How to test the degree of an Almon Distributed Lag Model?

A section on Polynomial Distributed (Almon) Lag Models can be found in the Chapter called "Distributed Lag Models" within the SHAZAM Reference Manual. These can be specified on the OLS, GLS, AUTO, BOX or POOL (Panel Data) methods and the order and endpoint restrictions can be specified differently for each independent variable.

The choice of lag length and order (degree) is rarely known in practice and detecting the correct order requires studying the fit of the models you estimate - in particular compare the $R^2$, AIC and BIC statistics.

In general a good strategy is to settle the lag length first by starting with a large number of lags in the unrestricted case and reduce the lags until the fit of the model deteriorates sharply. Once the lag length is known then determine the degree of the polynomial starting with a large one and reducing it. An F test can be used to test between models where the lag length is the same but the order differs. However, an F test cannot be used between models where the lag length differs. The F test and degrees of freedom adjustments are described in the SHAZAM manual

See also Baltagi (2008) - pg. 131 and Davidson & Mackinnon (1993) pg. 674-676