Question :- A well-known tool, which is employed by monetary authorities to track monetary policy, is the so-called Taylor rule. The aim of this exercise is to apply that tool to UK monetary policy. Data for this exercise are in Question_1.xlsx, where IR is the interest rate set by central bank, CPI is the consumer price index and GDP is the UK GDP volume, using 2005 as reference year. Data span from 1960q1 to 2004q4.

The Taylor rule can be represented as follows:

i_t = α + β₁inflationt_t + β₂output_gap_t + ξ_t

where i_t is the log of the interest rate, nflationt_t is the inflation rate and output_gap_t is the difference between the actual level of output and the potential one.

a. Using the data contained in the dataset, construct the variables that you need in order to estimate eq. (1).

b. Estimate eq. (1), report the results and comment on them. Are the results consistent with Taylor’s theory? Explain.

c. It is suggested that output_gap should weight half of inflation in determining the interest rate. Write correctly the null hypothesis and the alterative hypothesis of this test. Report the test and comment on its significance. Construct the test, report it and comment on its significance.

d. Someone suggests that if the coefficient associated to the inflation is equal to 0.8, output_gap is not relevant in explaining the variability of the dependent variable. Write down the correct null hypothesis and the alternative. Construct an appropriate test, report it and comment its significance.

e. A researcher suggests that the presence of heteroscedasticity in the residuals does not affect the results. Explain this fully and comment the result of such a test. Then, construct an appropriate test for detecting the presence of heteroscedasticity, explain it, report and comment the result of such a test.

f. A researcher suggests that the LM test should be always used to test for the presence of serial correlation. Do you agree? Suppose that you have a first order serial correlation. Explain two tests that you can use to detect the presence of serial correlation, report and comment their results.

g. If either serial correlation or heteroscedasticity is detected, apply the appropriate correction to your estimation. Report and explain your estimation results, by also commenting the difference with the estimations in point (b).