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BEA611S - BASIC ECONOMETRICS FOR AGRICULTURE -1ST OPP - NOV 2022 |
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nAmI BI A un IVE RSITY
OF SCIEn CE Ano TECHn OLOGY
FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES
DEPARTMENT OF AGRICULTUREAND NATURALRESOURCESSCIENCES
QUALIFICATION:BACHELOROF SCIENCE.INAGRICULTURE(AGRIBUSINESSMANAGEMENT)
QUALIFICATIONCODE: 07BAGA
COURSECODE: BEA611S
LEVEL: 7
COURSENAME: BASIC ECONOMETRICS FOR
AGRICULTURE
DATE: NOVEMBER 2022
DURATION: 3 HOURS
MARKS: 100
FIRSTOPPORTUNITY 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.
PERMISSIBLEMATERIALS
1. Examination question paper
2. Answering book
THIS QUESTION PAPERCONSISTSOF 10 PAGES(Excluding this front page)
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Section 1 Multiple choice
Questions 1
Which of the following statements is NOT CORRECTabout Econometrics?
A. There is no difference between econometrics, statistics and mathematics
B. Econometrics empirically measure relationships among economic variables
C. Econometrics is an amalgam of economic theory, mathematical economics, economic
statistics and mathematical statistics
D. Econometrics is a collection of statistical techniques for testing economic theories
Question 2
The methods or steps taken in econometrics to estimate economic relationships are as
follows:
1. Develop and test a hypothesis
2. Specify the econometrics model.
3. Collect the data.
4. Identify the variables.
5. State the economic theory or hypothesis to be investigated.
6. Do predictions and forecast based on the estimated parameters.
7. Estimate the parameters of the model.
8. Use the model to inform policy.
Which of the following CORRECTLYdescribes the econometrics steps?
A. 2, 5, 4, 3, 8, 1, 7 & 6
B. 4, 2, 6, 5, 7, 1, 3 & 8
C. 5, 2, 4, 3, 7, 1, 6 & 8
D. 5, 2, 1, 3, 7, 4, 6 & 8
Question 3
An economic model is represented by the equation
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Y=a+bX
Which of the following statements is NOT correct?
A. a has no economic interpretation
B. b is the slope while a is the intercept
C. X influences Y according to the value taken by b
D. For the model to be linear X must be raised to the power of two or more
Question 4
Which of the following is NOT CORRECTabout the name of the variable X in the equation,
Y=a+bX
A. Predictor
B. Repressor
C. Independent variable
D. Explanatory variable
Question 5
Which of the following BESTdescribes the models in equations {1) and {2)?
Y = a +bX ...................................................................................................................................... (1)
Y = a+bX +&................................................................................................................................ (2)
A. Both are the same
B. Equation (1) is used by statisticians whereas, (2) is an econometric model
C. The & is the disturbance or error term which is a random (stochastic) variable
D. Irrespective of the & there is an exact relationship between Y and X .
Question 6
/J 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
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Question 7
Which of the following statement about R2 is NOTcorrect?
A. It is a non-negative quantity
B. Its value is between zero and one
C. It is the proportion of Y that is explained by X
D. It is the best estimate of the goodness of fit.
Question 8
Assuming an equation is expressed as
Y; = /Ji+ /J2X+1/J2X2 + A
Which of the following best describes the formula to test the Hypothesis that /32 is not
statistically different from zero?
/J A) t = 2 - /32 I se(/J2 )
B) t = /32 - /J2 / se(/2 J)
/J C) t = /32 - 2 / se(/32 )
/J /J D) t = 2 - 2 / se(/Ji)
Question 9
Instead of using the Null hypothesis to test the significance of an estimate, a shortcut known
as the "2-t "rule of thumb can be used. This rule says, "Reject the null that /32 = 0 if the
computed t-statistics value exceeds
A) Absolute value of three
B) Absolute value of one
C) Absolute value of two
D) Absolute value of four
Question 10
Which of the following is NOTan econometric model?
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C).r; = /31+ /31X;
D). r; = /31+ (0.75 - /31)e-Pi(X;-2) + A
Question 11
The relationship between a farmer's consumption expenditure (Y) and income (X) is
expressed as follows, E(y IX;)= f(x;) .Which of the following statements about the
equation is incorrect?
A) It is known as the conditional expectation function
B) It is known as the population regression function
C) It is known as the population regression
D) It is known as the sample regression function
Question 12
Which of the following is incorrect about the interpretation of the
equation Y; = /31 + /32x 1 + /32x 2 + A ?
A) The expected mean value of y is conditionally related to X;
B) The values of x are unobservable
C) The expected mean value or average response of Y varies with X
D) The equation of a linear function
Question 13
Y; /J µ;. /J If an estimable model is given as, = 1 + 2X; + Which of the following statements is
incorrect?
A) The equation is a sample regression function
/3 B) The 2 is the estimator for /32
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C)The value of /J?is known as the parameter estimate
D) The value of /32 cannot be negative
Question 14
Y; /J /J Which of the following parameters in the equation = 1 + 2Xi + µi can be calculated
I'x°y' / , using the formula?
where xi= (X -X) and Y; = (Y -Y).
~xi
Question 15
The function y = f(x) is said to be a linear function of ( x ), which of the following
statements is incorrect about this linear function?
A) x must appear with power or index of 1 only.
B) x must not be multiplied or divided by any other variable
C) The rate of change of y with respect to x must be independent of the value of x
D) x can appear as a square root (
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Section 2 True or False
Question 1
The t-test of significance requires that the sampling distribution of estimators follow a
normal distribution. True or False
Question 2
Even though the disturbance term is not normally distributed, the Ordinary Least Square
estimators are still unbiased. True or False
Question 3
If there is no intercept in the regression model, the estimated error (residual) will not sum to
zero. True or False
Question 4
The p-value and the size of a test statistic mean the same thing. True or False
Question 5
In a regression model that contains the intercept, the sum of the residual is always zero.
True or False
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
iv).
Linear regression line
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(1 mark)
(1 mark)
(1 mark)
(1 mark)
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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)
Question 1.2.
Using hypothetical data, the relationship between child nutrition and stunting was
estimated as follows.
Where, Y =Average height of pupils aged 5 (measured in meters) and X =Household Dietary
Diversity Score (a measure of the diversity of food intake).
The estimated coefficients are
/31 = 0.088
(0.0412),
/32 = 0.7165
(0.2547),
2
R
= 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 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 = I, ...,N, the following sample moments have been calculated
from 10 observations.
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Icx -X)(Y-Y) = 20
Icx-.x)2= 200, and
2.1. Estimate the slope parameter
2.2. Estimate the intercept parameter
2.2. Determine the function j,
2.3. Calculate the value j, for x = 10
2.4. Obtain the 95% confidence interval for the calculated j,
(4 marks)
(4 marks)
(3 marks)
(3 marks)
(6 marks)
Question 3
Consider the following regression model, y1 = /Ji + /J2x1 + &1 • Where, y1 = consumption
expenditure, x =income, /Ji= Constant, /32 = 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 regression analysis (model) to determine the relationship between inventory and sales
gives the following post-regression test results.
Description
Durbin Watson Statistics
Skewness
Kurtosis
R-Squared
Observation
Probability
Statistics
1.8690
-0.1639
1.8084
0.9855
13
0.6612
4.1 What is the name of this test?
(2 marks)
4.2. Calculate the test statistics for this test
(2 marks)
4.3. What is the null hypothesis for this test
(2 marks)
4.4. Do you reject or fail to reject this null? Why?
(2 marks)
4.5 At 5% probability, using the attached Durbin-Watson Table test whether the residual
of this regression is first-order autocorrelated.
(4 marks)
4.6. What is the null hypothesis of this test?
(2 marks)
4.7. What are the implications of an autocorrelated residual on the parameter estimates
of a regression?
(6 marks)
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Statistical formula
var(/J ) - ~~~)--X- ; -X)2
1 - nL(X; -X)2
L(Y;-Y)(X; -X)
/J2 = L (X; -X)2
se(/J1) =
:I:x/
nL(X; -X)2
JB=n
[-S+62---
(K-3)2]
24
See the attached Dubin Watson table
(Y
se(/J2 ) =--=====
-X)2
JB=n
[
-S--2--
6
(K
-3)
2
]
22
k·' = 1
n
dL
du
6- 0.610
7 0.700
8- 0.76:3
g. 0.824
10
0.879
11
0_927
12
0.971
13
1 _010
14
1.04S
15
1_077
16
1.106
17
1.13-3
18- 1.158
11.400
1.356
1.332
11.320
1.320
11.324-
1.331
11.340
1,_350
11.361
1.371
11 .381
11.391
k' = 2
cjf...
dv
K=3
dL
du
0.467
0.559
0.6-29
0.697
0_658
0_812
0_861
0_905
0_946
0_982
71_015
1_046
1.896
1.777
1.699
1.641
1.604
1.579
1.562
1.551'
1.543
1.539
1.53 16
1.535
END
0.368
0_455
0.525
0.595
0.658
0.715
0.767
0.814
0.857
0.897
0.933
2.287
2.1.2.S
2.,016
1 .'928
1.864
1.816
1. 779
1.750
1.728
1.710
1.696
k' =4
dL
du
0_296
0_376
0.444
0_512
0.574
0_632
0_685
0_734
0_779
Q_820
2:.588
2.414
2 ..2:83
2.177
2.094
2.030
1.977
1.935
1.900
1.872