Ceris-Cnr, W.P. N° 12/2001 arbitrary equation (in this case SMS) and estimate the remaining factor-share equations by the SUR procedure.20 So, applying [2] to [1], we obtain the following equations to estimate jointly with [1]: S i = > i + > iy ln Y + > ik ln K + å > ij ln Pj + > iSP ln SP + O i [3] j i Î { L, F } ; j Î { L, MS, F } where Oi is a random noise reflecting the stochastic structure of the cost-share i. 5. Data Data set relates to 45 municipal local transit companies associated to Federtrasporti,21 operating over the years 1996, 1997 and 1998, for a total of 135 pooled observations.22 The sample includes operators providing both urban and extra-urban services.23 The data was collected from the annual reports of Federtrasporti and was integrated with a detailed questionnaire addressed to each firm. In our model, we use a composite measure of the output (Y) to reflect the global productive structure of the firm. It is well-known in transport literature, as for the network services, that the definition of the output is contrivers and can lead to different results, for example in terms of economies of scale. Our measure of output is computed by multiplying the transit firm’s fleet size, measured in terms of total places offered,24 and the total traveled kilometers. We want to point out some remarks about this kind of output. If we consider the operative context of the LPT industry, a firm must supply the service on a certain number of lines, offering a certain number of places and trips on this network. Our definition of output allows us to take into account the length of the network, the frequency of the service and the size of the fleet. Furthermore, this 20 21 22 23 24 It should be mentioned that the parameter estimates are invariant to the choice of which equation is deleted as long as the Iterated SUR (or Maximum Likelihood) estimation method is employed on the M – 1 factor-share equations. Federtrasporti associate the public firms of LPT Italian industry. Since we were working on a panel data in which each firm was observed over a period of three years, we had to choose whether to do a simple pooling on cross-section and time-series data, or to add to the model a fixed effect for every year or eventually a time-trend variable. For this reason, we did a Wald test on the joint significance of the time dummies for the first and third year added to the model. We also did the Wald test when we included in the model a time-trend variable. At the usual confidence levels, both the null hypothesis of constancy of the intercept over time and the null hypothesis of not significant time-trend effect could not be rejected, so we opted for a simple regression on the whole sample. Data mainly refers to bus transit mode. Only 8 companies provide tramway, trolley-line or railways service. The total places offered were calculated by multiplying the number of bus and their average capacity. 15