**3. Methodology**

Literature on the nexus of bank capital, risk, and efficiency has considerable growth. However, there is paucity in the studies that investigate the directional causality of triumvariate relationship [6, 8, 10, 22, 24]. Yet the focus of those studies is still on developed economies. Few studies address the dynamic intertwinning of the three variables through the use of novel vector autoregression method for panel data (PVAR) [7, 25]. However, there has not been any study looking at the comprehensive causality of the three contemporaneous factors of bank capital, risk, and efficiency using the same PVAR framework. This method combines the traditional vector autoregression with panel data technique to encounter the issue of endogeneity while allowing for inclusion of fixed effects in the model [27]. Apart from analyzing causality, the method also helps identify the response of a factor from the change in another and variance is decomposed to analyze the percentage of explanation by each component.

### **3.1 The hypotheses**

We hypothesize the dynamic interdependencies among risk, efficiency, and capital. The relations between bank efficiency and risk can be either positive or negative and causal direction can be two-way.

*Causal Relationship Among Bank Capitalization, Efficiency, and Risk-Taking in ASEAN… DOI: http://dx.doi.org/10.5772/intechopen.109120*

**Hypothesis 1a.** Bank risk causes a change in bank efficiency.

**Hypothesis 1b.** Bank efficiency causes a change in bank risk.

Hypothesis 1a with a negative sign is the *bad luck hypothesis*. Hypothesis 1b with a negative sign is the *bad management hypothesis.* Hypothesis 1b with a positive sign is the *skimping hypothesis*. [8].

The level of capital and hence bank leverage affects efficiency because of agency costs, which arise from conflicts of interest between shareholders and managers or between shareholders and debtholders.

**Hypothesis 2a.** Bank capital causes a change in bank efficiency.

**Hypothesis 2b.** Bank efficiency causes a change in bank capital.

Hypothesis 2a with a negative sign is the *agency costs shareholders-managers hypothesis*: high equity capital and less pressure of debt give managers more cash to invest and may lead to wasteful investment, lowering efficiency. Hypothesis 2a with a positive sign is the *agency costs shareholders-debtholders hypothesis*: if shareholders are tempted to maximize their value at the expense of debtholders, a higher capital ratio will reduce agency costs and thus increase efficiency [22].

Hypothesis 2b with a negative sign is *the efficiency-risk hypothesis*: more efficient banks can generate higher returns, which can partially substitute for equity capital to protect banks in the event of financial distress. Hypothesis 2b with a positive sign is the *franchise-value hypothesis*: efficient banks will maintain a high capital ratio to protect the franchise value associated with high efficiency [10].

Bank decisions on the levels of risk and capital are interrelated, as both decisions are affected by leverage, deposit insurance, and regulation.

**Hypothesis 3a.** Bank capital causes a change in bank risk.

**Hypothesis 3b.** Bank risk causes a change in bank capital.

Negative relationship between capital and risk indicates the *moral hazard behavior* as low capitalization Granger causes high nonperforming loans, because managers have less capital to lose in the event of default, and they benefit from higher returns on risky investments [8]. Causation of bank risk on bank capital supports the *regulatory hypothesis* where regulators require banks to hold capital commensurate with their risk [28], so an increase in the risk of problem loans can force managers to replenish bank capital [9].

The baseline analysis is extended in several dimensions to study whether these hypothesized relationships are stronger for certain types of banks. "Cost skimping" is expected to occur in efficient banks [8]. Managers of efficient banks are tempted to pursue expansion through investing in risky assets or controlling cost to attain higher efficiency, thereby increasing risk. Therefore, we look at subsamples of high- and low-efficiency banks to analyze the difference in behavior of the two groups of banks.

We extend our work to assess the relationships among risk, capital, and efficiency with subsamples of different size, ownership structure, and pre- and postcrisis periods. Literature finds the impact of market structure on bank risk taking [29–31] and efficiency [4, 17, 32, 33]. Large banks span their operations in both domestic and international markets, thus having a diversified portfolio. Small banks operate in smaller geographical or regional areas, so they have limited power in the market [34]. Large banks can improve efficiency and reduce risk, as they benefit from economies of scale and portfolio diversification [15, 17, 35]. Large banks also have easier access to the capital market and thus can operate with proportionately smaller capital [19, 36, 37]. In addition, several studies have found differences in the behavior of banks with different ownership. Udell et al. [38] find that on average foreign banks perform less

well than private domestic counterparts in developed countries, while reverse result is found in developing countries [39]. Finally, the 2008 global financial adversely hit the global banking sector and ASEAN banking system experiences the same effect. Banks may behave differently in response to the global crisis; therefore, subsamples of the two different periods of before and after crisis need further investigation.

### **3.2 The model**

We model the contemporaneous relationship of capital, risk, and efficiency using panel vector autoregration (VAR), initially developed by [40] and subsequently elaborated by [41]. Panel VAR treats all variables as endogenous and can capture their dynamic interdependencies. Impulse response functions (IRFs) identify the reaction (response) of one variable to a shock (impulse/innovation) in another variable while holding all other shocks at zero [40]. This process can explain the underlying causality among endogenous variables of the model.

The system of simultaneous equations from the model is regressed using systembased GMM. Dynamic simulations are implemented involving the estimation of impulse response functions and variance decompositions [7]. There is a key identifying assumption in setting the order of variables: variables that occur earlier in the ordering affect the following variables contemporaneously, while variables that appear later in the ordering affect previous variables only with lag [40]. This sequential order is a preferred identification strategy, which is referred to as Choleski decomposition. In this study, we make an assumption that risk could be more exogenous in relation to the other variables. An economic shock, or "bad luck" [8], immediately increases nonperforming loans, which proxy for risk. Banks respond by adjusting their capital cushion. Bank capital directly affects costs by providing a source of funding other than deposits [42]. Hence, capital and cost efficiency come later in the order.

We specify the three-variable VAR model as follows:

$$\text{CE}\_{i\downarrow} = a\_{10} + \beta\_{11} \text{RISK}\_{i\downarrow -1} + \beta\_{12} \text{CAP}\_{i\downarrow -1} + \beta\_{13} \text{CE}\_{i\downarrow -1} + f\_{\downarrow i} + d\_{\text{1c}\downarrow} + e\_{\text{1i}\downarrow} \tag{1}$$

$$\text{CAP}\_{i\sharp} = a\_{20} + \rho\_{21} \text{RISK}\_{i\sharp -1} + \rho\_{22} \text{CAP}\_{i\sharp -1} + \rho\_{23} \text{CE}\_{i\sharp -1} + f\_{\sharp i} + d\_{\sharp \sharp t} + \varepsilon\_{\sharp i\sharp} \tag{2}$$

$$R \text{ISK}\_{i,t} = a\_{30} + \beta\_{31} R \text{ISK}\_{i,t-1} + \beta\_{32} \text{CAP}\_{i,t-1} + \beta\_{33} \text{CE}\_{i,t-1} + f\_{j\_{\dot{\imath}i}} + d\_{\&,t} + \varepsilon\_{\dot{\imath}i,t} \tag{3}$$

where CEi,t, CAPi,t, and RISKi,t represent cost efficiency, capital, and risk respectively. fi denotes fixed effects that allow for individual heterogeneity. dc,t are time dummies.

Equation (1) tests the impacts of risk and capital on cost efficiency. The estimated coefficients for risk (*β*11) and capital (*β*12) constitute evidence for the bad luck hypothesis (H1a), agency cost, the shareholders-managers/shareholders-debtholders hypothesis (H2a).

Equation (2) examines the effects of risk and cost efficiency on capital. The estimated coefficients for cost efficiency (*β*23) and risk (*β*21) are used to test the efficiency-risk hypothesis/franchise value hypothesis (H2b) and the regulatory hypothesis (H3b).

Equation (3) investigates the impact of capital and cost efficiency on risk. The coefficients for cost efficiency (*β*33) and capital (*β*32) provide evidence of the bad management/cost skimping hypothesis (H1b) and the moral hazard/regulatory hypothesis (H3a, H3b).

### *Causal Relationship Among Bank Capitalization, Efficiency, and Risk-Taking in ASEAN… DOI: http://dx.doi.org/10.5772/intechopen.109120*

We also introduce fixed effects, denoted fi in the model above, to allow for individual heterogeneity in variables [42]. The fixed effects are correlated with the regressors because the dependent variables are lagged, so in order to create unbiased coefficients, we need to eliminate fixed effects by using forward mean differencing, known as the Helmert procedure [43]. This process removes the forward mean and preserves the orthogonality between transformed variables and lagged regressors. So we can use the lagged regressors as instruments in our system GMM regression.

In addition, country-specific time dummies, dc,t, are included to capture the country-specific macroeconomic variables. These dummies are eliminated by subtracting the means of each variable calculated for each country-year.

We analyze the impulse response functions (IRFs) to examine the reaction of one variable to a shock in another to infer the causality of the variables. Monte Carlo simulations method is used to derive a draw of coefficients. Then the matrix of variance decompositions is determined to explain the cumulative percentage of variation in a variable explained by the shock in another.

### **3.3 Data and variables**

Our data comprise 1404 observations of 146 commercial banks in Thailand, Malaysia, the Philippines, Indonesia, and Vietnam for the period from 2005 to 2015 in an unbalanced panel data. Banks' financial statements were obtained from Bankscope. To measure bank risk, we use the ratio of loan loss provisions (LLOSS) to loans to be the proxy for credit risk. This measure is commonly used to account for bank risk [6, 9, 15] as it focuses on credit risk and derives from accounting data. The ratio of equity to total assets is used as a measure of bank capital (CAP). This widely used proxy captures the bank's financial cushion to absorb loan losses [6, 8, 9]. To measure bank efficiency, we opt to use cost efficiency (CE) determined by stochastic frontier approach, which is widely used in literature [14, 44].
