In π = α 0 + ∑ α i InQ i

1. terms. So, the translog form in Eq(4) can be extended into FF form as following: 3 i 1 3 j 1 3 ∑k 1γ ik InQi InQk j 21 13 3 h 1 1 3 2 i 1 Inπ = α 0 + ∑ α i InQi β j InPj θ jh InPj InPh 3 3 3 i 1 j 1 i 1 3 3 + ∑∑[φij cos(Qi Qj ) λij sin(Qi Qj )] i 1 j 1 (5) In vaπ + In uaπ It can be noted that since input prices do not vary much over time, they are not spcecified in trigonometric terms. The FF model is more flexible than the translog and is a global approximation to virtually any cost or profit function (Berger and Mester, 1997). By adding the trigonometric terms to the stochastic model, the frontier will provide a greater flexibility to fit the data wherever it is most needed. To get estimates of the inefficiencies, u, in either Eq (4) or Eq (5), we will use a maximum likelihood procedure (see Cebenoyan et al, 1993, Karapakis et al, 1994). The choice between the two equations depends on whether the trigonometric terms are significant at the 5% level. The maximum likelihood estimation involves three steps. The first step involves obtaining OLS estimates of Eq (4) or (5). The OLS estimates are unbiased except the estimate of the α0. Second, the OLS estimates are used to obtain the starting values. The estimates corresponding to the largest log-likelihood value in the second step are used as starting values in the iterative maximization procedure in the third step. Jondrow et al (1982) have shown that inefficiency (in logarithm) of firm n can be calculated by using the distribution of the inefficiency term un conditional on εn , i.e., E(un/εn). The mean of this conditional distribution for the half normal model is shown as: 29