ECONOMICS 210-Multiple Linear Regression-Problem Set 3 Partial Solutions.-GRADRD A

Document Content and Description Below

ECON 210: Problem Set 3 Multiple Linear Regression Due April 25th, 2018 at the beginning of class 1 (10 points) Let X be a random column vector of size 2, X = (X1; X2)T with E(X1) = 1, E(X2) = 2, ... and V ar(X) = "3 4 4 5# Also let A = "a b c d# 1. Calculate E(AX) 2. Calculate V ar(AX) Solution: Full points only for fully simplified answers 2 (15 points) Levitt and Venkatesh investigate Chicago street gangs by modeling the determinants of the wages paid to \foot soldiers" in the gangs. Specifically, they estimate the model wage = β0 + β1war + β2large + u where, wage is the hourly pay to the foot soldiers, war equals 1 if the gang is currently involved in a gang war else 0, and large equals 1 if the gang is \large" else 0. They find β^0 = 1:83; β^1 = 1:3; β^2 = 4:07 1. According to their estimates, what is the average wage paid to a foot soldier in a small gang that is not at war? 2. Why did they include a dummy variable for the gang being large but not also for the gang being small? 3. How would you modify their regression to allow for the effects of a gang war on wages to be different for members of large versus small gangs? Solution: 1. $1.83 2. The dummies for large and small would be perfectly co-linear with the constant{thereby breaking the needed NPC assumption 3. Include the interaction of war * large [Show More]

Last updated: 1 year ago

Preview 1 out of 4 pages