This is a quick course on econometric theory and methods, along with the underlying ideas from probability, statistics and linear algebra that budding econometricians should know. The focus is on foundations and general principles. Although it was written to teach from, there are many solved exercises, making the text well suited to self-study. Worked examples and sample code are used to reinforce ideas.
The level of the text is calibrated towards the first year of graduate school—perhaps even to the first semester of the first year of graduate school—as an initial upper level course on econometrics and statistics. Those who work through the book will be well placed to take more specialized or applied quantitative courses in topics such as microeconometrics, time series analysis, or finance, to read graduate econometrics texts, and to begin to study papers from the econometrics literature and research from the wider world of statistics and data science.
One aim in writing the text was to link core topics in econometrics and statistics, identifying unifying principles and common themes. For example, the orthogonal projection theorem bestrides much of the technical material, from least squares to conditional expectation, while the concept of empirical risk minimization ties together most of our estimation theory. Another aim was to blend traditional econometrics with some of the theoretical ideas emanating from the data science and statistical learning communities.
I have emphasized the value of modern programming tools not only for data analysis but also for studying econometric theory. I’m certain that the best way to understand a result in econometric theory is to first work through the proof and then run a simulation that shows the theory in action. Sample code is provided in a mix of three programming languages: Julia, Python, and R. Python and R are the heavyweights of data science, and their popularity is now spilling over to econometrics. Julia is a new language for scientific programming with much to recommend it. All three are fun, high productivity languages. All three are open source.
Note that this text is not an encyclopedic treatment, nor a reference manual. I have tried to keep the book concise—suitable for a one semester course rather than anything longer. As a result, many well known econometric methods have been omitted or given only cursory treatments. As such, this book is intended as a complement or companion to the existing graduate level econometrics texts, most of which are cited in what follows.
I have freely borrowed ideas and results from a large number of sources. Some of these are listed in the "Further Reading" section at the end of each chapter. Doubtless some are missing. Many of the proofs in the text are "new" in the sense of being written from first principles, although they are certainly just remixes of what is already in the literature.
This book has benefited from the input of many students and colleagues. In particular, I wish to thank Blair Alexander, Frank Cai, Yiyong Cai, Tim Christensen, Bikramaditya Datta, Chenghan Hou, Takashi Kamihigashi, Paul Kitney, Qingyin Ma, Matthew McKay, Kieron Meagher, José L. Montiel Olea, Alex Olssen, Guanlong Ren, Tom Sargent, Stefan Webb, and Varang Wiriyawit. Extra thanks go to Cleo, my wife, for sharing the journey and helping with proofreading, and to Akshay Shanker, for reading the book so closely.