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Consider the following nonlinear regression model: š‘¦ š‘” = š›¼ š‘„ š‘” š›½ + šœ€ š‘” Assume i.i.d. data and š”¼ [ šœ€ š‘” | š‘„ š‘” ] = 0 . To estimate š›¼ and š›½ by GMM, we use the following moment conditions: š”¼ [ š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ] = 0 š”¼ [ ( š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ) š‘„ š‘” ] = 0 We have an i.i.d. sample with š‘‡ = 2000 observations, with āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” = 3000 and āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” 2 = 5000 . We obtain point estimates š›¼ Ģ‚ = āˆ’ 1 and š›½ Ģ‚ = 2 . To compute the variance of the estimates, we need to estimate the matrix š›¤ 0 , š›¤ Ģ‚ 0 = [ š›¤ Ģ‚ 11 š›¤ Ģ‚ 12 š›¤ Ģ‚ 21 š›¤ Ģ‚ 22 ] Then, the value š›¤ Ģ‚ 11 is:

选锹
A.š›¤ Ģ‚ 11 = āˆ’ 1.5
B.š›¤ Ģ‚ 11 = 1.5
C.There is not enough information to compute š›¤ Ģ‚ 11 .
D.š›¤ Ģ‚ 11 = āˆ’ 2.5
E.š›¤ Ģ‚ 11 = 5000
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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 āˆ’ α x_t β] = 0 and E[(y_t āˆ’ α x_t β) x_t] = 0. An i.i.d. sample with T = 2000 observations is provided, along with sample averages: (1/T)āˆ‘ x_t = 3000 and (1/T)āˆ‘ x_t^2 = 5000. The GMM estimates are α̂ = āˆ’1 and β̂ = 2. We are asked to determine the estimated value of Γ̂11, the (1,1) element of the matrix Γ̂0, where Ī“0 is the Jacobian (matrix of partial derivatives) of the moment conditions with respect to the parameters Īø = (α, β). Step-by-step analysis of each option: Option A: Γ̂11 = āˆ’1.5 - To obtain Γ̂11,......Login to view full explanation

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Consider the following nonlinear regression model: š‘¦ š‘” = š›¼ š‘„ š‘” š›½ + šœ€ š‘” Assume i.i.d. data and š”¼ [ šœ€ š‘” | š‘„ š‘” ] = 0 . To estimate š›¼ and š›½ by GMM, we use the following moment conditions: š”¼ [ š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ] = 0 š”¼ [ ( š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ) š‘„ š‘” ] = 0 To compute the variance of the estimates, we need to estimate the matrices š›¤ 0 and š›· 0 .

Consider the following nonlinear regression model: yi=α+βxi+εi, Assume i.i.d. data and š”¼[εi|xi]=0. To estimate α and β by GMM, we need at least two moment conditions, and we use š”¼[yiāˆ’Ī±āˆ’Ī²xi]=0 š”¼[(yiāˆ’Ī±āˆ’Ī²xi)xiβxiāˆ’1]=0 Chose the correct answer below.

Consider the following nonlinear regression model: š‘¦ š‘” = š›¼ š‘„ š‘” š›½ + šœ€ š‘” Assume i.i.d. data and š”¼ [ šœ€ š‘” | š‘„ š‘” ] = 0 . To estimate š›¼ and š›½ by GMM, we use the following moment conditions: š”¼ [ š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ] = 0 š”¼ [ ( š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ) š‘„ š‘” ] = 0 We have an i.i.d. sample with š‘‡ = 1000 observations, with āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” = 3000 and āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” 2 = 5000 . We obtain point estimates š›¼ Ģ‚ = āˆ’ 3 and š›½ Ģ‚ = 2 . To compute the variance of the estimates, we need to estimate the matrix š›¤ 0 , š›¤ Ģ‚ 0 = [ š›¤ Ģ‚ 11 š›¤ Ģ‚ 12 š›¤ Ģ‚ 21 š›¤ Ģ‚ 22 ] Then, the value š›¤ Ģ‚ 11 is:

Consider the following nonlinear regression model: š‘¦ š‘” = š›¼ š‘„ š‘” š›½ + šœ€ š‘” Assume i.i.d. data and š”¼ [ šœ€ š‘” | š‘„ š‘” ] = 0 . To estimate š›¼ and š›½ by GMM, we use the following moment conditions: š”¼ [ š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ] = 0 š”¼ [ ( š‘¦ š‘” āˆ’ š›¼ š‘„ š‘” š›½ ) š‘„ š‘” ] = 0 We have an i.i.d. sample with š‘‡ = 1000 observations, with āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” = 100 , āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” 2 = 200 and āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” 3 = 800 . We obtain point estimates š›¼ Ģ‚ = āˆ’ 1 and š›½ Ģ‚ = 3 . To compute the variance of the estimates, we need to estimate the matrix š›¤ 0 , š›¤ Ģ‚ 0 = [ š›¤ Ģ‚ 11 š›¤ Ģ‚ 12 š›¤ Ģ‚ 21 š›¤ Ģ‚ 22 ] Then, the value š›¤ Ģ‚ 11 is:

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