2. Serially Correlated Error Terms

Question 1

When do we have serially uncorrelated errors?

Answer 1

When corr(Ut, Ut-k)=0

Question 2

Possible sources of serial correlation in errors

Answer 2

• variables omitted that are correlated across periods
• incorrect functional form
• systematic errors in measurement

Question 3

What happens if we plot an AR(1) and vary p from 0 to -0.9?

Answer 3

The absolute magnitude of the process increases a lot. The process crosses the sero line in more periods

Question 4

What happens if we plot an AR(1) and vary p from 0 to +0.9

Answer 4

The magnitude increases. There are much less crosses of the zero line

Question 5

Consequences of serial correlation

Answer 5

• bias

- inference

Question 6

In relation to serial correlation, when is a model biased?

Answer 6

It will be biased when the model contains lags of the dependent variable and there is serial correlation

Question 7

How do serial correlated errors lead to poor inference?

Answer 7

The convential OLS forumla for calculating standard errors is incorrect in the presence of seriallly correlated errors.

Question 8

What does positive correlation do to the standard errors under convential OLS formula?

Answer 8

It makes the standard errors too small

Question 9

Methods for testing serial correlation

Answer 9

• graphical approach- examine a plot of residuals
• using residual correlogram
• durbin-watson test, durbin’s alternative test, breusch godfrey test

Question 10

When can the durbin watson test be performed?

Answer 10

• regression model has intercept
• serial correlation in residual u is of first order
• regression model doesnt include lagged dependent variables

Question 11

Steps of Durbin watson test

Answer 11

1. Estimate model parameters using OLS and obtain residuals
2. Calculate the Durbin- Watson test stat
3. Based on DW stat and CV make a decaion whether to reject Ho

Question 12

In a Durbin Watson test when do we reject Ho in favour of positive correlation ?

Answer 12

When DW stat< lower bound

Question 13

In a Durbin Watson test when do we reject Ho in favour of negative correlation ?

Answer 13

When DW stat> 4- lower bound

Question 14

Advantages of Durbin’s alternative test compared to the Durbin Watson test?

Answer 14

• 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

Question 15

When do we reject Ho in Durbin’s alternative test?

Answer 15

If coefficients on lagged residuals are jointly different from zero

Question 16

How do you compute the test stat for the Breusch Godfrey test?

Answer 16

T x R^2

Where T is the number of observations in the regression in step 2

Question 17

When do we reject Ho for a Breusch Godfrey test?

Answer 17

When the calculated value is greater than the critical value

Question 18

What are Newey west standard errors?

Answer 18

They are robust standard errors to arbitrary autocorrelation up to the order of the chosen log

Question 19

Feasible Generalised Least Squares estimator

Answer 19

Arbitrary autocorrelation robust standard errors which require us to specify the functional form but if correct are very efficient

Question 20

Steps of FGLS

Answer 20

1. Lag the original model
2. Multiply the lagged model by P and subtract it from the original model
3. Estimate P by regressing ût on ût-1 and repeating