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In general F-tests (including Chow tests) can be used to test for changes in a regression model over time. F-tests can be constructed using the TEST command and this is in the Chapter 8 of the SHAZAM 11 manual under Hypothesis Testing and Confidence Intervals here: SHAZAM 11 Manual.

The Chow test can be calculated using option CHOWTEST (see page 199).

See page 305 in the manual within the section on Pooled Cross Section Time Series models. The POOL command outputs the Lagrange Multiplier statistic for testing cross-section heteroskedasticity. The Breusch-Pagan LM test is also printed out. The manual provides some guidance on their meaning.

A Hausman test can be used to compare two estimators - a Fixed Effects estimator (consistent always) and a Random effects estimator which is consistent only under the Null of the random effect being uncorrelated with the X-variables. An example using the Hausman Specification Test can be found here: Hausman Test