Questions from Econometrics

Q: Derive the results in (8-32a) and (8

Derive the results in (8-32a) and (8-32b) for the measurement error model. Note the hint in Footnote 4 in section 8.5.1 that suggests you use result (A-66) when you need to invert

Q: At the end of section 8.7, it is suggested

At the end of section 8.7, it is suggested that the OLs estimator could have a smaller mean squared error than the 2sLs estimator. Using (8-4), the results of Exercise 1, and Theorem 8.1, show that th...

Q: Consider the linear model, / Let z be

Consider the linear model, Let z be an exogenous, relevant instrumental variable for this model. Assume, as well, that z is binary—it takes only values 1 and 0. Show the algebraic f...

Q: This is easy to show. In the expression for /

This is easy to show. In the expression for , if the kth Colum n in X is one of the columns in Z, say the lth, then the kth column in (Z'Z)-1Z'X will be the lth column of an L * L identity matrix. T...

Q: Prove that the control function approach in (8-16)

Prove that the control function approach in (8-16) produces the same estimates as 2SLS.

Q: Prove that in the control function estimator in (8-16

Prove that in the control function estimator in (8-16), you can use the predictions, z'p, instead of the residuals to obtain the same results apart from the sign on the control function itself, which...

Q: What is the covariance matrix, / of the GLS

What is the covariance matrix, of the GLS estimator and the difference between it and the OLs estimator, The result plays a pivotal role in the development of specification tests in Hausman (1978)....

Q: For the model in Exercise 9, what is the probability limit

For the model in Exercise 9, what is the probability limit of Note that s2 is the least squares estimator of the residual variance. It is also n times the conventional estimator of the variance of th...

Q: To continue the analysis in Application 5, consider a nonparametric regression

To continue the analysis in Application 5, consider a nonparametric regression of G/Pop on the price. Using the nonparametric estimation method in Section 7.5, fit the nonparametric estimator using a...

Q: For the model in Exercise 9, suppose that is normally distributed

For the model in Exercise 9, suppose that is normally distributed, with mean zero and variance 2[1 + (x)2]. Show that 2 and 2 can be consistently estimated by a regression of the least squares res...