If we use a quasi instrument for to estimate a 2SLS, than the probability limit for the 2SLS estimate of B1^ is: (Note s=standard deviation) A) plimB1^=B1+(corr(X,e)/corr(Z, e) )*($\sigma$_e/$\sigma$_X1) B) plimB1^=B1+(corr(Z,e)/corr(Z, X))*($\sigma$_e/$\sigma$_X1) C) plimB1^=B1+(corr(Z,e)/corr(X, e) )*($\sigma$_e/$\sigma$_X1) D) plimB1^=B1+(corr(Z,e)/corr(Z, Y))*( $\sigma$_e/$\sigma$_X1)

Question

Quizplus · Accepted Answer

The correct formula for the probability limit of the 2SLS estimate of B1^ using a quasi instrument is plimB1^=B1+(corr(Z,e)/corr(Z, X))*(F1F1F1S1F1F1F10_e/F1F1F1S1F1F1F10_X1). This is because when we use a quasi instrument, the correlation between the instrumental variable (Z) and the error term (e) is not equal to zero, but rather correlated with the endogenous variable (X). Therefore, we need to use the correlation between Z and X in the formula. Choice A is incorrect because it includes the terms U1B1e and U1B0, which are not necessary for the 2SLS estimation. Choice C is incorrect because it uses the correlation between Z and e, which is not what we need when using a quasi instrument. Choice D is incorrect because it uses the correlation between Z and Y, which is not relevant for the 2SLS estimation.

If We Use a Quasi Instrument for to Estimate a 2SLS