Introduction to Econometrics

1
Introduction to Econometrics

• Lecture week 12
• Time series econometrics
• Cointegration Error Correction

2
Cointegration

• A regression of one random walk series
  (nonstationary) on another random walk series
  gives a spurious regression b/c one of the basic
  assumptions of the CLRM (i.e. time invariant
  mean and variance of the error term) will be
  violated. Exception to this is the case where the
  series are cointegrated (i.e. the linear
  combination of these series is stationary).
• ut lagprot ?1 ?2lagprprice (t-1)
• If ut is stationary, lagpro lagprprice are
  cointegrated i.e. there exists long-run
  relationship between the variables. Thus, ?2 is
  the cointegrating parameter. The regression is
  not spurious.
• If ut is not stationary, the variables are not
  cointegrated. This means that the mean variance
  of the residuals changes over time (i.e. the CLRM
  assumptions are violated. Thus, the regression is
  spurious. The solution in such cases is to remove
  trends from the series through differencing.
• Tests for cointegration Correlogram of the
  residuals, augmented Engle-Granger (AEG) Test,
  Cointegrating Regression Durbin-Watson (CRDW)
  Test

3
Long-run equation a regression of LAGPRO on
LAGPRPRICE possible outlier detected in year 1972
4
Test for the significance of the outlier
confirmed overall result improved, outlier
removed
5
Test for cointegration cointegration confirmed
using augmented Engle-Granger Test (5 critical
is -3.78)
6
Conclusion on the cointegration test

• Augmented Engel-Granger test confirmed the
  presence of stable long-run relationship between
  the SAs agricultural production and SAs
  producer price index.
• The regression of agricultural production on
  producer price is not spurious.

7
Error Correction Mechanism (ECM)

• The error term ut in the cointegration regression
  is the equilibrium error.
• The error correction mechanism corrects for
  disequilibrium and serves as a link between the
  short-run behavior of the dependent variable and
  its long-run value.
• If ?2 is statistically significant, it tells us
  the proportion of disequilibrium in lagpro in one
  period which is corrected in the next the larger
  ?2, the quicker the adjustment back to
  equilibrium.

8
Error Correction Mechanism variables have the
expected sign, 64 of the disequilibrium in year
t-1 is corrected in year t.