Monash University Malaysia
ETW3510 Applied Econometrics Methods
Individual Assignment 1
Weight: 10% of Total Assessment
DUE DATE: 2 April 2021, Friday, 11.00PM (Week 5)
Instructions
1. This is an individual assessment and is worth 10% of the final mark.
2. Online Assignment Submission on Moodle and the submission must be in pdf.
File format: Firstname_studentID.pdf
3. All submissions should be attached with an Assignment Cover Sheet.
4. No submission will be allowed after the due date. Late assignment: A penalty of 10%
of the mark allocated to the assignment will be deducted for each day that the
assignment is late. Deadline extension: Request from your lecturer/ tutor 24 hours
before the due date should you have a legitimate excuse, or no extension will be
granted.
5. All workings must be clearly shown as marks will be awarded for workings.
6. Please ensure that you read the policy with regards to Plagiarism and Collusion.
This assignment will assess the understanding of the theoretical aspects of the first
learning outcome of the unit on the theory of micro-econometrics, as stated in the Unit
Guide.
Question 1
Suppose that X is a random variable which follows a normal distribution with an expected
value of µ and variance s 2 . Show that the CDF of X evaluated at a real number c may
be written as
F (c ) = F (
c-µ
s
)
[4 marks]
Question 2
What is a latent variable? Write down a model with the use of a latent variable. Explain
how it is possible to estimate the utility function with the use of the conditional model for
binary data.
[5 marks]
Question 3
Describe advantages and disadvantages of linear probability model, probit and logit
models.
[6 marks]
Question 4
The Organic Trade Association recently conducted a survey to determine the factors that
influence fruit buyers to buy more organic fruits than regular fruits. Random samples of
556 organic food buyers were surveyed in several supermarkets in the Klang Valley. The
dependent variable indicates whether the shopper bought more “environmentally friendly”
(i.e., grown without the use of chemical fertilizers and pesticides) fruits than regular fruits.
In total 5 variables were identified to influence the buying of organic fruits and the
variables are given as follows:
Variables
yi : 1 if shopper bought more organic fruits than regular fruits, 0 otherwise.
[Mean price RM1.08]
X 1i : Price of organic fruits (RM/lb.)
[Mean price RM0.88]
X 2i : Price of regular fruits (RM/lb)
[Mean income RM54.52]
X 3i : Family income of the buyer in 1000 Ringgit
X 4i : 1 if buyer male, 0 otherwise
[Mean years of schooling 14.36]
X 5i : Buyer’s education in years
(a) The linear relationship between Y and X’s were estimated using the Ordinary Least
Squares (OLS) estimation method and the following results were obtained:
Yi = 0.434 - 0.907 X 1i + 0.948 X 2i + 0.001X 3i - 0.106 X 4i + 0.017 X 5i
(0.159) (0.124)
(0.149)
(0.001)
(0.045)
(0.009)
(1.1)
Standard errors are given in parenthesis in (1.1). Interpret the results given in
(1.1). Discuss the limitations of the model estimated in (1.1). Use a =0.05.
[4 Marks]
(b) The following logit model was estimated for yi with log( X 1i ), log( X 2i ), log( X 3i ), X 4i
and X 5i as explanatory variables.
yi = L ( b 0 + b1log ( X 1i ) + b 2log ( X 2i ) + b3log ( X 3i ) + b 4 X 4i + b5 X 5i )
The results are reported in Table 1.1.
Table 1.1
Dependent Variable: Y
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
LOG(X1)
LOG(X2)
LOG(X3)
X4
X5
-0.955376
-4.044001
3.434111
0.296643
-0.483207
0.068339
0.700091
0.590506
0.571816
0.143870
0.207678
0.042827
-1.364646
-6.848365
6.005621
2.061885
-2.326708
1.595681
0.1724
0.0000
0.0000
0.0392
0.0200
0.1106
S.E. of regression
0.468478
Sum squared resid
120.7092
Log likelihood
-346.7208
Restricted log likelihood -380.7148
(i) Do the signs of the estimated parameters of income and price variables make
sense? Briefly explain.
[3 Marks]
(ii) Test the overall significance of the model at the 5% level of significance. Explain
your results and show all your workings.
[3 Marks]
(iii) Test the following hypothesis, H 0 : b k = 0 for k=1,2,3,4 and 5 at the 5% level of
significance. Interpret your results.
[3 marks]
(iv) How much discount should the shopkeepers give to their male customers to ensure
that a male customer has the same probability of buying more organic fruits than
regular fruits as a female customer with the same characteristics? (Assume that
the customers have mean characteristics).
[4 Marks]
Question 5
Provide an intuitive explanation of the maximum likelihood estimation technique for binary
dependent variable models.
[4 Marks]
Question 6
Explain the McFadden’s R2 and the percentage correctly predicted measures. How are
these measures different from R-square for the OLS.
[4 Marks]
End