1. Excel file "E1.1.xls" contains data on annual returns and estimated betas for a number of firms over several years. Use this data to estimate the following model,
ERit = θ0 + θ1βit + eit (1)
where Eit ≡ excess return on asset i at time t, βit is the estimated beta for asset i at time t, and θ0 and θ1 are the parameters to estimate. Estimate the model using OLS and another estimator that may be appropriate. Are the OLS results unbiased?
Test and explain. Motivate why the alternative estimator you chose may be appropriate and provide a test to choose between the OLS and the alternative. Are parameter estimates consistent? Explain.
Additional data is provided in "E1.1f.xls". Using this additional data, predict excess returns and the 80% confidence interval around these predicted returns for both of the models estimated above. Simulate and evaluate the forecast. Which model provides the better forecast? Is there room for improvement in the forecast? Explain.
2. A proposed model to forecast the monthly AAA corporate bond rate is
RAAAt = β0 + β1 R3t-1+ β2IPt-1 + β3GPWt-1 + et
where RAAA=AAA corporate bond rate.
R3 = 3 month treasury bill rate.
IP = Federal Reserve Board Index of industrial production.
GPW = rate of growth in the producer price index for all commodities.
The 3 month treasury bill is hypothesized to be positively related to the AAA corporate bond rate. The index of industrial production is intended as a measure of the demand for liquid assets (i.e., increases in production imply increases in demand, which would be expected to increase interest rates). Changes in commodity prices are expected to positively affect interest rates (e.g., an increase in the rate of inflation leads to an increase in interest rates). Use the data in "E1.2.csv" to estimate the model specified above and specifically address the following questions.
(a) Are the estimated parameters of this model significantly different from 0?
(b) Do your results from estimating the model match the theoretical hypotheses specified above? Explain.
(c) Test the hypothesis that β1 ≤ .5 at the .01 level of significance.
(d) Is there any evidence of a multicollinearity problem? Explain how this may cause a problem in hypothesis testing. Compute and explain collinearity diagnostics for this model. How does multicollinearity affect the power of hypothesis tests?
(e) Is there evidence of a permanent structural break in 1989? Test and explain the results.
(f) Test the hypothesis that β1 + β2 + β3 = 1 at the .05 significance level. Explain.
(g) Are the joint restrictions H0 : β2 = -β3 and R3t-1 = .1 GPWt-1 valid for the data generating process? Provide a test and explain the result.
(h) Are estimates of (2) unbiased, consistent, efficient? Provide tests and explain the implications in terms of addressing versus ignoring any problems found, in particular in the context of the above results.
Attachment:- final.rar