Topic 2: Properties of Regression Coefficients & Hypothesis Testing
2.20* (qn on one sided t-test)
(extracted from exercise 2.15) A researcher with a sample of 50 individuals
with similar educationbut differing amounts of training hypothesises that
hourly
ECON107
Applied Econometrics
MULTIPLE REGRESSION
(Two or more explanatory variables)
Chapter 3
(3.4 postponed & skip 3.6)
INTRODUCTION
In the real world one explanatory variable is not
enough
We extend the simple linear regression model, and
allow for t
Topic 3: Multiple Regression Analysis
A3.7
A researcher hypothesises that, for a typical enterprise, V, the logarithm of
value added per worker, is related to K, the logarithm of capital per worker, and
S, the logarithm of the average years of schooling o
Topic 4: Multicollinearity & Testing of linear restrictions
3.16*
A researcher investigating the determinants of the demand for public transport
in a certain city has the following data for 100 residents for the previous
calendar year: expenditure on publ
Elements of econometrics
C. Dougherty
EC2020, 2790020
2011
Undergraduate study in
Economics, Management,
Finance and the Social Sciences
This is an extract from a subject guide for an undergraduate course offered as part of the
University of London Intern
Singapore Management University
Econ 107: Applied Econometrics
Homework 5 Questions
Due Date: N/A
1. A classical example of an instrumental variable is the draft lottery number, used by Angrist (1990,
American Economic Review 80, pp. 313-336) to help meas
SingaporeManagementUniversity
SchoolofEconomics
ECON107AppliedEconometrics
Term1,AY20132014
SectionsG3G5(ProfessorChowHweeKwan)
Assignment2(Topics:Weeks510)
Question 1
For this question, you are required to download the EAEF (Educational Attainment and
E
ECON107
Applied Econometrics
MULTICOLINEARITY & TESTING OF
LINEAR RESTRICTIONS
Chapters 3 (3.4)
& 6 (6.5)
PROPERTIES OF THE MULTIPLE REGRESSION
COEFFICIENTS
A.1
The model is linear in parameters and correctly specified.
Y = 1 + 2 X 2 + . + k X k + u
A.2
T
Chapter 7: Heteroscedasticity
Chapter 7: Heteroscedasticity
Overview
This chapter begins with a general discussion of homoscedasticity and
heteroscedasticity: the meanings of the terms, the reasons why the
distribution of a disturbance term may be subject
Review for Econ 107 Final
Spring, 2013
1
Nonlinear Regressions (Topic 7, SW, Ch 8)
1. Modeling nonlinear regressions: Understand that in a quadratic regression model, the marginal
eect is a linear function of the regressor. Calculation of marginal eects.
TOPIC 9A: INSTRUMENTAL VARIABLES (IV)
REGRESSION
Instrumental variables
IV estimator with a single regressor and
a single instrument
1
2SLS/TSLS
estimator
WHERE ARE WE?
Randomization
Consider Y = 0 + 1X + u
From previous topics, we know that X and u are
u
WELCOME TO
ECON 107
APPLIED ECONOMETRICS
Professor JIN Sainan
Email: snjin@smu.edu.sg
Office hours: Friday 9-11am at SOE 5030 or by appointment
1
TEXTBOOK
Required:
Introduction to
Econometrics:
International Edition,
3/e
Author : Stock, James H. and
Mark
TOPIC 8: INTERNAL AND EXTERNAL VALIDITY
Internal and external validity
Threats to internal validity
Threats to external validity
Example: test score and class size (self-study)
1
1. INTERNAL AND EXTERNAL VALIDITY
Internal validity: A statistical analysis
TOPIC 6: MULTIPLE LINEAR REGRESSION:
INFERENCE
Hypothesis tests and confidence intervals for a
single coefficient
Tests of joint hypotheses
Testing single restrictions involving multiple
coefficients
Confidence sets for multiple coefficients
Model specifi
TOPIC 7b: NONLINEAR REGRESSIONS
Modeling nonlinear regressions
Interactions between regressors
Detection of omitted nonlinearity
1
INTERACTION BETWEEN REGRESSORS
The nonlinear models we have considered thus far allow for the
possibility that the change in
TOPIC 3: SIMPLE LINEAR REGRESSION: ESTIMATION
Simple linear regression models
OLS estimation
Measure of goodness-of-fit
OLS Assumptions
Sampling distribution of OLS estimators
1
1. SIMPLE LINEAR REGRESSION MODEL
Here we are interested in estimating a line
TOPIC 4: SIMPLE LINEAR REGRESSION: INFERENCE
Hypothesis testing
Confidence Intervals
Binary independent variables
Heteroskedasticity and homoskedasticity
Gauss-Markov theorem
Inference in small samples
1
WHERE ARE WE?
We have estimated 1which is the OLS e
Review for Econ 107 Final
Fall, 2012
1
Internal and External Validity (Topic 8)
1. Definitions of internal and external validity
2. Internal validity:
(a) Two components of internal validity: () The estimator of the causal eect should be
unbiased (asympto
TOPIC 7a: NONLINEAR REGRESSIONS
Modeling nonlinear regressions
Nonlinear regressions of a single
independent variable
1
1. MODELING NONLINEAR REGRESSIONS
In the linear regression model, we assume that the
conditional expectation of Yi given X1i , . . . ,X
Review for Econ 107 Midterm (G1, G2, G3)
Fall, 2012
Three types of data: cross sectional, time series, panel
1
Review of Probability (SW, Ch 2)
1. Random variables and distributions: basic concepts,
2. Expectation, mean and variance: basic denitions and p
A Quiz for Econ 107
February, 2013
True or false.
1. Let U 2 (p) and V 2 (q) . Then U + V 2 (p + q) .
2. Let U 2 (p) and V 2 (q) . Then
U/p
V /q
F (p, q).
3. Let n be an estimator of based on n observations. n is consistent for if MSE(n ) 0
as n .
4. The
TOPIC 9B: IV REGRESSION & 2SLS:
MULTIPLE REGRESSION
Introduction
Multiple regression: IV and 2SLS
Instrument relevance
Instrument
exogeneity
1
Applications
1. INTRODUCTION: GENERALIZING THE 2SLS METHOD
1. Adding exogenous regressors to the model
Suppose n
Review for Econ 107 Midterm (G1, G2, G3)
Fall, 2012
Three types of data: cross sectional, time series, panel
1
Review of Probability (SW, Ch 2)
1. Random variables and distributions: basic concepts,
2. Expectation, mean and variance: basic definitions and
Review for Econ 107 Final
Fall, 2012
1
Internal and External Validity (Topic 8)
1. Denitions of internal and external validity
2. Internal validity:
Pay attention to (a) Two components of internal validity: ( ) The estimator of the causal e ect should be
Quiz for Econ 107
Fall, 2012
True or false.
Topic 8
1. A statistical analysis does not have internal validity if the statistical inferences about causal
eects are not valid for the population being studied.
2. A statistical analysis does not have external
Review for Econ 107 Midterm
Spring, 2013
Three types of data: cross sectional, time series, panel.
1
Review of Probability (SW, Ch 2)
1. Random variables and distributions: basic concepts,
2. Expectation, mean and variance: basic denitions and properties;
TOPIC 5: MULTIPLE LINEAR
REGRESSION: ESTIMATION
Omitted variable bias (OVB)
Multiple linear regression model (LRM)
OLS estimator in multiple LRM
Goodness-of-fit in multiple LRM
Assumptions in multiple LRM
Distribution of the OLS estimators in multiple
LRM
TOPIC 2: REVIEW OF STATISTICS
Estimation of the population mean
Hypothesis testing for the population
mean
Confidence intervals for the population
mean
Difference in means
Treatment effects
Small sample t statistics
Covariance and correlation
1
PROBABILIT
Singapore Management University
Econ 107: Applied Econometrics
Homework 4 Questions
Due on 26 March 2013 for G1
27 March , 2013 for G2
Questions 1-2 (from Chapter 8) and 6-8 (from Chapter 9) in this homework are taken from the
required textbook Introducti
Singapore Management University
Econ 107: Applied Econometrics
Homework 2 Questions
Due on 16 Feb 2013 for G1
13 Feb , 2013 for G2
Questions 7-9 in this homework are taken from the required textbook Introduction to Econometrics
(3rd Edition, by James H. S
WELCOME TO
ECON 107
INTRODUCTION TO ECONOMETRICS
Professor Sainan JIN
Email: snjin@smu.edu.sg
1
Office hours: Tuesday 8-11am at SOE 5030
or by appointment
[Introduction to Econometrics] [ECON107]
Introduction to
Econometrics: Updated,
Global Edition, 3/E
Singapore Management University
Econ 107: Introduction to Econometrics
Homework 1 Questions
Due on 7 Sep. 2016 for G1 and G2
Due on 8 Sep. 2016 for G3
Some questions in this homework are taken from the textbook Introduction to Econometrics (Updated 3rd Ed
REVIEW OF STATISTICS (SW CHAPTER 3)
Sampling distribution
Estimation of the population mean
Hypothesis testing for the population mean
Confidence intervals for the population mean
Difference in means
Treatment effects
Small sample t statistics
Covariance
TOPIC 2: SIMPLE LINEAR REGRESSION: ESTIMATION
(PART A)
Simple linear regression models
OLS estimation
Measure of goodness-of-fit
1
1. SIMPLE LINEAR REGRESSION MODEL
Here we are interested in estimating a linear equation that
describes the relationship be
TOPIC 2: SIMPLE LINEAR REGRESSION: ESTIMATION
(PART B)
OLS Assumptions
Sampling distribution of OLS estimators
1
4. OLS ASSUMPTIONS
Why do we use the OLS estimator?
What are the properties of the OLS estimator?
Under what conditions is the OLS estimator n