Pooled Ordinary Least Squares Model

A pooled OLS model is the application of OLS to panel data.

Description

A panel dataset includes repeated measurements of the same units in varying time periods.

A simple approach to modeling with this data is to flatten it first, such that each unit-time pair is treated as a separate sample member. This is now called a pooled model.

The major issues with a pooled model are that the errors are often expected to correlate with the predictors, either within the unit or over time. An example of the former could be local or geographic effects. An example of the latter could be cumulative effects.

At a minimum, there should be examination of whether there is a panel effect in a dataset. Introduce dummy variables for the time periods (or rather T-1 dummy variables for T time periods) and use a joint test of whether the coefficients for those time period parameters are 0. This will not work well for small values of T.

More generally, fixed effects estimators will be more consistent.

Even if panel effects can be ruled out, there remains a potential for serially correlated errors. It is helpful to establish a decomposition for the unit error term ε_it into time-variant and time-invariant components: u_it and α_i. Even assuming the independence of these components, and assuming the independence of time-variant errors over time, The covariance of ε_it and ε_is for time periods t and s will at minimum be Cov(u_it + α_i, u_is + α_i) = Cov(α_i, α_i) = Var(α_i). A random effects model addresses this problem.

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