Consider the double-log regression equation log(S_t) = f(I_t, V_c) + epsilon_r =
ID: 3236818 • Letter: C
Question
Consider the double-log regression equation log(S_t) = f(I_t, V_c) + epsilon_r = beta_b+ + beta_1 log (I_t) + beta_2 log(V_c) + epsilon_t and obtain the estimated result as follows: where S_1 = the average daily spread between the bid and asking prices for the US dollar on the Brazilian black market in month t I_ = the average interest rate in month t V_t = the variance of the daily premium between the black market rate and the official exchange rate for the dollar in month t (a) Supple you were told to use the Park to teat whether the V_t is a potential proportionality factor of Z_r that might be the cause of in the residuals of the above equation. (i) Describe the procedures of the Park test (ii) Does likely appear in such a double log equation? Why or why not? Explain. (b) Why do you believe a logical reformulation of the equation might get rid of the ? (c) If you decided to apply Weighted Least Squares to the equation, what will be the transformed equation that you would estimate?Explanation / Answer
A.i.
Step 1 : Run ordinary least squares on your data. Make sure the regression produces a table of residuals.
Step 2 : Square the residuals from Step 1.
Step 3 : Take the natural log of the squared residuals from Step 2.
Step 4 : Take the natural log of Z, the variable which you suspect is causing the heteroscedastic behavior.
Step 5 : Run OLS again, this time for the natural log of Z (Step 4) against the natural log of the squared residuals (Step 3). In other words, LN of Z is your independent variable and LN(residuals2) is your dependent variable for the regression.
Step 6 : Find the T-Statistic for the Z variable. A large t-statistic (i.e. over 2) indicates the presence of heteroscedasticity.
ii.
Heteroscedasticity.may appear in double log equation if it is an incorrect functional form, also if the log transformation skewed any variable too much that can also bring heteroscedasticity. The presence of outlier can also induce heteroscedasticity.
B.
Sometimes model misspecification can also induce heteroscedasticity, thus some other transformation can also be tried and tested for heteroscedasticity.
C. Equation form will remain same only the coefficients will change. to determine exact coefficients we need data which is not provided here.