econometrics

FIN421 Econometrics for Finance Group Coursework (worth 30% of the total grade)

Submission deadline: December 24, 2021 Learning outcomes:

 Undertake data analysis using statistical software from the viewpoint of financial analysts.

 Understand how to conduct cross-sectional data analysis such as the instrumental variable regression, model diagnostic, and checking the weakness of instrumental variables.

 Analyse the properties of multiple time series and examine the long-run relationship among the selected time series by cointegration tests.

 Describe the underlying economic hypothesis and discuss the empirical results. Project background:

This coursework assignment comprises two projects.

I. The first project is an exercise that investigates if the central bank’s interest rate decision is affected by the stock market movement. The central bank’s mandate is to conduct monetary policy aimed at inflation stability and production growth. The interest rate decision should not be influenced by the stock market fluctuation. Nonetheless, the macroeconomic factors which the central bank is targeting could also affect the stock market return, and thus raise the potential endogeneity issue that complicates the task of estimating the reaction of monetary policy to stock market.

II. The second project is modelling the long-run relationships of multiple financial time series. Many economic or financial time series are non-stationary data, which are hard, if not impossible, to forecast accurately. The cointegration framework allows the researcher to utilize the equilibrium relations among the economic variables so that a potentially better prediction model could be built.

Project content:

I. Suppose a researcher proposes the following model:

𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡. 𝑟𝑎𝑡𝑒 = α + 𝛽 ∗ 𝑠𝑡𝑜𝑐𝑘. 𝑟𝑒𝑡𝑢𝑟𝑛 + 𝑋 𝛾 + 𝜖 𝑠𝑡𝑜𝑐𝑘. 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝛿 + 𝑋 𝜃 + 𝜖

where X is the vector of macroeconomic variables that could affect both interest rate and stock market return. The researcher is interested in the estimation of 𝛽; that is, the effect of stock return on interest rate. Download the “data_coursework.csv” from the dashboard (learningmall). The file contains the monthly data on stock return, fed fund rate, and other 4 variables (credit_spread, term_spread, inflation, ch_indprod) that would serve as the macroeconomic factors (X). These macroeconomic factors are selected as the proxies for the economic activity and consumer price condition the central bank is targeting. credit_spread is the difference in yield between the BAA and AAA corporate bonds, term_spread is the difference in yield between 10-year and 3-month government bond, inflation is the percentage change in the consumer price index, and ch_inprod is the change in the industrial production index.

a. Estimate the two specified models using ordinary least squares (OLS) and report the regression results. Are there multicollinearity issues in these models? And please briefly explain if the sign for each coefficient estimate is consistent with the economic theory.

b. Explain why the simple OLS might not be used to consistently estimate 𝛽. Because instrumental variables (IVs) are hard to obtain, the researcher attempts to employ Lewbel (2012, “Using heteroscedasticity to identify and estimate mis-measured and endogenous regressor models.”)’s method to construct the IVs as follows:

i. Obtain the residuals 𝜖̂ with OLS. ii. Calculate the 𝑋𝜖̂ as the instrumental variables Z. That is, Z =

(credit_spread*𝜖̂ , …, ch_indprod*𝜖̂ ).

c. Estimate the instrumental variable regression using Z as the instruments and summarize the results.

d. Compare the results from OLS and IV regression and discuss the empirical findings. Could we conclude that interest rate decision is affected by stock returns? If so, can we say anything about the extent of the stock returns driving the interest rate decision?

II. Select two or more financial time series that might exhibit long-run equilibrium

relationship. That is, you should expect or have a hypothesis that they are potentially cointegrated. The time series may be stock market index, foreign exchange rates, commodities price, or other macroeconomic variables. The choice of frequency could be daily, weekly, or monthly. The sampling period should cover the events of financial crises. The minimum length of sample is 10 years. In this project, you should discuss the following points:

a. Why should we be interested in the proposed model and which time series is the variable of main interest? Please explain the economic mechanism that drives the equilibrium relationship.

b. For each time series, describe their properties individually. Are they stationary or non-stationary? If it is non-stationary, what kind of transformation you use to obtain the stationary time series? What is the most appropriate model for each time series?

c. Are the multiple time series cointegrated as expected? That is, does the vector error correction model (VECM) conform with the formulated hypothesis?

d. Compare the forecasting performance between the univariate and multivariate time series models. Which approach is the superior one? What are the criteria you use to examine the forecasting performance?

e. Are the models stable? Here you could try splitting the sample into two non- overlapping subsamples: one that includes financial crises and the other does not. Another option is to split them into two equal-length subsamples. For each subsample, repeat the modelling exercises (univariate and multivariate) and compare their estimated results.

How to create groups Each group shall include 3-4 students. Students are free to choose their group members until November 19, 2021. Project output A report which answers the questions asked in the project content. In the report, you should also give a detailed explanation of the methodology to obtain your results. The sources of the data and cited references must be included in the Appendix. Each group must fill in and sign the group contribution form together with the submission (the form is in the Appendix A at the end of this document). The report must contain a minimum of 2,000 words and does not exceed 6,000 words, excluding the tables, appendix, and references. Assessment The final mark will be based on the instructor’s evaluation of the report using the following criteria:

 The methodology is explained with sufficient details.  The estimation results are reported along with clear explanation.  The numerical results are very clear and interpreted for the reader.  The source for the data is clearly specified.  The references are listed alphabetically and follows the standard of any international

journal.

Appendix B

Assessment Form for FIN421 Group Coursework (For Tutor Use)

Group ID

Max points Mark Project I

a. OLS estimation results 10

b. Explanation of endogeneity issue 5

c. IV regression results 10

d. Interpretation of empirical findings 10

Project II

a. Explanation of the proposed model 10

b. Univariate time series analysis 10

c. Cointegration test 10

d. Comparison of forecasting performance between univariate and multivariate time series models

20

e. Model stability analysis 15

Total marks 100

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