Topic 3: N

Apuntes

Topic 3: Nuts & Bolts of Linear Regression ECON30130: Econometrics Dr. Enda Hargaden Autumn 2025 Please remember that reading slides is like watching a movie with the sound off. You will likely miss out on key details if you rely on slides to “understand the script”. The “Classical Model” and Gauss-Markov Under “reasonable” assumptions, we have the Gauss-Markov Theorem. OLS delivers estimates with lower variance than any other unbiased estimator. The theoretical underpinning for OLS: there is no estimator that gives you an unbiased estimate of the true β with lower variance. This is sometimes, annoyingly, called BLUE Best Linear Unbiased Estimator. This is catchy but stupid. We will discuss violations of these assumptions in the this segment of the module. These assumptions are that the errors are mean zero, homoskedastic, and uncorrelated with each other. Heteroskedasticity An intuitive definition of homoskedasticity Homoskedastic errors: var(ui) = σ2 e.g. σ2 = 6.8 Heteroskedastic errors: var(ui)̸ = σ2 i.e. variance is not well captured by a single number. Heteroskedasticity— what is it?-400 -200 0 200 400 Residuals 0 1000 2000 3000 4000 Some explanatory variable, e.g. x2 Example ...