The effect of bank m&As on efficiency: the portuguese experience victor Mendes
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3. The ModelsIn this paper we want to study the effect of size on efficiency. The measurement of productive (in)efficiency and the estimation of production frontiers have been jointly done since Farrel’s (1957) seminal paper. The so-called X-inefficiency, or deviations from the efficient cost frontier, are the result of technical inefficiency (the firm could produce the same output with lower levels of inputs) and allocative inefficiency (given their relative prices, the used combination of inputs is different from the cost-minimizing combination). The DEA (data envelopment analysis) method is a non-parametric method widely used. The method uses linear programming techniques in the estimation of frontier (cost, in our case) functions; firms on the frontier are considered efficient. Other firms are compared with the ‘best practice’ units and inefficiency levels are computed using the estimated frontier. For a firm s facing input price vector ws and producing the output vector ys, x*s is the cost minimizing input vector. The operating productive efficiency index (EPG) is computed as EPGs = wsx*s/wsxs, that is, EPGs=minimum cost/actual cost. For the case of a bank producing three outputs with three inputs we need to solve the following linear programming problem
subject to yjs <= zsyjs , j = 1, 2, 3. s (1) xis >= zsxis , i = 1, 2, 3. s zs >= 0 , s = 1, ..., n zs = 1 s
The SFA-T (Stochastic Frontier Approach - Traditional) method assumes that banks are cost minimizing firms; their production process can be represented by the stochastic frontier cost function (2) 
where C represents variable cost, Y is the output vector, w is the input price vector, t represents time and captures possible technological changes, represents the vector of parameters to be estimated, u is the one-sided, non negative, stochastic element that represents cost inefficiency3, and v is a classical random error term, independent from u. It immediately follows that the stochastic and deterministic models are equivalent when v=0. We assume the following translog variable cost function,  where Cst = variable cost for observation s in year t; yist = output i (i=1, 2, 3) for observation s in year t; wkst = price of input k (k=1, 2, 3) for observation s in year t; Greek symbols = parameters to be estimated; vst = cost inefficiency for observation s in year t; ust = random error term. Symmetry restrictions on the second order parameters and linear homogeneity in input prices were imposed prior to the estimation of the model. Variable costs, the cost of deposits and labor costs are expressed in terms of w3. T  he SFA-E (Stochastic Frontier Approach – Endogenous) method assumes that inefficiency is endogenously explained. The model, suggested by Battese el al (1999), includes equation (3) along with the equation (4) below, describing the behavior of inefficiency. It is assumed that v follows the truncated (at zero) normal distribution with unknown variance, and mean which is a function of exogenous factors, that is  where Dj represents dummy variables equal to one if the bank is private (D1), privatized (D2), new (in the market after 1990 – D3), foreign (D4) and if it is a member of a bank group (D5). Z is a time trend. The parameters of equations (3) and (4) are simultaneously estimated by maximum likelihood using the software frontier 4.1 (  Coelli 1996). The variance parameters are reparametrized using Upon estimation of the model parameters, bank indices of technical inefficiency are computed using the Jondrow et al (1982) method. Download 0.67 Mb. Share with your friends:
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