[Sebastian Kripfganz]

With small samples, you should use the finite-sample critical values provided in Kripfganz and Schneider (2020, Oxford Bulletin of Economics and Statistics), which are available from the ardl postestimation command estat ectest. If the sample is really small, the command may not report such critical values because they are too unreliable. You could still use asymptotic critical values from PSS or resort to the bootstrap, but they won't be more reliable.

[ahmed mohamed ak]

Why is it necessary for the variables to have the same order of integration to apply the ARDL approach, when the original paper indicates that it is applicable regardless of whether the variables are are purely I(0), purely I(1), or mutually cointegrated?

[Sebastian Kripfganz]

It is not necessary for the vaiables to have the same order of integration.

[ahmed mohamed ak]

We would appreciate it if you could explain Hypothesis 5b to us, Professor.

[Kamel AKRICHE]

Dear Sebastian,

Can Kripfganz and Schneider (2020) critical values be used for a sample size of 22 observations? What are the sample size limits for which we use these critical values?

[Sebastian Kripfganz]

22 observations are very few for an ARDL estimation. You cannot have many regressors and need to tightly restrict the maximum lag order. Even if you do so, there won't be many degrees of freedom left. Think about a model with 3 variables y, X1, X2 and to 2 lags each. That would be 2 coefficients for the lagged dependent variable, 3 coefficients for X1 and X2 each, plus an intercept. That's a total of 9 coefficients to be estimated from 22 observations, which is just a little more than 2 observations per coefficient. You cannot expect any reliable estimates in such a situation.

The question about which critical values to be used then becomes quite irrelevant, because there is no way to properly approximate the distribution of a test statistic in such a small sample with hardly any degrees of freedom left.

[Kamel AKRICHE]

Thank you very much for your detailed and insightful response to my question.