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SAS/Ets 9.22 User's Guide 137. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 1352 F Chapter 19 The PANEL Procedure where r is a T x T matrix with elements tyts as follows j ÿ t - if t - s m Cov eit eis 0 if t s m where ÿ k 02 P k ajaj k for k t s . For the definition of In It Jn and Jr see the section Fuller and Battese s Method on page 1340. The covariance matrix denoted by V can be written in the form m V T2 In Jt o Jn It X In0 k 0 where V 0 It and for k 1 . m V 0 is a band matrix whose kth off-diagonal elements are 1 s and all other elements are 0 s. Thus the covariance matrix of the vector of observations y has the form m 3 Var y X vk vk k 1 where v1 o2 V2 Ob Vk k 3 k 3 . m 3 Vi In 0Jt V2 Jn It Vk In t 30 k 3 . m 3 The estimator of 0 is a two-step GLS-type estimator that is GLS with the unknown covariance matrix replaced by a suitable estimator of V. It is obtained by substituting Seely estimates for the scalar multiples Vk k 1 2 . . m 3. Seely 1969 presents a general theory of unbiased estimation when the choice of estimators is restricted to finite dimensional vector spaces with a special emphasis on quadratic estimation of functions of the form 1 St Vi. The parameters Vi i 1 . n are associated with a linear model E y X fl with covariance matrix i 1 Vi Vi where Vi i 1 . n are real symmetric matrices. The method is also discussed by Seely 1970a 1970b and Seely and Zyskind 1971 . Seely and Soong 1971 consider the MINQUE principle using an approach along the lines of Seely 1969 . Dynamic Panel Estimator For an example on dynamic panel estimation using GMM option see Example 19.6 The Cigarette Sales Data Dynamic Panel Estimation with GMM on page 1390. Dynamic Panel Estimator F 1353 Consider the case of the following general model yit 1 1 S Plyi t-l k rxilk yi at fit The x variables can include ones that are correlated or uncorrelated to the individual effects predetermined or strictly exogenous. The y and a are cross-sectional and time series fixed effects respectively. Arellano and Bond 1991 show that it is possible to define conditions
