Econometrics A

Question 1

What are the two types of data

Answer 1

1. Cross-Sectional = observations at a point in time.
2. Time-Series = observations of variables over time.

Question 2

What are the properties of OLS estimators

Answer 2

1. Efficiency = lowest variance.
2. Unbiasedness = the sampling distribution of the estimator is centred on Q.
3. Consistency.

Question 3

What are errors in hypothesis testing

Answer 3

Type 1 error = rejecting null when it is true.
Type 2 error = not rejecting a false hypothesis.

Question 4

What are the classical linear regression assumptions

Answer 4

CLRA1 - Model written.
CLRA2 - Explanatory variable is fixed.
CLRA3 - Variation in the X variable.
CLRA4 - Error has expected value of 0.
CLRA5 - No autocorrelation.
CLRA6 - Homoscedasticity.
CLRA7 - Population error is normally distributed.

Question 5

What are the theoretical results of CLRAs

Answer 5

TR1 - OLS estimators are unbiased.
TR2 - BLUE.
TR3 - Minimum Variance Unbiased Estimator.

Question 6

CLRAs zero conditional mean

Answer 6

CLRA1 - Model.
CLRA2 - Variation in the X variable.
CLRA3 - Error has expected value of 0.
CLRA4 - Disturbances are conditionally uncorrelated.
CLRA5 - Each disturbance has the same finite variance.
CLRA6 - Population error normally distributed.

Question 7

What is R^2 and what is the formula

Answer 7

Goodness of fit. R^2 = 1 - (RSS/TSS) = ESS/TSS.

Question 8

CLRAs multiple regressions

Answer 8

CLRA1 - Model.
CLRA2 - Error has expected value of 0.
CLRA3 - No regressors are constant.
CLRA4 - Not conditionally autocorrelated.
CLRA5 - Conditionally homoscedastic.
CLRA6 - Population error, conditional on the regressors, normally distributed.

Question 9

What affects standard error of OLS estimators

Answer 9

1. Variance of the error - increase variance of error = increase variance of estimator.
2. Variance in X variable - decrease variance in X variable = increase standard error.
3. Correlation between X and Z - increase correlation = increase standard error.
4. Sample size, n - increase n = reduced standard error.
5. Number of regressors, k - increase k = increase standard error.

Question 10

What is mulitcollinearity and how to identify, detect and deal with them

Answer 10

Identify: high variance, low t-values, high R^2 value, wrong signs.

Detecting: use regression results, look at R^2 values.

Dealing: dropping one of the problem variables, use a different source of sample of data, change functional form, use estimated values from previous literature.

Question 11

What are autocorrelated errors, sources, consequences, how to test for them and how to deal with them

Answer 11

A variable that is correlated with itself at different points in time. Violates CLRA4, errors are now autocorrelated.

Sources: Omission of explanatory variables or dynamic structure.

Consequences: OLS estimators still unbiased, equations for the variances of the OLS estimators are incorrect, OLS is no longer the best estimator (GLS).

Testing: DW test and Breusch-Godfrey test.

Dealing: GLS and Cochrane-Orcutt iterative procedure.

Question 12

What are heteroscedastic errors, consequences, how to test for them and how to deal with them

Answer 12

Violates CLRA5 - disturbances are now heteroscedastic, the variances are different for each i.

Consequences: OLS estimators are still unbiased, equations for the variances of the OLS estimators are incorrect, OLS no longer best estimator (WLS).

Testing: White’s test, Breusch-Pagan test and Goldfield-Quandt test.

Dealing: Weighted Least Squares (WLS).