题目
题目
单项选择题

Consider the following nonlinear regression model: 𝑦 𝑖 = 𝛼 + 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 at least two moment conditions. Chose the correct answer below.

选项
A.We can estimate the model using the following theoretical moments 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 𝛽 𝑥 𝑖 − 1 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 ] = 0
B.We can estimate the model using the following theoretical moments 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 ] = 0
C.We can estimate the model using the following theoretical moments 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 𝛽 𝑥 𝑖 − 1 ] = 0
D.Any of the answers provides appropriate moment conditions for estimation.
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思路分析
Examining the problem, we are dealing with a simple linear regression y_i = α + β x_i + ε_i, with E[ε_i | x_i] = 0 and i.i.d. data. In a GMM framework, valid moment conditions come from the orthogonality between the structural error and instruments (here, the regressor and a constant). Option 1: E[y_i − α − β x_i] = 0 and E[(y_i − α − β x_i) x_i] = 0. These are the standard mean and slope-related moment conditions one can deriv......Login to view full explanation

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