The coefficients of a cointegrated equation are interpreted as the long run relationships. If you aim to estimate the short run relationships then you should run the ECM model whose coefficients are interpreted as the short run relationships. The error coefficient in the ECM model is the adjustment coefficient.

If you do not understand, I can help you since I have worked on this model. Moreover, you can find more about the cointegration equations in my my paper which is attached.

Article Price and Income Elasticities of Gasoline Demand in Iran: Us...

Great! So does it matter if it's positive or negative?

The error coefficient in the ECM model should be negative and less than one but the other coefficients are not limited to any sign or quantity. The error coefficient which shows the adjustment speed, links the short term equilibrium to the long run equilibrium, so it should be negative and less than one. 

I am ready to explain more if you have more questions...

Thanks! It helps a lot! I would be greatful if you could explain, in simple words, how to interpret the coefficients of a cointegrated equation. In your paper, they are interpreted as elasticities. Is that only applicable in a static model (logarothmic)?

The coefficients of a cointegrated equation are interpreted as the long run relationships among the variables.

In my paper, they are interpreted as the long run elasticities since the variables are in natural logarithm. However, they can not be considered as the elasticities if the variables are not in the natural logarithm form.

So if a coefficient of a cointegrated equation is negative, it means there is a long run negative relationship? This doesn't fit my data.  I have two series that clearly move in the same direction over the long run, but where the coefficient of the theorized independent variable in the cointegrated equation is negative, when the dependent variable is normalized to 1 in the equation. Any explanations on that would be appreciated. 

Here are some pics of how the excel-graphs look like, and some output from Stata on cointegration and VECM. Can you explain this?

Dear Lars

I think Chuck A Arize  is very skillful. I am following your timeline to know what will be the final results.

Best Regards

Vahid

 I have addressed this issue with my good friend, Lars. I have no doubt, whatsoever, in my answer 

Yes, I'm making a lot of progress now! :)

Hello, I am doing the time-series analysis by using STATA too. As I understand, a "-" need to be added in front of the coefficients that VEC model tells us. Is that correct?

I believe, I have talked with my good friend Lars on this earlier in a post. You are supposed to normalize and multiply by "-1". For example, Eviews and probably Stata require normalization.  MICROFIT by Persaran and Persaran produces normalized estimates> For eample, if you have entered the variables in this order y x v z then it will produce estimates normalized on Y; if you arranged it x Y v z , it will produce estimates normalized on X etc. 

Thank you very much“

By the way, how to fix the endogenous problem in time-series analysis?

Hi Yichen: Can you explain more because the word "fix" can mean many things. Make us understand exactly, your question and we will be glad to help you!

I am studying the influence of education inequality on income inequality in China, and now I am doing the time-series analysis. But I know there is also an impact of income inequality on educational inequality. When doing panel data analysis, we usually use IV to solve the endogeneity problem. But what can I do in the VECM to solve the endogeneity? Sorry to confuse you guys. & Really thanks a lot!

All variables are endogenous in VECM assuming that you are using a system estimator. The exceptions are the seasonal dummies and outliers

Yichen: Was my answer to your endogeneity question satisfactory to you? You didn't say anything. Just checking!!

I just wonder does it mean there is no exact difference between dependent variable and independent variable in VECM？And the cointegrating equations I get from STATA is different from the OLS regression？ 

Sorry to delay my thanks！I just notice you put your answer，Chuck！Thank you very much！

In the VECM,  it is you who will normalize on the vector you want to because all variables are treated as the dependent variable so when you normalize you will see the lagged differences of the other variables plus the equation error correction variable . All that I am saying is that there is  no independent variable except the constant and dummy variables 

Excellent! Thanks aaaaaa lot!

Am happy that you are absorbing it and in no time you will be an expert and help other people.!!

Hi Professor Chuck A Arize, I need some assistance in regards with the issue of identification in multiple cointegrating vectors. I am empirically testing the Monetary Approach to Exchange Rate Determination model w.r.t UK's nominal exchange rate, and using US as the foreign country. In accordance with Johansen's cointegration rank test, 2 possible cointegrating vectors were discovered. I attempted to identify the two equations based on economic theory. The first Cointegration Vector (CV) is of course normalised w.r.t exchange rate, and the second CV (which I am not interested in but I am aware it still has to make economic sense since it impacts on the first CV's coefficients) is normalised w.r.t to money demand (while restricting exchange rate to equal zero). Now, with the identification, literature suggests imposing restrictions on the proportionality between relative monies and exchange rate, as well as the symmetry (equal and opposite signs) of the domestic and foreign outputs and interest rate. This is where I am having problems with. I do not wish to impose these restrictions since I want to have unique coefficients for the individual variables. What other restrictions can I make in order to satisfy both the order and rank conditions for identification? For information, I have tried to impose weak exogeneity on both CVs but Eviews will not give me t-statistics, reporting that one of the CV is not properly identified. Interestingly however, Eviews produces t-statistics when weak exogeneity is imposed on the second CV only. I have attached my estimating equation and the restrictions I imposed. Grateful if you or anyone can assist.

Sorry, I did see the attachment because I am using my phone. I am away because of holidays. Nevertheless, you need to ensure that you have the centered dummies, possible outlier dummies taken care of (you did mot tell me your type of data (e.g., monthly, quarterly etc). I have to assume that everything diagnostics are okay. Concerning E-Views, you need to normalize on exchange rate  by multiplying by -1 so that you have the right signs.  The testable restrictions are that the coefficient on  domestic money supply(a) is 1, foreign ms(b) is -1;

 plus a= -b

rgnp (c) and foreign rgnp (d) so that the resriction is C= -d

domestic interest rate (i) and foreign interest rate (ifor) so that i = -ifor. Therefore,  you have 5 restrictions.

I have broken it into parts but you should impose the restrictions as noted. Focus on the trace test so that you get one vector. Remember to apply small sample size corrector if necessary. Then, use the coefficients to create an ecm term for your error-correction model. This allows you to cross-check your work because ECM(-1) should enter only the exchange rate equation. Also, you may find that some of the restrictions may not hold and that shouldn't bother you because you are testing an unrestricted setup. 

If the trace is more than one cointegrating vector, maybe you have not chosen an appropriate lag length.