Question

For each of the Gauss-Markov Theorem assumptions (A0-A3), do the following: 

(a) State the assumption in mathematical terms. 

(b) State the intuitive meaning of the assumption. 

(c) For bonus points, state what might cause the assumption to be violated.

Answer 1

(a) Ideal conditions have to be met so that we can say that OLS is a good estimate.

Assumptions in mathematical terms.

1. (betas are parameters OLS estimates and epsilon is random error)

2,i=1,2,3... where is the i th error term.

3.

4.=0,i not equal to j.Cov-covariance

5.Cov()=0(Xi is independent variable and epsilon is the error term)

(b) Assumption numbers are correspondingly mentioned with respect to above answer.

1.It states that regression model is linear when all terms in model are constant or parameter multiplied by independent variable.

2.Expected value of error terms is 0 for all observations

3.Homoskedasticity It implies that model uncertainity is identical across observations.That is variance of errors should be consistent across all observations.

4. Error terms are independently distributed and not correlated

5. All independent variables are uncorrelated with error terms.

(c)Assumption numbers are correspondingly mentioned with respect to above answer

1.This assumption is wrong if model doest fit linear pattern.

2.If the expected value of error term takes a value other than 0 part of error term becomes predictable.

3.Heteroskedasticity-variance of error term is different across observations which is dependent on unobserved variables.

Possible cause of this includes omission of variables from calculation.

4.Spacial correlation or auto correlation.

This is caused by error term in t1 being dependent on error term in t0.Not accounting for this violates basic assumptions of OLS.

5.Ommited variable bias,simultaneity between independent and dependent variables.

Thanks for the question.Keep Chegging.