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Usually when we talk about a medical diagnosis,

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there's this expectation of precision. It feels,

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I don't know, almost like engineering, right?

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Oh, absolutely. Very cut and dry. Yeah, like

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you break your arm, the x -ray shows that jagged

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white line, and the doctor just points and says,

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there it is. Right. It's binary, broken or not

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broken. It's clean. And frankly, it's comforting.

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We really like things to be visible. But then

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you step into the world of empirical data. Oh,

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yeah. And that comfort just... Vanishes. Completely

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vanishes, especially when you are trying to figure

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out if one specific variable actually like caused

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a specific outcome. Suddenly that X -ray machine

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is just broken. We're looking at a diagnostic

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landscape that is entirely murky. I take it a

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step further, actually. It isn't just murky.

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Without the proper mathematical architecture,

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it's actively deceptive. Deceptive? Yeah. Wow.

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Yeah, because you were essentially looking at

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shadows and trying to infer the existence of

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a three -dimensional object that you can never,

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you know, actually touch. Which is exactly why

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we are plunging into paintings of first course

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in causal inference. Because for you listening,

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our mission today on this deep dive is to conquer

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this text. And it is quite a text. It really

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is. It's the distillation of seven years of teaching

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at UC Berkeley. It pulls together the statistical,

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the biostatistical, and econometric perspectives

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of figuring out basically what causes what. Right.

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Getting to the actual root of it. Exactly. So

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we are going to unpack the heavy math and translate

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it into profound real -world analytical tools.

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Because that traditional aphorism we all learned

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in Stats 101, you know, correlation does not

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imply causation. Right. The golden rule. Yeah.

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It's safe, but it's... fundamentally a dead end.

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This text argues that statistics is absolutely

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crucial for understanding causality. We just

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need like a rigorous formal language for it.

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And that formal language has to start with a

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philosophical grounding. I mean, the author anchors

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the text initially not in equations, but actually

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in antiquity. Oh, right. The Democritus quote.

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Exactly. Democritus said, I would rather discover

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one causal law than be king of Persia. Which

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is a massive statement. It is. And Aristotle

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argued that we do not have knowledge of a thing

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until we grasp its cause. It really highlights

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that causal inference isn't just like a niche

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statistical tool. It is the core engine of human

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epistemology. But classic statistics, the kind

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focused purely on drawing lines of best fit and

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finding associations, frequently falls into traps.

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OK, let's unpack this idea of traps, because

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the text highlights a famous one right out of

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the gate, the Ewell -Simpson paradox. Ah, yes.

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I think a lot of people vaguely remember Simpson's

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paradox from school as a quirky math trick. Like

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a trend appears in different groups of data,

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but then magically disappears when you combine

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them. Yeah, and it is often taught as a quirk,

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which honestly does a massive disservice to how

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dangerous it actually is in empirical research.

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Dangerous how? Well, the Yule -Simpson paradox

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demonstrates that an unmeasured binary confounder

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can completely overturn an observed association.

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I mean, it isn't just the magnitude of the effect

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that changes. The entire direction of the causal

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arrow can completely flip. Right. And the real

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-world example the book uses here is the Lalonde

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job training data, which, if you study econometrics,

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is legendary. Oh, totally foundational. So you

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have this data set evaluating a job training

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program designed to boost future earnings. If

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you run a naive, simple regression model, just

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regressing future earnings on a binary indicator

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of whether they took the training, doing absolutely

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nothing to control for other variables. Just

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a straight -up raw comparison. Yeah, exactly.

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The model spits out a coefficient of negative

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$8 ,506. Which, if you take that at face value,

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suggests the program was a catastrophic failure.

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Like actively ruining lives. Exactly. It implies

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that participating in this training actively

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destroyed over $8 ,000 of a person's future earning

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potential. Right. But then the text demonstrates

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that if you take that exact same data and run

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a multiple regression controlling for covariates.

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Things like age, education. Yeah, and crucially

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prior earnings. If you control for those, the

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coefficient on the training program flips to

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a positive $1 ,067. The harmful program is suddenly

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beneficial. Because the mechanism at play here

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is omitted variable bias. Right. See, in the

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naive regression, the error term is heavily correlated

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with the treatment variable. Why? Because the

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people who opted into this job training program

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were predominantly individuals who were already

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economically disadvantaged. They had lower education

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or a history of lower earnings to begin with.

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Exactly. So the naive regression wasn't measuring

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the causal effect of the training at all. It

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was simply measuring the structural disadvantage

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of the people who were enrolled. So relying on

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the raw correlation is basically like, it's like

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trying to deduce the shape of a complex object

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purely from its two -dimensional shadow on a

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wall. I like that. Depending on the angle of

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the light, which in our data represents the covariates

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we choose to look at, the shadow completely changes.

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A cylinder looks like a circle from the top down,

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but a rectangle from the side. That's a really

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helpful visualization. But let's push it further.

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If you don't account for the angle of the light,

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the confounders, you aren't just seeing a distorted

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shape. You are drawing conclusions that will

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dictate real -world policy, and you will be completely,

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entirely wrong. Which is terrifying for policymakers.

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Exactly. The shadow is just the association.

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The true shape is the causal effect. To move

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from the shadow to the object, we have to formally

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define what a cause even is. which requires abandoning

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the purely associative view of statistics. Which

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brings us to the bedrock of modern causal inference,

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right? The potential outcomes framework. Yes.

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Formalized by Nyman in 1923 and expanded by Rubin

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in 1974. And the text pairs this with an aphorism

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from Rubin in Holland, which is no causation

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without manipulation. Right. And that phrase

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is a hard boundary line for experimentalists.

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How so? It means if you cannot conceive of a

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mechanism to manipulate a treatment, even hypothetically,

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discussing its causal effect is mathematically

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incoherent. Wow. Okay. Yeah. You can talk about

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the causal effect of a drug or a tutoring program

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because you can intervene and change it. You

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cannot strictly talk about the causal effect

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of being tall or being born in 1990. Because

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those are immutable attributes. Exactly. Wait,

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I'm stuck on that limitation. People do studies

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all the time claiming things like height causes

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higher salaries. Are you saying the potential

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outcomes framework rejects that entirely? Well,

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it forces you to redefine what you are actually

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studying. Are you studying the immutable physical

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attribute of height? Or are you studying the

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perception of height by the employer? Oh. Because

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if it's the latter, you can manipulate that in

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an experiment, say by altering the height listed

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on a medical profile during a hypothetical hiring

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exercise. The manipulation constraint, it forces

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precision. Okay, that makes sense. It forces

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us to define the treatment clearly. So let's

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look at how potential outcomes actually works.

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The core idea is that for every single unit in

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your population, there exist two parallel realities.

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Two potential outcomes. There is the outcome

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that would happen if they received the treatment,

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denoted as Y of 1. And there is the outcome if

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they received the control, denoted as Y of 0.

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So the individual causal effect is literally

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just the mathematical difference. Right. Y of

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1 minus Y of 0. And if we scale that up, we get

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what the text calls the science table. Yeah.

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Imagine a massive spreadsheet. Every row is an

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individual unit. The columns are Y of 1 and Y

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of 0. If we had that complete table. causal inference

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would be a trivial exercise in subtraction. Just

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simple math. But we have a fundamental problem.

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We only ever get to observe half of the science

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table. Half of it is always missing. Right. I

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can't take the headache medicine and simultaneously

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not take the headache medicine at the exact same

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moment in time under the exact same conditions.

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Exactly. This is known as the fundamental problem

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of causal inference. For every unit, one potential

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outcome is realized and observed while the other...

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The counterfactual is forever unobservable. So

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we are left with this massive missing data problem.

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And to even attempt to fill in those missing

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values mathematically, the framework demands

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a really rigid assumption called SATFA. SATFA.

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The Stable Unit Treatment Value Assumption. Which

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is one of those acronyms that sounds incredibly

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dry. Oh, incredibly dry. But its implications

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literally dictate whether a study is actually

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valid or just statistical noise. So... SUTVA

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requires two specific conditions. First, no interference

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between units. Second, no hidden variations of

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treatments. Let's break down no interference

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first. The text uses the example of flu shots.

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Right. So interference occurs when the treatment

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assigned to unit A affects the potential outcomes

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of unit B. Okay. With vaccines, this is herd

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immunity. If I am studying the effect of a flu

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shot on whether you... contract the virus, your

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outcome doesn't solely depend on your treatment

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status. If I get the shot, I'm less likely to

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become a vector. Which lowers my probability

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of getting sick, even if I got the control. Exactly.

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Another brilliant example the book highlights

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is social media advertising. If a platform is

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trying to measure the causal effect of an ad

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on my purchasing behavior, they can't just randomize

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who sees the ad. Because of the network effect.

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Right. Because if my friend sees the ad and buys

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the product, they might... text me about it.

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My potential outcome just changed based on my

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friend's treatment status. The math of basic

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causal inference assumes a vacuum. It assumes

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each unit is an isolated island. When you have

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network effects, which, by the way, happen constantly

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in epidemiology, economics, and sociology. Yeah,

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the real world. Right. SUDFA is violated. You

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have to move to much more complex models of spillover

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effects. And the second part of SUDFA, no hidden

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variations of treatments, is just as crucial.

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If we are trying to measure the causal effect

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of a college education, Sutva demands that college

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education is a uniform treatment. Which we know

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it isn't. Far from it. A degree in computer science

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from MIT is a fundamentally different treatment

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than a degree in poetry from a small liberal

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arts college. If the treatment is a chaotic mixed

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bag, the Y of one column in our science table

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just loses its meaning. Which brings us to the

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necessity of precisely defining the experimental

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unit. And the text illustrates this beautifully

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with what we can call the headache pill paradox.

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OK, here's where it gets really interesting,

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because this kind of broke my brain a little.

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Let's hear it. Let's say I have a headache at

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2 p .m. I take a pill. At 3 p .m., my headache

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is gone. The sloppy everyday logic is I had a

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headache. I took a pill. Headache is gone. Therefore,

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the pill cured it. I observed my state before

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and my state after. Why is that logically invalid

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under this framework? Because you are conflating

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time with counterfactuals. The experimental unit

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is not you across all of time. The experimental

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unit is a specific slice of space -time. A slice?

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Yes. You at 2 p .m. is one unit. You at 3 p .m.

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is a completely different unit. Oh, because my

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body has naturally metabolized things, my stress

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levels might have dropped. The ambient temperature

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changed. Literally anything could have happened.

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Precisely. You have four potential outcomes happening

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here. Four? Yeah. U before the pill has an observed

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Y of zero and an unobserved Y of one. U after

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the pill has an observed Y of one and an unobserved

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Y of zero. You cannot simply subtract your historical

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before state from your current after state and

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declare it a causal effect. Because I don't know

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what U... after the pill would have felt like

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if I had refrained from taking it. The headache

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might have simply resolved on its own. Exactly.

259
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This level of strictness feels almost paralyzing.

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It forces you to acknowledge the vastness of

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the unobservable counterfactuals. And since we

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can't observe them, we have to rely on the mechanism

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that assigns people to the treatment or control

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in the first place, right? The treatment assignment

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mechanism? Right. And the book uses a fantastic

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hypothetical to contrast assignment mechanisms.

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The omniscient perfect doctor versus the clueless

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doctor. OK, let's talk about the perfect doctor.

269
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Let's say we have this doctor who knows the exact

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unobservable individual causal effect for every

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patient who walks in the door. A literal mind

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reader. Yeah. They know exactly who will benefit

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from the pill and who won't. So acting ethically,

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they only prescribe the pill to the people it

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actively helps. Okay, so now imagine you were

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a researcher looking at this perfect doctor's

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clinical data a year later. You look at the treated

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group. They all had fantastic outcomes. You look

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at the control group. They had worse outcomes.

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Right. If you calculate the naive difference

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in means between the two groups, the drug looks

282
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like a miracle cure. But wait, doesn't that contradict

283
00:13:24,779 --> 00:13:26,799
what we just said? The doctor sorted everyone

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00:13:26,799 --> 00:13:29,080
perfectly. Doesn't that prove the drug works?

285
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It proves the drug works for some, but... It

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00:13:32,720 --> 00:13:34,759
completely ruins your ability to estimate the

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00:13:34,759 --> 00:13:36,960
average causal effect for the whole population.

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Because the groups aren't comparable anymore.

289
00:13:39,639 --> 00:13:42,659
Exactly. By acting with perfect knowledge, the

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00:13:42,659 --> 00:13:45,539
doctor introduced massive, insurmountable selection

291
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bias. The treated group and the control group

292
00:13:48,279 --> 00:13:50,139
are fundamentally different kinds of people.

293
00:13:50,379 --> 00:13:52,360
Because the treatment assignment was perfectly

294
00:13:52,360 --> 00:13:54,620
correlated with the potential outcomes. Yep.

295
00:13:54,720 --> 00:13:57,240
Okay, so contrast that with the clueless doctor.

296
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This doctor doesn't know anything about medicine.

297
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They just flip a coin for every patient. Heads,

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00:14:01,980 --> 00:14:04,240
you get the pill. Tails, you don't. From a medical

299
00:14:04,240 --> 00:14:06,480
ethics standpoint, it's a total nightmare. Sure.

300
00:14:06,659 --> 00:14:09,639
But from an epistemological standpoint, it is

301
00:14:09,639 --> 00:14:13,379
perfection. By assigning the pill randomly, the

302
00:14:13,379 --> 00:14:15,820
assignment mechanism is rendered entirely independent

303
00:14:15,820 --> 00:14:18,960
of the patient's potential outcomes. It's totally

304
00:14:18,960 --> 00:14:22,620
blind. Yes. And as your sample size grows...

305
00:14:22,799 --> 00:14:24,620
The group that gets the pill and the group that

306
00:14:24,620 --> 00:14:27,399
gets the control will become statistically identical

307
00:14:27,399 --> 00:14:30,220
in their baseline characteristics. Both the things

308
00:14:30,220 --> 00:14:32,960
we can measure and, crucially, the things we

309
00:14:32,960 --> 00:14:35,519
cannot measure. So when we take the difference

310
00:14:35,519 --> 00:14:37,879
in means from the clueless doctor's clinic, we

311
00:14:37,879 --> 00:14:40,399
are actually uncovering the true average causal

312
00:14:40,399 --> 00:14:43,580
effect. By stripping away human choice and relying

313
00:14:43,580 --> 00:14:46,600
on random chance, we eliminate the bias. The

314
00:14:46,600 --> 00:14:49,200
clueless doctor is doing superior science. They

315
00:14:49,200 --> 00:14:52,309
really are. And this brings us out of the theoretical

316
00:14:52,309 --> 00:14:54,750
and into the foundational mathematics of part

317
00:14:54,750 --> 00:14:57,070
two of the text, which is all about randomized

318
00:14:57,070 --> 00:15:00,570
experiments. Right. When we formalize the clueless

319
00:15:00,570 --> 00:15:03,450
doctor's coin flip, we are utilizing the bedrock

320
00:15:03,450 --> 00:15:06,830
laid down by R .A. Fisher in his 1935 work, The

321
00:15:06,830 --> 00:15:09,690
Design of Experiments. Let's talk about Fisher's

322
00:15:09,690 --> 00:15:12,370
randomization test, because the text frames randomization

323
00:15:12,370 --> 00:15:15,049
as having this sort of mathematical superpower.

324
00:15:15,509 --> 00:15:19,049
It really is a superpower. A completely randomized

325
00:15:19,049 --> 00:15:22,129
experiment neutralizes unmeasured confounding

326
00:15:22,129 --> 00:15:25,870
by design. Think back to the missing half of

327
00:15:25,870 --> 00:15:29,129
the science table. The unobservable counterfactuals.

328
00:15:29,129 --> 00:15:31,950
Right, because the treatment assignment is independent

329
00:15:31,950 --> 00:15:34,970
of the potential outcomes. The distribution of

330
00:15:34,970 --> 00:15:37,110
any test statistic under the null hypothesis

331
00:15:37,110 --> 00:15:40,470
is completely deterministically dictated by the

332
00:15:40,470 --> 00:15:43,629
randomization mechanism itself. We need to define

333
00:15:43,629 --> 00:15:46,129
Fisher's sharp null hypothesis here because it's

334
00:15:46,129 --> 00:15:49,389
an extreme stance. It isn't just saying the treatment

335
00:15:49,389 --> 00:15:52,250
has no average effect. Oh, no. Fisher's sharp

336
00:15:52,250 --> 00:15:54,870
null hypothesis posits that the treatment has

337
00:15:54,870 --> 00:15:58,190
absolutely zero effect on any individual unit

338
00:15:58,190 --> 00:16:01,610
in the study. For every single person, Y of 1

339
00:16:01,610 --> 00:16:05,929
is exactly equal to Y of 0. So under Fisher's

340
00:16:05,929 --> 00:16:08,429
sharp null, this pill is essentially a sugar

341
00:16:08,429 --> 00:16:10,809
pill for everyone. It literally does nothing.

342
00:16:11,009 --> 00:16:14,730
Yes. And if we assume that it's true, something

343
00:16:14,730 --> 00:16:17,889
mathematically magical happens. We suddenly don't

344
00:16:17,889 --> 00:16:20,590
have any missing data in our science table. Wait,

345
00:16:20,610 --> 00:16:23,190
I'm trying to visualize this. If I know for a

346
00:16:23,190 --> 00:16:26,350
fact that y of 1 equals y of 0 for me... Under

347
00:16:26,350 --> 00:16:28,710
the null hypothesis, yeah. And I observe that

348
00:16:28,710 --> 00:16:30,350
my headache went away after taking the pill,

349
00:16:30,570 --> 00:16:33,190
then I know with absolute certainty that my headache

350
00:16:33,190 --> 00:16:35,570
would have gone away even if I hadn't taken the

351
00:16:35,570 --> 00:16:38,669
pill. Precisely. Under the sharp null, whatever

352
00:16:38,669 --> 00:16:41,070
outcome you observe under your assigned treatment,

353
00:16:41,350 --> 00:16:43,450
is exactly the outcome you would have observed

354
00:16:43,450 --> 00:16:47,049
under the alternative. We can seamlessly impute

355
00:16:47,049 --> 00:16:50,090
the missing counterfactuals. Wow. And once we

356
00:16:50,090 --> 00:16:52,570
have a fully imputed, complete science table,

357
00:16:52,769 --> 00:16:56,289
we can run a permutation test. Okay, let's unpack

358
00:16:56,289 --> 00:16:59,389
the permutation test. Is this basically asking

359
00:16:59,389 --> 00:17:01,929
what are the odds I would see a result this extreme

360
00:17:01,929 --> 00:17:04,269
if the treatment assignment was just random noise,

361
00:17:04,450 --> 00:17:07,430
like shuffling a deck of cards over and over?

362
00:17:07,630 --> 00:17:10,559
I like the card analogy. If I deal out a hand

363
00:17:10,559 --> 00:17:13,279
a thousand times and the hand the dealer originally

364
00:17:13,279 --> 00:17:16,680
gave me is better than 999 of those random shuffles,

365
00:17:16,799 --> 00:17:20,269
I reject the idea that the deck is fair. That's

366
00:17:20,269 --> 00:17:23,089
the exact logic. In the Fisher randomization

367
00:17:23,089 --> 00:17:25,750
test, you take the fully imputed science table

368
00:17:25,750 --> 00:17:28,609
and you computationally reassign the treatments

369
00:17:28,609 --> 00:17:31,470
based on the randomization mechanism thousands

370
00:17:31,470 --> 00:17:34,650
of times. For every permutation, you calculate

371
00:17:34,650 --> 00:17:37,509
the difference in means. This generates an exact

372
00:17:37,509 --> 00:17:40,420
null distribution. If your originally observed

373
00:17:40,420 --> 00:17:43,200
test statistic falls way out in the tail of the

374
00:17:43,200 --> 00:17:46,240
simulated distribution, you reject the sharp

375
00:17:46,240 --> 00:17:49,500
null hypothesis. You have proven that the treatment

376
00:17:49,500 --> 00:17:52,500
did something to someone. But the text draws

377
00:17:52,500 --> 00:17:54,779
a sharp distinction between Fisher's permutation

378
00:17:54,779 --> 00:17:58,220
approach from 1935 and Yersey -Naman's approach

379
00:17:58,220 --> 00:18:01,019
from 1923. What's the fundamental difference

380
00:18:01,019 --> 00:18:04,079
there? What's fascinating here is that they were

381
00:18:04,079 --> 00:18:07,069
solving slightly different problems. Fisher was

382
00:18:07,069 --> 00:18:10,210
the rigorous skeptic asking, is there any effect

383
00:18:10,210 --> 00:18:13,160
at all? Neyman, on the other hand, was focused

384
00:18:13,160 --> 00:18:16,700
on estimation. He wanted a number. He wanted

385
00:18:16,700 --> 00:18:19,539
to know the average causal effect across the

386
00:18:19,539 --> 00:18:22,339
population. So he introduced repeated sampling

387
00:18:22,339 --> 00:18:25,440
inference. Neyman proved that the simple difference

388
00:18:25,440 --> 00:18:28,460
in sample means is an unbiased estimator of the

389
00:18:28,460 --> 00:18:31,480
finite population average causal effect. But

390
00:18:31,480 --> 00:18:33,660
Neyman's math gets tricky when it comes to the

391
00:18:33,660 --> 00:18:36,220
variance, right? The text mentions that Neyman's

392
00:18:36,220 --> 00:18:38,319
estimator for the variance is inherently conservative.

393
00:18:38,599 --> 00:18:40,720
Why is that? I'm really glad you brought that

394
00:18:40,720 --> 00:18:42,980
up because it hits right back at the core of

395
00:18:42,980 --> 00:18:45,779
the missing data problem. To calculate the exact

396
00:18:45,779 --> 00:18:48,779
true variance of the average causal effect, the

397
00:18:48,779 --> 00:18:51,539
mathematical formula requires knowing the covariance

398
00:18:51,539 --> 00:18:55,059
between y of 1 and y of 0 for each individual.

399
00:18:55,420 --> 00:18:57,579
But we can never know that. Because we never

400
00:18:57,579 --> 00:19:00,119
observe y of 1 and y of 0 for the same person.

401
00:19:00,460 --> 00:19:03,579
Exactly. The covariance of counterfactuals is

402
00:19:03,579 --> 00:19:07,130
fundamentally unidentifiable. Neyman recognized

403
00:19:07,130 --> 00:19:10,190
this, so he derived a variance estimator that

404
00:19:10,190 --> 00:19:12,710
essentially assumes a constant additive effect,

405
00:19:12,950 --> 00:19:15,609
which provides an upper bound. So it plays it

406
00:19:15,609 --> 00:19:18,470
safe. Very safe. It is a conservative estimate,

407
00:19:18,670 --> 00:19:21,410
meaning your confidence intervals might be slightly

408
00:19:21,410 --> 00:19:24,230
wider than they theoretically need to be, but

409
00:19:24,230 --> 00:19:26,490
they won't falsely claim precision you don't

410
00:19:26,490 --> 00:19:29,750
actually have. So Fisher proves the drug isn't

411
00:19:29,750 --> 00:19:32,960
a total placebo. And Neyman gives us a safe,

412
00:19:33,039 --> 00:19:35,940
unbiased estimate of how much it helps on average.

413
00:19:36,180 --> 00:19:38,299
Right. And the text also bridges a critical gap

414
00:19:38,299 --> 00:19:40,720
here regarding populations, because Neyman's

415
00:19:40,720 --> 00:19:43,859
original 1923 math was strictly for a finite

416
00:19:43,859 --> 00:19:46,519
population, meaning it only mathematically applied

417
00:19:46,519 --> 00:19:48,700
to the exact people sitting in the room participating

418
00:19:48,700 --> 00:19:50,799
in the trial. Which is pretty limiting because

419
00:19:50,799 --> 00:19:53,980
researchers almost never care only about the

420
00:19:53,980 --> 00:19:56,180
people in the trial. They want to generalize

421
00:19:56,180 --> 00:19:58,660
to a superpopulation. The whole world. Or...

422
00:19:58,859 --> 00:20:01,579
at least a larger demographic. The book demonstrates

423
00:20:01,579 --> 00:20:03,720
that if you treat your experimental units as

424
00:20:03,720 --> 00:20:06,779
a random sample drawn from a broader superpopulation,

425
00:20:07,220 --> 00:20:10,079
Neyman's estimators still hold. The variance

426
00:20:10,079 --> 00:20:12,660
calculations shift to account for the sampling

427
00:20:12,660 --> 00:20:14,519
uncertainty from the superpopulation, but the

428
00:20:14,519 --> 00:20:17,440
core logic remains totally intact. It's really

429
00:20:17,440 --> 00:20:20,279
elegant. Yeah. When we can shuffle the deck,

430
00:20:20,420 --> 00:20:22,940
when we can rely on the clueless doctor to randomize,

431
00:20:23,019 --> 00:20:25,859
the math provides these clear answers. But that

432
00:20:25,859 --> 00:20:28,259
brings us to the threshold of part three of the

433
00:20:28,259 --> 00:20:30,920
book. The messy part. Very messy. The real world

434
00:20:30,920 --> 00:20:32,759
is messy. We can't run randomized controlled

435
00:20:32,759 --> 00:20:35,339
trials for everything. We can't force a random

436
00:20:35,339 --> 00:20:37,599
half of a town to smoke cigarettes for 20 years

437
00:20:37,599 --> 00:20:39,940
to see if they get cancer. Right. Highly unethical.

438
00:20:40,039 --> 00:20:42,039
We can't force people to drop out of high school

439
00:20:42,039 --> 00:20:44,839
to measure the impact on their wages. So when

440
00:20:44,839 --> 00:20:46,599
people self -select their treatments, we are

441
00:20:46,599 --> 00:20:49,339
thrust into the Wild West of observational studies.

442
00:20:49,799 --> 00:20:52,259
And navigating observational studies requires

443
00:20:52,259 --> 00:20:55,109
a completely different mindset. It's anchored

444
00:20:55,109 --> 00:20:57,450
by what the text introduces as Dorn's Question

445
00:20:57,450 --> 00:21:01,210
from 1953, which is, how would the study be conducted

446
00:21:01,210 --> 00:21:04,329
if it were possible to do it by controlled experimentation?

447
00:21:05,119 --> 00:21:07,799
So whenever we are staring at messy, real -world

448
00:21:07,799 --> 00:21:09,900
data, our first conceptual step is to design

449
00:21:09,900 --> 00:21:12,480
the hypothetical perfect experiment we wish we

450
00:21:12,480 --> 00:21:15,819
could have run? Yes. Dorn's Question forces you

451
00:21:15,819 --> 00:21:19,000
to identify the target trial, because in observational

452
00:21:19,000 --> 00:21:21,779
data, you are immediately confronted with selection

453
00:21:21,779 --> 00:21:24,799
bias. As we saw with the Lalonde job training

454
00:21:24,799 --> 00:21:27,480
data, when people choose their own treatment,

455
00:21:27,680 --> 00:21:31,779
the potential outcomes, Y of 1 and Y of 0, are

456
00:21:31,779 --> 00:21:33,779
no longer independent of the treatment assignment.

457
00:21:34,299 --> 00:21:36,779
Right. The people who take the medicine might

458
00:21:36,779 --> 00:21:39,000
be fundamentally sicker than the people who don't.

459
00:21:39,200 --> 00:21:42,380
Exactly. The book defines selection bias mathematically

460
00:21:42,380 --> 00:21:45,420
as the difference between the prima facie causal

461
00:21:45,420 --> 00:21:48,180
effect, which is just the naive difference in

462
00:21:48,180 --> 00:21:50,480
means between the treated and untreated groups,

463
00:21:51,150 --> 00:21:54,410
and the true average causal effect. And to close

464
00:21:54,410 --> 00:21:56,930
that gap, to eliminate that bias without randomization,

465
00:21:57,230 --> 00:22:00,150
causal inference relies on a monumental theoretical

466
00:22:00,150 --> 00:22:03,730
pillar, the ignorability assumption. Frequently

467
00:22:03,730 --> 00:22:06,930
called unconfoundedness. Unconfoundedness, right.

468
00:22:07,130 --> 00:22:10,490
Okay, let's unpack ignorability. It states that

469
00:22:10,490 --> 00:22:13,289
conditional on a set of observed covariates,

470
00:22:13,329 --> 00:22:15,509
which we'll call X, the treatment assignment

471
00:22:15,509 --> 00:22:19,349
is independent of the potential outcomes. Translating

472
00:22:19,349 --> 00:22:22,769
that from mathematical notation to reality, we

473
00:22:22,769 --> 00:22:24,789
are assuming that if we measure enough characteristics

474
00:22:24,789 --> 00:22:28,970
about our subjects, age, gender, income, detailed

475
00:22:28,970 --> 00:22:31,390
medical history, we can essentially recreate

476
00:22:31,390 --> 00:22:34,450
a randomized experiment inside strata of the

477
00:22:34,450 --> 00:22:37,750
data. Inside the subgroups. Right. We are declaring

478
00:22:37,750 --> 00:22:39,849
that if two people have the exact same values

479
00:22:39,849 --> 00:22:43,230
across all measured X variables, the fact that

480
00:22:43,230 --> 00:22:45,029
one received the treatment and the other didn't

481
00:22:45,029 --> 00:22:48,490
is essentially a coin flip. It's random. So what

482
00:22:48,490 --> 00:22:50,829
does this all mean for a researcher? It means

483
00:22:50,829 --> 00:22:53,130
we are taking a massive leap of faith that we

484
00:22:53,130 --> 00:22:54,930
have measured everything that influences both

485
00:22:54,930 --> 00:22:57,069
the choice to take the treatment and the final

486
00:22:57,069 --> 00:22:59,829
outcome. We are assuming there are no invisible

487
00:22:59,829 --> 00:23:02,549
variables, no hidden confounders lurking in the

488
00:23:02,549 --> 00:23:06,029
shadows. It is a profound, untestable leap of

489
00:23:06,029 --> 00:23:08,950
faith. But if you are willing to make that assumption,

490
00:23:09,210 --> 00:23:12,470
the text provides an arsenal of estimation strategies.

491
00:23:12,970 --> 00:23:15,490
What's the most basic one? The most basic is

492
00:23:15,490 --> 00:23:18,349
outcome regression. You simply regress the outcome

493
00:23:18,349 --> 00:23:20,890
on the treatment variable and all your covariates

494
00:23:20,890 --> 00:23:23,609
X. But the text warns that regression relies

495
00:23:23,609 --> 00:23:26,809
on parametric assumptions. It forces the data

496
00:23:26,809 --> 00:23:29,289
into specific shapes, usually assuming linear

497
00:23:29,289 --> 00:23:31,950
relationships. And if the true relationship between,

498
00:23:31,970 --> 00:23:35,710
say, age and income isn't a straight line, your

499
00:23:35,710 --> 00:23:38,109
regression will spit out a biased causal estimate.

500
00:23:38,529 --> 00:23:41,309
Which is why statisticians sought more flexible,

501
00:23:41,470 --> 00:23:44,369
elegant solutions. And this led to a paradigm

502
00:23:44,369 --> 00:23:48,049
shift in 1983 with Rosenbaum and Rubin's introduction

503
00:23:48,049 --> 00:23:51,589
of propensity scores. Oh, man, propensity scores.

504
00:23:51,710 --> 00:23:54,349
Here is a concept that completely dominates modern

505
00:23:54,349 --> 00:23:57,130
research. What exactly is a propensity score?

506
00:23:57,309 --> 00:23:59,950
A propensity score is simply the conditional

507
00:23:59,950 --> 00:24:02,750
probability of receiving the treatment given

508
00:24:02,750 --> 00:24:05,809
your observed covariates. Mathematically, it's

509
00:24:05,809 --> 00:24:09,809
EX equals the probability that T equals 1 given

510
00:24:09,809 --> 00:24:14,450
X. OK. It's real genius lies in dimension reduction.

511
00:24:15,200 --> 00:24:18,460
Right, because if I have 50 different covariates,

512
00:24:18,500 --> 00:24:21,319
exact age, exact income, zip code, blood pressure,

513
00:24:21,400 --> 00:24:24,519
finding two people in my data set who match perfectly

514
00:24:24,519 --> 00:24:27,380
across all 50 dimensions is basically statistically

515
00:24:27,380 --> 00:24:30,619
impossible. It is. It's called the curse of dimensionality.

516
00:24:30,960 --> 00:24:33,799
But Rosenbaum and Rubin proved a vital theorem.

517
00:24:34,099 --> 00:24:36,839
If treatment assignment is strongly ignorable

518
00:24:36,839 --> 00:24:40,039
given the full vector of covariates X, It is

519
00:24:40,039 --> 00:24:42,460
also strongly ignorable given just the scalar

520
00:24:42,460 --> 00:24:45,660
propensity score, EX. So I don't need to match

521
00:24:45,660 --> 00:24:49,339
people on all 50 variables. Exactly. You just

522
00:24:49,339 --> 00:24:52,359
run a model, usually a logistic regression, to

523
00:24:52,359 --> 00:24:54,559
calculate each person's probability of getting

524
00:24:54,559 --> 00:24:57,319
the treatment based on their traits. This collapses

525
00:24:57,319 --> 00:24:59,900
50 dimensions down to a single number between

526
00:24:59,900 --> 00:25:03,970
0 and 1. Wow. So if two people both have a propensity

527
00:25:03,970 --> 00:25:07,509
score of 0 .75, they have the exact same baseline

528
00:25:07,509 --> 00:25:10,210
likelihood of being treated. And once we have

529
00:25:10,210 --> 00:25:12,230
that score, one of the most powerful things we

530
00:25:12,230 --> 00:25:15,470
can do with it is inverse propensity score weighting,

531
00:25:15,470 --> 00:25:18,549
or IPW. Let's really drill down into the mechanics

532
00:25:18,549 --> 00:25:21,849
of IPW because it's brilliant but honestly counterintuitive.

533
00:25:22,109 --> 00:25:26,559
It can be. IPW operates by constructing a pseudopopulation,

534
00:25:26,720 --> 00:25:29,180
where the treatment assignment is no longer confounded

535
00:25:29,180 --> 00:25:32,180
by the covariates. It achieves this by weighting

536
00:25:32,180 --> 00:25:34,859
each individual in your dataset by the inverse

537
00:25:34,859 --> 00:25:36,880
of the probability of receiving the treatment

538
00:25:36,880 --> 00:25:39,710
they actually received. Let me test an analogy

539
00:25:39,710 --> 00:25:42,130
here to see if I'm grasping the math. Go for

540
00:25:42,130 --> 00:25:45,170
it. Let's say we are evaluating a grueling extreme

541
00:25:45,170 --> 00:25:48,569
fitness boot camp. The covariates tell us that

542
00:25:48,569 --> 00:25:51,430
young elite athletes have a 95 % probability

543
00:25:51,430 --> 00:25:54,309
of signing up. Older sedentary individuals have

544
00:25:54,309 --> 00:25:57,450
a 5 % probability of signing up. A classic case

545
00:25:57,450 --> 00:25:59,990
of selection bias. The treated group will be

546
00:25:59,990 --> 00:26:02,650
overwhelmingly young and fit. The control group

547
00:26:02,650 --> 00:26:05,799
will be older and sedentary. So in my data set,

548
00:26:05,859 --> 00:26:08,099
I have hundreds of elite athletes who took the

549
00:26:08,099 --> 00:26:11,140
boot camp, but I only have one sedentary guy

550
00:26:11,140 --> 00:26:13,519
who accidentally wandered in and took it. To

551
00:26:13,519 --> 00:26:15,279
figure out the average effect of this boot camp

552
00:26:15,279 --> 00:26:18,859
for the general population, IPW acts like a massive

553
00:26:18,859 --> 00:26:21,400
mathematical megaphone for the unusual cases.

554
00:26:21,880 --> 00:26:25,519
The athlete's weight is 1 divided by 0 .95, barely

555
00:26:25,519 --> 00:26:28,880
over 1. Their voice is quiet. But the sedentary

556
00:26:28,880 --> 00:26:32,440
guy's weight is 1 divided by 0 .05. He gets a

557
00:26:32,440 --> 00:26:34,809
weight of 20. His single outcome gets amplified

558
00:26:34,809 --> 00:26:37,829
20 times to balance out the population. Does

559
00:26:37,829 --> 00:26:40,670
that track? That is an exceptionally precise

560
00:26:40,670 --> 00:26:44,049
analogy. By upweighting the treated individuals

561
00:26:44,049 --> 00:26:47,430
who were unlikely to be treated, and conversely

562
00:26:47,430 --> 00:26:49,289
upweighting the control individuals who were

563
00:26:49,289 --> 00:26:52,789
unlikely to be controls, IPW perfectly balances

564
00:26:52,789 --> 00:26:55,430
the covariate distribution across the two groups.

565
00:26:55,789 --> 00:26:58,470
It's like magic. You have synthetically generated

566
00:26:58,470 --> 00:27:01,829
the clueless doctor's random coin flip. But wait,

567
00:27:01,910 --> 00:27:04,950
I see a glaring mathematical hazard here. What

568
00:27:04,950 --> 00:27:07,730
if the denominator is practically zero? What

569
00:27:07,730 --> 00:27:10,369
if the propensity score for that sedentary guy

570
00:27:10,369 --> 00:27:15,250
was 0 .001? His weight becomes 1 ,000. Doesn't

571
00:27:15,250 --> 00:27:17,849
that one single data point completely hijack

572
00:27:17,849 --> 00:27:21,299
the entire analysis? Ah, you've just identified

573
00:27:21,299 --> 00:27:25,000
the fatal flaw of IPW. Extreme propensity scores

574
00:27:25,000 --> 00:27:27,700
cause the variance of the estimator to absolutely

575
00:27:27,700 --> 00:27:31,170
explode. If your model for calculating the propensity

576
00:27:31,170 --> 00:27:33,789
score is misspecified, or if you have weights

577
00:27:33,789 --> 00:27:36,529
approaching infinity, your causal estimate becomes

578
00:27:36,529 --> 00:27:40,029
dangerously unstable. So IPW is powerful but

579
00:27:40,029 --> 00:27:43,210
fragile. How do we build a safety net? Well,

580
00:27:43,210 --> 00:27:45,869
the text introduces the pinnacle of these estimation

581
00:27:45,869 --> 00:27:51,069
strategies, doubly robust estimators. These estimators

582
00:27:51,069 --> 00:27:53,869
mathematically synthesize both outcome regression

583
00:27:53,869 --> 00:27:57,009
and inverse propensity score weighting into a

584
00:27:57,009 --> 00:28:00,059
single equation. Doubly robust. It sounds like

585
00:28:00,059 --> 00:28:03,059
wearing a belt and suspenders. It's exactly that.

586
00:28:03,539 --> 00:28:06,220
The mathematical architecture of a doubly robust

587
00:28:06,220 --> 00:28:09,599
estimator is astonishing. It is designed so that

588
00:28:09,599 --> 00:28:12,099
if you get one of your models wrong, let's say

589
00:28:12,099 --> 00:28:14,759
your logistic regression for the propensity score

590
00:28:14,759 --> 00:28:17,960
is completely misspecified, but your outcome

591
00:28:17,960 --> 00:28:20,819
regression model is correct, the estimator still

592
00:28:20,819 --> 00:28:23,140
converges to the true average causal effect.

593
00:28:23,660 --> 00:28:26,880
And vice versa. If my outcome regression assumes

594
00:28:26,880 --> 00:28:29,259
a linear relationship, that is totally wrong,

595
00:28:29,440 --> 00:28:32,059
but my propensity score model correctly captures

596
00:28:32,059 --> 00:28:34,400
the treatment assignment mechanism, it still

597
00:28:34,400 --> 00:28:38,140
works? Yes. It gives you two chances to be right.

598
00:28:38,519 --> 00:28:41,799
The math involves taking the IPW estimator and

599
00:28:41,799 --> 00:28:44,720
adding an augmentation term. If the outcome model

600
00:28:44,720 --> 00:28:48,480
is correct, the IPW error cancels out. If the

601
00:28:48,480 --> 00:28:51,140
propensity model is correct, the expected value

602
00:28:51,140 --> 00:28:53,789
of the augmentation term becomes zero. It is

603
00:28:53,789 --> 00:28:56,329
a brilliant mathematical safety net. The book

604
00:28:56,329 --> 00:28:58,809
also touches on matching algorithms, where you

605
00:28:58,809 --> 00:29:01,289
essentially search the data for statistical twins,

606
00:29:01,450 --> 00:29:04,069
and modern approaches using machine learning,

607
00:29:04,190 --> 00:29:06,730
like Bayesian additive regression trees, BART,

608
00:29:06,829 --> 00:29:09,230
or causal forests developed by researchers like

609
00:29:09,230 --> 00:29:12,009
Wager and Athe. Right, moving past standard regression.

610
00:29:12,349 --> 00:29:14,250
They use machine learning to calculate these

611
00:29:14,250 --> 00:29:16,869
conditional expectations without relying on rigid

612
00:29:16,869 --> 00:29:19,640
parametric formulas. Machine learning is incredibly

613
00:29:19,640 --> 00:29:22,299
effective at identifying nonlinear relationships

614
00:29:22,299 --> 00:29:25,779
and complex interactions between covariates that

615
00:29:25,779 --> 00:29:28,160
a human researcher would never ever think to

616
00:29:28,160 --> 00:29:30,619
specify in a standard regression model. But,

617
00:29:30,619 --> 00:29:34,619
and this is a massive neon flashing but, whether

618
00:29:34,619 --> 00:29:37,180
we are using basic regression, the megaphone

619
00:29:37,180 --> 00:29:40,140
of IPW, the belt and suspenders of doubly robust

620
00:29:40,140 --> 00:29:42,920
estimators, or the most advanced machine learning

621
00:29:42,920 --> 00:29:46,529
AI, every single one of them still fundamentally

622
00:29:46,529 --> 00:29:50,269
relies on the ignorability assumption. Yes, all

623
00:29:50,269 --> 00:29:52,470
the mathematical gymnastics in the world cannot

624
00:29:52,470 --> 00:29:55,549
save you if you fail to measure a critical compounder.

625
00:29:55,630 --> 00:29:58,109
Which hurls us into part four of the book, when

626
00:29:58,109 --> 00:30:01,430
ignorability fails. Chapters 16 through 20, because

627
00:30:01,430 --> 00:30:04,089
let's be honest, we can never definitively prove

628
00:30:04,089 --> 00:30:05,950
we've measured everything. There could always

629
00:30:05,950 --> 00:30:08,230
be a ghost in the machine. And acknowledging

630
00:30:08,230 --> 00:30:10,869
that ghost is the hallmark of rigorous science.

631
00:30:11,500 --> 00:30:14,740
To navigate this, the text introduces Judea Pearl's

632
00:30:14,740 --> 00:30:18,579
directed acyclic graphs, or DAGs. DAGs. For those

633
00:30:18,579 --> 00:30:20,819
who haven't used them, these are visual models.

634
00:30:20,920 --> 00:30:23,759
You draw nodes representing your variables and

635
00:30:23,759 --> 00:30:26,799
draw arrows representing causal pathways. They

636
00:30:26,799 --> 00:30:29,160
are visual, but they are underpinned by rigorous

637
00:30:29,160 --> 00:30:31,720
rules of conditional independence, specifically

638
00:30:31,720 --> 00:30:35,339
a concept called de -separation. DAGs are crucial

639
00:30:35,339 --> 00:30:37,119
because they prevent researchers from making

640
00:30:37,119 --> 00:30:41,220
a very common, very dangerous mistake. over -adjustment.

641
00:30:41,339 --> 00:30:44,160
I think the instinct for most people doing data

642
00:30:44,160 --> 00:30:47,440
analysis is, I have this massive data set with

643
00:30:47,440 --> 00:30:49,819
100 variables. I'm just going to throw every

644
00:30:49,819 --> 00:30:51,900
single one of them into my regression model as

645
00:30:51,900 --> 00:30:54,380
a control variable just to be safe. That is the

646
00:30:54,380 --> 00:30:57,480
kitchen sink approach. And DAGs prove mathematically

647
00:30:57,480 --> 00:31:00,859
why it is disastrous. The text highlights two

648
00:31:00,859 --> 00:31:03,079
specific structures that will ruin your analysis

649
00:31:03,079 --> 00:31:06,559
if you blindly control for them, M -bias and

650
00:31:06,559 --> 00:31:09,210
Z -bias. I really want to spend time on this

651
00:31:09,210 --> 00:31:11,990
because it's counterintuitive. Let's start with

652
00:31:11,990 --> 00:31:15,130
M bias. How does controlling for a variable actually

653
00:31:15,130 --> 00:31:18,690
create bias? Imagine a DAG shaped like the letter

654
00:31:18,690 --> 00:31:21,150
M. You have your treatment on the bottom left,

655
00:31:21,250 --> 00:31:24,130
your outcome on the bottom right. Now imagine

656
00:31:24,130 --> 00:31:26,710
two unmeasured hidden confounders at the top

657
00:31:26,710 --> 00:31:29,450
points of the M. And in the bottom middle, you

658
00:31:29,450 --> 00:31:32,609
have a measured variable, M. Okay, holding that

659
00:31:32,609 --> 00:31:35,430
shape in my head. The first hidden confounder

660
00:31:35,430 --> 00:31:38,269
causes both the treatment... and variable M.

661
00:31:38,490 --> 00:31:41,670
The second hidden confounder causes both the

662
00:31:41,670 --> 00:31:45,329
outcome and variable M. Crucially, the treatment

663
00:31:45,329 --> 00:31:48,769
does not cause M, and M does not cause the outcome.

664
00:31:49,230 --> 00:31:52,509
M is what we call a collider variable. It is

665
00:31:52,509 --> 00:31:54,829
an effect of two separate independent causes.

666
00:31:55,210 --> 00:31:57,829
So because the treatment doesn't cause the outcome

667
00:31:57,829 --> 00:32:01,369
through M, and M is in a traditional confounder,

668
00:32:01,490 --> 00:32:04,269
what happens if I decide to include M in my regression

669
00:32:04,269 --> 00:32:07,670
model? If you condition on a collider, You open

670
00:32:07,670 --> 00:32:10,769
a spurious path. In the raw data, the treatment

671
00:32:10,769 --> 00:32:13,430
and the outcome are not confounded through this

672
00:32:13,430 --> 00:32:16,910
M pathway. But the moment you control for M,

673
00:32:17,049 --> 00:32:19,369
you mathematically induce a correlation between

674
00:32:19,369 --> 00:32:22,410
the two hidden confounders, which suddenly opens

675
00:32:22,410 --> 00:32:24,930
a backdoor path from the treatment to the outcome.

676
00:32:25,250 --> 00:32:29,210
Wow. By trying to be safe and controlling for

677
00:32:29,210 --> 00:32:32,569
M, you literally injected bias into your estimate

678
00:32:32,569 --> 00:32:35,529
that wasn't there to begin with. That is terrifying.

679
00:32:35,750 --> 00:32:37,410
It's like trying to put out a small grease fire

680
00:32:37,410 --> 00:32:39,069
by throwing a bucket of water on it. You just

681
00:32:39,069 --> 00:32:42,630
spread the flames. And what about Z -bias? Z

682
00:32:42,630 --> 00:32:45,069
-bias occurs when you improperly control for

683
00:32:45,069 --> 00:32:47,789
an instrumental variable, a variable that strongly

684
00:32:47,789 --> 00:32:50,470
predicts the treatment but has no direct effect

685
00:32:50,470 --> 00:32:53,769
on the outcome. Including it in an outcome regression

686
00:32:53,769 --> 00:32:56,609
doesn't necessarily introduce confounding, like

687
00:32:56,609 --> 00:32:59,869
M -bias, but it can severely inflate the variance

688
00:32:59,869 --> 00:33:03,019
of your estimate. and actually amplify any residual

689
00:33:03,019 --> 00:33:05,299
confounding that you've failed to measure. The

690
00:33:05,299 --> 00:33:07,500
overarching lesson of DAGs is that you must think

691
00:33:07,500 --> 00:33:09,599
deeply about the causal mechanics generating

692
00:33:09,599 --> 00:33:11,839
your data before you ever touch a regression

693
00:33:11,839 --> 00:33:15,200
formula. But even with perfect DAGs, the ultimate

694
00:33:15,200 --> 00:33:18,220
threat is the unmeasured confounder, the ghost.

695
00:33:18,339 --> 00:33:20,880
The ghost in the machine. And the book grounds

696
00:33:20,880 --> 00:33:23,859
this in a legendary historical debate. R .A.

697
00:33:23,880 --> 00:33:26,799
Fisher's 1957 critique of the link between smoking

698
00:33:26,799 --> 00:33:30,099
and lung cancer. This is one of the most... instructive

699
00:33:30,099 --> 00:33:33,279
episodes in the history of statistics. By the

700
00:33:33,279 --> 00:33:36,019
late 1950s, observational studies were showing

701
00:33:36,019 --> 00:33:38,480
a massive association between smoking and lung

702
00:33:38,480 --> 00:33:41,220
cancer. The medical community was ready to declare

703
00:33:41,220 --> 00:33:43,900
causation. Ready to close the book on it. But

704
00:33:43,900 --> 00:33:46,559
Fisher, the genius who invented the randomization

705
00:33:46,559 --> 00:33:49,160
test we discussed earlier, stepped in and said,

706
00:33:49,259 --> 00:33:53,059
not so fast. Fisher basically played the ultimate

707
00:33:53,059 --> 00:33:55,619
devil's advocate. He pointed out that we didn't

708
00:33:55,619 --> 00:33:58,019
randomize who smoked. People self -selected.

709
00:33:58,140 --> 00:34:01,329
So, He hypothesized a ghost. What if there is

710
00:34:01,329 --> 00:34:04,869
a hidden, unmeasured genetic mutation, a gene

711
00:34:04,869 --> 00:34:08,110
that simultaneously makes a person crave nicotine

712
00:34:08,110 --> 00:34:11,110
and makes them highly susceptible to lung cancer?

713
00:34:11,349 --> 00:34:14,650
If that common cause gene exists, Fisher argued,

714
00:34:14,809 --> 00:34:17,409
then the entire association between smoking and

715
00:34:17,409 --> 00:34:20,510
cancer is spurious. Smoking doesn't cause cancer.

716
00:34:20,670 --> 00:34:24,019
The gene causes both. Which, I mean, sounds like

717
00:34:24,019 --> 00:34:26,179
corporate propaganda today, but from a strict

718
00:34:26,179 --> 00:34:29,219
causal inference standpoint, Fisher was mathematically

719
00:34:29,219 --> 00:34:32,199
justified in raising the objection. He pointed

720
00:34:32,199 --> 00:34:34,400
directly at the weakness of the ignorability

721
00:34:34,400 --> 00:34:38,099
assumption. So how did the field defeat Fisher's

722
00:34:38,099 --> 00:34:40,099
argument if they couldn't find the gene? They

723
00:34:40,099 --> 00:34:43,179
defeated him with math, specifically Jerome Kornfield

724
00:34:43,179 --> 00:34:46,519
in 1959. Kornfield didn't run a new biological

725
00:34:46,519 --> 00:34:49,579
study. He pioneered what we now call sensitivity

726
00:34:49,579 --> 00:34:52,630
analysis. He essentially said, Okay, Fisher,

727
00:34:52,769 --> 00:34:56,170
let's assume your hypothetical gene exists. How

728
00:34:56,170 --> 00:34:58,730
powerful would that gene have to be to completely

729
00:34:58,730 --> 00:35:01,269
explain away the massive association we observe

730
00:35:01,269 --> 00:35:03,610
in the data? And the data showed that smokers

731
00:35:03,610 --> 00:35:05,889
were roughly nine times more likely to develop

732
00:35:05,889 --> 00:35:09,030
lung cancer than nonsmokers. Exactly. Kornfield

733
00:35:09,030 --> 00:35:11,429
proved mathematically that for an unmeasured

734
00:35:11,429 --> 00:35:14,429
confounder to entirely explain away a nine -fold

735
00:35:14,429 --> 00:35:17,289
increase in risk, that hidden confounder itself

736
00:35:17,289 --> 00:35:20,349
would have to be at least nine times more prevalent

737
00:35:20,349 --> 00:35:22,469
in the smoking group than in the non -smoking

738
00:35:22,469 --> 00:35:25,769
group. So if smoking increases cancer risk nine

739
00:35:25,769 --> 00:35:28,570
times, this invisible cancer gene would have

740
00:35:28,570 --> 00:35:31,309
to be incredibly, almost impossibly concentrated

741
00:35:31,309 --> 00:35:34,309
specifically among people who chose to smoke.

742
00:35:34,550 --> 00:35:37,809
Yes. Kornfield's inequality demonstrated that

743
00:35:37,809 --> 00:35:40,829
while Fisher's hypothesis was technically possible

744
00:35:40,829 --> 00:35:45,119
under the math, it was biologically absurd. A

745
00:35:45,119 --> 00:35:47,179
genetic factor that perfectly segregated itself

746
00:35:47,179 --> 00:35:51,320
among smokers at a 9 to 1 ratio defied all understanding

747
00:35:51,320 --> 00:35:54,320
of genetics. Kornfield shifted the burden of

748
00:35:54,320 --> 00:35:56,800
proof. And the text details how this historical

749
00:35:56,800 --> 00:35:59,420
concept was recently generalized by Vanderweel

750
00:35:59,420 --> 00:36:02,199
and the author, Peng Ding, into a modern metric

751
00:36:02,199 --> 00:36:05,400
called the E -value. The E -value is a formal

752
00:36:05,400 --> 00:36:08,760
quantification of Kornfield's logic. It calculates

753
00:36:08,760 --> 00:36:11,719
the minimum strength of association that an unmeasured

754
00:36:11,719 --> 00:36:13,960
confounder would need to have with both the treatment,

755
00:36:14,300 --> 00:36:17,059
and the outcome to fully explain away your observed

756
00:36:17,059 --> 00:36:19,960
causal effect. So if we connect this to the bigger

757
00:36:19,960 --> 00:36:22,760
picture, the E -value is essentially a mathematically

758
00:36:22,760 --> 00:36:26,780
rigorous BS detector. Well, I wouldn't use those

759
00:36:26,780 --> 00:36:29,559
terms in a peer -reviewed paper, but conceptually,

760
00:36:29,559 --> 00:36:33,199
yes. It changes the nature of peer review. Instead

761
00:36:33,199 --> 00:36:35,780
of a critic saying, you might have unmeasured

762
00:36:35,780 --> 00:36:38,380
confounding, which is a lazy critique because

763
00:36:38,380 --> 00:36:41,139
the answer is always yes, the researcher can

764
00:36:41,139 --> 00:36:44,130
publish their E -value and say, Yes, there might

765
00:36:44,130 --> 00:36:47,030
be a hidden confounder, but my e -value is 15.

766
00:36:47,570 --> 00:36:50,030
Your hypothetical confounder would have to increase

767
00:36:50,030 --> 00:36:53,190
the likelihood of treatment 15 times and increase

768
00:36:53,190 --> 00:36:56,710
the outcome 15 times, beyond all the covariates

769
00:36:56,710 --> 00:36:59,440
I already controlled for. Does such a variable

770
00:36:59,440 --> 00:37:02,599
exist in reality? It grounds theoretical skepticism

771
00:37:02,599 --> 00:37:05,780
in numerical reality. Now, what happens when

772
00:37:05,780 --> 00:37:08,219
the assumptions fail, not because of hidden variables,

773
00:37:08,420 --> 00:37:10,599
but because of the structure of the treatment

774
00:37:10,599 --> 00:37:13,579
assignment itself? What if the overlap assumption

775
00:37:13,579 --> 00:37:18,300
fails entirely? Ah, overlap, or positivity, assumes

776
00:37:18,300 --> 00:37:21,619
that every individual has at least some non -zero

777
00:37:21,619 --> 00:37:23,880
probability of receiving either the treatment

778
00:37:23,880 --> 00:37:27,099
or the control, meaning the probability is strictly

779
00:37:27,099 --> 00:37:30,920
between 0 and 1. But in many policy settings,

780
00:37:31,079 --> 00:37:33,659
treatment is determined by a strict deterministic

781
00:37:33,659 --> 00:37:36,780
cutoff. The text dedicates Chapter 20 to this

782
00:37:36,780 --> 00:37:40,480
exact scenario, regression discontinuity. Let's

783
00:37:40,480 --> 00:37:43,019
paint the picture. Imagine a university scholarship

784
00:37:43,019 --> 00:37:45,400
that is automatically awarded to any student

785
00:37:45,400 --> 00:37:47,739
who scores an 80 or above on a standardized test.

786
00:37:47,940 --> 00:37:51,659
If you score 79 .9, you get nothing. In this

787
00:37:51,659 --> 00:37:54,880
scenario, overlap is completely violated. The

788
00:37:54,880 --> 00:37:57,099
probability of treatment for someone with a 75

789
00:37:57,099 --> 00:38:02,500
is 0%. For someone with an 85, it's 100%. You

790
00:38:02,500 --> 00:38:05,219
cannot use propensity score weighting. You cannot

791
00:38:05,219 --> 00:38:08,039
do standard matching because there are no untreated

792
00:38:08,039 --> 00:38:11,269
students with an 85 to compare to. It seems like

793
00:38:11,269 --> 00:38:14,230
a dead end, but economists realize the strict

794
00:38:14,230 --> 00:38:16,489
rule is actually hiding a secret experiment.

795
00:38:16,750 --> 00:38:19,429
Yes. We look at the forcing variable, the test

796
00:38:19,429 --> 00:38:22,489
score, and we zoom in microscopically on the

797
00:38:22,489 --> 00:38:25,130
threshold. The fundamental assumption of regression

798
00:38:25,130 --> 00:38:27,909
discontinuity is that potential outcomes are

799
00:38:27,909 --> 00:38:31,349
continuous at the cutoff. We assume that the

800
00:38:31,349 --> 00:38:34,630
student who scored a 79 .9 and the student who

801
00:38:34,630 --> 00:38:38,400
scored an 80 .1 are... on average identical in

802
00:38:38,400 --> 00:38:41,159
their unmeasured traits their motivation and

803
00:38:41,159 --> 00:38:44,099
their background the only reason one got an 80

804
00:38:44,099 --> 00:38:47,780
.1 and the other got 79 .9 was just random noise

805
00:38:47,780 --> 00:38:50,340
a lucky guess on a multiple choice question a

806
00:38:50,340 --> 00:38:54,019
momentary distraction exactly right at that invisible

807
00:38:54,019 --> 00:38:56,860
boundary line nature has artificially generated

808
00:38:56,860 --> 00:39:00,260
a randomized experiment for us by comparing the

809
00:39:00,260 --> 00:39:02,739
outcomes of the students just barely above the

810
00:39:02,739 --> 00:39:06,199
line to those just barely below, we can estimate

811
00:39:06,199 --> 00:39:09,159
the causal effect of the scholarship. But I imagine

812
00:39:09,159 --> 00:39:11,420
the caveat here is that we are only estimating

813
00:39:11,420 --> 00:39:13,719
the effect for those specific boundary students,

814
00:39:13,900 --> 00:39:15,920
right? We aren't estimating the effect of the

815
00:39:15,920 --> 00:39:18,780
scholarship for the kid who scored up 40. You've

816
00:39:18,780 --> 00:39:22,019
hit on a critical limitation. Regression discontinuity

817
00:39:22,019 --> 00:39:26,280
yields a local average treatment effect, or LATE.

818
00:39:27,099 --> 00:39:30,280
It is internally highly valid, but externally

819
00:39:30,280 --> 00:39:32,829
limited. Furthermore, it assumes researchers

820
00:39:32,829 --> 00:39:36,210
are dealing with a sharp discontinuity. If the

821
00:39:36,210 --> 00:39:39,190
cutoff can be manipulated, say, students near

822
00:39:39,190 --> 00:39:41,429
the boundary lobby the teachers for an extra

823
00:39:41,429 --> 00:39:44,130
fraction of a point, the random noise assumption

824
00:39:44,130 --> 00:39:47,269
breaks, and you have to use more complex, fuzzy

825
00:39:47,269 --> 00:39:50,719
RD models. Regression discontinuity is an incredible

826
00:39:50,719 --> 00:39:53,460
hack for finding causality in arbitrary rules.

827
00:39:53,780 --> 00:39:56,860
But what if we are dealing with messy observational

828
00:39:56,860 --> 00:39:59,420
data where there is no clean threshold and we

829
00:39:59,420 --> 00:40:02,139
know we have unmeasured confounders? This brings

830
00:40:02,139 --> 00:40:04,760
us to section six of our deep dive, instrumental

831
00:40:04,760 --> 00:40:08,239
variables. This is the absolute hallmark of econometric

832
00:40:08,239 --> 00:40:11,760
methodology covered in chapters 21 and 23. If

833
00:40:11,760 --> 00:40:14,519
DAGs and propensity scores are about measuring

834
00:40:14,519 --> 00:40:18,320
everything, instrumental variables, or IV, is

835
00:40:18,320 --> 00:40:20,599
a strategy for when you accept that you can't

836
00:40:20,599 --> 00:40:22,960
measure everything. It's a completely different

837
00:40:22,960 --> 00:40:25,679
paradigm. At the center of this paradigm is the

838
00:40:25,679 --> 00:40:28,219
instrument itself. Let's call it variable Z.

839
00:40:28,599 --> 00:40:31,659
The text requires an instrument to meet two strict

840
00:40:31,659 --> 00:40:35,059
criteria. First, relevance. The instrument Z

841
00:40:35,059 --> 00:40:37,780
must actually affect whether you take the treatment

842
00:40:37,780 --> 00:40:41,909
D. Second, the exclusion restriction. The instrument

843
00:40:41,909 --> 00:40:45,630
Z must have absolutely zero direct causal effect

844
00:40:45,630 --> 00:40:49,030
on the outcome Y, except through its effect on

845
00:40:49,030 --> 00:40:51,489
the treatment. The exclusion restriction is a

846
00:40:51,489 --> 00:40:54,389
massive assumption. The instrument must be perfectly

847
00:40:54,389 --> 00:40:57,349
unconfounded with the outcome. To really understand

848
00:40:57,349 --> 00:40:59,329
how this math works, the book transitions from

849
00:40:59,329 --> 00:41:01,829
pure observational data back to randomized experiments,

850
00:41:02,210 --> 00:41:05,289
specifically focusing on Chapter 21, noncompliance,

851
00:41:05,429 --> 00:41:08,050
because human beings ruin perfect experiments.

852
00:41:08,469 --> 00:41:11,199
They really do. In a textbook randomized controlled

853
00:41:11,199 --> 00:41:13,940
trial, you assign someone to take a drug and

854
00:41:13,940 --> 00:41:18,260
they take it. In reality, you suffer from noncompliance.

855
00:41:18,559 --> 00:41:20,780
Some people assigned to the treatment group experience

856
00:41:20,780 --> 00:41:24,119
side effects and stop taking the pill. Some people

857
00:41:24,119 --> 00:41:25,960
assigned to the control group get desperate,

858
00:41:26,159 --> 00:41:28,739
go to another doctor and secure the drug anyway.

859
00:41:29,440 --> 00:41:32,079
So the treatment assigned by the researcher is

860
00:41:32,079 --> 00:41:33,920
no longer the treatment received by the patient.

861
00:41:33,960 --> 00:41:36,980
We have a divergence. And this divergence forces

862
00:41:36,980 --> 00:41:39,260
us to define what we are actually measuring.

863
00:41:39,849 --> 00:41:42,510
The most basic metric is the intention -to -treat

864
00:41:42,510 --> 00:41:46,429
effect, or ITT. The ITT is essentially the causal

865
00:41:46,429 --> 00:41:48,789
effect of the prescription, right? We just compare

866
00:41:48,789 --> 00:41:51,010
the average outcome of everyone we told to take

867
00:41:51,010 --> 00:41:53,610
the drug against everyone we told not to, ignoring

868
00:41:53,610 --> 00:41:55,809
what they actually put in their bodies. Yes.

869
00:41:56,239 --> 00:41:59,519
The ITT is mathematically pure because it relies

870
00:41:59,519 --> 00:42:02,960
solely on the original randomization. It's unbiased.

871
00:42:03,300 --> 00:42:07,039
But scientifically, it's often unsatisfying.

872
00:42:07,469 --> 00:42:09,889
A biological researcher doesn't care about the

873
00:42:09,889 --> 00:42:12,590
effect of a doctor's advice. They want to know

874
00:42:12,590 --> 00:42:15,070
the physiological effect of the molecule on the

875
00:42:15,070 --> 00:42:17,590
human body. But we can't just compare the people

876
00:42:17,590 --> 00:42:19,449
who actually swallowed the pill to the people

877
00:42:19,449 --> 00:42:21,949
who didn't because of selection bias. The people

878
00:42:21,949 --> 00:42:24,070
who complied and took the pill might be fundamentally

879
00:42:24,070 --> 00:42:26,070
more health conscious than the people who ignored

880
00:42:26,070 --> 00:42:28,769
the doctor. Exactly. If you just look at the

881
00:42:28,769 --> 00:42:31,670
treatment received, you are back in the murky

882
00:42:31,670 --> 00:42:34,920
waters of confounded observational data. This

883
00:42:34,920 --> 00:42:37,500
conundrum was elegantly solved by the Nobel Prize

884
00:42:37,500 --> 00:42:40,000
-winning framework developed by Angrist, Invens,

885
00:42:40,139 --> 00:42:42,980
and Rubin. They showed how to use the randomized

886
00:42:42,980 --> 00:42:45,639
assignment itself as an instrumental variable.

887
00:42:46,199 --> 00:42:48,880
Okay, let's walk through this carefully. The

888
00:42:48,880 --> 00:42:50,820
random assignment, the doctor's prescription,

889
00:42:51,039 --> 00:42:54,460
is our instrument, Z. It is relevant because

890
00:42:54,460 --> 00:42:57,320
telling someone to take a pill definitely influences

891
00:42:57,320 --> 00:43:00,170
whether they take it. And it meets the exclusion

892
00:43:00,170 --> 00:43:02,750
restriction because merely hearing the words,

893
00:43:02,869 --> 00:43:05,449
take this pill, does not magically cure a disease.

894
00:43:05,570 --> 00:43:08,469
It only works if you swallow the pill. Perfect.

895
00:43:09,070 --> 00:43:12,190
To deploy the math, Angerist, Imbens, and Rubin

896
00:43:12,190 --> 00:43:14,750
conceptually divided the population into four

897
00:43:14,750 --> 00:43:17,489
latent strata based on how they respond to the

898
00:43:17,489 --> 00:43:19,849
instrument. It was before compliance groups.

899
00:43:20,670 --> 00:43:23,369
First, the compliers. These are the rule followers.

900
00:43:23,610 --> 00:43:25,949
If assigned the pill, they take it. If assigned

901
00:43:25,949 --> 00:43:29,510
the control, they don't. Second, the always takers.

902
00:43:29,530 --> 00:43:31,570
They will take the pill no matter what group

903
00:43:31,570 --> 00:43:34,989
they are put in. Third, the never takers. They

904
00:43:34,989 --> 00:43:38,230
refuse the pill even if assigned to it. And fourth,

905
00:43:38,369 --> 00:43:41,010
the defiers. They do the exact opposite of whatever

906
00:43:41,010 --> 00:43:44,309
you tell them. Trolls, basically. We typically

907
00:43:44,309 --> 00:43:47,150
invoke an assumption called monotonicity, which

908
00:43:47,150 --> 00:43:50,210
posits that there are no defiers. We assume the

909
00:43:50,210 --> 00:43:52,309
instrument only pushes people in one direction.

910
00:43:52,610 --> 00:43:55,690
So we are left with compliers, always takers,

911
00:43:55,690 --> 00:43:58,769
and never takers. Here is where the math feels

912
00:43:58,769 --> 00:44:00,949
like magic. We want the causal effect of the

913
00:44:00,949 --> 00:44:04,269
pill. The text explains that the IV method isolates

914
00:44:04,269 --> 00:44:08,130
the complier average causal effect, CACE, also

915
00:44:08,130 --> 00:44:10,190
known as the local average treatment effect,

916
00:44:10,369 --> 00:44:14,210
or LATE. Let's trace the logic. We observe the

917
00:44:14,210 --> 00:44:17,010
overall ITT, the effect of the assignment on

918
00:44:17,010 --> 00:44:19,769
the outcome. But we know the assignment had zero

919
00:44:19,769 --> 00:44:22,869
effect on the always takers. Why? Because they

920
00:44:22,869 --> 00:44:25,090
were going to take the pill regardless. The assignment

921
00:44:25,090 --> 00:44:27,849
didn't change their behavior, so... It couldn't

922
00:44:27,849 --> 00:44:30,110
have changed their outcome. And the exact same

923
00:44:30,110 --> 00:44:32,570
logic applies to the never -takers. The assignment

924
00:44:32,570 --> 00:44:34,750
didn't change their behavior either. They refused

925
00:44:34,750 --> 00:44:37,869
the pill in both alternate realities. Therefore,

926
00:44:38,070 --> 00:44:40,909
100 % of the difference in outcomes we observe

927
00:44:40,909 --> 00:44:43,809
in the overall ITT is being driven exclusively

928
00:44:43,809 --> 00:44:46,929
by the compliers, the only group whose behavior

929
00:44:46,929 --> 00:44:49,550
was actually manipulated by the instrument. I

930
00:44:49,550 --> 00:44:51,309
want to use an analogy here to make the math

931
00:44:51,309 --> 00:44:53,809
concrete. Let's say I want to study the causal

932
00:44:53,809 --> 00:44:56,389
effect of exercising at a specific gym on weight

933
00:44:56,389 --> 00:44:59,170
loss. But gym attendance is horribly confounded

934
00:44:59,170 --> 00:45:01,530
by personal motivation. Highly motivated people

935
00:45:01,530 --> 00:45:03,909
go to the gym and lose weight. If I just run

936
00:45:03,909 --> 00:45:07,429
a regression, motivation acts as a massive, unmeasured

937
00:45:07,429 --> 00:45:11,050
confounder. Right. So I need an instrument. I

938
00:45:11,050 --> 00:45:14,329
randomly mail a massive 50 % off coupon to Half

939
00:45:14,329 --> 00:45:16,610
the Tone. The coupon is randomly assigned so

940
00:45:16,610 --> 00:45:19,630
it's unconfounded. Now I look at my data. The

941
00:45:19,630 --> 00:45:21,650
ITT is the difference in weight loss between

942
00:45:21,650 --> 00:45:23,429
the people who received the coupon in the mail

943
00:45:23,429 --> 00:45:26,550
and those who didn't. But the ITT just measures

944
00:45:26,550 --> 00:45:29,409
the effect of receiving a piece of mail. Exactly.

945
00:45:29,789 --> 00:45:32,590
To find the late, the actual effect of going

946
00:45:32,590 --> 00:45:35,550
to the gym, I take that ITT and I divide it by

947
00:45:35,550 --> 00:45:37,710
the proportion of people who are actually influenced

948
00:45:37,710 --> 00:45:40,309
by the coupon. I divide by the compliance rate.

949
00:45:40,570 --> 00:45:43,110
Because the always -takers were already going.

950
00:45:43,389 --> 00:45:45,789
Right. The always -takers were already going

951
00:45:45,789 --> 00:45:47,929
to the gym at full price. The coupon didn't change

952
00:45:47,929 --> 00:45:50,179
their behavior. The never -takers aren't leaving

953
00:45:50,179 --> 00:45:52,519
their couch even with a discount. The IV math

954
00:45:52,519 --> 00:45:54,940
essentially strips away the always -takers and

955
00:45:54,940 --> 00:45:57,119
never -takers and calculates the exact causal

956
00:45:57,119 --> 00:45:59,559
effect of the gym specifically for the people

957
00:45:59,559 --> 00:46:02,420
who went only because they got the coupon. That

958
00:46:02,420 --> 00:46:04,920
is exactly how the Wald Estimator functions mathematically.

959
00:46:05,659 --> 00:46:09,400
Late is the ITT of the outcome divided by the

960
00:46:09,400 --> 00:46:12,179
ITT of the treatment. But this raises an important

961
00:46:12,179 --> 00:46:15,099
question. It's a profound admission of limits.

962
00:46:15,199 --> 00:46:17,840
We are admitting that we can never know the average

963
00:46:17,840 --> 00:46:20,539
causal effect of the gym for the always takers.

964
00:46:20,579 --> 00:46:22,920
We can never know it for the never takers. We

965
00:46:22,920 --> 00:46:25,739
can only know it for this invisible subgroup

966
00:46:25,739 --> 00:46:29,539
of compliers. Yes, and that is a massive paradigm

967
00:46:29,539 --> 00:46:32,960
shift in statistics. It forces researchers to

968
00:46:32,960 --> 00:46:35,579
be incredibly specific about who their data is

969
00:46:35,579 --> 00:46:38,480
actually speaking for. You cannot generalize

970
00:46:38,480 --> 00:46:41,760
a late estimate. to the entire population, unless

971
00:46:41,760 --> 00:46:44,619
you make incredibly strong, usually unjustifiable

972
00:46:44,619 --> 00:46:48,579
assumptions. IV is a scalpel. It cuts precisely,

973
00:46:48,820 --> 00:46:51,980
but it only cuts a very small area. Instrumental

974
00:46:51,980 --> 00:46:54,539
variables elegantly handle the messiness that

975
00:46:54,539 --> 00:46:57,199
happens before the treatment is taken, the noncompliance,

976
00:46:57,199 --> 00:46:59,719
the self -selection. But as we move into the

977
00:46:59,719 --> 00:47:01,900
final leg of our journey, part six of the book,

978
00:47:01,980 --> 00:47:05,219
chapters 26 through 29, we encounter a totally

979
00:47:05,219 --> 00:47:07,900
different type of messiness. What happens when

980
00:47:07,900 --> 00:47:10,429
the complications occur? after the treatment

981
00:47:10,429 --> 00:47:13,269
is administered. We are entering the domain of

982
00:47:13,269 --> 00:47:16,269
post -treatment traps. This is where causal inference

983
00:47:16,269 --> 00:47:19,150
ceases to be just mathematics and bumps hard

984
00:47:19,150 --> 00:47:21,989
against the metaphysical limits of science. We

985
00:47:21,989 --> 00:47:24,130
are dealing with principal stratification and

986
00:47:24,130 --> 00:47:26,949
mediation analysis. Let's define the scenario.

987
00:47:27,250 --> 00:47:30,010
You administer a treatment. That treatment affects

988
00:47:30,010 --> 00:47:32,889
a mediator variable, and that mediator variable

989
00:47:32,889 --> 00:47:35,650
subsequently affects the final outcome. A classic

990
00:47:35,650 --> 00:47:38,530
example, a doctor prescribes a new diet, the

991
00:47:38,530 --> 00:47:41,179
treatment. The diet lowers the patient's cholesterol,

992
00:47:41,380 --> 00:47:44,659
the mediator. The lower cholesterol reduces the

993
00:47:44,659 --> 00:47:47,619
risk of a heart attack, the outcome. Clinically,

994
00:47:47,699 --> 00:47:49,500
we want to know the mechanics of the treatment.

995
00:47:49,840 --> 00:47:52,500
Does the diet work exclusively because it lowers

996
00:47:52,500 --> 00:47:55,280
cholesterol? Or does the diet work through some

997
00:47:55,280 --> 00:47:58,320
other unmeasured pathway, like reducing inflammation,

998
00:47:58,659 --> 00:48:01,579
independent of cholesterol? We want to mathematically

999
00:48:01,579 --> 00:48:04,659
separate the indirect effect, through cholesterol,

1000
00:48:04,900 --> 00:48:08,300
from the direct effect, the other pathways. It

1001
00:48:08,300 --> 00:48:10,960
sounds totally reasonable. Just control for cholesterol

1002
00:48:10,960 --> 00:48:14,199
in a regression, right? No. Remember the DAGs.

1003
00:48:14,739 --> 00:48:17,500
Cholesterol is a post -treatment variable. It

1004
00:48:17,500 --> 00:48:19,960
is caused by the treatment. If you control for

1005
00:48:19,960 --> 00:48:22,539
it in a standard regression, you are likely inducing

1006
00:48:22,539 --> 00:48:25,940
Z -bias or M -bias. You will completely scramble

1007
00:48:25,940 --> 00:48:28,679
the causal estimate. Okay, so how does the potential

1008
00:48:28,679 --> 00:48:31,260
outcomes framework solve this without relying

1009
00:48:31,260 --> 00:48:33,679
on standard regression? It attempts to solve

1010
00:48:33,679 --> 00:48:36,789
it using nested potential outcomes. To calculate

1011
00:48:36,789 --> 00:48:39,670
a natural direct effect, the math requires us

1012
00:48:39,670 --> 00:48:44,289
to define a variable like y of 1 m sub 0. This

1013
00:48:44,289 --> 00:48:47,010
is where the math gave me vertigo. Let's translate

1014
00:48:47,010 --> 00:48:51,489
y of 1 comma m sub 0 into reality. The notation

1015
00:48:51,489 --> 00:48:55,469
y of 1 comma m sub 0 represents the potential

1016
00:48:55,469 --> 00:48:59,070
outcome, y, that an individual would experience

1017
00:48:59,070 --> 00:49:01,750
if they were exposed to the treatment, the 1,

1018
00:49:01,969 --> 00:49:05,610
but their mediator, m, was artificially held

1019
00:49:05,610 --> 00:49:08,190
at the exact, specific level it would have been

1020
00:49:08,190 --> 00:49:11,769
if they had received the control, the zero. Wait,

1021
00:49:11,809 --> 00:49:14,849
I need to map this to the diet example. We want

1022
00:49:14,849 --> 00:49:17,710
to measure the direct effect of the diet. The

1023
00:49:17,710 --> 00:49:20,289
math says we must imagine a parallel universe

1024
00:49:20,289 --> 00:49:22,650
where a patient is strictly adhering to this

1025
00:49:22,650 --> 00:49:25,230
new, super healthy diet, so treatment equals

1026
00:49:25,230 --> 00:49:28,969
one, but... Somehow, we reach into their biology

1027
00:49:28,969 --> 00:49:31,610
and magically hold their cholesterol level exactly

1028
00:49:31,610 --> 00:49:34,389
at the terrible high level it would have been

1029
00:49:34,389 --> 00:49:35,969
if they had spent the last month eating fast

1030
00:49:35,969 --> 00:49:40,789
food. So mediator equals zero. Yes, we are conceptually

1031
00:49:40,789 --> 00:49:43,349
decoupling the treatment from its natural biological

1032
00:49:43,349 --> 00:49:46,329
consequence to isolate the alternative pathways.

1033
00:49:46,710 --> 00:49:49,909
But that is physically impossible. We cannot

1034
00:49:49,909 --> 00:49:52,190
biologically separate the healthy diet from the

1035
00:49:52,190 --> 00:49:54,809
cholesterol response in that specific counterfactual

1036
00:49:54,809 --> 00:49:57,940
way. And if we can't physically do it, even in

1037
00:49:57,940 --> 00:50:00,699
a hypothetical experiment, some statisticians

1038
00:50:00,699 --> 00:50:03,099
argue this entire exercise is basically science

1039
00:50:03,099 --> 00:50:06,019
fiction. This raises the most profound philosophical

1040
00:50:06,019 --> 00:50:10,250
clash in the book, found in chapter 27. Researchers

1041
00:50:10,250 --> 00:50:13,349
like Frangakis and Rubin label these nested potential

1042
00:50:13,349 --> 00:50:17,969
outcomes as a priori counterfactuals. They argue

1043
00:50:17,969 --> 00:50:22,010
that because y of 1, m sub 0, cannot be observed

1044
00:50:22,010 --> 00:50:25,400
in any conceivable physical experiment, Utilizing

1045
00:50:25,400 --> 00:50:28,260
it crosses a hard line. You are no longer doing

1046
00:50:28,260 --> 00:50:31,320
empirical science. You are doing metaphysics.

1047
00:50:31,880 --> 00:50:35,670
Metaphysics. The book literally brings the philosopher

1048
00:50:35,670 --> 00:50:38,789
Karl Popper into the statistical debate. Yes.

1049
00:50:39,010 --> 00:50:42,329
Popper's demarcation of science is based on falsifiability.

1050
00:50:42,940 --> 00:50:46,000
A scientific hypothesis must be capable of being

1051
00:50:46,000 --> 00:50:48,639
tested and proven false by physical observation.

1052
00:50:49,579 --> 00:50:52,940
Because the state of y of 1 m sub 0 is fundamentally

1053
00:50:52,940 --> 00:50:56,579
universally unobservable, any mathematical claim

1054
00:50:56,579 --> 00:50:59,929
you make about it cannot be falsified. The strict

1055
00:50:59,929 --> 00:51:02,210
Popperian statistician looks at natural direct

1056
00:51:02,210 --> 00:51:05,269
effects and mediation analysis and says, this

1057
00:51:05,269 --> 00:51:07,929
is mathematical poetry. It is not statistics.

1058
00:51:08,349 --> 00:51:11,289
That is a staggering critique. You have these

1059
00:51:11,289 --> 00:51:13,449
elegant equations that work perfectly on paper,

1060
00:51:13,489 --> 00:51:17,469
but the reality they describe cannot exist. It

1061
00:51:17,469 --> 00:51:19,630
feels like a devastating blow to mediation analysis.

1062
00:51:20,309 --> 00:51:23,050
Does the book offer a way out, or does it just

1063
00:51:23,050 --> 00:51:26,030
leave us hanging in an existential crisis? Pingding

1064
00:51:26,030 --> 00:51:28,570
does not leave us hanging. The text presents

1065
00:51:28,570 --> 00:51:30,969
alternatives that satisfy the Popperian requirement

1066
00:51:30,969 --> 00:51:34,829
for physical observation. Specifically, the controlled

1067
00:51:34,829 --> 00:51:38,789
direct effect in Chapter 28. How does the controlled

1068
00:51:38,789 --> 00:51:42,170
direct effect differ from the metaphysical natural

1069
00:51:42,170 --> 00:51:45,789
direct effect? Instead of imagining a magical,

1070
00:51:46,070 --> 00:51:48,889
unobservable, counterfactual world where cholesterol

1071
00:51:48,889 --> 00:51:52,539
is held at what it would have been, the controlled

1072
00:51:52,539 --> 00:51:54,860
direct effect asks a fundamentally different

1073
00:51:54,860 --> 00:51:58,119
question. What is the effect of the diet if we

1074
00:51:58,119 --> 00:52:01,300
physically, medically intervene and force everyone's

1075
00:52:01,300 --> 00:52:04,559
cholesterol to a specific, observable, fixed

1076
00:52:04,559 --> 00:52:08,519
level, say, exactly 150 milligrams per deciliter?

1077
00:52:08,880 --> 00:52:12,630
Oh, I... could theoretically run that experiment.

1078
00:52:12,730 --> 00:52:15,429
I could put people on the diet and then use separate

1079
00:52:15,429 --> 00:52:18,130
statin medications to clamp everyone's cholesterol

1080
00:52:18,130 --> 00:52:22,510
at exactly 150. That is a physical observable

1081
00:52:22,510 --> 00:52:26,150
intervention. Exactly. It grounds the mathematics

1082
00:52:26,150 --> 00:52:29,690
back in observable reality. It forces the researcher

1083
00:52:29,690 --> 00:52:32,489
to be incredibly precise about what they are

1084
00:52:32,489 --> 00:52:35,489
actually claiming to know. If you cannot describe

1085
00:52:35,489 --> 00:52:37,610
a physical experiment that corresponds to your

1086
00:52:37,610 --> 00:52:40,610
mathematical equation, you must think very carefully

1087
00:52:40,610 --> 00:52:42,289
about whether you should be claiming to have

1088
00:52:42,289 --> 00:52:45,989
calculated it at all. It is a stunning reminder

1089
00:52:45,989 --> 00:52:48,750
that causal inference isn't just about crunching

1090
00:52:48,750 --> 00:52:51,670
numbers in a black box algorithm. It requires

1091
00:52:51,670 --> 00:52:54,730
a deep philosophical interrogation of the physical

1092
00:52:54,730 --> 00:52:56,650
reality those numbers are meant to represent.

1093
00:52:57,250 --> 00:52:59,849
Which is the core thesis of the entire textbook.

1094
00:53:00,190 --> 00:53:02,510
And it brings us to the end of our journey today.

1095
00:53:02,980 --> 00:53:05,139
We have covered an immense amount of intellectual

1096
00:53:05,139 --> 00:53:08,219
ground, unpacking the architecture of Peng Ding's

1097
00:53:08,219 --> 00:53:10,739
A First Course in Causal Inference. We really

1098
00:53:10,739 --> 00:53:12,940
have. We've traversed the dangerous illusions

1099
00:53:12,940 --> 00:53:15,619
of simple association and the Yule -Simpson paradox.

1100
00:53:15,980 --> 00:53:18,920
We built the rigorous, demanding foundation of

1101
00:53:18,920 --> 00:53:21,360
potential outcomes, counterfactuals, and the

1102
00:53:21,360 --> 00:53:24,349
strict rules of sattva. We explored the mathematical

1103
00:53:24,349 --> 00:53:27,309
magic of Fisher's randomization and Nyman's estimation

1104
00:53:27,309 --> 00:53:30,550
and navigated the treacherous, unconfounded waters

1105
00:53:30,550 --> 00:53:33,110
of observational studies using propensity scores

1106
00:53:33,110 --> 00:53:36,750
and doubly robust safety nets. We deployed DAGs

1107
00:53:36,750 --> 00:53:39,610
and E -values against hidden ghosts, leveraged

1108
00:53:39,610 --> 00:53:41,909
the econometric hacks of instrumental variables

1109
00:53:41,909 --> 00:53:45,010
in late. And finally, we brushed right up against

1110
00:53:45,010 --> 00:53:47,690
the epistemological limits of science with mediation

1111
00:53:47,690 --> 00:53:50,789
and post -treatment traps. It truly is a masterclass

1112
00:53:50,789 --> 00:53:52,489
in how to think critically about the universe.

1113
00:53:53,090 --> 00:53:55,230
And I want to leave you, the listener, with a

1114
00:53:55,230 --> 00:53:58,349
final provocative thought to mull over. The next

1115
00:53:58,349 --> 00:54:00,570
time you are staring at a spreadsheet, using

1116
00:54:00,570 --> 00:54:02,610
historical data to make a major decision in your

1117
00:54:02,610 --> 00:54:04,829
life or your business, maybe you're evaluating

1118
00:54:04,829 --> 00:54:07,969
the ROI of a massive marketing campaign or trying

1119
00:54:07,969 --> 00:54:11,090
to trace the root cause of a health issue. Stop

1120
00:54:11,090 --> 00:54:13,150
and ask yourself this question. It's an important

1121
00:54:13,150 --> 00:54:15,869
one. Are you relying on an assumption that can

1122
00:54:15,869 --> 00:54:18,230
actually be tested in the real physical world?

1123
00:54:18,900 --> 00:54:22,320
Or are you hidden deep in your own logic, implicitly

1124
00:54:22,320 --> 00:54:24,920
making a metaphysical claim about a parallel

1125
00:54:24,920 --> 00:54:27,860
universe that can never exist? Because as we've

1126
00:54:27,860 --> 00:54:30,440
learned today from Peng Ding, data isn't just

1127
00:54:30,440 --> 00:54:33,360
a collection of numbers. It is a philosophy of

1128
00:54:33,360 --> 00:54:36,460
reality. And mastering that philosophy is the

1129
00:54:36,460 --> 00:54:39,139
only way we can ever truly understand what causes

1130
00:54:39,139 --> 00:54:41,780
what. Thank you for joining us on this rigorous,

1131
00:54:42,019 --> 00:54:44,019
custom -tailored deep dive into the architecture

1132
00:54:44,019 --> 00:54:46,639
of causal inference. We hope your diagnostic

1133
00:54:46,639 --> 00:54:48,880
x -ray machine for empirical data is looking

1134
00:54:48,880 --> 00:54:52,300
a whole lot sharper. Until next time, keep questioning

1135
00:54:52,300 --> 00:54:52,840
the causes.