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Misspecification of the Panzar-Rosse Model:
Assessing Competition in the Banking Industry
Jacob A. Bikker∗ Laura Spierdijk† Paul Finnie‡
July 30, 2007
Abstract
This paper demonstrates that the level of competition in the existing Panzar Rosse
(P-R) literature is systematically overestimated and that the tests on both monopoly
and perfect competition are distorted. This is due to the use of bank revenues divided
by total assets as dependent variable in the P-R model instead of unscaled bank rev-
enues. We provide both theoretical and empirical evidence to illustrate the impact of
the misspecification on the estimation of competition and the statistical tests on the
market structure. Inclusion of scale variables as explanatory variables, which is com-
mon practice in the current literature, has a similar distorting effect. Our overview
of the extensive P-R literature reveals that all 28 studies considered suffer from these
types of misspecification. The empirical evidence provided in this paper is based on a
large sample of more than 18,000 banks in 101 countries over 16 years. We find that
monopoly cannot be rejected in 28% of the countries (against 0% under misspecifi-
cation) and that perfect competition cannot be rejected in 38% of the cases (against
20-30% under misspecification).
Keywords: competition, banking industry, Panzar-Rosse model, market structure
JEL Classification: C52, G21, L11, L13
∗Jacob Bikker, De Nederlandsche Bank (DNB), Supervisory Policy Division, Strategy Department, P.O.Box 98, 1000AB Amsterdam, The Netherlands. Phone: +31 20 524 2352. Fax: +31 20 524 1885. Email:[email protected].
†Laura Spierdijk, University of Groningen, Faculty of Economics, Department of Econometrics, P.O.Box 800, 9700AV Groningen, The Netherlands. Phone: +31 50 363 5929. Fax: +31 50 363 3720. Email:[email protected].
‡Paul Finnie, UBS AG, GTP Risk Management, Bahnhofstrasse 102, 8001 Zurich, Switzerland. Email:[email protected]. Paul Finnie was affiliated to De Nederlandsche Bank during the writing of thispaper. The authors are grateful to the participants of the DNB research seminar for valuable commentsand suggestions, and to Jack Bekooij for extensive data support. The usual disclaimer applies. The viewsexpressed in this paper are not necessarily shared by DNB or UBS.
1 Introduction
In recent years, a continuously increasing number of articles has investigated competition
in the banking industry. Internationalization, worldwide liberalization of financial markets
and banking harmonization in the European Union have raised broad interest in this
topic. Obviously, competition in the banking sector has a major impact on the wealth of
consumers and companies and affects the performance and financial health of banks.
Another explanation for the vast amount of studies on this topic is that competition
cannot be measured directly due to the lack of detailed information on prices and costs
of the various banking products. Therefore, various indirect measurement techniques have
been proposed, divided into two main streams: structural and non-structural approaches.
For an overview, see e.g. Bikker (2004).
One of the most popular methods used to assess competition in the banking industry
is the model of Panzar and Rosse (P-R). Seminal articles by Rosse and Panzar (1977) and
Panzar and Rosse (1982, 1987) provide an excellent framework for assessing degrees of
competition in the banking industry. However, the empirical translation of this approach
into an econometric specification is not unambiguous and allows for some degrees of free-
dom. The P-R model uses cross-sectional data to assess the competitive behavior of banks
on the basis of the comparative static properties of reduced-form revenue equations. It
explains revenues from input prices, among other factors. In this setting, the sum of the
elasticities of a bank’s total revenues to its input prices provides a pivotal statistic to
test for monopoly (or perfect cartel) and perfect competition. Moreover, under certain
assumptions this statistic can also serve as a measure of the degree of competition in the
banking sector.
One of the principal choices underlying the P-R approach concerns the dependent
variable, which is usually interest income or total income. Most studies use a scaled version
of bank income as the dependent variable in the P-R model and work with revenues divided
by total assets. The resulting variable can be interpreted as the lending rate or ‘price’.
However, the key result of this paper is that scaling fundamentally changes the nature
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of the model, since it transforms the revenue equation into a price equation. We show
how this misspecification distorts the measurement of competition and the statistical tests
on the market structure. Furthermore, we also provide empirical evidence that the scaled
P-R model is misspecified. Additionally, this paper demonstrates that the ‘wrong’ choice
of explanatory variables may cause a similar disruption of the assessment of competition.
Throughout, we use a large sample of 18,467 banks in 101 countries over 16 years, covering
a total of 112,343 bank-year observations. With the correctly specified P-R model we find
that monopolistic competition is indeed the most common market structure: it is rejected
in only one of the 101 countries. Monopoly or perfect cartel cannot be rejected in 28% of
the countries analyzed (against 0% in the misspecified model) and that perfect competition
cannot be rejected in 38% of the cases (against 20-30% with misspecification).
The setup of this paper is as follows. Section 2 presents the P-R approach and pro-
vides a literature survey. Subsequently, we use some intuitive arguments to point out how
misspecification affects the measurement of competition and the statistical tests on the
market structure. As a next step, Section 3 develops a theoretical framework to show how
misspecification in the P-R model may result in severely biased estimates of the key mea-
sure of competition. Section 4 discusses the data used in the empirical part of this paper
and Section 5 is devoted to the empirical implementation of the P-R model. We present
and discuss the empirical results in Section 6. Finally, Section 7 concludes the paper.
2 The P-R model
This section presents the P-R approach and discusses the literature on this topic, focusing
on the empirical implementation of this model.
2.1 The P-R model
Following Bikker and Haaf (2002), the empirical translation of the P-R approach assumes
a log-linear marginal cost (MC) function of the form
lnMC = α0 + α1 ln OUT +m∑
i=1
βi ln FIPi +p∑
j=1
γj ln EXCOSTj , (1)
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where OUT is the output of the bank, FIP the factor input prices and EXCOST repre-
sents other variables exogenous to the cost function. Similarly, the marginal revenue (MR)
function is assumed to have a log-linear form, thus
lnMR = δ0 + δ1 lnOUT +q∑
k=1
ξk ln EXREVk, (2)
where EXREV represents variables related to the bank-specific demand function. For a
profit-maximizing bank marginal costs equal marginal revenues in equilibrium. This results
in the equilibrium value
lnOUT∗ = (α0 − δ0 +m∑
i=1
βi ln FIPi +p∑
j=1
γj ln EXCOSTj
−q∑
k=1
ξk ln EXREVk)/(δ1 − α1). (3)
The reduced-form revenue equation is obtained as the product of equilibrium output and
the common price level. The latter is determined by the inverse-demand equation, which
in logarithms writes as
ln p∗ = ξ + ln(∑
i
OUT∗i ), (4)
where the asterisk refers to the equilibrium value. Building on this framework, Bikker and
Haaf (2002) arrive at the following empirical reduced-form equation
ln II = α + β lnAFR + γ ln PPE + δ ln PCE
+∑
j
ξj lnBSFj + η ln OI + error, (5)
where II denotes interest income, AFR the annual funding rate, PPE the price of personnel
expenses, PCE the price of capital expenditure and other expenses, BSF bank-specific
exogenous factors and OI the ratio of other income to total assets. Equation (5) is similar
to what is commonly used in the literature, but the choice of dependent and explanatory
variables may vary.
Rosse and Panzar (1977) and Panzar and Rosse (1987) use Equation (5) to construct
the ‘H statistic’, which allows for a quantitative assessment of the competitive nature
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of banking markets and the market power of banks. H is calculated as the sum of the
elasticities of a bank’s total revenue with respect to the bank’s input prices. Hence, based
on Equation (5) H = β + γ + δ. The banking industry is characterized by monopoly
or perfect cartel for H ≤ 0, monopolistic competition or oligopoly for 0 < H < 1, and
perfect competition for H = 1. Furthermore, under certain conditions, H increases with
the competitiveness of the banking industry (see Vesala (1995)).1
2.2 Dependent and explanatory variables
Estimation of Equation (5) requires choosing a dependent variable. Several studies base
‘revenues’ on interest income, assuming that financial intermediation is the core business of
most banks. Financial intermediation is, in fact, the type of banking activity underlying the
P-R framework. Other studies take into account that the share of non-interest revenues
(such as fee-based products, services and off-balance sheet credit substitutes) in total
revenues has doubled over the period 1990− 1998 and focus on total income instead. Also
the choice between relative and absolute measures of (either total or interest) income as
the dependent variable in Equation (5) is of crucial importance. Whereas many articles use
(the natural logarithm of) the ratio of income and total assets as their dependent variable,
others simply take the (natural logarithm of) total or interest income, without dividing
by total assets. As we will formally prove in the next section, Equation (5) reduces to
a price equation if the logarithm of relative income is taken as the dependent variable,
while it becomes a revenue specification if it is based on the logarithm of absolute income.
This has far-reaching implications, as we will show that the input price elasticities in a
price equation sum to one. Basing the H statistic on a price equation instead of a revenue
equation will cause a bias towards one.
Besides input prices, most studies on the P-R model include a wide range of explanatory1We may observe changes in the competitive structure of the banking industry over time, due to
e.g. liberalization, harmonization, deregulation, technological progress, and internationalization. Therefore,Bikker and Haaf (2002) include time-dependent coefficients in Equation (5), assuming that the long-term equilibrium market structure changes gradually over time. They do this through multiplication ofthe input price variables with the term exp(εTIME) in Equation (5), where the case ε = 0 refers toa situation where the competitive structure is constant over time. The time-dependent H statistic thenequals H(TIME) = exp(εTIME)(β + γ + δ).
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variables in Equation (5), depending in part on the availability of these variables. Many
studies use one or more capacity or scaling variables as covariates, to account for economies
of scale. However, a revenue equation with (the natural logarithm of) total assets (TA)
as scaling variable is indistinguishable from a price equation. To see this, suppose that
we add κ ln(TA) to the right-hand side of Equation (5), where κ represents the unknown
coefficient of ln TA. This is equivalent to adding (κ− 1) ln(TA) to the right-hand side of
this equation while rewriting the equation in such a way that the dependent variable on
the left-hand side equals ln(II/TA). Hence, adding a scaling factor also results in the type
of misspecification that occurs when we work with a scaled dependent variable. Obviously,
the use of other explanatory variables that reflect scale (e.g. size of deposits or equity)
will lead to similar misspecification.
2.3 Literature survey
Table 1 summarizes the vast empirical literature on the Panzar-Rosse approach since Shaf-
fer (1982) and additionally classifies each study on the basis of its dependent variable and
the included capacity or scaling variables. Moreover, this table also provides information
on the countries analyzed, the period of the corresponding data set and the average value
of the estimated H statistic in each study. The lower pane of Table 1 provides prelimi-
nary evidence that the estimates of the H statistic obtained from the P-R price equation
(0.64, the average over seven studies, see second column) are closer to the theoretical value
H = 1 than those based on the ‘true’ revenue equation (0.49, the average over six studies,
see first column). This type of bias is indeed what we expect and what will later follow
from our theoretical model in Section 3. Obviously, the studies in Table 1 show substantial
heterogeneity if one looks at the choice between interest and total income as the dependent
variable, the set of explanatory variables, and the countries analyzed. This suggests that,
to some extent, when we consider average values of H across these studies, we are com-
paring apples and oranges. Therefore, we will proceed in a different way to obtain more
convincing empirical evidence for the misspecification implied by the P-R price equation.
In Section 5, we will estimate several empirical P-R specifications using a large uniform
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data set. But first we will provide some theoretical evidence for misspecification of the
P-R model in the next section.
3 Misspecification in the P-R model
In this section, we theoretically assess the misspecification problem in the P-R approach
under three competition regimes: monopoly or perfect cartel, oligopoly and perfect com-
petition.
3.1 Misspecification in a simple monopoly model
This section investigates misspecification of the P-R approach using a simple single-
product monopoly model as described by Panzar and Rosse (1987, page 446). We first
present this illustration of the P-R approach and subsequently explain the effect of mis-
specification. The assumptions underlying the simple monopoly model below merely fa-
cilitate our illustrative example. The P-R approach is valid for a much broader range of
models, as it does not require any particular assumptions about the specification of the
demand curve or the production technology.
Suppose that the monopolist faces a demand curve with constant price elasticity e > 1
that reads as
y = (γ−1Z−αp)−e, (6)
where y is the demand for the single product, p is its price, and Z a vector of exogenous
variables that shift the bank’s demand function, with parameter α. In this case the bank’s
revenue function R is equal to
R(y, Z) = yp = γZαy(e−1)/e. (7)
One way to explain why the price elasticity of demand e should satisfy e > 1, is that
otherwise the revenue R would not increase with output y. For simplicity’s sake, we also
assume that the monopolist employs a constant return to scale Cobb-Douglas technology,
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so that its cost function C can be written as
C(y, W,X) = yXβ∏
j
waj
j
[aj > 0,
∑
j
aj = 1]. (8)
Here W is a vector of m factor prices, exogenous to the bank, with parameters aj (j =
1, . . . , m), which are equal to the cost shares of the respective input factors, and X is a
vector of exogenous variables that shift the bank’s cost function, with parameter β. Profit
maximization follows from the first derivative of profit π = R− C, and results in
∂π/∂y = γ((e− 1)/e)Zαy−1/e −Xβ∏
j
waj
j = 0. (9)
Hence, equilibrium output equals
y∗ = (Xβ∏
j
waj
j /(γZα(e− 1)/e))−e. (10)
Here the asterisk refers to the equilibrium value. Substitution of Equation (10) into Equa-
tion (7) and taking logarithms leads to the non-stochastic version of the bank’s reduced-
form revenue equation
ln R(y∗, Z, X) = γ0 + eα ln Z − (e− 1)β lnX − (e− 1)∑
j
aj lnwj , (11)
where the intercept satisfies γ0 = e ln γ − (1 − e) ln((e − 1)/e). The sum of input price
elasticities H − the indicator of competition − is thus equal to −(e− 1)∑
aj = 1− e ≤ 0.
Hence H is negative, since e > 1. Note that e > 1 is also required by the second order
condition for monopoly profit maximization (i.e. −(e − 1)/e < 0). Because of the simple
structure of the model, estimation of the reduced-form equation does not only provide a
way to test the hypothesis of monopoly profit maximization, it also yields estimates of all
structural parameters of interest. In particular, this example makes clear that both the
magnitude and the sign of H may be of interest. Since the model provides an estimate of
the price elasticity of demand e, the H statistic also yields an estimate of the Lerner index
of monopoly power L = (e− 1)/e = H/(H − 1).
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3.1.1 Misspecification
The equilibrium price follows from substitution of Equation (10) into Equation (6), which
yields
p∗ = γZα(y∗)−1/e = Xβ∏
j
waj
j /((e− 1)/e). (12)
In logarithms, we get
ln p∗ = − ln((e− 1)/e)) + β ln X +∑
j
aj lnwj . (13)
The equilibrium price is determined by the input prices, a constant multiplicative mark-up
depending on the price elasticity of demand e, and a mark-up depending on the explanatory
variables X in the bank’s cost function. Comparison of Equations (11) and (13) makes
clear that if the revenue R in the left-hand side of Equation (11) were replaced by the price
p, the sum of input price elasticities H would be equal to one instead of below zero. Hence,
misspecification caused by the use of a price equation rather than a revenue equation leads
to wrong inference about the market structure and the degree of competitiveness through
a strong bias of H towards one. Also note that the coefficients of the exogenous variables
X also have different parameter values in the price equation. Furthermore, the coefficients
of the shift variables Z in the demand function become zero.
We are aware that our argument is a conclusive proof only for the described type
of monopoly with a demand curve of constant price elasticity and a constant return to
scale Cobb-Douglas technology. It should be considered as an important example of a
framework in which misspecification occurs, disqualifying the traditional choice of the
dependent variable in the existing P-R literature.
3.2 Misspecification in an oligopoly model
This section is based on a common oligopoly model of N profit maximizing banks.2 We
assume that all costs are variable (in the long-run) and that all outputs are perfect com-
plements with zero cross-price elasticity. For each output in the output vector Yi, bank i
2See Cowling (1976), Cowling and Waterson (1976), Stigler (1964), and Bikker and Bos (2005).
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(i = 1, . . . , N) sets its price pi based on the inverse demand function pi = f(Y ) = f(∑
j Yj).
Profits Πi of bank i are defined as revenues piYi minus costs YiXβ
∏j w
aj
j , in line with the
model of the previous section. Profits are maximized when
∂Πi/∂Yi = p∗i + Yif′(Y )[dY/dYi]−Xβ
∏
j
waj
j = 0, (14)
where a prime denotes the first derivative. Rewriting Equation (14) yields the equilibrium
prices
p∗i = Xβ∏
j
waj
j − Yif′(Y )[dY/dYi]. (15)
We further rewrite and rearrange Equation (15), to obtain an equation that is more closely
in line with what is found in the empirical literature on bank performance. Writing Y as∑
j Yj , we start by defining λi as
∂Y/∂Yi = 1 + ∂∑
j 6=i
Yj/∂Yi = 1 + λi, (16)
where λi is known as the conjectural variation of bank i’s output (−1 ≤ λi ≤ 1)3. Fur-
thermore, for a demand function similar to Equation (6), we recognize that
f ′(Y )Y/p∗i = −1/e (17)
where e is the price elasticity of demand. Substitution of Equations (15) and (16) into (14)
and reshuffling yields
(p∗i −Xβ∏
j
waj
j )/p∗i = (Yi/Y )(1/e)(1 + λi). (18)
Hence, the bank’s mark-up over its total costs can be decomposed into bank i’s market
share, the inverse of the market price elasticity of demand, and bank i’s expectations about
the reactions of its rivals (strengthening the oligopolistic behavior on this market). After
solving of Equation (18) for p∗i and taking logarithms, we obtain:
ln p∗i = β lnX +∑
j
aj ln wj − ln(1− ((Yi/Y )(1/e)(1 + λi))). (19)
3A high value of λi means a bank has a high awareness of its interdependence with other banks. Ifbanks are indeed myopic, their λi equals zero.
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If the revenue R in the revenue equation for an oligopolistic market were replaced by the
price p∗i , the sum of input price elasticities H would be equal to unity instead of having
a value in the interval (0, 1).4 Hence, misspecification caused by using a price equation
rather than a revenue equation leads to wrong inference about the market structure and
its degree of competitiveness through a serious bias of H towards one, similar to the bias
under monopoly.
Again, we realize that our argument is not a conclusive proof for all types of oligopoly,
monopolistic competition and the like, but an illustrative example of a context in which
misspecification arises.
3.3 Misspecification under perfect competition
Finally, we have the perfect competition case. We know that under perfect competition
there are no excess profits, so that output prices are fully determined by input prices,
including a charge for invested equity, without any mark-up based on market power. In
this situation, the sum of input price elasticities H would be equal to unity in both the
price and the revenue equations. That is, in case of perfect competition, misspecification
caused by the use of a price equation rather than a revenue equation will not lead to wrong
conclusions about the market structure.
Since the misspecification does not result in a bias in the case of perfect competition,
but does biases H under monopoly and oligopoly, we expect that the impact of misspecifi-
cation will be larger the lower the value of H will be in the − correctly specified − revenue
equation.
4 Bank data sample
This paper uses a detailed data set obtained from Bankscope. The data set covers 25,000
private and public banks throughout the world with standardized reporting data that
facilitate comparison across different accounting systems. The panel data set, prior to4We assume that the mark-up (consisting of market share, market price elasticity of demand and
conjectural variation) is not proportional to the production costs.
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outlier reduction, is fairly extensive covering banks in 120 countries and spanning the
years 1986 − 2005. The data set is unbalanced as (for various reasons) not all banks are
included throughout the entire period, with particularly, strong underrepresentation in the
earlier years.
We focus on consolidated data (where available) from commercial, cooperative and sav-
ings banks and remove all observations pertaining to other types of financial institutions,
such as securities houses, medium and long term credit banks, specialized governmental
credit institutions and mortgage banks. The latter types of institutions may be less de-
pendent on the traditional intermediation function and may have a different financing
structure compared to our focus group. In any case, we favor a more homogeneous sam-
ple. We apply a number of selection rules to the most important variables and eliminate
data of banks under special circumstances (e.g. holding companies, banks in start-up or
discontinuity phases), erroneous data and abnormally high or low ratios between key vari-
ables. To compensate for structural differences across countries, we adjust the bounds as
necessary. This allows for some flexibility regarding the inclusion of countries that have
experienced (extremely) high inflation rates and hence (extremely) high interest rates, or
which are more labor-intensive. This operation reduces the number of observations by 6%.
For the complete set of selection rules and exclusion rates, we refer to Bikker et al. (2006).
Finally, we exclude all countries for which the number of bank-year observations over the
sample period is less than 50, a minimum number needed to obtain a sufficiently accurate
estimate of the country’s H statistic. This reduces our sample from 120 to 101 countries
(see Table 2).
The final sample consists of 112,343 bank-year observations on 18,467 different banks,
with the numbers from later years dominating the sample. The United States has by far the
largest number of bank-year observations at 54,466, followed by Germany (19,137), Italy
(6,149), France (3,641), and Japan (3,028). The data set has not been adjusted for bank
mergers, which means that merged banks are treated as two separate entities until the
point of merger, whereafter only one bank is reported. As also noted by other authors (in
particular Kishan and Opiela (2000) and Hempell (2002)), our approach implicitly assumes
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that the merged banks’ behavior in terms of their competitive stance and business mix
does not deviate from before the merger and of the other banks. This is because most
mergers take place between small cooperative banks that are assumed to have the same
features as regards their competitive stance and business mix. Table 2 provides a detailed
overview of the countries in the sample and the data period considered.
5 The empirical P-R model
This section discusses the translation of the theoretical P-R model into an empirical spec-
ification.
5.1 The model
In order to apply the P-R approach to our data, we estimate for each country the following
empirical reduced form equation of bank revenues, in line with Equation (5):
ln II = α + β lnAFR + γ ln PPE + δ ln PCE + η1 ln LNS/TA
+η2 lnONEA/TA + η3 lnDPS/F + η4 ln EQ/TA
+η5OI/II + ξ1COMdum + ξ2COOdum + error. (20)
For simplicity of notation, we leave out the subscripts i (banks) and t (year) in Equa-
tion (20). The dependent variable II denotes interest income. Regarding the input factor
prices, AFR stands for annual funding rate, PPE denotes price of personnel expenses,
and PCE is the price of physical capital expenditure. We cannot observe the three input
prices directly. Therefore, we use the ratio of interest expense to total funds (IE/FUN)
as a proxy for the average funding rate, the ratio of annual personnel expenses to total
assets (PE/TA) as an approximation to the price of personnel expenses, and the ratio of
other non-interest expenses to (modeled5) fixed assets (ONIE/FA) as proxy for the price of5To deal with possible inaccuracies in the measurement of fixed assets, we make an adjustment to this
variable. Following Resti (1997) and Bikker and Haaf (2002), we regress the natural logarithm of fixedassets on the logarithm of total assets and loans, including quadratic and cross terms of these variables.Subsequently, we use the regression forecasts of fixed assets to calculate PCE.
12
capital expenditure. Of course, using the ratio of annual personnel expenses to the number
of fulltime employees would be a better measure of the unit price of labor. However, due
to the limited data available on employee numbers and their poor quality, we use the total
assets configuration instead.
Additionally, we include a number of bank-specific factors as control variables, mainly
balance-sheet ratios that reflect bank behavior and risk profile, which may affect revenues.
The ratio of customer loans to total assets (LNS/TA) represents credit risk. Generally,
banks compensate themselves for this risk by means of a surcharge on the prime lend-
ing rate, which affects interest income. ONEA/TA equals the ratio of other non-earning
assets to total assets, which mirrors characteristics of the asset composition. The ratio
of customer deposits to the sum of customer deposits and short term funding (DPS/F)
captures features of the funding mix. The equity to total assets ratio (EQ/TA) accounts
for the leverage reflecting differences in the risk preferences across banks. Furthermore,
to take into account the increasing role of banking activities other than financial inter-
mediation, which draw partially on the same inputs, we complement the analysis by the
inclusion of the ratio of other income to interest income (OI/II). The specification of this
explanatory variable uses the fact that all inputs are used to generate total income (TI),
so that ln(TI) = ln(II + OI) ≈ ln(II) + OI/II. Using OI/II as an additional explanatory
variable with coefficient η5, this equation by approximation encompasses the models ex-
plaining only II (η5 = 0), or merely TI (η5 = 1). Furthermore, COMdum and COOdum are
dummy variables for, respectively, commercial and cooperative banks. They accommodate
for differences in asset sizes and revenue structures across banking types, not accounted
for by the other covariates. Since the P-R model is estimated per country, we obtain a
country-specific H statistic. As some banks are also active in foreign countries, our mea-
sure of competition in a particular country reflects the average level of competition on the
markets where the banks of this country operate.
To assess the impact of misspecification, we compare the H statistics obtained from
the P-R revenue equations with and without capacity variables and from the P-R price
equation. For this purpose, we estimate three different variants of Equation (20). The
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first variant explains the natural logarithm of interest income (II), whereas the second
model is based on the ratio of interest income and total assets (II/TA).6 The third spec-
ification takes the natural logarithm of interest income as the dependent variable (as in
Equation (20)), but additionally includes the natural logarithm of total assets as scaling
variable in the right-hand side of Equation (20). As a robustness test (and to address the
misspecification in the literature), we re-estimate these three specifications with total in-
come instead of interest income as the dependent variable. All models are estimated using
ordinary least squares, with White (1980)’s heteroskedasticity robust standard errors.7
5.2 Hypothesis testing
The relation between the value of H and the market structure provides a direct way to
test for the degree of competition in the banking sector. We apply the usual statistical
framework to test the value of H.
We consider the following tests: (1) one-sided test for monopoly: H0 : H ≤ 0 versus
H1 : H > 0, (2) two-sided test for the value of H: H0 : H = 0 versus H1 : H 6= 0,
(3) two-sided test for monopolistic competition or oligopoly: H0 : 0 < H < 1 versus
H1 : H ≤ 0 or H ≥ 1, and (4) two-sided test for perfect competition: H0 : H = 1 versus
H1 : H 6= 1. We use a one-sided t-test for the one-sided hypotheses and a two-sided t-test
for the two-sided ones. The distinction between one-sided and two-sided tests (referring to
the form of the alternative hypothesis) seems to be ignored in almost all studies dealing
with the P-R model.8 However, this difference is crucial and strongly affects the outcomes
of the tests. For instance, a test on monopoly only needs to be rejected when H is large.
However, a two-sided test will erroneously rejects when H is strongly negative. Therefore,
we explicitly distinguish between one-sided and two-sided tests. Test (2) does not have a
clear interpretation, but has been applied in the literature as a test for monopoly.6Obviously, this model does not include OI/II as explanatory variable.7For some countries, data are unavailable for some of the bank-specific factors, or available only for a
limited number of banks. In the latter case, we accept only a slight reduction in the sample and otherwisedisregard that particular variable. Sensitivity analysis confirms that the H estimates are only slightly, ifat all, affected by the deletion of these variables.
8All studies in Table 1 ignore this, except Vesala (1995) and Drakos and Kanstantinou (2005) whoapply the test correctly, Murjan and Ruza (2002) who use t-tests everywhere, and Claessens and Laeven(2004) who do not test. Yeyati and Micco (2003) do not explain their type of test.
14
6 The empirical P-R model: estimation results
Table 3 reports the estimated values of H (including standard errors, t-values, and average
R2 over the 101 countries) for each of the six different model specifications based on
Equation (20).9
6.1 Summary of estimation results
To assess the impact of misspecification on the value of H, Table 4 reports the average
values of H for each of the six specifications calculated over all 101 countries in the
sample.10 Also, this table provides standard errors corresponding to the estimates of H.
The summary statistics in Table 4 show that the average value of H obtained from the
P-R revenue equation is much smaller than the average value resulting from the P-R price
equation (0.504 versus 0.742, respectively). Such a difference persists when total income
instead of interest income is taken as the dependent variable in the model, or when total
assets is added to the model as a scaling variable. Since the number of observations used to
estimate H varies considerably across countries, we have also calculated weighted averages
to account for this.11 When we weight each H statistic by the number of observations
used to estimate the statistic and subsequently use these weighted H’s to calculate sample
averages, we find similar results as in the unweighted case.12
The average value of H based on the price model may seem less close to the theoretical
value H = 1 than expected. A possible explanation for this is the presence of errors-in-9Also, we note that the coefficients of the explanatory variables in Equation (5) have the expected sign.
The full estimation results are available upon request.10Although China is included in our sample, we realize that the application of the P-R model might not
be appropriate in this case since interest rate margins of banks were determined by the Chinese governmentduring the sample period. However, the P-R model wrongly suggests perfect competition. Moreover, it isnot unlikely that the Chinese data are not reliable, since banks may have an incentive to report resultsthat are closer to the state targets that they actually are. For this country, the outcomes for China shouldbe interpreted with great caution.
11To save space, we do not report these results here. However, they are available from the authors uponrequest.
12There are also studies that include bank-specific fixed or random effects in the P-R model. Sinceinclusion of these effects does hardly affect the values of the H-statistic, we do not report full estimationresults. For example, when we allow for bank-specific random or fixed effects in the P-R model with log IIas the dependent variable, the average H statistic over the 101 countries in the sample equals 0.45 (fixedeffects) respectively 0.48 (random effects). Average standard errors equal 0.57, respectively 0.48. Averagestandard errors are substantially larger than with pooled estimation, which is likely to be due to therelatively limited number of banks in many countries.
15
variables (see e.g. Greene (2000)), which causes a downward bias in the estimates of H in
both in the ‘right’ and the misspecified model. This phenomenon is often referred to as
‘attenuation’. These errors-in-variables may occur when we approximate the input prices
as described in Section 5.
The price equation’s estimates of H are not only biased towards H = 1, they also
exhibit less variability. This appears from Table 4, which shows that the standard deviation
of H calculated over all countries is substantially smaller when the statistic is based on
the price equation. This finding can be explained by the fact that H is bounded from
above by the theoretical restriction H = 1 in the price equation, which puts a limit on its
variability. Additionally, estimations of H seem to be more ‘accurate’ in the price model,
in the sense that the average standard error of H is smaller in the price model than in the
revenue specification. Of course, this apparent precision is spurious, being based on the
misspecification inherent to the price equation.13
Finally, we consider the correlations between the estimates of H obtained with the
various model specifications. The correlation between the correctly specified model and the
misspecified models is consistently around 0.30, with asymptotic standard error of about
0.09. Although the correlations are significantly positive at a 5% level14, their values are
relatively low, which underlines once more that the misspecified models produce seriously
biased estimates of the degree of competition in the banking industry.15
6.2 Hypothesis testing
For each country, Table 3 reports the results of the hypothesis testing with respect to the
market structure. Additionally, the lower pane of Table 4 summarizes the outcomes of
hypothesis testing for the various specifications, applied to all 101 countries.
The test results based on the correct specification (the revenue equation) make clear13Throughout, we use two-sample t-tests and χ2-tests to test whether the differences in means and
variances are significance. We adjust the t-tests to deal with unequal population variances. In all cases,the differences are significant and each reasonable significance level.
14Unless stated otherwise, we do all tests at a 5% significance level.15We also find that the correlation between the values of H obtained from the model based on ln(II/TA)
and the model with ln II as the dependent and ln TA as the scaling variable equals 0.97 with standarderror 0.009. Similar values are found for the same models in terms of TI instead of II.
16
that the banking sector in most countries is in a condition of monopolistic competition.
This market structure is rejected for one single country only (China). The null hypothesis
of monopoly is rejected for 72 countries in the sample, whereas perfect competition is
rejected for 62 out of 101 countries. Note that the statistical tests, as usual, suffer from the
limitation that they are not mutually exclusive. For instance, while for some countries the
null hypothesis of monopolistic competition is not rejected, the null hypothesis of perfect
competition cannot be rejected either. This merely means that the statistical evidence
supporting either hypothesis is inconclusive.
Although we may expect to find a significant tendency of H towards the theoretical
value H = 1 when estimating from the price equation, the lower pane of Table 4 presents
a different picture. For instance, in the price model the null hypothesis H = 1 is rejected
even more often than in the revenue model. This is due to the fact that the misspecification
also affects the standard errors of H. Since they are substantially smaller in the revenue
model, some null hypotheses are rejected more often in the price model. As a consequence
of the misspecification, inference about the value of H based on the price equation often
leads to erroneous conclusions. For instance, for 20 countries the price model indicates
perfect competition (i.e. H0 : H = 1 is not rejected), whereas the revenue model rejects
this hypothesis. Similarly, for 32 cases H0 : H = 0 is rejected in favor of H1 : H 6= 0 in the
price model, whereas this hypothesis is not rejected according to the revenue specification.
6.3 Robustness check
One of the key assumptions underlying the P-R model is that the banks analyzed are in a
state of long-run competitive equilibrium (see Panzar and Rosse (1987) and Nathan and
Neave (1989)). In such a situation risk-adjusted rates of returns are equalized across banks,
and returns on assets (ROA) and returns on equity (ROE) are uncorrelated with input
prices in equilibrium. An empirical test for long-run competitive equilibrium is obtained
from the regression model in Equation (20), with the dependent variable replaced by ROA
or ROE. Testing for H0 : H = 0 (equilibrium) against H1 : H < 0 (disequilibrium) in this
model by means of a one-sided t-test provides a direct empirical way to test for long-run
17
equilibrium. Based on a one sided t-test applied to the model based on ROA, we reject
the null hypothesis of long-run equilibrium at a 5% significance level for 17 countries, or
roughly 17% of our sample.16
To ensure that the previously calculated averages of the H statistic are not contami-
nated by countries that are not in equilibrium, we recalculate the sample averages over the
group of countries in equilibrium.17 The resulting averages are very similar to the figures
in Table 4, which underlines the robustness of our findings.
Finally, as mentioned by Shaffer (1985), if the sample is not in long-run equilibrium,
negative values of the H statistic no longer prove monopoly. However, it remains true
that positive H values disprove monopoly or that conjectural variation rejects short-run
oligopoly. Hence, even though Canada has a negative H value, it is not in long-run equilib-
rium, so nothing can be said about its market structure. In all other countries that are not
in long-run equilibrium we reject the monopoly market hypothesis, since the estimation
results report positive values of H.
7 Conclusions
This paper discusses the specification of the P-R model, in particular the choice of the
dependent variable. Theoretical equations of the model under monopoly (or perfect cartel)
as well as oligopoly suggest that the dependent variable of the revenue equation should be
(the logarithm of) interest income or total income. That is, income in levels rather than
scaled with total assets. Scaling transforms the revenue equation into a price equation,
which introduces a bias towards perfect competition (H = 1) in the estimate of the
degree of competition (H). The misspecification also distorts statistical tests on the market
structure, as it makes particularly monopoly (H = 0) less likely. Similar misspecification16The countries not in equilibrium are Argentina, Australia, Canada, Columbia, Denmark, El Salvador,
France, Korea, Kuweit, Mexico, Monaco, Nigeria, Pakistan, Paraguay, Saudi Arabia, Sweden, Thailand,United States, and Uruguay. In terms of ROE we find very similar results. However, it is a well-knownresult, articulated by Granger (1998), that any null hypothesis will almost certainly be rejected for any verylarge data set. He advocates focusing more on the results’ economic significance than on their statisticalsignificance. Hence, we must interpret the results with some caution, in particular for countries with largenumbers of observations, such as the United States.
17More detailed results are available upon request.
18
occurs when total assets or another scaling factor is included in the P-R model as an
explanatory variable.
Empirical evidence for over 100 countries covering more than 100,000 bank-year ob-
servations provides overwhelming support for our theory of misspecification and confirms
the assumed bias in both the level of competition and the tests for market structure. The
correct specification results in a worldwide average value of H of about 0.50, with above
average values for North and South America and below-average values for the Middle East
and East and Central Europe. By contrast, the misspecified model produces estimates of
around 0.75. We find that monopolistic competition is the prevailing market structure in
the banking sector. It is rejected in only one of the 101 countries, namely China. Monopoly
or perfect cartel forming cannot be rejected in 28 of the countries analyzed (against 0%
in the misspecified model) and perfect competition cannot be rejected in 38% (against
20-30% with misspecification).
Our overview of the extensive literature on the P-R model reveals that all 28 stud-
ies considered suffer from the type of misspecification we address. That means that the
literature systematically overestimates the degree of competition in the banking industry.
19
References
Al-Muharrami, S., Mathews, K. and Khabari, Y. (2006). Market structure and competi-
tive conditions in the Arab GCC banking system. Cardiff Economic Working Papers. No
2006/8.
Bikker, J.A. (2004). Competition and efficiency in a unified European banking market,
Edward Elgar.
Bikker, J.A. and Groeneveld, J.M. (2000). Competition and concentration in the EU bank-
ing industry. Kredit und Kapital 30, 62-98.
Bikker, J.A and Haaf, K. (2002). Competition, concentration and their relationship: An
empirical analysis of the banking industry. Journal of Banking and Finance 26, pp. 2191-
2214.
Bikker, J.A. and Bos, J.W.B. (2005). Trends in competition and profitability in the banking
industry: a basic framework. Suerf Series 2005/2.
Bikker, J.A., L. Spierdijk, and P. Finnie (2006). The impact of bank size on market power.
DNB Working Paper 120, De Nederlandsche Bank, Amsterdam.
Casu, B. and Girardone, G. (2005). Bank competition, concentration and efficiency in
the single European market. University of Essex, Department of Accounting, Finance and
Management.
Claessens, S. and Laeven, L. (2004). What drives bank competition? Some international
evidence. Journal of Money, Credit and Banking 36, 563-584.
Coccorese, P. (1998). Assessing the competitive conditions in the Italian banking system:
some empirical evidence. Banca Nazionale del Lavoro Quarterly Review 51, pp. 171-191.
Coccorese, P. (2003). Banking competition and macroeconomic conditions: A disaggregate
analysis. Journal of International Financial Markets, Institutions and Money 14, pp. 203-
219.
20
Cowling, K. (1976), On the theoretical specification of industrial structure-performance
relationships. European Economic Review 8, 1-14.
Cowling, K. and Waterson, M. (1976). Price cost margins and market structure. Economica
43, pp. 267-274.
De Bandt, O. and Davis, E.P. (2000). Competition, contestability and market structure
in European banking sectors on the eve of EMU. Journal of Banking & Finance 24, pp.
1045-1066.
Drakos K. and Konstantinou, P. (2005). Competition and contestability in transition bank-
ing: An empirical analysis. South-Eastern Europe Journal of Economics 2, pp. 183-209.
Granger, C. (1998). Extracting information from mega panels and high frequency data.
Statistica Neerlandica 52, pp. 258-272.
Greene, W.H. (2000). Econometric Analysis, Fourth edition, Prentice Hall, London.
Gunalp, B. and Celik, T. (2006), Competition in the Turkish banking industry. Applied
Economics 38, pp. 1335-1342.
Hempell, H. (2002). Testing for competition among German banks. Economic Research
Centre of the Deutsche Bundesbank. Discussion paper 04/02.
Hondroyiannis, L., Lolos, S. and Papapetrou, E. (1999). Assessing competitive conditions
in the Greek banking system. Journal of International Financial Markets, Institutions &
Money 9, pp. 377-391.
Jiang, G., Wong, J., Tang, N. and Sze, A. (2004). Banking sector competition in Hong
Kong - Measurement and evolution over time. Hong Kong Monetary Authority.
Kishan, R.P. and Opiela, T.P. (2000), Bank size, bank capital and the bank lending chan-
nel. Journal of Money, Credit and Banking 32, pp. 121-141.
Koutsomanoli-Fillipaki, N. and Staikouras, C. (2005). Competition and concentration in
the new European banking landscape. Department of Accounting and Finance, Athens
21
University of Economics and Business.
Lang, G. (1997), Wettbewerbsverhalten deutscher Banken: Eine Panelanalyse auf Basis der
Rosse-Panzar Statistik, Jahrbuch fur Wirtschaftswissenschaften. Review of Economics 48,
pp. 21-38.
Lee, S. and Lee, J. (2005). Bank consolidation and bank competition: An empirical analysis
of the Korean banking industry. Bank of Korea Economic Papers 8, pp. 102-144.
Mamatzakis, E., Staikouras, C. and Koutsomanoli-Fillipaki, N. (2005). Competition and
concentration in the banking sector of the south eastern European region. Emerging Mar-
kets Review 6, pp. 192-209.
Mkrtchyan (2005). The evolution of competition in banking in a transition economy: an
application of the Panzar-Rosse model to Armenia. European Journal of Comparative
Economics 2, pp. 67-82.
Molyneux, P., Lloyd-Williams, D.M. and Thornton, J. (1994). Competitive conditions in
European banking. Journal of Banking and Finance 18, pp. 445-459.
Molyneux, P., Thornton, J. and Lloyd-Williams, D.M. (1996). Competition and market
contestability in Japanese commercial banking. Journal of Economics and Business 48, pp.
33-45.
Murjan, W. and Ruza, C. (2002). The competitive nature of the Arab Middle Eastern
banking markets. International Advances in Economic Research 8, pp. 267-274.
Nathan, A. and Neave, E.H. (1989). Competition and contestability in Canada’s financial
system: empirical results. Canadian Journal of Economics 3, pp. 576-594.
Panzar, J.C. and J.N. Rosse (1982). Structure, conduct and comparative statistics. Bell
Laboratories Economic Discussion Paper.
Panzar, J. and Rosse, J. (1987). Testing for ‘Monopoly’ Equilibrium. Journal of Industrial
Economics 35, pp. 443-456.
22
Resti, A. (1997). Evaluating the cost-efficiency of the Italian banking system: what can be
learnt from the joint application of parametric and non-parametric techniques. Journal of
Banking & Finance 21, pp. 221-250.
Rime, B. (1999). Mesure de degre de concurrence dans le systeme bancaire Suisse a l’aide
du modele de Panzar et Rosse. Revue Suisse d’Economie Politique et de Statistique 135,
pp. 21-40.
Rosse, J. and Panzar, J. (1977). Chamberlin vs Robinson: an empirical study for monopoly
rents, Bell Laboratories Economic Discussion Paper.
Shaffer, S. (1982). A non-structural test for competition in financial markets. Proceedings
of a Conference on Bank Structure and Competition, Federal Reserve Bank of Chicago.
pp. 225-243.
Shaffer, S. (2002). Conduct in bank monopoly. Review of Economic Organization 20, pp.
221-238.
Stigler, G. (1964). A Theory of Oligopoly. Journal of Political Economy, 72, pp. 44-61.
Vesala, J. (1995). Testing for competition in banking: behavioral evidence from Finland.
Bank of Finland Studies.
Yeyati, E. and Micco, A. (2003). Banking competition in Latin America. Latin American
Competition Forum.
Yildirim, H.S, Philippatos, G.C. (2006). A note on restructuring, consolidation and compe-
tition in Latin American banking markets. Forthcoming Journal of Banking and Finance.
White, H. (1980). Heteroskedasticity consistent covariance matrix estimator and a direct
test for heteroskedasticity. Econometrica, 48, pp. 817-838.
23
Table
1:Sum
mary
ofth
ePanzar-R
oss
elite
ratu
re
auth
ors
dependent
scaling
years
countr
ies
avg.
Hresu
lts
Shaffer
(1982)
lnII
lnTA
1979
New
York
MC
Nath
an
and
Nea
ve
(1989)
lnT
Iln
TA
1982/84
Canada
0.8
21982:P
C;198384:re
stM
CM
oly
neu
xet
al.
(1994)
ln(I
I/TA
)ln
TA
1986/89
Fra
nce
,G
erm
any,
Italy
0.3
7M
:It
aly
;M
C:Fra
nce
,G
erm
any,
Spain
and
UK
Spain
,U
KVes
ala
(1995)
lnII
lnE
Q,ln
FA
1985/92
Fin
land
0.5
81989-1
990:M
;re
stM
CM
oly
neu
xet
al.
(1996)
lnII
lnTA
,ln
TD
1986/88
Japan
0.1
71986:M
;1988:M
CLang
(1997)
lnT
Iln
TA
1998/92
Ger
many
MC
Cocc
ore
se(1
998)
lnT
Iln
TD
1988/96
Italy
0.7
4M
CR
ime
(1999)
lnII
lnTA
1987/94
Sw
itze
rland
0.7
7M
CH
ondro
yia
nnis
etal.
(1999)
ln(T
I/TA
)ln
TA
1993/95
Gre
ece
0.1
8M
CB
ikker
and
Gro
enev
eld
(2000)
ln(I
I/TA
)ln
TA
1989/96
15
EU
countr
ies
0.8
2M
CD
eB
andt
and
Davis
(2000)
lnII
,ln
EQ
,1992/96
Fra
nce
,G
erm
any
and
Italy
0.2
8M
C:la
rge
banks;
small
banks:
lnT
Iln
FA
CB
NE
AM
Cin
Italy
;M
inFra
nce
,G
erm
any
Hem
pel
l(2
002)
ln(T
I/TA
)N
/A
1993/98
Ger
many
0.6
8M
CShaffer
(2002)
1984/99
Jayto
n,Tex
as
MC
Bik
ker
and
Haaf(2
002)
ln(I
I/TA
)ln
TA
1988/98
23
OE
CD
countr
ies
0.7
MC
Cocc
ore
se(2
003)
lnII
or
lnT
Iln
TA
1997/99
Italy
0.9
2M
CM
urj
an
and
Ruza
(2002)
lnII
lnTA
,ln
EQ
1993/97
Ara
bM
iddle
East
0.2
2M
CYey
ati
and
Mic
co(2
003)
ln(T
I/TA
)ln
TA
1993/02
Lati
nA
mer
ica
0.6
PC
:C
hile;
MC
:A
rgen
tina,B
razi
l,C
olo
mbia
,C
ost
aR
ica,Per
u,E
lSalv
ador
Cla
esse
ns
and
Lea
ven
(2004)
ln(I
I/TA
)and
ln(T
I/TA
)ln
TA
1994/2001
50
countr
ies
0.6
9M
CJia
ng
etal.
(2004)
1)
ln(T
I/TA
)1)
None
1992/2002
Hong
Kong
0.9
1P
C2)
lnT
I2)
lnTA
Mam
atz
akis
etal.
(2004)
ln(I
I/TA
)or
ln(T
I/TA
)N
/A
1998/2002
South
-East
ern
0.7
3M
CE
uro
pea
nco
untr
ies
Dra
kos
and
Konst
anti
nou
(2005)
lnT
Iln
TA
1992/2000
Form
erSovie
tU
nio
n0.3
2N
E:Latv
ia,U
kra
ine;
MC
:re
stM
krt
chyan
(2005)
ln(I
I/TA
)ln
TA
1998/2002
Arm
enia
0.6
9M
CC
asu
and
Gir
ard
one
(2005)
ln(T
I/TA
)ln
TA
1997/2003
EU
15
0.3
6M
CLee
and
Lee
(2005)
1)
ln(I
I/TA
)1)
None
1992/2002
Kore
a0.4
7M
C(d
ecre
asi
ng
com
pet
itiv
ele
vel
s)2)
ln(T
I/TA
)2)
None
3)
lnII
3)
lnTA
4)
lnT
I4)
lnTA
24
Table
1–
conti
nued
from
previo
us
page
auth
ors
dependent
scaling
years
countr
ies
avg.
Hresu
lts
Yildir
imand
Philip
pato
s(2
005)
ln(T
I/TA
)ln
TA
,ln
EQ
,1993/2000
11
Lati
nA
mer
ican
0.7
1M
Cln
FA
countr
ies
Kouts
om
anoli-F
illipaki
ln(I
I/TA
)or
ln(T
I/TA
)N
one
1998/2002
EU
10
vs.
EU
15
0.5
8M
C&
Sta
ikoura
s(2
005)
Al-M
uharr
am
iet
al.
(2006)
lnT
Iln
TA
1993/2002
Ara
bG
CC
countr
ies
0.6
2P
C:K
uw
ait
,SaudiA
rabia
,U
AE
;M
C:B
ahra
in,Q
ata
r;M
:O
man:(a
ppro
x.)
Gunalp
and
Cel
ik(2
006)
lnII
or
lnT
Iln
TA
1990/2000
Turk
ey0.3
7M
C
Nota
tion:
II(i
nte
rest
inco
me)
,TA
(tota
lass
ets)
,T
I(t
ota
lin
com
e),E
Q(e
quity),
FA
(fixed
ass
ets)
,T
D(t
ota
ldep
osi
ts),
FA
CB
NE
A(fi
xed
ass
ets,
cash
and
due
from
banks,
oth
ernon-e
arn
ing
ass
ets)
;M
(monopoly
),M
C(m
onopolist
icco
mpet
itio
n),
PC
(per
fect
com
pet
itio
n),
NE
(no
equilib
rium
).
Average
valu
es
of
Hst
ati
stic
sin
the
lite
ratu
re
This
pane
report
sth
eaver
age
valu
esof
Hover
vari
ous
studie
s,dis
tinguis
hin
gbet
wee
ndiff
eren
tch
oic
esofdep
enden
tand
scaling
vari
able
s.
lnII
aver
age
(tota
l)ln
(II/
TA
)aver
age
(tota
l)ln
TI
aver
age
(tota
l)ln
(TI/
TA
)aver
age
(tota
l)
wit
hln
TA
0.4
9(6
)w
ith
lnTA
0.6
5(4
)w
ith
lnTA
0.6
4(8
)w
ith
lnTA
0.5
5(4
)w
ith
lnE
Q0.4
0(2
)w
ith
lnE
Q-
wit
hln
EQ
-w
ith
lnE
Q0.7
1(1
)no
lnE
Q0.5
8(4
)no
lnE
Q0.6
5(4
)no
lnE
Q0.6
4(8
)no
lnE
Q0.3
8(3
)
wit
hout
lnTA
-w
ithout
lnTA
0.6
3(3
)w
ithout
lnTA
-w
ithout
lnTA
0.6
7(5
)w
ith
lnE
Q-
wit
hln
EQ
-w
ith
lnE
Q-
wit
hln
EQ
no
lnE
Q-
no
lnE
Q0.6
3(3
)no
lnE
Q-
no
lnE
Q0.6
7(5
)
Nota
tion:
II(i
nte
rest
inco
me)
,TA
(tota
lass
ets)
,T
I(t
ota
lin
com
e),E
Q(e
quity).
The
tota
lnum
ber
ofst
udie
sis
inpare
nth
eses
.
25
Table 2: Data sample
This table displays the countries included in the sample, as well as the country ID’s, the data period, the numberof banks, and the number of observations considered for each country.
country ID period # # country ID period # #banks obs. banks obs.
Algeria DZ 1987 2004 10 51 Lebanon LB 1990 2004 63 492Andorra AD 1988 2004 9 75 Liechtenstein LI 1989 2004 12 80Arab Emirates AE 1989 2004 17 120 Lithuania LT 1993 2004 13 67Argentina AR 1990 2004 122 448 Luxembourg LU 1988 2004 140 1,340Armenia AM 1996 2004 14 59 Macau MO 1992 2004 9 60Australia AU 1987 2005 41 240 Macedonia MK 1992 2004 14 63Austria AT 1987 2004 205 1,339 Malaysia MY 1992 2005 46 337Azerbaijan AZ 1996 2004 12 50 Malta MT 1989 2004 10 62Bahamas BS 1991 2004 38 68 Mauritius MU 1991 2004 12 50Bahrain BH 1988 2004 12 117 Mexico MX 1989 2004 49 112Bangladesh BD 1992 2004 33 270 Moldova MD 1993 2004 13 61Belgium BE 1987 2004 92 596 Monaco MC 1992 2004 14 135Bermuda BM 1989 2004 5 53 Morocco MA 1987 2004 14 72Bolivia BO 1991 2004 16 136 Mozambique MZ 1992 2004 12 51Botswana BW 1990 2004 6 50 Nepal NP 1992 2004 15 90Brazil BR 1990 2004 176 900 Netherlands NL 1987 2004 63 375Canada CA 1987 2004 68 536 New Zealand NZ 1987 2004 10 89Cayman Isl. KY 1992 2004 27 58 Nigeria NG 1989 2005 72 319Chile CL 1988 2004 36 232 Norway NO 1987 2004 68 417China PR CN 1988 2004 60 52 Oman OM 1988 2004 9 78Colombia CO 1989 2004 40 293 Pakistan PK 1988 2004 25 207Costa Rica CR 1991 2004 52 174 Panama PA 1989 2004 94 131Cote d’Ivoire CI 1992 2004 12 56 Paraguay PY 1990 2004 26 189Croatia HR 1991 2004 58 280 Peru PE 1991 2004 26 186Cyprus CY 1989 2004 20 113 Philippines PH 1988 2004 49 369Czech Rep. CZ 1989 2004 35 210 Poland PL 1992 2004 59 261Denmark DK 1988 2004 103 976 Portugal PT 1988 2004 33 290Dominican Rep. DO 1991 2004 31 170 Romania RO 1993 2004 34 135Ecuador EC 1987 2004 29 120 Russian Fed. RU 1992 2004 233 632El Salvador SV 1993 2004 14 72 Saudi Arabia SA 1987 2004 11 142Estonia EE 1993 2004 12 58 Senegal SN 1993 2004 10 50Finland FI 1988 2004 14 110 Singapore SG 1987 2004 27 93France FR 1986 2004 440 3,641 Slovakia SK 1990 2004 24 102Germany DE 1987 2004 2327 19,137 Slovenia SI 1993 2004 28 109Ghana GH 1991 2004 16 87 South Africa ZA 1987 2004 39 189Greece GR 1988 2004 28 162 Spain ES 1988 2004 171 1,513Hong Kong HK 1988 2004 44 329 Sri Lanka LK 1992 2004 12 72Hungary HU 1989 2004 31 136 Sweden SE 1987 2004 93 417Iceland IS 1990 2004 29 100 Switzerland CH 1987 2004 433 2,818India IN 1989 2004 78 648 Taiwan TW 1988 2005 46 69Indonesia ID 1987 2004 106 696 Thailand TH 1988 2004 19 153Ireland IE 1988 2004 40 219 Trinidad & Tobago TT 1992 2004 11 74Israel IL 1988 2004 18 145 Turkey TR 1987 2004 54 210Italy IT 1987 2004 829 6149 Ukraine UA 1993 2004 47 181Japan JP 1987 2004 781 3,028 United Kingdom GB 1987 2005 194 1,007Jordan JO 1989 2004 11 115 United States US 1989 2004 9534 54,466Kazakhstan KZ 1993 2004 27 114 Uruguay UY 1990 2004 44 154Kenya KE 1989 2004 49 188 Venezuela VE 1987 2004 57 280Korea KR 1991 2004 33 108 Vietnam VN 1991 2004 24 135Kuwait KW 1988 2004 6 77 Zambia ZM 1990 2004 11 57Latvia LV 1992 2004 29 141
26
Table
3:Est
imate
dvalu
esofH
base
don
diff
erentm
odelsp
ecifi
cati
ons
countr
yln
IIln
(II/
TA
)ln
II(+
lnTA
)ln
TI
ln(T
I/TA
)ln
TI
(+ln
TA
)
Hσ(H
)H
σ(H
)H
σ(H
)H
σ(H
)H
σ(H
)H
σ(H
)
Alg
eria
0.2
4616
0.5
18
0.7
064
0.1
86
0.6
558
0.2
26
0.2
2416
0.4
69
0.6
842
0.1
47
0.6
222
0.1
78
Andorr
a0.8
914
0.0
65
0.8
784
0.0
75
0.8
762
0.0
87
0.8
592
0.0
59
0.8
452
0.0
62
0.8
442
0.0
66
Ara
bE
mir
ate
s0.4
232
0.1
07
0.6
242
0.1
25
0.5
982
0.1
16
0.4
202
0.1
08
0.6
222
0.1
27
0.5
972
0.1
18
Arg
enti
na
0.4
122
0.1
57
0.8
224
0.0
92
0.7
852
0.0
85
0.3
502
0.1
65
0.7
642
0.0
90
0.7
282
0.0
85
Arm
enia
0.5
132
0.2
36
0.7
014
0.2
31
0.6
858
0.2
39
0.4
742
0.2
27
0.6
614
0.2
35
0.6
244
0.2
38
Aust
ralia
0.5
618
0.2
98
0.8
712
0.0
37
0.8
722
0.0
39
0.5
558
0.3
01
0.8
652
0.0
41
0.8
692
0.0
42
Aust
ria
0.0
6614
0.1
38
0.7
502
0.0
34
0.7
312
0.0
37
0.0
9114
0.1
38
0.7
752
0.0
29
0.7
662
0.0
31
Aze
rbaijan
0.1
1014
0.4
35
0.6
152
0.1
66
0.6
648
0.1
82
0.2
3316
0.4
24
0.7
384
0.1
37
0.7
764
0.1
47
Baham
as
0.5
312
0.1
49
0.7
452
0.0
71
0.8
022
0.0
81
0.3
722
0.0
96
0.5
852
0.0
93
0.5
872
0.1
15
Bahra
in0.5
2116
0.3
89
0.7
094
0.1
49
0.6
848
0.1
54
0.5
4616
0.4
06
0.7
342
0.1
28
0.7
192
0.1
38
Bangla
des
h0.9
834
0.0
90
0.9
664
0.0
64
0.9
688
0.0
65
0.9
914
0.0
92
0.9
744
0.0
68
0.9
754
0.0
69
Bel
giu
m0.4
922
0.1
46
0.8
802
0.0
36
0.8
672
0.0
35
0.4
842
0.1
46
0.8
722
0.0
34
0.8
552
0.0
32
Ber
muda
0.7
552
0.1
13
0.7
642
0.1
08
0.7
828
0.1
10
0.7
752
0.0
92
0.7
832
0.0
86
0.7
982
0.0
85
Bolivia
0.9
874
0.1
01
0.8
564
0.0
74
0.9
062
0.0
74
0.9
774
0.0
98
0.8
452
0.0
71
0.8
944
0.0
71
Bots
wana
0.0
8414
0.3
12
0.4
812
0.1
65
0.6
192
0.1
48
0.1
4514
0.2
91
0.5
412
0.1
48
0.6
712
0.1
32
Bra
zil
0.3
152
0.1
01
0.7
752
0.0
42
0.7
322
0.0
39
0.3
702
0.1
03
0.8
292
0.0
36
0.8
032
0.0
34
Canada
-0.0
1114
0.2
18
0.7
922
0.0
40
0.8
002
0.0
40
-0.0
0114
0.2
21
0.8
022
0.0
42
0.8
122
0.0
42
Caym
an
Isla
nds
0.5
8816
0.3
82
0.7
932
0.0
73
0.7
982
0.0
81
0.4
3416
0.3
95
0.6
382
0.0
92
0.6
472
0.1
03
Chile
0.9
544
0.1
45
0.8
974
0.0
96
0.9
078
0.1
03
0.8
314
0.1
30
0.7
742
0.0
67
0.7
852
0.0
67
Chin
aP
R1.5
651
0.2
00
0.8
134
0.1
33
0.9
188
0.1
20
1.5
321
0.1
98
0.7
804
0.1
34
0.8
734
0.1
24
Colo
mbia
0.5
574
0.2
38
0.7
882
0.0
64
0.7
582
0.0
58
0.5
404
0.2
38
0.7
712
0.0
63
0.7
392
0.0
56
Cost
aR
ica
1.0
824
0.3
05
0.8
832
0.0
57
0.8
782
0.0
62
1.0
834
0.3
05
0.8
842
0.0
57
0.8
792
0.0
61
Cote
d’Ivoir
e0.3
912
0.1
67
0.4
502
0.1
65
0.4
392
0.0
97
0.4
582
0.1
75
0.5
162
0.1
71
0.5
022
0.1
08
Cro
ati
a0.4
352
0.1
24
0.5
422
0.0
63
0.5
462
0.0
63
0.4
582
0.1
27
0.5
652
0.0
65
0.5
682
0.0
64
Cypru
s-0
.11014
0.3
66
1.0
024
0.1
22
0.9
668
0.1
14
-0.2
7614
0.3
81
0.8
374
0.1
13
0.8
904
0.1
27
Cze
chR
epublic
0.7
704
0.3
14
0.8
364
0.0
88
0.8
372
0.0
92
0.7
324
0.3
09
0.7
982
0.0
90
0.7
982
0.0
94
Den
mark
0.3
342
0.0
44
0.7
392
0.0
38
0.7
232
0.0
38
0.2
942
0.0
47
0.6
982
0.0
37
0.6
932
0.0
38
Dom
inic
an
Rep
ublic
0.7
084
0.3
09
0.9
204
0.1
14
0.9
258
0.1
12
0.5
578
0.2
93
0.7
692
0.0
75
0.7
712
0.0
75
Ecu
ador
0.6
2916
0.6
31
0.7
524
0.1
29
0.7
402
0.1
42
0.5
9616
0.6
46
0.7
192
0.1
33
0.7
112
0.1
45
ElSalv
ador
0.4
102
0.1
07
0.3
902
0.0
70
0.3
952
0.0
74
0.4
112
0.1
06
0.3
922
0.0
68
0.3
962
0.0
72
Est
onia
0.4
5316
0.2
92
0.7
244
0.2
38
0.7
258
0.2
41
0.4
4616
0.2
85
0.7
174
0.2
37
0.7
264
0.2
39
Fin
land
-0.2
7414
0.5
31
0.8
032
0.0
71
0.8
102
0.0
84
-0.3
0514
0.5
13
0.7
732
0.0
85
0.7
542
0.0
86
Fra
nce
0.5
992
0.0
78
0.7
162
0.0
19
0.7
112
0.0
22
0.5
392
0.0
80
0.6
562
0.0
19
0.6
522
0.0
21
Ger
many
0.6
452
0.0
66
0.7
912
0.0
15
0.7
882
0.0
16
0.6
462
0.0
65
0.7
902
0.0
12
0.7
872
0.0
13
Ghana
0.6
474
0.2
83
0.7
562
0.1
14
0.7
578
0.1
10
0.6
544
0.2
80
0.7
642
0.1
12
0.7
642
0.1
08
Gre
ece
0.5
122
0.1
21
0.8
292
0.0
65
0.8
258
0.0
65
0.5
722
0.1
24
0.8
894
0.0
74
0.8
774
0.0
75
27
Table
3–
conti
nued
from
previo
us
page
countr
yln
IIln
(II/
TA
)ln
II(+
lnTA
)ln
TI
ln(T
I/TA
)ln
TI
(+ln
TA
)
Hσ(H
)H
σ(H
)H
σ(H
)H
σ(H
)H
σ(H
)H
σ(H
)
Hong
Kong
0.0
0214
0.4
30
0.5
752
0.0
74
0.5
752
0.0
75
-0.0
0114
0.4
30
0.5
732
0.0
78
0.5
732
0.0
78
Hungary
0.1
6514
0.2
61
0.7
472
0.1
01
0.7
832
0.1
01
0.1
7414
0.2
58
0.7
562
0.0
97
0.7
862
0.0
98
Icel
and
-0.1
4416
0.6
37
0.8
604
0.1
36
0.7
948
0.1
33
-0.1
4516
0.6
40
0.8
604
0.1
33
0.7
944
0.1
31
India
0.4
782
0.1
09
0.7
362
0.0
22
0.7
212
0.0
25
0.4
502
0.1
14
0.7
082
0.0
19
0.7
052
0.0
22
Indones
ia0.0
6514
0.1
28
0.7
472
0.0
41
0.7
332
0.0
42
0.0
1614
0.1
27
0.6
992
0.0
43
0.6
762
0.0
43
Irel
and
1.1
134
0.3
39
0.8
984
0.0
61
0.8
938
0.0
59
1.0
734
0.3
38
0.8
582
0.0
66
0.8
542
0.0
63
Isra
el0.1
1514
0.3
94
0.7
134
0.1
56
0.7
412
0.1
58
0.1
2014
0.3
87
0.7
184
0.1
48
0.7
434
0.1
51
Italy
0.0
9414
0.0
90
0.7
602
0.0
17
0.7
522
0.0
18
0.0
8314
0.0
89
0.7
482
0.0
18
0.7
452
0.0
19
Japan
0.4
962
0.0
56
0.5
672
0.0
30
0.5
632
0.0
30
0.4
982
0.0
57
0.5
692
0.0
33
0.5
642
0.0
33
Jord
an
0.2
712
0.0
95
0.5
902
0.0
70
0.5
202
0.0
76
0.2
722
0.0
94
0.5
912
0.0
69
0.5
192
0.0
74
Kaza
khst
an
0.2
5314
0.3
50
0.5
792
0.0
84
0.5
712
0.0
82
0.2
6914
0.3
40
0.5
942
0.0
97
0.5
832
0.0
95
Ken
ya
0.7
874
0.2
78
0.6
632
0.0
81
0.6
562
0.0
72
0.7
864
0.2
74
0.6
612
0.0
78
0.6
572
0.0
71
Kore
a0.5
1116
0.4
57
0.6
422
0.0
37
0.6
432
0.0
39
0.5
2816
0.4
56
0.6
582
0.0
38
0.6
602
0.0
40
Kuw
ait
0.6
954
0.2
46
0.9
264
0.1
26
0.9
548
0.1
18
0.6
944
0.2
46
0.9
244
0.1
25
0.9
524
0.1
17
Latv
ia0.5
662
0.1
10
0.9
064
0.0
83
0.8
448
0.0
82
0.5
562
0.1
22
0.8
974
0.1
03
0.8
334
0.1
02
Leb
anon
0.4
372
0.0
71
0.7
352
0.0
46
0.7
232
0.0
46
0.4
252
0.0
73
0.7
222
0.0
46
0.7
142
0.0
47
Lie
chte
nst
ein
0.7
104
0.1
52
1.0
284
0.1
18
0.8
918
0.1
39
0.7
534
0.1
97
1.0
714
0.2
07
0.8
134
0.2
01
Lit
huania
0.4
5216
0.5
03
0.8
684
0.2
30
0.8
598
0.2
60
0.4
5416
0.4
97
0.8
704
0.2
34
0.8
524
0.2
66
Luxem
bourg
0.3
092
0.1
01
0.8
632
0.0
24
0.8
682
0.0
25
0.2
982
0.1
01
0.8
522
0.0
25
0.8
522
0.0
26
Maca
u0.3
716
0.2
20
0.7
002
0.1
41
0.6
682
0.1
39
0.3
786
0.2
19
0.7
072
0.1
33
0.6
772
0.1
31
Mace
donia
1.0
814
0.3
09
0.7
624
0.1
44
0.6
492
0.1
33
0.8
754
0.3
20
0.5
562
0.1
62
0.4
732
0.1
57
Mala
ysi
a0.7
282
0.1
29
0.9
002
0.0
45
0.9
112
0.0
49
0.7
272
0.1
30
0.8
982
0.0
42
0.9
104
0.0
47
Malt
a-0
.21814
0.2
41
0.8
022
0.0
77
0.7
452
0.0
84
-0.1
5714
0.2
33
0.8
644
0.0
99
0.7
702
0.1
01
Mauri
tius
0.5
808
0.3
11
0.8
532
0.0
62
0.8
878
0.0
58
0.5
968
0.3
16
0.8
694
0.0
82
0.9
014
0.0
78
Mex
ico
0.8
464
0.3
49
0.8
654
0.2
29
0.8
648
0.2
56
0.8
054
0.3
19
0.8
244
0.1
29
0.8
244
0.1
39
Mold
ova
0.6
382
0.1
15
0.6
692
0.0
56
0.6
682
0.0
55
0.6
172
0.1
00
0.6
482
0.0
67
0.6
432
0.0
58
Monaco
0.3
766
0.2
16
0.8
362
0.0
50
0.8
352
0.0
50
0.3
616
0.2
15
0.8
202
0.0
47
0.8
142
0.0
47
Moro
cco
0.1
9714
0.1
32
0.2
482
0.0
88
0.2
352
0.0
92
0.3
742
0.1
28
0.4
242
0.0
57
0.4
182
0.0
63
Moza
mbiq
ue
0.5
188
0.3
08
0.4
1916
0.3
05
0.3
9610
0.3
10
0.5
238
0.2
69
0.4
2414
0.2
65
0.4
0214
0.2
68
Nep
al
0.5
934
0.2
12
0.9
594
0.1
24
0.9
688
0.1
14
0.6
034
0.2
12
0.9
694
0.1
26
0.9
754
0.1
15
Net
her
lands
0.7
794
0.1
97
0.8
382
0.0
41
0.8
382
0.0
42
0.8
014
0.1
95
0.8
592
0.0
39
0.8
592
0.0
39
New
Zea
land
0.3
5314
0.2
28
0.7
602
0.0
96
0.7
362
0.1
13
0.3
5614
0.2
26
0.7
632
0.0
96
0.7
362
0.1
12
Nig
eria
0.6
802
0.0
56
0.7
362
0.0
48
0.7
312
0.0
46
0.6
732
0.0
58
0.7
302
0.0
55
0.7
262
0.0
54
Norw
ay
0.4
742
0.0
87
0.8
332
0.0
42
0.7
972
0.0
44
0.4
732
0.0
88
0.8
322
0.0
41
0.7
952
0.0
43
Om
an
0.3
872
0.0
73
0.5
132
0.0
33
0.4
882
0.0
31
0.3
872
0.0
74
0.5
132
0.0
33
0.4
882
0.0
31
Pakis
tan
0.4
706
0.2
61
0.7
242
0.0
68
0.7
342
0.0
64
0.4
576
0.2
61
0.7
102
0.0
74
0.7
192
0.0
70
Panam
a0.5
772
0.1
04
0.6
252
0.0
55
0.6
262
0.0
55
0.5
782
0.1
02
0.6
262
0.0
53
0.6
262
0.0
52
28
Table
3–
conti
nued
from
previo
us
page
countr
yln
IIln
(II/
TA
)ln
II(+
lnTA
)ln
TI
ln(T
I/TA
)ln
TI
(+ln
TA
)
Hσ(H
)H
σ(H
)H
σ(H
)H
σ(H
)H
σ(H
)H
σ(H
)
Para
guay
0.6
212
0.0
71
0.6
902
0.0
53
0.6
772
0.0
49
0.6
132
0.0
72
0.6
822
0.0
59
0.6
662
0.0
54
Per
u0.6
342
0.1
51
0.9
314
0.0
97
0.8
822
0.0
93
0.6
622
0.1
51
0.9
584
0.0
97
0.9
084
0.0
92
Philip
pin
es0.6
572
0.0
93
0.7
152
0.0
55
0.7
212
0.0
54
0.6
602
0.0
93
0.7
182
0.0
55
0.7
242
0.0
55
Pola
nd
0.0
8314
0.2
08
0.7
832
0.0
58
0.7
862
0.0
56
0.0
7614
0.2
06
0.7
762
0.0
56
0.7
762
0.0
54
Port
ugal
-0.1
5314
0.2
06
0.8
422
0.0
40
0.8
012
0.0
38
-0.3
7014
0.2
01
0.6
252
0.0
62
0.6
052
0.0
66
Rom
ania
0.6
404
0.2
17
0.7
984
0.1
45
0.7
778
0.1
41
0.6
624
0.2
13
0.8
204
0.1
45
0.7
974
0.1
40
Russ
ian
Fed
erati
on
0.3
992
0.0
89
0.6
332
0.0
49
0.6
202
0.0
48
0.4
332
0.0
67
0.6
692
0.0
42
0.6
402
0.0
39
SaudiA
rabia
0.4
742
0.1
44
0.6
052
0.1
46
0.5
712
0.1
50
0.3
192
0.1
04
0.4
502
0.1
01
0.4
072
0.0
92
Sen
egal
1.0
564
0.2
75
1.1
434
0.2
13
1.0
958
0.2
45
1.0
264
0.2
72
1.1
134
0.2
15
1.0
684
0.2
40
Sin
gapore
0.3
2916
0.6
86
0.6
712
0.0
58
0.6
752
0.0
61
0.3
2216
0.6
88
0.6
632
0.0
56
0.6
662
0.0
58
Slo
vakia
0.2
712
0.1
21
0.5
942
0.0
79
0.5
792
0.0
87
0.2
712
0.1
20
0.5
942
0.0
54
0.5
592
0.0
65
Slo
ven
ia0.3
822
0.1
86
0.7
062
0.0
79
0.6
472
0.0
72
0.3
822
0.1
85
0.7
062
0.0
80
0.6
472
0.0
73
South
Afr
ica
0.8
8016
0.9
40
0.5
852
0.1
01
0.5
942
0.1
09
0.9
5316
0.9
28
0.6
582
0.0
83
0.6
652
0.0
86
Spain
0.8
684
0.2
80
0.7
792
0.0
40
0.7
802
0.0
46
0.8
124
0.2
84
0.7
222
0.0
35
0.7
232
0.0
40
Sri
Lanka
0.6
904
0.3
38
0.8
664
0.1
40
0.8
868
0.1
30
0.6
874
0.3
38
0.8
634
0.1
41
0.8
834
0.1
30
Sw
eden
0.4
396
0.2
44
0.6
902
0.0
64
0.7
012
0.0
61
0.4
406
0.2
45
0.6
912
0.0
65
0.7
022
0.0
61
Sw
itze
rland
0.8
614
0.0
80
0.5
552
0.0
34
0.5
742
0.0
32
0.9
674
0.0
81
0.6
612
0.0
47
0.6
902
0.0
45
Taiw
an
0.9
284
0.1
15
0.9
114
0.0
79
0.9
118
0.0
78
0.9
274
0.1
14
0.9
114
0.0
78
0.9
104
0.0
77
Thailand
0.5
242
0.1
43
0.5
802
0.1
20
0.5
892
0.1
20
0.5
282
0.1
45
0.5
842
0.1
23
0.5
932
0.1
23
Tri
nid
ad
and
Tobago
0.0
8214
0.2
07
0.3
732
0.1
39
0.3
292
0.1
22
0.0
9814
0.2
05
0.3
892
0.1
35
0.3
392
0.1
16
Turk
ey0.3
8416
0.3
16
0.6
512
0.0
94
0.6
632
0.0
93
0.4
2714
0.2
91
0.6
942
0.0
60
0.7
002
0.0
59
Ukra
ine
0.4
742
0.1
16
0.7
232
0.0
90
0.6
332
0.0
82
0.4
862
0.1
15
0.7
352
0.0
95
0.6
412
0.0
84
Unit
edK
ingdom
0.7
704
0.1
30
0.7
762
0.0
35
0.7
762
0.0
36
0.7
764
0.1
31
0.7
822
0.0
35
0.7
812
0.0
36
Unit
edSta
tes
0.4
902
0.0
36
0.5
832
0.0
08
0.5
832
0.0
07
0.5
122
0.0
36
0.6
042
0.0
08
0.6
052
0.0
08
Uru
guay
0.5
202
0.1
08
0.8
744
0.0
96
0.8
462
0.0
98
0.5
062
0.0
90
0.8
602
0.0
70
0.8
372
0.0
70
Ven
ezuel
a0.7
914
0.2
21
0.7
432
0.0
94
0.7
472
0.1
04
0.7
904
0.2
19
0.7
412
0.0
93
0.7
452
0.1
04
Vie
tnam
0.7
362
0.1
12
0.7
742
0.0
67
0.7
712
0.0
66
0.7
352
0.1
11
0.7
732
0.0
66
0.7
692
0.0
65
Zam
bia
0.4
972
0.1
42
0.5
322
0.1
28
0.5
312
0.1
26
0.4
852
0.1
39
0.5
192
0.1
20
0.5
202
0.1
19
avg.adj.
R2
0.9
00.8
40.9
90.8
90.8
10.9
9
This
table
report
ses
tim
ate
dvalu
esof
H(d
enote
dby
H)
and
corr
espondin
gst
andard
erro
rs(σ
(H))
for
each
ofth
esi
xm
odel
spec
ifica
tions.
The
model
sden
ote
dby
‘ln
II(+
lnTA
)’and
‘ln
TI
(+ln
TA
)’re
fer
toth
esp
ecifi
cati
on
wit
h,re
spec
tivel
y,ln
IIand
lnT
Ias
the
dep
enden
tvari
able
and
lnTA
as
the
scaling
vari
able
.T
he
num
ber
sin
super
scri
pt
refe
rto
the
follow
ing
resu
lts
regard
ing
hypoth
esis
test
ing
(at
a5%
signifi
cance
level
):1−
8:re
ject
ion
ofm
onopoly
;1−
4,9−
12:re
ject
ion
of
H=
0(m
onopoly
acc
ord
ing
toth
ein
feri
or
test
),odd
num
ber
s:re
ject
ion
ofper
fect
com
pet
itio
n;1,2
,5,6
,9,1
0,1
3,1
4:re
ject
ion
ofm
onopolist
icco
mpet
itio
n,16:no
hypoth
esis
reje
cted
.
29
Table 4: Sample statistic for estimated H statistic
For each of the six model specifications, the upper panel of this table summarizes some sample statistics for Hbased on the sample of 101 countries. The middle panel reports the correlations (and corresponding asymptoticstandard errors) between the estimates of H obtained in the different models. The lower panel contains the resultsof market structure hypothesis testing and reports the number of times a particular null hypothesis is rejected ineach of the six model specifications.
dependent scaling avg. H std. dev. H avg. std. dev. Hvariable variable
ln II none 0.504 0.315 0.224ln(II/TA) none 0.742 0.148 0.090ln II ln TA 0.734 0.147 0.091ln TI none 0.495 0.315 0.221ln(TI/TA) none 0.732 0.138 0.087ln TI ln TA 0.722 0.139 0.087
models corr. in H’s std. dev. corr.
ln II and ln(II/TA) 0.30 0.09
ln II and ln II with scaling 0.34 0.09
ln TI and ln(TI/TA) 0.29 0.08
ln TI and ln TI with scaling 0.32 0.09
null hypothesis
dependent scaling ‘monopoly’ ‘H = 0’ ‘monopolistic ‘perfectvariable variable competition’ competition’
ln II none 72 65 1 62ln(II/TA) none 100 100 0 70ln II ln TA 100 100 0 75ln TI none 73 65 1 63ln(TI/TA) none 100 100 0 79ln TI ln TA 100 100 0 78
Notation: avg. H =Pn
i=1 Hi = H, std. dev. H =q
1n
Pni=1(Hi −H)2, avg. std. dev. H = 1
n
Pni=1 σ(Hi), where
σ(Hi) refers to the estimated standard error of Hi. Throughout, n = 101.
30