Consider the following nonlinear regression model: 𝑦 𝑡 = 𝛼 𝑥 𝑡 𝛽 + 𝜀 𝑡 Assume i.i.d. data and 𝔼 [ 𝜀 𝑡 | 𝑥 𝑡 ] = 0 . To estimate 𝛼 and 𝛽 by GMM, we use the following moment conditions: 𝔼 [ 𝑦 𝑡 − 𝛼 𝑥 𝑡 𝛽 ] = 0 𝔼 [ ( 𝑦 𝑡 − 𝛼 𝑥 𝑡 𝛽 ) 𝑥 𝑡 ] = 0 We have an i.i.d. sample with 𝑇 = 8000 observations, with ∑ 𝑡 = 1 𝑇 𝑥 𝑡 = 2000 , ∑ 𝑡 = 1 𝑇 𝑥 𝑡 2 = 4000 and ∑ 𝑡 = 1 𝑇 𝑥 𝑡 3 = 8000 . We obtain point estimates 𝛼 ̂ = − 5 and 𝛽 ̂ = 3 . To compute the variance of the estimates, we need to estimate the matrix 𝛤 0 , 𝛤 ̂ 0 = [ 𝛤 ̂ 11 𝛤 ̂ 12 𝛤 ̂ 21 𝛤 ̂ 22 ] Then, the value 𝛤 ̂ 11 is: 单项选择题

A

𝛤 ̂ 11 = 4000

B

𝛤 ̂ 11 = 0.5

C

𝛤 ̂ 11 = − 1

D

There is not enough information to compute 𝛤 ̂ 11 .

E

𝛤 ̂ 11 = − 0.25

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Consider the following nonlinear regression model: yi=α+eβxi+εi, Assume i.i.d. data and 𝔼[εi|xi]=0. To estimate α and β by GMM, we use the two theoretical moment conditions 𝔼[yi−α−eβxi]=0 𝔼[(yi−α−eβxi)xi]=0 To compute the variance of the GMM estimator we need the matrices Γ0 and Φ0.

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