Keywords: JEL classification: G21, D4 Banking, competition, convergence, Central and Eastern European countries

Many reforms of banking market liberalization in CEE countries raised the question on the convergence of banks' competitive behaviour, particularly because of the presence of foreign banks from same European regions. We find within-country convergence of three used bank competition measures, with higher convergence levels of market power and of competitive behaviour, and with faster convergence trend for foreign banks. Despite the efforts for banking market integration, there is no general movement toward across-countries convergence of competitive behaviour of CEE banks, neither for foreign nor for domestic institutions, higher dispersion of countries being however observed for the former.

Introduction

Governments in Central and Eastern European (CEE) countries succeeded in establishing of a competitive banking environment [START_REF] Bonin | Banking in Transition Countries[END_REF], in opening their banking markets to foreign participation and the integration of these markets to the European banking market. Among many other competitive-enhancing regulation measures, they had to adopt the principle of home country control for banks and the principle of single banking licence that authorizes any bank of any EU state to provide banking services in another EU member without additional authorization. The latter aims particularly to favour the EU cross-border expansion of banking products and thus to increase the bank competition. Consequently, the intention of all competitive-enhancing measures to create a single EU banking market should favour a homogeneous competitive environment for CEE banks and should lead to the convergence of bank competition.

At the beginning of the transition, foreign banks were eager to enter CEE markets. As members of same large European banking groups, they proposed similar products across all CEE banking markets, some being very innovative and other more efficient. Their relative advantage in terms of expertise, technology and know-how for credit screening and risk management, as well as the reputation of their parents, might have reduced the price of their products in order to enter these markets [START_REF] De Haas | Foreign banks and credit stability in Central and Eastern Europe. A panel data analysis[END_REF][START_REF] Claeys | Modes of Foreign Bank Entry and Effects on Lending Rates: Theory and Evidence[END_REF], spreading the pressures of competition on domestic banks as well and contributing to the convergence of competition in banking. However, the same factors might have increased the price once these markets have been conquered.

The main objective of this paper is thus to investigate the integration of CEE banking markets in terms of the convergence of bank competition. A perfect banking integration implies convergence toward the same price behaviour, which might be expected at least for foreign banks. However, different regulatory environments, various entry policies into these banking markets and different privatisation procedures of state-owned banks, among many other factors, would hamper foreign banks in CEE countries to behave alike.

No study, to the best of our knowledge, explored this important issue on CEE banks. Few papers on the subject focusing on the EU-15 banking markets emphasize different levels of European banks' competitiveness, in spite of a global increase in competition among these institutions [START_REF] De Bandt | Competition, contestability and market structure in European banking sector on the eve of EMU[END_REF]. [START_REF] Molyneux | Competitive conditions in European banking[END_REF] have firstly mentioned that these different competition levels are sign of lack of integration of European banks.

Our intention is thus, firstly, to assess the bank competition and its evolution in CEE economies and to examine if there is a difference between foreign and domestic banks. Our findings will contribute to a better understanding of the role of many competition-enhancing measures, as opening of the banking market and the entry of new banks, as well as competition-reducing measures, as merger-and-acquisition wave in these banking industries. A divergent competitive behaviour between foreign and domestic banks may hamper the homogenization process on CEE banking markets, which hastened after EU accession. Secondly, we aim to study whether there is convergence in bank competition both within and across CEE banking industries. This issue is of a great importance at least for the following three reasons. First, the within-country convergence is, as mentioned, a sign of harmonization in banking industry: domestic banks performs more and more new activities introduced by foreign counterparts, such as underwriting and trading securities, brokerage and investment, and therefore approach closer to practices of foreign banks. This might imply lower prices for banking products and more efficient and complete banking market. Second, the acrosscountries convergence is necessary for euro-zone accession perspective, some CEE countries being already members of euro-zone. In banking-oriented economies as CEE countries are, the transmission of the monetary policy depends mostly on the willingness of banks to adjust their loan and deposit rates on the evolution of the central bank's instruments. Since the reaction of banking institutions depends itself on their market power and competitive behaviour, different convergent levels across countries may imply an asymmetric effect of the monetary policy. Finally, with different convergence levels between foreign and domestic banks, an asymmetric impact may occur within CEE economies too, but at lesser extent due to compensation measures.

Other contribution to the banking literature of transition countries is precisely the estimation of convergence levels for different measures of bank competition. In order to test the convergence, we apply the two major concepts of convergence, β-convergence and σconvergence. Unlike other studies [START_REF] Weill | Convergence in banking efficiency across European countries[END_REF][START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF], we make these tests at microeconomic level, that is, across banks of each country and not across banking markets. Thus, βconvergence implies that banks with less competitive behaviour know faster increase of their competitiveness than banks with more competitive incentives. σ-convergence is considered when each bank's competitive measure is converging to the country's average level. More precisely, it implies that the deviation from the average level diminishes over time.

Finally, unlike previous studies, our microeconomic approach allows the examination of the convergence of bank competitive measures within each CEE country and the global convergence across all studied CEE banking markets. For the latter, using the results for within-country convergence, we determine with precision the groups of countries, whose banks have a similar competitive behaviour. This approach also allows the examination of the role of ownership profile on the convergence of bank competition.

In order to investigate the convergence of CEE banks' competitive behaviour and the role of ownership profile, we firstly briefly present the literature survey on the bank competition in European countries, especially in CEE banking markets, and emphasize the lack of convergence obtained by previous works. In section 3, we outline the methodology used to estimate the bank competitive measures, that is, the Lerner index, the Boone indicator and the H-statistic, and our approach for convergence tests. In section 4, we describe our data and variables, and explain and comment our empirical results. Finally, we conclude in section 5.

Related literature

Expected effects in the banking industry of CEE countries' accession to EU were an increased competition with new banking products and lower bank prices. However, few studies on EU old members find an imperfect competition in 1990s and some divergences across types of banks [START_REF] De Bandt | Competition, contestability and market structure in European banking sector on the eve of EMU[END_REF] and across countries [START_REF] Molyneux | Competitive conditions in European banking[END_REF][START_REF] Hondroyiannis | Assessing competitive conditions in the Greek banking system[END_REF][START_REF] Coccorese | Banking competition and macroeconomic conditions: a disaggregate analysis[END_REF].

The lack of convergence of bank competition is also observed for CEE countries. Considering [START_REF] Panzar | Testing for "monopoly" equilibrium[END_REF] methodology to estimate the H-statistic as measure of bank competition, [START_REF] Gelos | Consolidation and Market Structure in Emerging Market Banking Systems[END_REF] find that bank competition increased in the Czech Republic and decreased in Hungary and Poland from 1994 to 1999. With the same methodology, [START_REF] Mamatzakis | Competition and concentration in the banking sector of the South Eastern European region[END_REF] investigate the competitive conditions in the banking industry in the South and Eastern European region over the period 1998-2002, and find a monopolisitic competition for these banking industries. [START_REF] Dracos | Competition and Contestability in transition banking: an empirical analysis[END_REF] obtained similar results.

The main shortcoming of the previous approach is the estimation of an average measure of bank competition over the time sample, which therefore does not allow the determination of the evolution of competition level. Considering a translog revenue function instead of a linear form, [START_REF] Lapteacru | Impact of competition on bank efficiency: the case of Eastern and Central Europe[END_REF] overcome this problem and estimate the H-statistic for each bank and for each year over 1999-2006 period. They find that the competitive behaviour of Hungarian, Latvian, Lithuanian, Romanian, and Czech banks weakens and it strengthens for Slovak and Slovenian banking institutions. Lapteacru (2014) also highlights huge differences. Thus, these first studies clearly show either different levels or different trends of bank competition, presuming lack of convergence.

A divergence in banks' competitive behaviour is also found with the Lerner index, which is defined as mark-up of output price over marginal cost and measures the market power of banks. [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF] points out that these two measures are conceptually completely different and shows, on the example of CEE countries, that banks with higher H-statistic can have higher market power, and vice versa. Only in Slovakia does fierce market competition imply a decrease in market power. [START_REF] Agoraki | Regulations, competition and bank risktaking in transition countries[END_REF] find an increase in market power for Bulgarian, Czech, Hungarian, Estonian and Latvian banks and a decrease of the Lerner index of banking institutions of Poland andSlovakia over 1998-2005 period. The results of [START_REF] Lapteacru | Impact of competition on bank efficiency: the case of Eastern and Central Europe[END_REF] suggest the same evolution for Czech, Hungarian and Estonian banking institutions and no trend for Latvian, Slovak and Slovenian banks. Thus, with the Lerner index we also may presume the lack of convergence of CEE banks' competitiveness. However, none of these studies made convergence tests and none of them considered the role of foreign banks in the creation of convergence groups.

The only paper that made convergence tests on bank competition in the EU, including in CEE countries, is that of [START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF]. Applying both competitive measures, he finds no trend in market power of CEE banks and opposite evolution of the H-statistic: decreases for Bulgaria, the Czech Republic, Latvia, Poland, Romania and Slovenia, and increases for Estonia, Hungary, Lithuania and Slovakia. His convergence test imposes the determination of a global convergence level for all EU banking markets. Consequently, even if he concludes on the convergence in bank competition across European countries, his results do not provide information neither about the convergence within each country nor about the convergence groups of countries.

All these subjects (or their omission) guide our empirical investigation. In the following, we provide a methodological overview of applied measures of bank competition, which are the Lerner index, the Boone indicator and the H-statistic.

Methodology

In this section, we present the methodology used to estimate employed measures of bank competition. We then explain our within-country convergence tests and the creation of group of countries with same levels of bank competition, which will precisely uncover the acrosscountries convergence.

Measures of bank competition

We will apply the Lerner index, the Boone indicator and the H-statistic, because they do not measure the same aspects of competition [START_REF] Degryse | Microeconometrics of Banking: Methods, Applications, and Results[END_REF][START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF].

Lerner Index

The Lerner index is a structural measure that is defined as the mark-up of price over the bank's marginal cost:

𝐿𝐿 𝑖𝑖𝑖𝑖 = 𝑝𝑝 𝑖𝑖𝑖𝑖 - 𝜕𝜕𝐶𝐶 𝑖𝑖𝑖𝑖 𝜕𝜕𝑦𝑦 𝑖𝑖𝑖𝑖 𝑝𝑝 𝑖𝑖𝑖𝑖 , ( 1
)
where 𝑝𝑝 𝑖𝑖𝑖𝑖 represents the average price of bank i's output at time t, 𝐶𝐶 𝑖𝑖𝑖𝑖 is the bank's total cost and 𝑦𝑦 𝑖𝑖𝑖𝑖 is its output. Banks have no market power if 𝐿𝐿 𝑖𝑖𝑖𝑖 = 0, and the bank's market power increases with an increase in 𝐿𝐿 𝑖𝑖𝑖𝑖 . The Lerner index is computed for each bank and for each year and has been applied to assess the evolution bank competition (Fernández de Guevara et al., 2007;[START_REF] Carbó | Cross-country comparisons of competition and pricing power in European banking[END_REF][START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF] and to determine its factors [START_REF] Berger | Bank competition and financial stability[END_REF][START_REF] Fungacova | Does competition influence bank failures? Evidence from Russia[END_REF].

The econometric methodology consists in the estimation of the marginal cost of banks.

The banking literature mostly uses either the total amount of loans [START_REF] Pruteanu-Podpiera | Banking competition and cost efficiency: a micro-data analysis on the Czech banking industry[END_REF][START_REF] Solís | The social costs of bank market power: Evidence from Mexico[END_REF] or total assets [START_REF] Fernández De Guevara | Integration and competition in the European financial markets[END_REF][START_REF] Carbó | Cross-country comparisons of competition and pricing power in European banking[END_REF][START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF] as bank output. This study considers three bank products that are principal sources of revenue for CEE banks: non-financial loans, bank loans and investment assets, which are produced with funds, labour and physical capital. The translog cost function consists, therefore, of three inputs and three types of outputs as following:

ln𝐶𝐶 𝑖𝑖𝑖𝑖 = 𝑐𝑐 0 + 𝛼𝛼 𝑖𝑖 + 𝜇𝜇 𝑖𝑖 + � 𝛽𝛽 𝑗𝑗 ln𝑤𝑤 𝑗𝑗,𝑖𝑖𝑖𝑖 3 𝑗𝑗=1 + � 𝛾𝛾 𝑚𝑚 ln𝑦𝑦 𝑚𝑚,𝑖𝑖𝑖𝑖 3 𝑚𝑚=1 + 1 2 � � 𝜑𝜑 𝑘𝑘𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 3 𝑘𝑘=1 + � � 𝜒𝜒 𝑚𝑚𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 ln𝑦𝑦 𝑚𝑚,𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 3 𝑚𝑚=1 + 1 2 � � 𝜌𝜌 𝑚𝑚𝑚𝑚 ln𝑦𝑦 𝑚𝑚,𝑖𝑖𝑖𝑖 3 𝑚𝑚=1 ln𝑦𝑦 𝑚𝑚,𝑖𝑖𝑖𝑖 3 𝑚𝑚=1 + � 𝜔𝜔 1𝑚𝑚 ln𝑦𝑦 𝑚𝑚,𝑖𝑖𝑖𝑖 ln𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑚𝑚=1 + 𝜀𝜀 𝑖𝑖𝑖𝑖 + � 𝜔𝜔 2𝑚𝑚 ln𝑦𝑦 𝑚𝑚,𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑚𝑚=1 + 𝜀𝜀 𝑖𝑖𝑖𝑖 , (2)
where total costs Cit comprise operational and non-operational costs. ym is the banking product of type m: non-financial loans, bank loans and other earning-assets. w1 is the price of funds that is measured as the ratio of interest expenses to total interest-bearing liabilities, w2 is the price of labour that is calculated as the ratio of wage expense to total assets 1 , and w3 is the price of other inputs that is estimated as the ratio of other operational expenses to total assets 2 . 𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 represents real GDP in year t of the country of bank i, and 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 is real GDP growth. The evolution of banks' costs may also be affected by the business cycle, which explains the presence of economic indicators related to cross-product terms.

As homogeneous function of degree 1, the cost function must respect the following homogeneity conditions:

� 𝛽𝛽 𝑗𝑗 = 1 3 𝑗𝑗=1 � 𝜒𝜒 𝑚𝑚𝑘𝑘 = 0 3 𝑘𝑘=1 (𝑚𝑚 = [1,3]) � 𝜑𝜑 𝑘𝑘𝑘𝑘 = 0 3 𝑘𝑘=1 (𝑙𝑙 = [1,3]).
(3)

Similarly, the conditions of symmetry are also considered:

φkl=φlk (l,k = [1,3]), ρms=ρsm (m,s = [1,3]).
Equation ( 2) is regressed using a panel data model with fixed individual effects, αi, and fixed time effects, 𝜇𝜇 𝑖𝑖 , and the results are applied in the estimation of the marginal cost according to the following expression:

𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 = 𝜕𝜕𝐶𝐶 𝑖𝑖𝑖𝑖 𝜕𝜕�𝑦𝑦 1,𝑖𝑖𝑖𝑖 + 𝑦𝑦 2,𝑖𝑖𝑖𝑖 + 𝑦𝑦 3,𝑖𝑖𝑖𝑖 � = � � 𝛾𝛾 𝑚𝑚 3 𝑚𝑚=1 + � � 𝜒𝜒 𝑚𝑚𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 + � � 𝜌𝜌 𝑚𝑚𝑚𝑚 ln𝑦𝑦 𝑚𝑚 3 𝑚𝑚=1 3 𝑚𝑚=1 3 𝑚𝑚=1 + � 𝜔𝜔 1𝑚𝑚 ln𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑚𝑚=1 + � 𝜔𝜔 2𝑚𝑚 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑚𝑚=1 � × 𝐶𝐶 𝑖𝑖𝑖𝑖 𝑦𝑦 1,𝑖𝑖𝑖𝑖 + 𝑦𝑦 2,𝑖𝑖𝑖𝑖 + 𝑦𝑦 3,𝑖𝑖𝑖𝑖 . ( 4
)
The results are then employed in the estimation of the Lerner index Lit (eq. 1), computing the average price of bank output as the ratio of total revenues to interest-earning assets, 𝑝𝑝 𝑖𝑖𝑖𝑖 = 𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 �𝑦𝑦 1,𝑖𝑖𝑖𝑖 + 𝑦𝑦 2,𝑖𝑖𝑖𝑖 + 𝑦𝑦 3,𝑖𝑖𝑖𝑖 � ⁄ .

1 Following many other studies [START_REF] Fernández De Guevara | Integration and competition in the European financial markets[END_REF][START_REF] Maudos | The cost of market power in banking: Social welfare loss vs. cost inefficiency[END_REF][START_REF] Solís | The social costs of bank market power: Evidence from Mexico[END_REF][START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF] and because of the data availability, we use total assets instead of the number of employees. This will not qualitatively affect our results because total assets correlate significantly and positively with the number of employees.

2 Many authors use the price of physical capital instead of the price of other inputs. We employ the latter because the data for its calculation are available for the most of banks and because it comprises all other inputs and not a particular one.

Boone indicator

Boone (2008) suggests to measure how (cost) inefficiency, as reflected by differences in marginal cost, influences bank profitability. He proposes an indicator of competition based on idea that more efficient firms gain higher market shares, and that this effect will be stronger in more competitive banking market. Thanks to its important advantages, namely strong theoretical foundations and the consideration of efficiency-competitive behaviour nexus, this indicator has begun to be intensely used in recent banking literature: to measure the role of bank competition on the firms' access to finance [START_REF] Love | How bank competition affects firms' access to finance[END_REF], to assess the impact of financial reforms on bank competition through different institutional regimes [START_REF] Delis | Bank competition, financial reform, and institutions: the importance of being developed[END_REF], to revisit the relationship between banking market competition and risk-taking [START_REF] Tabak | The relationship between banking market competition and risk-taking: do size and capitalization matter?[END_REF], or just to measure the bank competition [START_REF] Van Leuvensteijn | A new approach to measuring competition in the loan markets of the euro area[END_REF].

It is often calculated as the elasticity of profits to marginal cost, based on idea that more efficient firms, that is, with lower marginal cost, earn more profits [START_REF] Degryse | Microeconometrics of Banking: Methods, Applications, and Results[END_REF][START_REF] Buch | Do banks benefit from internationalization? Revisiting the market-power risk nexus[END_REF][START_REF] Leon | Does bank competition alleviate credit constraints in developing countries?[END_REF]. However, higher profits do not necessarily mean more market shares, towards should lead the concept of [START_REF] Boone | A new way to measure competition[END_REF] of bank competitiveness. Van Leuvensteijn et al. (2013) develop the theoretical approach of [START_REF] Boone | A new way to measure competition[END_REF] for banking industry and support the idea that the Boone indicator must be directly considered as the elasticity of market share to marginal cost as in [START_REF] Bikker | Competition and efficiency in the Dutch life insurance industry[END_REF]. We follow this direct competitive effect of bank efficiency on market share gain, and apply the following econometric model to compute the Boone indicator:

ln𝑚𝑚𝑚𝑚 𝑖𝑖𝑖𝑖 = 𝜋𝜋 0 + 𝜋𝜋 1𝑖𝑖 + 𝜈𝜈 𝑖𝑖 + 𝜃𝜃 1 ln𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 + 𝜃𝜃 2 ln𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 × ln𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 + 𝜃𝜃 3 ln𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 × ln𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 +𝜃𝜃 4 ln𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 × 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 + 𝜀𝜀 𝑖𝑖𝑖𝑖 , (5) where 𝑚𝑚𝑚𝑚 𝑖𝑖𝑖𝑖 = 𝑒𝑒𝑒𝑒𝑔𝑔𝑒𝑒. 𝑒𝑒𝑚𝑚𝑚𝑚𝑒𝑒𝑎𝑎𝑚𝑚 𝑖𝑖𝑖𝑖 ∑ 𝑒𝑒𝑒𝑒𝑔𝑔𝑒𝑒. 𝑒𝑒𝑚𝑚𝑚𝑚𝑒𝑒𝑎𝑎𝑚𝑚 𝑖𝑖𝑖𝑖 𝑖𝑖 ⁄
stands for earning assets share for bank i in year t. As for bank costs, business cycle may also affect the evolution of market share. As the elasticity of market share to marginal cost, the Boone indicator is calculated as following:

𝐵𝐵𝐵𝐵𝐵𝐵𝑒𝑒𝑒𝑒 𝑖𝑖𝑖𝑖 = 𝜃𝜃 1 + 2𝜃𝜃 2 ln(𝑚𝑚𝑐𝑐 𝑖𝑖𝑖𝑖 ) + 𝜃𝜃 3 ln(𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 ) + 𝜃𝜃 4 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 .
(6)

H-statistic

Other aspect about the competitive behaviour of banks is addressed by the H-statistic of [START_REF] Panzar | Testing for "monopoly" equilibrium[END_REF], which is the aggregate elasticity of banks' revenue to input prices. Its authors show that the way in which the variation of input prices is transmitted to banks' revenue depends on the level of competition in the market. The H-statistic equals to one in a perfectly competitive market and ranges between 0 and 1 for banks operating under monopolistic competition. It is less than or equal to zero for banks that collude.

Regarding its concept, to compute the H-statistic we firstly must determine the revenue function of banks and, as it may also change with the economic context, we use the following translog form:

ln𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 = a 0 + ϑ i + 𝜐𝜐 𝑖𝑖 + � 𝜆𝜆 𝑗𝑗 ln𝑤𝑤 𝑗𝑗,𝑖𝑖𝑖𝑖 3 𝑗𝑗=1 + 𝜓𝜓 1 ln𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 + 𝜓𝜓 2 ln𝐿𝐿𝐵𝐵𝑒𝑒𝑒𝑒 𝑖𝑖𝑖𝑖 + 1 2 � � 𝜅𝜅 𝑘𝑘𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 3 𝑘𝑘=1 + � 𝜙𝜙 1𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 ln𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 + � 𝜙𝜙 2𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 𝐿𝐿𝐵𝐵𝑒𝑒𝑒𝑒 𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 + � 𝜙𝜙 3𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 ln𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑘𝑘=1 + � 𝜙𝜙 4𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑘𝑘=1 + 𝜀𝜀 𝑖𝑖𝑖𝑖 , (7)
where 𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 stands for total revenue of bank i in year t, 𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 represents total assets and 𝐿𝐿𝐵𝐵𝑒𝑒𝑒𝑒 𝑖𝑖𝑖𝑖 ratio of loans on total assets. The last two variables take into account the differences in size and business model, akin to De Bandt and Davis (2000), [START_REF] Bikker | Competition, concentration and their relationship: an empirical analysis of the banking industry[END_REF], [START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF]. Thus, the H-statistic is equal to

𝐻𝐻 𝑖𝑖𝑖𝑖 = � 𝜕𝜕𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 𝜕𝜕𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 × 𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 = � 𝜆𝜆 𝑗𝑗 3 𝑘𝑘=1 + � � 𝜅𝜅 𝑘𝑘𝑘𝑘 ln𝑤𝑤 𝑘𝑘,𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 3 𝑘𝑘=1 + � 𝜙𝜙 1𝑘𝑘 ln𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 + � 𝜙𝜙 2𝑘𝑘 𝐿𝐿𝐵𝐵𝑒𝑒𝑒𝑒 𝑖𝑖𝑖𝑖 3 𝑘𝑘=1 + � 𝜙𝜙 3𝑘𝑘 ln𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑘𝑘=1 + � 𝜙𝜙 4𝑘𝑘 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑝𝑝 𝑖𝑖 3 𝑘𝑘=1 . ( 8
)
Related to works of [START_REF] Carbó | Cross-country comparisons of competition and pricing power in European banking[END_REF], [START_REF] Lapteacru | Impact of competition on bank efficiency: the case of Eastern and Central Europe[END_REF] and [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF], our method allows the determination of individual H-statistics and thus the implementation of a homogeneous approach for all three competition measures.

Convergence measures and tests

We now present the methodology used to determine the convergence levels and to test the equality between them in order to uncover convergence groups of countries.

Estimation of convergence levels and within-country convergence tests

In order to estimate the convergence levels of bank competitive measures, 𝐵𝐵𝐶𝐶 (𝐿𝐿, 𝐵𝐵𝐵𝐵𝐵𝐵𝑒𝑒𝑒𝑒 and 𝐻𝐻), we apply a dynamic equation based on an autoregressive process according to which the convergence level is obtained for 𝐸𝐸(𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖 ) = 𝐸𝐸(𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖-𝑘𝑘 ) (∀𝑘𝑘 = 1, … , 𝑝𝑝). To test the convergence of bank competitiveness within each country and to find the convergence level, we thus regress the following equation using a panel data model with fixed individual and time effects:

𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖 = 𝑒𝑒 0 + 𝛼𝛼 𝑖𝑖 + 𝜇𝜇 𝑖𝑖 + � 𝑒𝑒 𝑘𝑘 𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖-𝑘𝑘 𝑝𝑝 𝑘𝑘=1 + 𝑢𝑢 𝑖𝑖𝑖𝑖 . ( 9
)
Obtained when the expected value of bank competitiveness does not change over time, the convergence level is calculated as follows:

𝐶𝐶𝐿𝐿 = 𝑒𝑒 0 1 -∑ 𝑒𝑒 𝑘𝑘 𝑝𝑝 𝑘𝑘=1 . ( 10
)
The 𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖 is converging if the 𝑝𝑝 solutions with respect to 𝜆𝜆 of the homogeneous equation

𝜆𝜆 𝑝𝑝 -� 𝜆𝜆 𝑝𝑝-𝑘𝑘 𝑒𝑒 𝑘𝑘 𝑝𝑝 𝑘𝑘=1 = 0 (11) are �𝜆𝜆 ̂𝑖𝑖� < 1 for any 𝑖𝑖 = 1, . . . , 𝑝𝑝.
This statistical convergence meaning is completed with other two concepts of convergence: β-convergence and σ-convergence [START_REF] Barro | Convergence across states and regions[END_REF]. The former means that banks with less competitiveness experience faster increase in their competitive behaviour. Some limits of this test have been, nevertheless, evoked by [START_REF] Quah | Empirics for economic growth and convergence[END_REF]. First, the banks with low previous level of competition could overpass the banks with high previous level and the evolution of bank competition become divergent. Second, taking into account that the reduction in dispersion implies convergence, the β-convergence test provides no information on the dispersion of bank competition measure.

In the banking literature, the β-convergence test has been performed for the convergence of bank efficiency [START_REF] Weill | Convergence in banking efficiency across European countries[END_REF] and competition [START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF] across European countries. Unlike to these studies, we check the convergence of bank competition within each country applying the following equation:

𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖 -𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖-1 = 𝛽𝛽 0 + 𝛼𝛼 𝑖𝑖 + 𝜇𝜇 𝑖𝑖 + 𝛽𝛽 1 𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖-1 + 𝜀𝜀 𝑖𝑖𝑖𝑖 .
(12) There is β-convergence if 𝛽𝛽 1 < 0. Moreover, higher is its absolute value, faster pervious 𝐵𝐵𝐶𝐶 values approach to current values. However, the value of 𝛽𝛽 1 cannot really allow to test the convergence because, for high absolute values, previous levels of 𝐵𝐵𝐶𝐶 could overpass the current ones and the process become divergent.

Contrary to the β-convergence test, σ-convergence test aims to investigate the evolution of the dispersion. There is then convergence if the dispersion diminishes over time and we thus overcome the divergent effect of the previous test. The σ-convergence test measures how quickly each bank's competition measure converges to countries' average level for each year and the estimation is made with the following equation:

𝐷𝐷𝑒𝑒𝐷𝐷 𝑖𝑖𝑖𝑖 = 𝜎𝜎 0 + 𝛼𝛼 𝑖𝑖 + 𝜎𝜎 1 𝑎𝑎𝑖𝑖𝑚𝑚𝑒𝑒 𝑖𝑖 + 𝜀𝜀 𝑖𝑖𝑖𝑖 , ( 13
) where 𝐷𝐷𝑒𝑒𝐷𝐷 𝑖𝑖𝑖𝑖 denotes the deviation of the bank competition 𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖 from its across-banks average level in year t, 𝐵𝐵𝐶𝐶 ���� 𝑖𝑖 , that is, 𝐷𝐷𝑒𝑒𝐷𝐷 𝑖𝑖𝑖𝑖 = |𝐵𝐵𝐶𝐶 𝑖𝑖𝑖𝑖 -𝐵𝐵𝐶𝐶 ���� 𝑖𝑖 |. There is σ-convergence if the coefficient 𝜎𝜎 1 is negative and its absolute value indicates the speed of convergence.

Across-countries tests of convergence

The most important contributions of our paper are the determination of convergence levels of bank competition measures and the establishment of groups of countries with same levels. The Wald test of equality between competition levels of k different countries will allow to bring together the countries for which it cannot reject the null hypothesis 𝐶𝐶𝐿𝐿 1 = 𝐶𝐶𝐿𝐿 2 = ⋯ = 𝐶𝐶𝐿𝐿 𝑘𝑘 . The Wald statistic for nonlinear restriction is (Greene, 2012, p. 172

): 𝑊𝑊 = (𝐜𝐜̂-𝐪𝐪) ′ {Var(𝐜𝐜)} -1 (𝐜𝐜̂-𝐪𝐪), ( 14
)
where 𝐜𝐜̂-𝐪𝐪 is the vector of 𝑘𝑘 -1 differences between a reference convergence level and other levels and Var(𝐜𝐜) = 𝐆𝐆 � Var�𝛃𝛃 � �𝐆𝐆 � ′ . Other formulas are: 𝐆𝐆 � = ∂𝐜𝐜�𝛃𝛃 � � ∂𝛃𝛃 � ′ ⁄ , where 𝐜𝐜�𝛃𝛃 � � is the vector of tested convergence levels that are computed with equation ( 10) and 𝛃𝛃 � is the vector of estimated coefficients of equation ( 9) that appear in equation ( 10). Var�𝛃𝛃 � � is the variance-covariance matrix of regressions of equation ( 9) for convergence levels that are subject of the Wald test. Finally, the Wald statistic W has a chi-squared distribution with degrees of freedom equal to the number of restrictions, that is 𝑘𝑘 -1.

Data and results

In this section, we firstly present our data and describe our variables. We then provide our main findings for CEE banks' competitiveness, their convergence levels and our results about groups of countries with same bank competitive environment.

Data and variables

Our sample of countries consists of 322 banks from ten CEE economies, including Bulgaria, the Czech Republic, Hungary, Estonia, Latvia, Lithuania, Poland, Romania, Slovakia and Slovenia. Accounting data for individual banks are extracted on an annual basis from Bankscope Fitch IBCA in millions of USD. Macroeconomic variables, as real GDP, real GDP growth and consumption price index, are obtained from DataStream for all transition countries. The sample period is from 1995 to 2013 and includes crisis events from nineties and from 2008.

For the 322 banks, 3,494 observations were collected for a 19-year period. Table 1 displays some descriptive statistics for the bank sample, which consists of banks of all sizes and covers almost entirely the CEE banking markets. Bank loans and other earning assets account for a substantial share of total outputs and were therefore considered separately in our regression equations.

All the regressions, with the exception of those for Estonia, are performed by considering the auto-correlation and the heteroscedasticity of the error term. The auto-correlation test for Estonian banks cannot reject the hypothesis of the absence of auto-correlation and therefore only the heteroscedasticity is corrected. All the regressions are also made with individual and time fixed effects. For equation ( 13), the time fixed effects are not included.

Evolution of bank competition

We investigate the evolution of bank competition measured with the Lerner index, the Boone indicator and with the H-statistic for CEE banks between 1995 and 2013 and examine the difference in competitive behaviour between domestic and foreign banks. The mean values for each country and each year are displayed in Table 2 and they unveil some important observations. First, the mean values of our three bank competition measures range globally within theoretical limits. The Lerner index is around 0.25 and the H-statistic around 0.65, with important deviations depending on years and countries. Therefore, the CEE banks have some market power, which corresponds to works of [START_REF] Lapteacru | Impact of competition on bank efficiency: the case of Eastern and Central Europe[END_REF], [START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF] and [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF] on CEE banks and corroborate also the findings of Fernández de Guevara et al. ( 2007) and [START_REF] Carbó | Cross-country comparisons of competition and pricing power in European banking[END_REF] on EU banks.

Second, as suggested and proved by [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF] on the experience of CEE banks, the market power, measured by the Lerner index, and the competitive behaviour, expressed by the H-statistic, are conceptually very different. The former measures the capability of banks to set a price higher than their marginal cost and the latter assesses the adjustment of bank revenues on the evolution of input prices. As such, more competitive banks do not always have less market power, because of the revenue and production reactions of banks to total costs. More precisely, if the elasticities of revenue and of earning assets with respect to costs evolve in the same direction, then the Lerner index and the H-statistic provide the same information about the competitiveness of banks. Our results are in the same vein as those of [START_REF] Weill | Bank competition in the EU: How has it evolved?[END_REF] and [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF] and suggest that more competitive banks do not always have less market power. The Lerner index is, for example, very sensitive to crisis events, when the price of bank product and services is set very close to marginal cost and sometimes it is even lower than the latter. Except for Poland and Slovenia, the banks of all other CEE countries have either negative or very close to zero Lerner indices during the crises of nineties and of 2008. On the other hand, except for Lithuania, the H-statistic does not show any important changing during the crisis events and, except for Slovakia, this is also the case of the Boone indicator.

Overall, with the exception of crisis periods when market power of banks decreases a lot, the evolution of the Lerner index of each country shows no discernible trend. As for an overall analysis, the market power of CEE banks lowers until 2005 and becomes stronger after ('All counties' side of table 2). This result does not corroborate the evolution of the Boone indicator and of the H-statistic. The bank competition slightly increases with the Boone indicator and it slightly decreases with the H-statistic. However, when we make an examination across CEE countries, we observe different patterns. In Bulgaria, the Czech Republic and Slovakia the market power of banks increases and competitive behaviour lowers with the H-statistic and accentuates with the Boone indicator. The same patterns of the Boone indicator and of the H-statistic but with a decrease in banks' market power are observed in Hungary and Romania. Lithuania is the only country where the Boone indicator and the Hstatistic suggest simultaneously the reduction of bank competition, and Poland is the only country where no measure unveils a trend.

Third, foreign banks have, on average, different competitive behaviour than their domestic counterparts and ownership matters for all bank competition measures ('All countries' side of table 2). In normal periods, foreign banks have lower market power and they resist better to crises, setting higher prices than marginal cost, particularly after 2008. The evolution of the Boone indicator registers a reversal of trend in 2005; after this year, foreign banks become more competitive than their domestic counterparts. And the H-statistic shows higher competition for foreign banking institutions over all period. Since all three measures consider different meanings of competition, we cannot conclude on contradictory results. As showed by [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF], the relationship between the Lerner index and the Hstatistic depends on the evolution of banks' revenue and production reactions to costs. He shows that in many CEE countries banks that are more competitive could have more market power, and vice versa. As for the Boone indicator, the increase in absolute value of 𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 cannot be explained by the same reactions of banks. Lower marginal cost leads to continuous raise of a bank's market share not only due to increase in bank competition, as suggested by [START_REF] Boone | A new way to measure competition[END_REF], but also due to a continuous consolidation process of CEE banking markets.

After the financial crisis of nineties, huge financial restructuring programs were implemented with liquidation of many small insolvent banks, privatization of public banks to foreign institutions that were already, in most, on these markets [START_REF] Bonin | Banking in Transition Countries[END_REF], and this concentration process has continued in 2000s with the merger of parent banks of CEE foreign institutions. Perhaps, this is precisely why after 2005 foreign banks gained more market share than their domestic counterparts did, being, at the same time, more efficient [START_REF] Bonin | Bank performance, efficiency and ownership in transition countries[END_REF][START_REF] Fries | Cost efficiency of bank in transition: Evidence from 289 banks and 15 post-communist countries[END_REF][START_REF] Havrylchyk | Efficiency of the Polish banking industry: Foreign versus domestic banks[END_REF][START_REF] Zajc | A comparative study of bank efficiency in central and eastern Europe: The role of foreign ownership[END_REF]. Finally, a thorough country-by-country analysis shows that during the crises of nineties the foreign banks do not do better in terms of price setting with respect to marginal cost. In Bulgaria, the Czech Republic, Latvia and Poland, they have lower market power than the domestic banks. Such difference is observed also in normal periods in Baltic countries, Slovakia and Slovenia, and only for some years in other CEE countries. In contrast, with the exception of Latvia, the foreign banks of all countries resist better during the recent financial crisis and have higher difference between the price of their products and their marginal cost. This is consistent with better performance found for foreign banks in CEE countries, which has improved during the 2000s because of better knowledge of these markets. Early Greenfield installations [START_REF] Majnoni | The Dynamics of Foreign Bank Ownership: Evidence from Hungary[END_REF][START_REF] Bonin | Banking in Transition Countries[END_REF], with more products and services and lower interest rates and prices [START_REF] De Haas | Foreign banks and credit stability in Central and Eastern Europe. A panel data analysis[END_REF][START_REF] Claeys | Modes of Foreign Bank Entry and Effects on Lending Rates: Theory and Evidence[END_REF], were changed into acquisitions of domestic entities, in order to alleviate the asymmetry of information [START_REF] Van Tassel | Asymmetric information and the mode of entry in foreign credit markets[END_REF] 3 . Moreover, during the same period, foreign banks acquired through the privatization the formerly state-owned banks. And, besides their better performance, they gained more market shares. Their Boone indicator is in absolute value higher than that of domestic banks in Bulgaria after 2002, in Estonia and in Latvia over all period sample, and in Poland after 2001. The effect of an increasing competition is well revealed by the evolution of the H-statistic. In all countries, the revenue of foreign banks is more adjusted to changing on input prices either after a certain year, which could correspond to a huge increase in their market share, or over all period sample, as in Hungary, Lithuania and Romania.

To summarize, there is a difference in market power and competitive behaviour between foreign and domestic CEE banks. The former have lower market power and higher elasticity of their revenue to input prices. The Boone indicator also shows that foreign banks are more competitive, but after a certain year. We will now study whether there is a convergence of these three measures of bank competition and whether the convergence levels are similar across banks with different ownership profile and across countries.

Findings of convergence levels

The convergence levels are estimated with equation (10) after the regression of fixed effects panel model (9). As previously, when appropriate, the regressions are performed by considering the auto-correlation and the heteroscedasticity of the error term. The bank competition measures converge if and only if the solutions of equation ( 11) are �𝜆𝜆 ̂𝑖𝑖� < 1. For all countries, the market power of foreign and domestic banks converges, but its convergence levels (CL) are different, including across CEE countries (see Table 3).

Although their values are at levels obtained with year-by-year and country-by-country computations (see Table 2), the market power of foreign banks converges to higher levels than those of domestic institutions for all countries, with the exception of Latvia and Romania. This result is explained by a higher impact of previous levels of the Lerner index on its current value for foreign banks. More precisely, for 'all countries' the coefficient of 𝐿𝐿 𝑖𝑖-1 is 0.550 for foreign banks and 0.246 for domestic entities. Higher values for the former are observed for almost all countries with similar levels of intercept (Const.). Same explanations are considered for the Boone indicator (see Table 4), which, for 'all countries' regression, convergences to same levels for foreign and domestic banks around of -0.68. This is consistent with previous year-by-year findings (see Tabe2), which divide period sample in two equal sides: before 2005 when domestic banks are more competitive and after 2005 when foreign institutions are. In absolute value, it is higher for foreign banks in Bulgaria, Estonia, Latvia and Romania. Although the year-by-year estimations do never show this for Romanian banks (see Table 2), the increase rate is nevertheless higher for foreign institutions, which leads to higher convergence level.

The results for 'all countries' show slightly higher elasticity of foreign banks' revenue to input prices (see Table 5), which is also consistent with year-by-year results that show higher H-statistic for foreign institutions over all period sample. The convergence levels vary from one country to another, with higher values for foreign banks in Estonia, Lithuania, Poland, Slovakia and Slovenia.

Overall, although convergence levels are different for foreign and domestic banks but also across countries, general trend is that foreign institutions have slightly higher market power and, at the same time, express slightly more competitive behaviour. The difference is so small that it could be explained by the statistical error. Nevertheless, the foreign banks in CEE countries can have a higher market power because their innovative products, more investment opportunities that they offer, their relative advantages in terms of risk management and the reputation of their parents can allow them to set higher price with respect to their marginal cost on a conquered banking market. At the same time, the increase in their cost is associated with much more rise in their assets than in their revenues, which, according to [START_REF] Lapteacru | Do more competitive banks have less market power? The evidence from Central and Eastern Europe[END_REF], explains the divergence between the Lerner index and the Hstatistic.

Our objective is also to test the across-countries convergence. The latter is made with the nonlinear Wald statistic (eq. 14), which tests the null hypothesis of equality between previously estimated convergence levels. For the Lerner index, it cannot reject this hypothesis for domestic banks of all countries (see Table 6). All CEE domestic banks have therefore a market power that converges at a level ranging between 0.11 and 0.27, which could be the level found previously for all countries with equations ( 9) and (10), that is 0.205 (see Table 3). The across-countries convergence test reveals two groups of countries for foreign banks: the foreign institutions of Bulgaria and the Czech Republic have a market power that converges to a same level spreading between 0.30 and 0.39, and those of other countries to a same level ranging between 0.18 and 0.30.

For other two measures, we observe different convergence levels across countries. In other words, there is an across-countries divergence for both foreign and domestic banks. More precisely, only the foreign banks of Bulgaria, Hungary, Latvia and Poland have a Boone indicator that converges to the same level and those of Lithuania and Slovenia to another level. The convergence levels for other countries are very different and the test rejects the hypothesis of equality between them. The Boone indicator of domestic banks is less dispersed, which allows the establishment of two large groups of countries: the Czech Republic, Estonia, Lithuania and Slovakia on the one hand, and Bulgaria, Hungary, Latvia, Poland and Romania on the other. The test for the H-statistic provides so many divergent groups for both foreign and domestic banks, the former being however more dispersed.

We can conclude that, despite the bank regulatory integration and the presence of the same major foreign banks, there is no general movement toward convergence of competitive behaviour of CEE banks, neither for foreign nor for domestic institutions. The latter have a homogeneous behaviour concerning the setting of prices and interest rates with respect to marginal cost, which is a little less homogeneous for foreign banks. Even if we observed an overall divergence in convergence levels of the Boone indicator and H-statistic, it is more marked for foreign banks: same foreign banks but different strategies and price policies, concerning the gain of market shares and the revenue reaction to input prices. Their behaviour still depends heavily on local specific regulatory environment, practices and businesses.

Findings of β-convergence and σ-convergence tests

The last convergence test aims to uncover the way in which the convergence is happened for each country and for both types of ownership, and they are made with the regression of equations ( 12) and ( 14). Our results, displayed in Table 7, provide evidence about βconvergence and σ-convergence in bank competition with an overall examination ('All countries' side of Table 7). Indeed, the coefficients 𝛽𝛽 1 and 𝜎𝜎 1 are, with the exception of domestic banks for the Lerner index, statistically significant for all bank competition measures and both types of ownership. Moreover, the Lerner index and the Boone indicator of foreign banks converge more rapidly than those of domestic institutions, and there is no difference for the H-statistic.

However, a country-by-country analysis provides support for faster convergence for the all competition measures of foreign banks only in Latvia, Poland and Slovenia. Hungary and Lithuania are the only countries where the convergence in competition among domestic institutions is faster with all three measures. For other countries, some competition measures converge more rapidly for foreign banks and others for domestic institutions. Consequently, even if there is a β-convergence for all countries and both ownership types, the speed of convergence diverges.

The σ-convergence test does not provide the same pattern. Even if the results bring to light the convergence of type σ of all bank competition measures of CEE banks in overall analysis, for many countries the dispersion, especially of the Lerner index, does not diminish over time and for some of them it even increases. In the latter case, as in Estonia and Lithuania, the deviation of the yearly competition measures from their yearly across-banks average rises. Since the convergence is already proved and found above (see Tables 345), this signifies that the yearly across-banks average values diverge themselves from the convergence levels estimated with equations ( 9) and (10).

Based on these two tests, we provide support for the β-convergence in bank competition for all countries and both types of ownership. The banks with less competitiveness (less market power) in previous year have known a faster increase in their competitive behaviour (in their market power). And generally the competition measures converge more rapidly for foreign banks. Another result concerns the σ-convergence. Even if, for some countries, the test rejects this type of convergence, there is σ-convergence for all competition measures of foreign banks and only for the Boone indicator and H-statistic of domestic institutions when we examine all countries together.

Conclusion

Even if the CEE countries followed different ways to join the European Union, all of them adopted the same liberalizing banking reforms with the view to join the European banking market. Therefore, we can wonder whether all these efforts led to the convergence of competitive behaviour of CEE banks, because only within an integrated banking market banks should price identically their products and services. Thus, we have examined the within-country convergence of bank competition, that is, the within-country banking integration, and the across-countries convergence, that is, the CEE banking integration. This issue is especially important for CEE economies where the presence of foreign banks increased continuously, reaching for some countries more than 90% of their banking market. As members of same large European banking groups, these institutions are supposed to increase the bank competition and, at the same time, to enhance the convergence of competitive behaviour of CEE banks. To determine the difference in bank competitiveness and its convergence between foreign and domestic banks, we have firstly estimated the three most used bank competition measures in banking literature, which are the Lerner index, the Boone indicator and the H-statistic. We have then applied innovative convergence tests.

We find that the Lerner index, the Boone indicator and the H-statistic show different trends, which are observed for both foreign and domestic banks. This does not mean contradictory results, because these measures are conceptually very different and each of them provides specific information about the competitiveness of banks. There is however some difference between foreign and domestic institutions. The former have lower market power until the recent financial crisis to which they resist better. They also have an enhanced competitive behaviour after 2004 with the Boone indicator and over all period with the Hstatistic. One has to mention that these results are very different across CEE countries.

Consequently, even though all competition measures converge for all countries and for both types of ownership, the convergence levels are different. Therefore, only the market power of CEE domestic banks converges to the same level. The lack of convergence across CEE countries of the Boone indicator and of the H-statistic is confirmed for both foreign and domestic banks. However, the foreign institutions show for all three measures more dispersed convergence groups. Despite the efforts for banking market integration and the presence of the same major foreign banks, there is no general movement toward convergence of competitive behaviour of CEE banks, neither for foreign nor for domestic institutions.

Finally, β-convergence test supports the view that banks with less competitiveness (less market power) in previous year have known a faster increase in their competitive behaviour (in their market power) and that the competition measures converge more rapidly for foreign banks. Despite the rejection by many countries of the σ-convergence test, the overall test confirms the reduction of the deviation of competition measures from their yearly acrossbanks average value, with different speeds for foreign and domestic banks. Consequently, bank ownership matters in the convergence of bank competition. Foreign banks have not only an enhanced competitive behaviour but also more dispersed convergence levels. Further research is however needed in order to determine the specific role of foreign banks in the integration of CEE banking markets from the point of view of banks' competitive behaviour. It could focus, in more details, on the impact of foreign ownership on the convergence process: an accelerating effect or, on the contrary, a slowing effect.

Table 1 .

 1 Descriptive statistics on used variables, 1995Descriptive statistics on used variables, -2013. .

		Nr. of	Total	Total	Non-fin.	Bank	Other earn.	Pr. of borr.	Pr. of	Pr. of	Total	Loan on	Real	GDP
		obs.	costs	revenues	loans	loans	assets	funds	labour	other inp.	assets	assets	GDP	growth
	Bulgaria	365	454	525	845	392	476	0.044	0.020	0.032		0.54	27,257	2.62
	Czech Rep.	373	275	386	2,957	1,253	1,359	0.044	0.008	0.019		0.46	123,572	2.59
	Hungary	414	288	351	1,785	450	674	0.066	0.017	0.030		0.53	99,883	1.93
	Estonia	118	101	152	1,888	204	170	0.027	0.019	0.022		0.57	12,270	4.91
	Latvia	341	35	48	474	142	97	0.024	0.017	0.026	764	0.45	13,845	4.50
	Lithuania	174	62	79	944	132	167	0.032	0.022	0.022		0.58	65,614	4.41
	Poland	687	310	410	2,584	468	1,087	0.061	0.017	0.021		0.54	301,662	4.28
	Romania	409	593	773	2,130	515	421	0.082	0.028	0.034		0.51	97,359	2.37
	Slovakia	304	159	203	1,487	380	482	0.044	0.010	0.022		0.51	61,047	4.29
	Slovenia	303	125	158	1,475	245	492	0.038	0.014	0.014		0.61	26,985	3.28
	Average	3,494	240	309	1,657	418	543	0.046	0.017	0.024		0.53	82949	3.52

Notes: This table displays descriptive statistics for the variables used in our estimations. The financial results, outputs and real GDP are in constant millions of USD. Output and input prices are unitless and real GDP growth rate is expressed as a percentage. The number of observations is 3,494.

Table 2 .

 2 Estimations of bank competition.

		1995	1996	1997 1998	1999 2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013
	Bulgaria
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	-	0.417 0.659 -0.109 0.155 0.192 0.147 0.197 0.285 0.328 0.364 0.356 0.319 0.312 0.314 0.332 0.252 0.241 0.289
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.161 0.340 0.472 0.173 0.323 0.289 0.267 0.241 0.234 0.261 0.216 0.188 0.298 0.118 0.271 0.156 0.096 0.008 0.026
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.161 0.351 0.513 0.094 0.261 0.252 0.201 0.216 0.265 0.301 0.311 0.297 0.313 0.247 0.300 0.270 0.190 0.148 0.172
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-	-0.078 -0.329 -0.483 -0.463 -0.442 -0.510 -0.589 -0.629 -0.688 -0.742 -0.780 -0.814 -0.792 -0.665 -0.742 -0.743 -0.732 -0.795
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.087 0.203 -0.194 -0.469 -0.452 -0.495 -0.520 -0.565 -0.605 -0.635 -0.649 -0.683 -0.787 -0.708 -0.604 -0.697 -0.722 -0.705 -0.748
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.087 0.163 -0.223 -0.473 -0.456 -0.475 -0.515 -0.578 -0.620 -0.666 -0.709 -0.747 -0.805 -0.764 -0.645 -0.726 -0.735 -0.721 -0.774
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	-	0.609 0.582 0.598 0.567 0.582 0.554 0.535 0.519 0.505 0.476 0.460 0.445 0.417 0.333 0.391 0.394 0.376 0.382
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.777 0.688 0.641 0.624 0.580 0.571 0.537 0.534 0.523 0.511 0.471 0.445 0.438 0.396 0.316 0.376 0.385 0.373 0.369
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.777 0.676 0.629 0.617 0.575 0.575 0.546 0.535 0.521 0.508 0.474 0.455 0.443 0.410 0.327 0.386 0.390 0.375 0.376
	Czech Rep.
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	0.283 0.279 0.262 -0.250 0.234 0.231 0.247 0.300	0322	0.318 0.365 0.391 0.404 0.452 0.464 0.482 0.201 0.221 0.295
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.173 0.044 0.091 -0.043 0.066 -0.303 0.296 0.309 0.350 0.261 0.399 0.369 0.454 0.395 0.420 0.429 0.394 0.424 0.430
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.224 0.151 0.185 -0.124 0.169 0.022 0.263 0.302 0.328 0.304 0.374 0.385 0.414 0.438 0.453 0.465 0.258 0.277 0.335
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-0.114 -0.195 -0.291 -0.335 -0.260 -0.190 -0.221 -0.223 -0.189 -0.186 -0.186 -0.204 -0.278 -0.334 -0.419 -0.308 -0.348 -0.390 -0.364
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.181 -0.271 -0.358 -0.334 -0.270 -0.198 -0.232 -0.179 -0.200 -0.227 -0.198 -0.249 -0.279 -0.341 -0.440 -0.329 -0.359 -0.369 -0.322
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.151 -0.237 -0.320 -0.328 -0.260 -0.193 -0.225 -0.212 -0.192 -0.195 -0.189 -0.215 -0.278 -0.336 -0.424 -0.315 -0.351 -0.384 -0.351
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	0.845 0.806 0.725 0.794 0.836 0.840 0.816 0.787 0.782 0.781 0.801 0.768 0.724 0.637 0.545 0.627 0.603 0.557 0.572
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.903 0.903 0.847 0.829 0.812 0.893 0.823 0.751 0.713 0.686 0.663 0.659 0.613 0.591 0.494 0.551 0.559 0.570 0.562
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.878 0.859 0.802 0.827 0.831 0.861 0.818 0.778 0.768 0.758 0.765 0.739 0.701 0.625 0.532 0.603 0.590 0.560 0.569
	Hungary
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	0.293 0.266 0.202 0.151 0.139 0.169 0.227 0.215 0.215 0.226 0.234 0.175 0.054 0.108 0.192 0.272 0.272 0.197 0.233
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.170 0.175 0.085 -0.213 0.176 0.223 0.241 -0.102 0.142 0.346 0.331 0.307 0.253 0.175 0.254 0.022 -0.003 0.049 0.047
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.238 0.230 0.165 0.030 0.149 0.182 0.232 0.146 0.201 0.247 0.254 0.201 0.102 0.120 0.207 0.184 0.167 0.141 0.159
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-0.086 -0.109 -0.120 -0.138 -0.195 -0.247 -0.300 -0.340 -0.405 -0.434 -0.506 -0.548 -0.579 -0.585 -0.580 -0.542 -0.571 -0.568 -0.566
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.050 -0.076 -0.085 -0.108 -0.184 -0.246 -0.324 -0.360 -0.409 -0.475 -0.526 -0.563 -0.594 -0.608 -0.609 -0.534 -0.548 -0.545 -0.552
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.070 -0.096 -0.109 -0.128 -0.192 -0.246 -0.308 -0.344 -0.406 -0.441 -0.510 -0.551 -0.582 -0.590 -0.587 -0.539 -0.562 -0.559 -0.560
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	0.875 0.860 0.853 0.842 0.828 0.812 0.790 0.774 0.730 0.717 0.693 0.667 0.668 0.645 0.666 0.658 0.636 0.650 0.639
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.832 0.839 0.848 0.843 0.815 0.785 0.765 0.753 0.749 0.695 0.700 0.679 0.678 0.612 0.639 0.695 0.697 0.694 0.667
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.856 0.851 0.851 0.842 0.825 0.806 0.782 0.769 0.734 0.713 0.695 0.669 0.670 0.639 0.659 0.671 0.659 0.667 0.650

Table 2 .

 2 Estimations of bank competition (cont.)

		1995	1996	1997 1998	1999 2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013
	Estonia
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	-	-	-	-	0.235 0.160 0.176 0.156 0.237 0.267 0.264 0.279 0.261 0.223 0.115 0.190 0.129 0.169 0.238
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.122 0.127 0.157 -0.112 0.000 0.166 0.212 0.207 0.181 0.249 0.254 0.414 0.626 0.543 -1.002 0.321 0.291 0.359 0.447
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.122 0.127 0.157 -0.112 0.059 0.163 0.197 0.182 0.209 0.258 0.259 0.356	0322	0.287 -0.108 0.234 0.175 0.223 0.298
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-	-	-	-	-0.626 -0.614 -0.586 -0.566 -0.547 -0.525 -0.501 -0.465 -0.417 -0.398 -0.440 -0.491 -0.465 -0.445 -0.432
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.729 -0.711 -0.687 -0.637 -0.614 -0.614 -0.586 -0.567 -0.544 -0.516 -0.491 -0.451 -0.436 -0.443 -0.426 -0.465 -0.459 -0.429 -0.420
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.729 -0.711 -0.687 -0.637 -0.617 -0.614 -0.586 -0.567 -0.545 -0.520 -0.496 -0.457 -0.420 -0.407 -0.437 -0.482 -0.464 -0.441 -0.428
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	-	-	-	-	0.514 0.431 0.406 0.433 0.522 0.579 0.579 0.406 0.219 0.183 0.482 0.689 0.578 0.725 0.886
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.616 0.626 0.590 0.460 0.450 0.460 0.542 0.620 0.611 0.669 0.614 0.386 0.376 0.489 0.871 0.397 0.386 0.388 0.446
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.616 0.626 0.590 0.460 0.466 0.448 0.488 0.526 0.567 0.624 0.596 0.395 0.245 0.244 0.560 0.592 0.523 0.629 0.760
	Latvia
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	-	0.235 -0.885 -0.026 0.185 0.240 0.185 0.237 0.256 0.240 0.272 0.213 0.158 0.143 0.109 0.043 0.176 0.253 0.338
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.233 0.321 0.352 -0.353 0.127 0.159 0.248 0.240 0.310 0.265 0.356 0.299 0.286 0.245 0.165 0.079 0.300 0.191 0.016
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.233 0.307 0.146 -0.271 0.141 0.178 0.227 0.239 0.294 0.256 0.323 0.263 0.229 0.191 0.137 0.063 0.238 0.218 0.168
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-	-0.378 -0.486 -0.469 -0.468 -0.538 -0.604 -0.662 -0.726 -0.807 -0.873 -0.941 -0.969 -0.791 -0.524 -0.721 -0.832 -0.866 -0.883
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.306 -0.377 -0.507 -0.429 -0.467 -0.542 -0.613 -0.669 -0.731 -0.798 -0.868 -0.930 -0.963 -0.796 -0.529 -0.714 -0.838 -0.864 -0.863
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.306 -0.377 -0.503 -0.439 -0.467 -0.541 -0.610 -0.667 -0.729 -0.801 -0.870 -0.934 -0.966 -0.794 -0.526 -0.717 -0.835 -0.865 -0.872
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	-	0.693 0.650 0.670 0.669 0.655 0.682 0.646 0.584 0.534 0.573 0.591 0.594 0.646 0.656 0.613 0.567 0.526 0.423
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.717 0.626 0.617 0.730 0.682 0.656 0.664 0.607 0.586 0.551 0.560 0.584 0.594 0.598 0.603 0.588 0.521 0.541 0.512
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.717 0.637 0.622 0.715 0.679 0.656 0.670 0.619 0.585 0.545 0.565 0.587 0.594 0.623 0.629 0.599 0.544 0.534 0.470
	Lithuania
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	-	-	-	-	-1.050 -0.025 -0.129 0.042 0.193 0.206 0.225 0.190 0.181 0.184 0.043 0.183 0.227 0.249 0.247
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.144 -0.039 0.026 0.126 0.143 0.118 0.110 0.189 0.190 0.213 0.207 0.243 0.232 0.092 -0.263 -0.041 -0.104 0.177 0.085
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.144 -0.039 0.026 0.126 0.024 0.103 0.030 0.107 0.192 0.209 0.218 0.211 0.201 0.143 -0.096 0.081 0.080 0.222 0.187
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-	-	-	-	-0.642 -0.496 -0.666 -0.475 -0.309 -0.222 -0.127 -0.175 -0.103 -0.239 -0.332 -0.248 -0.156 -0.116 -0.063
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-1.027 -0.881 -0.769 -0.786 -0.805 -0.729 -0.664 -0.600 -0.460 -0.368 -0.297 -0.283 -0.289 -0.443 -0.596 -0.422 -0.350 -0.248 -0.228
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-1.027 -0.881 -0.769 -0.786 -0.788 -0.706 -0.665 -0.531 -0.376 -0.287 -0.195 -0.218 -0.177 -0.329 -0.452 -0.327 -0.242 -0.166 -0.125
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	-	-	-	-	-0.649 0.137 0.619 0.374 0.462 0.428 0.499 0.623 0.668 0.674 0.131 0.632 0.536 0.344 0.168
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.607 0.488 0.422 0.428 0.066 0.343 0.504 0.311 0.404 0.293 0.312 0.369 0.636 0.444 -0.374 0.200 0.059 -0.316 -0.260
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.607 0.488 0.422 0.428 -0.006 0.323 0.543 0.346 0.436 0.368 0.424 0.521 0.655 0.571 -0.099 0.435 0.324 0.097 0.008

Table 2 .

 2 Estimations of bank competition (cont.)

		1995	1996	1997 1998	1999 2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013
	Poland
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	0.280 0.065 0.180 0.154 0.148 0.165 0.124 0.143 0.154 0.212 0.188 0.264 0.258 0.204 0.254 0.262 0.274 0.258 0.279
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.212 0.203 0.178 0.170 0.167 0.156 0.135 0.164 0.066 0.247 0.114 0.225 0.268 0.053 0.106 0.186 0.214 0.197 0.239
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.229 0.159 0.178 0.163 0.159 0.160 0.128 0.149 0.127 0.223 0.167 0.253 0.260 0.164 0.215 0.241 0.256 0.242 0.264
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-0.753 -0.778 -0.845 -0.828 -0.693 -0.850 -0.742 -0.647 -0.589 -0.680 -0.666 -0.730 -0.832 -0.861 -0.702 -0.724 -0.803 -0.782 -0.699
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.797 -0.811 -0.861 -0.830 -0.769 -0.881 -0.733 -0.614 -0.625 -0.714 -0.697 -0.713 -0.779 -0.852 -0.728 -0.837 -0.881 -0.843 -0.727
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.786 -0.800 -0.856 -0.829 -0.738 -0.866 -0.739 -0.638 -0.600 -0.691 -0.675 -0.725 -0.818 -0.859 -0.709 -0.755 -0.826 -0.798 -0.710
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	0.762 0.709 0.754 0.694 0.712 0.704 0.623 0.644 0.773 0.818 0.754 0.868 0.886 0.821 0.722 0.797 0.795 0.740 0.744
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.805 0.788 0.800 0.750 0.744 0.703 0.632 0.654 0.742 0.775 0.720 0.861 0.890 0.799 0.724 0.763 0.771 0.736 0.739
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.794 0.763 0.784 0.726 0.731 0.704 0.626 0.647 0.764 0.804 0.744 0.866 0.887 0.815 0.723 0.787 0.788 0.736 0.742
	Romania
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	-	-	0.265 0.233 0.188 0.201 0.187 0.229 0.207 0.213 0.208 0.211 0.234 0.200 0.186 0.269 0.208 0.137 0.186
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.393 0.328 0.226 0.203 0.213 0.177 0.240 0.216 0.257 0.259 0.216 0.294 0.272 0.169 0.161 -0.466 -0.343 -0.061 0.177
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.393 0.328 0.241 0.218 0.198 0.192 0.202 0.225 0.218 0.223 0.210 0.225 0.240 0.196 0.182 0.133 0.102 0.096 0.184
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-	-	-0.429 -0.396 -0.430 -0.480 -0.579 -0.608 -0.660 -0.770 -0.764 -0.887 -0.930 -1.050 -0.791 -0.780 -0.868 -0.826 -0.828
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.638 -0.662 -0.505 -0.433 -0.504 -0.565 -0.630 -0.655 -0.691 -0.829 -0.772 -0.891 -0.942 -1.063 -0.810 -0.816 -0.875 -0.845 -0.836
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.638 -0.662 -0.476 -0.414 -0.461 -0.510 -0.593 -0.623 -0.668 -0.783 -0.766 -0.888 -0.932 -1.052 -0.794 -0.787 -0.869 -0.830 -0.830
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	-	-	0.954 0.826 0.879 0.842 0.852 0.853 0.820 0.789 0.755 0.725 0.685 0.662 0.647 0.706 0.702 0.691 0.692
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.712 0.722 0.770 0.797 0.824 0.854 0.813 0.800 0.744 0.756 0.699 0.797 0.757 0.647 0.578 0.657 0.652 0.621 0.608
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.712 0.722 0.839 0.811 0.856 0.847 0.841 0.837 0.802 0.782 0.743 0.737 0.698 0.660 0.636 0.697 0.692 0.676 0.674
	Slovakia
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	-0.039 0.170 0.220 0.220 0.211 0.288 0.200 0.129 0.140 0.198 0.205 0.229 0.217 0.214 0.197 0.296 0.237 0.228 0.277
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.161 0.087 0.017 -0.033 -0.011 0.128 0.099 0.254 0.359 0.402 0.205 0.466 0.398 0.463 0.323 0.120 0.339 0.404 0.265
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.116 0.103 0.064 0.051 0.055 0.178 0.135 0.170 0.204 0.229 0.205 0.271 0.239 0.243 0.213 0.271 0.252 0.253 0.275
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-0.090 -0.078 -0.043 -0.053 0.019 -0.056 -0.057 -0.127 -0.172 -0.226 -0.303 -0.340 -0.411 -0.356 -0.229 -0.398 -0.379 -0.381 -0.399
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.049 -0.041 0.027 0.006 0.037 -0.007 -0.087 -0.137 -0.234 -0.260 -0.326 -0.386 -0.489 -0.436 -0.264 -0.403 -0.438 -0.411 -0.453
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.058 -0.048 0.011 -0.013 0.031 -0.022 -0.077 -0.133 -0.190 -0.231 -0.306 -0.348 -0.420 -0.366 -0.233 -0.399 -0.387 -0.385 -0.407
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	1.097 0.822 0.549 0.505 0.437 0.538 0.623 0.518 0.581 0.539 0.644 0.595 0.598 0.407 0.238 0.541 0.466 0.426 0.443
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.775 0.655 0.469 0.429 0.176 0.261 0.455 0.448 0.608 0.505 0.690 0.613 0.568 0.419 0.191 0.658 0.676 0.446 0.884
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.846 0.688 0.488 0.454 0.253 0.348 0.514 0.498 0.590 0.541 0.651 0.598 0.594 0.408 0.233 0.558 0.496 0.429 0.511

Table 2 .

 2 Estimations of bank competition (cont.)

		1995	1996	1997 1998	1999 2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013
	Slovenia
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	0.258 0.369 0.399 0.336 0.259 0.338 0.223 0.268 0.270 0.288 0.035 0.184 0.196 0.200 0.259 0.300 0.288 0.284 0.271
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.360 0.384 0.366 0.375 0.407 0.397 0.361 0.331 0.332 0.358 0.318 0.324 0.321 0.216 0.300 0.333 0.266 0.224 0.182
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.343 0.382 0.370 0.368 0.382 0.387 0.335 0.313 0.311 0.335 0.212 0.272 0.277 0.211 0.285 0.321 0.274 0.247 0.216
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-0.143 -0.176 -0.201 -0.270 -0.245 -0.224 -0.232 -0.196 -0.162 -0.093 0.050 0.025 0.008 -0.095 -0.216 -0.038 -0.060 -0.081 -0.071
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.240 -0.241 -0.241 -0.240 -0.161 -0.181 -0.215 -0.221 -0.188 -0.098 -0.042 0.015 0.033 -0.092 -0.223 -0.033 -0.073 -0.145 -0.148
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.224 -0.229 -0.237 -0.245 -0.175 -0.188 -0.219 -0.214 -0.179 -0.097 -0.008 0.019 0.024 -0.093 -0.220 -0.035 -0.068 -0.121 -0.119
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	0.628 0.583 0.625 0.625 0.655 0.665 0.688 0.707 0.764 0.816 0.947 0.850 0.819 0.798 0.943 0.948 0.919 0.946 0.957
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.577 0.605 0.605 0.632 0.700 0.700 0.664 0.663 0.717 0.788 0.816 0.812 0.799 0.793 0.892 0.868 0.840 0.861 0.869
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.586 0.601 0.607 0.631 0.692 0.694 0.669 0.676 0.733 0.797 0.865 0.826 0.806 0.795 0.911 0.898 0.870 0.893 0.902
	All countries
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑓𝑓	0.264 0.213 0.167 0.089 0.163 0.200 0.176 0.198 0.220 0.243 0.239 0.253 0.231 0.221 0.236 0.275 0.235 0.218 0.261
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔 𝑑𝑑	0.208 0.198 0.214 0.060 0.180 0.167 0.224 0.219 0.244 0.281 0.260 0.296 0.304 0.191 0.164 0.122 0.147 0.165 0.156
	𝐿𝐿𝑒𝑒𝑔𝑔𝑒𝑒𝑒𝑒𝑔𝑔	0.223 0.202 0.200 0.072 0.175 0.182 0.199 0.205 0.228 0.256 0.246 0.267 0.253 0.212 0.214 0.223 0.205 0.201 0.221
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑓𝑓	-0.279 -0.341 -0.394 -0.417 -0.381 -0.431 -0.472 -0.459 -0.464 -0.511 -0.527 -0.579 -0.621 -0.665 -0.559 -0.583 -0.619 -0.597 -0.578
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑑𝑑	-0.444 -0.442 -0.468 -0.455 -0.432 -0.467 -0.448 -0.479 -0.509 -0.543 -0.528 -0.535 -0.583 -0.582 -0.535 -0.540 -0.582 -0.583 -0.567
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒	-0.399 -0.415 -0.444 -0.439 -0.410 -0.451 -0.461 -0.465 -0.479 -0.521 -0.527 -0.564 -0.610 -0.641 -0.552 -0.568 -0.606 -0.593 -0.574
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑓𝑓	0.834 0.766 0.750 0.729 0.729 0.735 0.710 0.676 0.700 0.696 0.689 0.687 0.673 0.626 0.560 0.661 0.640 0.609 0.602
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑑𝑑	0.756 0.704 0.662 0.664 0.608 0.630 0.636 0.623 0.644 0.643 0.637 0.644 0.680 0.629 0.538 0.617 0.605 0.581 0.592
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎	0.777 0.721 0.691 0.691 0.659 0.677 0.675 0.656 0.679 0.678 0.672 0.673 0.675 0.627 0.553 0.646 0.628 0.600 0.598

Notes: This table presents the results of Lerner index (Lerner), Boone indicator (Beta) and H-statistic (Hstat) for foreign, domestic and all CEE banks. The subscript 'f' stands for foreign and 'd' for domestic banks. Measures without any subscript are for all banking institutions.

Table 4 .

 4 Convergence levels of Boone indicator. This table presents the results of convergence levels (CL) for the Boone indicator, according to equations (9) and (10). The roots 𝜆𝜆 𝑖𝑖 are the solutions of equation (11) and indicate convergence if their absolute values are lower than one. ***, ** and * are statistical significances at 0.01, 0.05 and 0.10 level, respectively.

	Countries	Foreign banks	Domestic banks		All banks
		Coef.	�𝝀𝝀 � 𝒊𝒊 �	CL	Coef.	�𝝀𝝀 � 𝒊𝒊 �	CL	Coef.	�𝝀𝝀 � 𝒊𝒊 �	CL
	Bulgaria
	Const.	-0.230***			-0.216***			-0.224***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.567***	0.177		0.640***	0.079		0.607***	0.127
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	0.132***	0.745	-0.766***	0.057	0.719	-0.712***	0.093**	0.734	-0.746***
	Czech Rep.
	Const.	-0.088***			-0.110***			-0.088***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.928***	0.499		0.818***	0.443		0.892***	0.455
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	-0.249***	0.499	-0.276***	-0.196*	0.443	-0.290***	-0.207***	0.455	-0.280***
	Hungary
	Const.	-0.062***			-0.046***			-0.054***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	1.059***	0.171		1.155***	0.246		1.107***	0.206
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	-0.152	0.888	-0.673***	-0.224***	0.908	-0.670***	-0.185**	0.901	-0.689***
	Estonia
	Const.	-0.122***			-0.022			-0.041***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	1.086***	0.595		0.966***	0.044		1.183***	0.334
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	-0.354***	0.595	-0.455***	-0.041	0.922	-0.289**	-0.283***	0.850	-0.408***
	Latvia
	Const.	-0.259***			-0.174***			-0.196***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.920***	0.498		0.962***	0.265		0.965***	0.371
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	-0.248***	0.498	-0.791***	-0.185***	0.697	-0.780***	-0.220***	0.594	-0.770***
	Lithuania
	Const.	-0.012			-0.037***			0.004
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	1.021***	0.317		0.920***	0.053		0.964***	0.056
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	-0.223	0.705	-0.060	-0.046	0.867	-0.291***	-0.051	0.908	0.041
	Poland
	Const.	-0.372***			-0.185***			-0.375***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.482***	0.026		0.569***	0.247		0.469***	0.064
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	0.013	0.508	-0.738***	0.202***	0.817	-0.808***	0.034	0.533	-0.756***
	Romania
	Const.	-0.239***			-0.162***			-0.213***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.595***	0.168		0.745***	0.074		0.640***	0.144
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	0.128***	0.763	-0.861***	0.060	0.818	-0.832***	0.113***	0.784	-0.861***
	Slovakia
	Const.	-0.084***			-0.020***			-0.044***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.700***	0.102		0.940***	0.017		0.836***	0.071
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	0.082**	0.803	-0.388***	0.016	0.957	-0.465***	0.064**	0.906	-0.441***
	Slovenia
	Const.	-0.040***			-0.039***			-0.035***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.660***	0.220		0.761***	0.058		0.761***	0.061
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	-0.097	0.440	-0.091***	-0.041	0.704	-0.138***	-0.043	0.699	-0.124***
	All countries
	Const.	-0.057***			-0.042***			-0.044***
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-1	0.850***	0.071		0.914***	0.026		0.887***	0.055
	𝐵𝐵𝑒𝑒𝑎𝑎𝑒𝑒 𝑖𝑖-2	0.066**	0.922	-0.681***	0.024	0.940	-0.687***	0.051**	0.942	-0.721***
	Notes:

Table 5 .

 5 Convergence level of H-statistic index. This table presents the results of convergence levels (CL) for the H-statistic, according to equations (9) and (10). The roots 𝜆𝜆 𝑖𝑖 are the solutions of equation (11) and indicate convergence if their absolute values are lower than one. ***, ** and * are statistical significances at 0.01, 0.05 and 0.10 level, respectively.

	Countries	Foreign banks		Domestic banks		All banks
		Coef.	�𝝀𝝀 � 𝒊𝒊 �	CL	Coef.	�𝝀𝝀 � 𝒊𝒊 �	CL	Coef.	�𝝀𝝀 � 𝒊𝒊 �	CL
	Bulgaria
	Const.	0.030***			0.041***			0.034***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.671***	0.243		0.700***	0.202		0.692***	0.218
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	0.222***	0.914	0.278***	0.183***	0.903	0.350***	0.199***	0.910	0.310***
	Czech Rep.
	Const.	0.078***			0.159***			0.113***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.934***	0.077		0.727***	0.040		0.841***	0.022
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.066	0.857	0.590***	0.031	0.767	0.658***	-0.018	0.818	0.634***
	Hungary
	Const.	0.058***			0.049***			0.050***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	1.005***	0.117		1.013***	0.106		1.022***	0.121
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.104	0.889	0.589***	-0.096	0.907	0.585***	-0.109	0.901	0.580***
	Estonia
	Const.	0.328***			0.173***			0.243***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.753***	0.598		0.738***	0.173		0.808***	0.529
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.355***	0.598	0.546***	-0.098	0.561	0.480***	-0.280***	0.529	0.515***
	Latvia
	Const.	0.111***			0.100***			0.118***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.925***	0.175		0.691***	0.152		0.734***	0.068
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.131***	0.750	0.539***	0.128**	0.843	0.551***	0.054	0.802	0.555***
	Lithuania
	Const.	0.199*			0.061			0.093**
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.518***	0.025		0.612***	0.261		0.593***	0.177
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.012	0.493	0.401***	0.228***	0.873	0.384**	0.137***	0.770	0.344***
	Poland
	Const.	0.346***			0.099***			0.331***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.664***	0.335		0.836***	0.028		0.694***	0.357
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.112**	0.335	0.773***	0.024	0.864	0.708***	-0.127***	0.357	0.763***
	Romania
	Const.	0.170***			0.102***			0.128***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.819***	0.086		0.796***	0.074		0.842***	0.034
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.063	0.734	0.696***	0.064	0.870	0.728***	-0.028	0.808	0.691***
	Slovakia
	Const.	0.215***			0.343***			0.263***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.566***	0.017		0.271	0.038		0.474***	0.021
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	0.010	0.583	0.506***	-0.009	0.233	0.465***	-0.009	0.454	0.492***
	Slovenia
	Const.	0.113***			0.192***			0.163***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.769***	0.130		0.938***	0.259		0.914***	0.137
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	0.117	0.900	0.999***	-0.176***	0.679	0.805***	-0.106	0.778	0.850***
	All countries
	Const.	0.200***			0.152***			0.174***
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-1	0.701***	0.016		0.675***	0.104		0.691***	0.046
	𝐻𝐻𝑚𝑚𝑎𝑎𝑒𝑒𝑎𝑎 𝑖𝑖-2	-0.011	0.686	0.646***	0.081	0.779	0.623***	-0.011	0.737	0.633***
	Notes:

As the foreign banks lack information about customers and business environment, they prefer acquire an existing customer portfolio by the acquisition of a domestic bank.

th group: RO -0.861

Notes: This table provides the results of the across-countries convergence test for all three measures of competition. p-value is the probability of rejection of the null hypothesis that the convergence levels (CL), estimated with equations ( 9) and ( 10), and presented in tables 3-5, are statistically equally for the countries of determined groups.


Sonia Bouzidi
email: sonia.bouzidi@inria.fr

Fabien Lahoche
email: fabien.lahoche@inria.fr

Isabelle Herlin
email: isabelle.herlin@inria.fr

Volker Hochschild

Helmut Staudenrausch

Land use classification at meso-scale using remotely sensed data

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Image classification is a widely used method for extracting information on surface land cover from remotely sensed images. The resulting cartography is helping decision makers in different research fields such as hydrology, agriculture and deforestation. At local scale a classification of images at high spatial resolution (as Landsat TM or SPOT data) improved with ground truthing gives a good information about land cover. However, high spatial resolution data or ground truthing are not always available at least for important surfaces. On these large areas, the NOAA/AVHRR sensors provide daily acquisitions with an important coverage; but due to the size of a pixel (1:1 1:1k m), which is generally larger than a single field, each pixel includes several covers. In order to extract information from such daily data, we propose a method to access the sub-pixel content. We define a process having as input a low spatial resolution temporal sequence of images (a NOAA sequence). It exploits the high temporal frequency of these acquisitions in order to estimate within each pixel the surface percentage of each land cover type. The approach is based on a mixture modeling of the pixel's response. This process will be called in this paper "NOAA unmixing". The result of this analysis is not a map of labels corresponding to different land covers (thematic classification) but a set of images (with the same size as the original NOAA image), giving the percentage of each land cover type for each pixel. The mixture model is described in section 2. The inversion of this model to estimate land cover proportions is explained in section 3. Lastly results are presented and evaluated in section 4.

THE MIXTURE MODEL

The basic physical assumption underlying the linear mixture model is that the different occupations present in a pixel contribute independently to its reflectance. The reflectance of that pixel can be considered as a sum of the individual land covers reflectances weighted by their area proportions. This model was used in different studies to un-mix pixels [START_REF] Quarmby | Linear mixture modelling applied to AVHRR data for crop area estimation[END_REF][START_REF] Settle | Linear mixing and the estimation of ground cover proportions[END_REF]. The quoted authors consider the pixel's response in different spectral bands of satellite images and resolve a system of nb linear equations where nb corresponds to the number of bands. This approach restricts the number of studied land cover types. In fact, only the case for which we have fewer interesting components than the number of acquisition bands can be evaluated. In other words, if we are dealing with NOAA/AVHRR data, only three land cover types can be studied because of the only three available channels measuring the reflectance in the visible and near infrared bands. To avoid this restriction, we propose to exploit the temporal information offered by the NOAA/AVHRR sensor. We make use of the whole sequence with a daily frequency and covering the vegetative cycle.

The number of linear equations is then important and we can study all land covers of a scene. At each date t we consider the linear relation between the pixel's reflectance and the individual reflectances of its components in the visible (channel 1) and near infrared (channel 2) channels:

R k i t = Nc X j=1 ij R k j t k = 1 2
(1) where:

Bouzidi, Sonia N c is the number of land covers, R k i t the reflectance of a NOAA pixel i in channel k (k = 1 or 2), at date t, R k j t the individual reflectance of the land cover type j in channel k (k = 1 or 2), at date t, ij the proportion of the land cover j within a NOAA pixel i.

We first use this model within a learning process to estimate the individual temporal reflectances R k j t for each land cover type in the visible and near infrared channels. For this purpose, we consider a small learning area for which ground truthing and high spatial resolution remote sensing data are simultaneously available. A precise land cover thematic classification image is obtained for this area from the remote sensing and the ground truthing [START_REF] Flügel | Classification of the Mkomazi river catchment[END_REF]. Then, after geometrical registration, we superpose the Landsat classification image and the NOAA images. Consequently, for each NOAA pixel, its composition in terms of percentage of land cover can be obtained by directly counting pixels on the Landsat classification image. We then obtain the ij values for this learning area. At each date t, we consider the linear model (1) for several pixels i; knowing the ij , the inversion of the obtained linear system allows the estimation of individual values R k j for this date. By repeating this process for all the dates, the temporal profiles R k j t are computed. This method and its results are detailed in (Bouzidi et al., 1997a[START_REF] Bouzidi | Subpixel mixture modeling applied for vegetation monitoring[END_REF]. In this paper, we use the hypothesis that these temporal profiles are spatially constant. At each pixel i, we consider the linear model (1) for several dates t; knowing the R k i t from the NOAA image and the individual temporal profiles R k j t from the learning process, the inversion of the obtained linear system allows the estimation of the proportions ij of each land cover j within the pixel. This point is described in the next section.

LAND COVER PROPORTIONS ESTIMATION

Our task is to estimate for each pixel i in the NOAA image the proportion ij of land cover j. We then consider, for this given pixel i, its reflectance in the visible and near infra-red channels for a number of dates. These dates are selected to avoid bad quality acquisitions and only images containing at least 80 of free clouds pixels are considered. Moreover, the acquisitions are constraint to cover an important part of the vegetative cycle in order to discriminate at best the different land covers. An over-determined system (S) of M linear equations (M denotes the number of dates) and N c unknown variables ( ij j = 1 : : : N c ) is then obtained:

S R k i t = Nc X j=1 ij R k j t k = 1 2 t = 1 : : : M (2)
with the following constraints:

Nc X j=1 ij = 1 (3) 0 ij 1 j = 1 : : : N c (4)
To solve these equations, we formulate the problem as an optimization problem. We aim to minimize, for a given pixel i, the difference between the different observed reflectance and that estimated by the linear model. This leads to the minimization of a set of functions for each pixel i:

jR k i t , Nc X j=1 ij R k j tj k = 1 2 t = 1 : : : M (5)
under the constraints (3) and (4). This minimization is performed using an algorithm based on sequential quadratic programming described in [START_REF] Zhou | Nonmonotone line search for minimax problems[END_REF]. This process, that we call "NOAA unmixing process" outputs, for each pixel, N c values corresponding to the proportions: percentage of each land cover type. This process allows the generation of N c images, each one having the size of the original NOAA image and giving for the studied land cover type its proportion within each pixel.

RESULTS AND VALIDATION

The test area chosen to evaluate the results is the Mkomazi catchment in Kwazulu-Natal (South Africa The process of validation is explained in figure 1. We consider a test zone covered simultaneously by the Landsat image and the NOAA acquisitions. We first establish the pixels' composition using the classification image obtained from Landsat data (only ground pixels are considered, and a mask is applied on pixels containing water). In fact, each NOAA pixel contains approximately 37 37 Landsat pixels which can be localized by the geometrical registration. From this set of Landsat pixels and from the classification image we compute the composition of the NOAA pixels in terms of the different land cover percentages. The obtained compositions serve as reference ones and are compared to the pixels proportions obtained after unmixing process of the NOAA data. This can be done for each land cover type. We present in figure 2 and figure 3 results obtained respectively for bare soil and grass. The lighter a pixel is, the greater the value of proportion or composition (in%) is.

In order to evaluate the difference between the pixels' compositions from the Landsat classification and the proportions obtained after the unmixing process of the NOAA data, we compute an euclidian distance between both results. So, for each land cover type j, a distance value is computed using the equation ( 6):

d j = v u u u t n X i=1 P j i , C j i 2 n (6)
where :

P j i denotes the proportion of land cover j in pixel i obtained after the unmixing process of the NOAA pixels, C j i denotes the composition of NOAA pixel i in land cover j obtained after the counting process on the thematic Landsat classification image, n is the number of NOAA pixels used for the evaluation.

The 26:79, field 12:7). These euclidian distances are computed from exact numerical values of composition and proportion and are not so easy to interpret even if we can see that fields and grass seem to be the land cover types difficult to analyse.

We then propose to consider a qualitative criterion for comparison of results. So, for each land cover type, for each process (counting process to compute composition, unmixing process to compute proportion), and for each pixel, we define a label according to table 3. Consequently, for each land cover, we generate two new images of labels values (1... corresponding to the two process (counting for composition, unmixing for proportion) as it is illustrated by figures 4 et 5, respectively for bare soil and grass. Then, we compute for each land cover, a 5 5 matrix L, where each value lc u (c u = 1 :::5) represents the quantity of pixels belonging to label c for composition (computed after the counting process of the Landsat classification image) and retrieved with a label u for the proportion (computed after the unmixing process of the NOAA data). The normalized trace of this matrix is then a global measure of accuracy for the unmixing process, compared with the classification process of the Landsat images. The table 4 displays the results obtained for the different land covers. High rates of label recognition are obtained for the land covers urban, forest and bare soil. However, the errors observed for the land covers grass and field are important. We are currently wondering about the kind of qualitative labels to create. We also suppose a confusion between these two classes because of their similar visible and near infra-red behaviors which have been used for the unmixing process of NOAA data. This is illustrated on figure 6 by displaying the NDVI (Normalized Derived Vegetation Index) curves estimated from the visible and near infra-red NOAA/AVHRR channels (N D V I = nir , vis=nir + vis): the curves are quite similar and that surely explains the difficulty to discriminate grass and fields in the visible and near infra-red channels. A future task is then to compute a differentiation criterion between these two land covers, in order to minimize this confusion. To do this, we propose to make use of the thermal channels and to compute proportions by considering the physical based mixture model that has been discussed in [START_REF] Lahoche | Fusion of Landsat TM and NOAA/AVHRR data for generating evapotranspiration maps in a semi-arid catchment[END_REF].

CONCLUSION

We describe a method for land use classification at meso-scale using coarse spatial resolution remotely sensed data acquired by the NOAA/AVHRR sensors. We define a model for the pixels' content and a process allowing to compute the individual proportions of the land covers for each pixel. This process exploits the temporal information of the NOAA data and is based on inverting a linear mixture model of reflectance, we call it the "unmixing process". The result provides a description in terms of land covers percentage within each NOAA pixel. Results evaluation is carried out on a test site and show that the method gives a global idea about land cover proportion inside the NOAA pixels. If this method seems to be promising, it must still be improved: define which types of land cover can be discriminated, and with which precision level. On another hand, for the inversion of the linear mixture model, we have considered a determinist resolution. A new formulation based on a probabilistic framework is under investigation, in order to estimate proportion values and also the associated likelihood.

Figure 2 :

 2 Figure 2: Bare soil. On the left, composition computed from the classification image; on the right, proportion obtained after the unmixing process of the NOAA pixels.

Figure 3 :

 3 Figure 3: Grass. On the left, composition computed from the classification image; on the right, proportion obtained after the unmixing process of the NOAA pixels.

  Labels and their corresponding values for proportion and composition.

Figure 4 :

 4 Figure 4: Bare soil. On the left, labels of composition; on the right, labels of proportion.

Figure 5 :

 5 Figure 5: Grass. On the left, labels of composition; on the right, labels of proportion.

Figure 6 :

 6 Figure 6: Temporal profiles of NDVI, for field and grass.

Table 1 :

 1 The available images are the following: a temporal sequence of NOAA images covering an important part of southern Africa, a Landsat TM image covering the main part of the catchment, a land cover classification computed from the Landsat TM image and enhanced by ground truthing. It is described in table 1. Characteristics of the Mkomazi Landsat thematic classification image.

	Name of land cover Relative surface of land cover
		in the thematic classification
		image
	indeterminate	8.69%
	water	18.36%
	urban	6.91%
	field	12.70%
	bare soil	4.47%
	grass	26.79%
	bushland	11.40%
	woodland	1.16%
	forest	9.52%

). The data available for this site are obtained within the context of the European INCO-PED IWRMS project (Integrated Water Resources Management System).

Table 2 :

 2 table 2 gives the euclidian distance values obtained for the different land cover types. The highest error values Euclidian distances for each land cover.

	Land cover Euclidian Distance
	urban	0.07
	field	0.16
	bare soil	0.05
	grass	0.16
	bushland	0.09
	forest	0.11

(measured by the euclidian distance) are observed for land covers occupying important surfaces of the test area (grass

Bouzidi, Sonia

International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.

Table 4 :

 4 Percentage of identical labels for each land cover type.

International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.

Bouzidi, SoniaInternational Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.

ACKNOWLEDGMENTS

This research is made within the context of the European INCO-PED IWRMS project (Integrated Water Resources Management System http://www.iwrms.uni-jena.de/) funded by European Commission under the contract ERBIC18CT97044.

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