12 port users. The model must thus be able to allow the regulator to track down the average evolution of efficiency in the sector but also to track down over time, as effectively as possible, the absolute and relative efficiency ranking of a panel of ports to identify outliers-i.e. systematic laggards or leaders. The estimation of the model is allowed by the access to a panel of data which covers a four year period-i 99699-- that follows a two year implementation period which should have already built in the frontier shift these reforms tend to introduce. In other words, catch up is the expected outcome measure to come from this sampel rather than technological progress at this stage of the reforms.

Following the literature in the field, we tested two functional forms for a stochastic producion function, a Cobb-Douglas and a Translog. The estimates are based on the maximum likelihood method relying on the FRONTIER package, version 4.1. The specific functional formal tested are the following: ln _Q,, = 83o_ + _,I_ ln K,, + /82 ln _L,,_ + 833 ln _I,, + 84T + /5_ ln(K,, )2 + /6 ln(K,, )ln(L,,) _/87 ln(KJ,)ln(IJ,)+_ 38 _ln(K,,)T_ + _89_ ln(LJ,)<sup>2</sup> + Ao0 ln(LJ,)ln(IJ)+ _1/3 ln(LJ,)T_ + (l) _+ A12 In(Ii, )2 + A13 In(lJ,T + A4T_ 2 _+ Vi, __ **_Ui,_** where: the variables are all deviations from the geometric mean and defined as follows: _i =_ 1,...,N and t=1,...,N _Qit is_ the volume of merchandise handled in port i during period t _Kit_ is the capital used by port i in period t as defined in the text _Lit_ is the number of workers employed in port i in period t _Iit_ are intermediate inputs costs in port i in period t _T_ is a time trend _vit_ is the random error assumed to be iid distributed as a normal _N(O, c2v)_ and independently distributed from uit which is a non negative random variable associated with technical inefficiency and supposed to be distributed independently as a N(O, _ou_<sup>_2_</sup> _)14._ Since the specification of the residual can in fact take various forms, we need a test to chose between the various models. This can be done through a ratio of likelihood test which works as follows: _LR =_ -2{1n[L(H0 )] - _ln[L(H,_ )D (2) where L(HO) and L(HI) are the value of the likelihood function under the null assumption (Ho) and the alternative (H,), respectively. If H. is correct, this statistic LR is distributed as a x2 with as many diegree of freedom as there are restrictions imposed.

Applied to the specification of the distribution of the inefficiency term, the tests leads sometimes to reject the assumption of a normal. This rejection combined with the difficulty of estimating a model

> 14 The term -ui cannot be observed in practice. Since the frontier has been estimated, the only thing observable is the difference vi-ui, the only solution is to rely on a predictor of this tern. The best one is the expected value of **_vj_** conditioned to the value of _vi-ui_ . When the models includes explanatory variables for the efficiency of ports, it becomes a _N(,uit,_ au") where

> ,U = **_z it J,_** and _zit_ is the vector of all variables which could influence the efficiency of ports and S is a vector of parameters to estimate in the modes including explanatory variables for port inefficiency