[SOLVED] ECON772 Homework 2 -Linear Model

Linear Model

• 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.

• 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: