How to check the Taylor principle is satisfied in historical data?

Taylor (1999) checks whether the Taylor principle is satisfied in historical data for specific periods by estimating his proposed rule (the original rule). For 1987:1-1997:3, for example, the Taylor principle is satisfied.

But if we extend the original Taylor rule to include other variables and allow for interest rate smoothing, the coefficient on \pi may not be greater than one.

In the empirical literature, others have used different specifications of the central bank’s reaction function to make similar statements like, “the Taylor principle is satisfied for period A.” But, of course, it depends on the model. I tried to say somewhere that the Taylor principle is satisfied for some period for my country based on an estimation of the original rule…similar to the table above. But one comment I got was that it is not satisfied because, in other specifications (allowing for lags and other variables) that I also showed, the coefficient on \pi is less than 1. So it seems we cannot really make a general statement that “the Taylor principle” is satisfied for some period, right? Like there is no consensus on a specific empirical model that one should use to answer whether or not the Taylor principle is satisfied, it seems. I guess the best answer is it depends (on the model).

In the Taylor paper, he mentioned, “I abstract from lags…”. And sure, others will specify the rule differently from the original rule. Is it fair to say that there cannot be a definite answer or consensus on whether the Taylor principle is satisfied for some period? Here, I mean in empirical models, not structural models.

It’s not even clear you can estimate the Taylor rule outside of a structural model. That is a point forcefully made by Cochrane (2011) in the JPE.
But yes, all model estimates are dependent on the model and the data may not be informative to select between models. You will never be able to test all the potential models that people may put prior mass on.

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