With the references from stochastic costs frontier model originated by Aigenr et al XXXXXXXXXXand Meeusen and van den Broeck (1977), Kumbhajar et al XXXXXXXXXXand Coccorse XXXXXXXXXXhave interpreted...


Equation (3) has to be estimated by using MLE and substituted the estimated parameters into Equation (2) to obtain the cost elasticity with respect to output. Then using the conditional mean estimator of from estimating Equation (3) and calculated in Equation (5). Eventually, the stochastic Lerner index can be calculated by Equation (6).


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With the references from stochastic costs frontier model originated by Aigenr et al. (1977) and Meeusen and van den Broeck (1977), Kumbhajar et al. (2012) and Coccorse (2014) have interpreted their idea into the following: (1) where is the stochastic frontier, i.e. the minimum level that revenue-cost ratio () can reach, in which is the deterministic part and is the stochastic part. is a non-negative tern which is the amount that revenue-cost ratio fails to reach the minimum. Since the revenue-cost ratio and so as the revenue and/or costs may be influenced by some unobserved factors, has to be included that represents a symmetric noise term. By adopting a similar translog cost function, the cost elasticity with respect to output is (2) By substituting Equation (2) into Equation (1), the cos function should be shown as: (3) : total revenue/ total costs for bank at time is the total assets, are input prices which include: (1) personnel expense/total assets (), (2) other operating costs/fixed (), and (3) interest expenses/total deposits and short-term funding (), is the term trend. By rearranging Equation (1) and omitting the noise term: (4) With further manipulation, Equation (5) becomes the following: (5) where the left-hand side is the standard Lerner index which is labelled as . It is equivalent to the “stochastic” version of the Lerner index which can can be calculated by: (6) In order to get the above Lerner index, Equation (3) has to be estimated by using MLE and substituted the estimated parameters into Equation (2) to obtain the cost elasticity with respect to output. Then using the conditional mean estimator of from estimating Equation (3) and calculated in Equation (5). Eventually, the stochastic Lerner index can be calculated by Equation (6).
Feb 08, 2022
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