Final Exam Solutions
August 8, 2013
This exam has two sections. Section 1 consists of two questions, both of which are required. Section 2 consists
of three questions, and you can choose which two you want to answer. Note that each question has a number o
Computational Assignment 1
ECON 4211
Fall 2016
Your assignment must consist of a do le, containing your code, and a typed document
which summarizes what you did, answers the assignment questions, and contains your
results. Make sure that your do le works,
ECON 4211
Principle of Econometrics
Fall 2016
ECON 4211: Midterm
Instructions
Write your name and student number clearly in the space provided below. You have
50 minutes to nish the exam.
Name:
Student ID:
Score:
Page 1
ECON 4211
Principle of Econometrics
Heteroscedasticity
ECON 4211
Deparment of Economcis
University of Minnesota
ECON 4211 (University of Minnesota)
1/6
R&D expenditure and sales in 18 industry groupings in the
United States
Model : R&Di = 1 + 2 Salesi + u
ECON 4211 (University of Minnesota)
Problem set 8
November 17, 2016
ECON 4211
Fall 2016
1. Consider the following model
Yi = 1 + 2 X + ui
Since we can't observe
Y
directly. Thus, we use
Y
as a proxy of
Y.
Yi = Yi + i
a)Write the model that we estimates.
b)Assume that E() = E(u) = 0. Show th
Computational Assignment 1
ECON 4211
Fall 2016
Your assignment must consist of a do le, containing your code, and a typed document
which summarizes what you did, answers the assignment questions, and contains your
results. Make sure that your do le works,
Problem set 7
November 10, 2016
ECON 4211
Fall 2016
1. Consider the true model
Yi = 1 + 2 X2i + ui
and overtting model
Yi = 1 + 2 X2i + 3 Z3i + u2i
a)Write the true model in deviation form.
b)Show that OLS estimator, 2 , is unbiased. (2 =
where x and y ar
Problem set 8
December 3, 2016
ECON 4211
Fall 2016
1. Consider the following model
Yi = 1 + 2 X + ui
Since we can't observe Y directly. Thus, we use Y as a proxy of Y.
Yi = Yi + i
a)Write the model that we estimates.
A:
Y = 1 + 2 Xi + (i + ui )
= 1 + 2 X
Part A
Why does the sum of squared errors go down as more independent variables are included in a
regression?
Based on the equation Sum of Squared Errors + Total Sum of the Regression Squares = Total Sum of
Squares, the more independent variables added, t
Homework Solutions
August 4, 2013
Homework 1
1. For simplicity, lets assume that xi has one dimension. Our assumptions imply that
N
log(L) =
i=1
1
1 yi xi
log() log()
2
2
2
This function is maximized at some (M LE , M LE ). To nd them, we take derivati
Problem set 6
November 10, 2016
ECON 4211
Fall 2016
1. Consider a model without a constant terms
Yi = Xi + ui
and var(ui ) = . Assume that the from of i2 is known.
a) Write down the objective function for GLS estimator.
i2
A:
Transformed model becomes
Yi
Problem set 6
November 2, 2016
ECON 4211
Fall 2016
1. Consider a model without a constant terms
Yi = Xi + ui
and var(ui ) = i2 . Assume that the from of i2 is known.
a) Write down the objective function for GLS estimator.
b) Write down the rst-order condi
Problem set 3
ECON 4211
Fall 2016
1. R2
P
a) Derive R2 = 1 P(YiuiY )2 in two-variable regression model.
2
b) What is the meaning of R2 in the multiple variable regression model? what is the
problem of R2 in the multiple variable regression model?
) Explai
Problem set 1
ECON 4211
Fall 2016
1. Consider
Y = (Y1, Y2 , , Yn )
for the sample size
n.
a) LetYi be expenditure in family i and Xi be income in family i. Explain the meaning
of cov (Yi , Yj ) = 0, for i 6= j .
b) Recall Assumption 1: Y = 1 + 2 X + u and
Problem set 2
ECON 4211
Fall 2016
1. Math review
Let:
1 2
1 0
1 3
A=
B=
C=
3 1
2 1
2 6
a) A B
b) B A
c) Is A B = B A?
d) A1
e) B 1
f) Solve x for Ax = b where
1
b=
0
g) Are A,B,C full rank ? Why or Why not?
1
2. Consider the following regression model :
Problem set 3
ECON 4211
Fall 2016
1. R2
P
a) Derive R2 = 1 P(YiuiY )2 in two-variable regression model.
2
A. see hapter 1 on the Moodle website.
b) What is the meaning of R2 in the multiple variable regression model? what is the
problem of R2 ?
A. R2 meas
Problem set 5
October 12, 2016
ECON 4211
Fall 2016
1.Consider the set of hypothetical data in the table. Suppose you want
to t the model
Yi = 1 + 2 X2i + 3 X3i + ui
Y
X2
X3
-10
1
1
-8
2
3
-6
3
5
-4
4
7
-2
5
9
0
6
11
2
7
13
4
8
15
6
9
17
8
10
19
10
11
21
a
Problem set 2
ECON 4211
Fall 2016
1. Math review
Let:
A=
a) A B
b) B A
c) Is A B = B A?
1
3
2
1
B=
1
2
0
1
C=
1
2
3
6
5 2
1 2
AB =
6=
=BA
5 1
5 5
d) A1
e) B 1
f) Solve x for
1
Ax = b where b =
0
1
1 1
1
1 2
1
5
1
=
=
x=A b=
3
0
1 6 3 1
5 3
5
We can
Problem set 5
October 17, 2016
ECON 4211
Fall 2016
1.Consider the set of hypothetical data in the table. Suppose you want
to t the model
Yi = 1 + 2 X2i + 3 X3i + ui
Y
X2
X3
-10
1
1
-8
2
3
-6
3
5
-4
4
7
-2
5
9
0
6
11
2
7
13
4
8
15
6
9
17
8
10
19
10
11
21
a
Problem set 4
October 12, 2016
ECON 4211
Fall 2016
1. Consider the following data.
We have quarterly data on the demand of roses for the period 1971-1975. We will
consider the demand of roses as a function of the prices of roses and carnations. Y is
the q
Problem set 1
ECON 4211
Fall 2016
1. Consider
Y = (Y1, Y2 , , Yn )
for the sample size
n.
a) LetYi be expenditure in family i and Xi be income in family i. Explain the meaning
of cov (Yi , Yj ) = 0, for i 6= j .
A: Expenditure in ith family is not correla
Problem set 7
November 17, 2016
ECON 4211
Fall 2016
1. Consider the true model
Yi = 1 + 2 X2i + ui
and overtting model
Yi = 1 + 2 X2i + 3 Z3i + u2i
a)Write the true model in deviation form.
A:
yi = 2 x2i + (ui u)
where yi = (Yi Y ), xi = (Xi X)
1
b)Show t
Problem set 4
Otober 4, 2016
ECON 4211
Fall 2016
1. Consider the following data
We have quarterly data on the demand of roses for the period 1971-1975.
We will onsider the demand of roses as a funtion of the pries of roses and
arnations. Y is the quantity