ECON 4000
TEST #2 ANSWER KEY
SPRING 2011
Instructions: All questions must be answered on this examination paper; no extraneous
sheets of paper will be graded. Point values for each question are in parentheses to the
left of the corresponding numerals. You
3
Autocorrelation
3.1 Consequences for OLS
Consider the GM assumptions for time-series models.
What are the consequences for OLS if TS.5 does not hold?
Is OLS still BLUE? Consistent? Does a CLT still hold?
What about inference?
How would you answer these
2
Multiple Regression
2.1 Estimation
2.1.1 Derivation of the OLS Estimators
Multiple regression model:
yi = 0 + 1 xi1 + + K xiK + ui
OLS estimators minimize
Q=
(yi 0 1 xi1 K xiK )2 .
i
FOC:
(yi 0 1 xi1 K xiK ) =
u
i = 0
i
i
xi1 (yi 0 1 xi1 K xiK ) =
i
xi1
TIME-SERIES REGRESSION
1
Implications for OLS
Basic time-series regression model:
yt = 0 + 1 xt1 + + K xtK + ut ,
t = 1, . . . , T
(1)
How do you distinguish the population from the sample in a time-series
context?
We think of time-series data as realizat
2
Trending Series
2.1 Deterministic Trends
Including a trend among the regressors does not violate any ts assumptions;
omitting a trend when present in the underlying process can result in a
spurious regression.
Common trend specifications:
Linear
yt = 0
5
Proxy Variables and Measurement Error
5.1 Proxy Variables
5.1.1 Conditions for Unbiasedness and Consistency
Consider
y = 0 + 1 x1 + 2 x2 + 3 x3 + u,
where x3 is unobserved and primary interest is in 1 and 2 .
Under what conditions can a proxy be used fo
7
Panel Data
7.1 Repeated Cross-sections vs Panels
In cross-section data, we assume the random variables that comprise the
regression model are iid draws from some population.
In repeated cross-sections, new units are repeated drawn over multiple time
per
6
Instrumental Variables
6.1 Motivation
IV motivated by violations of MLR.4, which implies
E(xik ui ) = 0,
k = 1, . . . , K
A variable that does not satisfy the uncorrelatedness conditions implied by
MLR.4 is endogenous.
Lets say that xi1 is endogenous. T
# Reading the data
# make sure to check if there is a heading or not, if so add ,h=T
data1= read.table("data2.1.txt")
# creating a regression from data
g=lm(sr~pop15+pop75+dpi+ddpi,data=savings)
# gives a summary of the variables in your regression
summar
STAT 4220
R Introduction and Preliminaries
1.1
The R Environment and Language
R is an integrated suite of software facilities for data manipulation, calculation and
graphical display.
The benefits of R for an introductory student are
R is free. R is open-
CROSS-SECTION REGRESSION
1
Simple Regression
1.1 Introduction
Simple regression model:
E(yi | xi ) = 0 + 1 xi ,
where yi is the dependent variable or regressand and xi is the explanatory
variable or regressor.
In terms of yi :
yi = 0 + 1 xi + ui
Implicati
ECON 4000
ECONOMICS OF HUMAN RESOURCES
Professor Warren
Course Syllabus: Spring 2011
The syllabus is a general plan for the course; deviations
announced to the class by the instructor may be necessary.
Office Hours: 1:15 2:15 p.m. MW and by appointment, B
ECON 4000
TEAM PROJECT
SPRING 2011
Deliverables:
Resume: You must submit a resume to me by the beginning of class on Wednesday, January 26th. In
completing your resume, you should carefully adhere to the Resume Checklist and Resume
Guidelines provided on
ECON 4000
TEST #1
ANSWER KEY
SPRING 2011
Instructions: All questions must be answered on this examination paper; no extraneous
sheets of paper will be graded. Point values for each question are in parentheses to the
left of the corresponding numerals. You
ECON 4000
TEST #1
SPRING 2011
Instructions: All questions must be answered on this examination paper; no extraneous
sheets of paper will be graded. Point values for each question are in parentheses to the
left of the corresponding numerals. You are not pe
ECON 4000
TEST #2
SPRING 2011
Instructions: All questions must be answered on this examination paper; no extraneous
sheets of paper will be graded. Point values for each question are in parentheses to the
left of the corresponding numerals. You are not pe
FALL 16
ECONOMICS 4750
PROBLEM SET 2
Solutions
CORNWELL
Part A
1.1. (8 points) Some obvious factors are income, age and number of siblings. Each of these could be
correlated with education: income, positively; age, negatively; and number of siblings, nega
Fall 2016
Economics 4750
Problem set 1
Solutions
Cornwell
Appendix B
B.1 (5 points)
Before the student takes the SAT exam, we do not know nor can we predict with certainty
what the score will be? The actual score depends on numerous factors, many of whic
FALL 15
ECONOMICS 4750
PROBLEM SET 4
Solutions
CORNWELL
Part A
Chapter 3
9.1. (6 points) House prices should fall with pollution (1 < 0) and rise with the number of rooms
(2 > 0).
9.2. (6 points) If rooms is positively correlated with home quality, and hi
4
Heteroscedasticity
4.1 Consequences for OLS
Recall MLR.5:
var(ui | xi1 , . . . , xiK ) = 2 ,
which says that 2 does not depend on the regressors.
OLS is unbiased and consistent, even if (MLR.5) is violated.
Under MLR.5,
var(k ) =
and
se(k ) =
2
SSTk (1
ECON 4000
DETAILED COURSE OBJECTIVES
SPRING 2011
After completing this course, you will be able to:
1. Explain the costs and benefits that should be considered in deciding how many workers to hire and
whether or not to hire a particular job candidate.
2.