ECON 208D Introduction to Econometrics
Solutions to Problem Set 4
Question 1 (Graded by Veronica Montalva)
(a) See the picture below.
Figure 1: joint pdf: f (x, y )
(b) Keep in mind that we need to take into account that x y :
1/2
1/2
y
Pr[0 x 1/2, 0 y 1/
ECON 208D Introduction to Econometrics
Solutions to Problem Set 2
Question 1 (Graded by Veronica Montalva)
(a) Using STATA we calculate the correlation coecient: 0.561.
(b) Using STATA we run the regression of T on D and obtain:
Table 1: Regression of T o
ECON 208D Introduction to Econometrics
Solutions to Problem Set 3
Question 1 (Graded by James Thomas)
Part a
One way to solve this problem is to rst calculate the expected prot from one randomly
drawn worker and then multiply this by 10 to obtain the expe
ECON 139
Duke University
Spring 2007
Midterm 1
Instructions (PLEASE READ CAREFULLY before starting):
This test has a total of 4 problems and 70 points.
You have 75 minutes to nish it.
Remember to Show Your Work and please be sure that your handwriting is
ECON 208D Introduction to Econometrics
Solutions to Problem Set 6
Question 1 (Graded by C.Y. Lee)
(a) The regression results are presented in the following table. The estimate of coecient on
lnPCE is 1 and the p-value (0.001) is less than 5%. Thus housing
ECON 139
Duke University
Spring 2008
Midterm 1
Instructions (PLEASE READ CAREFULLY before starting):
This test has a total of 3 problems and 72 points.
You have 75 minutes to nish it.
Remember to Show Your Work and please be sure that your handwriting is
ECON 208D Introduction to Econometrics
Solutions to Problem Set 5
Question 1 (a-d graded by James Thomas, e-h
graded by CY Lee)
Part a
Item 1
wage
lnwage
Mean
47,852
10.09
Median
28,923
10.27
Variance 3,440,000,000 1.7956
Skewness
2.443
-.8232
Kurtosis
9.
Duke University, practice problems for Introduction to Econometrics
February 16, 2011
1
Properties of Expectations, Variances and Covariances, Distributions
1. (5 points) You know that income per head in Italy (denoted by y ), expressed in Euros, is norma
Econ 139: Midterm 1 Review
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2010
Econ 139 Review 1 (Duke)
Review 1
Spring 2010
1 / 30
1
Basic Statistics
2
Properties of Estimators (Bias, Consistency, Asymptotic Normality)
3
Properties of O
Midterm 2 2010
Notes:
1. Use a calculator where necessary.
2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.
3. If you want to make any additional assumptions to simplify a problem, please state them clearly.
5.
Econ 139: Midterm 2 Review
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Review 2 (Duke)
Review 2
Spring 2011
1 / 33
1
Multivariate Regression (esp. Testing)
2
Modelling nonlinearities
3
Maximum Likelihood and Limited Depe
Probability and Statistics
Cumulative Distribution Function (CDF) of a Random Variable (RV) X
CDFX (z ) = Pr (X z )
Pn
Discrete: i=1 1 (xi z ) PrR(X = xi ) ; where 1 (E ) = 1 if E is true, and 0 otherwise.
Rz
z
Continuous:
f (x)dx = 1 1 (x z ) f (x) dx
1
Probability and Statistics
Cumulative Distribution Function (CDF) of a Random Variable (RV) X
CDFX (z ) = Pr (X z )
Pn
Discrete: i=1 1 (xi z ) PrR(X = xi ) ; where 1 (E ) = 1 if E is true, and 0 otherwise.
Rz
z
Continuous:
f (x)dx = 1 1 (x z ) f (x) dx
1
ECON 139
Duke University
Spring 2007
Final
Instructions (PLEASE READ CAREFULLY before starting):
This test has a total of 4 problems and 102 points.
You have 120 minutes to nish it.
Remember to Show Your Work and please be sure that your handwriting is le
ECON 139
Duke University
Spring 2008
Final Exam
Instructions (PLEASE READ CAREFULLY before starting):
This test has a total of 4 problems and 100 points.
You have 150 minutes to nish it.
Remember to Show Your Work and please be sure that your handwriting
139-Spring 2010 FINAL
Name:.NetID .
DO NOT TURN OVER UNTIL TOLD TO DO SO
Notes:
1. Use a calculator where necessary.
2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.
3. If you want to make any additional assump
139-Spring 2010 FINAL
Name:.NetID .
DO NOT TURN OVER UNTIL TOLD TO DO SO
Notes:
1. Use a calculator where necessary.
2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.
3. If you want to make any additional assump
139-Spring 09 FINAL
Name .
DO NOT TURN OVER UNTIL TOLD TO DO SO
Notes:
1. Use a calculator where necessary.
2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.
3. If you want to make any additional assumptions to
139-Spring 09 Midterm 2
Name .
DO NOT TURN OVER UNTIL TOLD TO DO SO
Notes:
1. Use a calculator where necessary.
2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.
3. If you want to make any additional assumptions
ECON 139
Duke University
Fall 2010
Midterm 1
Name:.
User ID:.
Notes:
1. Use a calculator where necessary
2. On questions 1 and 2 you do not need to show working. You should show your working on the other questions.
3. Make use of the cheat sheet. If you t
Introduction to Econometrics
Andrew Sweeting1
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 1 (Duke)
Course Intro & Probability Review
Spring 2011
1 / 38
Course Policies and Details
My background.
Class slides & course website (co
Introduction to Econometrics
Andrew Sweeting1
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 2 (Duke)
Probability
Spring 2011
1 / 48
An Unusual Case
In this course, we will usually work with distributions that are
well-behaved, and
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 3 (Duke)
Statistics Review
Spring 2011
1 / 36
Populations and Samples
Population:
Total collection of objectives or
people to be
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 4 (Duke)
Hypothesis Testing
Spring 2011
1 / 47
Condence Intervals and Hypothesis Testing (Chapter 3)
We usually estimate somethin
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 5 (Duke)
Univariate Regression
Spring 2011
1 / 38
Relating Two Variables
Econometrics is concerned with understanding the relatio
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 6 (Duke)
Univariate Regression (2)
Spring 2011
1 / 30
A Pharmaceutical Testing Example
Let look at a real world example.
s
Ritali
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 7 (Duke)
Univariate Regression (3)
Spring 2011
1 / 38
Regression When X is a Binary Variable
So far, we have only looked at examp
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 8 (Duke)
Multivariate Regression
Spring 2011
1 / 74
Omitted Variable Bias
The methodology we covered so far has (at least) one bi
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 9 (Duke)
Nonlinear Regression Functions
Spring 2011
1 / 57
Nonlinear Regression Functions
Up until now, we have assumed that the
Econ 139: Introduction to Econometrics
Andrew Sweeting
1 Department
of Economics
Duke University
Spring 2011
Econ 139 Handout 10 (Duke)
Binary Dependent Variables
Spring 2011
1 / 85
Regression with Binary Dependent Variables
Up to this point, the examples