AgEc 541 Econometrics.doc - RUFORUM

AgEc 541 - Econometrics Acknowledgements This course was authored by:
Dr. Jemma Haji
Department of Rural Development & Agricultural Extension
Haramaya University, Ethiopia
Email: jemmahaji@gmail.com
The following organisations have played an important role in facilitating
the creation of this course:
1. The Bill and Melinda Gates Foundation
(http://www.gatesfoundation.org/)
2. The Regional Universities Forum for Capacities in Agriculture,
Kampala, Uganda (http://ruforum.org/)
3. Haramaya University, Ethiopia (http://www.haramaya.edu.et/)
These materials have been released under an open license: Creative Commons
Attribution 3.0 Unported License
(https://creativecommons.org/licenses/by/3.0/). This means that we
encourage you to copy, share and where necessary adapt the materials to
suite local contexts. However, we do reserve the right that all copies and
derivatives should acknowledge the original author.
Course Description This course introduces you to the theory and practice in econometrics for
graduate students. While a sound understanding of econometric theory will
be beneficial, the course emphasizes the techniques for basic empirical
research, interpretation of quantitative results and model evaluations. The
contents will cover basics of ordinary least square methods, model
specification, maximum likelihood estimation and Limited dependent variable
models. Course Pre-Requisites Students should have a minimum of one junior-level (intermediate)
undergraduate courses in statistics and two mathematics courses. Students
are expected to be good in some statistical software such as SPSS, STATA
and LIMDEP. Course Objectives This course aims to provide an introduction to analyze economic problems
using quantitative methods by linking essentials of econometric theory to
estimation techniques. At the end of this course, students will be expected
to have gained basic skills in developing and interpreting models as
applied to a variety of economic problems and data. Additional emphasis is
placed on how to deal with economic data, developing a research project,
and in developing critical thinking skills in applied economic analysis. By
the end of this course the students should be able to:
. Apply econometric theory to real world problems;
. Describe the application of statistical concepts to economic
analysis;
. Analyze econometric models using real world data;
. Perform research projects
Course Introduction
In this course we discuss the basic ideas and the tools used for analyzing
economic data. We start with the definition of the subject: Econometrics is
the application of statistical techniques and analyses to the study of
problems and issues in economics. The word econometrics was coined in 1926
by Frisch, a Norwegian economist who shared the first Nobel Prize in
Economics in 1969 with another econometrics pioneer, Tinbergen. Even if
many economists had used data and made calculations long before 1926,
Frisch felt he needed a new word to describe how he interpreted and used
data in economics. Today, econometrics is a broad area of study within
economics. The field changes constantly as new tools and techniques are
added. Its center, however, contains a stable set of fundamental ideas and
principles. This course is about the core of econometrics. We will
elucidate the basic logic and methodology of econometrics, concentrating on
getting the core ideas exactly right. We divide the study of econometrics
in this course into the following two fundamental parts: Description and
Inference. In each Topic, regression analysis will be the primary tool. By showing
regression again and again in a variety of contexts, we strengthen the idea
that it is influential, flexible method that defines much of econometrics.
At the same time, however, we illustrate the conditions that must be met
for its appropriate use and the situations in which regression analysis may
lead to unfortunately wrong conclusions if these conditions are not met. Course Learning Outcomes Upon successful completion of this course students will be able to:
. Explain important statistical and econometric concepts.
. Apply basic simple and multiple linear regression, and Ordinary Least
Squares (OLS) estimation procedure to real world problems.
. Generate and test hypotheses.
. Explain basic assumptions of the OLS, test their validity in practical
situations, and deal with their violations.
. Describe the features of different types of economic data, and command
some basic tools and techniques of econometric analysis.
. Manage basic data.
. Use several statistical and econometric analyzing tools and techniques
e.g. statistical package Stata.
Course Reading Materials Gujarati, D. N., 2005. Basic Econometrics. McGraw Hill, Fourth edition.
Gujarati, D. N., 1999. Essentials of Econometrics. McGraw-Hill, Second
edition.
Maddala, G. S., 2001. Introduction to Econometrics. John Wiley, Third
Edition.
Wooldridge J. M., 2009. Introductory Econometrics. A Modern Approach.
South-Western, Fourth edition. Course Outline
Topic 1: Introduction to Econometrics 7
1.1 What is Econometrics? 7
1.1.1. Why econometrics? 9
1.1.2. The methodology of econometrics 9
1.2 Uses of Econometrics 12
1.2.1 Examples of questions that econometrics is useful for 13
1.3 The Four Basic Elements of Econometrics 13
1.4 Review of Basic Statistics 15
1.4.1 Some fundamental statistical quantities 16
1.4.2. Probability concepts and laws 18
1.4.3. Probability distributions 21
1.4.4. The normal distribution 22
1.4.5. Testing for significance using the normal distribution 23
1.4.6. Hypothesis testing 28
1.5. Summary 30
Topic 2: Simple Linear Regression 33
Introduction 33
2.1 Simple linear regression models 34
2.2 Assumptions Underlying Simple Linear Regression 37
2.2.1 Assumptions about the error term 37
2.3 Fitting the Model 38
2.3.1 The principle of least squares 39
2.3.2 Coefficient of determination 44
2.4 Inference in Simple Linear Regression 47
2.4.1 Inference on the regression parameters 49
2.5 Summary 52
Topic 3: Multiple Linear Regression 56
3.1 Assumptions Underlying Multiple Regression 59
3.1.1 Requirements of regression 59
3.1.2 Assumptions about the error term 60
3.2 Matrix Notation 61
3.3 Fitting the Model 65
3.3.1 The least squares line 66
3.3.2 Coefficient of multiple determination 73
3.3.3 Estimating the variance 74
3.4. Summary 76
Topic 4 Other Estimation Methods 79
4.1 Instrumental Variables (IV) 81
4.1.1 IV defined 81
4.1.2 One instrument for an endogenous regressor 82
4.1.3 More than one instruments for an endogenous regressor 83
4.2 Generalized Least Squares (GLS) 85
4.2.1 Homoscedasticty and no autocorrelation assumptions 85
4.2.2 The variance covariance matrix 86
4.2.3 Generalised Least Squares (GLS) method 86
4.3 Maximum Likelihood (MLH) Method 87
4.3.1 Some general properties of the Maximum Likelihood Method 89
4.4 Summary 90
Topic 5. Classical Linear Regression "Problems" 93
5.1 Heteroscedasticity 94
5.1.1 Consequences of heteroscedasticity 95
5.1.2 Detection of heteroscedasticity 95
5.2.3 Remedies for heteroscedasticity 100
5.2 Autocorrelation 103
5.2.1 Structure of autocorrelation 104
5.2.2 Consequences of Autocorrelation 106
5.2.3 Detection of autocorrelation 106
5.2.4 Remedies for autocorrelation 110
5.3 Multicollinearity 113
5.3.1 Sources of multicollinearity 114
5.3.2 Consequences of multicollinearity 114
5.3.3 Detection of multicollinearity 115
5.3.4 Remedies of multicollinearity 116
5.4 Specification Errors 119
5.5 Nonnormality 120
5.6 Summary 121
Topic 6: Limited Dependent Variable Models 124
6.1 Dummy Dependent Variables 125
6.1.1 Linear Probability Model (LPM) 125
6.1.2 The Logit Model 128
6.1.3 Probit Model 130
6.1.4 The models compared 131
6.2 The Tobit model 131
6.2.1Variables with discrete and continuous responses 131
6.2.2 Some terms and definitions 131
6.2.3 Conceptualizing censored data 133
6.2.5 The regression part of the Tobit Model 135
6.3 Summary 137 Topic 1: Introduction to Econometrics
Learning Objectives By the end of this topic, students should be able to:
. Define econometrics as a discipline;
. List the important uses of econometrics;
. Identify the basic components of econometrics;
. Use statistical concepts in econometrics;
. Apply statistical tests on some economic problems. Key Terms: Econometrics, DGP, Estimation, Specification, Descriptive
statistics, Inferential statistics, hypothesis testing. Introduction Under this topic we begin with the definition of econometrics. Different
authors defined econometrics differently, but the core idea remains
similar. The term econometrics was coined in 1926 by a Norwegian economist
Frisch who shared the first Nobel Prize in Economics in 1969 with another
econometrics pioneer, Tinbergen. Although many economists had used data and
made calculations long before 1926, Frisch felt he needed a new word to
describe how he interpreted and used data in economics. Today, econometrics
is a broad area of study within economics. The field changes constantly as
new tools and techniques are added. Its center, however, contains a stable
set of fundamental ideas and principles. Its uses and basic elements will
also be presented under this topic. Finally we will review basic
statistical concepts that have wider applications in Econometrics.
1.1 What is Econometrics?
In the field of Economics, more and more emphasis is being placed on
developing a