(Requires Matrix Algebra)The Population Multiple Regression Model Can Be Written

question 44

Essay

(Requires Matrix Algebra)The population multiple regression model can be written in matrix form as
Y = Xβ + U
where
Y = ,U = ,X = ,and β = Note that the X matrix contains both k endogenous regressors and (r +1)included exogenous regressors (the constant is obviously exogenous).
The instrumental variable estimator for the overidentified case is where Z is a matrix,which contains two types of variables: first the r included exogenous regressors plus the constant,and second,m instrumental variables.
Z = It is of order n × (m+r+1).
For this estimator to exist,both ( Z)and [ Z( Z)-1 X] must be invertible.State the conditions under which this will be the case and relate them to the degree of overidentification.

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