Positive ECM is not a good sign for your model. It implies that the process it not converging in the long run. Thus, there are some instabilities. Usually this means that there are some specification problems with the model itself, or maybe there are some data issues. It could also be an indication of structural changes, as you have suggested, but you should specify those in your model, if you suspect that there are some in the analyzed period. Also, there are time series tests for structural breaks, so you could first test for those and maybe include them in the model if they are significant.

Dear Valerija,

Thanks for your valuable suggestion. I will test the presence of structural shifts in the data and model specification.

Many thanks

Kifle

Adding to Valerija, If you checked the assumptions and they are fulfilled. In this situation the positive sign of ECM depicts that due to any structural change in your variables they will converge towards equilibrium rather it will diverge from equilibrium. Also keep in mind the value of Durbin Watson Test, which tells us about the problem of autocorrelation. Sometimes the ECM sign is positive due to the presence of autocorrelation.

Thanks Muhammad. I checked for autocorrelation and the number of lag included in the model has addressed it and the test result showed that there is no autocorrelation problem. But if the equilibrium relationship between the prices shifts, such as due to significant income and population change as well as a change in taste, if all prices adjust towards the new equilibrium position, can we still exclude the possibility of positive coefficient of one or more of the EC terms. Your comment is highly appreciated.

It would be useful to know exactly what you are estimating. In particular, Hendry (1995), Dynamic Econometrics would distinguish between Equilibrium and pure error correction (I might suggest you obtain a copy of this book). The traditional models relate back to the Sargan (1964) Wage Equation reproduced in the Festschrift edited by Hendry and Wallis (1984), Econometrics and Quantitative Economics and subsequent articles by Davidson, Hendry and Mizon amongst others in 1978. If you are estimating the models with unit coefficients, then my concern would be that such restriction would not usually hold in a well formulated demand equation and this could lead you not to find a stable model. If the model is logarithmic then you cannot anticipate unitary elasticity.

Simple error correction models are only really valid when the system is bivariate when this is not correct then there may be more error correction terms and thus what the late Sir Clive Granger has termed hidden cointegration may arise. The single error correction is not sufficient to explain the long-run corrections that drive the system. So prices may be driven by some sort of cost mark-up while quantity is explained by a demand equation and you are modeling a mixture of these relations. There may be further issues that may arise when single equation methods are being applied especially the cointegrating regression approach. It is possible to identify such models and James Davidson, Econometric Theory (2000) includes a chapter explaining how this might be done. However, care must be taken with the inclusion of stationary terms as near non-stationary variables may cause significant distortion in the cointegrating regression equations.

I would also suggest looking at the demand literature as the log-log formulation does not satisfy adding up so this suggests flexible function forms such as almost ideal systems that can also give rise to dynamic models. These models approximate a wide range of demand equations and subject to quasi linear Engle curves aggregate perfectly across individuals. The models are quasi linear depending on the nature of the price index used, but there are also non-linear generalisations of these formulations.

An example of this type of model is the almost ideal system (AIDS) of Deaton and Muellbauer (a start point might be their book Consumer Theory (1980), OUP). However, this model uses the budget share as the dependent variable and this is bounded to lie in the region zero to one so there is a degree of skepticism as to whether such series can be I(1). However, there is an error correction form of this model called dynamic AIDS where the results are discussed in terms of the long-run of a dynamic system that may still relate to stationary variables or variables that may be thus restricted.

The latter were all the variables in the model real and price homogeneity imposed in relation to the long-run variables might be estimated as a VAR or under restriction via SURE; otherwise endogeneity may be an issue.

Hi John many thanks for your valuable comment. I will explore the issues you raised and do  wider reading. For your information, I am trying to find if crop prices, such as prices of wheat and maize , are close substitutes and also which of these prices have a price leading role.  Based on utility maximization as my theoretical framework, I derived a theoretical model which suggests that crop prices have a stable equilibrium price differences. I am testing if this holds in different spatial locations and also trying to find to what extent the government can stabilize the overall crop prices movements by stabilizing  only the crops that have price leading role.  

Can ECM term be lower than -1? the attached paper reports ECM coefficient as -1.27.

Can ECM term be lower than -1? How to interpret a value lower than -1? Does it suggest that something wrong with the model?

Any help?

Thank you in advance.

The easiest way to consider the size of the coefficient on the ECM is in terms of the Engle-Granger approach as the ADF test procedure applied to the residual from the cointegrating regression:

In the context of potentially cointegrating regressions the primary regression is static and the DF coefficient provides a one step estimate of the first order autoregressive coefficient plus one. So for this variant of ECM the AR coefficient is zero when the ECM term is -1 and the cointegrating regression has no first order error autocorrelation.

When the common factor restriction holds:

Here when the ECM coefficient is less than -1 then the cointegrating regression exhibits positive error autocorrelation so a coefficient that is less than -1 is not a problem unless the associated serial correlation coefficient is less than or equal to -1 and there is a -ve unit root. The associated cut off for this coefficient is -2.

If the above does not apply then the precise link to the error behaviour is not as clear, but ECM terms less than -2 are an issue, but fortunately -ve autoregression in economic and finance data in the non-stationary form is not so usual.

In the VAR then again the link to the autoregression in the error is less precise even with a single cointegrating vector as the alpha loadings depend on the normalisation and relative scaling of the data. With as mentioned in my previous response the error correction coefficient being +ve when the associated term in the cointegrating vector  is -ve.

These conclusions do not hold with more than one cointegrating vectors.

Usually with economic and finance data the first order autoregression in the data is positive. If a linear regression with this data is estimated then except in highly unusual cases the model will suffer from first order error autocorrelation with a positive coefficient. For example a cointegrating regression can have an uncorrelated error as the regressor or regressors capture all the lagged error behaviour and the stochastic trends. Such an example occurs in the case considered in the simulations in Burke and Hunter (2007) available to the interested reader on RG. It may be possible with appropriate scaling as mentioned in the previous answer to find -ve serial correlation and as a result an error correction coefficient that is less than -1. However, care must be taken of -ve unit roots. 

if ECT value is between 0 to -1 and statistically significant, what it means . and further in the presence of controlled variables the Value of ECT is between 0 to -1 but long run coefficients of primary explanatory variables are positive but insignificant then how we will interpret the model.

It is actually possible in some instances.

Express the pace of conditioning from the short term to the long term which is required to be Negative and moral to provide a practical guide to the existence of a long-term relationship between the variables of the study, and in your study the presence of positive reference raises the question of whether it is significant or not? Or there is an error in appreciation from the ground up

What if ETC is positive but significant? How we will interpret it?

What if ETC is positive but significant? How we will interpret it? If it means, mis-specification, then how can we correct the model?

My ECT is positive and significant. How can I correct it?

Its usual case though. Did you double check your codes? Because I faced same problem before and later fixed it by editing code.

Thank you Mohammed for your response. What codes, sir? I don't understand.

check stata list

I'm using eviews