TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 135

SAS/Ets User's Guide 135. 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 | 1332 F Chapter 19 The PANEL Procedure The total number of observations M pN 1 Ti. For the balanced data case Ti T for all i. The MxM covariance matrix of uit is denoted by V. Let X and y be the independent and dependent variables arranged by cross section and by time within each cross section. Let Xs be the X matrix without the intercept. All other notation is specific to each section. The One-Way Fixed-Effects Model The specification for the one-way fixed-effects model is uit Yi eit where the yi s are nonrandom parameters to be estimated. Let Qo diagCE . with Jt Jr. Ti and Er It Jr where Jr is a matrix of Ti ones. The matrix Qo represents the within transformation. In the one-way model the within transformation is the conversion of the raw data to deviations from a cross section s mean. The vector xit is a row of the general matrix Xs where the subscripted 5 implies the constant column of ones is missing. Let Xs Q0Xs and y Qoy. The estimator of the slope coefficients is given by 0 0 s Xs Xs 1XS y Once the slope estimates are in hand the estimation of an intercept or the cross-sectional fixed effects is handled as follows. First you obtain the cross-sectional effects Yi yi- - 3 sXi- for i 1 . N If the NOINT option is specified then the dummy variables coefficients are set equal to the fixed effects. If an intercept is desired then the ith dummy variable is obtained from the following expression Di Yi - Yn for i 1 . N - 1 The intercept is the Nth fixed effect yN. The within model sum of squared errors is SSE X E yt - Yi - Xs s 2 i 1 t 1 The estimated error variance can be written n SSE M - N - K - 1 Alternatively an equivalent way to express the error variance is f2 U0QoU M - N - K - 1 The One-Way Fixed-Effects Model F 1333 where the residuals u are given by u Im jM j M M y Xs fls if there is an intercept and by u y Xs s if there is not. The drawback is that the formula changes but the results do not with the inclusion of a constant. The variance covariance matrix .

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