Whenever I encounter two vectors I would generally interpret it as misspecification and would work hard to come up with a single interpretable vector.

Chuck A Arize 's advice will certainly simplify your analysis. It is very important that you start with your economic theory/ common sense and work out in advance how many equilibrium relationships are in your model and how they can be identified. I have explained some points relating to the table you attached. I particular I don't think that Johansen's model 5 is not producing sensible results

I presume that you are using quarterly data.

You have two equilibrium relationships (ecm1 and ecm2)

Ecm1 is the equilibrium relationship

lgdpr = 2.56 lvisitors - 8.02 lemployed + 0.02 t +29.58

or the error correction mechanism (disequilibrium)

ecm1 = lgdpr - 2.56 lvisitors + 8.02 lemployed - 0.02 t -29.58

In the dlgdpr equation, the coefficient 0.05 means 5% of the disequilibrium is restored in the next quarter. This means that half of any disequilibrium in any one period is dissipated in about 14 quarters. There is a similar adjustment for each of the other variables arising from ecm1. Ecm2 and its adjustment speeds are defined similarly. It is nearly impossible to determine stability from these adjustments. Stability is determined by the roots of the companion matrix of the estimated system. I would hope that Eviews does this analysis.

Your software is producing two identified equations

Ecm1 determines an equilibrium for lgdpr by imposing a zero restriction on ltaking

Ecm2 determines an equilibrium for ltaking by imposing a zero restriction on lgdpr. I suspect that your economic reasoning may question this relationship as I would think that the equilibrium of this variable depends on lgdpr. If you enter the variables in a different order in your estimation Eviews will likely produce a completely different set of equilibrium relationships. The VECM procedure estimates the space of the cointegrating vectors. This means that if you have two cointegrating vectors, then any two independent linear combinations of those two cointegrating vectors are also cointegrating vectors. You must use economic theory/common sense to identify the appropriate pair of cointegrating vectors. Econometrics can not do this.

I would also be concerned that a t term is included in the ecm. Have you considered the economic meaning of ecm1? The t term implies that other things being equal, gdpr grows by 2% per quarter or 8% per annum. This does not sound correct.

I would also warn you that it is unlikely that the t-statistics on the error correction terms do not follow a standard t-distribution. This should be clarified in your Eviews manual.

I agree with all comments made above by John C Frain

Let me add an obvious point he needs to check. The equation has no significant error correction term, even though he claims he has two vectors. In no case did the dynamics translate into the steady-state. Take out the trend variable and ensure that appropriate outliers have been handled with dummies vars, including seasonality, and avoid extreme models (i.e., without intercept and inclusion trend variable, Johansen 5).

The last sentence in my first paragraph should read

Johansen model 4 (unrestricted constant, restricted trend) is not producing sensible results.

Dear Tran Nhat Duy Nguyen ,

I completely concur with the advice and insights provided by both Chuck A Arize and John C Frain .

In addition, please advise what is the economic theory underpinning your study? – which concomitantly further extends to the theoretical framework.

Kindly recall that the error correction term; also called the “cointegration term”, reflects the speed of adjustment at which the deviation by endogenous variables (x, y, etc) from the long-run equilibrium course gradually corrects through a sequence of partial short-run adjustments. The error correction term, thus, indicates the long-run behaviour of the respective endogenous variables towards convergence to their long-run cointegrating relationship.

In the case of your results, the occurrence of steady adjustment to the long-run equilibrium through the short-run partial adjustment mechanism is unsubstantiated by the statistically insignificant statistics relating to deviations from the long-run equilibrium path. Results of the short-run dynamics of your specified equation do not show evidence of correction of the temporary deviation from the long-run equilibrium relationship between the specified variables in the first period (eg. quarter, year, etc – depending on the frequency of your data) after the occurrence of the deviation.

Best!

I want to stress John's point for a careful specification of the (theoretical) model. It seems that this has not be done here. It is not clear what variables are used. Even for GDP, one must guess, whether it is nominal or real. EMPLOYED can mean employees of a whole economy, one sector or an enterprise (as the term VISITERS suggests). I do not know what TAKING is.

One should therefore not put too much trouble into the interpretation of the results. They are not accepatable. More than 90% of the coefficients are not signicicant. As John pointed out, a constant of 2.2% for the quarterly (I think that his assumption that quarterly data were used) growth of GDP (i.e. 9% p.a.) cannot be true. If one deletes all insignificant variables from the dlnGDP equation, one gets %GDP=2.2%-0,75%GDP-1-0.5%GDP-2-0.65GDP-3 (of course, the coefficients would change for an estimate only with these variables). This is a result similar to one would get for a variable with a trend and seasonal pattern plus a white noise.

Dear Tran.

Kindly take time to check your model specification for clarity.

Regards

Tran Nhat Duy Nguyen

if you have not solved your problem, please look carefully at LTAKING variable, it is plausible that your problem is coming from there. Thank you for giving us this assignment.