Econometrics · University level
Econometrics,
by stage
The econometrics pages on this site, sorted by what you need to do next: learn it from the start, check what you know, or get through an exam or a dissertation. Where a topic has more than one page, its row says which is the explainer, which the course lesson and which the lecture notes.
Written by a Cambridge PhD econometrician who lectured in econometrics at two UK universities and now tutors it one-to-one.
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Introduction to Econometrics
A free course, published lesson by lesson, from first-year statistics to regression, causes and a first look at time series. One idea a lesson, real data, worked examples, marked questions.
Start the course → I want to test myselfMarked questions
One hundred and forty-seven questions so far, from random variables to forecasting: five at the end of each of lessons 2 to 14 and 21 to 25, six on each of the OLS and hypothesis-testing explainers and five on each of the other nine explainers. Each is marked on the page, with an explanation for every option, right or wrong.
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How it works →The lecture notes, problem sets and videos from the university courses are on the teaching page, and Econometrics explained is the one-page map of the subject. This page lists what fits each stage.
Foundations: data, chance and sampling
First-year statistics. Part 1 of the course (lessons 2 to 5) teaches these step by step. The study notes below are the reference pages: the theorem statements, the animations and the table of rules.
- Random variables and distributionsFirst yearLesson 2: probability functions and the CDF, densities as areas, the normal and standardising, joint distributions, independence, five marked questions
- Expectation, variance, covariance and correlationFirst yearLesson 3: centre, spread and how two variables move together, on Premier League goals, wages and births; the variance of a sum; why the sample variance divides by n - 1; five marked questions
- Sampling distributions, the law of large numbers and the central limit theoremFirst yearLesson 4: the sample mean over 10,000 samples of 25 births, its centre and variance, both theorems, how large n must be, five marked questions
- Standard deviation versus standard errorFirst yearLesson 5: where s/√n comes from, why four times the data halves the standard error, which spread to report, error bars, five marked questions
- Econometrics basics: the ideas in orderFirst yearStudy-notes hub: five notes in reading order, what each gives the next, what to know first and links to the matching lessons
- Expectation, variance and covarianceFirst yearStudy notes: the variance and covariance rules in one table with their conditions, a real portfolio, two dice checked against all 36 outcomes
- The law of large numbersFirst yearStudy notes with animation: the weak law and what it needs, an animated running mean, Chebyshev's inequality, what the law does not say
- The central limit theoremFirst yearStudy notes with animation: the theorem and what it needs, a flat and a skewed population, how large n must be, infinite variance
- The normal, t, chi-squared and F distributionsFirst yearExplainer: how the four are built, which test uses which, quiz
Inference: tests, p-values and intervals
Part 2 of the course. The explainers below are the reference versions.
- Hypothesis testing, p-values and powerFirst yearExplainer: one worked example, a real test, quiz · Lesson 7 · Lesson 8 · lecture notes
- Confidence intervals and t-testsFirst yearExplainer: what 95% means, intervals and tests, quiz · Lesson 6
Regression: OLS and how to read it
Parts 3 and 4 of the course. Start with the explainer for the definition, the lesson to do it by hand, the derivation for the proof.
- What OLS isFirst yearExplainer: meaning, formula, worked example, quiz · Lesson 9: fitting the line by hand · derivation in matrix form
- Reading regression outputFirst yearExplainer: a real table line by line, with Stata, R and Python code and output, quiz · Lesson 11: reading regression output
- Multiple regression and holding other things fixedSecond yearLesson 12: what a coefficient means with several regressors, holding other things fixed as a comparison, partialling out, and when adding a regressor moves the others; five marked questions
- Omitted variable biasSecond yearLesson 13: the identity that links the short and long regressions, the sign and size of the bias, and why more data do not remove it; five marked questions
- R-squared and goodness of fitFirst yearExplainer: TSS, ESS and RSS, what counts as good, adjusted R-squared, quiz · Lesson 10: residuals, fit and R-squared
- The Gauss-Markov theorem and BLUESecond yearExplainer
- Logs, elasticities and dummiesSecond yearExplainer: the four cases, exact against approximate, worked on real wages, quiz · Lesson 14: dummies, logs and interactions
- Heteroskedasticity, multicollinearity and diagnostic testsSecond yearExplainer · lecture slides · robust and cluster standard errors (MSc)
Causes: experiments, panels and instruments
Part 5 of the course. The explainer is the first-year version; the MSc notes are the full treatment.
- Correlation versus causationFirst yearExplainer
- Treatment effects and causal inferenceMScLecture notes
- Difference-in-differences and panel dataMScPolicy analysis with panel data · fixed and random effects
- Instrumental variables and weak instrumentsSecond year to MScExplainer · lecture slides
Time series
Part 6 of the course (lessons 21 to 25) is the slow route. The explainers are the reference versions, and the module notes carry the algebra.
- What a time series isSecond yearLesson 21: one history and the paths that could have been, on UK inflation since 1989; four simulated histories from one rule; why dependent observations carry less information; five marked questions · Explainer: time series econometrics notes · part 2 · module notes with exercises
- Reading a time-series graphSecond yearLesson 22: trend, seasonality, persistence, volatility, outliers and shifts in the mean, each on a real series; five marked questions
- Autocorrelation and the correlogramSecond yearLesson 23: r(1) by hand, how much data it needs, the band, one real correlogram; five marked questions · Explainer: how to read a correlogram · serial correlation in regression errors
- Stationarity, white noise and random walksSecond yearLesson 24: the three conditions, white noise, the random walk, differences and spurious regression; five marked questions
- AR, MA and ARMA models and forecastingSecond yearLesson 25: the AR(1) fitted to UK GDP growth, forecasts by hand and their bands; five marked questions · Explainer: AR, MA, ARMA and ARIMA models · estimation and model selection
- Vector autoregressionsMScVAR basics · impulse response functions
- Random walks and the efficient market hypothesisSecond yearExplainer
Advanced methods and financial econometrics
MSc and research level. No course lessons here; these stand on their own.
- Maximum likelihoodMScExplainer · slides
- Generalised method of momentsMScExplainer
- Identification-robust inferenceResearchExplainer · research papers
- GARCH and volatilityMScExplainer · slides
- Stock returns, CAPM and the market modelMScDistribution of returns · CAPM and beta
- Mathematical methods for economicsSecond yearLinear algebra and calculus notes
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