Nonstationary panel data, spurious regression

Question

I would like a more detailed explanation of this quote:

"Unlike the single time series spurious regression literature, the panel data spurious regression estimates give a consistent estimate of the true value of the parameter as both N and T tend to infinity. This is because, the panel estimator averages across individuals and the information in the independent cross-section data in the panel leads to a stronger overall signal than the pure time series case."
(from Baltagi's Econometric Analysis of Panel Data).

I find it odd. How can spurious regression provide consistent estimate of the true value (typical spurious regression yields non-zero coefficient estimates, while the true value is zero)?

The quote above gives me the impression that in a panel environment, one does not need to worry about the nonstationarity of the variables. Is this correct?

Answer 1

Admittedly a bit confusing wording from Baltagi in this specific excerpt. But unfortunately, the expression "spurious regression" has come to be used in the econometrics literature as a synonym for "non-stationary and non-cointegrated regression"

Let's first attempt to clarify what the "spurious regression phenomenon" is:

Spurious regression : when the estimation method produces a statistically significant relation between two variables, irrespective of whether such a relation exists or not.

And the phenomenon typically arises when the processes are not-stationary, and not co-integrated.

Note carefully that a relation may indeed exist -under "spurious regression" we do not describe the case where such a relation does not exist, but the estimator produces a phoney one. The problem lies in the fact that since we will get a statistically significant relation in all cases, we cannot tell whether what we see is actual or an artifact.

Then, Philips and Moon (see this 2000 paper of theirs for an accessible exposition) showed that in a panel-data setting, the regression stops being spurious, but it consistently estimates what actually is there -if there is a relation, it will estimate the relation, if there is not a relation, it will estimate zero. But, this will happen under two-dimensional asymptotics, i.e. as both $n$ and $T$ go to infinity. After all, the intuition behind this result, is exactly the exploitation of the two-dimensional information provided by a panel-data structure.

But I would refrain from general assertions like "we don't have to worry about non-stationary (and non-cointegrated) panels" - one should first study and understand the theoretical results and under which conditions (and for which kind of panels) do they hold.