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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” = 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:
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B.There is not enough information to compute
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D.š¤
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E.š¤
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We need to evaluate each proposed value for ĪĢ11 given the moment conditions and the provided sample moments.
Option A: ĪĢ11 = ā3. The element ĪĢ11 corresponds to the expected derivative of the first moment with respect to α, i.e., ām1/āα evaluated at the estimated parameters. If m1,t = y_t ā α x_t^β with β known (here Ī²Ģ = 2 from the estimation), then ām1,t/āα = ā x_t^β = ā x_t^2. The GMM cross-derivative ĪĢ1......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” = 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:
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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