2. (30 Marks) Edward Saunders published an article that tested the possibility that the stock market is affected by the weather on Wall Street. Using daily data from 28 years, he estimated an equation with the following variables D.J. = Bo + 0.10Rf-1 + 0.0010J, - 0.017M + 0.0005Ct N = 6911 (daily), R = 0.02 where DJt = the percentage change in the Dow Jones industrial average on day t Rt = the daily index capital gain or loss for day t = a dummy variable equal to 1 if the ith day was in January, 0 otherwise Mt = a dummy variable equal to 1 if the ith day was a Monday, 0 otherwise Ct = a variable equal to 1 if the cloud cover was 20 percent or less, equal to -1 if the cloud cover was 100 percent, 0 otherwise (a) Saunders did not include an estimate of the constant term in his published regres- sion results. Which of the Classical Assumptions supports the conclusion that you shouldn't spend much time analyzing estimates of the constant term? Explain. (b) Which of the Classical Assumptions would be violated if you decided to add four more dummy variables to the equation that was equal to 1 if the ith day was a Tuesday, Wednesday, Thursday, or Friday, and equal to 0 otherwise? (Hint: The stock market is not open on weekends.) (c) Carefully state the meaning of the coefficients of R and M. being sure to take into account the fact that R is lagged (one time period behind) in this equation for valid theoretical reasons. (d) The variable C is a measure of the percentage of cloud cover from sunrise to sunset on the ith day and reflects the fact that approximately 85 percent of all New York's rain falls on days with 100 percent cloud cover. Is C a dummy variable? What assumptions (or conclusions) did the author have to make to use this variable? What constraints does it place on the equation? (e) Saunders concludes that these findings cast doubt on the hypothesis that security markets are entirely rational. Based just on the small portion of the author's work that we include in this question, would you agree or disagree? Why? (Hint: Consider the overall fit of the estimated model R and compare the four estimated coefficients BR. BJ; BM; and Be.)