2. Serially Correlated Error Terms Flashcards
When do we have serially uncorrelated errors?
When corr(Ut, Ut-k)=0
Possible sources of serial correlation in errors
- variables omitted that are correlated across periods
- incorrect functional form
- systematic errors in measurement
What happens if we plot an AR(1) and vary p from 0 to -0.9?
The absolute magnitude of the process increases a lot. The process crosses the sero line in more periods
What happens if we plot an AR(1) and vary p from 0 to +0.9
The magnitude increases. There are much less crosses of the zero line
Consequences of serial correlation
- bias
- inference
In relation to serial correlation, when is a model biased?
It will be biased when the model contains lags of the dependent variable and there is serial correlation
How do serial correlated errors lead to poor inference?
The convential OLS forumla for calculating standard errors is incorrect in the presence of seriallly correlated errors.
What does positive correlation do to the standard errors under convential OLS formula?
It makes the standard errors too small
Methods for testing serial correlation
- graphical approach- examine a plot of residuals
- using residual correlogram
- durbin-watson test, durbin’s alternative test, breusch godfrey test
When can the durbin watson test be performed?
- regression model has intercept
- serial correlation in residual u is of first order
- regression model doesnt include lagged dependent variables
Steps of Durbin watson test
- Estimate model parameters using OLS and obtain residuals
- Calculate the Durbin- Watson test stat
- Based on DW stat and CV make a decaion whether to reject Ho
In a Durbin Watson test when do we reject Ho in favour of positive correlation ?
When DW stat< lower bound
In a Durbin Watson test when do we reject Ho in favour of negative correlation ?
When DW stat> 4- lower bound
Advantages of Durbin’s alternative test compared to the Durbin Watson test?
- it can be carried out even when regressors contain lagged dependent variables
- can also be used to test serial correlation against higher order serial correlations
When do we reject Ho in Durbin’s alternative test?
If coefficients on lagged residuals are jointly different from zero
How do you compute the test stat for the Breusch Godfrey test?
T x R^2
Where T is the number of observations in the regression in step 2
When do we reject Ho for a Breusch Godfrey test?
When the calculated value is greater than the critical value
What are Newey west standard errors?
They are robust standard errors to arbitrary autocorrelation up to the order of the chosen log
Feasible Generalised Least Squares estimator
Arbitrary autocorrelation robust standard errors which require us to specify the functional form but if correct are very efficient
Steps of FGLS
- Lag the original model
- Multiply the lagged model by P and subtract it from the original model
- Estimate P by regressing ût on ût-1 and repeating
