-by-step guide to its implementation. Examples of its use
in the monetary policy process are discussed in Clark and Ravazzolo (2015) and Lubik
and Matthes (2015b), while Canova and Gambetti (2009) and Lubik et al. (2016) detail
some of its limitations.

Lubik and Matthes: How Likely Is the Zero Lower Bound?

45

deep, underlying relationships that govern the joint behavior of aggregate variables. Perhaps more importantly, a TVP-VAR can in principle
capture nonlinear behavior in the underlying time series, such as the
ZLB, where movements in the interest rate are capped by a lower bound
of 0 percent, without specifying the precise source of the nonlinearity.
TVP-VARs have also proved useful in forecasting because they allow
researchers to distinguish between structural or long-lasting changes in
the economy and shorter-term ‡uctuations in a consistent and transparent manner. The former a¤ect trends and forecasts thereof, while
the latter are often driven by changes in the volatility of shocks hitting
the economy. Allowing for time variation in both elements of the model
helps researchers di¤erentiate these sources of aggregate ‡uctuations.

A TVP-VAR for the US Economy
We specify a TVP-VAR in quarterly data on real GDP growth, PCE
in‡ation, and the federal funds fate, which are collected in a column
vector yt . We assume that the joint evolution of these variables is
governed by the law of motion:
yt =

t+

2
X

Aj;t yt

j

+ et :

(1)

j=1

t is a drift term that can contain deterministic and stochastic components. It is of particular importance for capturing the changing trends
in the variables, such as the decline of GDP growth over the last …fty
years or the ZLB, which can be regarded as trend break in this context.
The Aj;t are conformable coe¢ cient matrices that contain time-varying
parameters, the evolution of which we detail below. et is a vector of
residuals. We set the lag length equal to two, which is standard for
quarterly data in the TVP-VAR literature (see Primiceri 2005). We
can de…ne Xt0 I (1; yt0 1 :::; yt0 2 ) to provide a compact representation of the dynamics of yt . We then rewrite equation (1) as:

yt = Xt0

t

+ et :

(2)

We assume that the law of motion for the time-varying parameters
in the coe¢ cient matrices Aj;t is given by a random walk process:
t

=

t 1

+ ut ;

(3)

where ut is a zero mean i.i.d. Gaussian process. We model the process
for stochastic volatility by assuming that the covariance matrix of the
one-step-ahead forecast error et can be decomposed as follows:
et =

1
t

t "t ;

(4)

46

Federal Reserve Bank of Richmond Economic Quarterly

where the standardized residuals are distributed as "t N (0; I). t is
a lower triangular matrix with ones on the main diagonal and representative non…xed element it . t is a diagonal matrix with representative
non…xed element jt . The dynamics of the non…xed elements of t and
t are given by:
log

i
t
j
t

=

i
t 1

= log

+

i
t:

j
t 1

+

(5)
j
t:

(6)

We assume that all these innovations are normally distributed with
covariance matrix V . In order to provide some structure for the estimation, we restrict the joint behavior of the innovations as follows
(following Primiceri 2005):
20
13 2
3
"t
I 0 0 0
6B ut C7 6 0 Q 0 0 7
B
C7 6
7
V = V ar 6
(7)
4@ t A5 = 4 0 0 S 0 5 :
0 0 0 W
t

S is further restricted to be block diagonal, which simpli…es inference.
We use a Gibbs-sampling algorithm to generate draws from the posterior. The implementation of the Gibbs-sampling approach used for
Bayesian inference follows Del Negro and Primiceri (2015) and is also
described in more detail in Lubik and Matthes (2015a).
A key choice for TVP-VAR modeling is how to set the prior. In
order to achieve sharp inference, given the multiple sources of variation
in TVP-VAR models, a researcher needs to impose restrictions on the
relationship between the covariance matrices of the parameters. The
trade-o¤, however, is that a too-restrictive prior may not leave room for
the time-variation to appear. In our benchmark, we impose a typical
choice of prior as recommended in Primiceri (2005). Speci…cally, we
assume the following:
Q

IW (

W
S

IW (
IW (

2
Q
2
W
2
S

40 V (

OLS ); 40);

2 I; 2);
2 V ( OLS ); 2);

(8)
(9)
(10)

where IW denotes the Inverted Wishart distribution. Priors for all
other parameters are the same as in Primiceri (2005). For the prior
hyperparameters Q ; W ; and S ; we use the values Q = 0:01, W =
0:01, and S = 0:1.

Computing ZLB Probabilities
The probability that the economy will reach or fall below the ZLB in the
future is based on a forecast of the joint evolution of the variables in the

Lubik and Matthes: How Likely Is the Zero Lower Bound?

47

statistical model. This is not a point forecast but rather a collection of
forecasts that detail all likely paths the economy will take given where
it is now. The ZLB probability then simply captures how many times
the interest rate will be at or below zero. In order to operationalize this
idea, we proceed as follows. In the …rst step, we estimate the TVPVAR over the entire sample period. Our posterior sampler delivers the
posterior distribution of parameters for any point in the sample, which
we will exploit later. We then …x the coe¢ cients at their last estimated
posterior mean and keep them …xed over the forecast horizon. This
assumption is made for computational expediency as it does not require
simulating paths of parameters. Recall that all coe¢ cients in the model
are varying over time, including the trends, the lag coe¢ cients, and the
parameters governing the volatility of the shocks. In the simulation
exercise we do not draw from the innovation distributions of the TVPVAR parameters as this would add an additional layer of uncertainty.
This approach is consistent with the idea of an unchanged forecast
where the structure of the economy is not expected to change. This
assumption seems reasonable as a baseline, especially in light of the
fact that we model the evolution of parameters as random walks. In
addition, it is a well-known drawback of TVP-VARs that because of all
the moving parts uncertainty about forecasts is generally higher. Forecasting the paths of parameters as well would thus just compound this
uncertainty. In that sense, there would be too much parameter variation to make the forecasts meaningful, or alternatively, current conditions would be uninformative about the future. We therefore choose
to err on the side of sharper predictions. What we might miss are, at
lower frequencies, changes in trend growth, as we have seen over the
last decades for real GDP and the real rate of interest, and periods
of excess volatility, such as we have seen during deep recessions and
…nancial crises. At the same time, such events are notoriously di¢ cult
to forecast. We show an example of this and its implications for our
exercise below.
Given this structure of the TVP-VAR, we produce forecasts over
a ten-year horizon. The forecasts are such that for each future date
we generate realizations of the shocks hitting the economy; that is, we
draw from the estimated distribution of the innovations to the exogenous processes and record how they propagate through the economy.
This generates sample trajectories of the model’s endogenous variables
that can be collected at every point in time as a distribution of likely
outcomes. From this collection of sample paths, we can then compute
the probability that the interest rate will be at or below the ZLB.
In principle, one can think of two alternative measures. The …rst
gives an answer to the question: What is the probability that at a given

48

Federal Reserve Bank of Richmond Economic Quarterly

point in time the FFR is forecast to be at or below zero? We measure
this by counting how many times the interest rate is subject to the ZLB
at a given date under all simulated trajectories. The ZLB probability
is then found by dividing this count by the total number of simulations
at the speci…c point in time. We label this measure ‘unconditional’as
it represents the marginal probability of being at the ZLB at a given
time period. In terms of our forecasting exercise, it is a simple count
of ZLB events at every point in time, normalized by the total number
of forecast paths.
We also consider an alternative measure that we label ‘conditional.’
This measure represents the probability that the economy has been at
the ZLB at least once up to and including the current period. It thereby
takes into account the dependency of the ZLB episodes. As the forecast
horizon increases, the count is accumulated. For instance, consider a
trajectory of the FFR that is below zero in period t + 1 and period t + 2
and is above zero in period t + 3. For the …rst, unconditional measure,
we record a count of one, one, and zero, since the measure focuses on
the ZLB episodes in any period. For the second, conditional measure,
the count is one, one, one, since this hypothetical path features two
incidences of a ZLB episode. In this case, the trajectory still enters
the ZLB count in the last period since the given incidence of shocks
resulted in a ZLB episode in prior periods and thus contributed to the
overall “risk” of the ZLB. In this sense, it is a cumulative probability
measure for the question at hand. From a policymaker’s point of view,
it conveys the information that even if a trajectory is not subject to the
ZLB at a particular date, it may have been so in prior periods and may
therefore have to be avoided. Naturally, the unconditional measure is
bounded from above by the conditional measure.

2.

THE PROBABILITY OF BEING AT THE ZLB

We report the key …ndings of this article in Figures 1 and 2, which
report the two measures of the ZLB probabilities discussed above.
We consider a forecast horizon of ten years at a quarterly frequency.
The …gures show the ZLB probabilities for three sample periods each,
namely ending in 2018Q1, 2018Q2, and 2018Q3, respectively, but with
the same start date, 1963Q1. The samples are real time in that we
have used the data actually available to policymakers at that time. For
the sample with the most recent data, up to and including 2018Q3, the
…gures show that for both measures the probability is essentially zero
for one year out. It rises gradually toward a long-run level of 7 percent
in the case of the unconditional measure in Figure 1 and around 13
percent for the alternative measure in Figure 2. As can be seen from

Lubik and Matthes: How Likely Is the Zero Lower Bound?

49

the …gures, the ZLB probabilities are rising over time. This stems from
the fact that uncertainty is expanding as we forecast further out into
the future and that the conditional probability is cumulative.
As discussed above, the probabilities shown in Figure 1 give policymakers an unconditional view that the ZLB may occur again in the
future. From this perspective it indicates that there is less than a one
in ten chance that in 2028 the economy will be in a situation where the
FFR is again constrained at zero. Since the ZLB has been observed in
the dataset, the model deems it likely to happen again, given the estimated historical patterns of shocks when extrapolated forward. This
is irrespective of whether any trajectory has been at the ZLB before or
not. The estimates in Figure 2 show a similar pattern with virtually
zero probability for one year from now. It is then rising to a long-run
level of close to 15 percent. The interpretation of this conditional measure is that in 2028 roughly one-eighth of all forecast trajectories of the
federal funds rate will have hit the ZLB at some point, either only once
or repeatedly.
The ZLB probabilities for the sample ending in 2018Q2 are essentially identical to the most recent sample, with the latter’s unconditional probability slightly higher in the …rst half of the sample but
slightly lower in the second half. In contrast, the ZLB probabilities for
the 2018Q1 sample are considerably higher, rising to a long-run level
of 15 percent in the case of the unconditional measure and around 30
percent for the other measure. Still, for one year out, the probability is
e¤ectively zero. This shift in the estimated ZLB probabilities is driven
by the strong GDP growth data in the second and third quarters of
2018, which imply a higher forecast FFR path and thus a larger distance from the ZLB for all trajectories. Moreover, the stronger growth
data may lead the model to reevaluate the underlying properties of
GDP, which also support a higher FFR path. In addition, a stronger
economy in 2018 reduces the likelihood of a recession in the near term,
thus reducing the ZLB probabilities.
This discussion raises the question of how reliable the estimates of
the ZLB probabilities are. The quality of the estimates rests crucially
on how well the model captures past experiences, including the ZLB
period during 2009–14. The future is, of course, uncertain, but we can
get a sense of how well the TVP-VAR has performed in the past by
conducting a pseudo out-of-sample forecasting exercise. We proceed as
follows. As a starting point, we use the baseline estimated posterior
distribution of parameters at di¤erent points in time. The posterior
estimates of parameters at any point in time are a function of all available data— data at time t + j; j
1 are generally informative about
the parameter values in place at time t. Using this approach instead of

50

Federal Reserve Bank of Richmond Economic Quarterly

a true out-of-sample exercise, where we would have to reestimate the
model period by period, is computationally much more tractable but
is naturally subject to the caveat that it is based on information that
could not have been known at that time.7
We then perform the same forecasting exercise as discussed above.
At each date we simulate the model forward using the posterior estimates of the coe¢ cients, which are held …xed over the forecast horizon.
We produce the same counts as in the prior exercise, namely how many
times the interest rate is at or below the ZLB for each quarter. Figure
3 shows results from this exercise. We focus on four forecast horizons:
one quarter ahead, four, eight, and then twenty. The horizontal axis in
the …gure denotes the period in which the forecast is made, while each
panel reports results for a speci…c forecast horizon. The four panels in
the …gure depict the unconditional ZLB probabilities at the respective
forecast horizons as they change over time.
The upper left-hand panel shows the one-step-ahead ZLB probability. For almost the entire sample period the probability is zero on
account of high interest rates (and high in‡ation during the 1970s).
This changes in early 2009 as this probability shoots up to 80 percent
with the onset of the Great Recession. This is driven by the sharp
decline in real GDP growth, which, given historical patterns embedded in the estimated model, prompts a sharp drop in the interest rate.
The one-step-ahead forecast at the next data point drops to below 50
percent and hovers around 20 percent until 2015 with the start of the
exit from the quantitative easing period. The ZLB probabilities during
this period are punctuated by occasional spikes that line up with weak
data on GDP growth and low in‡ation numbers.
Nevertheless, these estimates indicate one weak point of the TVPVAR, namely that it exhibits something akin to mean reversion.8 Despite having observed policy rates at zero for several years, the TVPVAR continues to predict an immediate rise in rates and hence a low
7

Another caveat associated with this exercise is that we use …nal data for the estimates. This presumes knowledge that policymakers at that time could not have had,
as initial data releases are typically subject to measurement errors and later revisions.
The TVP-VAR estimates thereby do not re‡ect the actual decision-making environment
that policymakers faced, which can result in biased estimates of the implicit policy rule.
Lubik and Matthes (2016) show that policymaking under this type of data mismeasurement can considerably a¤ect macroeconomic outcomes.
8
To be clear, the TVP-VAR does not per se exhibit mean reversion as the coe¢ cients are modeled as random walk processes and the underlying data are allowed to be
nonstationary. In that sense, there is no ergodic distribution, but this does not rule out
a proper posterior distribution. In addition, in our forward simulation exercise, we are
holding the coe¢ cients …xed at their last estimated value. It can be seen from Figures
1 and 2 that the ZLB probabilities seem to stabilize. It is in that sense that we apply
the moniker mean reversion.

Lubik and Matthes: How Likely Is the Zero Lower Bound?

51

ZLB probability. As outside observers, the persistence of a ZLB policy is apparent, not least from Federal Reserve communication; yet it
is not straightforward to capture this feature in a statistical model.9
Overall, this serves as a caveat for the …ndings above, namely that the
TVP-VAR does not fully capture the underlying dynamics in the data.
The other three panels in Figure 3 show similar patterns. There is
a spike of the ZLB probabilities at the onset of the Great Recession,
which then settle at a lower level before dropping to almost zero with
the beginning of the tightening period. What di¤ers across panels
is the time horizon along which the probabilities are estimated. As
the horizon expands from one quarter ahead to twenty quarters, the
initial ZLB probability drops. For instance, at …ve years out, the model
implies a 50 percent chance that the economy will be at the ZLB.
In that sense, the TVP-VAR captures the underlying ZLB dynamics
reasonably well as it incorporates the sharp interest rate drop to …ght
the downturn and ascribes persistence to it.
Moreover, the same panel shows that the slowdown in growth observed around the middle of the 2000s translates into an increased ZLB
probability. In a sense, the TVP-VAR shows that there was information available before the actual onset of the Great Recession that put
increased likelihood on very low interest rates at a …ve-year mark. Finally, the results for longer time horizons also show higher ZLB probabilities in the mid-1970s, the early 1980s, and the early 2000s. All
three periods are characterized by large interest rate movements and
higher macroeconomic volatility around and during recessions. This
translates into more forecast uncertainty, which is re‡ected in higher
ZLB probabilities.

3.

CONCLUSION

This article discusses an approach to how policymakers can think about
the risk of having to face the zero lower bound on the nominal interest
rates. It is based on a forecasting model for the US economy that is
‡exible enough to capture nonlinearities such as the ZLB. Our main
…nding is that the probability of being at the ZLB is small but not insigni…cant for the US economy over a ten-year time horizon. Depending
on how one interprets the notion of being at the ZLB, either over the
course of a time path (our conditional measure) or as a pure point-intime forecast (our unconditional measure), this likelihood is close to
9

DSGE models have struggled with this feature of the data, too. See, for instance,
Kiley and Roberts (2017). Jones (2017) does better than most by incorporating forward
guidance explicitly into the policy rule.

52

Federal Reserve Bank of Richmond Economic Quarterly

one-…fth in the longer run, albeit it is close to zero over a shorter time
horizon. A robustness exercise shows that our methodology is reasonably successful in capturing the probability of being at the ZLB before
and during the Great Recession.
Our …ndings can inform the discussion on the pace of interest rate
increases since the probability of being at the ZLB is inversely related
to its distance from the interest rate, other things being equal. Whether
a more aggressive path of hikes has the potential to tip the economy
into recession, thereby stimulating interest rate cuts and an increased
risk of the ZLB, depends on the underlying structure of the economy
and its monetary transmission mechanism. It goes much beyond the
scope of this article to assess whether the employed TVP-VAR is a
good descriptor of this mechanism. Nevertheless, our estimated ZLB
probabilities are also a convenient way of summarizing forecasts by
condensing a lot of information into a single statistic. Overall, we
regard the ZLB probabilities discussed in this article as a useful tool
for policymakers to assess the current stance of monetary policy in light
of the estimated likelihood that the policy will be constrained by the
ZLB.

Lubik and Matthes: How Likely Is the Zero Lower Bound?

53

REFERENCES
Canova, Fabio, and Luca Gambetti. 2009. “Structural Changes in the
US Economy: Is There a Role for Monetary Policy?” Journal of
Economic Dynamics and Control 33 (February): 477–90.
Chung, Hess, Jean-Philippe Laforte, David Reifschneider, and John
C. Williams. 2012. “Have We Underestimated the Likelihood and
Severity of Zero Lower Bound Events?” Journal of Money, Credit
and Banking 44 (February): 47–82.
Clark, Todd E., and Francesco Ravazzolo. 2015. “Macroeconomic
Forecasting Performance under Alternative Speci…cations of
Time-Varying Volatility.” Journal of Applied Econometrics 30
(June/July): 551–75.
Del Negro, Marco, and Giorgio E. Primiceri. 2015. “Time Varying
Structural Vector Autoregressions and Monetary Policy: A
Corrigendum.” Review of Economic Studies 82 (October):
1342–45.
Doh, Taeyoung, and Michael Connolly. 2012. “The State Space
Representation and Estimation of a Time-Varying Parameter
VAR with Stochastic Volatility.” Federal Reserve Bank of Kansas
City Working Paper 12-04 (July).
Jones, Callum. 2017. “Unanticipated Shocks and Forward Guidance
at the ZLB.” Manuscript (October).
Kiley, Michael, and John M. Roberts. 2017. “Monetary Policy in a
Low Interest Rate World.” Brookings Papers on Economic
Activity (Spring): 317–72.
Laubach, Thomas, and John C. Williams. 2016. “Measuring the
Natural Rate of Interest Redux.” Business Economics 51 (April):
57–67.
Lubik, Thomas A., and Christian Matthes. 2015a. “Time-Varying
Parameter Vector Autoregressions: Speci…cation, Estimation, and
an Application.” Federal Reserve Bank of Richmond Economic
Quarterly 101 (Fourth Quarter): 323–52.
Lubik, Thomas A., and Christian Matthes. 2015b. “Calculating the
Natural Rate of Interest: A Comparison of Two Alternative
Approaches.” Federal Reserve Bank of Richmond Economic Brief
15-10 (October).

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Federal Reserve Bank of Richmond Economic Quarterly

Lubik, Thomas A., and Christian Matthes. 2016. “Indeterminacy and
Learning: An Analysis of Monetary Policy in the Great In‡ation.”
Journal of Monetary Economics 82 (September): 85–106.
Lubik, Thomas A., Christian Matthes, and Andrew Owens. 2016.
“Beveridge Curve Shifts and Time-Varying Parameter VARs.”
Federal Reserve Bank of Richmond Economic Quarterly 102
(Third Quarter): 197–223.
Primiceri, Giorgio E. 2005. “Time Varying Structural Vector
Autoregressions and Monetary Policy.” Review of Economic
Studies 72 (July): 821–52.

Lubik and Matthes: How Likely Is the Zero Lower Bound?

55

Figure 1 Estimated Probabilities of Being at the Zero Lower
Bound for Three Sample Periods

56

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Estimated Probabilities of Being at the Zero Lower
Bound for Three Sample Periods

Lubik and Matthes: How Likely Is the Zero Lower Bound?

57

Figure 3 Probabilities of the Zero Lower Bound at Di erent
Time Horizons