The ‘wrong skewness’ problem: a re-specification of stochastic frontiers

In this paper, we study the ‘wrong skewness phenomenon’ in stochastic frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error, and causes the ‘wrong skewness problem’, for which the estimated inefficiency in the whole industry is zero. We propose a more general and flexible specification of the SF model, introducing dependences between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error into three components, namely: (i) the asymmetry of the inefficiency term; (ii) the asymmetry of the random error; and (iii) the structure of dependence between the error components. This decomposition suggests that the wrong skewness anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF has the wrong skewness, an estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. More importantly, we estimate a non-zero inefficiency, thus solving the wrong skewness problem. In the second dataset, where the classic SF does not yield any anomaly, an estimation of our model provides evidence for the presence of dependence. In such situations, we show that there is a remarkable difference in the efficiency distribution between the classic SF and our class of models.     

基于随机需求的物流配送中心选址离散模型研究

针对物流需求不确定情况下的物流配送中心选址问题,对传统模型进行改进,将随机需求变量引入离散型选址模型,利用随机规划理论和遗传算法对实例模型进行求解。结果显示物流需求不确定情况下的随机规划模型的求解结果比假设已知需求情况下的结果真实可信,所需物流费用较少。     

A simple approach for the analysis of generalizea linear mixed models

A broad class of generalized linear mixed models, e.g. variance components models for binary data, percentages or count data, will be introduced by incorporating additional random effects into the linear predictor of a generalized linear model structure. Parameters are estimated by a combination of quasi-likelihood and iterated MINQUE (minimum norm quadratic unbiased estimation), the latter being numerically equivalent to REML (restricted, or residual, maximum likelihood). First, conditional upon the additional random effects, observations on a working variable and weights are derived by quasi-likelihood, using iteratively re-weighted least squares. Second, a linear mixed model is fitted to the working variable, employing the weights for the residual error terms, by iterated MINQUE. The latter may be regarded as a least squares procedure applied to squared and product terms of error contrasts derived from the working variable. No full distributional assumptions are needed for estimation. The model may be fitted with standardly available software for weighted regression and REML.     

Some results on an additive hazards model

In the present paper, we study the analytical properties of an addictive hazards model. The ageing properties of the baseline random variable and the induced random variable are compared. Various stochastic orders that relate these two variables are also explored.     

Stochastic error specification in primal and dual production systems

In this paper we derive both primal and dual‐cost systems in which the stochastic specifications arise from the model (random environment or measurement errors and optimization errors)—not tacked on at the end after the deterministic system is worked out. Derivation of the error structures is based on cost‐minimizing behavior on the firms. The primal systems constitute the production function and the first‐order conditions of cost minimization. We consider two dual‐cost systems. The first dual system is based on the cost function and cost share equations. The second dual system is based on a multiplicative general error production model that is an alternative to McElroy's additive general error production model. Our multiplicative general error model gives a clear and intuitive economic meaning to the error components. The resulting cost system is easy to estimate compared to the alternative cost systems. The error components in the multiplicative general error model can capture heterogeneity in the technology parameters even in a cross‐sectional model. Panel data are not necessary to estimate either the primal or dual systems. The models are estimated using data on 72 fossil fuel‐fired steam electric power generation plants (observed for the period 1986–1999) in the USA. Copyright © 2009 John Wiley & Sons, Ltd.     

Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes

This paper examines the impact of an endogenous cost function variable on the inefficiency estimates generated by stochastic frontier analysis (SFA). The specific variable of interest in this application is endogenous quality in nursing homes. We simulate a dataset based on the characteristics of for-profit nursing homes in California, which we use to assess the impact on SFA-generated inefficiency estimates of an endogenous regressor under a variety of scenarios, including variations in the strength and direction of the endogeneity and whether the correlation is with the random noise or the inefficiency residual component of the error term. We compare each of these cases when quality is included and excluded from the cost equation. We provide evidence of the impact of endogeneity on inefficiency estimates yielded by SFA under these various scenarios and when the endogenous regressor is included and excluded from the model.     

Panel estimators and the identification of firm-specific efficiency levels in parametric,semiparametric and nonparametric settings

The paper analyzes a number of competing approaches to modeling efficiency in panel studies. The specifications considered include the fixed effects stochastic frontier, the random effects stochastic frontier, the Hausman–Taylor random effects stochastic frontier, and the random and fixed effects stochastic frontier with an AR(1) error. I have summarized the foundations and properties of estimators that have appeared elsewhere and have described the model assumptions under which each of the estimators have been developed. I discuss parametric and nonparametric treatments of time varying efficiency including the Battese–Coelli estimator and linear programming approaches to efficiency measurement. Monte Carlo simulation is used to compare the various estimators and to assess their relative performances under a variety of misspecified settings. A brief illustration of the estimators is conducted using U.S. banking data.     

FIRM HETEROGENEITY,PERSISTENT AND TRANSIENT TECHNICAL INEFFICIENCY: A GENERALIZED TRUE RANDOM‐EFFECTS model

This paper considers a panel data stochastic frontier model that disentangles unobserved firm effects (firm heterogeneity) from persistent (time‐invariant/long‐term) and transient (time‐varying/short‐term) technical inefficiency. The model gives us a four‐way error component model, viz., persistent and time‐varying inefficiency, random firm effects and noise. We use Bayesian methods of inference to provide robust and efficient methods of estimating inefficiency components in this four‐way error component model. Monte Carlo results are provided to validate its performance. We also present results from an empirical application that uses a large panel of US commercial banks. Copyright © 2012 John Wiley & Sons, Ltd.     

A Bayesian estimator for stochastic frontier models with errors in variables

A Bayesian estimator is proposed for a stochastic frontier model with errors in variables. The model assumes a truncated-normal distribution for the inefficiency and accommodates exogenous determinants of inefficiency. An empirical example of Tobin??s Q investment model is provided, in which the Q variable is known to suffer from measurement error. Results show that correcting for measurement error in the Q variable has an important effect on the estimation results.     

Nonparametric stochastic frontiers: A local maximum likelihood approach

This paper proposes a new approach to handle nonparametric stochastic frontier (SF) models. It is based on local maximum likelihood techniques. The model is presented as encompassing some anchorage parametric model in a nonparametric way. First, we derive asymptotic properties of the estimator for the general case (local linear approximations). Then the results are tailored to a SF model where the convoluted error term (efficiency plus noise) is the sum of a half normal and a normal random variable. The parametric anchorage model is a linear production function with a homoscedastic error term. The local approximation is linear for both the production function and the parameters of the error terms. The performance of our estimator is then established in finite samples using simulated data sets as well as with a cross-sectional data on US commercial banks. The methods appear to be robust, numerically stable and particularly useful for investigating a production process and the derived efficiency scores.     

Stochastic comparisons for the number of working components of a system in random environment

In terms of stochastic orders, the purpose of this paper is to show how the random environment can affect the number of working components of a system with heterogeneous components sharing a common random environment. Applications to a class of semiparametric mixture models, stress-strength model and warm standby system are presented.     

基于随机需求的军事物流中心选址研究

军事物流中心的合理选择,对于提高后勤与装备保障水平,降低军事物流成本具有重要意义。文章针对军用装备的特点,当需求量为随机变量时,建立了军事物流中心选址的随机数学模型。通过等价变换。将该随机数学模型转换成确定性等价问题。结果表明：在随机需求条件下,该方法在保障军事目标实现的同时,能够有效降低军事物流成本,实现了军事效益和经济效益的和谐统一。     

Usefulness of proxy variables in linear models with stochastic regressors

This paper considers a linear model with two stochastic regressors where one regressor is not observed directly but may be observed with error (proxy variable). The interest is focussed upon the estimation accuracy of the regression coefficient of the observable regressor. The possibility of estimating this coefficient more accurately using a proxy variable in regression instead of omitting the non-observable variable is considered, and an approximate condition for this to occur is given and discussed.     

Stochastic comparisons of multivariate reversed frailty model

Multivariate frailty approaches are most commonly used to define distributions of random vectors, which represent lifetimes of individuals or components and stochastically compare them in terms of various multivariate orders. In this paper, we study a multivariate shared reversed frailty model and a general multivariate reversed frailty mixture model, and derive sufficient conditions for some of the stochastic orderings to hold among the random vectors. We also consider a particular case of a general multivariate mixture model in which the baseline distribution function is represented in terms of a copula and study stochastic comparisons (stochastic and lower orthant order) among the two random vectors.     

A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models

This paper derives an analytic closed-form formula for the cumulative distribution function (cdf) of the composite error of the stochastic frontier analysis (SFA) model. Since the presence of a cdf is frequently encountered in the likelihood-based analysis with limited-dependent and qualitative variables as elegantly shown in the classic book of Maddala (Limited-dependent and qualitative variables in econometrics. Cambridge University Press, Cambridge, 1983), the proposed methodology is useful in the framework of the stochastic frontier analysis. We apply the formula to the maximum likelihood estimation of the SFA models with a censored dependent variable. The simulations show that the finite sample performance of the maximum likelihood estimator of the censored SFA model is very promising. A simple empirical example on the modeling of reservation wage in Taiwan is illustrated as a potential application of the censored SFA.     

The occurrence of outliers in the explanatory variable considered in an errors-in-variables framework

Summary The problem of estimating the slope of a linear relationship between two jointly normally distributed random variables is considered when outliers may occur in the explanatory variable. It will be studied as a special case of an errors-in-variables problem where the explanatory variable is measured which a nonnormally distributed error. In this more general model and under certain conditions a consistent estimator can be given with a normal limiting distribution. Applications to cases of outliers in the explanatory variable will be presented.     

UNCERTAINTY ANALYSIS FOR MULTI-REGION INPUT–OUTPUT MODELS – A CASE STUDY OF THE UK'S CARBON FOOTPRINT

This paper reviews and demonstrates methods available for estimating standard deviations for carbon multipliers in a multi-regional input–output (MRIO) framework. We attempt to capture all possible variations of underlying data and calculation procedures in a global MRIO model constructed with particular focus on the UK. We consider these variations to be random, and determine the stochastic variation of the whole MRIO system using Monte Carlo techniques. 5000 simulation runs were carried out to determine the standard deviations of multipliers. From these, the standard deviations of components of the UK's carbon footprint were estimated using error propagation. We estimate an 89% probability that the UK's carbon footprint has increased between 1994 and 2004.     

Stochastic model specification search for Gaussian and partial non-Gaussian state space models

Model specification for state space models is a difficult task as one has to decide which components to include in the model and to specify whether these components are fixed or time-varying. To this aim a new model space MCMC method is developed in this paper. It is based on extending the Bayesian variable selection approach which is usually applied to variable selection in regression models to state space models. For non-Gaussian state space models stochastic model search MCMC makes use of auxiliary mixture sampling. We focus on structural time series models including seasonal components, trend or intervention. The method is applied to various well-known time series.     

Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy

This paper develops methods for stochastic search variable selection (currently popular with regression and vector autoregressive models) for vector error correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model. Copyright © 2011 John Wiley & Sons, Ltd.     

A non-linear model of the real US/UK exchange rate

This paper provides a framework for building and estimating non-linear real exchange rate models. The approach derives the stationary distribution from a continuous time error correction model and estimates this by MLE methods. The derived distribution exhibits a wide variety of distributional shapes including multimodality. The main result is that swings in the US/UK rate over the period 1973:3 to 1990:5 can be attributed to the distribution becoming bimodal with the rate switching between equilibria. By capturing these changes in the distribution, the non-linear model yields improvements over the random walk, the speculative efficiency model, and Hamilton's stochastic segmented trends model.