## Threshold regression cross sample equality test

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jerrychang
Posts: 2
Joined: Tue Jun 16, 2015 12:52 am

### Threshold regression cross sample equality test

I have a question regarding the estimation of the threshold regression model (TAR) in eviews.
I am estimating a threshold model with three regimes and two thresholds.
According to theories, I am supposed to get three regimes, and the test also suggests so.
Thus, everything went as planned. I used the fixed number sequential method for the TAR estimation. In other words, I pre-specified two thresholds for the estimation.
However, for some economic reasons and the sake of interpretation, I need to estimate the model separately for two subsamples, namely high debt capacity and low debt capacity subsamples. As I said, for each subsample, I am supposed to get two thresholds with three different regimes. Here my threshold variable is another variable, say Z.

Basically, the model will look something like below:
Y=c+bX , for high debt capacity subsample, estimated using TAR with two thresholds.
Y=c+aX, for low debt capacity subsample, estimated using TAR with two thresholds.

Because I got three regimes for each subsample, the results for each separate estimation will give me something like below:
b1 (i.e. regime1, high debt) , b2 (i.e. regime2, high debt), b3(i.e. regime3, high debt)
a1 (i.e. regime1, low debt), a2 (i.e. regime2, low debt), a3 (i.e. regime3, low debt)

My question is how do I test if b1=a1, b2=a2 and b3=a3 across the two samples in this case?

For a simple cross sample equality test, I can go with the chow test. But the issue here is obviously more complicated. For one thing, I am not really sure how to refer to the estimated coefficients when I do the test. In other words, how do I specify Eq1_b1=Eq2_a1 in eviews? For another, the chow test simply disappears in the stability diagnostic drop-Down menu, after the TAR estimation.

I also checked the Eviews forum. Someone suggested that we combine two subsamples and use a dummy variable indicator with interaction terms for the cross-sample equality test. But this will get tricky as well. Say we create a dummy for one subsample (i.e. 1) and 0 for the other. How do we put it in the TAR model? Do we list the dummy as non_varying regressors and the interaction as threshold varying regressor? That is not what I wanted here.

What I am supposed to do is to test the coefficient equality for each of the three regimes for the two different subsamples. I imagine there might be some debates on if the TAR model is fit for the estimation and if I should pre-specify two thresholds. Despite those possible arguments, is there a way to do the cross-sample equality test for the TAR model?
Many thanks in advance.

Jerry