Are hospitals seasonally inefficient? Evidence from Washington State

Abstract

Efficiency measurement has been one of the most extensively explored areas of health services research over the past two decades. Despite this attention, few studies have examined whether a provider's efficiency varies on a monthly, quarterly or other, sub-annual basis. This article presents an empirical study that looks for evidence of seasonal inefficiency. Using a quarterly panel of general, acute-care hospitals from Washington State, we find that hospital efficiency does vary over time; however, the nature of this dynamic inefficiency depends on the type of efficiency being measured. Our results suggest that technical and cost efficiency vary by quarter. Allocative and scale efficiency also vary on a quarterly basis, but only if the data are jointly disaggregated by quarter and another, firm-specific factor such as size or operating status. Thus, future research, corporate decisions and government policies designed to improve the efficiency of hospital care need to account for seasonal trends in hospital efficiency.

Notes

¹ The primary difference between SFA and DEA lies in how the efficient frontier is calculated. Stochastic frontier analysis employs regression analysis to estimate the efficient frontier, and calculates individual efficiency scores by decomposing the error term of the regression equation. Because regression analysis is used, the efficiency scores can be analysed using standard statistical techniques. However, a drawback to SFA is that the results may be subject to parametric specification bias; if one miss-specified the regression equation, the efficiency scores will be biased. Data envelopment analysis uses linear-programming methods to calculate both the efficient frontier and the efficiency scores. The advantage of DEA is that it is nonparametric in nature; that is, it does not require the researcher to specify a functional form for the production process being analysed. Unlike SFA, DEA also allows the researcher to simultaneously examine several different types of efficiency (including technical, allocative, cost and scale), and allows for the specification of multiple outputs, especially when calculating technical and scale efficiency. A potential drawback is that DEA-generated efficiency scores are usually not normally distributed, and thus cannot be analysed with standard, parametric hypothesis tests.

² Several studies utilize both SFA and DEA; for example, see Bryce et al . (2000), Giuffrida and Gravelle (2001), Jacobs (2001) and Rosenman and Friesner (2004).

³ Generally these inputs are capital goods. However, in certain instances  – for example, if the firm has a binding contract with a labour union  – other inputs such as labour may also exhibit seasonal under-utilization.

⁴ The Friedman and Pauly study (1981) is over two decades old, and the Jack and Powers (2004) analysis is a single case study.

⁵ Expanding this argument to include multiple inputs, outputs or seasons should not significantly impact our analysis, as doing so merely adds extra dimensions to Figs 1–3.

⁶ By definition, cost efficiency is the product of allocative and technical efficiencies. Thus, if a firm is cost efficient it is also allocatively and technically efficient.

⁷ By definition, all distance functions are bounded between zero and one, with one representing a completely efficient firm and zero representing a completely inefficient firm. Thus, for example, if the ratio 0F/0A is 0.8, then we say that the firm in question is 80% technically efficient.

⁸ The same interpretation discussed in footnote 5 also applies here.

⁹ Measuring technical efficiency in this case depends on the returns to scale. Point A is efficient regardless of whether one assumes VRS or CRS. Point B leads to inefficiency regardless of the frontier chosen. Under CRS, inefficiency is given by the ratio B ₀ B _crs/B ₀ B, while under VRS, inefficiency is given by B ₀ B _vrs/B ₀ B.

¹⁰ Given that one can reject, but never accept a null hypothesis, this specification also allows us to make a stronger conclusion about whether hospitals are seasonally inefficient.

¹¹ An additional argument for allowing all inputs to be discretionary is that we have no a priori reason to believe that one type of input (for example, capital) is more likely to lead to seasonal inefficiency. This is especially true given the fact that the data used in this study are quarterly in nature. Had we used data of shorter frequency (for example, monthly data) this assumption would be less likely to hold. At the same time, this also implies that one is more likely to find evidence of seasonal inefficiency as the frequency of the data is shorter. We leave this possibility as a suggestion for future research.

¹² This program was written by Tim Coelli and is available from the Center for Efficiency and Productivity Analysis at the University of Queensland in Australia. The program can be downloaded at http://www.uq.edu.au/economics/cepa/index.htm

¹³ A common approach in the literature is to use Tobit regressions to see how different hospital characteristics affect efficiency. However, recent work by Simar and Wilson (2000, 2003) among others has demonstrated that such estimates (whether estimated with a Tobit model or other maximum likelihood approaches) are biased and very likely inconsistent. Thus, we avoid regression techniques in favour of an analysis of variance approach.

¹⁴ We required hospitals to have at least 25 inpatient days for each patient group, and at least 25 total outpatient visits. As a check, we implemented several variations on these minimum criteria (from as low as 10 to approximately 50) and found very few changes in the resulting data set.

¹⁵ Unfortunately, while we have quarterly data on all other outputs, our casemix data is measured annually. However, since annual casemix data will likely bias the results against a finding of seasonal inefficiency (and since our approach is to use an input oriented technique, which adjusts inputs holding outputs constant), this should not affect the reliability of our results, particularly if evidence of seasonal inefficiency is found.

¹⁶ All input prices vary by quarter, as does the number of paid hours. Not surprisingly, the number of licensed beds and hospital square footage exhibit no quarterly variation.

¹⁷ Tests were conducted using both parametric (one-way ANOVA) and nonparametric tests (Kruskal–Wallis test) for the mean. The sign test was also used to test these same hypotheses at the median. Among all of these tests, the lowest probability value obtained was 0.239, with most probability values ranging between 0.5 and 0.9. Further details of these tests are available from the authors upon request.

¹⁸ Full results are available from the corresponding author.

¹⁹ Full results are available for the corresponding author.