Can i-invariant but t-variant variables be used together with time dummy?

[Alex Mai]

In a previous answer, Jeff Wooldridge mentioned that

......it doesn't make sense to include a full set of time dummies along with any function of time. Putting in time dummies allows for any kind of trend, of which a linear trend is a special case. A program like Stata will drop either the linear time trend or one of the dummies. Now, if h gets an i subscript then the model makes sense.

Incidentally, it's not just a linear time trend or other functions of time that are redundant. Any macro variables that don't change across i are perfectly collinear with a full set of time dummies. That's an advantage of including the time dummies: one need not restrict the time trend or collect data on aggregate variables.

Whether time trend can be used together with time dummy seems to be subject to debates. So how about an individual-invariant but time-invariant variable (e.g. world GDP growth rate in a cross-country panel)? Such a variable is very similar to a time trend in some senses. My understanding of Wooldridge's words is that such a variable should not be used with time dummy. But I am not quite sure about my interpretation.

Thank you very much.

[Sebastian Kripfganz]

It is not a debate. It is a fact. There is nothing to be added to Jeff's wise words.

You cannot have both time dummies and world GDP in a cross-country panel regression.

[Clyde Schechter]

You cannot have both time dummies and world GDP in a cross-country panel regression.

The operative word here is "have." You can code both time dummies and world GDP, but one of them will inevitably get omitted due to colinearity.