## Instrumental regressions

Consider the limited information (LI) structural regression model:

y = Ye + Xayі + u = Z5 + u, |
(23.3) |

Y = Xana + X2n2 + V, |
(23.4) |

where Y and Xj are n x m and n x k matrices which respectively contain the observations on the included endogenous and exogenous variables, Z = [Y, Xa], 5 = (P’, y1)’ and X2 refers to the excluded exogenous variables. If more than m variables are excluded from the structural equation, the system is said to be overidentified. The associated LI reduced form is:

п 1 = ПіР + y1/ п2 = П2р.

The necessary and sufficient condition for identification follows from the relation п2 = П2р. Indeed P is recoverable if and only if

rank(n2) = m. (23.7)

To test the general linear hypothesis R5 = r, where R is a full row rank q x (m ...

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