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On the effect of prospective payment on local hospital competition in Germany

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The introduction of prospective hospital reimbursement based on diagnosis related groups (DRG) in 2004 has been a conspicuous attempt to increase hospital efficiency in the German health sector. As a consequence of the reform a rise of competition for (low cost) patients could be expected. In this paper the competition between hospitals, quantified as spatial spillover estimates of hospital efficiency, is analyzed for periods before and after the reform. We implement a two-stage efficiency model that allows for spatial interdependence among hospitals. Hospital efficiency is determined by means of non-parametric and parametric econometric frontier models. We diagnose a significant increase of negative spatial spillovers characterizing hospital performance in Germany, and thus, confirm the expected rise of competition.

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  1. As it turns out, empirical results on the effect of prospective payment on spatial spillovers are qualitatively similar for alternative threshold values applied for outlier detection.

  2. Regarding the applied two-stage approach some remarks are in order. Firstly, two-step estimation of the effects of explanatory variables on \(\theta^{S}_{i}\) might obtain biased results in both steps [27, 49]. In the first step, the estimation of the stochastic production function 1 ignoring the explanatory variables z i yield biased efficiency scores. This leads to biased results in the second step. Wang and Schmidt [49] show in a simulation experiment that the biases persist asymptotically. Unfortunately, to our knowledge, a one-step treatment of SFA models accounting for spatial error and lag dependence has not been proposed yet. Since the focus of this study is rather on the comparison of estimated spatial spillovers over time we consider the neglect of the bias problem as tenable. Secondly, Simar and Wilson [42] mention that in finite samples the estimated DEA efficiency scores are biased and serially correlated in a complicated fashion. The convergence rate of \(\theta^{D}_{i}\) depends on the number of inputs and outputs and is typically lower than the parametric convergence rate. Maximum Likelihood estimates of regressions involving \(\theta^{D}_{i}\) are consistent, but inference based on the inverse of the negative Hessian of the log-likelihood is generally invalid. To analyze the robustness of inferential results, we apply a bootstrap procedure suggested by Simar and Wilson [42]. However, the difference between bootstrap based and asymptotic results is negligible and, therefore, we only document the latter.

  3. As a robustness check we have applied two further input specifications. Firstly, the number of employees is replaced by wage expenditures. Secondly, in order to minimize measurement errors in the labor variables the number of full time equivalent employees is used instead of the number of employees. However, for these variables data are only available for physicians and non-physicians. In summary, the diagnostic results are qualitatively very similar across all considered input measures.

  4. For the SARAR model, we only document results for specifications with the same imposed pattern for the spatial lag and error dependence, since log-likelihood statistics of alternative specifications (W d and M n , and W n and M d ) do not offer any improvements.

  5. Augurzky et al. [2] mention the importance of the geographic area where the market share is built up. In a rural area a higher market share can be the result of being the only provider of inpatient treatments invoking an inefficient production of medical care, due to the lack of competitors. At the opposite, a higher market share in an urban area might be the result of efficient performance under strengthened competition. We incorporate an interaction of ms and an agglomeration dummy variable. However, there is no considerable difference between the market share impact in rural and urban areas.

  6. As a robustness check we have estimated a more restricted Cobb–Douglas production function, i.e. δ kl  = 0 ∀ k,l in Eq. 1. It obtains positive effects of the inputs on output for almost all years. Due to space considerations results are not shown here, but available from the authors upon request. A comparison of the corresponding log-likelihood statistics is in favor of the more general translog model. Diagnostic results of the hypothesis about the effect of prospective payment on spatial spillovers are qualitatively similar for the translog and Cobb-Douglas production function.

  7. We consider Spearman rank correlation rather than linear correlation to account for a potentially non-linear relationship between SFA and DEA efficiency scores.


  1. Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic Publishers, Boston

    Google Scholar 

  2. Augurzky B, Engel D, Schwierz C (2006) Who gets the credit? Determinants of the probability of default in the German hospital sector. RWI discussion papers 0054, Rheinisch-Westfälisches Institut für Wirtschaftsforschung

  3. Banker RD, Morey RC (1986) Efficiency analysis for exogenously fixed inputs and outputs. Oper Res 34(4):513–521

    Article  Google Scholar 

  4. Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage Sci 30:1078–1092

    Article  Google Scholar 

  5. Banker RD, Gadh VM, Gorr WL (1993) A Monte Carlo comparison of two production frontier estimation methods: corrected ordinary least squares and data envelopment analysis. Eur J Oper Res 67(3):332–343

    Article  Google Scholar 

  6. Barbetta GP, Turati G, Zago AM (2007) Behavioral differences between public and private not-for-profit hospitals in the Italian national health service. Health Econ 16(1):75–96

    Article  Google Scholar 

  7. Biorn E, Hagen TP, Iversen T, Magnussen J (2003) The effect of activity-based financing on hospital efficiency: a panel data analysis of DEA efficiency scores 1992–2000. Health Care Manage Sci 6(4):271–283

    Article  Google Scholar 

  8. Böcking W, Ahrens U, Kirch W, Milakovic M (2005) First results of the introduction of DRGs in Germany and overview of experience from other DRG countries. J Public Health 13(3):128–137

    Article  Google Scholar 

  9. Chang H (1998) Determinants of hospital efficiency: the case of central government-owned Hospitals in Taiwan. Omega 26(2):307–317

    Article  Google Scholar 

  10. Chirikos TN, Sear AM (2000) Measuring hospital efficiency: a comparison of two approaches. Health Serv Res 34(6):1389–1408

    Google Scholar 

  11. Dranove D, Ludwick R (1999) Competition and pricing by nonprofit hospitals: a reassessment of Lynk’s analysis. J Health Econ 18(1):87–98

    Article  Google Scholar 

  12. Ellis RP (1998) Creaming, skimping and dumping: provider competition on the intensive and extensive margins. J Health Econ 17(5):537–555

    Article  Google Scholar 

  13. Ellis RP, McGuire TG (2002) Hospital response to prospective payment: moral hazard, selection, and practice-style effects. J Health Econ 15(3):257–277

    Article  Google Scholar 

  14. Evans RG, Walker HD (1972) Information theory and the analysis of hospital cost structure. Can J Econ 5(3):398–418

    Article  Google Scholar 

  15. Farsi M, Filippini M (2008) Effects of ownership, subsidization and teaching activities on hospital costs in Switzerland. Health Econ 17(3):335–350

    Article  Google Scholar 

  16. Giuffrida A, Gravelle H (2001) Measuring performances in primary care: econometric analysis and DEA. Appl Econ 33:163–175

    Google Scholar 

  17. Greer I, Schulten T, Böhlke N (2010) Deutsche Gründlichkeit: liberalization and local industrial relations in German hospitals. CERIC working paper no. 9

  18. Helmig B, Lapsley I (2001) On the efficiency of public, welfare and private hospitals in Germany over time—a sectoral DEA-study. Health Serv Manag Res 14(4):263–274

    Article  Google Scholar 

  19. Hensen P, Beissert S, Bruckner-Tuderman L, Luger TA, Roeder N, Müller ML (2008) Introduction of diagnosis-related groups in Germany: evaluation of impact on in-patient care in a dermatological setting. Eur J Public Health 18(1):85–91

    Article  Google Scholar 

  20. Herr (2008) Cost and technical efficiency of German hospitals: does ownership matter? Health Econ 17(9):1057–1071

    Article  Google Scholar 

  21. Herr A, Schmitz H, Augurzky B (2011) Profit efficiency and ownership of German hospitals. Health Econ 20(6):660–674

    Article  Google Scholar 

  22. Hollingsworth B (2008) The measurement of efficiency and productivity of health care delivery. Health Econ 17(10):1107–1128

    Article  Google Scholar 

  23. Jacobs R (2001) Alternative methods to examine hospital efficiency: data envelopment analysis and stochastic frontier analysis. Health Care Manage Sci 4(2):103–115

    Article  Google Scholar 

  24. Jacobs R, Smith PC, Street A (2006) Measuring efficiency in health care: analytic techniques and health policy. Cambridge University Press, Cambridge

    Book  Google Scholar 

  25. Johnson AL, McGinnis LF (2008) Outlier detection in two-stage semiparametric DEA models. Eur J Oper Res 187(2):629–635

    Article  Google Scholar 

  26. Jondrow J, Lovell CAK, Materov I, Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. J Econom 19(2–3):233–238

    Article  Google Scholar 

  27. Kim M, Schmidt P (2008) Valid tests of whether technical inefficiency depends on firm characteristics. J Econom 144(2):409–427

    Article  Google Scholar 

  28. Krieger N, Williams DR, Moss NE (1997) Measuring social class in US public health research: concepts, methodologies, and guidelines. Annu Rev Public Health 18:341–378

    Article  Google Scholar 

  29. Kumbhakar SC, Lovell CAK (2000) Stochastic frontier analysis. Cambridge, Cambridge University Press

    Google Scholar 

  30. Kumbhakar SC, Ghosh S, McGuckin JT (1991) A generalized production frontier approach for estimating determinants of inefficiency in US dairy farms. J Bus Econ Stat 9(3):279–286

    Article  Google Scholar 

  31. Lee K, Chun K, Lee J (2008) Reforming the hospital service structure to improve efficiency: urban hospital specialization. Health Policy 87(1):41–49

    Article  Google Scholar 

  32. Lungen M, Lapsley I (2003) The reform of hospital financing in Germany: an international solution? J Health Organ Manag 17(5):360–372

    Article  Google Scholar 

  33. Mielck A (2000) Soziale Ungleichheit und Gesundheit: Einführung in die aktuelle Diskussion. Bern u.a., Hans Huber

  34. Mielck A (2005) Soziale Ungleichheit und Gesundheit: Empirische Ergebnisse, Erklärungsansätze, Interventionsmöglichkeiten. Bern u.a., Hans Huber

  35. Mörsch M (2010) Bestandsaufnahme zur Krankenhausplanung und Investitionsfinanzierung in den Bundeslandern. Deutsche Krankenhausgesellschaft. Dezernat II, Berlin

    Google Scholar 

  36. Norton EC, Van Houtven CH, Lindrooth RC, Normand S-LT, Dickey B (2002) Does prospective payment reduce inpatient length of stay? Health Econ 11(5):377–387

    Article  Google Scholar 

  37. Perelman J, Shmueli A, Closon M-C (2008) Deriving a risk-adjustment formula for hospital financing: integrating the impact of socio-economic status on length of stay. Soc Sci Med 66:88–98

    Article  Google Scholar 

  38. Picone G, Wilson RM, Chou S-Y (2003) Analysis of hospital length of stay and discharge destination using hazard functions with unmeasured heterogeneity. Health Econ 12(12):1021–1034

    Article  Google Scholar 

  39. Propper C, Burgess S, Green K (2004) Does competition between hospitals improve the quality of care? Hospital death rates and the NHS internal market. J Public Econ 11(7–8):1247–1272

    Article  Google Scholar 

  40. Rosko MD, Chillingerian JA (1999) Estimating hospital inefficiency: does case mix matter? Health Care Manage Sci 23(1):57–71

    Google Scholar 

  41. Schreyögg J, Stargardt T, Tiemann O (2011) Costs and quality of hospitals in different health care systems: a multi-level approach with propensity score matching. Health Econ 20(1):85–100

    Article  Google Scholar 

  42. Simar L, Wilson PW (2007) Estimation and inference in two-stage, semi-parametric models of production processes. J Econom 136(1):31–64

    Article  Google Scholar 

  43. Staat M (2006) Efficiency of hospitals in Germany: a DEA-bootstrap approach. Appl Econ 38(19):2255–2263

    Article  Google Scholar 

  44. Statistisches Bundesamt (2008) Krankenhaus- Landschaft im Umbruch. Begleitmaterial zur Pressekonferenz am 10. Dezember 2008 in Berlin

  45. Steinmann L, Dittrich G, Karmann A, Zweifel P (2004) Measuring and comparing the (in)efficiency of German and Swiss hospitals. Eur J Health Econ 5(3):216–226

    Article  Google Scholar 

  46. Tiemann O, Schreyögg J (2009) Effects of ownership on hospital efficiency in Germany. BuR Bus Res J 2(2):115–145

    Google Scholar 

  47. Town R, Vistnes G (2001) Hospital competition in HMO networks. J Health Econ 20(5):733–753

    Article  Google Scholar 

  48. Van Biesebroeck J (2007) Robustness of productivity estimates. J Ind Econ 55(3):529–569

    Article  Google Scholar 

  49. Wang H, Schmidt P (2002) One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. Journal of Productivity Analysis 18(2):129–144

    Article  Google Scholar 

  50. Webster TM, Baumgartner R, Sprunger JK, Baldwin DD, McDougall EM, Herrell SD (2005) A clinical pathway for laparoscopic pyeloplasty decreases length of stay. J Urol 173(6):2081–2084

    Article  Google Scholar 

  51. Werblow A, Karmann A, Robra BP (2010) Effizienz, Wettbewerb und regionale Unterschiede in der stationären Versorgung. In: Klauber J, Geraedts M, Friedrich J (eds) Krankenhaus-Report 2010—Schwerpunkt: Krankenhausversorgung in der Krise? Stuttgart, Schattauer, pp 41–71

    Google Scholar 

  52. Werblow A, Robra BP (2007) Einsparpotenziale im medizinfernen Bereich deutscher Krankenhäuser—eine regionale Effizienzfront-Analyse. In: Klauber J, Schellschmidt H, Robra BP (eds) Krankenhaus-Report 2006—Schwerpunkt: Krankenhausmarkt im Umbruch. Stuttgart, Schattauer, pp 133–151

    Google Scholar 

  53. Wilson PW (1995) Detecting influential observations in data envelopment analysis. Journal of Productivity Analysis 6(1):27–45

    Article  Google Scholar 

  54. Zweifel P, Breyer F, Kifmann M (2009) Health economics. Springer, Berlin

    Book  Google Scholar 

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We thank three anonymous referees, Uwe Jensen, Andrew Street, the participants of the XVth. Spring meeting of young economists 2010 in Luxembourg, Jahrestagung des Vereins für Socialpolitik 2010 in Kiel and 15. Nachwuchsworkshop der DStatG 2009 in Merseburg for helpful comments and discussions on earlier versions of this manuscript. We also thank Alexander Vogel and Hendrik Tietje of the Forschungsdatenzentrum der Statistischen Landesämter—Standort Kiel/Hamburg for their cooperation.

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Correspondence to Christoph Strumann.


A Efficiency measurement

1.1 A.1 DEA efficiency scores

The efficiency score, \(\theta^{D}_{i}\), is obtained under the assumption of variable returns to scale [4] by solving the following linear program

$$ \begin{array}{rll} \theta^{D}_{i}=\arg \min\limits_{\theta^{D}_{i}, \, \tau} \Big\{\theta^{D}_{i}>0 \Big| \sum\limits_{l} \tau_{l} q_{pl} \geq q_{pi} \; &\forall& \; p \in \{1,...,s\} \\ \theta^{D}_{i} x^D_{ki} \sum\limits_{l} \tau_{l} x^D_{kl} \; &\forall& \; k \in \{1,...,m^D\} \\ x^N_{ji} \geq \sum\limits_{l} \tau_{l} x^N_{jl}\; &\forall& \; j \in \{1,...,m^N\} \\ \sum\limits_{l} \tau_{l} =1, \; \tau_{l}>0 \; &\forall& \; l =1,...,N \Big\}, \end{array} $$

where q ri , \(x^N_{ji}\) and \(x^D_{ki}\) denote output, non-discretionary and discretionary input variables of hospital i. The numbers of outputs, non- and discretionary inputs, and reference hospitals are s, m N, m D, and N, respectively.

1.2 A.2 SFA efficiency scores

Given Maximum Likelihood estimates of the model parameters in Eq. 1 the technical efficiency of the i-th hospital is obtained as [26]

$$ \begin{array}{rll} \theta^{S}_i &=& \exp\left\{-\mathrm{E}\left[ u_i|v_i-u_i \right] \right\} \quad \mathrm{with} \\ && {\kern6pt}\mathrm{E}\left[ u_i|v_i-u_i \right]= \hat{\mu}_i^* + \hat{\sigma}^* \frac{\phi\left(\hat{\mu}_i^*/\hat{\sigma}^*\right)}{\Phi\left(\hat{\mu}_i^*/\hat{\sigma}^*\right)}, \\ \hat{\mu}_i^*&=&\frac{\hat{\sigma}^2_v \hat{\gamma}'h_i - \hat{\sigma}^2_u \hat{\nu}_i}{\hat{\sigma}^2_v + \hat{\sigma}^2_u} \quad \mathrm{and} \quad \hat{\sigma}^{*}=\sqrt{\frac{\hat{\sigma}^2_v \hat{\sigma}^2_u}{\hat{\sigma}^2_v + \hat{\sigma}^2_u}}, \end{array} $$

where \(\hat{\nu}_i\!=\!\ln q_i - \hat{\alpha}_0 - \sum\limits_{k} \hat{\alpha}_k \ln x_{ik} - \sum\limits_{k} \sum\limits_{k\geq l} \hat{\delta}_{kl} \ln x_{ik} \ln x_{il}\), and Φ and ϕ are the Gaussian cumulative and probability density function, respectively [29].

B Maximum Likelihood estimation

Model 2 can be written as

$$ {\textbf{\emph B}}{\textbf{\emph A}}y = {\textbf{\emph B}}{\textbf{\emph Z}}\beta + \epsilon, $$

where B = I N  − ρ W and A = I N  − λ W. Assuming a multivariate normal distribution of the error terms, the log likelihood function is given by

$$ \mathrm{ln}L = -\frac{N}{2}\mathrm{ln}(2\pi\sigma^2) + \ln|{\textbf{\emph A}}| + \ln|{\textbf{\emph B}}| - \frac{\epsilon'\epsilon}{2\sigma^2}, $$

where ϵ = B \(\left(\boldsymbol{A} y - \boldsymbol{Z}\beta\right)\) and σ 2 = ϵϵ/N. The ML estimator is

$$ \hat{\beta}_{ML} = \left(\boldsymbol{Z}'\widehat{\boldsymbol{B}}' \widehat{\boldsymbol{B}} \boldsymbol{Z}\right)^{-1} \boldsymbol{Z}'\widehat{\boldsymbol{B}}'\widehat{\boldsymbol{B}}\widehat{\boldsymbol{A}}y $$

where \(\widehat{\boldsymbol{B}}= \boldsymbol{I}_N-\hat{\rho}_{ML} \boldsymbol{M}\) and \(\widehat{\boldsymbol{A}}=\boldsymbol{I}_N-\hat{\lambda}_{ML} \boldsymbol{W}\).

C Construction of case mix weights

The more time the treatments of cases belonging to the j-th clinical department take relative to all other treatments, the higher the weight, π j , of the respective cases. Let c ij be the number of cases in the j-th clinical department of the i-th hospital. Then, the weighted cases of hospital i are calculated as

$$ wc_i= \sum\limits_{j=1}^J \pi_j \, c_{ij}, $$

where π j  = los j /los G , \(los_j=(\sum_{i=1}^N days_{ij}/c_{ij})/N\) is the mean length of stay for the cases belonging to the j-th clinical department over all hospitals and \(los_G=(\sum_{j=1}^J los_j) /J\) is the mean length of stay over all clinical departments and all hospitals.

D Outlier detection

Table 5 shows the share of hospitals in the population and in the sample of the first and second stage over different subgroups characterized by the number of beds and ownership form. In the sample of both stages hospitals with less than 100 beds and profit oriented hospitals are under-represented.

Table 5 Distribution of hospitals pooled over all time periods

E First stage results

This appendix provides further details on the results of the parameter estimates of the SFA model and descriptive statistics of SFA and DEA efficiency scores.

1.1 E.1 SFA parameter estimates

The results of the SFA model are shown in Table 6. The parameter estimates are characterized by substantial heterogeneity over time. The estimated variance of the noise component, \(\sigma_v^2\), decreases remarkably after 1996 and 2001 suggesting less measurement errors and a higher quality of the data. Similarly, the estimated variance of the inefficiency term, \(\sigma_u^2\), shrinks after 2001. Moreover, the ratio of both variances, \(\sigma_u^2/\sigma_v^2\), indicates a lower proportion of signal to noise after 2001.

Table 6 Estimates of the SFA translog model

To facilitate the interpretation of the estimated translog input coefficients output elasticities with respect to inputs are also reported. The estimated output elasticities are mostly significantly positive for the most years and, similar to other estimates, vary substantially over time. After 2001 the amount of material expenses and the number of non-medical employees appear to have a (theoretically implausible) negative effect on the number of weighted treated cases. However, these estimates are mostly insignificant. The exogenously fixed input variable beds obtains a negative estimate, indicating a positive effect of the number of beds on efficiency. The magnitude of the estimated impact is decreasing after 2001.Footnote 6

The variation in the estimates over time might be explained by two reasons. Firstly, the definition of the costs has changed in 1996 and 2002. Secondly, the application of minimally invasive procedures has been expanded over the last years leading to shorter rehabilitation time and decreased hospital costs [50]. Both instances might have an effect on the stochastic noise in the hospital data and, thus, influence the parameter estimates.

1.2 E.2 DEA and SFA efficiency scores

Descriptive statistics of estimated DEA and SFA efficiency scores are shown in Table 7. For all subgroups mean SFA efficiency scores are markedly higher than their DEA counterparts. This could be seen as a reflection of the fact that in the DEA model all deviations from the frontier are assigned as inefficiency, while it is separated from stochastic noise in the SFA model. The difference between both efficiency measures varies over beds and ownership form. For instance, profit oriented hospitals are characterized by the highest DEA but lowest SFA efficiency scores. In total, 3% of the hospitals are DEA-efficient, i.e. \(\theta^D_i=1\). The share of these hospitals varies over the groups. Almost 11% of small (<100 beds) and privately owned hospitals are clarified as efficient by means of DEA, while in the other groups the share varies between 0.87% (100–299 beds) to 3.97% (>500 beds). Similar to the SFA parameter estimates the Spearman rank correlation between the alternative efficiency measures vary over time.Footnote 7 In the years 1995 and 1996, the correlation between both efficiency scores is negative. This might be explained by the poor quality of the data as suggested by the relative large variance of the noise component \(\hat{\sigma}^2_{v}\) (Table 6). Measurement errors are in general more detrimental to DEA, since it exploits the noise as inefficiency (e.g. [5, 48]). In the SFA model an assumption about the distribution of the inefficiency term is required to separate inefficiency from noise. However, the decomposition of the error term could fail under large measurement errors [48]. Therefore, in the presence of large amounts of noise both methods may perform poorly. This might explain the remarkable differences between the efficiency scores. After 1996 the variance of the noise component drops to one third of its previous magnitude and the correlation between DEA and SFA efficiency scores reaches almost 78% in 1997. It decreases over time to 40% in 2006. The decline in the correlation is in line with the higher proportion of the noise component after 2001 as indicated by the decreased ratio of estimated variances \(\hat{\sigma}^2_u/\hat{\sigma}^2_v\). Hospitals with more than 300 beds are characterized by the strongest similarity between both efficiency measures. In summary, the statistics document the heterogeneity between parametric and non-parametric efficiency measures as also documented in other comparative studies of hospital performance (e.g. [10, 16, 23, 24]).

Table 7 Summary statistics and correlation of DEA and SFA efficiency scores (in %)

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Herwartz, H., Strumann, C. On the effect of prospective payment on local hospital competition in Germany. Health Care Manag Sci 15, 48–62 (2012).

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