[texhax] TexLive 6b
Patric Glöde
Patric.Gloede at t-online.de
Sat Mar 26 17:43:11 CET 2005
Dear support,
I just wanted to compile a TeX-file with Dante's TeXLive 6b system. The
file has been compiled (without problems) with another TeX system
before. Unfortunately, I cannot tell you which TeX system this was. In
any case, my TeXLive 6b is not able to compile the file. I guess the
file requires packages not included in Dante's TeXLive 6b. As I am not a
professional with LaTeX I am not able to check this. I have attached the
relevant files to this email. You would do me a great favour to tell me
what is going wrong, where I could download the missing packages, and to
which folders I have to copy them so that TeX can work with them.
I would appreciate a quick answer as I urgently need the document as pdf
file for a seminar.
Thanks a lot for your help
Patric Gloede
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\begin{titlepage}
\title{Measuring Competition in the Banking Industry - A Review}
\author{Patric Karl Gl\"{o}de, E-Mail:
snpagloe at mi.uni-erlangen.de}
\end{titlepage}
\begin{document}
%\title{Measuring Competition in the Banking Industry}
\maketitle
\begin{abstract}
This paper gives an overview of the existing approaches to
competition measuring in the banking industry. Literature offers a
great number of studies on competition. Most studies use either
the approach of Panzar and Rosse or a conjectural variations
model. The SCP paradigm provides a method which allows inferences
from industry structure on the degree of competition. Empirical
evidence of the SCP paradigm, however, is far from being
unambiguous. Studying the banking sector poses specifical
problems, in particular due to poor data availability and the lack
of a clear definition of banks' output and input.
\end{abstract}
\section{Introduction}
Literature offers a great number of studies about competition.
Most articles tackle the problem of competition measuring with the
Panzar-Rosse or a conjectural variations model. All approaches
have shortcomings. Mostly, strong assumptions have to been made
and inferences about the real form of market organisation are
problematic. Often, the only unambiguous proceeding is to test for
one extreme case, e.g. monopoly or perfect competition. In
addition, bank specific problems arise from the definition of
input and output. There are four main approaches\footnote{cf. for
example \cite{freixas}, \cite{goddard} or \cite{hempell}}.\\
(1) The production approach views the bank as a firm producing
services related to loans and deposits. Interest payments for
funds are not included in the cost function. Main costs are
expenditures for personnel and physical capital. This model is
applied by \cite{suominen}, who measures competition
in the Finnish banking market.\\
(2) The intermediation approach assumes that banks employ labor
and physical capital to produce loans. Deposits and other funds
are taken as inputs. Accordingly costs consist of interest
payments for funds as well as of expenses for labour and physical
capital. This is the most commonly chosen model.\\
(3) An alternative model by Hancock (1991) regards user cost and
classifies services with negative user cost (such as loans and
demand deposits) as output and those with positive user cost (for
instance savings deposits) as inputs. Hancock also suggests a test
for input and output. Therefore banks' profits are linearly
regressed on the real balances of the different items in the
balance sheet. Negative coefficients indicate inputs, positive
coefficients indicate output. This is intuitively plausible: an
increase of output increases profit, whereas an increase of input
decreases profit. Hancock finds that loans and demand deposits are
output. Inputs contain labor, physical capital, materials, time
deposits, and borrowed money.\\
(4) In a more recent study \cite{hughes} introduce risk in the
definition of what banks produce. Banks' business relies much on
their comparative advantage in monitoring and assessing risk.
Hence, risk should not be neglected in banks' production and cost
functions. In addition, Hughes et al. present a method of how the
function of deposits can be tested. He finds that there is strong
empirical evidence that deposits are input. He proceeds as
follows: he differentiates an operating cost function (which
includes costs of labour and physical capital, but excludes
deposits) with respect to deposits. If deposits are output, an
increase in the production of deposits will require more input.
Hence, the above derivative should bear a positive sign, and
vice versa.\\
\\
In addition to the mentioned problems, a big constraint in all
studies are data problems, particularly with output prices.\\
\\
In the following sections I give an overview of the existing
approaches to competition measuring. Each section contains a brief
description of the economic background, gives an example of how
the model can be described empirically and discusses advantages
and shortcomings of the respective model. I also present some
empirical results (focusing on studies on the German banking
sector). Completeness, of course, is not assured.
%I am grateful to my colleagues, Stephanie Becker, Michael Koetter,
%Thorsten Nestmann, Monika Trapp and Stefan Weiss for a lot of
%interesting and productive discussions.
\section{Structural approaches}
Structural approaches are based on the SCP\footnote{SCP is short
for "Structure-Conduct-Performance".} paradigm, the efficiency
hypothesis and oligopoly models. The SCP paradigm posits a
relationship between market structure, firm conduct and market
performance. It says that in highly concentrated markets with a
small number of large, dominant firms it is easy for these firms
to collude and raise profits to levels not compatible with perfect
competition. The bulk of studies opts for the $k$-firm
concentration ratio ($CR_k$) or the Herfindahl-Hirschmann index
($HHI$) as a measure of market concentration. With $s_i$ denoting
the market share of firm $i$ ($i=1,...,n$, $k \leq n$)these
indices are defined as follows:
\begin{equation}
\label{CRK}
CR_k := \sum_{i=1}^k s_i \; \; \hbox{ where } s_i < s_j
\hbox{
for } i<j
\end{equation}
and
\begin{equation}
\label{HHI}
HHI := \sum_{i=1}^n (s_i)^2 \; .
\end{equation}
The popularity of the $HHI$ and $CR_k$ may be due to the easy
applicability of these indices as well as to the fact that
attempts to derive a formal relationship between structure and
performance lead directly to the $HHI$ or the $CR_k$.
\cite{cetorelli}, however, challenges the formal derivation of the
$HHI$ since it needs far too strong assumptions. \cite{bosdiss} or
\cite{bos} enhances the SCP and creates a Cournot based model
establishing a testable relationship between market share ($MS_i$)
and profitability (cf. below). In his tests for market power he
finds that, while $HHI$ in the traditional SCP model proves not to
be significant, the $MS_k$ variable in his enhanced model does.
\cite{berger95} comes to a comparable result for US banks. The
$CR_k$ would be applicable for countries with a small couple of
dominant banks and a competitive fringe of small institutes. This
is certainly not the case in Germany.
\\\cite{eibmoly} points out that empirical evidence for the SCP
hypothesis is very weak. In addition, even if there is evidence
for a relationship between structure, conduct and performance the
causality is not clear. The efficiency hypothesis proposes that
high performance of dominant firms as well their dominance itself
may be due to efficiency. The SCP could also give misleading
signals if markets are contestable. Then, even players in highly
concentrated markets may behave competitively.\\
\\
As empirical results from SCP based studies are ambiguous
structural approaches are not granted much space in this paper.
\subsection{SCP tests}
The SCP\footnote{SCP is short for
"Structure-Conduct-Performance".} model can be formulated as
follows:
\begin{equation}
\label{scp}
P_t = f(M_t,D_t,C_t) \; ,
\end{equation}
where $t$ is time, $P$ is a performance measure, $M$ are market
structure variables, $D$ is a set of demand variables and $C$ is a
set of firm or product-specific control variables (e.g. cost
variables).\\
Possible performance measures are return on equity ($ROE$) and
return on assets ($ROA$). In his study on the Dutch banking market
\cite{bosdiss}\footnote{I opt for this study for two reasons:
first it is one of the most recent studies applying the SCP model
and second the Dutch banking sector is highly concentrated and we
thus would expect the SCP hypothesis to hold.} chooses $ROA$
because it is not affected by changes in market capitalisation.
Market share variables are commonly the said $HHI$ or $CR_3$.
Control variables in \cite{bosdiss} are $RISK = \frac{\hbox{total
net loans}}{\hbox{total assets}} \cdot 100 \%$, $LIQUIDITY =
\frac{\hbox{liquid assets}}{\hbox{total assets}} \cdot 100 \%$,
$COST = \frac{\hbox{total operating expenses}}{\hbox{total
operating
income}}$ and $MARKET = \hbox{total deposits}$. \\
Surprisingly both market structure variables ($HHI$ and $CR_3$)
carry a negative sign and are significant at the $5 \%$ level.
Thus, the SCP models do not indicate any market power. This is
even more astonishing regarding the fact that the Dutch $CR_3$
hovers around $80 \%$ in the observed period (1992-1998).\\
\\
If concentration had no negative influence on competition fears of
current consolidation in the European banking sector would be
unfounded. Exactly these fears have contributed to boost interest
in competition measuring. US anti trust authorities, however, do
rely on the SCP model. Their decisions whether to accept a merger
or not are based on the $HHI$. \cite{cetorelli} reviews the
appropriateness of the use of the $HHI$ as a main screening factor
in merger analysis. In easy numerical examples he shows that the
$HHI$ can give misleading signals and indicate, for instance,
higher concentration even if competitiveness would obviously be
enhanced by a merger. He concludes that market structure does not
allow to detect anticompetitive conditions. \cite{cetorelli} also
reviews literature focusing on the SCP model and finds evidence
for the SCP hypothesis\footnote{cf. \cite{berger89} and
\cite{neumark}} as well as results which suggest a non-monotonic
(U-shaped) market-concentration relationship\footnote{cf.
\cite{jackson92} and \cite{jackson97}}. In his own study
Cetorelli estimates a Bresnahan like conduct parameter and
compares it with SCP paradigm based inferences from $HHI$ in the
Italian banking sector. Surprisingly, both methods yield
contradictory results. \cite{eibmoly} cites Gilbert's
comprehensive article (\cite{gilbert}), which reviews 45 studies,
just 27 of which find results supporting the SCP paradigm. As
mentioned above, \cite{berger95} finds that (economies of scale
and) market structure has (have) no effect on performance but that
(X-efficiency and) market power does (do) have some, however weak,
explanatory power for bank performance. He concludes that "it does
not appear that any of the efficiency or market power hypotheses
are of great importance n explaining bank profits". In line with
\cite{eibmoly}, I claim that the SCP hypothesis has no major
importance for competition measuring.
\subsection{A Cournot Model}
This model, developed by \cite{cowling}, is based on a Cournot
model and establishes a formal relationship between industry
concentration and performance\footnote{The approach is very
similar to the Bresnahan model described below.}. A major problem
of the SCP model is that the choice of the market structure
measure implies an a priori assumption on the influence of
different players on the market (e.g. the $CR_k$ underestimates
the competitive fringe). Thus, in order to allow for asymmetries
in market structures as well as for differences in cost structures
and collusive behaviour \cite{bosdiss} modifies Cowling's model by
testing a \emph{firm} performance/market share relationship
instead of an \emph{industry} performance/market structure
relationship. This proceeding might be suggested by the above
mentioned results of \cite{berger95} .\\
The model setup is based on a profit maximising collusive Cournot
oligopolist and yields the following equation:
\begin{equation}
\label{boscournot}
\frac{\Pi _i + F_i}{R_i} = \left( - \frac{1}{\eta _D} \right)
\cdot (MS_i) \cdot (1+ \lambda _i) \; ,
\end{equation}
defining profit $\Pi _i$, fixed cost $F_i$, revenue $R_i$, market
share $MS_i$, price elasticity of demand $\eta _D$, and the
conjectural variation (CV) $\lambda _i$\footnote{The conjectural
variation is defined as $\lambda _i := \frac{\partial X}{\partial
x_i} - 1 = \frac{\partial \sum_{j \neq i} x_j}{\partial{ x_j}}$
with the firm output $x_i$ and industry output $X$. The CV
measures the expectations firm $i$ has about the reaction of
rivals to its own change in output. $\lambda$ without subscript
usually refers to the expression$\frac{\partial X}{\partial x_i}$.
For further details about the CV cf. $\lambda ^*$ below.}
respectively for firm $i$. For the estimation Bos assumes $\eta_D$
to be constant, which is justified regarding the brevity of the
analysed period. Further, he shows that, assuming collusive
behaviour, $\lambda _i$ is a function of $MS_i$. This allows
interpreting the combined impact of $\lambda _i$ and $MS_i$ on
profitability and omitting $\lambda _i$ does not change the sign
of the joint coefficient in the regression equation\footnote{Bos
notes that interpreting the magnitude of the coefficient, however,
is no longer possible.}. Thus, we get the following regression
equation:
\begin{equation}
\label{bosregress}
\ln \frac{\Pi_{i,t}+F_{i,t}}{R_{i,t}} = \beta_{0,t} + \beta_1 \ln
MS_{i,t} + \epsilon
\end{equation}
The proceeding seems to me not completely consistent, as Bos
employs equation (\ref{bosregress}) to test for perfect
competition. However, equation (\ref{bosregress}) has been
obtained under the
assumption of collusion.\\
\\
Testing for perfect competition yielded the following results: The
coefficient of the variable $MS$, although not very large, is
highly significant. Thus, there is evidence for market power in
the Dutch banking market. This is important since SCP tests have
failed to detect it.
\section{NEIO approaches}
NEIO\footnote{NEIO is short for "New Empirical Industrial
Organisation".} approaches try to measure competitive conduct
directly and do not rely on a relationship between structure,
conduct and performance. They have a sound theoretical
underpinning. Beyond testable hypotheses NEIO approaches provide a
kind of continuous measure of competition. %\cite{corts} points to
%the important "as-if" constraint in the interpretation of the
%results in Bresnahan studies. It is due to the fact that Bresnahan
%studies assume a priori that the underlying market is a
%conjectural variations market.
%The same problems occur in the Panzar-Rosse model
%substituting Chamberlinian monopolistic competition for
%conjectural variations market.
\subsection{A conjectural variations model \ref{cv}}
The conjectural variations model determines the degree of market
power of the average, profit-maximising, oligopoly bank in the
short run. It indirectly measures price-cost margins. The key
parameter is the conjectural variations (CV) parameter, which
originally is a conduct parameter giving information about the
conduct of firms in the market of interest. The CV concept
generalises the traditional Cournot model and makes it possible to
parameterise the range between perfect competition and perfect
collusion. Empirically the conduct parameter is obtained by
estimating simultaneously a demand and a supply equation.
\cite{bresnahan} gives a comprehensive description of this
approach. This is why literature sometimes refers to this model as
'Bresnahan approach'.\\
\\
If we have $n$ banks in the industry supplying a homogenous
product the first order condition for profit maximising of the
average bank $i$, summing over all banks in the industry and
dividing through $n$ yields\footnote{For details cf. Appendix.}:
\begin{equation}
\label{firstorder}
P = -\lambda ^* P'(X,EX_D) X +
\frac{1}{n}\sum_{i=1}^{n}c'_i(x_i,EX_{S_i}) \; \; ,
\end{equation}
where $P$ denotes the inverse demand function, $X = \sum_{i=1}^{n}
x_i$ is industry output, $EX_D$ are exogenous variables affecting
industry demand but not marginal costs, $c'_i$ are marginal costs
of bank $i$, $EX_{S_i}$ are exogenous variables affecting the
marginal costs of bank $i$ but not the industry demand function
and $\lambda ^*$ is the CV, i.e.:
\begin{equation}
\label{lambdastar}
\lambda^* := \frac{1}{n} \frac{\partial X}{\partial x_i} =
\frac{1}{n} \left( 1 + \frac{\partial \sum_{j \neq i}
x_j}{\partial x_i} \right) \; \; .
\end{equation}
$\lambda ^*$ has values in the interval from 0 to 1, which have
the following economic implications:
$$
\begin{tabular}{|c|c|c|} \hline
\multicolumn{3}{|c|}{Conjectural variations parameter} \\ \hline
$\lambda ^* = 1$ & $\lambda _i = n-1$ & Monopoly or perfect collusion \\
$\lambda ^* = \frac{1}{n}$ & $\lambda _i = 0$ & Cournot oligopoly \\
$\lambda ^* = 0$ & $\lambda _i = -1$ & Perfect competition\\
\hline
\end{tabular}
$$
$\lambda ^*$ has several equivalent economic interpretations which
are easily seen from (\ref{firstorder}) and (\ref{lambdastar}) or
slightly transformed terms. (1) It represents the conjectured
degree of output change of the competitors if bank $i$ changes its
output; (2) it indicates how much of the monopoly markup (which
equals inverse elasticity) is actually charged by the
players of the observed market; (3) alternatively $\lambda^*$ can
be interpreted as an elasticity adjusted Lerner index; (4)
$-\lambda^*$ measures the percentage deviation of the aggregate
output from the competitive
equilibrium level\footnote{For details cf. Appendix.}.\\
Sticking to the CV language (which corresponds to interpretation
(1)) the above listed implications can easily be derived from
economic intuition. Therefore it is important to remember that
$\lambda^*$ says something about the \emph{expectations} of firms.
A Cournot oligopolist assumes by definition that the other players
won't change their output. Thus $\frac{\partial X}{\partial
x_i}=1$. In perfect competition price is exogenously given. Thus
industry output is expected to remain constant and $\frac{\partial
X}{\partial x_i}=0$. In a perfectly collusive oligopoly each
player wants to maintain its market share $\frac{1}{n}$. Hence an
output increase by player $i$ will cause a proportional increase
in output of each "partner". Thus industry output $X$ increases
proportionally and $\frac{\partial X}{\partial x_i}=n$.\\
Some articles present equation (\ref{firstorder}) in a more
"purist" form without deriving it from a Cournot first order
condition:
\begin{equation}
\label{firstorder2}
P = - \lambda^* P' X + c \; ,
\end{equation}
where $c$ denotes average marginal cost. Of course,
(\ref{firstorder2}) is equal to (\ref{firstorder}). The
implication $\lambda^*$ as a parameter representing the degree of
competition is even more obvious\footnote{which is the reason why
I present this equation as well.}.\\
\\
The empirical model shall now briefly be exemplified following
\cite{bresnahan82} and \cite{bikkerbres}: Bikker chooses a
one-product banking model. However, he considers two products in
this sense that he first tests for the hypothesis with deposits as
"the" product (or rather the services attributed to deposits
approximated by the real value of total deposits) and later with
loans as "the" product. Of course costs are different in both
cases. For deposits the equations estimated are:
\begin{equation}
\label{dep}
DEP_t = \alpha _{0,t} + \alpha _{1,t}1 r_{dep,t} + \alpha _{2,t}
EX_{D,t} + \alpha _{3,t} EX_{D,t} r_{dep,t} + \epsilon_t \; \;
\hbox{and}
\end{equation}
\begin{equation}
\label{rdep}
r_{dep,t} = -\lambda^* \frac{DEP_t}{\alpha _{1,t} + \alpha _{3,t}
EX_{D,t}} + \beta _{0,t} + \beta _{1,t} ^* DEP + \beta _{2,t} ^*
EX_{S,t} + \nu_t \; .
\end{equation}
These equations yield the conduct parameter $\lambda ^*$. The
cross term in (\ref{dep}) must be included for reasons of
identification. The variables are defined as follows:
\begin{eqnarray*}
DEP & = & \hbox{the real value of deposits} \\
r_{dep} & = & \hbox{the market deposit rate} \\
EX_D & = & \hbox{exogenous variables affecting industry demand for
deposits but not marginal} \\ & & \hbox{costs, such as disposable
income, unemployment, interest rates for alternative} \\ & &
\hbox{investments and the
number of branches} \\
\epsilon & = & \hbox{error term} \\
EX_S & = & \hbox{exogenous variables influencing the supply of
deposits, such as costs of input} \\ & & \hbox{factors for the
production of deposits}
(wages etc.) \\
\nu & = & \hbox{error term}
\end{eqnarray*}
Substituting $LOANS$ and $DEP$ for $r_{lend}$ and $r_{dep}$
yields (\ref{dep}) and (\ref{rdep}) for loans.\\
\cite{bikkerbres} cannot reject perfect competition for almost all
countries. For those countries, where it is rejected, he finds a
very low degree of collusion only. The results are very similar
for deposit and for loan markets.\footnote{This may be astonishing
because Germany is among those countries where perfect competition
can be rejected (even if the actual market equilibrium seem snot
be too far away from it). On the other hand concentration measures
unanimously yield comparatively low levels of concentration. SCP
thus would predict exactly the opposite of
what \cite{bikkerbres} found with Bresnahan's model.}\\
\\
\cite{suominen} extends the Bresnahan model to a two product model
and thus can apply the production approach.\\
\\
We now come to the problems associated with the CV model. At first
glance, the above interpretation of the CV parameter might seem
very accessible and beyond doubts. This is right for perfect
competition and Cournot oligopoly. For monopoly or perfect
collusion, however, there is some inconsistency. The question is:
which inferences can we draw from the estimation result if
$\lambda^*=1$? It is right to say that in perfect collusion one
player \emph{expects} its partners to proportionally match its
increase in quantity. As all firms act as one monopolist collusive
output maximises every one firm's profit. If one firm deviates
from common optimum output others will perfectly match this
deviation and profits will drop. Thus, as firms \emph{expect}
retaliation (with negative consequences for their profits) they
actually will never deviate from collusive output\footnote{This is
right provided that perfect collusion is a stable, efficient
equilibrium. If the game allows for the possibility that cheating
will raise profits despite retaliation in the periods to come (a
possible retaliation might be: playing a Cournot game from the
respective round on) the "monopolistic" equilibrium may break
down. \cite{corts} simulates an efficient supergame where exactly
this happens.}. But this means that the econometrician will never
observe deviations from the collusive output. The expected
matching behaviour described by $\lambda^*$ therefore will remain
unobserved. Returning to the above question, the observed value of
$\lambda^*$ cannot be seen as result of the "collusive
expectation". Since, if the incumbent firms had theses
expectations we should not observe $\lambda^*=1$. Theses
considerations do not cast a good light on the "conjectural
variations interpretation". As a solution to this problem
literature tends to interpret the parameter $\lambda^*$ as an
"as-if" parameter who tells us that the degree of competition is
as high "as if" it was produced in a conjectural variations market
with this level of competition. \cite{corts} notes: "The as-if
interpretation of the conduct parameter is based on the
observation that, for given demand and cost conditions, one can
compute the conjecture that would yield the observed price-cost
margins if firms were playing a conjectural variations
equilibrium, even if observed behavior is in fact generated by
some other oligopoly game." The "conjectural variations problem"
might be evaded by just taking $\lambda^*$ as an
elasticity-adjusted Lerner index\footnote{Appendix A shows how
this interpretation can easily be derived from equation
(\ref{firstorder}).}.
\\
Another question is: in which cases is '$\lambda^*=1$' consistent
with a stable equilibrium? Obviously equilibrium is just
guarantied if the incentive to collude is compatible with market
conditions. However, transitory demand shocks and low discount
factors might disturb the equilibrium\footnote{cf. again
\cite{corts} for details on this topic}.\\
\\
Apart from the theoretical interpretation of the conduct parameter
\cite{corts} challenges its \emph{estimation}. %This estimated parameter usually is
%interpreted as an "as-if\," conjectural variations parameter
%indexing intermediate levels of collusive behaviour.
Corts proves that the estimated parameter is biased as soon as the
actual underlying behaviour is not the result of a conjectural
variations equilibrium and establishes a formal sufficient and
necessary condition for the "as-if" interpretation being correct.
He simulates an efficient supergame collusion and shows that, if
the demand shocks the market undergoes are not permanent, the
estimated conduct parameter underestimates the actual degree of
collusion. If the demand shocks are completely transitory it may
not detect any market power even if there are monopolistic
price-cost margins. %Apart from potential transitory demand shocks
%the discount factor for profits in future periods plays an
%important role. The discounted value of future profit losses which
%are due to retaliation decreases, of course, with the discount
%factor. In an extreme case the discount factor equals zero.
One may argue that the model can at least be used to test for
extreme behaviour (e.g. perfect competition) instead of being used
to measure the degree of market power. However Corts shows that
$\lambda = 1$ may be consistent with any level of market power and
a rejection of this hypothesis may actually not allow any
inference. The intuition behind Corts' argumentation is easy: the
framework of CV analysis is based on the \emph{static} first-order
condition of a profit-maximising Cournot oligopolist. In a
\emph{dynamic} setting, however, the first-order condition may
depend as well on the incentive compatibility constraint
associated with collusion. After a demand shock a player might
find that cheating (despite retaliation by rivals) would earn him
higher profits. Such behavior can bias the estimated conduct
parameter.\\
The criticism in \cite{corts} somewhat relativises the outcome of
CV studies. Since the late nineties a couple of articles have been
published, which try to "test" the accuracy of CV methods. They
focus on industries with virtually perfect data availability,
where markups can be measured directly. The "direct" results are
compared with the outcome of CV estimates. \cite{genesove}
concentrate on the US sugar industry between 1890 and 1914. They
find that the CV model provide a quite correct estimate of market
conditions; deviation from the actual degree of competition are is
not large. \cite{knittel} studies the Californian electricity
market covering the period from 1998 to 2000. Their result is that
the accuracy of the parameter estimate depends on the functional
form of demand (e.g. linear or loglinear).\\
\\
Finally it is worth pointing to the article of \cite{ribon}, which
analyses if competition had been affected by financial
liberalisation in Israel. Ribon and Yosha introduce a couple of
new features into the Bresnahan approach. First they
simultaneously determine the competitive conduct in an input
market (deposits) and an output market (loans). Second they allow
for dynamics, i.e. the conduct parameters are not assumed to be
constant over time. This is achieved by either interacting the
conduct parameters with time dummies or by modelling the conduct
parameters as functions of time. Third, they extensively include
alternative funding sources, as central bank sealed bid auctions,
and also account for additional aspects, e.g. reserve rates
regulated by the Bank of Israel or the inflation rate. Ribon and
Yosha use marginal cost, which are specified as the marginal cost
of funding from the central bank. Data needed to compute the
industry average of these cost can easily be obtained. The authors
further note that identification of the conduct parameters needs
varying inflation rates. Unfortunately, this point might make the
approach - in the form used by Ribon and Yosha - inapplicable to
the German banking sector. Nevertheless, this approach to the
Bresnahan concept is very worth reading as it introduces a couple
of aspects other
studies omit.\\
\\
%\footnote{It seems important to note that
%\cite{corts}does not appear in the references of
%\cite{bikkerbres}, a paper dated from 2003 and thus after Corts'
%article.}
%We
%will see below that this constraint allows unambiguous inferences
%of the Panzar-Rosse $H$-statistic.
I will shortly report the outcome of \cite{bikkerbres}, the only
Bresnahan-based study of competition in German banking, which is
available to me. For the deposit market\footnote{where deposits
are the only product} the hypothesis $\lambda ^* = 0$ (attributed
to perfect competition) can be rejected on a $95 \%$-level of
significance. Nevertheless the deviation from zero is not great.
Testing for Cournot equilibrium ($\lambda ^* = 1/n$) the
hypothesis cannot be rejected. On the German loans market both
perfect competition and Cournot equilibrium can be rejected. The
estimated value of
$\lambda ^*$ lies somewhere in between.\\
Apart from Germany, Spain was the only country for which the
hypothesis "perfect competition in the deposit market" could be
rejected\footnote{The sample contains Belgium, France, Germany,
Italy, the Netherlands, Portugal, Spain, Sweden and the UK.}. For
all other countries it could not be rejected (Bikker notes,
however, that taking perfect competition as hypothesis implies an
a priori bias towards perfect competition.). The result is
somewhat astonishing. At least for countries with a very high
concentration ratio, like the Netherlands, we would have expected
evidence supporting some abuse of market power. On the other hand,
in Germany, which has a relatively low concentration, the
Bresnahan model detects collusion. In the loan market nonperfect
competition is found in Portugal, Spain, Sweden and the UK (and
Germany).
\subsection{The Panzar-Rosse (P-R) approach} Originally\footnote{cf. \cite{pr}}
Panzar and Rosse develop a testable implication of monopolistic
profit-maximisation. The model is then extended to other market
equilibria. They therefore analyse the comparative static
properties of the reduced form revenue equation at the firm level.
The key parameters are the factor price elasticities of the
reduced form revenue equation. Data requirements are relatively
modest. Output price data are not required.\\
The model is based on the reduced form revenue function $R^* =
R^*(w,z,t)$, where $z$ are exogenous variables shifting the firm's
revenue function, $t$ are exogenous variables shifting the firm's
cost function and $w$ are factor prices. The key parameter is the
$H$-statistic which is defined as follows:
\begin{equation}
H := \sum_{i=1}^{n}\frac{\partial R^*}{\partial w_i}
\frac{w_i}{R^*}
\end{equation}
We need the following assumptions:
\begin{enumerate}
\item linearly homogenous cost functions (or homothetic production
function)
\item factor prices exogenous to the individual firm
\item free market entry and exit
\item long-run equilibria\footnote{
This is not necessary if one just wants to test for monopoly.}
\item the elasticity of perceived demand facing the individual
firm is a nondecreasing function of the number of symmetric rivals
\item $\frac{\partial P}{\partial y},\frac{\partial P}{\partial n}
< 0$ with the inverse demand function $P$ and the number of
symmetric rivals $n$.
\end{enumerate}
The following table shows the implications of different values of
$H$:
$$
\begin{tabular}{|c|c|} \hline
\multicolumn{2}{|c|}{Competitive environment test} \\ \hline
$H \leq 0$ & Monopoly or perfect collusion \\
$H \leq 1$ &
Symmetric Chamberlinian equilibrium \\
$H = 1 $ & Long-run competitive equilibrium \\
\hline
\end{tabular}
$$
It is important to note that in the literature this classification
is not completely consistent. For example \cite{hempell} does not
allow equality for monopolistic competition. Therefore I have
sticked to the original article of Panzar and Rosse (\cite{pr}).
The intuitive derivation of this classification is easy:\\
Monopoly: An increase in input factor prices produces an upward
shift of cost functions. Thus prices rise and output falls. As
monopolists produce on the elastic portion of the inverse demand
schedule this has a negative total effect on revenues. Hence an
increase in
input factor prices causes a decrease in revenues.\\
Perfect competition: Suppose all input factor prices rise by 1\%.
As we have assumed linear homogeneous cost functions the average
total costs curve shifts upward by 1\% for all output levels. Thus
prices increase by 1\% as well. As the minimum point of the
average total cost curve does not move optimum output remains
constant. Thus revenues rise by 1\%. The effect of a 1\% increase
of factor input prices is a 1\% increase in revenues.\\
There is no easy intuitive explanation for the $H$ values in the
case of Chamberlinian monopolistic competition.\\
\cite{moly} points out that there is a second interpretation of
the $H$-statistic which allows to test for equilibrium. In this
case one has to substitute elasticities of \emph{returns} for
elasticities of \emph{revenues}. Since the P-R approach is based
on comparative static models inferences from the $H$-statistic are
actually not possible if markets are not in a long-run
equilibrium. Hence, testing for equilibrium should precede testing
for market power.
$$
\begin{tabular}{|c|c|} \hline
\multicolumn{2}{|c|}{Equilibrium test} \\ \hline
$H < 0$ & Disequilibrium \\
$H = 0$ & Equlibrium \\ \hline
\end{tabular}
$$
Again, economic intuition can illuminate these interpretations of
$H$: In competitive capital markets risk-adjusted rates of return
must be equal for all banks. Thus, in equilibrium rates of return
should not be statistically correlated with input prices. \\
In the regression equation, returns have to be substituted for
revenues as the left-hand variable.
\\
\\
We will now shortly discuss the pros and cons of the P-R approach.
The most striking advantage are the limited data requirements.
Output prices are not required. In addition we have a sound
theoretical underpinning and with some additional assumptions $H$
can be interpreted as a continuous measure of
competition\footnote{\cite{bikkerhaaf}}. As we use firm-level data
it is possible to differentiate between different markets.
\cite{hempell}, for instance, classifies banks into big, small and
medium-sized ones or she tests savings banks, cooperative banks,
credit banks and foreign banks separately. At last, the
disaggregation of the $H$-statistic can give insight into which
factor contributed most
to the total effect.\\
Problems arise from the fact that the model (if applied to test
other scenarios than monopoly) works for long-run equilibria only.
The model does not allow for differences in maturity structure of
banks' asset portfolio. This might cause a downward bias as longer
maturities prevent banks from direct price adjustments. In
addition P-R do not account for multi-product banks. Maybe the
most problematic aspect of the model is the assumption that banks
are price takers on input
markets.\footnote{(\cite{bikkerbres})finds a quite high degree of
competition in deposit markets. In addition, if more and more
substitutes for traditional deposits are offered there may also be
a positive effect on the competition in this segment. Thus, at
least one of the input markets might be highly competitive.}\\
The "one-product constraint" is sometimes solved by running the
tests for two product bundles separately. \cite{rime} in his study
of the Swiss banking market, for instance, takes two pairs of
products: (1) loans and bonds and (2) total assets and service
fees. Of course costs have to be adapted adequately.\\
\\
The estimation equation is a loglinear reduced form revenue
equation. We cite the version used by \cite{hempell}:
\begin{eqnarray}
\label{presteq}
\ln TIN1tTA_{i,t} & = & a_1 + b_1 \ln IETF2_{i,t} + b_2 \ln
wage1_{i,t} + b_3 \ln aCEtFA_{i,t} + c_1 LtTL_{i,t} \nonumber \\
& & + c_2 IDtTD_{i,t} + c_3 lmab1t_{i,t} + c_4 cashi_{i,t} + d_1 t
+ \lambda _t + \mu _i + u _{i,t} \; ,
\end{eqnarray}
where
\begin{eqnarray*}
TIN1tTA & = & \hbox{total income to total assets} \\
IEtF2 & = & \hbox{interest expenses to total funds} \\
wage1 & = & \hbox{personnel expenses to total assets} \\
CEtFA & = & \hbox{capital expenses to fixed assets} \\
LtTL & = & \hbox{customer loans to total loans} \\
IDtTD & = & \hbox{interbank deposits to total deposits} \\
lmab11 & = & \hbox{maturity structure of customer loan portfolio}
\\
cashi & = & \hbox{cash flow to business volume by sector of the
borrower, weighted} \\
& & \hbox{with the portfolio of loans to enterprises.}
\end{eqnarray*}
Hempell estimates (\ref{presteq}) with a fixed effect panel
regression. $\lambda _t$ represents the time specific constant
accounted for by including time dummies and $\mu _i$ the bank
specific constant. $u_{i,t}$ are the error terms corresponding to
the endogenous variable\footnote{\cite{hempell} also gives a good
overview of the variables other studies employed.}. The vast
majority of studies estimates a loglinear revenue function.
\cite{perrakis} criticises this functional form. \cite{lang}
therefore applies a translog function. \cite{moly} also try a
translog model but drop it because of massive
problems with collinearity of explanatory variables.\\
In the estimation equation for the equilibrium test \cite{moly}
choose 'return on assets' ($ROA$) as left-hand variable\footnote{
The right-hand variables differ as well, but this is not due to
the equilibrium test.}.\\
\\
Most studies using the P-R statistic find different degrees of
monopolistic competition. For the German banking sector the
reviewed studies have the following results: As mentioned above
\cite{hempell} runs her test for the whole sample as well as for
different subgroups. The period covered is 1993 - 1998. She finds
monopolistic competition for all groups. However, cooperative
banks, savings banks, credit banks and foreign banks have
increasing $H$-values. Distinguishing between small, medium-sized
and large banks\footnote{"small" includes all banks with assets
below 1 billion DM, "medium-sized" means banks with assets between
1 and 5 billion DM and "large" covers the remainder.} $H$
increases with size. Thus bigger banks operate in a more
competitive
environment than small banks.\\
\cite{lang} analyses data from the period between 1988 and 1992 to
get virtually the same results as Hempell, i.e. monopolistic
competition and a higher $H$ value for credit banks than for
savings and cooperative banks.\\
\cite{bikkerhaaf} study the period from 1988 to 1998. They find
that competitive behaviour increases with size. For small and
medium-sized banks both hypotheses $H=0$ and $H=1$ can be rejected
(level of confidence: $99.9\%$). This indicates monopolistic
competition. For large banks however they obtain $H=1.05$ and thus
cannot reject the hypothesis that this group operates in a
perfectly competitive environment (level of confidence: $95 \%$).
The following table gives an overview of which hypotheses could
not be rejected\footnote{The levels of confidence are always over
$95\%$. See \cite{bikkerhaaf}, Appendix 1} in the countries
analysed in \cite{bikkerhaaf}:
$$
\begin{tabular}{|c||c|c|} \hline
\textbf{country} & $H=1$ \textbf{not rejected} & $H=0$ \textbf{not rejected} \\
& (group) & (group) \\ \hline
Austria & small & \\
Belgium & small & \\
Denmark & large & \\
Finland & small & \\
Germany & large & \\
Greece & large & small \\
Ireland & small, large & \\
Japan & & small \\
South Korea & medium, large & \\
Netherlands & small, large & \\
New Zealande& medium & \\
Sweden & large & \\
Switzerland & medium, large & \\
\hline
\end{tabular}
$$
This shows that the German result "the larger the bank the more
competitive its environment" cannot easily be generalised.
However, monopoly seems to be very scarce. The whole sample
includes 23 countries. In almost half of them there are no
indications at all for either perfect competition or monopoly.\\
\cite{moly} studies competitive conditions in various European
banking markets between 1986 and 1989. He also runs an equilibrium
test. For Germany he finds equilibrium for the whole period. In
the competition test for Germany both perfect competition and
monopoly can be rejected for 1986, 1988 and 1989. The 1987 data
suggest perfect competition.\\
\\
The above mentioned problems all arise from the theoretical
framework of the P-R model itself. There is, however, another flaw
associated with the empirical setup, which shall now shortly be
described: Input factor prices entering the estimation equation
always include personnel expenses, costs of physical capital and
costs of deposits. Equity capital as input factor and costs of
equity capital, however, are neglected. This might be due to
problems associated with measuring costs of equity capital. The
gravity of this problematic might be demonstrated by means of the
following example: \cite{hempell} classifies deposits as input.
Consequently she accounts for interest expenses in the calculation
of costs. These funding costs are approximated by $IEtF2$, which
is defined as "interest expenses to total funds". Assume that the
bank in question substitutes risky loans for, say, government
securities. In this case, the bank has to increase its equity
capital to account for the higher risk in its portfolio. As a
certain amount of equity capital will be substituted for debts and
liabilities interest expenses will fall. The nominator of the
proxy for funding costs will decrease (since: funds = deposits +
equity capital). Thus, the proxy for input costs will fall. This
might produce a paradoxical effect: if costs for equity capital
are higher than costs of foreign capital funding costs will rise.
The cost measure, however, will indicate lower costs\footnote{Of
course, the example is very rough. If the bank takes higher risks
it might have to pay higher rates on deposits, which also affect
the new funding costs. The scenario shall just demonstrate the
general problem.}. Appendix B describes how a shadow price
for equity capital could be estimated.\\
\subsection{An approach by Hannan and Liang}
\cite{hannan} have developed a method to test for price-taking
behavior in the deposit market. They apply it to the US banking
market. The method has been adopted by \cite{ashton} in a study on
competition in the UK retail banking sector. In addition, it
allows to test the SCP hypothesis. Hannan and Liang note that
testing for perfect collusion would need unacceptable assumptions,
such as product homogeneity. However, the parameter they estimate
enables to draw ordinal conclusions about the degree of
competition. Thus, it is possible to compare competition in
different product markets. The test requires time-series
information on bank deposit rates, security rates, and bank
marginal costs. The main outcome of the study is that perfect
competition can be rejected and that the degree of competition is
lower for money market deposit accounts (MMDA) than for two-year
certificates of deposits (2YCD) and three-year certificates of
deposits (3YCD). The theoretical background relies on the analysis
of the margin between exogenous gouvernment securities rates and
deposits rates of respective maturities. Comparison of a market
where individual banks might exercise some price-setting power and
a market where an individual bank is price-taker allows inferences
on the level of market power. The estimated parameter measures the
supply elasticity. It gives information on both a bank's
conjecture on how rivals will react to its interest rate change
and the degree of product differentiation.
%Interpretation of the parameter:
%The elasticity measures the percentage change of supply,
%if the interest rate is reduced by one percentage point.
%If the other banks do not react at all, all customers (suppliers)
%will deposit all their money at my rivals. Thus my perceived supply
%will break down completely, elasticity is infinite.
%If the others collude with me nothing will happen
%to my supply and elasticity is zero. "perceived" refers to the fact
%that it is the individual elasticity I face and not industry
%elasticity.
%Thus alpha is also kind of a conduct parameter.
Defining $r_d^i$ bank $i$'s deposit rate, $c_d^i$ bank $i$'s
marginal cost of employing a dollar of deposits to fund
securities, $r_s$ the security rate and $e_d^i$ bank $i$'s
perceived deposit-supply elasticity\footnote{Deposit-supply
elasticities are bank specific since Hannan and Liang allow for
the existence of product differentiation. Thus, elasticity is
affected by the reactions of rivals as well as by the degree of
product differentiation} the profit-maximising rate for each type
of deposit must satisfy the following equation:
\begin{equation}
\label{hannantheo}
r_d^i \cdot \left( 1 + \frac{1}{e_d^i} \right) = r_s - c_d^i
\Longleftrightarrow r_d^i = \underbrace{\frac{e_d^i}{1 +
e_d^i}}_{=: \; \alpha ^i} \cdot (r_s - c_d^i) \; .
\end{equation}
In words: the additional expenses due to an an additional dollar
"produced" must equal the marginal net gain from investing that
dollar in securities.\\
In the absence of market power the perceived supply elasticity is
infinite. As $\alpha ^i \stackrel{e_d^i \to
\infty}{\longrightarrow} 1$, perfect competition is equivalent
with $\alpha ^i = 1$. Thus, if time-series regression of $r_d^i$
on $r_s - c_d^i$ yields values for $\alpha ^i$ significantly less
than unity perfect competition can be rejected. Further, we can
note that $\alpha _i$ is an isotonic function of elasticity and,
hence, a lower degree of competition coincides with lower values
of $\alpha ^i$.\\
Some attention should be paid to the choice of the three deposit
categories. MMDAs require frequent contact between customers and
banks and thus they may be competed for on an local basis. The
market for 2YCDs and 3YCDs is likely to be geographically broader.
This approach to distinction of different markets (where
'different' mainly refers to the geographic dimension) is similar
to our proceeding in the Bresnahan and the P-R model where market
delineation has been achieved by product differentiation (deposits
and loans) and separation of different banking groups (large,
medium-sized and small or savings,
cooperative, credit and foreign banks).\\
The variable $c_d^i$ in equation (\ref{hannantheo}) cannot be
measured directly . Hannan and Liang derive it from a
multi-product cost function following \cite{berger95}.
\cite{ashton} show the procedure
for a couple of UK banks.\\
The time series estimation equation is specified as follows:
\begin{equation}
\label{hannanemp}
r_d^i = \alpha _0 + \alpha _1^i (r_s - c_d^i) + \hbox{error term}
\end{equation}
The estimation results\footnote{Hannan and Liang excluded those
banks from the sample, for which $\alpha ^i$ proved to be not
constant over time.} show that $94\%$ respectively $80\%$ and
$77\%$ of $\alpha^i$ were significantly ($95\%$ level of
confidence) less than one in the MMDA, the 2YCD and the 3YCD case.\\
\\
As the Hannan/Liang approach also provides a test for the SCP
paradigm we will briefly return to this model. The above
discussion of the coefficient $\alpha ^i$ suggests that it can be
interpreted as a rough measure of market power. Thus, a negative
relationship between $\alpha ^i$ and market concentration could be
interpreted as evidence for the SCP paradigm. Therefore Hannan and
Liang run cross-section regressions of $\alpha _1^i$ on a
concentration measure and other explanatory variables. The
estimation equation is of the form:
\begin{equation}
\label{hannanscp}
\tilde{\alpha}_1^i = \gamma_0 + \gamma_1 CR_i + \gamma X_i + u_i
\; ,
\end{equation}
where $\tilde{\alpha}_1^i$ is the estimated value of $\alpha_1^i$,
$CR_i$ represents the 3-firm concentration index of bank $i$'s
market, $X_i$ is a vector of explanatory variables, e.g. bank
size, and $u_i$ is an error term\footnote{Markets are defined as
Metropolitan Statistical Areas (MSAs) or counties in the case of
banks located outside of MSAs.}. The regressions results are not
surprising: for the MMDA market, which is a relatively local
market, Hannan and Liang find a negative relationship between
$\tilde{\alpha}_1^i$ and $CR_i$. For the CDs the coefficients of
$CR_i$ are not significant. This is in line with the notion that
in broader geographic markets market power associated with
concentration is not perceivable\footnote{This is kind of a
contestability argument.}. The result may be interpreted in this
sense that the SCP paradigm generally is plausible, but
contestability matters.
\subsection{The Iwata model}
\cite{iwata} has developed another model which is based on an
oligopolistic market and measures the conjectural variation.
According to the Cournot and the Bresnahan model, it is derived
from the first order conditions of a profit-maximising
oligopolist. \cite{overview} note that this model has apparently
been applied only once to the banking industry by
\cite{shafferdisalvo} to a duopoly. Iwata himself applies it to
the Japanese flat glass industry. A shortcoming of the model is
that it requires micro-data for the structure of cost and
production for homogenous products. This is why I will not go into
further detail and just present the term which determines the
conjectural variation:
\begin{equation}
\label{iwata}
\lambda _i = \eta _D \cdot \frac{c'(x_i) - p}{p} \cdot
\frac{X}{x_i} - 1 \; ,
\end{equation}
where $\eta _D$ is the price elasticity of demand, $x_i$
individual firm output, $X$ industry output and $p$ price. To
obtain $\lambda _i$ one has to estimate a market demand function
and individual cost functions. Therefore one has to assume that
$p$ and $x_i/X$ are strict functions of exogenous variables and
that the price elasticity of demand is constant.
%!!!!!!! Check this in Iwata.
\section{Conclusion}
The paper has presented an overview of the existing approaches to
the measurement of competition. It shows that bank specific
problems are not yet resolved perfectly. In particular the
question of how to introduce risk and equity capital , at least in
the papers I reviewed, remains unanswered. Structural approaches
to the measurement of competition seem not reliable. Thus recent
literature has focussed on NEIO models, mainly the co´njectural
variations approach and the Panzar-Rosse approach. The latter
seems to be the most applicable model. The empirical outcome is
more or less similar in all studies indicating a relatively high
degree of competition.
\newpage
%\setcounter{page}{1}
\bibliographystyle{plainnat}
\bibliography{yyy}
\newpage
%\begin{appendix}
\appendix
\begin{Large}\textbf{Appendix} \end{Large}
\section{The formal framework of the conjectural variations
approach}
We assume $n$ banks in an oligopolistic market supplying
one homogenous product. Profit of bank $i$ is given by:
\begin{equation}
\label{oligoprofit}
\pi_i = P(X,EX_D) x_i - c_i(x_i,EX_{S_i}) - F_i \; ,
\end{equation}
where $P$ is price, $c_i$ is the marginal cost of bank $i$, $x_i$
is the output of bank $i$, $X$ is industry output, $EX_{S_i}$ are
exogenous factors affecting bank $i$'s cost but not industry
demand, $EX_{D}$ are exogenous factors affecting industry demand
but not marginal cost and $F_i$ is bank $i$'s fixed cost. Defining
$c'_i$ the marginal cost of bank $i$, the first-order condition
for profit-maximisation is:
\begin{equation}
\label{oligofirstorder}
0 = P(X,EX_D) + x_i \frac{\partial P}{\partial X} \frac{\partial
X}{\partial x_i} - c'_i \; .
\end{equation}
Summing over all banks and dividing through $n$ yields:
\begin{equation}
\label{oligosum}
0 = P + \frac{1}{n} X P' \, \frac{\partial X}{\partial x_i} -
\frac{1}{n} \sum_{i=1}^n c'_i \; ;
\end{equation}
hence,
\begin{equation}
\label{oligoresult}
P = - \lambda^* X P' + \frac{1}{n} \sum_{i=1}^n c'_i \; .
\end{equation}
With the semi-elasticity of demand $\eta_D^*$ and average marginal
cost $c$ one has:
\begin{equation}
\label{oligoelast}
P = \lambda ^* (\eta^*)^{-1} + c \; .
\end{equation}
This relationship reflects how prices are affected by demand
elasticities and costs where the oligopolist is assumed to
maximise perceived profits through consideration of the reaction
of other players.\\
Another re-arrangement illuminates the interpretation of $\lambda
^*$ as part of the Lerner index $L := \frac{P-c}{P}$ which measures the
markup:
\begin{equation}
\label{oligolerner}
L = \frac{P-c}{P} = \lambda^* \frac{1}{\eta^*} \; .
\end{equation}
In a monopoly the Lerner index equals inverse elasticity. This is
consistent with assigning the value 1 to $\lambda^*$ in case of monopoly
as done in sub-section 3.1.
Dividing through $L$ and defining the elasticity-adjusted Lerner
index $L_{\eta}$ yields:
\begin{equation}
\label{oligoadjustedlerner}
\lambda^* = \eta \frac{P-c}{P} =: L_{\eta} \; .
\end{equation}
Sometimes the CV parameter even \emph{is defined} as the
elasticity-adjusted Lerner index. The elasticity adjusted Lerner
index has an important feature: it differentiates whether high
price-cost margins are due to the abuse of market power or to
low elasticities.\\
At last, \cite{shaffercan} presents the interpretation of the CV
parameter as the percentage deviation from competitive output.
This goes as follows:
\begin{equation}
\label{oligooutput1}
\underbrace{P \cdot \frac{\hbox{d} X}{\hbox{d}
P}}_{\hbox{\small{equlibrium output}}} - \underbrace{c \cdot
\frac{\hbox{d} X}{\hbox{d} P}}_{\hbox{competitive output}} =
\hbox{ deviation} \; .
\end{equation}
Re-arrangement and devising through $X$ produces:
\begin{equation}
\label{oligooutput2}
\frac{P \cdot \frac{\hbox{d} X}{\hbox{d} P}-c \cdot \frac{\hbox{d}
X}{\hbox{d} P}}{X} = - \lambda^* \; .
\end{equation}
\section{The cost of equity capital}
\cite{hughes} offers an interesting method how to derive the
shadow price of equity capital. He also estimates the mean shadow
price for different size groups of US banks (where size refers to
asset size). Starting point of the formal derivation is the
cash-flow cost function
\begin{equation}
\label{cfcost}
C_{CF}(\mathbf{y},n,p,\mathbf{w_p},\mathbf{w_d},k) =
\min_{\mathbf{x_p},\mathbf{x_d}} (\mathbf{w_p x_p} + \mathbf{x_d
w_d}) \hbox{ s.t. } T(\mathbf{y},n,p,\mathbf{x},k) \leq 0 \hbox{
and } k = k^0 \; ,
\end{equation}
with the transformation function $T$; $\mathbf{y}$,
information-intensive loans and financial services; $k$, equity
capital; $\mathbf{x_d}$, demandable debt and other types of debt;
$\mathbf{x_p}$, labour and physical capital; $\mathbf{x} =
(\mathbf{x_p},\mathbf{x_d})$; and $w_i$, the price of the $i$-th
type of input. In order to allow for the asset quality two
controls are included: the amount of nonperforming loans, $n$, and
the average contractual interest rate on loans, $p$. Then,
economic cost can be described as follows:
\begin{equation}
\label{cost}
C(\mathbf{y},n,p,\mathbf{w_p},\mathbf{w_d},w_k) =
C_{CF}(\mathbf{y},n,p,\mathbf{w_p},\mathbf{w_d},k) + w_k k \; ,
\end{equation}
The first-order condition for cost minimisation yields:
\begin{equation}
\label{equitycost}
w_k = - \frac{\partial C_{CF}}{\partial k} \; .
\end{equation}
If the shadow price equals the market price it reflects the
marked-priced risk of a bank's portfolio\footnote{Higher risks
increase the required return on equity.}. But, besides possible
problems with estimating $-\partial C_{CF}/\partial k$, it is not
assured that the level of equity observed minimises cost. If not,
the estimated shadow price may not equal the market price.
Regulation, for instance, might demand levels of equity capital,
which exceed cost-minimising levels. Another incentive for banks
to hold more equity capital may be the signalling function of
equity capital. \\
The outcome of the estimations in \cite{hughes} suggest that banks
do not minimise cost. Shadow price values for small banks seem to
be smaller than market prices, those of large banks seem to exceed
market prices.
%\end{appendix}
\end{document}
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\begin{titlepage}
\title{Measuring Competition in the Banking Industry - A Review}
\author{Patric Karl Gl\"{o}de, E-Mail:
snpagloe at mi.uni-erlangen.de}
\end{titlepage}
\begin{document}
%\title{Measuring Competition in the Banking Industry}
\maketitle
\begin{abstract}
This paper gives an overview of the existing approaches to
competition measuring in the banking industry. Literature offers a
great number of studies on competition. Most studies use either
the approach of Panzar and Rosse or a conjectural variations
model. The SCP paradigm provides a method which allows inferences
from industry structure on the degree of competition. Empirical
evidence of the SCP paradigm, however, is far from being
unambiguous. Studying the banking sector poses specifical
problems, in particular due to poor data availability and the lack
of a clear definition of banks' output and input.
\end{abstract}
\section{Introduction}
Literature offers a great number of studies about competition.
Most articles tackle the problem of competition measuring with the
Panzar-Rosse or a conjectural variations model. All approaches
have shortcomings. Mostly, strong assumptions have to been made
and inferences about the real form of market organisation are
problematic. Often, the only unambiguous proceeding is to test for
one extreme case, e.g. monopoly or perfect competition. In
addition, bank specific problems arise from the definition of
input and output. There are four main approaches\footnote{cf. for
example \cite{freixas}, \cite{goddard} or \cite{hempell}}.\\
(1) The production approach views the bank as a firm producing
services related to loans and deposits. Interest payments for
funds are not included in the cost function. Main costs are
expenditures for personnel and physical capital. This model is
applied by \cite{suominen}, who measures competition
in the Finnish banking market.\\
(2) The intermediation approach assumes that banks employ labor
and physical capital to produce loans. Deposits and other funds
are taken as inputs. Accordingly costs consist of interest
payments for funds as well as of expenses for labour and physical
capital. This is the most commonly chosen model.\\
(3) An alternative model by Hancock (1991) regards user cost and
classifies services with negative user cost (such as loans and
demand deposits) as output and those with positive user cost (for
instance savings deposits) as inputs. Hancock also suggests a test
for input and output. Therefore banks' profits are linearly
regressed on the real balances of the different items in the
balance sheet. Negative coefficients indicate inputs, positive
coefficients indicate output. This is intuitively plausible: an
increase of output increases profit, whereas an increase of input
decreases profit. Hancock finds that loans and demand deposits are
output. Inputs contain labor, physical capital, materials, time
deposits, and borrowed money.\\
(4) In a more recent study \cite{hughes} introduce risk in the
definition of what banks produce. Banks' business relies much on
their comparative advantage in monitoring and assessing risk.
Hence, risk should not be neglected in banks' production and cost
functions. In addition, Hughes et al. present a method of how the
function of deposits can be tested. He finds that there is strong
empirical evidence that deposits are input. He proceeds as
follows: he differentiates an operating cost function (which
includes costs of labour and physical capital, but excludes
deposits) with respect to deposits. If deposits are output, an
increase in the production of deposits will require more input.
Hence, the above derivative should bear a positive sign, and
vice versa.\\
\\
In addition to the mentioned problems, a big constraint in all
studies are data problems, particularly with output prices.\\
\\
In the following sections I give an overview of the existing
approaches to competition measuring. Each section contains a brief
description of the economic background, gives an example of how
the model can be described empirically and discusses advantages
and shortcomings of the respective model. I also present some
empirical results (focusing on studies on the German banking
sector). Completeness, of course, is not assured.
%I am grateful to my colleagues, Stephanie Becker, Michael Koetter,
%Thorsten Nestmann, Monika Trapp and Stefan Weiss for a lot of
%interesting and productive discussions.
\section{Structural approaches}
Structural approaches are based on the SCP\footnote{SCP is short
for "Structure-Conduct-Performance".} paradigm, the efficiency
hypothesis and oligopoly models. The SCP paradigm posits a
relationship between market structure, firm conduct and market
performance. It says that in highly concentrated markets with a
small number of large, dominant firms it is easy for these firms
to collude and raise profits to levels not compatible with perfect
competition. The bulk of studies opts for the $k$-firm
concentration ratio ($CR_k$) or the Herfindahl-Hirschmann index
($HHI$) as a measure of market concentration. With $s_i$ denoting
the market share of firm $i$ ($i=1,...,n$, $k \leq n$)these
indices are defined as follows:
\begin{equation}
\label{CRK}
CR_k := \sum_{i=1}^k s_i \; \; \hbox{ where } s_i < s_j
\hbox{
for } i<j
\end{equation}
and
\begin{equation}
\label{HHI}
HHI := \sum_{i=1}^n (s_i)^2 \; .
\end{equation}
The popularity of the $HHI$ and $CR_k$ may be due to the easy
applicability of these indices as well as to the fact that
attempts to derive a formal relationship between structure and
performance lead directly to the $HHI$ or the $CR_k$.
\cite{cetorelli}, however, challenges the formal derivation of the
$HHI$ since it needs far too strong assumptions. \cite{bosdiss} or
\cite{bos} enhances the SCP and creates a Cournot based model
establishing a testable relationship between market share ($MS_i$)
and profitability (cf. below). In his tests for market power he
finds that, while $HHI$ in the traditional SCP model proves not to
be significant, the $MS_k$ variable in his enhanced model does.
\cite{berger95} comes to a comparable result for US banks. The
$CR_k$ would be applicable for countries with a small couple of
dominant banks and a competitive fringe of small institutes. This
is certainly not the case in Germany.
\\\cite{eibmoly} points out that empirical evidence for the SCP
hypothesis is very weak. In addition, even if there is evidence
for a relationship between structure, conduct and performance the
causality is not clear. The efficiency hypothesis proposes that
high performance of dominant firms as well their dominance itself
may be due to efficiency. The SCP could also give misleading
signals if markets are contestable. Then, even players in highly
concentrated markets may behave competitively.\\
\\
As empirical results from SCP based studies are ambiguous
structural approaches are not granted much space in this paper.
\subsection{SCP tests}
The SCP\footnote{SCP is short for
"Structure-Conduct-Performance".} model can be formulated as
follows:
\begin{equation}
\label{scp}
P_t = f(M_t,D_t,C_t) \; ,
\end{equation}
where $t$ is time, $P$ is a performance measure, $M$ are market
structure variables, $D$ is a set of demand variables and $C$ is a
set of firm or product-specific control variables (e.g. cost
variables).\\
Possible performance measures are return on equity ($ROE$) and
return on assets ($ROA$). In his study on the Dutch banking market
\cite{bosdiss}\footnote{I opt for this study for two reasons:
first it is one of the most recent studies applying the SCP model
and second the Dutch banking sector is highly concentrated and we
thus would expect the SCP hypothesis to hold.} chooses $ROA$
because it is not affected by changes in market capitalisation.
Market share variables are commonly the said $HHI$ or $CR_3$.
Control variables in \cite{bosdiss} are $RISK = \frac{\hbox{total
net loans}}{\hbox{total assets}} \cdot 100 \%$, $LIQUIDITY =
\frac{\hbox{liquid assets}}{\hbox{total assets}} \cdot 100 \%$,
$COST = \frac{\hbox{total operating expenses}}{\hbox{total
operating
income}}$ and $MARKET = \hbox{total deposits}$. \\
Surprisingly both market structure variables ($HHI$ and $CR_3$)
carry a negative sign and are significant at the $5 \%$ level.
Thus, the SCP models do not indicate any market power. This is
even more astonishing regarding the fact that the Dutch $CR_3$
hovers around $80 \%$ in the observed period (1992-1998).\\
\\
If concentration had no negative influence on competition fears of
current consolidation in the European banking sector would be
unfounded. Exactly these fears have contributed to boost interest
in competition measuring. US anti trust authorities, however, do
rely on the SCP model. Their decisions whether to accept a merger
or not are based on the $HHI$. \cite{cetorelli} reviews the
appropriateness of the use of the $HHI$ as a main screening factor
in merger analysis. In easy numerical examples he shows that the
$HHI$ can give misleading signals and indicate, for instance,
higher concentration even if competitiveness would obviously be
enhanced by a merger. He concludes that market structure does not
allow to detect anticompetitive conditions. \cite{cetorelli} also
reviews literature focusing on the SCP model and finds evidence
for the SCP hypothesis\footnote{cf. \cite{berger89} and
\cite{neumark}} as well as results which suggest a non-monotonic
(U-shaped) market-concentration relationship\footnote{cf.
\cite{jackson92} and \cite{jackson97}}. In his own study
Cetorelli estimates a Bresnahan like conduct parameter and
compares it with SCP paradigm based inferences from $HHI$ in the
Italian banking sector. Surprisingly, both methods yield
contradictory results. \cite{eibmoly} cites Gilbert's
comprehensive article (\cite{gilbert}), which reviews 45 studies,
just 27 of which find results supporting the SCP paradigm. As
mentioned above, \cite{berger95} finds that (economies of scale
and) market structure has (have) no effect on performance but that
(X-efficiency and) market power does (do) have some, however weak,
explanatory power for bank performance. He concludes that "it does
not appear that any of the efficiency or market power hypotheses
are of great importance n explaining bank profits". In line with
\cite{eibmoly}, I claim that the SCP hypothesis has no major
importance for competition measuring.
\subsection{A Cournot Model}
This model, developed by \cite{cowling}, is based on a Cournot
model and establishes a formal relationship between industry
concentration and performance\footnote{The approach is very
similar to the Bresnahan model described below.}. A major problem
of the SCP model is that the choice of the market structure
measure implies an a priori assumption on the influence of
different players on the market (e.g. the $CR_k$ underestimates
the competitive fringe). Thus, in order to allow for asymmetries
in market structures as well as for differences in cost structures
and collusive behaviour \cite{bosdiss} modifies Cowling's model by
testing a \emph{firm} performance/market share relationship
instead of an \emph{industry} performance/market structure
relationship. This proceeding might be suggested by the above
mentioned results of \cite{berger95} .\\
The model setup is based on a profit maximising collusive Cournot
oligopolist and yields the following equation:
\begin{equation}
\label{boscournot}
\frac{\Pi _i + F_i}{R_i} = \left( - \frac{1}{\eta _D} \right)
\cdot (MS_i) \cdot (1+ \lambda _i) \; ,
\end{equation}
defining profit $\Pi _i$, fixed cost $F_i$, revenue $R_i$, market
share $MS_i$, price elasticity of demand $\eta _D$, and the
conjectural variation (CV) $\lambda _i$\footnote{The conjectural
variation is defined as $\lambda _i := \frac{\partial X}{\partial
x_i} - 1 = \frac{\partial \sum_{j \neq i} x_j}{\partial{ x_j}}$
with the firm output $x_i$ and industry output $X$. The CV
measures the expectations firm $i$ has about the reaction of
rivals to its own change in output. $\lambda$ without subscript
usually refers to the expression$\frac{\partial X}{\partial x_i}$.
For further details about the CV cf. $\lambda ^*$ below.}
respectively for firm $i$. For the estimation Bos assumes $\eta_D$
to be constant, which is justified regarding the brevity of the
analysed period. Further, he shows that, assuming collusive
behaviour, $\lambda _i$ is a function of $MS_i$. This allows
interpreting the combined impact of $\lambda _i$ and $MS_i$ on
profitability and omitting $\lambda _i$ does not change the sign
of the joint coefficient in the regression equation\footnote{Bos
notes that interpreting the magnitude of the coefficient, however,
is no longer possible.}. Thus, we get the following regression
equation:
\begin{equation}
\label{bosregress}
\ln \frac{\Pi_{i,t}+F_{i,t}}{R_{i,t}} = \beta_{0,t} + \beta_1 \ln
MS_{i,t} + \epsilon
\end{equation}
The proceeding seems to me not completely consistent, as Bos
employs equation (\ref{bosregress}) to test for perfect
competition. However, equation (\ref{bosregress}) has been
obtained under the
assumption of collusion.\\
\\
Testing for perfect competition yielded the following results: The
coefficient of the variable $MS$, although not very large, is
highly significant. Thus, there is evidence for market power in
the Dutch banking market. This is important since SCP tests have
failed to detect it.
\section{NEIO approaches}
NEIO\footnote{NEIO is short for "New Empirical Industrial
Organisation".} approaches try to measure competitive conduct
directly and do not rely on a relationship between structure,
conduct and performance. They have a sound theoretical
underpinning. Beyond testable hypotheses NEIO approaches provide a
kind of continuous measure of competition. %\cite{corts} points to
%the important "as-if" constraint in the interpretation of the
%results in Bresnahan studies. It is due to the fact that Bresnahan
%studies assume a priori that the underlying market is a
%conjectural variations market.
%The same problems occur in the Panzar-Rosse model
%substituting Chamberlinian monopolistic competition for
%conjectural variations market.
\subsection{A conjectural variations model}
The conjectural variations model determines the degree of market
power of the average, profit-maximising, oligopoly bank in the
short run. It indirectly measures price-cost margins. The key
parameter is the conjectural variations (CV) parameter, which
originally is a conduct parameter giving information about the
conduct of firms in the market of interest. The CV concept
generalises the traditional Cournot model and makes it possible to
parameterise the range between perfect competition and perfect
collusion. Empirically the conduct parameter is obtained by
estimating simultaneously a demand and a supply equation.
\cite{bresnahan} gives a comprehensive description of this
approach. This is why literature sometimes refers to this model as
'Bresnahan approach'.\\
\\
If we have $n$ banks in the industry supplying a homogenous
product the first order condition for profit maximising of the
average bank $i$, summing over all banks in the industry and
dividing through $n$ yields\footnote{For details cf. Appendix.}:
\begin{equation}
\label{firstorder}
P = -\lambda ^* P'(X,EX_D) X +
\frac{1}{n}\sum_{i=1}^{n}c'_i(x_i,EX_{S_i}) \; \; ,
\end{equation}
where $P$ denotes the inverse demand function, $X = \sum_{i=1}^{n}
x_i$ is industry output, $EX_D$ are exogenous variables affecting
industry demand but not marginal costs, $c'_i$ are marginal costs
of bank $i$, $EX_{S_i}$ are exogenous variables affecting the
marginal costs of bank $i$ but not the industry demand function
and $\lambda ^*$ is the CV, i.e.:
\begin{equation}
\label{lambdastar}
\lambda^* := \frac{1}{n} \frac{\partial X}{\partial x_i} =
\frac{1}{n} \left( 1 + \frac{\partial \sum_{j \neq i}
x_j}{\partial x_i} \right) \; \; .
\end{equation}
$\lambda ^*$ has values in the interval from 0 to 1, which have
the following economic implications:
$$
\begin{tabular}{|c|c|c|} \hline
\multicolumn{3}{|c|}{Conjectural variations parameter} \\ \hline
$\lambda ^* = 1$ & $\lambda _i = n-1$ & Monopoly or perfect collusion \\
$\lambda ^* = \frac{1}{n}$ & $\lambda _i = 0$ & Cournot oligopoly \\
$\lambda ^* = 0$ & $\lambda _i = -1$ & Perfect competition\\
\hline
\end{tabular}
$$
$\lambda ^*$ has several equivalent economic interpretations which
are easily seen from (\ref{firstorder}) and (\ref{lambdastar}) or
slightly transformed terms. (1) It represents the conjectured
degree of output change of the competitors if bank $i$ changes its
output; (2) it indicates how much of the monopoly markup (which
equals the standard Lerner index) is actually charged by the
players of the observed market; (3) alternatively $\lambda^*$ can
be interpreted as an elasticity adjusted Lerner index; (4)
$-\lambda^*$ measures the percentage deviation of the aggregate
output from the competitive
equilibrium level\footnote{For details cf. Appendix.}.\\
Sticking to the CV language (which corresponds to interpretation
(1)) the above listed implications can easily be derived from
economic intuition. Therefore it is important to remember that
$\lambda^*$ says something about the \emph{expectations} of firms.
A Cournot oligopolist assumes by definition that the other players
won't change their output. Thus $\frac{\partial X}{\partial
x_i}=1$. In perfect competition price is exogenously given. Thus
industry output is expected to remain constant and $\frac{\partial
X}{\partial x_i}=0$. In a perfectly collusive oligopoly each
player wants to maintain its market share $\frac{1}{n}$. Hence an
output increase by player $i$ will cause a proportional increase
in output of each "partner". Thus industry output $X$ increases
proportionally and $\frac{\partial X}{\partial x_i}=n$.\\
Some articles present equation (\ref{firstorder}) in a more
"purist" form without deriving it from a Cournot first order
condition:
\begin{equation}
\label{firstorder2}
P = - \lambda^* P' X + c \; ,
\end{equation}
where $c$ denotes average marginal cost. Of course,
(\ref{firstorder2}) is equal to (\ref{firstorder}). The
implication $\lambda^*$ as a parameter representing the degree of
competition is even more obvious\footnote{which is the reason why
I present this equation as well.}.\\
\\
The empirical model shall now briefly be exemplified following
\cite{bresnahan82} and \cite{bikkerbres}: Bikker chooses a
one-product banking model. However, he considers two products in
this sense that he first tests for the hypothesis with deposits as
"the" product (or rather the services attributed to deposits
approximated by the real value of total deposits) and later with
loans as "the" product. Of course costs are different in both
cases. For deposits the equations estimated are:
\begin{equation}
\label{dep}
DEP_t = \alpha _{0,t} + \alpha _{1,t}1 r_{dep,t} + \alpha _{2,t}
EX_{D,t} + \alpha _{3,t} EX_{D,t} r_{dep,t} + \epsilon_t \; \;
\hbox{and}
\end{equation}
\begin{equation}
\label{rdep}
r_{dep,t} = -\lambda^* \frac{DEP_t}{\alpha _{1,t} + \alpha _{3,t}
EX_{D,t}} + \beta _{0,t} + \beta _{1,t} ^* DEP + \beta _{2,t} ^*
EX_{S,t} + \nu_t \; .
\end{equation}
These equations yield the conduct parameter $\lambda ^*$. The
cross term in (\ref{dep}) must be included for reasons of
identification. The variables are defined as follows:
\begin{eqnarray*}
DEP & = & \hbox{the real value of deposits} \\
r_{dep} & = & \hbox{the market deposit rate} \\
EX_D & = & \hbox{exogenous variables affecting industry demand for
deposits but not marginal} \\ & & \hbox{costs, such as disposable
income, unemployment, interest rates for alternative} \\ & &
\hbox{investments and the
number of branches} \\
\epsilon & = & \hbox{error term} \\
EX_S & = & \hbox{exogenous variables influencing the supply of
deposits, such as costs of input} \\ & & \hbox{factors for the
production of deposits}
(wages etc.) \\
\nu & = & \hbox{error term}
\end{eqnarray*}
Substituting $LOANS$ and $DEP$ for $r_{lend}$ and $r_{dep}$
yields (\ref{dep}) and (\ref{rdep}) for loans.\\
\cite{bikkerbres} cannot reject perfect competition for almost all
countries. For those countries, where it is rejected, he finds a
very low degree of collusion only. The results are very similar
for deposit and for loan markets.\footnote{This may be astonishing
because Germany is among those countries where perfect competition
can be rejected (even if the actual market equilibrium seem snot
be too far away from it). On the other hand concentration measures
unanimously yield comparatively low levels of concentration. SCP
thus would predict exactly the opposite of
what \cite{bikkerbres} found with Bresnahan's model.}\\
\\
\cite{suominen} extends the Bresnahan model to a two product model
and thus can apply the production approach.\\
\\
We now come to the problems associated with the CV model. At first
glance, the above interpretation of the CV parameter might seem
very accessible and beyond doubts. This is right for perfect
competition and Cournot oligopoly. For monopoly or perfect
collusion, however, there is some inconsistency. The question is:
which inferences can we draw from the estimation result if
$\lambda^*=1$? It is right to say that in perfect collusion one
player \emph{expects} its partners to proportionally match its
increase in quantity. As all firms act as one monopolist collusive
output maximises every one firm's profit. If one firm deviates
from common optimum output others will perfectly match this
deviation and profits will drop. Thus, as firms \emph{expect}
retaliation (with negative consequences for their profits) they
actually will never deviate from collusive output\footnote{This is
right provided that perfect collusion is a stable, efficient
equilibrium. If the game allows for the possibility that cheating
will raise profits despite retaliation in the periods to come (a
possible retaliation might be: playing a Cournot game from the
respective round on) the "monopolistic" equilibrium may break
down. \cite{corts} simulates an efficient supergame where exactly
this happens.}. But this means that the econometrician will never
observe deviations from the collusive output. The expected
matching behaviour described by $\lambda^*$ therefore will remain
unobserved. Returning to the above question, the observed value of
$\lambda^*$ cannot be seen as result of the "collusive
expectation". Since, if the incumbent firms had theses
expectations we should not observe $\lambda^*=1$. Theses
considerations do not cast a good light on the "conjectural
variations interpretation". As a solution to this problem
literature tends to interpret the parameter $\lambda^*$ as an
"as-if" parameter who tells us that the degree of competition is
as high "as if" it was produced in a conjectural variations market
with this level of competition. \cite{corts} notes: "The as-if
interpretation of the conduct parameter is based on the
observation that, for given demand and cost conditions, one can
compute the conjecture that would yield the observed price-cost
margins if firms were playing a conjectural variations
equilibrium, even if observed behavior is in fact generated by
some other oligopoly game." The "conjectural variations problem"
might be evaded by just taking $\lambda^*$ as an
elasticity-adjusted Lerner index\footnote{Appendix A shows how
this interpretation can easily be derived from equation
(\ref{firstorder}).}.
\\
Another question is: in which cases is '$\lambda^*=1$' consistent
with a stable equilibrium? Obviously equilibrium is just
guarantied if the incentive to collude is compatible with market
conditions. However, transitory demand shocks and low discount
factors might disturb the equilibrium\footnote{cf. again
\cite{corts} for details on this topic}.\\
\\
Apart from the theoretical interpretation of the conduct parameter
\cite{corts} challenges its \emph{estimation}. %This estimated parameter usually is
%interpreted as an "as-if\," conjectural variations parameter
%indexing intermediate levels of collusive behaviour.
Corts proves that the estimated parameter is biased as soon as the
actual underlying behaviour is not the result of a conjectural
variations equilibrium and establishes a formal sufficient and
necessary condition for the "as-if" interpretation being correct.
He simulates an efficient supergame collusion and shows that, if
the demand shocks the market undergoes are not permanent, the
estimated conduct parameter underestimates the actual degree of
collusion. If the demand shocks are completely transitory it may
not detect any market power even if there are monopolistic
price-cost margins. %Apart from potential transitory demand shocks
%the discount factor for profits in future periods plays an
%important role. The discounted value of future profit losses which
%are due to retaliation decreases, of course, with the discount
%factor. In an extreme case the discount factor equals zero.
One may argue that the model can at least be used to test for
extreme behaviour (e.g. perfect competition) instead of being used
to measure the degree of market power. However Corts shows that
$\lambda = 1$ may be consistent with any level of market power and
a rejection of this hypothesis may actually not allow any
inference. The intuition behind Corts' argumentation is easy: the
framework of CV analysis is based on the \emph{static} first-order
condition of a profit-maximising Cournot oligopolist. In a
\emph{dynamic} setting, however, the first-order condition may
depend as well on the incentive compatibility constraint
associated with collusion. After a demand shock a player might
find that cheating (despite retaliation by rivals) would earn him
higher profits. Such behavior can bias the estimated conduct
parameter.\\
The criticism in \cite{corts} somewhat relativises the outcome of
CV studies. Since the late nineties a couple of articles have been
published, which try to "test" the accuracy of CV methods. They
focus on industries with virtually perfect data availability,
where markups can be measured directly. The "direct" results are
compared with the outcome of CV estimates. \cite{genesove}
concentrate on the US sugar industry between 1890 and 1914. They
find that the CV model provide a quite correct estimate of market
conditions; deviation from the actual degree of competition are is
not large. \cite{knittel} studies the Californian electricity
market covering the period from 1998 to 2000. Their result is that
the accuracy of the parameter estimate depends on the functional
form of demand (e.g. linear or loglinear).\\
\\
Finally it is worth pointing to the article of \cite{ribon}, which
analyses if competition had been affected by financial
liberalisation in Israel. Ribon and Yosha introduce a couple of
new features into the Bresnahan approach. First they
simultaneously determine the competitive conduct in an input
market (deposits) and an output market (loans). Second they allow
for dynamics, i.e. the conduct parameters are not assumed to be
constant over time. This is achieved by either interacting the
conduct parameters with time dummies or by modelling the conduct
parameters as functions of time. Third, they extensively include
alternative funding sources, as central bank sealed bid auctions,
and also account for additional aspects, e.g. reserve rates
regulated by the Bank of Israel or the inflation rate. Ribon and
Yosha use marginal cost, which are specified as the marginal cost
of funding from the central bank. Data needed to compute the
industry average of these cost can easily be obtained. The authors
further note that identification of the conduct parameters needs
varying inflation rates. Unfortunately, this point might make the
approach - in the form used by Ribon and Yosha - inapplicable to
the German banking sector. Nevertheless, this approach to the
Bresnahan concept is very worth reading as it introduces a couple
of aspects other
studies omit.\\
\\
%\footnote{It seems important to note that
%\cite{corts}does not appear in the references of
%\cite{bikkerbres}, a paper dated from 2003 and thus after Corts'
%article.}
%We
%will see below that this constraint allows unambiguous inferences
%of the Panzar-Rosse $H$-statistic.
I will shortly report the outcome of \cite{bikkerbres}, the only
Bresnahan-based study of competition in German banking, which is
available to me. For the deposit market\footnote{where deposits
are the only product} the hypothesis $\lambda ^* = 0$ (attributed
to perfect competition) can be rejected on a $95 \%$-level of
significance. Nevertheless the deviation from zero is not great.
Testing for Cournot equilibrium ($\lambda ^* = 1/n$) the
hypothesis cannot be rejected. On the German loans market both
perfect competition and Cournot equilibrium can be rejected. The
estimated value of
$\lambda ^*$ lies somewhere in between.\\
Apart from Germany, Spain was the only country for which the
hypothesis "perfect competition in the deposit market" could be
rejected\footnote{The sample contains Belgium, France, Germany,
Italy, the Netherlands, Portugal, Spain, Sweden and the UK.}. For
all other countries it could not be rejected (Bikker notes,
however, that taking perfect competition as hypothesis implies an
a priori bias towards perfect competition.). The result is
somewhat astonishing. At least for countries with a very high
concentration ratio, like the Netherlands, we would have expected
evidence supporting some abuse of market power. On the other hand,
in Germany, which has a relatively low concentration, the
Bresnahan model detects collusion. In the loan market nonperfect
competition is found in Portugal, Spain, Sweden and the UK (and
Germany).
\subsection{The Panzar-Rosse (P-R) approach} Originally\footnote{cf. \cite{pr}}
Panzar and Rosse develop a testable implication of monopolistic
profit-maximisation. The model is then extended to other market
equilibria. They therefore analyse the comparative static
properties of the reduced form revenue equation at the firm level.
The key parameters are the factor price elasticities of the
reduced form revenue equation. Data requirements are relatively
modest. Output price data are not required.\\
The model is based on the reduced form revenue function $R^* =
R^*(w,z,t)$, where $z$ are exogenous variables shifting the firm's
revenue function, $t$ are exogenous variables shifting the firm's
cost function and $w$ are factor prices. The key parameter is the
$H$-statistic which is defined as follows:
\begin{equation}
H := \sum_{i=1}^{n}\frac{\partial R^*}{\partial w_i}
\frac{w_i}{R^*}
\end{equation}
We need the following assumptions:
\begin{enumerate}
\item linearly homogenous cost functions (or homothetic production
function)
\item factor prices exogenous to the individual firm
\item free market entry and exit
\item long-run equilibria\footnote{
This is not necessary if one just wants to test for monopoly.}
\item the elasticity of perceived demand facing the individual
firm is a nondecreasing function of the number of symmetric rivals
\item $\frac{\partial P}{\partial y},\frac{\partial P}{\partial n}
< 0$ with the inverse demand function $P$ and the number of
symmetric rivals $n$.
\end{enumerate}
The following table shows the implications of different values of
$H$:
$$
\begin{tabular}{|c|c|} \hline
\multicolumn{2}{|c|}{Competitive environment test} \\ \hline
$H \leq 0$ & Monopoly or perfect collusion \\
$H \leq 1$ &
Symmetric Chamberlinian equilibrium \\
$H = 1 $ & Long-run competitive equilibrium \\
\hline
\end{tabular}
$$
It is important to note that in the literature this classification
is not completely consistent. For example \cite{hempell} does not
allow equality for monopolistic competition. Therefore I have
sticked to the original article of Panzar and Rosse (\cite{pr}).
The intuitive derivation of this classification is easy:\\
Monopoly: An increase in input factor prices produces an upward
shift of cost functions. Thus prices rise and output falls. As
monopolists produce on the elastic portion of the inverse demand
schedule this has a negative total effect on revenues. Hence an
increase in
input factor prices causes a decrease in revenues.\\
Perfect competition: Suppose all input factor prices rise by 1\%.
As we have assumed linear homogeneous cost functions the average
total costs curve shifts upward by 1\% for all output levels. Thus
prices increase by 1\% as well. As the minimum point of the
average total cost curve does not move optimum output remains
constant. Thus revenues rise by 1\%. The effect of a 1\% increase
of factor input prices is a 1\% increase in revenues.\\
There is no easy intuitive explanation for the $H$ values in the
case of Chamberlinian monopolistic competition.\\
\cite{moly} points out that there is a second interpretation of
the $H$-statistic which allows to test for equilibrium. In this
case one has to substitute elasticities of \emph{returns} for
elasticities of \emph{revenues}. Since the P-R approach is based
on comparative static models inferences from the $H$-statistic are
actually not possible if markets are not in a long-run
equilibrium. Hence, testing for equilibrium should precede testing
for market power.
$$
\begin{tabular}{|c|c|} \hline
\multicolumn{2}{|c|}{Equilibrium test} \\ \hline
$H < 0$ & Disequilibrium \\
$H = 0$ & Equlibrium \\ \hline
\end{tabular}
$$
Again, economic intuition can illuminate these interpretations of
$H$: In competitive capital markets risk-adjusted rates of return
must be equal for all banks. Thus, in equilibrium rates of return
should not be statistically correlated with input prices. \\
In the regression equation, returns have to be substituted for
revenues as the left-hand variable.
\\
\\
We will now shortly discuss the pros and cons of the P-R approach.
The most striking advantage are the limited data requirements.
Output prices are not required. In addition we have a sound
theoretical underpinning and with some additional assumptions $H$
can be interpreted as a continuous measure of
competition\footnote{\cite{bikkerhaaf}}. As we use firm-level data
it is possible to differentiate between different markets.
\cite{hempell}, for instance, classifies banks into big, small and
medium-sized ones or she tests savings banks, cooperative banks,
credit banks and foreign banks separately. At last, the
disaggregation of the $H$-statistic can give insight into which
factor contributed most
to the total effect.\\
Problems arise from the fact that the model (if applied to test
other scenarios than monopoly) works for long-run equilibria only.
The model does not allow for differences in maturity structure of
banks' asset portfolio. This might cause a downward bias as longer
maturities prevent banks from direct price adjustments. In
addition P-R do not account for multi-product banks. Maybe the
most problematic aspect of the model is the assumption that banks
are price takers on input
markets.\footnote{(\cite{bikkerbres})finds a quite high degree of
competition in deposit markets. In addition, if more and more
substitutes for traditional deposits are offered there may also be
a positive effect on the competition in this segment. Thus, at
least one of the input markets might be highly competitive.}\\
The "one-product constraint" is sometimes solved by running the
tests for two product bundles separately. \cite{rime} in his study
of the Swiss banking market, for instance, takes two pairs of
products: (1) loans and bonds and (2) total assets and service
fees. Of course costs have to be adapted adequately.\\
\\
The estimation equation is a loglinear reduced form revenue
equation. We cite the version used by \cite{hempell}:
\begin{eqnarray}
\label{presteq}
\ln TIN1tTA_{i,t} & = & a_1 + b_1 \ln IETF2_{i,t} + b_2 \ln
wage1_{i,t} + b_3 \ln aCEtFA_{i,t} + c_1 LtTL_{i,t} \nonumber \\
& & + c_2 IDtTD_{i,t} + c_3 lmab1t_{i,t} + c_4 cashi_{i,t} + d_1 t
+ \lambda _t + \mu _i + u _{i,t} \; ,
\end{eqnarray}
where
\begin{eqnarray*}
TIN1tTA & = & \hbox{total income to total assets} \\
IEtF2 & = & \hbox{interest expenses to total funds} \\
wage1 & = & \hbox{personnel expenses to total assets} \\
CEtFA & = & \hbox{capital expenses to fixed assets} \\
LtTL & = & \hbox{customer loans to total loans} \\
IDtTD & = & \hbox{interbank deposits to total deposits} \\
lmab11 & = & \hbox{maturity structure of customer loan portfolio}
\\
cashi & = & \hbox{cash flow to business volume by sector of the
borrower, weighted} \\
& & \hbox{with the portfolio of loans to enterprises.}
\end{eqnarray*}
Hempell estimates (\ref{presteq}) with a fixed effect panel
regression. $\lambda _t$ represents the time specific constant
accounted for by including time dummies and $\mu _i$ the bank
specific constant. $u_{i,t}$ are the error terms corresponding to
the endogenous variable\footnote{\cite{hempell} also gives a good
overview of the variables other studies employed.}. The vast
majority of studies estimates a loglinear revenue function.
\cite{perrakis} criticises this functional form. \cite{lang}
therefore applies a translog function. \cite{moly} also try a
translog model but drop it because of massive
problems with collinearity of explanatory variables.\\
In the estimation equation for the equilibrium test \cite{moly}
choose 'return on assets' ($ROA$) as left-hand variable\footnote{
The right-hand variables differ as well, but this is not due to
the equilibrium test.}.\\
\\
Most studies using the P-R statistic find different degrees of
monopolistic competition. For the German banking sector the
reviewed studies have the following results: As mentioned above
\cite{hempell} runs her test for the whole sample as well as for
different subgroups. The period covered is 1993 - 1998. She finds
monopolistic competition for all groups. However, cooperative
banks, savings banks, credit banks and foreign banks have
increasing $H$-values. Distinguishing between small, medium-sized
and large banks\footnote{"small" includes all banks with assets
below 1 billion DM, "medium-sized" means banks with assets between
1 and 5 billion DM and "large" covers the remainder.} $H$
increases with size. Thus bigger banks operate in a more
competitive
environment than small banks.\\
\cite{lang} analyses data from the period between 1988 and 1992 to
get virtually the same results as Hempell, i.e. monopolistic
competition and a higher $H$ value for credit banks than for
savings and cooperative banks.\\
\cite{bikkerhaaf} study the period from 1988 to 1998. They find
that competitive behaviour increases with size. For small and
medium-sized banks both hypotheses $H=0$ and $H=1$ can be rejected
(level of confidence: $99.9\%$). This indicates monopolistic
competition. For large banks however they obtain $H=1.05$ and thus
cannot reject the hypothesis that this group operates in a
perfectly competitive environment (level of confidence: $95 \%$).
The following table gives an overview of which hypotheses could
not be rejected\footnote{The levels of confidence are always over
$95\%$. See \cite{bikkerhaaf}, Appendix 1} in the countries
analysed in \cite{bikkerhaaf}:
$$
\begin{tabular}{|c||c|c|} \hline
\textbf{country} & $H=1$ \textbf{not rejected} & $H=0$ \textbf{not rejected} \\
& (group) & (group) \\ \hline
Austria & small & \\
Belgium & small & \\
Denmark & large & \\
Finland & small & \\
Germany & large & \\
Greece & large & small \\
Ireland & small, large & \\
Japan & & small \\
South Korea & medium, large & \\
Netherlands & small, large & \\
New Zealande& medium & \\
Sweden & large & \\
Switzerland & medium, large & \\
\hline
\end{tabular}
$$
This shows that the German result "the larger the bank the more
competitive its environment" cannot easily be generalised.
However, monopoly seems to be very scarce. The whole sample
includes 23 countries. In almost half of them there are no
indications at all for either perfect competition or monopoly.\\
\cite{moly} studies competitive conditions in various European
banking markets between 1986 and 1989. He also runs an equilibrium
test. For Germany he finds equilibrium for the whole period. In
the competition test for Germany both perfect competition and
monopoly can be rejected for 1986, 1988 and 1989. The 1987 data
suggest perfect competition.\\
\\
The above mentioned problems all arise from the theoretical
framework of the P-R model itself. There is, however, another flaw
associated with the empirical setup, which shall now shortly be
described: Input factor prices entering the estimation equation
always include personnel expenses, costs of physical capital and
costs of deposits. Equity capital as input factor and costs of
equity capital, however, are neglected. This might be due to
problems associated with measuring costs of equity capital. The
gravity of this problematic might be demonstrated by means of the
following example: \cite{hempell} classifies deposits as input.
Consequently she accounts for interest expenses in the calculation
of costs. These funding costs are approximated by $IEtF2$, which
is defined as "interest expenses to total funds". Assume that the
bank in question substitutes risky loans for, say, government
securities. In this case, the bank has to increase its equity
capital to account for the higher risk in its portfolio. As a
certain amount of equity capital will be substituted for debts and
liabilities interest expenses will fall. The nominator of the
proxy for funding costs will decrease (since: funds = deposits +
equity capital). Thus, the proxy for input costs will fall. This
might produce a paradoxical effect: if costs for equity capital
are higher than costs of foreign capital funding costs will rise.
The cost measure, however, will indicate lower costs\footnote{Of
course, the example is very rough. If the bank takes higher risks
it might have to pay higher rates on deposits. The scenario shall
show the general problem.}. Appendix B describes how a shadow
price
for equity capital could be estimated.\\
\subsection{An approach by Hannan and Liang}
\cite{hannan} have developed a method to test for price-taking
behavior in the deposit market. They apply it to the US banking
market. The method has been adopted by \cite{ashton} in a study on
competition in the UK retail banking sector. In addition, it
allows to test the SCP hypothesis. Hannan and Liang note that
testing for perfect collusion would need unacceptable assumptions,
such as product homogeneity. However, the parameter they estimate
enables to draw ordinal conclusions about the degree of
competition. Thus, it is possible to compare competition in
different product markets. The test requires time-series
information on bank deposit rates, security rates, and bank
marginal costs. The main outcome of the study is that perfect
competition can be rejected and that the degree of competition is
lower for money market deposit accounts (MMDA) than for two-year
certificates of deposits (2YCD) and three-year certificates of
deposits (3YCD). The theoretical background relies on the analysis
of the margin between exogenous gouvernment securities rates and
deposits rates of respective maturities. Comparison of a market
where individual banks might exercise some price-setting power and
a market where an individual bank is price-taker allows inferences
on the level of market power. The estimated parameter measures the
supply elasticity. It gives information on both a bank's
conjecture on how rivals will react to its interest rate change
and the degree of product differentiation.
%Interpretation of the parameter:
%The elasticity measures the percentage change of supply,
%if the interest rate is reduced by one percentage point.
%If the other banks do not react at all, all customers (suppliers)
%will deposit all their money at my rivals. Thus my perceived supply
%will break down completely, elasticity is infinite.
%If the others collude with me nothing will happen
%to my supply and elasticity is zero. "perceived" refers to the fact
%that it is the individual elasticity I face and not industry
%elasticity.
%Thus alpha is also kind of a conduct parameter.
Defining $r_d^i$ bank $i$'s deposit rate, $c_d^i$ bank $i$'s
marginal cost of employing a dollar of deposits to fund
securities, $r_s$ the security rate and $e_d^i$ bank $i$'s
perceived deposit-supply elasticity\footnote{Deposit-supply
elasticities are bank specific since Hannan and Liang allow for
the existence of product differentiation. Thus, elasticity is
affected by the reactions of rivals as well as by the degree of
product differentiation} the profit-maximising rate for each type
of deposit must satisfy the following equation:
\begin{equation}
\label{hannantheo}
r_d^i \cdot \left( 1 + \frac{1}{e_d^i} \right) = r_s - c_d^i
\Longleftrightarrow r_d^i = \underbrace{\frac{e_d^i}{1 +
e_d^i}}_{=: \; \alpha ^i} \cdot (r_s - c_d^i) \; .
\end{equation}
In words: the additional expenses due to an an additional dollar
"produced" must equal the marginal net gain from investing that
dollar in securities.\\
In the absence of market power the perceived supply elasticity is
infinite. As $\alpha ^i \stackrel{e_d^i \to
\infty}{\longrightarrow} 1$, perfect competition is equivalent
with $\alpha ^i = 1$. Thus, if time-series regression of $r_d^i$
on $r_s - c_d^i$ yields values for $\alpha ^i$ significantly less
than unity perfect competition can be rejected. Further, we can
note that $\alpha _i$ is an isotonic function of elasticity and,
hence, a lower degree of competition coincides with lower values
of $\alpha ^i$.\\
Some attention should be paid to the choice of the three deposit
categories. MMDAs require frequent contact between customers and
banks and thus they may be competed for on an local basis. The
market for 2YCDs and 3YCDs is likely to be geographically broader.
This approach to distinction of different markets (where
'different' mainly refers to the geographic dimension) is similar
to our proceeding in the Bresnahan and the P-R model where market
delineation has been achieved by product differentiation (deposits
and loans) and separation of different banking groups (large,
medium-sized and small or savings,
cooperative, credit and foreign banks).\\
The variable $c_d^i$ in equation (\ref{hannantheo}) cannot be
measured directly . Hannan and Liang derive it from a
multi-product cost function following \cite{berger95}.
\cite{ashton} show the procedure
for a couple of UK banks.\\
The time series estimation equation is specified as follows:
\begin{equation}
\label{hannanemp}
r_d^i = \alpha _0 + \alpha _1^i (r_s - c_d^i) + \hbox{error term}
\end{equation}
The estimation results\footnote{Hannan and Liang excluded those
banks from the sample, for which $\alpha ^i$ proved to be not
constant over time.} show that $94\%$ respectively $80\%$ and
$77\%$ of $\alpha^i$ were significantly ($95\%$ level of
confidence) less than one in the MMDA, the 2YCD and the 3YCD case.\\
\\
As the Hannan/Liang approach also provides a test for the SCP
paradigm we will briefly return to this model. The above
discussion of the coefficient $\alpha ^i$ suggests that it can be
interpreted as a rough measure of market power. Thus, a negative
relationship between $\alpha ^i$ and market concentration could be
interpreted as evidence for the SCP paradigm. Therefore Hannan and
Liang run cross-section regressions of $\alpha _1^i$ on a
concentration measure and other explanatory variables. The
estimation equation is of the form:
\begin{equation}
\label{hannanscp}
\tilde{\alpha}_1^i = \gamma_0 + \gamma_1 CR_i + \gamma X_i + u_i
\; ,
\end{equation}
where $\tilde{\alpha}_1^i$ is the estimated value of $\alpha_1^i$,
$CR_i$ represents the 3-firm concentration index of bank $i$'s
market, $X_i$ is a vector of explanatory variables, e.g. bank
size, and $u_i$ is an error term\footnote{Markets are defined as
Metropolitan Statistical Areas (MSAs) or counties in the case of
banks located outside of MSAs.}. The regressions results are not
surprising: for the MMDA market, which is a relatively local
market, Hannan and Liang find a negative relationship between
$\tilde{\alpha}_1^i$ and $CR_i$. For the CDs the coefficients of
$CR_i$ are not significant. This is in line with the notion that
in broader geographic markets market power associated with
concentration is not perceivable\footnote{This is kind of a
contestability argument.}. The result may be interpreted in this
sense that the SCP paradigm generally is plausible, but
contestability matters.
\subsection{The Iwata model}
\cite{iwata} has developed another model which is based on an
oligopolistic market and measures the conjectural variation.
According to the Cournot and the Bresnahan model, it is derived
from the first order conditions of a profit-maximising
oligopolist. \cite{overview} note that this model has apparently
been applied only once for the banking industry by
\cite{shafferdisalvo} to a duopoly. Iwata himself applies it to
the Japanese flat glass industry. A shortcoming of the model is
that it requires micro-data for the structure of cost and
production for homogenous products. This is why I will not go into
further detail and just present the term which determines the
conjectural variation:
\begin{equation}
\label{iwata}
\lambda _i = \eta _D \cdot \frac{c'(x_i) - p}{p} \cdot
\frac{X}{x_i} - 1 \; ,
\end{equation}
where $\eta _D$ is the price elasticity of demand, $x_i$
individual firm output, $X$ industry output and $p$ price. To
obtain $\lambda _i$ one has to estimate a market demand function
and individual cost functions. Therefore one has to assume that
$p$ and $x_i/X$ are strict functions of exogenous variables and
that the price elasticity of demand is constant.
%!!!!!!! Check this in Iwata.
\section{Conclusion}
The paper has presented an overview of the existing approaches to
the measurement of competition. It shows that bank specific
problems are not yet resolved perfectly. In particular the
question of how to introduce risk and equity capital , at least in
the papers I reviewed, remains unanswered. Structural approaches
to the measurement of competition seem not reliable. Thus recent
literature has focussed on NEIO models, mainly the co´njectural
variations approach and the Panzar-Rosse approach. The latter
seems to be the most applicable model. The empirical outcome is
more or less similar in all studies indicating a relatively high
degree of competition.
\newpage
%\setcounter{page}{1}
\bibliographystyle{plainnat}
\bibliography{yyy}
\newpage
%\begin{appendix}
\appendix
\begin{Large}\textbf{Appendix} \end{Large}
\section{The formal framework of the conjectural variations
approach}
We assume $n$ banks in an oligopolistic market supplying
one homogenous product. Profit of bank $i$ is given by:
\begin{equation}
\label{oligoprofit}
\pi_i = P(X,EX_D) x_i - c_i(x_i,EX_{S_i}) - F_i \; ,
\end{equation}
where $P$ is price, $c_i$ is the marginal cost of bank $i$, $x_i$
is the output of bank $i$, $X$ is industry output, $EX_{S_i}$ are
exogenous factors affecting bank $i$'s cost but not industry
demand, $EX_{D}$ are exogenous factors affecting industry demand
but not marginal cost and $F_i$ is bank $i$'s fixed cost. Defining
$c'_i$ the marginal cost of bank $i$, the first-order condition
for profit-maximisation is:
\begin{equation}
\label{oligofirstorder}
0 = P(X,EX_D) + x_i \frac{\partial P}{\partial X} \frac{\partial
X}{\partial x_i} - c'_i \; .
\end{equation}
Summing over all banks and dividing through $n$ yields:
\begin{equation}
\label{oligosum}
0 = P + \frac{1}{n} X P' \, \frac{\partial X}{\partial x_i} -
\frac{1}{n} \sum_{i=1}^n c'_i \; ;
\end{equation}
hence,
\begin{equation}
\label{oligoresult}
P = - \lambda^* X P' + \frac{1}{n} \sum_{i=1}^n c'_i \; .
\end{equation}
With the semi-elasticity of demand $\eta_D^*$ and average marginal
cost $c$ one has:
\begin{equation}
\label{oligoelast}
P = \lambda ^* (\eta^*)^{-1} + c \; .
\end{equation}
This relationship reflects how prices are affected by demand
elasticities and costs where the oligopolist is assumed to
maximise perceived profits through consideration of the reaction
of other players.\\
Another re-arrangement illuminates the interpretation of $\lambda
^*$ as coefficient of the Lerner index $L := \left( -
\frac{\hbox{d} X}{\hbox{d} P} \frac{P}{X} \right)^{-1}$ which
equals the markup in a monopoly:
\begin{equation}
\label{oligolerner}
\frac{P-c}{P} = \lambda^* L \; .
\end{equation}
Dividing through $L$ and defining the elasticity-adjusted Lerner
index $L_{\eta}$ yields:
\begin{equation}
\label{oligoadjustedlerner}
\lambda^* = \eta \frac{P-c}{P} =: L_{\eta} \; .
\end{equation}
Sometimes the CV parameter even \emph{is defined} as the
elasticity-adjusted Lerner index. The elasticity adjusted Lerner
index has an important feature: it differentiates whether high
price-cost margins are due to the abuse of market power or to
low elasticities.\\
At last, \cite{shaffercan} presents the interpretation of the CV
parameter as the percentage deviation from competitive output.
This goes as follows:
\begin{equation}
\label{oligooutput1}
\underbrace{P \cdot \frac{\hbox{d} X}{\hbox{d}
P}}_{\hbox{\small{equlibrium output}}} - \underbrace{c \cdot
\frac{\hbox{d} X}{\hbox{d} P}}_{\hbox{competitive output}} =
\hbox{ deviation} \; .
\end{equation}
Re-arrangement and devising through $X$ produces:
\begin{equation}
\label{oligooutput2}
\frac{P \cdot \frac{\hbox{d} X}{\hbox{d} P}-c \cdot \frac{\hbox{d}
X}{\hbox{d} P}}{X} = - \lambda^* \; .
\end{equation}
\section{The cost of equity capital}
\cite{hughes} offers an interesting method how to derive the
shadow price of equity capital. He also estimates the mean shadow
price for different size groups of US banks (where size refers to
asset size). Starting point of the formal derivation is the
cash-flow cost function
\begin{equation}
\label{cfcost}
C_{CF}(\mathbf{y},n,p,\mathbf{w_p},\mathbf{w_d},k) =
\min_{\mathbf{x_p},\mathbf{x_d}} (\mathbf{w_p x_p} + \mathbf{x_d
w_d}) \hbox{ s.t. } T(\mathbf{y},n,p,\mathbf{x},k) \leq 0 \hbox{
and } k = k^0 \; ,
\end{equation}
with the transformation function $T$; $\mathbf{y}$,
information-intensive loans and financial services; $k$, equity
capital; $\mathbf{x_d}$, demandable debt and other types of debt;
$\mathbf{x_p}$, labour and physical capital; $\mathbf{x} =
(\mathbf{x_p},\mathbf{x_d})$; and $w_i$, the price of the $i$-th
type of input. In order to allow for the asset quality two
controls are included: the amount of nonperforming loans, $n$, and
the average contractual interest rate on loans, $p$. Then,
economic cost can be described as follows:
\begin{equation}
\label{cost}
C(\mathbf{y},n,p,\mathbf{w_p},\mathbf{w_d},w_k) =
C_{CF}(\mathbf{y},n,p,\mathbf{w_p},\mathbf{w_d},k) + w_k k \; ,
\end{equation}
The first-order condition for cost minimisation yields:
\begin{equation}
\label{equitycost}
w_k = - \frac{\partial C_{CF}}{\partial k} \; .
\end{equation}
If the shadow price equals the market price it reflects the
marked-priced risk of a bank's portfolio\footnote{Higher risks
increase the required return on equity.}. But, besides possible
problems with estimating $-\partial C_{CF}/\partial k$, it is not
assured that the level of equity observed minimises cost. If not,
the estimated shadow price may not equal the market price.
Regulation, for instance, might demand levels of equity capital,
which exceed cost-minimising levels. Another incentive for banks
to hold more equity capital may be the signalling function of
equity capital. \\
The outcome of the estimations in \cite{hughes} suggest that banks
do not minimise cost. Shadow price values for small banks seem to
be smaller than market prices, those of large banks seem to exceed
market prices.
%\end{appendix}
\end{document}
-------------- next part --------------
\Sort{
Mode{on}
Collation{mixed}
SortTypeOrder{name}
NameOrder{ascending}
}
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author = {Bos, J.},
year = 2002,
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volume = 48,
number = 1,
pages = {21-38}
}
@ARTICLE{rime,
author = {Rime, B.},
year = 1999,
title = {Mesure du degr\'{e} de concurrence dans le syst\`{e}me bancaire suisse \`{a} l'aide du mod\`{e}le de {P}anzar et {R}osse},
journal = {Revue suisse d'Economie politique et de Statistique},
volume = 135,
number = 1,
pages = {21-40}
}
@UNPUBLISHED{bikkerhaaf,
author = {Bikker, J.A. and Haaf, K.},
year = 2000,
title = {Competition, Concentration and their Relationship: An Empirical Analysis of the Banking Industry},
note = {De Nederlandsche Bank, Research Series Supervision, vol. 30}
}
@UNPUBLISHED{easteuro,
author = {Yildrim, H.S. and Philippatos, G.C.},
year = 2003,
title = {Competition and Contestability in Central and Eastern European Banking Markets},
note = {University of Saskatchewan, Working Paper}
}
@UNPUBLISHED{hempell,
author = {Hempell, H.},
year = 2002,
title = {Testing for Competition Among German Banks},
note = {Economic Research Centre of the Deutsche Bundesbank, Discussion paper 04/02 }
}
@ARTICLE{moly,
author = {Molyneux, P. and Lloyd-Williams, D.M. and Thornton J.},
year = 1994,
title = {Competitive conditions in {E}uropean banking},
journal = {Journal of Banking and Finance},
volume = 18,
pages = {445-459}
}
@ARTICLE{corts,
author = {Corts, K.S.},
year = 1999,
title = {Conduct parameters and the measurement of market power},
journal = {Journal of Econometrics},
volume = 88,
number = 2,
pages = {227-250}
}
@ARTICLE{iwata,
author = {Iwata, G.},
year = 1974,
title = {Measurement of Conjectural Variations in Oligopoly},
journal = {Econometrica},
volume = 42,
number = 5,
pages = {947-966}
}
@ARTICLE{cowling,
author = {Cowling, W. and Waterson, M.},
year = 1976,
title = {Price-Cost Margins and Market Structure},
journal = {Economica},
volume = 43,
pages = {267-274}
}
@UNPUBLISHED{overview,
author = {Bikker, J.A. and Haaf, K.},
year = 2000,
title = {Measures of competition and concentration in the banking industry: a review of the literature},
note = {De Nederlandsche Bank, Research Series Supervision, vol. 27}
}
@UNPUBLISHED{ashton,
author = {Ashton, J.},
year = 1999,
title = {A test of perfect competition in the UK retail-banking deposit market},
note = {Bournemouth University, School of Finance \& Law, Working Paper Series, No. 15 }
}
@ARTICLE{hannan,
author = {Hannan, T.H. and Liang, J.N.},
year = 1993,
title = {Inferring market power from time-series data, The case of the banking firm},
journal = {International Journal of Industrial Organization},
volume = 11,
pages = {205-218}
}
@ARTICLE{shafferdisalvo,
author = {Shaffer, S. and DiSalvo, J.},
year = 1994,
title = {Conduct in a banking duopoly},
journal = {Journal of Banking $\&$ Finance},
volume = 18,
pages = {1063-1082}
}
@BOOK{varian,
author = {Varian, H.},
year = 1989,
title = {Grundzüge der Mikro{\"{o}}konomik},
series = {Internationale Standardlehrbücher der Wirtschafts- und Sozialwissenschaften},
publisher = {Oldenbourg},
address = {München}
}
@ARTICLE{hughes,
author = {Hughes, J.P. and Lang, W.W. and Mester, L.J. and Moon, C.G.},
year = 2001,
title = {Are scale economies in banking elusive or illusive? Evidence obtained by incorporating capital structure and risk-taking into models of bank production},
journal = {Journal of Banking and Finance},
volume = 25,
pages = {2169-2208}
}
@BOOK{freixas,
author = {Freixas, X. and Rochet, J.-C.},
year = 1998,
title = {Microeconomics of Banking},
publisher = {The MIT Press},
address = {Cambridge, Mass.}
}
@ARTICLE{berger89,
author = {Berger, A. and Hannan, T.},
year = 1989,
title = {The price-concentration relationship in banking},
journal = {Review of Economics and Statistics},
volume = 71,
pages = {291-299}
}
@ARTICLE{neumark,
author = {Neumark, D. and Sharpe, S.},
year = 1992,
title = {Market structure and the nature of price rigidity: {E}vidence from the market for consumer deposits},
journal = {Quartely Journal of Economics},
volume = 107,
pages = {656-680}
}
@ARTICLE{jackson97,
author = {Jackson III, W.},
year = 1997,
title = {Market structure and the speed of adjustment: Evidence of non-monotonicity},
journal = {Review of Industrial Organization},
volume = 71,
pages = {291-299}
}
@ARTICLE{jackson92,
author = {Jackson III, W.},
year = 1992,
title = {The price-concentration relatioship in banking: {A} comment},
journal = {Review of Economics and Statistics},
volume = 74,
pages = {373-376}
}
@ARTICLE{bresnahan,
author = {Bresnahan, T.F.},
year = 1989,
title = {Empirical studies of industries with market power},
journal = {Handbook of Industrial Organization},
volume = 2,
pages = {1011-1055}
}
@ARTICLE{bergercost,
author = {Berger, A.N.},
year = 1995,
title = {Allen},
journal = {Journal of Econometrics},
volume = 88,
number = 2,
pages = {227-250}
}
@ARTICLE{hannan2,
author = {Hannan, H.H.},
year = 1991,
title = {Foundations of Structure-Conduct-Performance Paradigm in Banking},
journal = {Journal of Money, Credit and Banking},
volume = 23,
number = 1,
pages = {68-84}
}
@ARTICLE{perrakis,
author = {Perrakis, S.},
year = 1991,
title = {Assesing competition in {C}anada's finacial system: {A} note},
journal = {Canadian Journal of Economics},
volume = 223,
number = 3,
pages = {727-732}
}
@ARTICLE{genesove,
author = {Genesove, D. and Mullin, W.P.},
year = 1998,
title = {Testing static oligopoly models: conduct and cost in the sugar industry, 1890-1914},
journal = {RAND Journal of Economics},
volume = 29,
number = 2,
pages = {355-377}
}
@BOOK{goddard,
author = {Goddard, J. and Molyneux, P. and Wilson J.O.S.},
year = 2001,
title = {European banking},
series = {Finance},
publisher = {Wiley},
address = {Chichester}
}
@UNPUBLISHED{knittel,
author = {Kim, D.-W. and Knittel C.R.},
year = 2003,
title = {Biases in {S}tatic {O}ligopoly {M}odels?: {E}vidence from the {C}alifornian {E}lectricity {M}arket},
note = {University of California, Davis}
}
@UNPUBLISHED{ribon,
author = {Ribon, S. and Yosha, O.},
year = 1999,
title = {Financial {L}iberalization and {C}ompetition in {B}anking: {A}n {E}mpirical {I}nvestigation},
note = {The Eitan Berglas School of Economics, Tel-Aviv University, Working Paper No. 23-99}
}
@ARTICLE{gilbert,
author = {Gilbert, R.A.},
year = 1984,
title = {Bank market structure and competition - a survey},
journal = {Journal of Money, Credit and Banking},
volume = 16,
number = 2,
pages = {617-645}
}
@ARTICLE{bresnahan82,
author = {Bresnahan, T.F.},
year = 1982,
title = {The oligopoly solution concept is identified},
journal = {Economics Letters},
volume = 10,
pages = {87-92}
}
-------------- next part --------------
-------------- next part --------------
\Sort{
Mode{on}
Collation{mixed}
SortTypeOrder{name}
NameOrder{ascending}
}
% SCP
@BOOK{bosdiss,
author = {Bos, J.},
year = 2002,
title = {European Banking: Market Power and Efficiency},
publisher = {Universitaire Pers Maastricht},
address = {Maastricht}
}
@ARTICLE{eib/Moly,
author = {Molyneux, P.},
year = 1999,
title = {Increasing concentration and competition in European banking: The end of anti-trust?},
journal = {EIB Papers, European banking after EMU},
volume = 4,
number = 1,
pages = {127-136}
}
} @UNPUBLISHED{bos03,
author = {Bos, J.W.B.},
year = 2003,
title = {Improving Market Power Tests: Does it matter for the Dutch Banking Market?},
journal = {De Nederlandsche Bank, Research Series Supervision, vol. 56}
}
} @UNPUBLISHED{cetorelli,
author = {Cetorelli, N.},
year = 1999,
title = {Competitive analysis in banking: Appraisal of the methologies},
journal = {The Federal Reserve Bank of Chicago, Economic Perspectives}
}
@ARTICLE{berger,
author = {Berger, A.N.},
year = 1995,
title = {The profit-structure relationship in banking - tests of market power and efficient structure hypothesis},
journal = {Journal of Money, Credit and Banking},
volume = 27,
number = 2,
pages = {404-431}
}
%Bresnahan
} @UNPUBLISHED{bikker/bres,
author = {Bikker, J.A.},
year = 2003,
title = {Testing for imperfect competition on EU deposit and loan markets with Bresnahan's market power model},
journal = {De Nederlandsche Bank, Research Series Supervision, vol. 52}
}
@ARTICLE{shaffer/can,
author = {Shaffer, S.},
year = 1993,
title = {A Test of Competition in Canadian Banking},
journal = {Journal of Money, Credit and Banking},
volume = 25,
number = 1,
pages = {49-61}
}
%Panzar-Rosse
@ARTICLE{pr,
author = {Panzar, J.C. and Rosse, J.N.},
year = 1987,
title = {Testing for "Monopoly" Equilibrium},
journal = {The Journal of Industrial Economics},
volume = XXXV,
number = 4,
pages = {443-456}
}
@ARTICLE{rime,
author = {Rime, B.},
year = 1999,
title = {Mesure du degr\acute{e} de concurrence dans le syst\grave{e}me bancaire suisse \grave{a} l'aide du mod\grave{e}le de Panzar et Rosse},
journal = {Revue suisse d'Economie politique et de Statistique},
volume = 135,
number = 1,
pages = {21-40}
}
@UNPUBLISHED{bikkerhaaf,
author = {Bikker, J.A. and Haaf, K.},
year = 2000,
title = {Competition, Concentration and their Relationship: An Empirical Analysis of the Banking Industry},
note = {De Nederlandsche Bank, Research Series Supervision, vol. 30}
}
@UNPUBLISHED{easteuro,
author = {Yildrim, H.S. and Philippatos, G.C.},
year = 2003,
title = {Competition and Contestability in Central and Eastern European Banking Markets},
note = {University of Saskatchewan, Working Paper}
}
@UNPUBLISHED{hempell,
author = {Hempell, H.},
year = 2002,
title = {Testing for Competition Among German Banks},
note = {Economic Research Centre of the Deutsche Bundesbank, Discussion paper 04/02 }
}
%General
@ARTICLE{iwata,
author = {Iwata, G.},
year = 1974,
title = {Measurement of Conjectural Variations in Oligopoly},
journal = {Econometrica},
volume = 42,
number = 5,
pages = {947-966}
}
%@ARTICLE{cowling,
author = {Cowling, W. and Waterson, M},
year = ? ,
title = {Price-Cost Margins and Market Structure},
journal = {Economica},
volume = 43,
pages = {267-274}
}
@UNPUBLISHED{overview,
author = {Bikker, J.A. and Haaf, K.},
year = 2000,
title = {Measures of competition and concentration in the banking industry: a review of the literature},
note = {De Nederlandsche Bank, Research Series Supervision, vol. 27}
}
@UNPUBLISHED{ashton,
author = {Ashton, J.},
year = 1999,
title = {A test of perfect competition in the UK retail-banking deposit market},
note = {Bournemouth University, School of Finance \& Law, Working Paper Series, No. 15 }
}
-------------- next part --------------
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{The nlinproc class already includes natbib coding,\MessageBreak
so you should not add it explicitly}
{Type <Return> for now, but then later remove\MessageBreak
the command \protect\usepackage{natbib} from the document}
\endinput}{}
\@ifclassloaded{egs}{\PackageError{natbib}
{The egs class already includes natbib coding,\MessageBreak
so you should not add it explicitly}
{Type <Return> for now, but then later remove\MessageBreak
the command \protect\usepackage{natbib} from the document}
\endinput}{}
% Define citation punctuation for some author-year styles
% One may add and delete at this point
% Or put additions into local configuration file natbib.cfg
\newcommand\bibstyle at chicago{\bibpunct{(}{)}{;}{a}{,}{,}}
\newcommand\bibstyle at named{\bibpunct{[}{]}{;}{a}{,}{,}}
\newcommand\bibstyle at agu{\bibpunct{[}{]}{;}{a}{,}{,~}}%Amer. Geophys. Union
\newcommand\bibstyle at egs{\bibpunct{(}{)}{;}{a}{,}{,}}%Eur. Geophys. Soc.
\newcommand\bibstyle at agsm{\bibpunct{(}{)}{,}{a}{}{,}\gdef\harvardand{\&}}
\newcommand\bibstyle at kluwer{\bibpunct{(}{)}{,}{a}{}{,}\gdef\harvardand{\&}}
\newcommand\bibstyle at dcu{\bibpunct{(}{)}{;}{a}{;}{,}\gdef\harvardand{and}}
\newcommand\bibstyle at aa{\bibpunct{(}{)}{;}{a}{}{,}} %Astronomy & Astrophysics
\newcommand\bibstyle at pass{\bibpunct{(}{)}{;}{a}{,}{,}}%Planet. & Space Sci
\newcommand\bibstyle at anngeo{\bibpunct{(}{)}{;}{a}{,}{,}}%Annales Geophysicae
\newcommand\bibstyle at nlinproc{\bibpunct{(}{)}{;}{a}{,}{,}}%Nonlin.Proc.Geophys.
% Define citation punctuation for some numerical styles
\newcommand\bibstyle at cospar{\bibpunct{/}{/}{,}{n}{}{}%
\gdef\NAT at biblabelnum##1{##1.}}
\newcommand\bibstyle at esa{\bibpunct{(Ref.~}{)}{,}{n}{}{}%
\gdef\NAT at biblabelnum##1{##1.\hspace{1em}}}
\newcommand\bibstyle at nature{\bibpunct{}{}{,}{s}{}{\textsuperscript{,}}%
\gdef\NAT at biblabelnum##1{##1.}}
% The standard LaTeX styles
\newcommand\bibstyle at plain{\bibpunct{[}{]}{,}{n}{}{,}}
\let\bibstyle at alpha=\bibstyle at plain
\let\bibstyle at abbrv=\bibstyle at plain
\let\bibstyle at unsrt=\bibstyle at plain
% The author-year modifications of the standard styles
\newcommand\bibstyle at plainnat{\bibpunct{[}{]}{,}{a}{,}{,}}
\let\bibstyle at abbrvnat=\bibstyle at plainnat
\let\bibstyle at unsrtnat=\bibstyle at plainnat
\newif\ifNAT at numbers \NAT at numbersfalse
\newif\ifNAT at super \NAT at superfalse
\DeclareOption{numbers}{\NAT at numberstrue
\ExecuteOptions{square,comma,nobibstyle}}
\DeclareOption{super}{\NAT at supertrue\NAT at numberstrue
\renewcommand\NAT at open{}\renewcommand\NAT at close{}
\ExecuteOptions{nobibstyle}}
\DeclareOption{authoryear}{\NAT at numbersfalse
\ExecuteOptions{round,colon,bibstyle}}
\DeclareOption{round}{%
\renewcommand\NAT at open{(} \renewcommand\NAT at close{)}
\ExecuteOptions{nobibstyle}}
\DeclareOption{square}{%
\renewcommand\NAT at open{[} \renewcommand\NAT at close{]}
\ExecuteOptions{nobibstyle}}
\DeclareOption{angle}{%
\renewcommand\NAT at open{$<$} \renewcommand\NAT at close{$>$}
\ExecuteOptions{nobibstyle}}
\DeclareOption{curly}{%
\renewcommand\NAT at open{\{} \renewcommand\NAT at close{\}}
\ExecuteOptions{nobibstyle}}
\DeclareOption{comma}{\renewcommand\NAT at sep{,}
\ExecuteOptions{nobibstyle}}
\DeclareOption{colon}{\renewcommand\NAT at sep{;}
\ExecuteOptions{nobibstyle}}
\DeclareOption{nobibstyle}{\let\bibstyle=\@gobble}
\DeclareOption{bibstyle}{\let\bibstyle=\@citestyle}
\newif\ifNAT at openbib \NAT at openbibfalse
\DeclareOption{openbib}{\NAT at openbibtrue}
\DeclareOption{sectionbib}{\def\NAT at sectionbib{on}}
\def\NAT at sort{0}
\DeclareOption{sort}{\def\NAT at sort{1}}
\DeclareOption{sort&compress}{\def\NAT at sort{2}}
\@ifpackageloaded{cite}{\PackageWarningNoLine{natbib}
{The `cite' package should not be used\MessageBreak
with natbib. Use option `sort' instead}\ExecuteOptions{sort}}{}
\newif\ifNAT at longnames\NAT at longnamesfalse
\DeclareOption{longnamesfirst}{\NAT at longnamestrue}
\DeclareOption{nonamebreak}{\def\NAT at nmfmt#1{\mbox{\NAT at up#1}}}
\def\NAT at nmfmt#1{{\NAT at up#1}}
\renewcommand\bibstyle[1]{\@ifundefined{bibstyle@#1}{\relax}
{\csname bibstyle@#1\endcsname}}
\AtBeginDocument{\global\let\bibstyle=\@gobble}
\let\@citestyle\bibstyle
\newcommand\citestyle[1]{\@citestyle{#1}\let\bibstyle\@gobble}
\@onlypreamble{\citestyle}\@onlypreamble{\@citestyle}
\newcommand\bibpunct[7][, ]%
{\gdef\NAT at open{#2}\gdef\NAT at close{#3}\gdef
\NAT at sep{#4}\global\NAT at numbersfalse\ifx #5n\global\NAT at numberstrue
\else
\ifx #5s\global\NAT at numberstrue\global\NAT at supertrue
\fi\fi
\gdef\NAT at aysep{#6}\gdef\NAT at yrsep{#7}%
\gdef\NAT at cmt{#1}%
\global\let\bibstyle\@gobble
}
\@onlypreamble{\bibpunct}
\newcommand\NAT at open{(} \newcommand\NAT at close{)}
\newcommand\NAT at sep{;}
\ProcessOptions
\newcommand\NAT at aysep{,} \newcommand\NAT at yrsep{,}
\newcommand\NAT at cmt{, }
\newcommand\NAT at cite%
[3]{\ifNAT at swa\NAT@@open\if*#2*\else#2\ \fi
#1\if*#3*\else\NAT at cmt#3\fi\NAT@@close\else#1\fi\endgroup}
\newcommand\NAT at citenum%
[3]{\ifNAT at swa\NAT@@open\if*#2*\else#2\ \fi
#1\if*#3*\else\NAT at cmt#3\fi\NAT@@close\else#1\fi\endgroup}
\newcommand\NAT at citesuper[3]{\ifNAT at swa
\unskip\hspace{1\p@}\textsuperscript{#1}%
\if*#3*\else\ (#3)\fi\else #1\fi\endgroup}
\providecommand
\textsuperscript[1]{\mbox{$^{\mbox{\scriptsize#1}}$}}
\providecommand\@firstofone[1]{#1}
\newcommand\NAT at citexnum{}
\def\NAT at citexnum[#1][#2]#3{%
\NAT at sort@cites{#3}%
\let\@citea\@empty
\@cite{\def\NAT at num{-1}\let\NAT at last@yr\relax\let\NAT at nm\@empty
\@for\@citeb:=\NAT at cite@list\do
{\edef\@citeb{\expandafter\@firstofone\@citeb}%
\if at filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
\@ifundefined{b@\@citeb\@extra at b@citeb}{%
{\reset at font\bfseries?}
\NAT at citeundefined\PackageWarning{natbib}%
{Citation `\@citeb' on page \thepage \space undefined}}%
{\let\NAT at last@num\NAT at num\let\NAT at last@nm\NAT at nm
\NAT at parse{\@citeb}%
\ifNAT at longnames\@ifundefined{bv@\@citeb\@extra at b@citeb}{%
\let\NAT at name=\NAT at all@names
\global\@namedef{bv@\@citeb\@extra at b@citeb}{}}{}%
\fi
\ifNAT at full\let\NAT at nm\NAT at all@names\else
\let\NAT at nm\NAT at name\fi
\ifNAT at swa
\ifnum\NAT at ctype>1\relax\@citea
\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\ifnum\NAT at ctype=2\relax\NAT at test{\NAT at ctype}%
\else\NAT at alias
\fi\hyper at natlinkend\else
\ifnum\NAT at sort>1
\begingroup\catcode`\_=8
\ifcat _\ifnum\z@<0\NAT at num _\else A\fi
\global\let\NAT at nm=\NAT at num \else \gdef\NAT at nm{-2}\fi
\ifcat _\ifnum\z@<0\NAT at last@num _\else A\fi
\global\@tempcnta=\NAT at last@num \global\advance\@tempcnta by\@ne
\else \global\@tempcnta\m at ne\fi
\endgroup
\ifnum\NAT at nm=\@tempcnta
\ifx\NAT at last@yr\relax
\edef\NAT at last@yr{\@citea \mbox{\noexpand\citenumfont{\NAT at num}}}%
\else
\edef\NAT at last@yr{--\penalty\@m\mbox{\noexpand\citenumfont{\NAT at num}}}%
\fi
\else
\NAT at last@yr \@citea \mbox{\citenumfont{\NAT at num}}%
\let\NAT at last@yr\relax
\fi
\else
\@citea \mbox{\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
{\citenumfont{\NAT at num}}\hyper at natlinkend}%
\fi
\fi
\def\@citea{\NAT at sep\penalty\@m\NAT at space}%
\else
\ifcase\NAT at ctype\relax
\ifx\NAT at last@nm\NAT at nm \NAT at yrsep\penalty\@m\NAT at space\else
\@citea \NAT at test{1}\ \NAT@@open
\if*#1*\else#1\ \fi\fi \NAT at mbox{%
\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
{\citenumfont{\NAT at num}}\hyper at natlinkend}%
\def\@citea{\NAT@@close\NAT at sep\penalty\@m\ }%
\or\@citea
\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at test{\NAT at ctype}\hyper at natlinkend
\def\@citea{\NAT at sep\penalty\@m\ }%
\or\@citea
\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at test{\NAT at ctype}\hyper at natlinkend
\def\@citea{\NAT at sep\penalty\@m\ }%
\or\@citea
\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at alias\hyper at natlinkend
\def\@citea{\NAT at sep\penalty\@m\ }%
\fi
\fi
}}%
\ifnum\NAT at sort>1\relax\NAT at last@yr\fi
\ifNAT at swa\else\ifnum\NAT at ctype=0\if*#2*\else
\NAT at cmt#2\fi \NAT@@close\fi\fi}{#1}{#2}}
\newcommand\NAT at test[1]{\ifnum#1=1 \ifx\NAT at nm\NAT at noname
{\reset at font\bfseries(author?)}\PackageWarning{natbib}
{Author undefined for citation`\@citeb'
\MessageBreak
on page \thepage}\else \NAT at nm \fi
\else \if\relax\NAT at date\relax
{\reset at font\bfseries(year?)}\PackageWarning{natbib}
{Year undefined for citation`\@citeb'
\MessageBreak
on page \thepage}\else \NAT at date \fi \fi}
\let\citenumfont=\relax
\newcommand\NAT at citex{}
\def\NAT at citex%
[#1][#2]#3{%
\NAT at sort@cites{#3}%
\let\@citea\@empty
\@cite{\let\NAT at nm\@empty\let\NAT at year\@empty
\@for\@citeb:=\NAT at cite@list\do
{\edef\@citeb{\expandafter\@firstofone\@citeb}%
\if at filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
\@ifundefined{b@\@citeb\@extra at b@citeb}{\@citea%
{\reset at font\bfseries ?}\NAT at citeundefined
\PackageWarning{natbib}%
{Citation `\@citeb' on page \thepage \space undefined}\def\NAT at date{}}%
{\let\NAT at last@nm=\NAT at nm\let\NAT at last@yr=\NAT at year
\NAT at parse{\@citeb}%
\ifNAT at longnames\@ifundefined{bv@\@citeb\@extra at b@citeb}{%
\let\NAT at name=\NAT at all@names
\global\@namedef{bv@\@citeb\@extra at b@citeb}{}}{}%
\fi
\ifNAT at full\let\NAT at nm\NAT at all@names\else
\let\NAT at nm\NAT at name\fi
\ifNAT at swa\ifcase\NAT at ctype
\if\relax\NAT at date\relax
\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\NAT at date\hyper at natlinkend
\else
\ifx\NAT at last@nm\NAT at nm\NAT at yrsep
\ifx\NAT at last@yr\NAT at year
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at exlab
\hyper at natlinkend
\else\unskip\
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at date
\hyper at natlinkend
\fi
\else\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}%
\hyper at natlinkbreak{\NAT at aysep\ }{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend
\fi
\fi
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at alias\hyper at natlinkend
\fi \def\@citea{\NAT at sep\ }%
\else\ifcase\NAT at ctype
\if\relax\NAT at date\relax
\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\hyper at natlinkend
\else
\ifx\NAT at last@nm\NAT at nm\NAT at yrsep
\ifx\NAT at last@yr\NAT at year
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at exlab
\hyper at natlinkend
\else\unskip\
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at date
\hyper at natlinkend
\fi
\else\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}%
\hyper at natlinkbreak{\ \NAT@@open\if*#1*\else#1\ \fi}%
{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend\fi
\fi
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at alias\hyper at natlinkend
\fi \if\relax\NAT at date\relax\def\@citea{\NAT at sep\ }%
\else\def\@citea{\NAT@@close\NAT at sep\ }\fi
\fi
}}\ifNAT at swa\else\if*#2*\else\NAT at cmt#2\fi
\if\relax\NAT at date\relax\else\NAT@@close\fi\fi}{#1}{#2}}
\newif\ifNAT at par \NAT at partrue
\newcommand\NAT@@open{\ifNAT at par\NAT at open\fi}
\newcommand\NAT@@close{\ifNAT at par\NAT at close\fi}
\newcommand\NAT at alias{\@ifundefined{al@\@citeb\@extra at b@citeb}{%
{\reset at font\bfseries(alias?)}\PackageWarning{natbib}
{Alias undefined for citation `\@citeb'
\MessageBreak on page \thepage}}{\@nameuse{al@\@citeb\@extra at b@citeb}}}
\let\NAT at up\relax
\newcommand\NAT at Up[1]{{\let\protect\@unexpandable at protect\let~\relax
\expandafter\NAT at deftemp#1}\expandafter\NAT at UP\NAT at temp}
\newcommand\NAT at deftemp[1]{\xdef\NAT at temp{#1}}
\newcommand\NAT at UP[1]{\let\@tempa\NAT at UP\ifcat a#1\MakeUppercase{#1}%
\let\@tempa\relax\else#1\fi\@tempa}
\newcommand\shortcites[1]{%
\@bsphack\@for\@citeb:=#1\do
{\edef\@citeb{\expandafter\@firstofone\@citeb}%
\global\@namedef{bv@\@citeb\@extra at b@citeb}{}}\@esphack}
\newcommand\NAT at biblabel[1]{\hfill}
\newcommand\NAT at biblabelnum[1]{\bibnumfmt{#1}}
\newcommand\bibnumfmt[1]{[#1]}
\def\@tempa#1{[#1]}
\ifx\@tempa\@biblabel\let\@biblabel\@empty\fi
\newcommand\NAT at bibsetnum[1]{\settowidth\labelwidth{\@biblabel{#1}}%
\setlength{\leftmargin}{\labelwidth}\addtolength{\leftmargin}{\labelsep}%
\setlength{\itemsep}{\bibsep}\setlength{\parsep}{\z@}%
\ifNAT at openbib
\addtolength{\leftmargin}{\bibindent}%
\setlength{\itemindent}{-\bibindent}%
\setlength{\listparindent}{\itemindent}%
\setlength{\parsep}{0pt}%
\fi
}
\newlength{\bibhang}
\setlength{\bibhang}{1em}
\newlength{\bibsep}
{\@listi \global\bibsep\itemsep \global\advance\bibsep by\parsep}
\newcommand\NAT at bibsetup%
[1]{\setlength{\leftmargin}{\bibhang}\setlength{\itemindent}{-\leftmargin}%
\setlength{\itemsep}{\bibsep}\setlength{\parsep}{\z@}}
\newcommand\NAT at set@cites{\ifNAT at numbers
\ifNAT at super \let\@cite\NAT at citesuper
\def\NAT at mbox##1{\unskip\nobreak\hspace{1\p@}\textsuperscript{##1}}%
\let\citeyearpar=\citeyear
\let\NAT at space\relax\else
\let\NAT at mbox=\mbox
\let\@cite\NAT at citenum \def\NAT at space{ }\fi
\let\@citex\NAT at citexnum
\ifx\@biblabel\@empty\let\@biblabel\NAT at biblabelnum\fi
\let\@bibsetup\NAT at bibsetnum
\def\natexlab##1{}%
\else
\let\@cite\NAT at cite
\let\@citex\NAT at citex
\let\@biblabel\NAT at biblabel
\let\@bibsetup\NAT at bibsetup
\def\natexlab##1{##1}%
\fi}
\AtBeginDocument{\NAT at set@cites}
\AtBeginDocument{\ifx\SK at def\@undefined\else
\ifx\SK at cite\@empty\else
\SK at def\@citex[#1][#2]#3{\SK@\SK@@ref{#3}\SK@@citex[#1][#2]{#3}}\fi
\ifx\SK at citeauthor\@undefined\def\HAR at checkdef{}\else
\let\citeauthor\SK at citeauthor
\let\citefullauthor\SK at citefullauthor
\let\citeyear\SK at citeyear\fi
\fi}
\AtBeginDocument{\@ifpackageloaded{hyperref}{%
\ifnum\NAT at sort=2\def\NAT at sort{1}\fi}{}}
\newif\ifNAT at full\NAT at fullfalse
\newif\ifNAT at swa
\DeclareRobustCommand\citet
{\begingroup\NAT at swafalse\def\NAT at ctype{0}\NAT at partrue
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\newcommand\NAT at citetp{\@ifnextchar[{\NAT@@citetp}{\NAT@@citetp[]}}
\newcommand\NAT@@citetp{}
\def\NAT@@citetp[#1]{\@ifnextchar[{\@citex[#1]}{\@citex[][#1]}}
\DeclareRobustCommand\citep
{\begingroup\NAT at swatrue\def\NAT at ctype{0}\NAT at partrue
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\cite
{\begingroup\def\NAT at ctype{0}\NAT at partrue\NAT at swatrue
\@ifstar{\NAT at fulltrue\NAT at cites}{\NAT at fullfalse\NAT at cites}}
\newcommand\NAT at cites{\@ifnextchar [{\NAT@@citetp}{%
\ifNAT at numbers\else
\NAT at swafalse
\fi
\NAT@@citetp[]}}
\DeclareRobustCommand\citealt
{\begingroup\NAT at swafalse\def\NAT at ctype{0}\NAT at parfalse
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\citealp
{\begingroup\NAT at swatrue\def\NAT at ctype{0}\NAT at parfalse
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\citeauthor
{\begingroup\NAT at swafalse\def\NAT at ctype{1}\NAT at parfalse
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\Citet
{\begingroup\NAT at swafalse\def\NAT at ctype{0}\NAT at partrue
\let\NAT at up\NAT at Up
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\Citep
{\begingroup\NAT at swatrue\def\NAT at ctype{0}\NAT at partrue
\let\NAT at up\NAT at Up
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\Citealt
{\begingroup\NAT at swafalse\def\NAT at ctype{0}\NAT at parfalse
\let\NAT at up\NAT at Up
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\Citealp
{\begingroup\NAT at swatrue\def\NAT at ctype{0}\NAT at parfalse
\let\NAT at up\NAT at Up
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\Citeauthor
{\begingroup\NAT at swafalse\def\NAT at ctype{1}\NAT at parfalse
\let\NAT at up\NAT at Up
\@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
\DeclareRobustCommand\citeyear
{\begingroup\NAT at swafalse\def\NAT at ctype{2}\NAT at parfalse\NAT at citetp}
\DeclareRobustCommand\citeyearpar
{\begingroup\NAT at swatrue\def\NAT at ctype{2}\NAT at partrue\NAT at citetp}
\newcommand\citetext[1]{\NAT at open#1\NAT at close}
\DeclareRobustCommand\citefullauthor
{\citeauthor*}
\newcommand\defcitealias[2]{%
\@ifundefined{al@#1\@extra at b@citeb}{}
{\PackageWarning{natbib}{Overwriting existing alias for citation #1}}
\@namedef{al@#1\@extra at b@citeb}{#2}}
\DeclareRobustCommand\citetalias{\begingroup
\NAT at swafalse\def\NAT at ctype{3}\NAT at parfalse\NAT at citetp}
\DeclareRobustCommand\citepalias{\begingroup
\NAT at swatrue\def\NAT at ctype{3}\NAT at partrue\NAT at citetp}
\renewcommand\nocite[1]{\@bsphack
\@for\@citeb:=#1\do{%
\edef\@citeb{\expandafter\@firstofone\@citeb}%
\if at filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
\if*\@citeb\else
\@ifundefined{b@\@citeb\@extra at b@citeb}{%
\NAT at citeundefined \PackageWarning{natbib}%
{Citation `\@citeb' undefined}}{}\fi}%
\@esphack}
\newcommand\NAT at parse[1]{{%
\let\protect=\@unexpandable at protect\let~\relax
\let\active at prefix=\@gobble
\xdef\NAT at temp{\csname b@#1\@extra at b@citeb\endcsname}}%
\expandafter\NAT at split\NAT at temp
\expandafter\NAT at parse@date\NAT at date??????@@%
\ifciteindex\NAT at index\fi
}
\newcommand\NAT at split[4]{%
\gdef\NAT at num{#1}\gdef\NAT at name{#3}\gdef\NAT at date{#2}%
\gdef\NAT at all@names{#4}%
\ifx\NAT at noname\NAT at all@names \gdef\NAT at all@names{#3}\fi}
\newcommand\NAT at parse@date{}
\def\NAT at parse@date#1#2#3#4#5#6@@{%
\ifnum\the\catcode`#1=11\def\NAT at year{}\def\NAT at exlab{#1}\else
\ifnum\the\catcode`#2=11\def\NAT at year{#1}\def\NAT at exlab{#2}\else
\ifnum\the\catcode`#3=11\def\NAT at year{#1#2}\def\NAT at exlab{#3}\else
\ifnum\the\catcode`#4=11\def\NAT at year{#1#2#3}\def\NAT at exlab{#4}\else
\def\NAT at year{#1#2#3#4}\def\NAT at exlab{{#5}}\fi\fi\fi\fi}
\newcommand\NAT at index{}
\let\NAT at makeindex=\makeindex
\renewcommand\makeindex{\NAT at makeindex
\renewcommand\NAT at index{\@bsphack\begingroup
\def~{\string~}\@wrindex{\NAT at idxtxt}}}
\newcommand\NAT at idxtxt{\NAT at name\ \NAT at open\NAT at date\NAT at close}
\@ifundefined{@indexfile}{}{\let\NAT at makeindex\relax\makeindex}
\newif\ifciteindex \citeindexfalse
\newcommand\citeindextype{default}
\newcommand\NAT at index@alt{{\let\protect=\noexpand\let~\relax
\xdef\NAT at temp{\NAT at idxtxt}}\expandafter\NAT at exp\NAT at temp\@nil}
\newcommand\NAT at exp{}
\def\NAT at exp#1\@nil{\mbox{}\index[\citeindextype]{#1}}
\AtBeginDocument{%
\@ifpackageloaded{index}{\let\NAT at index=\NAT at index@alt}{}}
\newcommand\NAT at ifcmd{\futurelet\NAT at temp\NAT at ifxcmd}
\newcommand\NAT at ifxcmd{\ifx\NAT at temp\relax\else\expandafter\NAT at bare\fi}
\def\NAT at bare#1(#2)#3(@)#4\@nil#5{%
\if @#2
\expandafter\NAT at apalk#1, , \@nil{#5}\else
\stepcounter{NAT at ctr}%
\NAT at wrout{\arabic {NAT at ctr}}{#2}{#1}{#3}{#5}
\fi
}
\newcommand\NAT at wrout[5]{%
\if at filesw
{\let\protect\noexpand\let~\relax
\immediate
\write\@auxout{\string\bibcite{#5}{{#1}{#2}{{#3}}{{#4}}}}}\fi
\ignorespaces}
\def\NAT at noname{{}}
\renewcommand\bibitem{%
\@ifnextchar[{\@lbibitem}{%
\global\NAT at stdbsttrue
\stepcounter{NAT at ctr}\@lbibitem[\arabic{NAT at ctr}]}}
\def\@lbibitem[#1]#2{%
\if\relax\@extra at b@citeb\relax\else
\@ifundefined{br@#2\@extra at b@citeb}{}{%
\@namedef{br@#2}{\@nameuse{br@#2\@extra at b@citeb}}}\fi
\@ifundefined{b@#2\@extra at b@citeb}{\def\NAT at num{}}{\NAT at parse{#2}}%
\item[\hfil\hyper at natanchorstart{#2\@extra at b@citeb}\@biblabel{\NAT at num}%
\hyper at natanchorend]%
\NAT at ifcmd#1(@)(@)\@nil{#2}}
\ifx\SK at lbibitem\@undefined\else
\let\SK at lbibitem\@lbibitem
\def\@lbibitem[#1]#2{%
\SK at lbibitem[#1]{#2}\SK@\SK@@label{#2}\ignorespaces}\fi
\newif\ifNAT at stdbst \NAT at stdbstfalse
\AtEndDocument
{\ifNAT at stdbst\if at filesw\immediate\write\@auxout{\string
\global\string\NAT at numberstrue}\fi\fi
}
\providecommand\bibcite{}
\renewcommand\bibcite[2]{\@ifundefined{b@#1\@extra at binfo}\relax
{\NAT at citemultiple
\PackageWarningNoLine{natbib}{Citation `#1' multiply defined}}%
\global\@namedef{b@#1\@extra at binfo}{#2}}
\AtEndDocument{\NAT at swatrue\let\bibcite\NAT at testdef}
\newcommand\NAT at testdef[2]{%
\def\NAT at temp{#2}\expandafter \ifx \csname b@#1\@extra at binfo\endcsname
\NAT at temp \else \ifNAT at swa \NAT at swafalse
\PackageWarningNoLine{natbib}{Citation(s) may have
changed.\MessageBreak
Rerun to get citations correct}\fi\fi}
\newcommand\NAT at apalk{}
\def\NAT at apalk#1, #2, #3\@nil#4{\if\relax#2\relax
\global\NAT at stdbsttrue
\NAT at wrout{#1}{}{}{}{#4}\else
\stepcounter{NAT at ctr}%
\NAT at wrout{\arabic {NAT at ctr}}{#2}{#1}{}{#4}\fi}
\newcommand\citeauthoryear{}
\def\citeauthoryear#1#2#3(@)(@)\@nil#4{\stepcounter{NAT at ctr}\if\relax#3\relax
\NAT at wrout{\arabic {NAT at ctr}}{#2}{#1}{}{#4}\else
\NAT at wrout{\arabic {NAT at ctr}}{#3}{#2}{#1}{#4}\fi}
\newcommand\citestarts{\NAT at open}
\newcommand\citeends{\NAT at close}
\newcommand\betweenauthors{and}
\newcommand\astroncite{}
\def\astroncite#1#2(@)(@)\@nil#3{\stepcounter{NAT at ctr}\NAT at wrout{\arabic
{NAT at ctr}}{#2}{#1}{}{#3}}
\newcommand\citename{}
\def\citename#1#2(@)(@)\@nil#3{\expandafter\NAT at apalk#1#2, \@nil{#3}}
\newcommand\harvarditem[4][]%
{\if\relax#1\relax\bibitem[#2(#3)]{#4}\else
\bibitem[#1(#3)#2]{#4}\fi }
\newcommand\harvardleft{\NAT at open}
\newcommand\harvardright{\NAT at close}
\newcommand\harvardyearleft{\NAT at open}
\newcommand\harvardyearright{\NAT at close}
\AtBeginDocument{\providecommand{\harvardand}{and}}
\newcommand\harvardurl[1]{\textbf{URL:} \textit{#1}}
\providecommand\bibsection{}
\@ifundefined{chapter}%
{\renewcommand\bibsection{\section*{\refname
\@mkboth{\MakeUppercase{\refname}}{\MakeUppercase{\refname}}}}}
{\@ifundefined{NAT at sectionbib}%
{\renewcommand\bibsection{\chapter*{\bibname
\@mkboth{\MakeUppercase{\bibname}}{\MakeUppercase{\bibname}}}}}
{\renewcommand\bibsection{\section*{\bibname
\ifx\@mkboth\@gobbletwo\else\markright{\MakeUppercase{\bibname}}\fi}}}}
\@ifclassloaded{amsart}%
{\renewcommand\bibsection{\section*{\refname}}}{}
\@ifclassloaded{amsbook}%
{\renewcommand\bibsection{\chapter*{\bibname}}}{}
\@ifundefined{bib at heading}{}{\let\bibsection\bib at heading}
\newcounter{NAT at ctr}
\renewenvironment{thebibliography}[1]{%
\bibsection\parindent \z@\bibpreamble\bibfont\list
{\@biblabel{\arabic{NAT at ctr}}}{\@bibsetup{#1}%
\setcounter{NAT at ctr}{0}}%
\ifNAT at openbib
\renewcommand\newblock{\par}
\else
\renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
\fi
\sloppy\clubpenalty4000\widowpenalty4000
\sfcode`\.=1000\relax
\let\citeN\cite \let\shortcite\cite
\let\citeasnoun\cite
}{\def\@noitemerr{%
\PackageWarning{natbib}
{Empty `thebibliography' environment}}%
\endlist\vskip-\lastskip}
\let\bibfont\relax
\let\bibpreamble\relax
\providecommand\reset at font{\relax}
\providecommand\bibname{Bibliography}
\providecommand\refname{References}
\newcommand\NAT at citeundefined{\gdef \NAT at undefined {%
\PackageWarningNoLine{natbib}{There were undefined citations}}}
\let \NAT at undefined \relax
\newcommand\NAT at citemultiple{\gdef \NAT at multiple {%
\PackageWarningNoLine{natbib}{There were multiply defined citations}}}
\let \NAT at multiple \relax
\AtEndDocument{\NAT at undefined\NAT at multiple}
\providecommand\@mkboth[2]{}
\providecommand\MakeUppercase{\uppercase}
\providecommand{\@extra at b@citeb}{}
\gdef\@extra at binfo{}
\providecommand\hyper at natanchorstart[1]{}
\providecommand\hyper at natanchorend{}
\providecommand\hyper at natlinkstart[1]{}
\providecommand\hyper at natlinkend{}
\providecommand\hyper at natlinkbreak[2]{#1}
\@ifundefined{bbl at redefine}{}{%
\bbl at redefine\nocite#1{%
\@safe at activestrue\org at nocite{#1}\@safe at activesfalse}%
\bbl at redefine\@lbibitem[#1]#2{%
\@safe at activestrue\org@@lbibitem[#1]{#2}\@safe at activesfalse}%
}
\AtBeginDocument{\@ifundefined{bbl at redefine}{}{%
\bbl at redefine\@citex[#1][#2]#3{%
\@safe at activestrue\org@@citex[#1][#2]{#3}\@safe at activesfalse}%
\bbl at redefine\NAT at testdef#1#2{%
\@safe at activestrue\org at NAT@testdef{#1}{#2}\@safe at activesfalse}%
\@ifundefined{org@@lbibitem}{%
\bbl at redefine\@lbibitem[#1]#2{%
\@safe at activestrue\org@@lbibitem[#1]{#2}\@safe at activesfalse}}{}%
}}
\ifnum\NAT at sort>0
\newcommand\NAT at sort@cites[1]{%
\@tempcntb\m at ne
\let\@celt\delimiter
\def\NAT at num@list{}%
\def\NAT at cite@list{}%
\def\NAT at nonsort@list{}%
\@for \@citeb:=#1\do{\NAT at make@cite at list}%
\edef\NAT at cite@list{\NAT at cite@list\NAT at nonsort@list}%
\edef\NAT at cite@list{\expandafter\NAT at xcom\NAT at cite@list @@}}
\begingroup \catcode`\_=8
\gdef\NAT at make@cite at list{%
\edef\@citeb{\expandafter\@firstofone\@citeb}%
\@ifundefined{b@\@citeb\@extra at b@citeb}{\def\NAT at num{A}}%
{\NAT at parse{\@citeb}}%
\ifcat _\ifnum\z@<0\NAT at num _\else A\fi
\@tempcnta\NAT at num \relax
\ifnum \@tempcnta>\@tempcntb
\edef\NAT at num@list{\NAT at num@list \@celt{\NAT at num}}%
\edef\NAT at cite@list{\NAT at cite@list\@citeb,}%
\@tempcntb\@tempcnta
\else
\let\NAT@@cite at list=\NAT at cite@list \def\NAT at cite@list{}%
\edef\NAT at num@list{\expandafter\NAT at num@celt \NAT at num@list \@gobble @}%
{\let\@celt=\NAT at celt\NAT at num@list}%
\fi
\else
\edef\NAT at nonsort@list{\NAT at nonsort@list\@citeb,}%
\fi}
\endgroup
\def\NAT at celt#1{\ifnum #1<\@tempcnta
\xdef\NAT at cite@list{\NAT at cite@list\expandafter\NAT at nextc\NAT@@cite at list @@}%
\xdef\NAT@@cite at list{\expandafter\NAT at restc\NAT@@cite at list}%
\else
\xdef\NAT at cite@list{\NAT at cite@list\@citeb,\NAT@@cite at list}\let\@celt\@gobble%
\fi}
\def\NAT at num@celt#1#2{\ifx \@celt #1%
\ifnum #2<\@tempcnta
\@celt{#2}%
\expandafter\expandafter\expandafter\NAT at num@celt
\else
\@celt{\number\@tempcnta}\@celt{#2}%
\fi\fi}
\def\NAT at nextc#1,#2@@{#1,}
\def\NAT at restc#1,#2{#2}
\def\NAT at xcom#1,@@{#1}
\else
\newcommand\NAT at sort@cites[1]{\edef\NAT at cite@list{#1}}\fi
\InputIfFileExists{natbib.cfg}
{\typeout{Local config file natbib.cfg used}}{}
%%
%% <<<<< End of generated file <<<<<<
%%
%% End of file `natbib.sty'.
-------------- next part --------------
\def\NAT at citex% very dirty hack for german natbib users
[#1][#2]#3{%
\NAT at sort@cites{#3}%
\if*#1*\else#1\ \fi% 1st opt. arg. at first.
\let\@citea\@empty
\@cite{\let\NAT at nm\@empty\let\NAT at year\@empty
\@for\@citeb:=\NAT at cite@list\do
{\edef\@citeb{\expandafter\@firstofone\@citeb}%
\if at filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
\@ifundefined{b@\@citeb\@extra at b@citeb}{\@citea%
{\reset at font\bfseries ?}\NAT at citeundefined
\PackageWarning{natbib}%
{Citation `\@citeb' on page \thepage \space undefined}\def\NAT at date{}}%
{\let\NAT at last@nm=\NAT at nm\let\NAT at last@yr=\NAT at year
\NAT at parse{\@citeb}%
\ifNAT at longnames\@ifundefined{bv@\@citeb\@extra at b@citeb}{%
\let\NAT at name=\NAT at all@names
\global\@namedef{bv@\@citeb\@extra at b@citeb}{}}{}%
\fi
\ifNAT at full\let\NAT at nm\NAT at all@names\else
\let\NAT at nm\NAT at name\fi
\ifNAT at swa\ifcase\NAT at ctype
\if\relax\NAT at date\relax
\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\NAT at date\hyper at natlinkend
\else
\ifx\NAT at last@nm\NAT at nm\NAT at yrsep
\ifx\NAT at last@yr\NAT at year
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at exlab
\hyper at natlinkend
\else\unskip\
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at date
\hyper at natlinkend
\fi
\else\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}%
\hyper at natlinkbreak{\NAT at aysep\ }{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend
\fi
\fi
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at alias\hyper at natlinkend
\fi \def\@citea{\NAT at sep\ }%
\else\ifcase\NAT at ctype
\if\relax\NAT at date\relax
\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\hyper at natlinkend
\else
\ifx\NAT at last@nm\NAT at nm\NAT at yrsep
\ifx\NAT at last@yr\NAT at year
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at exlab
\hyper at natlinkend
\else\unskip\
\hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at date
\hyper at natlinkend
\fi
\else\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}%
%\hyper at natlinkbreak{\ \NAT@@open\if*#1*\else#1\ \fi}%
\hyper at natlinkbreak{\ \NAT@@open}% suppress first opt. arg.
{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend\fi
\fi
\or
\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at nmfmt{\NAT at nm}\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at date\hyper at natlinkend
\or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
\NAT at alias\hyper at natlinkend
\fi \if\relax\NAT at date\relax\def\@citea{\NAT at sep\ }%
\else\def\@citea{\NAT@@close\NAT at sep\ }\fi
\fi}}\ifNAT at swa\else\if*#2*\else\NAT@@close%
\let\NAT@@close\@empty% relax the closing brace, really dirty
\NAT at cmt#2\fi\if\relax\NAT at date\relax\else
\NAT@@close\fi\fi}{}{#2}%
% ^ #1 removed to avoid doubled 1st opt. arg.
}%
\endinput
-------------- next part --------------
%% File: `plainnat.bst'
%% A modification of `plain.bst' for use with natbib package
%%
%% Copyright 1993-1999 Patrick W Daly
%% Max-Planck-Institut f\"ur Aeronomie
%% Max-Planck-Str. 2
%% D-37191 Katlenburg-Lindau
%% Germany
%% E-mail: daly at linmpi.mpg.de
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN
%% archives in directory macros/latex/base/lppl.txt; either
%% version 1 of the License, or any later version.
%%
% Version and source file information:
% \ProvidesFile{natbst.mbs}[1999/05/11 1.6 (PWD)]
%
% BibTeX `plainnat' family
% version 0.99b for BibTeX versions 0.99a or later,
% for LaTeX versions 2.09 and 2e.
%
% For use with the `natbib.sty' package; emulates the corresponding
% member of the `plain' family, but with author-year citations.
%
% With version 6.0 of `natbib.sty', it may also be used for numerical
% citations, while retaining the commands \citeauthor, \citefullauthor,
% and \citeyear to print the corresponding information.
%
% For version 7.0 of `natbib.sty', the KEY field replaces missing
% authors/editors, and the date is left blank in \bibitem.
%
% Includes fields ISBN and ISSN.
%
% Includes field URL for Internet addresses (best used with
% with the url.sty package of Donald Arseneau
%
ENTRY
{ address
author
booktitle
chapter
edition
editor
howpublished
institution
isbn
issn
journal
key
month
note
number
organization
pages
publisher
school
series
title
type
url
volume
year
}
{}
{ label extra.label sort.label short.list }
INTEGERS { output.state before.all mid.sentence after.sentence after.block }
FUNCTION {init.state.consts}
{ #0 'before.all :=
#1 'mid.sentence :=
#2 'after.sentence :=
#3 'after.block :=
}
STRINGS { s t }
FUNCTION {output.nonnull}
{ 's :=
output.state mid.sentence =
{ ", " * write$ }
{ output.state after.block =
{ add.period$ write$
newline$
"\newblock " write$
}
{ output.state before.all =
'write$
{ add.period$ " " * write$ }
if$
}
if$
mid.sentence 'output.state :=
}
if$
s
}
FUNCTION {output}
{ duplicate$ empty$
'pop$
'output.nonnull
if$
}
FUNCTION {output.check}
{ 't :=
duplicate$ empty$
{ pop$ "empty " t * " in " * cite$ * warning$ }
'output.nonnull
if$
}
FUNCTION {fin.entry}
{ add.period$
write$
newline$
}
FUNCTION {new.block}
{ output.state before.all =
'skip$
{ after.block 'output.state := }
if$
}
FUNCTION {new.sentence}
{ output.state after.block =
'skip$
{ output.state before.all =
'skip$
{ after.sentence 'output.state := }
if$
}
if$
}
FUNCTION {not}
{ { #0 }
{ #1 }
if$
}
FUNCTION {and}
{ 'skip$
{ pop$ #0 }
if$
}
FUNCTION {or}
{ { pop$ #1 }
'skip$
if$
}
FUNCTION {new.block.checka}
{ empty$
'skip$
'new.block
if$
}
FUNCTION {new.block.checkb}
{ empty$
swap$ empty$
and
'skip$
'new.block
if$
}
FUNCTION {new.sentence.checka}
{ empty$
'skip$
'new.sentence
if$
}
FUNCTION {new.sentence.checkb}
{ empty$
swap$ empty$
and
'skip$
'new.sentence
if$
}
FUNCTION {field.or.null}
{ duplicate$ empty$
{ pop$ "" }
'skip$
if$
}
FUNCTION {emphasize}
{ duplicate$ empty$
{ pop$ "" }
{ "{\em " swap$ * "}" * }
if$
}
INTEGERS { nameptr namesleft numnames }
FUNCTION {format.names}
{ 's :=
#1 'nameptr :=
s num.names$ 'numnames :=
numnames 'namesleft :=
{ namesleft #0 > }
{ s nameptr "{ff~}{vv~}{ll}{, jj}" format.name$ 't :=
nameptr #1 >
{ namesleft #1 >
{ ", " * t * }
{ numnames #2 >
{ "," * }
'skip$
if$
t "others" =
{ " et~al." * }
{ " and " * t * }
if$
}
if$
}
't
if$
nameptr #1 + 'nameptr :=
namesleft #1 - 'namesleft :=
}
while$
}
FUNCTION {format.key}
{ empty$
{ key field.or.null }
{ "" }
if$
}
FUNCTION {format.authors}
{ author empty$
{ "" }
{ author format.names }
if$
}
FUNCTION {format.editors}
{ editor empty$
{ "" }
{ editor format.names
editor num.names$ #1 >
{ ", editors" * }
{ ", editor" * }
if$
}
if$
}
FUNCTION {format.isbn}
{ isbn empty$
{ "" }
{ new.block "ISBN " isbn * }
if$
}
FUNCTION {format.issn}
{ issn empty$
{ "" }
{ new.block "ISSN " issn * }
if$
}
FUNCTION {format.url}
{ url empty$
{ "" }
{ new.block "URL \url{" url * "}" * }
if$
}
FUNCTION {format.title}
{ title empty$
{ "" }
{ title "t" change.case$ }
if$
}
FUNCTION {format.full.names}
{'s :=
#1 'nameptr :=
s num.names$ 'numnames :=
numnames 'namesleft :=
{ namesleft #0 > }
{ s nameptr
"{vv~}{ll}" format.name$ 't :=
nameptr #1 >
{
namesleft #1 >
{ ", " * t * }
{
numnames #2 >
{ "," * }
'skip$
if$
t "others" =
{ " et~al." * }
{ " and " * t * }
if$
}
if$
}
't
if$
nameptr #1 + 'nameptr :=
namesleft #1 - 'namesleft :=
}
while$
}
FUNCTION {author.editor.full}
{ author empty$
{ editor empty$
{ "" }
{ editor format.full.names }
if$
}
{ author format.full.names }
if$
}
FUNCTION {author.full}
{ author empty$
{ "" }
{ author format.full.names }
if$
}
FUNCTION {editor.full}
{ editor empty$
{ "" }
{ editor format.full.names }
if$
}
FUNCTION {make.full.names}
{ type$ "book" =
type$ "inbook" =
or
'author.editor.full
{ type$ "proceedings" =
'editor.full
'author.full
if$
}
if$
}
FUNCTION {output.bibitem}
{ newline$
"\bibitem[" write$
label write$
")" make.full.names duplicate$ short.list =
{ pop$ }
{ * }
if$
"]{" * write$
cite$ write$
"}" write$
newline$
""
before.all 'output.state :=
}
FUNCTION {n.dashify}
{ 't :=
""
{ t empty$ not }
{ t #1 #1 substring$ "-" =
{ t #1 #2 substring$ "--" = not
{ "--" *
t #2 global.max$ substring$ 't :=
}
{ { t #1 #1 substring$ "-" = }
{ "-" *
t #2 global.max$ substring$ 't :=
}
while$
}
if$
}
{ t #1 #1 substring$ *
t #2 global.max$ substring$ 't :=
}
if$
}
while$
}
FUNCTION {format.date}
{ year duplicate$ empty$
{ "empty year in " cite$ * warning$
pop$ "" }
'skip$
if$
month empty$
'skip$
{ month
" " * swap$ *
}
if$
extra.label *
}
FUNCTION {format.btitle}
{ title emphasize
}
FUNCTION {tie.or.space.connect}
{ duplicate$ text.length$ #3 <
{ "~" }
{ " " }
if$
swap$ * *
}
FUNCTION {either.or.check}
{ empty$
'pop$
{ "can't use both " swap$ * " fields in " * cite$ * warning$ }
if$
}
FUNCTION {format.bvolume}
{ volume empty$
{ "" }
{ "volume" volume tie.or.space.connect
series empty$
'skip$
{ " of " * series emphasize * }
if$
"volume and number" number either.or.check
}
if$
}
FUNCTION {format.number.series}
{ volume empty$
{ number empty$
{ series field.or.null }
{ output.state mid.sentence =
{ "number" }
{ "Number" }
if$
number tie.or.space.connect
series empty$
{ "there's a number but no series in " cite$ * warning$ }
{ " in " * series * }
if$
}
if$
}
{ "" }
if$
}
FUNCTION {format.edition}
{ edition empty$
{ "" }
{ output.state mid.sentence =
{ edition "l" change.case$ " edition" * }
{ edition "t" change.case$ " edition" * }
if$
}
if$
}
INTEGERS { multiresult }
FUNCTION {multi.page.check}
{ 't :=
#0 'multiresult :=
{ multiresult not
t empty$ not
and
}
{ t #1 #1 substring$
duplicate$ "-" =
swap$ duplicate$ "," =
swap$ "+" =
or or
{ #1 'multiresult := }
{ t #2 global.max$ substring$ 't := }
if$
}
while$
multiresult
}
FUNCTION {format.pages}
{ pages empty$
{ "" }
{ pages multi.page.check
{ "pages" pages n.dashify tie.or.space.connect }
{ "page" pages tie.or.space.connect }
if$
}
if$
}
FUNCTION {format.vol.num.pages}
{ volume field.or.null
number empty$
'skip$
{ "\penalty0 (" number * ")" * *
volume empty$
{ "there's a number but no volume in " cite$ * warning$ }
'skip$
if$
}
if$
pages empty$
'skip$
{ duplicate$ empty$
{ pop$ format.pages }
{ ":\penalty0 " * pages n.dashify * }
if$
}
if$
}
FUNCTION {format.chapter.pages}
{ chapter empty$
'format.pages
{ type empty$
{ "chapter" }
{ type "l" change.case$ }
if$
chapter tie.or.space.connect
pages empty$
'skip$
{ ", " * format.pages * }
if$
}
if$
}
FUNCTION {format.in.ed.booktitle}
{ booktitle empty$
{ "" }
{ editor empty$
{ "In " booktitle emphasize * }
{ "In " format.editors * ", " * booktitle emphasize * }
if$
}
if$
}
FUNCTION {empty.misc.check}
{ author empty$ title empty$ howpublished empty$
month empty$ year empty$ note empty$
and and and and and
key empty$ not and
{ "all relevant fields are empty in " cite$ * warning$ }
'skip$
if$
}
FUNCTION {format.thesis.type}
{ type empty$
'skip$
{ pop$
type "t" change.case$
}
if$
}
FUNCTION {format.tr.number}
{ type empty$
{ "Technical Report" }
'type
if$
number empty$
{ "t" change.case$ }
{ number tie.or.space.connect }
if$
}
FUNCTION {format.article.crossref}
{ key empty$
{ journal empty$
{ "need key or journal for " cite$ * " to crossref " * crossref *
warning$
""
}
{ "In {\em " journal * "\/}" * }
if$
}
{ "In " key * }
if$
" \citep{" * crossref * "}" *
}
FUNCTION {format.book.crossref}
{ volume empty$
{ "empty volume in " cite$ * "'s crossref of " * crossref * warning$
"In "
}
{ "Volume" volume tie.or.space.connect
" of " *
}
if$
editor empty$
editor field.or.null author field.or.null =
or
{ key empty$
{ series empty$
{ "need editor, key, or series for " cite$ * " to crossref " *
crossref * warning$
"" *
}
{ "{\em " * series * "\/}" * }
if$
}
{ key * }
if$
}
'skip$
if$
", \citet{" * crossref * "}" *
}
FUNCTION {format.incoll.inproc.crossref}
{ editor empty$
editor field.or.null author field.or.null =
or
{ key empty$
{ booktitle empty$
{ "need editor, key, or booktitle for " cite$ * " to crossref " *
crossref * warning$
""
}
{ "In {\em " booktitle * "\/}" * }
if$
}
{ "In " key * }
if$
}
{ "In " }
if$
" \citet{" * crossref * "}" *
}
FUNCTION {article}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.title "title" output.check
new.block
crossref missing$
{ journal emphasize "journal" output.check
format.vol.num.pages output
format.date "year" output.check
}
{ format.article.crossref output.nonnull
format.pages output
}
if$
format.issn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {book}
{ output.bibitem
author empty$
{ format.editors "author and editor" output.check
editor format.key output
}
{ format.authors output.nonnull
crossref missing$
{ "author and editor" editor either.or.check }
'skip$
if$
}
if$
new.block
format.btitle "title" output.check
crossref missing$
{ format.bvolume output
new.block
format.number.series output
new.sentence
publisher "publisher" output.check
address output
}
{ new.block
format.book.crossref output.nonnull
}
if$
format.edition output
format.date "year" output.check
format.isbn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {booklet}
{ output.bibitem
format.authors output
author format.key output
new.block
format.title "title" output.check
howpublished address new.block.checkb
howpublished output
address output
format.date output
format.isbn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {inbook}
{ output.bibitem
author empty$
{ format.editors "author and editor" output.check
editor format.key output
}
{ format.authors output.nonnull
crossref missing$
{ "author and editor" editor either.or.check }
'skip$
if$
}
if$
new.block
format.btitle "title" output.check
crossref missing$
{ format.bvolume output
format.chapter.pages "chapter and pages" output.check
new.block
format.number.series output
new.sentence
publisher "publisher" output.check
address output
}
{ format.chapter.pages "chapter and pages" output.check
new.block
format.book.crossref output.nonnull
}
if$
format.edition output
format.date "year" output.check
format.isbn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {incollection}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.title "title" output.check
new.block
crossref missing$
{ format.in.ed.booktitle "booktitle" output.check
format.bvolume output
format.number.series output
format.chapter.pages output
new.sentence
publisher "publisher" output.check
address output
format.edition output
format.date "year" output.check
}
{ format.incoll.inproc.crossref output.nonnull
format.chapter.pages output
}
if$
format.isbn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {inproceedings}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.title "title" output.check
new.block
crossref missing$
{ format.in.ed.booktitle "booktitle" output.check
format.bvolume output
format.number.series output
format.pages output
address empty$
{ organization publisher new.sentence.checkb
organization output
publisher output
format.date "year" output.check
}
{ address output.nonnull
format.date "year" output.check
new.sentence
organization output
publisher output
}
if$
}
{ format.incoll.inproc.crossref output.nonnull
format.pages output
}
if$
format.isbn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {conference} { inproceedings }
FUNCTION {manual}
{ output.bibitem
format.authors output
author format.key output
new.block
format.btitle "title" output.check
organization address new.block.checkb
organization output
address output
format.edition output
format.date output
format.url output
new.block
note output
fin.entry
}
FUNCTION {mastersthesis}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.title "title" output.check
new.block
"Master's thesis" format.thesis.type output.nonnull
school "school" output.check
address output
format.date "year" output.check
format.url output
new.block
note output
fin.entry
}
FUNCTION {misc}
{ output.bibitem
format.authors output
author format.key output
title howpublished new.block.checkb
format.title output
howpublished new.block.checka
howpublished output
format.date output
format.issn output
format.url output
new.block
note output
fin.entry
empty.misc.check
}
FUNCTION {phdthesis}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.btitle "title" output.check
new.block
"PhD thesis" format.thesis.type output.nonnull
school "school" output.check
address output
format.date "year" output.check
format.url output
new.block
note output
fin.entry
}
FUNCTION {proceedings}
{ output.bibitem
format.editors output
editor format.key output
new.block
format.btitle "title" output.check
format.bvolume output
format.number.series output
address output
format.date "year" output.check
new.sentence
organization output
publisher output
format.isbn output
format.url output
new.block
note output
fin.entry
}
FUNCTION {techreport}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.title "title" output.check
new.block
format.tr.number output.nonnull
institution "institution" output.check
address output
format.date "year" output.check
format.url output
new.block
note output
fin.entry
}
FUNCTION {unpublished}
{ output.bibitem
format.authors "author" output.check
author format.key output
new.block
format.title "title" output.check
format.url output
new.block
note "note" output.check
format.date output
fin.entry
}
FUNCTION {default.type} { misc }
MACRO {jan} {"January"}
MACRO {feb} {"February"}
MACRO {mar} {"March"}
MACRO {apr} {"April"}
MACRO {may} {"May"}
MACRO {jun} {"June"}
MACRO {jul} {"July"}
MACRO {aug} {"August"}
MACRO {sep} {"September"}
MACRO {oct} {"October"}
MACRO {nov} {"November"}
MACRO {dec} {"December"}
MACRO {acmcs} {"ACM Computing Surveys"}
MACRO {acta} {"Acta Informatica"}
MACRO {cacm} {"Communications of the ACM"}
MACRO {ibmjrd} {"IBM Journal of Research and Development"}
MACRO {ibmsj} {"IBM Systems Journal"}
MACRO {ieeese} {"IEEE Transactions on Software Engineering"}
MACRO {ieeetc} {"IEEE Transactions on Computers"}
MACRO {ieeetcad}
{"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}
MACRO {ipl} {"Information Processing Letters"}
MACRO {jacm} {"Journal of the ACM"}
MACRO {jcss} {"Journal of Computer and System Sciences"}
MACRO {scp} {"Science of Computer Programming"}
MACRO {sicomp} {"SIAM Journal on Computing"}
MACRO {tocs} {"ACM Transactions on Computer Systems"}
MACRO {tods} {"ACM Transactions on Database Systems"}
MACRO {tog} {"ACM Transactions on Graphics"}
MACRO {toms} {"ACM Transactions on Mathematical Software"}
MACRO {toois} {"ACM Transactions on Office Information Systems"}
MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"}
MACRO {tcs} {"Theoretical Computer Science"}
READ
FUNCTION {sortify}
{ purify$
"l" change.case$
}
INTEGERS { len }
FUNCTION {chop.word}
{ 's :=
'len :=
s #1 len substring$ =
{ s len #1 + global.max$ substring$ }
's
if$
}
FUNCTION {format.lab.names}
{ 's :=
s #1 "{vv~}{ll}" format.name$
s num.names$ duplicate$
#2 >
{ pop$ " et~al." * }
{ #2 <
'skip$
{ s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
{ " et~al." * }
{ " and " * s #2 "{vv~}{ll}" format.name$ * }
if$
}
if$
}
if$
}
FUNCTION {author.key.label}
{ author empty$
{ key empty$
{ cite$ #1 #3 substring$ }
'key
if$
}
{ author format.lab.names }
if$
}
FUNCTION {author.editor.key.label}
{ author empty$
{ editor empty$
{ key empty$
{ cite$ #1 #3 substring$ }
'key
if$
}
{ editor format.lab.names }
if$
}
{ author format.lab.names }
if$
}
FUNCTION {author.key.organization.label}
{ author empty$
{ key empty$
{ organization empty$
{ cite$ #1 #3 substring$ }
{ "The " #4 organization chop.word #3 text.prefix$ }
if$
}
'key
if$
}
{ author format.lab.names }
if$
}
FUNCTION {editor.key.organization.label}
{ editor empty$
{ key empty$
{ organization empty$
{ cite$ #1 #3 substring$ }
{ "The " #4 organization chop.word #3 text.prefix$ }
if$
}
'key
if$
}
{ editor format.lab.names }
if$
}
FUNCTION {calc.short.authors}
{ type$ "book" =
type$ "inbook" =
or
'author.editor.key.label
{ type$ "proceedings" =
'editor.key.organization.label
{ type$ "manual" =
'author.key.organization.label
'author.key.label
if$
}
if$
}
if$
'short.list :=
}
FUNCTION {calc.label}
{ calc.short.authors
short.list
"("
*
year duplicate$ empty$
short.list key field.or.null = or
{ pop$ "" }
'skip$
if$
*
'label :=
}
FUNCTION {sort.format.names}
{ 's :=
#1 'nameptr :=
""
s num.names$ 'numnames :=
numnames 'namesleft :=
{ namesleft #0 > }
{ nameptr #1 >
{ " " * }
'skip$
if$
s nameptr "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}" format.name$ 't :=
nameptr numnames = t "others" = and
{ "et al" * }
{ t sortify * }
if$
nameptr #1 + 'nameptr :=
namesleft #1 - 'namesleft :=
}
while$
}
FUNCTION {sort.format.title}
{ 't :=
"A " #2
"An " #3
"The " #4 t chop.word
chop.word
chop.word
sortify
#1 global.max$ substring$
}
FUNCTION {author.sort}
{ author empty$
{ key empty$
{ "to sort, need author or key in " cite$ * warning$
""
}
{ key sortify }
if$
}
{ author sort.format.names }
if$
}
FUNCTION {author.editor.sort}
{ author empty$
{ editor empty$
{ key empty$
{ "to sort, need author, editor, or key in " cite$ * warning$
""
}
{ key sortify }
if$
}
{ editor sort.format.names }
if$
}
{ author sort.format.names }
if$
}
FUNCTION {author.organization.sort}
{ author empty$
{ organization empty$
{ key empty$
{ "to sort, need author, organization, or key in " cite$ * warning$
""
}
{ key sortify }
if$
}
{ "The " #4 organization chop.word sortify }
if$
}
{ author sort.format.names }
if$
}
FUNCTION {editor.organization.sort}
{ editor empty$
{ organization empty$
{ key empty$
{ "to sort, need editor, organization, or key in " cite$ * warning$
""
}
{ key sortify }
if$
}
{ "The " #4 organization chop.word sortify }
if$
}
{ editor sort.format.names }
if$
}
FUNCTION {presort}
{ calc.label
label sortify
" "
*
type$ "book" =
type$ "inbook" =
or
'author.editor.sort
{ type$ "proceedings" =
'editor.organization.sort
{ type$ "manual" =
'author.organization.sort
'author.sort
if$
}
if$
}
if$
" "
*
year field.or.null sortify
*
" "
*
title field.or.null
sort.format.title
*
#1 entry.max$ substring$
'sort.label :=
sort.label *
#1 entry.max$ substring$
'sort.key$ :=
}
ITERATE {presort}
SORT
STRINGS { longest.label last.label next.extra }
INTEGERS { longest.label.width last.extra.num number.label }
FUNCTION {initialize.longest.label}
{ "" 'longest.label :=
#0 int.to.chr$ 'last.label :=
"" 'next.extra :=
#0 'longest.label.width :=
#0 'last.extra.num :=
#0 'number.label :=
}
FUNCTION {forward.pass}
{ last.label label =
{ last.extra.num #1 + 'last.extra.num :=
last.extra.num int.to.chr$ 'extra.label :=
}
{ "a" chr.to.int$ 'last.extra.num :=
"" 'extra.label :=
label 'last.label :=
}
if$
number.label #1 + 'number.label :=
}
FUNCTION {reverse.pass}
{ next.extra "b" =
{ "a" 'extra.label := }
'skip$
if$
extra.label 'next.extra :=
extra.label
duplicate$ empty$
'skip$
{ "{\natexlab{" swap$ * "}}" * }
if$
'extra.label :=
label extra.label * 'label :=
}
EXECUTE {initialize.longest.label}
ITERATE {forward.pass}
REVERSE {reverse.pass}
FUNCTION {bib.sort.order}
{ sort.label 'sort.key$ :=
}
ITERATE {bib.sort.order}
SORT
FUNCTION {begin.bib}
{ preamble$ empty$
'skip$
{ preamble$ write$ newline$ }
if$
"\begin{thebibliography}{" number.label int.to.str$ * "}" *
write$ newline$
"\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi"
write$ newline$
"\expandafter\ifx\csname url\endcsname\relax" write$ newline$
" \def\url#1{{\tt #1}}\fi" write$ newline$
}
EXECUTE {begin.bib}
EXECUTE {init.state.consts}
ITERATE {call.type$}
FUNCTION {end.bib}
{ newline$
"\end{thebibliography}" write$ newline$
}
EXECUTE {end.bib}
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