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POOLED CROSS SECTION TIME SERIES MODELS

Pooled Cross Section Time Series Models refers to the method of combining time series (quarterly) data with cross sectional (state level) data. This method has the advantage of capturing a larger portion of the variability in the data (making the parameter estimates more robust) while allowing a framework to be designed to test a variety of hypotheses.

For example, lets say we are interested in developing a forecasting model to explain unit sales for the Southeast region as a function of disposable income, product price, average age of the adult population, and advertising dollars. Given 36 quarters of history, you could build an regional model using 36 data points and forecast the total unit sales for the Southeast. Alternatively, you could construct a regression model for the 9 state region and use the data for each state as individual cross sections - a model that would have 36 * 9 = 324 total observations. By including dummy variables for each state, your model could be made to describe differentials at the state level rather than simple at the region level.

Estimation for the Pooled Cross-Section Time Series Model is generally accomplished through a Generalized Least Squares (GLS) procedure. The estimation procedure often suggested for this type of data is referred to as the KMENTA [1986] Model. The pooling technique described by KMENTA employs a set of assumptions on the disturbance covariance matrix that gives a cross-sectionally heteroscedastic and timewise autoregressive model. In general, the procedure is accomplished in four steps:

* Ordinary Least Squares is used to estimate preliminary coefficients and residuals needed in subsequent steps.

* The residuals are used to compute autocorrelations throughout the cross- sections.

* The auto-correlation estimates are used to transform the observations and OLS is then applied. The error variances and covariances are estimated from the residuals of the transformed model.

* The GLS estimator is obtained and certain assumptions are made as to the full or partial use of the GLS Phi matrix.


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