An Essay On Cointegration And Error Correction Models

Thus the LR (or static) equilibrium requires the deviation to be stationary (not to grow over time), to be I(0).

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We can reparameterize this equation in several ways: 1.

LR and SR multipliers e e    2L     2  yt  1  xt  t  xt  t and the LR solution is yt  1 1  L 1   1  L   1   or yt xt  ut ---the cointegrating relation.

In many instances, it is difficult to establish a general model.

The conceptual difficulties with general models led to a wide adoption of the: 3.

I have posted a similar question at But anyway, after finding out that (x, y) are cointegrated, do I run the usual OLS or use a error correction model?

If the latter, how do I get a error correction model and run a regression on it?    --   1 2  = the LR multiplier of xt on yt ; 1 = the SR multiplier. 1   -- Cointegrating vector = (1,  ) If  0 then y and x must have the same stochastic trend, otherwise e would not be I(0). Error Correction Model Subtract yt  1 from both sides and add and subtract 1 xt  1 from the RHS: yt 1xt  (1   )( yt  1  xt  1 )  et ---The Error Correction Model (ECM).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.We want to see if there is a linear combination of these two variables that does not have a stochastic trend, i.e. One simple way is to see if the residual from the cointegrating relation is stationary.For this: Multivariate Models I: CI& ECM 5 Test critical values: 1% level -3.463235 5% level -2.875898 10% level -2.574501 Cointegration refers to LR relation.It shows how yt responds in the SR to changes in xt and to deviations from LR equilibrium ( yt  1  xt  1 ) .Note that the LR equilibrium derived in (1.) is now nested in the dynamic model.Econometricians estimated large models assuming that some variables were exogenous (or predetermined) and affected the endogenous variables –Cowles Foundation approach-- The estimates were interpreted as the multipliers (static or dynamic) representing the reaction of the economic variables (endogenous) to policy variables (exogenous).Restrictions on equations were imposed based on theoretical assumptions.


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