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Hospital cost efficiency: an examination of US acute care inpatient hospitals

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Abstract

The use of stochastic frontier models for inference on hospital efficiency is complicated by the inability to fully control for quality differences across hospitals. Additionally, the potential existence of cross-sectional dependence due to the presence of unobserved common factors leads to endogeneity problems that can bias both cost function and efficiency estimates. Using a panel consisting of 1518 hospitals for the years 1996–2013 (T = 18), I adopt techniques for dealing with long, cross-sectionally dependent panel data in order to estimate cost parameters and hospital specific efficiency. In particular, I employ the estimation technique proposed by Bai (Econometrica 77(4):1229–1279, 2009), which assumes that the unobservable heterogenous effects have a factor structure. I find evidence of considerable scale economies and that hospital cost inefficiencies have been increasing during the period of 1996–2013, and that the growth in expenditures is, in part, driven by spending that increases patient satisfaction, but that does not significantly contribute to improved patient health outcomes.

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Notes

  1. For details on hospital value based purchasing see: https://www.cms.gov/Medicare/Quality-Initiatives-Patient-Assessment-Instruments/hospital-value-based-purchasing/index.html?redirect=/Hospital-Value-Based-Purchasing/

  2. Of particular relevance to this study are SFA studies, with a health care focus, that have used panel data; these include: Chirikos (1998), Chirikos and Sear (2000), Deily et al. (2000), Li and Rosenman (2001), Rosko (2001, 2004), Sari (2003), McKay and Deily (2005), Deily and McKay (2006), Furukawa et al. (2010), Rosko and Mutter (2010, 2014).

  3. For excellent reviews of the SFA literature, see: Kumbhakar and Lovell (2000), Greene (2008) and Belotti (2012). For recent applications of the factor model methodology to production frontier analysis, see: Ahn et al. (2007), Mastromarco and Serlenga (2009), Kneip et al. (2012), Ahn et al. (2013), Filippini and Tosetti (2014) and Mastromarco et al. (2015).

  4. Additional details on the potential empirical benefits of the factor model approach are provided within Appendix A.

  5. Rather than having to imposing a set structure upon the modeled inefficiency, a factor model approach allows the researcher to use data-driven tests to determine the appropriate number of factor components to include. For details on these tests, see, e.g., Bai and Ng (2002), Bai (2004), Onatski (2009), Alessi et al. (2010), Kneip et al. (2012), Ahn and Horenstein (2013).

  6. For additional details on the within-group interpretation of the interactive fixed effects model, please see Bai (2009, pp. 1248–1249).

  7. In practice, this means that a interactive fixed effects approach will results in the same estimates as the fixed effects model, assuming this is indeed the true underlying model. However, in the presence of cross-sectional dependence within the data, due to latent common factors, the interactive fixed effects model is able to capture and control these latent features. As such, in motivating the use of an interactive fixed effects approach it is important to test for cross-sectional dependence using, e.g., the Pesaran (2014) cross-sectional dependence test.

  8. An alternative example of a possible latent factor would be trends in the adoption/use of state-of-the-art medical technologies within the US health care market. For a more detailed explanation of the endogeneity problem caused due to such latent structures, please see Appendix A.

  9. Regarding the notation throughout: the linear form is due to having taken logs. The “ln” prefix is omitted to ease the notation. That is, e.g. \(TC_{it}\) should really say ln\(TC_{it}\). Also, bold notation denotes vectors, e.g. \(x_{it}\) is not a vector, but \({\textbf{x}}_{it}\) is.

  10. The literature on stochastic cost frontier analysis in health care has mainly consisted of working with either the Cobb-Douglas functional form or the more flexible specification of a trans-log form that nests the former as a special case (see e.g. Rosko et al., 2008 for a relevant survey of this literature). The choice to work with the Cobb-Douglas form is done for its simplicity here, however, a robustness check using the translog cost functional form is also provided within Appendix D.

  11. For additional details on the estimation procedure see Bai (2009) and Bada and Liebl (2014); and/or Appendix A.

  12. The notation \({\overline{z}}_{i}\) denotes the average across the time dimension. That is, \({\overline{z}}_{i}=\frac{1}{T}\left( \sum _{t}^{T}z_{it}\right)\).

  13. The choice of taking the min(.) operator over both i, t or just i will affect the results and a discussion of this is provided within the results section.

  14. Note that since the given Cobb-Douglas form does not allow for second-order terms, the value of scale economies is assumed to be constant irrespective of the output level (see e.g. Farsi et al. (2005b, p. 75)).

  15. This section provides only some basic information regarding the data sources, for additional data details please see Appendix B.

  16. For additional details, see: https://www.cms.gov/Research-Statistics-Data-and-Systems/Downloadable-Public-Use-Files/Cost-Reports/?redirect=/CostReports/

  17. See: https://www.cms.gov/Medicare/Medicare-Fee-for-Service-Payment/AcuteInpatientPPS/Historical-Impact-Files-for-FY-1994-through-Present.html

  18. The first of these comes from the Dartmouth atlas data, while the rest (including all variables in Table 3) are from the CMS’s hospital compare data.

  19. This section draws on two computational resources for the purpose of performing estimation and various specification tests. These are: (i) the plm package by Croissant and Millo (2008), and (ii) the phtt package by Bada and Liebl (2015).

  20. The tests for establishing the optimal number of factors vary in their recommendations from 1 to 4 factors (for details see Appendix C). Within the main analysis I employ a specification that controls for individual fixed effects and that allows for two factors.

  21. The global CD test considers dependence across all hospitals within the whole of the US. The local CD test, on the other hand, considers dependence on a state level.

  22. Running additional specification tests recommended by Bai (2009) and Kneip et al. (2012) I find that both of these tests reject the null hypothesis of there only being additive two-way-effects–again, lending support to a richer specification with interactive fixed effects. For additional details on these tests and the results from Augmented Dickey Fuller tests that reject the null of a unit root, see Appendix C.

  23. This result appears robust when using even broader (25 or 50 mile) radius measures.

  24. The finding of increasing scales within health care seems supported by the high volume of hospital mergers and system formation within the industry (again, for a nice review of this literature please see Gaynor and Town (2012)).

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  1. Department of Medicine, Division of General Internal Medicine, Medical College of Wisconsin, 9200 West Wisconsin Avenue, Milwaukee, WI, 53226, USA

    Sebastian Linde PhD

  2. Center for Advancing Population Science, Medical College of Wisconsin, Milwaukee, WI, USA

    Sebastian Linde PhD

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Linde, S. Hospital cost efficiency: an examination of US acute care inpatient hospitals. Int J Health Econ Manag. 23, 325–344 (2023). https://doi.org/10.1007/s10754-023-09356-x

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