What type of regression to use here


Fortran must die
This article shows two regression models an older simpler one and a later more complex one. They never identify the type of regression used. The later, more complex model, differences some of the IV. My question is, can you do this with linear regression or do you have to use something like regression with autoregressive error or other time series approach to use differenced variables.

The article also does something I have tried to get an explanation of for a very long time without success :p They difference some variables and not others (so the integration - the order- of the variables will not be the same). I know you can do that with ARIMA, but some accounts I have seen of regression suggest this is invalid with regression. That is they say the variables all have to be integrated of the same order.