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Endogeneity refers to a situation where an explanatory variable in a model is correlated with the error term. Endogeneity induces biased parameter estimates. This is an important problem when working with observational data and the goal is causal inference.

2 votes

Does confounding always imply endogeneity?

But if the confounding variable is measured, then it's no longer endogeneity. … .$ $X$ is confounded with $U_Y,$ which is the definition of endogeneity. Typically, $U_Y$ is not measured. …
Adrian Keister's user avatar
0 votes

Measuring the causal impact of a policy that is not binding

You want to know if there is an endogeneity problem. The answer is that it depends. … Now you have a backdoor path from $I$ to $Y,$ and you have an endogeneity problem. …
Adrian Keister's user avatar
1 vote

How to deal with treatment variable which is determined by the outcome variable

Here's a partial answer: for any moment in time $t$, think about the outcomes at $t$, the messages at $t+1,$ and the outcomes at $t+2,$ like so: Obviously, this diagram leaves out traffic, weather, a …
Adrian Keister's user avatar
10 votes
Accepted

An intuitive explanation of the instrumental variable

I think the most intuitive explanation lies in the causal Directed Acyclic Graph (DAG) approach taken by Judea Pearl, where $A\to B$ means $A$ causes $B$. The typical setup for an instrumental variabl …
Adrian Keister's user avatar
2 votes

My instrument (z) only affects y through x, but y affects z directly. Is my instrument valid?

If it is the case that $Y$ affects $Z,$ then $Z$ cannot be an instrument. By definition, an instrumental variable has to be $d$-separated from $Y$ in $G_{\alpha}$ and $d$-connected to $X.$ Your instru …
Adrian Keister's user avatar
4 votes

Does an endogenous variable bias the coefficient of the exogenous one?

Well, except in the multivariate normal case, zero covariance does not imply independence. You have not specified any distributions, so we cannot assume multivariate normal distributions. So technical …
Adrian Keister's user avatar
2 votes

Instrumental variables- unconfoundness vs exclusion restriction

On page 86 of Causal Inference in Statistics: A Primer, by Pearl, Glymour, and Jewell, the authors state that A variable is called an "instrument" if it is $d$-separated from $Y$ in $G_\alpha$ and, i …
Adrian Keister's user avatar