Anon

Model Estimation 287

values for Y for some of the observations are different. If we repeat the same
calculations as above, we find the following empirical moments:

m

m

m

1.8600

4.5220

13.9608

1

2

3

=

=

=

If we apply the MOM and equate the first two theoretical and empirical
moments, using equation (13.21) we obtain

μ

σ

=

=−=

186

(^22186)

.

4.5220. 1.0624

Using these parameters we can now compute the first three theoretical
moments:

m

m

m

1.8600 1.8600

4.5220 4.5220

12.3630 13.9608

11

22

33

μ= =

μ= =

μ= =

While the first two theoretical and empirical moments coincide by con-
struction as in the previous case, there is a significant difference between the
theoretical and empirical values of the third moment. The vector g in equa-
tion (13.22) assumes the following values:

g

0

0

–1. 5978

=





















table 13.2 Sample Data to Illustrate the GMM

Observation Y X

1 0.7 0.7

2 1.3 1.3

3 1.1 2.9

4 1.7 4.2

5 1.6 5.5

6 1.4 6.7

7 1.6 7.4

8 1.7 8.1

9 3.1 9.2

10 4.4 10.6