Fair premium rate of the deposit insurance system based on banks' creditworthiness

Yoshino, Naoyuki; Taghizadeh-Hesary, Farhad; Nili, Farhad Working Paper Fair premium rate of the deposit insurance system based on banks' creditworthiness ADBI Working Paper, No. 757 Provided in Cooperation with: Asian Development Bank Institute (ADBI), Tokyo Suggested Citation: Yoshino, Naoyuki; Taghizadeh-Hesary, Farhad; Nili, Farhad (2017) : Fair premium rate of the deposit insurance system based on banks' creditworthiness, ADBI Working Paper, No. 757, Asian Development Bank Institute (ADBI), Tokyo This Version is available at: https://hdl.handle.net/10419/179213 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. 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. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/ ADBI Working Paper Series FAIR PREMIUM RATE OF THE DEPOSIT INSURANCE SYSTEM BASED ON BANKS’ CREDITWORTHINESS N. Yoshino, F. TaghizadehHesary, and F. Nili No. 757 July 2017 Asian Development Bank Institute The Working Paper series is a continuation of the formerly named Discussion Paper series; the numbering of the papers continued without interruption or change. ADBI’s working papers reflect initial ideas on a topic and are posted online for discussion. ADBI encourages readers to post their comments on the main page for each working paper (given in the citation below). Some working papers may develop into other forms of publication. Suggested citation: Yoshino, N., F. Taghizadeh-Hesary, and F. Nili. 2017. Fair Premium Rate of the Deposit Insurance System based on Banks’ Creditworthiness. ADBI Working Paper 757. Tokyo: Asian Development Bank Institute. Available: https://www.adb.org/publications/fair-premiumrate-deposit-insurance-system-based-banks-creditworthiness Please contact the authors for information about this paper. Email: nyos[email protected], [email protected], [email protected] Naoyuki Yoshino is the dean of the Asian Development Bank Institute. Farhad Taghizadeh-Hesary is an assistant professor of economics at Keio University, and a visiting professor at the Graduate School of Economics, University of Tokyo, Japan. Farhad Nili is senior advisor to the executive director of the World Bank Group. The views expressed in this paper are the views of the author and do not necessarily reflect the views or policies of ADBI, ADB, its Board of Directors, or the governments they represent. ADBI does not guarantee the accuracy of the data included in this paper and accepts no responsibility for any consequences of their use. Terminology used may not necessarily be consistent with ADB official terms. Working papers are subject to formal revision and correction before they are finalized and considered published. Asian Development Bank Institute Kasumigaseki Building, 8th Floor 3-2-5 Kasumigaseki, Chiyoda-ku Tokyo 100-6008, Japan Tel: +81-3-3593-5500 Fax: +81-3-3593-5571 URL: www.adbi.org E-mail: [email protected] © 2017 Asian Development Bank Institute ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Abstract Purpose Deposit insurance is a key element in modern banking, as it guarantees the financial safety of deposits at depository financial institutions. It is necessary to have at least a dual fair premium rate system based on the creditworthiness of financial institutions, as considering a singular premium system for all banks will have a moral hazard. In this paper, we develop a theoretical as well as an empirical model for calculating dual fair premium rates. Design/methodology/approach Our definition of a fair premium rate in this paper is a rate that can cover the operational expenditures of the deposit insuring organization, provides it with sufficient funds to enable it to pay a certain percentage share of deposit amounts to depositors in the case of bank default, and provides it with sufficient funds as precautionary reserves. To identify and classify healthier and more stable banks, we use credit rating methods that employ two major dimensional reduction techniques. For forecasting nonperforming loans (NPLs), we develop a model that can capture both macro shocks and idiosyncratic shocks to financial institutions in a vector error correction model (VECM). Findings The response of NPLs/loans to macro shocks and idiosyncratic innovations shows that using a model with macro variables only is insufficient, as it is possible that under favorable economic conditions some banks perform negatively for bank-level reasons such as mismanagement, or vice versa. Final results show that deposit insurance premium rates need to vary in relation to banks’ creditworthiness. Value The results provide interesting insight for financial authorities to assist them in setting fair deposit insurance premium rates. A high premium rate reduces the capital adequacy of individual financial institutions, which endangers the stability of the financial system; a low premium rate reduces the security of the financial system. Keywords: deposit insurance premium rate, forecasting nonperforming loans, idiosyncratic shocks JEL Classification: G28, G21, E44 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Contents 1. INTRODUCTION ......................................................................................................... 1 1.1 Who Pays the Deposit Insurance Premium? ................................................... 2 2. MODEL ........................................................................................................................ 3 2.1 Dual Premium Rate Model .............................................................................. 3 2.2 Forecasting Banks’ Nonperforming Loans: Macro Shocks versus Idiosyncratic Shocks ............................................................................ 6 3. AN ANALYSIS OF BANKS’ CREDIT RATING ............................................................ 7 3.1 Selection of Variables ...................................................................................... 8 3.2 Principal Component Analysis ......................................................................... 9 3.3 Cluster Analysis ............................................................................................. 12 3.4 Robustness Check of Banks’ Credit Rating................................................... 13 4. EMPIRICAL ANALYSIS ............................................................................................ 14 4.1 Forecasting Banks’ Nonperforming Loans .................................................... 14 4.2 Fair Deposit Insurance Premium Rate for Each Group of Banks .................. 20 5. CONCLUSION .......................................................................................................... 21 REFERENCES ..................................................................................................................... 23 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili 1. INTRODUCTION Since the start of the recent global financial crisis, triggered by the collapse of Lehman Brothers in September 2008, there has been an ongoing international debate about the reform of financial regulation and supervision intended to prevent the recurrence of a similar crisis. Strengthening deposit insurance systems is one of the fundamental steps in this reform. Deposit insurance is a key element in modern banking, as it guarantees the financial safety of deposits at depository financial institutions. If an insured depository institution fails to fulfill its obligations to its depositors, the insuring agency will step in to honor the principal and accrued interests up to a predetermined ceiling. An important issue under this system is how to price deposit insurance (Horvitz 1983; Kane 1986; Yoshino, Taghizadeh-Hesary, and Nili 2013). For determining fair premium rates to be paid by depository financial institutions to the insuring agency, the consensus method tends toward the adoption of a risk-based deposit insurance scheme according to bank defaults. To achieve this goal, several models for assessing bank defaults have been proposed: Buser, Chen, and Kane (1981); Acharya and Dreyfus (1989); Bartholdy, Boyle, and Stover (2003); and, more recently, Yoshino and Hirano (2011). However, in the literature on banking and finance we have found only a few studies dealing with the deposit insurance system (Horvitz 1983; Hwang, Lee, and Liaw 1997; Inakura and Shimizutani 2010; Yoshino, Taghizadeh-Hesary, and Nili 2013) and hardly any studies on how to estimate and forecast fair premium rates for deposit insurance. In one of the most recent studies, Yoshino, Taghizadeh-Hesary, and Nili (2013) provide a model for calculating fair premium rates for the deposit insurance system. Using this model, they estimate the fair premium rate for the deposit insurance system of Japan and find that it is much higher than the actual current premium rate in that country. In another study, they conclude that, to secure financial stability, Japan needs to raise the deposit insurance premium rate. It is crucial for each country to set fair premium rates to maintain financial system stability, thereby protecting depositors and ensuring an appropriate settlement of funds when financial institutions fail. In this paper, a fair rate refers to a rate that covers the operational expenditures of an insuring agency (e.g. personnel costs and equipment costs) and provides it with sufficient funds to financially assist any failed depository financial institutions. The insuring agency is also obliged to keep adequate precautionary reserves at the end of each financial period to secure itself against further possible failures. A high premium rate reduces the capital adequacy of individual financial institutions, which endangers the stability of the financial system; a low premium rate reduces the security of the financial system. In this paper, we expand the model first introduced by Yoshino, Taghizadeh-Hesary, and Nili (2013) for estimating one fair premium rate for the whole deposit insurance system. We conclude that many countries need to adopt a system that uses more than one fair premium rate. Depending on the soundness and stability of banks, varying premium rates should be adopted as it is unfair for all banks, irrespective of whether they are healthy or unhealthy, to pay the same premium rate to the insuring agency. Unsound and riskier banks that endanger the stability of the financial system should pay higher premiums than healthy banks and financial institutions that keep their nonperforming loans (NPLs) at adequate levels and perform well financially. Hence, it is necessary to have at least a dual fair premium rate system, which is the main argument of this paper. In Section 2 of this paper, we present a model for calculating dual fair premium rates that would allow healthier banks to pay a lower rate. For this 1 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili purpose, we need to have a mechanism for credit rating and classification of banks based on their financial soundness, which is presented in Section 3. For our empirical analysis, presented in Section 4, we use the deposit insurance system of an Asian economy that is currently in the process of establishing a deposit insurance system. 1.1 Who Pays the Deposit Insurance Premium? As its name suggests, a deposit insurance system is intended primarily to provide for the payment of insurance claims when an insurable contingency occurs. Specifically, there are two methods of protection: the insurance payout method, whereby insurance payouts are made directly to depositors; and a method whereby the business of a failed financial institution is transferred to a different financial institution, and the deposit insurance agency or corporation (DIC) provides assistance to this second institution. When checking the DIC websites of various countries, we typically find a sentence along the following lines: “You [depositors] do not pay for the deposit insurance. Financial institutions that are a member of our deposit insurance system pay premiums to us.” Although member banks or financial institutions of the deposit insurance system do indeed pay the premium rate to the DIC, in practice the deposit insurance premium rate burden is divided between banks and depositors and/or banks and corporations. Figure 1 illustrates how the burden of the deposit insurance premium is shared. Figure 1: Who Pays the Deposit Insurance Premium? Source: Authors’ compilation. In Figure 1, τ is the deposit insurance premium banks should pay to the DIC. Paying this premium increases the banks’ costs, so they have to lower the interest they pay out on customer deposits and/or raise their interest rates on loans granted. In the left-hand-side graph of Figure 1, it is assumed that banks compensate for their premium burden only by lowering the interest they pay out on deposits. In this scenario, banks are not the only parties that bear the burden of the deposit insurance cost, as it is shared between depositors and banks. As can be seen in the figure, the higher costs incurred by banks due to the launch of a deposit insurance system decrease the demand for deposits and consequently the demand curve shifts to the left. The result is 2 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili a decrease in interest rates on deposits. “AB” signifies the share of the burden of the deposit insurance premium borne by the banks, “BC” is the depositors’ share of the burden of the deposit insurance premium, and “AC” is the total decrease in the interest paid out on deposits, which is equal to τ . In the right-hand-side graph of Figure 1, a scenario in which the premium burden of banks is compensated only by raising their lending rates on loans to corporations is presented. In this case, the increase in cost incurred by the banks due to the launch of a deposit insurance system results in a decrease in the provision of loans to customers and consequently the supply curve shifts to the left. As a result, banks’ lending rates for loans rise. This tends to divide the premium burden between banks and corporations that are demanders of loans. The corporations’ share is depicted by “ba,” the banks’ share by “cb,” and “ca” depicts the total change in the banks’ lending rate as a result of paying premiums to the DIC, which is equal to τ . 2. MODEL In this paper we present two models—the first one is for estimating dual premium rates of deposit insurance; the second is for forecasting NPLs for each group of banks, which is a requirement for estimating the premium rates of deposit insurance. In Section 2.1 we define the dual premium rate model, and in Section 2.2 we explain how to forecast banks’ NPLs using our model. 2.1 Dual Premium Rate Model In the development of our model we were inspired by Yoshino, Taghizadeh-Hesary, and Nili (2013). They provide a model using a discounted present value mechanism to calculate a single fair premium rate for deposit insurance systems through which they estimate the fair premium rate for the deposit insurance system of Japan. Their model enables us to calculate a single premium rate for all financial institutions, which is what many countries use. However, in many other countries the monetary authorities prefer to use dual or multiple premium rates for their deposit insurance system, which means healthier financial institutions pay a lower premium to the DIC. This gives financial institutions an incentive to improve their soundness, so they can attain higher credit rating levels for paying lower premiums. In this paper, we expand the Yoshino, Taghizadeh-Hesary and Nili (2013) model, and use a discounted present-value mechanism to calculate dual fair premium rates for the deposit insurance system. It can be expanded further to calculate multi-premium rates, should a particular DIC wish to use more than two premium rates. Figure 2 shows the general outline of our new model for calculating the different premium rates for each group of banks: As Figure 2 shows, according to our model, the premium income the DIC earns from each group of banks (A, B) has to be equal to the total amount of financial assistance the DIC provides to each group in the case of a banking default in that group, operational expenditures incurred by the DIC for each group, and precautionary future reserves kept by the DIC for each group separately. 3 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Figure 2: Income and Expenditure of DIC in the Case of Dual Premium Rates DIC = deposit insurance agency/corporation. Note: “A” banks are healthier banks than “B” banks. A τ is the premium rate for Group “A,” B τ is the premium rate for Group “B” of banks. , AB II are the premium income of the DIC from Group A and Group B of banks, respectively. , AB DD are the cumulative deposit of Group A and Group B of banks, respectively. Source: Authors. According to our model, the discounted cumulative amounts of these variables are important, meaning: Discounted cumulative premium income of the DIC from each group of banks (including future expected income) = Discounted cumulative operational expenditures of the DIC toward each group of banks (including future expected operational expenditures) + Discounted cumulative financial assistance of the DIC to failed financial institutions of each groups (including future expected financial assistance) + discounted precautionary future reserves of the DIC at the end of the period for each group of banks. Below, in Equations 1–8, we present each of these elements: Present value of income (including future income) of the DIC from Group A banks: (1) Present value of income (including future income) of the DIC from Group B banks: (2 ) where A PVI and B PVI denote the present value of income (including future income) of the DIC from Group A and Group B banks, respectively; A i D and B i D are the cumulative amount of eligible deposits of Group A and Group B banks, respectively, in each year; A τ and B τ are the deposit insurance premium rates for Group A and Group B banks, respectively; and i τ stands for the average long-term interest rate used for discounting values in each. ( ) ( ) ( ) ( ) n n A n AAA A r D r D r D r D PVI A AAA + ++ + + + + + =1 ... 11 12 2 2 1 1 1 0 0 0 ττττ () ( ) ( ) ( ) n n B n BB B B r D r D r D r D PVI B BBB + ++ + + + + + =1 ... 111 2 2 2 1 1 1 0 0 0 ττ ττ 4 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Table 4: Component Correlation Matrix Component Z1 Z2 Z3 Z1 1 (0.282) 0.059 Z2 (0.282) 1 0.162 Z3 0.059 0.162 1 (…) = negative value. Note: The extraction method is principal component analysis. The rotation method is direct oblimin rotation with Kaiser Normalization. Figure 3 shows the distribution of the three components (Z1, Z2, and Z3) for 28 out of a total of 32 banks of an Asian country. Figure 3: Distribution of Factors for 28 Banks continued on next page 11 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Figure 3 continued Note: Each star represents one bank; these are named alphabetically, A, B, C, …, Z, AA, BB, CC, DD, EE, and FF, for 32 banks of an Asian economy. Four banks (banks B, G, H, and M) are outliers in positive parts of the graphs and are not visible in the above graphs. 3.3 Cluster Analysis In this section, we take the three components obtained in the previous section and identify those banks that have similar traits. We then generate clusters and place the banks in distinct groups. To do this, we employ cluster analysis, which organizes a set of data into groups so that observations from a group with similar characteristics can be compared with those from a different group (Martinez and Martinez 2005). In this case, banks are organized into distinct groups according to the three components derived from the PCA obtained in the previous section. Cluster analysis techniques can themselves be broadly grouped into three classes: hierarchical clustering, optimization clustering,3 and model-based clustering. We use the method most prevalent in the literature—hierarchical clustering. This produces a nested sequence of partitions by merging (or dividing) clusters. At each stage of the sequence, a new partition is optimally merged with (or separated from) the previous partition according to some adequacy criterion. The sequence of partitions ranges from a single cluster containing all the individual banks to a number of clusters (n) containing a single bank. The series can be described by a tree display called a “dendrogram” (Figure 4). Agglomerative hierarchical clustering proceeds by means of a series of successive fusions of the n objects into groups. By contrast, divisive hierarchical methods divide the n individuals into progressively finer groups. Divisive methods are not commonly used because of the computational problems they pose (see Everitt et al. [2001] and Landau and 3 The main difference between the hierarchical and optimization techniques is that in hierarchical clustering the number of clusters is not known beforehand. The process consists of a sequence of steps in which two groups are either merged (agglomerative) or divided (divisive) according to the level of similarity. Eventually, each cluster can be subsumed as a member of a larger cluster at a higher level of similarity. The hierarchical merging process is repeated until all subgroups are fused into a single cluster (Martinez and Martinez 2005). Optimization methods, on the other hand, do not necessarily form hierarchical classifications of the data as they produce a partition of the data into a specified or predetermined number of groups by either minimizing or maximizing some numerical criteria (Feger and Asafu-Adjaye 2014). 12 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Chis Ster [2010]). Below, we use the average linkage method, which is a hierarchical clustering technique. Figure 4 shows the dendrogram that results from this hierarchical clustering: Figure 4: Dendrogram Using Average Linkage The resulting dendrogram (hierarchical average linkage cluster tree) provides a basis for determining the number of clusters by sight. In the dendrogram shown in Figure 4, the horizontal axis shows 28 banks, which are named alphabetically. As mentioned above, 32 banks are the subject of our examination. However, four banks have outlying positive data that are far removed from the data for the other 28 banks. We do not include these four banks in our cluster analysis as our result is not a rational clustering. This is the reason Figure 4 shows only 28 banks on the horizontal axis. The dendrogram classifies the banks into two main clusters (Group 1 and Group 2), but it does not show which of these two clusters contain the financially healthier banks, so we have to take one further step. By comparing the classification resulting from cluster analysis and the distributions of factors in Figure 3, we can conclude that the sequence of banks on the horizontal axis of our dendrogram is based on their soundness. Among these 28 banks, bank “F” has the highest stability and soundness, whereas bank “W” has the lowest. 3.4 Robustness Check of Banks’ Credit Rating For robustness, we check the rankings of three banks out of the 28 banks for all eight examined financial variables. We randomly pick one bank from Group 1 and one from Group 2, and the bank that is in the middle of the credit ranking selected. The results are summarized in Table 5: Table 5: Robustness Check for Three Sample Banks Bank Credit Rank Rank of L–D Rank of PR–L Rank of (SD+LD) –D Rank of A–L Rank of SC–L Rank of CA–D Rank of CBR–D Rank of OBR–D I 2 24 1 16 3 5 8 21 2 R 14 14 17 12 15 9 11 9 7 W 28 11 20 22 20 6 10 3 18 Note: Credit rank is the ranking shown by our dendrogram—the lower this number, the healthier the bank. For definitions of the variables, please refer to Table 1. 13 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili The first randomly picked bank from Group 1 is bank I. Bank I is the second most sound and stable bank according to our credit rating result, and as is clear from Table 5, the robustness check supports this result. This bank shows a fairly stable and healthy status in most of our eight financial variables. It is the top bank for PR–L (properties/loans), meaning this bank has a relatively large amount of properties compared with the amount of loans, which means it is stable. It ranks second for OBR–D (accounts receivable from other banks/total deposits), fifth for SC–L (securities/loans), and third for A–L (assets/loans)—these results indicate that this bank has sufficient assets, which favors its stability and soundness. Although it has one of the lowest ranks for L–D (loans/deposits), this suggests this bank is trusted by depositors, and therefore the amount of deposits is large compared with loans. The second bank in our robustness check is bank R, which can be found in the middle of the horizontal axis of our dendrogram with a credit rank of 14, which is close to the middle of these 28 banks. When considering bank R’s ranking in terms of the eight variables, for most of these variables it appears in the middle of the ranking. If we take a simple average of the rank of this bank in our eight variables, the result is almost 12, which is close to the credit rank of 14 suggested by our method. The third bank in our robustness check is bank W, a bank we pick randomly from Group 2. Bank W has the lowest soundness and stability in this group and among all 28 banks. When considering the ranking of this bank in our eight variables in Table 5, it is apparent that this bank is not sound. It has very low rankings for PR–L (properties/loans), (SD+LD)/D ((saving deposits + long-term deposits)/total deposits), A–L (assets/loans), and OBR–D (accounts receivable from other banks/total deposits), which suggests this bank is unsound and unstable—it has the lowest credit rank of the banks examined. 4. EMPIRICAL ANALYSIS In Section 4.1, we first use the model developed in Section 2.2 to forecast NPLs for each group of banks. We then use the results of the estimations obtained in Section 4.1 to calculate a fair deposit insurance premium rate for each group of banks, using the model we develop in Section 2.1 of this paper. 4.1 Forecasting Banks’ Nonperforming Loans There are several recent works on forecasting banks’ nonperforming loans and stress testing. For instance, Kahlert and Wagner (2017) stress tested Eurozone banks of systemic importance by applying a historical simulation approach. To forecast each group of banks’ NPLs, we run regressions using the vector autoregression or vector error correction (VAR/VEC) model. As mentioned above, for our empirical analysis in this paper we use data from an Asian economy, so we use macroeconomic data and all 32 banks’ financial profiles to forecast the NPLs for each group of banks (Group 1 and Group 2). As per Eq. 9, we need to use macroeconomic variables (real GDP, price of land, price of stock, government bond interest rate) and Zi, which represents the financial profile of banks and captures idiosyncratic shocks, to forecast NPLs. In our empirical analysis, for the macroeconomic variables we employ real GDP, and instead of the price of stock and price of land, due to lack of data, we use the consumer price index (CPI), which is the best representative for the price level in an economy and can be used as a substitute for these two price levels. In this study, using the government bond interest rate is not practical since the selected Asian country has implemented Islamic banking and fiscal rules, which are quite different from conventional rules. And as interest rates are affected by monetary policy, instead of the real interest rate, we 14 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili use another monetary variable, M1, which has a high correlation with the interest rate, as shown in many previous studies. Eq. 9 has two categories of variables for forecasting NPLs—the first category consists of the macroeconomic variables described above; the second element is Zi, reflecting the financial profile of banks. The latter category is made up of three significant components—Z1, Z2, and Z3—obtained using principal component analysis in Section 3.2 with their factor loadings presented in Table 3. Using the loadings of all eight financial ratios (Table 3), we obtain Z1, Z2, and Z3 for each group of banks (Group 1 and Group 2), and since those eight financial ratios of banks are time series variables, Z1, Z2, and Z3 will also be time series variables. For our empirical analysis, we use monthly data from 2011M1 to 2013M12 from the Central Bank. Since we have two groups of banks, we should run two regressions—one for each group. The left-hand side of Eq. 9 for each group’s regression is the sum of NPLs of that group/total loans of that group of banks; the right-hand side of Eq. 9 is the macroeconomic variables and Z1, Z2, and Z3 for that group of banks. 4.1.1 Data Analysis To evaluate the stationarity of all series, we use an augmented Dickey–Fuller (ADF) test. The results we obtain imply that all variables are nonstationary. These variables include GDP growth rate; CPI inflation rate (inflation rate of each month compared to the same month of the previous year); M1 growth rate (growth rate of M1 in each month compared with the same month of the previous year—the original quarterly data are converted to monthly data); sum of NPLs/sum of total loans for Group 1 and Group 2 of the banks; and Z1, Z2, and Z3 for each group of banks. However, when we apply the unit root test to their first differences, we are able to reject the null hypothesis of unit roots for each of the variables. These results suggest that all variables each contain a unit root. When we perform the unit root test and discover that the variables are nonstationary in level and stationary at the first difference level, they are integrated of order one. The next step is to conduct a cointegration analysis to examine whether a long-run relationship exists among these variables. 4.1.2 Cointegration Analysis We conduct a cointegration analysis using Johansen’s technique by assuming a linear deterministic trend and for two cases—with intercept, and with intercept and trend. Given the short period of our data, the Akaike information criterion (AIC) suggests using variables with one lag. The results of the cointegration rank test using trace are presented in Table 6. As is clear from Table 6, the above test rejects the null hypothesis of noncointegrating variables for Group 1 and Group 2. This means that all variables are cointegrated and there is a long-run association among variables, or, in other words, in the long run, these seven variables (NPL/L, GDP growth rate, CPI inflation rate, M1 growth rate, Z1, Z2, and Z3) for each group of banks move together. Hence, we should run a vector error correction model (VECM). The AIC results of our linear deterministic VEC model indicate that estimating the model by including trend and intercept is slightly better than including just intercept for both bank groups, so we also retain this finding. 15 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Table 6: Cointegration Rank Test (Trace) Group 1 of Banks Intercept Intercept and Trend Hypothesized no. of CEs Eigenvalue Trace Statistic Prob. Eigenvalue Trace Statistic Prob. None 0.80 192.62* 0.00 0.80 217.14* 0.00 At most 1 0.75 136.33* 0.00 0.75 160.38* 0.00 At most 2 0.61 87.91* 0.00 0.62 111.82* 0.00 At most 3 0.53 55.01* 0.01 0.55 77.80* 0.00 At most 4 0.39 28.35 0.07 0.51 49.89* 0.01 At most 5 0.25 11.06 0.21 0.35 24.98 0.06 At most 6 0.02 0.86 0.35 0.25 10.10 0.12 Group 2 of Banks Intercept Intercept and Trend Hypothesized no. of CEs Eigenvalue Trace Statistic Prob. Eigenvalue Trace Statistic Prob. None 0.80 167.96* 0.00 0.81 200.61* 0.00 At most 1 0.75 112.06* 0.00 0.80 141.91* 0.00 At most 2 0.48 64.19 0.13 0.58 86.33 0.07 At most 3 0.46 41.23 0.18 0.47 55.63 0.20 At most 4 0.24 19.41 0.46 0.38 33.63 0.31 At most 5 0.21 9.58 0.31 0.24 16.82 0.43 At most 6 0.03 1.17 0.28 0.19 7.34 0.31 CE = cointegrating equation; prob. = probability. Note: * denotes rejection of the noncointegrating hypothesis at the 5% level. Prob. shows MacKinnon–Haug–Michelis p-values. 4.1.3 Vector Error Correction Model (VECM) We estimate Model 9 in a VECM setting including the seven variables—NPL/L, GDP growth rate, CPI inflation rate, M1 growth rate, Z1, Z2, and Z3—for each group. The VECM can be defined as follows (see Yoshino et al. 2014): (10 ) for (11 ) where d denotes the first differences, O is the lag operator, and ε is an error term. can be written as αβ ′ Π= , where α and β are pr× matrices, and p is the number of variables in V. gdp is GDP growth rate, cpi is CPI inflation rate, and m1 is M1 growth rate. β is a vector of the cointegrating relationship and α is a loading matrix defining the adjustment speed of the variables in V to the long-run equilibrium defined by the cointegrating relationship. The rank of Π is denoted by r. As mentioned above, the AIC standard suggests one lag. tttt VdVOAdV ε +Π+= −1 )( ( ) Z3, Z2 Z1,m1, cpi, gdp, NPL/L,=V Π 16 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili Model 12 shows our VECM for Group 1 with four cointegrating equations and one lag for each variable: d(NPL1/L1) = Φ1[Z1,1(–1) – 47.45 NPL1/L1(-1) – 33.89 P(–1) + 1.82 Y(–1) + 0.34 trend – 12.36] + Φ2[Z1,2(–1) – 8.83 NPL1/L1(–1) – 5.43 P(–1) + 0.75 Y(–1) + 0.05 trend – 1.55] + Φ3[Z1,3(–1) – 23.10 NPL1/L1(–1) – 17.63 P(–1) + 6.89 Y(–1) + 0.24 trend – 9.12 ] + Φ4[ M(–1) – 0.92 NPL1/L1(–1) – 2.17 P(–1) + 2.35 Y(–1) + 0.03 trend – 1.59] + Φ5 d[Z1,1(–1)] + Φ6 d[Z1,2(–1)] + Φ7d[Z1,3(–1)] + Φ8d[M(–1)] + Φ9d[NPL1/L1(–1)] + Φ10d[P(–1)] + Φ11d[Y(–1)] + Φ12 (12 ) where NPL1/L1 is the ratio of NPLs over total loans for Group 1; Z1,1 denotes the first component, Z1,2 is the second component, and Z1,3 is the third component, all three for Group 1; d(Z1,1), d(Z1,2), d(Z1,3), d(M), d(NPL1/L1), d(P), and d(Y) are first differences of the first component, the second component, the third component (all three for Group 1), M1 growth rate, NPLs over total loans for Group 1, CPI inflation rate, and GDP growth rate, respectively. In this VECM, trend is also included, since we calculate the cointegration with intercept and trend. Φ1, Φ2, Φ3, and Φ4 are the coefficients of the four cointegrating equations; Φ5 … Φ11 are the coefficients of the lagged variable for the seven variables of our model; and Φ12 is a constant. Model 13 shows our VECM for Group 2 with one cointegrating equation and one lag for each variable: d(NPL2/L2) = Φ13[Z2,1(–1) + 0.67 Z2,2(–1) – 3.90 Z2,3(–1) + 0.03 M(– 1) – 2.04 NPL2/L2 (–1) – 1.11 P(–1) – 0.04 Y(–1) + 0.008 trend – 0.97] + Φ14 d[Z2,1(–1)] + Φ15 d[Z2,2(–1)] + Φ16d[Z2,3(–1)] + Φ17d[M(–1)] + Φ18d[NPL2/L2(–1)] + Φ19d[P(–1)] + Φ20d[Y(–1)] + Φ21 (13 ) where NPL2/L2 is the ratio of NPLs over total loans for Group 2; Z2,1 denotes the first component, Z2,2 is the second component, and Z2,3 is the third component, all three for Group 2; d(Z2,1), d(Z2,2), d(Z2,3), d(M), d(NPL2/L2), d(P), and d(Y) are first differences of the first component, the second component, the third component (all three for Group 2), M1 growth rate, NPLs over total loans for Group 2, CPI inflation rate, and GDP growth rate, respectively. In this VECM, trend is also included since we calculate the cointegration with intercept and trend. Φ13 is the coefficient of the cointegrating equation; Φ14 … Φ20 are the coefficients of the lagged variable for the seven variables of our model; and Φ21 is a constant. We use models 12 and 13 to forecast the NPL/L for each group of banks. To do so, we need some assumptions. As mentioned above, in developing our VECM we use monthly data from 2011M1 to 2013M12. We assume real GDP growth of 2.8%, year on year, for 2014 and 2.9% for 2015. We assume a CPI inflation rate of 23%, year on year, for 2014 and for 2015 we expect 18%. As for the M1 growth rate, the selected country under a new governor continues to pursue tightening monetary policies, as it did in 2013, to control the high inflation rate. Hence, we assume that in 2014 and 2015, M1 grows at the same rate as in 2013M09–2013M12. Also for NPL/L and the three components for each group of banks for 2014 and 2015, we assume they stay on the same growth path as in 2013M09–2013M12. Using these assumptions, we forecast the NPL/L for each group and use these to calculate the premium rates for each group of banks (which are presented in Section 4.2). 17 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili 4.1.4 Impulse Response Analysis In this section, we conduct impulse response (IR) analysis to provide further evidence of the dynamic response of NPL/L to macro and idiosyncratic innovations. (For more information on IR analysis, see Yoshino and Taghizadeh-Hesary [2014c].) The accumulated response of NPL/L to macro and idiosyncratic innovations for Group 1 of the banks is shown in Figure 5. Figure 5: Response of NPL/L to Innovations (Group 1 of Banks) Note: Accumulated response to Cholesky one-standard deviation innovations. NPL1/L1 is the ratio of NPLs over total loans for Group 1 of the banks; Z1,1 denotes the first component, Z1,2 the second component, and Z1,3 the third component, all three for Group 1; M1 denotes M1 growth rate, P denotes CPI inflation rate, and Y denotes GDP growth rate. The three graphs in the first row of Figure 5 show accumulated responses of NPL/L to an unanticipated positive shock to Z1, Z2, and Z3 for Group 1 of the banks. The response of NPL/L to Z1 is statistically negative and very persistent. This means a positive shock to Z1, which mainly represents assets, decreases the NPL/L of Group 1. An unanticipated positive shock to Z2, which represents deposits, has a statistically negative effect on the NPL/L of Group 1 and builds up over the first 3 months, after which it becomes insignificant, meaning an unanticipated increase in deposits reduces the NPL/L for Group 1. An unanticipated positive shock to Z3, which represents 1/loans, has a statistically negative effect on NPL/L of Group 1 and builds up over the first 3 months, after which it becomes insignificant. The four other graphs in Figure 5 show accumulated responses of the NPL/L of Group 1 of the banks to positive shocks to macro variables and to lagged NPL/L. The response of NPL/L to M1 growth rate shocks is statistically positive and builds up over the first 5 months, after which it becomes insignificant. An unanticipated positive shock to P (CPI inflation) has a 18 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili statistically negative and persistent effect on the NPL/L of Group 1, which is consistent with Yoshino and Hirano (2011, 2013). An unanticipated positive shock to Y (GDP growth rate) has a statistically negative effect on the NPL/L of Group 1 and builds up over the first 2 months, after which time it becomes insignificant. Figure 6 depicts the accumulated responses of NPL/L to macro and idiosyncratic innovations for Group 2 of the banks. Figure 6: Response of NPL/L to Innovations (Group 2 of Banks) Note: Accumulated response to Cholesky one-standard deviation innovations. NPL2/L2 is the ratio of NPLs over total loans for Group 2 of the banks; Z2,1 denotes the first component, Z2,2 the second component, and Z2,3 the third component, all three for Group 2; M1 denotes the M1 growth rate, P the CPI inflation rate, and Y the GDP growth rate. Group 2 shows similar responses to innovations to macro variables. It means that focusing only on a model based on macro variables for forecasting NPLs of different groups of banks leads to misinterpretation as it is possible that under good economic conditions some banks show a negative financial performance and have a high default risk. The responses of the NPL/L of Group 2 of the banks to an unanticipated positive shock to Z1 and Z3 are similar to Group 1’s responses, but for shocks to Z2 the responses differ. The response of the NPL/L of Group 2 to positive shocks to Z2 is statistically positive and persistent, which goes against our finding for Group 1. This means that increasing deposits, which are good news for banks, tend to result in an increase in NPL/L for Group 2. This shows that Group 2 does not manage their NPL/L well—by expanding their business and accepting more deposits the NPL/L ratio increases, which indicates that Group 2 is not as sound as Group 1. -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to Z2,1 -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to Z2,2 -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to Z2,3 -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to M -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to NPL2/L2 -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to P -.03 -.02 -.01 .00 .01 .02 12345678910 Accumulated Response of NPL2/L2 to Y 19 ADBI Working Paper 757 Yoshino, Taghizadeh-Hesary, and Nili These results confirm our findings in the previous sections of this paper. Moreover, they back up our suggestion that macro variables are not sufficient in an NPL forecasting model for different groups of banks. The model also needs to have the capability to capture idiosyncratic shocks, as does our Model 9 above. 4.2 Fair Deposit Insurance Premium Rate for Each Group of Banks In this paper, a fair premium rate is defined as a rate that covers the operational expenditures of an insuring agency (e.g. personnel costs and equipment costs), provides it with sufficient funds to enable it to pay a certain percentage of deposit amounts to depositors in the case of a banking default, and provides it with sufficient funds as precautionary reserves to secure itself against further failures. High premium rates reduce the capital adequacy of individual financial institutions, which can in turn endanger the stability of the financial system. Low premium rates reduce the overall safety of the financial system. Figure 7 shows a bank’s balance sheet in the case of default. In order to calculate the fair deposit insurance premium rate, we need to calculate the financial assistance of the deposit insurance. Figure 7: Financial Assistance of the Deposit Insurance Corporation/Agency in a Failed Bank’s Balance Sheet Source: Authors’ compilation. To estimate fair premium rates for each group of banks, we need to make some assumptions regarding: the percentage share of insurance coverage for each type of deposit; the level of the insuring agency’s operational expenditures; the estimated default ratio of NPLs; and the percentage share of excess over the forecasted financial assistance from the DIC and operational expenditures that need to be kept by this organization as precautionary reserves. 20