Structure and Temporal Change of the Credit Network between Banks and Large Firms in Japan

Iyetomi, Hiroshi; Ikeda, Yuichi; Aoyama, Hideaki; Fujiwara, Yoshi; Souma, Wataru Article Structure and Temporal Change of the Credit Network between Banks and Large Firms in Japan Economics: The Open-Access, Open-Assessment E-Journal Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Iyetomi, Hiroshi; Ikeda, Yuichi; Aoyama, Hideaki; Fujiwara, Yoshi; Souma, Wataru (2009) : Structure and Temporal Change of the Credit Network between Banks and Large Firms in Japan, Economics: The Open-Access, Open-Assessment E-Journal, ISSN 1864-6042, Kiel Institute for the World Economy (IfW), Kiel, Vol. 3, Iss. 2009-7, pp. 1-18, https://doi.org/10.5018/economics-ejournal.ja.2009-7 This Version is available at: https://hdl.handle.net/10419/27527 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en Vol. 3, 2009-7| March 16, 2009 | http://www.economics-ejournal.org/economics/journalarticles/2009-7 Structure and Temporal Change of the Credit Network between Banks and Large Firms in Japan Yoshi Fujiwara ATR/NiCT CIS Applied Network Science Laboratory, Kyoto Hideaki Aoyama Department of Physics, Kyoto University, Kyoto Yuichi Ikeda Hitachi Ltd., Hitachi Research Laboratory, Ibaraki Hiroshi Iyetomi Department of Physics, Niigata University, Ikarashi, Niigata Wataru Souma ATR/NiCT CIS Applied Network Science Laboratory, Kyoto Abstract We present a new approach to understanding credit relationships between commercial banks and quoted firms, and with this approach, examine the temporal change in the structure of the Japanese credit network from 1980 to 2005. At each year, the credit network is regarded as a weighted bipartite graph where edges correspond to the relationships and weights refer to the amounts of loans. Reduction in the supply of credit affects firms as debtor, and failure of a firm influences banks as creditor. To quantify the dependency and influence between banks and firms, we propose a set of scores of banks and firms, which can be calculated by solving an eigenvalue problem determined by the weight of the credit network. We found that a few largest eigenvalues and corresponding eigenvectors are significant by using a null hypothesis of random bipartite graphs, and that the scores can quantitatively describe the stability or fragility of the credit network during the 25 years. Special issue “Reconstructing Macroeconomics” JEL: E51, E52, G21 Keywords: Banking; credit topology; bipartite network; systemic risk Correspondence Yoshi Fujiwara, ATR CIS Applied Network Science Lab., Kyoto 619-0288, Japan; e-mail: [email protected]m We would like to thank M. Gallegati and G. De Masi for discussions during a preliminary stage of this work. Y.F. thanks them for the collaboration (De Masi et al., 2008). We acknowledge the Nikkei Media Marketing, Inc. for technical assistance. © Author(s) 2009. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany Economics: The Open-Access, Open-Assessment E-Journal 1 1 Introduction The credit-debt relation between banks and firms is one of the most important relationships among economic agents. Credit is a source of profit for a bank, and it is fuel for growth of a firm. The flip side of the relation is, however, the path where failures take place and their propagation occurs often at a nation-wide scale, and sometimes to a world-wide extent, as we experience today. It is well known that the Japanese banking system suffered a considerable deterioration in its financial condition during the 1990s. Financial institutions in private-sector had accumulated loan losses, more than 80 trillion yen (nearly 15% of GDP), which reduced the bank capitalization, and led to the failure of three major and other small banks. Even though two major banks were nationalized in 1997, and other political decisions were made in order to maintain the stability of financial system, most banks, major and minor, decreased the supply of credit immediately; even by reducing existing loans to firms. A lot of firms, especially small and medium-sized firms, eventually suffered loss of funding. See Brewer et al. (2003). Financial systems are, at an aggregate level, subject to the tails of distributions for economic variables. This perspective has been recognized increasingly in economics; personal income, firm-size, number of relationships among firms and banks (ownership, supplier-customer, etc.), and so on. It has been recognized that distributions and fluctuations are the keys for understanding many phenomena in macro-economy (see Aoki and Yoshikawa (2007) and Delli Gatti et al. (2008)). Figure 1: Historical data of the total amount of debt from banks during the calendar years, 1980 to 2005. For large firms (filled circles) and for small and medium firms (squares). 300 200 100 0 1980 1985 1990 1995 2000 2005 Debt from banks (billion yen) Year (calendar) Large firms Small-Medium Fig. 1shows the historical data of the total amount of debt from banks for large firms and for small and medium firms1. For the year 2005, 1.25% (33,833) 1Source: 2008 white papers on small and medium enterprises in Japan, Small and Medium Enterprise Agency. Here large firms are the companies capitalized at 100 million yen or more, and small-medium firms are the others. Calendar years are used here and throughout this paper. www.economics-ejournal.org 2Economics: The Open-Access, Open-Assessment E-Journal of domestic firms are the large firms according to the classification, while the rest 98.75% are the small-medium firms2. Yet the total loans for the large firms amount to be 160 billion yen, which is nearly equal to those for the small-medium firms as shown in the figure. Thus, only a small fraction of firms account for half of all loans. Conversely, as we shall show in this paper, a large part of loans is provided by a few large banks — the tail of another distribution. Suppose a large firm is heavily indebted with banks. Then a failure of the firm, or a default, may cause a considerable effect on the balance sheets of the banks. If the banks reduce their supply of credit, then the total supply of loans will be decreased resulting in the adverse shocks to other firms. Therefore, the study of structure of credit relationships or credit network between banks and firms, and its temporal change would give us an insight to understand the financial stability or fragility. This is precisely the purpose of this paper. There are several related works in the literature. For example, Ogawa et al. (2007) carried out an analysis of dependency of the number of long-term credit relationships on characteristics of firms. Uchida et al. (2008) studied the relation between bank-size and credit links. Kano et al. (2006) investigated the credit of small and medium-sized firms. Studies such as Ogawa et al. (2007) focus on multiple lending relationships. Recently, complex network analysis (see Caldarelli (2007) and references therein) has been applied to financial systems (e.g., Inaoka et al. (2004), Imakubo and Soejima (2008), Iori et al. (2008) for inter-bank relationships, De Masi and Gallegati (2007), De Masi et al. (2008) for bank-firm relationships). In this paper, we shall study on the credit network between banks and large firms by regarding the network as a weighted bipartite graph, develop quantification of fragility of banks, and apply it to credit networks in Japan for the past 25 years. In Section 2, we describe our credit network dataset. In Section 3.1, we consider a credit network as a weighted bipartite graph, and show several statistical properties of heavy-tailed distributions. Then, in Section 3.2, we propose a set of scores for banks and firms which measure potential influences that one agent exerts on the other. It is shown that the scores can be calculated by solving an eigenvalue problem. In Section 3.3, we apply this method to our dataset from the year 1980 to 2005. The results are discussed in Section 4.Appendix A: is for proving mathematical properties for the eigenvalue problem which appeared in Section 3.2. 2 Dataset Our dataset is based on a survey of firms quoted in the Japanese stock-exchange markets (Tokyo, Osaka, Nagoya, Fukuoka and Sapporo, in the order of market size). The data were compiled from the firms’ financial statements and survey by Nikkei Media Marketing, Inc. in Tokyo, and are commercially available. They include the information about each firm’s borrowing obtained from financial institutions such as the amounts of borrowing and their classification into short-term and longterm borrowings. We examined the period from the years 1980 to 2005, for which incomplete data are few, and study the time development of credit relationships by 2Source: statistics of corporations by industry, annual report, 1980 to 2005, Ministry of Finance. www.economics-ejournal.org Economics: The Open-Access, Open-Assessment E-Journal 3 Figure 2: The number of commercial banks and quoted firms. 0 50 100 150 200 250 1980 1985 1990 1995 2000 2005 0 500 1000 1500 2000 #banks #firms (quoted) Year (calendar) #banks #firms Table 1: Classification of commercial banks. # denotes the net number of institutions in each corresponding category during the years, 1980 to 2005. The leftmost column, ato j, is defined as a short-hand notation. id Classification # aLong-term credit banks 3 bCity banks 16 cRegional banks 64 dSecondary regional banks 71 eTrust banks 20 fLife insurance companies 23 gNon-life insurance companies 23 hCredit associations (Shinkin banks) 4 iAgricultural financial institutions 4 jShoko Chukin bank 1 Total 229 using the total of long and short-term credit. For financial institutions, we select commercial banks as a set of leading suppliers of credit. The set comprises long-term, city, regional (primary and secondary), trust banks, insurance companies and other institutions including credit associations. During the examined period, more than 200 commercial banks existed, which are summarized in Table 1. We remark that failed banks are included until the year of failure, and that merger and acquisition of banks are processed consistently. For quoted firms, we choose only surviving firms that are quoted in the stock markets mentioned above3. 3Based on the lists of surviving firms and quoted firms in September and December 2007 respectively. Firms registered on over-the-counter (OTC) market and/or on JASDAQ (the present OTC market) are excluded. The dataset includes the OTC and JASDAQ data since 1996, so we exclude them also by checking the listing date of the firms added in the dataset. www.economics-ejournal.org 4Economics: The Open-Access, Open-Assessment E-Journal Table 2: Sectors of quoted firms in the dataset. # denotes the net number of firms in each sector during the years, 1980 to 2005. The total number of the firms amounts to 2,330. manufacturing # non-manufacturing # Foods 105 Marine products 5 Textile products 60 Mining 7 Pulp & paper 18 Construction 148 Chemicals 156 Wholesale trade 233 Drugs & medicines 33 Retail trade 153 Petroleum & coal 11 Securities 18 Rubber products 20 Credit & leasing 75 Ceramic, etc. 49 Real estate 75 Iron & steel 49 Railway transport. 27 Non-ferrous metals 106 Road transport. 28 General machinery 182 Water transport. 15 Electronics 203 Air transport. 4 Shipbuilding 6 Warehousing 38 Motor vehicles 65 Information Tech. 20 Transportation equip. 11 Utilities (electric) 11 Precision instruments 40 Utilities (gas) 13 Other manufacturing 82 Services 264 The number of banks and firms in each year is summarized in Fig. 2. The classification of banks and industrial sectors of firms are shown in Table 1and Table 2respectively. 3 Analysis of Credit Network 3.1 Credit Network as a Weighted Bipartite Graph Each yearly statement, or snapshot, of the credit network in our dataset can be regarded as a bipartite graph. Nodes are either banks or firms4. Banks and firms are denoted by Greek letters µ(µ= 1,...,n) and Latin letters i(i= 1,...,m) respectively. nis the number of banks, and mis that of firms. An edge between a bank µand a firm iis defined to be present if there is a credit relationship between them. In addition, a positive weight wµi is associated with the edge, which is defined to be the amount of the credit. We can depict the network as shown in Fig. 3. wµi is the amount of lending by bank µto firm i, which precisely equals to the amount of borrowing by firm ifrom bank µ. The total amount of lending by bank 4Note that banks are not included in the side of firms, even if they are borrowing from other banks. Because our dataset includes banks’ borrowing only partially, the interbank credit is not considered here, though it is no less important than the bank-firm credit studied here. www.economics-ejournal.org Economics: The Open-Access, Open-Assessment E-Journal 5 Figure 3: Credit network as a bipartite graph. An edge connecting between bank µ and firm iis associated with an amount of credit wµi as a weight. µis wµ:= ∑ i wµi ,(1) and the total amount of borrowing by firm iis wi:= ∑ µ wµi .(2) We note that a same value wµi has different meanings as a weight to the bank µ and to the firm i. For example, even if 90% of the total lending of the bank µgoes to the firm i, it may be the case that idepends on µby only 20% for all the loans from banks. It would be natural to define an (n×m) matrix Awhose component is given by Aµi := wµi wµ .(3) Aµi represents the relative amount of lending by bank µto firm i. We have ∑ i Aµi = 1 for all µ . (4) Similarly, we define an (m×n) matrix Bby Biµ := wµi wi .(5) Biµ represents the relative amount of borrowing by firm ifrom bank µ. We have ∑ µ Biµ = 1 for all i . (6) The degree kµof bank µis the number of edges emanating from it to firms, and the degree kiof firm iis the number of edges to banks. When the weights wµi are all equal to 1, it is obvious that kµ=wµand ki=wi. The distributions for wµ,wi,kµ,kihave long-tails. They are shown, for the data of credit relationships in the year 2005, in Fig. 4(a) to (d). The long-tails for the www.economics-ejournal.org 6Economics: The Open-Access, Open-Assessment E-Journal banks’ amount of credit and number of firms for lending, in Fig. 4(a) and (c) for wµand kµrespectively, are comprised of city banks, long-term credit banks, several of trust banks and insurance companies (see the classification in Table 1). Similar long-tails are observed for firms, as shown in Fig. 4(b) and (d) for wiand ki. There is a significant correlation between wµand kµin a natural way, and also for wiand ki, as shown in Fig. 4(e) and (f) respectively. We calculated rank correlation in terms of Kendall’s τ, which gave significant values of τ= 0.825(16.0σ) and τ= 0.450(28.3σ) respectively, where σis the value under the null hypothesis of statistical independence. In particular, from the Fig. 4(e), we can observe an empirical relation of kµ∝wa µ, where a≈0.69 ±0.03 (least-square fit; error 95% level). This implies the relation of wµ/kµ∝k0.44±0.07 µmeaning that the average loan is larger for the larger degree kµ, or roughly speaking, for the larger banks. This observation is consistent with known empirical facts (see Uchida et al. (2008) on similar relation for borrowing by small and medium-sized enterprises). We refer the reader to De Masi et al. (2008) for extensive study on statistical properties of credit topology and weights. 3.2 Fragility Scores of Banks Bank and firm establish a credit relationship for obvious reasons. Bank supplies credit in anticipation of interest margin, and firm uses credit as an important source of financing in anticipation of growth in its business. An edge of credit, therefore, represents dependency of one agent on the other in two ways. Aµi quantifies the dependency of bank µon firm ias a source of profit. Also Biµ is the dependency of firm ion bank µas a source of financing from financial institutions. The flip side of dependency is a potential influence which one agent exerts on the other, as we argue below. Suppose that one can quantify a change in the level of bank µ’s financial deterioration by a variable or score, xµ, which is to be defined in a consistent way by the following argument. Bank µwith increasing xµwill behave in various ways; it may shrink the amount of its supplied credit, increase interest-rate, shorten the due time of payment by firms, and so forth. In any case, it would influence firm ito an extent that can be quantified by Biµ, because it represents the dependency of firm ion bank µfor the source of financing. Suppose additionally that a change in the level of firm i’s financial degradation is quantified by another score, yi, it would be reasonable to assume that yiis proportional to Biµ xµsummed over banks µ, or yi∝∑µBiµ xµ, as the influence from banks to firms. Fig. 5(a) illustrates this direction of influence. Similarly for the reverse direction of influence, from firms to banks. Firm iwith yimay delay its repayment, have defaults, even fail into bankruptcy, and so forth, due to its financial difficulties. Then the lending banks will not be able to fully enjoy profits in expected amounts due to the delay, may possibly have bad loans partially, if not totally, for the credit given to bankrupted firms. Any of them would result in the banks’ financial deterioration, the level of which was assumed to be quantified by xµat the outset of our argument. Such influence to bank µfrom www.economics-ejournal.org Economics: The Open-Access, Open-Assessment E-Journal 7 Figure 4: (a) Cumulative distribution P>(wµ) for banks’ lending wµ. (b) P>(wi) for firms’ borrowing. (c) P>(kµ) for the number of banks’ lending relationships. (d) P>(ki) for the number of firms’ borrowing relationships. (e) Scatter plot for banks’ wµand kµ. (f) Scatter plot for firms’ wiand ki. All the plots are for the data in the year 2005. In the plots (a),(c) and (e) for banks, the points are drawn according to the classification given in Table 1. Rank correlations (Kendall’s τ) for (e) and (f) are τ= 0.825(16.0σ) and τ= 0.450(28.3σ) respectively (σcalculated under the null hypothesis of statistical independence). 10-2 10-1 100 10-1 100101102103104 P>(wµ) wµ (billion yen) a, b c, d e f, g h, i, j 10-3 10-2 10-1 100 102103104105106107 P>(wi) wi (million yen) 10-2 10-1 100 100101102103 P>(kµ) kµ a, b c, d e f, g h, i, j 10-3 10-2 10-1 100 100101102 P>(ki) ki 100 101 102 103 10-1 100101102103104 kµ wµ (billion yen) a, b c, d e f, g h, i, j 100 101 102 102103104105106107 ki wi (million yen) (a) (b) (c) (d) (e) (f) www.economics-ejournal.org 14 Economics: The Open-Access, Open-Assessment E-Journal the matrix A: (aµ)i:= Aµi ,(19) it is possible to define a similarity in the lending patterns for a pair of banks µand ν, for example, by the inner product of the corresponding vectors aµand aν. Then one can perform the clustering by standard methods including multi-dimensional scaling and hierarchical clustering. Indeed, De Masi et al. (2008) showed the minimum spanning tree (MST) calculated by a similarity measure ignoring the information of weight but considering only the connectivity from banks to firms. The resulting MST corresponds to clusters of co-financing relationships of banks, which strongly reflect the geographical regions especially for the regional banks. It would be interesting to investigate how the eigen-structure is related to those clusters. It is also remarked that, as described in Section 2, we did not include the firms that went into bankruptcy. It should be interesting to include them in the credit network in order to evaluate the effect to banks and to compare the evaluation with the structural change that followed after the bankruptcy. It would be possible to model such propagation based on our consideration in defining the scores. 5 Conclusion We studied the structure and its temporal change of Japanese credit relationships between commercial banks and quoted firms for the 25 years from 1980 to 2005. Each snapshot of the credit network is regarded as a weighted bipartite graph, where each node is either a bank or a firm, and an edge between a bank and a firm is defined to be present if there is a credit relationship between them. The edge has a weight that represents the amount of credit. Suppose that a bank shrinks the amount of its supplied credit, a firm as debtor would be influenced to a certain extent that might be quantified by a matrix that can be calculated by the weight. Similarly, if a firm fails, then its effect to a bank as debtor would propagate to an extent that is measurable from the weight. To quantify the propagation, we introduced a set of score named fragility and its dual, and proved mathematical properties among them. The set of scores can be obtained by solving an eigenvalue problem. By comparing the eigen-structure with that obtained in random bipartite graphs, which have same distributions for degrees of banks and firms and for normalized weight of banks, we found that the largest few (non-trivial) eigenvalues for the scores are significant. We performed historical analysis for our datasets, and showed that there are periods when the eigen-structure is stable or unstable, and that a particular set of banks, mostly a few regional banks, have large values of the fragility scores. Drastic change occurs in the late 80s during the bubble and also at the epochs of financially unstable periods including the financial crisis. Further investigation might be necessary to relate our results based on complex network analysis to the characteristic of banks, but we believe that our approach is a potentially valuable quantification of the structure and its temporal change of credit relationships. www.economics-ejournal.org Economics: The Open-Access, Open-Assessment E-Journal 15 Appendix A: Mathematical Properties of the Eigenvalue Problem As shown in Section 3.2, the set xof fragility scores of banks is the right eigenvector of the weight matrix Pas in Eq.(9), and the set uof dual scores of banks satisfy the left eigenvector of Pas in Eq.(12). In this Appendix, we prove mathematical properties on eigenvalues and eigenvectors. Let us first show that the score ucan be calculated directly from the score x. Eq.(9) is written explicitly in components as 1 wµ∑ i,ν 1 wi wµiwνixν=λxµ,(A.1) which we rewrite as ∑ i,ν 1 wi wµiwνixν=λwµxµ.(A.2) On the other hand, Eq.(12) is ∑ µ uµ 1 wµ∑ i 1 wi wµiwνi =λuν,(A.3) which, after exchanging µ↔ν, reads as ∑ i,ν 1 wi wµiwνi uν wν =λuµ.(A.4) By comparing Eq.(A.2) and Eq.(A.4), we find that they are equivalent under the identification: uµ∝wµxµ.(A.5) This also proves that left-eigenvalues and the right-eigenvalues have a same spectrum. Let us consider two sets of eigenvalues and corresponding eigenvectors, (λ(k),u(k),x(k)) and (λ(`),u(`),x(`)). We have u(k)TPx(`)=λ(k)u(k)T·x(`)=λ(`)u(k)T·x(`).(A.6) This means that 0 = (λ(k)−λ(`))u(k)T·x(`)=(λ(k)−λ(`))∑ µ u(k) µx(`) µ,(A.7) www.economics-ejournal.org 16 Economics: The Open-Access, Open-Assessment E-Journal which, by the use of Eq.(A.5), implies that 0 = (λ(k)−λ(`))∑ µ wµx(k) µx(`) µ.(A.8) Therefore, the eigenvectors should be orthonormal under the weight wµas a metric5. That is, ∑ µ wµx(k) µx(`) µ=δk` .(A.9) It follows from Eq.(A.9) the orthonormality: ∑ k wµx(k) µx(k) ν=δµν .(A.10) This consideration of the inner product implies that we should take a look at the product of Eq.(A.2) and xµ. This leads us to λ=∑ i 1 wi(∑ µ wµixµ)2 ∑ µ wµx2 µ .(A.11) This proves that λis real and positive, although the matrix Pis not symmetric. Also we have the following inequality that holds for any value of q. 0≤∑ µ wµi(q−xµ)2=wiq2−2(∑ µ wµixµ)q+∑ µ wµix2 µ.(A.12) This leads to the inequality for the discriminant: (∑ µ wµixµ)2 −wi∑ µ wµix2 µ≤0,(A.13) from which it proves that the largest eigenvalue is 1. 0< λ ≤1.(A.14) This proves Eq.(13). It is obvious from Eq.(A.11) that λ= 1 if and only if xµ=q. In fact, one can easily see, from Eq.(4) and Eq.(6) that xµ= 1 (µ= 1,...,n) is the eigenvector corresponding to λ= 1, provided that the bipartite graph is connected (i.e. any node of bank or firm is reachable from any other)6. This proves Eq.(14). 5Mathematically, xis a covariant vector, uis a contravariant vector, and the metric that connects them is given by gµν =δµν wµ. The orthogonalization of eigenvectors is done with respect to this metric. 6For a disconnected graph, xµis constant in each connected components. The multiplicity of λ= 1 is equal to the number of the connected components. www.economics-ejournal.org Economics: The Open-Access, Open-Assessment E-Journal 17 In addition, by applying the orthogonal relation in Eq.(A.10) to Eq.(A.2), it can be shown after a short calculation that the summation formula holds: ∑ k λk=∑ µ,i AµiBiµ = tr P.(A.15) This proves Eq.(15). To summarize, the eigenvector ucan be calculated directly from the eigenvector x. Also the eigenvalues satisfy 0 < λ ≤1, where the largest eigenvalue corresponds to a trivial eigenvector. On the other hand, the dual scores, u, corresponding to the largest eigenvalue λ= 1 simply represents the total amount of loans, namely uµ∝wµdue to Eq.(A.5), so we can focus on non-trivial eigenvectors, x(2),x(3) and so on in the main text. www.economics-ejournal.org 18 Economics: The Open-Access, Open-Assessment E-Journal References Aoki, M., and H. Yoshikawa (2007). Reconstructing Macroeconomics — A Perspective from Statistical Physics and Combinatorial Stochastic Processes. Cambridge: Cambridge University Press. Brewer E., H. Genay, and G. G. Kaufman (2003). Banking Relationships during Financial Distress: The Evidence from Japan. Economic Perspectives, 27(3),2–19. Caldarelli, G. (2007). Scale-Free Networks. Oxford: Oxford University Press. De Masi, G., Y. Fujiwara, M. Gallegati, B. Greenwald, and J. E. Stiglitz (2008). An Analysis of the Japanese Credit Network. arXiv:0901.2384v1 [q-fin.ST]. De Masi, G., and M. Gallegati (2007). Bank-Firm Topology in Italy. Submitted. 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Some Evidence from Firm-Level Data. Economic Systems, 31(1),49–70. Uchida, H., G. F. Udell, and W. Watanabe (2008). Bank Size and Lending Relationships in Japan. Journal of the Japanese and International Economies, 22, 242–267. www.economics-ejournal.org Please note: You are most sincerely encouraged to participate in the open assessment of this article. You can do so by either rating the article on a scale from 1 (bad) to 5 (excellent) or by posting your comments. Please go to: www.economics-ejournal.org/economics/journalarticles/2009-7 The Editor © Author(s) 2009. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany