Random Versus Explained Inefficiency in Stochastic Frontier Analysis: The Case of Queensland Hospitals
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Estimation of (in)efficiency became a popular practice that witnessed applications in virtually any sector of the economy over the last few decades. Many different models were deployed for such endeavors, with Stochastic Frontier Analysis (SFA) models dominating the econometric literature. Among the most popular variants of SFA are Aigner, Lovell, and Schmidt (1977), which launched the literature, and Kumbhakar, Ghosh, and McGuckin (1991), which pioneered the branch taking account of the (in)efficiency term via the so-called environmental variables or determinants of inefficiency. Focusing on these two prominent approaches in SFA, the goal of this chapter is to try to understand the production inefficiency of public hospitals in Queensland. While doing so, a recognized yet often overlooked phenomenon emerges where possible dramatic differences (and consequently very different policy implications) can be derived from different models, even within one paradigm of SFA models. This emphasizes the importance of exploring many alternative models, and scrutinizing their assumptions, before drawing policy implications, especially when such implications may substantially affect people's lives, as is the case in the hospital sector.Keywords:
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This article focuses on the lessons learned from stochastic frontier analysis studies of U.S. hospitals, of which at least 27 have been published. A brief discussion of frontier techniques is provided, but a technical review of the literature is not included because overviews of estimation issues have been published recently. The primary focus is on the correlates of hospital inefficiency. In addition to examining the association of market pressures and hospital inefficiency, the authors also examined the relationship between inefficiency and hospital behavior (e.g., hospital exits) and inefficiency and other measures of hospital performance (e.g., outcome measures of quality). The authors found that consensus is emerging on the relationship of some factors to hospital efficiency; however, further research is needed to better understand others. The application of stochastic frontier analysis to specific policy issues is in its infancy; however, the methodology holds promise for being useful in certain contexts.
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Abstract This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.
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Abstract The median is proposed as an alternative to the expectation of the conditional distribution in order to predict the technical inefficiency in stochastic frontier production models with panel data. Numerical comparison reveals that the two predictors can take different values when the distribution is skewed.
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In this paper, we examine the application of SFA method with time-invariant inefficiency and assess its estimation of inefficiency when applied to cross section and panel data. By using simulation methods, we look at the effect of unobserved heterogeneity on the estimates of inefficiency in both cross section and panel. In the presence of unobserved heterogeneity and significant variance in the inefficiency term, stochastic frontier estimation of inefficiency can be significantly different in panel and in cross section. This finding accords with analysis of actual data from the postal sector. We then suggest an estimation method for cost frontier when inefficiency is time-invariant and with unobserved heterogeneity.(This abstract was borrowed from another version of this item.)
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In this paper, we examine the application of SFA method with time-invariant inefficiency and assess its estimation of inefficiency when applied to cross section and panel data. By using simulation methods, we look at the effect of unobserved heterogeneity on the estimates of inefficiency in both cross section and panel. In the presence of unobserved heterogeneity and significant variance in the inefficiency term, stochastic frontier estimation of inefficiency can be significantly different in panel and in cross section. This finding accords with analysis of actual data from the postal sector. We then suggest an estimation method for cost frontier when inefficiency is time-invariant and with unobserved heterogeneity.
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Current literature on public hospital efficiency in Australia only reveals information on how efficient public hospitals are in the short run. The presence of persistent technical inefficiency arising from long‐term systemic problems and government‐related regulatory constraints does not appear to have been addressed. Using the aggregated hospital panel data for the period 2002–2018 on eight Australian states and territories, this study incorporates the measure of both transient and persistent technical inefficiency while controlling for unobserved heterogeneity to obtain a more precise measure of technical efficiency. This study’s findings estimate the national average transient efficiency to be 0.96. In contrast, the national average persistent efficiency is estimated to be 0.83. Further, Queensland (0.67), Victoria (0.66) and New South Wales (0.60) posted the lowest overall technical efficiency driven by the high level of persistent inefficiency. On the other hand, Northern Territory (0.96), Australian Capital Territory (0.95) and Tasmania (0.95) are the top performers. This study’s findings call on policy‐makers and regulators to disclose hospital‐level data to researchers to gain further insight into the causes of persistence in inefficiency, especially among bigger states, which will help formulate more targeted policy interventions.
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This paper presents a new stochastic frontier (SF) model for panel data. The new model moves the SF approach one step further by taking into account unobserved firm heterogeneity, short- run and long-run inefficiency. By doing so the model can not only separate firm heterogeneity from long-run (persistent) inefficiency, but it can also estimate both short-run and long-run inefficiency. Previous panel data models either confounded persistent inefficiency with firm effects (heterogeneity) or firm effects were incorrectly treated as persistent inefficiency. Both formulations are misspecified and are likely to give wrong estimates of overall inefficiency. The model presented in this paper avoids this problem by disentangling persistent inefficiency com- ponent from firm-effects while accommodating short-run inefficiency. Each of these components is treated as independent random effects. We use results from closed-skew normal distribution to derive both the log-likelihood function of the model in closed form and the posterior expected values of the random effects. These posterior expected values are used to estimate short-run and long-run (in)efficiency as well as random firm effects. The proposed model is general enough to nest all the currently used panel SF models and thus appropriateness of these models can be tested against the general model empirically. We provide empirical results from three different applications using our general model as well as several popular models that are currently used in the literature.
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