Consider the following linear regression model: 𝑦 𝑖 = 𝛼 + 𝛽 𝑥 𝑖 + 𝛾 𝑥 𝑖 2 + 𝜀 𝑖 , Assume i.i.d. data and 𝔼 [ 𝜀 𝑖 | 𝑥 𝑖 ] = 0 . To estimate 𝛼 , 𝛽 and 𝛾 by GMM, we use the three theoretical moment conditions 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 − 𝛾 𝑥 𝑖 2 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 − 𝛾 𝑥 𝑖 2 ) 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 − 𝛾 𝑥 𝑖 2 ) 𝑥 𝑖 2 ] = 0 To compute the variance of the GMM estimator we need the matrices 𝛤 0 and 𝛷 0 . Single choice

A

The matrix 𝛤 0 is: 𝛤 0 = 𝔼 [ 1 𝑥 𝑖 𝑥 𝑖 2 𝑥 𝑖 − 𝑥 𝑖 2 − 𝑥 𝑖 3 𝑥 𝑖 2 𝑥 𝑖 3 𝑥 𝑖 4 ] .

B

The matrix 𝛤 0 is: 𝛤 0 = 𝔼 [ − 1 − 𝑥 𝑖 − 𝑥 𝑖 2 − 𝑥 𝑖 − 𝑥 𝑖 2 − 𝑥 𝑖 3 ] .

C

The matrix 𝛤 0 is: 𝛤 0 = 𝔼 [ − 1 − 𝑥 𝑖 − 𝑥 𝑖 − 𝑥 𝑖 2 − 𝑥 𝑖 2 − 𝑥 𝑖 3 ] .

D

The matrix 𝛤 0 is: 𝛤 0 = 𝔼 [ − 1 − 𝑥 𝑖 − 𝑥 𝑖 2 − 𝑥 𝑖 − 𝑥 𝑖 2 − 𝑥 𝑖 3 − 𝑥 𝑖 2 − 𝑥 𝑖 3 − 𝑥 𝑖 4 ] .

E

There is not enough information to compute the matrix 𝛤 0 .

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