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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 lively discussion of bad controls ensued, during which I offered one of my favorite examples: a good instrument is a bad control.
Last updated on Aug 28, 2025
10 min read
econometrics
,
causal inference
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 predictor by carrying out additional “auxiliary” regressions that adjust for all other predictors.
Last updated on Aug 14, 2025
10 min read
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 the outcome variable on the fitted values, what will I get?
Last updated on Jul 24, 2025
3 min read
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 pose a question that requires only introductory econometrics knowledge, but has an unexpected answer.
Last updated on Jul 13, 2025
7 min read
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 introductory econometrics course that ordinary least squares (OLS) is the best linear unbiased estimator (BLUE) in a linear regression model under the Gauss-Markov assumptions.
Frank DiTraglia
Last updated on Aug 10, 2024
33 min read
shrinkage
,
decision theory
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