Econ 837: Probability Theory and Statistics

First year PhD econometrics.

Background material: Hansen’s textbook

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The first part of the course covers measure theoretic probability essential for research in fields where probability is used in applications.

Topics to be covered include:

1. Measure and integration from a probabilistic perspective.

2. Basic probabilistic notions of random variables, expectation, independence.

3. Limit theorems: laws of large numbers, convergence in distribution, central limit theorems.

Relevant References

• Probability and Random Processes by Grimmett and Stirzaker
• A First Look at Rigorous Probability Theory by Rosenthal
• Probability and Measure by Billingsley
• The Borel Cantelli Lemma by Chandra, T.K.
• Gut, Allan. Probability: A Graduate Course
• Measure Theory by Halmos, P.R.

A good basic reference for those who never took econometrics is:

• Hogg, McKean, and Craig. Introduction to Mathematical Statistics.

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The second part of the course looks at topics in identification and estimation in econometrics.

1. Identification.

• Definition of identification. Identification in linear models, binary response models, and in some nonlinear models.
• Mean independence vs Median independence.
• Difference between assumptions regarding DGP (behavioral and statistical), and data collection methods (missing data, measurement error, censoring, attrition).

2. Statistical Inference. DGP. Sampling.

3. Extremum Estimators: Consistency and Asymptotic Normality.

Relevant References

• Lewbel’s Identification Zoo
• Imbens/Wooldridge notes
• Manski (2005)
• Molinari (2008)
• Tamer (2010)
• Hayashi, Ch. 7 and slides
• Newey and McFadden (1994)
• Newey (1991)
• Andrews (1994)