代写 ETF2100/5910 Introductory Econometrics assignment

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代写 ETF2100/5910 Introductory Econometrics assignment

Department of Econometrics and Business Statistics

ETF2100/5910 Introductory Econometrics

Assignment 2, Semester 1, 2016

Worth 15% of Final Mark

Due 4pm Friday May 6

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

Note:

• This assignment comprises three (3) questions.

• Question 3 is an extra question for ETF5910 students.

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

of answers.

• Total marks for ETF2100 and ETF5910 students are 90 and 108, 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.

Q UESTION 1 (50 marks)

Consider the following total cost function where

TC represents total cost for the ith firm and

Q represents quantity of output.

2 3

1 2 3 4 i i i i i

TC Q Q Q e =β +β +β +β + (1.1)

Two other costs that may be of interest are average cost per quantity of output and marginal

cost for an extra output. Average cost is obtained by dividing total cost by quantity of output.

Using total cost as defined in equation (1.1) average cost function can be defined as:

2 1 3 4

i i i i

AC Q Q v

=β +β +β +β + (1.2)

where the new error term is

i i i

v e Q = . Note that the parameters

1 2 3 4

, , and β β β β are the same

parameters as those in equation (1.1).

Marginal cost is obtained from taking derivative of total cost with respect to output. From the

total cost function defined in (1.1) marginal cost function can be derived as:

2 3 4

2 3

i i i

MC Q Q =β + β + β (1.3)

Data on a sample of 28 firms in the clothing industry are in the file clothes.wf1.

(a) What sign would you expect for

2 3

, β β and

β ? Explain. (5 marks)

(b) Estimate the total cost function (1.1) and report results. Are the signs for the estimated

coefficients turn out as expected? (5 marks)

2 3 4

, and β β β .

(6 marks)

(d) Using 0.01 α = test the significance of the model. (3 marks)

(e) Obtain and report the correlations between the explanatory variables. Is there evidence

of multicollinearity? What could be the symptoms of multicollinearity in the regression

results in (b)? (5 marks)

(f) Test whether the data suggest that a linear total cost function will suffice. (5 marks)

(g) What parameter restrictions imply a linear average cost function? Test these

restrictions. (4 marks)

(h) Calculate the predicted total, average and marginal cost for output 1,2, ,10

Q =  using

the parameter estimates from (b). (3 marks)

(i) Graph the predicted total, average and marginal cost for output 1,2, ,10

Q = 

calculated in (h) (3 marks)

(j) It is believed that it is profitable for firms to produce when price exceeds average cost

and firms will decide to shut down if price is less than average cost. Also, average cost

is at minimum when

i i

AC MC = . From the graph in (i) roughly find the output level

where

i i

AC MC = . Calculate the minimum average cost implied by the estimated

parameters in (b). At what price should the firm make a decision to shut down?

(5 marks)

(k) Find estimates of

1 2 3 4

, , and β β β β by applying least squares to the average cost function

defined in (1.2). Report the results. Is it possible to make any decision about which set

of estimates might be "best"? (6 marks)

Question 2 (40 marks)

Suppose that you are trying to explain marketing performance of Heinz tomato sauce at a

supermarket. Weekly sales is considered to be one of the obvious marketing performance

measures. The file promotion.xlsx contains 124 observations on the sales of Heinz tomato sauce

(

S ) and the weekly average price (

P ) for the t-th week, both measured in dollars. For each

week we also recorded whether there is coupon promotion (

CP ), major display promotion (

DP) or combined promotion (

TP ). The variables

CP ,

DP and

TP are dummy variables.

CP = for the week with coupon promotion only. 1

DP = when there is major display

promotion only. 1

TP = for the week where there are coupon and display promotion at the

same time. In the analysis below we will consider sales (

t

代写 ETF2100/5910 Introductory Econometrics assignment

S ) and price (

P ) after taking natural

logarithms.

(a) Plot a scatter diagram of ln

S versus ln

P . Comment on the correlation between the

two variables. (3 marks)

(b) Consider first the model below.

0 1 2 3 4

ln ln

t t t t t t

S P CP DP TP e =β +β +β +β +β +

What signs would you expect

1 2 3 4

, , and β β β β to be? Explain why? (Answer this before

using regression.) (4 marks)

(d) Carefully interpret the estimated coefficients. Have the signs of the estimates turned out

as you expected? (4 marks)

(e) Use a p-value approach to test whether there is a significant relationship between

ln and ln

t t

S P . Is the result of the test consistent with the result from the plot in (a)?

Explain why. (5 marks)

(f) Use a critical value approach at 5% level of significance to test whether a combined

promotion has any impact on sales. Be sure to explain your methodology. Are your

results surprising? (5 marks)

(g) It is of interest to investigate the difference in the impact on weekly sales between the

two promotions – coupon and display. Obtain a 95% interval estimate for ( )

2 3

β −β .

Use the result to discuss the relative effectiveness of the two promotions. Explain the

benefit of reporting interval estimate instead of the point estimate. (7 marks)

(h) Test at the 0.5 α = level of significance whether the impact on sales from having

combined promotion is more than the impact of having coupon and display promotion

separately. (7 marks)

(i) Predict the sales for the week where the price is $1.05 and there is only a coupon

promotion. (2 marks)

Question 3 For ETF5910 only (18 marks)

Consider again the data in the file promotion.xlsx.

(a) Plot a scatter diagram of ln

S against (

ln ln

t t

P P − − ). Comment on the relationship

between ln

S and (

ln ln

t t

P P − − ). (3 marks)

(b) The model in Question 2 is expanded to include the dynamic structure of the sales. We

expand the model by including first-order lags of

P − and

−

. The model

becomes:

0 1 1 2 3 1 4 5 6

ln ln ln ln

t t t t t t t t

S S P P CP DP TP v

− −

= α +α +α +α +α +α +α +

Interpret the coefficient

α . (2 marks)

(d) Explain if the model in part (b) is a better model than the one in Question 2. Why?

(3 marks)

(e) How would you modify the model in part (b) (of this question) if you have a strong

belief that the percentage change in current sales resulting from percentage change in

this week price is the same as percentage change in current sales resulting from

percentage change in the price last week. Explain your reasons. Test this belief.

(7 marks)
代写 ETF2100/5910 Introductory Econometrics assignment