Simultaneous equations with error components

In this paper we derive a limited as well as a full information estimator for the structural parameters of a simultaneous equations model with error components. Under this model, the gain in efficiency by performing these estimators rather than the classical two-stage and three-stage least squares procedures is demonstrated. It is shown that the full information estimator will reduce to the limited information estimator when the disturbances of different structural equations are uncorrelated with each other but not necessarily when all structural equations are just identified. This is different from the analogous situation in the classical case.     

Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach

In this paper, we propose simulation-based Bayesian inference procedures in a cost system that includes the cost function and the cost share equations augmented to accommodate technical and allocative inefficiency. Markov chain Monte Carlo techniques are proposed and implemented for Bayesian inferences on costs of technical and allocative inefficiency, input price distortions and over- (under-) use of inputs. We show how to estimate a well-specified translog system (in which the error terms in the cost and cost share equations are internally consistent) in a random effects framework. The new methods are illustrated using panel data on U.S. commercial banks.     

Some aspects of bivariate regression subject to linear constraints

This paper considers a two-equation linear model when a subset of the parameters in one of the equations is subject to zero constraints. Inference procedures are presented both in the Bayesian and sampling theory framework. Specifically, posterior distributions and confidence distributions of the parameters, as well as various test procedures, are derived and illustrated with examples. The effect of the zero constraints on these procedures are discussed, and a comparison of the Bayesian with the sampling results is given.     

灰色预测模型在公路货运量预测中的应用

论述了灰色预测模型在公路货运量预测中的应用技术、方法与程序。该方法利用了累加生成手段和微分方程描述的灰色模型,与目前常规货运量预测理论和模型相比,可有效地处理小样本、贫信息的不确定系统,并在一定预测时段内具有良好的预测精度和实用性。     

Multivariate residual‐based finite‐sample tests for serial dependence and ARCH effects with applications to asset pricing models

In this paper, we propose several finite‐sample specification tests for multivariate linear regressions (MLR). We focus on tests for serial dependence and ARCH effects with possibly non‐Gaussian errors. The tests are based on properly standardized multivariate residuals to ensure invariance to error covariances. The procedures proposed provide: (i) exact variants of standard multivariate portmanteau tests for serial correlation as well as ARCH effects, and (ii) exact versions of the diagnostics presented by Shanken ( 1990 ) which are based on combining univariate specification tests. Specifically, we combine tests across equations using a Monte Carlo (MC) test method so that Bonferroni‐type bounds can be avoided. The procedures considered are evaluated in a simulation experiment: the latter shows that standard asymptotic procedures suffer from serious size problems, while the MC tests suggested display excellent size and power properties, even when the sample size is small relative to the number of equations, with normal or Student‐t errors. The tests proposed are applied to the Fama–French three‐factor model. Our findings suggest that the i.i.d. error assumption provides an acceptable working framework once we allow for non‐Gaussian errors within 5‐year sub‐periods, whereas temporal instabilities clearly plague the full‐sample dataset. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical inference on seemingly unrelated non‐parametric regression models with serially correlated errors

This article is concerned with the inference on seemingly unrelated non‐parametric regression models with serially correlated errors. Based on an initial estimator of the mean functions, we first construct an efficient estimator of the autoregressive parameters of the errors. Then, by applying an undersmoothing technique, and taking both of the contemporaneous correlation among equations and serial correlation into account, we propose an efficient two‐stage local polynomial estimation for the unknown mean functions. It is shown that the resulting estimator has the same bias as those estimators which neglect the contemporaneous and/or serial correlation and smaller asymptotic variance. The asymptotic normality of the resulting estimator is also established. In addition, we develop a wild block bootstrap test for the goodness‐of‐fit of models. The finite sample performance of our procedures is investigated in a simulation study whose results come out very supportive, and a real data set is analysed to illustrate the usefulness of our procedures.     

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

Single-equation estimators and aggregation restrictions when equations have the same sets of regressors

It is well known that linear equations subject to cross-equation aggregation restrictions can be ‘stacked’ and estimated simultaneously. However, if every equation contains the same set of regressors, a number of single-equation estimation procedures can be employed. The applicability of ordinary least squares is widely recognized but the article demonstrates that the class of applicable estimators is much broaders than OLS. Under specified conditions, the class includes instrumental variables, generalized least squares, ridge regression, two-stage least squares, k-class estimators, and indirect least squares. Transformations of the original equations and other related matters are discussed also.     

Multiple imputation of incomplete zero‐inflated count data

Empirical count data are often zero‐inflated and overdispersed. Currently, there is no software package that allows adequate imputation of these data. We present multiple‐imputation routines for these kinds of count data based on a Bayesian regression approach or alternatively based on a bootstrap approach that work as add‐ons for the popular multiple imputation by chained equations (mice ) software in R (van Buuren and Groothuis‐Oudshoorn , Journal of Statistical Software, vol. 45, 2011, p. 1). We demonstrate in a Monte Carlo simulation that our procedures are superior to currently available count data procedures. It is emphasized that thorough modeling is essential to obtain plausible imputations and that model mis‐specifications can bias parameter estimates and standard errors quite noticeably. Finally, the strengths and limitations of our procedures are discussed, and fruitful avenues for future theory and software development are outlined.     

A semi-parametric Bayesian approach to the instrumental variable problem

We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components. We demonstrate that this procedure is both feasible and sensible using actual and simulated data. Sampling experiments compare inferences from the non-parametric Bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics. When errors are non-normal, our procedure is more efficient than standard Bayesian or classical methods.     

Local and global identification and strong consistency in time series models

We define local and global identification with respect to a sequence of criterion functions and show how global identification is related to a proof of strong consistency. We also show that local identification of the parameters is needed to ensure that common estimation procedures are well defined. We illustrate the results by an application to the simultaneous ARMAX model. Finally, we motivate and generalize a local identification result for dynamic, simultaneous equations models given by Hatanaka (1976).     

Efficient minimum distance estimation with multiple rates of convergence

This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations.Possible applications include econometric problems with two dimensions of asymptotics, due to trimming, tail estimation, infill asymptotic, social interactions, kernel smoothing or any kind of regularization.     

A Note on Properties of Iterative Procedures of Asymptotic Inference

This note deals with the article 'On iterative procedures of asymptotic inference' by K.O. DZHAPARIDZE (1983), in which an informal discussion is given on performing an unconstrained maximization or solving non–linear equations of statistics by iterative methods with the quadratic termination property. It discusses the theorem that if a maximized function, e.g. the likelihood function, is asymptotically quadratic, then for asymptotically efficient inference finitely many iterations are needed.
It is argued here that the theory still applies if certain well specified inexact (hence computationally cheaper) line searches are used in the optimization.     

Several efficient two-step estimators for the dynamic simultaneous equations model with autoregressive disturbances

Several asymptotically efficient methods are suggested on both the full and the limited information approach to estimate the simultaneous equations model in which the lagged endogenous variables and the autoregressive disturbances coexist. They are two-step procedures and do not involve iterations. A method is suggested also for the case where any portion of the autoregressive parameter matrix is specified to be zero. Since the consistency and efficiency depend upon the asymptotic, local identifiability, the necessary and sufficient condition is derived for it. It does not depend on the exclusion of the lagged endogenous variables.     

A note on the estimation of seemingly unrelated regression systems

In a system of simultaneous equations, one obtains the same results for the overidentified equations by applying three-stage least squares to those equations alone as one would obtain by applying three-stage least squares to the entire system. This paper obtains an analogous result for a system of seemingly unrelated regressions. In doing so it generalizes earlier results of several other authors.     

Legendre小波求解Fredholm-Volterra方程

本文运用Legendre小波求解Fredholm-Volterra方程,建立了Legendre小波的算子矩阵,利用Legendre小波方法求解积分方程的基本思想是将求解积分方程的问题转化为求解一组代数方程组的问题。     

Correction of errors in Vetschera's (2004) model of behavioral uncertainty and investment

Modelling of behavioural uncertainty has been a concern for researchers for some time. This paper briefly reviews modelling related to uncertainty and the focuses on the model presented by Vetschera (2004). A model of decision behaviour has been developed in the paper with regard to investment and cooperation taking into account the uncertainty and lack of information. The model is an important contribution for it focuses on situations that are not usual to the normal principle agent problems. The present review however reveals some errors in the paper. Sometimes errors may appear editorial but the same errors may lead the interested reader or researcher to inappropriate paths, particularly those who may fail to follow an argument or comprehend the underlying meanings of the equations and analytical solutions. In this manner, further work on this important topic may be hindered if researchers accept forms as presented in the paper literally as facts to further work. The main contribution of this paper is that it presents the correct forms of the mathematical aspects and procedures of the Vetschera (2004) paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Deriving benefits from conflict resolution: A macrojustice assessment

Effective conflict resolution procedures serve to minimize dysfunctional effects of conflict and maximize functional effects. In the literature on conflict resolution procedures, the effectiveness of procedures has been evaluated primarily from the perspective of the individual. This article suggests that a system-level analysis of the pattern of outcomes resulting from different conflict resolution procedures is a necessary component in formulating a comprehensive framework for the design and evaluation of conflict resolution systems in organizations. The analytic questions addressed by this study concern associations between resolution procedures and outcome patterns in a system created specifically for conflict resolution within organizations: the grievance system. The pattern of outcomes was found to vary with the conflict resolution procedure. It is suggested that this has important implications for effective conflict resolution systems.