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The spatial Probit model—An application to the study of banking crises at the end of the 1990’s
Physica A 415 (2014) 251–260
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Physica A journal homepage: www.elsevier.com/locate/physa
The spatial Probit model—An application to the study of banking crises at the end of the 1990’s✩ Andrea Amaral a , Margarida Abreu a,b , Victor Mendes c,d,∗ a
ISEG (Lisboa School of Economics & Management), University of Lisbon, Rua do Quelhas, 6, 1200-781 Lisboa, Portugal
b
UECE (Research Unit on Complexity and Economics), Rua Miguel Lupi, 20, 1200 Lisboa, Portugal
c
CMVM - Portuguese Securities Commission, Rua Laura Alves, 4, 1050-138 Lisboa, Portugal
d
CEFAGE-UE (Center for Advanced Studies in Management and Economics), Largo dos Colegiais, 2, 7000-803 Évora, Portugal
highlights • • • •
Spatial Probit (SP) excels traditional probit in the study of financial contagion. SP allows the accounting of cross and feedback effects of contagion. Contagion may result from institutional similarities between banking systems. Or from business connections between institutions of different countries.
article
info
Article history: Received 9 January 2014 Received in revised form 19 May 2014 Available online 30 July 2014 Keywords: Spatial probit Banking crises Contagion
abstract We use a spatial Probit model to study the effect of contagion between banking systems of different countries. Applied to the late 1990s banking crisis in Asia we show that the phenomena of contagion is better seized using a spatial than a traditional Probit model. Unlike the latter, the spatial Probit model allows one to consider the cascade of cross and feedback effects of contagion that result from the outbreak of one initial crisis in one country or system. These contagion effects may result either from business connections between institutions of different countries or from institutional similarities between banking systems. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Most of the existing empirical research on the predictability and contagion of financial crises evaluates the probability of a banking system going into crisis using the traditional Probit/Logit models. Ref. [1] is one of the first studies in this area using a Probit model to study the determinants of currency crashes in developing countries, and decisively contributes to the development of the early warning system literature. The works by Berg and Pattillo [2], Edison [3] and Berg et al. [4] use the new indicators suggested by Kaminsky and Reinhart [5] and a more general Probit model applied to the Asian crisis in the eighties. Demirgüç-Kunt and Detragiache [6] use a multivariate Logit model for the prediction of banking crises. More recently, Bussière and Fratzscher [7] show that binomial discrete-dependent-variable models are subject to what the authors refer to as ‘‘post-crisis bias’’. However, the correction of this bias is done in the context of a multinomial Logit model. Finally,
✩ This article is part of the Strategic Project (PEst-OE/EGE/UI0436/2011).
∗ Corresponding author at: CMVM - Portuguese Securities Commission, Rua Laura Alves, 4, 1050-138 Lisboa, Portugal. Tel.: +351 213177000; fax: +351 213537077. E-mail addresses: [email protected] (M. Abreu), [email protected] (V. Mendes). http://dx.doi.org/10.1016/j.physa.2014.07.044 0378-4371/© 2014 Elsevier B.V. All rights reserved.
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Schularick and Taylor [8] and Jordá et al. [9] use a Logit model to study rare events associated with episodes of financial crisis, and Duca and Peltonen [10] use a multivariate discrete choice model for assessing and predicting systemic financial events. Although this literature contributed to a deeper understanding of banking and financial crisis, the traditional Probit/Logit models do not allow one to consider the effect of the connections between the different banking/financial systems in the outbreak of a financial crisis.1 As such, the validity of the estimators lays on the assumption that the observations/countries are different, but not connected. This means that these traditional models do not take into account that the occurrence of a systemic crisis in one country may also be a function of the neighboring banking system’s health or even of the similarity of the banking structure and legal and institutional environment of another country with which it has strong financial ties, independently of the physical or trade proximity between the countries. It may also be a function of the banking regulation culture in each country.2 In this paper we use a spatial Probit model in which the probability of a banking system suffering a crisis is also a function of the occurrence of crisis in ‘nearby’ banking systems. As referred in Ref. [14], this model does not only identify a ‘‘first victim’’ who’s banking system is in crisis; it allows one to take into consideration all the feedback effects, i.e., to consider that the crisis in a given banking system stimulates a series of impacts in other systems. In turn, these effects generate new actions, namely from the country in which the crisis episode has begun. The spatial model considers, therefore, the existence of a ‘‘cascade’’ of effects that is not present in the traditional model. The spatial Probit model lays on a web of connections between observations, through which instability waves propagate, summarized in the proximity matrix. In this paper we consider two ways of interpreting proximity. Firstly, we consider that two banking systems are close because flows of funds take place between them, and contagion is the spreading of a crisis to neighboring economies which are strongly dependent and connected (contagion based on the fundamentals and interdependence of economies—[15]). Secondly, we identify structurally similar banking systems: they may not be operationally connected, but have similar characteristics; therefore agents expect that whatever has affected banks in one country will also affect banks in other countries and react accordingly (mimetic contagion). The paper is structured as follows. The spatial Probit model is presented in Section 2. In Section 3 we discuss the dataset and variables used in the empirical application. Results are discussed (and compared with those from the traditional model) in Section 4, while Section 5 concludes the paper. 2. The spatial Probit model The spatial Probit model (version ‘‘Lag’’) is modeled as Yi∗ = ρwi1 Y1∗ + ρwi2 Y2∗ + · · · + ρwiN YN∗ + Xi β + εi
(1)
where Yi∗ is a latent variable, Xi is the vector of exogenous variables, β is a parameter vector, ρ is the dependence parameter, wij represents the proximity between observations (i, j), and εi is an i.i.d. random disturbance. Given that Yi∗ is not observable, the observables are only binary variables Yi , with
Yi =
1, 0,
if Yi∗ > 0 if Yi∗ < 0.
The model represents a substantive spatial dependence [16]; what happens with the ith observation depends on its links with all the other observations. In matrix notation (1) becomes Y ∗ = ρ WY ∗ + X β + ε
(1a)
where Y = (Y1 , . . . , YN ) , W (N × N ) is a spatial weight matrix that captures the dependence structure between neighboring observations, and ε ∼ N 0, σ 2 IN .3 If ρ = 0 the model reduces to the standard Probit model.4 If ρ ̸= 0 the estimators used in the traditional Probit model are inconsistent. The error terms ε are heteroskedastic and autocorrelated. Maximum likelihood estimation techniques are not suitable for limited dependent variable spatial autoregressive models because they yield inconsistent estimators [19,20]. Moreover, the spatial likelihood function involves the evaluation of an n-dimensional integral; the estimation becomes more complex because a multidimensional integration is necessary to account for all these factors.5 ∗
∗
∗ ′
1 Lehar [11] tries to measure contagion via asset portfolio correlation (high correlation meaning contagion). In the context of a traditional Probit, Santor [12] uses a proxy for informational contagion and González-Hermosillo [13] uses the total bank loans to GDP ratio. These are, however, added as independent variables in the model. 2 In fact, in the eighties banking regulation became weaker due to competitive (de)regulation. 3 See Refs. [16,17], for example, on the Spatial Probit Model. 4 See Ref. [18] on the standard Probit model. 5 A recent example of an application of spatial Probit models is Ref. [21].
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On first glance, it would seem that the differences of model (1a) against the traditional Probit model are not significant; it is just about including an ‘‘average contagion indicator’’ in the model. However, this procedure has profound implications on the information necessary to estimate the model and on the parameter interpretation because the spatial Probit model lays on a connection’s web between observations, through which the instability waves propagate. One other possibility is to consider the links between observations as secondary: the agent’s actions are correlated because they suffer the influence of a common shock. It is the ‘‘Error’’ version of the model, in which λ is the contagion parameter: Yi∗ = Xi β + εi
with εi = λ
n
wij εj + ui
(2)
j =1
or, in matrix notation Y ∗ = X β + ε,
with ε = λW ε + u, u ∼ N 0, σu2 IN .
(2a)
The intensity with which the banking crisis propagates is directly dependent on the countries’ economic and financial integration. The proximity between the agents, being commercial, political or plain informative, has a central role in all the contagious processes, and as such the understanding of the phenomenon goes through the connection’s web between the agents, summarized in the proximity matrix. W is the spatial weights matrix. It captures the observations’ structure of dependency. Each generic element wij reflects the distance separating the element i from the element j. The elements of the spatial weights matrix are typically rowstandardized, such that for each i, j wij = 1, and this means that the spatial lag may be interpreted as a weighted average (the wij being the weights) of the neighbors. In general, the elements wij are based on the geographic arrangement of the observations, or contiguity, but alternative specifications exist,6 and the weights must be exogenous to the model in order to avoid identification problems [26]. Two ways of interpreting proximity are considered. The first is to accept that two banking systems are similar because an effective exchange of transactions exists, either by way of trade or capital participation. In this case, contagion is the spreading of a crisis to neighbor economies, strongly dependent and interconnected. It is what Dornbusch et al. [15] refers to as contagion with a real fundament, based on the basic fundamentals and interdependence of the economies. The second is to assume that banking systems are close when they are structurally similar. Here we have contagion by imitation, i.e., operationally the banking systems may not be connected, but as they have similar characteristics, agents expect that whatever has affected comparable banks in one country will also affect their own country and react accordingly. In this case contagion is attached to the behavior of the financial agents and also to the possibility of a shock being transmitted from one economy to another, with fundamental connections not having to necessarily exist. If the investor anticipates any added risk relatively to his portfolio, he will have increased preference for liquidity and will try to reduce his exposure namely in similar markets or in the same region. One other aspect is to do with the fact that the processing of the information specific to each country that should support the investor’s performance is complex and costly. Therefore the information that a country is in a crisis causes ‘‘wake up calls’’ in other economies. In either of the cases, the investors’ herding (i.e., imitation) behavior increases with the integration of the banking systems.7 The spatial Probit model integrates the complexity that characterizes the relations between the banking systems, and that complexity materializes in the proximity matrix. That matrix, exogenously defined, assumes central importance in these models, conditioning the dimension of the multiplying effects. By recurring to this proximity matrix the model gets close to the essays of Sheldon and Maurer [28], Furfine [29], Wells [30], Upper and Worms [31], Degryse and Nguyen [32], Lelyveld and Liedorp [33] and Mistrulli [34]. In these studies the interconnections’ matrix between the institutions is used in simulations to survey the existence of contagion. However, in the spatial Probit model, the probability of a country being in crisis is, among other things, function of the occurrence of crisis in ‘nearby’ countries, and this allows the accounting of a ‘‘cascade’’ effect that is not present in the traditional Probit model. 3. Dataset and variables We apply the spatial Probit model to the late 1990s banking crisis in Asia.8 The sample includes information for 87 countries9 in 1998, and the following variables: CRIS = 1 if the country’s banking system is in crisis (the Caprio and
6 Spatial weights can be based on distance decay [22], on the structure of a social network [23], on economic distance [24], on trade-based interaction measures [25], for example. 7 Herding behavior has been found in both institutional and retail investors. Friedman [27], for example, states that there are some characteristics of the professional investment community (importance of relative performance, asymmetry of incentives) which suggest that institutional investors will herd. 8 A preliminary version of the paper was published in 2010 (see Ref. [35]). 9 The sample includes developed, developing and less developed countries, so that the traditional model and the spatial model are estimated with the same number of observations in order to compare the results. The sample is conditioned by the higher demand of information of the spatial Probit model. The World Bank has information for 207 countries in 1998 (but not for all the variables of the model), and 26 of them were in crisis in 1998. In the sample used the percentage of countries in crisis (17%) is similar.
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Klingebiel’s [36] chronology to identify countries that have gone through systemic banking crisis is used); Inf = Inflation Rate; GDPg = GDP real growth rate; PubExpenses = Public expenses as a % of GDP; PCI = per capita income; Dep = 1 if there is a deposit insurance scheme in the country; ETA = Equity-to-Total Assets ratio10 ; ROA = Return on Assets; LIQ = Loan-to-deposit ratio; SDAssets = standard deviation of the log (total assets); Quality = Loan loss reserves-to-total assets ratio; CV_ROA = Coefficient of variation of ROA; CV_LIQ = Coefficient of variation of LIQ; HighROA = Percentage of banks with above average ROA; HighLIQ = Percentage of banks with above average LIQ.11 The sources of information are the World Bank,12 IMF13 and Bankscope.14 The construction of the model’s independent variables is explained, in detail, in the Appendix. It is important, however, to mention that to try and measure the importance of the microeconomic characteristics of the diverse institutions that make up the system, the return on assets and on equity, liquidity, structure of assets and of capital indicators which are included as independent variables, are averages for the banking system, but obtained based on the financial information available to the diverse institutions (more precisely commercial banks) which compose it.15 The proximity matrix is a proxy for the operational connections between banking systems. To measure the mesh of connections between banking systems the ideal would be to have available information relating to, for instance, the trade volumes between them, the capital participation between the systems or between the banks, or even information as to the banks indebtedness to foreign institutions. In whichever case it would be necessary disaggregated information, i.e., taking the last example, it is not enough to know what indebtedness a banking system i has to foreign institutions; it is necessary to know exactly what indebtedness a banking system i has to each one of the remaining banking systems in the sample. This information is not, however, available, and so one has to use a proxy.16 A reasonable approach could be achieved through the capital movements between countries, but we only have access to aggregate information on capital movements, being unknown in what way the flows that come out or go in to a country are divided between the destiny and origin country. One alternative is the use of exports, disaggregated by exchange partners. Although it is not an ideal solution, in fact countries with large trade exchanges are countries in which the banks have, as a consequence, strong connections. The point here is not to use the exports because the international trade is a channel of contagion, but to use the exports as a proxy of the level of interaction of the banks.17 We use the exports (Wx ), disaggregated by destination, and assume that countries with intense trade flows are countries with strongly connected banks.18 A second matrix (Wba ) is also built with the objective of measuring the existence of contagion by imitation, and to test the robustness of our results. It captures the similarities between the banking structures of each pair of countries via the degree of the restrictions imposed on bank activities.19 Countries with similar banking structures exhibit equivalent values and therefore the distance between them is smaller.20 , 21 Summing up, the proximity matrices are built to recreate the real mesh of connections between banking systems and not through entropy maximization, as in Refs. [28,30–33]. Entropy maximization assumes that each element establishes equal relations with all the others. This is not realistic in our study because each country does have different connections with all the other countries.
10 ‘Assets’ is defined as commercial banks’ total assets. 11 See Refs. [37–39], for example, on the use of inflation, GDP growth and public expenses, Ref. [6] on the use of deposit insurance and institutional environment, Ref. [13] and Ref. [40] on the use of microeconomic variables in the context of banking crises. 12 World Development Indicators, Bank Regulation and Supervision, and Bank Concentration and Crisis. 13 Direction of Trade Statistics Yearbook. 14 Bankscope is used to get (commercial) bank specific balance sheet and income statement information. 15 These variables are also referred to as ‘bank-specific variables’ in the remainder of the paper. 16 The possible fragility of the proxies used in the construction of the proximity matrices has motivated the non-realization of the statistical tests proposed by Pinkse [41] for the spatial correlation existence. The results of these tests are significantly affected by bad proximity matrices specification problems [42]. Besides, if the spatial dependence is not significant then the method will reflect this in the estimation of the ρ and λ coefficients. 17 The idea that banks ‘follow their customers abroad’ when those client firms engage in a growing volume of international trade and investment goes at least as far back as the seventies. A natural corollary is that banks become more multinational, and financial systems more connected. See, for example, Refs. [43,44]. 18 This matrix is computed for a sample of only 84 countries. Novo [14], in his study of the 1992 European exchange rate crises shows that trade connections, more than political proximity, are the primary contagion channel. We also use an (imports + exports) matrix since the interconnections between banks can be related to both imports and exports, thus unveiling additional trade/connection bilaterality. This allows one to check the robustness of the results. 19 The degree of restrictions to commercial bank access to the activities of brokerage, real estate, insurance and property ownership of non-financial firms are included in the analysis (see the variable definition in the Appendix). Barth et al. [45] show the existence of a relationship between bank regulation, particularly restrictions on bank activity, and crisis. 20 Again, we use an alternative bank activity matrix to test the robustness of our results. This alternative includes variables related to the structure of the banking sector (the market share of the three largest banks, bank return on equity, restrictions on banks’ activities), relevance of the banking sector (deposits as a percentage of GDP) and other characteristics of the banking sector (bank’s external loans and deposits as a percentage of domestic bank deposits). Other characteristics of the banking sector are included as independent variables. 21 W is based on indicators for which there is no times-series information. Besides, these indicators are related to sector characteristics that suffer ba
slow transformations and therefore present rather stable values in the short and medium term. As Barth et al. [46] refer, the regulation and supervision characteristics are relatively stable over a period of one or two decades. That is not the case of Wx as it depends on the export volumes in each year.
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Table 1 Estimation results, spatial Probit (dependent variable: CRIS). Wba Lag Const
5.794 (+9.05) **
Inf GDPg PubExpenses PCI Dep ETA ROA LIQ SDAssets Quality CV_ROA CV_LIQ HighROA
ρ
6.607 (+14.21) **
−0.062
−0.059
−0.058
(−16.25) **
(−16.51) **
(−17.19) **
−0.299
−0.314
−0.329
−0.298
(−25.77) **
(−24.16) **
(−20.92) **
(−25.04) **
−0.155
−0.155
−0.171
−0.155
(−19.51) **
(−19.14) **
(−19.30) **
(−19.05) **
−0.022
−0.023
−0.024
−0.022
(−15.10) **
(−14.69) **
(−14.18) **
(−14.75) **
−0.354
−0.251
−0.213
−0.303
(−3.96) **
(−2.83) **
(−2.34) **
(−3.46) **
−0.047
−0.043
−0.074
−0.046
(−6.43) **
(−5.90) **
(−7.96) **
(−6.31) **
−0.444
−0.452
−0.491
−0.438
(−19.10) **
(−19.06) **
(−18.16) **
(−18.49) **
−0.028
−0.029
−0.027
−0.027
(−10.94) **
(−10.98) **
(−10.39) **
(−10.53) **
0.236
0.217
0.204
0.260
(+2.53) **
(+2.32) **
(+2.12) **
(+2.78) **
−0.010
−0.013
−0.035
−0.012
(−3.01) **
(−3.05) **
(−2.16) **
(−2.91) **
−0.032
−0.031
−0.035
−0.032
(−6.71) **
(−6.53) **
(−5.89) **
(−6.61) **
1.336
1.344
(+7.83) **
(+7.93) **
−0.004
−0.002 (−0.72)
1.814 (8.38) **
−0.009 (−2.84) **
1.374 (+8.02) **
−0.003 (−0.92)
−0.049
−0.051
−0.048
−0.048
(−13.59) **
(−13.69) **
(−13.11) **
(−13.24) **
−0.479
4.473 (+1.50)
−0.039 (−1.81) *
−0.204 (−2.71) **
−0.105 (−2.01) **
−0.015 (−1.55)
−0.208 (−0.37)
−0.032 (−0.68)
−0.301 (−1.98) **
−0.018 (−1.13)
0.180 (+0.29)
−0.009 (−0.33)
−0.022 (−0.71)
0.945 (+0.87)
−0.002 (−0.12)
−0.032 (−1.39)
(+7.81) **
−1.056
0.004
(−7.27) **
87
Traditional Probit
0.31
(−1.89) *
n **
8.211 (+14.27) **
Wx Error
−0.054
λ
*
6.891 (+14.69) **
Wx Lag
(−14.99) **
(−1.54)
HighLIQ
Wba Error
87
(+0.05)
84
84
87
Indicates statistical significance at 10%. Indicates statistical significance at 5% (or less).
4. Results The estimates of the traditional Probit model are in the last column of Table 1. At the 5% significance level, only the GDP real growth rate, the weight of public expenses in the GDP and the return on assets are statistically significant in explaining the probability of a banking crisis. According to our results, recession periods and poor banking sector performance are favorable to the occurrence of banking crises. Data also indicates that an increase of the public expenses’ weight in the GDP is a stabilizing factor. However, if all the microeconomic variables are excluded from the model, the GDP real growth is the only statistically significant variable, and if only the microeconomic variables are included in the model, ROA is the sole statistically significant variable (results not shown). Although the results of the several published empiric studies about banking crises are not directly comparable, as neither the samples nor the independent variables, nor even the dependent, are coincident, our results are less expressive than those from prior studies. Demirgüç-Kunt and Detragiache [37] have empirically confirmed the statistical relationship between the probability of a banking crisis and the GDP real growth rate and the inflation rate, as well as with the deposit insurance and per capita income. Many other authors obtain statistical significance for the GDP real growth rate and for the inflation rate, even in the case in which these variables are not the central objective of the study but are used as controls ([47–49], among others). Other studies show an association between the existence of a deposit insurance scheme, or the quality of the banking regulation, and the occurrence of systemic banking crisis [6,45,46]. That is not our case. As for the bank-specific variables, Demirgüç-Kunt and Detragiache [49,37], Eichengreen and Rose [38] and Domaç and Peria [50] mostly report non-significant variables as well. The spatial Probit model is estimated by the Recursive Importance Sampling (RIS) method [51,52], taking the estimates of the traditional model as initialization parameters. Results are in Table 1, and are structurally more robust than those of the traditional model. With respect to the coefficient estimates, results are similar in the four models we present in the first four columns of Table 1, in terms of both magnitude and statistical significance. The macroeconomic and institutional variables are statistically significant. The inflation rate has a negative impact, as opposed to the one obtained by Demirgüç-Kunt and
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Detragiache [37,53]. One possible justification may be the fact that the sample’s average inflation rate is low,22 and therefore any rise allows bank profitability to increase [54]. The negative sign of PubExpenses may be linked to the frequent use of public expenses as a policy mechanism, and is consistent with Ref. [53]. Countries with higher per capita income levels and with deposit insurance schemes are more stable [45,46]. Results suggest that the minor incentive to deposit runs resulting from the implementation of deposit insurance schemes overcompensates the negative effects of moral hazard.23 Countries in which banks have higher ETA achieve greater stability. The negative sign of LIQ indicates that a reduction in the average banking system liquidity harnesses its stability. Although increased liquidity heterogeneity contributes to stability, one cannot say the same in regard to the profitability heterogeneity. Estimates for the ROA, asset quality and heterogeneity coefficients are equally robust. Finally, the ρ estimate associated with the Wx matrix is positive, and negative in the sample ‘‘Banking Activity’’.24 Thus, if a country is in crisis this increases the probability of neighboring countries to which it is connected, directly or indirectly (by way of third countries), being equally affected. Contagion motivated by a common shock is only confirmed with the ‘‘Banking Activity’’ sample. 4.1. Marginal effects In the traditional model a one-unit increase in GDPg, for example, will cause a 0.204 latent variable decrease in the same country. The impact on all the other countries is null. In the spatial Probit model, that one-unit increase immediately causes a reduction (between 0.329 and 0.298-units, depending on the model) in the latent variable. However, because the countries are interdependent, whatever affects one country has repercussions in all those connected to it, and these changes will feedback the country where the process began. The total impact is given by
1Cris∗ = βGDPg (I − ρ W)−1 1XiGDPg
(3)
where Cris is the latent variable (n × 1) vector, βGDPg is the coefficient of GDPg, I is the identity matrix, W is the proximity matrix, and 1XiGDPg is an (n × 1) vector of zeros except the i element which is the unit. The indirect impact, motivated by the interlinks, is given by ∗
i
1Cris∗ − 1Cris∗ = βGDPg [(I − ρ W)−1 − I]1XiGDPg
(4)
in which i
1Cris∗ = βGDPg 1XiGDPg
(5)
represents the direct impact. In our example, the total impact is given by an (84 × 1) vector and for each one of the independent variables there are 84 different vectors, according to the country in which the GDPg change is assumed. However, the analysis of the impact matrix [55] is more interesting than a meticulous, thorough analysis of these results. It condenses the importance of the connections between countries and is given by
(I − ρ W)−1 .
(6)
Each element of the main diagonal gives the total (direct plus feedback) impact of country i on itself. The elements outside the main diagonal (γij ) measure the indirect impact of country j on country i. The (incomplete) impact matrix for the Lag/Wx case and the GDPg variable is in Table 2. One-unit changes in France, the USA or the United Kingdom have different impacts than those produced by identical changes in Indonesia or Korea, for example. The indirect impact that the USA (Indonesia) has on itself is 0.056 (0.001) and the impact of the USA on Indonesia is 0.085, while that of Indonesia on the USA is only 0.002. Finally, while in the traditional model the marginal impact is constant to all observations, in the spatial model we have as many marginal impacts as the sample observations. Again using the simplification of the latent variable, in the traditional model the marginal impact of GDPg is given by
∂ Cris∗ i = βGDPg , ∂ GDPgi
∀i
(7)
whereas in the spatial model it is
∂ Cris∗ i = βGDPg γij , ∂ GDPgj
∀i, j.
(8)
22 Excluding Indonesia and Romania, the average inflation rate in the crisis (stable) countries is 6% (6.6%). 23 This contradicts the findings of Demirgüç-Kunt and Detragiache [37,6]. 24 The sign of ρ adequately varies according to the use of a distance matrix (negative) or a proximity matrix (positive). W is a distance matrix; the ba bigger wij the bigger is the distance between observations (i, j), and so it is expected that the occurrence of a crisis becomes less likely when the distance increases.
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Table 2 Impact matrix (Lag/Wx /GDPg case).
France Indonesia Korea Malaysia Thailand United Kingdom USA ... Average
France
Indonesia
Korea
Malaysia
Thailand
United Kingdom
USA
1.016 0.011 0.011 0.011 0.013 0.051 0.016 ... 0.029
0.001 1.001 0.006 0.006 0.008 0.021 0.002 ... 0.002
0.005 0.023 1.004 0.012 0.008 0.004 0.012 ... 0.008
0.003 0.015 0.014 1.006 0.017 0.003 0.007 ... 0.005
0.003 0.010 0.006 0.014 1.002 0.002 0.004 ... 0.004
0.059 0.017 0.021 0.022 0.024 1.015 0.028 ... 0.038
0.057 0.085 0.100 0.110 0.116 0.081 1.056 ... 0.091
Thus, the marginal impact resulting from the change in GDPg in the country will have to be considered, but also the impact resulting from GDPg changes in the neighbor countries. In the traditional model the marginal effect of GDPg is −0.204 in each country. In the spatial model a 1-unit increase in the USA’s GDPg has a marginal impact on the latent variable of the USA itself of −0.347 (= − 0.329 ∗ 1.056), and of −0.028 (= − 0.329 ∗ 0.085) in Indonesia’s, or −0.019 (= − 0.329 ∗ 0.057) in France’s, for example. 4.2. Robustness tests We perform a set of tests to investigate the robustness of our key findings. Firstly, instead of using the exports as a proxy for the countries’ connections in the proximity matrix, we use the sum of exports and imports because trade flows are bilateral and by doing so one hopes to capture (additional) connection bilaterality. A second alternative matrix related to banking activity is also tested. This matrix includes variables that give a different characterization of the structure and organization of the banking sector (concentration—the market share of the three largest banks; profitability—bank return on equity; range of permissible activities—as in Wba ), relevance of the banking sector in the economy (deposits as a percentage of GDP) and other characteristics of the banking sector (bank’s external loans and deposits as a percentage of domestic bank deposits; banking freedom—captures restrictions on de novo bank entry, degree of bank regulation, existence of state-owned banks, degree of government interference in the credit-granting activity). This is done bearing in mind that the proximity matrix needs to be exogenous, so that other characteristics of the banking sector are kept as independent variables. Secondly, and given that, most probably, the proximity matrices suffer from discrepancies between actual and reported bilaterality, we estimate the ARMA (i.e., the lag + error) spatial model for all the proximity matrices used. In general, results are very similar to those reported in Table 1, and thus are not shown.25 Thirdly, we estimate all our models with only the macro and institutional variables as explanatory variables, and, on the other hand, with only the explanatory bank-specific variables. With one exception (the deposit insurance variable), all the remaining variables retain their respective sign and statistical significance. However, we find that the relevance of the macro and institutional variables is stronger, but the bank-specific variables add accuracy to the model. Using again the lag model with the exports proximity matrix as an example, we find that the macro/institutional variables are better at predicting the crises than the bank-specific ones in the sense that they correctly identify more countries in crisis. In fact, the lag model with macro/institutional variables correctly predicts nine of the 15 in-sample crises (Table 3, column (2)), but the lag model with bank-specific variables correctly predicts seven (column (3)). Nevertheless, adding the bank-specific variables to the macro/institutional ones allows the model to increase the accuracy of the results, for the model now correctly predicts twelve countries in crisis (column (1)).26 , 27 These in-sample predictions are better than the out-of-sample predictions obtained when we estimate a similar model for the crises in year 1995 and use the estimates thus obtained to predict the countries in crisis in 199828 : in this case the model correctly predicts seven of the 15 countries in crisis in 1998 (Table 3, column (4)). Nevertheless, considering all the in-sample and the out-of-sample predictions, Vietnam is the only country in crisis without a crisis being predicted by any model. 5. Conclusion The study of banking crises through a traditional Probit model is not satisfactory. The results from the spatial model are statistically more reliable, and more robust than those from the traditional model. If the observations are inter-related, 25 Results are available from the authors upon request. 26 Rather than defining a certain threshold above which a country is considered in crisis, we assume that the top 15 probabilities are the countries in crises. There are three crises in the lag/Wx case which were not correctly identified (neither using the macro/institutional variables, nor the bank-specific variables nor all the variables). Also, using only the bank-specific variables produces a higher number of ‘false positive’ cases. 27 In our sample, the (average) estimated contribution of contagion to the likelihood of banking crises measured by the ratio ρ WY /(ρ WY + X β) is around 8.8%. In 11 countries this ratio is well above 15%. 28 We estimate a similar lag/W spatial Probit model for the year 1995 crises (17 countries in our sample were in crisis in 1995, many of them Latinx American and eastern countries) and use the estimates thus obtained to forecast the crisis countries in 1998.
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A. Amaral et al. / Physica A 415 (2014) 251–260 Table 3 Model predictions (Lag/Wx case). Real data
Brazil China, People’s Rep. of Indonesia Jamaica Japan Korea Latvia Malaysia Nigeria Philippines Romania Russia Slovak Republic Thailand Vietnam
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
In-sample
Out-of-sample
All variables (1)
Macro variables (2)
Micro variables (3)
All variables (4)
1 1 1 1
1 1
1 1
1
1
1 1
1 1 1 1 1 1 1
1 1 1 1 1
1 1
1
1
1
1 1 1
1 1 1
Legend: 1 means that the country is in crisis in 1998 (real data column—see Ref. [36]), or the model predicts that the country is in crisis in 1998.
the maximization of the usual likelihood function in the Probit model produces inconsistent and inefficient estimators. The estimates here reported for the traditional model are an example of it, and this lack of quality of the estimators and of the reliability of the statistic inference probably explains why previous studies did not find significant relationships between the occurrence of crises and the characteristics of the banking sector [38] or bank liquidity [37,50]. Contagion is crucial to understanding the occurrence of systemic banking crises but the phenomenon may result from business connections between institutions or from similarities between banking structures. Our results show little sensitivity to the proximity concept used, which could be a sign that the contagion channels are diverse. However, our results clearly show that the spatial model is a better methodology to study contagion. Acknowledgments Financial support by FCT (Fundação para a Ciência e a Tecnologia), Portugal, is gratefully acknowledged by second author. The third author gratefully acknowledges partial financial support from FCT (Fundação para a Ciência e a Tecnologia) and FEDER/COMPETE (grant PEst-C/EGE/UI4007/2011). The views stated herein are those of the author and are not necessarily those of the CMVM. Appendix A.1. Countries included in the sample Argentina (a), Armenia, Australia, Azerbaijan, Bahrain, Bangladesh (a), Belarus, Bhutan, Bolivia, Botswana, Brazil (a, b), Bulgaria (a), Canada, Chile, China (b), Croatia, Cyprus, Czech Republic (a), Denmark, Egypt, Estonia (a), Finland, France, Georgia, Ghana, Greece, Guatemala, Guyana, Honduras, Hungary (a), Iceland, India, Indonesia (b), Ireland, Israel, Italy, Jamaica (b), Japan (a, b), Jordan, Kazakhstan, Kenya, Kuwait, Latvia (a, b), Lebanon, Lithuania (a), Luxembourg, Macao, Macedonia, Malawi, Malaysia (b), Malta, Mauritius, Mexico (a), Moldova, Morocco, Namibia, Nepal, Netherlands, New Zealand, Nigeria (a, b), Oman, Panama, Peru, Philippines (b), Portugal, Republic of Korea (b), Romania (a, b), Russian Federation (a, b), Rwanda, Saudi Arabia, Singapore, Slovak Republic (a, b), Slovenia, South Africa, Spain, Sri Lanka, St. Kitts and Nevis, Sweden, Switzerland, Thailand (b), Trinidad and Tobago, Turkey, United Kingdom, United States of America, Venezuela (a), Vietnam (b), Zambia. (a) Countries with banking crisis in 1995 (according to Caprio and Klingebiel [36]). (b) Countries with banking crisis in 1998 (according to Caprio and Klingebiel [36]).
A.2. Variable definition CRIS = 1 if the country’s banking system is in crisis (the Caprio and Klingebiel’s [36] chronology to identify countries that have gone through systemic banking crisis is used); Inf = Inflation Rate, in percentage (GDP Deflator). Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html.
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GDPg = GDP real growth rate. Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html. PubExpenses = General Government final consumption expenditure as a % of GDP. Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html. PCI = per capita income, in percentage; computed as a country’s per capita income divided by the US per capita income. Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html. Dep = 1 if there is an explicit deposit insurance scheme in the country. Source: World Bank http://siteresources. worldbank.org/INTRES/Resources/469232-1107449512766/Caprio_2000_banking_regulation_database.xls. ETA = Equity-to-Total Assets ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ETA. Source: Bankscope. It is a leverage indicator; higher ratios mean that the bank’s capital buffer is stronger, with a negative impact on the likelihood of a bank crises. ROA = Return on Assets ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ROA. Source: Bankscope. Higher profitability is a critical determinant of bank equilibrium. LIQ = Loan-to-deposit ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ‘‘Net Loans/Customer & Short Term Funding’’ ratio. Source: Bankscope. Higher ratios are associated with lower liquidity due to the loan/deposit maturity mismatch, and it becomes more difficult to redeem deposits should there be higher demand. Thus, higher liquidity is a stabilizing factor. SDAssets = standard deviation of the commercial banks’ log(total assets). Source: Bankscope. It measures the degree of similitude of the bank sizes. Lower SDAssets means that banks are more similar in terms of size; this could mean that it is more difficult to supervise fewer and larger banks because problems in one bank may quickly become systemic. Quality = Loan loss reserves-to-total assets ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ‘‘Loan Loss Reserves/Total Assets’’ ratio. Source: Bankscope. Used as an indicator of asset quality; there are always bad bank loans and if banks are able to increase their loan loss reserves and yet be profitable and reward their shareholders then this may be a sign of bank stability. CV_ROA = Coefficient of variation of ROA. Source: Bankscope. Higher coefficient of variation means that there are a lot of different banks with higher and lower than the average sector profitability, meaning that we have a diversified sector. Diversification can be good insofar as the eventual existence of problem banks can benefit from the buffer provided by more profitable ones. CV_LIQ = Coefficient of variation of LIQ. Source: Bankscope. A stronger dispersion of liquidity among banks may help contain ‘propagation waves’ in case of a sudden disruption in some (but not all) financial institutions. HighROA = Percentage of banks with above average ROA. Source: Bankscope. If the banking sector in composed of a large percentage of banks with above average profitability, then this could be a stabilizing factor insofar as only a smaller number of financial institutions is pushing profits down. HighLIQ = Percentage of banks with above average LIQ. Source: Bankscope. Similar to HighROA, except with the opposite sign given the construction of the liquidity variable. A.3. Proximity matrices Wx : Exports Matrix—Each wij element represents exports from country i to country j, and these are row-standardized, so that for each i, j wij = 1. Source: IMF—Direction of Trade Statistics Yearbook, 2001. An alternative definition, using exports plus imports was also used. Wba : Banking Activity Matrix—Each wij element is measured by the absolute value of the difference between the ‘‘Banking Activity’’ index for each pair (i, j) of countries. From the original version of the Barth et al. [46] database, an index of the degree of restriction to commercial bank access to the activities of brokerage, real estate, insurance and property ownership of non-financial firms is constructed. For each activity we attribute a 0–3 score if there is unrestricted access, access allowed with some limitations, access restricted and access prohibited, respectively. The average of the scores for the 4 activities is an indicator of the degree of restrictions imposed to the banking sector, which is higher the closer the average gets to 3. An alternative definition, using other characteristics of the banking sector, was also used. Source: World Bank http:// siteresources.worldbank.org/INTRES/Resources/469232-1107449512766/Caprio_2000_banking_regulation_database.xls. References [1] [2] [3] [4]
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Contents lists available at ScienceDirect
Physica A journal homepage: www.elsevier.com/locate/physa
The spatial Probit model—An application to the study of banking crises at the end of the 1990’s✩ Andrea Amaral a , Margarida Abreu a,b , Victor Mendes c,d,∗ a
ISEG (Lisboa School of Economics & Management), University of Lisbon, Rua do Quelhas, 6, 1200-781 Lisboa, Portugal
b
UECE (Research Unit on Complexity and Economics), Rua Miguel Lupi, 20, 1200 Lisboa, Portugal
c
CMVM - Portuguese Securities Commission, Rua Laura Alves, 4, 1050-138 Lisboa, Portugal
d
CEFAGE-UE (Center for Advanced Studies in Management and Economics), Largo dos Colegiais, 2, 7000-803 Évora, Portugal
highlights • • • •
Spatial Probit (SP) excels traditional probit in the study of financial contagion. SP allows the accounting of cross and feedback effects of contagion. Contagion may result from institutional similarities between banking systems. Or from business connections between institutions of different countries.
article
info
Article history: Received 9 January 2014 Received in revised form 19 May 2014 Available online 30 July 2014 Keywords: Spatial probit Banking crises Contagion
abstract We use a spatial Probit model to study the effect of contagion between banking systems of different countries. Applied to the late 1990s banking crisis in Asia we show that the phenomena of contagion is better seized using a spatial than a traditional Probit model. Unlike the latter, the spatial Probit model allows one to consider the cascade of cross and feedback effects of contagion that result from the outbreak of one initial crisis in one country or system. These contagion effects may result either from business connections between institutions of different countries or from institutional similarities between banking systems. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Most of the existing empirical research on the predictability and contagion of financial crises evaluates the probability of a banking system going into crisis using the traditional Probit/Logit models. Ref. [1] is one of the first studies in this area using a Probit model to study the determinants of currency crashes in developing countries, and decisively contributes to the development of the early warning system literature. The works by Berg and Pattillo [2], Edison [3] and Berg et al. [4] use the new indicators suggested by Kaminsky and Reinhart [5] and a more general Probit model applied to the Asian crisis in the eighties. Demirgüç-Kunt and Detragiache [6] use a multivariate Logit model for the prediction of banking crises. More recently, Bussière and Fratzscher [7] show that binomial discrete-dependent-variable models are subject to what the authors refer to as ‘‘post-crisis bias’’. However, the correction of this bias is done in the context of a multinomial Logit model. Finally,
✩ This article is part of the Strategic Project (PEst-OE/EGE/UI0436/2011).
∗ Corresponding author at: CMVM - Portuguese Securities Commission, Rua Laura Alves, 4, 1050-138 Lisboa, Portugal. Tel.: +351 213177000; fax: +351 213537077. E-mail addresses: [email protected] (M. Abreu), [email protected] (V. Mendes). http://dx.doi.org/10.1016/j.physa.2014.07.044 0378-4371/© 2014 Elsevier B.V. All rights reserved.
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Schularick and Taylor [8] and Jordá et al. [9] use a Logit model to study rare events associated with episodes of financial crisis, and Duca and Peltonen [10] use a multivariate discrete choice model for assessing and predicting systemic financial events. Although this literature contributed to a deeper understanding of banking and financial crisis, the traditional Probit/Logit models do not allow one to consider the effect of the connections between the different banking/financial systems in the outbreak of a financial crisis.1 As such, the validity of the estimators lays on the assumption that the observations/countries are different, but not connected. This means that these traditional models do not take into account that the occurrence of a systemic crisis in one country may also be a function of the neighboring banking system’s health or even of the similarity of the banking structure and legal and institutional environment of another country with which it has strong financial ties, independently of the physical or trade proximity between the countries. It may also be a function of the banking regulation culture in each country.2 In this paper we use a spatial Probit model in which the probability of a banking system suffering a crisis is also a function of the occurrence of crisis in ‘nearby’ banking systems. As referred in Ref. [14], this model does not only identify a ‘‘first victim’’ who’s banking system is in crisis; it allows one to take into consideration all the feedback effects, i.e., to consider that the crisis in a given banking system stimulates a series of impacts in other systems. In turn, these effects generate new actions, namely from the country in which the crisis episode has begun. The spatial model considers, therefore, the existence of a ‘‘cascade’’ of effects that is not present in the traditional model. The spatial Probit model lays on a web of connections between observations, through which instability waves propagate, summarized in the proximity matrix. In this paper we consider two ways of interpreting proximity. Firstly, we consider that two banking systems are close because flows of funds take place between them, and contagion is the spreading of a crisis to neighboring economies which are strongly dependent and connected (contagion based on the fundamentals and interdependence of economies—[15]). Secondly, we identify structurally similar banking systems: they may not be operationally connected, but have similar characteristics; therefore agents expect that whatever has affected banks in one country will also affect banks in other countries and react accordingly (mimetic contagion). The paper is structured as follows. The spatial Probit model is presented in Section 2. In Section 3 we discuss the dataset and variables used in the empirical application. Results are discussed (and compared with those from the traditional model) in Section 4, while Section 5 concludes the paper. 2. The spatial Probit model The spatial Probit model (version ‘‘Lag’’) is modeled as Yi∗ = ρwi1 Y1∗ + ρwi2 Y2∗ + · · · + ρwiN YN∗ + Xi β + εi
(1)
where Yi∗ is a latent variable, Xi is the vector of exogenous variables, β is a parameter vector, ρ is the dependence parameter, wij represents the proximity between observations (i, j), and εi is an i.i.d. random disturbance. Given that Yi∗ is not observable, the observables are only binary variables Yi , with
Yi =
1, 0,
if Yi∗ > 0 if Yi∗ < 0.
The model represents a substantive spatial dependence [16]; what happens with the ith observation depends on its links with all the other observations. In matrix notation (1) becomes Y ∗ = ρ WY ∗ + X β + ε
(1a)
where Y = (Y1 , . . . , YN ) , W (N × N ) is a spatial weight matrix that captures the dependence structure between neighboring observations, and ε ∼ N 0, σ 2 IN .3 If ρ = 0 the model reduces to the standard Probit model.4 If ρ ̸= 0 the estimators used in the traditional Probit model are inconsistent. The error terms ε are heteroskedastic and autocorrelated. Maximum likelihood estimation techniques are not suitable for limited dependent variable spatial autoregressive models because they yield inconsistent estimators [19,20]. Moreover, the spatial likelihood function involves the evaluation of an n-dimensional integral; the estimation becomes more complex because a multidimensional integration is necessary to account for all these factors.5 ∗
∗
∗ ′
1 Lehar [11] tries to measure contagion via asset portfolio correlation (high correlation meaning contagion). In the context of a traditional Probit, Santor [12] uses a proxy for informational contagion and González-Hermosillo [13] uses the total bank loans to GDP ratio. These are, however, added as independent variables in the model. 2 In fact, in the eighties banking regulation became weaker due to competitive (de)regulation. 3 See Refs. [16,17], for example, on the Spatial Probit Model. 4 See Ref. [18] on the standard Probit model. 5 A recent example of an application of spatial Probit models is Ref. [21].
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On first glance, it would seem that the differences of model (1a) against the traditional Probit model are not significant; it is just about including an ‘‘average contagion indicator’’ in the model. However, this procedure has profound implications on the information necessary to estimate the model and on the parameter interpretation because the spatial Probit model lays on a connection’s web between observations, through which the instability waves propagate. One other possibility is to consider the links between observations as secondary: the agent’s actions are correlated because they suffer the influence of a common shock. It is the ‘‘Error’’ version of the model, in which λ is the contagion parameter: Yi∗ = Xi β + εi
with εi = λ
n
wij εj + ui
(2)
j =1
or, in matrix notation Y ∗ = X β + ε,
with ε = λW ε + u, u ∼ N 0, σu2 IN .
(2a)
The intensity with which the banking crisis propagates is directly dependent on the countries’ economic and financial integration. The proximity between the agents, being commercial, political or plain informative, has a central role in all the contagious processes, and as such the understanding of the phenomenon goes through the connection’s web between the agents, summarized in the proximity matrix. W is the spatial weights matrix. It captures the observations’ structure of dependency. Each generic element wij reflects the distance separating the element i from the element j. The elements of the spatial weights matrix are typically rowstandardized, such that for each i, j wij = 1, and this means that the spatial lag may be interpreted as a weighted average (the wij being the weights) of the neighbors. In general, the elements wij are based on the geographic arrangement of the observations, or contiguity, but alternative specifications exist,6 and the weights must be exogenous to the model in order to avoid identification problems [26]. Two ways of interpreting proximity are considered. The first is to accept that two banking systems are similar because an effective exchange of transactions exists, either by way of trade or capital participation. In this case, contagion is the spreading of a crisis to neighbor economies, strongly dependent and interconnected. It is what Dornbusch et al. [15] refers to as contagion with a real fundament, based on the basic fundamentals and interdependence of the economies. The second is to assume that banking systems are close when they are structurally similar. Here we have contagion by imitation, i.e., operationally the banking systems may not be connected, but as they have similar characteristics, agents expect that whatever has affected comparable banks in one country will also affect their own country and react accordingly. In this case contagion is attached to the behavior of the financial agents and also to the possibility of a shock being transmitted from one economy to another, with fundamental connections not having to necessarily exist. If the investor anticipates any added risk relatively to his portfolio, he will have increased preference for liquidity and will try to reduce his exposure namely in similar markets or in the same region. One other aspect is to do with the fact that the processing of the information specific to each country that should support the investor’s performance is complex and costly. Therefore the information that a country is in a crisis causes ‘‘wake up calls’’ in other economies. In either of the cases, the investors’ herding (i.e., imitation) behavior increases with the integration of the banking systems.7 The spatial Probit model integrates the complexity that characterizes the relations between the banking systems, and that complexity materializes in the proximity matrix. That matrix, exogenously defined, assumes central importance in these models, conditioning the dimension of the multiplying effects. By recurring to this proximity matrix the model gets close to the essays of Sheldon and Maurer [28], Furfine [29], Wells [30], Upper and Worms [31], Degryse and Nguyen [32], Lelyveld and Liedorp [33] and Mistrulli [34]. In these studies the interconnections’ matrix between the institutions is used in simulations to survey the existence of contagion. However, in the spatial Probit model, the probability of a country being in crisis is, among other things, function of the occurrence of crisis in ‘nearby’ countries, and this allows the accounting of a ‘‘cascade’’ effect that is not present in the traditional Probit model. 3. Dataset and variables We apply the spatial Probit model to the late 1990s banking crisis in Asia.8 The sample includes information for 87 countries9 in 1998, and the following variables: CRIS = 1 if the country’s banking system is in crisis (the Caprio and
6 Spatial weights can be based on distance decay [22], on the structure of a social network [23], on economic distance [24], on trade-based interaction measures [25], for example. 7 Herding behavior has been found in both institutional and retail investors. Friedman [27], for example, states that there are some characteristics of the professional investment community (importance of relative performance, asymmetry of incentives) which suggest that institutional investors will herd. 8 A preliminary version of the paper was published in 2010 (see Ref. [35]). 9 The sample includes developed, developing and less developed countries, so that the traditional model and the spatial model are estimated with the same number of observations in order to compare the results. The sample is conditioned by the higher demand of information of the spatial Probit model. The World Bank has information for 207 countries in 1998 (but not for all the variables of the model), and 26 of them were in crisis in 1998. In the sample used the percentage of countries in crisis (17%) is similar.
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Klingebiel’s [36] chronology to identify countries that have gone through systemic banking crisis is used); Inf = Inflation Rate; GDPg = GDP real growth rate; PubExpenses = Public expenses as a % of GDP; PCI = per capita income; Dep = 1 if there is a deposit insurance scheme in the country; ETA = Equity-to-Total Assets ratio10 ; ROA = Return on Assets; LIQ = Loan-to-deposit ratio; SDAssets = standard deviation of the log (total assets); Quality = Loan loss reserves-to-total assets ratio; CV_ROA = Coefficient of variation of ROA; CV_LIQ = Coefficient of variation of LIQ; HighROA = Percentage of banks with above average ROA; HighLIQ = Percentage of banks with above average LIQ.11 The sources of information are the World Bank,12 IMF13 and Bankscope.14 The construction of the model’s independent variables is explained, in detail, in the Appendix. It is important, however, to mention that to try and measure the importance of the microeconomic characteristics of the diverse institutions that make up the system, the return on assets and on equity, liquidity, structure of assets and of capital indicators which are included as independent variables, are averages for the banking system, but obtained based on the financial information available to the diverse institutions (more precisely commercial banks) which compose it.15 The proximity matrix is a proxy for the operational connections between banking systems. To measure the mesh of connections between banking systems the ideal would be to have available information relating to, for instance, the trade volumes between them, the capital participation between the systems or between the banks, or even information as to the banks indebtedness to foreign institutions. In whichever case it would be necessary disaggregated information, i.e., taking the last example, it is not enough to know what indebtedness a banking system i has to foreign institutions; it is necessary to know exactly what indebtedness a banking system i has to each one of the remaining banking systems in the sample. This information is not, however, available, and so one has to use a proxy.16 A reasonable approach could be achieved through the capital movements between countries, but we only have access to aggregate information on capital movements, being unknown in what way the flows that come out or go in to a country are divided between the destiny and origin country. One alternative is the use of exports, disaggregated by exchange partners. Although it is not an ideal solution, in fact countries with large trade exchanges are countries in which the banks have, as a consequence, strong connections. The point here is not to use the exports because the international trade is a channel of contagion, but to use the exports as a proxy of the level of interaction of the banks.17 We use the exports (Wx ), disaggregated by destination, and assume that countries with intense trade flows are countries with strongly connected banks.18 A second matrix (Wba ) is also built with the objective of measuring the existence of contagion by imitation, and to test the robustness of our results. It captures the similarities between the banking structures of each pair of countries via the degree of the restrictions imposed on bank activities.19 Countries with similar banking structures exhibit equivalent values and therefore the distance between them is smaller.20 , 21 Summing up, the proximity matrices are built to recreate the real mesh of connections between banking systems and not through entropy maximization, as in Refs. [28,30–33]. Entropy maximization assumes that each element establishes equal relations with all the others. This is not realistic in our study because each country does have different connections with all the other countries.
10 ‘Assets’ is defined as commercial banks’ total assets. 11 See Refs. [37–39], for example, on the use of inflation, GDP growth and public expenses, Ref. [6] on the use of deposit insurance and institutional environment, Ref. [13] and Ref. [40] on the use of microeconomic variables in the context of banking crises. 12 World Development Indicators, Bank Regulation and Supervision, and Bank Concentration and Crisis. 13 Direction of Trade Statistics Yearbook. 14 Bankscope is used to get (commercial) bank specific balance sheet and income statement information. 15 These variables are also referred to as ‘bank-specific variables’ in the remainder of the paper. 16 The possible fragility of the proxies used in the construction of the proximity matrices has motivated the non-realization of the statistical tests proposed by Pinkse [41] for the spatial correlation existence. The results of these tests are significantly affected by bad proximity matrices specification problems [42]. Besides, if the spatial dependence is not significant then the method will reflect this in the estimation of the ρ and λ coefficients. 17 The idea that banks ‘follow their customers abroad’ when those client firms engage in a growing volume of international trade and investment goes at least as far back as the seventies. A natural corollary is that banks become more multinational, and financial systems more connected. See, for example, Refs. [43,44]. 18 This matrix is computed for a sample of only 84 countries. Novo [14], in his study of the 1992 European exchange rate crises shows that trade connections, more than political proximity, are the primary contagion channel. We also use an (imports + exports) matrix since the interconnections between banks can be related to both imports and exports, thus unveiling additional trade/connection bilaterality. This allows one to check the robustness of the results. 19 The degree of restrictions to commercial bank access to the activities of brokerage, real estate, insurance and property ownership of non-financial firms are included in the analysis (see the variable definition in the Appendix). Barth et al. [45] show the existence of a relationship between bank regulation, particularly restrictions on bank activity, and crisis. 20 Again, we use an alternative bank activity matrix to test the robustness of our results. This alternative includes variables related to the structure of the banking sector (the market share of the three largest banks, bank return on equity, restrictions on banks’ activities), relevance of the banking sector (deposits as a percentage of GDP) and other characteristics of the banking sector (bank’s external loans and deposits as a percentage of domestic bank deposits). Other characteristics of the banking sector are included as independent variables. 21 W is based on indicators for which there is no times-series information. Besides, these indicators are related to sector characteristics that suffer ba
slow transformations and therefore present rather stable values in the short and medium term. As Barth et al. [46] refer, the regulation and supervision characteristics are relatively stable over a period of one or two decades. That is not the case of Wx as it depends on the export volumes in each year.
A. Amaral et al. / Physica A 415 (2014) 251–260
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Table 1 Estimation results, spatial Probit (dependent variable: CRIS). Wba Lag Const
5.794 (+9.05) **
Inf GDPg PubExpenses PCI Dep ETA ROA LIQ SDAssets Quality CV_ROA CV_LIQ HighROA
ρ
6.607 (+14.21) **
−0.062
−0.059
−0.058
(−16.25) **
(−16.51) **
(−17.19) **
−0.299
−0.314
−0.329
−0.298
(−25.77) **
(−24.16) **
(−20.92) **
(−25.04) **
−0.155
−0.155
−0.171
−0.155
(−19.51) **
(−19.14) **
(−19.30) **
(−19.05) **
−0.022
−0.023
−0.024
−0.022
(−15.10) **
(−14.69) **
(−14.18) **
(−14.75) **
−0.354
−0.251
−0.213
−0.303
(−3.96) **
(−2.83) **
(−2.34) **
(−3.46) **
−0.047
−0.043
−0.074
−0.046
(−6.43) **
(−5.90) **
(−7.96) **
(−6.31) **
−0.444
−0.452
−0.491
−0.438
(−19.10) **
(−19.06) **
(−18.16) **
(−18.49) **
−0.028
−0.029
−0.027
−0.027
(−10.94) **
(−10.98) **
(−10.39) **
(−10.53) **
0.236
0.217
0.204
0.260
(+2.53) **
(+2.32) **
(+2.12) **
(+2.78) **
−0.010
−0.013
−0.035
−0.012
(−3.01) **
(−3.05) **
(−2.16) **
(−2.91) **
−0.032
−0.031
−0.035
−0.032
(−6.71) **
(−6.53) **
(−5.89) **
(−6.61) **
1.336
1.344
(+7.83) **
(+7.93) **
−0.004
−0.002 (−0.72)
1.814 (8.38) **
−0.009 (−2.84) **
1.374 (+8.02) **
−0.003 (−0.92)
−0.049
−0.051
−0.048
−0.048
(−13.59) **
(−13.69) **
(−13.11) **
(−13.24) **
−0.479
4.473 (+1.50)
−0.039 (−1.81) *
−0.204 (−2.71) **
−0.105 (−2.01) **
−0.015 (−1.55)
−0.208 (−0.37)
−0.032 (−0.68)
−0.301 (−1.98) **
−0.018 (−1.13)
0.180 (+0.29)
−0.009 (−0.33)
−0.022 (−0.71)
0.945 (+0.87)
−0.002 (−0.12)
−0.032 (−1.39)
(+7.81) **
−1.056
0.004
(−7.27) **
87
Traditional Probit
0.31
(−1.89) *
n **
8.211 (+14.27) **
Wx Error
−0.054
λ
*
6.891 (+14.69) **
Wx Lag
(−14.99) **
(−1.54)
HighLIQ
Wba Error
87
(+0.05)
84
84
87
Indicates statistical significance at 10%. Indicates statistical significance at 5% (or less).
4. Results The estimates of the traditional Probit model are in the last column of Table 1. At the 5% significance level, only the GDP real growth rate, the weight of public expenses in the GDP and the return on assets are statistically significant in explaining the probability of a banking crisis. According to our results, recession periods and poor banking sector performance are favorable to the occurrence of banking crises. Data also indicates that an increase of the public expenses’ weight in the GDP is a stabilizing factor. However, if all the microeconomic variables are excluded from the model, the GDP real growth is the only statistically significant variable, and if only the microeconomic variables are included in the model, ROA is the sole statistically significant variable (results not shown). Although the results of the several published empiric studies about banking crises are not directly comparable, as neither the samples nor the independent variables, nor even the dependent, are coincident, our results are less expressive than those from prior studies. Demirgüç-Kunt and Detragiache [37] have empirically confirmed the statistical relationship between the probability of a banking crisis and the GDP real growth rate and the inflation rate, as well as with the deposit insurance and per capita income. Many other authors obtain statistical significance for the GDP real growth rate and for the inflation rate, even in the case in which these variables are not the central objective of the study but are used as controls ([47–49], among others). Other studies show an association between the existence of a deposit insurance scheme, or the quality of the banking regulation, and the occurrence of systemic banking crisis [6,45,46]. That is not our case. As for the bank-specific variables, Demirgüç-Kunt and Detragiache [49,37], Eichengreen and Rose [38] and Domaç and Peria [50] mostly report non-significant variables as well. The spatial Probit model is estimated by the Recursive Importance Sampling (RIS) method [51,52], taking the estimates of the traditional model as initialization parameters. Results are in Table 1, and are structurally more robust than those of the traditional model. With respect to the coefficient estimates, results are similar in the four models we present in the first four columns of Table 1, in terms of both magnitude and statistical significance. The macroeconomic and institutional variables are statistically significant. The inflation rate has a negative impact, as opposed to the one obtained by Demirgüç-Kunt and
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Detragiache [37,53]. One possible justification may be the fact that the sample’s average inflation rate is low,22 and therefore any rise allows bank profitability to increase [54]. The negative sign of PubExpenses may be linked to the frequent use of public expenses as a policy mechanism, and is consistent with Ref. [53]. Countries with higher per capita income levels and with deposit insurance schemes are more stable [45,46]. Results suggest that the minor incentive to deposit runs resulting from the implementation of deposit insurance schemes overcompensates the negative effects of moral hazard.23 Countries in which banks have higher ETA achieve greater stability. The negative sign of LIQ indicates that a reduction in the average banking system liquidity harnesses its stability. Although increased liquidity heterogeneity contributes to stability, one cannot say the same in regard to the profitability heterogeneity. Estimates for the ROA, asset quality and heterogeneity coefficients are equally robust. Finally, the ρ estimate associated with the Wx matrix is positive, and negative in the sample ‘‘Banking Activity’’.24 Thus, if a country is in crisis this increases the probability of neighboring countries to which it is connected, directly or indirectly (by way of third countries), being equally affected. Contagion motivated by a common shock is only confirmed with the ‘‘Banking Activity’’ sample. 4.1. Marginal effects In the traditional model a one-unit increase in GDPg, for example, will cause a 0.204 latent variable decrease in the same country. The impact on all the other countries is null. In the spatial Probit model, that one-unit increase immediately causes a reduction (between 0.329 and 0.298-units, depending on the model) in the latent variable. However, because the countries are interdependent, whatever affects one country has repercussions in all those connected to it, and these changes will feedback the country where the process began. The total impact is given by
1Cris∗ = βGDPg (I − ρ W)−1 1XiGDPg
(3)
where Cris is the latent variable (n × 1) vector, βGDPg is the coefficient of GDPg, I is the identity matrix, W is the proximity matrix, and 1XiGDPg is an (n × 1) vector of zeros except the i element which is the unit. The indirect impact, motivated by the interlinks, is given by ∗
i
1Cris∗ − 1Cris∗ = βGDPg [(I − ρ W)−1 − I]1XiGDPg
(4)
in which i
1Cris∗ = βGDPg 1XiGDPg
(5)
represents the direct impact. In our example, the total impact is given by an (84 × 1) vector and for each one of the independent variables there are 84 different vectors, according to the country in which the GDPg change is assumed. However, the analysis of the impact matrix [55] is more interesting than a meticulous, thorough analysis of these results. It condenses the importance of the connections between countries and is given by
(I − ρ W)−1 .
(6)
Each element of the main diagonal gives the total (direct plus feedback) impact of country i on itself. The elements outside the main diagonal (γij ) measure the indirect impact of country j on country i. The (incomplete) impact matrix for the Lag/Wx case and the GDPg variable is in Table 2. One-unit changes in France, the USA or the United Kingdom have different impacts than those produced by identical changes in Indonesia or Korea, for example. The indirect impact that the USA (Indonesia) has on itself is 0.056 (0.001) and the impact of the USA on Indonesia is 0.085, while that of Indonesia on the USA is only 0.002. Finally, while in the traditional model the marginal impact is constant to all observations, in the spatial model we have as many marginal impacts as the sample observations. Again using the simplification of the latent variable, in the traditional model the marginal impact of GDPg is given by
∂ Cris∗ i = βGDPg , ∂ GDPgi
∀i
(7)
whereas in the spatial model it is
∂ Cris∗ i = βGDPg γij , ∂ GDPgj
∀i, j.
(8)
22 Excluding Indonesia and Romania, the average inflation rate in the crisis (stable) countries is 6% (6.6%). 23 This contradicts the findings of Demirgüç-Kunt and Detragiache [37,6]. 24 The sign of ρ adequately varies according to the use of a distance matrix (negative) or a proximity matrix (positive). W is a distance matrix; the ba bigger wij the bigger is the distance between observations (i, j), and so it is expected that the occurrence of a crisis becomes less likely when the distance increases.
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Table 2 Impact matrix (Lag/Wx /GDPg case).
France Indonesia Korea Malaysia Thailand United Kingdom USA ... Average
France
Indonesia
Korea
Malaysia
Thailand
United Kingdom
USA
1.016 0.011 0.011 0.011 0.013 0.051 0.016 ... 0.029
0.001 1.001 0.006 0.006 0.008 0.021 0.002 ... 0.002
0.005 0.023 1.004 0.012 0.008 0.004 0.012 ... 0.008
0.003 0.015 0.014 1.006 0.017 0.003 0.007 ... 0.005
0.003 0.010 0.006 0.014 1.002 0.002 0.004 ... 0.004
0.059 0.017 0.021 0.022 0.024 1.015 0.028 ... 0.038
0.057 0.085 0.100 0.110 0.116 0.081 1.056 ... 0.091
Thus, the marginal impact resulting from the change in GDPg in the country will have to be considered, but also the impact resulting from GDPg changes in the neighbor countries. In the traditional model the marginal effect of GDPg is −0.204 in each country. In the spatial model a 1-unit increase in the USA’s GDPg has a marginal impact on the latent variable of the USA itself of −0.347 (= − 0.329 ∗ 1.056), and of −0.028 (= − 0.329 ∗ 0.085) in Indonesia’s, or −0.019 (= − 0.329 ∗ 0.057) in France’s, for example. 4.2. Robustness tests We perform a set of tests to investigate the robustness of our key findings. Firstly, instead of using the exports as a proxy for the countries’ connections in the proximity matrix, we use the sum of exports and imports because trade flows are bilateral and by doing so one hopes to capture (additional) connection bilaterality. A second alternative matrix related to banking activity is also tested. This matrix includes variables that give a different characterization of the structure and organization of the banking sector (concentration—the market share of the three largest banks; profitability—bank return on equity; range of permissible activities—as in Wba ), relevance of the banking sector in the economy (deposits as a percentage of GDP) and other characteristics of the banking sector (bank’s external loans and deposits as a percentage of domestic bank deposits; banking freedom—captures restrictions on de novo bank entry, degree of bank regulation, existence of state-owned banks, degree of government interference in the credit-granting activity). This is done bearing in mind that the proximity matrix needs to be exogenous, so that other characteristics of the banking sector are kept as independent variables. Secondly, and given that, most probably, the proximity matrices suffer from discrepancies between actual and reported bilaterality, we estimate the ARMA (i.e., the lag + error) spatial model for all the proximity matrices used. In general, results are very similar to those reported in Table 1, and thus are not shown.25 Thirdly, we estimate all our models with only the macro and institutional variables as explanatory variables, and, on the other hand, with only the explanatory bank-specific variables. With one exception (the deposit insurance variable), all the remaining variables retain their respective sign and statistical significance. However, we find that the relevance of the macro and institutional variables is stronger, but the bank-specific variables add accuracy to the model. Using again the lag model with the exports proximity matrix as an example, we find that the macro/institutional variables are better at predicting the crises than the bank-specific ones in the sense that they correctly identify more countries in crisis. In fact, the lag model with macro/institutional variables correctly predicts nine of the 15 in-sample crises (Table 3, column (2)), but the lag model with bank-specific variables correctly predicts seven (column (3)). Nevertheless, adding the bank-specific variables to the macro/institutional ones allows the model to increase the accuracy of the results, for the model now correctly predicts twelve countries in crisis (column (1)).26 , 27 These in-sample predictions are better than the out-of-sample predictions obtained when we estimate a similar model for the crises in year 1995 and use the estimates thus obtained to predict the countries in crisis in 199828 : in this case the model correctly predicts seven of the 15 countries in crisis in 1998 (Table 3, column (4)). Nevertheless, considering all the in-sample and the out-of-sample predictions, Vietnam is the only country in crisis without a crisis being predicted by any model. 5. Conclusion The study of banking crises through a traditional Probit model is not satisfactory. The results from the spatial model are statistically more reliable, and more robust than those from the traditional model. If the observations are inter-related, 25 Results are available from the authors upon request. 26 Rather than defining a certain threshold above which a country is considered in crisis, we assume that the top 15 probabilities are the countries in crises. There are three crises in the lag/Wx case which were not correctly identified (neither using the macro/institutional variables, nor the bank-specific variables nor all the variables). Also, using only the bank-specific variables produces a higher number of ‘false positive’ cases. 27 In our sample, the (average) estimated contribution of contagion to the likelihood of banking crises measured by the ratio ρ WY /(ρ WY + X β) is around 8.8%. In 11 countries this ratio is well above 15%. 28 We estimate a similar lag/W spatial Probit model for the year 1995 crises (17 countries in our sample were in crisis in 1995, many of them Latinx American and eastern countries) and use the estimates thus obtained to forecast the crisis countries in 1998.
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A. Amaral et al. / Physica A 415 (2014) 251–260 Table 3 Model predictions (Lag/Wx case). Real data
Brazil China, People’s Rep. of Indonesia Jamaica Japan Korea Latvia Malaysia Nigeria Philippines Romania Russia Slovak Republic Thailand Vietnam
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
In-sample
Out-of-sample
All variables (1)
Macro variables (2)
Micro variables (3)
All variables (4)
1 1 1 1
1 1
1 1
1
1
1 1
1 1 1 1 1 1 1
1 1 1 1 1
1 1
1
1
1
1 1 1
1 1 1
Legend: 1 means that the country is in crisis in 1998 (real data column—see Ref. [36]), or the model predicts that the country is in crisis in 1998.
the maximization of the usual likelihood function in the Probit model produces inconsistent and inefficient estimators. The estimates here reported for the traditional model are an example of it, and this lack of quality of the estimators and of the reliability of the statistic inference probably explains why previous studies did not find significant relationships between the occurrence of crises and the characteristics of the banking sector [38] or bank liquidity [37,50]. Contagion is crucial to understanding the occurrence of systemic banking crises but the phenomenon may result from business connections between institutions or from similarities between banking structures. Our results show little sensitivity to the proximity concept used, which could be a sign that the contagion channels are diverse. However, our results clearly show that the spatial model is a better methodology to study contagion. Acknowledgments Financial support by FCT (Fundação para a Ciência e a Tecnologia), Portugal, is gratefully acknowledged by second author. The third author gratefully acknowledges partial financial support from FCT (Fundação para a Ciência e a Tecnologia) and FEDER/COMPETE (grant PEst-C/EGE/UI4007/2011). The views stated herein are those of the author and are not necessarily those of the CMVM. Appendix A.1. Countries included in the sample Argentina (a), Armenia, Australia, Azerbaijan, Bahrain, Bangladesh (a), Belarus, Bhutan, Bolivia, Botswana, Brazil (a, b), Bulgaria (a), Canada, Chile, China (b), Croatia, Cyprus, Czech Republic (a), Denmark, Egypt, Estonia (a), Finland, France, Georgia, Ghana, Greece, Guatemala, Guyana, Honduras, Hungary (a), Iceland, India, Indonesia (b), Ireland, Israel, Italy, Jamaica (b), Japan (a, b), Jordan, Kazakhstan, Kenya, Kuwait, Latvia (a, b), Lebanon, Lithuania (a), Luxembourg, Macao, Macedonia, Malawi, Malaysia (b), Malta, Mauritius, Mexico (a), Moldova, Morocco, Namibia, Nepal, Netherlands, New Zealand, Nigeria (a, b), Oman, Panama, Peru, Philippines (b), Portugal, Republic of Korea (b), Romania (a, b), Russian Federation (a, b), Rwanda, Saudi Arabia, Singapore, Slovak Republic (a, b), Slovenia, South Africa, Spain, Sri Lanka, St. Kitts and Nevis, Sweden, Switzerland, Thailand (b), Trinidad and Tobago, Turkey, United Kingdom, United States of America, Venezuela (a), Vietnam (b), Zambia. (a) Countries with banking crisis in 1995 (according to Caprio and Klingebiel [36]). (b) Countries with banking crisis in 1998 (according to Caprio and Klingebiel [36]).
A.2. Variable definition CRIS = 1 if the country’s banking system is in crisis (the Caprio and Klingebiel’s [36] chronology to identify countries that have gone through systemic banking crisis is used); Inf = Inflation Rate, in percentage (GDP Deflator). Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html.
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GDPg = GDP real growth rate. Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html. PubExpenses = General Government final consumption expenditure as a % of GDP. Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html. PCI = per capita income, in percentage; computed as a country’s per capita income divided by the US per capita income. Source: World Bank, World Development Indicators (WDI) http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20398986~menuPK:64133163~ pagePK:64133150~piPK:64133175~theSitePK:239419,00.html. Dep = 1 if there is an explicit deposit insurance scheme in the country. Source: World Bank http://siteresources. worldbank.org/INTRES/Resources/469232-1107449512766/Caprio_2000_banking_regulation_database.xls. ETA = Equity-to-Total Assets ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ETA. Source: Bankscope. It is a leverage indicator; higher ratios mean that the bank’s capital buffer is stronger, with a negative impact on the likelihood of a bank crises. ROA = Return on Assets ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ROA. Source: Bankscope. Higher profitability is a critical determinant of bank equilibrium. LIQ = Loan-to-deposit ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ‘‘Net Loans/Customer & Short Term Funding’’ ratio. Source: Bankscope. Higher ratios are associated with lower liquidity due to the loan/deposit maturity mismatch, and it becomes more difficult to redeem deposits should there be higher demand. Thus, higher liquidity is a stabilizing factor. SDAssets = standard deviation of the commercial banks’ log(total assets). Source: Bankscope. It measures the degree of similitude of the bank sizes. Lower SDAssets means that banks are more similar in terms of size; this could mean that it is more difficult to supervise fewer and larger banks because problems in one bank may quickly become systemic. Quality = Loan loss reserves-to-total assets ratio, in percentage. For each country, computed as the unweighted average of each commercial bank’s ‘‘Loan Loss Reserves/Total Assets’’ ratio. Source: Bankscope. Used as an indicator of asset quality; there are always bad bank loans and if banks are able to increase their loan loss reserves and yet be profitable and reward their shareholders then this may be a sign of bank stability. CV_ROA = Coefficient of variation of ROA. Source: Bankscope. Higher coefficient of variation means that there are a lot of different banks with higher and lower than the average sector profitability, meaning that we have a diversified sector. Diversification can be good insofar as the eventual existence of problem banks can benefit from the buffer provided by more profitable ones. CV_LIQ = Coefficient of variation of LIQ. Source: Bankscope. A stronger dispersion of liquidity among banks may help contain ‘propagation waves’ in case of a sudden disruption in some (but not all) financial institutions. HighROA = Percentage of banks with above average ROA. Source: Bankscope. If the banking sector in composed of a large percentage of banks with above average profitability, then this could be a stabilizing factor insofar as only a smaller number of financial institutions is pushing profits down. HighLIQ = Percentage of banks with above average LIQ. Source: Bankscope. Similar to HighROA, except with the opposite sign given the construction of the liquidity variable. A.3. Proximity matrices Wx : Exports Matrix—Each wij element represents exports from country i to country j, and these are row-standardized, so that for each i, j wij = 1. Source: IMF—Direction of Trade Statistics Yearbook, 2001. An alternative definition, using exports plus imports was also used. Wba : Banking Activity Matrix—Each wij element is measured by the absolute value of the difference between the ‘‘Banking Activity’’ index for each pair (i, j) of countries. From the original version of the Barth et al. [46] database, an index of the degree of restriction to commercial bank access to the activities of brokerage, real estate, insurance and property ownership of non-financial firms is constructed. For each activity we attribute a 0–3 score if there is unrestricted access, access allowed with some limitations, access restricted and access prohibited, respectively. The average of the scores for the 4 activities is an indicator of the degree of restrictions imposed to the banking sector, which is higher the closer the average gets to 3. An alternative definition, using other characteristics of the banking sector, was also used. Source: World Bank http:// siteresources.worldbank.org/INTRES/Resources/469232-1107449512766/Caprio_2000_banking_regulation_database.xls. References [1] [2] [3] [4]
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