Question 2 [34 marks]

A researcher wants to analyse the relationship between the three-month T-bill rate,

tb3, the annual inflation rate, inf based on the consumer price index, and the federal

budget deficit, def as a percentage of GDP and develops the following model. The

data is stored under the file name is tb3.xlsx

tb3₂ = a + α₁ inf₂ + a₂ defe + €₂

(a) Use Gretl to obtain a line plot among these three variables (one graph) and

comment on the plot. (Hint: to make the graph in Gretl: highlight all three

variables right click →→time series plot on a single graph →OK.) [4 marks]

(b) Obtain sample correlation coefficient between these variables and comment

on the strength of the relationships? (Hint: to obtain correlation in Gretl: →

highlight all three variables right click correlation matrix → Ok.) [4 marks]

(c) Estimate the above regression model and provide the Gretl output. (Hint:

Model ordinary least squares select the appropriate variables to the boxes ➜Ok).

[4 marks]

(d) Interpret the coefficients a, and a₂. Does the sign of the coefficients agree with

your expectations? Explain. [4 marks]

(e) Provide and interpret the coefficient of determination, R². [4 marks]

(f) Plot the residuals of the model and comment on any pattern. (Gretl: in your

regression output window, select the menu Graph →Residual plot →Against

Time ok.) [2 marks]

(g) Add a one lag of inf and def to the equation in part (a) and re-estimate your

model and report the result. Are the coefficients for the two lag variables

individually significant at the 5% level? In Gretl: Model ordinary least

squares →A dialog box will appear. Choose the "tb3" to the dependent variables box

and "inf" and "def" as regressors. From the left bottom corner select →lags→→add 1

lag for "inf" and "def" and then click ok.) [4 marks]

(h) Conduct the second order autocorrelation test for the model in part (c) at the

5% significance level. Attach your Gretl results. Clearly states all steps in your

test; Null and alternative hypotheses, the auxiliary regression and the test

statistic, critical value, your decision and the conclusion. (Gretl:

Tests →Autocorrelation Make lags order for test =2→Ok.) [6 marks]

(i) Re-estimate your model with Robust standard errors and provide your

output. Compare your results with the output in part (c). Comment.

(Model →OLS → Choose the "tb3" to the dependent variables box and "inf" and

"def" as regressors. From the left bottom corner check the box "Robust standard

errors".) [2 marks]