cointegrating regression and Error correction Model

[hongweiyuan1501]

Hi :D ,
I have to estimate if certain macroeconomic variables can have significant impact on the housing price in both long term and short term. The method I used is Engle-Granger 2 step and error-correction mechanism. I have around 9 variables, which 8 of them are independent variables. The model is ln(house_price_index)=f(lninflation, loglong_term_interest_rate, lnreal_disposable_income, lnechange_rate, lnloan_amount, logbuilding_cost_index, loghousing_starts, loghousing_completions).

Here are the procedures I have used to estimate the both long term and short term relationships:
1. Check the unit roots of each variables. I found the dependent variable and 7 independent variables have unit root. 1 independent variable does not have unit root, so it is excluded for the model. The rest of the variables do not have unit roots after first difference, so they are I(1).
2. I estimated the static model 1 by OLS, then I use ADF test to test if the residual of the model 1 is stationary or not. Then I found the residual is stationary, which implies the unit root test rejects the null hypothesis that there is no cointegration by comparing the t statistics with critical values from Mackinnon (1991). This means the static model 1 is the long term relationship.
3. Then I calculated the first difference of both the dependent and independent variables and also the lagged one period of the residual of the model 1 to form the error-correction model by using OLS. The short term relationship is only found when all the independent variables (including lagged variables) are all significant and the coefficient of the lagged one period of the residual of the model 1 has to smaller than 0 but greater than -1.

Thus, I would like to ask that:
• Are my procedures correct? Did I miss anything or any indications I need to be aware of when I have my models?
• How should I interpret the results of the long term model as some of the variables are significant while some of the variables are not? Because of the causes of the spurious regression problem, therefore the t statistics, as well as the probability, are not correct. Should I just interpret sign of the coefficient of each variable?
• Also how should I interpret the short term results?
• My short run model’s R square is only around 64%, is this good enough?
Thank you very much in advance! :)