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:j.a.bikker@dnb.nl.

†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:l.spierdijk@rug.nl.

‡Paul Finnie, UBS AG, GTP Risk Management, Bahnhofstrasse 102, 8001 Zurich, Switzerland. Email:paul.finnie@gmail.com. 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

1

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)

2

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

3

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).

4

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

5

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,

6

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).

7

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).

8

(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.

9

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.

10

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

11

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

13

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

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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