In π = α 0 + ∑ α i InQ i

1. measured efficiency may be biased with random deviations from the true efficiency frontier. On the other hand, parametric procedures are more developed and avoid some of the problems associated with the non-parametric techniques. For instance, the stochastic frontier techniques not only allow for an error term but also distinguish between firm-specific effects and random noise. But the stochastic frontier analysis has its own problems. For instance, the stochastic frontier techniques impose a particular functional form that affects the shape of the frontier.9 If the functional form is mis-specified, measured efficiency may be confounded with specification errors. 10 Berger and Humphry (1997) argue that it is not possible to determine which of the two major approaches dominates the other since level of efficiency is unknown. In our study, we use the stochastic frontier approach and address the main limitation of the functional form specification by specifying flexible forms. In fact, the translog model is the most popular form in the literature, which is a flexible functional form and is expanded by a second-order Taylor series. The translog model of the alternative profit efficiency in Eq (3) can be written as following: 3 i 1 3 j 1 3 1 ∑γ ik InQi InQk 13 2 j 1 3 h 1 1 3 2 i Inπ = α 0 + ∑α i InQi β j InPj θ jh InPj InPh k 1 3 3 ∑i 1∑j ϕ1 ij InQi InPj (4) In vaπ + In u aπ The Fourier flexible functional specification has recently become the most acceptable and increasingly applied parametric functional form in measuring banking efficiency. The Fourier flexible specification (FF) includes the standard translog terms, as in Eq (4), plus the trigonometric 9 that fits the banking cost and production technology. 10 28