Open Access Open Badges Research article

Efficacy of a numerical value of a fixed-effect estimator in stochastic frontier analysis as an indicator of hospital production structure

Hiroyuki Kawaguchi1*, Hideki Hashimoto2 and Shinya Matsuda3

Author Affiliations

1 Economics Faculty, Seijo University, 6-1-20 Seijo, Setagaya-ku, Tokyo, Japan

2 Graduate School of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan

3 Department of Public Health, University of Occupational and Environmental Health, 1-1 Iseigaoka, Yahatanishi-ku, Kitakyushu, Fukuoka, Japan

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BMC Health Services Research 2012, 12:334  doi:10.1186/1472-6963-12-334

Published: 22 September 2012



The casemix-based payment system has been adopted in many countries, although it often needs complementary adjustment taking account of each hospital’s unique production structure such as teaching and research duties, and non-profit motives. It has been challenging to numerically evaluate the impact of such structural heterogeneity on production, separately of production inefficiency. The current study adopted stochastic frontier analysis and proposed a method to assess unique components of hospital production structures using a fixed-effect variable.


There were two stages of analyses in this study. In the first stage, we estimated the efficiency score from the hospital production function using a true fixed-effect model (TFEM) in stochastic frontier analysis. The use of a TFEM allowed us to differentiate the unobserved heterogeneity of individual hospitals as hospital-specific fixed effects. In the second stage, we regressed the obtained fixed-effect variable for structural components of hospitals to test whether the variable was explicitly related to the characteristics and local disadvantages of the hospitals.


In the first analysis, the estimated efficiency score was approximately 0.6. The mean value of the fixed-effect estimator was 0.784, the standard deviation was 0.137, the range was between 0.437 and 1.212. The second-stage regression confirmed that the value of the fixed effect was significantly correlated with advanced technology and local conditions of the sample hospitals.


The obtained fixed-effect estimator may reflect hospitals’ unique structures of production, considering production inefficiency. The values of fixed-effect estimators can be used as evaluation tools to improve fairness in the reimbursement system for various functions of hospitals based on casemix classification.

Casemix classification; Efficiency estimation; Fixed effects