Consider the following two least-squares estimates of the relationship between interest rates and the federal budget deficit
Question:
Consider the following two least-squares estimates of the relationship between interest rates and the federal budget deficit in the United States:
Model A: Ŷ1 = 0.103 - 0.079X1 R2 = .00
Where:
Y1 = the interest rate on Aaa corporate bonds
X1 = the federal budget deficit as a percentage of GNP (quarterly model: N = 56)
Model T: Ŷ2 = 0.089 + 0.369X2 + 0.887X3 R2 = .40
Where:
Y2 = the interest rate on 3-month Treasury bills
X2 = the federal budget deficit in billions of dollars
X3 = the rate of inflation (in percent) (quarterly model: N = 38)
a. What does “least-squares estimates” mean? What is being estimated? What is being squared? In what sense are the squares “least”?
b. What does it mean to have an R2 of .00? Is it possible for an R2 to be negative?
c. Based on economic theory, what signs would you have expected for the estimated slope coefficients of the two models?
d. Compare the two equations. Which model has estimated signs that correspond to your prior expectations? Is Model T automatically better because it has a higher R2? If not, which model do you prefer and why?
Step by Step Answer:
a The squares are least in the sense that they are being mi...View the full answer
