It measures the speed of adjustment towards long-run equilibrium.

thank professors for your valuabel response.

what exactly does the speed of adjustmment mean?

for example if the coefficient of error correction term is -0.15 or +0.15, how to interpret that value and sign?

thanks in advance.

Suppose we have some cointegrating relationship x -ay = 0 between the two variables x and y, Now suppose that there is disequilibrium and x-ay=d. a coefficient of -0.15 means that 15% of that disequilibrium is dissipated before the next time period and 85% remains. (of course other new shocks may also add or subtract from the disequilibrium in the next period). It is often of interest to estimate how long it will take for an existing disequilibrium to be reduced by 50% (half life of disequilibrium). For your -.15 this is given by n in the solution of

0.85^n = 0.5

Take logs of both sides to get

n = 4.265

Half a disequilibrium will occur in about 4 1/4 years. Even when the coefficient is significant but small it may take a very long time for the disequilium to be halved

thank you prof. John C Frain

you explained about negative value of error correction coefficient excellently.

if the value fo error correction coefficient is positive, how do you interpret it.

thanks in advance

The coefficient on the error correction term is expected to be between -1 and 0. The negative sign indicates the degree of correction.

In a single equation ecm, the coefficient on the error correction mechanism must be between -2 and 0. Otherwise, the error correction term is explosive. In a single equation (Engle-Granger or ARDL estimates or ... ) a coefficient outside the accepted range is an indication of model misspecification. Possibly the single equation methodology is not valid.

If you are dealing with a multivariate system this is not necessary. Consider the two-equation system

\Delta x_t = -0.5 ( x - ay)_{t-1} + \epsilon_{1t} (where a>0)

\delta y_t = -0.25( x - ay)_{t-1}} + \epsilon_{2t}

where x_t and y_t are I(1) and are cointegrated and the equilibrium cointegrating relationship is x-ay.

In the first equation, the coefficient is -0.5 and clearly tends to reduce the equilibrium term. In the second equation, the coefficient is in effect positive when regarded as an adjustment to y and thus tends to increase the disequilibrium in y. However, the reduction effect on x is larger than that on y and the overall system will be drawn back to equilibrium.

If you are interested in the dynamics of your system have a look at the impulse Responses and possibly the eigenvalues of the companion matrix. If any of the Impulse responses are explosive reconsider your model.

In general, the stability of the system is determined by the eigenvectors of the estimated dynamic system.

thank you prof. John C Frain

Read the article in this link and see how positive and significant ECM coefficient is interpreted

https://www.google.com/url?q=http://ricardo.ecn.wfu.edu/~cottrell/ecn215/extra/error_corr_2004.pdf&sa=U&ved=0ahUKEwjmg-74qOnhAhUCURUIHRy3CLwQFggYMAU&usg=AOvVaw3AQKoiqkWCqgtY_w_Sokld

Hello all, noticed most of the new generation estimates has no ECT (eg DCCE), may i please know if it's ok to report the result without the ECT or i have to run for a different estimate that shows ECT (eg PMG)?

I appreciate ur comments.

what is the econometrics magnitude of ecm

It has to be negative. If positive, re-evaluate the variables in the model

the magnitudes of ecm indicates for any shocks the speed of recovery from short-run disequilibrium to long-run equilibrium convergence

If the value of ECM term is -1.62 then is it ok or should we recalculate the model? Thanks

Please enlighten me if we have to compare two models one with error correction term 0.04 and high magnitude of slope coefficients or one with 0.80 error correction term but magnitude of slope coefficients very low. which one is better?

The coefficient of the error correction term is expected to be between -1 and 0. The negative sign indicates the degree of correction. In a single equation error correction model, the coefficient on the error correction mechanism must be between -1 and 0. Otherwise, the error correction term is explosive. A negative and statistically significant coefficient on the error-correction term implies that roughly 87% of the disequilibrium in the previous years is corrected within one year. Common Method Bias (CMB) is a systematic error that occurs when the same method is used to measure multiple variables in a study. It can lead to spurious relationships between variables and can affect the validity of the results. There are several methods to test and control for CMB, including Harman’s one-factor test, marker variable technique, and partially out the first unrotated factor as a “general factor” attributable to social desirability or common method bias. Ergodicity economics is an approach to economic theory which emphasizes the ergodicity question, namely whether expectation values of stochastic processes are equal to their time averages. This yields alternative solutions to classic problems in economics. In essence, ergodicity economics explores what aspects of economics can be informed by avoiding implicit assumptions of ergodicity. It insists on a physical justification when expectation values are used. In ergodicity economics, expectation values are replaced, where necessary, by averages that account for the ergodicity or non-ergodicity of the observables involved.

The coefficient of the error correction term (ECT) is expected to be between -1 and 0. The negative sign indicates the degree of correction. The error-correction term relates to the fact that last-period’s deviation from a long-run equilibrium, the error, influences its short-run dynamics. The magnitude of the coefficient suggests a fairly high speed of adjustment in the aftermath of a shock. The error correction term is defined as e c t t := z t − x t − y t (= ε t)

Srikanth Potharla Looking back over this discussion one part of your question was never answered. In relation to the coefficient of the error correction term - "How to interpret its statistical significance?"

I have seen software producing t-statistics for this coefficient. |These t-statistics do not have a standard t-distribution and therefore the evaluation of the coefficient is not valid. In a VECM if you wish to test the statistic you must use a Likelihood ratio test.

Your software may have some routine to do this calculation. It is important if you wish to consider the weak exogeneity of an explanatory variable.

Many of your replies discuss the interpretation of an error correction coefficient that is between 0 and -2. It is important to understand that it is not, except in special cases necessary that the coefficient is between these two limits. The stability of a VECM depends on the eigenvalues of the dynamic system created by the VECM. When these eigenvalues are of modulus 1 or less the system is stable.

For example, even when the coefficient of the error correction term is between these limits the short-run adjustments could be overshooting and cause disequilibrium. A valid VECM must have stable dynamics.

I have asked this question before and have not received any answer.

Can anyone give a reference to a textbook that says that the coefficient of the error correction in an ecm must be between 0 and -2 or between 0 and -1? This is not true. There may be some blogs that say so and these should be corrected. They are based on a misunderstanding of the dynamics of such systems.