Kyoo il Kim Department of Economics University of Minnesota

Introduction to Econometrics, Econ4261 Spring 2013

P ROBLEM S ET 1 (D UE F EBRUARY 7, T HURSDAY IN CLASS )

Answer the Followings 1. Calculate: a) E[X], E[Y ] b) V ar[X], V ar[Y ] c) Cov[X, Y ] d) ρ(X, Y ) from the distribution below Y =1 X = 5000 X = 10, 000 X = 15, 000 0 1/8 1/3 Y =0 1/4 1/8 1/6 (1)

2. Suppose E[X] = 1 and E[Y ] = 2 and suppose X and Y are independent. Evaluate: a) E[2X + 1] b) E[X + Y ] c) E[X − 2Y ] d) E[XY + 1] 3. Suppose V ar[X] = 2, V ar[Y ] = 1, Cov[X, Y ] = 0. Evaluate: a) V ar[X + 2Y ] b) V ar[X − Y ] c) Cov[2X − Y, X − 1] n

i=1 [Xi

4. Suppose c)

n

i=1 Xi

= 2 and

+ 2]

n

i=1 Yi

= 3. Evaluate: a)

n

i=1 [Xi

+ Yi ]

b)

n

i=1 [Xi

− 2Yi ]

5. Let X = 1 with n = 100. What is

6. Show that V ar[X] = E[X 2 ] when E[X] = 0.

n

i=1 Xi ? What is

n

i=1 [Xi −X]? and What is

n

i=1

X +1 ?

7. Show that Cov[X, Y ] = E[XY ] when E[X] = 0 or E[Y ] = 0. 8. Suppose V ar[X] = 1, V ar[Y ] = 2, V ar[Z] = 2, Cov[X, Y ] = 0, Cov[X, Z] = −1, and Cov[Y, Z] = 2. Obtain V ar[X − Y + 3Z] 1

9. Show that (a) (b)
n n
i=1 (Xi i=1 (Xi

− X)2 =

− X)(Yi − Y ) =

n

2 i=1 Xi

10. Let b be an estimator of β. The Mean Squared Error is deﬁned as M SE(b) = E[(b − β)2 ]. Show that M SE(b) = V ar(b) + bias2 (b) = E[(b − E[b])2 ] + (E[b] − β)2

n

−X

i=1 Xi Yi

n

i=1 Xi

=

−X

n

n

2 i=1 Xi

i=1 Yi

=

n

− nX

2

i=1 Xi Yi

− nXY

11. Do questions 2.6, 2.10, 2.15, 2.24 in Stock and Watson 12. Do questions 3.3, 3.6, 3.10, 3.13, 3.19 in Stock and Watson

...ProblemSet11. (Star Wars) Real GDP = 461.0(214.5/60.6) = 1,631.76
(E.T.) Real GDP = 399.9(214.5/96.5) = 888.90
(Titanic) Real GDP = 600.8(214.5/160.5) = 802.94
(Shrek 2) Real GDP = 437.2(214.5/188.9) = 496.45
(Avatar) Real GDP = 760.5(214.5/214.5) = 760.5
Real GDP in Order of Largest to Smallest
Movies
Nominal
Box Office Receipts (millions)
CPI in Year Released
Real Box Office Receipts (millions)
Star Wars (1977)
461.0
60.6...

...ProblemSet1Problem1
Which project should the firm select? Why?
Project B: Managers should try to maximize their stock’s intrinsic value while also bringing in revenue. The P/E ratio shows the dollar amount investors will pay for $1 of current earnings.
Problem 2
If most investors expect the same cash flows from Companies A and B but are more confident that A’s cash flows will be...

...INSTRUCTIONS: You must show all of your work where calculations are required and you must include a brief explanation of approximately 50 words for each answer to receive full credit:
1. Markets, Demand and Supply, part 1 (10pts):
a. What effect will each of the following have on the DEMAND for coffee (i.e. Increase Demand, Decrease Demand, or NO CHANGE)? You must include a brief explanation of approximately 50 words for each answer to receive full credit:
i....

...Professor MacDonald
Your Name: _______________________________
ProblemSet1
Question 1 (2 points): Explain how each of the following events affects the equilibrium price and
quantity in the associated market. Hint: in each case, either the supply or the demand curve shifts, but
not both. Explain your answer in one sentence and draw a graph to accompany your answer, being sure
to correctly label all parts of the graph.
Event...

...Department of Economics
Economics 011
Section 14
Prof. Steve Suranovic
Fall 2012
ProblemSet #2 – Answers
Answer all of the following questions from the book and those below. HW #2 is due in class on
Wednesday Feb 22nd .
A. Questions from Text and Readings
R&T Chapter 2-5 (online), Chapter 2.4 Review and Practice (in printed textbook);
Concept Problems 2, 3;
(for Extra Practice complete Numerical Problems1 –...

...73-240 | Recitation A
ProblemSet1Problem1: Nominal GDP, Real GDP, Price Indices, and Inflation
A. Nominal GDP in Year 1 = $430
Nominal GDP in Year 2 = $617.50
Growth Rate of Nominal GDP = 44%
B. RGDP(1) in Year 1 = $430
RGDP(1) in Year 2 = $410
RGDP(1) growth = -4.65%
RGDP(2) in Year 1 = $655
RGDP(2) in Year 2 = $617.50...

...ProblemSet1
Name: Christen Brown
ProblemSet1 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 2.
1. Based on the information provided for the market for video games, answer the following questions.
PRICE
Q DEMANDED
Q SUPPLIED
$50
5
9
$45
7
7
$40
9
5
$35
11
3
$30
13
1
a.) Draw and properly label the demand and supply graphs (this means you must label the axes...

...PROBLEMSET # 1
Instructions:
1) Open book, open notes limited to only class materials.
2) Unlimited time.
3) This must be reflective of your individual effort. GMU Honor Code applies.
4) The ProblemSet #1 (only the question solutions portion) is due at the end of the day on September 24th.
5) Show all work, as partial credit will be given for each question’s...

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