Lecture 11 Cointegration

Question 1

Cointegration

Answer 1

(If they are stationary you can use OLS, most of the time they arent)
.. deviation from long run equil -> errort = betaxt
1. Cointegration refers to a linear combination of non stationary variables. If (b1..bn) is cointegrating vector, than (lambda b1,…lambdabn) also coint iff lambda =! 0
To normalize the coint vector w.r.t. xyt simple select lambda = 1/beta1
2. Equation must be balanced in that the order of integration of the two sides must be equal.
3. If xt has m components there may be as many as m-1 linearly indep. coint. vectors.

Question 2

Granger Representation Theorem

Answer 2

IN ECM the short term dynamics of the variables in the system are influenced by the deviation from equil. GRT stating that for any set of I(1) variables, error correction and cointegration are equivalent representations.

Question 3

Engle Granger Methodology:

Answer 3

1. Pretest the variables for their order of integration
2. Estimate the long run equil relationship. If the results of step 1 indicate that both yt and zt are I(1) ->estimate -> Consider the autoregress. of the residuals., Test alpha1 = 0.
3. Estimate ECM deltayt, deltazt

Question 4

Speed of adjustment coefficients

Answer 4

alphay and alphaz have important applications for the dynamics. Large value of alphaz is associated with large deltazt .
If alphay is zero, zt does all of the correction to eliminate any deviation from long run equil. yt doesnt do any of the error correction. yt is weakly exogenous.

Question 5

Problems with EG Method

Answer 5

1. It is possible to find that one regression indicates the variables are cointegrated whereas reversing the order indicates no integration.
2. In test using three or more variables, there could be more than one cointegrating vector. (no procedure for the seperate estim. of the multiple coint. vectors)
3. Relies on a two step estimator.

Question 6

Read Johansen Methodology on the paper!

Answer 6

If (A1 - I) is full rank, each of xt converge to a point.
If consists of all zeros, all of xit would follow a unit root process
ln(1-lambda) = 0, if the variables are cointegrated, Johansen use pi = alpha*beta’, testing follows a chi2 distribution
Process can be modified to include a drift and seasonal dummy variables.

Question 7

Lag length and causality tests.

Answer 7

To determine lag length use multivariate AIC, SBC– If you want to test the lag lengths for a single equation Ftest is approp.
From VAR follows a VECM…

Question 8

Basic VAR

Answer 8

no autocorrelation residuals is particulary important, the residuals should at least be distributed symmetrically.
The bearing length should not be too great