A Primer in Econometric Theory

by John Stachurski

ISBN: 9780262337458 | Copyright 2016

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This book offers a cogent and concise treatment of econometric theory and methods along with the underlying ideas from statistics, probability theory, and linear algebra. It emphasizes foundations and general principles, but also features many solved exercises, worked examples, and code listings. After mastering the material presented, readers will be ready to take on more advanced work in different areas of quantitative economics and to understand papers from the econometrics literature. The book can be used in graduate-level courses on foundational aspects of econometrics or on fundamental statistical principles. It will also be a valuable reference for independent study.

One distinctive aspect of the text is its integration of traditional topics from statistics and econometrics with modern ideas from data science and machine learning; readers will encounter ideas that are driving the current development of statistics and increasingly filtering into econometric methodology. The text treats programming not only as a way to work with data but also as a technique for building intuition via simulation. Many proofs are followed by a simulation that shows the theory in action. As a primer, the book offers readers an entry point into the field, allowing them to see econometrics as a whole rather than as a profusion of apparently unrelated ideas.

This important book fills a gap in the existing curriculum by providing a firm foundation in linear algebra, statistics, and coding for students who want to study advanced econometrics. And there's more: it also exposes students to methods of machine learning and computational statistics, offering a broader perspective on modern data analytic techniques.

Hal Varian Chief Economist, Google

A Primer in Econometric Theory presents key foundations and supplements them with good examples. It vividly shows the benefits given to us by decades of technical progress in econometrics and computational methods. Stachurski’s writing style presents technical arguments in attractive and accessible ways.

Thomas J. Sargent New York University

John Stachurski's text, A Primer in Econometric Theory is a concise and elegant book that provides a more conceptual introduction to econometrics that coincides well with my own preferred way of teaching the subject to first-year graduate students. It is clear, rigorous, and provides a large number of interesting exercises with solutions. I will use it in my own econometrics teaching and recommend it to complement other applied econometrics books.

John Rust Gallagher Family Professor of Economics, Georgetown University

When I learned the fundamentals of linear algebra and economic theory as a graduate student, I found most textbooks and courses had an emphasis on theory but very little in terms of software. The emphasis on teaching these ideas through modern programming tools such as Julia, Python, and R not only makes the material far more accessible but also equips the readers of this book for their professional careers. I wish I had such a book when I was in grad school!

Viral Shah Co-inventor of Julia programming language, Co-founder of Julia Computing, Co-author of Rebooting India
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Contents (pg. vii)
Preface (pg. xv)
Common Symbols (pg. xvii)
Chapter 1: Introduction (pg. 1)
1.1: The Nature of Econometrics (pg. 1)
1.2: Data versus Theory (pg. 3)
1.3: Comments on the Literature (pg. 5)
1.4: Further Reading (pg. 5)
Part I: Background (pg. 7)
Chapter 2: Vector Spaces (pg. 9)
2.1: Vectors and Vector Space (pg. 9)
2.2: Orthogonality (pg. 27)
2.3: Further Reading (pg. 34)
2.4: Exercises (pg. 35)
Chapter 3: Linear Algebra and Matrices (pg. 45)
3.1: Matrices and Linear Equations (pg. 45)
3.2: Properties of Matrices (pg. 53)
3.3: Projection and Decomposition (pg. 60)
3.4: Further Reading (pg. 70)
3.5: Exercises (pg. 70)
Chapter 4: Foundations of Probability (pg. 79)
4.1: Probabilistic Models (pg. 79)
4.2: Distributions (pg. 99)
4.3: Further Reading (pg. 116)
4.4: Exercises (pg. 116)
Chapter 5: Modeling Dependence (pg. 125)
5.1: Random Vectors and Matrices (pg. 125)
5.2: Conditioning and Expectation (pg. 141)
5.3: Further Reading (pg. 154)
5.4: Exercises (pg. 154)
Chapter 6: Asymptotics (pg. 161)
6.1: LLN and CLT (pg. 161)
6.2: Extensions (pg. 169)
6.3: Further Reading (pg. 174)
6.4: Exercises (pg. 174)
Chapter 7: Further Topics in Probability (pg. 177)
7.1: Stochastic Processes (pg. 177)
7.2: Markov Processes (pg. 184)
7.3: Martingales (pg. 197)
7.4: Simulation (pg. 200)
7.5: Further Reading (pg. 206)
7.6: Exercises (pg. 206)
Part II: Foundations of Statistics (pg. 211)
Chapter 8: Estimators (pg. 213)
8.1: The Estimation Problem (pg. 213)
8.2: Estimation Principles (pg. 222)
8.3: Some Parametric Methods (pg. 233)
8.4: Further Reading (pg. 244)
8.5: Exercises (pg. 244)
Chapter 9: Properties of Estimators (pg. 247)
9.1: Sampling Distributions (pg. 247)
9.2: Evaluating Estimators (pg. 255)
9.3: Further Reading (pg. 270)
9.4: Exercises (pg. 270)
Chapter 10: Confidence Intervals and Tests (pg. 275)
10.1: Confidence Sets (pg. 275)
10.2: Hypothesis Tests (pg. 280)
10.3: Further Reading (pg. 294)
10.4: Exercises (pg. 295)
Part III: Econometric Models (pg. 297)
Chapter 11: Regression (pg. 299)
11.1: Linear Regression (pg. 299)
11.2: The Geometry of Least Squares (pg. 308)
11.3: Further Reading (pg. 315)
11.4: Exercises (pg. 315)
Chapter 12: Ordinary Least Squares (pg. 323)
12.1: Estimation under OLS (pg. 323)
12.2: Problems and Extensions (pg. 338)
12.3: Further Reading (pg. 347)
12.4: Exercises (pg. 347)
Chapter 13: Large Samples and Dependence (pg. 355)
13.1: Large Sample Least Squares (pg. 355)
13.2: MLE for Markov Processes (pg. 363)
13.3: Further Reading (pg. 370)
13.4: Exercises (pg. 370)
Chapter 14: Regularization (pg. 377)
14.1: Nonparametric Density Estimation (pg. 377)
14.2: Controlling Complexity (pg. 386)
14.3: Further Reading (pg. 399)
14.4: Exercises (pg. 399)
Part IV: Appendix (pg. 403)
Chapter 15: Appendix (pg. 405)
15.1: Sets (pg. 405)
15.2: Functions (pg. 408)
15.3: Cardinality and Measure (pg. 411)
15.4: Real-Valued Functions (pg. 413)
Bibliography (pg. 415)
Index (pg. 425)
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