pharmaceutical drugs, medical instruments, transplants, etc )and the number of installed beds (beds ) 7 The technical efficiency frontier is constructed by choosing the number of weighted cases weighted cases, cp. following subsection)as the output variable. Additional to the labour variables described above, the number of installed beds is used as a proxy for capital input b)The erogenous variables concur in both models and are included to control for observable heterogeneity, and to measure their direct effects on inefficiency. First, public hospitals are com- pared to private and non-profit hospitals. Since public subsidies, in particular investments in the hospital's infrastructure, only have an intermediate effect on inefficiency, we use the subsidy sta- tus of the previous year(no. subst-1). A closer look at the non-subsidised hospitals reveals that private hospitals, while forming the minority in the overall sample(15%), are strongly overrepre- sented in this subgroup(76-80%). As a consequence of this observation, we include interactions of subsidy status with ownership type(e.g.(no-subsx private)t-1) to allow for heterogeneous effects The regional dummy(east) differentiates between hospitals located in eastern Germany(including Berlin)and those located in western Germany. Analogously to Zuckerman et al.(1994), the ratio of female patients (female ratio), of patients of at least 75 years of age(plus 75 ratio) and of patients receiving surgeries(surgery ratio) are used to control for further case-mix differences c)The nurse per bed ratio (nurse/bed), which had been shown to decrease efficiency(Farsi and Filippini, 2006), is minimal for private(for-profit)hospitals. The unweighted average length of stay in the final sample turns out to be 3.52 days higher in private than in public institutions in 2000 and declines over time(cf. figure 1). This decline may be due to the expected change payment schemes towards the capitation fee system introduced in 2004 th of Since the health insurance type cannot be observed in the data, it is assumed that privately and statutory ("gesetzlich)insured patients(10% and 85% of the German population in 2003, respectively)are proportionally distributed across all hospital ownership types 2.3 Constructing Case-Mix Weights Demographic and geographic factors and specialisation of hospitals constitute structural differences regarding the severity of illness of the patients and related treatment costs. Most authors add a scalar measure of patient mix, which is based on cost information, such as the Medicare Case-Mix Index(MCI)for US hospitals(Ozcan and Luke, 1992; Rosko, 1999, 2001, 2004) or similar indices for Finland and UK(Linna and Hakkinen, 1997; Linna, 1998; Jacobs, 2001) to their model. The number of beds given in the hospital statistics is the annual average of installed beds for inpatient treatment as opposed to semi-inpatient and post-inpatient treatment) independent of the source of funding. This number does neither include those beds rented out to external physicians nor does it reflect the number of actually used SThe German dataset neither provides information on a patient's DRG nor on costs per patient
(pharmaceutical drugs, medical instruments, transplants, etc.) and the number of installed beds (beds).7 The technical efficiency frontier is constructed by choosing the number of weighted cases (weighted cases, cp. following subsection) as the output variable. Additional to the labour variables described above, the number of installed beds is used as a proxy for capital input. b) The exogenous variables concur in both models and are included to control for observable heterogeneity, and to measure their direct effects on inefficiency. First, public hospitals are compared to private and non-profit hospitals. Since public subsidies, in particular investments in the hospital’s infrastructure, only have an intermediate effect on inefficiency, we use the subsidy status of the previous year (no subst−1). A closer look at the non-subsidised hospitals reveals that private hospitals, while forming the minority in the overall sample (15%), are strongly overrepresented in this subgroup (76-80%). As a consequence of this observation, we include interactions of subsidy status with ownership type (e.g. (no subs×private)t−1) to allow for heterogeneous effects. The regional dummy (east) differentiates between hospitals located in eastern Germany (including Berlin) and those located in western Germany. Analogously to Zuckerman et al. (1994), the ratio of female patients (female ratio), of patients of at least 75 years of age (plus75 ratio) and of patients receiving surgeries (surgery ratio) are used to control for further case-mix differences. c) The nurse per bed ratio (nurse/bed), which had been shown to decrease efficiency (Farsi and Filippini, 2006), is minimal for private (for-profit) hospitals. The unweighted average length of stay in the final sample turns out to be 3.52 days higher in private than in public institutions in 2000 and declines over time (cf. figure 1). This decline may be due to the expected change in payment schemes towards the capitation fee system introduced in 2004. Figure 1: Unweighted average length of stay by ownership type and year Since the health insurance type cannot be observed in the data, it is assumed that privately and statutory (“gesetzlich”) insured patients (10% and 85% of the German population in 2003, respectively) are proportionally distributed across all hospital ownership types. 2.3 Constructing Case-Mix Weights Demographic and geographic factors and specialisation of hospitals constitute structural differences regarding the severity of illness of the patients and related treatment costs. Most authors add a scalar measure of patient mix, which is based on cost information, such as the Medicare Case-Mix Index (MCI) for US hospitals (Ozcan and Luke, 1992; Rosko, 1999, 2001, 2004) or similar indices for Finland and UK (Linna and H¨akkinen, 1997; Linna, 1998; Jacobs, 2001) to their model.8 7The number of beds given in the hospital statistics is the annual average of installed beds for inpatient treatment (as opposed to semi-inpatient and post-inpatient treatment) independent of the source of funding. This number does neither include those beds rented out to external physicians nor does it reflect the number of actually used beds. 8The German dataset neither provides information on a patient’s DRG nor on costs per patient. 6
However, Medicare patients do not cover all available treatments such that the Mci might be biased In this paper, severity of illness weights are constructed using the average length of stay(los) of each inpatient diagnosis in Germany. A mean los by year and main diagnosis m = l,...,M (ICD-10 Version 2.0, three digits) over all N= 2, 290 German hospitals is calculated: los N2s,(daysmi/casesmi ). The mean length of stay over all diagnoses and all hospitals is denoted by losG. The weight Tm Josm is bigger(smaller)than one if the treatment of diagnosis m takes more(less) time than the overall average los. These weights rely on the idea that length of stay is a good proxy for resource use. However, weights of rehabilitation care diagnoses may b upward biased compared to their costs, while weights for severe cases with high mortality rates may be biased downwards. Comparing the variable cases with the number of cases of each diagnosis multiplied by Tm( denoted by weighted cases), between -7, 065 and 6, 250 cases(-60% and 140 are added due t 3 Result 3.1 Cross Sectional Analysi Cross section estimation results for the three years 2001 to 2003 are reported in Table 2(cost efficiency) and Table 3(technical efficiency ). The hypothesis that there is no inefficiency(which means ou=0)can be rejected for each year under study. Over the three years, the signs of most coefficient estimates coincide in both models. Although standard errors and point estimates differ between the years and the models, both tables show similar and consistent results. The estimated effect of input prices on the cost frontier and of the inputs on the technical frontier are presented in the first part of Tables 2 and 3. The variation across time within each model is small and all but two coefficients are significantly different from zero at a one per cent level. They also show the expected positive effects on the respective dependent variables. The coefficient estimates of the exogenous factors in the second part of Tables 2 and 3, are read as effects on inefficiency. First and most importantly, they reveal that both private and non-profit hospitals are less efficient than public hospitals in Germany. This finding confirms the results of international hospital efficiency studies. Although in germany the health insurance coverage of treatments is highly regulated and hospitals cannot negotiate prices, we find differences in the hospitals efficiency. Studies analysing profits and debts of german hospitals show that public hospitals face a much higher risk of insolvency and closure(Augurzky et al., 2004). One explanation of this paradox is the regulatory regime. The former system of cost reimbursement including per diem payments offers profit maximising hospitals an incentive to boost revenues by increasing the lengths of stay. This conclusion is derived from the descriptive statistics in Table 1, from Figure 1 and from the rank correlation matrix in the Appendix (Table A-2). The pairwise correlation matrix reveals that efficiency rankings are negatively correlated with length of stay by at least 43% at the 1% significance level across all models. Thus, a further decrease of the average lengths of stay in private hospitals due to the introduction of capitation fees in 2004 may reduce the differences in efficiency across the ownership types in the long run. This question will be left to further research when more data points are available and the transformation process has proceeded. Finally, one may argue that public authorities mainly privatised unprofitable hospitals in order to rehabilitate their finances. However, the calculated efficiency scores of the 43 privatised hospitals are, on average, only slightly below those of all other hospitals. The result that private hospitals are less efficient than public hospitals does not imply that hospitals which have been privatised are less or more efficient than if they had not been privatised gThe time index t is suppressed for ease of illustration
However, Medicare patients do not cover all available treatments such that the MCI might be biased. In this paper, severity of illness weights are constructed using the average length of stay (los) of each inpatient diagnosis in Germany. A mean los by year9 and main diagnosis m = 1, . . . , M (ICD-10 Version 2.0, three digits) over all N = 2, 290 German hospitals is calculated: losm = 1 N PN i=1(daysmi/casesmi). The mean length of stay over all diagnoses and all hospitals is denoted by losG. The weight πm = losm losG is bigger (smaller) than one if the treatment of diagnosis m takes more (less) time than the overall average los. These weights rely on the idea that length of stay is a good proxy for resource use. However, weights of rehabilitation care diagnoses may be upward biased compared to their costs, while weights for severe cases with high mortality rates may be biased downwards. Comparing the variable cases with the number of cases of each diagnosis multiplied by πm (denoted by weighted cases), between −7, 065 and 6, 250 cases (−60% and 140%) are added due to weighting. 3 Results 3.1 Cross Sectional Analysis Cross section estimation results for the three years 2001 to 2003 are reported in Table 2 (cost efficiency) and Table 3 (technical efficiency). The hypothesis that there is no inefficiency (which means σu = 0) can be rejected for each year under study. Over the three years, the signs of most coefficient estimates coincide in both models. Although standard errors and point estimates differ between the years and the models, both tables show similar and consistent results. The estimated effect of input prices on the cost frontier and of the inputs on the technical frontier are presented in the first part of Tables 2 and 3. The variation across time within each model is small and all but two coefficients are significantly different from zero at a one per cent level. They also show the expected positive effects on the respective dependent variables. The coefficient estimates of the exogenous factors in the second part of Tables 2 and 3, are read as effects on inefficiency. First and most importantly, they reveal that both private and non-profit hospitals are less efficient than public hospitals in Germany. This finding confirms the results of international hospital efficiency studies. Although in Germany the health insurance coverage of treatments is highly regulated and hospitals cannot negotiate prices, we find differences in the hospitals’ efficiency. Studies analysing profits and debts of German hospitals show that public hospitals face a much higher risk of insolvency and closure (Augurzky et al., 2004). One explanation of this paradox is the regulatory regime. The former system of cost reimbursement including per diem payments offers profit maximising hospitals an incentive to boost revenues by increasing the lengths of stay. This conclusion is derived from the descriptive statistics in Table 1, from Figure 1 and from the rank correlation matrix in the Appendix (Table A-2). The pairwise correlation matrix reveals that efficiency rankings are negatively correlated with length of stay by at least 43% at the 1% significance level across all models. Thus, a further decrease of the average lengths of stay in private hospitals due to the introduction of capitation fees in 2004 may reduce the differences in efficiency across the ownership types in the long run. This question will be left to further research when more data points are available and the transformation process has proceeded. Finally, one may argue that public authorities mainly privatised unprofitable hospitals in order to rehabilitate their finances. However, the calculated efficiency scores of the 43 privatised hospitals are, on average, only slightly below those of all other hospitals. The result that private hospitals are less efficient than public hospitals does not imply that hospitals which have been privatised are less or more efficient than if they had not been privatised. 9The time index t is suppressed for ease of illustration. 7