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Consider the following nonlinear regression model: š¦ š” = š¼ š„ š” š½ + š š” Assume i.i.d. data and š¼ [ š š” | š„ š” ] = 0 . To estimate š¼ and š½ by GMM, we use the following moment conditions: š¼ [ š¦ š” ā š¼ š„ š” š½ ] = 0 š¼ [ ( š¦ š” ā š¼ š„ š” š½ ) š„ š” ] = 0 We have an i.i.d. sample with š = 1000 observations, with ā š” = 1 š š„ š” = 1000 and ā š” = 1 š š„ š” 2 = 4000 . We obtain point estimates š¼ Ģ = 1 and š½ 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:
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To analyze this GMM setup, we consider the moment condition g1,t = y_t ā α x_t^β. The derivative of g1,t with respect to α is āg1,t/āα = ā x_t^β. The population counterpart is Ī11 = E[ āg1,t/āα ] = ā 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, Ī11 = ā E[x_t^......Login to view full explanationē»å½å³åÆę„ēå®ę“ēę”
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Consider the following nonlinear regression model: š¦ š” = š¼ š„ š” š½ + š š” Assume i.i.d. data and š¼ [ š š” | š„ š” ] = 0 . To estimate š¼ and š½ by GMM, we use the following moment conditions: š¼ [ š¦ š” ā š¼ š„ š” š½ ] = 0 š¼ [ ( š¦ š” ā š¼ š„ š” š½ ) 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 š¼[εi|xi]=0. To estimate α and β by GMM, we need at least two moment conditions, and we use š¼[yiāαāβxi]=0 š¼[(yiāαāβxi)xiβxiā1]=0 Chose the correct answer below.
Consider the following nonlinear regression model: š¦ š” = š¼ š„ š” š½ + š š” Assume i.i.d. data and š¼ [ š š” | š„ š” ] = 0 . To estimate š¼ and š½ by GMM, we use the following moment conditions: š¼ [ š¦ š” ā š¼ š„ š” š½ ] = 0 š¼ [ ( š¦ š” ā š¼ š„ š” š½ ) š„ š” ] = 0 We have an i.i.d. sample with š = 1000 observations, with ā š” = 1 š š„ š” = 3000 and ā š” = 1 š š„ š” 2 = 5000 . We obtain point estimates š¼ Ģ = ā 3 and š½ 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” = š¼ š„ š” š½ + š š” Assume i.i.d. data and š¼ [ š š” | š„ š” ] = 0 . To estimate š¼ and š½ by GMM, we use the following moment conditions: š¼ [ š¦ š” ā š¼ š„ š” š½ ] = 0 š¼ [ ( š¦ š” ā š¼ š„ š” š½ ) š„ š” ] = 0 We have an i.i.d. sample with š = 1000 observations, with ā š” = 1 š š„ š” = 100 , ā š” = 1 š š„ š” 2 = 200 and ā š” = 1 š š„ š” 3 = 800 . We obtain point estimates š¼ Ģ = ā 1 and š½ 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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