The 3-year average of the estimated efficiency was around 0.60, which was lower than 0.896 reported by Jacobs, Smith, and Street (2006), 0.78 by Kawaguchi (2008), and 0.79 by Takatsuka and Nishimura (2008) [8–10]. This discrepancy could be attributed to differences in the nature of sampled hospitals, the functional form of estimation models, and inclusion of a quality indicator in our model. Jacobs, Smith, and Street (2006) used a simple linear cost function with 4-year panel data of 185 samples from public hospitals in the United Kingdom . Kawaguchi (2008) analyzed 5-year panel data of 862 municipal hospitals in Japan with a Cobb–Douglas cost function, accounting for patient characteristics and proxy indicators of care quality . Takatsuka and Nishimura (2008) investigated the effects of introducing a new ordering system on efficiency with 5-year panel data of 408 municipal hospitals using a translog production function . When we removed the quality indicator from our model, the 3-year average efficiency increased to 0.744, a level similar to that reported in the previously published studies described above. Thus, we speculate that previous studies may fail to discriminate the efficiency of quantity production from the quality of production. Additionally, Mutter et al. (2008) reported that the mortality rate of Medicare patients had a negative coefficient of correlation with the cost function, implying that higher quality production increased costs .
Previous economic studies of hospital production efficiency focused on estimated efficiency, and conducted a secondary regression analysis to identify factors related to the efficiency. Our idea to use the estimated fixed-effect value as an indicator of structural hospital properties of the production function is unique. The estimated hospital-specific fixed effects were statistically independent of estimated efficiency scores, and had wide variance across hospitals. The secondary regression analysis confirmed that the fixed-effect estimators were significantly associated with hospitals’ advanced functions and local competitiveness, as hypothesized. These results indicate that the numerical value of the fixed-effect estimator may reflect the unobserved time-invariant heterogeneity of hospitals that corresponds to the structural properties of their location and function.
Identifying the contribution of these structural properties to a hospital’s production function has an important policy implication, especially under rigid price regulation as is the case in Japan, Canada, and some European countries. Non-profit hospitals are expected to meet societal demands of high quality and quantity of service provision regardless of unprofitable external conditions . Because inclusive payment mainly covers variable cost, non-profit hospitals with high functional and academic duties or those in remote rural areas often need complementary subsidization. However, subsidies discourage efficiency. Our new method may provide an approach for discriminating the contribution of external structural properties and efficiency per se, and for tailoring the finance method of non-profit hospitals under non-profitable external conditions without discouraging improvements in efficiency.
Limitations and future directions
Similar to previous studies on hospital production efficiency, our study suffers several limitations. First, a relatively small sample size and a short time interval of 3 years may limit the generalizability and estimation efficiency of our results. Despite our best efforts to obtain the necessary information to construct our production function model, data in panel form were only available from 127 DPC hospitals. As a result, our sample is not representative of all Japanese hospitals, and reflects only advanced, acute-care hospitals. Greene (2005a) argued that when a fixed-effect model is used for data in a relatively short period, and a period of three years is short in this context, the estimated parameters may be biased and there may be an "incidental parameters" problem . Chen, Schmidt, and Wang (
2011) investigated the effects of the incidental parameter problem on the fixed-effect parameters
. The effect on E [
] is still unclear. They also suggested that the incidental problem would be reduced by adopting data covering periods from 5 to 10 years []. Thus, our results and the usefulness of fixed-effect parameters in discriminating hospital structural properties should be confirmed with a larger and longer panel dataset.
Second, we used a simple production function as the first step in testing our hypothesis. Because a simple empirical model was used in this study, there is a possibility of the omitted variables problem, which may bias the estimation of time-variant component of hospital production efficiency. However, fixed effect model should allow us to obtain time-consistent component of productive efficiency more free from such misspecification, and we believe the second regression would tell how such time consistent characteristics of hospital production function were related to regional healthcare needs and demographic characteristics.
Finally, in our estimation, the minimum efficiency score was negative and the maximum efficiency score was not 1. The same problem was reported by Jacobs, Smith, and Street (2006) in their analysis of National Health Service hospitals in the United Kingdom using the same method . This is apparently a limitation of statistical modeling, and further studies are needed to resolve this issue.