Measurement error and latent variables in econometrics (Q2707383)

In applied econometrics researchers are often plagued with data which are either measured with errors or unobservable in practice because the underlying theoretical concept calls for a latent variable, e.g., the permanent income or the potential output in macroeconomics. To deal with the problems when one or more of the regressors in a linear regression model are either measured with errors or are unobservable, a huge amount of literature on this topic helps the researcher to overcome the problems involved in the estimation procedures at least to some extent. In this sense this book also falls into this tradition, but with the remarkable exception that the book is written as a textbook. Therefore, most topics dealt with are not new, although some of the mathematical derivations are. The emphasis is on gaining insight into a wide range of problems and solutions coming from a wide variety of backgrounds. Additionally, the ``it can be shown''-phrase is used only to a minimum extent, but instead most of the results are explicitly derived and/or proved. Due to this structure the reader should have a solid background in econometrics, statistics, matrix algebra and calculus at an intermediate level.NEWLINENEWLINENEWLINEThe book starts with the deficiencies of regression estimates when the regressors are measured with error. Usually, the parameter estimates will be inconsistent, with inconsistency typically towards zero, but this statement does not hold generally. The region where estimators may lie given the true parameter values is characterized. In chapter 3, the question is reversed, and the region where the true regression coefficients may lie given the inconsistent estimator is characterized. Chapter 4 paves the way for a discussion of solutions to the measurement error problem. The authors show that the inconsistency problem is not only due to the choice of estimator, but due to an identification problem which calls for additional information to be able to obtain reliable consistent estimators. The additional information required is discussed in the following two chapters. One sort of additional information relates to sufficient prior knowledge about functions of the parameters, and the other sort concentrates on the form of instrumental variables.NEWLINENEWLINENEWLINEIn chapter 7 the instrumental variables approach is extended to the case of multiple regression equations with measurement error. This extension leads in its simplest form to the factor analysis model with a single factor. The concept of factor analysis is further explored in chapter 8 by introducing restrictions on the parameters of the factor model on the one hand, and by relating the factors to background variables on the other hand. Factor analysis models belong to the class of structural equations models. Structural equations models impose a structure on the covariance matrix of the observations, and estimation takes place by minimizing the distance between the theoretical structure and the observed covariance matrix in some way.NEWLINENEWLINENEWLINEThis approach to estimation is a particular instance of the generalized method of moments (GMM), where parameters are estimated by minimizing the length of a vector function in parameters and statistics. Due to the importance of the GMM-estimator, chapter 9 deals exclusively with the properties of GMM-estimation procedures. Testing and model evaluation in the context of GMM proceeds in chapter 10. The final chapter 11 is devoted to a discussion of nonlinear models.NEWLINENEWLINENEWLINETo sum up, for all researchers who are concerned with measurement error and latent variables the book is highly recommended. It presents the most recent research results in a comprehensive way, derives most of the results and thus, is equally well suited for teaching purposes as well as for applied research.