Instability of threshold regression

[wxhdiy01]

I'm using Eviews 9.0, and have been experimenting with the threshold model. I see in a pure AR model where only dependent variable and its lags are included, the lag length affects which variable is chosen as the threshold variable. This is understandable since models with different number of lags are basically different models. However, when I use the same model (same lag length), the pool of possible threshold variables affects which variable is chosen as the threshold variable. For example, although variable X1 and X2 are never chosen as the threshold variable, if I include X1 and X2 as possible threshold, then X3 is chosen as the threshold, whereas if X1 and X2 are not included as possible thresholds, X4 is chosen as the threshold. The only reason I can think of is that X1 and X2 have shorter time series, so it might affect the number of observations when they are included. However, when they are included and X3 is chosen, eviews shows that it is using the full time series, not the short time series restricted by X1 and X2. So it doesn't seem to explain the problem.

Since the threshold chosen by Eviews changes when the pool of possible threshold variables changes, I become skeptical of the results in general. Could you help explain why this happens, and what factors affects the selection of threshold variable? Many thanks!

[EViews Gareth]

Including or not including a variable will impact inferences on other variables.

[wxhdiy01]

Could you explain more in detail or refer to a source where I can get more information? Thank you!

[EViews Gareth]

https://en.wikipedia.org/wiki/Omitted-variable_bias

[wxhdiy01]

Thanks for the reply, but I don't think that's the reason. Using the example before, X1 and X2 are only "possible threshold variables", I don't think they are used as normal right hand side variables. Also as stated in the original question, either X3 or X4 is selected as the real threshold variable, the number of observations is not restricted and is still 175 (the total sample size is 175, while X1 and X2 only have 75 observations). This shows even if X1 and X2 are in the pool, they don't need to be in the regression. So I think there must be other reasons relating to the selection mechanism.

Hope the question is clear; if not, please just let me know. Thank you!

[EViews Glenn]

Model selection requires the use of observations which are common across all possible specifications. So different samples related to the exclusion or inclusion of X1 and X2 from the selection list will be employed.

Once the model selection determines the selected variable, EViews will estimate the specification using the full sample available for the selected model. As you have seen, this estimation sample may differ from the selection sample.

If you wish to enforce consistency across all of the possibilities, you can put all of your selection variables in a group, and set the sample so that @rnas is eqwual to zero.