You need to copy and paste relevant
output from Gretl onto a word document to accompany your analysis. However,
inclusion of irrelevant output will lead to deduction of marks. Your report should be
neatly set out and provide clear answers to the assignment questions. For the final
question you need to convince the marker that your choice is valid so you should use
results from previous questions to support your choice of a preferred model.
The data tuna.gdt contains 52 observations. This data file is on the weekly sales of a
major brand of canned tuna by a supermarket chain in a large midwestern U.S. city
during a mid-1990s calendar year. The variables listed in the file are:
SB1= Unit sales of brand 1 canned tuna
PB1= Average price per can of brand 1 canned tuna ($)
PB2= Average price per can of brand 2 canned tuna ($)
PB3= Average price per can of brand 3 canned tuna ($)
(4 Marks) Multiply the observation in each of the variables, PB1, PB2 and PB3 by 100 to express them in terms of cents and call the new variables PB1C, PB2C and PB3C, respectively. (To make a new variable in Gretl select ‘Add’ ‘define new variables’ and type in the box as ‘PB1C=PB1*100’ then click ‘OK’.
Repeat the same steps to make the other two variables, PB2C and PB3C and type as follows. (PB2C=PB2*100, PB3C=PB3*100). Estimate the following regression model and report the results. Interpret the estimates of a2, a3 and a4?
????1 = ??! + ??!??1?? + ??!????2?? + ??!????3?? + ??
(3 Marks) Using a 1% significance level and a suitable one sided hypothesis, test each of the above slope coefficients equal to zero against your one sided alternative and comment on the results.
(4 Marks) Test the hypothesis that the effect of a price increase in brand one on sales of brand one is equal to three times the price decrease of brand three on the sales of brand one. Use the t-test and a 5% significance level.
(4 Marks) Create relative price variables RP2 and RP3 as it is shown below and estimate the following model. (RP2=PB1/PB2 and RP3=PB1/PB3)
????1 = ??! + ??!??2 + ??!????3 + ??!
What do you anticipate the relationship between sales (SB1) and the relative price variables to be? Do the signs of the estimates agree you’re your expectations? Explain. (Create a new variable in Gretl select “Add” then “define new variable” and type in the box as ‘RP2=PB1/PB2’ click “ok”. Similarly to make the next variable repeat the above steps and type in the box as ‘RP3=PB1/PB3).
(3 Marks) Re estimate the model in Q4 by changing the variables in to logarithms and interpret the slope coefficients. (To take logs in Gretl first highlight the variable/s to be changed in to logs then choose the menu ‘Add’ then select ‘logs of selected variables’)
ln ????1 = ??! + ??! ln ????2 + ??!ln (????3) + ??
(2 Marks)Which brand, no. 2 or no. 3, is the strongest competitor to brand no. 1? Why?
(3 Marks) Calculate the relative price elasticity of brand 1 tuna sales at the mean relative price for the models in Q4 and Q5 and interpret them.
(4 Marks) Test the overall significance of the model in Q5 at the 5% significance level and comment on your results. (Use the restricted and unrestricted version of the F test)
(2 marks) Plot the residuals of the double log model estimated in Q5 and comment on it.
(6 marks) compare the two models in Q4 and Q5 and what econometric problem(s), if any, do the models appear to have? Which model do you prefer? Clearly state your reasons for selecting the model you chose.