Econometrics

Question 3(C ):

Used constant values for x, u, z and r in all the trails.

x u z r

N(0.6,1.2) N(0,0.2) N(0.5,1) N(0,0.4)

Case 1:

β1 β2 δ1 δ2

1 2 0.3 0.4

Result:

Samples β1 obtained β 2 obtained

50 1.017105 1.973811

500 1.012906 1.996428

5000 1.001158 1.999286

From the above results it can be seen that the estimated values of β1 and β2 are almost equal to the set values of β1 and β2 when the sample size is 50 and 500. But comparing the set values and estimated values of the β1 and β2 for the sample size of 5000, the values are more precise.

Case 2:

β1 β2 δ1 δ2

0.5 0.5 0.5 0.5

Result:

Samples β1 obtained β 2 obtained

50 0.4873854 0.5053234

500 0.4967929 0.5068216

5000 0.5023603 0.4999937

From the above results it can be seen that the estimated values of β1 and β2 are having similar features as the case 1. The estimated values of β1 and β2 are almost equal to the set values of β1 and β2 when the sample size is 50 and 500. But comparing the set values and estimated values of the β1 and β2 for the sample size of 5000, the values are more precise.

Case 3:

β1 β2 δ1 δ2

10 20 0.1 5

Result:

Samples β1 obtained β 2 obtained

50 10.03987 19.99735

500 9.996189 19.99693

5000 10.00146 19.99931

The model seems to work for smaller samples as well as when the sample size is increased. The estimated values obtained are almost the same as the estimators fed to the model.

Question 3(C ):

Used constant values for x, u, z and r in all the trails.

x u z r

N(0.6,1.2) N(0,0.2) N(0.5,1) N(0,0.4)

Case 1:

β1 β2 δ1 δ2

1 2 0.3 0.4

Result:

Samples β1 obtained β