Gemeinderatssitzungsprotokoll 2010.12.15 - St. Marein bei Knittelfeld

3.3 The cost frontier speci…cationThe empirical application requires the speci…cation of a functional form for thetotal cost frontier. A popular form in this type of studies is the translog function,that is a second degree Taylor approximation of an arbitrary cost function. Inour case, we specify a two output, three input cost frontier, taking the followingform: T Citln = 0 + X r ln y r +X ps s ln(21)p Fit+ Xp FitXr2(D;R) s2(L;K)+ 1 2Xr2(D;R) psit rs ln y s ln + 1 p Fit 2Xs2(L;K) m2(L;K) psit sm ln lnp Fits2(L;K)XXr2(D;R) l2(D;R)pmit rl ln y r ln y lp Fit+ u it + v itIn Equation (21) the residual is composed of a one-sided (u it ) term, which followsa truncated normal distribution with mean it , and a symmetric random noise(v it ). We further assume that v it and u it are homoskedastic and independentof each other and uncorrelated with the output and input price vectors, y r andp s .The outputs y r are represented by the volume of MSW disposed (r = D)and the volume of MSW recycled (r = R). On the side of productive factors,prices refers to labor (s = L), capital (s = K) and fuel (s = F).Cost and input prices are divided by the price of fuel (p F ) to ensure homogeneityof degree one in input prices while sr = rs and sm = ms imposesymmetry. Other non imposed properties, in particular concerning the concavityof the cost function in input prices, are checked ex post.We model the expected value of the pre-truncation normal distribution ofcost ine¢ ciency in accordance to the theoretical predictions derived in Section2. In particular, we test three subsequent models:MODEL 1: it = 0 + ACC ln ACCOUNT it (22)MODEL 2: it = 0 + ACC ln ACCOUNT it + CORR ln CORRUP T it (23)MODEL 3: it = 0 + ln ACCOUNT it ACC + ACC_CORP CORP it (24)+ ln CORRUP T it CORR + CORR_LW LW P OL it+ CORP CORP it + LW LW P OL it17