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and Posner(2006)analyse antitrust issues theoretically and find that the same incentives to re- strain trade exist in the non-profit sector as in the private(for-profit)sector. In his overview about non-profit ownership and hospital behaviour, Sloan(2000) also concludes that there is no clear em- pirical evidence for a difference between these two ownership types. Duggan(2000) uses a change in financing US hospitals to reveal that the difference between the three types is driven by the soft budget constraint of public hospitals. Empirical studies of US hospital efficiency(Zuckerman et al., 1994; Rosko, 1999, 2001, 2004; Ozcan et al., 1992; Rosko and Chilingerian, 1999; Folland and Hofler, 2001)using different estimation strategies come to the conclusion that investor-owne hospitals or private(proprietary)hospitals are less cost efficient than their respective base groups (different combinations of public, non-profit or non-profit teaching hospitals). To our knowledge there are only two studies applying this approach to measure technical efficiency of hospitals(Web- steret al., 1998; Brown, 2003). Brown finds non-profit hospitals to be the most technically efficient In Switzerland, hospital cost efficiency does not differ by ownership type(Farsi and Filippini, 2006 2008) The efficiency of german hospitals has only been investigated with Data Envelopment Analysis DEA)so far, and results with respect to the ownership type are mixed. Helmig and Lapsley (2001)use data from 1991 to 1996 aggregated on the three ownership types(public, non-profit and private) and measure the highest inefficiency scores for the group of private hospitals. Staat(2006) applies dea to two different samples of comparable hospitals in western Germany using data from 1994. Differences between ownership types are not significant when comparing group means of the estimated efficiency scores. This lack of precision may be attributed to small subsamples. Werblow and Robra(2006)calculate high saving potentials in non-medical departments using aggregated non-medical costs from 2004 differentiated by the three ownership types and 16 federal states(48 observations). Calculated mean efficiency varies greatly over ownership types and federal states On average, however, the group of public hospitals is least efficient compared to the other two The remainder of the paper is organised as follows: The estimation strategy is explained in Subsection 2.1, the dataset is described in Subsection 2.2, and the problem of adjusting cases for severity of illness is discussed in Subsection 2.3. The results are presented in Section 3. Section 4 tains conclusions 2 Estimation Strategy and Data 2.1 Estimation Strategy In the case of technical efficiency, the log-linear technical stochastic frontier assuming a Cobb- Douglas production function is defined as A+∑Anm江n i.e. for each hospital i the output yi (the weighted number of cases)is maximised given inputs I CLi,., IKi and given an environment characterised by standard normally distributed random noise vi and systematic hospital specific inefficiency ui. The inefficiency term ui is assumed to b truncated at zero to assure that efficiency is smaller than 1 To measure cost efficiency for each hospital i, the K input prices w;=wli,., wki of inputs r: are calculated. The cost frontier to be estimated is defined as C +n1 +By ln lki 2Kumbhakar and Lovell(2000) provide a complete summary of both the theory and techniques used in Stochastic Frontier Production, Cost, and Profit Analysis. Another detailed review is provided by Greene(1997)and Posner (2006) analyse antitrust issues theoretically and find that the same incentives to re￾strain trade exist in the non-profit sector as in the private (for-profit) sector. In his overview about non-profit ownership and hospital behaviour, Sloan (2000) also concludes that there is no clear em￾pirical evidence for a difference between these two ownership types. Duggan (2000) uses a change in financing US hospitals to reveal that the difference between the three types is driven by the soft budget constraint of public hospitals. Empirical studies of US hospital efficiency (Zuckerman et al., 1994; Rosko, 1999, 2001, 2004; Ozcan et al., 1992; Rosko and Chilingerian, 1999; Folland and Hofler, 2001) using different estimation strategies come to the conclusion that investor-owned hospitals or private (proprietary) hospitals are less cost efficient than their respective base groups (different combinations of public, non-profit or non-profit teaching hospitals). To our knowledge, there are only two studies applying this approach to measure technical efficiency of hospitals (Web￾ster et al., 1998; Brown, 2003). Brown finds non-profit hospitals to be the most technically efficient. In Switzerland, hospital cost efficiency does not differ by ownership type (Farsi and Filippini, 2006, 2008). The efficiency of German hospitals has only been investigated with Data Envelopment Analysis (DEA) so far, and results with respect to the ownership type are mixed. Helmig and Lapsley (2001) use data from 1991 to 1996 aggregated on the three ownership types (public, non-profit and private) and measure the highest inefficiency scores for the group of private hospitals. Staat (2006) applies DEA to two different samples of comparable hospitals in western Germany using data from 1994. Differences between ownership types are not significant when comparing group means of the estimated efficiency scores. This lack of precision may be attributed to small subsamples. Werblow and Robra (2006) calculate high saving potentials in non-medical departments using aggregated non-medical costs from 2004 differentiated by the three ownership types and 16 federal states (48 observations). Calculated mean efficiency varies greatly over ownership types and federal states. On average, however, the group of public hospitals is least efficient compared to the other two groups. The remainder of the paper is organised as follows: The estimation strategy is explained in Subsection 2.1, the dataset is described in Subsection 2.2, and the problem of adjusting cases for severity of illness is discussed in Subsection 2.3. The results are presented in Section 3. Section 4 contains conclusions. 2 Estimation Strategy and Data 2.1 Estimation Strategy In the case of technical efficiency, the log-linear technical stochastic frontier assuming a Cobb￾Douglas production function is defined as2 ln yi = β0 + X n βn ln xni + vi − ui , (1) i.e. for each hospital i the output yi (the weighted number of cases) is maximised given inputs xi = [x1i , . . . , xKi] and given an environment characterised by standard normally distributed random noise vi and systematic hospital specific inefficiency ui . The inefficiency term ui is assumed to be truncated at zero to assure that efficiency is smaller than 1. To measure cost efficiency for each hospital i, the K input prices wi = [w1i , . . . , wKi] of inputs xi are calculated. The cost frontier to be estimated is defined as ln Ci wki = β0 + X n6=k βn ln wni wki + βy ln yi + vi + ui , (2) 2Kumbhakar and Lovell (2000) provide a complete summary of both the theory and techniques used in Stochastic Frontier Production, Cost, and Profit Analysis. Another detailed review is provided by Greene (1997). 3
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