This coursework uses a data set from Stock and Watson’s ‘Introduction to Econometrics’ textbook. The two variables are a three-month interest rate (R90_{t}) and a one-year interest rate (R1yr_{t}). Use of the GRETL econometrics software is required. The data set is on the class MyPlace page. Using data for 1964Q1 to 1999Q4 throughout:
(a) Obtain time series plots of R90t, R90t, R1yr_{t}, and R1yr_{t}. Obtain plots of R90t against R1yr_{t} and of R90t against R1yr_{t}. Comment.
Consider the equation
ΔX_{t} =α + ρX_{t−1 }+ γ1 ΔX_{t−1} + γ2 ΔX_{t−2 }+ γ3 ΔX_{t−3 }+ u_{t}.
(b) Run the regression corresponding to (1) when Xt is R90_{t} (the three month interest rate) and test H0 : ρ = 0 against Ha : ρ< 0 using appropriate Dickey-Fuller critical values.
(c) Repeat step (b) but for R1yr_{t} (the one year interest rate).
(d) Repeat step (b) but for R90_{t} − R1yr_{t}.
(e) Discuss the implications of your estimations and your tests in parts (b),
(c), and (d).
(f) Estimate and discuss an ‘error correction mechanism’ type equation to describe ΔR90_{t}, reporting tests for both (i) autocorrelation and (ii) parameter stability, as well as parameter estimates and standard errors.