Question

Can I please get an answer to this problem?

3. Suppose we would like to estimate the effect of city credit ratinglon the municipal bond interest rate mbr. Other factors affecting mbr are tax rate tr, unemployment rate ue, and the ratio of citizens in working age to total population of the city watp. Credit rate classes are indicated as B, BB, BBB, A, AA, AAA, with B the lowest and AAA the highest. a) Define appropriate dummy variables for the credit rating classes and form a (linear) regression model to test whether credit rating affects mbr. b) Present in terms of the model parameter the null hypothesis for testing the hypothesis. c) Given that there are n observations (cities), what test statistic would you use and what are/is the degrees of freedom?

Answer 1

Using dummy variable concept, we introduce 6 dummy variables for each type of rating category , & drop intercept term to avoid any dummy variable trap

& Then using F statistic ( via restricted least squares test) to find out the significance of the dummy variables

Now introducing 6 dummies for each type of category of Rating and so to avoid dummy variable Trap, drop the intercept term, Thus mbr = beta_1 D_1 + beta D_2 + beta_3 D_3 + beta_4 D_4 + beta_5 D_5 + beta_6 D_6 + beta_7 + beta_8 u e + beta 9 w T p Thus mbr = sigma_i = 1^6 beta i Di + beta_7 + beta_8 u e + beta 9 wapt Now D_1 = {1 if Rating is B 0 o/w D_2 = { 1 if Rating is BB 0 o/w D_3 = {1, if rating is B beta B 0 o/w ans so on D_4 for A, D_5 for AA D_6 for AAA b) Now Null type: beta_2 - beta_2 = = beta_5 = 0 c) Now if H_) is true then mbr = beta_4 tr + beta_8 ve + beta_9 watp Reg^n eq^n R_Restricted^2 so using F statistics for Restricted least squares f = (R_Ur^2 - R_R^2)/m/(1 - R_UR^2)/n - R m rightarrow No of Restrictions = 6