Adding variables in levels to cointegrating equation

[ripieter]

Hi everyone,

I'm doing research about the Belgian real estate market and I have a question concerning the use of first differences of variables and levels in the same equations.
In some model I tested cointegration in the equation "ln(real house price) = a*ln(number of households) + b*ln(real income)", using Engle-Granger (so testing wheter the residuals of that regressions are I(0) basically). In the second step I used the one time lag of these residuals (error correction term, ECT) and regressed them with the first differences of the above equation, to get my long-term equation:

"D[ln(real house price)] = a*D[ln(number of households)] + b*D[ln(real income)] + ECT"

Now I want to test the short run influence of unemployment (which is not included in the long term equation because it was I(0) and the variables in the long run eq have to be I(1)) and my question is, can I include unemployment in levels, or should I test the influence in first difference in order to get results that are correct?

I cannot use the ARDL, because I only have 15 observations, so the question really is wheter the interpretation of my coefficients will be correct if there are variables in levels added to my cointegrating regression or that I should only add first differences (or lagged first diff)?
Many thanks for the help guys!