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 CrossSection 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 crosssectionally
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 autocorrelation 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.
