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I am really struggling with whether to include lagged dependent variables or not.

I have read the logic (on this website) that a lagged dependent variable should include if its current value is linked to its past value, i.e. the AR(1) coefficient is significant.

However, I read a paper from Vialsuso (2001),

"Results of Monte Carlo simulations suggest that conclusions drawn from least squares causality tests may lead to an erroneous claim that a statistically significant causal relation exists. Misleading inference associated with least squares may be traced to two explanations. First, because the set of regressors in a VAR includes lagged-dependent variables, least-squares standard errors are not consistent and may not support correct statistical inference (Engle et al., 1985)".

Can anyone explain why including a lagged dependent variable may lead to erroneous results? Should I or should I not include it?

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