The TSCSREG Procedure

Overview

The TSCSREG (Time Series Cross Section Regression) procedure analyzes a class of linear econometric models that commonly arise when time series and cross-sectional data are combined. The TSCSREG procedure deals with panel data sets that consist of time series observations on each of several cross-sectional units. Such models can be viewed as two-way designs with covariates

$y_{it}=\sum_{k=1}^K{X_{itk}{\beta}_{k}}+u_{it} \hspace*{1em} i=1, { ... }, N;\hspace*{1em} t=1, { ... }, T$

where N is the number of cross sections, T is the length of the time series for each cross section, and K is the number of exogenous or independent variables.

The performance of any estimation procedure for the model regression parameters depends on the statistical characteristics of the error components in the model. The TSCSREG procedure estimates the regression parameters in the preceding model under several common error structures. The error structures and the corresponding methods the TSCSREG procedure uses to analyze them are as follows:

one and two-way fixed and random effects models. If the specification is dependent only on the cross section to which the observation belongs, such a model is referred to as a model with one-way effects. A specification that depends on both the cross section and the time series to which the observation belongs is called a model with two-way effects.
Therefore, the specifications for the one-way model are
$u_{it}={\nu}_{i}+{\epsilon}_{it}$
and the specifications for the two-way model are
$u_{it}={\nu}_{i}+e_{t} + {\epsilon}_{it}$
where ${{\epsilon}_{it}}$ is a classical error term with zero mean and a homoscedastic covariance matrix.
Apart from the possible one-way or two-way nature of the effect, the other dimension of difference between the possible specifications is that of the nature of the cross-sectional or time-series effect. The models are referred to as fixed effects models if the effects are nonrandom and as random effects models otherwise.
first-order autoregressive model with contemporaneous correlation
$u_{it}= {\rho}_{i} u_{i,t-1}+ {\epsilon}_{it}$
The Parks method is used to estimate this model. This model assumes a first-order autoregressive error structure with contemporaneous correlation between cross sections. The covariance matrix is estimated by a two-stage procedure leading to the estimation of model regression parameters by GLS.
mixed variance-component moving average error process
u_it= a_i+ b_t+ e_it

$e_{it}= {\alpha}_{0} {\epsilon}_{t}+ {\alpha}_{1} {\epsilon}_{t-1}+{ ... }+ {\alpha}_{m} {\epsilon}_{t-m}$
The Da Silva method is used to estimate this model. The Da Silva method estimates the regression parameters using a two-step GLS-type estimator.

The TSCSREG procedure analyzes panel data sets that consist of multiple time series observations on each of several individuals or cross-sectional units. The input data set must be in time series cross-sectional form. See Chapter 2, "Working with Time Series Data," for a discussion of how time series related by a cross-sectional dimension are stored in SAS data sets. The TSCSREG procedure requires that the time series for each cross section have the same number of observations and cover the same time range.

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