Matrix Differential Calculus with Applications in Statistics and Econometrics

(2003). Comparison Methods for Stochastic Models and Risks. Technometrics: Vol. 45, No. 4, pp. 370-371.

Comparison Methods for Stochastic Models and Risks

Estimation of technical efficiency is widely used in empirical research using both cross-sectional and panel data. Although several stochastic frontier models for panel data are available, only a few of them are normally applied in empirical research. In this article we chose a broad selection of such models based on different assumptions and specifications of heterogeneity, heteroskedasticity and technical inefficiency. We applied these models to a single dataset from Norwegian grain farmers for the period 2004–2008. We also introduced a new model that disentangles firm effects from persistent (time-invariant) and residual (time-varying) technical inefficiency. We found that efficiency results are quite sensitive to how inefficiency is modeled and interpreted. Consequently, we recommend that future empirical research should pay more attention to modeling and interpreting inefficiency as well as to the assumptions underlying each model when using panel data.

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Technical efficiency in competing panel data models: a study of Norwegian grain farming

Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding.

Foundations of Linear and Generalized Linear Models

Technical efficiency in competing panel data models: A study of Norwegian grain farming

This paper considers the estimation of Kumbhakar et al. (J Prod Anal. doi:
 10.1007/s11123-012-0303-1
 , 2012) (KLH) four random components stochastic frontier (SF) model using MLE techniques. We derive the log-likelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closed-form expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three different applications.

Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency

We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continu- ation type which may be more suitable with ordinal data. We introduce a general definition of marginal interaction parameters and show that this parameterization constitutes a link function so that linear models defined by equality and inequality constraints may be fitted and tested by extending the methods of Colombi and Forcina (2001). Computation and asymptotic properties of maximum likelihood estimators are discussed, and the asymptotic distribution of the likelihood ratio test is derived.

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An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints

Given a set of discrete response variables, some of which are ordinal, and an arbitrary set of discrete explanatory variables, we propose a simple matrix formulation for parameterising the saturated model as in Glonek (1996). This is such that, within a hierarchical structure, marginal logits and log-odds ratios of various possible types, together with the remaining log-linear interactions of high order, may be modelled by equality and inequality constraints. Inequality constraints are particularly relevant for specifying models of positive association. Efficient algorithms are provided for computing maximum likelihood estimates under such constraints. The asymptotic distribution of the likelihood ratio test is derived and an extension of the usual analysis of deviance is outlined which incorporates inequality constraints.

Marginal regression models for the analysis of positive association of ordinal response variables

In this paper, we extend the 4-random-component closed skew-normal stochastic frontier model by including exogenous determinants of hospital persistent (long-run) and transient (short-run) inefficiency, separated from unobserved heterogeneity We apply this new model to a dataset composed by 133 Italian hospitals during the period 2008-2013 We show that average total inefficiency is about 23%, higher than previous estimates; hence, a model where the different types of inefficiency and hospital unobserved characteristics are not confounded allows us to get less biased estimates of hospital inefficiency Moreover, we find that transient efficiency is more important than persistent efficiency, as it accounts for 60% of the total one Last, we find that ownership (for-profit hospitals are more transiently inefficient and less persistently inefficient than not-for-profit ones, whereas public hospitals are less transiently inefficient than not-for-profit ones), specialization (specialized hospitals are more transiently inefficient than general ones; ie, there is evidence of scope economies in short-run efficiency), and size (large-sized hospitals are better than medium and small ones in terms of transient inefficiency) are determinants of both types of inefficiency, although we do not find any statistically significant effect of multihospital systems and teaching hospitals

https://onlinelibrary.wiley.com/doi/pdf/10.1002/hec.3557

Determinants of transient and persistent hospital efficiency: The case of Italy

This paper presents a new stochastic frontier model for panel data. The model takes into account firm unobservable heterogeneity and short-run and long-run sources of inefficiency. Each of these features is modeled by a specific random effect. In this way, firms’ latent heterogeneity is not wrongly modeled as inefficiency, and it is possible to disentangle a time-persistent component from the total inefficiency. Under reasonable assumptions, we show that the closed-skew normal distribution allows us to derive both the log-likelihood function of the model and the posterior expected values of the random effects. The new model is compared with nested models by analyzing the efficiency of firms belonging to different sectors.

/pdf/a-stochastic-frontier-model-with-short-run-and-long-run-4obhsq243b.pdf

Roberto Colombi

Papers

Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency

An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints

Marginal regression models for the analysis of positive association of ordinal response variables

Determinants of transient and persistent hospital efficiency: The case of Italy

A Stochastic Frontier Model with short-run and long-run inefficiency random effects