Fixed and Random Effects in Stochastic Frontier Models

Received stochastic frontier analyses with panel data have relied on traditional fixed and random effects models. We propose extensions that circumvent two shortcomings of these approaches. The conventional panel data estimators assume that technical or cost inefficiency is time invariant. Second, the fixed and random effects estimators force any time invariant cross unit heterogeneity into the same term that is being used to capture the inefficiency. Inefficiency measures in these models may be picking up heterogeneity in addition to or even instead of inefficiency. A fixed effects model is extended to the stochastic frontier model using results that specifically employ the nonlinear specification. The random effects model is reformulated as a special case of the random parameters model. The techniques are illustrated in applications to the U.S. banking industry and a cross country comparison of the efficiency of health care delivery.JEL classification: C1, C4     

On divergence and convergence of sums of nonnegative random variables

Abstract  If X ₁, X ₂,… are exponentially distributed random variables thenσ^∞_{k= 1} X_k=∞ with probability 1 iff σ^∞_{k= 1} EX_k=∞. This result, which is basic for a criterion in the theory of Markov jump processes for ruling out explosions (infinitely many transitions within a finite time) is usually proved under the assumption of independence (see FREEDMAN (1971), p. 153–154 or BREI-MAN (1968), p. 337–338), but is shown in this note to hold without any assumption on the joint distribution. More generally, it is investigated when sums of nonnegative random variables with given marginal distributions converge or diverge whatever are their joint distributions.     

The asymptotic distribution of the determinant of a random correlation matrix

Our main result gives the asymptotic distribution of the determinant of a random correlation matrix sampled in a particular way from the space of d ×d correlation matrices. Several spin‐off results are proven along the way, and an interesting connection with the law of the determinant of general random matrices is investigated. As different methods for generating random correlation matrices are proposed in the literature, one application of our result is that in can be employed to differentiate between those methods.     

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。     

Testing for Multicointegration in Panel Data with Common Factors*

This paper addresses the concept of multicointegration in a panel data framework and builds upon the panel data cointegration procedures developed in Pedroni [Econometric Theory (2004), Vol. 20, pp. 597–625]. When individuals are either cross‐section independent, or cross‐section dependence can be removed by cross‐section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes. The paper also deals with the issue of cross‐section dependence using approximate common‐factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating an inventories, sales and production relationship for a panel of US industries.     

A note on mixed Poisson approximation

Conditions sufficient for the weak convergence of sums of 0–1 random variables indexed by k -sets to a mixed Poisson law are presented. An example of applications concerning "distance" random variables is also provided.     

Application of discrete transforms in reliability of a parallel redundant system

This paper introduces the application of Discrete Transform in order to study the reliability of a redundant system consisting of more than one identical components that are connected in parallel. Successive failure times of each individual component are assumed to be positive random variables having a common general distribution, while the repair times of the system are governed by another independent general distribution. Further, it is assumed that the repair is carried out when all the components in the system have failed. TheLaplace Transform of the transient state probabilities associated with the system have been obtained. In the last section, the asymptotic behaviour of the system has also been examined.     

Bias in dynamic panel estimation with fixed effects,incidental trends and cross section dependence

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N→∞$N\to \infty$. The results extend earlier work by Nickell [1981. Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426] and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.     

House Price Dynamics in Mumbai, 1989–1995

The objective of this paper is to study the importance of price index methodology to analyzing intra-metropolitan house price variations in Mumbai. Two hedonic regression-based approaches – cross section and explicit time variable – are compared. The results indicate conclusively that the former is better than the latter. This paper also contributes to the literature on intra-metropolitan house price variations by explaining them based on urban development, population and employment patterns in Mumbai.     

Inference on stochastic time-varying coefficient models

Recently, there has been considerable work on stochastic time-varying coefficient models as vehicles for modelling structural change in the macroeconomy with a focus on the estimation of the unobserved paths of random coefficient processes. The dominant estimation methods, in this context, are based on various filters, such as the Kalman filter, that are applicable when the models are cast in state space representations. This paper introduces a new class of autoregressive bounded processes that decompose a time series into a persistent random attractor, a time varying autoregressive component, and martingale difference errors. The paper examines, rigorously, alternative kernel based, nonparametric estimation approaches for such models and derives their basic properties. These estimators have long been studied in the context of deterministic structural change, but their use in the presence of stochastic time variation is novel. The proposed inference methods have desirable properties such as consistency and asymptotic normality and allow a tractable studentization. In extensive Monte Carlo and empirical studies, we find that the methods exhibit very good small sample properties and can shed light on important empirical issues such as the evolution of inflation persistence and the purchasing power parity (PPP) hypothesis.     

Generalized cumulative residual entropy and record values

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts.     

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

Maximum score estimation of the stochastic utility model of choice

This paper introduces a class of robust estimators of the parameters of a stochastic utility function. Existing maximum likelihood and regression estimation methods require the assumption of a particular distributional family for the random component of utility. In contrast, estimators of the ‘maximum score’ class require only weak distributional assumptions for consistency. Following presentation and proof of the basic consistency theorem, additional results are given. An algorithm for achieving maximum score estimates and some small sample Monte Carlo tests are also described.     

Another look at risk apportionment

This paper presents a general result on the random selection of an element from an ordered sequence of risks and uses this result to derive additive and cross risk apportionment. Preferences favoring an improvement of the sampling distribution in univariate or bivariate first-order stochastic dominance are those exhibiting additive or cross risk apportionment. The univariate additive and multiplicative risk apportionment concepts are then related to the notion of bivariate cross risk apportionment by viewing the single-attribute utility function of an aggregate position (sum or product of attributes) as a 2-attribute utility function. The results derived in the present paper allow one to further explore the connections between the different concepts of risk apportionment proposed so far in the literature.     

On the possibility of extinction in a class of Markov processes in economics

We analyze the possibility of eventual extinction of a replenishable economic asset (natural resource or capital) whose stocks follow a stationary Markov process with zero as an absorbing state. In particular, the stochastic process of stocks is determined by a given sequence of i.i.d. random variables with bounded support and a positive-valued transition function that maps the current level of the stock and the current realization of the random variable to the next period’s stock. Such processes arise naturally in stochastic dynamic models of economic growth and exploitation of natural resources. Under a minimal set of assumptions, the paper identifies conditions for almost sure extinction from all initial stocks as well as conditions under which the stocks enter every neighborhood of zero infinitely often almost surely. Our results emphasize the crucial role played by the nature of the transition function under the worst realization of the random shock and clarifies the role of the “average” rate of growth in the context of extinction.     

Life Expectancies for Small Areas: A Bayesian Random Effects Methodology

Monitoring small area contrasts in life expectancy is important for health policy purposes but subject to difficulties under conventional life table analysis. Additionally, the implicit model underlying conventional life table analysis involves a highly parametrized fixed effect approach. An alternative strategy proposed here involves an explicit model based on random effects for both small areas and age groups. The area effects are assumed to be spatially correlated, reflecting unknown mortality risk factors that are themselves typically spatially correlated. Often mortality observations are disaggregated by demographic category as well as by age and area, e.g. by gender or ethnic group, and multivariate area and age random effects will be used to pool over such groups. A case study considers variations in life expectancy in 1 118 small areas (known as wards) in Eastern England over a five-year period 1999–2003. The case study deaths data are classified by gender, age, and area, and a bivariate model for area and age effects is therefore applied. The interrelationship between the random area effects and two major influences on small area life expectancy is demonstrated in the study, these being area socio-economic status (or deprivation) and the location of nursing and residential homes for frail elderly.     

A residual inaccuracy measure based on the relevation transform

Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given.     

Input–Output Models with Stochastic Matrices and Time Lags

In this paper, the random balanced growth factor to forward-lag-type and mixed-lag-type input–output (IO) models is considered. The instability of IO and capital matrices is taken into account by stochastic methods. Exact and approximate characteris-tics of stochastic solutions are given.     

On parameter estimation of partly observed bilinear discrete-time stochastic systems

The parameter estimation problem of a partly observed nonlinear discrete-time stochastic system is considered. The unobserved component of the system is a q-dimensional stable autoregressive process of the pth order with random parameters, observed in the presence of multiplicative and additive noises. The distributions of all the noises of the system are supposed to be unknown. The problem is to estimate the mean of the drifting parameters of the object and variances of the additive noises of the system. Asymptotic correlation estimators of all these parameters are investigated and sequential estimators with given mean square accuracy of the mean of the drifting autoregressive parameters are obtained.     

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.