Consider the nonlinear model yt=θ1x θ2 t +εt where the sample data (y1,x1),...,(yT,xT) are i.i.d. and E(εt|xt)=0. We know that the nonlinear least square estimator is asymptotically normal, that is √ T ( ˆ θ NL−θ0) d ⤳ N(0,A −1 0 Ω0A −1 0 ) To compute the standard errors we need to estimate Ω0, ˆ Ω 0=[ 1 T ∑ T t=1 ˆ ε 2 t x 2 ˆ θ 2 t 1 T ∑ T t=1 ˆ ε 2 t ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ ε 2 t ˆ θ 2 1 x 2 ˆ θ 2 t log2(xt)] What is the missing entry in the matrix ˆ Ω 0? Single choice

A

1 T ∑ T t=1 ˆ ε 2 t ˆ θ 2 1 x 2 ˆ θ 2 t log2(xt)

B

𝔼( ˆ ε 2 t ˆ θ 2 1 x 2 ˆ θ 2 t log2(xt))

C

𝔼( ˆ ε 2 t x 2 ˆ θ 2 t )

D

1 T ∑ T t=1 ˆ ε 2 t x 2 ˆ θ 2 t

E

𝔼( ˆ ε 2 t ˆ θ 1x 2 ˆ θ 2 t log(xt))

F

1 T ∑ T t=1 ˆ ε 2 t ˆ θ 1x 2 ˆ θ 2 t log(xt)

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Consider the nonlinear model yt=θ1x θ2 t +εt where the sample data (y1,x1),...,(yT,xT) are i.i.d. and E(εt|xt)=0. We know that the nonlinear least square estimator is asymptotically normal, that is √ T ( ˆ θ NL−θ0) d ⤳ N(0,A −1 0 Ω0A −1 0 ) To compute the standard errors we need to estimate A0, ˆ A 0=[ 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ θ 2 1 x 2 ˆ θ 2 t log2(xt)] What is the missing entry in the matrix ˆ A 0?

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