4.4 Methodology and Data
4.4.5 Variable Selection and Regressions
As previously noted the dependant variables will be the parametric SFA and non-parametric DEA. In order to compare with an accounting based efficiency ratio the cost to income ratio (CIR) will be used. The ratio is calculated by dividing the operating costs (administrative and fixed costs, such as salaries and property expenses, but not non-performing loans) by operating income. According to Chiaramonte, Croci, and Poli (2015) managerial quality is approximated by CIR, a low value indicates better managerial quality as they are able to keep costs down (or stable) whilst increasing income. The following independent variables will examine the impact of banking risk characteristics and regulatory variables on cost (in)efficiency while controlling for profitability and size. See Table 4.5 for a descriptive summary of the variables uses within this study24 and Table 4.6 for a
statistical summary. As this paper focuses on the USA banking industry only, other country-specific characteristics are not required as controls. Such variables would be required if this was a cross-country study.
A proxy for Diversification (DIV) is the magnitude of non-interest income to operating income, which greatly reflects bank participation in financial markets
24All the data used was deflated by their corresponding years consumer price index (CPI) to the
year 2000 price levels to control for inflation effects, a similar approach to Abuzayed et al. (2009); Gardener, Molyneux, and Nguyen-Linh (2011); Molyneux and Williams (2013)inter alia.
such as securities trading, asset management services, to name a few. The expected relationship with efficiency is uncertain. On the one hand, a negative relationship would suggest that diversification leads to excess risk and therefore lower cost efficiency. Otherwise, the sign may be positive if diversification is seen as a way for financial institutions to increase income streams more than it costs to achieve this extra income.
To account for banks’ asset quality the variable CreditRisk is used. Financial institutions which provide more loans, especially in the context of pre-crisis, are expected to incur higher credit risk. This variable is expected to have an inverse relationship with cost efficiency, as higher credit risk would theoretically increase costs (via write off and the redress process) and lower profitably. A similar relationship is expected for Leverage (FLVRG) as another proxy for credit risk.
The Tier One Capital Ratio (T1CR) is a regulatory variable that could have a positive or negative effect on cost efficiency. It could possibly enhance cost efficiency as banking regulations enhance market discipline (Pasiouras et al., 2009) which makes the institutions safer. On the contrary having to hold extra capital could be seen as costly, as capital affects costs through its use as a source of funding (Berger & Mester, 1997). Within Table 4.1 on regulation impact on efficiency, all authors found that capital requirement had a positive impact on cost efficiency. Typically previous studies have applied dummy variables or capital requirement indexes rather than the individual bank level measures.
A liquidity (LIQ) variable similar to Williams and Nguyen (2005) can also be positive or negative in relation to efficiency. If increased loans helps banks to diversify their credit risk and/or enhance interest income, a positive relationship might be expected. However, if this enhances credit risk (due to non-performing loans) and increases the asset/liabilities gaps this could negatively impact cost efficiency due to the need to source extra funds.
The Net Stable Funding Ratio (NSFR) is another regulatory variable with an unknown relationship with cost efficiency. This variable to the best of my knowledge has not been tested in relation to efficiency before. This ratio as discussed in section 3.4.3 is required to be above 100% to demonstrate the financial institution has
sufficient access to longer term funding in the event of a liquidity shortage. This is approximated using equation 4.4.5 (Chiaramonte & Casu, 2017).
N SF R=
Equity+F undingT otalLT +
T erm Customer Deposits ∗0.95 ! + Current Customer Deposits ∗0.9 ! + Other Deposits andST Borrowing ∗0.5 Other Assets+ Government Securities + OBS Items ∗0.05+ Other Securities+ Loans and Advances toBanks ! ∗0.5 ! +M ortgageLoans ∗0.65+ Retail and Corporate Loans ∗0.85 !≥100% (4.4.5)
If this ratio is seen as a onus on the institutions to hold/source more funding this would increase cost negativity affecting cost efficiency. However, as with LIQ if it helps banks to diversify other risks and makes them safer (bringing funding costs down) this will enhance cost efficiency.
As a control variable for profitability, Return on Assets (ROA) is expected to have a positive relationship with cost efficiency, with the assumption that profitable institutions are more efficient at transforming inputs into outputs. In the event of profitability due to higher credit risk, this could result in lower cost efficiency.
To investigate the role of size (and indirectly enhanced regulation) on cost efficiency, the dummy variable to indicated whether a financial institution is classed as a SIFI or G-SIB. SIF I is included as another control variable (only applicable from 2011). This variable to the best of my knowledge has not been tested in relation to efficiency before. Due to mixed previous empirical results regarding size, noa priori expectation is expected.
Year effects (year dummies, excluding the first year) capture the influence of aggregate (time-series) trends. It allows to control for the exogenous increase in the dependent variable which is not explained by the other variables. For example, the likes of an external shock where it’s impact is restricted to a given time-period, affecting all panel units that are not controlled by other explanatory variables.
In the first instance this study applies OLS (Tobit in the case of SFA) regression, followed by Generalized Method of Moments (GMM) regression to study the relationship between banking variables and cost efficiency. The cost efficiency scores (as the explained variable) calculated via SFA are limited to values between 0 and 1. Thus, this dependent variable cannot be expected to have a normal distribution. If ordinary least squares (OLS) regression was applied in
Table 4.5: Individual Bank Explanatory Variables Symbol Variable Name Description Expected Sign Authors
DIV Diversification Proxy for a bank’s business model calculated by net non- interest income to net operating income.
+/– Beck et al. (2016)
CreditRisk Credit Risk Ratio of Non-performing loans divided by total loans. The higher the ratio, the lower the quality of the loan portfolio.
– Ariff and Luc (2008); Luo et al. (2016)
FLVRG Leverage Financial Leverage is defined as the ratio of total assets to total common equity. A lower figure represents less leverage
– F¨are, Grosskopf, and Weber (2004)
T1CR Tier 1 Capital Ratio
The ratio of Tier 1 capital to risk-weighted assets.
+/– N/A
LIQ Liquidity Liquidity is measured by the ratio of net loans to deposits and short term funding. Lower figure represents higher liquidity
+/– Williams and Nguyen (2005)
NSFR Net Stable Funding Ratio
A regulatory ratio to measure long-term funding
+/– N/A
ROA Return on assets (control variable)
Indicator of how profitable a company is relative to its total assets, as a percentage. Provides an idea of how efficient management is at using its assets to generate earnings
+ Berger and Mester (2003); Ariff and Luc (2008)
SIFI SIFI Bank (control
variable)
A dummy variable 1= classified as a systemically important institution or a domestically important institution, otherwise 0
+/– N/A
Year Time (control variable)
Table 4.6: US Bank Efficiency Determinants Statistics Summary Variable Obs Mean Std. Dev. Min Max SFAEFF 3728 .751 .085 .548 .954 ProdGrowth 3495 2.144 .261 .89 4.366 CIR 10400 68.345 24.623 -9.565 580.645 DIV 10370 .862 3.899 -81.368 89.286 CreditRisk 6359 .019 .209 0 16.562 FLVRG 9353 11.818 16.229 1.142 1043.228 T1CR 9326 13.243 7.72 -4.15 438.98 LIQ 7718 .815 .197 .001 6.468 NSFR 4675 .938 .057 .646 1.787 ROA 9372 .167 53.059 -5133.206 16.126
this case the result may be biased and/or produce inconsistent parameter estimates (Greene, 1981). Typically, the empirical literature applies the Tobit estimation (Tobin, 1958) to avoid this issue (Ariff & Luc, 2008; J. R. Barth, Lin, et al., 2013; Delis & Papanikolaou, 2009; S. H. Lee, 2013), using the Stata12 command xttobit for the following model:
yit=αi+βnXit+εit, εit ∼N(0, σt2) (4.4.6)
where αi is the firm-specific constant effect, Xit is a 1×L vector of bank level
financial explanatory variable which are time-varying, βn are the corresponding
vector parameters to be estimated, finally the error term, εit, which is assumed to
be normally distributed. Also, the technique of bootstrapping will be applied to assess whether this alters the explanatory power of the variables. Simar and Wilson (2007) first advocated the use of single and double bootstrapping as it enhanced the statistics significance of efficiency in their empirical evidence from the US banking sector. Further, Delis and Papanikolaou (2009) found that when a bootstrapping technique is applied the explanatory power of certain variables was enhanced. Tortosa-Ausina et al. (2008) also found that bootstrapping allows for more careful analysis at firm level25. In the context of this study the model 4.4.7
outlines the equation to determine bank efficiency.
EF Fit=αi+β1DIVit+β2CreditRiskit+β3F LV RGit+β4T1CRit
+β5LIQit+β6N SF Rit+β7ROAit+β8SIF Iit+Y ear+εit (4.4.7)
where EF Fit will be SFA, ProdGrowth and CIR. Following the application of
Tobit and OLS regression, GMM regression is applied to the same explanatory variables. The purpose of applying GMM is to incorporate the lag dependant variable to test whether the previous efficiency level significantly impacts future efficiency scores.
yit=αi+β1yit−1+βnXit+uit, i= 1, . . . , N, t = 1, . . . T (4.4.8)
where αi is the firm-specific constant effect, yit−1 is an endogenous lagged
dependant variable, Xit is a 1 × L vector of bank level financial explanatory
variable (see Table 4.5 for more details) which are time-varying and not strictly exogenous, βn are the vector parameters to be estimated, finally the error term,
uit, assumes a mean of zero and is probably serially correlated. Daraio and Simar
(2005) acknowledged possible serial correlation as a shortcoming of multistage DEA and SFA analysis among estimated coefficients.
Due to yit−1 being an endogenous explanatory variable (with respect to both αi
and uit). The conventional covariance estimators of equation 4.4.8 are no longer
consistent26. Endogeneity can arise by: (i) omitted variables (correlation with errors); (ii) measurement error in the independent variable (e.g. the efficiency or market power calculations); and (iii) reversed causality (from the lag or selection bias) (Hall, 2005). This provides justification for adopting GMM to obtain consistent estimates (Arellano, 2003). Further, due to the use of panel data the GMM estimations are mostly valid for data with small T and large N. This is the case within this paper’s sample, thus the GMM method proposed by Ahn and
bootstrapping, However, not every banks Malmquist productivity index was significantly different from the original value before bootstrapping.
Sickles (2000) is used. Using Stata12, a two-step system dynamic GMM approach was applied with windmeijer-corrected standard errors (Windmeijer, 2005) to control for potential instances of endogeneity (Blundell & Bond, 1998) and for the downward bias in the estimated asymptotic standard errors. The issue of endogeneity arises due to the possibility of reverse causality that certain bank characteristics may be determined by performance (efficiency and asset quality) or that such characteristics may be derived by underlying unobservable factors that impact performance. To ensure the GMM models fit correctly it is expected that AR(1) is statistically significant due to the way it is constructed and statistically insignificant AR(2). Therefore the output requires the p-values of AR(2) and Hansen tests to be greater than 0.1 (10% significance) (Dovonon & Hall, 2018). The Hansen J-statistics of over identifying restrictions should be statistically insignificant as this indicates that the instruments are valid in the two-step system GMM estimation. If the previous holds this implies that the models fit correctly with statistically insignificant test statistics of second-order autocorrelation in second differences (AR(2)) and the Hansen J-statistics (Matousek, Nguyen, & Stewart, 2016).