Sometimes in macro models, something causes instability. For example, when the Taylor principle is not satisfied or you hit the lower bound under some conditions, you get instability.

But, say, I estimate the Taylor rule i_t = \alpha + \beta_1 \pi + \beta_2 y_t + e_t for economy A (say, with OLS or GMM), and I find that \beta_1 <1, which is a violation of the Taylor principle. But there is no instability in the data for economy A. Actually, output and inflation are stable. Then I guess there is only one reason why instability didn’t happen as the theory predicts, which is, there were no shocks to spur the instability?

John Cochrane humorously once said, ‘we all know what happens when you hit the lower bound, nothing’.

I guess the correct way to think about it is that if you believe the theory and ‘take it seriously’, then you should, sort of, investigate why the instability didn’t happen as the theory predicts.

I find the literature on indeterminacy hard to distill into simple messages. For example, we know that in regime-switching contexts, there may be determinacy as long as people assign a sufficiently high probability to return to a normal regime. See

https://www.jstor.org/stable/30035014

For that reason I don’t assign too much weight to estimates in one particular regime/sample.

Oh, I see. Thanks!!

Does this statement also apply to other parameters in the model? Or only parameters in equations not derived from FOCs. Maybe even parameters in policy functions derived from FOCs may have this regime-switching behavior.

Also, thanks for the paper. I have not read all of it yet, but it seems the point they make is that instability is not always due to indeterminacy. I guess we can also say stability is not always due to determinacy (the point in my question).

Instability is not the same as indeterminacy. The point of the paper is that there are can be periods of both instability and indeterminacy that are still consistent with overall stability and determinacy as long as there is a high enough probability to move to a stable and determinate regime at some point.