The European Journal of Health Economics

, Volume 18, Issue 4, pp 481–494 | Cite as

Estimation of a physician practice cost function

  • Lukas Kwietniewski
  • Mareike Heimeshoff
  • Jonas Schreyögg
Original Paper



The goal of the present paper is to provide evidence on the behavior of physician practice cost functions.

Data sources

Our study is based on the data of 3686 physician practices in Germany for the years 2006 to 2008.

Study design

We apply a translog functional form and include a comprehensive set of variables that have not been previously used in this context. A system of four equations using three-stage least squares is estimated.

Principal findings

We find that a higher degree of specialization leads to a decrease in costs, whereas quality certification increases costs. Costs of group practices are higher than of solo practices. The latter finding can be explained by the existence of indivisibilities of expensive technical equipment. Smaller practices do not reach the critical mass to invest in certain technologies, which leads to differences in the type of health care services provided by different practice types.


This is the first study to use physician practices as the unit of observation and to consider the endogenous character of physician input. Our results suggest that identifying factors that influence physician practice costs is important for providing evidence-based physician payment systems and to enable decision-makers to set incentives effectively.


Physician practice cost function Three-stage least squares Specialization Economies of scale 

JEL Classification

I20 C33 D22 


  1. 1.
    Busse, R., Schreyögg, J., Smith, P.C.: Editorial: hospital case payment systems in Europe. Health Care Manag. Sci. 9(3), 211–213 (2006)CrossRefPubMedGoogle Scholar
  2. 2.
    Bonastre, J., Le Vaillant, M., De Pouvourville, G.: The impact of research on hospital costs of care: an empirical study. Health Econ. 20(1), 73–84 (2011)CrossRefPubMedGoogle Scholar
  3. 3.
    Farsi, M., Filippini, M.: Effects of ownership, subsidization and teaching activities on hospital costs in Switzerland. Health Econ. 17(3), 335–350 (2008)CrossRefPubMedGoogle Scholar
  4. 4.
    Schreyögg, J., Stargardt, T., Tiemann, O., Busse, R.: Methods to determine reimbursement rates for diagnosis related groups (DRG): a comparison of nine European countries. Health Care Manag. Sci. 9(3), 215–223 (2006)CrossRefPubMedGoogle Scholar
  5. 5.
    Escarce, J.J., Pauly, M.V.: Physician opportunity costs in physician practice cost functions. J. Health Econ. 17(2), 129–151 (1998)CrossRefPubMedGoogle Scholar
  6. 6.
    Pope, G.C., Burge, R.T.: The marginal practice cost of physicians’ services. Socio Econ. Plan. Sci. 29(1), 1–16 (1995)CrossRefGoogle Scholar
  7. 7.
    Gunning, T.S., Sickles, R.C.: A multi-product cost function for physician private practices. J. Prod. Anal. 35(2), 119–128 (2011)CrossRefGoogle Scholar
  8. 8.
    Breyer, F.: The specification of a hospital cost function: a comment on the recent literature. J. Health Econ. 6(2), 147–157 (1987)CrossRefPubMedGoogle Scholar
  9. 9.
    Christensen, E.W.: Scale and scope economies in nursing homes: a quantile regression approach. Health Econ. 13(4), 363–377 (2004)CrossRefPubMedGoogle Scholar
  10. 10.
    Frech, I.H.E.T., Ginsburg, P.B.: Optimal scale in medical practice: a survivor analysis. J. Bus. 47(1), 23–36 (1974)CrossRefGoogle Scholar
  11. 11.
    Marder, W.D., Zuckerman, S.: Competition and medical groups: a survivor analysis. J. Health Econ. 4(2), 167–176 (1985)CrossRefPubMedGoogle Scholar
  12. 12.
    Baltagi, B.H., Bratberg, E., Holmås, T.H.: A panel data study of physicians’ labor supply: the case of Norway. Health Econ. 14(10), 1035–1045 (2005)CrossRefPubMedGoogle Scholar
  13. 13.
    Rizzo, J.A., Blumenthal, D.: Physician labor supply: do income effects matter? J. Health Econ. 13(4), 433–453 (1994)CrossRefPubMedGoogle Scholar
  14. 14.
    Sloan, F.A.: Physician supply behavior in the short run. Ind. Lab. Relat. Rev. 28, 549 (1974)CrossRefGoogle Scholar
  15. 15.
    Lin, H.-C., Chen, C.-S., Liu, T.-C., Lee, H.-C.: Differences in practice income between solo and group practice physicians. Health Policy 79(2), 296–305 (2006)CrossRefPubMedGoogle Scholar
  16. 16.
    Shephard, R.W.: Cost and production functions. Princeton University Press, Princeton (1953)Google Scholar
  17. 17.
    Varian, H.R.: Microeconomic analysis. Norton, New York (1984)Google Scholar
  18. 18.
    Reinhardt, U.: A production function for physician services. Rev. Econ. Stat. 54(1), 55–66 (1972)CrossRefGoogle Scholar
  19. 19.
    Pope, G.C., Burge, R.T.: Economies of scale in physician practice. Med. Care Res. Rev. 53(4), 417–440 (1996)CrossRefPubMedGoogle Scholar
  20. 20.
    Thurston, N.K., Libby, A.M.: A production function for physician services revisited. Rev. Econ. Stat. 84(1), 184–191 (2002)CrossRefGoogle Scholar
  21. 21.
    Diewert, W.E.: An application of the Shephard duality theorem: a generalized Leontief production function. J. Polit. Econ. 79(3), 481–507 (1971)CrossRefGoogle Scholar
  22. 22.
    Gaynor, M., Pauly, M.V.: Compensation and productive efficiency in partnerships: evidence from medical groups practice. J. Polit. Econ. 98(3), 544–573 (1990)CrossRefGoogle Scholar
  23. 23.
    DeFelice, L.C., Bradford, W.D.: Relative inefficiencies in production between solo and group practice physicians. Health Econ. 6(5), 455–465 (1997)CrossRefPubMedGoogle Scholar
  24. 24.
    Sarma, S., Devlin, R.A., Hogg, W.: Physician’s production of primary care in Ontario. Canada. Health Econ. 19(1), 14–30 (2010)PubMedGoogle Scholar
  25. 25.
    Briggs, A., Clark, T., Wolstenholme, J., Clarke, P.: Missing…. presumed at random: cost-analysis of incomplete data. Health Econ. 12(5), 377–392 (2002)CrossRefGoogle Scholar
  26. 26.
    Grieve, R., Cairns, J., Thompson, S.G.: Improving costing methods in multicentre economic evaluation: the use of multiple imputation for unit costs. Health Econ. 19(8), 939–954 (2010)CrossRefPubMedGoogle Scholar
  27. 27.
    Wagner, T.H., Hu, T., Hibbard, J.H.: The demand for consumer health information. J. Health Econ. 20(6), 1059–1075 (2001)CrossRefPubMedGoogle Scholar
  28. 28.
    Schafer, J.L.: Analysis of incomplete multivariate data. Chapman & Hall/CRC, Boca Raton (1997)CrossRefGoogle Scholar
  29. 29.
    Blough, D.K., Ramsey, S., Sullivan, S.D., Yusen, R.: The impact of using different imputation methods for missing quality of life scores on the estimation of the cost-effectiveness of lung-volume-reduction surgery. Health Econ. 18(1), 91–101 (2009)CrossRefPubMedGoogle Scholar
  30. 30.
    Dayhoff, D.A., Cromwell, J.: Measuring differences and similarities in hospital caseloads: a conceptual and empirical analysis. Health Serv. Res. 28(3), 292 (1993)PubMedCentralGoogle Scholar
  31. 31.
    Zwanziger, J., Melnick, G.A., Simonson, L.: Differentiation and specialization in the California hospital industry 1983 to 1988. Med. Care 34(4), 361 (1996)CrossRefPubMedGoogle Scholar
  32. 32.
    Busse, R.: Disease management programs in Germany’s statutory health insurance system. Health Affair 23(3), 56–67 (2004)CrossRefGoogle Scholar
  33. 33.
    Griffin, R.C., Montgomery, J.M., Rister, M.E.: Selecting functional form in production function analysis. Western J. Agr. Econ. 12(2), 216–227 (1987)Google Scholar
  34. 34.
    Christensen, L.R., Jorgenson, D.W., Lau, L.J.: Transcendental logarithmic production frontiers. Rev. Econ. Stat. 55(1), 28–45 (1973)CrossRefGoogle Scholar
  35. 35.
    Bilodeau, D., Cremieux, P.Y., Ouellette, P.: Hospital cost function in a non-market health care system. Rev. Econ. Stat. 82(3), 489–498 (2000)CrossRefGoogle Scholar
  36. 36.
    Conrad, R.F., Strauss, R.P.: A multiple-output multiple-input model of the hospital industry in North Carolina. Appl. Econ. 15(3), 341–352 (1983)CrossRefGoogle Scholar
  37. 37.
    Cowing, T.G., Holtmann, A.G., Powers, S.: Hospital cost analysis: a survey and evaluation of recent studies. Adv. Health Econ. Health Serv. Res. 4, 257 (1983)PubMedGoogle Scholar
  38. 38.
    Vita, M.G.: Exploring hospital production relationships with flexible functional forms. J. Health Econ. 9(1), 1–21 (1990)CrossRefPubMedGoogle Scholar
  39. 39.
    Li, T., Rosenman, R.: Estimating hospital costs with a generalized Leontief function. Health Econ. 10(6), 523–538 (2001)CrossRefPubMedGoogle Scholar
  40. 40.
    Kopetsch, T.: Studie zur Altersstruktur- und Arztzahlentwicklung. Bundesärztekammer und Kassenärztliche Vereinigung. (2010). Accessed 08 Feb 2016
  41. 41.
    Lin, D.Y., Wie, L.J.: The robust inference for the Cox proportional hazards model. J. Am. Stat. Assoc. 84(408), 1074–1078 (1989)CrossRefGoogle Scholar
  42. 42.
    Hardin, J.W.: The robust variance estimator for two-stage models. Stata J 2(3), 253–266 (2002)Google Scholar
  43. 43.
    Kleibergen, F., Paap, R.: Generalized reduced rank tests using the singular value decomposition. J Econometrics 133(1), 97–126 (2006)CrossRefGoogle Scholar
  44. 44.
    Staiger, D.O., Stock, J.H.: Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586 (1997)CrossRefGoogle Scholar
  45. 45.
    Stock, J.H., Yogo, M.: Testing for Weak Instruments in IV Regression. In: Andrews, D.W.K., Stock, J.H. (eds.) Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, 80–108. Cambridge University Press, New York (2005)Google Scholar
  46. 46.
    Greene, W.H.: Econometric analysis 4th edition. Macmillan (2000)Google Scholar
  47. 47.
    Auquier, A.A.: Sizes of firms, exporting behavior, and the structure of French industry. J. Ind. Econ. 29(2), 203–218 (1980)CrossRefGoogle Scholar
  48. 48.
    You, J.I.: Small firms in economic theory. Cambridge J. Econ. 19(3), 441–462 (1995)CrossRefGoogle Scholar
  49. 49.
    Newhouse, J.P.: The economics of group practice. J. Hum. Resour. 8(1), 37–56 (1973)CrossRefGoogle Scholar
  50. 50.
    Daidone, S., D’Amico, F.: Technical efficiency, specialization and ownership form: evidences from a pooling of Italian hospitals. J. Prod. Anal. 32(3), 203–216 (2009)CrossRefGoogle Scholar
  51. 51.
    Lee, K., Chun, K., Lee, J.: Reforming the hospital service structure to improve efficiency: urban hospital specialization. Health Policy 87(1), 41–49 (2008)CrossRefPubMedGoogle Scholar
  52. 52.
    Carey, K., Burgess Jr, J.F.: On measuring the hospital cost/quality trade-off. Health Econ. 8(6), 509–520 (1999)CrossRefPubMedGoogle Scholar
  53. 53.
    Hvenegaard, A., Arendt, J.N., Street, A., Gyrd-Hansen, D.: Exploring the relationship between costs and quality: does the joint evaluation of costs and quality alter the ranking of Danish hospital departments? Eur. J. Health Econ. 12(6), 541–551 (2011)CrossRefPubMedGoogle Scholar
  54. 54.
    Jha, A.K., Orav, E.J., Dobson, A., Book, R.A., Epstein, A.M.: Measuring efficiency: the association of hospital costs and quality of care. Health Affair 28(3), 897–906 (2009)CrossRefGoogle Scholar
  55. 55.
    Schreyögg, J., Stargardt, T.: The trade-off between costs and outcomes: the case of acute myocardial infarction. Health Serv. Res. 45, 1585–1601 (2010)Google Scholar
  56. 56.
    Angrist, J.D., Krueger, A.B.: The effect of age at school entry on educational attainment: an application of instrumental variables with moments from two samples. J. Am. Stat. Assoc. 96(2), 238–336 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Lukas Kwietniewski
    • 1
  • Mareike Heimeshoff
    • 1
  • Jonas Schreyögg
    • 1
  1. 1.Hamburg Center for Health EconomicsUniversity of HamburgHamburgGermany

Personalised recommendations