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BEA611S - BASIC ECONOMETRICS FOR AGRICULTURE -2ND OPP - JAN 2023 |
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n Am I 8 I A Un IVE RS ITV
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH, NATURAL RESOURCESAND APPLIED SCIENCES
DEPARTMENT OF AGRICULTUREAND NATURAL RESOURCESSCIENCES
QUALIFICATION: BACHELOR OF SCIENCE IN AGRICULTURE (AGRIBUSINESS MANAGEMENT)
QUALIFICATION CODE: 07BAGA
COURSE CODE: BEA611S
LEVEL: 7
COURSE NAME: BASIC ECONOMETRICS FOR
AGRICULTURE
DATE: JANUARY 2023
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER(S) PROF DAVID UCHEZUBA
MODERATOR: MR MWALA LUBINDA
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
1. Examination question paper
2. Answering book
THIS QUESTION PAPER CONSISTS OF 9 PAGES (Excluding this front page)
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Section 1 Multiple choice
Question 1
Consider the following models
E(y / X;) = /31+ f32X; 2 + µ; ······················.·.·.·..·.·.·..·.·.·.............................(.A)
E(y / X;) = /31+ /Ji X; + µ;···················································(·B··)···················
Which of the following statements about equations (A) and (B) is incorrect?
A) Equation (A) is linear in parameter and (B) is non-linear in parameter
B) Equation (A) is linear in variable and (B) is non-linear in variable
C) Equation (A) is non-linear in variable and (B) is linear in variable
D) Equation (A) is linear in parameter and (B) linear in variable
Question 2
The farmer's consumption function is fitted as
Y; = /31+ /J2X;+ A
Which of the following is INCORRECTabout why A was included in the model?
A) We do not know other variables affecting consumption expenditure ( y)
B) Even if we know, we may not have information (data) about all factors affecting ( y)
C) There may be measurement errors in the way data was collected
D) We include A because it is a non-random and systematic component of the model
Question 3
According to the Gauss-Markov theorem, which of the following statements is NOT CORRECT?
/3 An estimator says the ordinary least square (OLS}estimator 2 , is said to be the best linear
unbiased estimator of /32, if the following conditions hold.
/3 A) 2 , must be a linearfunction of the dependent variable ( y)
/3 E(/3 B) 2 , must be unbiased, i.e, its average or expected value
/3 2 ), must be equal to 2
/3 C) 2 , must have minimum variance
/3 D) 2 , must have a mean of zero
Question 4
/3 An unbiased estimator such as 2 , with the least (minimum) variance is said to be
A) An inefficient estimator
B) An efficient estimator
C) A random noise
D) An asymptote
Question 5
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Consider the following regression model estimated using the OLSmethod
y =463.5136-0.390lx 1 +0.17925x 2
(91.2835) (0.1213) (0.0477)
(Standard errors are in parenthesis)
Using equation (12.1), calculate the t-statistic for the x 1 and x2 variables
A) 3.2159 and 3.710
B) 3.2801 and 3.7578
C) 3.2159 and 3.7578
D) 3.2009 and 3.7011
Question 6
Which one of the following incorrectly defines the coefficient of correlation between variables?
A. Its value is between -1 and +l.
B. It can be positive or negative
C. It is a measure of association
D. It is independent of the origin and scale
E It is the same as R2
Question 7
The statistical significance of a parameter in a regression model refers to:
a) The conclusion of testing the null hypothesis that the parameter is equal to zero,
against the alternative that it is non-zero.
b) The probability that the OLSestimate of this parameter is equal to zero.
c) The interpretation of the sign (positive or negative) of this parameter.
d) All of the above
Question 8
All of the following are possible effects of multicollinearity EXCEPT:
a) the variances of regression coefficients estimators may be larger than expected
b) the signs of the regression coefficients may be opposite of what is expected
O)a significant F ratio may result even though the t ratios are not significant
d) removal of one data point may cause large changes in the coefficient estimates
6} the VIP is zero
Question 9
Suppose that you estimate the model Y =50 +B1X+ u. You calculate residuals and find that
the explained sum of squares is 400 and the total sum of squares is 1200. The R-squared is
a) 0.25
b) 0.33
c) 0.5
d) 0.67
Question 10
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In linear regression, the assumption of homoscedasticity is needed for
I. unbiasedness
II simple calculation of variance and standard errors of coefficient estimates.
Ill. the claim that the OLSestimator is BLUE.
a) I only.
b) II only.
c) Ill only.
d) II and Ill only.
e) I, II, and Ill.
Question 11
Which of the following is/are consequences of over-specifying a model (including
irrelevant variables on the right-hand side)?
I. The variance of the estimators may increase.
II. The variance of the estimators may stay the same.
Ill. Bias of the estimators may increase.
a) I only.
b) 11only.
c) Ill only.
d) I and II only.
e) I, II, and Ill.
Question 12
Heteroscedasticity means that
a) Homogeneity cannot be assumed automatically for the model.
b) the observed units have different preferences.
c) the variance of the error term is not constant.
d) agents are not all rational.
Question 13
By including another variable in the regression, you will
a) look at the t-statistic of the coefficient of that variable and include the variable
only if the coefficient is statistically significant at the 1% level.
b) eliminate the possibility of omitted variable bias from excluding that variable.
c) decrease the regression R2 if that variable is important.
d) decrease the variance of the estimator of the coefficients of interest.
Question 14
Which of the following statements is TRUEconcerning OLSestimation?
a) OLSminimises the sum of the vertical distances from the points to the line
b) OLSminimises the sum of the squares of the vertical distances from the points to
the line
c) OLSminimises the sum of the horizontal distances from the points to the line
(d) OLSminimises the sum ofthe squares of the horizontal distances from the points
to the line.
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Question 15
The residual from a standard regression model is defined as
a) The difference between the actual value, y, and the mean, y
y, b) The difference between the fitted value, and the mean, y
c) The difference between the actual value, y, and the fitted value, y
y, d) The square of the difference between the fitted value, and the mean, y
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Section 2 True or False
Question 1
If the null hypothesis is not rejected, it is true. True or False.
Question 2
/J The higher the value of the a-2 , the larger the variance of 2 given in question 4. True or
False
Question 3
The conditional and unconditional means of a random variable are the same thing. True or
False.
Question 4
In the two-variable population regression function (PRF),if the slope coefficient /32 is zero,
the intercept /31 is estimated by the sample mean Y.
Question 5
The conditional variance, var ( .Y;IX;) = a-2 , and the unconditional variance of Y, var ( Y) =
a-2r, will be the same if X had no influence on Y.
Section 3 - General
Question 1
Question 1.1. What is the meaning of the following econometrics terms
i).
Intercept (constant)
ii).
Cross-section data
iii).
Response variable
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(1 mark)
(1 mark)
(1 mark)
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iv).
Linear regression line
v).
Predictor
vi).
Linear model
vii). Multivariate model
viii). Regression analysis
ix).
Residual
x).
Slope coefficient
(1 mark)
{1 mark)
{1 mark)
{1 mark)
(1 mark)
(1 mark)
{1 mark)
Question 1.2.
Using hypothetical data, the relationship between child nutrition and stunting was
estimated as follows.
A
A
A
Y;=/3,+ f32X;
Where, Y =Average height of pupils aged 5 (measured in metres) and X =Household Dietary
Diversity Score (a measure of the diversity of food intake).
The estimated coefficients are
/3A
1
=
0.088
(0.0412),
/3A
2
=
0.7165
(0.2547),
R2 = 0.91.
(Figures in parenthesis are standard errors).
1.2.1. Interpret the slope coefficient
1.2.2. Calculate the T-statistic for the slope coefficient.
1.2.3. Calculate the T-statistic for the intercept coefficient
1.2.4. Interpret the the R2 value
1.2.5. Give two properties of the coefficient of correlation between Y and X
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
Question 2
In a model Y; =a+ /Jx; +u;,i = 1,...,N, the following sample moments have been calculated
from 10 observations.
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2.1. Estimate the slope parameter
2.2. Estimate the intercept parameter
y 2.2. Determine the function
y 2.3. Calculate the value for x = 10
y 2.4. Obtain the 95% confidence interval for the calculated
(4 marks)
(4 marks)
(3 marks)
{3 marks)
(6 marks)
Question 3
Consider the following regression model, y 1 = /31 + /32x1 + &1 • Where, y1 = consumption
expenditure, x =income, /J1= Constant, /J2 = Slope, & = Error term. Which of the above
3.1. Has fixed values in repeated sampling.
(2 mark)
3.2
Is a stochastic variable.
{2 mark)
3.3
Is a non-stochastic variable
(2 mark)
3.4
Has zero mean in a classical linear regression.
(2 mark)
3.5
Is a parameter.
(2 mark)
3.6. The analysis of the variance of a regression model is given below.
df
Regression
1
Residual
Total
12
ss
0.0040
0.2741
MS
0.2701
F
Significance F
745.9286 0.0000
i).
Complete the table
ii)
What is the null hypothesis of this test?
iii) Do you reject or fail to reject this null? Why?
{6 marks)
{2 marks)
(2 marks)
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Question 4
A post-regression Breusch-Pagan-Godfrey test was conducted to test for a violation of a
classical linear regression assumption. The result results of the test are shown below.
Description
F-statistics
P-value (Fl, 11)
Statistics
3.1405
0.1040
4.1 What is the name of this test?
4.2. What is the null hypothesis for this test
4.3. Do you reject or fail to reject this null? Why?
4.4. What are the implications of violating this assumption
4.5. How do you detect this assumption is violated?
4.6. What measure would you adopt to remedy this problem?
(2 marks)
(2 marks)
(2 marks)
(4 marks)
(6 marks)
(4 marks)
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Statistical formula
se(/31)= nI(Xi -X)2 a-
JB=n
[
-S+2-'----('K----3)2]
6
24
See the attached Durbin Watson table
k··= 1
n
dL
du
6 0_610
7 0.700
a 0.7,63
9 0_824-
10
0_579
11: 0_927
12
0..971
13
1_010
14
1 _04-5
15
1.077
16
1 _106
17
1 .13-3
18
1.1.58
11.400
11_356
11.332
1! _320
11.320
1i .324
11.331
11.340
11.3.SO
11.361
11_371
11.381
1.3.91
k·'=2
dL
du
K=3
dL
du
k"'=4
dL
du
0_467
0_55,g
0_629
0_697
0_658
0_812·
0_861
0.905
0.94-6
0.98.2
1.015
1.04-6
1 .8.96
1 ..777
1_699
1 _,641]
1.604
1.579
1 _562
1 _5511
1.543
1 _539
1.536
1.535
END
0_368
0_455
0_525
0_595
0.658
0_715
0_767
0_814
o_8s7
o_agy
0_933
2-2'87
2_ 1:2a
2_0"16
1 _,92:8
1.,8,64
1 .816
1_779
1.750
1.72.S
-a.710
1 .,69,6
0_296
0_376
o,_444
0.512
0.574
Q,_632
0.685
o,_734
0.779
0.820
2_saa
2_41.4
2.28'3
2.177
2.094-
2.030
1 ..977
1 _935
1.900
1.872
9