RECURSOS Humanos

DEA was formed in Farrell (1957) seminal work and built on by Charnes, Cooper, and Rhodes (1978), the non-parametric methodology applies linear programming to measure the distance of individual firms (refered to as Desision Making Units (DMU)) from the efficient or best practice frontier. In other words, DMUs are compared to other identified best practice DMUs (Cook & Seiford, 2009). DEA identifies the inefficiency in firms by comparing it to efficient firms. This is as oppose to relating a firm’s performance with statistical averages which may not be relevant to that firm. Also, DEA does not assume any functional structure imposed on the data in determining efficient firms. DEA allows for multiple inputs and outputs which are readily available via published financial accounts. Input

18_{lnT C and input price terms are normalised by the last input price, in order to impose linear}

homogeneity of degree one on the input prices.

19_{Equity capital is treat without any associated price as quasi-fixed in the frontier model this}

is because equity levels is more difficult to alter in the short-term (compared to the outputs). Furthermore, it is used to control for insolvency risk and the different risk preferences of banks.

20_{Hence in stata12 the true fixed-effects model (Greene, 2005) half-normal distribution for the}

and output weights are endogenously derived, thus avoiding subjective weights or externally imposed weights from other samples. They are used to produce a parsimonious scalar estimate where multidimensional interactions are simultaneously captured (Avkiran, 2013). Mathematical programming eliminates the impact of market prices and other exogenous components affecting actual bank performance, as is thus superior over accounting ratios. Wang and Huang (2007) argue that typical financial ratios from annual reports such as ROA and cost to revenue are often compounded with other effects irrespective of the managers performance. Halkos and Salamouris (2004) also advocate that frontier efficiency estimation via DEA is superior to simple ratio analysis. Most early empirical studies showed that using DEA to estimate the efficient frontier yielded robust results (Seiford & Thrall, 1990).

However, DEA does not assume statistical noise and that the data is free of any measurement errors, which can allow the error term to be attributed to inefficiency. This is due to DEA assuming random variants to cancel each other. Further, as the inputs and outputs indicators are relative to the sample, results can be influenced by idiosyncratic risk such as regional price differences and extreme observations. Therefore, it is common practice to scrutinise the data for outliers to reduce the impact of measurement error. Distributions of parameter estimates are known asymptotically and statistical significance tests such as the T-test can be designed, however DEA makes no distribution assumption. Horsky and Nelson (2006) acknowledged this in developing statistical significance tests for linear programming methods. Further, Asmild and Zhu (2016) warn that traditional DEA may potentially be biased during crisis period as it does not control for extreme weights. For example, during the recent financial crisis a number of institutions, (i) relied on wholesale funding rather than retail funding (skewing input, price of deposits) (ii) and/or relied on risky asset portfolios via exposure to the property sector (skewing outputs). In such cases it would be inappropriate to class these banks as efficient, for the given level of risk. Following a meta-analysis of the global microfinance efficiency, Fall, Akim, and Wassongma

(2018) argued that use of SFA should be increased over DEA because it suffers from inherent weaknesses such as being highly sensitive to the data and sample size which may lead to biased estimates if there are measurement errors or outliers. Earlier Staat (2001) also evidenced how DEA efficiency scores can be affected by various sample sizes.

The DEA production technology constitutes a convex relationship, which is determined by using piecewise combinations of all efficient banks. Similar to Koetter and Meesters (2013) a formal program to obtain this set is given by:

min Θ,λ Θ subject to −yi+Yλ≥0, Θxi−Xλ≥0, λ≥0 (4.4.4)

Θis the component that reflects the efficiency of the DMUi, which is minimized. Accordingly, the production function is put as far as possible to the outside. yi and xi are vectors of outputs produced and inputs consumed respectively (the same

output and inputs used in 4.4.1). Y and X are matrices with all the output and inputs of all DMUs respectively. λ is a weighted vector, which uses the linear combination of producers corresponding to the lowest Θ. It therefore represents the vector that measures which DMUs outperforms DMUi21. Fukuyama and Weber (2009) pointed out that when the optimal solution to the cost function using DEA allows for slack in the constraints that define the technology efficiency it is possible to increase at least one output without increasing costs. This may result in two banks being deemed equally cost efficient even though one may produce more of at least one output.

21_{The constant returns to scale assumptions in equation 4.4.4 can be relaxed by factors of the}

variables return to scale assumption by adding a convexity constraint (i.e. the sum of the elements ofλshould be equal to 1) (Coelli, Rao, O’Donnell, & Battese, 2005).

Malmquist Productivity Index using DEA Frontier

Using DEA and the cost efficiency input and outputs highlighted previously (similar to Al-Sharkas et al. (2008); Duygun et al. (2016); Guzman and Reverte (2008); Kirkwood and Nahm (2006); Tortosa-Ausina, Grifell-Tatj´e, Armero, and Conesa (2008) inter alia) the Malmquist productivity index (MPI) (Malmquist, 1953) will be used to calculated DEA using the panel data which requires bivariate density estimation, which was performed via kernel smoothing. The MPI measures the productivity changes along with time variations and can be decomposed DEA into changes in efficiency and taking into account of time variants of technology (F¨are, Grosskopf, Norris, & Zhang, 1994). The input oriented geometric mean of MPI change (similar to Total Factor Productivity change, (TFPCH)), can be decomposed using the concept of input oriented technical change (TECHCH) and input oriented efficiency change (EFFCH); while the technical efficiency change can be further decomposed into scale efficiency change (SECH) and pure technical efficiency change (PECH) components. Park and Weber (2006) following Chambers’ (2002) Luenberger productivity indicator, combining EFFCH and TECHCH obtains a proxy from Productivity growth (ProdGrowth). Boussemart, Briec, Kerstens, and Poutineau (2003) showed that the Malmquist index is a linear approximation of the Luenberger indicator of productivity growth, but they did not discuss their exact relationship. Later Balk, F¨are, Grosskopf, and Margaritis (2008) provided this relationship.