Signs on independent variables change in VECM results I am estimating a VECM model and it was determined by the trace tests that there are two cointegration equations.  From this,  I proceeded  to estimate the β under this restriction that provides the normalized cointegration equation. The independent variables are significant at the 5 percent levels.  
Now after obtaining the normalized equations, I treated the normalized variable as the   “dependent” variable and the remaining independent variables move to the RHS and the signs change.  In the normalized equation the sign is correct, but after this transformation the sign is the opposite. How can this be interpreted?   
 A: When you look at your normalized eigenvectors $\hat{\beta}_{i}^{\prime}$ then the variable you normalized on should be one and the rest of the variables should appear in whatever sign they have divided by the normalized variable, e.g.: 
$$\hat{\beta}_{1}^{\prime}=\left(0.07\,:\,-0.03\,:\,1.00\,:\,-0.29\,:\,0.57\right)$$ 
$$\hat{\beta}_{2}^{\prime}=\left(1.00\,:\,-1.02\,:\,-3.45\,:\,-8.51\,:\,8.00\right)$$
$$\vdots$$
$$\hat{\beta}_{i}^{\prime}=\cdots$$
here the vecotor of variables is given as:
$$X_{t}=\left(m_{t}^{r}\,:\, y_{t}^{r}\,:\,\Delta p_{t}\,:\, R_{m,t}\,:\, R_{b,t}\right)^{\prime}$$.
In the above example it should be clear that we have normalized on $\Delta p_{t}$ in the first vector and $m_{t}^{r}$ in the second vector. When we want to interpret the relationship we can treat the normalized variables as the dependent variables in a linear regression so the signs of the other variables will change as we now interpret each vector as a relationship explaining the normalized variable (dependent variable if you want a comparison to linear regression), i.e. we move the variables to the other side. Using this, the first vector above can be interpreted as a relationship explaining the inflation rate:
$$\Delta p=0.29R_{m}-0.57R_{b}-0.07m^{r}+0.03y^{r}$$ and the second relationship can be interpreted as a money demand relationship:
$$m^{r}=1.02y^{r}+3.45\Delta p+8.51R_{m}-8.00R_{b}$$
We use the normalization so we are able to uniquely identify the $\beta$ vectors and by choosing to normalize on variables which lead to a meaningful economic relationship its a convenient way to let us interpret the cointegrating vectors as economic equilibrium relationships.
See the "The Cointegrated VAR Model: Methodology and Applications" by Katarina Juselius sections 7.5 and 7.6 which discusses exactly this and where the above has been adapted from.
Alternatively you cant take a look Eric Zivot's lecture notes on cointegration, section 12.2.2 or  "New Introduction to Multiple Time Series Analysis" by Lütkepohl.
