17 questions linked to/from do(x) operator meaning?
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### Mathematical definition of causality

Let $Y$ and $X$ be random variables. $E(Y|X)$ is the conditional mean of $Y$ given $X$. We say $Y$ is not causally related to $X$ if $E(Y|X)$ does not depend on $X$, which implies it is equal to $E(Y)$...
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### How is causation defined mathematically?

What is the mathematical definition of a causal relationship between two random variables? Given a sample from the joint distribution of two random variables $X$ and $Y$, when would we say $X$ causes ...
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### T-consistency vs. P-consistency

Francis Diebold has a blog post "Causality and T-Consistency vs. Correlation and P-Consistency" where he presents the notion of P-consistency, or presistency: Consider a standard linear regression ...
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### Is causal inference only from data possible?

Suppose we are given a dataset but not the capability of performing some AB testing. We do some regression using X as predictor and Y as response and get a model. Can we actually say something about ...
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### Is a regression causal if there are no omitted variables?

A regression of $y$ on $x$ need not be causal if there are omitted variables which influence both $x$ and $y$. But if not for omitted variables and measurement error, is a regression causal? That is, ...
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### Is there a simpler probabilistic causal model that describes this data generating process?

Consider the following data generating process: A person with gender male or female is selected from a population with probability $\alpha$ of selecting female. The person is offered a drug to treat ...
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### Causal effect by back-door and front-door adjustments

If we wanted to calculate the causal effect of $X$ on $Y$ in the causal graph below, we can use both the back-door adjustment and front-Door adjustment theorems, i.e., P(y | \textit{do}(X = x)) = \...
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### Are causal effects constant over time?

The possibility that correlations are unstable over time is a matter of fact. Just for example we can consider that models included in these articles: https://www.sciencedirect.com/science/article/abs/...
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### Relationship between Causal Calculus (in the sense of the Book of Why) and other existing modeling formalisms?

I am watching this video on youtube: https://youtu.be/zvrcyqcN9Wo?t=2896 about Causal Calculus (CC), namely this section on causal graphs, and it seems to me that this theory of causality is not that ...
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### What's the DGP in causal inference?

This question come from this discussion (Under which assumptions a regression can be interpreted causally? ). That discussion touch too arguments and is not possible to speak about all things there. ...
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### non stochastic regressors

In the multiple linear regression analysis if regressors are non-stochastic the causal interpretation of parameters is automatically permitted? I think so, because it seems me that the model can be ...
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### non stochastic regressors and causation

Randomized controlled experiment is base case for causality (also) in regression. However currently I’m analyzing the role of causality in linear regression as shown in many econometrics textbook. ...
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### regression and causation

In the Chen and Pearl (2013) article there are several critics about econometrics textbooks. Currently I try to understand more about it. In particular the Authors written (pag 4, footnote 5): From ...
Pearl defines (see Causality, Judea Pearl, 2nd ed., Definition 7.1.1) a Structural Causal Model (SCM) as a triple $(\mathscr U, \mathscr V, F)$ where $\mathscr U$ is a set of "exogenous variables," \$\...