Recently, I received an email from Ozan, who wrote:
"I’ve a simple but not explicitly answered question within the text books on stationary series. I’m estimating a model with separate single equations (I don’t take into account the interactions among them ). I’ve only non-stationary series in some equations (type 1), only stationary in some (type 2), and a combination of the both in the others (type 3). For the first two cases I apply the usual procedures and for the last case the Pesaran (2011) test. I want to find the short term effects of some variables on the others. I’ve two questions:
1) If the Pesaran test turns out inconclusive or rejects cointegration, what’s the next step ? Differencing all the series and applying an OLS? Or differencing only the non-stationary ones? Or another method?
2) As I mentioned I’m looking for the short-run effects. In the type 2 equations, I guess running an OLS in levels gives the long-run effects. Therefore I run an OLS in differences. Some claim that differencing an already stationary series causes problems. I’m confused. What do you think?"
Let's start out by making sure what Ozan means by "the usual procedures" for his "Type 1" and "Type 2" equations.