Homework Set 3, ECO 311

Due Date: Check the class schedule on syllabus

Instruction: Each question is worth 4 points. You need to submit the answers of all three questions. The maximum point you can get is 12 points. Please do not ask me to go through the homework before the due date.

**Q1: Omitted Variable Bias**

Use the House data. Please run a simple regression rprice = β0 + β1baths + u. Suppose the error term u includes only one omitted variable area, which measures the size of a house

1. Please explain in detail whether βˆ1 in the simple regression underestimates or overestimates the marginal effect of baths on rprice. You need to explicitly specify the sign

of β2 and δ1 in formula 3.46 or Table 3.2 in the textbook.

2. How to empirically check the sign of correlation between baths and area?

**Q2: Frisch-Waugh Theorem**

Please understand Equation 3.22 in the textbook

1. Use House data and report the multiple regression rprice = β0 +β1baths+β2age+u.

Interpret βˆ1.

2. Suppose the key regressor is baths. Please show the stata code and result that implement the two-step procedure of the Frisch-Waugh Theorem to obtain βˆ1

**Q3: F Test of Overall Significance**

Use the House data. Please run a multiple regression rprice = β0 + β1baths + β2age + u.

Consider testing the joint null hypothesis

H0 : β1 = 0, β2 = 0

1. Please run the restricted regression and obtain RSS restricted

2. Please compute the F-statistic and find the p-value using stata function Ftail