[Sebastian Kripfganz]

1. There are certainly different acceptable labels, but we should be precise about the terminology: The ECT(-1) term is not just y_t-1 but instead the whole term in parentheses on slide 12, i.e. (y_t-1 - theta x__t-1). The ADJ coefficient is not the error correction term. It is the coefficient of the error correction term.

2. I do not have a clear preference. It depends on the interpretation of the error correction term and its coefficient. If you interpret the ADJ coefficient as a response to a current-period change in the equilibrium, then choose ec. If you interpret it as a response to a previous-period change in the equilibrium, then choose ec1. Most people probably do not worry about this distinction.

3. I am not sure I understand the question. The answer might be the same as for question 2.

[John Costopoulos]

Dear Sebastian,

Thank you for your prompt response and your patience.

1. I'm sorry for any inconvenience caused to you by coming back to question 1, but I have some good reasons to believe that the label ADJ might incorrectly be considered as denoting the ECT. The formulas in Slide of your 2018 presentation indicate clearly that ADJ (α) represents the coefficient of the ECT(-1) term, i.e. of the term (y_t-1 - theta x__t-1). However, when we are looking at the ADJ section of the regression output, we see that ADJ is actually obtained by the y(t-1) coefficient. In addition, what we see at the LR section is not actually the results of the OLS regression per se, but the results - through nlcom - of a normalization of the original LR coefficients on -α. Based on the above, it is clear that all the work is done on only one equation, which is a completely different approach from the traditional one, which derived the ECT(-1) from the equation in levels (all variables being I(1)) and then used it in the restricted ECM in order to obtain the speed of adjustment and the SR coefficients. For the above reasons, what I'm actually looking for is just to find a label which: (a) would be more lengthy/self-explanatory from the label ADJ, and (b) would not cause any confusion to readers who are more familiar with the "traditional" ECT(-1) term.

2. I summarize below some things to see I have understood them correctly:

• In the ec representation, the ADJ coefficient refers to a contemporaneous change in the equilibrium, while a SR (not lagged) coefficient describes two things: (a) the contemporaneous (i.e. in time t) effect of the corresponding x variable (as if the system were still in equilibrium ?), and (b) the reaction in time t of the system to its deviation from its the long-run equilibrium due the change in this x variable which destroyed the equilibrium.
• In the ec1 representation, the ADJ coefficient refers to a change in the equilibrium which occurred in a previous period (t-1 or even earlier ?), while the SR (not lagged) coefficient measures, as described in an older post, "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".

[Eric de Souza]

In answer to #32, I don't see where the problem lies. Dy(t) = SR + alpha.y(t-1) + beta.x(t-1) = alpha [y(t-1) + (beta / alpha).x(t-1).].
alpha is the adjustment coefficient, the speed of adjustment to a new equilibrium -if negative. ADJ is alpha

[John Costopoulos]

Dear Eric,

Thank your for your prompt response.

I think you are right to wonder. I see now that my reference "I have some good reasons to believe that the label ADJ might incorrectly be considered as denoting the ECT" was confusing, since I did not want to report any problem regarding the ardl program. What I actually referred to is the misconception, which I have so far encountered twice in the empirical literature, that the ADJ denotes the ECT. I should have stated it more explicitly from the beginning. Starting from this, I tried to explain to anyone who might be interested, that both the ADJ and the LR coefficients are produced by the ardl program by following a different approach than that of the traditional way to extract the ECT(-1) from the levels equation and then using it in a restricted ECM. Based on the above, please consider my post as a (rather unsuccessful) attempt to offer some additional information, than to report any problems regarding the ardl program, whose I am a big fun!

[JIBRIN SABA]

what are the maximum number of variables for ardl model

[JIBRIN SABA]

Please help me regards to ARDL maximum number of variables that can be use in the models

[JIBRIN SABA]

Please Sebastian help me about the maximum number of variables that can be use in the ARDL models.

[Sebastian Kripfganz]

You can put in as many variables as you want, provided you have sufficiently many observations. If you do not have many observations, you need to restrict yourself to a few key variables. I cannot give you an exact number. There is a natural trade off between bias (not enough variables) and efficiency (not enough degrees of freedom).