题目
题目

BU.232.630.W1.SP25 Quiz 2 solutions

单项选择题

Consider the following nonlinear regression model: yt=αx β t +εt Assume i.i.d. data and 𝔼[εt|xt]=0. To estimate α and β by GMM, we chose among the following moment conditions: 𝔼[yt−αx β t ]=0 𝔼[(yt−αx β t )xt]=0 𝔼[(yt−αx β t ) 1 xt ]=0 Choose the most appropriate answer below:

选项
A.Only the first and third equations are valid moment conditions to estimate α and β by GMM.
B.Only the second and third equations are valid moment conditions to estimate α and β by GMM.
C.All equations are valid moment conditions to estimate α and β by GMM.
D.Only the first and second equations are valid moment conditions to estimate α and β by GMM.
E.None of the equations above are valid moment conditions to estimate α and β by GMM.
查看解析

查看解析

标准答案
Please login to view
思路分析
We begin by restating the setup and the available moment conditions to be evaluated for GMM estimation of α and β in the nonlinear regression y_t = α x_t^β_t + ε_t with E[ε_t | x_t] = 0 and i.i.d. data. Option A: Only the first and third equations are valid moment conditions. - The first condition E[y_t − α x_t^β_t] = 0 leverages the standard moment condition arising from the mean-zero regression error given x_t, which is valid under E[ε_t | x_t] = 0. In words, the average misfit must vanish, which is a classic unconditional moment. - The third condition E[(y_t − α x_t^β_t) (1/x_t)] = 0 uses a function of x_t as a weighting in the moment. Since E[ε_t | x_t] = 0, multiplying ε_t by any function of x_t and taking expectation yiel......Login to view full explanation

登录即可查看完整答案

我们收录了全球超50000道考试原题与详细解析,现在登录,立即获得答案。

类似问题

Consider the following nonlinear regression model: yt=αx β t +εt Assume i.i.d. data and 𝔼[εt|xt]=0. To estimate α and β by GMM, we use the following moment conditions: 𝔼[yt−αx β t ]=0 𝔼[(yt−αx β t )xt]=0 To compute the variance of the estimates, we need to estimate the matrices Γ0 and Φ0.

Consider the following nonlinear regression model: yi=α+x β i +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−x β i ]=0 𝔼[(yi−α−x β i )xi]=0 To compute the variance of the GMM estimator we need the matrices Γ0 and Φ0.

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, and we use 𝔼 [ 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ] = 0 𝔼 [ ( 𝑦 𝑖 − 𝛼 − 𝛽 𝑥 𝑖 ) 𝑥 𝑖 𝛽 𝑥 𝑖 − 1 ] = 0 Chose the correct answer below.

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 .

更多留学生实用工具

加入我们，立即解锁 海量真题 与 独家解析，让复习快人一步！