Consider the following nonlinear regression model: 𝑦 𝑖 = 𝛼 + 𝑒 𝛽 𝑥 𝑖 + 𝜀 𝑖 , Assume i.i.d. data and 𝔼 [ 𝜀 𝑖 | 𝑥 𝑖 ] = 0 . To estimate 𝛼 and 𝛽 by GMM, we need two moment conditions. Choose the best answer below: 单项选择题

A

The two moments are 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝑒 𝛽 𝑥 𝑖 ] = 0 𝔼 [ 𝑥 𝑖 𝑒 𝛽 𝑥 𝑖 ] = 0

B

There is not enough information to write two moment conditions.

C

The two moments are 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝑒 𝛽 𝑥 𝑖 ] = 0 𝔼 [ 𝑦 𝑖 − 𝑒 𝛽 𝑥 𝑖 ] = 0

D

The two moments are 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝑒 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝑒 𝛽 𝑥 𝑖 ) ] = 𝔼 ( 𝜀 𝑖 )

E

The two moments are 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝑒 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝑒 𝛽 𝑥 𝑖 ) 𝑥 𝑖 3 ] = 0

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