Linked Questions
52 questions linked to/from Under which assumptions a regression can be interpreted causally?
105
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17
answers
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Under what conditions does correlation imply causation?
We all know the mantra "correlation does not imply causation" which is drummed into all first year statistics students. There are some nice examples here to illustrate the idea.
But sometimes ...
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76
votes
6
answers
9k
views
Criticism of Pearl's theory of causality
In the year 2000, Judea Pearl published Causality. What controversies surround this work? What are its major criticisms?
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22
votes
6
answers
68k
views
Does simple linear regression imply causation?
I know correlation does not imply causation but instead the strength and direction of the relationship. Does simple linear regression imply causation? Or is an inferential (t-test, etc.) statistical ...
- 221
24
votes
3
answers
17k
views
Unconfoundedness in Rubin's Causal Model- Layman's explanation
When implementing Rubin's causal model, one of the (untestable) assumptions that we need is unconfoundedness, which means
$$(Y(0),Y(1))\perp T|X$$
Where the LHS are the counterfactuals, the T is the ...
- 1,229
21
votes
5
answers
4k
views
Definition and delimitation of regression model
An embarrassingly simple question -- but it seems it has not been asked on Cross Validated before:
What is the definition of a regression model?
Also a support question,
What is not a regression ...
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30
votes
2
answers
8k
views
do(x) operator meaning?
I have seen the $do(x)$ operator everywhere in some literature review I am doing on Causality (see, for instance this wikipedia entry). However, I cannot find a formal and general definition of this ...
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17
votes
3
answers
1k
views
Which OLS assumptions are colliders violating?
The following webpage says that:
We should not control for a collider variable!
Which OLS assumptions are colliders violating?
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9
votes
2
answers
1k
views
Incorrectly Using the Word "Causal" to Describe a Regression Model?
Suppose we take the classical linear regression model:
$$y_i = \beta_0 + \beta_1 x_i + \epsilon_i$$
Over the years, I have heard so many people say that such an interpretation can be drawn from this ...
15
votes
5
answers
11k
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What are the differences between stochastic and fixed regressors in linear regression model?
If we have stochastic regressors, we are drawing random pairs $(y_i,\vec{x}_i)$ for a bunch of $i$, the so-called random sample, from a fixed but unknown probabilistic distribution $(y,\vec{x})$. ...
- 502
19
votes
4
answers
9k
views
Difference Between Simultaneous Equation Model and Structural Equation Model
Can anybody please help me to understand the differences between simultaneous equations models and structural equation models (SEM)? It will be great if somebody can provide me some literature on it.
...
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15
votes
2
answers
2k
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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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18
votes
1
answer
4k
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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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13
votes
3
answers
3k
views
Regression and causality in econometrics
In regression in general and in linear regression in particular, causal interpretation of parameters is sometimes permitted. At least in econometrics literature, but not only, when causal ...
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6
votes
2
answers
12k
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Strict exogeneity and lagged variables
I am confused why strict exogeneity must be violated when we have lagged time series variables. My understanding of strict exogeneity is that a variable must be uncorrelated with error terms in all ...
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4
votes
3
answers
2k
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Conditional probability and causality
I would like to understand the link between conditional probabilities and causality. More precisely:
Assume we have two variables $A=\{0,1\}$ and $B=\{0,1\}$ and we observe:
$P(A=1|B=1)>P(A=1|B=0)...
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9
votes
2
answers
2k
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What is the relationship between minimizing prediction error versus parameter estimation error?
With the advent of statistical learning techniques, people are talking a lot about prediction error, while in classical statistics, one is focusing on parameter estimation error. What is the ...
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5
votes
3
answers
2k
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Measurement error in one indep variable in OLS with multiple regression
Suppose I regress (with OLS) $y$ on $x_1$ and $x_2$. Suppose I have i.i.d. sample of size n, and that $x_1$ is observed with error but $y$ and $x_2$ are observed without error. What is the probability ...
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18
votes
2
answers
1k
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How would econometricians answer the objections and recommendations raised by Chen and Pearl (2013)?
In their article, Chen and Pearl (2013), critically examined 6 econometric textbooks, among these the textbooks written by Wooldridge (2009) {the introductory book}, and Stock & Watson (2011). ...
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3
votes
2
answers
2k
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Regression and the CEF
I recently read in this page (https://www.timlrx.com/2018/02/26/notes-on-regression-approximation-of-the-conditional-expectation-function/#fn1) that:
"Regression offers a way of approximating ...
8
votes
3
answers
887
views
Are all statistical models also causal models?
I'm just starting to learn about causal inference methods, focused on Pearl's do-calculus.
So the point between Pearl's causal graphs and rules for manipulating causal graphs appears to be to turn a ...
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5
votes
2
answers
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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 ...
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3
votes
2
answers
2k
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Interpreting interaction term when X1 effect on Y depends on X2 but X2 effect on Y does not depend on X1
Imagine a set of variables, X1, X2, and Y, all continuous variables.
There is a simple case where X1 and X2 affect Y such that:
Y = alpha + β1 X1 + β2 X2 + error
Using R syntax, a model to analyze ...
- 327
2
votes
3
answers
2k
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Endogeneity testing using correlation test
I am currently testing my linear model using OLS method. The last thing I have to test is endogeneity issue. Is it enough if I test each explanatory variable for correletion with error term? Than ...
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8
votes
1
answer
1k
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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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3
votes
2
answers
1k
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Is it possible for the zero conditional mean assumption to fail?
I have a questions about the so-called "zero conditional mean" assumption often made in the context of regression analysis. I am struggling to see how it could be violated, or rather where ...
- 303
1
vote
2
answers
1k
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Regression's population parameters
Suppose I've specified a linear regression model:
$$
Y = \beta_0 + \beta_1 X + \epsilon
$$
where $\beta_0$, $\beta_1$ are the population parameters. My question is: why are these parameters ...
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2
votes
2
answers
358
views
Why are error properties in linear regression assumptions if they are true by construction?
The following two results on the residuals ($\epsilon$) in the case of linear regression get stated as assumptions of the linear regressions
$E(\epsilon) = 0$
$cov(X, \epsilon) = 0$
Here is MIT 18....
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0
votes
2
answers
3k
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Zero conditional expectation of error in OLS regression
Suppose we have a dependent variable $Y$ and an independent variable $X$ in a population, and we want to estimate the linear model
$$
Y = \beta_{0} + \beta_{1}X + \varepsilon
$$
Using the least-...
- 245
0
votes
1
answer
3k
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OLS Assumption-No correlation should be there between error term and independent variable and error term and dependent variable
My question is that does endogeneity exists if there is correlation between dependent variable and error term, but not in between error term and independent variable. So for Ex, we know there should ...
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8
votes
1
answer
847
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conditional and interventional expectation
Conditional expectation $E[Y|X]$ and interventional expectation $E[Y|do(X)]$ are related but conceptually very different things.
I know that if $X$ is a randomly assigned by an experiment, we have ...
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