Comments on the econometrics of female labor supply and children by alice and masao nokalnura

Abstract

The present paper focuses attention on the sensitivity of technical inefficiency to most commonly used one‐sided distributions of the inefficiency error term, namely the truncated normal, the half‐normal, and the exponential distributions. A generalized version of the half‐normal, which does not embody the zero‐mean restriction, is also explored. For each distribution, the likelihood function and the counterpart of the estimator of technical efficiency are explicitly stated (Jondrow, J., Lovell, C. A. K., Materov, I. S., Schmidt, P. ([1982] Jondrow, J., Lovell, C. A. K., Materov, I. S. and Schmidt, P. 1982. On estimation of technical inefficiency in the stochastic frontier production function model. J. Econometrics, 19: 233–238. [Crossref], [Web of Science ®] , [Google Scholar]), On estimation of technical inefficiency in the stochastic frontier production function model, J. Econometrics19:233–238). Based on our panel data set, related to Tunisian manufacturing firms over the period 1983–1993, formal tests lead to a strong rejection of the zero‐mean restriction embodied in the half normal distribution. Our main conclusion is that the degree of measured inefficiency is very sensitive to the postulated assumptions about the distribution of the one‐sided error term. The estimated inefficiency indices are, however, unaffected by the choice of the functional form for the production function.     

Semiparametric Estimation of Stochastic Production Frontier Models

This article extends the linear stochastic frontier model proposed by Aigner, Lovell, and Schmidt to a semiparametric frontier model in which the functional form of the production frontier is unspecified and the distributions of the composite error terms are of known form. Pseudolikelihood estimators of the parameters characterizing the two error terms of the model are constructed based on kernel estimation of the conditional mean function. The Monte Carlo results show that the proposed estimators perform well in finite samples. An empirical application is presented. Extensions to a partially linear frontier function and to more flexible one-sided error distributions than the half-normal are discussed     

The “wrong skewness” problem in stochastic frontier models: A new approach

Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generalizing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and nondegenerate efficiency measures. We discuss the statistical properties of the model, and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958–2005 and show that for a number of years our model suggests technical efficiencies well below the frontier while the classical one estimates no inefficiency in those years.     

Distribution of cost inefficiency in stochastic frontier approach: evidence from Spanish banking

The aim of the paper is to demonstrate the appropriateness of an a priori analysis to determine the distributional assumption of the inefficiency term in a stochastic frontier model. To this end, theoretical distributions of estimated inefficiency were obtained when the inefficiency term is assumed to be distributed as a half normal and an exponential in a cost frontier model. Comparisons of such theoretical distributions with the respective cost inefficiency estimators using the goodness of fit test allow selecting the most appropriate distributional assumption. The application on three data sets of Spanish banking system in 2009 demonstrated the relevance of the research question. First, the results of estimated cost inefficiency with a half normal assumption are larger than with an exponential distribution significantly. Besides, half normal assumption was rejected and exponential was not rejected as the most appropriate distribution of inefficiency term in Spanish banking data set. However, the adjustment of saving banks data had been better with the former distribution than the latter. In the case of banks, any distribution results appropriate. To sum up, this work demonstrate that the distributional assumption on inefficiency term in Stochastic Frontier Approach must be established in a justified way, as it can significantly bias the results of estimated inefficiency and therefore, influences improving policies and strategies in the Spanish banking sector.     

On the Detection of Contemporaneous Relationships Among Multiple Time Series

A study is carried out of a sampling from a half-normal and exponential distributions to develop a test of hypothesis on the mean. Although these distributions are similar, the corresponding uniformly most paerful test statistics are different. The exact distributions of these statistics my be written in terms of the incomplete gamma function. If the experimental data my be fitted by either distributions, it is advisable to carryout the test based on the half-normal distribution as it is generally more powerful than the one based on the exponential one.     

Inferences from Cross-Sectional,Stochastic Frontier Models

Conventional approaches for inference about efficiency in parametric stochastic frontier (PSF) models are based on percentiles of the estimated distribution of the one-sided error term, conditional on the composite error. When used as prediction intervals, coverage is poor when the signal-to-noise ratio is low, but improves slowly as sample size increases. We show that prediction intervals estimated by bagging yield much better coverages than the conventional approach, even with low signal-to-noise ratios. We also present a bootstrap method that gives confidence interval estimates for (conditional) expectations of efficiency, and which have good coverage properties that improve with sample size. In addition, researchers who estimate PSF models typically reject models, samples, or both when residuals have skewness in the “wrong” direction, i.e., in a direction that would seem to indicate absence of inefficiency. We show that correctly specified models can generate samples with “wrongly” skewed residuals, even when the variance of the inefficiency process is nonzero. Both our bagging and bootstrap methods provide useful information about inefficiency and model parameters irrespective of whether residuals have skewness in the desired direction.     

企业技术效率的影响分析

 本文以上海市166家大中型企业五年的面板数据为研究对象,设定两种不同的生产函数和两种误差分布,利用随机前沿方法分别进行了技术效率的估计。我们发现不同测算方法的结果差异不大,且对企业的评价具有一致性。结果表明上海市工业企业的技术效率整体水平不高。通过研究影响企业技术效率的外生性因素,发现企业的所有制结构、规模、R&D经费支出与R&D人员投入、资本密集程度和企业的垄断程度等因素都对上海市工业企业的技术效率水平具有显著影响。基于研究结果,我们给出了提高企业技术效率的一些建议。     

General properties for the beta extended half-normal model

We formulate and study a four-parameter lifetime model called the beta extended half-normal distribution. This model includes as sub-models the exponential, extended half-normal and half-normal distributions. We derive expansions for the new density function which do not depend on complicated functions. We obtain explicit expressions for the moments and incomplete moments, generating function, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. In addition, the model parameters are estimated by maximum likelihood. We provide the observed information matrix. The new model is modified to cope with possible long-term survivors in the data. The usefulness of the new distribution is shown by means of two real data sets.     

A new weighted distribution as an extension of the generalized half-normal distribution with applications

In this study, a new extension of generalized half-normal (GHN) distribution is introduced. Since this new distribution can be viewed as weighted version of GHN distribution, it is called as weighted generalized half-normal (WGHN) distribution. It is shown that WGHN distribution can be observed as a single constrained and hidden truncation model. Therefore, the new distribution is more flexible than the GHN distribution. Some statistical properties of the WGHN distribution are studied, i.e. moments, cumulative distribution function, hazard rate function are derived. Furthermore, maximum likelihood estimation of the parameters is considered. Some real-life data sets taken from the literature are modelled using the WGHN distribution. It is seen that for these data sets the WGHN distribution provides better fitting than the GHN and slashed generalized half-normal (SGHN) distributions.     

An extension of the generalized half-normal distribution

In this paper we propose an extension of the generalized half-normal distribution studied in Cooray and Ananda (Commun Stat 37:1323–1337, 2008). This new distribution is defined by considering the quotient of two random variables, the one in the numerator being a generalized half normal distribution and the one in the denominator being a power of the uniform distribution on \((0,1)\) , respectively. The resulting distribution has greater kurtosis than the generalized half normal distribution. The density function of this more general distribution is derived jointly with some of its properties and moments. We discuss stochastic representation, maximum likelihood and moments estimation. Applications to real data sets are reported revealing that the proposed distribution can fit real data better than the slashed half-normal, generalized half-normal and Birnbaum–Saunders distributions.     

Sample size selection in clinical trials when population means are subject to a partial order: one-sided ordered alternatives

The statistical methodology under order restriction is very mathematical and complex. Thus, we provide a brief methodological background of order-restricted likelihood ratio tests for the normal theoretical case for the basic understanding of its applications, and relegate more technical details to the appendices. For data analysis, algorithms for computing the order-restricted estimates and computation of p-values are described. A two-step procedure is presented for obtaining the sample size in clinical trials when the minimum power, say 0.80 or 0.90 is specified, and the normal means satisfy an order restriction. Using this approach will result in reduction of 14-24% in the sample size required when one-sided ordered alternatives are used, as illustrated by several examples.     

Exploring the distribution for the estimator of Rosenthal's ‘fail-safe’ number of unpublished studies in meta-analysis

The present article discusses the statistical distribution for the estimator of Rosenthal's ‘file-drawer’ number N_R, which is an estimator of unpublished studies in meta-analysis. We calculate the probability distribution function of N_R. This is achieved based on the central limit theorem and the proposition that certain components of the estimator N_R follow a half-normal distribution, derived from the standard normal distribution. Our proposed distributions are supported by simulations and investigation of convergence.     

On the Joint Estimation of Heterogeneous Technologies,Technical, and Allocative Inefficiency

In this article, we provide a semiparametric approach to the joint measurement of technical and allocative inefficiency in a way that the internal consistency of the specification of allocative errors in the objective function (e.g., cost function) and the derivative equations (e.g., share or input demand functions) is assured. We start from the Cobb–Douglas production and shadow cost system. We show that the shadow cost system has a closed-form likelihood function contrary to what was previously thought. In turn, we use the method of local maximum likelihood applied to a system of equations to obtain firm-specific parameter estimates (which reveal heterogeneity in production) as well as measures of technical and allocative inefficiency and its cost. We illustrate its practical application using data on U.S. electric utilities.     

Cox Regression with Covariate Measurement Error

This article deals with parameter estimation in the Cox proportional hazards model when covariates are measured with error. We consider both the classical additive measurement error model and a more general model which represents the mis-measured version of the covariate as an arbitrary linear function of the true covariate plus random noise. Only moment conditions are imposed on the distributions of the covariates and measurement error. Under the assumption that the covariates are measured precisely for a validation set, we develop a class of estimating equations for the vector-valued regression parameter by correcting the partial likelihood score function. The resultant estimators are proven to be consistent and asymptotically normal with easily estimated variances. Furthermore, a corrected version of the Breslow estimator for the cumulative hazard function is developed, which is shown to be uniformly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process. Simulation studies indicate that the asymptotic approximations work well for practical sample sizes. The situation in which replicate measurements (instead of a validation set) are available is also studied.     

A Comparison Between Maximum Likelihood and Bayesian Estimation of Stochastic Frontier Production Models

In this paper, the finite sample properties of the maximum likelihood and Bayesian estimators of the half-normal stochastic frontier production function are analyzed and compared through a Monte Carlo study. The results show that the Bayesian estimator should be used in preference to the maximum likelihood owing to the fact that the mean square error performance is substantially better in the Bayesian framework.     

Objective Bayesian Inference for the Half-Normal and Half-t Distributions

In this article, Bayesian inference for the half-normal and half-t distributions using uninformative priors is considered. It is shown that exact Bayesian inference can be undertaken for the half-normal distribution without the need for Gibbs sampling. Simulation is then used to compare the sampling properties of Bayesian point and interval estimators with those of their maximum likelihood based counterparts. Inference for the half-t distribution based on the use of Gibbs sampling is outlined, and an approach to model comparison based on the use of Bayes factors is discussed. The fitting of the half-normal and half-t models is illustrated using real data on the body fat measurements of elite athletes.     

SEMIPARAMETRIC ESTIMATION OF THE ERROR DISTRIBUTION IN MULTIVARIATE REGRESSION USING COPULAS

A semiparametric method is developed to estimate the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonparametric part of the method treats the marginal distributions of the error term as unknown, and estimates them using suitable empirical distribution functions. Then the dependence parameter is estimated by either maximizing a pseudolikelihood or solving an estimating equation. It is shown that this estimator is asymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric method is better than the parametric ones available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic efficiency as a result of the estimation of regression parameters. An empirical example on portfolio management is used to illustrate the method.     

Estimating technical efficiency with non-neutral shift of the frontier

In the literature, technical efficiency is measured as the ratio of the observed output to potential output. Although there is no a priori theoretical reasoning, in the stochastic framework of measuring technical efficiency, potential output has been conventionally assumed as a neutral shift from observed output, owing solely to a larger intercept term in the frontier production function and without change in the input response coefficients. The objective of this paper is to propose and apply a method to measure technical efficiency without the above assumption. Furthermore, this methodology does not require the restrictive assumption of a particular distribution for the efficiency-related error term, as has been the case until now in the stochastic production function literature. A random sample of farmers from Madurai district in Tamil Nadu, India, was used. The analysis revealed substantial variation in the farm-specific input response coefficients between farms, which means that the contributions of individual inputs to the output differ from farm to farm, because the methods of application of the individual inputs vary. The frontier production function, which defines the potential of a technology, is determined by the highest values of the coefficients of each individual input which may come from one or more farms. Farm-specific frontier functions generally showed a considerable potential for improving the technical.performance of each input.     

Numerical Algorithms Group Manual Mark 7

We consider the estimation of the 90 and 95 percentiles of a normal distribution and also the construction of one-sided 90% and 95% -normal ranges. Three methods are proposed -the sample percentile method, and two based on kernel estimates of the density function using Fryer's method and the leaving-one-out method for choosing a smoothing parameter.

A simulation study compares the methods in terms of bias, variance and mean square error of the population percentile estimates and of the eovers of the consequent normal ranges.