1. Which of the following is one of the Classical Linear Regression Model assumptions?

a) The error term follows a t distribution

b) The expected value of the error term is zero

c) The variance of the error term is heteroscedastic

d) The covariance between the error term and the independent variable is constant

2. Which one of the following is NOT the BLUE properties of OLS estimators 1   and 2   in simple regression models?

a) 1  and 2  have the lowest variances

b) 1  and 2  are linear functions of Y

c) 1  and 2 are random variables

d) (2) = 2

3. What is the value of the coefficient of determination (R2) in the following estimation results where se represents standard error?

i  = 0.518 + 0.707Xi

se = (0.315)  (0.305)

RSS  =  0.157 and (Y − )2  =  0.208

a) 0.198

b) 0.245

c) 0.755

d) Cannot be determined

4. In the regression model: lnYt  = β1  + β 2Xt  + ut , what does β2 represent where X is time?

a) The elasticity of Y with respect to X

b) The change of Y with respect to X

c) The growth rate of Y

d) The value of Y given that X = 0

5. Given the following estimation results, what is the value of F-statistic for the null hypothesis that 0 : β 2  = β 3  = β4  = 0 ? The model was estimated using 75 observations.

t  = −104.807 + 0.167X2t  + 0.210X3t  + 0.077X4t

se = (39.48)     (0.068)        (0.189)        (0.008)

R2  = 0.874

RSS = 0.6707

a) 164.595

b) 235.841

c) 6.937

d) 464.746

6. Consider the following two regression models:

= 1  + 2X2i  + 3X3i  + 4X4i  +

= 1  + 2X2i  +

The models were estimated based on 71 observations. The residual sum of squares of the first model is 0.1618 and the residual sum of squares of the second model is 0.1784. What is the value of the Wald statistic to test the null hypothesis that H0 : β3=0 and β4=0?

a) -3.117

b) 3.437

c) 3.642

d) 7.284

7. Regression on standardised variables is suggested when:

i.  All independent variables are measured using the same metric.

ii.  The objective is to identify the relative importance of the independent variables in a multiple regression model.

iii.  All independent variables are measured using different measurement units.

iv.  All independent variables are normally distributed.

a)   (i) and (iii) only

b)   (ii) and (iv) only

c)   (ii), and (iii) only

d)   (i), (ii), (iii), and (iv)

8. What will be the properties of the OLS estimator in the presence of multicollinearity?

a)  It will be consistent, unbiased and efficient

b)  It will be consistent and unbiased but not efficient

c)  It will be consistent but not unbiased

d)  It will not be consistent

9. Which of the following could be used as a test for autocorrelation up to third order?

a)  The Durbin-Watson test

b)  White’s test

c)  The RESET test

d)  The Breusch-Godfrey test

10.Suppose that the Durbin-Watson (DW) test is applied to a regression containing two explanatory variables plus a constant with 50 data points. The DW test statistic takes a value of 1.43. What is the appropriate conclusion at the 5 percent significance level?

a)  Residuals appear to be positively autocorrelated

b)  Residuals appear to be negatively autocorrelated

c)  Residuals appear not to be autocorrelated

d)  The test result is inconclusive

11.Which of the following are plausible approaches to dealing with a regression model that exhibits heteroscedasticity:

i.  Take logarithms of each of the variables

ii.  Use the robust standard errors

iii.   Use the weighted least square (WLS) procedure

iv.  Add lagged values of the dependent variable to the regression equation

a)  (i) and (iii) only

b)  (ii) and (iv) only

c)  (i), (ii), and (iii) only

d)  (i), (ii), (iii), and (iv)

12.A parsimonious model is one that

a)  Includes too many variables

b)  Includes as few variables as possible to explain the data

c)  Is a well-specified model

d)  Is a mis-specified model

13.Which of the following are characteristics of a stationary process?

i.   It crosses its mean value frequently

ii.   It has constant mean and variance

iii.   It contains no trend component

iv.   It will be stationary in first difference form

a)  (i) and (iii) only

b)  (ii) and (iv) only

c)  (i), (ii), and (iii) only

d)  (i), (ii), (iii), and (iv)

14.Consider the following correlogram and suggest a model from the following list that best characterises the process:

a)  AR(1)

b)  MA(2)

c)  AR(2)

d)  ARMA(1,1)

15.Which of these features in the time-series data are captured by an E-GARCH (1,1) model?

i.  Mean-reverting

ii.  Leverage effect

iii.  Volatility clustering

iv.  Volatility affecting return

a)  (i) and (iii) only

b)  (ii) and (iv) only

c)  (i), (ii), and (iii) only

d)  (i), (ii), (iii), and (iv)

16.To examine the determinants of CEOs’ salary  in the financial  industry , a  researcher constructed the following population regression function:

= 1  + 22 + 33 + 44 + 55 +

where represents the annual salary of CEOs, 2  is years of education, 3  is years of work experience, 4  denotes years with current employer, 5  is age, is the error term.

Using data for the most influential financial firms in the United Kingdom, the following sample regression function has been estimated to explain the annual salary earned in 2020 by the CEOs (in thousands of pounds):

= 6.476 + 0.0658 2 + 0.0267 3 + 0.0094 4 − 0.0209 5 (2.356)   (0.0374)        (0.0125)         (0.0042)         (0.0483)

= 0.3522 = 53

where is the sample standard deviation, is the number of firms included in the analysis and the total variation in the dependent variable equals 8.7533.

a) Interpret the partial slope coefficients and comment on the sign of the estimates.    (20 marks)

b) A   researcher  claims  that   CEOs  who   obtain  a  one-year   Master  of   Business Administration degree receive an incremental salary increase of 100%. Do you agree with the researcher?

(20 marks)

c) Using the confidence interval approach, test the hypothesis that working experience is a key determinant of the CEO’s salary.

(20 marks) d) Test the overall significance of the model.

(20 marks) e) Calculate the value of adjusted 2  and support its use over normal 2 .

(20 marks)

17.

a) Suppose that the total output  () for a given factory  is given  by a  Cobb-Douglas production function in the form of:

=

where A is the total factor productivity, L denotes labour, K represents capital, and alpha and delta are input shares of labour and capital, respectively. Jointly test the hypotheses that the total factor productivity is unity and that the function exhibits constant returns to scale. State the null and alternative hypotheses. What would be the appropriate testing procedure and steps to test the two hypotheses jointly?

(40 marks)

b) To estimate the impact of gender and marital status on individual earnings, a researcher modelled the population regression function as follows:

= 0   + 1 + 2 + 3 + 4 i +

where is average hourly earnings for individual , is a binary variable that takes on the value of one if the individual is a female and zero otherwise, is a binary variable that takes on the value of one if the individual is married and zero otherwise, takes on the value of one if the individual is not married and zero otherwise.  Finally, i  is a  binary variable that takes on the value of one  if the individual is educated and zero otherwise.

Does the population regression model specified correctly? Can you identify any potential

problem? If yes what would be the remedy?                                             (20 marks)

c) Consider the following regression model: = 0  + 1 +

i)  Show that the coefficient of determination  R2  equals the squared value of the correlation coefficient between X and Y, that is 2  = ( )2 .              (20 marks)

ii)  Suppose that 1  = 0 , derive the value of the coefficient of determination 2 .

(20 marks)

18.

a)  A  researcher  estimates  the  following  model  for  stock  returns  (standard  errors  in parentheses) but thinks that there may be a problem with it. By calculating the t-ratios

and considering the value of R2 , suggest what the problem might be.

= 0.838 + 0.3022 − 0.9813 2  = 0.96, 2  = 0.89 (0.634)    (0.197)    (0.863)

What are the steps that the researcher can take to mitigate the problem?

(40 marks)

b)  The following regression was run using 70 monthly observations:

t  = 0.78 − 0.89Pt  + 0.35St

(0.56)    (0.78)    (0.12)

R2  = 0.76, DW = 1.57, White = 27.2

where B is the demand for brokerage services, P is the price of the services and S is the total  number of brokers and all variables are  in  logarithms (standard errors  in parentheses). DW is the Durbin-Watson statistic. White is the White’s test statistic.

i)   Comment on the specification of the above model.                             (20 marks)

ii)   Does the model suffer from heteroscedasticity? If so how might this have arisen?

19.

a)  What do you understand by the term ‘autocorrelation’?

(40 marks)

(20 marks)

b)  An econometrician suspects that the residuals of her model might be autocorrelated.

Explain the steps involved in testing this theory using the Durbin–Watson (DW) test.

(40 marks)

c)  The econometrician follows your guidance in part (a) and calculates a value for the DW statistic of 1.65. The regression has 80 quarterly observations and three explanatory variables (plus a constant term). Perform the test. What is your conclusion?

(40 marks)

20.

a)  Define the term “unit root” and explain why it is important to test for unit root in time series data before attempting to build an empirical model.

(20 marks)

b)  A researcher wants to test for the presence of unit root in time series data and decides

to use the Dickey-Fuller (DF) test. He estimates a regression of the form ∆ = + −1 +

and obtains the estimate = −0.82 with standard error = 0.14

i)   Given the data and a critical value of -2.88, perform the DF test. What are the null and alternative hypotheses for this test? What is the main conclusion from this test?

(40 marks)

ii)   Another researcher suggests that there may be a problem with this methodology since it assumes that the disturbances (ut) are white noise. Suggest a possible source of difficulty and how the researcher might in practice get around it.

(40 marks)