Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market return minus one-month T-bill return). She is also familiar with evidence showing how US stock market returns differ by the political party affiliation of the US President. Chiesa estimates a multiple regression model to predict monthly excess stock market returns accounting for business conditions and the political party affiliation of the US President:
Excess stock marker return t
= a0 + a1 default spread t-1 + a2 Term spread t-1 + a3 Pres party dummy t-1 + e t
Default spread is equal to the yield on Baa bonds minus the yield on Aaa bonds. Term spread is equal to the yield on a 10-year constant-maturity US Treasury index minus the yield on a 1-year constant-maturity US Treasury index. Pres party dummy is equal to 1 if the US President is a member of the Democratic Party and 0 if a member of the Republican Party.
Chiesa collects 432 months of data (all data are in percent form, i.e., 0.01 = 1 percent). The regression is estimated with 431 observations because the independent variables are lagged one month. The regression output is in Exhibit 1. Exhibits 2 through 5 contain critical values for selected test statistics.
Number of observations………………………………………431
Test statistic from Breusch-Pagan (BP) test…………………7.35
R2……………………………………………………………0.053
Adjusted R2…………………………………………………0.046
Durbin-Watson (DW) ……………………………………….1.65
Sum of squared errors (SSE)………………………………19,048
Regression sum of squares (SSR)……………………………1,071
An intern working for Chiesa has a number of questions about the results in Exhibit 1:
Question 1 How do you test to determine whether the overall regression model is significant?
Question 2 Does the estimated model conform to standard regression assumptions?
For instance, is the error term serially correlated, or is there conditional heteroskedasticity?
Question 3 How do you interpret the coefficient for the Pres party dummy variable?
Question 4 Default spread appears to be quite important. Is there some way to assess the precision of its estimated coefficient? What is the economic interpretation of this variable?
After responding to her intern’s questions, Chiesa concludes with the following statement: “Predictions from Exhibit 1 are subject to parameter estimate uncertainty, but not regression model uncertainty.”
EXHIBIT 3
Table of the Student’s t-Distribution………….(One-Tailed Probabilities for df = )
P………………………………………………………….t
0.10……………………………………………………1.282
0.05……………………………………………………1.645
0.025…………………………………………………..1.960
0.01……………………………………………………2.326
0.005…………………………………………………..2.576
Regarding the intern’s Question 1, is the regression model as a whole significant at the 0.05 level?
A. No, because the calculated F-statistic is less than the critical value for F.
B. Yes, because the calculated F-statistic is greater than the critical value for F.
C. Yes, because the calculated Ï2 statistic is greater than the critical value for Ï2.
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