ARDL short run and long run Interpretation

[Nga Do]

Hi everyone,
This is the first time I use Stata for my paper so I am confused a lot. I’m doing my research with the Autoregressive Distributed Lag (ARDL) via Stata 16
There is one question that is getting on my nerves.
There is co-integration among variables because I already checked it with the bounds test. There is one of my independent variables which has 0 lag so that It doesn’t appear in the SR panel because it has 0 lag when I run a command with ec. But with ec1, it appears in the SR panel. I posed the results as 2 pictures below.
1) Could you please tell me which one I should choose to interpret results in the long run?
2) Could you please tell me which one I should choose to interpret results in the short run?
3) Is this correct that I interpret the long-run relationship in the LR panel and short-run relationship in the SR panel between the independent variables and the dependent variable?
4) in the long run, I put: lFDI as a dependent variable and In the short run, I put D.lFDI as a dependent variable. am I right?

I am sorry if I ask such a simple question, but I tried to search for it a lot on the internet but I have not found a reasonable answer.
Thank everyone so much in advance! I really appreciate it.

distributed lag model (ARDL).

[Sebastian Kripfganz]

Welcome to Statalist and thank you for your interest in our ardl command.

1) The long-run coefficients are identical in the two specifications and the interpretation is also the same.
2) In the ec1 specification, because the first lag of INT is used in the long-run relationship but no lag was present in the underlying ARDL model, the term D1.INT needs to be added artifically to offset adding the lag of INT to the long-run relationship. However, this is not an independently estimated coefficient. Its value equals the negative product of the ADJ coefficient and the INT long-run coefficient: -6.933688 = - (-0.5518688 * -12.56401). This short-run coefficient cannot be interpreted independently from the long-run adjustment, which is why the ec representation might be easier to interpret.
3) All of the variables in the LR and the SR sections give you effects of those independent variables on the dependent variable.
4) For the interpretation, that is correct.

More on ARDL estimation:

• Kripfganz, S. and D. C. Schneider (2018). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Proceedings of the 2018 London Stata Conference.
• ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Nga Do]

Hi Sebastian Kripfganz,
I would like to thank you so much for your kind reply.
I am sorry that I still have one question. if I choose the ec representation in my model for the interpretation, can I conclude that in the short run, there is no relationship between INT which has 0 lag and the dependent variable independently? if I am wrong, could you please tell me how to say about INT in the short run with the ec representation?
I hope that I can hear your comments. Thank you so much!

[Sebastian Kripfganz]

There is still a short-run reaction to a change in INT via the error-correction term. Starting from the long-run equilibrium, if there is a change in INT, the equilibrium relationship is no longer satisfied. Therefore, the dependent variable reacts to this deviation from the long-run relationship. The strength of this (short-run) reaction is measured by the ADJ coefficient.

[Nga Do]

Hi Sebastian Kripfganz,
I would like to thank you for your kind reply. I still have some questions. Please kindly help me to explain it.
1) In the slide No.16: "The short-run coefficients ψyi, ψxi (and ω) are reported in the output section SR. They account for short-run fluctuations not due to deviations from the long-run equilibrium."
so, I can say that with the ec interpretation, in the SR panel, the impact of INT on the dependent variable in the short-run is measured by the ADJ coefficient and the short-run impacts of the other variables are independent with the long-run impacts. Am I right?
2) in slide 26, ec(t) is generated from Y(t-1) and X(t) after ardl, ec and; ec(t) is generated from Y(t-1) and X(t-1) after ardl, ec1
I feel that it is suitable to choose the ec1 representation to interpret the output in the long run because X at the time (t-1) has an impact on Y(t-1) but for the ec representation, I say X(t) has an impact with something in the past?
I am so sorry if I ask such simple questions, but these things make me very confused.
I am looking forward to hearing from you. Thank you so much!

[Sebastian Kripfganz]

1) That's basically right.
2) I understand your confusion. If there exists a long-run equilibrium between X and Y, then in the equilibrium time subscripts do not matter. You should essentially interpret these long-run level terms without time subscripts. In the long-run, a change of X by 1 unit has an effect on Y by 'theta' units (given by the long-run coefficient). If the system is out of the equilibrium, then the dependent variable will adjust in the current period (this is where time matters again for the short-run adjustment) by 'alpha' units (the negative ADJ coefficient) to a 1 unit deviation from the equilibrium. This could also be given a percentage interpretation: 'alpha'*100% of the equilibrium deviation will be corrected in the current period.

[Nga Do]

Hi Sebastian Kripfganz,
I would like to thank you for your kind reply. I feel grateful for it. May I still ask a question?
1) In the slide No.16: "The short-run coefficients ψyi, ψxi (and ω) are reported in the output section SR. They account for short-run fluctuations not due to deviations from the long-run equilibrium."
I understand the ec representation but I am still wondering about the ec1 representation because I want to make sure that I can understand both the representations.
With the ec1 interpretation, in the SR panel, the impact of INT on the dependent variable in the short-run is measured by the ADJ coefficient and the INT long-run coefficient. I understand this one because you already explained it.
However, Regrading to the other variables, with the ec1 representation, the short-run impacts of the other variables (shown in the SR panel) are still independent with the long-run impacts. Therefore, these interpretations are the same as the ec representation for these variables. am I correct? if I am wrong, could you please help me with how to interpret these variables in the SR for the ec1 representations?
I am looking forward to hearing from you. Thank you so much!

[Sebastian Kripfganz]

I think my previous explanations were a bit confusing. I apologize for that.

The interpretation of the SR coefficients of the contemporaneous (not lagged) first-differenced terms varies slightly depending on the ec or ec1 representation, for all variables.

• For the ec representation, it measures the contemporaneous effect that we observe in addition to the reaction to any deviation from the long-run equilibrium caused by the same change in the regressor.
• For the ec1 representation, it measures the contemporaneous effect that we would observe if the system was still in equilibrium before that change, not accounting for the distortion of the long-run relationship caused by that change in the regressor.

All lagged SR effects have the same interpretation in both representations. (Their coefficients are identical.)

[Nga Do]

Hi Sebastian Kripfganz,
I would like to thank you so much for your reply. I really appreciate it.

[Shruti Gungabissoon]

Hello, I am doing a thesis on the impact of Foreign Direct Investment on Employment for Mauritius and so, I adopted the ARDL model because there was a mix of I(1) and I(0) variables. However, all my tests are significant and good. I just had the issue of multicollinearity and so, I wanted to know if multicollineaity matters in ARDL and should I leave it?

[Justin Niakamal]

See https://www.statalist.org/forums/for...=1587500490135 for the response to post #10.