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Microsoft Word - Assignment_Econ6034_Final.docx Econometrics and Business Statistics tal Marks 80 The assignment relates to the following learning outcomes: • Apply basic statistical techniques to...

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Microsoft Word - Assignment_Econ6034_Final.docx


Econometrics and Business Statistics

tal Marks 80

The assignment relates to the following learning outcomes:
• Apply basic statistical techniques to problems in economics and business
• Use econometric tools to model, estimate and forecast economic data
• Engage into further studies in econometrics
• Demonstrate the ability to work effectively in a group
Submission:
• No extensions will be granted except for cases in which an application for
Special Consideration is made and approved.
• Late submissions will be accepted up to 96 hours after the due date and time.
• There will be a deduction of 10% of the total available marks made from the
total awarded mark for each 24-hour period or part thereof that the
submission is late (for example, 25 hours late in submission incurs a 20%
penalty).
• Include following details in your submission file: Family Name, Given name,
Your student ID number and the Econ6034_Assignment.
• Type your assignment in MSWORD (font size 12) and save it as a pdf and
submit your PDF document. No other format will be accepted.
• Use Microsoft word equation editor to type your formulae or equation. The
Following links may be helpful in getting started with the equation editor.
• https:
www.uwyo.edu/ceas
esources/cu
ent-
students/classes/esig%20help/windows%20help%20files/microsoft%20office
word-equations.pdf
• https:
www.officetooltips.com/word_2016/tips/working_with_microsoft_equ
ation.html
• You CANNOT submit the assignment in Handwritten or scanned formats.
• Your answers must be preceded with the assignment questions and your
answers must be in the same order.
• Unless it requested in the question otherwise do not attach Eviews output.
• If required, charts and output from EViews may be copied as an image into
the document.
• Marks will be deducted for poor quality presentation.
• No appendices in your assignment.
• Maximum pages 12
• You can ONLY submit ONCE to Turnitin.

Plagiarism:
• Each assignment must represent the student's own work.
• The copying of another student's answer or textbooks, or part thereof, is
clearly regarded as plagiarism.
• Students who have plagiarised will be awarded a mark of zero, will not be
permitted to resubmit, and may be reported to the University Disciplinary
Committee for further action.
• Students should be aware of the University’s Academic Integrity Policy and
the Student Code of Conduct: https:
students.mq.edu.au/study/getting-
started/student-conduct

Acknowledgement:
� I agreed and submit my assignment.



Assignment Questions

Question 1 [46 marks]

Suppose we wish to estimate the relationship between food expenditure and some of
its determinants. The file Foodexp.xlsx contains 200 observations from a cross-
section of households for the following variables.

Foodexpi: Weekly expenditure on food (excluding restaurants) in dollars.
Incomei: Weekly household income in dollars.
Childreni: Number of dependent children living in the household.
Retiredi: A binary (0/1) indicator of whether head of the household is retired
{ret.=1}.

(a) Consider a regression model
???????! = ?" + ?# log(??????!) + ?$?ℎ??????! + ?%???????! + ?!
Estimate the model using Eviews and provide the summary results (A
summary results should include fitted equation with coefficients, standard
e
or, t-statistic, p-value, sample size, F-statistic and R-squared). [4 marks]
(b) Interpret the coefficient estimates and their significance at the 5% significance
level. [4 marks]
(c) Does the sign of the coefficients agree with your expectations? Comment.
[4 marks]
(d) Based on the regression output, if Income increases by 10% what is the
estimated change in Foodexp, holding Children and Retired constant. [4 marks]
(e) Test the overall validity of the regression model at the 5% significance level.
State the hypotheses, restricted and unrestricted model, test statistics and its
distribution when null hypothesis is true, critical value and your conclusion.
[4 marks]
(f) Construct 95% confidence interval for ?#, the slope of the log(Income) variable
and interpret your results. [4 marks]
(g) Based on your answer in part (f), without performing a hypothesis test,
would you reject the hypothesis ?": ?$ = 100,                ?#: ?$ ≠ 100. Explain? [4
marks]
(h) Plot the least squares residuals against log(Income) and comment on the
pattern. Is there any evidence of heteroscedasticity? [4 marks]
(i) Test for the existence of heteroscedasticity at the 5% significance level. Use
the Breusch-Pagan-Godfrey test and attach your Eviews results. Clearly states
all steps in your test; null and alternative hypotheses, the auxiliary regression
and the test statistic, critical value, your decision and the conclusion. [6
marks]
(j) Re-estimate your model with robust standard e
ors and attach your Eviews
output. Compare your results with the output in part (a). Comment.
[4 marks]
(k) Now run the following regression model:
???????! = ?" + ?# log(??????) + ?!
(l) Compare your model that with part (a). Which model would you choose?
And Why? [4 marks]
Question 2 [34 marks]

A researcher wants to analyse the relationship between the three-month T-bill rate,
tb3, the annual inflation rate, inf based on the consumer price index, and the federal
udget deficit, def as a percentage of GDP and develops the following model. The
data is stored under the file name is intdef_A.xlsx

??3& = ?" + ?#???& + ?$    ???& + ?&
(a) Use Eviews to obtain a line plot among these three variables (one graph) and
comment on the plot. (Hint: to make the graph in Eviews: Quick à Graph à tb3
inf def àOk àLine & Symbol à OK.) [4 marks]
(b) Obtain sample co
elation coefficient between these variables and comment
on the strength of the relationships? (Hint: to obtain co
elation in Eviews: Quick
à Group Statistics à Co
elations à tb3 inf def à Ok.) [4 marks]
(c) Estimate the above regression model and provide the Eviews output.
[4 marks]
(d) Interpret the coefficients ?#and    ?$. Does the sign of the coefficients agree with
your expectations? Explain. [4 marks]
(e) Provide and interpret the coefficient of determination, ?$. [4 marks]
(f) Plot the residuals of the model and comment on any pattern. [2 marks]
(g) Add a one lag of inf and def to the equation in part (a) and re-estimate your
model. and report the result. Are the coefficients for the two lag variables
individually significant at the 5% level? To add lag variables in Eviews type
inf(-1) def(-1) [4 marks]
(h) Conduct the second order autoco
elation test for the model in part (c) at the
5% significance level. Attach your Eviews results. Clearly states all steps in
your test; Null and alternative hypotheses, the auxiliary regression and the
test statistic, critical value, your decision and the conclusion. [6 marks]
(i) Re-estimate your model with Newey-West standard e
ors and provide your
output. Compare your results with the output in part (c). Comment.
[2 marks]


Microsoft Word - Tables-Guj.docx
Answered Same Day May 30, 2021 ECON6034 Macquaire University

Solution

Komalavalli answered on May 31 2021
134 Votes
Question 1:
Model 1:
(a)
yi = ?0 + ?1 x1i+ ?2 x2i + ?3 x3di + ?i
yi - Weekly expenditure on food (excluding restaurants) in dollars
x1i - Log of weekly household income in dollars
x2i - Number of dependent children living in the household
x3di = 1 If head of the household is retired
    0 If head of the household is not retired
Log linear Regression equation: Foodexp = 174.09+ 0.0432*log(Income) + 22.8*Children - 13.8*Retired.
Summary of Income variable; t statistics-7.406, standard e
or-0.005, p-value -0.00
Summary of Children variable; t statistics-4.541, standard e
or-5.028.005, p-value -0.00
Summary of Retired dummy variable; t statistics is -0.947, standard e
or-14.569, p-value -0.3445
Summary of overall Model:
Prob (F-statistics) is 0.000; value of F statistic is 34.342, Adjusted R-squared is 0.33, R squared value is 0.34.Sample size of the model is 1200.
(b)
Expect the variable retired rest of all 2 variables, income and children are significant at 5 % level of significance.
Interpretation of coefficient:
By holding retired and children variable constant for a one percent increase in weekly household income on an average increases the weekly expenditure on food by $0.04 retired. Increase in one dependent children living in the household on an average increases the weekly expenditure on food by $22.82 by holding other variables constant. We can’t interpret the coefficient value of Retired variable, because it is insignificant at 1%, 5%, and 10% level of significance. Insignificant variable does not have influence on the regression model
(c)
From the model we can observe that there is a positive relationship between food expenditure and income, food expenditure and dependent children. When we look in real life relation between these variable, it will also have a positive relationship between these variable. It indicating the food expenditure increases when dependent children in the household and weekly income of the household increases. Therefore the sign of the model coefficients is similar to what I have expected.
(d)
Predicted change in food expenditure when income increases by 10 % by holding other things constant. Log linear Regression equation:
Log linear Regression Model y = 174 + 0.0432x1i + 22.8 x2i - 13.8 x3di.
For 10% increase in income: y = 174 + 0.0432(10) + 22.8 (0) - 13.8 (0).
y = 174 + 0.432
y = 174.432
The model predicted that when income increases by 10 % on an average expenditure on food is $174.432 by holding other variable constant.
(e)
Hypothesis of this model is H0 null hypothesis: β0= β1= β2= β3=0,by indicating all the coefficient variable equal to zero we assume that none of the variable in this model has influence on food expenditure.H1 β0≠β1≠β2≠β3≠0, we assume that all variables has influence on the food expenditure .
Unrestricted or full model is y = β0+ β1 x1+ β2 x2 + β3 x3d and restricted model is y = 0.If null hypothesis is true we use restricted model and we use unrestricted model when alternate hypothesis is true
Here the critical value of F stasticts (3,196) is 2.7 .The value of F statistics is 34.342 which is greater than the value critical value of F test .Therefore we reject null hypothesis and accept alternate hypothesis H1.Furthure we will use unrestricted model.
(f)
Variable log income of 95% confidence interval is (0.031719, 0.054742) stating that the population mean lies between the 0.031719 and 0.054742
(g)
Above analysis show that the population mean is does not include the value of null hypothesis .So we reject the null hypothesis ?0: ?2 = 100 and accept the alternate hypothesis ?1: ?2 ≠ 100, which indicates the variable log (income) has influence on the model.
(h)
Residual plot against log(income)
The above plot shows an upward line pattern, indicating the presence of heteroscedasticity indicates that there is no evidence for constant variance of residuals.
(i)
    Heteroskedasticity Test: Breusch-Pagan-Godfrey
    Null hypothesis: Homoskedasticity
    
    
    
    
    
    
    
    
    
    
    F-statistic
    21.74638
        Prob. F(3,196)
    0.0000
    Obs*R-squared
    49.94591
        Prob. Chi-Square(3)
    0.0000
    Scaled explained SS
    46.42366
        Prob. Chi-Square(3)
    0.0000
    
    
    
    
    
    
    
    
    
    
    
    Test Equation:
    
    
    
    Dependent Variable: RESID^2
    
    
    Method: Least Squares
    
    
    Sample: 1 200
    
    
    
    Included observations: 200
    
    
    
    
    
    
    
    
    
    
    
    
    Variable
    Coefficient
    Std. E
o
    t-Statistic
    Prob.  
    
    
    
    
    
    
    
    
    
    
    C
    1833.589
    1041.575
    1.760401
    0.0799
    INCOME
    4.092107
    0.528356
    7.744979
    0.0000
    CHILDREN
    -1618.538
    454.8451
    -3.558437
    0.0005
    RETIRED
    -539.9479
    1318.818
    -0.409418
    0.6827
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    R-squared
    0.249730
        Mean dependent va
    5642.232
    Adjusted R-squared
    0.238246
        S.D....
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