It is noted that our studies on the performance of Vietnamese banks are based on the assumption that all banks are undertaking similar activities and producing comparable products or services under common technologies. According to Dyson et al. (2001, p. 247), “there is an unwritten assumption that the units are operating in similar environments… however, this assumption can rarely be safely made, and, as a consequence, environmental variables are often brought into the analysis” as supplements.
In SFA, Battese and Coelli (1995) modeled the cost inefficiency component as
ݑ ൌ ߜݖ ݓ (59)
127 Remember that the time series frontier as well as the index number approach (of which SPFI belongs to)
where u is the cost inefficiencies derived from equation (27), z is the vector of environmental factors, w is a random variable distributed as a truncated-normal distribution with zero mean and variance ߪ௨ଶ, and ߜ is the vector of coefficients to be estimated.
Meanwhile, efforts were made in order to account for these environmental factors directly within the DEA model in a single-stage (Banker & Morey, 1986a, b), however, since it has some limits,128 the multi-stage DEA models are preferred (Charnes et al., 1981; Ray, 1988; Fried et al., 1999; Muñiz, 2002; Hoff, 2007; and so on). An advantage of this approach is that it allows for the examination of environmental variables (on the dependent variable) in both sign and significance (Fried et al., 1999). Therefore, for the RA and DEA approaches, we check for the effects of bank’s ownerships and sizes (expected finding E2, section 1.2.3) using a second-stage regression model:
ܻ ൌ ߚ ߚଵܻܶܲܧ ߚଶܵܫܼܧ ߚଷܻܶܲܧ כ ܵܫܼܧ ߝ (60) where Y is the dependent variable that vary depending on the model used in the first stage (CE in SFA and PI or CAMELS ratios in RA); TYPE is a dummy variable represents the ownership of the bank (TYPE = 1 if the bank is SOCB, otherwise TYPE = 0); SIZE is the logarithmic value of the bank’s total assets; and İ is the error component. We also control for the interaction between TYPE and SIZE, as one may argue that the SOCBs tend to have bigger size compared to the JSCBs, by using an addition variable TYPE*SIZE.
The above environmental factors or bank’ specific characters (i.e. TYPE and SIZE) help explain the differences between efficiency measures (CE or PI) as well as key ratios of
128 For example, the incorporation of environmental variables directly into the linear problem of DEA will
increase the number of variables and thus, may bias the efficiency measures as DEA is sensitive to the “dimensional issue” (Sexton et al., 1986; Dyson et al., 2001; Hughes & Yaisawarng, 2004). More detailed commentary on the single-stage DEA is provided by Fried, Schmidt, and Yaisawarng (1999) and Fried, Lovell, Schmidt, and Yaisawarng (2002), among others.
different banks (CAMELS ratios) in the examined duration. Due to data limitation (more discussion are in the following section), these studies only cover the 2003-2010 period and thus could not reflect the whole financial liberalization process in Vietnam. Our FI-DEA model helps overcome that limitation utilizing the time-series data of macro-level information of the whole Vietnamese banking system instead of the individual bank-level data. Consequently, to examine the effect of liberalization on the performance of the Vietnamese banking system, we employ a set of macroeconomic variables ܺ in the second- stage regression of the FI-DEA study.
ܻ ൌ ߚ ߚଵܺ ߝ (61)
This macroeconomic set is chosen following the literature (e.g. McKinnon, 1973; Shaw, 1973; Bandiera et al., 2000; Laeven, 2003; Lane & Milesi-Ferretti, 2007; Chinn & Ito, 2008). We notice that these variables also proxy for the financial liberalization progress proposed by McKinnon as in Figure 1 of section 1.2.1 above. In addition, to analyse the effect of important turning points in the financial liberalization process, we divide our regression model into two sub-models. In each model, we introduce a crisis dummy variable with zero-year lag (C0) or one-year lag (C1), assuming that the effect of the crisis may happen at the time the crisis occurred or one year later, respectively. Descriptive information on these environmental variables is presented in the following section (Table 11). The dependent variable Yi, however, will differ in each model (see Table 6).
Table 5. Independent variables of the second-stage FI-DEA study
ࢄ Explanations and Sources
Associations with FI measures KA Kaopen index, measuring the financial openness of the country (extracted
from Chinn & Ito, 2008) +
BD Budget deficit (extract from ADB statistical online database) -
TB Trade balance (extract from ADB statistical online database) +
CB Capital account balance (extract from ADB statistical online database) +
NB Number of banking institutions in the system (from SBV reports) +
NS Number of equitized SOCBs in the system (from SBV reports) +
BC Bank concentration ratios (extracted from Beck et al., 2000) -
RR Reserve requirement ratios, announced by the SBV (from SBV reports) -
LI Nominal interest rates on working capital loans (extracted from the
Vietnam Annual Statistical reports from the IMF) -
RD
Real interest rates on deposits (calculated from IMF data on nominal interest rates on 3-month household loans and quartile average inflation rates, using the exact Fisher equation)
+
C0 Zero-year crisis effect, dummy variable (equals 1 if the year is 1997 and
2007; else equals 0) -
C1 One-year crisis lag effect, dummy variable (equals 1 if the year is
1998and 2008; else equals 0) -
There are several regression methods to estimate the correlation between the efficiency/performance/productivity scores in the first-stage with the independent variables of the second-stage, including the OLS, Tobit, and logit. Regarding that performance and efficiency scores (e.g. CE or PI) are censored/bounded between 0 and 1, the Tobit regression is preferred (Fethi & Pasiouras, 2010).129 For CAMELS ratios or other TFP (and its components) changesthe basic regression model OLS is justified. Additionally, for the regression part of our FI-DEA study, since the sample size is small (we have only 21 observations by looking at the Vietnamese banking system in each year of the 1990-2010
period as an individual DMU), we also employ the backward step-wise regression technique (Mark, 1988; Harrell, 2001). This technique begins with all variables included in the Tobit regression, and then it eliminates one variable at a time that has the highest p- value (or the most insignificant variable) until the eliminating could not improve the significance of the model. Hence, it reduces the environmental variables into an acceptable number that allows for valid conclusions could be made, regarding our small sample size.
Table 6. Second-stage regression: Dependent variables and techniques
Dependent variable (Y) Obs. Regression technique
Ratio Analysis 96 Tobit
ǡǡǡǡǡ 96 OLS SFA 96 Tobit ܥܧሶ, ܶܧܥܪሶ , ܵܧሶ, ܴܲܧሶ , ܶܨܲܥܪሶ 96 OLS MI-DEA 96 Tobit ǡǡ 96 OLS FI-DEA 21 Step-wise Tobit οܶܧோௌ, οܵܧ, οܣܧ, FI 21 Step-wise OLS Note: Obs.: Observations,
EF in MI-DEA is the efficiency scores calculated using a pooled data for 12 banks in 8 years; while the EF in FI-DEA is calculated using the time-series DEA model.