In this course, we shall discuss the consistency and asymptotic normality of extremum estimators (such as MLE and GMM), under classical smoothness assumptions. We shall also discuss how these results provide a basis for asymptotically valid inferential procedures.
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.
Seven lectures will be held: on Mon 9:30--11:00 (Weeks 1--4) and Thu 14:30--16:00 (Weeks 1--3), in Seminar Room A.
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. Please note that some sections of these notes (particularly Section 2) differ considerably from those used in last year's iteration of this course. I will start posting solutions to the exercises from week 2 onwards
Asymptotics: a review [updated 14/10/16]
Asymptotic normality: the smooth case [updated 02/11/16]
Inference
C. Solutions to exercises [Sections 1--4]
Errata [updated 02/11/16]
Please email me if you find any errors in the notes, typographical or otherwise.
Some guidelines for revising for this course, and what to expect in the exam
'Specimen' exam question, with solutions