ARDL and multicollinearity

[NipNip]

Hello!
Would you agree on the following?

"The ARDL approach does not address multicollinearity problems. In fact, when the sample size is relatively small, multicollinearity problems can easily arise when the lag order is set too high".

"But, We also are differencing the data when estimating an ARDL model".

Could you, please, share your experience? How robust is ARDL against multicollinearity?

[startz]

A first question is why you care about multicollinearity???

For many macro time series determining exact timing of effects is quite hard. So ARDL models do have a lot of multicollinearity. That means individual coefficients are not well identified. But functions of the coefficients, such as long-run effects are often very well identified.

[NipNip]

Thank you, startz. Please, correct me if I'm wrong. There is a distinction between short run and long run multipliers, even Interim/delay multipliers. What about them? What really matter are the functions of the coefficients, such as long-run effects? the Does sample (thinking of 20 or 30 observations) affect of SR and LR multipliers validity?

[startz]

You are right that there is a distinction. Of course, once you've run the ARDL you get estimates and standard errors for trhe case at hand.

In principle 20 or 30 observations might be okay. In practice I would say it likely isn't enough.

[cheriedavy]

The ARDL (Autoregressive Distributed Lag) approach can help mitigate multicollinearity to some extent by differencing the data, which can reduce the correlation between independent variables. However, it's not immune to multicollinearity issues, especially when you include a high number of lag terms. When the lag order is set too high in ARDL models, it can still lead to multicollinearity problems, especially with a small sample size.
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Therefore, it's essential to carefully select the lag order and consider other methods like variable selection or regularization techniques to address multicollinearity effectively in ARDL modeling.

[NipNip]

If the ARDL model has multicollinearity, heteroskedasticity, serial correlation, etc., then any functions from it, say Short-run/Long-run multipliers and so will be affected by these problems. Right?

[startz]

Yes. But these problems have very different consequences. What problem do you think multicollinearity causes?

[NipNip]

I think is affects the standard errors of the estimates, which translates to uncertainty on the estimates. Also, Shouldn't this bother us?
Also, OLS can't clearly distinguish the effects of correlated covariates.
Please, correct me if I'm wrong.

[startz]

Correct. But this is a consequence of the data and the model. Basically, ols is optimal in the presence of multicollinearity.

[NipNip]

I think you meant "this is a consequence of the data and NOT the model". The model requires lags, tho. So. The issue is how the variables are encoded.
Using lags will come up with multicollinearity. Why time-series analysts are ok with them?

[startz]

Specifying lags is part of specifying a model.

You still haven’t said why you think an estimate with multicollinearity is bad.

[NipNip]

It is bad because we are not sure about the true effect of the regressors. They can change from one sample to another.

[startz]

Okay. So it is nice if there is little multicollinearity. It is also nice if we have many observations and other things. For a given dataset and a correctly specified number of lags, ols is the best we can do…multicollinearity or not.

[NipNip]

Even if multicollinearity translates to "instability in the coefficients", we might need to just accepted it because of the available data and as long as the model specification has the best fit. Particularly when working with time-series in a regression setting.

[startz]

Makes sense