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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‘‡ = 1000 observations, with āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” = 1000 and āˆ‘ š‘” = 1 š‘‡ š‘„ š‘” 2 = 4000 . We obtain point estimates š›¼ Ģ‚ = 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
B.š›¤ Ģ‚ 11 = 1000
C.There is not enough information to compute š›¤ Ģ‚ 11 .
D.š›¤ Ģ‚ 11 = 4000
E.š›¤ Ģ‚ 11 = āˆ’ 4
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To analyze this GMM setup, we consider the moment condition g1,t = y_t āˆ’ α x_t^β. The derivative of g1,t with respect to α is āˆ‚g1,t/āˆ‚Ī± = āˆ’ x_t^β. The population counterpart is Ī“11 = E[ āˆ‚g1,t/āˆ‚Ī± ] = āˆ’ E[x_t^β]. Given the model context, β is estimated as 2, so x_t^β = x_t^2. Therefore, at the true parameter values, Ī“11 = āˆ’ E[x_t^......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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