Linked Questions
49 questions linked to/from Under which assumptions a regression can be interpreted causally?
4
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703
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linear causal model
Currently I’m focused on linear causal model expressed as a structural equation like this:
$y = \beta_1 x_1 + \beta_2 x_2 + … + \beta_k x_k + u$
where $E[u|x_1,x_2,…,x_k]=0$ (exogenous error)
we ...
- 4,636
2
votes
1
answer
183
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Causal discovery for pairwise independent joint dependent variables
Consider the standard example for variables that are pairwise independent but joint dependent.
$$
(x,y,z)=
\begin{cases}
(0,0,0) & \text{probability 1/4} \\
(1,1,0) & \text{probability 1/4} \\
...
2
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1
answer
211
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Clarification on the assumptions $E[u|x]=0$ and the $x_i$ being fixed in repeated samples in Wooldridge Introductory Econometrics
The author is writing on the assumption $E[u|x]=0$.
The part of the text which is not clear to me is this (the red lines emphasize where the critical portions are located) :
In the first piece I don'...
- 346
2
votes
1
answer
377
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endogenous regressor and correlation
In a widely cited paper by Antonakis et al. (2010), they mention:
If the relation between x and y is due, in part, to other reasons,
then x is endogenous, and the coefficient of x cannot be ...
- 487
1
vote
1
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54
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What exactly is a "true" population model in linear regression?
What do we mean by a true population model when talking about linear regression? Say I want to study the effects of years of schooling $S$ on wages. I posit the following two models:
$log(wage)=β_0+...
- 65
1
vote
1
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347
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OLS Estimation, Bias and Causality
I wish to ask about the bias of an OLS estimator. In what follows I assume that the regression that we are dealing with is an approximation to a linear conditional expectations function. That is we ...
- 151
1
vote
1
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74
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What are the main methods for estimating the Average Treatment Effect in Observational Studies outside of matching?
I am wondering what the main methods for estimating the Average Treatment Effect in Observational Studies are outside of matching. In matching, there are weighting, stratification, propensity score ...
- 2,682
1
vote
1
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193
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Econometrics meaning of structural versus regression model
I want to make sure my understanding is correct. Particularly in econometrics, when authors write down a model:
$Y_i = \beta_0 + \beta_1 X_i + \epsilon$
Can I think of this as a 'structural model'- or ...
- 601
1
vote
1
answer
1k
views
Does homoscedasticity imply that the regressor variables and the errors are uncorrelated?
By OLS regression equation:
$$Y = a + bX + e$$
My thoughts are that homoscedasticity by definition imply that $Var(Y|X) = Var(e|X)=$ constant, then this would imply that $Var(e|X) = Var(e)$ which ...
- 23
0
votes
1
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174
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Endogeneity and Regression Interpretation: how does it work? is it possible?
My question is not particularly straightforward. I will explain my reasoning, and then give the question at the end to avoid any confusion.
$\ Y_{i} = \beta_{0}+\beta_{1}X_{i}+\varepsilon_{i} $
...
- 151
0
votes
1
answer
123
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simple linear regression causality
lets say we have a perfect linear regression, i.e. we have included all relevant variables (to prevent OVB: omitted variable bias), and also such that there is no other problems like mutli-...
- 143
0
votes
1
answer
308
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Random Sampling: Weak and Strong Exogenity
$Y \ = \ X' \beta \ + \ e $
Where $Y = (y_1, ..., y_n)$ and $\beta = (\beta_0,..., \beta_k)$.
Why would Weak Exogenity under random sampling produce Strong Exogenity?
I know that weak exogenity is ...
- 232
0
votes
1
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2k
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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 ...
- 151
6
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0
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412
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Structural equation and causal model in economics
Structural equations is a useful language for causal analysis in economics. In Causality Pearl (2009 cap 5) we can find the best discussion about this.
My question: is possible to use the concept of ...
- 4,636
1
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0
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Causal assumptions when treating time series as a bunch of points
Suppose there are two time series, $x_t$ and $y_t$, that capture daily counts of some sort. $x_t$ is believed to have causal impact on $y_t$. Suppose further that a simple regression is fit to the ...
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