Description
The purpose of this paper is to investigate whether there are any differences in the
capitalization speed-of-adjustment across regulatory capitalization buckets of commercial banks in the
USA, for the period 2002-2009
Journal of Financial Economic Policy
US banks' capitalization speed-of-adjustment: a microeconometric approach
Konstantinos Drakos
Article information:
To cite this document:
Konstantinos Drakos, (2012),"US banks' capitalization speed-of-adjustment: a microeconometric
approach", J ournal of Financial Economic Policy, Vol. 4 Iss 3 pp. 270 - 286
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US banks’ capitalization
speed-of-adjustment:
a microeconometric approach
Konstantinos Drakos
Department of Accounting and Finance,
Athens University of Economics and Business, Athens, Greece
Abstract
Purpose – The purpose of this paper is to investigate whether there are any differences in the
capitalization speed-of-adjustment across regulatory capitalization buckets of commercial banks in the
USA, for the period 2002-2009.
Design/methodology/approach – The Federal Deposit Insurance Corporation (FDIC) monitors
banks’ capital ratio using the bucketing approach. Thus, this discrete and ordered variable is modeled
in the context of a partial adjustment speci?cation, controlling for initial conditions and cross-sectional
heterogeneity. Parameters are estimated with the generalized dynamic random effects ordered probit
technique that is ?exible enough to allow for differential effects of covariates across capitalization
categories.
Findings – The main result is that the speed of adjustment is monotonically increasing for banks
belonging in lower capitalization buckets, after controlling for bank-speci?c capitalization
determinants. In addition, substantial differential impacts of capitalization drivers across regulatory
buckets are uncovered.
Practical implications – This an important ?nding both for regulators and market participants
since it sheds light on a very crucial aspect of banks’ behaviour.
Originality/value – This is the ?rst paper that adopts the FDIC bucketing in the actual modelling.
In addition, it uses the generalized dynamic random effects ordered probit technique in order to
explore potential differential impact of capital ratio determinants across buckets.
Keywords United States of America, Commercial banks, Capitalization,
Federal Deposit Insurance Corporation,
Speed-of-Adjustment
Paper type Research paper
1. Introduction
An emphatic lesson learnt during the past century is that bank failures have an
increasing capacity to impose large negative externalities directly on their depositors,
and indirectly via the signi?cant budgetary consequences in the event that governments
bear the cost of bailout. More importantly, due to the cross cutting and crucial role of
banks in the payments system and facilitation of credit, banking systemic risk may
produce severe adverse effects to the real economy. Thus, it comes as no surprise that the
banking sector has traditionally been one of the most heavily regulated sectors with the
aim to minimize the likelihood banking crises occur. In addition, the increased
cross-border banking activities tend to generate crises transcending the geographic
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – C25, G21, G32
The author acknowledges ?nancial support by the Athens University of Economics and
Business Research Center (ELKE).
JFEP
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270
Journal of Financial Economic Policy
Vol. 4 No. 3, 2012
pp. 270-286
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381211245980
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boundaries of the originating country. Moreover, the need to avoid gaining advantages
stemming from unsound banking activity led to the adoption of a common set of rules
internationally. A basic building block of these rules, that emerged from the
international Basel Accord, is that banks are subject to the regulatory constraint of
maintaining a capital ratio (CAR) of at least 8 percent. Capital Ratio is de?ned as the ratio
of total risk capital Tier1 þ Tier2 to risk weighted assets (RWA).
Regulators closely monitor the level and the trajectory of banks’ capital ratios, paying
special attention to undercapitalized banks, those below the 8 percent threshold. In fact,
for such banks regulators have the ability to call for prompt corrective action in the form
of adjusting upwards their capital ratio within a speci?ed time horizon, and even force
themto foreclosure in case of no compliance. However, froma regulatory perspective the
distinction between banks who are undercapitalized and those who are not, although
useful, turns out to be rather crude. This becomes immediately apparent if we consider
two banks who are both undercapitalized, but their distance from the regulatory
threshold differs. For instance, the likelihood of failure[1] would dramatically differ
between a bank with a capital ratio of 2 percent and another with 7 percent. In order to
have a ?ner and more informative assessment of capital status, the Federal Deposit
Insurance Corporation (FDIC), which is the US regulator, classi?es banks into ?ve
capitalization buckets according to their CAR as follows[2]:
(1) Critically undercapitalized if CAR , 2 percent.
(2) Signi?cantly undercapitalized if 2 percent #CAR , 6 percent.
(3) Undercapitalized if 6 percent # CAR , 8 percent.
(4) Adequately capitalized if 8 percent # CAR , 10 percent.
(5) Well capitalized if CAR $ 10 percent.
Given that the FDIC employs the above classi?cation it would naturally be interested
in having information pertinent to each capitalization bucket. However, academic
research typically treats capital ratio in a continuous fashion, creating a misalignment
between the research questions addressed by the academic literature and those
relevant for regulatory purposes. For instance there are several questions that remain
unanswered such as whether the factors affecting capital ratios of banks belonging in
different buckets are identical, or whether a given factor exerts the same quantitative
and/or qualitative impact across buckets. Perhaps one of the most important issues is
whether the capitalization speed-of-adjustment differs across capitalization buckets.
In particular, one would expect the corrective action mentioned earlier and banks’ own
self-correcting mechanism, to result in a higher speed-of-adjustment for banks
belonging to lower capitalization buckets.
These are exactly the gaps we aim to ?ll with the present study, where instead of
using the continuous capital ratio, we model the discrete and ordered variable that the
FDIC monitors. Moreover, we will allow and test for possible differential effects of
covariates, paying particular attention to the speed-of-adjustment parameters across
capitalization buckets, within the context of a formal econometric setup. Note that the
set of covariates includes all potential capitalization determinants such as size, risk,
pro?tability, asset quality and market discipline (Demstez et al., 1996; Flannery and
Sorescu, 1996; Goldberg and Hudgins, 2002; Lindquist, 2004; Jokipii and Milne, 2008).
The analysis is based on a large microeconometric panel consisting of all FDIC-insured
US banks’
capitalization
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commercial banks in the USA for the period 2002-2009. The estimation technique is the
generalized dynamic random effects ordered probit (Boes, 2007), where we will control
for initial conditions (Wooldridge, 2005) and cross-sectional heterogeneity (Mundlack,
1978; Chamberlain, 1984). The study mainly makes a twofold contribution to the
literature. First, to the best of our knowledge it is the ?rst time that capitalization is
modeled as a discrete ordered variable that matches the FDIC buckets. Second, it
employs a generalized setup that allows covariates to exert diverse effects across
capitalization categories and therefore allows a formal statistical investigation of a
differential speed-of-adjustment.
Let us brie?y discuss the ?ndings from the analysis. First, we uncover evidence
for a differential impact of several capitalization determinants across categories, which
suggests that banks cannot be treated as a uniform group. Second, although the present
analysis ?nds similar impacts of capitalization determinants with previous studies – in
terms of direction – there is ample evidence that their impact differs across capitalization
groups. Third, we document substantial differences in the capitalization speed-of-
adjustment, which increases monotonically as one moves to lower capitalization buckets.
For instance, the critically undercapitalized category covers 50 percent of its distance from
the (latent) targeted level within 0.7 years, while the adequately capitalized group clears the
same distance in about 2.5 years. These ?ndings may be attributed to the impact of the
prompt corrective action and/or to banks’ self-correcting behavior.
The remainder of the paper is structured as follows. Section 2 provides a brief
review of the relevant literature. Section 3 presents the econometric methodology.
Section 4 describes the dataset. Section 5 discusses the estimation results and ?nally
Section 6 concludes and discusses policy implications.
2. Literature review
The literature has proposed several factors as potential determinants of bank
capitalization capturing diverse associated incentives and costs. In short these factors
re?ect size, risk, pro?tability, asset quality and market discipline. In what follows we
will brie?y discuss the theoretical arguments for using each factor.
There are several ?nancial rationales suggesting a negative effect of bank’s size on
its capital ratio. One of them takes into account the costs of:
.
screening potential borrowers; and
.
monitoring the behavior of approved borrowers.
To the extent that there are economies of scale in such activities we expect larger banks
to be more able to achieve them, hence reducing capital holding requirements. In
addition, one would reach a similar conclusion if the bene?ts of portfolio diversi?cation
are increasing with bank size (Demsetz and Strahan, 1997; Alfon et al., 2004; Stolz and
Wedow, 2005; Jokippi and Milne, 2008). Furthermore, larger banks may hold lower
capital reserves because they might:
.
face less severe liquidity constraints; and
.
have lower transaction costs in adjusting capital levels (Alfon et al., 2004).
Another reason for expecting a negative relationship between size and capital held is
the so-called “too big to fail” hypothesis according to which large banks enjoy implicit
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government guarantees. Since the potential failure of a large institution is more likely
to affect the whole system, the likelihood of a safety net provided by authorities is
perceived as being higher (Ayuso et al., 2004; Lindquist, 2004; Stolz and Wedow, 2005).
The main reason banks are required to hold capital is to cover their potential
unexpected losses, which clearly are a function of the overall risks the bank assumes.
Thus, we expect banks assuming higher risk to tend to hold more capital. However, there
are various studies who report a negative association between risk and capital, ?nding
which can be indicative of a moral hazard problem (Alfon et al., 2004; Ayuso et al., 2004;
Lindquist, 2004). Apart from the riskiness of a bank’s assets, which to some extent
re?ects prior assessments based on the type of asset, one may also ?nd important
information embedded in their quality. Again we expect banks with lower asset quality
to hold more capital.
There are two arguments that support a positive relationship between a bank’s
pro?tability and its capital. First, according to the pecking-order theory (Myers and
Majluf, 1984) one expects banks to have a preference for internal funding because it
is less costly compared to external sources of ?nancing. Second, according to the
charter value hypothesis, more pro?table banks would opt for higher capital ratios
to protect their charter value (Marcus, 1983; Keeley, 1990; Demstez et al., 1996;
Hellmann et al., 2000).
There is a literature advocating a market discipline effect on capital ratio, much like
leverage ratios (Flannery and Sorescu, 1996; Morgan and Stiroh, 2001; Gropp et al., 2006;
Flannery and Rangan, 2007). The essence of market discipline in the banking sector is
that at-risk private sector claimants will impose “constraints” on bank behavior to
protect their interests. The literature has suggested that such disciplinary effects can be
brought about by uninsured depositors and/or subordinated debt holders. Both groups
are exposed to potentially non-prudential bank behavior, and in the event of default face
losses with high likelihood. The former group obviously because of a lack of deposit
insurance coverage, and the latter group due to their lowpriority of claims. So uninsured
depositors may penalize riskier banks by requiring higher interest rates or by
withdrawing their deposits (Goldberg and Hudgins, 1996, 2002; Park and Peristiani,
1998; Peria and Schmukler, 2001; Davenport and McDill, 2006), and in a similar vein,
subordinated debt holders will either require a higher premium or withdraw their funds
(Avery et al., 1988; Sironi, 2003; Covitz et al., 2004). Hence, we expect banks exposed to
higher market disciplinary effect to hold more capital.
3. Econometric methodology
Let the indices i,t denote the cross-sectional unit (bank) and time period (year),
respectively. Using the FDIC buckets as exogenously given, we de?ne a new variable
CAP
i,t
as follows:
CAP
i;t
¼
0; if bank i is critically undercapitalized in year t
1; if bank i is significantly undercapitalized in year t
2; if bank i is undercapitalized in year t
3; if bank i is adequately capitalized in year t
4; if bank i is well capitalized in year t
8
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>
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>
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>
>
>
>
>
>
:
ð1Þ
US banks’
capitalization
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It becomes apparent that the variable under scrutiny is not continuous, but rather
shows a discrete ordered response, which should be modeled by an Ordered Probit
model. Assume that CAP is derived by a latent target variable model determined by:
CAP
*
i;t
¼ x
0
i;t
b þ c
i
þ e
i;t
ð2Þ
where x
i,t
is a vector of covariates, c
i
is the unobserved heterogeneity, e
i,t
jx , N(0,1),
and b denotes a vector of constant parameters.
Let a
1
, a
2
, a
3
, a
4
be cut points (also known as threshold parameters) and
de?ne:
CAP
i;t
¼
0; if CAP
*
i;t
# a
1
1; if a
1
, CAP
*
i;t
# a
2
2; if a
2
, CAP
*
i;t
# a
3
3; if a
3
, CAP
*
i;t
# a
4
4; if CAP
*
i;t
. a
4
8
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ð3Þ
Given the assumption e
i,t
jx , N(0,1) one can derive the conditional distribution of CAP
given x
i,t
:
PrðCAP
i;t
¼ 0jx
i;t
Þ ¼ PrðCAP
*
i;t
#a
1
jx
i;t
Þ ¼ Prðx
0
i;t
bþc
i
þe
i;t
,a
1
jx
i;t
Þ ¼Fða
1
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 1jx
i;t
Þ ¼ Prða
1
,CAP
*
i;t
#a
2
jx
i;t
Þ ¼ . . . ¼Fða
2
2x
0
i;t
b2c
i
Þ 2Fða
1
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 2jx
i;t
Þ ¼ Prða
2
,CAP
*
i;t
#a
3
jx
i;t
Þ ¼ . . . ¼Fða
3
2x
0
i;t
b2c
i
Þ 2Fða
2
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 3jx
i;t
Þ ¼ Prða
3
,CAP
*
i;t
#a
4
jx
i;t
Þ ¼ . . . ¼Fða
4
2x
0
i;t
b2c
i
Þ 2Fða
3
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 4jx
i;t
Þ ¼ PrðCAP
*
i;t
.a
4
jx
i;t
Þ ¼ . . . ¼ 1 2Fða
4
2x
0
i;t
b2c
i
Þ
ð4Þ
where Pr( · ) and F( · ) denote probability and the normal cumulative distribution
function, respectively.
The various costs associated with adjusting CAP, make full adjustment to the
target unlikely, and therefore we assume that its observed trajectory obeys a partial
adjustment law (Flannery and Rangan, 2006; Berger et al., 2008)[3]. According to this
mechanism, banks adjust their current CAP relative to its previous level, at a fraction
of last year’s deviation from the latent desired level:
CAP
i;t
2CAP
i;t21
¼ u · CAP
*
i;t
2CAP
i;t21
ð5Þ
where u denotes the speed-of-adjustment parameter, CAP
i,t21
is the vector of
indicators 1{CAP
i,t21
¼ j, j ¼ 0,1,2,3,4, denoting last year’s capitalization status and
CAP
*
i;t
is the latent desired level.
Combining (2) and (5) gives us the following dynamic ordered probit model for
banks’ observed choices:
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CAP
i;t
¼ ð1 2uÞ · CAP
i;t21
þ x
0
i;t
b þ c
i
þ e
i;t
ð6Þ
From equation (6) one can easily see that as a direct consequence of the partial
adjustment assumption a dynamic element is introduced in the model. In the
econometric terminology (1 2 u) would capture any persistence in CAP, which clearly is
a negative function of the speed-of-adjustment parameter. It is apparent that in the case
of full adjustment (u ¼ 1) there would be no persistence, while partial adjustment would
necessarily generate some persistence.
However, the estimation of parameters appearing in equation (6) involves several
complications that need to be addressed. In particular, unobserved heterogeneity
cannot be eliminated with standard ways such as differencing. Here, c
i
will be treated
as random giving rise to a dynamic random effects ordered probit. In addition, the
presence of the dynamic component (lagged dependent variable) creates two further
problems. First, it implies that CAP
i,t
is affected by initial conditions given that any
working sample does not observe the dependent variable from its actual onset.
Wooldridge (2005) has suggested the inclusion of initial conditions, in our case CAP
i,0
,
as a covariate. Second, signi?cant persistence maybe erroneously attributed to state
dependence, while it may simply re?ect unobserved heterogeneity which has not been
properly accounted for. This problem can be surpassed by using a “correlated
random effects” model, which essentially includes the sample time means x
0
i
of all
explanatory variables as additional covariates (Mundlack, 1978; Chamberlain, 1984).
The intuition behind this tactic is that the (between) variation of time means would
capture a portion of unobserved heterogeneity. Hence, the full speci?cation of the
model is as follows:
CAP
i;t
¼ ð1 2uÞ · CAP
i;t21
þx
0
i;t
b þ x
0
i
g þd · CAP
i;0
þ c
i
þ e
i;t
ð7Þ
where x
i
denotes the sample time means of covariates for each cross-sectional unit
(bank), b,g and d are vectors and a scalar, respectively, of estimable parameters.
Equation (7) can be written more compactly as:
CAP
i;t
¼ z
0
i;t
l þ c
i
þ e
i;t
ð8Þ
where z
i;t
¼ ðCAP
i;t21
; x
i;t
; x
i
; CAP
i;0
Þ
0
and l ¼ ½ð1 2uÞ; b; g; d?:
Another important issue is that a standard ordered probit estimation procedure
would assume that the parameters do not vary between groupings, the so-called
parallel lines assumption (Long, 1997). This view ignores possible heterogeneous
effects of some or even all covariates across categories and in any case the conjecture of
equal thresholds for all banks is at least questionable (Greene and Hensher, 2010).
To tackle this issue we resort to the generalized random effects ordered probit
(Boes, 2007), which allows for differences in the cut points, and therefore in the slope
coef?cients. Recall that for the jth outcome the following holds:
PrðCAP
i;t
¼ jjz
i;t
Þ ¼ Fða
jþ1
2z
0
i;t
l 2c
i
Þ 2Fða
j
2z
0
i;t
l 2c
i
Þ ð9Þ
One can relax the assumption of equal thresholds across categories allowing them
to depend on the covariates in the following manner:
~ a
j
¼ a
j
þz
0
i;t
c
j
ð10Þ
US banks’
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where c
j
are the loading factors of the covariates on the thresholds. Substituting
equation (10) into equation (9) leads to:
PrðCAP
i;t
¼jjz
i;t
Þ ¼Fða
jþ1
þz
0
i;t
c
jþ1
2z
0
i;t
l2c
i
Þ 2Fða
j
þz
0
i;t
c
j
2z
0
i;t
l2c
i
Þ ð11Þ
or equivalently:
PrðCAP
i;t
¼ jjz
i;t
Þ ¼ Fða
jþ1
2z
0
i;t
j
jþ1
2c
i
Þ 2Fða
j
2z
0
i;t
j
j
2cÞ ð12Þ
where:
j
j
¼ l 2c
j
:
Pfarr et al. (2010) developed aniterative ?tting process, building on the automated ?tting
procedure for cross-sectional data (Williams, 2006). This process starts with the
estimation of an unconstrained model (where all coef?cients are allowed to vary),
followed by a sequence of Wald tests (for each covariate) examining whether coef?cients
statistically differ across groupings. Insigni?cant values of the Wald test indicate that
the coef?cient is constrained, i.e. has an identical effect across all groupings. Finally, the
model is re?tted with the constraints imposed and an overall (global) Wald test on the
full model is applied to con?rm the null hypothesis that the parallel lines assumption is
not violated.
To gauge the importance of allowing parameters to vary across categories, consider
the speed at which banks adjust their capitalization to the target. In a simple ordered
probit setup the speed-of-adjustment parameter is (ad hoc constrained to be) identical
across all capitalization groupings. In contrast, the herein proposed setup allows for the
possibility that speed-of-adjustment parameters vary across capitalization groups. This
is veryuseful information for the regulator who wouldbe more interested inknowing the
speed-of-adjustment of undercapitalized banks compared to that of adequately
capitalized banks. Stretching this a bit more, for the regulator and in fact for the banking
system, it would be essential that the speed-of-adjustment is higher for lower buckets of
capitalization. Berger et al. (2008) point out that differential speeds-of-adjustment are to
be expected since banks further away from their desired capital ratio may adjust faster.
Moreover, banks that are below the regulatory threshold may experience more pressure
fromauthorities to adjust, while at the other end, banks that are above their target capital
ratios may exhibit a lower speed-of-adjustment.
Furthermore, the setup permits revisiting earlier ?ndings regarding the direction
and magnitude of effects of each and every capitalization determinant. For instance,
previous studies have documented the so-called size effect, under which larger banks
tend to hold lower capital ratios. Similarly, banks with higher risk have been reported
as also exhibiting lower capital ratios (?nding indicative of moral hazard), while in
contrast more pro?table banks tend to be associated with higher. Now we can explore
whether these effects are valid across capitalization categories in a systematic and
holistic econometric framework.
4. Data issues
4.1 Dependent variable
The dataset consists of all FDIC-insured commercial banks in the USA for the period
2002-2009, providing us a sample with a total of 79,272 observations. Our starting point
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is the capital ratio, de?ned as total risk capital (the sum of Tiers 1 and 2) divided by risk
weighted assets. The dependent variable in our analysis, CAP, is de?ned according to
which FDIC bucket a bank’s capital ratio falls. Table I shows the distribution of banks
across CAP categories by year. The unconditional overall distributions are quite similar
across years, with the vast majority of banks belonging to the well capitalized category,
followed by those belonging to the adequately capitalized category. However, one can
immediately see that inthe last two years of the sample (2008, 2009), which correspond to
the ongoing severe ?nancial crisis, there has been a notable increase in the percentage of
undercapitalized banks. In particular, critically undercapitalized banks in 2009 showed
a ?vefold increase in comparison to 2002. Even more pronounced changes are found in
the signi?cantly undercapitalized and undercapitalized banks, which in comparison to
their 2002 magnitude they have increased by 47 and 57 times, respectively.
4.2 Control variables
In order to arrive at solid statistical inferences about the speed-of-adjustment
parameters it is vital to adequately model the bank-speci?c factors that may drive the
choice of capital ratio. As discussed earlier the literature has proposed several such
factors capturing diverse incentives and costs associated with selecting a given level of
capitalization. In short these are size, risk, asset quality, pro?tability, and market
discipline.
Table II provides the bank-speci?c variables that will be used as proxies for those
factors, obtained from FDIC’s “Statistics on Depository Institutions”. Since the choice
of covariates does not re?ect any structural model it is imperative to employ different
controls to ensure the robustness of our ?ndings. So the table offers two sets of
controls, one to be used in the baseline model and another to be used in the sensitivity
analysis model.
Finally note that the covariates’ vector will also include each US State’s time
series mean of (log) real per capita GDP. This variable is time-invariant but differs
between States and would therefore capture unobserved factors common for banks
operating in the same geographic area (State). The standard way to proceed would
be to use a set of State dummy variables, which however would further increase
CAP
bucket
Critically
undercapitalized
Signi?cantly
undercapitalizeed Undercapitalized
Adequately
capitalized
Well
capitalized
No. of
banks
Year
2002 0.02 0.02 0.06 1.39 98.50 9,325
2003 0.02 0.03 0.03 0.99 98.92 9,154
2004 0.00 0.02 0.02 0.94 99.02 8,951
2005 0.00 0.02 0.06 0.76 99.16 8,809
2006 0.01 0.00 0.07 0.64 99.28 8,657
2007 0.00 0.06 0.11 1.03 98.80 8,513
2008 0.10 0.37 0.74 2.28 96.51 8,288
2009 0.25 0.94 1.15 2.15 95.51 7,994
All years 0.05 0.16 0.25 1.37 98.17 79,272
Notes: Numbers denote percentages; the number of banks decreases each year due to M&A’s and
bank defaults; sums may differ from 100 due to rounding errors
Table I.
Distribution of banks
across capitalization
categories by year
US banks’
capitalization
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the already high computational dif?culty. The proposed solution is computationally
less burdensome but serves the same purpose.
5. Empirical results
5.1 Preliminary analysis
Before estimating the formal econometric model it would be useful to gain some
insights about movements between CAP categories by calculating the unconditional
sample transition matrix, provided in Table III. We present two transition matrices,
one that includes the default state and another based only on surviving banks. Clearly
the latter presents transition probabilities across capitalization categories, conditional
on the event that a bank has not defaulted, and therefore should be interpreted
accordingly. We will discuss the contents of Panel A, where default is accounted for.
As expected, banks belonging to any of the undercapitalized categories run the highest
default risk within a year. What is interesting is that the signi?cantly undercapitalized
category has the highest probability of default (about 67 percent), while one would
expect the critically undercapitalized group to exhibit the highest default probability.
The adequately capitalized and well capitalized categories have substantially lower
probabilities of default, estimated at 4.9 and 0.11 percent, respectively.
Important information is also embodied in the main diagonal elements which
capture the degree of persistence (i.e. tendency to remain in the same capitalization
groupings between any two adjacent years). Persistence is substantially stronger at the
high end of the capitalization spectrum. In particular, well capitalized banks
(with CAP ¼ 4) tend to remain in the same category almost with certainty
(with unconditional probability of 98.5 percent). The other category with notable,
but much lower, persistence is that of adequately capitalized banks which tend to retain
their status with an unconditional probability of almost 21 percent.
Equally vital information is conveyed in the remaining off-diagonal elements since
they show how the probability mass is distributed across transitions. There are two
?ndings that clearly stand out. First, it is noteworthy that within one year there is a
large fraction of banks completing transitions between rather distant states. For
instance, about 35.5 percent of critically capitalized banks and about 33 percent of
signi?cantly undercapitalized, transit to the well capitalized category. A smaller
Proxy used in (expected sign)
Factor Baseline model Sensitivity analysis
Size Logarithm of total assets (2) Logarithm of number of employees (2)
Risk Risk weighted assets/total assets (þ) Provisions for loan losses/total loans (þ)
Pro?tability (Total interest income 2 total interest
expense)/total assets (þ)
Net operating income/total assets (þ)
Asset quality
a
Noncurrent assets/total assets (þ) (Gross loan and lease ?nancing
receivable charge-offs 2 gross
recoveries)/total loans and lease
?nancing receivables (þ)
Market
discipline
Uninsured deposits/total deposits (þ) Subordinated debt/total liabilities (þ)
Note:
a
Both proxies are inverse measures of asset quality
Table II.
Bank-speci?c factors
and proxies used
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Table III.
Empirical transition
matrix across
capitalization categories
US banks’
capitalization
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fraction of critically capitalized banks (about 8 percent) improve their capitalization
status, but continue to remain undercapitalized. Second, banks which belong to the
undercapitalized group face a probability of about 37 percent to improve their
capitalization status (about 11 percent towards the adequately capitalized group, and
about 26 percent towards the well capitalized group) or deteriorate their status with a
probability of about 22 percent (about 17 percent to the signi?cantly undercapitalized
category, and about 5 percent to the critically undercapitalized category).
These ?ndings suggest that persistence is substantially smaller at low
capitalization categories. Recalling that the speed-of-adjustment is negatively related
to persistence, we then have prima facie evidence for a higher speed-of-adjustment in
lower capitalization categories. Of course, these are only tentative observations that
may or may not be veri?ed in a formal conditional model.
5.2 Estimation results from the generalized dynamic random effects ordered probit
model
As a prelude we report in Table IV the estimation results from the constrained
dynamic random effects ordered probit[4]. We document signi?cant and large
persistence, which implies that banks on average cover 50 percent of the distance from
their latent desired capitalization in about 1.9 years. Size, risk and asset quality tend to
decrease capitalization, while pro?tability and market discipline to increase it. Initial
conditions also emerge as a signi?cant determinant of capitalization status.
Baseline Sensitivity
CAP
i,t21
0.743
* * *
(15.94) 0.876
* * *
(18.54)
Size 20.543
* * *
(217.00) 20.659
* * *
(212.94)
Risk 20.006
* * *
(25.90) 20.033
* *
(22.26)
Pro?tability 0.099
* * *
(4.07) 0.029
* * *
(3.14)
Asset quality 20.115
* * *
(215.54) 20.049
* * *
(23.95)
Market discipline 0.004
* *
(2.58) 20.035 (20.54)
CAP
i,0
0.056
* * *
(3.34) 0.084
* * *
(5.79)
Mean(size) 0.614
* * *
(16.36) 0.586
* * *
(11.12)
Mean(risk) 20.013
* * *
(28.02) 0.075
* * *
(2.90)
Mean(pro?tability) 0.061
* *
(2.05) 0.093
* * *
(6.72)
Mean(asset quality) 20.117
* * *
(29.09) 20.089
* * *
(23.07)
Mean(market discipline) 20.003 (21.36) 0.136 (1.52)
Mean(state real per capita GDP) 20.225
* *
(22.01) 20.085 (20.84)
Cut_1 24.054
* * *
(23.27) 21.258 (21.13)
Cut_2 23.358
* * *
(22.72) 20.652 (20.59)
Cut_3 22.935
* *
(22.38) 20.301 (20.27)
Cut_4 22.233
*
(21.81) 0.307 (0.28)
Diagnostics
Log-likelihood 25,571.20 26,219.60
Likelihood ratio test 2,391.81 1,095.01
Observations 67,728 67,728
Notes: Statistical signi?cance at:
*
10,
* *
5 and
* * *
1 percent levels; numbers in brackets denote
z-scores; mean() stands for a given covariate’s time series mean calculated for each cross-sectional unit
(bank); denotes the signi?cance test of the estimated model against the constant alternative; denotes
the estimated threshold points
Table IV.
Dynamic random effects
ordered probit
(constrained
model-parallel lines
imposed)
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In Table V we report the estimation results from the generalized dynamic random
effects ordered probit model. Let us start with the parallel lines assumption tests
for each covariate. The null that a given covariate exerts an identical effect across
all categories was not rejected in six cases (for pro?tability and its time series mean;
for risk; for market discipline and its time series mean, and for the time series mean
of size), while for all other cases there were emphatic rejections. These ?ndings suggest
that there is suf?cient evidence for differential impacts of covariates across
capitalization groups. Also note that after the imposition of the constraints, the overall
parallel lines test is not rejected, indicating that the choice of a generalized model is
statistically appropriate.
Before we turn our attention to the speed-of-adjustment coef?cients it would be
fruitful to discuss the ?ndings regarding the control variables. Initial conditions seemto
play an important role in determining capitalization status across all categories. In
particular, banks with higher initial capitalization tend to continue to have higher
capitalization status, but this effect is monotonically decreasing across capitalization
categories. Size is found to exert a negative impact on capitalization across all groups,
?nding which is in line with previous ?ndings that analyzed CARwho report that larger
banks tend to hold lower capital ratios. Also in line with the literature, we encounter a
negative impact of risk on capitalization, which as mentioned earlier is found as having a
uniform effect across all capitalization categories. Similarly pro?tability has an equal
effect across all groups, and the direction of impact is positive as has been reported in
past studies. The asset quality proxy is signi?cant and carries a negative coef?cient,
which suggests that lower asset quality tends to decrease capitalization. This ?nding in
conjunction with the negative effect of risk provide evidence in favor of a moral hazard
phenomenon, since one would expect institutions with worse asset quality and higher
risk to hold, ceteris paribus, more capital. Another interesting ?nding is the positive
and signi?cant effect of market discipline, which implies that there is a systematic
disciplinary process imposed on banks’ capitalization choices. Finally. the majority of
longitudinal means of covariates are signi?cant suggesting that serve their purpose of
capturing a portion of the unobserved heterogeneity.
Moving now to the parameters of main interest we see that the lagged capitalization
status enters with a signi?cantly positive coef?cient in all categories. What is important
is that the relevant coef?cients increase for higher capitalization groups. Recall that the
estimated coef?cients’ distance from unity is a measure for the speed-of-adjustment.
Hence, there is evidence that the speed-of-adjustment differs across groups, and in fact is
higher for lower capitalization categories. Essentially, if we transform the estimated
coef?cients into time periods needed to cover 50 percent of the distance from the latent
desired capitalization we ?nd the following. critically undercapitalized banks cover this
distance in about 0.7 years, signi?cantly undercapitalized banks in about 1.4 years,
undercapitalized banks in about 1.6 years, while adequately capitalized banks need
about 2.5 years to clear the same distance. Thus, we uncover evidence infavor of a higher
speed-of-adjustment for lower capitalization banks. This is consistent both with a
systematic effect of the prompt correction action as well as with a banks’ self-correcting
(capitalization) mechanism behavior.
The sensitivity analysis provides qualitatively similar conclusions. Again, the lowest
capitalization group is estimated as having the highest speed-of-adjustment, parameter
which decreases as we move to higher capitalization categories. The estimated time
US banks’
capitalization
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Baseline Sensitivity
Critically undercapitalized category; CAP
i,t
¼ 0
CAP
i,t21
0.276
* *
(2.15) 0.458
* *
(3.53)
Size 20.636
* * *
(29.13) 20.094 (20.37)
Risk 20.006
* * *
(25.73) 0.001 (0.02)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.057
* * *
(22.75) 20.049
* * *
(23.85)
Market discipline 0.004
* *
(2.57) 20.435
* * *
(23.14)
CAP
i,0
0.192
* * *
(3.53) 0.026 (0.49)
Mean(size) 0.611
* * *
(16.23) 20.061 (20.23)
Mean(risk) 0.015
* * *
(2.98) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.177
* * *
(3.69)
Mean(asset quality) 20.161
* * *
(23.78) 20.275
*
(21.92)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 1.037
*
(1.89) 20.093 (20.92)
Intercept 29.369 (21.56) 3.451
* * *
(2.74)
Signi?cantly undercapitalized category; CAP
i,t
¼ 1
CAP
i,t21
0.653
* * *
(8.50) 0.725
* * *
(10.00)
Size 20.678
* * *
(215.84) 20.847
* * *
(27.38)
Risk 20.006
* * *
(25.73) 20.127
* * *
(24.00)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.118
* * *
(28.85) 20.049
* * *
(23.85)
Market discipline 0.004
* * *
(2.57) 20.139 (21.31)
CAP
i,0
0.138
* * *
(4.07) 0.036 (1.19)
Mean(size) 0.611
* * *
(16.23) 0.688
* * *
(5.82)
Mean(risk) 20.001 (20.35) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.177
* * *
(7.03)
Mean(asset quality) 20.201
* * *
(26.94) 20.259
* * *
(23.41)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 20.641
* * *
(22.75) 20.093 (20.92)
Intercept 8.755
* * *
(3.41) 2.160
*
(1.89)
Undercapitalized category; CAP
i,t
¼ 2
CAP
i,t21
0.696
* * *
(10.68) 0.763
* * *
(12.34)
Size 20.624
* * *
(217.47) 20.922
* * *
(212.28)
Risk 20.006
* * *
(25.73) 20.158
* * *
(26.70)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.148
* * *
(215.43) 20.049
* * *
(23.85)
Market discipline 0.004
* *
(2.57) 20.011 (20.14)
CAP
i,0
0.062
* *
(2.41) 0.038
*
(1.84)
Mean(size) 0.611
* * *
(16.23) 0.807
* * *
(10.37)
Mean(risk) 20.009
* * *
(24.02) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.130
* * *
(7.37)
Mean(asset quality) 20.153
* * *
(27.36) 20.177
* * *
(24.06)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 20.641
* * *
(23.27) 20.093 (20.92)
Intercept 8.422
* * *
(3.97) 1.458 (1.30)
Adequately capitalized category; CAP
i,t
¼ 3
CAP
i,t21
0.803
* * *
(16.38) 0.936
* * *
(19.02)
Size 20.531
* * *
(216.61) 20.639
* * *
(212.37)
Risk 20.006
* * *
(25.73) 20.016 (20.87)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.113
* * *
(214.47) 20.049
* * *
(23.85)
(continued)
Table V.
Generalized dynamic
random effects ordered
probit
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needed for banks belonging in the critically undercapitalized group to cover 50 percent
of the distance from the latent target is about 0.9 years. For the signi?cantly
undercapitalized banks is about 1.8 years, undercapitalized banks is about 2.08 years.
For these groups the estimates between the baseline and the sensitivity models are quite
close. However, the sensitivity model for adequately capitalized banks implies that they
need about seven years to clear the same distance, which substantially higher than the
2.5 years estimated from the baseline model.
6. Conclusions
Based on all FDIC-insured banks during the period 2002-2009 we estimated the
capitalization speed-of-adjustment across different FDIC capitalization buckets, using a
generalizeddynamic randomeffects orderedprobit model. The reduced-formspeci?cation
was based on a partial adjustment model, controlling for all standard capitalization
determinants, initial conditions and unobserved cross-sectional heterogeneity. An
attractive feature of the estimation technique is that it allows to test for differential effects
Baseline Sensitivity
Market discipline 0.004
* *
(2.57) 0.021 (0.29)
CAP
i,0
0.050
* * *
(2.93) 0.087
* * *
(5.97)
Mean(size) 0.611
* * *
(16.23) 0.569
* * *
(10.66)
Mean(risk) 20.014
* * *
(28.52) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.091
* * *
(6.44)
Mean(asset quality) 20.112
* * *
(28.51) 20.086
* * *
(22.91)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 20.196
*
(21.73) 20.093 (20.92)
Intercept 1.652 (1.33) 20.501 (20.45)
Diagnostics
Parallel lines assumption tests by covariate (p-value)
CAP
i,t21
0.00 0.00
Size 0.00 0.00
Risk 0.16 0.00
Pro?tability 0.55 0.93
Asset quality 0.00 0.30
Market discipline 0.05 0.00
CAP
i,0
0.00 0.03
Mean(size) 0.06 0.00
Mean(risk) 0.00 0.75
Mean(pro?tability) 0.38 0.00
Mean(asset quality) 0.00 0.01
Mean(market discipline) 0.39 0.33
Mean(state real per capita GDP) 0.00 0.07
Overall parallel lines assumption test ( p-value) 0.08 0.37
Log-likelihood 25,471.61 26,112.10
Wald test 2,213.79
* * *
1,651.43
Observations 67,728 67,728
Notes: Statistical signi?cance at:
*
10,
* *
5 and
* * *
1 percent levels; numbers in brackets denote
z-scores; mean() stands for a given covariate’s time series mean calculated for each cross-sectional unit
(bank); the null hypothesis is that the slope parameter of each covariate is equal across categories;
overall test that slope parameters are equal across categories; denotes the overall signi?cance test Table V.
US banks’
capitalization
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of covariates across capitalization categories. According to our ?ndings there is suf?cient
evidence supporting a higher speed-of-adjustment for lower capitalization banks, ?nding
which can be attributed to FDIC’s prompt corrective action and/or banks’ self-correcting
behavior. This an important ?nding both for regulators and market participants since it
sheds light on a very crucial aspect of banks’ behavior. In addition, we ?nd effects similar
to those reported in the previous literature regarding the standard capitalization
determinants. However, for several of themwe conclude that theyexert impacts of unequal
magnitude across capitalization categories.
Future research could explore further issues such as what is the effect of banks’
loan, asset and liabilities composition on the speed-of-adjustment. In addition, potential
fruitful extensions may also explore bank ownership and competition effects.
Notes
1. Of course the likelihood of failure is not uniquely determined by a bank’s capitalization.
However, ceteris paribus, a bank’s ability to avoid failure is an increasing function of its
capitalization (Estrella et al., 2000).
2. These thresholds were initially introduced in the Federal Deposit Insurance Corporation
Improvement Act of December 1991, which determines what supervisory actions would be
taken by bank regulators.
3. For instance capital ratios can be increased either by increasing capital and/or by reducing
risk-weighted assets. Raising new capital is costly, especially for troubled banks with capital
ratios below the regulatory threshold. Moreover, reduction of risk-weighted assets is bound
to be constrained by the amount of assets maturing in the current period and the capital
losses that might be produced by disposing assets prior to their maturity (Berger et al., 2008).
4. Note that all time-varying covariates will enter the model with a one period lag to avoid
potential simultaneity.
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About the author
Dr Konstantinos Drakos holds a PhD in Economics from the University of Essex (UK). Currently
he is Assistant Professor of Finance at the Department of Accounting and Finance (Athens
University of Economics and Business). Previously he held appointments at the University of
Patras (Greece) and the University of Essex (UK). Dr Konstantinos Drakos can be contacted at:
[email protected]
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doc_869693381.pdf
The purpose of this paper is to investigate whether there are any differences in the
capitalization speed-of-adjustment across regulatory capitalization buckets of commercial banks in the
USA, for the period 2002-2009
Journal of Financial Economic Policy
US banks' capitalization speed-of-adjustment: a microeconometric approach
Konstantinos Drakos
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US banks’ capitalization
speed-of-adjustment:
a microeconometric approach
Konstantinos Drakos
Department of Accounting and Finance,
Athens University of Economics and Business, Athens, Greece
Abstract
Purpose – The purpose of this paper is to investigate whether there are any differences in the
capitalization speed-of-adjustment across regulatory capitalization buckets of commercial banks in the
USA, for the period 2002-2009.
Design/methodology/approach – The Federal Deposit Insurance Corporation (FDIC) monitors
banks’ capital ratio using the bucketing approach. Thus, this discrete and ordered variable is modeled
in the context of a partial adjustment speci?cation, controlling for initial conditions and cross-sectional
heterogeneity. Parameters are estimated with the generalized dynamic random effects ordered probit
technique that is ?exible enough to allow for differential effects of covariates across capitalization
categories.
Findings – The main result is that the speed of adjustment is monotonically increasing for banks
belonging in lower capitalization buckets, after controlling for bank-speci?c capitalization
determinants. In addition, substantial differential impacts of capitalization drivers across regulatory
buckets are uncovered.
Practical implications – This an important ?nding both for regulators and market participants
since it sheds light on a very crucial aspect of banks’ behaviour.
Originality/value – This is the ?rst paper that adopts the FDIC bucketing in the actual modelling.
In addition, it uses the generalized dynamic random effects ordered probit technique in order to
explore potential differential impact of capital ratio determinants across buckets.
Keywords United States of America, Commercial banks, Capitalization,
Federal Deposit Insurance Corporation,
Speed-of-Adjustment
Paper type Research paper
1. Introduction
An emphatic lesson learnt during the past century is that bank failures have an
increasing capacity to impose large negative externalities directly on their depositors,
and indirectly via the signi?cant budgetary consequences in the event that governments
bear the cost of bailout. More importantly, due to the cross cutting and crucial role of
banks in the payments system and facilitation of credit, banking systemic risk may
produce severe adverse effects to the real economy. Thus, it comes as no surprise that the
banking sector has traditionally been one of the most heavily regulated sectors with the
aim to minimize the likelihood banking crises occur. In addition, the increased
cross-border banking activities tend to generate crises transcending the geographic
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – C25, G21, G32
The author acknowledges ?nancial support by the Athens University of Economics and
Business Research Center (ELKE).
JFEP
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Journal of Financial Economic Policy
Vol. 4 No. 3, 2012
pp. 270-286
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381211245980
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boundaries of the originating country. Moreover, the need to avoid gaining advantages
stemming from unsound banking activity led to the adoption of a common set of rules
internationally. A basic building block of these rules, that emerged from the
international Basel Accord, is that banks are subject to the regulatory constraint of
maintaining a capital ratio (CAR) of at least 8 percent. Capital Ratio is de?ned as the ratio
of total risk capital Tier1 þ Tier2 to risk weighted assets (RWA).
Regulators closely monitor the level and the trajectory of banks’ capital ratios, paying
special attention to undercapitalized banks, those below the 8 percent threshold. In fact,
for such banks regulators have the ability to call for prompt corrective action in the form
of adjusting upwards their capital ratio within a speci?ed time horizon, and even force
themto foreclosure in case of no compliance. However, froma regulatory perspective the
distinction between banks who are undercapitalized and those who are not, although
useful, turns out to be rather crude. This becomes immediately apparent if we consider
two banks who are both undercapitalized, but their distance from the regulatory
threshold differs. For instance, the likelihood of failure[1] would dramatically differ
between a bank with a capital ratio of 2 percent and another with 7 percent. In order to
have a ?ner and more informative assessment of capital status, the Federal Deposit
Insurance Corporation (FDIC), which is the US regulator, classi?es banks into ?ve
capitalization buckets according to their CAR as follows[2]:
(1) Critically undercapitalized if CAR , 2 percent.
(2) Signi?cantly undercapitalized if 2 percent #CAR , 6 percent.
(3) Undercapitalized if 6 percent # CAR , 8 percent.
(4) Adequately capitalized if 8 percent # CAR , 10 percent.
(5) Well capitalized if CAR $ 10 percent.
Given that the FDIC employs the above classi?cation it would naturally be interested
in having information pertinent to each capitalization bucket. However, academic
research typically treats capital ratio in a continuous fashion, creating a misalignment
between the research questions addressed by the academic literature and those
relevant for regulatory purposes. For instance there are several questions that remain
unanswered such as whether the factors affecting capital ratios of banks belonging in
different buckets are identical, or whether a given factor exerts the same quantitative
and/or qualitative impact across buckets. Perhaps one of the most important issues is
whether the capitalization speed-of-adjustment differs across capitalization buckets.
In particular, one would expect the corrective action mentioned earlier and banks’ own
self-correcting mechanism, to result in a higher speed-of-adjustment for banks
belonging to lower capitalization buckets.
These are exactly the gaps we aim to ?ll with the present study, where instead of
using the continuous capital ratio, we model the discrete and ordered variable that the
FDIC monitors. Moreover, we will allow and test for possible differential effects of
covariates, paying particular attention to the speed-of-adjustment parameters across
capitalization buckets, within the context of a formal econometric setup. Note that the
set of covariates includes all potential capitalization determinants such as size, risk,
pro?tability, asset quality and market discipline (Demstez et al., 1996; Flannery and
Sorescu, 1996; Goldberg and Hudgins, 2002; Lindquist, 2004; Jokipii and Milne, 2008).
The analysis is based on a large microeconometric panel consisting of all FDIC-insured
US banks’
capitalization
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commercial banks in the USA for the period 2002-2009. The estimation technique is the
generalized dynamic random effects ordered probit (Boes, 2007), where we will control
for initial conditions (Wooldridge, 2005) and cross-sectional heterogeneity (Mundlack,
1978; Chamberlain, 1984). The study mainly makes a twofold contribution to the
literature. First, to the best of our knowledge it is the ?rst time that capitalization is
modeled as a discrete ordered variable that matches the FDIC buckets. Second, it
employs a generalized setup that allows covariates to exert diverse effects across
capitalization categories and therefore allows a formal statistical investigation of a
differential speed-of-adjustment.
Let us brie?y discuss the ?ndings from the analysis. First, we uncover evidence
for a differential impact of several capitalization determinants across categories, which
suggests that banks cannot be treated as a uniform group. Second, although the present
analysis ?nds similar impacts of capitalization determinants with previous studies – in
terms of direction – there is ample evidence that their impact differs across capitalization
groups. Third, we document substantial differences in the capitalization speed-of-
adjustment, which increases monotonically as one moves to lower capitalization buckets.
For instance, the critically undercapitalized category covers 50 percent of its distance from
the (latent) targeted level within 0.7 years, while the adequately capitalized group clears the
same distance in about 2.5 years. These ?ndings may be attributed to the impact of the
prompt corrective action and/or to banks’ self-correcting behavior.
The remainder of the paper is structured as follows. Section 2 provides a brief
review of the relevant literature. Section 3 presents the econometric methodology.
Section 4 describes the dataset. Section 5 discusses the estimation results and ?nally
Section 6 concludes and discusses policy implications.
2. Literature review
The literature has proposed several factors as potential determinants of bank
capitalization capturing diverse associated incentives and costs. In short these factors
re?ect size, risk, pro?tability, asset quality and market discipline. In what follows we
will brie?y discuss the theoretical arguments for using each factor.
There are several ?nancial rationales suggesting a negative effect of bank’s size on
its capital ratio. One of them takes into account the costs of:
.
screening potential borrowers; and
.
monitoring the behavior of approved borrowers.
To the extent that there are economies of scale in such activities we expect larger banks
to be more able to achieve them, hence reducing capital holding requirements. In
addition, one would reach a similar conclusion if the bene?ts of portfolio diversi?cation
are increasing with bank size (Demsetz and Strahan, 1997; Alfon et al., 2004; Stolz and
Wedow, 2005; Jokippi and Milne, 2008). Furthermore, larger banks may hold lower
capital reserves because they might:
.
face less severe liquidity constraints; and
.
have lower transaction costs in adjusting capital levels (Alfon et al., 2004).
Another reason for expecting a negative relationship between size and capital held is
the so-called “too big to fail” hypothesis according to which large banks enjoy implicit
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government guarantees. Since the potential failure of a large institution is more likely
to affect the whole system, the likelihood of a safety net provided by authorities is
perceived as being higher (Ayuso et al., 2004; Lindquist, 2004; Stolz and Wedow, 2005).
The main reason banks are required to hold capital is to cover their potential
unexpected losses, which clearly are a function of the overall risks the bank assumes.
Thus, we expect banks assuming higher risk to tend to hold more capital. However, there
are various studies who report a negative association between risk and capital, ?nding
which can be indicative of a moral hazard problem (Alfon et al., 2004; Ayuso et al., 2004;
Lindquist, 2004). Apart from the riskiness of a bank’s assets, which to some extent
re?ects prior assessments based on the type of asset, one may also ?nd important
information embedded in their quality. Again we expect banks with lower asset quality
to hold more capital.
There are two arguments that support a positive relationship between a bank’s
pro?tability and its capital. First, according to the pecking-order theory (Myers and
Majluf, 1984) one expects banks to have a preference for internal funding because it
is less costly compared to external sources of ?nancing. Second, according to the
charter value hypothesis, more pro?table banks would opt for higher capital ratios
to protect their charter value (Marcus, 1983; Keeley, 1990; Demstez et al., 1996;
Hellmann et al., 2000).
There is a literature advocating a market discipline effect on capital ratio, much like
leverage ratios (Flannery and Sorescu, 1996; Morgan and Stiroh, 2001; Gropp et al., 2006;
Flannery and Rangan, 2007). The essence of market discipline in the banking sector is
that at-risk private sector claimants will impose “constraints” on bank behavior to
protect their interests. The literature has suggested that such disciplinary effects can be
brought about by uninsured depositors and/or subordinated debt holders. Both groups
are exposed to potentially non-prudential bank behavior, and in the event of default face
losses with high likelihood. The former group obviously because of a lack of deposit
insurance coverage, and the latter group due to their lowpriority of claims. So uninsured
depositors may penalize riskier banks by requiring higher interest rates or by
withdrawing their deposits (Goldberg and Hudgins, 1996, 2002; Park and Peristiani,
1998; Peria and Schmukler, 2001; Davenport and McDill, 2006), and in a similar vein,
subordinated debt holders will either require a higher premium or withdraw their funds
(Avery et al., 1988; Sironi, 2003; Covitz et al., 2004). Hence, we expect banks exposed to
higher market disciplinary effect to hold more capital.
3. Econometric methodology
Let the indices i,t denote the cross-sectional unit (bank) and time period (year),
respectively. Using the FDIC buckets as exogenously given, we de?ne a new variable
CAP
i,t
as follows:
CAP
i;t
¼
0; if bank i is critically undercapitalized in year t
1; if bank i is significantly undercapitalized in year t
2; if bank i is undercapitalized in year t
3; if bank i is adequately capitalized in year t
4; if bank i is well capitalized in year t
8
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>
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ð1Þ
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It becomes apparent that the variable under scrutiny is not continuous, but rather
shows a discrete ordered response, which should be modeled by an Ordered Probit
model. Assume that CAP is derived by a latent target variable model determined by:
CAP
*
i;t
¼ x
0
i;t
b þ c
i
þ e
i;t
ð2Þ
where x
i,t
is a vector of covariates, c
i
is the unobserved heterogeneity, e
i,t
jx , N(0,1),
and b denotes a vector of constant parameters.
Let a
1
, a
2
, a
3
, a
4
be cut points (also known as threshold parameters) and
de?ne:
CAP
i;t
¼
0; if CAP
*
i;t
# a
1
1; if a
1
, CAP
*
i;t
# a
2
2; if a
2
, CAP
*
i;t
# a
3
3; if a
3
, CAP
*
i;t
# a
4
4; if CAP
*
i;t
. a
4
8
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ð3Þ
Given the assumption e
i,t
jx , N(0,1) one can derive the conditional distribution of CAP
given x
i,t
:
PrðCAP
i;t
¼ 0jx
i;t
Þ ¼ PrðCAP
*
i;t
#a
1
jx
i;t
Þ ¼ Prðx
0
i;t
bþc
i
þe
i;t
,a
1
jx
i;t
Þ ¼Fða
1
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 1jx
i;t
Þ ¼ Prða
1
,CAP
*
i;t
#a
2
jx
i;t
Þ ¼ . . . ¼Fða
2
2x
0
i;t
b2c
i
Þ 2Fða
1
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 2jx
i;t
Þ ¼ Prða
2
,CAP
*
i;t
#a
3
jx
i;t
Þ ¼ . . . ¼Fða
3
2x
0
i;t
b2c
i
Þ 2Fða
2
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 3jx
i;t
Þ ¼ Prða
3
,CAP
*
i;t
#a
4
jx
i;t
Þ ¼ . . . ¼Fða
4
2x
0
i;t
b2c
i
Þ 2Fða
3
2x
0
i;t
b2c
i
Þ
PrðCAP
i;t
¼ 4jx
i;t
Þ ¼ PrðCAP
*
i;t
.a
4
jx
i;t
Þ ¼ . . . ¼ 1 2Fða
4
2x
0
i;t
b2c
i
Þ
ð4Þ
where Pr( · ) and F( · ) denote probability and the normal cumulative distribution
function, respectively.
The various costs associated with adjusting CAP, make full adjustment to the
target unlikely, and therefore we assume that its observed trajectory obeys a partial
adjustment law (Flannery and Rangan, 2006; Berger et al., 2008)[3]. According to this
mechanism, banks adjust their current CAP relative to its previous level, at a fraction
of last year’s deviation from the latent desired level:
CAP
i;t
2CAP
i;t21
¼ u · CAP
*
i;t
2CAP
i;t21
ð5Þ
where u denotes the speed-of-adjustment parameter, CAP
i,t21
is the vector of
indicators 1{CAP
i,t21
¼ j, j ¼ 0,1,2,3,4, denoting last year’s capitalization status and
CAP
*
i;t
is the latent desired level.
Combining (2) and (5) gives us the following dynamic ordered probit model for
banks’ observed choices:
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CAP
i;t
¼ ð1 2uÞ · CAP
i;t21
þ x
0
i;t
b þ c
i
þ e
i;t
ð6Þ
From equation (6) one can easily see that as a direct consequence of the partial
adjustment assumption a dynamic element is introduced in the model. In the
econometric terminology (1 2 u) would capture any persistence in CAP, which clearly is
a negative function of the speed-of-adjustment parameter. It is apparent that in the case
of full adjustment (u ¼ 1) there would be no persistence, while partial adjustment would
necessarily generate some persistence.
However, the estimation of parameters appearing in equation (6) involves several
complications that need to be addressed. In particular, unobserved heterogeneity
cannot be eliminated with standard ways such as differencing. Here, c
i
will be treated
as random giving rise to a dynamic random effects ordered probit. In addition, the
presence of the dynamic component (lagged dependent variable) creates two further
problems. First, it implies that CAP
i,t
is affected by initial conditions given that any
working sample does not observe the dependent variable from its actual onset.
Wooldridge (2005) has suggested the inclusion of initial conditions, in our case CAP
i,0
,
as a covariate. Second, signi?cant persistence maybe erroneously attributed to state
dependence, while it may simply re?ect unobserved heterogeneity which has not been
properly accounted for. This problem can be surpassed by using a “correlated
random effects” model, which essentially includes the sample time means x
0
i
of all
explanatory variables as additional covariates (Mundlack, 1978; Chamberlain, 1984).
The intuition behind this tactic is that the (between) variation of time means would
capture a portion of unobserved heterogeneity. Hence, the full speci?cation of the
model is as follows:
CAP
i;t
¼ ð1 2uÞ · CAP
i;t21
þx
0
i;t
b þ x
0
i
g þd · CAP
i;0
þ c
i
þ e
i;t
ð7Þ
where x
i
denotes the sample time means of covariates for each cross-sectional unit
(bank), b,g and d are vectors and a scalar, respectively, of estimable parameters.
Equation (7) can be written more compactly as:
CAP
i;t
¼ z
0
i;t
l þ c
i
þ e
i;t
ð8Þ
where z
i;t
¼ ðCAP
i;t21
; x
i;t
; x
i
; CAP
i;0
Þ
0
and l ¼ ½ð1 2uÞ; b; g; d?:
Another important issue is that a standard ordered probit estimation procedure
would assume that the parameters do not vary between groupings, the so-called
parallel lines assumption (Long, 1997). This view ignores possible heterogeneous
effects of some or even all covariates across categories and in any case the conjecture of
equal thresholds for all banks is at least questionable (Greene and Hensher, 2010).
To tackle this issue we resort to the generalized random effects ordered probit
(Boes, 2007), which allows for differences in the cut points, and therefore in the slope
coef?cients. Recall that for the jth outcome the following holds:
PrðCAP
i;t
¼ jjz
i;t
Þ ¼ Fða
jþ1
2z
0
i;t
l 2c
i
Þ 2Fða
j
2z
0
i;t
l 2c
i
Þ ð9Þ
One can relax the assumption of equal thresholds across categories allowing them
to depend on the covariates in the following manner:
~ a
j
¼ a
j
þz
0
i;t
c
j
ð10Þ
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where c
j
are the loading factors of the covariates on the thresholds. Substituting
equation (10) into equation (9) leads to:
PrðCAP
i;t
¼jjz
i;t
Þ ¼Fða
jþ1
þz
0
i;t
c
jþ1
2z
0
i;t
l2c
i
Þ 2Fða
j
þz
0
i;t
c
j
2z
0
i;t
l2c
i
Þ ð11Þ
or equivalently:
PrðCAP
i;t
¼ jjz
i;t
Þ ¼ Fða
jþ1
2z
0
i;t
j
jþ1
2c
i
Þ 2Fða
j
2z
0
i;t
j
j
2cÞ ð12Þ
where:
j
j
¼ l 2c
j
:
Pfarr et al. (2010) developed aniterative ?tting process, building on the automated ?tting
procedure for cross-sectional data (Williams, 2006). This process starts with the
estimation of an unconstrained model (where all coef?cients are allowed to vary),
followed by a sequence of Wald tests (for each covariate) examining whether coef?cients
statistically differ across groupings. Insigni?cant values of the Wald test indicate that
the coef?cient is constrained, i.e. has an identical effect across all groupings. Finally, the
model is re?tted with the constraints imposed and an overall (global) Wald test on the
full model is applied to con?rm the null hypothesis that the parallel lines assumption is
not violated.
To gauge the importance of allowing parameters to vary across categories, consider
the speed at which banks adjust their capitalization to the target. In a simple ordered
probit setup the speed-of-adjustment parameter is (ad hoc constrained to be) identical
across all capitalization groupings. In contrast, the herein proposed setup allows for the
possibility that speed-of-adjustment parameters vary across capitalization groups. This
is veryuseful information for the regulator who wouldbe more interested inknowing the
speed-of-adjustment of undercapitalized banks compared to that of adequately
capitalized banks. Stretching this a bit more, for the regulator and in fact for the banking
system, it would be essential that the speed-of-adjustment is higher for lower buckets of
capitalization. Berger et al. (2008) point out that differential speeds-of-adjustment are to
be expected since banks further away from their desired capital ratio may adjust faster.
Moreover, banks that are below the regulatory threshold may experience more pressure
fromauthorities to adjust, while at the other end, banks that are above their target capital
ratios may exhibit a lower speed-of-adjustment.
Furthermore, the setup permits revisiting earlier ?ndings regarding the direction
and magnitude of effects of each and every capitalization determinant. For instance,
previous studies have documented the so-called size effect, under which larger banks
tend to hold lower capital ratios. Similarly, banks with higher risk have been reported
as also exhibiting lower capital ratios (?nding indicative of moral hazard), while in
contrast more pro?table banks tend to be associated with higher. Now we can explore
whether these effects are valid across capitalization categories in a systematic and
holistic econometric framework.
4. Data issues
4.1 Dependent variable
The dataset consists of all FDIC-insured commercial banks in the USA for the period
2002-2009, providing us a sample with a total of 79,272 observations. Our starting point
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is the capital ratio, de?ned as total risk capital (the sum of Tiers 1 and 2) divided by risk
weighted assets. The dependent variable in our analysis, CAP, is de?ned according to
which FDIC bucket a bank’s capital ratio falls. Table I shows the distribution of banks
across CAP categories by year. The unconditional overall distributions are quite similar
across years, with the vast majority of banks belonging to the well capitalized category,
followed by those belonging to the adequately capitalized category. However, one can
immediately see that inthe last two years of the sample (2008, 2009), which correspond to
the ongoing severe ?nancial crisis, there has been a notable increase in the percentage of
undercapitalized banks. In particular, critically undercapitalized banks in 2009 showed
a ?vefold increase in comparison to 2002. Even more pronounced changes are found in
the signi?cantly undercapitalized and undercapitalized banks, which in comparison to
their 2002 magnitude they have increased by 47 and 57 times, respectively.
4.2 Control variables
In order to arrive at solid statistical inferences about the speed-of-adjustment
parameters it is vital to adequately model the bank-speci?c factors that may drive the
choice of capital ratio. As discussed earlier the literature has proposed several such
factors capturing diverse incentives and costs associated with selecting a given level of
capitalization. In short these are size, risk, asset quality, pro?tability, and market
discipline.
Table II provides the bank-speci?c variables that will be used as proxies for those
factors, obtained from FDIC’s “Statistics on Depository Institutions”. Since the choice
of covariates does not re?ect any structural model it is imperative to employ different
controls to ensure the robustness of our ?ndings. So the table offers two sets of
controls, one to be used in the baseline model and another to be used in the sensitivity
analysis model.
Finally note that the covariates’ vector will also include each US State’s time
series mean of (log) real per capita GDP. This variable is time-invariant but differs
between States and would therefore capture unobserved factors common for banks
operating in the same geographic area (State). The standard way to proceed would
be to use a set of State dummy variables, which however would further increase
CAP
bucket
Critically
undercapitalized
Signi?cantly
undercapitalizeed Undercapitalized
Adequately
capitalized
Well
capitalized
No. of
banks
Year
2002 0.02 0.02 0.06 1.39 98.50 9,325
2003 0.02 0.03 0.03 0.99 98.92 9,154
2004 0.00 0.02 0.02 0.94 99.02 8,951
2005 0.00 0.02 0.06 0.76 99.16 8,809
2006 0.01 0.00 0.07 0.64 99.28 8,657
2007 0.00 0.06 0.11 1.03 98.80 8,513
2008 0.10 0.37 0.74 2.28 96.51 8,288
2009 0.25 0.94 1.15 2.15 95.51 7,994
All years 0.05 0.16 0.25 1.37 98.17 79,272
Notes: Numbers denote percentages; the number of banks decreases each year due to M&A’s and
bank defaults; sums may differ from 100 due to rounding errors
Table I.
Distribution of banks
across capitalization
categories by year
US banks’
capitalization
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the already high computational dif?culty. The proposed solution is computationally
less burdensome but serves the same purpose.
5. Empirical results
5.1 Preliminary analysis
Before estimating the formal econometric model it would be useful to gain some
insights about movements between CAP categories by calculating the unconditional
sample transition matrix, provided in Table III. We present two transition matrices,
one that includes the default state and another based only on surviving banks. Clearly
the latter presents transition probabilities across capitalization categories, conditional
on the event that a bank has not defaulted, and therefore should be interpreted
accordingly. We will discuss the contents of Panel A, where default is accounted for.
As expected, banks belonging to any of the undercapitalized categories run the highest
default risk within a year. What is interesting is that the signi?cantly undercapitalized
category has the highest probability of default (about 67 percent), while one would
expect the critically undercapitalized group to exhibit the highest default probability.
The adequately capitalized and well capitalized categories have substantially lower
probabilities of default, estimated at 4.9 and 0.11 percent, respectively.
Important information is also embodied in the main diagonal elements which
capture the degree of persistence (i.e. tendency to remain in the same capitalization
groupings between any two adjacent years). Persistence is substantially stronger at the
high end of the capitalization spectrum. In particular, well capitalized banks
(with CAP ¼ 4) tend to remain in the same category almost with certainty
(with unconditional probability of 98.5 percent). The other category with notable,
but much lower, persistence is that of adequately capitalized banks which tend to retain
their status with an unconditional probability of almost 21 percent.
Equally vital information is conveyed in the remaining off-diagonal elements since
they show how the probability mass is distributed across transitions. There are two
?ndings that clearly stand out. First, it is noteworthy that within one year there is a
large fraction of banks completing transitions between rather distant states. For
instance, about 35.5 percent of critically capitalized banks and about 33 percent of
signi?cantly undercapitalized, transit to the well capitalized category. A smaller
Proxy used in (expected sign)
Factor Baseline model Sensitivity analysis
Size Logarithm of total assets (2) Logarithm of number of employees (2)
Risk Risk weighted assets/total assets (þ) Provisions for loan losses/total loans (þ)
Pro?tability (Total interest income 2 total interest
expense)/total assets (þ)
Net operating income/total assets (þ)
Asset quality
a
Noncurrent assets/total assets (þ) (Gross loan and lease ?nancing
receivable charge-offs 2 gross
recoveries)/total loans and lease
?nancing receivables (þ)
Market
discipline
Uninsured deposits/total deposits (þ) Subordinated debt/total liabilities (þ)
Note:
a
Both proxies are inverse measures of asset quality
Table II.
Bank-speci?c factors
and proxies used
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Table III.
Empirical transition
matrix across
capitalization categories
US banks’
capitalization
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fraction of critically capitalized banks (about 8 percent) improve their capitalization
status, but continue to remain undercapitalized. Second, banks which belong to the
undercapitalized group face a probability of about 37 percent to improve their
capitalization status (about 11 percent towards the adequately capitalized group, and
about 26 percent towards the well capitalized group) or deteriorate their status with a
probability of about 22 percent (about 17 percent to the signi?cantly undercapitalized
category, and about 5 percent to the critically undercapitalized category).
These ?ndings suggest that persistence is substantially smaller at low
capitalization categories. Recalling that the speed-of-adjustment is negatively related
to persistence, we then have prima facie evidence for a higher speed-of-adjustment in
lower capitalization categories. Of course, these are only tentative observations that
may or may not be veri?ed in a formal conditional model.
5.2 Estimation results from the generalized dynamic random effects ordered probit
model
As a prelude we report in Table IV the estimation results from the constrained
dynamic random effects ordered probit[4]. We document signi?cant and large
persistence, which implies that banks on average cover 50 percent of the distance from
their latent desired capitalization in about 1.9 years. Size, risk and asset quality tend to
decrease capitalization, while pro?tability and market discipline to increase it. Initial
conditions also emerge as a signi?cant determinant of capitalization status.
Baseline Sensitivity
CAP
i,t21
0.743
* * *
(15.94) 0.876
* * *
(18.54)
Size 20.543
* * *
(217.00) 20.659
* * *
(212.94)
Risk 20.006
* * *
(25.90) 20.033
* *
(22.26)
Pro?tability 0.099
* * *
(4.07) 0.029
* * *
(3.14)
Asset quality 20.115
* * *
(215.54) 20.049
* * *
(23.95)
Market discipline 0.004
* *
(2.58) 20.035 (20.54)
CAP
i,0
0.056
* * *
(3.34) 0.084
* * *
(5.79)
Mean(size) 0.614
* * *
(16.36) 0.586
* * *
(11.12)
Mean(risk) 20.013
* * *
(28.02) 0.075
* * *
(2.90)
Mean(pro?tability) 0.061
* *
(2.05) 0.093
* * *
(6.72)
Mean(asset quality) 20.117
* * *
(29.09) 20.089
* * *
(23.07)
Mean(market discipline) 20.003 (21.36) 0.136 (1.52)
Mean(state real per capita GDP) 20.225
* *
(22.01) 20.085 (20.84)
Cut_1 24.054
* * *
(23.27) 21.258 (21.13)
Cut_2 23.358
* * *
(22.72) 20.652 (20.59)
Cut_3 22.935
* *
(22.38) 20.301 (20.27)
Cut_4 22.233
*
(21.81) 0.307 (0.28)
Diagnostics
Log-likelihood 25,571.20 26,219.60
Likelihood ratio test 2,391.81 1,095.01
Observations 67,728 67,728
Notes: Statistical signi?cance at:
*
10,
* *
5 and
* * *
1 percent levels; numbers in brackets denote
z-scores; mean() stands for a given covariate’s time series mean calculated for each cross-sectional unit
(bank); denotes the signi?cance test of the estimated model against the constant alternative; denotes
the estimated threshold points
Table IV.
Dynamic random effects
ordered probit
(constrained
model-parallel lines
imposed)
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In Table V we report the estimation results from the generalized dynamic random
effects ordered probit model. Let us start with the parallel lines assumption tests
for each covariate. The null that a given covariate exerts an identical effect across
all categories was not rejected in six cases (for pro?tability and its time series mean;
for risk; for market discipline and its time series mean, and for the time series mean
of size), while for all other cases there were emphatic rejections. These ?ndings suggest
that there is suf?cient evidence for differential impacts of covariates across
capitalization groups. Also note that after the imposition of the constraints, the overall
parallel lines test is not rejected, indicating that the choice of a generalized model is
statistically appropriate.
Before we turn our attention to the speed-of-adjustment coef?cients it would be
fruitful to discuss the ?ndings regarding the control variables. Initial conditions seemto
play an important role in determining capitalization status across all categories. In
particular, banks with higher initial capitalization tend to continue to have higher
capitalization status, but this effect is monotonically decreasing across capitalization
categories. Size is found to exert a negative impact on capitalization across all groups,
?nding which is in line with previous ?ndings that analyzed CARwho report that larger
banks tend to hold lower capital ratios. Also in line with the literature, we encounter a
negative impact of risk on capitalization, which as mentioned earlier is found as having a
uniform effect across all capitalization categories. Similarly pro?tability has an equal
effect across all groups, and the direction of impact is positive as has been reported in
past studies. The asset quality proxy is signi?cant and carries a negative coef?cient,
which suggests that lower asset quality tends to decrease capitalization. This ?nding in
conjunction with the negative effect of risk provide evidence in favor of a moral hazard
phenomenon, since one would expect institutions with worse asset quality and higher
risk to hold, ceteris paribus, more capital. Another interesting ?nding is the positive
and signi?cant effect of market discipline, which implies that there is a systematic
disciplinary process imposed on banks’ capitalization choices. Finally. the majority of
longitudinal means of covariates are signi?cant suggesting that serve their purpose of
capturing a portion of the unobserved heterogeneity.
Moving now to the parameters of main interest we see that the lagged capitalization
status enters with a signi?cantly positive coef?cient in all categories. What is important
is that the relevant coef?cients increase for higher capitalization groups. Recall that the
estimated coef?cients’ distance from unity is a measure for the speed-of-adjustment.
Hence, there is evidence that the speed-of-adjustment differs across groups, and in fact is
higher for lower capitalization categories. Essentially, if we transform the estimated
coef?cients into time periods needed to cover 50 percent of the distance from the latent
desired capitalization we ?nd the following. critically undercapitalized banks cover this
distance in about 0.7 years, signi?cantly undercapitalized banks in about 1.4 years,
undercapitalized banks in about 1.6 years, while adequately capitalized banks need
about 2.5 years to clear the same distance. Thus, we uncover evidence infavor of a higher
speed-of-adjustment for lower capitalization banks. This is consistent both with a
systematic effect of the prompt correction action as well as with a banks’ self-correcting
(capitalization) mechanism behavior.
The sensitivity analysis provides qualitatively similar conclusions. Again, the lowest
capitalization group is estimated as having the highest speed-of-adjustment, parameter
which decreases as we move to higher capitalization categories. The estimated time
US banks’
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Baseline Sensitivity
Critically undercapitalized category; CAP
i,t
¼ 0
CAP
i,t21
0.276
* *
(2.15) 0.458
* *
(3.53)
Size 20.636
* * *
(29.13) 20.094 (20.37)
Risk 20.006
* * *
(25.73) 0.001 (0.02)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.057
* * *
(22.75) 20.049
* * *
(23.85)
Market discipline 0.004
* *
(2.57) 20.435
* * *
(23.14)
CAP
i,0
0.192
* * *
(3.53) 0.026 (0.49)
Mean(size) 0.611
* * *
(16.23) 20.061 (20.23)
Mean(risk) 0.015
* * *
(2.98) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.177
* * *
(3.69)
Mean(asset quality) 20.161
* * *
(23.78) 20.275
*
(21.92)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 1.037
*
(1.89) 20.093 (20.92)
Intercept 29.369 (21.56) 3.451
* * *
(2.74)
Signi?cantly undercapitalized category; CAP
i,t
¼ 1
CAP
i,t21
0.653
* * *
(8.50) 0.725
* * *
(10.00)
Size 20.678
* * *
(215.84) 20.847
* * *
(27.38)
Risk 20.006
* * *
(25.73) 20.127
* * *
(24.00)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.118
* * *
(28.85) 20.049
* * *
(23.85)
Market discipline 0.004
* * *
(2.57) 20.139 (21.31)
CAP
i,0
0.138
* * *
(4.07) 0.036 (1.19)
Mean(size) 0.611
* * *
(16.23) 0.688
* * *
(5.82)
Mean(risk) 20.001 (20.35) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.177
* * *
(7.03)
Mean(asset quality) 20.201
* * *
(26.94) 20.259
* * *
(23.41)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 20.641
* * *
(22.75) 20.093 (20.92)
Intercept 8.755
* * *
(3.41) 2.160
*
(1.89)
Undercapitalized category; CAP
i,t
¼ 2
CAP
i,t21
0.696
* * *
(10.68) 0.763
* * *
(12.34)
Size 20.624
* * *
(217.47) 20.922
* * *
(212.28)
Risk 20.006
* * *
(25.73) 20.158
* * *
(26.70)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.148
* * *
(215.43) 20.049
* * *
(23.85)
Market discipline 0.004
* *
(2.57) 20.011 (20.14)
CAP
i,0
0.062
* *
(2.41) 0.038
*
(1.84)
Mean(size) 0.611
* * *
(16.23) 0.807
* * *
(10.37)
Mean(risk) 20.009
* * *
(24.02) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.130
* * *
(7.37)
Mean(asset quality) 20.153
* * *
(27.36) 20.177
* * *
(24.06)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 20.641
* * *
(23.27) 20.093 (20.92)
Intercept 8.422
* * *
(3.97) 1.458 (1.30)
Adequately capitalized category; CAP
i,t
¼ 3
CAP
i,t21
0.803
* * *
(16.38) 0.936
* * *
(19.02)
Size 20.531
* * *
(216.61) 20.639
* * *
(212.37)
Risk 20.006
* * *
(25.73) 20.016 (20.87)
Pro?tability 0.100
* * *
(4.09) 0.027
* * *
(2.83)
Asset quality 20.113
* * *
(214.47) 20.049
* * *
(23.85)
(continued)
Table V.
Generalized dynamic
random effects ordered
probit
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needed for banks belonging in the critically undercapitalized group to cover 50 percent
of the distance from the latent target is about 0.9 years. For the signi?cantly
undercapitalized banks is about 1.8 years, undercapitalized banks is about 2.08 years.
For these groups the estimates between the baseline and the sensitivity models are quite
close. However, the sensitivity model for adequately capitalized banks implies that they
need about seven years to clear the same distance, which substantially higher than the
2.5 years estimated from the baseline model.
6. Conclusions
Based on all FDIC-insured banks during the period 2002-2009 we estimated the
capitalization speed-of-adjustment across different FDIC capitalization buckets, using a
generalizeddynamic randomeffects orderedprobit model. The reduced-formspeci?cation
was based on a partial adjustment model, controlling for all standard capitalization
determinants, initial conditions and unobserved cross-sectional heterogeneity. An
attractive feature of the estimation technique is that it allows to test for differential effects
Baseline Sensitivity
Market discipline 0.004
* *
(2.57) 0.021 (0.29)
CAP
i,0
0.050
* * *
(2.93) 0.087
* * *
(5.97)
Mean(size) 0.611
* * *
(16.23) 0.569
* * *
(10.66)
Mean(risk) 20.014
* * *
(28.52) 0.065
* *
(2.35)
Mean(pro?tability) 0.059
* *
(1.98) 0.091
* * *
(6.44)
Mean(asset quality) 20.112
* * *
(28.51) 20.086
* * *
(22.91)
Mean(market discipline) 20.003 (21.36) 0.084 (0.94)
Mean(state real per capita GDP) 20.196
*
(21.73) 20.093 (20.92)
Intercept 1.652 (1.33) 20.501 (20.45)
Diagnostics
Parallel lines assumption tests by covariate (p-value)
CAP
i,t21
0.00 0.00
Size 0.00 0.00
Risk 0.16 0.00
Pro?tability 0.55 0.93
Asset quality 0.00 0.30
Market discipline 0.05 0.00
CAP
i,0
0.00 0.03
Mean(size) 0.06 0.00
Mean(risk) 0.00 0.75
Mean(pro?tability) 0.38 0.00
Mean(asset quality) 0.00 0.01
Mean(market discipline) 0.39 0.33
Mean(state real per capita GDP) 0.00 0.07
Overall parallel lines assumption test ( p-value) 0.08 0.37
Log-likelihood 25,471.61 26,112.10
Wald test 2,213.79
* * *
1,651.43
Observations 67,728 67,728
Notes: Statistical signi?cance at:
*
10,
* *
5 and
* * *
1 percent levels; numbers in brackets denote
z-scores; mean() stands for a given covariate’s time series mean calculated for each cross-sectional unit
(bank); the null hypothesis is that the slope parameter of each covariate is equal across categories;
overall test that slope parameters are equal across categories; denotes the overall signi?cance test Table V.
US banks’
capitalization
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of covariates across capitalization categories. According to our ?ndings there is suf?cient
evidence supporting a higher speed-of-adjustment for lower capitalization banks, ?nding
which can be attributed to FDIC’s prompt corrective action and/or banks’ self-correcting
behavior. This an important ?nding both for regulators and market participants since it
sheds light on a very crucial aspect of banks’ behavior. In addition, we ?nd effects similar
to those reported in the previous literature regarding the standard capitalization
determinants. However, for several of themwe conclude that theyexert impacts of unequal
magnitude across capitalization categories.
Future research could explore further issues such as what is the effect of banks’
loan, asset and liabilities composition on the speed-of-adjustment. In addition, potential
fruitful extensions may also explore bank ownership and competition effects.
Notes
1. Of course the likelihood of failure is not uniquely determined by a bank’s capitalization.
However, ceteris paribus, a bank’s ability to avoid failure is an increasing function of its
capitalization (Estrella et al., 2000).
2. These thresholds were initially introduced in the Federal Deposit Insurance Corporation
Improvement Act of December 1991, which determines what supervisory actions would be
taken by bank regulators.
3. For instance capital ratios can be increased either by increasing capital and/or by reducing
risk-weighted assets. Raising new capital is costly, especially for troubled banks with capital
ratios below the regulatory threshold. Moreover, reduction of risk-weighted assets is bound
to be constrained by the amount of assets maturing in the current period and the capital
losses that might be produced by disposing assets prior to their maturity (Berger et al., 2008).
4. Note that all time-varying covariates will enter the model with a one period lag to avoid
potential simultaneity.
References
Alfon, I., Argimon, I. and Bascunana-Ambros, P. (2004), “What determines how much capital is
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About the author
Dr Konstantinos Drakos holds a PhD in Economics from the University of Essex (UK). Currently
he is Assistant Professor of Finance at the Department of Accounting and Finance (Athens
University of Economics and Business). Previously he held appointments at the University of
Patras (Greece) and the University of Essex (UK). Dr Konstantinos Drakos can be contacted at:
[email protected]
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