[Sebastian Kripfganz]

Two comments:

1. My example in post #379 above, we have the special situation that the ec1 form is overparameterized because the underlying model is an ARDL(1,0,2) model with 0 lags for the ln_inc regressor. By forcing ln_inc to enter with its first lag in the long-run relationship, we have to artifically construct a corresponding short-run term that would not be present in the ec form. The coefficient of this short-run term is not freely estimated but determined by a nonlinear constraint. This overparameterization is not preserved when the results are stored with option regstore() because the covariance matrix of the coefficients would be singular. As you can see in the output, the regressor ln_consump (which has a positive number of lags) still appears with its first lag in the newey output when you use ardl with the ec1 option. You can avoid the problem for the ln_inc regressor by forcing it to have exactly 1 lag with the lags(. 1 .) option of the ardl command. Alternatively, there is the undocumented minlag1 option that enforces a minimum of 1 lag for each regressor.

2. The parameterization of the long-run coefficients cannot be preserved for the newey command because it is a nonlinear transformation of the underlying ARDL coefficients. That remark holds both for the ec and the ec1 option. To obtain the Newey West standard errors for the long-run coefficients, you would need to use the nlcom command directly after the newey command, as on slide 42 of my 2018 London Stata Conference presentation:

nlcom (_b[ln_inc] / (1 - _b[L.ln_inv])) (_b[L.ln_consump] / (1 - _b[L.ln_inv]))

[Arturo Galindo]

Thanks Sebastian Kripfganz for the prompt reply. I tried this, but again the output that I get corresponds to the parametrization of the ec option, not the one of the ec1. Any suggestion on how to obtain the Newey West covariance matrix for the alternative parametrization would be welcome.

[Sebastian Kripfganz]

The procedure outlined on slide 41 of my 2018 London Stata Conference presentation should still work if you add the ec1 option.

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump, ec1 regstore(ardlreg)
estimates restore ardlreg
local cmdline `"`e(cmdline)'"'
gettoken cmd cmdline : cmdline
newey `cmdline' lag(4)

The results are no longer separated into the three sections ADJ, LR, SR, but the coefficients still correspond to the ardl results.

[Arturo Galindo]

Hi Sebastian Kripfganz. Hope all is well. A quick question. Is there a way to use the NEWEY command keeping the structure of the alternative EC parametrization (ec1)? Thanks in advance.

[Sebastian Kripfganz]

1. There is no general answer to this question. Monthly data over an 11-years time span certainly allows you to use more lags. You might try to set maxlag(12) which would allow the same month of the previous year to have an effect on the current outcome.
2. It means that the short-run dynamics for this variable are completely determined by the adjustment to deviations from the long-run relationship.
3. The postestimation command for the bounds test is estat ectest. See slides 18 and following of my 2018 London Stata Conference presentation:

• Kripfganz, S. and D. C. Schneider (2018). ardl: Estimating autoregressive distributive lag and equilibrium correction models. Proceedings of the 2018 London Stata Conference.

[Ngoc Lan Do]

Dear Sir,
I am running ARDL model and I don't use statistic software very often, so there is something that I don't really understand after following the steps as instructed. Here are my questions:
1. I'm using monthly data in 11 year period, should I increase the maxlag in my model?
2. In the case that an independent variable has lag 0, in ec model there is no coefficient in SR, does it mean that there is no SR relationship between the dependent variable and that independent variable?
3. It is written in your paper that "If the bounds test does not reject the null hypothesis of no long-run relationship, an ARDL model purely in first differences (without an equilibrium correction term) might be estimated." Then what is the exact command I need to use in this case in order to consider the existence of long-run relationships between variables?

[Sebastian Kripfganz]

I guess it might make sense to do that in certain situations. The dummies in the LR relationship than might account for a structural break in that relationship. You can achieve this by simply specifying the dummy variables together with the other independent variables and assigning zero lags with the lags() option for them. Note however that the bounds test would no longer be valid in such a situation.

[Mette Marit Johansen]

Hi Sebastian Kripfganz

My supervisor advice me to include dummies also in the LR relationship. It seems like you only include the dummies in the SR relation (ref. www.stata.com/meeting/chicago16/slides/chicago16_kripfganz.pdf) ARDL.pdf ARDL.pdf ARDL.pdf . What are your thoughts on this?

Does it make sense to also include the dummies in the static long run equation? If so, what are the interpretation of the estimatet coefficients in the LR relation?

[Sebastian Kripfganz]

The ardl command is for use with a single time series only and does not support panel data. The bounds test itself is only valid for time series data.

[Slah Slimani]

Hello everyone,
I am using a PANEL ARDL model under STATA and I want to know if there is a stata command that allows to execute the Bound test .... Thank you very much for answering me

[Minyoung Yang]

Thank you for your rapid and clear answer.

Now, I can understand that I need to do more study on this topic.
Also, I will try to avoid applying it in the wrong way.

Thanks.

[Sebastian Kripfganz]

1. If X1 and X2 are relevant predictors of Y but you exclude them from your specification, then your estimates might suffer from an omitted variables bias. If you are using all variables together, i.e. ardl Y X1 X2 X3, ec, and you find that X3 is insignificant in the long-run relationship, then you could simplify your model by specifying X3 as an exogenous variable instead.

2. You cannot use the ARDL bounds test to perform these multiple checks. Running all of these tests would already violate the assumption that there is at most one long-run relationship involving Y. In other words, once you find a long-run relationship in the first model, the other three specifications immediately violate the underlying assumption and the corresponding bounds test becomes invalid.

3. Generally, you should only use differenced data if there is no long-run relationship among the variables. If you look at the regression output of the ec representation, then without a long-run relationship only differenced variables would remain. That means, if there is a long-run relationship but you only use differenced variables, you would have again an omitted variables problem.

[Minyoung Yang]

Thank you for your answer.

If possible, can I ask an additional question about your answer?

1. If I do the ARDL Bound test just with Y and X3 (in my previous question) and find there is no cointegration, can I use this variable as an exogenous variable?

2. According to the basic concept of cointegration, I can understand your answer. But then, I just confused about the concept of "multiple cointegrations".
Is that means I need to check the models like following using ARDL Bound test?

• Y ~ X1 X2 X3
• X1 ~ Y X2 X3
• X2 ~ Y X1 X3
• X3 ~ Y X2 X3

Of course, in this case, I just separate the independent and dependent variables (which means I didn't make the ARDL model because of convenience).

3. This one is an extra question about the variable itself. By the definition, we need to use "level" variance when we try to find a long-run relationship (not only the case of ARDL).
If we use differenced level variables, because it loses their long-run property, it can't appropriate analysis (sometimes spurious regression that all of us don't want).
But, sometimes, actually more frequently than I imagine, many papers and articles use differenced level variables.
Is that means, if we have enough number of data (so we can less concern about the loss of information), can we say differentiation of our variables as the econometric treatment?
If so, is it possible to do the ARDL approach with differenced level data?

Actually, the more I study, the more confusing it seems.
So I would be very grateful if you could give me an explanation about that.

Again, thank you very much for your favor.

[Sebastian Kripfganz]

1. If you can justify that X3 does not affect the long-run relationship, you can indeed use the exog() option. Note however that ardl will not obtain an optimal lag order for this variable in that case. If you want to include lags of X3, you need to specify them as well in the exog() option.

2. Basically, yes. But you can include multiple variables in the same cointegrating relationships, i.e. Y could be cointegrated with X1 and X2 jointly. Also, there could be multiple cointegrating relationships as long as there is only one that includes Y. For example, if there is a cointegrating relationship between Y and X1 and another one between X1 and X2, an ARDL model with Y as the dependent variable would be possible.

[Minyoung Yang]

Hello Everyone,

1. I tried to do bound testing using ARDL model with one dependent variable (Y) and three independent variables (X1, X2, X3).
In this case, if I want to know the long-run relationship with Y and X1, and Y and X2 separately, can I use code of "e"?
I mean, I thought variable X3 is necessary for variable Y, but I don't need to know the long-run relationship with Y and X3.
Which means, in this case,

code:

ardl Y X1, e(X2 X3) ec
estat btest

ardl Y X2, e(X1 X3) ec
estat btest

is available?

2. Also, as far as I know, if there are multiple cointegrations in the model, I can't use the ARDL approach.
Is that means I need to use Johansen and Juselius (1990) test and find the rank of the model?

3. Through the study about literature, I set the process about cointegration like this

• First, check the stationary and integrated status of variables.
• If the variables are I(0) or I(1), we can use the ARDL bound test (and preferred because of several advantages).
• Before using ARDL approach, we need to check the rank of the model for reducing unnecessary step (if there are multiple cointegrations, the ARDL approach is meaningless).
• After finding the number of ranks, do the bound testing.
• Because the Johansen cointegration test is appropriate for a model with a large number of sample, we need to check our model again by switching the position of independent and dependent variables.
• If there are bi-directional (not means direction of causality) relation within the model, we can't use the ARDL approach.
• If only one relation exists, we can say our model is cointegrated.

4. Finally, in the Stata, can we do "VECM Granger causality" process? How about using ARDL models residuals?

I'm very appreciated if anybody answers me (even partially, it's fine).
Thank you.