"Extremum estimator" is simply a pretentious term for "an estimator computed by maximising (or minimising) a criterion function". So essentially all the estimators you have seen to date -- e.g. OLS, GMM and MLE -- are of this type. (Even a sample mean and the 2SLS estimator can be fitted into this framework, as can be other things like quantile regression.) This course presents a unified asymptotic theory for these estimators.
In particular, I plan to cover the following topics:
Fundamental elements of asymptotic analysis: modes of stochastic convergence
Consistency under weak conditions
Asymptotic normality via linearisation of a FOC
Simulation-based estimators and indirect inference
Two-step estimation procedures
This course will thus cover similar to ground to last year's, but 4 and 5 are new. (Though probably I am being too ambitious at this stage and will have to leave some things out.)
No doubt you will have seen many of the results that we cover before: but you will have not seen a rigorous proof of them. 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. So 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.
Lectures will be held in Weeks 3--6 of Hilary term (8 lectures)
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.)
Wooldridge (2010), Econometric Analysis of Cross Section and Panel Data, Part III
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.)
Current version: posted 23/05/18, 13:00. Significant corrections to sections previously released are marked with (non-printing) annotations in the pdf.
The exam paper for Advanced Econometrics 2 will contain two questions related to this module.
All available past exam questions are listed below. Please note that because the course notes have been somewhat redrafted this year, some assumptions/conditions that are referred to in these questions have changed slightly.