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ECON 403 - Applied Econometrics Sample Exam

Section A – ANSWER ALL QUESTIONS

For each question you should include definitions, formulae and examples as appropriate. Marks will be awarded for the explanation provided.

Question 1 [30 marks]

a) Including an irrelevant variable will increase the variances ofthe parameter estimates.

(6 marks)

b) 2SLS estimates are Biased but the bias usually falls as sample size increases.

(6 marks)

c) In OLS regression, ifthe errors are heteroskedastic the estimated coefficients are inefficient.

(6 marks)

d) In a unit process OLS estimates converges but at a similar rate to that of stationary process.

(6 marks)

e) The problem of identification has to do with the specification ofthe model and has nothing to do with the sample size. (6 marks)

Question 2 [20 marks]

a) In the model yt x et where et et 1 vt , explain why it is typically assumed

that

1 (10 marks)

b) Discuss the results of the diagnostics tests provided below. For each test outline the null and alternative hypothesis and the conclusion reached. (10 marks)

Test	Statistic	p-value
Ramsey Reset	F-Statistics: 3.28950	(0.07293)
Jarque-Bera	Chi-square: 3.95104	(0.13871)
Breusch-Godfrey LM	F-Statistics: 2.70145	(0.02549)
ARCH Test	F-statistics:1.26877	(0.28823)
White Test	F-statistics: 1.603453	(0.16837)

Section B – ANSWER ONLY ONE QUESTION

Question 3 [25 marks]

a) What is heteroskedasticity? What are the consequences of pure heteroskedasticity for multiple regression models estimated by OLS? Use an example to illustrate your answer.

(9 marks)

b) Describe the step involved in obtaining a White test for the detection of heteroskedasticity. What are the degrees of freedom (df) for this test? Use an example to illustrate your answer.

(9 marks)

c) Describe how weighted least squares can be applied in order to account for pure heteroskedasticity? What other procedures can be used to account for pure heteroskedasticity? You can use an example to illustrate your answer. (7 marks)

Question 4 [25 marks]

a) Match the following processes with the Acfs below and outline which of these processes are not stationary. (15 marks)

zt 0.75zt 1 ut

zt zt 1 ut

zt 0.2zt 1 ut

(i) (ii)

(iii)

b) In the model = + where = −1 + , explain why it is typically assumed that || < 1. (5 marks)

c) If a time series is stationary implies that it is white noise, Discuss (5 marks)

Section C – ANSWER ONE QUESTION ONLY

Question 5 [25 marks]

a) Let rt et et 1 , where et is a white noise. Find the mean of and variance ofrt .

(5 marks)

b) Outline the difference between the autocorrelation function and the partial autocorrelation function. Explain why they are equal at lag 1. (10 marks)

c) In the context of OLS model building, explain the importance of balancing the tension between including irrelevant variables and omitting important variables. Illustrate your answer with an example. (10 marks)

Question 6 [25 marks]

We are given the following model:

= + +