econometrics.blog

Chris Sims - RIP

meta

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…

Francis J. DiTraglia

Overlapping Confidence Intervals: Part II

statistics

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…

Francis J. DiTraglia

Overlapping Confidence Intervals

statistics

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…

Francis J. DiTraglia

A Good Instrument is a Bad Control: Part II

econometrics

causal inference

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…

Francis J. DiTraglia

Two FWL Theorems for the Price of One

econometrics

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…

Francis J. DiTraglia

Econometrics Puzzler #2: Fitting a Regression with Fitted Values

econometrics

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…

Francis J. DiTraglia

Econometrics Puzzler #1: To Instrument or Not?

econometrics

causal inference

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…

Francis J. DiTraglia

Not Quite the James-Stein Estimator

statistics

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…

Francis J. DiTraglia

How to Do Regression Adjustment

causal inference

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…

Francis J. DiTraglia

Is it better to improve sensitivity or specificity?

statistics

teaching

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…

Francis J. DiTraglia

How to Read an Econometrics Paper

teaching

Reading and understanding econometrics papers can be hard work. Most published articles, even review articles, are written by specialists for specialists. Unless you’re…

Francis J. DiTraglia

Sims and Uhlig (1991) Replication

time series

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…

Francis J. DiTraglia

The Return of econometrics.blog!

meta

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…

Francis J. DiTraglia

A Good Instrument is a Bad Control

econometrics

causal inference

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…

Francis J. DiTraglia

The R Formula Cheatsheet

computing

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…

Francis J. DiTraglia

Random Variables Cheatsheet

statistics

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…

Francis J. DiTraglia

Why Econometrics is Confusing Part II: The Independence Zoo

econometrics

teaching

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…

Francis J. DiTraglia

From the Poisson Distribution to Stirling’s Approximation

statistics

computing

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…

Francis J. DiTraglia

Local Asymptotics: The Simplest Possible Example

econometrics

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…

Francis J. DiTraglia

Three Ways of Thinking About Instrumental Variables

econometrics

causal inference

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…

Francis J. DiTraglia

Why Econometrics is Confusing Part 1: The Error Term

econometrics

teaching

“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…

Francis J. DiTraglia

A New Way of Looking at Least Squares

econometrics

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…

Francis J. DiTraglia

The Wilson Confidence Interval for a Proportion

statistics

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…

Francis J. DiTraglia

Lessons from the Oxford Vaccination Survey

statistics

applied

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…

Francis J. DiTraglia

Street Fighting Numerical Analysis - Part 1

computing

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…

Francis J. DiTraglia

Don’t Use the Textbook CI for a Proportion

statistics

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…

Francis J. DiTraglia

Regressions with a Mis-measured, Binary Outcome

measurement error

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…

Francis J. DiTraglia

Beyond Classical Measurement Error

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…

Francis J. DiTraglia

Understanding the F Statistic

econometrics

teaching

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…

Francis J. DiTraglia

(Mis)understanding Selection on Observables

causal inference

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…

Francis J. DiTraglia

Untangling Cause and Effect Without Experiments

causal inference

teaching

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…

Francis J. DiTraglia

Thirty isn’t the magic number

statistics

teaching

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 \(\sigma^2\)

Francis J. DiTraglia

Econometricians Anonymous

meta

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…

Francis J. DiTraglia

UK Excess Deaths by Age Group and Sex

applied

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…

Francis J. DiTraglia

Past the Peak? Excess Deaths in England and Wales

applied

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:

Francis J. DiTraglia

Excess Deaths in England and Wales

applied

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…

Francis J. DiTraglia