Tom Wansbeek

Latent variable models in econometrics

Publisher Summary This chapter discusses latent variable models in econometrics. The essential characteristic of a latent variable is revealed by the fact that the system of linear structural equations in which it appears cannot be manipulated so as to express the variable as a function of measured variables only. It discusses that for a linear structural equation system to be called “latent variable model,” there is at least one more independent variable than the number of measured variables. Usage of the term “independent” variable as contrasted with “exogenous” variable, the more common phrase in econometrics, includes measurement errors and the equation residuals themselves. In the functional model, the true values of exogenous variables are fixed variates, and therefore, are best thought of as nuisance parameters that may have to be estimated en route to getting consistent estimates of the primary structural parameters of interest. Finally, restrictions on a models covariance structure, which are commonplace in sociometric and psychometric modeling, also serve to aid identification.

ESTIMATION OF THE ERROR-COMPONENTS MODEL WITH INCOMPLETE PANELS

Abstract The error-components model (ECM) is probably the most frequently used approach to analyze panel data in econometrics. When the panel is incomplete, which is the rule rather than the exception when the data come from large-scale surveys, standard estimation methods cannot be applied. We first discuss estimation in the fixed-effects analogue of the ECM, and then present two estimators (quadratic unbiased and maximum likelihood) for the ECM. Some simulation results are given to assess finite-sample properties and computational burden of the various methods.

Cross-Sectional Dependence in Panel Data Analysis

This article provides an overview of the existing literature on panel data models with error cross-sectional dependence (CSD). We distinguish between weak and strong CSD and link these concepts to the spatial and factor structure approaches. We consider estimation under strong and weak exogeneity of the regressors for both T fixed and T large cases. Available tests for CSD and methods for determining the number of factors are discussed in detail. The finite-sample properties of some estimators and statistics are investigated using Monte Carlo experiments.

An approach ton-mode components analysis

As an extension of Lastovickas four-mode components analysis ann-mode components analysis is developed. Using a convenient notation, both a canonical and a least squares solution are derived. The relation between both solutions and their computational aspects are discussed.

THE INDIVIDUAL WELFARE FUNCTION - A REVIEW

Abstract The Individual Welfare Function (IWF), introduced by Van Praag (1968), is a cardinal utility function. It can be measured by means of survey questions. Since its introduction, the IWF has been used extensively in both theoretical and empirical research. This research is reviewed, with an emphasis on policy applications.

A simple way to obtain the spectral decomposition of variance components models for balanced data

By means of an example it is shown how eigenvalues and eigenvectors of variance components models can be obtained straightforwardly when balanced data are available. Simple asymptotically efficient estimators of the variance components are presented.

GMM estimation in panel data models with measurement error

Griliches and Hausman (J. Econom. 32 (1986) 93) have introduced GMM estimation in panel data models with measurement error. We present a simple, systematic approach to derive moment conditions for such models under a variety of assumptions.

SOME NEW RESULTS ON CORRELATION-PRESERVING FACTOR SCORES PREDICTION METHODS

Anderson and Rubin and McDonald have proposed a correlation-preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables. Green has proposed a correlation-preserving method which minimizes the trace of a residual covariance matrix for factors. Krijnen, Wansbeek and Ten Berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix, and offered an iterative procedure to that effect. In the present paper it is shown that the iterative procedure can be replaced by a closed-form solution. When all unique variances are strictly positive, this solution is the same as McDonalds. The solution coincides with Greens solution in certain special cases, for instance, when the factors are orthogonal.

BLOCK KRONECKER PRODUCTS AND THE VECB OPERATOR

This paper is concerned with two generalizations of the Kronecker product and two related generalizations of the vec operator. It is demonstrated that they pairwise match two different kinds of matrix partition, viz. the balanced and unbalanced ones. Relevant properties are supplied and proved. A related concept, the so-called tilde transform of a balanced block matrix, is also studied. The results are illustrated with various statistical applications of the five concepts studied.

A Note on Spectral Decomposition and Maximum Likelihood Estimation in ANOVA Models with Balanced Data

A simple derivation of the spectral decomposition of the covariance matrix for a general multi-way variance components model is presented. So-called balanced data are assumed to be available. Spectral decomposition is exploited to derive the information matrix and the first-order conditions for the maximum likelihood estimation of the variance components parameters.