[SOLVED] BUSI4528 QUANTITATIVE RESEARCH METHODS FOR FINANCE AND INVESTMENT AUTUMN SEMESTER 2021-2022 Pyt

BUSI4528-E1

BUSINESS SCHOOL

A LEVEL 4 MODULE, AUTUMN SEMESTER 2021-2022

QUANTITATIVE RESEARCH METHODS FOR FINANCE AND INVESTMENT

1. a) Consider an experiment on student scores. Students were randomly assigned within schools into three types of classes: small classes with 13-17 students, regular-sized classes with 22-25 students, and regular-sized classes with a full-time teacher aide to assist the home teacher. Student scores on academic tests were recorded as well as some information about the students, teachers, and schools. The experiment considers two academic years data.

Score: total examine scores of each student.

Small: an indicator variable Small=1 if the student is in a small class, and 0 otherwise. Aide:  an indicator variable Aide=1 if there is a full-time teacher aide in the regular- sized classes, and 0 otherwise.

Tchexper: teacher’s experiences in terms of years.

Male: an indicator variable Male=1 if the student is male, and 0 otherwise.

Tchmasters: an indicator variable Tchmasters=1 if the teacher has a master degree, and 0 otherwise.

Absent: number of days the student is absent from school. tchid: individual teacher’s ID.

schid: individual school’s ID.

Using Stata, we  regress  by  OLS student score on small class size, teacher’s aide, student’s gender, teacher’s experience and education. The estimated results are shown below:

(i)          Write down the regression model and interpret the meaning and significance of each coefficient. Are the signs and relative magnitudes consistent with the intuition?   [25 marks]

(ii)          The table below shows the results of an alternative specification. Compare  the results from the table below to those in part (i). In particular, comment on the standard errors.

[10 marks]

(iii)         Let INCOME= income per capita (in thousands of U.S. dollars) and BACHELOR= percentage of the population with a bachelor’s degree or more for selected U.S. states,  a  total  of  N=52  observations.  The  results  from  a  simple  linear regression of INCOME and BACHELOR are

INCOM(̂)E=12.11+1.24BACHELOR se       (2.75)    (0.132)

Construct a 99% interval estimate of the coefficient for BACHELOR. Interpret the interval estimate.  [15 marks]

b) Explain the setup of the Logit model and how it provides a remedy to the shortcomings of the Linear Probability Model (LPM).  [35 marks]

c)  Explain  how  to  use  estimates  of  the  Logit  model  to  calculate  marginal  effects  of continuous explanatory variables and discrete effects of binary explanatory variables.  [15 marks]

Total [100 marks]

2.  a) Consider  the  experiment  and  initial  estimation  of  Question  1.a.  We  estimate  the determinants  of  Score  using  a  different  model,  and  the  results  are  shown  below. Compare the results of the new estimation and those in Question 1.a. State the difference between the two models.

[25 marks]

b) What is type I and type II error in hypothesis testing?   [15 marks]

c)  What are the main characteristics of t-distribution and under what circumstances should we use t-distribution rather than normal distribution?   [10 marks]

d) For time series data, outline the static model and the ARDL(1,1) model with serially correlated errors. Discuss the consequences for OLS estimators and standard errors.   [30 marks]

e) Outline the Dickey-Fuller test for the null hypothesis (H0) of the presence of a unit root in an autoregressive time series model against the alternative hypothesis (HA) that the autoregressive time series model is stationary around a zero mean.   [20 marks]

Total [100 marks]

3. a) Consider an experiment on whether government subsidies reduce the impact of recession on company’s bankruptcy. Suppose that, before the recession, the government provided subsidies to companies in some selected cities. Companies in the other cities received no subsidies. Before the recession, there were 102 companies receiving subsidies and 153 companies that  did  not.  After the  recession,  for  the  companies  that  received subsidies,  93  survived.  Among  the  companies  that  did  not  receive  subsidies,  123 survived after the recession.

(i)      Let the companies without subsidies before the recession be the control group and those that received subsidies be the treatment group. Draw a graph showing that treatment effect. Calculate the magnitude of the treatment effect.   [15 marks]

(ii)     Suppose that we have data of these two groups for 6 years including the recession year, so that N=12. Let AFTER t=1 for years after the recession and AFTER t =0 for years before the recession. Let TREATi=1 for the group whose companies received subsidies and TREATi=0 for the group whose companies did not receive subsides. Let Numcompi,t   be  the  number of companies in each group in each year. We obtained the estimation below:

Numcom(̂)pl,t  = 166 − 2.87TREATi  − 47AFTER t+ 20.3(TREATi  × AFTER t)

(se)                   (8.8)           (7.6)         (10.6)

What is the treatment effect from above equation? Is the estimated treatment effect significant at the 5% level?   [10 marks]

b) Explain what the Central Limit Theorem is.   [10 marks]

c)  What are the assumptions of estimating a multiple linear regression model?   [15 marks]

d) Outline the Linear Probability Model (LPM) and explain in detail its main limitations.   [30 marks]

e) What is meant by saying that a time series is stationary?  Is the following time series stationary or non-stationary?

yt  = yt−1  + vt

where error terms vt  are i.i.d. with mean zero and variance σv(2) , and t denotes the t-th time period. Justify your answer.   [20 marks]

Total [100 marks]

4. a) Define the term multicollinearity and explain how it can be detected. Also, list the

negative consequences of multicollinearity and explain how they can be mitigated.  [50 marks]

b) Consider the following time series model :

yt  =  β0  + β1xt  + β2xt−1  + yyt−1  + εt

It is suspected that the model suffers from serial correlation in the error term of the form.

εt  = Pεt−1  + ut

where ut   is an identically and independently distributed error term and t denotes the t– th time period. Describe in detail a test to detect serial correlation in the above form of the model.   [25 marks]

c)  Explain the Engle-Granger test for cointegration and write down the steps involved in the test.   [25 marks]

Total [100 marks]