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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 "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." I confused about if she applied any specific econometric test or not. If she applied, which test did she applied? Please help me.

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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.

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  • $\begingroup$ So 0.97 comes from Davidson and MacKinnon, right? $\endgroup$ – mfc Oct 26 '20 at 19:32
  • $\begingroup$ @mfc no that is their imposed restriction. The test works by comparing restricted model to an unrestricted model. You only asked what tests they used. These tests usually work by having several models some of them might be forced to have some coefficients based on theory and then the coefficients between two models are compared using the above mentioned tests. In this case for example they use the test in the NKPC vs. general model to test whether the freely estimated coefficients a,b,c satisfy the restrictions 0,0.97,0. You can learn more about these tests in above mentioned sources $\endgroup$ – 1muflon1 Oct 26 '20 at 19:38
  • $\begingroup$ Thank you very much 1muflon1. You answered my 2 questions since yesterday. You have done me great favors. I'm really grateful to you because you were helpful. $\endgroup$ – mfc Oct 26 '20 at 19:44
  • $\begingroup$ @mfc you are welcome $\endgroup$ – 1muflon1 Oct 26 '20 at 19:45

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