Estimation of Dynamic Models with Error Components
01 Sep 1981-Journal of the American Statistical Association (Taylor & Francis Group)-Vol. 76, Iss: 375, pp 598-606
TL;DR: In this paper, observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit.
Abstract: Observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit. Different assumptions about the initial conditions are (a) initial state fixed, (b) initial state random, (c) the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed, and (d) the unobserved individual effect independent of the unobserved dynamic process with initial value random. Asymptotic properties of the maximum likelihood and “covariance” estimators are obtained when T → ∞ and when N → ∞. The relationship between the pseudo and conditional maximum likelihood estimators is clarified. A simple consistent estimator that is independent of the initial conditions and the way in which T or N → ∞ is also suggested.
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TL;DR: In this article, the generalized method of moments (GMM) estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables.
Abstract: This paper presents specification tests that are applicable after estimating a dynamic model from panel data by the generalized method of moments (GMM), and studies the practical performance of these procedures using both generated and real data. Our GMM estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables. We propose a test of serial correlation based on the GMM residuals and compare this with Sargan tests of over-identifying restrictions and Hausman specification tests.
26,580 citations
TL;DR: In this paper, two alternative linear estimators that are designed to improve the properties of the standard first-differenced GMM estimator are presented. But both estimators require restrictions on the initial conditions process.
19,132 citations
TL;DR: The pooled mean group estimator (PMG) estimator as discussed by the authors constrains long-run coefficients to be identical but allows short run coefficients and error variances to differ across groups.
Abstract: It is now quite common to have panels in which both T, the number of time series observations, and N, the number of groups, are quite large and of the same order of magnitude. The usual practice is either to estimate N separate regressions and calculate the coefficient means, which we call the mean group (MG) estimator, or to pool the data and assume that the slope coefficients and error variances are identical. In this article we propose an intermediate procedure, the pooled mean group (PMG) estimator, which constrains long-run coefficients to be identical but allows short-run coefficients and error variances to differ across groups. We consider both the case where the regressors are stationary and the case where they follow unit root processes, and for both cases derive the asymptotic distribution of the PMG estimators as T tends to infinity. We also provide two empirical applications: Aggregate consumption functions for 24 Organization for Economic Cooperation and Development economies over th...
4,592 citations
TL;DR: In this article, the authors present a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed.
2,774 citations
TL;DR: This paper reviewed econometric methods for dynamic panel data models, and presented examples that illustrate the use of these procedures for the analysis of large number of individuals or firms observed for a small number of time periods.
Abstract: This paper reviews econometric methods for dynamic panel data models, and presents examples that illustrate the use of these procedures The focus is on panels where a large number of individuals or firms are observed for a small number of time periods, typical of applications with microeconomic data The emphasis is on single equation models with autoregressive dynamics and explanatory variables that are not strictly exogenous, and hence on the Generalised Method of Moments estimators that are widely used in this context Two examples using firm-level panels are discussed in detail: a simple autoregressive model for investment rates; and a basic production function
2,200 citations
Cites methods from "Estimation of Dynamic Models with E..."
...The basic first-differenced Two Stage Least Squares (2SLS) estimator for the AR(1) panel data model was proposed by Anderson and Hsiao (1981, 1982) , initially as a way of obtaining a consistent starting value for computation of Maximum Likelihood estimators....
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...The basic first-differenced Two Stage Least Squares (2SLS) estimator for the AR(1) panel data model was proposed by Anderson and Hsiao (1981, 1982), initially as a way of obtaining a consistent starting value for computation of Maximum Likelihood estimators....
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Book•
01 Jan 1971
TL;DR: The Wiley Classics Library as discussed by the authors is a collection of books that have become recognized classics in their respective fields, including some of the most important works of the 20th century in mathematics.
Abstract: The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 --Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory--Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Fsehbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Gerald d. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I--Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II--Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1--Power Series--lntegration--Conformal Mapping--Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2--Special Functions--Integral Transforms--Asymptotics--Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3--Discrete Fourier Analysis--Cauchy Integrals--Construction of Conformal Maps--Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochetadt Integral Equations Erwin O. Kreyezig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation All Hasan Nayfeh Introduction to Perturbation Techniques Emanuel Parzen Modern Probability Theory and Its Applications P.M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory, Volume I--Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II--Automorphic and Abelian integrals C. L Siegel Topics in Complex Function Theory, Volume III--Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems
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