Econometrics

Question 1 Consider the following IS-LM model, justify the importance of identification and evaluate whether the model is identified and choose an appropriate method to estimate the model. 𝑅𝑑 = 𝛽11 + 𝛽12𝑀𝑑 + 𝛽13π‘Œπ‘‘ + 𝛽14π‘€π‘‘βˆ’1 + 𝑒1𝑑 π‘Œπ‘‘ = 𝛽21 + 𝛽22𝑅𝑑 + 𝛽23𝐼𝑑 + 𝑒2𝑑 Where 𝑅𝑑 is interest rate, π‘Œπ‘‘ is GDP, 𝑀𝑑 is money stock, 𝐼𝑑 is investment. [30 marks] 

Question 2 Describe the characteristics of a non-stationary time series, and interpret the problems associated with regressing non-stationary variables on each other. Propose a formal test to test whether a time series has a unit root. [30 marks] 

Question 3 Discuss what cointegration is and how we can test whether two variables are cointegrated. If we find that our variables are cointegrated, formulate a model to express the relationship between them. Interpret the economic intuition with the model. [30 marks]

 Question 4 Compare the advantages and disadvantages of panel data and appraise the panel data model. Propose different methods of estimating simple linear panel data models. [30 marks] 

Section B continues on next page MN-M038 (January 2022) Page 3 SECTION B – Answer ALL Questions This section accounts for 40% of total marks 

Question 5 A researcher wants to study the determinants of housing prices in the UK. He/she builds the following regression model and uses the OLS method to estimate it. Tables 1 and 2 on page 4 show the regression results. Some of the values have been deleted. Use these results to answer all the questions (i) to (iv) below. ln(π‘Œπ‘‘ ) = 𝛽1 + 𝛽2 ln(π‘Œπ‘‘βˆ’1 ) + 𝛽3 ln(𝑋1 ) + 𝛽4 ln(𝑋2 ) + 𝛽5 ln(𝑋3 ) + 𝑒𝑑 Where π‘Œπ‘‘ is housing price index, 𝑋1 is disposable income, 𝑋2 is consumer price index and 𝑋3 is money supply. 

(i) Interpret the main results from the regression in Table 1, commenting on the economic meaning of the estimated parameters. Comment on the goodness of fit. [5 marks] 

(ii) Using the results from Table 1, evaluate whether the coefficient on last period housing price is significantly different from 0. Comment on the economic meaning. [5 marks]

(iii) The researcher suspects that the regression suffers from first-order autocorrelation. He/she wants to use the Durbin Watson statistics in Table 1, give some intuition about the values in the Durbin Watson critical values tables and propose a suitable autocorrelation test. [15 marks]

(iv) Table 2 shows the auxiliary regression of a heteroskedasticity test. Use the information provided to identify which heteroskedasticity test it is from and analyse whether heteroskedasticity is present. Give some intuition about how this test tests for heteroskedasticity. [15 marks]