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ECMT2150-无代写
时间：2023-09-17
ECMT2150
Lecture 1
Intermediate Econometrics
Semester 2, 2023
Coordinator: Dr Luke Hartigan
Office: Room 502, Social Sciences Building A02
Email: luke.hartigan@sydney.edu.au
Zoom Hours: Thursdays 11:00AM-12:00PM or by appt
Topics Today
Week 1
• Unit Overview
• See also the unit outline online
• Additional helpful info posted on our Canvas site
• Introduction to Econometrics
• Reference: Wooldridge Chapters 1 & 2
Unit Overview
What to expect from me?
• It’s wonderful to be teaching this unit – My goal is
to encourage many of you to:
• Think about a career as an economist (public or private)
• Develop an interest in learning more about the theory
and application of econometrics
What to expect from me - Logistics
• Lecture slides will generally be available on Monday
• I will try to respond to emails within 1-2 days (I teach
another course)
• Please use the Ed discussion board:
• Ask and discuss content questions there
• Can ask admin questions there too
• Please CHECK THERE & on the ANNOUNCEMENTS page FIRST
before emailing the teaching team. Especially if it’s an admin
question
Textbook
•Required:
Introductory Econometrics: A Modern
Approach, by J.M. Wooldridge 6th or 7th Ed.
Publisher (Cengage) discount code: WOW10
Other textbooks
• If you want extra reading, the following textbooks
are recommended:
• Microeconometrics Using Stata, by Cameron &
Trivedi, Stata Press, 2010
• Mostly Harmless Econometrics: An Empiricist's
Companion, by Angrist and Pischke, Princeton
University Press, 2008
• Mastering ‘Metrics: The Path from Cause to Effect, by
Angrist and Pischke, Princeton University Press, 2015
• Microeconometrics: Methods and Applications, by
Cameron & Trivedi, Cambridge University Press, 2005
Canvas and Ed
• Canvas
• Announcements
• Lecture Slides
• Tutorial Questions and Solutions
• Assignment
• Practice exam questions
• Marks (incl Quizzes)
• Please check Canvas regularly – at least 1-2 times every
week
• Ed
• Use and check the Ed discussion board regularly
Lectures and Tutorials
• Attend the lectures week by week
• Support your learning with
• Textbook & Lecture slides
• Read the assigned chapters and lecture notes before attending
• Tutorials
• Questions? consultation hours, Ed
• Attend your tutorial sessions!
• Tutorials will help you understand the materials covered in lectures
• Each week, tutorials will work on the same topic as the lecture for that week
• Tutorial questions will be posted the week before the tutorial
• Attempt to solve the questions before the tutorial so that you can follow the tutor
efficiently and get the most out of your tutorial time
Remember that learning economics (econometrics) is like learning to swim … you can’t
do it from the sidelines. You have to jump in the water. Try to be an active learner!
Tutorials and Tutors
• Unit Tutors:
Felipe Pelaio, Mingdi Chen, Longye Tian
• Tutorials:
• See your personal timetable for your tutorial times and locations
• Tutorials start this week (week 1)! This is an opportunity to get
help with (i.e. review) the important mathematical and statistical
tools used in the Unit (see Appendices A – C)
• Office hours – see Canvas for times and venues
STATA and Practical Data Analysis
STATA
• Students enrolled in this course can access a copy of STAT18 to install on your
own PC for use during the semester:
• To access STATA, please follow the instructions below:
• Navigate to STATA student licence request form:
https://forms.office.com/r/rsGzwA0RV4
• Log in using your university student account credentials.
• Enter you student ID and review the licence agreement.
• Submit the form.
• After you have submitted the form successfully, please stay on the
webpage, which will display instructions to download, installation, and
licencing.
STATA and Practical Data Analysis
STATA
• Getting help:
• STATA has very good help facilities. Lots of free online
guides to STATA are available on the STATA website:
https://www.stata.com/support/
• UCLA maintains an excellent website with lots of helpful
tutorials: https://stats.idre.ucla.edu/stata/
• Your tutors are also adept at using STATA so ask them for
help in tutorials or consultation times
• Post a question on Ed (you can do this anonymously)
Assessment
• For Special Consideration/Arrangement etc., check the UoS
Outline and see also University and Faculty Policies
TASK Weight Due date
Quizzes (5) 10% Each quiz will be available
from Mon 9AM – Sun
11:59PM of that week
Weeks:
4,6,9,11,
13
In-Semester
Exam
25% Wed, 20 Sep, 10:00AM Week 8
Assignment 15% Sun, 29 Oct, 11:59PM Week 12
Final Exam 50% Exam period
Quizzes
• There are 5 MCQ quizzes with 6 questions each
• Occur in weeks 4, 6, 9, 11 and 13
• Quizzes will be made available on the external
website: http://www.mcempirics.com/
• Use invitation to register on this website with your
USyd email address (xxxx@uni.sydney.edu.au)
• Each quiz open for 1 week but once you start only
have 60 minutes to complete it
In-Semester Exam
• Short-release assignment
• Exam comprising two parts: MCQ, short-answer
and questions requiring you to do STATA-based
computations
• Part 1 will involve MCQ and short-answer type
questions (60 minutes)
• Part 2 will require you to download a dataset and
answer questions using STATA (24 hours)
• Cover concepts from weeks 1-7
The University of Sydney Page 16
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In order to get assistance, students need to register
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Disability Services Office
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02-8627-8422
Topics and Schedule
Week Topics & Assessments Readings
1 Introduction to Econometrics & Some Concepts in Probability and StatisticsTutorials are on this week Chs 1 & 2, Appendix A,B & C
2 Simple and Multiple Linear Regression – Assumptions and Properties Chs 2 (2.1-2.4), 3 (3.1-3.2) & 6 (6.1-6.3)
3 Multiple Linear Regression – Further Properties
Chs 2 (2.3,2.5), 3 (3.3, 3.4) & 4
(4.1)
4 Inference in Linear Regression ModelsQuiz 1 Ch 4
5 Asymptotic Properties of the Linear Regression Model and Using Qualitative Data Chs 5 & 7 (7.1-7.5)
6 Specification Issues in Linear Regression ModelsQuiz 2 Chs 3 (3.3,3.4) & 9 (9.2)
7 Further Specification Issues in Linear Regression Models Ch 9 (9.1, 9.4-9.6)
8 In-Semester Exam (no lecture, but tutorials still on!)
Mid Semester Break
9 Heteroskedasticity and Introduction to GLSQuiz 3 Ch 8
10 Endogeneity and Instrumental Variables Chs 9 (9.4) & 15
11 Instrumental Variables – Further IssuesQuiz 4 Ch 15
12 Introduction to Panel Data MethodsAssignment is due Sunday 29 Oct at 11:59PM Chs 13 & 14 (mostly 13)
13 Further Topics in Panel Data Models and Review Chs 13 & 14 (mostly 14)
The Nature of Econometrics and Economic
Data
Reference: Chapter 1
The Nature of Econometrics
• What is econometrics?
• Econometrics => use of statistical methods to analyse economic data
• Econometricians typically analyse nonexperimental (i.e. observational) data
• Typical goals of econometric analysis
• Estimating relationships between economic variables
• Testing economic theories and hypotheses
• Predicting economic variables
• Evaluating and implementing government and business policy
Ask yourself why? What differs between the natural sciences and a social
science like economics?
1. Decide the topic and propose an economic model (theory)
2. Propose a corresponding econometric (or empirical) model,
which typically involves some unknown parameters
3. Collect appropriate data
4. Using some software, estimate the model (i.e. parameters)
from the data
5. Give economic interpretation to the estimation results
Steps in Econometric Analysis
Economic models
• Can be models of microeconomic (e.g. individuals or firms) or
macroeconomic (e.g. regions, countries) behaviour
• Can be formal (i.e. derived from first principles), informal (i.e.
conceptual frameworks based on economic understanding), or
atheoretical (i.e. based on intuition)
• Often use optimising behaviour, equilibrium modeling
• Establish relationships between economic variables
“Essentially, all models are wrong, but some are useful”
(Box, G. E. P., and Draper, N. R., (1987), Empirical Model Building and Response Surfaces, John Wiley & Sons, New York, NY p. 424.)
Econometrics vs Economics
• Economics suggests important relationships, often with
policy implications, but virtually never suggests quantitative
magnitudes (i.e. size) of causal effects:
• What is the quantitative effect of reducing class size on student
achievement?
• How does a bachelor’s degree change earnings?
• What is the price elasticity of cigarettes?
• What is the effect on output growth of a 1 percentage point increase
in the cash rate by the RBA?
• What is the effect on housing prices of changes to zoning laws?
The applied economist uses econometrics to get the best estimate of
the economic relationship being investigated. The econometrician
develops the tools (i.e. methods) applied economists use
• Becker (1968) Derives equation for criminal activity based on utility
maximization ... What determines amount of criminal activity?
• The functional form of relationship not specified because it depends on the
utility function which is not known
• We cannot estimate this relationship as is ... we will need to specify an
econometric model
"Wage" in criminal
activities
Hours spent in
criminal activities
Wage for legal
employment Other
income
Probability of
getting caught
Probability of
conviction if
caught
Expected
sentence
Age
Eonomic Model of Crime: Example 1
• The functional form has to be specified
• Variables may have to be approximated (i.e. parameterised) by other
quantities
Measure of criminal
activity
Other
income
Frequency of
prior arrests
Wage for legal
employment
Frequency of
conviction
Average sentence
length after conviction
Age
Unobserved determinants
of criminal activity
e.g. moral character,
wage in criminal activity,
family background …
Economic Model of Crime (cont.)
• What is effect of additional training on worker productivity?
• Formal economic theory not really needed to derive equation:
• Other factors may be relevant, but these are the most
important (?)
Hourly wage
Years of formal
education Years of work-
force experience
Weeks spent
in job training
Model of Job Training and Worker
Productivity
Model of Job Training and Worker
Productivity (cont.)
• Econometric analysis requires that we think seriously about the
specification of the error term u
• Econometric models may be used for hypothesis testing
• For example, the parameter β3 represents the effect of training on the wage
• How large is the effect? Is it different from zero? Is it positive?
Hourly wage
Years of work-
force experience
Weeks spent
in job training
Unobserved determinants
of wages
e.g. innate ability,
quality of education,
family background …
Years of formal
education
Causality and the notion of ceteris paribus
• Most economic questions are ceteris paribus questions
• It is important to define which causal effect one is interested in
• It is useful to describe how an experiment would have to be
designed to infer the causal effect in question
Definition of causal effect of x on y:
How does variable y change if variable x is changed
but all other relevant factors are held constant?
The Nature of Econometrics
• Causal effect of fertilizer on crop yield
• By how much will the production of soybeans increase if one increases
the amount of fertilizer applied to the ground?
• Implicit assumption: all other factors that influence crop yield such as
quality of land, rainfall, presence of parasites etc. are held fixed
• Experiment:
• Choose several one-acre plots of land; randomly assign different amounts
of fertilizer to the different plots; compare yields
• Experiment works because amount of fertilizer applied is
unrelated to other factors influencing crop yields
The Nature of Econometrics
• Measuring the return to education:
• If a person is chosen from the population and given another year of
education, by how much will his or her wage increase?
• Implicit assumption: all other factors that influence wages such as
experience, family background, intelligence etc. are held fixed
• Experiment:
• Choose a group of people; randomly assign different amounts of
eduction to them (infeasible!); compare wage outcomes
• Problem: without random assignment, amount of education is
related to other factors that influence wages (e.g. ability)
The Nature of Econometrics
• Effect of law enforcement on city crime level
• If a city is randomly chosen and given ten additional police officers, by how
much would its crime rate fall?
• Alternatively: If two cities are the same in all respects, except that city A
has ten more police officers, by how much would the two cities crime rates
differ?
• Experiment:
• Randomly assign number of police officers to a large number of cities
• In reality, number of police officers will be determined by crime rate
(i.e. simultaneous determination of crime and number of police)
The Nature of Econometrics
Econometrics vs Statistics
• Usually, we are interested in recovering causal relations, not just
correlation, among economic variables
• Ideally, we would like to conduct an experiment
• But typically, it is impossible (or impractical and expensive) to run
experiments in economics, and we only have observational data
• returns to education
• can we ask someone to smoke to study the effect smoking?
Causality and Ceteris Paribus
• Most propositions in economics are ceteris paribus by
nature. Therefore, the goal is to infer a causal effect of one
variable on another, holding all other factors constant
• To infer causality, we need to hold other factors constant
• Key question is usually:
• Have ‘enough’ other factors been held fixed to make a
case for causality?
• ‘Enough’ generally means all other relevant factors
• Properly applied, econometric methods can simulate a
ceteris paribus outcome
Correlation vs Causality
Econometrics deals with difficulties arising from
using observational data to estimate causal effects
Most common problems:
• confounding effects (i.e. omitted factors)
• simultaneous causality (i.e. x => y; y => x)
Correlation does not imply causation! But economic
theory and econometrics together can permit us to
infer causation from observational data
An Example: Homework and Obesity
Econometric analysis requires data
• Different kinds of economic datasets
1. Cross-sectional data
2. Time series data (not covered in ECMT2150)
3. Pooled cross-sections
4. Panel/Longitudinal data
• Econometric methods depend on the nature of the data used
• Use of inappropriate methods may lead to misleading results
Economic Data
• Sample of individuals, households, firms, cities, states, countries, or other
units of interest at a given point of time/in a given period (i.e. a snapshot)
• Cross-sectional observations are more or less independent
• For example, pure random sampling from a population
• Sometimes pure random sampling is violated, e.g. units refuse to respond
in surveys, or if sampling is characterised by clustering
• Cross-sectional data typically encountered in applied microeconomics
For the most part, we will assume that our data are sampled randomly from
a population, even if that‘s not always technically correct
Cross-Sectional Data
Cross-sectional data set on wages and other characteristics
Observation number Hourly wage
Indicator variables
(1=yes, 0=no)
Example: Cross-Sectional Data
• Cross-sectional data on growth rates and country characteristics
Adult secondary
education rates
Growth rate of real
per capita GDP
Government consumtion
as percentage of GDP
Example: Cross-Sectional Data
• Observations of a variable or several variables over time
• For example, share prices, interest rates, consumer price index,
gross domestic product, vehicle sales, …
• Time series observations are typically serially correlated
• Ordering of observations conveys important information
• Data frequency: daily, weekly, monthly, quarterly, annually, …
• Typical features of time series: trends and seasonality
• Typical applications: applied macroeconomics and finance
The analysis of time series data is covered in ECMT2160.
Time Series Data
• Time series data on minimum wages and related variables
Unemployment
rate
Average minimum
wage for given year
Average
coverage rate
Gross national
product
Time Series Data Example
• Two or more cross sections are combined in one data set
• Cross sections are drawn independently of each other (e.g. Implies
individuals/firms will differ in each cross-section)
• Pooled cross sections often used to evaluate policy changes
• Example:
• Evaluate effect of change in property taxes on house prices
• Random sample of house prices for the year 1993
• A new random sample of house prices for the year 1995
• Compare before/after (1993: before reform, 1995: after reform)
Pooled Cross-Sectional Data
• Pooled cross sections on housing prices
Number of bathrooms
Property tax
Size of house
in square feet
Before reform
After reform
Pooled Cross-Sectional Data Example
• The same cross-sectional units are followed over time
• Panel data have both cross-sectional and time series dimensions
• Panel data can be used to account for time-invariant unobservables
• Panel data can be used to model lagged responses
• Example: Police and crime
• City crime statistics; each city is observed in two years
• Time-invariant unobserved city characteristics may be modelled
• Effect of police on crime rates may exhibit time lag
Panel data have become extremely important in most applied work in
economics
Panel or Longitudinal Data
Each city has two time
series observations
Number of
police in 1986
Number of
police in 1990
Panel Data Example
(1) A reminder:
Simple Linear Regression
+
(2) A primer:
Seeking a Causal Interpretation
Simple linear regression
What’s the point?
Suppose x and y are two variables representing some
population. The objective is to:
• Explain y in terms of x
• Study how y changes with changes in x
Issues:
• How do we account for other factors that affect y?
• What is the functional relationship between x and y?
• How can we ensure that we are capturing a ceteris
paribus (i.e. causal) result … if that is the goal?
46
Simple linear regression
Linear regression is a simple method of examining the
relationship between y and x
• Specifically, we explain variable y in terms of variable x
47
dependent
(response)
variable
independent
(explanatory)
variable
Intercept
Slope
parameter Error term
(random and
unobserved)
Examples: X and Y
• Interest rates (y) explained by money supply (x)
• Sales (y) explained by advertising (x)
• Wages (y) explained by education (x)
• Household expenditure (y) explained by income (x)
• Housing prices (y) explained by location (x)
48
The Error Term
• u captures:
• randomness in behaviour
• variables left out of the model
• departures from linearity
• errors in measurement
49
• Example: Soybean yield and fertilizer
• Example: A simple wage equation
50
Measures the effect of fertilizer on
yield, holding all other factors fixed
Rainfall,
land quality,
presence of parasites …
Measures the change in hourly wage
given another year of education,
holding all other factors fixed
Labor force experience,
tenure with current employer,
work ethic, ability …
Examples: Simple Regression Model
Interpretation in the simple linear regression model:
The goal is to understand how y varies with changes in x:
• So the key question:
When is it reasonable to assume that ceteris paribus holds?
That is, when is there a causal interpretation?
51
By how much does the dependent
variable change if the independent
variable is increased by one unit?
as long as
Interpretation only correct if all other
things remain equal when the indepen-
dent variable is increased by one unit
Interpretation
Conditional mean independence
Answer: We need conditional mean independence!
That is:
• since u and x are random variables, we can define the
conditional distribution of u given x
• the key assumption of the regression model:
• u is mean independent of x
E(u|x) = E(u)
• i.e. knowing x does not imply anything about u
52
Zero Conditional Mean independence
Note: It is common to assume that:
E(u) = 0
• so long as there is an intercept in the model this assumption is not
at all restrictive;
• It simply implies a rescaling of the intercept
Putting this together: The zero conditional mean independence
assumption is:
E(u|x) = E(u) = 0
But the important bit is the conditional mean independence
assumption
53
When is there a causal interpretation?
Conditional mean independence assumption holds:
But this is very unrealistic in the simple regression model:
• Example: wage equation
54
e.g. ability etc…
The explanatory variable must not
contain information about the mean
of the unobserved factors
The conditional mean independence assumption is unlikely to hold
here because individuals with more education will also often have
more ability on average – not independent!
What about causality?
… another useful thing to know:
if conditional mean
independence holds…
The conditional mean independence assumption ALSO implies
This means that the average value of the dependent variable y
across the population can be expressed as a linear function of
the explanatory variable x.
This tells us how Y changes with X on average, (i.e. Expected
outcomes), not individual outcomes!
56
Population Regression Function (PRF)
57
Population
regression function
Population Regression Function
You could be
here
or
here
For individuals with x = x2,
the average value of y is
y2 = β0 + β1x2
How do we get our ordinary least
squares estimates?
• In order to estimate the regression model we need data:
• A random sample of n observations
59
First observation
Second observation
Third observation
n-th observation
Value of the
explanatory variable of
the i-th observation
Value of the dependent
variable of the i-th
observation
How do we get estimates of 0 and 1?
• Plot the data, and fit as good as possible a regression line through
the data points:
60
Fitted regression line
For example, the i-th
data point
Ordinary Least Squares
• What does as good as possible mean?
Let‘s think about this…
61
Ordinary Least Squares
• What does as good as possible mean?
• Regression residuals
• Answer: Minimise sum of squared regression residuals
• Ordinary Least Squares (OLS) estimates
62
Ordinary Least Squares
Bottom Line: the OLS estimates can be obtained by:
• fitting a line through the sample points
• where the sum of squared residuals is
minimised
• hence the term ‘least squares’ estimation
63
• CEO Salary and return on equity
• Fitted regression
• Causal interpretation?
64
Salary in thousands of dollars Return on equity of the CEO‘s firm
Intercept
If the return on equity increases by 1 percent,
then salary is predicted to change by $18,501
OLS Example
Example cont.
65
Unknown population
regression line
Fitted regression line
(depends on sample)
E.g., CEO number 11‘s salary was
$875.372 lower than predicted
using information on his firm‘s
return on equity
Example cont.
• Wage and education
• Fitted regression
• Causal interpretation?
67
Hourly wage in dollars Years of education
Intercept
In the sample, one more year of education was
associated with an increase in hourly wage by $0.54
More Examples
What else & Next Week
Appendices A – Mathematical Tools
• Carefully review this material
• It will come in handy throughout the course
Tutorial this week (week 1):
• Review of Probability and Statistics – (Textbook Appendix B & C)
• Material from these 3 (A, B & C) appendices will frequently come up
during the course
Lecture 2:
• Linear Regression Models – Multiple/multivariate
• Ordinary Least Squares (OLS)
• Chapters: 2 (2.1-2.4), 3 (3.1-3.2) & 6 (6.1-6.3)
Lecture 1
Intermediate Econometrics
Semester 2, 2023
Coordinator: Dr Luke Hartigan
Office: Room 502, Social Sciences Building A02
Email: luke.hartigan@sydney.edu.au
Zoom Hours: Thursdays 11:00AM-12:00PM or by appt
Topics Today
Week 1
• Unit Overview
• See also the unit outline online
• Additional helpful info posted on our Canvas site
• Introduction to Econometrics
• Reference: Wooldridge Chapters 1 & 2
Unit Overview
What to expect from me?
• It’s wonderful to be teaching this unit – My goal is
to encourage many of you to:
• Think about a career as an economist (public or private)
• Develop an interest in learning more about the theory
and application of econometrics
What to expect from me - Logistics
• Lecture slides will generally be available on Monday
• I will try to respond to emails within 1-2 days (I teach
another course)
• Please use the Ed discussion board:
• Ask and discuss content questions there
• Can ask admin questions there too
• Please CHECK THERE & on the ANNOUNCEMENTS page FIRST
before emailing the teaching team. Especially if it’s an admin
question
Textbook
•Required:
Introductory Econometrics: A Modern
Approach, by J.M. Wooldridge 6th or 7th Ed.
Publisher (Cengage) discount code: WOW10
Other textbooks
• If you want extra reading, the following textbooks
are recommended:
• Microeconometrics Using Stata, by Cameron &
Trivedi, Stata Press, 2010
• Mostly Harmless Econometrics: An Empiricist's
Companion, by Angrist and Pischke, Princeton
University Press, 2008
• Mastering ‘Metrics: The Path from Cause to Effect, by
Angrist and Pischke, Princeton University Press, 2015
• Microeconometrics: Methods and Applications, by
Cameron & Trivedi, Cambridge University Press, 2005
Canvas and Ed
• Canvas
• Announcements
• Lecture Slides
• Tutorial Questions and Solutions
• Assignment
• Practice exam questions
• Marks (incl Quizzes)
• Please check Canvas regularly – at least 1-2 times every
week
• Ed
• Use and check the Ed discussion board regularly
Lectures and Tutorials
• Attend the lectures week by week
• Support your learning with
• Textbook & Lecture slides
• Read the assigned chapters and lecture notes before attending
• Tutorials
• Questions? consultation hours, Ed
• Attend your tutorial sessions!
• Tutorials will help you understand the materials covered in lectures
• Each week, tutorials will work on the same topic as the lecture for that week
• Tutorial questions will be posted the week before the tutorial
• Attempt to solve the questions before the tutorial so that you can follow the tutor
efficiently and get the most out of your tutorial time
Remember that learning economics (econometrics) is like learning to swim … you can’t
do it from the sidelines. You have to jump in the water. Try to be an active learner!
Tutorials and Tutors
• Unit Tutors:
Felipe Pelaio, Mingdi Chen, Longye Tian
• Tutorials:
• See your personal timetable for your tutorial times and locations
• Tutorials start this week (week 1)! This is an opportunity to get
help with (i.e. review) the important mathematical and statistical
tools used in the Unit (see Appendices A – C)
• Office hours – see Canvas for times and venues
STATA and Practical Data Analysis
STATA
• Students enrolled in this course can access a copy of STAT18 to install on your
own PC for use during the semester:
• To access STATA, please follow the instructions below:
• Navigate to STATA student licence request form:
https://forms.office.com/r/rsGzwA0RV4
• Log in using your university student account credentials.
• Enter you student ID and review the licence agreement.
• Submit the form.
• After you have submitted the form successfully, please stay on the
webpage, which will display instructions to download, installation, and
licencing.
STATA and Practical Data Analysis
STATA
• Getting help:
• STATA has very good help facilities. Lots of free online
guides to STATA are available on the STATA website:
https://www.stata.com/support/
• UCLA maintains an excellent website with lots of helpful
tutorials: https://stats.idre.ucla.edu/stata/
• Your tutors are also adept at using STATA so ask them for
help in tutorials or consultation times
• Post a question on Ed (you can do this anonymously)
Assessment
• For Special Consideration/Arrangement etc., check the UoS
Outline and see also University and Faculty Policies
TASK Weight Due date
Quizzes (5) 10% Each quiz will be available
from Mon 9AM – Sun
11:59PM of that week
Weeks:
4,6,9,11,
13
In-Semester
Exam
25% Wed, 20 Sep, 10:00AM Week 8
Assignment 15% Sun, 29 Oct, 11:59PM Week 12
Final Exam 50% Exam period
Quizzes
• There are 5 MCQ quizzes with 6 questions each
• Occur in weeks 4, 6, 9, 11 and 13
• Quizzes will be made available on the external
website: http://www.mcempirics.com/
• Use invitation to register on this website with your
USyd email address (xxxx@uni.sydney.edu.au)
• Each quiz open for 1 week but once you start only
have 60 minutes to complete it
In-Semester Exam
• Short-release assignment
• Exam comprising two parts: MCQ, short-answer
and questions requiring you to do STATA-based
computations
• Part 1 will involve MCQ and short-answer type
questions (60 minutes)
• Part 2 will require you to download a dataset and
answer questions using STATA (24 hours)
• Cover concepts from weeks 1-7
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Topics and Schedule
Week Topics & Assessments Readings
1 Introduction to Econometrics & Some Concepts in Probability and StatisticsTutorials are on this week Chs 1 & 2, Appendix A,B & C
2 Simple and Multiple Linear Regression – Assumptions and Properties Chs 2 (2.1-2.4), 3 (3.1-3.2) & 6 (6.1-6.3)
3 Multiple Linear Regression – Further Properties
Chs 2 (2.3,2.5), 3 (3.3, 3.4) & 4
(4.1)
4 Inference in Linear Regression ModelsQuiz 1 Ch 4
5 Asymptotic Properties of the Linear Regression Model and Using Qualitative Data Chs 5 & 7 (7.1-7.5)
6 Specification Issues in Linear Regression ModelsQuiz 2 Chs 3 (3.3,3.4) & 9 (9.2)
7 Further Specification Issues in Linear Regression Models Ch 9 (9.1, 9.4-9.6)
8 In-Semester Exam (no lecture, but tutorials still on!)
Mid Semester Break
9 Heteroskedasticity and Introduction to GLSQuiz 3 Ch 8
10 Endogeneity and Instrumental Variables Chs 9 (9.4) & 15
11 Instrumental Variables – Further IssuesQuiz 4 Ch 15
12 Introduction to Panel Data MethodsAssignment is due Sunday 29 Oct at 11:59PM Chs 13 & 14 (mostly 13)
13 Further Topics in Panel Data Models and Review Chs 13 & 14 (mostly 14)
The Nature of Econometrics and Economic
Data
Reference: Chapter 1
The Nature of Econometrics
• What is econometrics?
• Econometrics => use of statistical methods to analyse economic data
• Econometricians typically analyse nonexperimental (i.e. observational) data
• Typical goals of econometric analysis
• Estimating relationships between economic variables
• Testing economic theories and hypotheses
• Predicting economic variables
• Evaluating and implementing government and business policy
Ask yourself why? What differs between the natural sciences and a social
science like economics?
1. Decide the topic and propose an economic model (theory)
2. Propose a corresponding econometric (or empirical) model,
which typically involves some unknown parameters
3. Collect appropriate data
4. Using some software, estimate the model (i.e. parameters)
from the data
5. Give economic interpretation to the estimation results
Steps in Econometric Analysis
Economic models
• Can be models of microeconomic (e.g. individuals or firms) or
macroeconomic (e.g. regions, countries) behaviour
• Can be formal (i.e. derived from first principles), informal (i.e.
conceptual frameworks based on economic understanding), or
atheoretical (i.e. based on intuition)
• Often use optimising behaviour, equilibrium modeling
• Establish relationships between economic variables
“Essentially, all models are wrong, but some are useful”
(Box, G. E. P., and Draper, N. R., (1987), Empirical Model Building and Response Surfaces, John Wiley & Sons, New York, NY p. 424.)
Econometrics vs Economics
• Economics suggests important relationships, often with
policy implications, but virtually never suggests quantitative
magnitudes (i.e. size) of causal effects:
• What is the quantitative effect of reducing class size on student
achievement?
• How does a bachelor’s degree change earnings?
• What is the price elasticity of cigarettes?
• What is the effect on output growth of a 1 percentage point increase
in the cash rate by the RBA?
• What is the effect on housing prices of changes to zoning laws?
The applied economist uses econometrics to get the best estimate of
the economic relationship being investigated. The econometrician
develops the tools (i.e. methods) applied economists use
• Becker (1968) Derives equation for criminal activity based on utility
maximization ... What determines amount of criminal activity?
• The functional form of relationship not specified because it depends on the
utility function which is not known
• We cannot estimate this relationship as is ... we will need to specify an
econometric model
"Wage" in criminal
activities
Hours spent in
criminal activities
Wage for legal
employment Other
income
Probability of
getting caught
Probability of
conviction if
caught
Expected
sentence
Age
Eonomic Model of Crime: Example 1
• The functional form has to be specified
• Variables may have to be approximated (i.e. parameterised) by other
quantities
Measure of criminal
activity
Other
income
Frequency of
prior arrests
Wage for legal
employment
Frequency of
conviction
Average sentence
length after conviction
Age
Unobserved determinants
of criminal activity
e.g. moral character,
wage in criminal activity,
family background …
Economic Model of Crime (cont.)
• What is effect of additional training on worker productivity?
• Formal economic theory not really needed to derive equation:
• Other factors may be relevant, but these are the most
important (?)
Hourly wage
Years of formal
education Years of work-
force experience
Weeks spent
in job training
Model of Job Training and Worker
Productivity
Model of Job Training and Worker
Productivity (cont.)
• Econometric analysis requires that we think seriously about the
specification of the error term u
• Econometric models may be used for hypothesis testing
• For example, the parameter β3 represents the effect of training on the wage
• How large is the effect? Is it different from zero? Is it positive?
Hourly wage
Years of work-
force experience
Weeks spent
in job training
Unobserved determinants
of wages
e.g. innate ability,
quality of education,
family background …
Years of formal
education
Causality and the notion of ceteris paribus
• Most economic questions are ceteris paribus questions
• It is important to define which causal effect one is interested in
• It is useful to describe how an experiment would have to be
designed to infer the causal effect in question
Definition of causal effect of x on y:
How does variable y change if variable x is changed
but all other relevant factors are held constant?
The Nature of Econometrics
• Causal effect of fertilizer on crop yield
• By how much will the production of soybeans increase if one increases
the amount of fertilizer applied to the ground?
• Implicit assumption: all other factors that influence crop yield such as
quality of land, rainfall, presence of parasites etc. are held fixed
• Experiment:
• Choose several one-acre plots of land; randomly assign different amounts
of fertilizer to the different plots; compare yields
• Experiment works because amount of fertilizer applied is
unrelated to other factors influencing crop yields
The Nature of Econometrics
• Measuring the return to education:
• If a person is chosen from the population and given another year of
education, by how much will his or her wage increase?
• Implicit assumption: all other factors that influence wages such as
experience, family background, intelligence etc. are held fixed
• Experiment:
• Choose a group of people; randomly assign different amounts of
eduction to them (infeasible!); compare wage outcomes
• Problem: without random assignment, amount of education is
related to other factors that influence wages (e.g. ability)
The Nature of Econometrics
• Effect of law enforcement on city crime level
• If a city is randomly chosen and given ten additional police officers, by how
much would its crime rate fall?
• Alternatively: If two cities are the same in all respects, except that city A
has ten more police officers, by how much would the two cities crime rates
differ?
• Experiment:
• Randomly assign number of police officers to a large number of cities
• In reality, number of police officers will be determined by crime rate
(i.e. simultaneous determination of crime and number of police)
The Nature of Econometrics
Econometrics vs Statistics
• Usually, we are interested in recovering causal relations, not just
correlation, among economic variables
• Ideally, we would like to conduct an experiment
• But typically, it is impossible (or impractical and expensive) to run
experiments in economics, and we only have observational data
• returns to education
• can we ask someone to smoke to study the effect smoking?
Causality and Ceteris Paribus
• Most propositions in economics are ceteris paribus by
nature. Therefore, the goal is to infer a causal effect of one
variable on another, holding all other factors constant
• To infer causality, we need to hold other factors constant
• Key question is usually:
• Have ‘enough’ other factors been held fixed to make a
case for causality?
• ‘Enough’ generally means all other relevant factors
• Properly applied, econometric methods can simulate a
ceteris paribus outcome
Correlation vs Causality
Econometrics deals with difficulties arising from
using observational data to estimate causal effects
Most common problems:
• confounding effects (i.e. omitted factors)
• simultaneous causality (i.e. x => y; y => x)
Correlation does not imply causation! But economic
theory and econometrics together can permit us to
infer causation from observational data
An Example: Homework and Obesity
Econometric analysis requires data
• Different kinds of economic datasets
1. Cross-sectional data
2. Time series data (not covered in ECMT2150)
3. Pooled cross-sections
4. Panel/Longitudinal data
• Econometric methods depend on the nature of the data used
• Use of inappropriate methods may lead to misleading results
Economic Data
• Sample of individuals, households, firms, cities, states, countries, or other
units of interest at a given point of time/in a given period (i.e. a snapshot)
• Cross-sectional observations are more or less independent
• For example, pure random sampling from a population
• Sometimes pure random sampling is violated, e.g. units refuse to respond
in surveys, or if sampling is characterised by clustering
• Cross-sectional data typically encountered in applied microeconomics
For the most part, we will assume that our data are sampled randomly from
a population, even if that‘s not always technically correct
Cross-Sectional Data
Cross-sectional data set on wages and other characteristics
Observation number Hourly wage
Indicator variables
(1=yes, 0=no)
Example: Cross-Sectional Data
• Cross-sectional data on growth rates and country characteristics
Adult secondary
education rates
Growth rate of real
per capita GDP
Government consumtion
as percentage of GDP
Example: Cross-Sectional Data
• Observations of a variable or several variables over time
• For example, share prices, interest rates, consumer price index,
gross domestic product, vehicle sales, …
• Time series observations are typically serially correlated
• Ordering of observations conveys important information
• Data frequency: daily, weekly, monthly, quarterly, annually, …
• Typical features of time series: trends and seasonality
• Typical applications: applied macroeconomics and finance
The analysis of time series data is covered in ECMT2160.
Time Series Data
• Time series data on minimum wages and related variables
Unemployment
rate
Average minimum
wage for given year
Average
coverage rate
Gross national
product
Time Series Data Example
• Two or more cross sections are combined in one data set
• Cross sections are drawn independently of each other (e.g. Implies
individuals/firms will differ in each cross-section)
• Pooled cross sections often used to evaluate policy changes
• Example:
• Evaluate effect of change in property taxes on house prices
• Random sample of house prices for the year 1993
• A new random sample of house prices for the year 1995
• Compare before/after (1993: before reform, 1995: after reform)
Pooled Cross-Sectional Data
• Pooled cross sections on housing prices
Number of bathrooms
Property tax
Size of house
in square feet
Before reform
After reform
Pooled Cross-Sectional Data Example
• The same cross-sectional units are followed over time
• Panel data have both cross-sectional and time series dimensions
• Panel data can be used to account for time-invariant unobservables
• Panel data can be used to model lagged responses
• Example: Police and crime
• City crime statistics; each city is observed in two years
• Time-invariant unobserved city characteristics may be modelled
• Effect of police on crime rates may exhibit time lag
Panel data have become extremely important in most applied work in
economics
Panel or Longitudinal Data
Each city has two time
series observations
Number of
police in 1986
Number of
police in 1990
Panel Data Example
(1) A reminder:
Simple Linear Regression
+
(2) A primer:
Seeking a Causal Interpretation
Simple linear regression
What’s the point?
Suppose x and y are two variables representing some
population. The objective is to:
• Explain y in terms of x
• Study how y changes with changes in x
Issues:
• How do we account for other factors that affect y?
• What is the functional relationship between x and y?
• How can we ensure that we are capturing a ceteris
paribus (i.e. causal) result … if that is the goal?
46
Simple linear regression
Linear regression is a simple method of examining the
relationship between y and x
• Specifically, we explain variable y in terms of variable x
47
dependent
(response)
variable
independent
(explanatory)
variable
Intercept
Slope
parameter Error term
(random and
unobserved)
Examples: X and Y
• Interest rates (y) explained by money supply (x)
• Sales (y) explained by advertising (x)
• Wages (y) explained by education (x)
• Household expenditure (y) explained by income (x)
• Housing prices (y) explained by location (x)
48
The Error Term
• u captures:
• randomness in behaviour
• variables left out of the model
• departures from linearity
• errors in measurement
49
• Example: Soybean yield and fertilizer
• Example: A simple wage equation
50
Measures the effect of fertilizer on
yield, holding all other factors fixed
Rainfall,
land quality,
presence of parasites …
Measures the change in hourly wage
given another year of education,
holding all other factors fixed
Labor force experience,
tenure with current employer,
work ethic, ability …
Examples: Simple Regression Model
Interpretation in the simple linear regression model:
The goal is to understand how y varies with changes in x:
• So the key question:
When is it reasonable to assume that ceteris paribus holds?
That is, when is there a causal interpretation?
51
By how much does the dependent
variable change if the independent
variable is increased by one unit?
as long as
Interpretation only correct if all other
things remain equal when the indepen-
dent variable is increased by one unit
Interpretation
Conditional mean independence
Answer: We need conditional mean independence!
That is:
• since u and x are random variables, we can define the
conditional distribution of u given x
• the key assumption of the regression model:
• u is mean independent of x
E(u|x) = E(u)
• i.e. knowing x does not imply anything about u
52
Zero Conditional Mean independence
Note: It is common to assume that:
E(u) = 0
• so long as there is an intercept in the model this assumption is not
at all restrictive;
• It simply implies a rescaling of the intercept
Putting this together: The zero conditional mean independence
assumption is:
E(u|x) = E(u) = 0
But the important bit is the conditional mean independence
assumption
53
When is there a causal interpretation?
Conditional mean independence assumption holds:
But this is very unrealistic in the simple regression model:
• Example: wage equation
54
e.g. ability etc…
The explanatory variable must not
contain information about the mean
of the unobserved factors
The conditional mean independence assumption is unlikely to hold
here because individuals with more education will also often have
more ability on average – not independent!
What about causality?
… another useful thing to know:
if conditional mean
independence holds…
The conditional mean independence assumption ALSO implies
This means that the average value of the dependent variable y
across the population can be expressed as a linear function of
the explanatory variable x.
This tells us how Y changes with X on average, (i.e. Expected
outcomes), not individual outcomes!
56
Population Regression Function (PRF)
57
Population
regression function
Population Regression Function
You could be
here
or
here
For individuals with x = x2,
the average value of y is
y2 = β0 + β1x2
How do we get our ordinary least
squares estimates?
• In order to estimate the regression model we need data:
• A random sample of n observations
59
First observation
Second observation
Third observation
n-th observation
Value of the
explanatory variable of
the i-th observation
Value of the dependent
variable of the i-th
observation
How do we get estimates of 0 and 1?
• Plot the data, and fit as good as possible a regression line through
the data points:
60
Fitted regression line
For example, the i-th
data point
Ordinary Least Squares
• What does as good as possible mean?
Let‘s think about this…
61
Ordinary Least Squares
• What does as good as possible mean?
• Regression residuals
• Answer: Minimise sum of squared regression residuals
• Ordinary Least Squares (OLS) estimates
62
Ordinary Least Squares
Bottom Line: the OLS estimates can be obtained by:
• fitting a line through the sample points
• where the sum of squared residuals is
minimised
• hence the term ‘least squares’ estimation
63
• CEO Salary and return on equity
• Fitted regression
• Causal interpretation?
64
Salary in thousands of dollars Return on equity of the CEO‘s firm
Intercept
If the return on equity increases by 1 percent,
then salary is predicted to change by $18,501
OLS Example
Example cont.
65
Unknown population
regression line
Fitted regression line
(depends on sample)
E.g., CEO number 11‘s salary was
$875.372 lower than predicted
using information on his firm‘s
return on equity
Example cont.
• Wage and education
• Fitted regression
• Causal interpretation?
67
Hourly wage in dollars Years of education
Intercept
In the sample, one more year of education was
associated with an increase in hourly wage by $0.54
More Examples
What else & Next Week
Appendices A – Mathematical Tools
• Carefully review this material
• It will come in handy throughout the course
Tutorial this week (week 1):
• Review of Probability and Statistics – (Textbook Appendix B & C)
• Material from these 3 (A, B & C) appendices will frequently come up
during the course
Lecture 2:
• Linear Regression Models – Multiple/multivariate
• Ordinary Least Squares (OLS)
• Chapters: 2 (2.1-2.4), 3 (3.1-3.2) & 6 (6.1-6.3)
