Econometrics
B.Sc. (Hons) Statistics · Semester V · Academic Session 2026–27
The course covers how econometric models are built and estimated, and what to do when the assumptions of the classical linear regression model fail: generalized least squares, multicollinearity and ridge regression, heteroskedasticity, autocorrelation, instrumental variables, and the identification and estimation of simultaneous equations models.
Slides
There is one deck for each lecture.
Introduction and generalized least squares · Lectures 1–15
| Lecture | Topics | Slides |
|---|---|---|
| 1 | Preliminaries: notation; differentiation with respect to a vector; expectations and variances | 9 slides |
| 2 | Positive definite matrices and eigenvalues; the OLS criterion and normal equations | 7 slides |
| 3 | Variance of OLS; estimating σ²; the Gauss–Markov theorem; a numerical example | 7 slides |
| 4 | Meaning and nature of econometrics; exact and econometric relationships | 9 slides |
| 5 | Types of data; sources and quality of data | 10 slides |
| 6 | Objectives of econometric models; stages of model building | 8 slides |
| 7 | From a question to an estimated model; role of econometrics | 9 slides |
| 8 | The model with a general covariance matrix; what happens to OLS | 8 slides |
| 9 | The GLS estimator by transforming the model | 8 slides |
| 10 | The GLS estimator by direct minimisation | 6 slides |
| 11 | Mean and variance of the Aitken estimator | 6 slides |
| 12 | Aitken’s theorem: statement and short proof | 6 slides |
| 13 | Aitken’s theorem: the direct proof; GLS versus OLS | 11 slides |
| 14 | A worked example of GLS | 8 slides |
| 15 | Feasible GLS; summary of key formulas | 7 slides |
Multicollinearity and heteroskedasticity · Lectures 16–30
| Lecture | Topics | Slides |
|---|---|---|
| 16 | The problem of multicollinearity; standardised form; sources | 10 slides |
| 17 | Implications: perfect and near multicollinearity; the variance inflation factor | 11 slides |
| 18 | OLS estimates too large on average; practical consequences; detection by |X′X| | 10 slides |
| 19 | Diagnostics: correlation matrix, |R|, partial regressions and VIFs | 10 slides |
| 20 | Diagnostics: condition indices and variance-decomposition proportions | 9 slides |
| 21 | Remedies: more data, dropping variables, prior information, generalized inverse, principal components | 13 slides |
| 22 | Ridge regression: the estimator, constrained least squares, bias and covariance | 12 slides |
| 23 | Mean squared error of the ridge estimator; the Hoerl–Kennard theorem | 11 slides |
| 24 | Why ridge regression works; choice of the biasing parameter; ridge trace and HKB | 12 slides |
| 25 | Limitations of ridge regression; summary of key formulas | 7 slides |
| 26 | Heteroskedasticity: concept, sources and consequences for OLS | 9 slides |
| 27 | Bartlett’s test | 10 slides |
| 28 | The Breusch–Pagan test | 8 slides |
| 29 | The Goldfeld–Quandt test; comparison of the three tests | 9 slides |
| 30 | Estimation under heteroskedasticity: WLS, transforming the model, feasible GLS | 13 slides |
Autocorrelation and instrumental variables · Lectures 31–45
| Lecture | Topics | Slides |
|---|---|---|
| 31 | Autocorrelation: concept, measures and causes; the AR(1) scheme | 6 slides |
| 32 | Moments of the AR(1) disturbances | 8 slides |
| 33 | Consequences of autocorrelated disturbances | 7 slides |
| 34 | Detection: graphical method; the Durbin–Watson statistic and its relation with ρ | 7 slides |
| 35 | The Durbin–Watson test: decision rule, examples and limitations | 8 slides |
| 36 | Durbin’s h test | 6 slides |
| 37 | ρ known: the generalized difference equation and the Prais–Winsten transformation | 9 slides |
| 38 | ρ unknown: estimating ρ; the Cochrane–Orcutt procedure | 6 slides |
| 39 | Durbin’s two-step method; the Hildreth–Lu method | 7 slides |
| 40 | A complete worked example; summary of key formulas | 9 slides |
| 41 | Why OLS fails: consistency; a regressor correlated with the disturbance | 7 slides |
| 42 | Instruments; the IV estimator in the simple regression | 7 slides |
| 43 | Consistency of the IV estimator; an IV calculation | 6 slides |
| 44 | The IV estimator in matrix form: consistency and variance | 6 slides |
| 45 | Relevance and weak instruments; more instruments than regressors; summary | 7 slides |
Simultaneous equations models · Lectures 46–60
| Lecture | Topics | Slides |
|---|---|---|
| 46 | Simultaneous equations models; endogenous, exogenous and predetermined variables | 6 slides |
| 47 | A demand–supply system: structural and reduced forms | 9 slides |
| 48 | General form of the system; the problem of identification | 9 slides |
| 49 | The order condition | 7 slides |
| 50 | The rank condition; working procedure for identification | 8 slides |
| 51 | The X/0 table method | 10 slides |
| 52 | Identification step by step: the market for milk | 8 slides |
| 53 | Examples of identification; summary of key points | 12 slides |
| 54 | OLS in a structural equation: inconsistency and where it is appropriate | 8 slides |
| 55 | Indirect least squares | 8 slides |
| 56 | Two-stage least squares: the method, derivation and consistency | 8 slides |
| 57 | 2SLS standard errors; an over-identified example; 2SLS, IV and ILS under exact identification | 9 slides |
| 58 | LIML: the least variance ratio and its minimisation | 10 slides |
| 59 | LIML under exact identification; the k-class; a LIML calculation | 8 slides |
| 60 | Properties of LIML; comparison of the methods; summary | 6 slides |
Syllabus
| Unit | Topics | Lectures |
|---|---|---|
| I | Introduction: objective behind building econometric models, nature of econometrics, model building and role of econometrics. Generalized least squares estimation, Aitken estimator, Gauss–Markov theorem for GLSE. | 15 |
| II | Problem of multicollinearity, its implications; sources of multicollinearity; tools for handling the problem; remedies for multicollinearity; ridge regression. Heteroskedasticity, consequences and tests for it, estimation procedures under heteroskedastic disturbances, Bartlett’s test, Breusch–Pagan test and Goldfeld–Quandt test. | 15 |
| III | Autocorrelation: concept, consequences of autocorrelated disturbances, detection and solution of autocorrelation. Instrumental variable estimation. | 15 |
| IV | Simultaneous equations model, problem of identification, necessary and sufficient condition for the identifiability of parameters in a structural equation, ordinary least squares, indirect least squares, two-stage least squares and limited information maximum likelihood method. | 15 |
Books
- Greene, W. H. (2018). Econometric Analysis, 8th Ed., Pearson, New York.
- Gujarati, D. N., Porter, D. C., and Pal, M. (2021). Basic Econometrics, 6th Ed., McGraw-Hill Education (India), Chennai.
- Johnston, J., and DiNardo, J. (1997). Econometric Methods, 4th Ed., McGraw-Hill, New York.
- Koutsoyiannis, A. (1977). Theory of Econometrics, 2nd Ed., Macmillan, London.
- Maddala, G. S., and Lahiri, K. (2009). Introduction to Econometrics, 4th Ed., John Wiley & Sons, Chichester.
- Montgomery, D. C., Peck, E. A., and Vining, G. G. (2021). Introduction to Linear Regression Analysis, 6th Ed., John Wiley & Sons, Hoboken.
The slides follow my lecture notes for the course. The complete notes, worked solutions, the R practicals with their data and assignments are shared with the students enrolled in the course.