I am estimating a single-equation VEC model from a seven-variable system. The Johansen Cointegration tests (both Trace and MaxEignvalue) reveal that the system have 4 distinct ranks. Will my single-equation estimation be valid if I just specify r=1 in my VEC estimation? Thanks in advance.
For clarity are you estimating a single equation error-correction model, as a VEC implies multiple equations. In short, if you have mutiple cointegrating equations but you only estimate one, your coefficients will contain bias (effectively your cointegrating equation will be averaging the effects of all four). You are essentially omitting information. Of course, you may primarily only be interested in the first cointegrating equation and it ultimately depends on why your are constructing the model (e.g. forecasting etc), but the coefficients will be biased.
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