econometrics.blog

Apr 26, 2026 7 min computing

Complex Step Differentiation

Street Fighting Numerical Analysis - Part 2
Sometimes we need a good approximation to the derivative \(f'(x)\) of a real-valued function \(f\) at some real value \(x\). So here’s a fun fact that you may not know. If \(…
Apr 9, 2026 1 min meta

A Makeover for econometrics.blog

Today econometrics.blog got a long-overdue update from blogdown to Quarto. Thanks to Claude Code, the transition was seamless: all existing links are preserved, along with…
Mar 15, 2026 3 min meta

Chris Sims - RIP

I was saddened to hear of Chris Sims’s passing yesterday. Although I’m not a macroeconometrician, his work has strongly influenced the way I think about econometrics. I…
Nov 22, 2025 11 min statistics

Overlapping Confidence Intervals: Part II

In my earlier post on Overlapping Confidence Intervals I asked what we can learn from the overlap, or lack thereof, between confidence intervals for two population means…
Nov 15, 2025 13 min statistics

Overlapping Confidence Intervals

Perhaps you’ve seen a claim like this in an applied paper: “the estimated effect for Group A is statistically significant, but the estimated effect for Group B is not; this…
Aug 28, 2025 10 min econometrics causal inference

A Good Instrument is a Bad Control: Part II

At a recent seminar dinner the conversation drifted to causal inference, and I mentioned my dream of one day producing a Lady Gaga parody music video called “Bad Control”.1 A…
Aug 14, 2025 10 min econometrics

Two FWL Theorems for the Price of One

The result that I prefer to call Yule’s Rule, more commonly known as the “Frisch-Waugh-Lovell (FWL) theorem”, shows how to calculate the regression slope coefficient for one…
Jul 24, 2025 3 min econometrics

Econometrics Puzzler #2: Fitting a Regression with Fitted Values

Suppose I run a simple linear regression of an outcome variable on a predictor variable. If I save the fitted values from this regression and then run a second regression of…
Jul 13, 2025 7 min econometrics causal inference

Econometrics Puzzler #1: To Instrument or Not?

Welcome to the first installment of the Econometrics Puzzler, a new series of shorter posts that will test and strengthen your econometric intuition. Here’s the format: I’ll…
Aug 10, 2024 37 min statistics

Not Quite the James-Stein Estimator

If you study enough econometrics or statistics, you’ll eventually hear someone mention “Stein’s Paradox” or the “James-Stein Estimator”. You’ve probably learned in your…
Aug 2, 2024 24 min causal inference

How to Do Regression Adjustment

By the end of a typical introductory econometrics course students have become accustomed to the idea of “controlling” for covariates by adding them to the end of a linear…
Jul 25, 2024 9 min statistics teaching

Is it better to improve sensitivity or specificity?

Here’s a slightly unusual exercise on the topic of Bayes’ Theorem for those of you teaching or studying introductory probability. Imagine that you’re developing a diagnostic…
Jul 20, 2024 13 min teaching

How to Read an Econometrics Paper

Reading and understanding econometrics papers can be hard work. Most published articles, even review articles, are written by specialists for specialists. Unless you’re…
Jul 15, 2024 8 min time series

Sims and Uhlig (1991) Replication

As a teaser for our upcoming (2024-07-23) virtual reading group session on Bayesian macro / time series econometrics, this post replicates a classic paper by Sims & Uhlig…
Jul 14, 2024 2 min meta

The Return of econometrics.blog!

After a year-long hiatus, I’m excited to return to regular blogging about econometrics! I have a long list of posts that I’m eager to write, and I hope you’ll find them…
Jun 29, 2023 9 min econometrics causal inference

A Good Instrument is a Bad Control

Here’s a puzzle for you. What will happen if we regress some outcome of interest on both an endogenous regressor and a valid instrument for that regressor? I hadn’t thought…
Apr 19, 2023 2 min computing

The R Formula Cheatsheet

R’s formula syntax is extremely powerful but can be confusing for beginners.1 This post is a quick reference covering all of the symbols that have a “special” meaning inside…
Jan 7, 2023 1 min statistics

Random Variables Cheatsheet

To do well in an econometrics or statistics course at any level, you need to have a large number of simple properties of random variables at your fingertips. Some years back…
Jan 1, 2023 19 min econometrics teaching

Why Econometrics is Confusing Part II: The Independence Zoo

In econometrics it’s absolutely crucial to keep track of which things are dependent and which are independent. To make this as confusing as possible for students, a typical…
Nov 18, 2022 7 min statistics computing

From the Poisson Distribution to Stirling's Approximation

The Poisson distribution is the most famous probability model for counts, non-negative integer values. Many real-world phenomena are well approximated by this distribution…
Nov 12, 2022 6 min econometrics

Local Asymptotics: The Simplest Possible Example

If you study enough econometrics, you will eventually come across an asymptotic argument in which some parameter is assumed to change with sample size. This peculiar notion…
Nov 6, 2022 11 min econometrics causal inference

Three Ways of Thinking About Instrumental Variables

In this post we’ll examine a very simple instrumental variables model from three different perspectives: two familiar and one a bit more exotic. While all three yield the…
Jul 24, 2022 5 min econometrics teaching

Why Econometrics is Confusing Part 1: The Error Term

“Suppose that \(Y = \alpha + \beta X + U\).” A sentence like this is bound to come up dozens of times in an introductory econometrics course, but if I had my way it would be…
Mar 14, 2022 12 min econometrics

A New Way of Looking at Least Squares

Have you got a ruler handy? Fantastic! Then hold out your right hand, extend your thumb and little finger as far as they’ll go, and measure the distance in centimeters…
Feb 5, 2022 24 min statistics

The Wilson Confidence Interval for a Proportion

This is the second in a series of posts about how to construct a confidence interval for a proportion. (Simple problems sometimes turn out to be surprisingly complicated in…
Dec 31, 2021 14 min statistics applied

Lessons from the Oxford Vaccination Survey

Sorry @UniofOxford, but this is wildly misleading. Students who choose to reply to a vaccination survey are likely very different from those who choose not to reply. If…
Oct 29, 2021 8 min computing

Street Fighting Numerical Analysis - Part 1

Computing is a crucial part of modern applied and theoretical econometrics but most economists, myself included, have little if any formal training in numerical analysis and…
Oct 4, 2021 11 min statistics

Don't Use the Textbook CI for a Proportion

In a previous post I showed an example in which the “textbook” confidence interval for a proportion performs poorly despite a fairly large sample size. My aim in that post…
Aug 30, 2021 16 min measurement error

Regressions with a Mis-measured, Binary Outcome

Many outcomes of interest in economics are binary. For example, we may want to learn how employment status \(Y^*\) varies with demographics \(X\), where \(Y^*=1\) means…
Aug 23, 2021 5 min measurement error

Beyond Classical Measurement Error

Pop Quiz: If \(D^*\) and \(D\) are binary random variables and \(D\) is a noisy measure of \(D^*\), is it possible for the measurement error \(W \equiv D - D^*\) to be classi…
Aug 15, 2021 20 min econometrics teaching

Understanding the F Statistic

The F-statistic for a test of multiple linear restrictions is a staple of introductory econometrics courses. In the simplest case, it can be written as \[F \equiv…
Aug 8, 2021 6 min causal inference

(Mis)understanding Selection on Observables

On a recent exam I asked students to extend the logic of propensity score weighting to handle a treatment that takes on three rather than two values: basically a…
Aug 1, 2021 8 min causal inference teaching

Untangling Cause and Effect Without Experiments

The following is a piece I wrote for the LMH News, based on a general interest webinar that I gave in November of 2020. If this post inspires you to learn more about causal…
May 8, 2021 15 min statistics teaching

Thirty isn't the magic number

The simplest version of the central limit theorem (CLT) says that if \(X_1, \dots, X_n\) are iid random variables with mean \(\mu\) and finite variance \(\sigma^2\)
Apr 1, 2021 4 min meta

Econometricians Anonymous

Some years back, I wrote a monologue for the Economics Department Skit Night at UPenn. It was a niche venue, granted, but the crowd seemed to enjoy my contribution. In honor…
May 13, 2020 3 min applied

Past the Peak? Excess Deaths in England and Wales

Since my previous post, the Office for National Statistics has posted updated data on weekly deaths, and we’ve updated rcovidUK accordingly. Here’s where things stand:
May 13, 2020 5 min applied

UK Excess Deaths by Age Group and Sex

In an earlier post I looked at regional differences in the effects of Covid-19 by calculating excess deaths in each week of 2020 relative to an average of the preceding five…
May 4, 2020 3 min applied

Excess Deaths in England and Wales

To get a better idea of the impact of Covid19 in the UK, Dan Mead and I put together an R package rcovidUK with weekly deaths in England and Wales, taken from the Office for…
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