Questions
Questions

BU.232.630.F2.SP25 Sample Quiz 2 2025

Single choice

Consider the following nonlinear regression model: yi=α+eβxi+εi, Assume i.i.d. data and 𝔼[εi|xi]=0. To estimate α and β by GMM, we use the two theoretical moment conditions 𝔼[yi−α−eβxi]=0 𝔼[(yi−α−eβxi)xi]=0 To compute the variance of the GMM estimator we need the matrices Γ0 and Φ0.

Options
A.There is not enough information to compute the matrix Γ0.
B.The matrix Γ0 is: Γ0=𝔼[−1 −xieβxi −xi −x 2 i eβxi].
C.The matrix Γ0 is: Γ0=𝔼[−1 βeβxi −xi −xieβxi].
D.The matrix Γ0 is: Γ0=𝔼[−1 −xieβxi −x 2 i eβxi −1].
E.The matrix Γ0 is: Γ0=𝔼[−xi −xieβxi −xi −x 2 i eβxi].
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Step-by-Step Analysis
We begin by restating the setup: a nonlinear regression yi = α + e^{β xi} + εi with moment conditions E[yi − α − e^{β xi}] = 0 and E[(yi − α − e^{β xi}) xi] = 0. For GMM, the matrix Γ0 is the expectation of the Jacobian of the moment conditions with respect to the parameters θ = (α, β) evaluated at the true parameter values. Specifically, if g_i(θ) = [ yi − α − e^{β xi}; (yi − α − e^{β xi}) xi ], then the partial derivatives are: - ∂/∂α of the first moment is −1, and ∂/∂β of the first moment is − xi e^{β xi}. - For the second moment, ∂/......Login to view full explanation

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