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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.
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.
I believe some of you do know the answer, please help.
Multivariate Models I: Cointegration and Error Correction Models Historically, econometricians used various approaches to estimate and forecast. Specific to general approach This was the earliest methodology.
Cointegration approach and VAR models: Most economic theory is based on equilibrium models which require the economy to get back to an equilibrium relation in the LR.
This relation imposes the condition that none of the dependent or independent variables can wander away from each other for an extended period of time, implying that the error term associated with the corresponding equilibrium relation has to be white noise.
-- 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).