Lecture 10 Error Correction Models

Question 1

SEM estimated in Error Correction Form

Answer 1

estimate the speed at which the dependent variable y returns to equil. after a change in an independent variable X.
useful for estimating both short term and long term effects of one time series on another
often mesh well with our theories of policital and social processes.
useful when dealing with integrated data, but can also be used with stationary.

Question 2

Basic structure SEM ECM

Answer 2

Error correction component of the model measures the speed at which prior deviations from equil are corrected.

ECM can be used to estimate the following quantitites of interest for all x variables:
Short term effects of x on y
long term effects of x on y
speed at which y returns to equil. after a deviation has occured.

Question 3

Application of ECMs ?

Answer 3

private Consumption, interest rates, economic expectations, consumer confidence, support for social security

Question 4

Stationary vs integrated time series?

Answer 4

Stationary time series data are mean reverting (finite mean and variance that dont depend on time)
Time series can be stationary but contains autocorrelation.
Often is data stationary but appear to be integrated:
Integrated time series data: are not mean reverting
appear to be on a rw
have current values that can be expressed as the sum of all previous changes
the effect of any shock is permanently incorporated on to the series
best predictor of the series at t is the value of t-1
have theoretically infinite variance and no mean

Question 5

Two Time Series are cointegrated if?

Answer 5

Both are integrated of the same order and there is a linear combination of the two time series that is I(0) i.e. stationary. yt = theta xt , zt = yt - theta xt
If the drunken belongs to the dog, they are likely to have an equil relationship and are cointegrated.
… xt - xt-1 = ut + errror correction mechanism

Question 6

Granger Representation Theorem

Answer 6

If y a x are I(1) and cointegrated, then the optimal regression for y takes deltayt = ….. with error correction term.

Question 7

Reactions to spurious regression:

Answer 7

If the series are I(1), then do regressions in differences
Cointegrations says: add the error correction term in z
Difference is critical: error correction coefficient gamma pushes y back toward the cointegration relationship.

Question 8

Engel and Granger Two Step ECM

Answer 8

It is really a 4 step model:

1) Determine that all time series are integrated of the same order
2) Demonstrate that the time series are cointegrated
3) Obtain an estimate of the cointegration vector Z by regressing Y on X and take the residuals
4) Enter the lagged residuals Z into a regression of deltayt on deltaxt-1

Residual has mean zero we dont need a constant.

Question 9

Two step vs Single Equation ECM

Answer 9

Integrate or stationary, sECM avoids this debate

sECM dont require cointegration and easy to interprete of causal relationship

Question 10

ADL vs sECM

Distributed lag models?

Answer 10

Equivalence, standard error for long term effects of variables is relatively easy to obtain in sECM.

DLM: possible multicollinearity, loss of degress of freedom. Use Koyck tranformation to produce a simple model with just Xt on Yt-1. More important long run multiplier from ADL