Linear Model

• Let

y = X + u;

and consider the restriction

R = c:

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

• Consider the model

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

• Let

Find the asymptotic distribution of

1. u0u=n;
2. ub0y=nbb ;
3. ubb0u=n: