Editorial-Board_2014_Journal-of-Banking---Finance.pdfJOURN.docx

Editorial-Board_2014_Journal-of-Banking---Finance.pdf
JOURNAL OF BANKING AND FINANCE
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The-determinants-of-U-S--banks--international-a_2014_Journal-
of-Banking---Fi.pdf
Journal of Banking & Finance 44 (2014) 233–247
Contents lists available at ScienceDirect
Journal of Banking & Finance
journal homepage: www.elsevier .com/locate / jbf
The determinants of U.S. banks’ international activities
http://dx.doi.org/10.1016/j.jbankfin.2014.04.014
0378-4266/� 2014 Elsevier B.V. All rights reserved.
⇑ Tel.: +1 315 859 4859; fax: +1 315 859 4477.
E-mail address: [email protected]
1 These foreign banking activities generally bring efficiency
and tech
improvements to host countries’ financial markets (Xu, 2011).
However, the
arising from financial contagion from parent banks can
destabilize host ec
during crisis periods (de Haas and van Lelyveld, 2011).
Judit Temesvary ⇑
Department of Economics, Hamilton College, 198 College Hill
Road, Clinton, NY 13323, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received 9 November 2012

Accepted 15 April 2014
Available online 26 April 2014
JEL classification:
C53
F37
G11
G15
G21
Keywords:
International banking
Bank behavior
Affiliate lending
Cross-border lending
Bank regulation
This paper develops a model and structural dynamic estimation
of bank behavior to map the relationship
between U.S. banks’ choices of foreign banking activities, and
bank and foreign market traits. This estima-
tion framework is applied to a unique bank-level dataset
compiled from regulatory sources, covering U.S.
banks’ foreign activities in 83 host markets over the 2003–2013
period. Bank traits are better able to
explain the evolving patterns of foreign banking than host
market characteristics. After controlling for
these traits, the post-financial crisis period shows a structural
shift away from cross-border claims
towards foreign affiliate activities. Structural estimates of
foreign market entry costs and regulatory
attitudes towards risk are derived. Simulation exercises confirm
the strong impact of banks’ and
regulators’ risk stance on bank profits and portfolio
composition.
� 2014 Elsevier B.V. All rights reserved.

1. Introduction
Global banking has become increasingly prevalent over the past
several decades. The average share of foreign banks now
reaches
20% in the OECD countries, with some as high as 50%
(Claessens
and van Horen, 2012). U.S. banks have also become more
involved
in foreign countries, with their foreign claims rising from
308 billion USD in 1998 to 3.4 trillion USD by 2012. Over this
time
period, U.S. banks invested an average of 18% of their portfolio
in
foreign claims.
Beyond its rising magnitude, the composition of this interna-
tional exposure has changed substantially over the past decade.
U.S. banks have noticeably moved away from cross-border
claims
(whereby U.S. banks acquire foreign assets directly from the
U.S.)
towards foreign affiliate claims (which are acquired via foreign
affiliates established in host countries). In 2003, U.S. banks
held
only 15 cents in affiliate claims for each dollar in cross-border
claims. By 2013, this number has risen to 33 cents per each
dollar’s worth of cross border claim. A further interesting
pattern
is that of U.S. banks’ foreign affiliate participation. Since 2003,
foreign market entries and exits averaged at 3.5 and 3.7 per
globally active U.S. bank, respectively. On average, U.S. banks
have
maintained an affiliate presence in one third of the countries
they
hold claims in.1

In light of these interesting patterns, the goal of this paper is to
explore the determinants and characteristics of U.S. banks’
foreign
activities over the course of the past ten years. The main
contribu-
tion of this paper is the development and estimation of a
dynamic
model of banks’ decisions concerning which countries to enter,
and
their choices of the volume and composition of claims to hold
there. The model is estimated using a two-step structural
dynamic
method, which is applied to a newly compiled bank-level
dataset
on U.S. banks’ foreign activities. The estimation procedure is a
version of the Bajari et al. (2007) dynamic structural two-step
estimation method. The first stage estimates banks’ foreign
claims
volume choices, as well as banks’ choices of foreign market
entry
and exit, as functions of a broad set of bank and host market
traits
in a reduced-form setting. The second stage then uses the policy
function estimates from the first stage to construct banks’ dis-
counted sum of expected profits over time, corresponding to
banks’
nological
volatility
onomies
http://crossmark.crossref.org/dialog/?doi=10.1016/j.jbankfin.20
14.04.014&domain=pdf
mailto:[email protected]

http://www.sciencedirect.com/science/journal/03784266
http://www.elsevier.com/locate/jbf
234 J. Temesvary / Journal of Banking & Finance 44 (2014)
233–247
observed foreign choices as well as a range of alternate choices.
Comparing these constructed values of the observed and
alternate
paths of action, the structural parameters (such as entry costs
and
banks’ and regulators’ attitudes towards market risk) are chosen
so
as to rationalize banks’ observed choices. The data set was
compiled by merging various regulatory databases, banks’
balance-sheet data and host-country macroeconomic indicators.
It covers 82 U.S. banks’ activities in 83 foreign countries
between
2003 Q1 and 2013 Q1.2
This paper’s approach to the microeconomic modeling of banks’
activities has three advantages. Since it is dynamic, it captures
the
interactions between banks’ foreign market entry/exit and
claims
choices. These dynamic interactions are important: market entry
enables banks to hold foreign affiliate claims in that market for
many periods to come. This foreign market involvement will
then
influence banks’ future entry and claims choices in other
markets
as well (via diversification benefits, substitution effects, etc.).
By
being able to capture these interactions, this method goes
beyond the reduced-form and static empirical methods applied
in previous related literature (Focarelli and Pozzolo, 2001;

Miller
and Parkhe, 1998).
The analysis also accounts for banks’ choice of the composition
of their claims as functions of bank and market traits. This is a
step
forward since the simultaneous cross-border and foreign
affiliate
claim choices are interconnected, yet respond to bank and
market
traits differently. For instance, banks tend to establish foreign
affil-
iates in host markets that have lower taxes, laxer regulatory
restrictions on bank activities and a majority of retail clients
(Cerutti et al., 2007), as well as substantial transfer risk
(Cetorelli
and Goldberg, 2008). On the other hand, cross-border claims,
which can draw on parent banks’ capital base, are more suitable
if the host country is less developed or smaller (Lehner, 2009),
or
if the majority of clients there are low-risk multinationals or
sover-
eigns. Home market conditions are also important in shaping the
composition of foreign claims (de Haas and van Lelyveld, 2006;
de Haas and van Lelyveld, 2010), especially when there are
risks
of regulatory arbitrage or financial contagion (Aiyar, 2011;
Cetorelli and Goldberg, 2011; Buch, 2003; Magri et al., 2005).
Bank
traits matter as well: previous literature has highlighted bank
size
(Focarelli and Pozzolo, 2001) and the health of the balance
sheet
(Popov and Udell, 2012) as particularly important. In fact,
results
of the following analysis show that bank traits are better able to

explain banks’ foreign activities than host market
characteristics.
Since the estimation is structural, it enables the identification of
parameters (such as entry costs and risk aversions) for which
the
reduced-form literature uses rough empirical proxies. Getting
structural estimates of these attitudes towards risk is a step
forward, in light of evidence that regulatory strictness matters:
a
lax bank-regulatory environment in the home country gives
banks a competitive advantage in global banking, while a strict
regulatory environment in the host market limits domestic and
cross-border bank activity (Fidrmuc and Hainz, 2013; Chen and
Liao, 2011). Results in this paper show that regulators have
become
more risk averse since the financial crisis, and confirms that
banks
have done so as well (de Haas and van Horen, 2010). The
analysis
also estimates the host-market specific fixed entry costs (brick
and
mortar expenses as well as administrative fees) that banks have
to
pay upon market entry, and the scrap value of these costs that
banks can recover upon exit. These entry costs form barriers to
banks’ foreign market entry (Lehner, 2009), and as such, can
significantly affect the pattern of global banking. The following
2 The number of banks for which bank-level data is available is
limited by
regulatory reporting requirements. Only U.S. banks with claims
in any given country
in excess of 1% of total assets, or 20% of capital, are required
to report foreign
exposure.
analysis shows that entry costs have grown substantially since

2008.
The paper contributes to a growing volume of literature by
examining the effect of the recent financial crisis on banks’
lending
activities (Cotugno et al., 2013; Kleimeier et al., 2013; Ivashina
and
Scharfstein, 2010). Previous work has found that U.S. banks’
foreign
activities have fallen significantly in the aftermath of the crisis
(Cetorelli and Goldberg, 2009; Cetorelli and Goldberg, 2011).
This
paper’s findings add to the picture by implying that the post-
crisis
reduction in foreign activities is the result of banks’ response to
deteriorating balance sheet and host market conditions. After
con-
trolling for the changes in bank and market traits over the crisis
period, there is evidence of a shift in the composition of foreign
banking: banks have shifted significantly away from cross-
border
loans towards foreign affiliate activities since the financial
crisis.
The paper proceeds as follows. Section 2 presents the model and
characterizes banks’ optimal domestic and foreign claims
choices
as a Markov perfect equilibrium. Section 3 describes the data
and
discusses the estimation method. Section 4 describes the results
of the estimation. Section 5 presents simulation exercises.
Section 6
concludes.
2. Model
The dataset that the model is ultimately estimated on specifies

the volumes of claims and liabilities at the level of bank-host
country pairs, but does not break them down by type (e.g. loans
or bonds as types of claims, or deposits as a type of liability).
None-
theless, for expositional purposes the following model treats
loans,
bonds and deposits as separate types of claims and liabilities,
each
with its own traits. The estimable claims equations described in
Section 3 can be thought of as composites of the various types
of
assets detailed in the model below.
2.1. Setup and notation
This section describes the model of a bank’s foreign market
entry/exit choices, as well as its decision on the volumes of
loans
to extend and deposits to take on. Let j ¼ 1 . . . J denote bank j.
Each
bank j is owned by shareholders, whose goal is to maximize the
lifetime discounted sum of mean–variance utilities on the bank
portfolio.3 Shareholders make foreign market entry/exit, as well
as
loan/deposit volume choices at the beginning of each period t.
There
are a total of T periods such that t ¼ 1 . . . :T. The bank can
operate in
any of I countries, such that i ¼ 1 . . . I. In what follows, the
time
indices t, the country indices i and bank indices j are
suppressed.
In each country, there are several markets m available to the
bank. Let m ¼ 1 denote the home (source-country) market. In
each
host (foreign) country, there are two markets available to the

bank.
First, the bank’s headquarters can extend cross-border loans
directly from the home market to any host country. Let m ¼ 2
denote this cross-border loan market. Alternatively, the bank
can
make foreign affiliate (local) loans in the host country by
establish-
ing an affiliate there. Let m ¼ 3 denote this foreign affiliate
market.
In each of the I � 1 foreign countries, the bank can engage in
two
markets: cross-border and foreign affiliate. Since by definition,
there is no cross-border loan market in the bank’s home, there
are a total of 2 � ðI � 1Þ þ 1 markets available. In addition to
making loans, the bank also has the option to take deposits in
all
markets. Foreign affiliate offices receive funding from their
parent via internal capital markets (Cetorelli and Goldberg,
2009;
3 The mean–variance formulation, also employed by (Buch et
al., 2010), is
appropriate since evidence shows that banks look for higher
returns and diversifi-
cation opportunities in host markets (Focarelli and Pozzolo,
2005).
J. Temesvary / Journal of Banking & Finance 44 (2014) 233–
247 235
Cetorelli and Goldberg, 2012). Let Km denote the amount of
capital that shareholders choose to transfer to the host country’s
market m at the beginning of the period. Since funds used to
make
cross-border loans originate from the home budget, the
capitaliza-

tion for the cross-border market m ¼ 2 is the same as for the
home
market m ¼ 1.
In each market, banking clients’ goal is to maximize utility over
their lifetime. After solving their lifetime utility maximization
problem (not explicitly modeled here), risk-averse banking
clients
in market m diversify by demanding a composite bundle of
banking services from banks of all nationalities present in that
market. As a result, banking markets m are monopolistically
competitive.4 Banks in market m make loans lm to clients at
interest
rate rlm, and take deposits dm at rate rdm. Loan and deposit
markets
are subject to random and market-specific aggregate shocks.
According to the Dixit-Stiglitz formulation, these shocks are
captured by the market-specific composite return indices on
loans
and deposits, denoted by am and bm respectively. These return
indices are composites of all banks’ rates operating in market
m.
ða; bÞ are determined at the market level within each market,
but
are exogenous and random from each individual bank’s
perspective.5
Let bars over parameters denote expectations and V is the
known
variance–covariance matrix of return indices across all
countries
and markets. The return indices are assumed to be jointly
normally
distributed as follows.
am

bm
� �
�N
�am
�bm
; V
� �
ð2:1Þ
Shareholders observe the Dixit-Stiglitz type monopolistically
competitive loan demand lm and deposit supply dm functions.
Let
�m denote the market-specific loan demand elasticity and gm is
the elasticity on clients’ deposit supply. The loan demand and
deposit supply the bank faces depend on how its rates ðrlm;
rdmÞ fare
relative to the composite loan and deposit indices in that
market.
ðam; bmÞ.
lm ¼
am
rlm
� ��m
ð2:2Þ
dm ¼
rdm
bm
� �gm

ð2:3Þ
In addition to taking deposits, the bank can also issue bonds Dm
in international financial markets, in order to finance its
activities.
The bank is a price-taker in these competitive bond markets.6
Investors take the health of the bank’s balance sheet into
account
when they decide the rate at which they are willing to lend to
the
bank. The rate rDm at which the bank can sell bonds to
investors
increases with the volume of bonds outstanding, i.e. investors
require a risk premium from banks with more debt. On the other
4 This choice is motivated by the facts that (1) most banking
markets around the
world are characterized by a high level of market concentration
(Beck et al., 2004) and
(2) the relationships that banks develop with customers provide
them with
informational capital, which translates into differentiated
services and market power.
5 Based on the Dixit-Stiglitz formulation, the indices are given
by
am ¼ Am
R
n rlmnð Þ
1��n @n
h i�1
with �m > 1 and bm ¼ Bm

R
n rdmnð Þ
1þ[email protected]
h i
, where Am
and Bm are market-specific constants. The aggregation is over
all banks of all
nationalities operating in market m.
6 The assumption that banks are price-takers in bond markets
but price-setters in
deposit-markets follows from the structure of the model.
Depositors in each market
of each country are restricted to deposit in the limited number
of banks that operate
in the given market in the client’s country. The fact that only a
limited number of
banks are available in that market in that country gives banks
market power in
deposit markets. In contrast, bond markets are international –
clients from any
country can invest in the bonds of banks in any other country.
As banks must compete
with all other countries’ banks for bond financing, banks are
price-takers in debt
markets.
hand, a better-capitalized bank can issue bonds at a lower rate.
How-
ever, the bond rate can never fall below the pre-specified
minimum
rate of �rm.
rDm ¼ �rm 1þ
Dm

Km
� �
ð2:4Þ
There are both fixed and variable costs associated with the
bank’s activities. The bank must pay a fixed entry cost Cm
when
it enters market m in the host country. This entry cost captures
all fixed costs of opening a foreign affiliate, such as brick and
mortar costs, administrative fees, etc. Furthermore, the bank can
recover scrap value Wm when it leaves the market (such that
Wm 6 Cm). This fixed scrap value is the amount the bank can
recover of the paid entry costs upon exit. As such, it includes
the
resale value of real estate, equipment, refunds, etc. In addition,
the bank also incurs proportional (marginal) costs of lending
and
deposit-taking, denoted by clm and cdm, respectively. Some
exam-
ples of such incremental costs are: the expenses of processing a
new loan application, meeting with clients, financial transaction
taxes, etc.
Before making their portfolio choice, the bank’s shareholders
observe a set of state variables P at the beginning of each
period.
These state variables consist of market-specific characteristics,
bank traits and variables which pertain to bank-market pairs. As
for market-specific state variables, shareholders observe the
following set of exogenous and known state variables: the
vector
of proportional costs ðcdm; clmÞ, the foreign income
repatriation tax
xm, the vector of market and country-specific bank income
taxes

sm, the required reserve ratios and minimum capital ratio
require-
ments ðdm;jmÞ; the joint normal distribution N of return
indices;
and the market-specific fixed entry costs and scrap values ðCm;
WmÞ.
In addition, shareholders can see a snapshot of the bank’s
current international position. That is to say, at the beginning of
the period shareholders can observe which markets the bank is
currently active in (based on past entry and exit choices). Let
ð{PÞm ¼ 1 if the bank is currently active in the host country’s
market m, and ð{PÞm ¼ 0 otherwise. Shareholders can observe
the
vector of the bank’s status in each country and market, denoted
by {P . Shareholders also observe K, which is the vector of
market-specific capitalizations Km allocated to market m at the
beginning of the period. Since profits are re-distributed to
share-
holders at the end of each period, the sum of these market-
specific
capitalizations is taken to be exogenous from the bank’s
perspec-
tive. Let ðem Pð Þ ¼ 1; em Pð Þ ¼ �1Þ denote the bank’s
decision to
enter and exit market m in the current period, respectively.
Then
the state vector at date t þ 1, denoted by Ptþ1, is drawn from a
probability distribution K Ptþ1jet ;Ptð Þ. The dependence of
this
function on et means that time t entry/exit decisions affect
the future strategic environment. However, not all states are
influenced by past actions.
Since profits are redistributed to shareholders at the end of each
period, shareholders choose loan and deposit volumes with only

the current period in mind.7 As Km is the amount of
capitalization
present in market m at the beginning of the period, eK m
denotes
the value of the bank’s end-period operations in market m.
Shareholders’ goal is to maximize their concave increasing
expected
utility function over the sum of the bank’s end-period
capitalizations
across all countries and all markets, given their expectations of
the
mean and variance–covariance of returns.
The random market shocks perturb loan demand and deposit
supply, and therefore affect bank revenue. As a result, the coun-
try-specific eK m’s are also random variables. Since cross-
border
7 Whereas market entry and exit choices are made with multi-
period consider-
ations in mind, when fixed costs are present.
233–247
loans all originate from the bank’s home budget, the bank’s
home
capitalization K1;2 takes the following form.8
eK 1;2 ¼ K1;2 þ 1� s1ð Þ � ðrl1 � cl1Þ � l1 � ðrd1 þ cd1Þ �
d1 � ðrD1 � D1;2Þ½ �
þ 1� s2ð Þ � rl2 � cl2ð Þ � l2 � ðrd2 þ cd2Þ � d2½ � � C2 1
: e2 ¼ 1ð Þ
þ � 2 1 : e2 ¼ �1ð Þ ð2:5Þ
In (2.5), the first term in the home-market capitalization eK 1;2

is
the initial home-market capitalization K1;2. The first square
brack-
ets contain domestic loan interest income net of costs, minus
domestic deposit expenses and bond-borrowing costs. This
home-market ’net revenue’ is adjusted for the domestic income
tax rate s1. The second bracketed term contains the revenue
from
cross-border lending, net of costs and income taxes and cross-
border deposit expenses. The last two terms are the costs of new
cross-border market entry e2 ¼ 1ð Þ if applicable, and the scrap
value collected from newly vacated markets e2 ¼ �1ð Þ.9
Recalling that m ¼ 3 denotes the foreign affiliate (local) market
in the host country, the end-period value of the bank’s foreign
affiliate is as follows.
eK 3 ¼ K3 þ 1� s3ð Þ
� 1�x3ð Þ rl3 � cl3ð Þ � l3 � rd3 þ cd3ð Þ � d3 � rD3 �
D3ð Þ½ �
� C3 1 : e3 ¼ 1ð Þ þ � 3 1 : e3 ¼ �1ð Þ ð2:6Þ
In (2.6), the first term in eK 3 is the initial host market
capitaliza-
tion K3. The square brackets contain loan interest income net of
costs, minus deposit expenses and bond-borrowing costs. This
’net revenue’ is adjusted for the host market income tax s3 and
income repatriation rate x3 before it is added on to K3. Fixed
entry
costs C3 come out of the foreign affiliate’s budgets at the time
of
entry e3 ¼ 1ð Þ, which also recover scrap values � 3 in case of
exit
e3 ¼ �1ð Þ. Let eK denote the column vector of market and
coun-

try-specific capitalizations, for all countries and markets. After
all
foreign income is repatriated to the bank’s source market, the
bank’s end-period aggregate capital is then {eK ¼PiPm eK im.
At this point, it is instructive to point out that the Dixit-Stiglitz
formulation implies that the loan revenue rlm � lm and deposit
expenditure rdm � dm functions are linear in the jointly
normally
distributed composite indices ðam; bmÞ.10 Since ðeK 1; ~K3Þ
are sums
of these terms, the end-period random capitalizations are also
jointly
normally distributed.
Bank activities are subject to minimum reserve and capital ade-
quacy requirements. The model considers the territorial
approach
to the regulation of U.S. bank affiliates in host countries. This
approach, increasingly implemented by the U.S. Federal
Reserve
in its rulemaking, calls for the regulation of foreign bank
subsidiar-
ies at the host country level. This territorial approach to bank
regulation subjects foreign affiliates to similar liquidity and
capital
requirements as domestic banks in the host market. While the
territorial approach remains controversial it is increasingly
likely
to be adopted by the main financial centers of the world.
In line with the territorial approach, domestic and cross-border
loans are subject to home country regulations. Furthermore,
foreign affiliate operations are bound by the host country’s laws
and regulations, since these operations are financed out of the
budget of each foreign affiliate separately. Recall that ðd;jÞ

denote
8 The double subsrcipts indicate the fact that domestic and
cross-border lending
both originate from the home country budget.
9 The bank is assumed to be always present in the home market,
where its
headquarters are located. This assumption implies that this
study does not consider
shareholders’ choice to set up a new bank or close an existing
one.
10 Based on the Dixit-Stiglitz formulation, the loan revenue and
deposit expenditure
functions in Eq. (2.6) take the forms rlm � lm ¼ amð Þ � lmð Þ
�m�1
�m and rdm � dm ¼ bmð Þ�
dmð Þ
gmþ1
gm respectively.
the required reserve ratio and the minimum capital adequacy
ratio,
respectively, and K3 is the initial capital allocated to the
foreign
affiliate. Then the budget constraints on the bank’s home and
host
country operations are as follows.
l1 þ l2 6 K1;2 þ D1;2 þ 1� d1;2ð Þ � d1 þ d2ð Þ ð2:7Þ
l3 6 K3 þ D3 þ 1� d3ð Þ � d3 ð2:8Þ
The host country bank regulator considers the bank’s risk-
weighted capitalization in its regulatory capital requirement, as
outlined in the Basel Accords. Let ðh1;2; h3Þ denote the home

and
host country bank regulator’s stance on risk, respectively. This
is
the regulator’s risk aversion parameter, i.e. the weight the
regula-
tor assigns to the market risk associated with the fraction of the
bank’s portfolio that originates from the bank regulator’s
country
of supervision. Let ðV1;2; V3Þ denote the variance–covariance
matrix
of the return indices within the home country and the host
country, respectively.11 The risk-weighted capital requirements
in
the home country and host country are then
E eK 1;2h i� h1;22 � eK 01;2V1;2 eK 1;2� �P j1;2 � l1 þ l2ð
Þ ð2:9Þ
E eK 3h i� h32 � eK 03V3 eK 3� �P j3 � l3ð Þ ð2:10Þ
The budget and regulatory constraints must hold in each period
and each country. At this point it is useful to re-introduce the
time
index t, country index i and bank index j.
Given the state Pt 2 P, banks choose actions simultaneously.
The two types of actions are the period-by-period loan/deposit
vol-
ume choices and the dynamic foreign market entry/exit
decisions.
Let Et ¼ e1t . . . eJt
�
denote the vector of all banks’ time t entry/exit
choices, and Ej ¼ ej1 . . . ejT
�

denotes bank j’s actions over time.
Then E ¼ E1 . . . EJ
�
is the matrix of all entry/exit decisions. Before
choosing its actions, each bank j receives a private shock mjt ,
drawn
independently across banks and over time from a distribution
G �jPtð Þwith support m. For example, the private shock might
derive
from variability in managerial drive for international portfolio
diversification. Let the vector mt ¼ m1t ; . . . ; mJt
�
denote the private
shocks of all banks.
The bank’s overall end-period capitalizations eK j is normally
distributed, since it is the sum of normally distributed random
variables. eK 0jV eK j� � is the variance–covariance of the
bank’s portfo-
lio. k is the bank’s constant risk aversion. Given its private
shock,
the entry/exit decision vector Ej and the set of state variables Pt
,
in each period t bank j chooses its loan and deposit volumes to
maximize its mean–variance expected utility as follows.
max
limj ;d
i

mj ;D
i
j ;K
i
j
u ej;P; mj
�
t ¼ E ~Kj
� �
t
� kj
2
� eK 0jV eK j� �
t
ð2:11Þ
subject to the budget and regulatory constraints described in
Eqs.
(2.7)–(2.10).
Let c < 1 denote the time-invariant discount factor. Bank j
makes foreign market entry and exit decisions to maximize its
dis-
counted sum of expected utilities over time as follows.
max
e1j ;...;eMj
E

XT
t¼0
ctuj ej;P; mj
�
tjPt
" #
ð2:12Þ
11 V1;2 represents the variance–covariance matrix of the bank’s
home country
operations. Accordingly, it is the variance–covariance matrix of
the returns on home
country loans l1, home country deposits d1, cross-border loans
l2 and cross-border
deposits d2. Similarly, V3 stands for the variance–covariance
matrix of the returns on
the bank’s foreign country operations (foreign affiliate loans l3
and deposits d3). Based
on these definitions, these country-specific covariance matrices
are not the same as
the overall variance–covariance matrix on the bank’s global
portfolio, denoted by V in
Eq. (2.1).
247 237
The expectation is over bank j’s private shock in the current
period, as well as over future values of the state variables P,
actions Ej, and private shocks mj. The final aspect of the model
is
the transition between states. As described above, the state
vector

at date t þ 1 is denoted by Ptþ1, and is drawn from a probability
distribution K Ptþ1jet ;Ptð Þ. The dependence of this function
on et
means that time t entry/exit decisions affect the future strategic
environment. However, not all states are influenced by past
actions.
The analysis of equilibrium behavior focuses on pure strategy
Markov perfect equilibria (MPE). In a MPE, each bank’s
behavior
depends only on the current state. Formally, a Markov strategy
for bank j is a function xj : P� mj # Ej. A profile of Markov
strate-
gies is a vector x ¼ x1; . . . ;xJ
�
where x : ðP; m1; . . . ; mJÞ# E. If
behavior is given by a Markov strategy profile x, bank j’s
expected
utility over time, given a state P can be written recursively:
Vj P;xð Þ¼Em uj x P;mð Þ;Pt;mjt
�
þc
Z
Vj P
0;xð ÞdK P0jx P;ð Þ;Pð ÞjP
� �
ð2:13Þ
In (2.13), Vj is bank j’s ex ante value function in that it reflects
expected profits at the beginning of a period before private

shocks
are realized. The profile x is a MPE if, given the opponent
profile
x�j, each bank j prefers its strategy xj to all alternative Markov
strategies x0j. That is, x is a MPE if for all banks j, states P,
and
Markov strategies x0j,
Vj P;xð ÞP Vj P;x0j;x�j
� �
ð2:14Þ
It is assumed that all the conditions for the existence of such a
MPE
are satisfied. Given the entry cost and scrap value vectors of C
and
� , bank j’s optimal entry/exit rule is then as follows.
Enter if Vj eimj¼1;eim�j;P;x
� �
�Cim PVj eimj¼0;eim�j;P;x
� �
;
Exit if Vj eimj¼�1;eim�j;P;x
� �
þ� im PVj eimj¼0;eim�j;P;x
� �
;
Stay ‘put’ if otherwise:

8>>><>>>:
ð2:15Þ
12 The sample captures an active period of U.S. bank mergers.
In order to avoid the
problem of big ‘jumps’ in balance sheets due to mergers, the
issue is handled as
follows. First, merger events are identified based on the
FFIEC’s National Information
Center’s Institution History feature. Starting with the time of
merger, the merging
banks are then eliminated from the sample. The merged banks
are then considered as
a newly created entity, which is assigned the original acquiring
bank’s balance sheet
and claims data from then on.
3. Data and estimation
3.1. Data
The estimation is based on a unique U.S. bank-level dataset
newly created from the merger of regulatory balance sheet data
and FFIEC 009a data on select U.S. banks’ foreign claims. This
paper
relies on two ‘versions’ of this dataset. The first, ‘unrestricted’
dataset contains detailed balance sheet data on all U.S. financial
institutions subject to reporting requirements. The second,
‘restricted’ dataset contains balance sheet and country-specific
foreign claims data for all U.S. financial institutions who report
to the FFIEC on the 009a form. This is referred to as the
‘restricted’
dataset.
The ‘unrestricted’ dataset incorporates various types of banking
organizations, including commercial banks, bank holding
compa-

nies, and edge and agreement corporations. The dataset was
created by merging regulatory balance sheet data from the Call
Reports with foreign claims data from the FFIEC 009a forms.
As
for the balance sheet data, data were collected from the Report
of Condition and Income, as reported on the FFIEC Central
Data
Repository’s Public Data Distribution site (for commercials
banks),
from the FR Y-9C forms as reported on the Chicago Fed’s
website
(for bank holding companies) and from the FR 2886b and
FFIEC
002 forms (for Edge and Agreement Corporations). This
combined
dataset consists of balance sheet and financial data for over
18,000 U.S. financial institutions. In order to identify those
banks
with significant foreign exposures, an indicator variable is
created
that takes on a value of ‘1’ if the bank reports on the FFIEC
009a
form, and ‘0’ otherwise.
The ‘restricted’ dataset contains information on the subset of
U.S. financial institutions that are required to report detailed
infor-
mation on international claims volumes and activities on the
FFIEC’s 009a Data Report form. U.S. financial institutions are
required to report foreign country-specific claims on this form
(the volumes broken down into cross-border and foreign
affiliate
claims) if exposure to that given country exceeds 1% of the
institu-
tion’s total assets, or 20% of its capital. This dataset contains
data

on 82 FFIEC-reporting banks’s foreign claims in 83 host
markets.
Of the reporting U.S. banks, 59% are commercial banks, 28%
are
offices of bank holding companies, 7% are trade financing
offices,
and the remainder are in the business of investment banking and
securities dealing or sales financing.12 Cross-border claims and
foreign affiliate claims are reported separately for each host
country-bank-time period combination.
The key dependent variables in the following econometric anal-
ysis are: host country-specific cross-border claims, foreign
affiliate
claims and market entry/exit choices. Data for cross-border
claims
are taken as Column 4 in the FFIEC 009a forms, and defined as:
‘Amount of Cross-border Claims Outstanding After Mandated
Adjustments for Transfer of Exposure (excluding derivative
prod-
ucts’ (Column 1) plus ‘Amount of Cross-border Claims
Outstanding
from Derivative Products after Mandated Adjustments for
Transfer
of Exposure’ (Column 3). Foreign affiliate claims are defined as
‘Amount of Net Foreign Office Claims on Local Residents
(including
derivative products)’ (Column 2). Total foreign assets in host
coun-
try i are therefore defined as the sum of the above three items.
U.S.
(home country) claims are calculated from the Call Reports as
described in detail in Table 1. Importantly, the model above
describes banks’ claims and liabilities as functions of bank and
market-specific characteristics. In order to include data on bank
traits (such as total capital and return on equity), the ‘restricted’

dataset is merged with data on the 82 FFIEC 009a-reporting
banks’
balance sheets from the regulatory sources above. In order to
incorporate data on host markets, the bank data is also merged
with data on the macro-indicators of the 83 foreign countries
that
U.S. banks hold claims in. Country-specific macro data come
from
the IMF’s International Financial Statistics, OECD’s Statistics,
the
EIU’s Country Data and the World Bank’s Bank Regulation and
Supervision database. The ‘restricted’ dataset therefore contains
quarterly balance sheet, financial and country-specific foreign
claims data for 82 banks in 83 foreign markets, broken down by
claims type.
The choice of the time frame for the analysis is motivated by
data availability considerations. On its website, the FFIEC
makes
009a data available starting with the 2003 Q1 quarter.
Therefore,
both the ‘unrestricted’ and the ‘restricted’ datasets cover the
period
spanning from the first quarter of 2003 to the first quarter of
2013,
a total of 41 quarters.
Some traits of this ‘restricted’ dataset warrants further discus-
sion. First, the 009a form reports data on an ‘ultimate risk’
basis,
i.e. adjusted for cross-country transfers of risk. As such, the
reported
claims reflect total claims acquired in that host market, minus
the
amount of claims for which the repayment responsibility has
been

Table 1
Summary of Explanatory Variables.
Variable name Notation Empirical measure
Cross-Border Claims claims2 Cross-border claims, millions
USD column 4 from the FFIEC 009a surveys
Affiliate Claims claims3 Net Affiliate claims, millions USD
from the FFIEC 009a Surveys
U.S. Domestic Claims claims1 Sum of U.S. public claims,
financial sector claims and non-financial private claims of
banks
a
Foreign Market Presence {P Taken as 1 if claims3 > 0 on FFIEC
009a form, 0 otherwise
Bank Capital Kj Bank’s total assets, millions USD
RCON/RCFD/RIAD/RCFD 3210 from the regulatory datasets
Expected Market Return �a Stockmarket return index, averaged
over 3-quarter rolling windows from the IMF’s IFS & EIU’s
Country Data
GDP Deflator – From EIU’s Country Data
Return on Equity – Calculated as RCON/RCFD/RIAD/RCFD
(4340/3210) � 100
Capital-Asset Ratio – RCON/RCFD/RIAD/RCFD (3210/8276) �
100
Cost-Asset Ratio – RCON/RCFD/RIAD/RCFD (4093 or
4073)/2170 � 100
Foreign Owner Percent – RCON/RCFD/RIAD/RCFD 9325
Income Tax Rate s Corporate Tax Rate in host market used in
structural stage only
Minimum Capital Ratio and Reserve

Requirement
ðj; dÞ Minimum Capital Adequacy & RRR from the World
Bank’s Bank Regulation and Supervision database and
national central bank websites
Host-U.S. covar. – Covariance between the U.S. and host
stockmarket growth, over 3-quarter rolling windows
Market Return Variance V Variance of stockmarket index
growth rate taken over 3-quarter rolling windows
Real GDP – From EIU’s Country Data
Inverse Mills (first) MR Inverse Mills ratio calculated from the
‘reporting’ probit regression
Inverse Mills (second) MP Inverse Mills ratio calculated from
the ‘market presence’ probit regression
Bank & Regulatory Risk Aversion, Entry &
Scrap values
ðk; h; C; WÞ Estimated from Model
a Note: U.S. public claims are the sum of items 0090, 0371,
8636, 1918, 2107, 3532, g421, 8635. U.S. financial sector
claims are the sum of items 0082, 1505, g418, 3171
minus c029). U.S. non-financial private claims are items 1761,
2182, g422, 1975 minus c028.
233–247
transferred to other countries (outward transfer of risk), plus the
amount of claims lent to other countries for which the given
host
country has taken responsibility (inward transfer of risk). As
such,
the actual amounts lent to any given country (on an ‘immediate

counterparty’ basis) can be quite different from the amounts the
country is responsible for repaying (on an ‘ultimate risk’
basis).13
Second, U.S. banks’ cross-border claims are reported on a
‘gross’ basis,
but foreign affiliate (local) claims are reported ‘net’ of affiliate
liabil-
ities. Therefore, the bank level dataset does not allow for the
separate
analysis of liabilities, and the foreign affiliate claim equations
are
estimated using ‘net’ foreign affiliate claims as the dependent
vari-
able. Third, as mentioned above the FFIEC 009a reports data on
‘claims’ as opposed to ‘loans’. As a result, the reported volumes
include assets other than loans (such as bonds, stocks, and
derivative
products). To reflect the structure of the dataset, loans l are
hereon
replaced with claims. The motivation for using stock market
indices
as measures of market returns comes from this composite nature
of
the dependent variable. These indices are likely to capture the
average returns on the various types of assets that are reported
as
‘claims’ on the FFIEC 009a form. Finally, the FFIEC 009a
dataset does
not provide information on the mode of foreign market entry,
i.e.
whether entry occurred via merger with an incumbent bank in
the
host market, or via greenfield investment. This distinction,
however,
should not matter for the following analysis since foreign

acquisition
and greenfield investment both imply the payment of some fixed
costs. If entry occurs via foreign acquisition rather than
greenfield
investment, the scrap value of market exit can be interpreted as
the
value of the sale of foreign participation.14
3.2. Estimation method
The estimation consists of two stages. The first stage examines
the role of a broad set of bank vs. market traits in claims
volume
and entry/exit decisions simultaneously. This, together with the
correction for the various data reporting and market selection
biases, is a step beyond previous practice. The second
(structural)
stage of the estimation addresses the question: what are banks’
13 Of course, at the global level the two types of exposure must
equal.
14 Many thanks to the anonymous referee for making this point.
and regulators’ stance on risk, and the entry costs and scrap
values
of foreign bank entry? The gist of this step is to allow data to
reveal
the values of these parameters that would rationalize observed
bank behavior. The following analysis proceeds under two main
assumptions. First, the model described above represents banks’
true behavior. Second, the market entry/exit and claims volume
choices observed in the data correspond to banks’ optimal
actions.
An important issue to address in the following estimation is that
the second-stage structural parameters already enter the first-
stage policy function. This is handled via an iterative
formulation.
First, the second stage of the estimation (described below) is
run

on actual bank data. This yields initial estimates for the
structural
parameters, used as data in the first stage estimations from then
onwards. The iterations continue until the structural estimates
converge. The second-stage structural estimators are consistent
and asymptotically normal if the sufficient conditions specified
in
Appendix C are met.
3.2.1. First-stage estimation
This section presents a brief outline of the estimation. The main
focus of the first stage is the reduced-form estimation of the
rela-
tionship between banks’ choices of foreign markets and claims
vol-
umes and the state variables in P. However, there are two
important selection biases that arise at this first (reduced form)
stage of the estimation, necessitating some auxiliary steps of
cor-
rection. One source of selection bias is the fact that only U.S.
banks
with significant foreign exposure are required to report on the
FFIEC 009a form. Another source of selection bias is inherent
in
the market entry/exit choices. Since the chosen markets are
funda-
mentally more attractive, banks are likely to acquire
significantly
more claims in these markets than they would in the average
market. Both biases are corrected via the Heckman-style two-
step
selection bias correction method.15 The reduced-form first
stage of
the estimation will consist of three steps: a probit equation of
banks’
reporting/non-reporting status, a probit equation of the market

entry/exit choice, and the claims volume choice equations.
15 In general, the two-step correction consists of (1) the
calculation of the inverse
Mills ratio from the selection equation and (2) the inclusion of
this inverse Mills ratio
as an extra estimator in the ‘biased’ equation.
247 239
First, the reporting bias is considered. Let Nj denote the bank’s
excess utility from holding claims in any given foreign country
in
excess of 20% of its capital or 1% of its assets.16 Nj is an
unobserved
function of bank traits. Let {Rj denote the indicator function
that
takes a value of 1 if the bank reports to the FFIEC via the 009a
form,
and 0 otherwise.17 Then the observation criterion is
Observe {Rj ¼ 1 if Nj ¼ /
R �PRj þ eRj P 0
Observe {Rj ¼ 0 otherwise:
(
ð3:1Þ
where PRj is the set of bank characteristics that affect banks’
report-
ing vs. non-reporting status (i.e. whether they maintain a high
enough foreign exposure to have to report). If eRj is normal, the
prob-
ability of reporting can be expressed as follows.

prob {Rj ¼ 1
� �
¼ Prob Nj P 0
�
¼ Prob / �Pj þ eRj P 0
� �
¼ U / �Pj
�
ð3:2Þ
This equation is estimated via random-effects probit, to take
account of the panel structure of the data. The dependent
variable
is an indicator variable that takes on a value of 1 if the bank
reports
on the FFIEC 009a form, and 0 otherwise. The set of bank traits
included in pRj are as follows: total capitalization, Return on
Equity,
Post-financial crisis indicator variable, capital-to-assets ratio,
cost-to-assets ratio, percent owned by foreigners, bank type
(bank
holding company, edge corporation, etc.), International Banking
Facility indicator, bank’s age (in years) and bank’s risk
aversion
(kj).18 After the estimation, the inverse Mills ratio is
calculated.19
Second, the market selection bias is examined. Recall that {Pj
denotes the ‘indicator’ function that takes a value of 1 if bank j
is

‘present’ in the market, and 0 otherwise. Information on {Pj is
avail-
able only if the bank reports on Form 009a, i.e. if it ‘passes’ the
first
stage selection with {Rj ¼ 1. Let X
i
j denote bank j’s excess utility
from holding claims in country i, which is an unobserved
function
of bank, market and country-specific traits. The observation
rule of
{P;ij is then as follows.
Observe {P;ij ¼ 1 if X
i
j ¼ j � ½{
P;i
j;t�1; P
P;i þ eP;ij P 0 and {
R
j ¼ 1
Observe {P;ij ¼ 0 otherwise:
(
ð3:3Þ
where PP;ij is the set of bank and host market traits that affect
banks’
choice of market presence. If eP;ij is normal, the probability of
affiliate presence can be expressed as follows.

prob {P;ij;t ¼ 1
� �
¼ Prob j � ½{P;ij;t�1; P
P;i
j ; M
R� þ eP;ij P 0
� �
¼ U j � ½{P;ij;t�1; P
P;i
j ; M
R�
h i
ð3:4Þ
where MR is the inverse Mills ratio from the estimation of Eq.
(3.2).
Eq. (3.4) is estimated via random-effects probit, to take account
of the panel structure of the data. The dependent variable is an
indicator variable that takes on a value of 1 if the bank is
present
in the given host market that period, and 0 otherwise. The set of
explanatory variables in pP;ij are: lagged presence indicator {
P;i
j;t�1,
total capitalization, capital-assets ratio, return on equity,
post-financial crisis indicator, gross domestic product, bank’s
cost-to-assets ratio, percentage owned by foreigners,
stockmarket

growth (market return), variance of stockmarket returns,
16 The reporting threshold on Form 009a.
17 The superscript R stands for ‘Reporting’.
18 The variables that appear in this initial equation but not in
any of the later-stage
equations (i.e. the identification variables) are: percent owned
by foreigners, bank
type, International Banking Facility indicator and bank’s age.
19 An important issue to address is that the second-stage
structural parameter in H
already enter the first-stage policy function. This is handled as
described in the first
paragraph of Section 3.2.
covariance of host market with U.S. stock market and GDP
deflator.
The following structural parameters are also included: fixed
entry
cost, scrap value, regulatory risk aversion and bank risk
aversion.
After Eq. (3.4) is estimated, marginal effects for the market
entry
subset with ð{P;ij;t ¼ 1j{
P;i
j;t�1 ¼ 0Þ are calculated. Marginal effects for
the market exit subset with ð{P;ij;t ¼ 0j{
P;i
j;t�1 ¼ 1Þ characterize banks’
market exit choice. After the estimation, predicted probabilities
are
calculated from Eq. (3.4). These are the transition probabilities
for

the ’market presence’ vector {P .
As a next step, the non-linear first order conditions taken from
(2.11) are log-linearized around the perfectly competitive
symmet-
ric certainty equilibrium, the steps of which are shown in
Appendix
A and B. This log-linearization yields estimable reduced-form
policy equations. In these log-linearized estimable equations, l
is
now replaced with claims to reflect the structure of the data.
Suppressing the time subscripts, the observation criteria for the
domestic, cross-border and foreign affiliate claims volumes are
as
follows.
For U:S: and foreign affiliate claims ðm¼1;3Þ :
ðclaimsÞi1;3;j¼pi1;3;j �P
i
1;3;jþ�i1;3;j if {
R
j ¼1 and {
P;i
j ¼1
for cross-border claims ðm¼2Þ :
ðclaimsÞi2;j¼pi2;j �P
i
2;mþ�i2;j if {
R
j ¼1

8>>>><>>>>:
ð3:5Þ
where ðP1; P2; P3Þ are the sets of explanatory variables and
ð�1; �2; �3Þ are error terms for the domestic, cross-border
and foreign
affiliate claims volumes, respectively. Inclusion of the inverse
Mills
ratios from the two selection equations eliminates the selection
bias
from the cross-border and foreign affiliate claims regressions.
ðclaimsÞi1;3;j ¼ pi1;3;j � ½P
i
1;3;j; M
R; MP � þ �i1;3;j
ðclaimsÞi2;j ¼ pi2;j � ½P
i
2;m; M
R� þ �i2;j
ð3:6Þ
The set of bank and market traits included in (3.6) are as fol-
lows: total capitalization, return on equity, bank’s capital-assets
ratio, post-financial crisis indicator, GDP, percent of foreign
owner,
minimum capital ratio, stockmarket growth, host market – U.S.
market covariance, variance of stockmarket returns and GDP
deflator. The following structural parameters are also included:
regulatory risk aversion and bank risk aversion. Eq. (3.6) is
estimated via random-effects maximum likelihood, to take
account

of the panel structure of the data.
A further important issue to address is: how do the state vari-
ables in P evolve over time? In order to be able to use Eq.
(2.12)
to approximate bank j’s expected utility, one needs numerous
predicted paths of the state variables in P to average over. Let
Pz denote the zth state variable. If Pz has the Markov property,
the following equation can be used to forward simulate values
of
Pz, given a starting value.
Pz;t ¼ nz �Pz;t�1 þ ez ð3:7Þ
Empirical estimates of ½n̂ z; ^varðezÞ� can be obtained by
running
the linear regression equation in (3.7) on the observed (actual)
data
for Pz. This regression yields coefficient estimates ½n̂ z� and
esti-
mated sample variance of the error term ^varðezÞ. Given an
initial
value for Pz, the coefficients ½n̂ z� and random error term
draws
from the normal distribution with moments Nð0; ^varðezÞÞ can
be
used to forward simulate N paths of Pz. Let Pn denote the set of
state variables resulting from the n’th simulation. Plugging Pn
into
Eq. (3.4) and random error term draws based on the estimated
var-
iance ^varðePÞ then yield simulated paths of the market
presence
vector {̂P (the endogenous state variable). Finally, the Pn’s
together
with the policy function estimates /̂ from (3.4) and (3.6) are
then

plugged into Eqs. (2.11). Taking the discounted sum of utilities
and
averaging over all simulations in N then becomes the empirical
approximation of the indirect utility in Eq. (2.12) as follows.
233–247
bV P;x; Hð Þ ¼ 1
N
RNn¼1
E
XT
t¼0
ctu x̂ n Pn:t; mn;tð Þ;Pn;t; mn;t; Hð ÞjP0 ¼ P; H
" #
: ð3:8Þ
3.2.2. Second step: structural parameter estimates
This second step of the estimation consists of finding the values
of the structural parameters in H that ensure that the bank’s
observed claims and market entry/exit choices are rational (i.e.
yield the highest expected lifetime value, as compared to other
possible paths of action). The goal is to estimates these
parameters
for each country separately, i.e. to get estimates of Hi
exploiting
variation across banks, markets and time periods. This is done
as
follows.

Let bV j P;xj;x�j; H0� denote the predicted value of bank j’s
expected lifetime value, corresponding to its optimal strategy
x ¼ ðxj;x�jÞ. Let ðx0j;x�jÞ denote the strategy that consists of
bank j taking a one-step deviation from its optimal strategy with
all other banks’ strategies unchanged. For instance, suppose that
one of the observed datapoints is that bank j entered market m
at time t. A one-step deviation would be for this bank to enter
market m at time t � 1 instead of t, all other actions unchanged.
Let bV P;x0; Hð Þ denote the value of this one-step deviation,
calcu-
lated from Eq. (3.8). Let k ¼ 1 . . . K index the one-step
deviations.
For each one of these deviations k, the corresponding expected
bank value can be calculated based on (3.8). If banks behave
rationally, the value of the observed set of actions in Eq. (3.8)
must
have a higher value than any of the considered one-step
deviations.
bV j P;xj;x�j; H0� P bV j P;x0j;x�j; H0� � ð3:9Þ
There are a total of K ¼ 2 � ðT � 1Þ � J �M one-step
deviations to
consider for any given country, across all banks, markets and
time
periods.20 The goal is to obtain country-specific estimates ^Hi
that
minimize violations of this K set of inequalities for each
country i
separately. 21
Let x denote the equilibrium conditions, and gð�Þ is the
‘excess
value’ the bank gets from its optimal set of choices over the
k’th
sub-optimal path.

gj;k x; H; /̂
� �
¼ bV j P;xj;x�j; H; /̂; ĵ; p̂ � �
� bV j P;x0j;k; x�j; H; /̂; ĵ; p̂ � � ð3:10Þ
Recall that /̂; ĵ; p̂
� �
denote the first-stage policy function
estimates. Then the mean squared deviation from the optimality
condition in Eq. (3.9) across all perturbations k ¼ 1 . . . K can
be
written as:
Q H; /̂; ĵ; p̂
� �
¼ 1
K
�
XK
k¼1
min gk H; /̂; ĵ; p̂
� �
;0
n o� �2
ð3:11Þ
The best estimates of the structural parameters in H are such
that

Ĥ :¼ arg min
H
Q H; /̂; ĵ; p̂
� �
ð3:12Þ
The estimators are consistent and asymptotically normal if the
sufficient conditions specified in Appendix C are met.
20 There are ðT � 1Þ � J entry and ðT � 1Þ � J exit
possibilities to consider for each
market.
21 Bank-specific kj are estimated from a first-pass at the model
where variation
across market, time and one-step deviations is used to identify
kj ’s. These values are
then used as given in the market-specific entry cost, scrap value
and risk aversion
estimations described in this section.
4. Estimation results
4.1. Market entry/exit choices and claims volumes
In the interest of space, detailed results on the FFIEC reporting/
non-reporting selection equation are not reported.22 It suffices
to
say that banks who report to the FFIEC on their foreign
exposures
(1) are bigger (in terms of total capitalization) and more cost-
effective, (2) have a higher percentage of foreign ownership, (3)
more likely to be international banking facilities, in particular
edge
or agreement corporations, and (4) younger, in terms of years
since

U.S. incorporation. Tables 1 and 2 describe and provide
summary
statistics for the explanatory variables used in the estimations,
respectively.
The first two columns in Table 3 list the effects of the set of
explanatory variables in PP on banks’ choice to set up (market
entry) or close (market exit) a foreign affiliate in a host
country.
Bank size (as proxied by total capital) is by far the most
important
determinant of foreign market entry and exit. A 1% rise in total
capital increases the probabilities of entry and exit by 1.73%
and
3.41% points, respectively. Furthermore, less cost-effective and
less
profitable banks are significantly more likely to enter, and less
capitalized banks are more likely to exit a host market. Among
host
market traits, a 1% increase in the co-movement of the U.S. and
host financial markets raises the probability of exit by as
much as 10.52% points. Interestingly, greater variance of host
market returns makes banks more likely to set up an affiliate
there
– perhaps as a way to ensure closer monitoring of volatile
projects.
Among the structural variables, 1% increases in entry costs and
the
risk aversion of regulators make market entry significantly less
likely (by 1.48% and 0.28% points, respectively). Greater scrap
values raise the probability of market exit, whereas the bank’s
risk
stance does not play a significant role.
The effect of the financial crisis warrants further discussion.
Recent literature has highlighted significant reductions in U.S.

banks’ foreign activities since the financial crisis (as outlined in
the Introduction). The results of this analysis qualify that state-
ment: much of the documented reduction is directly attributable
to detrimental changes in bank and market conditions. After
con-
trolling for changes in a broad set of market and bank traits
over
time, the positive coefficient on the post-crisis indicator
variable
remains significant and large – suggesting a structural shift
towards foreign market entry. All else equal, banks are 5.72%
points more likely to enter a new market in the period after
2008 Q3 than before.
The last two columns of Table 3 describe the cross-border
claims and foreign affiliate claims estimation results. In the
cross-border results of the third column, the dominance of bank
traits is apparent. Larger, worse capitalized and less profitable
banks hold significantly more cross-border claims. A 1% point
increase in foreign ownership raises C–B claims by as much as
0.80%. Among market traits, only the home-market (U.S.) mini-
mum capital ratio requirement (MCR) has a significant effect,
whereas most host market traits enter with the expected signs
but insignificantly. Controlling for changes in market and bank
traits, U.S. banks acquire significantly less cross-border claims
in
the post-crisis period than before, in line with previous
evidence
(Cetorelli and Goldberg, 2009). Importantly, the correlation
coeffi-
cient qR is positive and significant, validating the importance of
correcting the reporting bias. Those banks who report on the
FFIEC
009a form have unobservable traits that make them lend 10.10%
more in cross-border claims than the average U.S. bank would.
22 Detailed tables are available from the author upon request.

Table 2
Summary statistics of variables.
Name Minimum 25 ptile 50 ptile 75 ptile Maximum Mean
Standard dev.
Cross-border claims (logs) 0.00 2.89 4.84 7.52 11.86 5.26 2.86
Affiliate claims (logs) �0.99 4.09 6.27 8.02 13.55 6.10 2.72
Foreign market presence 0.00 0.00 0.00 1.00 1.00 0.25 0.43
Bank capital (log) �6.91 3.85 5.67 7.81 13.43 5.80 3.16
Exp. market return (%) �25.12 �2.71 3.03 8.38 69.08 2.63
10.88
GDP deflator 77.16 99.3 105.18 112.37 470.93 118.04 50.39
Return on equity (%) �11.55 1.30 4.24 8.97 126.24 7.40 13.26
Capital-asset ratio (%) 0.57 11.80 15.39 21.24 60.59 18.10 9.99
Foreign owner percent 0.00 0.00 0.00 99.00 100.00 37.68 46.41
Min capital ratio 8.00 8.00 8.00 9.00 13.00 8.62 1.40
Host-U.S. covar. �43.68 13.52 33.28 81.46 229.53 51.60 52.83
Market return variance 0.31 20.59 50.24 111.65 484.13 77.90
78.54
Inverse mills (1st stage) 0.13 0.22 0.28 0.37 1.20 0.35 0.21
Inverse mills (2nd stage) 0.26 0.35 0.41 0.82 3.78 0.76 0.72
Real GDP (logs) 1.49 4.64 6.29 6.84 9.52 5.96 1.90
Cost-asset ratio (%) 0.00 1.25 2.49 4.15 38.22 3.66 4.78
Income tax rate (%) 0.00 22.00 28.00 33.00 44.00 26.25 8.81
Reserve reqmnt. (%) 0.00 0.00 2.00 13.00 60.00 8.08 14.30
Note: Variable definitions can be found in Table 1.
247 241
Foreign affiliate claims results are reported in the last column
of

Table 3. Larger and better capitalized, as well as more
profitable,
foreign-owned and risk averse banks acquire significantly more
foreign affiliate claims. As expected, greater variance of foreign
market returns discourages foreign affiliate claims. All else
equal,
banks hold slightly (0.28%) more foreign affiliate claims in the
post-crisis period. The positive and statistically significant
correla-
tion coefficients ðqR;qPÞ highlights the importance of
correcting
the selection bias. Those banks who report on the FFIEC 009a
form
hold 5.70% more foreign affiliate claims than the average U.S.
bank
would. Furthermore, the ‘entered’ markets have special unob-
served traits that make the average U.S. bank hold 3% more
claims
in these markets than they would in the average foreign market.
Ignoring these selection issues would lead to biased coefficient
estimates.
Those variables which have different effects on the market
entry vs. the affiliate volumes choices warrant special attention.
In particular, banks with higher returns on equity (ROE) are
signif-
icantly less likely to enter a new market, but conditional on
having
entered, lend significantly more there. Similarly, banks are
signifi-
cantly less likely to enter host markets with strict bank
regulators
(higher values of the risk stance h), but lend significantly more
in
the presence of such regulators, conditional on having already
entered. The effect of the covariance between the returns of the

U.S. and host markets is also interesting. Stronger such
covariance
makes banks less likely to enter a host market, but lend
significantly more there once entry occurs. To the extent that
the
covariance of returns is a measure of how closely integrated the
host country financial market is with that of the U.S., the
implica-
tion is that financial integration provides a stronger lending
motive
than risk sharing considerations. However, it is the portfolio
diver-
sification motive that appears to drive the market entry/exit
decision.
A key implication of the results is that the aftermath of the
financial crisis has brought a compositional shift in foreign
bank-
ing, and not a general trend away from it. It appears that the
well-documented reduction in U.S. banks’ foreign activities (as
dis-
cussed in the Introduction) is due to the deterioration of bank
and
market conditions in the aftermath of the financial crisis, and
not
attitudes against foreign involvement. The first-stage results
imply
that after controlling for market and bank balance sheet
changes,
U.S. banks have shown a strong tendency towards foreign
affiliate
banking away from cross-border banking over the past 5 years.
4.2. Risk aversions, market entry costs and scrap values
This subsection describes the estimation results for the struc-
tural parameters of the model: banks’ risk aversion parameter

kj,
the country-specific regulatory risk stance hi, and the country-
specific entry costs Ci and scrap values � i (which are common
across banks and constant over time). The second stage of the
model is estimated for the pre- and post-crisis period separately.
All structural estimates are summarized in Table 4.
Bank risk aversion is the k term from the mean–variance objec-
tive of the bank. As such, it captures the weight that the bank
assigns to the market risk (global variance–covariance of
returns)
on its portfolio, relative to expected returns. The analysis yields
a
median estimate k ¼ 0:04 for the pre-crisis period, and k ¼ 0:07
for the post-crisis period. This value is significantly lower than
previous risk aversion estimates for U.S. banks’ domestic
activities,
at around 0.20 (Nishiyama, 2007). It is, however, in line with
expectations that the analysis of the global activities of large
international banks would indicate more risk-loving behavior
than
results derived from the local activities of domestic U.S. banks
of all
sizes.
Regulatory risk stance h is the weight that the given country’s
bank regulator attaches to the market risk on banks’ local
(country-level) portfolios. This is the weight that appears in the
risk-weighted minimum capital requirement in Eq. (2.9) and
(2.10). Greater risk aversion (higher weight) means that banks
are more limited in the amount of risk they can take on in their
local portfolio. The median country’s bank regulator is more
risk
averse than the median bank in both the pre-and post-crisis
periods. Looking across countries, the bank regulator is more
risk

averse than the median U.S. bank in 77% of the countries. The
median country’s bank regulator’s risk aversion has increased
since
the financial crisis (from 0.07 to 0.16, respectively).
Entry costs represent all fixed costs of entering a new banking
market, including brick and mortar costs, as well as
administrative,
bureaucratic and legal fees (such as costs of licences, permits
and
incorporation). Scrap values represent the amount that banks are
able to recover of these entry costs (via sale of real estate,
equip-
ment, refunds, liquidation, etc.) upon exiting the market. Entry
costs have increased threefold since before the financial crisis,
whereas scrap values have remained relatively stable. Before
the
crisis, U.S. banks were able to recover 75% of entry costs in the
form
of scrap. Since the crisis, however, this share has fallen to only
25%.
Table 3
Estimation Results. Foreign market entry & exit and claims
volume choices. Reported coefficients are elasticities and semi-
elasticities (indicated by s superscript).
Independent variables Dependent variables
Probabilities Claim volumes
Market entry Market exit Cross-border Affiliate
Total capitalization 1.73⁄⁄⁄ 3.41⁄⁄ 0.77⁄⁄⁄ 0.28⁄⁄⁄

(0.58) (1.62) (0.03) (0.09)
Capital-assets ratios �0.02 �0.51 �0.10⁄⁄⁄ 0.02⁄⁄
(0.07) (0.35) (0.01) (0.01)
Return on equitys �0.33⁄⁄⁄ �0.15 �0.10⁄⁄⁄ 0.10⁄
(0.12) (0.42) (0.01) (0.06)
Post-crisiss 5.72⁄⁄ �5.82 �0.17⁄⁄⁄ 0.28⁄
(2.61) (9.77) (0.06) (0.16)
GDP 0.71 �2.00 0.11 0.10
(0.64) (3.03) (0.08) (0.30)
Cost-to-assets ratios 0.66⁄⁄ 0.67 – –
(0.32) (1.41)
Foreign owner percents – – 0.80⁄⁄⁄ 0.01⁄
((0.01) (0.01)
Minimum capital ratios – – -0.05⁄⁄ �0.30
(0.02) (0.60)
Market return 0.05 0.02 0.10 0.10
(0.05) (0.57) (0.10) (0.10)
Host-U.S. return covariance �1.14 10.52⁄ 0.04 0.31⁄⁄
(0.94) (6.29) (0.04) (0.13)
Variance of returns 1.48⁄ �1.34 �0.20 �0.13⁄
(0.90) (4.45) (0.40) (0.07)
Fixed entry cost �1.48⁄ – –
(0.65)
Regulatory risk aversion �0.28⁄⁄ 0.28 0.01 0.30⁄⁄⁄

0.12) (0.32) (0.01) (0.10)
Fixed scrap value – 0.66⁄ – –
(0.38)
Bank’s risk aversion 2.15 �8.28 �0.12 0.57⁄⁄
(4.20) (14.67) (0.19) (0.23)
GDP Deflator – – 0.51⁄⁄ -0.02
(0.21) (0.25)
Constant �0.84 �10.34 0.92 11.56⁄⁄⁄
(15.41) (15.95) (1.87) (3.83)
qR: ‘Reporting’ bias 0.55 – 0.65⁄ 0.42⁄
(0.82) (0.36) (0.25)
qP: ‘Market Choice’ bias – – – 0.11⁄⁄⁄
(0.04)
Prob Pv2 0.01 0.06 0.00 0.00
No. of country-bank pairs 241 56 215 89
Observations 2232 1568 1985 1895
Notea: The left two columns present the results of the market
entry/exit random-effects probit estimations, described in Eq.
(3.4). The dependent variable is an indicator that
equals 1 if the bank is present in the given host market in that
time period, and 0 otherwise. For the market entry/exit
estimations, the reported marginal effects should be
interpreted as the % point change in the probability of entry or
exit, in response to a 1 unit (in case of semi-elasticities marked
by superscript s) or a 1% (in case of the
unmarked variables) change in the explanatory variable.
Noteb:The right two columns present the results of the cross-
border claim and foreign affiliate claims random effects

maximum likelihood estimations, described in Eq. (3.6).
The dependent variables are the logs of the total cross-border
claims and net affiliate claims that banks report on the FFIEC
009a form, by country. For the cross-border and
affiliate claim volume equations, the reported marginal effects
should be interpreted as the percent change in the volume of
claims, in response to a 1 unit (in case of
semi-elasticities marked by superscript s) or a 1% (in case of
the unmarked variables) change in the explanatory variable. All
explanatory variables are as in Table 1.
Notec: Reported coefficients are calculated elasticities and
semi-elasticities (s).
⁄ Statistical significance at 10% levels.
⁄⁄ Statistical significance at 5% levels.
⁄⁄⁄ Statistical significance at 1% levels.
Table 4
Summary statistics for structural estimation results.
Estimated parameters Minimum Median Maximum Mean St.
deviation Obs.
Bank risk stance 2003–2007 0.01 0.04 0.10 0.04 0.02 720
2008–2013 0.02 0.07 0.07 0.06 0.01 684
Entry cost 2003–2007 99.99 128.55 395.13 159.87 70.81 1444
2008–2013 244.00 395.19 1308.54 536.10 223.36 1368
Scrap value 2003–2007 5.54 96.38 193.11 – 46.97 1444
2008–2013 92.30 99.75 99.99 99.07 1.58 1368
Regulatory risk stance 2003–2007 0.03 0.07 0.42 0.12 0.12 2888
2008–2013 0.03 0.16 0.48 0.19 0.15 2736
Note: Summary statistics for estimated structural parameters,

across all countries. The ’Obs.’ column indicates the number of
simulated datapoints in the estimation.
233–247
Table 5
Correlations with macroconomic and regulatory indicators.
Variable Entry cost Scrap value Entry – scrap Regulatory risk
aversion
2003–2007 2008–2013 2003–2007 2008–2013 2003–2007 2008–
2013 2003–2007 2008–2013
Entry cost 1.00 1.00
Scrap value 0.34⁄⁄⁄ 0.64⁄⁄⁄ 1.00 1.00
Entry – scrap 0.99⁄⁄⁄ 0.92⁄⁄⁄ 0.27⁄⁄⁄ �0.13⁄⁄ 1.00 1.00
Regulatory 0.14⁄⁄ 0.13⁄⁄ 0.20⁄⁄⁄ �0.06 0.12⁄ �0.14⁄⁄ 1.00 1.00
Risk Stance
Tax rate 0.12 0.26 �0.25⁄⁄⁄ �0.09 0.14⁄ 0.35 0.27⁄⁄ �0.32
Reserve req. �0.37⁄⁄⁄ �0.46 0.15⁄ �0.33 �0.37⁄⁄⁄ 0.27 0.35⁄⁄⁄
�0.68⁄⁄
Market return �0.27⁄⁄⁄ �0.11⁄⁄ 0.15⁄⁄⁄ �0.10⁄⁄ �0.29⁄⁄⁄ �0.09⁄
0.07 0.15⁄⁄
Market variance 0.01 0.01 0.12⁄⁄ 0.08 �0.01 �0.03 0.37⁄⁄⁄ 0.09⁄
Real GDP �0.30⁄⁄⁄ 0.76⁄⁄⁄ �0.93⁄⁄⁄ 0.26⁄⁄⁄ �0.22⁄⁄⁄ 0.79⁄⁄⁄ �0.24⁄⁄⁄
�0.23⁄⁄⁄
Inflation �0.17⁄⁄⁄ �0.06 0.01 �0.17⁄⁄⁄ �0.17⁄⁄⁄ 0.03 0.26⁄⁄⁄ �0.03
Note: Reported values are correlation coefficients.
⁄ Statistical significance at 10% levels.

⁄⁄ Statistical significance at 5% levels.
⁄⁄⁄ Statistical significance at 1% levels.
247 243
In order to shed light on the meaning behind these numbers,
Table 5 examines how the structural estimates vary with
economic
and regulatory measures of markets. Countries with higher entry
costs also offer significantly more in scrap values upon exit.
Since
part of the entry costs is regulatory compliance, it makes sense
that
countries with stricter bank regulators also have higher entry
costs. High entry cost markets also offer significantly lower
market
returns. On the other hand, the entry-scrap difference (a
measure
of banks’ ability to recover fixed costs) is higher in these low
return
countries. Furthermore, results indicate that entry costs vary
significantly more across markets and over time than scrap
values
do. As expected, regulators take a much stricter stance on
banks’
ability to take on market risk in countries where the financial
market is chronically volatile. This regulatory risk aversion
tends
to be lower in larger economies (as measured by GDP).
5. Simulation exercises
This section conducts two types of exercises. The first subsec-
tion examines the effect of rising bank risk aversion k on the
aver-
age bank’s behavior, assuming all countries’ regulators hold
their

risk stances steady. The second subsection then explores the
impact of increases in all foreign regulators’ stance on risk,
assum-
ing all banks’ and U.S. regulators’ risk aversions stay constant.
The
goal is to explore the effects of these two types of changes on
(1)
banks’ probability of entering a new host market; (2) the
average
bank’s expected value from operating in a host country, (3) the
expected share of foreign assets, and (4) the expected ratio of
affil-
iate claims to cross-border claims in the average bank’s
portfolio.23
Simulations are carried out for the pre- and post-crisis periods
separately. As k and h are incrementally increased from 0.05 to
0.5,
respectively, the model is re-estimated at each stage and the
vari-
ables of interest in (1) through (4) are recorded. Table 6
summarizes
the information shown in Figs. 1 and 2.
24 Whereas controlling for changes in these bank and market
conditions over time
would show a trend towards foreign market entry.
25 This is the mean return minus the risk-weighted variance on
the bank’s portfolio
5.1. Increasing bank risk aversion
The amount of risk that banks are willing to take on has very
important implications for their profitability and choice of
foreign
exposure. The panels of Fig. 1 show how a rise in banks’ risk
aver-

sion k from 0.05 to 0.5 affects bank behavior. The top left panel
shows that all else equal, banks are slightly less likely to enter a
new market in the post-crisis period than before, due to the
23 ‘Expected’ implies that values are weighted by the
probability of market entry.
worsening bank and market conditions over the crisis period.24
The pre- and post-crisis effects of rising bank risk aversion on
entry
probabilities are small and very similar.
The top right panel shows that the pre- and post-crisis periods
are very different in how k affects banks’ average value from
oper-
ating in a host market.25 The rise in bank risk aversion lowers
this
value by over 4,000% in the post-crisis period, whereas the
compara-
ble effect is a 900% decline in the pre-crisis period. What
explains
this result? Given banks’ mean–variance utility, k affects the
value
of banks’ country-level operations in two ways. First, a rising k
con-
stitutes a larger weight on the variance term, lowering country
value
linearly. Second, k also affects the probability of market entry
as well
as the claims volume choices. Increasingly risk averse banks are
more likely to enter new markets (as shown in the top left
panel),
and hold relatively more affiliate claims in those markets (lower
right panel) – increasingly so in the aftermath of the crisis. The
deterioration of foreign market conditions in the post-2008
period,
combined with the response of increasingly risk averse banks to

shift
towards affiliate activities thus reduces, causes risk aversion to
reduce country value faster in the aftermath of the crisis.26
The lower right panel shows that in the aftermath of the crisis,
the expected share of affiliate to cross-border claims is lower
than
in the period leading up to it. This is partly due to the lower
entry
probabilities (as in the top left panel), and partly to the
worsening
of host market traits from before to after the crisis. This result
is
particularly interesting to put in the context of the first-stage
result that if bank and market traits had remained the same as
before, foreign affiliate claims would have actually increased
relative to cross-border claims in the post-crisis period (the
post-
crisis line would be above the pre-crisis line in the lower right
panel). Finally, the lower left panel highlights that the
deteriorated
bank and market conditions in the aftermath of the crisis have
caused risk appetite to have a weaker positive effect on foreign
investment.
5.2. Increasing foreign regulatory risk stance
Fig. 2 shows that increasing all foreign bank regulators’ risk
aversion from 0.05 to 0.5 has significant effects on all four
mea-
sures of bank behavior and performance. In line with first-stage
in that host market.
26 There are no diversification opportunities as the affiliate
claim is the only
available asset in the host country.

4
Bank Risk Aversion
Fig. 1. The impact of changes in bank risk aversion.
Table 6
Effects (in percent) of changes in risk aversion from 0.05 to 0.5.
Change in risk stance Affiliate to C–B ratio Share of foreign
assets Prob. of market entry Country ops. value
2003–2007 2008–2013 2003–2007 2008–2013 2003–2007 2008–
2013 2003–2007 2008–2013
Bank’s risk 9.80 13.34 26.06 60.32 0.31 0.36 �934.53 �4023
Stance k
Foreign regulator’s �58.65 �60.09 7.33 �48.29 �0.30 �0.33
�59.97 �33.31
Risk stance h
Note: Percent changes in respective variables as average k and h
change from 0.05 to 0.5. The median values of k and h are 0.08
and 0.07, respectively.
233–247
results, a stricter foreign market bank regulator makes it less
likely
that a U.S. bank would enter the market, although the effects
are
very small in magnitude. The probability of market entry is
slightly

lower in the post-crisis period, due to the worsening of bank
and
market indicators.
It is instructive to recall from the first stage results in Table 3
that increases in regulatory h significantly lower the probability
of foreign market entry, but promote affiliate lending
conditional
on market entry. The former result is confirmed by the top left
panel of Fig. 2. Furthermore, the lower right panel indicates
that
the reductions in affiliate lending due to the extensive margin
(forgone entry opportunities) dominate the positive effect of h
on
the intensive margin: the ratio of affiliate to C–B loans falls in
the portfolio as foreign regulators take a stricter stance on risk.
The overall effect is that increasing h reduces the value of
foreign
market operations for banks, as shown in the top right panel of
Fig. 2.
In addition, the pre-crisis patterns of bank behavior provide
some evidence of regulatory arbitrage leading up to the
financial
crisis. The slight pre-crisis increase in the share of foreign
assets
in the lower left panel and the falling affiliate to C–B claim
ratio
in the lower right panel suggest that banks would have shifted
slightly towards cross-border claims away from affiliate claims
in
response to stricter host market regulation (rising h) before the
cri-
sis. In the aftermath of the crisis such arbitrage opportunities
appear more limited as banks would respond to higher h’s by
turn-

ing more towards their home market.
4
Bank Risk Aversion
Fig. 2. The impact of changes in foreign regulatory risk stance.
247 245
The comparison of the effects of bank risk versus regulatory
risk
aversion highlights some interesting points about foreign
affiliate
banking. More risk averse banks tend towards entering new
markets and holding higher foreign affiliate claim volumes
there
– however, similar increases in the risk aversion of host country
bank regulators reverse this trend significantly.
6. Summary and conclusion
This paper has developed a two-stage dynamic structural
estimation framework to examine the patterns of U.S. banks’
foreign activities over the past ten years, looking at the pre-
and post-financial crisis periods separately. This estimation
framework is applied to a unique bank-level dataset, compiled
from various regulatory sources. This dataset of bank balance
sheet, foreign market activity and host market characteristics
covers 82 globally active U.S. banks’ operations in 83 foreign
markets over the 2003 Q1–2013 Q1 period. The first stage of
the estimation examines the empirical mapping between banks’
foreign market entry/exit and cross-border and foreign affiliate
claims choices on the one hand, and a broad set of bank and

market traits on the other. The second stage then uses these
policy function estimates and data on banks’ observed behavior
to find values of some key structural parameters (such as fixed
entry costs and regulatory risk stances) that rationalize banks’
observed choices.
The main results can be summarized as follows. First, the
first-stage results show that bank traits are better able to explain
the patterns of banks’ foreign activities than host market traits.
In particular, larger and less profitable (as measured by return
on
equity) banks tend to be the most globally active. Better
capitalized
banks tend to prefer affiliate over cross-border claims. It is
shown
that foreign claim volumes suffer from significant reporting and
market selection biases, which the current analysis was able to
correct.
Second, results are also able to qualify recent literature’s con-
clusion that U.S. banks have moved away from foreign markets
in the aftermath of the global financial crisis. First-stage
estimates
imply that this trend only reflects banks’ response to
deteriorating
balance sheet and host market conditions, as opposed to a
change
in attitudes about going abroad. After controlling for bank and
host
market characteristics, there is evidence of a shift in bank
portfolio
composition away from holding cross-border claims towards
entering foreign markets and holding affiliate claims there.
Third, structural estimates of bank and regulatory risk stances
imply that on average, regulators take a stricter stance on

market
risk than banks do. Both banks and host country bank regulators
have become more risk averse in the aftermath of the financial
233–247
crisis. The fixed entry costs that U.S. banks must face when
enter-
ing a new market have increased threefold since the onset of the
crisis, whereas scrap values have not increased.
Fourth, simulation exercises highlight the importance of the
structural parameters and the pre- vs. post-crisis distinction.
Increases in bank and host market regulatory risk aversions
affect
bank behavior more strongly in the aftermath of the crisis than
in
the period before the crisis. The opposing effects of bank vs.
regu-
latory risk aversion on affiliate activities is particularly
interesting.
More risk averse banks seek out more foreign affiliate claims,
but
host market regulators with a strict stance on risk substantially
counteract this trend.
A valuable future extension of this work would be to estimate
the model on a dataset that has information on the detailed types
of banks’ liabilities (deposits, bonds, etc.) as well as assets
(loans,
bonds, etc.) at the host country level. Furthermore, if such data
were available, the issue of mergers and acquisitions vs.
greenfield
investment as alternative forms of foreign market entry wsould

warrant further investigation as well.
Acknowledgements
I would like to thank Karl Shell, George Jakubson and Nicholas
Kiefer at Cornell University for their advice and helpful
comments
in this project. Special thanks to Karl Shell. I would also like to
thank my colleagues at Hamilton College and participants at the
2011 Annual Conference of the Hungarian Society of
Economics
in Budapest, the 2011 Liberal Arts Macro Workshop at Vassar
College and the Hamilton–Colgate Seminar Series at Hamilton
College for helpful comments.
Appendix A. Functional forms
A.1. Revenues and variances
From Eq. (2.2), the total and marginal lending revenues in mar-
ket m are:
TTRlm ¼ �aml
�m�1
�mð Þ
m
MRlm ¼ �aml�1=�mm
�m � 1
�m
� � ðA:1Þ
From Eq. (2.3), the total and marginal deposit expenses in mar-
ket m are:

TTEdm ¼ �bmd
gmþ1
gmð Þ
m
MEdm ¼ �bmd1=gmm
gm þ 1
gm
� � ðA:2Þ
Variance of the bank’s overall portfolio:
var eK� � ¼X
mn
1� smð Þ 1� snð Þ 1�xmð Þ 1�xnð Þ½ �
cov am; anð Þl
�m�1
�mð Þ
m l
�m�1
�nð Þ
n
þcov am; bnð Þl
�n�1
�mð Þ
m d
gmþ1

gnð Þ
n
þcov bm; bnð Þd
gmþ1
gmð Þ
m d
gnþ1
gnð Þ
n
266664
377775 ðA:3Þ
A.2. First order optimality conditions
This section describes the first-order optimality conditions
taken with respect to the variables ðlmj; dmj; Dj; Kj in Eq.
(2.11) and
the entry/exit choices ðe1j; . . . ; eMj in Eq. (2.12), subject to
the bud-
get constraints in (2.7) and (2.8) and the regulatory constraints
in
(2.9) and (2.10). Recall that m ¼ 1 denotes the home (source)
market, m ¼ 2 is the cross-border lending market in the host
coun-
try, and m ¼ 3 is the foreign affiliate market. Let cm denote the
multiplier on the budget constraint in market m, and /m denotes
the multiplier on the regulatory constraint in market m.
MRl1�cl1ð Þ 1�s1ð Þ 1þ/1ð Þ� kþ/1h1;2ð Þ
@var eK� �
@l1

�/1j1;2�c1¼0
ðA:4Þ
MRl2�cl2ð Þ 1�s1ð Þ 1þ/1ð Þ� kþ/1h1;2ð Þ
@var eK� �
@l2
�/1j1;2�c1¼0
ðA:5Þ
MRl3�cl3ð Þ 1�s3ð Þ 1�x3ð Þ 1þ/3ð Þ
� kþ/3h3ð Þ
@var eK� �
@l3
�/3j3�c3¼0 ðA:6Þ
MEd1 þ cd1ð Þ 1� s1ð Þ 1þ /1ð Þ
þ kþ /1h1;2ð Þ
@var eK� �
@d1
� c1 1� d1ð Þ ¼ 0 ðA:7Þ
MEd3 þ cd3ð Þ 1� s3ð Þ 1�x3ð Þ 1þ /3ð Þ
þ kþ /3h3ð Þ
@var eK� �
@d3
� c3 1� d3ð Þ ¼ 0 ðA:8Þ

c1 � 2 1� s1ð Þ�r1;2 1þ
D1
K1;2
� �
1þ /1ð Þ ¼ 0 ðA:9Þ
c3 � 2 1� s3ð Þ 1�x3ð Þ�r3 1þ
D3
K3
� �
1þ /3ð Þ ¼ 0 ðA:10Þ
c3þ/3þ 1þ/3ð Þ
�r3D
2
3
K23
" #
�c1�/1� 1þ/1ð Þ
�r1;2D21;2
K21;2
" #
¼0 ðA:11Þ
E eK 1;2� �� h1;22 var eK 1;2� �� j1;2 l1 þ l2ð Þ ¼ 0
ðA:12Þ
E eK 3� �� h32 var eK 3� �� j3 l3ð Þ ¼ 0 ðA:13Þ
K1;2 þ ðd1 þ d2Þ 1� d1;2ð Þ þ D1;2 � l1 � l2 ¼ 0 ðA:14Þ

K3 þ d3 1� d3ð Þ þ D3 � l3 ¼ 0 ðA:15Þ
Appendix B. Log-linearization
This section describes the log-linearization of the non-linear
first-order optimality conditions described above. The log-
lineari-
zation is around the perfectly competitive symmetric certainty
equilibrium. This is the equilibrium for an economy with � ¼ 0
and g ¼ 0. Furthermore, all elements of the variance–covariance
matrix V in Eq. (2.1) are zero. The equations are log-linearized
with
respect to each model parameter x. The log-linearized equations
presented below are generalized to many markets. Let subscript
m denote market m ¼ ð1;2;3Þ (Home; Cross-Border; Foreign
Affiliate) and subscript j denotes bank j. Let ðv;,;.;u; n; sÞ
denote
log-linearization constants. The log-linearized optimality condi-
tions are as described in Eqs. (B.1)–(B.8) below.
v1ljm � v2 �am þ v3clm þ v4sm þ v5
X
m
ljm þ v6
X
m
djm þ v7cjm
þ v8jm þ v9/jm þ v10�m ¼ 0 ðB:1Þ

247 247
,1djm þ ,2�bm þ ,3cdm þ ,4sm þ ,5
X
m
ljm þ ,6
X
m
djm ��,7cjm
þ ,8di þ ,9/jm � ,10gm ¼ 0 ðB:2Þ
.1�rm þ .2Djm � .3Kjm � .4sm � .5cjm þ .6/jm ¼ 0 ðB:3Þ
X
m
u1cjm þu2/jm þu3�rm þ 2u4Djm � 2u5Kjm
� �
¼ u1cjm þu2/jm þu3�rm þ 2u4Djm � 2u5Kjm ðB:4Þ
cjm þ Kjm þ djm � dm þ Djm � ljm ¼ 0 ðB:5Þ
/jm þ n1Kjm þ n2ljm þ n3 �am � n4clm � n5djm � n6�bm �
n7cdm
� n8
X
m
ljm � n9
X
m
djm � n10�rm � n11Djm � n12sm � n13jm ¼ 0

ðB:6Þ
X
m
Kjm ¼ Kj ðB:7Þ
V eK� � ¼ s1X
m
�am þ s2
X
m
lm � s3
X
m
�bm � s4
X
m
dm � s5
X
m
clm
� s6
X
m

cdm � s7
X
m
sm � s8
X
m
dm � s9
X
m
jm � s10
X
m
�m
þ s11
X
m
gm � s12
X
m
�rm � s13
X
m

Dm þ s14K � s15Cm ðB:8Þ
Eqs. (3.3) and (3.5) in the body of the paper are the reduced-
form equivalents of these log-linearized equations. The
estimated
coefficients in Section (3.2) are combinations of the log-
linearization
constants in the log-linearized equations above.
Appendix C. Sufficient conditions for consistent and
asymptotically normal structural estimators taken from
Assumption S2 of Bajari et al. (2007)
1. The inequalities Gj ¼ ðgj;1; . . . ; gj;k; gj;KÞ are independent
and
identically distributed.
2. For each gj;k, each V
̂ j is computed using independent draws
and
satisfies Eðð̂ VjÞÞ ¼ Vj <1. In addition, with probability 1, bV
is
twice differentiable in h and the first-stage coefficient estimates
/, and three times differentiable in h.
3. As the sample size h!1, both the number of simulations and
one – step deviations ðn; kÞ ! 1 and h=n2 ! 0.
4. The set H is compact and h0 ¼ arg minHQ H; /̂0
� �
.
5. There exists a full-rank matrix B0, such that, for h near h0,
@
@h

Q nðh; n̂ Þ ¼
@
@h
Q nðh0; p̂ hinÞ þ ðB0 þ opð1ÞÞðh� h0Þ
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