An Essay On Cointegration And Error Correction Models

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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.

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.

    --   1 2  = the LR multiplier of xt on yt ; 1 = the SR multiplier.

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 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.

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

 The vector of coefficients,  ' = cointegrating vector.

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