[Sarah Magd]

Dear Prof. Sebastian Kripfganz

I am investigating the drivers of a dependent variable shown in the figure below. In the first part of my analysis, I found a structural break in May 2023. Therefore, I ran the initial analysis on two subsamples.

However, to analyze the drivers of this variable, I want to conduct the analysis for the entire sample using the ARDL model. My questions are:

(i) Given that my dependent variable has a structural break, can I include a dummy variable in my ARDL model and interact it with the independent variables I have?
(ii) If so, should I treat the dummy variable for this structural break and the interaction terms as exogenous or endogenous variables?
(iii) Would there be any issues if I use this model with daily data?

Could you please provide guidance on this?


Thanks.

[Sebastian Kripfganz]

(i) You can do that; just note that the ardl command does not accept factor variable notation. You would need to create separate variables for the interaction terms first. Consequently, the command will not know that these are interaction terms and therefore computes any long-run effects as if they were separate variables. However, this is probably okay in your case because the structural break should also imply different long-run effects in the two subsamples.

(ii) There is really just one "endogenous" variable in an ARDL model, which is the dependent variable. You can specify the dummy variable itself with the exog() option, but interaction terms should usually still appear in the regular list of independent variables.

(iii) The main issue would be that the bounds test for existence of a long-run level relationship is no longer valid for a model with a structural break. It would only be applicable on each subsample individually.

[Sarah Magd]

Dear Prof. Sebastian Kripfganz

Thank you very much for the constructive answers.


Based on your answer, would the following steps be correct?

Step one: run the bounds test on the full sample and the subsamples without any dummy variables.
Step two: run the ARDL model on the full sample with a dummy variable for the subsample as an exogenous variable, but the interaction term would appear in the regular list of independent variables.


For the first step, the code will be:

*Bounds test for the second subsample
ardl Y X1 X2 X3  if t > 200, maxlags(6) aic maxcombs(15000) fast
matrix list e(lags)
ardl Y X1 X2 X3  if t > 200, ec1 lags(4 0 1 2)
estat ectest     
*Bounds test for the first subsample
ardl Y X1 X2 X3  if t < 200, maxlags(6) aic maxcombs(15000) fast
matrix list e(lags)
ardl Y X1 X2 X3  if t < 200, ec1 lags(2 0 3 4)
estat ectest  
*Bounds test for the full sample
ardl Y X1 X2 X3, maxlags(6) aic maxcombs(15000) fast
matrix list e(lags)
ardl Y X1 X2 X3, ec1 lags(6 0 5 4)
estat ectest

For the second step, the code will be:

 
X1_d = X1*d_s2
X2_d = X2*d_s2
X3_d = X3*d_s2
* d_s2 is a dummy variable that takes 1 if time > 200
ardl Y X1 X2 X3 X1_d  X2_d X3_d, ec1 exog(d_s2) lags(6 0 5 4)

Could you please let me know if there are any mistakes in my codes? Should I also control for the structural break by adding a dummy variable as an exogenous variable when testing for cointegration in the full sample?

[Sebastian Kripfganz]

If there is a structural break, then the bounds test for the full sample would be unreliable - with or without dummy/interaction terms.

Other than that, things look okay. You might have to re-optimize the lag orders when including the interaction terms.