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Stanford University Department of Economics
ECO 270: Econometrics I
Fall 2017
Annoucement: Exam Schedule according to the registrar's office
Final Exam: 12:15pm to 3:15pm, Thursday, December 14, Landau Economics
Building 140
Annoucement: The class on November 16 might need to be canceled or
rescheduled.
Course Description
This course is designed primarily to provide the necessary statistics background to
incoming PhD students in the economics department, in particular so that it might
be possible to continue with the more challenging econ 271 and econ 272 in the first
year econometrics sequence. You are required to be familiar with the materials
taught in econ 102A and econ 102B. You also need to be very good at linear algebra
and multivariate calculus, and should know some basic real analysis.
Part 2 of econ 270 introduces the statistical inference theory of estimation and
testing. Time permitting, an introduction to basic linear regression models might be
given.
Textbooks and Reading Materials
I will be drawing materials mostly from the following three books. As long as
you can survive the course, it is entirely up to you to decide whether you want
to purchase all, one, or none of these books.
George Casella and Roger Berger, "Statistical Inference", Duxbury
Advanced Series, 2002. 2nd edition.
Takeshi Amemiya, "Introduction to Statistics and Econometrics",
Harvard University Press, optional, 1994.
William Greene, "Econometric Analysis", 5th edition and above,
Prentice Hall, New Jersey.
You might also be interested in the following two books, but they are far more
advanced.
E.L.Lehmann and George Casella, "Theory of Point Estimation".
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E.L.Lehmann and Joseph Romano, "Testing Statistical Hypotheses".
Schedule and Staff
We meet on Tuesdays and Thursdays 11:30am to 1:20pm. There will be 19 or
20 lectures and a final exam.
The instructor is Professor Han Hong, Room 228, Landau Economics
Building.
Instructor office hours: Mondays 3:30pm -- 4:30pm, or by appointment.
The teaching assistant is Ben Mill.
TA office hours:
TA Sessions:
There will be weekly TA sessions unless announced otherwise.
While you are encouraged to discuss the problems, You are required to submit
independent solutions for the problem sets. There will be regular problem sets
and a final exam.
Course Outline
The following syllabus contains suggested pages from the textbooks for
reading. But you are responsible for reading other parts of the textbooks
and/or additional materials to understand the content of the course.
Since the Amemiya book is very concise and can be (and should be)
read from beginning to end, and only a small amount of material is
drawn from Greene, I will mostly only give page number for Casella
and Berger. You should also read Appendix A and Appendix B (and
maybe even Appendix E) of Greene's "Econometric Analysis".
Probability Theory, Random Variables and Distribution Functions
I will review this part VERY quickly.
Lecture Notes for Part 1, courtesy of Professor Joe Romano, can
be downloaded from Canvas.
Ch 1, Casella and Berger (CB afterwards)
Chs 2 and 3, Amemiya
Subtopics
Set Theory (CB pp 1-5)
Axiomatic Approach, Law of Total Probability, Bonferroni
Bound (CB pp 5-13)
Independence, Conditional Probability, Bayes Rule (CB pp
20-27)
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The Monte Hall (See CB pp 21 Three Prisoners)
Random Variables (CB pp 27--29)
Examples of Discrete and Continuous Random Variables
(CB pp 85-111)
Distribution and Density Functions (CB pp 29--37)
Transformations and Expectations
Ch 2, Casella and Berger
Chs 3 and 4 Amemiya
Subtopics
CDF and pdf of monotonic transformation (CB pp 47-54)
Inverse CDF transformation, random number generation
(CB pp 54--55)
CDF transformation, P-value (CB pp 54)
Centered and noncentered moments (CB pp 55--59)
Bias, Variance, Mean Square Error (CB pp 58)
Moment Generating Function (CB pp 59--68)
Charateristic Function (CB pp 84 and blackboard
supplement)
Common Families of Random Variables, Multivariate Random
Variables
Ch 3 and 4, Casella and Berger
Ch 5, Amemiya
Subtopics
Exponential Family (CB pp 111-116)
Location Scale Family (CB pp 117-121)
Markov Inequality (CB pp 136)
Chebyshev Inequality (CB pp 122)
Jensen's Inequality (CB pp 190)
Bivariate and Multivariate Random Variables (CB pp 139-
144)
Joint CDF and PDF (CB pp144-147)
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Marginal CDF and PDF (CB 147-152)
Independence (CB p153-156)
Multivariate transformations (CB p156-162, 185)
Joint Moments, Covariance and Correlation (CB 169-177)
Cauchy Schwartz Inequality (CB pp 187--188)
Best Linear Predictor (Amemiya pp 75--77)
Conditional Distribution (CB 147-152)
Law of Iterated Expectations (CB pp 164)
Law of Total Variance (CB pp 167)
Best Predictor (Amemiya pp 80--83)
Multivariate Normal Distribution (Amemiya pp 97-98)
Properties of Random Samples and Large Sample Theory
Lecture Notes, largesample.pdf
Ch 6, Amemiya
Ch 5, Casella and Berger
Appendix D. Greene
Subtopics
Sample Mean, Variance, Moments (CB pp 212 -- 214)
Unbiasedness Properties (CB pp 212 -- 214)
T-test statistic and t-distribution (CB 215-225)
Pivotal statistic and location-scale family (CB 116-121,
blackboard note)
Vector and Matrix differentiation (Greene, Appendix A.8)
Sample Variance and Chi square distribution (CB 218-222)
Convergence in probability, almost surely, in distribution,
in moments. ( CB 232-240, Joe's Lecture Note)
Limits of sequence of events (Joe Lecture Note)
Borel Cantelli Lemma (JOe Lecture Note)
Weak and Strong Law of Large Numbers (CB 232-240, Joe
Lecture note)
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Examples and Counter Examples
Vector Versions (Joe Lecture Note, Blackboard)
Continuous Mapping Theorem (Joe Lecture Note)
Slutsky's Lemma (CB 239-240, Joe Lecture Note)
Central Limit Theorems (CB 232-240, Joe Lecture note)
Proof using Moment Generating Functions (Joe Lecture
note)
Multivariate Central Limit Theorem, Cramer-Wold Device
(Joe Lecture Note)
Applications: t-statistics, binomial distributions
The Delta Method (CB 243, Joe Lecture Note)
Second Order Delta Method (CB 244)
Point and Interval Estimation
Point Estimation Lecture Notes
pointestimation.pdf
Additional Notes about Sandwich Variance, by Leon
Interval Estimation Lecture Notes
intervalestimation.pdf
Derivation of Normal Posterior Distribution, by Leon
Bayesian Asymptotics
Ch 7 and 8, Amemiya
Ch 7 and 9, Casella and Berger
Appendix C, Greenee
Subtopics
Point and Interval Estimation
Frequentist vs Bayesian vs Fiduciary Inference
(blackboard)
Parameters and Estimators
Finite and Large Sample properties of Estimators
Unbiasedness and Variance, mean square error (CB pp
330-331, 334-340)
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Admissibility and Bayes Estimators (Amemiya 122-124,
CB 324, 348-353)
Best Linear Unbiased Estimators (Amemiya 125-127)
Gauss Markov (Amemiya 128)
Counter Examples (Amemiya 131)
Consistency and Asymptotic Distribution and Efficiency
(CB 467-470, blackboard note)
Maximum Likelihood Estimator (CB pp 315--323)
Binomial and Normal Examples (Amemiya Ch7)
Numerical and Stochastic Optimation (Greene Appendix
E)
Newton Raphson and Gauss Newton Iterations
Newton Methods
Bisection for rooting finding
Root finding methods
Cramer Rao Lower Bound (CB 335-337, blackboard note)
Best Unbiased Estimators (see later)
Kullback Leibler Information Criterion (KLIC)
(blackboard note only)
Misspecification and Pseudo-Value (blackboard note only)
M-estimator Theory (Amemiya 141-145, CB 484-486,
blackboard note)
Uniform Convergence in Probability (blackboard note)
Identification and Misspecification for MLE (blackboard
note)
Asymptotic Normality (CB 467-470, Amemiya 141-145)
Score Function (blackboard note)
Information Matrix (In)equality (Amemiya 139,
blackboard note)
(Seemingly but not really) Robust Sandwich formula
(blackboard note)
Confidence Intervals (Amemiya 160-167, CB 417-430,
496-499)
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Exact and Asymptotic Coverage (CB 417-430, 496-499)
Confidence Set (CB 420-427)
Properties of Confidence Intervals (CB 417-430, 496-499)
Bayesian Inference
Hypothesis Testing
Testing Lecture Notes testing.pdf
LR test under linear equality constraints
LRtestlinearconstraints.pdf
Ch 9, Amemiya
Ch 8, Casella and Berger
Appendix C, Greene
Subtopics
(CB pp 382-393, topics below)
Simple and Composite Null
Simple and Composite Alternative
Size and Power
Most Powerful Test and Neyman Pearson Lemma
When NP Lemma is not useful
Bayesian Tests
Power function
Uniformly most power test
Admissible test
Likelihood Ration tests (CB pp 373-379)
One sided versus two sides tests
Size function, least favorable Null
P-values
Wald Tests
Local Power
Consistent Model Selection
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Asymptotic Equivalence of LR, Wald and LM tests
Duality between Confidence Interval and Hypothesis Testing
Ch 8, Amemiya
Ch 9, Casella and Berger
Appendix C, Greene
Principles of Data Reduction
Sufficiency and Completeness Lecture Notes
sufficiencyandcompleteness.pdf
Ch 6, Casella and Berger
Subtopics
Sufficient Statistics (CB pp 271-279, 285-286)
Factorization Theorem
Blackwell-Rao Theorem (CB 342)
Complete Statistics (CB pp 271-279, 285-286)
Exponential Family
Uniformly Minimum Variance Unbiased Estimator (CB pp
330-331, 334-340)
Lehmann Scheffe Theorem (CB 347, 349)
The Linear Regression Model
Least Square in the sample (without a model yet)
The Algebra and Geometry of Ordinary Least Square (GR
pp 19 -- 25)
Partitioned and Partial Regression (GR pp 26 -- 28)
R-Square and Adjusted R-square (GR pp31 -- 37)
Notes, updated 01/12/17
The "Classical" Linear Regression Model
Finite Sample Properties
Unbiasedness (GR pp 44-45)
Gauss Markov Thereom (GR pp 45-47)
Variance Estimation (GR pp 48-49)
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Inference Under Normality (GR pp 50-55)
Notes
Alternative to Lagrange Multiplier, pp 20-23,
Amemiya's "Advanced Econometrics"
Large Sample Properties
Consistency (GR pp 66--67)
Asymptotic Normality (GR pp 67--70)
Maximum Likelihood Estimation under Normality
(GR pp 492--496)
Notes
Problem Sets
Problem Set 1 Due on Thursday, October 12.
Problem Set 2 Due on Thursday, October 26.
Problem Set 3 Due on Tuesday, November 14.
Final Exam 2015
Final Exam 2014
Final Exam 2013
Final Exam 2012
Final Exam 2011
Final Exam 2010
Han Hong, February 2017
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