Questions
Questions
Single choice

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 = 2000 observations, with ∑ 𝑡 = 1 𝑇 𝑥 𝑡 = 3000 and ∑ 𝑡 = 1 𝑇 𝑥 𝑡 2 = 5000 . We obtain point estimates 𝛼 ̂ = − 1 and 𝛽 ̂ = 2 . 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:

Options
A.𝛤 ̂ 11 = − 1.5
B.𝛤 ̂ 11 = 1.5
C.There is not enough information to compute 𝛤 ̂ 11 .
D.𝛤 ̂ 11 = − 2.5
E.𝛤 ̂ 11 = 5000
View Explanation

View Explanation

Verified Answer
Please login to view
Step-by-Step Analysis
We start by restating the question setup to ensure clarity: we have a nonlinear regression model given by y_t = α x_t β (with ε_t as the error term and E[ε_t|x_t] = 0), and the GMM moment conditions are: E[y_t − α x_t β] = 0 and E[(y_t − α x_t β) x_t] = 0. An i.i.d. sample with T = 2000 observations is provided, along with sample averages: (1/T)∑ x_t = 3000 and (1/T)∑ x_t^2 = 5000. The GMM estimates are α̂ = −1 and β̂ = 2. We are asked to determine the estimated value of Γ̂11, the (1,1) element of the matrix Γ̂0, where Γ0 is the Jacobian (matrix of partial derivatives) of the moment conditions with respect to the parameters θ = (α, β). Step-by-step analysis of each option: Option A: Γ̂11 = −1.5 - To obtain Γ̂11,......Login to view full explanation

Log in for full answers

We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!

Similar Questions

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 To compute the variance of the estimates, we need to estimate the matrices 𝛤 0 and 𝛷 0 .

Consider the following nonlinear regression model: yi=α+βxi+εi, Assume i.i.d. data and 𝔼[εi|xi]=0. To estimate α and β by GMM, we need at least two moment conditions, and we use 𝔼[yi−α−βxi]=0 𝔼[(yi−α−βxi)xiβxi−1]=0 Chose the correct answer below.

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 = 1000 observations, with ∑ 𝑡 = 1 𝑇 𝑥 𝑡 = 3000 and ∑ 𝑡 = 1 𝑇 𝑥 𝑡 2 = 5000 . We obtain point estimates 𝛼 ̂ = − 3 and 𝛽 ̂ = 2 . 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 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 = 1000 observations, with ∑ 𝑡 = 1 𝑇 𝑥 𝑡 = 100 , ∑ 𝑡 = 1 𝑇 𝑥 𝑡 2 = 200 and ∑ 𝑡 = 1 𝑇 𝑥 𝑡 3 = 800 . We obtain point estimates 𝛼 ̂ = − 1 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:

More Practical Tools for Students Powered by AI Study Helper

Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!