# An Essay On Cointegration And Error Correction Models

I believe some of you do know the answer, please help.

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 Sims (1980): endogeneity of the policy variables. It consists of specifying a general model that can nest several special cases.

 Lucas critique: assumption of coefficient constancy. It should be general enough that the error terms are homoscedastic.

Often we are interested in the SR dynamics and convergence to the LR. Short-run dynamics, LR equilibrium and Error Correction Consider the dynamic model: y t y t  1   1 xt   2 xt  1  et where y, x ~ I(1) and e ~ I(0).

This can be a consumption model where y=consumption and x=income.

This approach also has its problems, not withstanding the Sims and Lucas critiques.

Elimination of variables is subjective and depends on the assessment by the researcher.

This is the LR equilibrium that acts as “attractor” towards which the sytem converges when there is a divergence from it due to nonstationarity (caused by stochastic trends).

You cannot infer cointegration from visual inspection.

Multivariate Models I: CI& ECM 1 More generally consider a model  ' xt et where  ' , xt denote vectors of coefficients (  ,  2 ,  3 ,...) and variables ( x1 , x2 , x3 ,....) of the model.

The system is in LR equilibrium when  ' xt 0 so we can define  et = the deviation from equilibrium.