Econ 703: Handout 1
Federico A. Bugni
August 24, 2015
1
Introduction
The objective of this handout is to introduce the basic concepts of probability theory. Following Casella
and Berger (2002), we adopt the axiomatic approach to define probability measure

Econ 341: Midterm exam
Federico A. Bugni
October 21, 2009
Instructions: Please make sure to write your name on the exam. Please take 5 minutes to read each
exercises carefully before answering the exam. Each exercise in the exam has a number of points ass

Econ 703: Midterm Exam
Federico A. Bugni
October 22, 2013
Instructions: Please make sure to write your name on each of your blue books. Before you begin to
complete the exam, you will be allowed 10 minutes to read the questions. If you cite a result deriv

Econ 703: Midterm Exam
Federico A. Bugni
October 25, 2012
Instructions: Please make sure to write your name on each of your blue books. Before you begin to
complete the exam, you will be allowed 8 minutes to read the questions. If you cite a result derive

Econ 341: Midterm Exam
Federico A. Bugni
October 21, 2010
Instructions: Please make sure to write your name on the exam. Please take 10 minutes to read each exercise
carefully before answering the exam. Each exercise in the exam has a number of points ass

Econ 703: Midterm Exam
Federico A. Bugni
October 16, 2014
Instructions: Please answer each question in a separate blue book and make sure to write your
name on each of them. Before you begin to complete the exam, you will be allowed 8 minutes to read the

Econ 703: Midterm Exam
Federico A. Bugni
October 15, 2015
Instructions: The exam is composed of three questions. Please answer each question on a
separate blue book and write your name on each of them. Before you begin to complete the exam,
you will be al

Econ 703: Final Exam
Federico A. Bugni
December 12, 2012
Instructions: The exam is composed of three questions. Please answer each question on a separate blue book
and write your name on each of them. Before you begin to complete the exam, you will be all

Econ 341: Final Exam
Federico A. Bugni
December 14, 2011
Instructions: Please make sure to write your name on each of your blue books. Before you begin to
complete the exam, you will be allowed 15 minutes to read the questions. If you cite a result derive

Econ 341: Final exam
Federico A. Bugni
December 18, 2009
Instructions: Please make sure to write your name on each of your blue books. Before you begin to complete the exam,
you will be allowed 15 minutes to read the questions. If you cite a result derive

Econ 703: Final Exam
Federico A. Bugni
December 13, 2015
Instructions: The exam is composed of three questions. Please answer each question on a separate blue
book and write your name on each of them. Before you begin to complete the exam, you will be all

Econ 703: Final Exam
Federico A. Bugni
December 15 & 16, 2012
Instructions: Please make sure to write your name on each of your blue books. Before you begin to
complete the exam, you will be allowed 15 minutes to read the questions. If you cite a result d

Econ 703: Final Exam
Federico A. Bugni
December 13, 2014
Instructions: The exam is composed of three questions. Please answer each question on a separate
blue book and write your name on each of them. Before you begin to complete the exam, you will be
all

Econ 341: Midterm exam
Federico A. Bugni
October 23, 2011
Instructions: Please make sure to write your name on each of your blue books. Before you begin to
complete the exam, you will be allowed 8 minutes to read the questions. If you cite a result derive

Econ 703: Handout 14
Federico A. Bugni
December 1, 2015
1
Introduction
The classical Assumptions (A 1.1)-(A 1.5), have allowed us to derive very strong finite sample properties for
the OLS estimator. Unfortunately, some of these assumptions were considere

Econ 703: Handout 2
Federico A. Bugni
August 26, 2015
1
Introduction
This handout introduces the concept of random variable, which is one of the building blocks this course. We
first consider a general definition of random variable and then we specialize

Econ 703: Handout 3
Federico A. Bugni
September 1, 2015
1
Introduction
This handout collects several topics of importance regarding random variables.
We define the concept of moments of a random variable, which is a useful way to summarize the
informatio

Econ 703: Handout 4
Federico A. Bugni
September 14, 2015
1
Introduction
The goal of this handout is to review examples of well-known distributions and describe their main properties.
These distributions will be important later in this course.
2
Discrete d

Econ 703: Handout 5
Federico A. Bugni
September 16, 2015
1
Introduction
This handout provides a brief introduction to statistical inference. Section 2 defines relevant concepts and
describes the two main routes for conducting statistical inference: finite

Econ 703: Handout 6
Federico A. Bugni
September 23, 2015
1
Introduction
The objective of inference is to use sample in order to learn about the population distribution we are interested
in. In order to conduct inference we construct a sample statistic, de

Econ 703: Handout 7
Federico A. Bugni
September 29, 2015
1
Introduction
The goal of this handout is to describe the main results in asymptotic theory, which are the law of large
number (LLN) and the central limit theorem (CLT). If cfw_Xi ni=1 is a sample

Econ 703: Handout 8
Federico A. Bugni
October 6, 2015
Statistical inference is the process of learning about the population distribution using the information of
the sample. In general, statistical inference has the following two goals:
estimating a cert

Econ 703: Handout 9
Federico A. Bugni
October 27, 2015
1
Introduction
The objective of this handout is to study an estimation method known as maximum likelihood estimator
(MLE). In order to apply this estimation method, we need to specify the likelihood o

Econ 703: Handout 10
Federico A. Bugni
November 6, 2015
1
Introduction
As we have seen in previous handouts, statistical inference is the process of learning about the population
distribution using the information of the sample. It has the following two g

Econ 703: Handout 11
Federico A. Bugni
November 10, 2015
1
Introduction
This handout presents the classical linear model and the ordinary least squares (OLS) estimator. Section
2 introduces a set of conditions known as the classical assumptions. Section 3

Econ 703: Handout 12
Federico A. Bugni
November 19, 2015
1
Introduction
This handout describes further finite sample properties of the ordinary least squares (OLS) estimator. Section
2 provides a practical interpretation of the parameter in the classical

Econ 703: Handout 13
Federico A. Bugni
November 16, 2015
1
Introduction
This handout discusses what happens to our OLS inference when we remove two of the classical assumptions
of the OLS model. The presentation follows Hayashi (2000, Chapters 1-2).
In or

Econ 341: Final exam
Federico A. Bugni
December 18, 2010
Instructions: Please make sure to write your name on each of your blue books. Before you begin to complete the exam,
you will be allowed 15 minutes to read the questions. If you cite a result derive