erved total adj the vectors of the respective coefficients to be estimated. Since a cost frontier must be linearl homogeneous in input prices, total costs and the other input prices wni are normalised by dividing them with one fixed input price Wki. Estimation results do not depend on this choice. Additionally, the more flexible translog production function is estimated adding interaction terms between the inputs and outputs to the frontier. These interaction terms capture different degrees of substitutability between inputs and possible increasing or decreasing returns to scale. 3 The translog cost function in a panel data setting" where the symmetry restriction that Bk= BI posed is defined by +∑Ah如t A1+5∑∑ m In -In (nya)2+A12003+ The literature offers several different approaches to model the non-negative systematic ineffi ciency component ui. This study follows an approach first suggested by Deprins and Simar(1989) assuming that hospital-specific factors zi=[2li,. zLil directly impact inefficiency. Formally, uiN*(=5, 02), i.e. ui has a normal distribution truncated at zero with mode 2i 5 varying over the hospitals and constant variance o,. Note that zi does not influence the deterministic part of the cost or technical frontier. These models are called 'normal truncated normal models since one component of the composite error is normally distributed, while the second is truncated normally distributed. In order to estimate our model, we use the one-step procedure by Huang and Liu (1994)which has been generalised to panel data by Battese and Coelli(1993, 1995) 4o Due to the assumption that the variance is constant, the signs of the coefficients correspond the signs of their marginal effects on the unconditional expected inefficiency(Wang, 2002) To derive the log likelihood function, it is necessary to assume that ui and vi are distributed independently of each other and of the regressors. Maximum Likelihood estimation delivers con- sistent parameter estimates, that means it allows inference about the deterministic part of the frontier and the impacts of the exogenous variables on inefficiency. Furthermore, the estimates allow us to compute hospital-specific cost(technical)efficiency scores CE(TEi)as the expected value of the efficiency conditional on the random composite error, i. e. CEi=Eexp(-uilui+ui Ei= Elexpl-uilvi-uil. These estimated scores, however, are inconsistent using cross sec- tional data because the variation associated with the distribution of (uivi t ui) is independent of i(Kumbhakar and Lovell, 2000). The inconsistency of the efficiency estimators can only be overcome with a long panel dataset that allows asymptotics along the time dimension 2.2 The Dataset The data used in this study are extracted from the annual hospital and patient statistics, which are collected and administered by the Statistical Offices of the Lander for the years 2000 to 2003. All German hospitals are, by statute, obliged to deliver this information($17b KHG). Our unbalanced samples consist of 1556 to 1635 general hospitals each year. Approximately 11%of the observations are dropped due to data inconsistencies, namely hospitals with zero costs for doctors or nurses(734 obs. ) where costs per nurse were higher than costs per doctor(additional 105 obs. ) and where the numbers of doctors and nurses were missing(90 obs. ) Exhibiting very short lengths of stay, these observations are mainly small private hospitals with a very specific organisational structure(e.g 3For a detailed discussion about functional form in production function analysis compare Griffin et al.(1987) 4 The translog panel production functio be derived analogously and is not presented.where Ci are the observed total adjusted costs of hospital i, yi is the output, and βn and βy are the vectors of the respective coefficients to be estimated. Since a cost frontier must be linearly homogeneous in input prices, total costs and the other input prices wni are normalised by dividing them with one fixed input price wki. Estimation results do not depend on this choice. Additionally, the more flexible translog production function is estimated adding interaction terms between the inputs and outputs to the frontier. These interaction terms capture different degrees of substitutability between inputs and possible increasing or decreasing returns to scale.3 The translog cost function in a panel data setting4 where the symmetry restriction that βkl = βlk is imposed is defined by ln Cit wkit = β0 + X n6=k βn ln wnit wkit + βy ln yit + 1 2 X n6=k X m6=k βnm ln wnit wkit ln wmit wkit + X n6=k βyn ln wnit wkit ln yit + 1 2 βyy(ln yit) 2 + βt2003 + vit + uit. (3) The literature offers several different approaches to model the non-negative systematic ineffi- ciency component ui . This study follows an approach first suggested by Deprins and Simar (1989) assuming that hospital-specific factors zi = [z1i , ..., zLi] directly impact inefficiency. Formally, ui ∼ N +(z 0 i δ, σ2 u ), i.e. ui has a normal distribution truncated at zero with mode z 0 i δ varying over the hospitals and constant variance σ 2 u . Note that zi does not influence the deterministic part of the cost or technical frontier. These models are called ‘normal truncated normal’ models, since one component of the composite error is normally distributed, while the second is truncated normally distributed. In order to estimate our model, we use the one-step procedure by Huang and Liu (1994) which has been generalised to panel data by Battese and Coelli (1993, 1995). Due to the assumption that the variance is constant, the signs of the coefficients correspond to the signs of their marginal effects on the unconditional expected inefficiency (Wang, 2002). To derive the log likelihood function, it is necessary to assume that ui and vi are distributed independently of each other and of the regressors. Maximum Likelihood estimation delivers con￾sistent parameter estimates, that means it allows inference about the deterministic part of the frontier and the impacts of the exogenous variables on inefficiency. Furthermore, the estimates allow us to compute hospital-specific cost (technical) efficiency scores CEi (T Ei) as the expected value of the efficiency conditional on the random composite error, i.e. CEi = E[exp(−ui)|vi + ui ] (T Ei = E[exp(−ui)|vi − ui ]). These estimated scores, however, are inconsistent using cross sec￾tional data because the variation associated with the distribution of (ui |vi ± ui) is independent of i (Kumbhakar and Lovell, 2000). The inconsistency of the efficiency estimators can only be overcome with a long panel dataset that allows asymptotics along the time dimension. 2.2 The Dataset The data used in this study are extracted from the annual hospital and patient statistics, which are collected and administered by the Statistical Offices of the L¨ander for the years 2000 to 2003. All German hospitals are, by statute, obliged to deliver this information (§17b KHG). Our unbalanced samples consist of 1556 to 1635 general hospitals each year. Approximately 11% of the observations are dropped due to data inconsistencies, namely hospitals with zero costs for doctors or nurses (734 obs.), where costs per nurse were higher than costs per doctor (additional 105 obs.), and where the numbers of doctors and nurses were missing (90 obs.). Exhibiting very short lengths of stay, these observations are mainly small private hospitals with a very specific organisational structure (e.g. 3For a detailed discussion about functional form in production function analysis compare Griffin et al. (1987). 4The translog panel production function can be derived analogously and is not presented. 4