Free course · First year to second year
Introduction to
Econometrics
A first course in econometrics in 25 planned lessons, from the statistics every economics degree starts with, through hypothesis tests and regression, to the questions the subject exists to answer: does schooling raise pay, did a minimum wage cost jobs, what can a forecast promise. Eighteen lessons are published so far (2 to 14 and 21 to 25); the list below says which. Each lesson teaches one idea with a real data set, a worked example you can repeat by hand and marked questions that explain every wrong answer as well as the right one.
Written from my university lecture notes and simplified for a first course. Start at lesson 2; lesson 1 is still to come. Part 1 (lessons 2 to 5) leads into part 2 (lessons 6 to 8). Lessons go up a few at a time, in the order students need them most. Where a lesson is not yet up, the line beneath it points to the page on this site that covers the topic now.
By Dr Nicky Grant, Cambridge PhD in economics. Former lecturer at Manchester (2013 to 2019) and St Andrews (2019 to 2025).
Part 1. Data, chance and sampling
First year. The statistics that regression stands on: random variables, how to summarise them, and the fact that an average computed from a sample is itself random.
- 1What econometrics is for: questions, data, causesIn preparation. For now, read Econometrics explained.
- 2Random variables and distributionsPublishedWhat a random variable is, its probability function and CDF, densities as areas, the normal and standardising, joint distributions and independence, on Premier League goals and birthweights. Five marked questions.
- 3Expectation, variance, covariance and correlationPublishedThe centre and spread of a distribution 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.
- 4Sampling distributions, the law of large numbers and the central limit theoremPublishedWhy a sample mean is unbiased and has variance σ²/n, shown on 10,000 samples of 25 births, then the two theorems and how large n must be. Five marked questions.
- 5Standard deviation versus standard errorPublishedWhere s/√n comes from, why four times the data halves the standard error, which spread to report and how to read error bars, on 1,388 birthweights. Five marked questions.
Part 2. Inference
First year. These three lessons say what a 95% interval promises, how a test is built, and what a p-value is the probability of.
- 6Confidence intervals: what 95% meansPublishedAn interval for 1,388 birthweights, what the 95% refers to (10,000 simulated samples), why small samples need a t multiple, and one interval by hand. Five marked questions.
- 7Hypothesis tests step by stepPublishedA test in five steps on a claim about the average grade, one tail or two, the t-test, and a test for home advantage in two Premier League seasons. Five marked questions.
- 8p-values, Type I and II errors, powerPublishedThe p-value as an area and as a count in a simulation, the two ways a test can be wrong, and how power depends on the truth and the sample size. Five marked questions.
Part 3. Regression
First year into second year. The OLS line by hand and by software: what it minimises, what the slope and intercept mean, how to read the printout, and what "holding other things fixed" does.
- 9Fitting the OLS line by handPublishedWhere the slope formula comes from, the calculation step by step on five workers, and the same arithmetic on 20 Premier League clubs. Five marked questions.
- 10Residuals, fit and R-squaredPublishedWhat the line leaves over, how big a typical residual is, and how TSS, ESS and RSS give R-squared, on five workers and then on 20 Premier League clubs. Five marked questions.
- 11Reading regression outputPublishedWhy every coefficient comes with a standard error, how to build the standard error, t and the 95% interval by hand, and two real printouts read line by line. Five marked questions.
- 12Multiple regression and holding other things fixedPublishedWhat a coefficient means when other regressors are in the model, shown on 526 US workers (1976): the schooling coefficient of 0.092 reproduced by partialling out, when adding a regressor moves the others, and the assumption needed to read a coefficient as an effect. Five marked questions.
- 13Omitted variable bias: sign and sizePublishedThe identity that links the short and long coefficients, the sign and the size of the bias, checked on 1,388 US births and in a simulation at three sample sizes; then an irrelevant variable, variables that cannot be measured, controls and instruments. Five marked questions.
Part 4. Making regression work
Second year. Dummies, logs and interactions; what to do when the error spread changes with x; why two overlapping regressors can each look insignificant.
- 14Dummies, logs, elasticities and interactionsPublishedA dummy variable as a difference in group means, the base group and the dummy variable trap, a logged outcome read as a percentage, roughly and exactly, a dummy in a log model, and an interaction drawn as two lines, on 526 US workers (1976) and 1,388 US births (1988). Five marked questions.
- 15Heteroskedasticity and robust standard errorsIn preparation. For now, read Diagnostic testing in linear regression.
- 16MulticollinearityIn preparation. For now, read Diagnostic testing in linear regression.
Part 5. Causes
Second year. Why a correlation is not an effect, what a randomised trial buys you, and two tools economists use when they cannot run one.
- 17Correlation, causation and selection biasIn preparation. For now, read Correlation versus causation.
- 18Potential outcomes and randomised trialsIn preparation. For now, the MSc notes on treatment effects and causal inference cover the ideas at a higher level.
- 19Difference-in-differencesIn preparation. For now, the MSc notes on policy analysis with panel data cover the method at a higher level.
- 20Instruments in plain EnglishIn preparation. For now, read Instrumental variables and weak instruments.
Part 6. Time series
Second year. A first look at data observed over time, written to need nothing beyond Parts 1 to 3: one history out of many possible ones, what a graph can show, the correlogram, random walks and a first forecast.
- 21One history, many possible paths: what a time series isPublishedUK inflation since 1989 as one path of a process that could have produced others: four simulated histories from one rule, 10,000 replays of a rule fitted to the data, and why 100 dependent observations can be worth 43 independent ones, or 6. Five marked questions.
- 22Reading a time-series graph: trend, seasonality, persistence, volatilityPublishedSix features to look for, each with a number from a real series: UK GDP, retail sales every December, unemployment, IBM's returns and the two pandemic quarters of 2020; then what a graph cannot settle. Five marked questions.
- 23Autocorrelation and the correlogramPublishedThe correlation of a series with its own past: r(1) by hand on eight quarters of GDP growth, how much data it needs, where the band ±1.96/√T comes from, and one real correlogram read in full. Five marked questions.
- 24Stationarity, white noise, random walks and spurious regressionPublishedWhat a process must keep constant for one history to teach us about it, why a random walk fails, what differencing does, and why regressing one random walk on an unrelated one reports a relationship in 77% of 10,000 simulated pairs. Five marked questions.
- 25AR(1) models and forecastingPublishedThe simplest model with memory, fitted to UK GDP growth: what its two numbers mean, forecasts one, two and h quarters ahead by hand, why the band widens and then levels off, and how the forecasts made at the end of 2015 fared. Five marked questions.
How the lessons are built
- One idea per lesson, taught with a real data set (UK macroeconomic series, Premier League results, published survey data) or a simulation with its recipe stated, so you can rerun it.
- The intuition in words and a picture before any formula; then a worked example with numbers small enough to check by hand, ending with the same answer the software prints.
- Three to five check questions at the end of each lesson, marked on the page, with an explanation for every option.
- Links up to the longer explainer on each topic and to the advanced notes.
- A level label on every part and every lesson: first year or second year. Part 6 is a simplified version of a third-year time-series course.
Free, no sign-up. If you want help beyond the lessons, one-to-one econometrics tuition starts with a free 30-minute consultation.
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