Which econometric test applied here? I have been reading an article about the Phillips Curve. But I got stuck in a part of econometric analysis. I am not good at econometric. Therefore I need help here. In this link you can read the article. If you search 0.97 with Ctrl+F, you can see the first finding that I want to ask about it. She says in there &quot;By applying Equations 5–7 to the data, one need not assume any specific form of nonrationality in expectations. Since the task here is to compare the different models on their own terms, the theoretical restrictions are imposed in the estimated specifications of the New Keynesian models. Thus, in the New Keynesian Phillips curve, the imposed value of β is 0.97 and as seen in Equation 7, the sum of forward- and backward-looking components is restricted to unity for the Hybrid Phillips curve.&quot; I confused about if she applied any specific econometric test or not. If she applied, which test did she applied? Please help me.
As they clearly say on pp 2267:

Alternative specifications were compared using the
specification test by Davidson and MacKinnon and
the Wald test of coefficient restrictions.

So they two tests Davidson and MacKinnon specification test and Wald test.
Wald test is a classic test for coefficient restrictions you can learn can learn more about it in any econometrics textbook, for example Verbeek (2008). Guide to modern econometrics. 4ed.
For Davidson and MacKinnon specification test you can have a look at the original Davidson and MacKinnon (1990) paper.