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On The Estimation Of Covariance Matrices Using Panel Data Artificial Regressions
Abstract
The use of artificial regressions to compute the variance of the difference of pairs of panel data estimators that cannot be ranked in terms of efficiency is considered. It is illustrated how it is possible to get (asymtotically) valid estimators of covariance matrices for differences between estimators when the assumption that the error term in the auxiliary model is IID is violated. We distinguish two possible deviations, one leading only to a non-spherical-within groups covariance matrix and the second leading to a non-spherical-between-groups covariance matrix also. It is shown to what extent the use of an artificial regression with panel data can lead to a robust estimator of the covariance matrix in the first case whereas it leads to a non valid estimator in the second. An alternative step by step procedure is presented. Keywords; artificial regression models, panel data, covariance matrices estimates, hypothesis testing. JEL Classification: C12, C13, C23
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Associated with every popular nonlinear estimationmethod is at least ont "artificial" linear regression. We define an artificial regression in terms of three conditions that it must satisfy. Then we show how artificial regressions can be useful for numerical optimization, testing hypotheses, and computing paremeter estimates. Several existing artificial regressions are discussed and are shown to satisfy the defining conditions, and a new artificial regression for regression models with heteroskedasticity of unknown form is introduced.
The classical econometric approach to modelling has been to specify a model up to a finite-dimensional parameter vector, and estimation and testing techniques have been widely used on these finite-dimensional parameter spaces. In the last fifteen years or so however, new methods have been developed to allow more flexible models which utilise infinite-dimensional parameters. Simultaneously, methods of moments estimation have also become more widely used and applied. In this book, the author provides a survey of these modern techniques and how they are applied to limited dependent variable (LDV) models. As well as covering many classical approaches, the topics covered include: instrumental variable estimation, the generalized method of moments, extremum estimators, methods of simulated moments, minimum distance estimation, nonparametric density and regression function estimation, and semiparametric methods for LDV. As a result, many graduate students and research workers will appreciate this up-to-date account. There is an appendix that describes the use of the software package GAUSS to implement these methods in conjunction with some real data sets.
Recent advances in establishing the nature and scope of estimators in econometrics have shed more light on the importance of instrumental variables. In this book, the authors argue that such methods may be regarded as a strong organizing principle for a wide variety of estimation and hypothesis testing problems in econometrics and statistics. In support of this claim they present and develop the methodology of instrumental variables in its most general and explanatory form. They show, for instance, that techniques commonly used to handle simultaneity and related problems can be reduced to one of two generic variables of instrumental variables estimators, allowing them to explore further the conditions under which different proposed estimators are efficient.
Using the result that under the null hypothesis of no misspecification an asymptotically efficient estimator must have zero asymptotic covariance with its difference from a consistent but asymptotically inefficient estimator, specification tests are devised for a number of model specifications in econometrics. Local power is calculated for small departures from the null hypothesis. An instrumental variable test as well as tests for a time series cross section model and the simultaneous equation model are presented. An empirical model provides evidence that unobserved individual factors are present which are not orthogonal to the included right-hand-side variable in a common econometric specification of an individual wage equation.
Discussion Paper, n. 99a04
- G R E Q A M Davidson
Davidson, G.R.E.Q.A.M. Discussion Paper, n. 99a04. R. and MacKinnon,J.G. (1998). Artificial Regressions,
Testing the Exogeneity Assumption in Panel Data Models with " Non Classical " Disturbances, Discussion Paper in Economics and Econometrics
- O 'brien
- R Patacchini
O'Brien, R. and Patacchini, E. (2003). Testing the Exogeneity Assumption
in Panel Data Models with " Non Classical " Disturbances, Discussion Paper
in Economics and Econometrics, University of Southampton, n. 0302.