econometrics.blog
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2d ago
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 regression model. But this familiarity can sometimes cause confusion when students later encounter regression adjustment, a widely-used approach to causal inference under the selection-on-observables assumption. While regression adjustment is simple in theory, the finer points of how and when to apply it in practice are much more subtle. One of these finer points is how to tell whether a particular covariate is a “good contro ..read more
econometrics.blog
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1w ago
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 test for a disease. The test is very simple: it either comes back positive or negative. You have a choice between slightly increasing either your test’s sensitivity or its specificity. If your goal is to maximize the positive predictive value (PPV) of your test, i.e. the probability that a patient has the disease given that the test comes back positive, which test characteristic should you choose to improve? An Open I ..read more
econometrics.blog
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2w ago
Reading and understanding econometrics papers can be hard work. Most published articles, even review articles, are written by specialists for specialists. Unless you’re already familiar with the literature, it can be a real uphill battle to make it through a recent paper. In grad school I remember our professors repeatedly admonishing me and the rest of the cohort to “read the papers!” But when I did my best to follow this advice, I nearly always felt like I was banging my head against a wall. Effective reading is a skill that can be learned, and the only way to learn is through practice. But ..read more
econometrics.blog
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2w ago
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 (1991) contrasting Bayesian and Frequentist inferences for a unit root. In the post I’ll focus on explaining and implementing the authors’ simulation design. In the reading group session (and possibly a future post) we’ll talk more about the paper’s implications for the Bayesian-Frequentist debate and relate it to more recent work by Mueller & Norets (2016). We’ll also be joined by special guest Frank Schorfheide who ..read more
econometrics.blog
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2w ago
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 interesting. To whet your appetite, here’s a preview of some of the topics I plan to cover in the coming weeks: Bayesian versus Frequentist Approaches to Unit Roots How Not To Do Regression Adjustment Understanding the James-Stein Estimator In the meantime, I have a few econometrics-related announcements: I’ll be teaching a summer course on causal inference at Oxford this September. If you’re interested in attending here are ..read more
econometrics.blog
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1y ago
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 about this question until 2018, when one of my undergraduate students asked it during class. If memory serves, my off-the-cuff answer left much to be desired.1 Five years later I’m finally ready to give a fully satisfactory answer; better late than never I suppose! The Model We’ll start by being a bit more precise about the setup. Suppose that $$Y$$ is related to $$X$$ according to the following linear causal model $Y \le ..read more econometrics.blog by 1y ago 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 I made a handout containing the most important properties for my undergraduate students at the University of Pennsylvania. In the hopes that this might be of use to others, I’ve released an updated pdf on github. You can fork the repository here. If you spot any errors or want to suggest any additions, feel free to raise an issue or send me a pull request ..read more econometrics.blog by 1y ago 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, including the number of German bombs that landed in 1/4km grid squares in south London during WWII. Formally, we say that a discrete random variable $$X$$ follows a Poisson distribution with rate parameter $$\mu > 0$$, abbreviated $$X \sim \text{Poisson}(\mu)$$, if $$X$$ has support set $$\{0, 1, 2, ...\}$$ and probability mass function \[ p(x) \equiv \mathbb{P}(X=x) = \frac{e^{-\mu }\mu^x}{x!}.$ Using some clever alge ..read more
econometrics.blog
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1y ago
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 goes by a variety of names including “Pitman drift,” a “sequence of local alternatives,” and “local mis-specification,” and crops up in a wide range of problems from weak instruments, to model selection, to power analysis.1 Whatever you choose to call it, the idea of a parameter that changes with sample size is bizarre, and I remember spending weeks trying to understand it when I was a graduate student. How could parameters ..read more
econometrics.blog
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1y ago
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 same solution in this particular model, they lead in different directions in more complicated examples. Crucially, each gives us a different way of thinking about the problem of endogeneity and how to solve it. The Setup Consider a simple linear causal model of the form $$Y \leftarrow \alpha + \beta X + U$$ where $$X$$ is endogenous, i.e. related to the unobserved random variable $$U$$. Our goal is to learn $$\beta$$, th ..read more

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