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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.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).
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?
If the estimation rejected the model then the model was deemed inappropriate and therefore modified.
This was an approach that went from specific to general.
Cointegration (Engle and Granger, 1987, Engle and Yoo, 1987, 91, Phillips and Ouliaris, 1990, Stock and Watson, 1988, Phillips, 1991) The idea is to look for linear combinations of variables that remove the common trend and make the combination I(0).
For instance in the case of two variables xi ,t and yi ,t , can we find a unique value of such that there is no unit root in the relation between the two variables and yt xt is I(0)?
-- 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 1xt (1 )( yt 1 xt 1 ) et ---The Error Correction Model (ECM).
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.