题目
题目
单项选择题

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 need two moment conditions. Choose the best answer below:

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We start by restating the problem in our own words to ensure clarity. The nonlinear regression model is yi = α + e^{β xi} + εi, with i.i.d. data and E[εi | xi] = 0. To estimate α and β by GMM, we need two moment conditions. The given option proposes two moments: E[ yi − α − e^{β xi} ] = 0 and E[ ( yi − α − e^{β xi} ) log(xi) ] = 0. Option analysis step by step: First moment option: E[ yi − α − e^{β xi} ] = 0 - This is a standard moment implied by E[εi | xi] = 0. Since E[εi] = E[ E[εi | xi] ] = 0, the residual yi − α − e^{β xi} has mean zero. In GMM terms, using a constant instrument 1 yields the first moment condition. This choice is typical and valid for identifying α and ......Login to view full explanation

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类似问题

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.

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:

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 use the two theoretical moment conditions 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 ] = 0 To compute the variance of the GMM estimator we need the matrices 𝛤 0 and 𝛷 0 .

Consider the following linear 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 use the three theoretical moment conditions 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 2 ] = 0 To compute the variance of the GMM estimator we need the matrices 𝛤 0 and 𝛷 0 .

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