FIN9028M Quantitative Methods for Economics and Finance - University of Lincoln

Assignment Questions:

Question 1: Interpret and Replicate an Academic Paper

Read teaching materials and the paper by Chow and Wang (2010) "The Empirics of Inflation in China" to answer the following questions. Chow and Wang (2010) paper could be downloaded from the Blackboard.

1) On the first page, paragraph 3, the authors report "The Augmented Dickey-Fuller tests strongly suggest the presence of a unit root in log(P) and log(M²/Y)." Verify this statement using the data provided in the paper. Report in detail the steps of your exercise with explanation.

2) On the first page, the last paragraph, the authors report "Let ut be the estimated trend deviation of the log price level or the error correction term. We then regress dlog(P_t) on dlog(M²t/Yt), dlog(P_t-1), and u_t-1 where dlog(X_t) is defined as log(X_t) - log(X_t-1), ...". What is "estimated trend" referred to in the first sentence and for what purpose it should be estimated? Replicate the last two regression results reported at the end of this page. Illustrate your understanding of this model. Specifically, what is the purpose for this regression? How to interpret the estimated coefficients for this model? Illustrate your understanding that the coefficient on ut is negative.

3) Replicate both Figure 1 and Figure 2. (Hint: To obtain exactly the same graphs, the following options of Stata graph commands are required: ylabel, xlabel, yscale, xscale, xmtick, and yaxis. Key in ‘help graph' in Stata command section to find out more). Provide your comments and interpretation on these graphs. Specifically, what can we learn from these two graphs?

4) On the second page, the second paragraph, the authors report "The following (table) reports the result of the Chow test for parameter stability using t = 1979 as the break point. The result provides extremely strong support for parameter stability of this equation."

Replicate the authors' F-test result in the described table and verify the authors' statement here. Why do we need to perform a structure break test in this case? What could be problematic if in this case we do have a structure break in the time series? Illustrate your understanding of the degrees of freedom of F-statistic reported in the table. Is there any limitation for this "Chow test for parameter stability" approach?

Question 2: Extend an Existing Study

Read teaching materials and the paper by Chow and Lawler (2003) "A Time Series Analysis of the Shanghai and New York Stock Price Indices" to answer the following questions.

Chow and Lawler (2003) paper could be downloaded from the Blackboard. Stata data file ‘cl_2003.dta' on the Blackboard contains data to be used for this question.1 A detailed description for this data set is given in PDF file ‘cl_2003_data description.pdf', which is also available from the Blackboard.

1) Verify the summary statistics reported in Table 1 - 4 of Chow and Lawler (2003) paper to confirm that ‘cl_2003.dta' made available by the authors is not far different from the one been used in the paper.

2) In the same paragraph, the authors state that "The above result is one indication that the Chinese capital market was not integrated with the world market, but the degree of integration may increase in the future as China has become a member of WTO." Collect data from FRED to extend the sample period of the current dataset up to the last week of June 2020. Provide empirical evidence to test the conjecture made by the author in this statement. Note that China officially became a member of WTO on 11 December 2001.

3) Construct an ADL(3, 3) model to conduct pseudo out-of-sample forecasts of weekly rate of return of Shanghai stock market using historical returns of both Shanghai and New York markets, over 2017 Week 1 - 2018 Week 25, using regressions that begin in 2001 Week 1. Illustrate in detail your estimation steps and your comments on the results obtained.

4) Using data for rate of return of Shanghai stock market, estimate an AR(1) model with GARCH(1,1) errors. Plot the residuals from this AR(1) model along with ±σt GARCH bands as in Figure 16.4 in Stock and Watson (2014). Do you observe any sharp increase or decrease in the variability? Provide your comments on the results obtained.

Question 3: From Theory to Empirical Study

Download from Federal Reserve Bank of St. Louis (FRED) the following quarterly variables for a country from 1980:Q1 to 2021:Q2 (or as early as possible and up to 2021:Q2):2

In Macroeconomics, the model for the demand for nominal money balances takes the following form: Md = P·(Y, R), where (Y, R), in an implicit functional form, denotes demand for liquidity which depends on real output and interest rate. Since the demand for nominal balances is proportional to the aggregate price level, we can divide both sides of the nominal money demand equation by P. This gives the liquidity demand function or the demand for real balances function:

For the second equality, the left-hand-side of the equation is the demand for nominal balances divided by the aggregate price level or the demand for real balances (the real purchasing power of money). The right-hand side is the liquidity demand function. The demand for real balances is now decomposed into a transactions demand for money (captured by Y) and a portfolio demand for money (captured by R). Now assume that (Y, R) has a linear functional form, we can construct the following empirical model based on theory for the exercises in this question:

1) Estimate a VAR(4) (a VAR model with four lags) for ?MDt and ?Yt. Does ?Y Granger- cause ?MD? Does ?MD Granger-cause ?Y? Repeat the same exercise to investigate the relationship between ?MD and ?R. Explain and comment on your results.

2) Should the VAR models estimated in 1) include more than four lags? Explain your answer with evidence.

3) Now estimate a three-variable VAR model for ?MD, ?Y, and ?R. Conduct impulse response analysis based on this VAR model and provide your comments on the results obtained.

Attachment:- Quantitative Methods for Economics.rar