In this course, we will discuss the consistency and asymptotic normality of extremum estimators (such as MLE and GMM), under classical smoothness assumptions. If there is enough time, we will also touch on how to conduct inference using the Wald statistic.
The ultimate purpose of this course is to introduce you to the style of mathematical reasoning used, in econometrics and statistics, to derive the large-sample properties of estimators and inferential procedures. In this sense, the results that we cover are less important than the arguments used to prove them.
The surest way to become familiar with these arguments is to work carefully through the proofs and -- most importantly -- attempt the exercises that I provide (in the course notes). You can only be sure that you really understand this material if you are able to complete (at least some of) the exercises.
The current plan is for the four lectures to be held on: Wed & Thu of Wk 3, Wed of Wk 4, and Wed of Wk 5. (Thus Marianne will give the first lecture on her module on Thu of Wk 4.) Wed lectures are at 11:30-13:00 in Seminar Room C, and Thu lectures at 14:30-16:00 in the Lecture Theatre (Manor Rd).
Consultation: I will next be available for consultation on Tuesday of Week 9 (8 Dec), at 15:30--17:30, in the Large Discussion Room of the Social Science Library (Manor Rd).
The only required reading is the course notes (below). For the benefit of those of you who may find it helpful to consult other sources, a few relevant references are indicated at the end of each section of the notes. These will generally refer to one or more of the following:
Newey & McFadden (1994), "Large sample estimation and hypothesis testing", Handbook of Econometrics. Covers very similar ground to this course (and much more), though I find some of their proofs a little terse.
Hayashi (2000), Econometrics, Chapters 2 & 7. Not so useful for proofs, but does give a wide range of examples that might help to illustrate the theory that we will cover. (We won't have time to cover very many examples.)
van der Vaart (1998), Asymptotic Statistics, Chapters 2, 3 and 5. Gives a more advanced treatment of these topics.
But please note that it is in no way expected that you will consult any of these texts. (Though I should add that van der Vaart (1998) is a terrific book, and anyone seriously interested in studying econometric theory should get hold of a copy.)
These will be posted during the course; my aim is to make the relevant sections available before we cover them in class. I will start posting solutions to the exercises from week 4 onwards (see below)
Extremum estimators: an introduction [updated for a second time on 11/11]
Asymptotics: a review [updated 18/11]
Consistency [updated 21/5/16]
Asymptotic normality: the smooth case [updated 6/12]
References [updated 11/11]
Errata [updated 21/5/16]
Solutions to exercises [updated 15/5/16: Exercises 4.4 and 4.5 still to be added]
How to revise for this course [updated 12/5/16]
Specimen exam question, with solutions [updated 21/5/16]
Since this is the first time that I have taught from these notes, they will undoubtedly contain some errors: please email me if you find any.