Research Model and Research Methodology to Analyze the Impact of Bad Debt on Bank Efficiency

Performance measures take into account undesirable factors, including: undesirable inputs; and undesirable outputs.

At this time, the thesis uses the DEA model with undesirable outputs to measure the bank efficiency score in the Vietnamese commercial banking system when taking into account the output factor of bad debt. With this model, the impact of bad debt on the bank efficiency score of each bank will be considered, and the optimal level of bad debt for the bank to achieve the efficiency margin.

The model inputs include: Staff costs, interest costs, fixed assets; the model outputs: customer deposits, investments, non-interest income, and bad debts (bad debts are undesirable outputs). The input/output factors are similar to those in the cost efficiency measurement model. The efficiency score represents: If it is 1, the bank is marginally efficient; above 1, it is inefficient. Josef Jablonský's DEA.RES 14 software is used to measure the DEA efficiency score with bad debts as undesirable outputs.

Model

Performance measurement model with output

unwanted

Efficiency measurement model with undesirable outputs (undesirable outputs DEA model)

max ℎ As, b t , b u= s + +( wb t+ Yb u )

MZ[ M #Z[ #

(3.3)

Provided:

;

WX # + b u = X #A

;W& M- b t= s& , r ∈ DO

Z[ M MA

; W&′ M − b t = s&′ M A , r ∉ DO

Z[ M

;

W= 1

W, b u , b t≥ 0

# M

b u , b tare the excess input and the shortage output of

# M

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bank

X #A , & MA are the inputs and outputs of the bank

DI and DO are sets of indices of desired inputs and desired outputs.

(desirable outputs), and X′ # = X YN2 − X # , U ∉ }~ , and

&′ M = & YN2 − & M , a ∉ }

Source: Seiford & Zhu (2002)

In addition, the thesis also uses the super-efficiency model to measure the efficiency order of banks that have reached the efficiency frontier and the super-efficiency model used is that of Andersen & Petersen (1993).

3.2. RESEARCH MODEL AND RESEARCH METHOD TO ANALYZE THE IMPACT OF BAD DEBT ON BANK EFFICIENCY

3.2.1. Proposed research model

Bad debt is one of the main causes affecting bank efficiency. At the same time, the efficiency in bank operations is also a factor affecting bad debt - this is one of the internal factors of the bank (bank specific). Therefore, studying the relationship between bad debt and bank efficiency in the context of the Vietnamese commercial banking system not only helps to understand the impact of bad debt on cost efficiency, but also: (i) Understand the opposite impact of cost efficiency on bad debt; (ii) analyze the causal relationship between bad debt and cost efficiency, meaning whether bad debt is the cause of changes in cost efficiency, or cost efficiency is the cause of changes in bad debt, or both; (iii) evaluate the reactions of cost efficiency when there is a shock to bad debt, and vice versa...

The selected variables are: Non-performing loan ratio (NPLR) and cost efficiency (CE). The existence of a relationship between these two variables will be used to test the research hypotheses, specifically as follows:

- First, the “bad luck” hypothesis H1 suggests that the increase in bad debt and the Granger-cause relationship reduce cost efficiency. At this time, the increase in bad debt is due to the influence of macroeconomic/industry factors such as GDP, inflation, unemployment, interest rate reduction, increased money supply, etc. That forces commercial banks to increase credit portfolio management activities, especially loans that are near maturity. The increase in management activities such as monitoring, collection, urging collection, proactive bad debt management, debt sale, etc. has led to increased costs, thereby reducing bank efficiency. Therefore:

H1 : Increasing bad debt is positively related to decreasing cost efficiency.

- Second, hypothesis H2 “bad management”. This hypothesis states that low cost efficiency is a signal of poor business management performance and has a Granger-cause relationship leading to high NPLs. The expectation in this relationship is negative between NPLs and cost efficiency. Therefore:

H2 : Low cost efficiency will positively affect the increase in bad debt of commercial banks.

- Third, the “skimping” hypothesis H3 is tested similarly to the “bad management” hypothesis but with the sign reversed, i.e. a negative Granger-cause from cost efficiency to NPLs. Therefore, higher cost efficiency will have a negative Granger-cause with NPLs. This negative relationship is assumed to be a trade-off of future loan performance for short-term bank cost efficiency.

H3 : Higher cost efficiency has a negative impact on bad debts of commercial banks.

Based on hypotheses H1, H2, H3, the thesis proposes the following research model:

". # ,= = % ". # ,=u[ , … , ". # ,=u; ; ÅÇÉj # ,=u[ , … , ÅÇÉj = u; + Ñ #+ Ö [ #,= (3.4)

ÅÇÉj # ,= = % ÅÇÉj # ,=u[ , … , ÅÇÉ # ,=u; ; ". # ,=u[ , … , ". = u; + Ñ #+ Ö [ #,= (3.5)

Where: n is the number of lags, Ñ # is the bank-specific effect that captures systematic differences across banks, Ö #,= is a randomly distributed error term

are independent and different, CE is cost efficiency, NPLR is non-performing loans ratio.

Equation (3.4) represents the total effect of the bad debt ratio on cost efficiency. If this effect is negative and statistically significant, the study data is consistent with the “bad luck” hypothesis; conversely, equation (3.5) represents the total effect of cost efficiency on the bad debt ratio. This effect can be positive or negative, and if statistically significant, the study data is consistent with the “skimping” or “bad management” hypothesis.

To perform the above analysis, the thesis uses the two-step S-GMM estimation method for dynamic panel data models, PVAR (Panel-Vector Autoregression) model and Granger Causality analysis technique to verify the proposed hypotheses.

3.2.2. S – GMM (system – Generalized method of moments) estimation method for dynamic panel data models

To solve the research objective of analyzing the impact of bad debt on cost efficiency, the thesis uses the generalized panel data estimation method on the system GMM moment (S – GMM) proposed by Arellano & Bond (1991) and Blundell & Bond (1998). The reason for using the GMM method is: (i) The panel data is unbalanced, and the explanatory variables are continuous; (ii) there is a correlation between the explanatory variables with the individual effects and the correlation between the explanatory variables with the error component; (iii) there is a linear relationship between the dependent variable and the explanatory variable; (iv) the dynamic model with one or both sides of the equation containing a lagged variable. Because of the above, the estimations by other methods are ineffective or biased.

In addition, the GMM method is commonly used for estimating dynamic panel data or panel data that violates heteroscedasticity and autocorrelation properties. With the GMM method proposed by Hansen (1982) based on the estimation

maximum likelihood estimation (MLE) of Fisher, and allows solving problems where classical MLE fails. However, Blunell & Bond (1998) argue that the estimates proposed by Hansen will encounter the problem of weak proxy when the coefficients approach 1. When the coefficients are equal to 1, the moment conditions will not relate the real parameters and the estimates will be time-dependent.

T. Later, two methods were developed to solve the above problem: (i) Difference GMM method (D – GMM) of Blundell & Bond (1998); (ii) System GMM method (S – GMM) based on the difference GMM of Arellano & Bond (1995) with certain constraints.

The GMM method also exploits the aggregated data of the panel and does not constrain the length of the time series of the panel units, so it will allow the use of an appropriate lag structure to exploit the dynamic characteristics of the data. However, the disadvantages of the model and the estimation method are low accuracy if the sample is small and high stability. To overcome this, the S-GMM method will perform better estimation than the D-GMM.

Now, consider the regression equation of the form:

& #== Ü á+ à #=Ü â+ Ö #+ ä # ,= (3.6)

In there:

U represents each bank, t represents time

& #= is the dependent variable

à #=is the explanatory variable

Ö # is the unobserved individual effect

ä #,= is the error

Equation (3.6) is rewritten in terms of dynamic regression:

& # ,= = ã& # ,=u[ + Ü â X # ,= + + #=i = 1,2,…N and t = 1,2,…T (3.7)

+ #= = Ö # + ä #=

. Ö # = 0, . ä #= = 0, . Ö # ä #= = 0 i = 1,2,…N and t = 1,2,…T

In there:

U represents each bank and t represents time.

& #,= = dependent variable for bank i at time t

X #,= = set of independent variables

Ö # = unobservable variables

ä #,= = error

+ #= = Ö # + ä #,= is the fixed effect containing the error

The regression coefficients of equation (3.7) are estimated by the GMM method proposed by Arellano & Bond (1991); later refined by Arellano & Bover (1995) and Blundell & Bond (1998). At this point, equation (3.7) is transformed into a difference equation of the form:

& #,= − & #,=u[ = ã & #,=u[ − & #,=uå + Ü âX # , = − # ,=

Where Δ is the first-order difference operator

Differentiation makes Δ& # ,=u[ correlated with Δ+ # ,= and biases the estimates of model (3.8). To deal with endogeneity, Arellano & Bond (1991) propose using the lag from & # ,=uå as an instrumental variable for Δ& # ,=u[ because & # ,=uå is correlated with Δ& # ,=u[ but not with Δ+ # ,= , under the condition that + # ,= is not serially correlated:

. & # ,=uw ∆+ # ,= = 0 for b ≥ 2 , t = 3,…,T

On the other hand, the assumption of complete exogeneity of the explanatory variables is no longer valid in the case of reverse causality ( . X # ,w + # ,= ≠ 0 for t < s). Therefore, for weakly endogenous or pre-determined explanatory variables, only their lags are suitable as instrumental variables:

. X # ,=uw Δ+ # ,= = 0 with b ≥ 2 , t = 3,…,T

With the above assumptions, equation (3.9) can be estimated with one-step S-GMM. Under the assumption of independent error terms and homoscedasticity, one-step GMM will give robust estimates. However, when serial correlation or heteroscedasticity of series components occurs, two-step GMM will give better results. Two-step S-GMM

Construct variance and covariance matrices based on residual estimates and use variance-covariance matrix adjustment and difference GMM.

At this time, the dynamic panel data model with the two-step S-GMM estimation method for the second research objective is to determine the impact of bad debt on cost efficiency as follows:

General model: & # ,= = ã& # ,=u[ + ÜX # ,= + + #=

Specific model:

". # ,= = ã". # ,=u[ + Ü [ ÅÇÉj # ,= + Ü å ÅÇÉj # ,=u[ + Ü å ÅÇÉj # ,=uå + + #=

i = 1,2,…N and t = 1,2,…T (3.9)

In which: ã and Ü are estimated parameters; + #= = Ö # + ä #,= is the fixed effect containing the error term; X #,= ( NPLR ) is the explanatory variable for CE at time t. However, the lag order of NPLR has a significant impact on CE, and the lag order 2 of NPLR is optimal through the information results AIC, BIC, QIC are the smallest; the values of CE and NPLR are determined by logarithms to ensure that the variables are in the range [- ∞ , + ∞] and are symmetrically distributed.

In addition, the thesis proposes an inverse model to examine the effects of cost efficiency on bad debt ratio, meaning that cost efficiency has a linear relationship with bad debt at time t and lag levels.

Specific model:

ÅÇ É #,= = íÅÇÉ #,=u[ + ì [ " . #,= + ì å " . #,=u[ + ì î " . #,=u[ + + #=

i = 1,2,…N and t = 1,2,…T (3.10)

Furthermore, the two variables NPLR and CE are identified as endogenous variables, meaning that they are correlated with the residuals. Other studies also identify them as endogenous variables such as: Fiordelisi et al . (2011); Tabak et al . (2011); Kwan & Eisenbeis (1997); Williams (2004); Altunbas et al. (2007). Therefore, the GMM method will help to estimate efficiently and without bias.

However, to check whether the choice of instrumental variables makes the estimation effective, and to check the suitability of the model, it is necessary to perform tests, specifically:

- Firstly, for the GMM method, when giving results, it is necessary to consider the following two rules: One is, the number of research years (the number of period) must always be less than the number of research units (the number of units); two is, the number of instruments (the number of instruments) must not exceed the number of research units (the number of units).

- Second, using Sargan and Arellano – Bond (AR) statistics will test the validity of the instruments in the GMM method. Accordingly, the Sargan test will determine the appropriateness of the instrumental variables, also known as testing the endogeneity limit of the model. Sargan test with the hypothesis ï á(instrumental variables are exogenous) – meaning they are not correlated with the model error. At this point, the p-value of the Sargan test should be as large as possible. The Arellano – Bond (AR(2)) test helps test for autocorrelation at all levels, the hypothesis is that ï á(no autocorrelation, and a p-value greater than 0.1 means that the initial hypothesis of no 2-order serial correlation is rejected.

3.2.3. Panel vector autoregression model and Granger causality analysis

In addition to the model assessing the correlation relationship through the level of impact of bad debt on cost efficiency, and vice versa. The thesis also considers the causal relationship between them through the PVAR model (panel vector autoregression model) using GMM estimation and Granger causality analysis techniques. The term autoregression is due to the appearance of the lagged value of the dependent variable on the right-hand side and the term vector is due to working with a vector of two (or more) variables. The two variables included in the model are cost efficiency, bad debt, and the lags of the two variables.

The assessment of the Granger causality relationship above has also been studied by Berger & DeYoung (1997) in the correlation between three variables: Cost efficiency (by SFA parameter method), bad debt, and bank capitalization. However,

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