Journal of Health Economics 20 2001 271–282
Omitted variable bias and hospital costs
Pierre-Yves Crémieux
a,b,∗
, Pierre Ouellette
a
a
Département des Sciences Économiques, Université du Québec à Montréal, Montreal, Canada
b
Analysis GroupEconomics, One Brattle Square, 5th floor, Cambridge MA 02138, USA Received 1 October 2000; received in revised form 1 November 2000; accepted 7 November 2000
Abstract
This research examines the impact of omitted variables on the accuracy of parametric hospital cost function estimations based on Québec hospital level data. We assess the effect of omitted
variables resulting from incomplete data on technology and performance measurement and on tests of the cost minimizing behavior of the institution. Our results show that important characteristics
of hospital technology, such as returns to scale, are extremely sensitive to omitted variable bias. Similarly, estimates of hospital performance are poor indicators of actual performance when data
are incomplete. © 2001 Elsevier Science B.V. All rights reserved.
JEL classification: I11; D24 Keywords: Hospital cost; Omitted variable; Technological progress
1. Introduction
Cost function estimations are commonly used to determine the production characteristics of a particular technology, to compare technologies across firms, industries or countries, and
to examine technological progress Diewert, 1971. In the hospital sector, cost functions have been used to identify the characteristics of the ‘optimal’ hospital returns to scale,
capital level, diversification of services and the effect of technological change Eakin and Knieser, 1988, 1992; Cowing and Holtmann, 1983; Cowing et al., 1983; Breyer, 1987; Dor
and Farley, 1996; Granneman et al., 1986; Lave and Lave, 1970; Lee and Wallace, 1973; Vita, 1990; Vitaliano, 1987. This approach has also been relied upon to identify performance
differences across ownership structures or to suggest optimal budget allocation in public health care systems Banks, 1993; Bilodeau et al., 2000b; Ministère de la Santé et des
∗
Corresponding author. Present address: Analysis GroupEconomics, One Brattle Square 5th Floor, Cambridge, MA 02138, USA. Tel.: +1-617-349-2135; fax: +1-617-864-3742.
E-mail address: pcremieuxanalysisgroup.com P.-Y. Cr´emieux. 0167-629601 – see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 6 2 9 6 0 0 0 0 0 8 5 - 0
272 P.-Y. Cr´emieux, P. Ouellette Journal of Health Economics 20 2001 271–282
Services Sociaux, 1992. For such exercises to be valid requires that both the underlying hospital production process and cost function exhibit certain theoretical properties and that
the estimation rely on complete data. From a theoretical point of view, at a minimum, hospitals must be short-run cost mini-
mizers. This determination should typically be made prior to examining the characteristics of hospital care. Second, the very accuracy of the testing for cost minimization and of the
overall analysis may be highly dependent on the quality of the underlying data. Some evidence exists of biases associated with incomplete data but, to date, no research
has quantified the effect of incomplete data on either the tests of theoretical properties or the characterization of hospital performance and production of health care based on parametric
cost function estimation. This is unfortunate since researchers often must rely on incomplete or unreliable data for some of the hospitals examined andor some of the inputs and outputs
of the production process Vitaliano, 1987; Eakin and Knieser, 1988; Koop and Carey, 1994; Ministère de la Santé et des Services Sociaux, 1992.
This article examines the impact of omitted variables on the accuracy of such analyses. Is it preferable to conduct the analysis with incomplete data or to refrain from cost function
estimation altogether? Using Monte Carlo analysis, Gagné and Ouellette 1998 have shown that cost function estimation can be effectively relied upon to characterize the technology
and test economic theory if the underlying data are reasonably good. Based on a data set with rather complete data on all inputs and outputs, we examine the effect of data omission on
technology and performance measurement as well as tests of the cost minimizing behavior of the firm. This is done by comparing results obtained from a benchmark model including all
available variables with those obtained from a model based on a subset of data. Differences between the models will serve as measures of bias associated with incomplete data. Although
it relies on unusually complete data, the benchmark model may itself suffer from bias resulting from data limitations. However, the magnitude of differences across models with
varying degrees of data completeness, remain indications of the sensitivity of parametric estimation to data limitations.
2. Data
