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Federal Reserve Bank of Chicago
BankCaR (Bank Capital-at-Risk):
A credit risk model for
US commercial bank charge-offs
Jon Frye and Eduard Pelz
WP 2008-03
BankCaR (Bank Capital-at-Risk):
A credit risk model
for US commercial bank charge-offs
Jon Frye
Senior Economist
Federal Reserve Bank of Chicago
230 South LaSalle Street
Chicago, IL 60604
Jon.Frye@chi.frb.org
312-322-5035
Eduard Pelz
Senior Supervision Analyst
Federal Reserve Bank of Chicago
230 South LaSalle Street
Chicago, IL 60604
Eduard.Pelz@chi.frb.org
312-322-6018
April 22, 2008
The authors are indebted to numerous individuals at the Federal Reserve who have
given contributions and insightful comments. These include members of the Research
and Bank Supervision Departments of the Federal Reserve Banks of Chicago,
Richmond, and Dallas, and the Federal Reserve Board of Governors. The views
expressed are the authors' and do not necessarily represent the views of the
management of the Federal Reserve Bank of Chicago or the Federal Reserve System.
BankCaR (Bank Capital-at-Risk):
A credit risk model for US commercial bank charge-offs
Abstract
BankCaR is a credit risk model that forecasts the distribution of a commercial
bank's charge-offs. The distribution depends only on systematic factors;
BankCaR takes each bank and projects its expected charge-off across a
distribution of good years and bad years. Since most bank failures occur in bad
years, this analysis has promise for both banks and bank supervisors.
In BankCaR, charge-offs depend on the bank's loan balances and the charge-off
rates of twelve categories of lending. A joint distribution of the twelve charge-off
rates is calibrated to a long history of regulatory reporting data. Applied to the US
banking system, BankCaR finds that credit risk is rising and is concentrated most
significantly in construction lending. Applied to individual banks, BankCaR
efficiently identifies those that have an adverse combination of credit risk and
capital.
BankCaR uses publicly available regulatory reporting data, the most common
credit portfolio model, and standard quantitative techniques. These generic
qualities can provide a standard of comparison between banks. They also can
provide an individual commercial bank with a benchmark for more elaborate
vended credit models.
Keywords: credit risk, risk screening, loan charge-offs, validation
JEL classification: G32, G21, G38
-2-
Introduction and summary
BankCaR (Bank Capital-at-Risk) is a credit risk model that forecasts the
distribution of charge-offs at commercial banks in the United States. Its goal is to
improve the identification, quantification, and management of inherent bank
credit risk. BankCaR can supplement a bank's internal credit risk model or
benchmark credit risk in the absence of other models.
BankCaR forecasts risks rather than outcomes. Traditionally, the analysis of bank
risk involves a forecast of what is likely to happen to a bank, a sector, or the
macro economy. Instead, BankCaR forecasts what can happen under a broad
range of circumstances. BankCaR's focus on risk represents a departure from
traditional analyses of bank losses.
Applied to the US banking system, BankCaR finds that credit risk is rising, and
that it is concentrated most significantly in construction lending. Applied to
individual banks, BankCaR identifies those that have an adverse combination of
credit risk and capital.
The paper begins with a brief discussion of the data employed. The data are
gathered from regulatory filings that are available on the public record since
1984. These filings do not contain all the information that is available to bank
managers and bank examiners. Where detailed information is not available,
BankCaR assumes uniformity between banks and over time.
An overview describes the model in general terms. BankCaR extends the model
employed in Basel II to include twelve risk factors corresponding to twelve
categories of lending. The probability distribution of a bank's annual charge-off
depends on the bank's twelve loan balances and on the statistical distribution of
the twelve charge-off rates. The assumptions are discussed in detail. Most of the
assumptions arise from the nature of the data in the regulatory filings. Following
the overview, the mathematics of the model and its calibration are presented.
Two sections report results at year-end 2006. First, BankCaR is applied to the
aggregated US banking system. The greatest potential for loss stems from three
categories: consumer, commercial and industrial (C&I), and construction.
Construction becomes increasingly likely to dominate at greater levels of overall
loss. This result departs from historical data, in which construction charge-offs
have never played the dominant role. Thus, BankCaR predicts that a year with
unusually high charge-offs will have an unusual primary source, namely, chargeoffs on construction loans.
Next, BankCaR is applied separately to each US commercial bank. The majority
of banks, if exposed to stressful conditions, charge off more construction loans
than any other category. Scenarios those that cause banks to become
undercapitalized tend to produce high levels of construction charge-offs.
-3-
BankCaR efficiently identifies banks that have an adverse combination of credit
risk and capital.
Bank loans and charge-offs
BankCaR begins its analysis with the outstanding loan balances in twelve
categories. The categories appear in Table 1.
Table 1. Loan categories and Call Report data elements
Call Report data elements
Commercial and industrial loans
Credit cards
Other revolving credit plans
Other consumer loans (includes single payment, installment, and all student loans)
Other
Other loans
Loans to foreign governments and official institutions (including foreign central banks)
Obligations (other than securities and leases of states and political subdivisions in the US)
Depository Institutions
Loans to depository institutions and acceptances of other banks
To commercial banks in the US
To other depository institutions in the US
To banks in foreign countries
Lease Financing
Lease financing receivables (net of unearned income)
Agriculture
Loans to finance agricultural production and other loans to farmers
Construction
Construction, land development, and other land loans
Non-farm non-residential Secured by nonfarm nonresidential properties
Multifamily
Secured by multifamily (5 or more) residential properties
Farm
Secured by farmland (including farm residential and other improvements)
1-4 Revolving
Revolving, open-end loans secured by 1–4 family residential properties and extended under lines of credit
1-4 Other
Closed-end loans secured by 1–4 family residential properties
Tier 1
Tier 1 Capital
ALLL
Allowance for Loan and Lease Losses
Total Assets
Total Assets
Loans are taken from Schedule RC-C Loans and Lease Financing Receivables , charge-offs from RI-B Charge-offs and Recoveries on
Loans and Leases and Changes in Allowance for Loan and Lease Losses , Tier 1 capital from RC-R Regulatory Capital and total assets
and ALLL from RC Balance Sheet . See http://www.chicagofed.org/economic_research_and_data/commercial_bank_data.cfm.
Category
C&I
Consumer
The data source is the Consolidated Reports of Condition and Income, generally
referred to as the call reports. Call reports are an authoritative source of both the
current loan balances for a bank and the historical charge-off rates for the
banking system. Banks are required by law to make timely and accurate call
report filings, and bank examiners verify that the filings reflect a bank's accounts.
Call report data are available to the public and useful beginning 1984—a period
significantly longer than most other credit loss data sets.
As shown in Table 1, some categories are combinations of several call report data
elements. Over time data elements have evolved, usually to provide greater detail.
This is most notably the case for the six real estate categories that became
separately available only beginning in 1991. 1
BankCaR uses the category data in two distinct ways: a bank's outstanding dollar
balances are the amounts subject to charge-off, and historical US aggregate
annual gross charge-off rates are used to calibrate the probability model. The
Real estate consists of four commercial real estate categories (construction, farm, multifamily,
and nonfarm nonresidential) and two residential categories (one-to-four-family revolving
residential and one-to-four-family other residential).
1
-4-
combination of a bank's current loans and the distribution of charge-off rates
produce assessments of bank risk.
Figure 1. Total bank loans outstanding with proportions
6
100%
C&I
Con su m er
5
80%
Ot h er
Deposi t or y In st .
60%
4
40%
3
Lea se Fi n a n cin g
A gr i cu l t u r e
Rea l Est a t e
T otal Loans,
$T rillions,
right scale
20%
Con st r u ct i on
NFNR
Mu l t i fa m i l y
2
Fa r m
1-4 Rev ol v i n g Res.
1
0%
1984
1988
1992
1996
2000
1-4 Ot h er Res.
2004
Figure 1 presents the recent history of outstanding loan balances for all US
commercial banks. Loans grow 6.9% per year on average over the sample period.
Also shown is the decomposition of loans into the twelve categories. Over the
sample period, the proportion devoted to C&I declines by about half while
proportion devoted to real estate approximately doubles.
Figure 2. Selected aggregate charge-off rates
Aggregate charge-off rate
4%
Con su m er
Con st r u ct i on
3%
C&I
2%
Non -fa r m n on - r esi den t i a l
1%
1-4 Ot h er r esi den t i a l
0%
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Figure 2 shows annual aggregate gross charge-off rates for US commercial banks
in five selected categories. Several characteristics stand out. Different categories
have different means, ranging from 0.15% (one-to-four-family other residential)
to 2.68% (consumer). Dispersion around these means also differ from category to
category. Further, the timing of cycles of different categories is not well
synchronized, for example, the 2001 recession has little or no effect on real estate
charge-offs; consumer lending has cycles of charge-off rates apparently unrelated
to other categories.
-5-
Overview of BankCaR
This section begins with an intuitive motivation for the statistical model
underlying BankCaR. It then describes BankCaR's distinguishing features, which
are correlated factors and charge-off rate scenarios. The section concludes with
definitions of the risk measures produced by BankCaR.
Figures 1 and 2 suggest the features that a statistical model of bank charge-off
rates should possess. The model should analyze at least to the category level,
because the categories have different average charge-off rates and the relative
weights of the categories can change. Categories should be allowed to differ not
only in mean but also in dispersion around the mean. Finally, categories should
be allowed to vary together, but with less than perfect synchrony. A single factor
model (such as employed in Basel II) cannot capture the sometimes contrary
behaviors of charge-off rates in different categories.
The model underlying BankCaR is designed to match these broad features. To
allow for lack of synchrony, BankCaR employs twelve separate, imperfectly
correlated risk factors. Each factor controls a category charge-off rate. To allow
different categories to have different means and different dispersions, each
charge-off distribution is governed by two parameters.
A random draw of twelve possible charge-off rates is referred to as a charge-off
scenario. Applied to a bank, a scenario produces an amount charged off.
BankCaR employs 100,000 scenarios in total. The set of 100,000 possible
charge-off amounts constitute the estimate of the bank's charge-off distribution.
Figure 3. From correlated normal factors to BankCaR scenarios
Charge-off rates
Correlated category factors
4
3
7%
2
6%
1
5%
0
Correlated charge-off rates
8%
4%
8%
7%
(1.2%, 6.6%)
-4
-3
-2
-1
0
1
2
3
Construction charge-off
Construction factor
Construction rate = 6.6%
4
3%
-1
2%
-2
6%
5%
4%
3%
2%
C&I rate = 1.2%
-3
(0.04, -2.35)
-4
C&I factor
1%
1%
0%
0%
-3
-2
-1
0
Category factor
1
2
0%
1%
2%
3%
4%
5%
C&I charge-off
6%
7%
8%
Figure 3 illustrates the production of 1,000 scenarios for two categories, C&I and
construction. BankCaR uses the same procedure to produce 100,000 scenarios
involving all twelve category charge-off rates.
The panel at the left shows 1,000 random draws from a pair of correlated
standard normal factors. They exhibit the degree of correlation calibrated
-6-
between C&I and construction, which is 59%. For illustrative purposes, a point is
chosen and highlighted with factor values of -2.35 (construction) and 0.04 (C&I).
The two curves in the center panel convert these two factors into charge-off rates.
There are of course twelve such curves within BankCaR, and all are calibrated to
the data. The illustrative draw of the construction factor produces the sizable
construction charge-off rate of 6.6%. The near-zero draw of the C&I factor
produces a middling C&I charge-off rate of 1.2%. This pair of simulated chargeoff rates is highlighted in the panel at the right.
The panel at the right shows the 1,000 scenarios that correspond to points in the
panel at the left. According to the right panel, there will many years with nearzero construction charge-off rates and a few years with highly elevated rates; the
charge-off rates for C&I are not forecast at either extreme. These stylized facts
reflect the general patterns apparent in the historical rates shown in Figure 2.
Normally, the mean of each simulated factor is equal to zero, and the mean of
each simulated charge-off rate is equal to the average historical charge-off rate. If
the next year's charge-off rate is expected to differ from the historical average, a
fixed amount can be added to draws of the associated factor. This adjustment
allows for nontrivial forecasting while maintaining other aspects of the statistical
distribution.
When new data become available, the statistical parameters are recalibrated and
new scenarios are generated. The same set of scenarios is used for all analyses
performed in a year. Using the same scenarios for different banks removes a
source of randomness that would otherwise affect comparisons between banks.
BankCaR produces several measures and indicators of risk: a bank's Capital-atRisk (CaR), its characteristic scenario, its risk type, and its stressed capital.
CaR is defined as the 99.5th percentile of a bank's loss. Operationally, this equals
the 500th worst among the 100,000 possible losses, stated as a percent of the
bank's total assets. CaR is the credit portfolio equivalent of Value-at-Risk,
commonly used to the measure the risk of portfolios of traded financial
instruments.
A bank's characteristic scenario portrays the average conditions under which loss
equals CaR. Conceptually, the characteristic scenario is the mathematically
expected scenario that produces loss equal to CaR. Operationally, BankCaR takes
the average among a subset of its scenarios. Scenario losses are sorted and
averages taken of the greatest two losses, the greatest three, and so forth. One of
these averages is closest to CaR. The average of the associated scenarios is the
characteristic scenario. In practice the characteristic scenario is the average of 12% of all scenarios. Thus, the characteristic scenario produces loss equal to CaR
and serves as a portrayal of the average scenario that produces loss at that level.
-7-
Taken together, CaR and the characteristic scenario provide a summary of the
bank's loss distribution. An even simpler summary is provided by CaR and risk
type. A bank's risk type is the category that contributes the bank's greatest
charge-off when the characteristic scenario is active. A given bank's risk type is
not the whole story since two or more categories might contribute nearly equally
to loss, but risk type can nonetheless be a useful summary.
BankCaR compares a bank's CaR to its financial resources. Specifically, stressed
capital is defined as equal to tier 1 capital plus allowances for loan and lease
losses (ALLL) less CaR. 2 Presumably, a bank having greater stressed capital
would be better able to survive a year of high credit loss. Finally, BankCaR
assigns a degree of inherent credit risk (High, Above Average, Average, or Low)
based on the bank's stressed capital compared to other banks.
Assumptions and limitations
Like all statistical models, BankCaR makes numerous assumptions. The most
important assumption is that every bank is vulnerable to the system-wide chargeoff scenario, irrespective of the bank's location, size, or other characteristics.
Although this assumption excludes some sources of bank risk, it facilitates a
direct comparison between different institutions. Naturally, nothing reported by
BankCaR can supplant detailed knowledge of an institution, its history, and its
competitive environment.
Some assumptions follow from the nature of call report data. Call report category
data are not distinguished by risk; therefore, BankCaR assumes that all loans
within a category are uniform in obligor quality, outstanding amount, and
potential for recovery. Call reports reflect only category-level outstanding loan
balances. BankCaR does not model gains or losses from investment accounts or
from contingent exposures such as loan commitments and off-balance sheet
derivatives. Call reports do not contain estimates of the marked-to-market values
of loan portfolios; BankCaR is calibrated only to amounts actually charged off.
Parameter values are assumed to be constant over time, as would be the case if
underwriting standards were unchanged. In calibrating parameters, two choices
are believed to have minor effects. The gross charge-off rate is used, in part
because net charge-offs can be negative for technical reasons. The annual time
step is used, in part because unobserved category factors are autocorrelated at the
quarterly time step.
BankCaR does not quantify many variables that are important to overall bank
risk, such as liquidity, control structures, technical and managerial quality, offbalance sheet exposures, hedging activities, and so forth. In particular, BankCaR
Not all of ALLL might be available to absorb charge-offs, because some provisions in ALLL are
associated with specific loans that might not default. The distinction between specific provisions
(FAS-5) and general provisions (FAS-114) cannot be observed in call report data.
2
-8-
is not a capital model. Banks hold capital to cover not only credit losses but also
to cover market losses, operational losses, and other losses. BankCaR is not
designed to arrive at an appropriate level of capital for a given bank or for the
banking system.
Probability model
This section describes the technical details of BankCaR's probability model. The
bulk of the section describes the marginal distribution of the charge-off rate
within a category. Once the marginal distributions are in place, they are readily
connected to each other.
The underlying model is the structural credit portfolio model based on the
insights of Robert Merton. The model produces the probability distribution of
loss, relative to the return of par, resulting from default. It is commonly used to
measure portfolio credit risk at banks. Recently, the model gained prominence as
the basis for the Basel II minimum capital requirement.
Merton's model produces the distribution of the default rate. In addition, loss
depends on the distribution of dollar exposure amounts and on the distribution
of loss given default (LGD), which is the fraction of par that is lost on a defaulted
instrument. BankCaR assumes that loan amounts are small enough that no single
loan can have an appreciable effect on a charge-off rate. The role of LGD is
developed later.
We begin with a particular loan made to a firm. The model assumes that when
the loan matures there is a comparison between the firm's assets and liabilities.
In the case of a surplus, the firm can refinance or find other ways to make
payment. In the case of a shortfall, the firm defaults.
The model assumes that the value of the firm's liabilities is known and that the
return on the firm's assets has a normal distribution. Standardizing the asset
return has no effect on the idea that default occurs if and only if asset return is
less than some fixed threshold. Symbolizing the standardized asset return as αi:
(1)
Firm i defaults if and only if α i < α i *, where α i ~ N[0,1]
The probability that Firm i defaults is designated PDi. Therefore, PDi = Φ(αi*),
where Φ(·) represents the standard normal cumulative distribution function
(CDF). Using the inverse CDF, αi* = Φ-1(PDi). In practice, PD refers to a fixed
interval of time. In BankCaR, the period is one year, which is equal to the forecast
horizon.
The asset returns of firms in the same category are assumed to be jointly normal.
As such, they can be represented by a factor model. BankCaR assumes that there
-9-
is a single systematic factor affecting the asset returns of all firms in the
category. 3 Each firm's asset return is also affected by an independent
idiosyncratic factor that is normally distributed. When the systematic and
idiosyncratic factors are standardized, a single parameter, ρi, decomposes αi into
sources of risk:
(2)
α i = ρ i Z + 1 − ρ i X i ; Z , X i ~ i . i . d . N [0,1]
Z is the average standardized asset return of firms in the category and is referred
to as the category factor. If Z takes a positive value, asset returns tend to be above
average. Because Xi is independent of other information, there is no opportunity
for Firm i to be affected by other firms that might share its industry, region, or
other characteristic.
BankCaR assumes that all firms in the category are statistically identical. Thus,
the parameters PD and ρ are uniform within the category. This implies that the
correlation between the asset returns of two firms in a category is equal to ρ:
Corr [α i , α h ] = Corr [ ρ Z + 1 − ρ X i , ρ Z + 1 − ρ X h ] = ρ
Because of this, the parameter ρ in structural models is often referred to as "asset
return correlation," and estimates of correlation based on asset returns are often
employed in credit models. This puts great faith in the validity of the model's
stylized assumptions. By contrast, BankCaR calibrates all parameters, including
its correlations, to call report data. To reinforce this distinction, we refer to
parameter ρ as "category correlation." Other things equal, a category with greater
correlation would exhibit greater dispersion of the default rate.
(3)
The centerpiece of the model is the conditional probability that Firm i defaults.
Supposing that the systematic factor Z takes the value z, the default of Firm i
depends completely on the realization of its idiosyncratic factor Xi. This insight
leads to an expression for the conditionally expected default rate that was first
provided by Oldrich Vasicek:
P [α i < α i * | Z = z ] = P [ ρ z + 1 − ρ X i < Φ −1 (PD )]
(4)
⎡Φ −1 (PD ) − ρ z ⎤
⎡
Φ −1 (PD ) − ρ z ⎤
=Φ⎢
= P ⎢X i <
⎥
⎥
1− ρ
1− ρ
⎢
⎥
⎢
⎥
⎣
⎦
⎣
⎦
Expression (4) states the conditionally expected default rate for a firm. In an
asymptotic portfolio, it is also the default rate for the category. If z is greater than
zero the default rate is less than PD, while if z is somewhat less than zero the
default rate is greater than PD.
In the terminology introduced by Michael Gordy, within a category BankCaR is an asymptotic
single risk factor model.
3
- 10 -
Allowing the subscript to distinguish categories and λ to represent the default
rate, λj is an invertible function of the category factor:
⎡Φ −1 (PD j ) − ρ j Z j ⎤
⎥;
λj = Φ ⎢
1− ρ j
⎢
⎥
⎣
⎦
(5)
Zj =
(6)
Z j ~ N[0,1]
Φ −1 (PD j ) − 1 − ρ j Φ −1 (λ j )
ρj
= z j (λ j )
The change-of-variable technique then provides the density of the category
default rate:
⎛ Φ −1 (PD j ) − 1 − ρ j Φ −1 (λ j ) ⎞
⎟
φ⎜
⎜
⎟
ρj
1− ρ j ⎝
d z j (λ j )
⎠
φ (z j (λ j )) =
f (λ j ) =
−1
d λj
φ (Φ (λ j ))
ρj
(7)
where φ(·) represents the standard normal probability density function (PDF).
Figure 4.
Conditionally expected default rates
Figure 5.
Distributions of default rates
5%
150
4%
120
Rate
3%
Density
PD = 0.75%
ρ = 22.2%
2%
PD = 0.74%
ρ = 2.9%
1%
90
PD = 0.74%
ρ = 2.9%
60
30
0%
PD = 0.75%
ρ = 22.2%
0
-3
-2
-1
0
1
Realization of Z
2
3
0%
1%
2%
3%
Default rate
4%
5%
Figures 4 and 5 illustrate these functions for cases of high correlation (PD =
0.75%, ρ = 22.2%) and low correlation (PD = 0.74%, ρ = 2.9%). 4 Figure 4 shows
that the two distributions are equally likely to produce default rates greater than
about 1.0%. Figure 5 shows that the high-correlation distribution is much more
likely to produce high rates of default. It should be apparent that this family of
distributions can produce a large range of shapes, including highly skewed
distributions.
To complete the specification of the probability model, BankCaR assumes that
the standard normal category factors are jointly normal. Any pair of category
4
These values reflect the estimates for construction and for lease financing, respectively.
- 11 -
factors is therefore connected by a factor correlation. Symbolizing the 12x12
matrix of factor correlations, Σ = [[ρij]], the joint PDF of the twelve default rates
is given by change-of-variable:
12
(8)
f (λ1 , λ 2 , ... , λ12 ) = φ12 (z 1 (λ1 ), z 2 (λ 2 ), ... , z 12 (λ12 ), Σ ) ∏
j =1
1− ρ j
ρ j φ (Φ −1 (λ j ))
where φ12(·, Σ) is the twelve-variable standard normal PDF with correlation
matrix equal to Σ. The resulting connection between the marginal charge-off rate
distributions is sometimes referred to as the Gauss copula.
Calibration
This section describes how BankCaR's parameters are calibrated to values that
best reflect historical charge-off rates, according to the principle of maximum
likelihood. The current values of the parameters appear in Table 2.
Four issues arise when calibration takes place. The first issue is that the theory
presented in the previous section derives a distribution of the default rate. A
default rate would be generally greater than a charge-off rate, because a bank
does not lose 100% of the balance of every loan in every case. Call reports do not
contain separate default rates and LGD rates. Lacking the data, BankCaR makes
an identifying assumption to bridge the gap.
A naïve identifying assumption would be to assume that in any year the LGD rate
equals the same fixed value. If this were 25%, a sequence of charge-off rates
{CR1, CR2, …, CRT} would imply a sequence of default rates {CR1/0.25,
CR2/0.25, …, CRT/0.25}. The distribution of the default rate would be calibrated
to these data, and the loss rate would equal one-quarter the default rate.
The naïve approach assumes that LGD does not vary with conditions, but the
opposite has become widely accepted. The Basel II capital requirement, for
example, recognizes that LGD can be greater in downturn conditions than in
average conditions. If LGD rises at the same time as the default rate, there is
more risk than if only the default rate rises in a downturn. For this reason, the
naïve approach understates risk.
Instead of the naïve approach, BankCaR assumes that the risk of a loan depends
on its expected loss and not on the decomposition of expected loss into PD and
expected LGD. In particular, BankCaR assumes that risk would be unaffected if
the unknown value of expected LGD were equal to 100%. This allows BankCaR to
apply the theory of the default rate directly to the data on charge-off rates.
Though for calibration purposes BankCaR assumes that LGD = 100%, there is no
inference regarding the values of expected LGD and PD, which remain unknown.
Implicitly, the annual average LGD varies in step with the default rate.
- 12 -
The second issue involves the maximization of the likelihood function. Many
likelihood functions must be maximized in all parameters simultaneously;
however, a two-stage approach finds the same results given the nature of the
BankCaR likelihood function. In the first stage, BankCaR analyzes each of the
twelve categories in turn. In a category j, the observed charge-off rate in year t is
CRj,t, and its unconditional expectation is ECRj. BankCaR assumes
independence between years and maximizes the likelihood function derived from
Expression (7):
(9) ln L(ECR j , ρ j ; {CR j ,t }) =
∏
t
1− ρ j
ρ
j
⎛ Φ −1 (ECR j ) − 1 − ρ j Φ −1 (CR j ,t ) ⎞
⎟
φ⎜
⎜
⎟
ρj
⎝
⎠
−1
φ (Φ (CR j ,t ))
This provides maximum likelihood estimates of ECRj and ρj. These in turn imply
estimates of zj,t according to Expression (6). In the second stage, all twelve
ˆ ˆ
ˆ
sequences { z 1,t , z 2 ,t ,..., z 12 ,t } are in hand, and correlations between them can be
calculated as usual to produce maximum likelihood estimates of the factor
correlations.
This two-stage approach produces exactly the same result as maximizing the joint
likelihood function simultaneously in all ninety parameters. In the first stage, the
parameters of categories are distinct. The parameters ECR1 and ρ1 do not appear
in the marginal distributions of CR2, CR3, …, or CR12. Therefore, those data tell
nothing about the values of ECR1 and ρ1; the maximum likelihood estimates of
ECR1 and ρ1 are the same whether they are obtained from the marginal
likelihoods or from the joint likelihood. Since the same is true of every category,
working category-by-category provides the same estimates of ECR and ρ as
would be found using simultaneous estimation.
In the second state, when the category-by-category estimates of ECRj, and ρj are
substituted into Expression (8), the only remaining unknowns appear in the
correlation matrix Σ:
12
ˆ
ˆ
ˆ
(10) ln L = ∏ φ12 (z1 (CR1,t ), z 2 (CR2 ,t ), ... , z12 (CR12 ,t ), Σ ) ∏
ˆ
1− ρ j
ˆ
ρ j φ (Φ −1 (CR j ,t ))
The maximum value of Expression (10) would therefore occur at the maximum
likelihood estimates of the correlations between the set of inferred category
ˆ
ˆ
ˆ
factors { z1 (CR1,t ), z 2 (CR 2 ,t ), ... , z12 (CR12 ,t )} . These are exactly the correlations
that BankCaR produces in the second stage of the calibration.
j =1
t
Thus, the special nature of BankCaR's likelihood function—the lockstep relation
between CR's and Z's, mediated by distinct PD's and ρ's—allows a two-step
- 13 -
procedure to produce the same estimates as would be found using simultaneous
estimation. In practice, the two-step procedure is superior because
multidimensional routines can converge to points along constraints rather than
to the interior global maximum found using the two-stage approach.
The third issue is that BankCaR departs from a common credit modeling practice
that takes literally the role of asset correlation. In that practice, estimates of
correlation based on asset return data are substituted into the credit risk model.
The distributions that result only partly reflect credit loss data. In part, they also
reflect the data used to calibrate asset return correlation. By contrast, the
parameters of BankCaR reflect only the historical charge-off rates that have
actually been experienced.
The fourth issue is that the charge-off series for the six real estate categories are
not available prior to 1991. To handle this missing data, BankCaR employs a
maximum likelihood technique provided by Donald Morrison. To improve the
statistical fit in the 1984-1990 sub-period, BankCaR employs a 13x13 matrix of
factor correlations that includes a factor for total real estate, for which charge-off
rates are available for all years. Once the factor correlation estimates are in hand,
no further use is made of the total real estate series.
Table 2. BankCaR parameter estimates and conditionally expected charge-off rates
Res.
R.E.
Comm.
R. E.
Not Real Estate
Category ECR j
C&I
Consumer
Other Lending
Depository Institutions
Lease Financing
Agriculture
Construction
Non-farm non-residential
Multifamily
Farm
1-4 Revolving
1-4 Other
1.44%
2.68%
1.23%
0.62%
0.74%
1.00%
0.75%
0.40%
0.37%
0.14%
0.20%
0.15%
ρj
CCR j
4.2%
2.3%
12.6%
26.8%
2.9%
10.8%
22.2%
10.6%
15.5%
2.3%
0.7%
1.3%
4.5%
6.0%
7.7%
8.7%
2.1%
5.9%
8.3%
2.7%
3.5%
0.4%
0.4%
0.4%
Factor correlations, ρ ij
-32%
-32%
46% -16%
60% -45%
83%
-8%
66% -76%
59% -57%
57% -61%
29% -21%
56%
-3%
-10%
1%
84% -63%
46% 60% 83% 66%
-16% -45%
-8% -76%
79% 32%
6%
79%
39% 48%
32% 39%
44%
6% 48% 44%
60% 65% 34% 50%
51% 63% 32% 56%
72% 58%
9%
6%
66% 51% 35%
11%
-6% -19% -40% -20%
25% 45% 60% 79%
59%
-57%
60%
65%
34%
50%
99%
85%
80%
13%
70%
57%
-61%
51%
63%
32%
56%
99%
81%
76%
10%
72%
29%
-21%
72%
58%
9%
6%
85%
81%
88%
17%
28%
56% -10% 84%
-3%
1% -63%
66%
-6% 25%
51% -19% 45%
35% -40% 60%
11% -20% 79%
80% 13% 70%
76% 10% 72%
88%
17% 28%
23% 47%
23%
10%
47% 10%
Table 2 shows the BankCaR parameter estimates for 2007, using data through
year-end 2006. Table 2 also shows the conditional charge-off rate (CCRj) for
each category. The CCR of a category is defined as the 99.5th percentile of the
category charge-off rate. It comes about when the category factor is at its 0.5th
percentile:
(11)
⎡Φ −1 (ECR j ) − ρ j Φ −1 (0.005) ⎤
⎥
CCR j = Φ ⎢
1− ρ j
⎢
⎥
⎣
⎦
Among the factor correlations appearing in Table 2, most are positive, consistent
with the commonplace observation that the economic cycle tends to affect most
firms irrespective of category. The four commercial real estate factors are
especially strongly related.
- 14 -
As we have seen, the identifying LGD assumption made by BankCaR infers
greater risk than the naïve approach assuming a fixed value of LGD. The
quantitative difference is not always great. Using the naïve approach with LGD
assumed equal to 30%, the difference is less than 10% of CCR for ten of the
twelve categories, and it is less than 20% of CCR in the remaining two categories.
Thus, the effect of LGD variation in BankCaR is not extreme.
Confidence regions can be derived from the asymptotic likelihood ratio, which
approaches the χ2 distribution as the number of years rises. Taking separately
each category, the following statistic has the χ22 distribution:
(12)
⎡ LnL (ECR j = ecr j , ρ j = rho j ) ⎤
2
− 2 Log ⎢
⎥ ~ χ2
Max LnL (ECR j , ρ j )
⎢
⎥
⎣
⎦
Figure 6. Parameter estimates, 95% confidence regions, and
level curves of CCR at 1% , 5% , 10% , 20% , 30% , 40%
50%
Category correlation
CCR
= 10%
40%
CCR
= 5%
Construction
Multifam ily
30%
CCR = 40%
Depository
CCR = 30%
CCR
= 1%
Agriculture
20%
Other
CCR = 20%
10%
C&I
NFNR
Consum er
Lease
0%
0%
1%
2%
Expected charge-off rate
3%
4%
Figure 6 shows the maximum likelihood estimates of ECRj and ρj and the 95%
confidence regions derived from Expression (12). For the three categories
appearing at the lower left (farm loans, one-to-four-family revolving residential
mortgages, and one-to-four-family other residential mortgages) the confidence
regions are small. For some other categories, the category-level data cannot reject
a large range of combinations of ECR and ρ.
The parameter uncertainty implies uncertainty regarding conditional charge-off
rates. Figure 6 illustrates this with level curves of CCR equal to 1%, 5%, 10%,
20%, 30%, and 40%. A separate indication is provided by bootstrapping. For
three categories, we resample the charge-off data, re-estimate the parameters,
and recalculate CCR 1,000 times. The bootstrapped 95% confidence intervals for
CCR are 3.3% to 5.3% for C&I, 4.6% to 7.1% for consumer, and 1.4% to 18.5% for
construction. The significant uncertainty in tail estimates is principally a
consequence of the available data: we seek the worst charge-off that would come
about once in 200 years, yet we have only sixteen years of construction charge-off
- 15 -
data to work with. Especially given the pattern of the rates in certain categories,
there is great uncertainty in projections of tail risk.
The US composite bank
This section shows some of the results that are available when BankCaR is
applied to a bank. The bank in the spotlight is the US composite bank—a
hypothetical bank representing the US banking sector as a whole. The loan
amounts of the composite bank equal to the sums of loans at all commercial
banks.
Table 3. Composite bank loss in an illustrative scenario
Lending Category
C&I
Consumer
Other Lending
Depository Institutions
Lease Financing
Agriculture
Construction
Non-farm non-residential
Multifamily
Farm
1-4 Revolving Residential
1-4 Other Residential
Non-Loan Assets
Totals
$Billions
Outstanding
970
752
176
106
124
54
497
808
106
52
467
1,430
4,497
10,038
Illustrative scenario
Charge-off rate
$B Charge-off
1.25%
12.1
1.47%
11.0
1.33%
2.3
0.21%
0.2
0.36%
0.4
0.71%
0.4
6.63%
33.0
2.11%
17.0
2.51%
2.7
0.28%
0.1
0.32%
1.5
0.21%
2.9
----83.8
Composite bank loss in the illustrative charge-off scenario
0.83%
Table 3 displays the composite bank loan balances as of year-end 2006. Table 3
also shows an illustrative scenario that is an extension of an earlier example. The
dollar charge-off in any category is the product of the loan balance and the
charge-off rate. No charge-off results from assets other than loans. Combining
charge-offs from all categories, the illustrative scenario produces a loss equal to
0.83% of assets. This would illustrate one of the 100,000 simulation runs that
build up the distribution of a bank's loss distribution.
- 16 -
Figure 7. Distribution of loss of the composite bank
and category making the greatest contribution to loss
100000
Consumer
Number of scenarios
10000
C&I
Construction
1000
100
10
1
0.0%0.2%
0.2%0.4%
0.4%0.6%
0.6%0.8%
0.8%1.0%
1.0%1.2%
1.2%1.4%
1.4%1.6%
1.6%1.8%
1.8%2.0%
Composite bank charge-off
The distribution of loss for the composite bank is shown in Figure 7. Loss is
highly concentrated in a narrow range: over 49% of scenarios produce loss in the
range 0.40%-0.60% of assets. Because of this concentration, the vertical axis
Figure 7 is shown on a logarithmic scale. Only one scenario in twenty produces
loss greater than 0.80%. CaR is equal to the 500th greatest loss, 1.32%.
For each scenario, BankCaR determines the category that contributes the greatest
amount of loss. Except in 0.04% of scenarios, the dominant category is consumer
(71.8%), C&I (25.6%), or construction (2.6%). This breakdown parallels the
breakdown of twenty-three years of historical data: consumer has been the
greatest contributor in fifteen years, C&I in eight years, and construction in none
of the years.
The breakdown is different, though, depending on the overall amount of loss. As
shown in Figure 7, if overall loss is low or moderate, the consumer category or the
C&I category is likely to produce the greatest loss. If overall loss is greater than
about 1.20% the construction category becomes dominant. Thus, if the US
banking system has a year of very high charge-offs overall, BankCaR projects that
primary source of charge-offs will differ from what has been observed
historically. An adverse year is likely to be dominated by construction charge-offs
and more generally by the broader grouping of commercial real estate.
The average of the 1,377 scenarios producing greatest loss is the characteristic
scenario for the composite bank. Not surprisingly, it projects a high rate of
charge-off in the construction category.
- 17 -
Figure 8. The characteristic scenario for the composite bank
(charge-off rate in parentheses next to category name)
C&I (3.59% )
Con su m er (1.71% )
Ot h er l en din g (4.95% )
Ou t st a n di n g l oa n ba l a n ce
Deposit or y In st it u t i on s (5.51% )
Loss i n ch a r a ct er i st i c scen a r i o
Lea se Fin a n cin g (1.35% )
A gr i cu l t u r e (2.90% )
Con st r u ct i on (7.80% )
Non -fa r m n on -r esi den t i a l (2.49% )
Mu l t i fa m i l y r esi den t i a l (2.53% )
Fa r m (0.37% )
1-4 Fa m i l y Rev ol v i n g (0.21% )
1-4 Fa m i l y Ot h er (0.30% )
0%
5%
10%
15%
20%
Pr opor t i on a t e a m ou n t
25%
30%
Figure 8 compares loan balances to loss amounts under the characteristic
scenario of the composite bank. The characteristic scenario itself appears in
parentheses next to the category names.
Though exposure to construction loans is only 9% of total loans, construction
contributes more loss than any other category under the characteristic scenario.
The composite bank is therefore said to have the construction risk type. C&I is a
close second.
The composite bank enjoys a diversification benefit because the twelve category
factors are correlated imperfectly. If instead we assume instead that all factors
correlations equal 100%, every factor would attain its 99.5th percentile in the
same scenario, and CaR would depend only on category CCRs. For the composite
bank, the loss would then equal 1.91%. The full-model value of CaR, 1.32%,
therefore represents a diversification benefit equal to 30.8%.
Individual US Banks
This section repeats the foregoing analysis for each of the 7264 commercial banks
observed by BankCaR at year-end 2006. On average, the diversification benefit is
20.6%. This is naturally less than for the better-diversified composite bank.
Among the individual banks, the diversification benefit ranges between 0% and
45%. Banks that specialize in a single category have the least diversification
benefit. The greatest diversification benefit is enjoyed by banks having the
consumer risk type because of the negative correlation between the consumer
factor and other factors.
- 18 -
Table 4. US commercial banks by risk type
RiskType
C&I
Consumer
Other
Depository Institutions
Lease Financing
Agriculture
Construction
Non-farm non-residential
Multifamily Residential
Farm
1-4 Family Revolving
1-4 Family Other
All Banks
Number of banks
564
226
36
17
5
1,039
4,921
287
9
1
1
158
7,264
Average CaR
1.36%
1.72%
1.35%
1.18%
1.45%
1.72%
2.01%
1.52%
1.59%
1.39%
0.12%
1.33%
1.87%
Table 4 shows the distribution of banks by risk type and the associated average
value of CaR. Three of the risk types contain 9o% of banks: C&I, agriculture, and
construction. Some other risk types are poorly represented either because few
banks have substantial exposure to the category (for example, lease financing), or
because the CCR of the category is low (for example, farm lending).
Construction, which has been shown to have outsized effects on the composite
bank, also plays an important role at the individual bank level. Over 2/3 of banks
have the construction risk type, and banks having the construction risk type have
the greatest average value of CaR. An detailed analysis of the source of risk is
available to regulators on a bank-by-bank basis as part of BankCaR's "dashboard"
report.
Figure 9. Designation of risk level by stressed capital
100%
25%
Low Risk
10.92%
10%
6.94%
5.57%
50%
Norm al Risk
20%
Above Norm al Risk
5%
High
Risk
1%
0
1000
2000
3000
4000
5000
6000
7000
7264 banks sorted by stressed capital
As a screening tool that compares credit risk between banks, BankCaR highlights
banks that have low levels of stressed capital. Specifically, the banks having the
lowest 5% of stressed capital are designated "High Risk", the next 20% are
designated "Above Normal Risk", the center 50% are designated "Normal Risk",
- 19 -
and the 25% with greatest Stressed Capital are designated "Low Risk". These
designations are somewhat arbitrary in that bank risk is a continuous spectrum
without definite break points, and yet a level of stressed capital at the risky end of
the spectrum should not be ignored by bank managers or examiners. The current
break points between designations are illustrated in Figure 9.
Figure 10. Stressed Capital
Figure 11. Capital-at-Risk
4%
12%
10%
75th percentile bank
75th percentile bank
2%
8%
6%
95th percentile bank
3%
25th percentile bank
25th percentile bank
1%
5th percentile bank
4%
00Q3
01Q3
02Q3
03Q3
04Q3
05Q3
06Q3
07Q3
0%
00Q3
01Q3
02Q3
03Q3
04Q3
05Q3
06Q3
07Q3
The break points are remarkably stable over time, as shown in Figure 10. This
results from offsetting influences. The corresponding percentiles of CaR have
risen over time, as shown in Figure 11. The general rise in CaR has been offset by
a simultaneous rise in bank holdings of Tier 1 capital plus ALLL, producing
stability in the distribution of stressed capital.
Figure 11 also shows that the inter-quartile range of CaR has increased over time.
Credit risk at different banks differs more than it did previously. This trend
toward diversity of risk increases the value of a risk-based tool such as BankCaR.
Figure 12. Banks highlighted by SR 2007-01 and BankCaR
15%
Stressed capital
12%
9%
Neither (61%)
2007-01 only (34%)
6%
BankCaR only (1%)
Both (4%)
3%
0
2
4
6
8
10
Commercial real estate loans / total capital
BankCaR's High Risk banks can be compared to the set of banks highlighted by
an exposure-based screen. In Figure 12, each dot represents a US commercial
- 20 -
bank. BankCaR would highlight banks lower in the diagram, that is, banks with
relatively low values of stressed capital. To make this definite, the diagram
isolates the 5% of banks that BankCaR designates as High Risk.
By contrast, an example of an exposure-based screen is Federal Reserve SR Letter
2007-01. This SR Letter highlights banks that have a high ratio of either CRE or
construction lending to total capital. 5 This is a not unreasonable screening
criterion, given that construction loans have statistically high risk as confirmed
by the analysis of BankCaR. And yet, since it is based on exposure rather than on
risk, it calls attention to banks having high levels of stressed capital. Those banks,
recall, would have substantial levels of tier 1 plus ALLL even if they were to
experience charge-off at the high level represented by CaR. An exposure-based
criterion is also likely to miss some banks that have low levels of stressed capital,
simply because those banks do not have the exposure that is being screened for.
A separate target of analysis is the set of BankCaR's scenarios. A particular
scenario might cause a well capitalized bank to become adequately capitalized,
undercapitalized, significantly undercapitalized, or critically undercapitalized. 6
Many BankCaR scenarios produce no change in the status of any bank, because
they involve low and moderate rates of charge-off. Some scenarios produce a few
status changes, and a few scenarios produce status changes at many banks.
Figure 13. Number of undercapitalized banks in the worst scenarios,
with the category producing the greatest loss
Number of undercapitalized banks
2500
2000
1500
1000
Construction
Categories other
than construction
500
0
99.0
99.1
99.2
99.3
99.4
99.5
Percentile
99.6
99.7
99.8
99.9
100.0
Figure 13 portrays scenarios that cause a well capitalized bank to become
undercapitalized. Only 1,000 scenarios are shown, sorted by the number of banks
affected. The worst scenario causes about 2,500 banks to become
undercapitalized. Of these, about 1,800 would have greater charge-offs in
construction than in any other category; the remaining 700 would have their
greatest charge-offs in a category other than construction. All told, Figure 13
SR 2007-01 also considers growth in the CRE portfolio and excludes lending on owner-occupied
buildings. These conditions are not reflected in this comparison because of data limitations.
6 These terms are defined in the FDIC Improvement Act of 1991, which places banks within
categories defined in part by the ratio between capital and assets.
5
- 21 -
portrays 539,920 events in which a bank becomes undercapitalized. In 80% of
those events, construction is the greatest source of loss.
The construction category has been encountered repeatedly in these analyses.
When the composite bank has an unusually great loss, the category making the
greatest contribution tends to be construction. Among individual banks, most
have the construction risk type. Banks having the construction risk type tend to
have a high level of CaR. In an adverse event, such as one of the scenarios
portrayed in Figure 13, banks that become undercapitalized are likely to find that
construction loans produce greater charge-offs than any other category. Despite
all this, a bank's exposure to the construction category is not the whole story
when it comes to forecasting its charge-off risk.
Conclusion
BankCaR forecasts the distribution of a commercial bank's charge-offs at the
horizon of one year. This departs from traditional styles of forecasting that
produce point estimates. One traditional style focuses on the asset quality of a
bank's loans using tools such as regulatory classifications, the level and trend of
loans past due, and other factors. Another style focuses on macroeconomic or
financial variables such as output, interest rates, equity returns, or other data.
Forecasts, for the bank or for the macro economy, are most accurate when the
forecast horizon is short. To the extent that such forecasts are valid for a longer
horizon, they could be incorporated into later versions of BankCaR.
Applied to the composite US commercial bank, BankCaR finds that the 99.5th
percentile of the distribution of charge-offs is equal to the moderate value of
1.32%. If the US aggregate charge-off were this high, BankCaR predicts that
construction lending would probably contribute more charge-offs than any other
category. By contrast, the greatest contributor has historically been consumer or
C&I lending. BankCaR predicts that a bad year would be dominated, for the first
time, by construction.
Applied separately to each US bank, BankCaR efficiently identifies banks that
have an adverse combination of credit risk and financial risk resources, defined
as tier 1 capital plus ALLL. The difference, stressed capital, is a natural metric for
comparing the inherent credit risk of banks. Over the last seven years, the
distribution of stressed capital has been stable as a result of offsetting increases
in risk and capital.
BankCaR uses publicly available regulatory reporting data, the most common
credit portfolio model, and standard quantitative techniques. These generic
qualities provide a standard of comparison between banks and a benchmark for
more detailed models developed for specific banking institutions.
- 22 -
References
Federal Financial Institutions Examination Council (FFIEC), 2007,
Consolidated Reports of Condition and Income,
https://cdr.ffiec.gov/Public/WelcomeAdditionalInfo.aspx
Frye, Jon, 2000, "Collateral Damage," Risk, April,
http://www.chicagofed.org/publications/publicpolicystudies/emergingissues/pd
f/S&R_2000_15.pdf
Gordy, Michael, 2000, "A comparative anatomy of credit risk models," Journal
of Banking and Finance 24, pages 119-149,
http://www.federalreserve.gov/Pubs/feds/1998/199847/199847pap.pdf
Gordy, Michael, 2002, "A Risk-Factor Model Foundation for Ratings-Based
Bank Capital Rules", Journal of Financial Intermediation, vol. 12 (July 2003),
pp. 199-232,
http://www.federalreserve.gov/pubs/feds/2002/200255/200255pap.pdf
McNeil, Alexander, Rudiger Frey and Paul Embrechts, 2005,
Quantitative Risk Management, Princeton University Press
Merton, Robert, 1973, "On the Pricing of Corporate Debt: The Risk Structure
of Interest Rates," Journal of Finance, Vol. 29, MIT (1974), pp. 449-470,
http://dspace.mit.edu/bitstream/1721.1/1874/1/SWP-0684-14514372.pdf
Morrison, Donald F, 2005, Multivariate Statistical Methods, Fourth Edition.
Brooks/Cole Publishing
Office of the Comptroller of the Currency, Federal Reserve System,
Federal Deposit Insurance Corporation, and Office of Thrift
Supervision, 2007, "Risk-Based Capital Standards: Advanced Capital Adequacy
Framework," Basel II Preamble: http://www.occ.gov/ftp/release/2007-123a.pdf
Basel II Final Rule: http://www.occ.gov/ftp/release/2007-123b.pdf
Vasicek, Oldrich, 2002, "Loan Portfolio Value," Risk, December, pp. 160-162,
http://www.moodyskmv.com/conf04/pdf/papers/dist_loan_port_val.pdf
- 23 -
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde
WP-05-01
Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse
WP-05-02
Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman
WP-05-03
Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton
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Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi
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What Determines Bilateral Trade Flows?
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Intergenerational Economic Mobility in the U.S., 1940 to 2000
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Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
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Working Paper Series (continued)
Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
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WP-05-15
Competition in Large Markets
Jeffrey R. Campbell
WP-05-16
Why Do Firms Go Public? Evidence from the Banking Industry
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Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
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WP-05-18
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WP-05-19
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Supplier Switching and Outsourcing
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Maude Toussaint-Comeau
WP-05-23
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WP-05-24
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Identification of Search Models with Initial Condition Problems
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Working Paper Series (continued)
Why are safeguards needed in a trade agreement?
Meredith A. Crowley
WP-06-06
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-06-07
A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon
WP-06-08
Mergers and Risk
Craig H. Furfine and Richard J. Rosen
WP-06-09
Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis
WP-06-10
Do Consumers Choose the Right Credit Contracts?
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles
WP-06-11
Chronicles of a Deflation Unforetold
François R. Velde
WP-06-12
Female Offenders Use of Social Welfare Programs Before and After Jail and Prison:
Does Prison Cause Welfare Dependency?
Kristin F. Butcher and Robert J. LaLonde
Eat or Be Eaten: A Theory of Mergers and Firm Size
Gary Gorton, Matthias Kahl, and Richard Rosen
Do Bonds Span Volatility Risk in the U.S. Treasury Market?
A Specification Test for Affine Term Structure Models
Torben G. Andersen and Luca Benzoni
WP-06-13
WP-06-14
WP-06-15
Transforming Payment Choices by Doubling Fees on the Illinois Tollway
Gene Amromin, Carrie Jankowski, and Richard D. Porter
WP-06-16
How Did the 2003 Dividend Tax Cut Affect Stock Prices?
Gene Amromin, Paul Harrison, and Steven Sharpe
WP-06-17
Will Writing and Bequest Motives: Early 20th Century Irish Evidence
Leslie McGranahan
WP-06-18
How Professional Forecasters View Shocks to GDP
Spencer D. Krane
WP-06-19
Evolving Agglomeration in the U.S. auto supplier industry
Thomas Klier and Daniel P. McMillen
WP-06-20
3
Working Paper Series (continued)
Mortality, Mass-Layoffs, and Career Outcomes: An Analysis using Administrative Data
Daniel Sullivan and Till von Wachter
The Agreement on Subsidies and Countervailing Measures:
Tying One’s Hand through the WTO.
Meredith A. Crowley
WP-06-21
WP-06-22
How Did Schooling Laws Improve Long-Term Health and Lower Mortality?
Bhashkar Mazumder
WP-06-23
Manufacturing Plants’ Use of Temporary Workers: An Analysis Using Census Micro Data
Yukako Ono and Daniel Sullivan
WP-06-24
What Can We Learn about Financial Access from U.S. Immigrants?
Una Okonkwo Osili and Anna Paulson
WP-06-25
Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?
Evren Ors and Tara Rice
WP-06-26
Welfare Implications of the Transition to High Household Debt
Jeffrey R. Campbell and Zvi Hercowitz
WP-06-27
Last-In First-Out Oligopoly Dynamics
Jaap H. Abbring and Jeffrey R. Campbell
WP-06-28
Oligopoly Dynamics with Barriers to Entry
Jaap H. Abbring and Jeffrey R. Campbell
WP-06-29
Risk Taking and the Quality of Informal Insurance: Gambling and Remittances in Thailand
Douglas L. Miller and Anna L. Paulson
WP-07-01
Fast Micro and Slow Macro: Can Aggregation Explain the Persistence of Inflation?
Filippo Altissimo, Benoît Mojon, and Paolo Zaffaroni
WP-07-02
Assessing a Decade of Interstate Bank Branching
Christian Johnson and Tara Rice
WP-07-03
Debit Card and Cash Usage: A Cross-Country Analysis
Gene Amromin and Sujit Chakravorti
WP-07-04
The Age of Reason: Financial Decisions Over the Lifecycle
Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson
WP-07-05
Information Acquisition in Financial Markets: a Correction
Gadi Barlevy and Pietro Veronesi
WP-07-06
Monetary Policy, Output Composition and the Great Moderation
Benoît Mojon
WP-07-07
4
Working Paper Series (continued)
Estate Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-07-08
Conflict of Interest and Certification in the U.S. IPO Market
Luca Benzoni and Carola Schenone
WP-07-09
The Reaction of Consumer Spending and Debt to Tax Rebates –
Evidence from Consumer Credit Data
Sumit Agarwal, Chunlin Liu, and Nicholas S. Souleles
WP-07-10
Portfolio Choice over the Life-Cycle when the Stock and Labor Markets are Cointegrated
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
WP-07-11
Nonparametric Analysis of Intergenerational Income Mobility
with Application to the United States
Debopam Bhattacharya and Bhashkar Mazumder
WP-07-12
How the Credit Channel Works: Differentiating the Bank Lending Channel
and the Balance Sheet Channel
Lamont K. Black and Richard J. Rosen
WP-07-13
Labor Market Transitions and Self-Employment
Ellen R. Rissman
WP-07-14
First-Time Home Buyers and Residential Investment Volatility
Jonas D.M. Fisher and Martin Gervais
WP-07-15
Establishments Dynamics and Matching Frictions in Classical Competitive Equilibrium
Marcelo Veracierto
WP-07-16
Technology’s Edge: The Educational Benefits of Computer-Aided Instruction
Lisa Barrow, Lisa Markman, and Cecilia Elena Rouse
WP-07-17
The Widow’s Offering: Inheritance, Family Structure, and the Charitable Gifts of Women
Leslie McGranahan
WP-07-18
Demand Volatility and the Lag between the Growth of Temporary
and Permanent Employment
Sainan Jin, Yukako Ono, and Qinghua Zhang
WP-07-19
A Conversation with 590 Nascent Entrepreneurs
Jeffrey R. Campbell and Mariacristina De Nardi
WP-07-20
Cyclical Dumping and US Antidumping Protection: 1980-2001
Meredith A. Crowley
WP-07-21
Prenatal Nutrition and Adult Outcomes: The Effect of Maternal Fasting During Ramadan
Douglas Almond and Bhashkar Mazumder
WP-07-22
5
Working Paper Series (continued)
The Spending and Debt Responses to Minimum Wage Increases
Daniel Aaronson, Sumit Agarwal, and Eric French
WP-07-23
The Impact of Mexican Immigrants on U.S. Wage Structure
Maude Toussaint-Comeau
WP-07-24
A Leverage-based Model of Speculative Bubbles
Gadi Barlevy
WP-08-01
Displacement, Asymmetric Information and Heterogeneous Human Capital
Luojia Hu and Christopher Taber
WP-08-02
BankCaR (Bank Capital-at-Risk): A credit risk model for US commercial bank charge-offs
Jon Frye and Eduard Pelz
WP-08-03
6
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