ECON 772 Homework 2- Linear Model Solved

Linear Model
1)     Let

y = X¯ + u;

and consider the restriction

R¯ = c:

Write down an unbiased estimate of ¯ that satis…es the restriction and derive its asymptotic distribution. Show that its asymptotic coviance matrix is smaller than the asymptotic covariance matrix of the OLS estimator.

2)     Consider the model

 

where there is no constant in the equation. Derive the properties of R2 for this model.

3)     Let

 Find the asymptotic distribution of 

a)      u0u=n;

b)     ub0y=nbb ;

c)      ubb0u=n: