Course : Econometrics

Part 1:

In the first part of the  course we introduced the multiple linear regression model, we derived the OLS estimators and we also discussed their geometric interpretation. Then, we discussed in detail the Gauss-Markov assumptions, we proved the Gauss-Markov theorem and the finite sample properties of the OLS estimators as well as results related to hypothesis testing with respect to the linear model. Subsequently, we proved large sample size properties of the OLS estimators such as consistency and asymptotic normality. Finally, we proved results for the estimation of the multiple linear regression model by using the likelihood principle and we also discussed the Generalised Least Squares method.

The exams’ questions can include theoretical and practical exercises related to the above notions as well as proofs of the Theorems that discussed in detail during the course.

All the lecture notes and tutorials have been uploaded in the e-class web page of the course within the folder “1^st Part Alexopoulos’’. 

Part 2:

The remark above about the exams' questions holds also for the 2nd part.

Also, notice that the updated lecture notes (24/01/23) can be found here and here (the relevant tutorial code can also be found here). Check the eclass of the course frequently in case of further updates.

Remember that the blog contains reviews of the 2^nd part’s lectures with links (among others) towards the notes, errors’ corrections, etc. Consult them!

The above (notes, blog posts) contain descriptions of the notions examined during the lectures. Some remarks on the material:

• The example involving stochastic Nash equilibria was indicative of how economic theory can structure an econometric model involving moment conditions. We did not have time to design inferential procedures on that. You will not be examined on that.
• The example involving the GARCH(1,1) model was indicative of how empirical economic phenomena can structure an econometric model, of a model involving non linearities, no closed forms for the associated estimators, numerical procedures for inference, etc. You should comprehend the previous, but you will not be examined on derivations involving that model-we did not actually perform any analytical derivations.
• The derivation of the IVE in the case where the parameter space is the whole Euclidean one (unrestricted IVE), was performed in the class, and more details lie in the notes (especially in the second part). They are important.
• The Lipschitz continuity of the (modified) criterion for the OLSE in the case where the parameter space is compact was not derived in the class. If it will be needed you will be given it.
• The derivation of the weak consistency for the IVE either in the case where the parameter space is the whole Euclidean space, or when it is compact, or when it is closed and convex, was not performed in the class due to time shortage. However it is somewhat analogous to the derivations of the weak consistency of the OLSE, and it is detailed in the second part of the notes. This lies in your exam material! (apart from the analogous derivation of the Lipschitz continuity which you will be given if needed).
• Please try to derive consistency for the OLSE, when the parameter space is compact, by using its’ representation as a minimizer of the Euclidean distance between the unrestricted OLSE and the parameter space. Use the high level conditions that guarantee consistency for the unrestricted OLSE and apply the theorem we have derived in the case where the criterion is the aforementioned distance (is it possibly less involved to establish the conditions of the theorem in this case!).