Class Problem Set 2
1-Which one of the following estimators of population mean () is unbiased? Which one is more
MSE efficient? (Y1,Y2, and Y3 are 3 random and independent observations)
M1=0.15Y1+0.25Y2+0.6Y3
M2=0.33Y1+0.34Y2+0.35Y3
2- Show that the follo
Class problem 1
Consider the following probability distribution for random variable X.
X
fx or P(X=x)
0
0.10
1
0.20
2
0.40
4
0.15
7
0.10
8
0.05
Find: (you need to show your work)
a.
b.
c.
d.
e.
f.
g.
h.
i.
Mean=E(X)
E(3X)
Is E(3X)=3E(X)?
2
Var(X)=
Var(X+2
Bora Kim (2924798272)
(Quiz 2 Econ 318 )
Problem 1
You are interested in the relationship between output (Q), Capital, and Labor.
Q = 0 + 1 Ln(Capital) + 2 Labor + 3 Labor2 + u
= 1.5 + 44.2Ln(Capital) + 1.28Labor 0.032Labor2
Q
(a)
How do you interpret pa
Bora Kim
(ECON 318 Solution to Test 1 )
Q1 (16 points)
Probability that any particular fund outperforms the market in all 10 years is 210 =
1/1, 024.
(a)
Although individual fund has a low probability of outperforming the market in all 10
years, in aggreg
Bora Kim
(ECON 318 Note on HW6 )
Q1
A priori we would expect all slope parameters (log(sales) , roe , ros ) to be all positive.
A posteriori estimation result conrms our a priori expectations. (e.g.) As sales increases
by one percent, the salary of CEO in
ECON 318
ASSIGNMENT 1
1. Let X be a random variable and let EX = show that
(a) E(X )2 = E(X 2 ) 2 .
(b) Var (aX + b) = a2 Var (X)
2. If X and Y are independent. Show Cov (X, Y ) = 0.
3. If X N (, 2 ), show
X
N (0, 1).
4. Let cfw_X1 , . . . , Xn be n ra
Class Assignment 6:
Use Data 7-6 to test for structural break (Chows Test) for the following model: Variable D90=0
for 1980 census and D90=1 for 1990 census.
(1) Povrte=0+ 1urb+ 2famsize+3unemp+4highschl+5college+6medinc+u
Method 1H0: There no structural
Eco 318
Assignment 4
Question 1
What is knowns as the characteristic line of modern investment analysis is simply the
regression line obtained from the following model:
‘Ht 2 ai+ﬂirmt+ut
where m = the rate of return on the ith security in time t
mm = the
Bora Kim
(ECON 318 Note on HW4 )
Q1
(a)
Null and alternative hypotheses are
H0 :
H1 :
Test statistic is
z=
2 = 1
2 > 1
1.0568 1
2 1
=
= 0.8214
0.0728
se(2 )
Test statistic follows the normal distribution by the central limit theorem. Also, since
Pr(Z > z
Class problem set 3
You need to show your work. All parts must be done manually without use of a software.
Sales
Experience
2100
17
2000
20
3500
28
2400
22
3300
32
2000
16
5100
40
3200
18
3400
25
3000
20
2
Total:
A department store is interested in the re
Use data GREENE7_8 for the following exercise.
Consider the following 2 models:
Model 1:
G = 0 + 1Pg + 2 ln(Y) + 3Pnc + u
Model 2:
ln(G) = 0 + 1Pg + 2 ln(Y) + 3Pnc + u
1- Estimate both models
Model 1: OLS, using observations 1960-1995 (T = 36), Dependent
Bora Kim
(ECON 318 Note on HW1 )
This is a very short note for HW1. Note that Im not required to make the answer sheet for
HWs.
Q1
Recall the formula
E[aX + b] = aE[X] + b
V [aX + b] = a2 V [X]
(a) implies that we can nd alternative formula for the varian
Bora Kim
(ECON 318 Note on HW5 )
Q1
Model B can be written as:
Y = 1 + (2 + 1)X2 + 3 X3 + u2
which is of the form of model A. Therefore 1 = 1 , 2 = 2 + 1, and 3 = 3 . It follows
that 1 = 1 , 2 = 2 + 1, and 3 = 3 . To see this, note that (1 , 2 , 3 ) a
ECON 318 Homework 1
Due Feb. 8th before 7PM (online submission)
Instructor: Yu-Wei Hsieh
Note: (1) Please submit your homework in either word or pdf format through Turnitin on the Blackboard.
(2) Please include all your answers, analysis and the key steps
R Mini Course
USC ECON 318
Yu-Wei Hsieh
January 19, 2017
1. Getting Started
Load Packages
# data sets
library(datasets)
library(gcookbook)
# graphics
library(ggplot2)
# data manipulation
library(dplyr)
library(data.table)
Case-sensitive: x and X are dif
R Mini Course
31/1/17 14:34
R Mini Course
USC ECON 318
Yu-Wei Hsieh
January 27, 2017
1. Getting Started
Install and Load Packages
install.packages("gcookbook")
install.packages("nycflights13")
install.packages("ggplot2")
install.packages("dplyr")
install.
Econometrics Summary
Algebraic and Statistical Preliminaries
Elasticity: The point elasticity of Y with respect to L is given by = (Y/L)/(Y/L).
The arc elasticity is given by (Y/L)/(Y/L), when L and Y may be chosen in various
ways, including taking the mi
ECON318
Chapter 4
Yun Woo Kim
5.
(i) .412 +/- 1.96(.094)
(ii) No, because the value .4 lies inside the 95% confidence interval.
(iii) Yes, because 1 is outside the 95% confidence interval.
10.
(i) n=142 and k=4: F = [.0395/(1-.0395)](137/4) = 1.41 (approx
ECON318
Assignment
28 September 2015
Yun Woo Kim
3.
(ii) The signs of B2 and B3 are not obvious, at least to me. One could argue that more
educated people like to get more out of life, and so, other things equal, they sleep
less (B2 < 0). The relationship
ECON318: Chapter 2 Yun Woo Kim
#5
(i) when income increases by 1 unit, consumption increases by 0.853 unit. This
means, as income increases, consumption expenditure also increases but less than
proportionately. When income is zero, consumption still occur
Eco 318
Assignment 5
Question 1
Consider the following models.
Model A: K = a1 + (12X2r + a3X3, + u“
1 Model B: (Y, —X2,) = ,3, + ﬂ2X2, + ,B3X3, +1.2,
1(a) Will OLS estimates of oil and ,8] be the same? Why?
- (b) Will OLS estimates of a3 and A. be the sa
Eco 318
Assignment 6
Question 1
From a sample of 209 ﬁrms, we obtained the following regression results:
log(salary) = 4.32 + 0.28010g(sales) + 0.0174r0e + 0.00024ros _
se = (0.32) (0.035) ' (0.0041) (0.00054) R2 = 0.283
where ‘
salary = salary of CE
sale
UNIVERSITY OF SOUTHERN CALIFORNIA
DEPARTMENT OF ECONOMICS
ECON 318: Introduction to Econometrics, Fall 2014
Instructor: Yu-Wei Hsieh
HOMEWORK 1
DUE TUESDAY SEP. 9th BEFORE 11:00AM
Problem 1. Suppose that a population consists of weekly incomes of college