A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry
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A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry Kai Sun1 Ruhul Salim2 ●
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Accepted: 28 October 2020 / Published online: 28 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper proposes a semiparametric smooth-varying coefficient input distance frontier model with multiple outputs and multiple inputs, panel data, and determinants of technical inefficiency for the Indonesian banking industry during the period 2000 to 2015. The technology parameters are unknown functions of a set of environmental factors that shift the input distance frontier non-neutrally. The computationally simple constraint weighted bootstrapping method is employed to impose the regularity constraints on the distance function. As a by-product, total factor productivity (TFP) growth is estimated and decomposed into technical change, scale component, and efficiency change. The distance elasticities, marginal effects of the environmental factors on the distance elasticities, temporal behavior of technical efficiency, and also TFP growth and its components are investigated. JEL codes: D24 G21 ●
Keywords Input distance function Semiparametric smooth coefficient model Stochastic frontier model Decomposition ●
1 Introduction In estimating a production technology, both primal (e.g., a production/output distance function (ODF)) and dual (e.g., a cost/input distance function (IDF)) approaches are employed in the literature (e.g., Esho 2001; Fries and Taci 2005; Feng and Serletis 2010; Bhaumik et al. 2012; Servin et al. 2012; Sun 2015, among others). Different representations of technology have different advantages/disadvantages. For example, the production function can only handle the single output case, while the input/output distance and cost functions can accommodate multiple outputs. In fact, the ODF reduces to the production function when there is only one output. The production function and ODF are susceptible to the endogeneity of inputs unless the constant returns to scale (CRS) restriction is imposed on
* Ruhul Salim [email protected]
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them—this is because the input ratios on the right-hand-side are exogenous (Kumbhakar 2013). However, the CRS assumption is problematic since it violates the second-order conditions of profit maximization.1 An IDF is dual to a cost function. However, like the ODF, the estimation of the IDF does not require input price information, which is usually difficult to obtain or subject to measurement issues. The IDF gives the maximum amount by which an input vector can be radially contracted to produce the same output vector, while the ODF gives the maximum amount by which an output vector can be radially expanded using the same input vector.2 Therefore, the IDF and ODF define input- and output-oriented technical inefficiencies, respectively. In view of the banking industry, the IDF is preferred because it can not only handle the banks’ multiple-input and multiple-output set
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