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ECON 2300 SEMESTER 2 2016

ECON 2300 SEMESTER 2 2016

ASSIGNMENT 1: Due Wednesday August 31st, 2016 by 5.00 pm

Maximum Marks 80. Weight in the final assessment: 10%

Question 1: (30 marks)

You are required to do all the parts of this question by hand (i.e. using summation notation and a nonprogrammable calculator).

Suppose that we are interested in the relationship between the agricultural sector and total

output in developing countries and we are given data on variables Y and X where Y measures

per capita GDP in thousands of $US and X measures the percentage of the labour force in the

agricultural sector. The data is

X

Y

a.

b.

c.

9

6

10

8

8

8

7

7

10

7

4

12

5

9

5

8

6

9

7

10

and assume that the Gauss Markov

Consider the relationship given by

(the sum of squared errors) and

.

theorem holds. Use this data to calculate , ,

Show your working. Then test the null hypothesis (at the 5% level) that the percentage of

workers in the labour force in agriculture does not affect per capita GDP, choosing a suitable

alternative for your test. Briefly justify your choice of an alternative hypothesis, and comment on

any additional assumptions that you need to make to perform the test. (18 marks)

Calculate the total sum of squares (SST) and R2 for this regression, and then comment on the fit

of this model. (5 marks)

Suppose that per capita GDP was measured in $US rather than thousands of $US. How would

that change the coefficients and the sum of squared errors for the equation in (a)? Show your

working. (7 marks)

Question 2: (50 marks)

Instructions: You should hand in your answers to the questions, together with an appendix which

contains appropriate computer output. Answers should be in sentence form (i.e. single word or single

number answers without explanation will be considered incomplete), but clarity of presentation is

important, so try to make your comments/discussion brief and to the point. Annotated output does not

constitute a sufficient answer to any question, but you should highlight those parts of your output that

you explicitly use in your answers, so that I know where your answers came from. If your answers do

not meet these criteria, they will necessarily lose marks. Be sure to answer all parts of each question.

Background: You have just learnt Engle?s Law which states that the share of household expenditure

spent on food decreases with income. You have decided to examine this law empirically. You have

come across data collected as a part of the British Family Expenditure surveys.

The file lon.wf1 is available on the Blackboard site. It is a cross section of 1215 households drawn from

the British Family Expenditure surveys. Data have been selected to include only households with one

or two children living in Greater London. Self-employed and retired households have been excluded.

The variables in the dataset are:

a.

b.

TOTEXP = total household expenditure (rounded to the nearest 10 UK pounds sterling)

WFOOD = budget share for food expenditure (i.e. the ratio of expenditure on food to total

expenditure)

Generate a scatter plot to examine the general nature of the relationship between the expenditure

share on food (WFOOD) and total expenditure (TOTEXP) of the household. Does there appear

to be a relationship between these two variables? If so, comment on whether the relationship

seems to follow Engel?s law. (3 marks)

Consider the three models given by

WFOOD 1 2 ln(TOTEXP) e ,

WFOOD 1 2 TOTEXP e and

ln(WFOOD) 1 2 ln(TOTEXP ) e

i.

ii.

iii.

iv.

v.

Estimate all the three different functional forms (semi-log; linear; and log-log). Present the

estimated equations from all the three models, including the standard errors of estimated

coefficients and R-squared. Interpret the slope coefficients. Are the signs of the slope

coefficients what you expected? Explain. (16 marks)

Evaluate the suitability of the semi-log, linear, and log-log models for fitting the data. Which

of them would you select as best, and why? (8 marks)

Your background in applied econometrics suggests that the slope coefficients from the three

models (semi-log, linear and log-log models) cannot be compared across the models. Compute

and interpret the expenditure elasticity for food share at the sample means in each case.

Compare the estimated elasticities from the three models. (9 marks)

Based on the elasticities computed, do these results suggest that food is a luxury or a

necessity? (2 marks)

Construct histograms of the least squares residuals from each of the models. Do the residuals

appear to be normally distributed? Use a Jarque-Bera test and a 5% level of significance to

test the null hypothesis of normality. (12 marks)

Submission of Assignment:

Unless otherwise specified, all reports must be lodged by the due date and time. Upload your report

and appendix as a single pdf file through the Turnitin link provided through the course?s Blackboard

site. Please Note: Reports must not be faxed or emailed to the Course Coordinator without prior

arrangement.

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