代写 Monash ETF2100/5910 Introductory Econometrics

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代写 Monash ETF2100/5910 Introductory Econometrics

Department of Econometrics and Business Statistics

ETF2100/5910 Introductory Econometrics

Assignment 1, Semester 1, 2016

Worth 10% of Final Mark

Due 4pm Friday April 8

(Hand in to Duangkamon’s mailbox – Building H Level 5)

Note:

• Notation used in the assignment needs to be written correctly and properly. It is

recommended that students submit hand-written assignments instead of typed ones.

• This assignment comprises three questions.

• Question 3 parts h) to k) are extra questions for ETF5910 students.

• Mark allocations are given for each question. Marks are also awarded for presentation

of graphs.

• Total marks for ETF2100 and ETF5910 students are 100 and 125, respectively.

• Marks will be deducted for late submission on the following basis:

10% for each day late, up to a maximum of 3 days.

Assignments more than 3 days late will not be marked.

Question 1 ((5+5)+(9+3+3+3)+2+5+2+5=42 marks)

(a) Show that

(i) ( )( )

1 1 1 1

N N N N

i i i i i i

i i i i

x x y y x y x y

= = = =

− − = −

∑ ∑ ∑ ∑

(ii)

2 2

1 1 1

( )

N N N

i i i

x x x x

= = =

 

− = −

 

 

∑ ∑ ∑

(b) In 1990, data were collected for 200 CEO Salaries (measured on thousands of dollars)

and their company’s return on equity, RoE (measured in percent) over the previous

three years. Consider the following linear regression model:

1 2 i i i

Salary RoE e =β +β +

Let’s y Salary = and x RoE = and

200 200 200 200

1 1 1 1

3470.7; 261752; 75159.15; 4801270;

i i i i i

i i i i

x y x x y

= = = =

∑ ∑ ∑ ∑

( )

388,006,092

y y

− =

∑

Fill in the blanks of the EViews output below using the information above and the

relevant information provided in the EViews output. Be sure to show your working and

any formulae used. In particular, find the following quantities.

(i) Calculate x , y ,

b ,

b and

2

代写 Monash ETF2100/5910 Introductory Econometrics

( ) se b .

(ii) Calculate the t statistic for testing the null hypotheses

0 2

: 0 H β = .

(iii) Calculate the sum squared error or SSE .

(iv) Calculate

R .

Dependent Variable: SALARY

Method: Least Squares

Sample: 1 200

Included observations: 200

Variable Coefficient Std. Error t-Statistic Prob.

C 220.8001 4.5642 0.0000

ROE 0.1294

R-squared Mean dependent var

Adjusted R-squared 0.006584 S.D. dependent var 1396.345

S.E. of regression 1391.741 Akaike info criterion 17.32445

Sum squared resid Schwarz criterion 17.35743

F-statistic 2.318811 Durbin-Watson stat 2.118519

Prob(F-statistic) 0.129413

b .

(d) Economic theory stated that return on equity should have a positive impact on salary.

Use a critical value approach to test this hypothesis at 10% level of significance. Be

sure to show all steps used to conduct your hypothesis test.

(e) Predict the expected CEO salary when the company’s return on equity is 10% for the

previous three years.

(f) Calculate salary elasticity with respect to return on equity when the return on equity is

10% for the previous three years. Calculate also its standard error. (Use the property

that ( ) ( )

var var aX a X = where X is a random variable and a is a constant.)

Question 2 (4 marks each =16 Marks)

Are the following statements true? Provide a brief explanation (not more than 3-4 sentences)

for your answer.

1. In the OLS model,

var( ) b increases as the sample size (N) increases.

2. A left-tailed significance test should be used for

0 2

: 0 H β = when economic theory

suggests that the dependent variable and the independent variable have a correlation

that is greater than 0.

3. When overall uncertainty in the model, as measured by σ 2 , is smaller, the forecast error

will also be smaller.

4. The Jarque-Bera test is a test of the hypothesis that the residuals have a constant

variance.

Question 3 (6 marks each for parts (a) to (g) = 42 marks; for (h) to (k) 11+2+2+10 = 25

marks)

Life expectancy is an indicator of how long a person can expect to live on average given the

environment s/he is in. It is a standard measure of population wellbeing in general. It is

commonly used by the government for policy planning related to future population ageing in a

country. It is also commonly used in calculating life insurance policy.

There are a number of studies done on the relationship between life expectancy and income. It

is believed that people with higher incomes tend to live longer than people with lower incomes

and the relationship can be linear or nonlinear.

Consider the data on life expectancy and income for the year 2011 from a number of countries

obtained from http://www.gapminder.org/ and reported in LifeExpectancy.xls. The variable LE

represents life expectancy at birth in years. The variable GDP represents the country’s Gross

Domestic Product (GDP) per capita in international dollar after adjusting for purchasing power

parity so that GDP from different countries are comparable.

Consider three functional forms for the relationship between life expectancy and income.

1 2 i i i

LE GDP e =β +β + (3.1)

( )

1 2 ln i i i

LE GDP v = α +α + (3.2)

1 2 i i i

LE GDP = γ + γ +ε (3.3)

(a) Explain what each of the above functional forms imply in terms of the relationship

between life expectancy and GDP?

(b) Using the data for 179 countries, estimate the 3 equations and report the results the

usual way.

match your observations? Explain why?

(d) Obtain and comment on residual plots against the explanatory variable for each

equation. Which model seems best specified?

(e) Obtain histograms of your residuals for each model and discuss if they resemble a

normal distribution. Perform a test of normality on each set of residuals.

(f) Interpret and compare the

R for each of your three equations, and explain why it is

possible to make this comparison.

(g) Which is your preferred model? Use your answers in parts b) to f) above to justify your

choice.

Parts h) to k) below are for ETF5910 students only

It may be of interest to compare life expectancy between two levels of incomes. Some previous

studies have shown that a big proportion of population around the world receive income in

2011 around 2,000 international dollars. At the same time, some people at the high end of the

global income distribution receive income more than 30,000 international dollars in 2011.

Using the preferred model in (g):

(h) Predict life expectancy values for the two levels of GDPs. Obtain a 99% prediction

interval for both predicted life expectancy values. Compare and comment on the

finding.

(i) Find the estimates of the slopes ( ) ( ) d LE d GDP at the points where 2,000 GDP = and

30,000 GDP = .

(j) Find estimates of the elasticities ( ) ( )

( ) ( )

d LE d GDP GDP LE at the point where

2,000 GDP = and 30,000 GDP = .

(k) Based on the finding from parts (h) to (j), write a short report (not more than half a

page) in terms of life expectancy between low and high income populations.

代写 Monash ETF2100/5910 Introductory Econometrics