This course is designed for students with a strong background in econometrics and statistics acquired in previous courses: Mathematics for Economics I and II, Statistics I and II, Econometrics, Econometric Techniques and Quantitative Economics.

This subject is part of the Quantitative Techniques and Applied Economics track. This course formally justifies the econometric methods discussed in previous courses (Econometrics, Econometric Techniques, and Quantitative Economics) and considers generalizations of them. Topics to be covered include: inferences based on Ordinary Least Squares (OLS), Maximum Likelihood (ML), and Generalized Method of Moments (GMM), in both single-equation and multiple-equation contexts. The course, like the rest of the track, is designed for students interested in preparing for work involving data processing and making inferences about causal relationships. Such jobs include econometrics, business analyst, financial analyst, quantitative analyst, risk analyst, policy analyst, consultant, marketing specialist, accounting specialist, auditor, and many more. The course is particularly useful for students intending to pursue postgraduate studies related to the Economics¡ discipline.

1. Ordinary least squares (OLS): The classical regression model. The algebra of least squares. Finite sample properties of OLS. Hypothesis testing under normality. Relation to maximum likelihood. Generalized least squares. 2. Large sample theory: Review of limit theorems for sequences of random variables. Fundamental concepts in time-series analysis. Large-sample distribution of the OLS estimator. Hypothesis testing. Consistent estimation of the asymptotic variance of OLS estimators. Implications of conditional homoscedasticity. Testing conditional homoscedasticity. Least squares projection. Consistent estimates of projection coefficients. Testing for lack of autocorrelation. 3. Single-equation generalized method of moments (GMM): Endogeneity bias. The general formulation. Generalized method of moments defined. Large sample properties of GMM. Testing overidentified restrictions. Hypothesis testing by likelihood-ratio principle. Implications of conditional homoscedasticity. 4. Multiple-equations GMM: The multiple-equations model. Multiple-equation GMM defined. Large sample theory. Single-equation versus multiple-equations estimation. Special cases of multiple equations GMM: FIVE, 3SLS and SUR. Common coefficients.

Assignments are used to guide the study of the subject. Each week the student has to apply results and techniques discussed in the lectures. The course is of a methodological nature and does not require the use of computers.