Questions from Econometrics

Q: Derive the final equality in Equation (13.10).

Derive the final equality in Equation (13.10). (Use the definition of the covariance, and remember that, because the actual treatment Xi is random, b1i and Xi are independently distributed.) Data fro...

Q: A researcher is interested in predicting average test scores for elementary schools

A researcher is interested in predicting average test scores for elementary schools in Arizona. She collects data on three variables from 200 randomly chosen Arizona elementary schools: average test s...

Q: You have a sample of size n = 1 with data y1

You have a sample of size n = 1 with data y1 = 2 and x1 = 1. You are interested in the value of  in the regression Y = X + u. (Note there is no intercept.) a. Plot the sum of squared residuals (y1 -...

Q: Let X1 and X2 be two positively correlated random variables, both

Let X1 and X2 be two positively correlated random variables, both with variance 1. a. (Requires calculus) The first principal component, PC1, is the linear combination of X1 and X2 that maximizes var...

Q: Consider the fixed-effects panel data model Yjt = j

Consider the fixed-effects panel data model Yjt = j + ujt for j = 1, ……, k and t = 1, ……, T. Assume t...

Q: Describe the relationship, if any, between the standard error of

Describe the relationship, if any, between the standard error of a regression and the square root of the MSPE of the regression’s out-of-sample predictions.

Q: Y is a random variable with mean  = 2 and variance

Y is a random variable with mean  = 2 and variance 2 = 25. a. Suppose you know the value of  i. What is the best (lowest MSPE) prediction of the value of Y? That is, what is the oracle prediction...

Q: In Exercise 14.5(b), suppose you predict Y

In Exercise 14.5(b), suppose you predict Y using Y/2 instead of Y. a. Compute the bias of the prediction. b. Compute the mean of the prediction error. c. Compute the variance of the prediction error....

Q: In Exercise 14.5(b), suppose you predict Y

In Exercise 14.5(b), suppose you predict Y using Y - 1 instead of Y. a. Compute the bias of the prediction. b. Compute the mean of the prediction error. c. Compute the variance of the prediction error...

Q: In any year, the weather can inflict storm damage to a

In any year, the weather can inflict storm damage to a home. From year to year, the damage is random. Let Y denote the dollar value of damage in any given year. Suppose that in 95% of the years Y = $0...