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19 votes
Accepted

Can an instrumental variable equation be written as a directed acyclic graph (DAG)?

Yes. For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$. The instrumental variable model for this DAG ...
Alexis's user avatar
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17 votes

Explain in layperson's terms why predictive models aren't causally interpretable

First of all, I don't think this should be treated as a strict dichotomy: "predictive models can never establish causal inference." There are various situations in which a predictive model ...
Graham Wright's user avatar
16 votes

Explain in layperson's terms why predictive models aren't causally interpretable

I think this explanation is best approached sequentially. Start with a simple story: When my dog Omey wags his tail, that indicates he is happy. For instance, he never wags it at the vet, wags it a ...
dimitriy's user avatar
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15 votes

Can an instrumental variable equation be written as a directed acyclic graph (DAG)?

Yes, they surely can. As a matter of fact, the SCM/DAG literature has been working on generalized notions of instrumental variables, you might want to check Brito and Pearl, or Chen, Kumor and ...
Carlos Cinelli's user avatar
15 votes

Why not use instrumental variable directly as a covariate in the regression?

The point of instrumental variable regression is to provide an unbiased estimate of the causal effect of exposure $X$ on outcome $O$, when there is some unmeasured—possibly unmeasureable—variable $U$ ...
Alexis's user avatar
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14 votes

Instrumental variable exclusion restriction

There are two criteria for good instruments: The instrument $z$ is correlated with the endogenous variable $x$ (relevance). The instrument $z$ affects dependent variable $y$ only through $x$. In ...
ChrisP's user avatar
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11 votes
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What are the differences between tests for overidentification in 2SLS

There are a lot of questions here, so I'll first give an overview, and then explain a bit more. You have 4 tests you're asking about: Hausman test, Sargan test, a Wald test of exogeneity, and a Hansen ...
doubled's user avatar
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11 votes
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DAGs: instrumental and adjusted variables

While drawing DAGs...what are instrumental and adjusted variables? An instrumental variable is an observed variable that is often used to help obtain an unbiased estimate for a causal effect that is ...
Robert Long's user avatar
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11 votes

Do I need to include confounding variables in my regression model when I use instrument variables?

The point of an instrumental variable (IV) is that it works even when the confounding variables are unknown. If they are all known, I'm not sure it makes sense to use an IV approach. In any case, if ...
Scriddie's user avatar
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10 votes
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How does IV 2SLS obtain a causal coefficient?

Start from the structural model, $$y_i = \alpha + \beta X_i + \epsilon_i$$ where the explanatory variable of interest $X_i$ has a correlation with the error term, $Cov(X_i,\epsilon_i)\neq 0$. In this ...
Andy's user avatar
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10 votes
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Can I ignore the negative R-squared value when I am using instrumental variable regression?

Yes, the linked STATA post answers your question in a single sentence: $R^2$ really has no statistical meaning in the context of 2SLS/IV. How can $R^2$ be negative? Wikipedia has a great ...
Frans Rodenburg's user avatar
10 votes
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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 ...
Adrian Keister's user avatar
10 votes

Explain in layperson's terms why predictive models aren't causally interpretable

I don't think you even need to posit a covariate adjustment set $\textbf{Z}$ nor the indexation of black-box models to convey in layman terms the main point. Assume the following: $y$ is number of ...
Kuku's user avatar
  • 1,471
9 votes

Definition of validity of an instrumental variable

Following Hernán and Robins' Causal Inference, Chapter 16: Instrumental variable estimation, instrumental variables have four assumptions/requirements: $Z$ must be associated with $X$. $Z$ must ...
Alexis's user avatar
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8 votes

Why doesn't measurement error in the dependent variable bias the results?

Regression analysis answers the question, "What is the AVERAGE Y value for those who have given X values?" or, equivalently, "How much is Y predicted to change ON AVERAGE if we change X by one unit?" ...
user175057's user avatar
8 votes
Accepted

How can I compute the standard error of the Wald estimator?

Here is my answer to my question. I hope there is no mistake in calculus. We have : $y_{1,i}$ a dichotomous random variable following a Bernouilli distribution with parameter $\mu_{y_1}$ $y_{0,i}$ a ...
PAC's user avatar
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8 votes
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R-square and Intrumental Regression

No. $R^2$ in instrumental variables regression is not useful. Since one of the explanatory variables $x$ is correlated with the error $\epsilon$ we can't decompose the variance of the outcome $y$ ...
Joe King's user avatar
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7 votes
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Definition of validity of an instrumental variable

Requirements for Z to be a valid instrument for X are: Relevance = Z needs to highly correlated with X Exogenous = Z is correlated with Y solely through its correlation with X; so Z is uncorrelated ...
dimitriy's user avatar
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7 votes

Time series and instrumental variables

Consider a series $Y_t$ generated as an $ARMA(1,1)$ process $$ Y_t=\phi Y_{t-1}+\epsilon_t+\theta\epsilon_{t-1} $$ Suppose our interest centers on estimating $\phi$. We have an endogeneity issue here, ...
Christoph Hanck's user avatar
7 votes
Accepted

Is Just-Identified 2SLS Median-Unbiased?

In simulation studies the term median bias refers to the absolute value of the deviations of an estimator from its true value (which you know in this case because it is a simulation so you choose the ...
Andy's user avatar
  • 19.2k
7 votes

Covariance, bernoulli distribution and instrumental variables

Consider the ordinary least squares fit of $Y$ to $Z$: Because the mean of univariate data minimizes the sum of squared residuals, this fit must rise from the mean of the $Y$ values associated with $...
whuber's user avatar
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7 votes
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What is difference between mediation analysis and mendelian randomization analysis?

IV in mediation analysis stands for independent variable not instrumental variable. There is no concept of instruments in mediation analysis. In mediation analysis, the variable of interest is the ...
Heteroskedastic Jim's user avatar
6 votes
Accepted

Why is the variance of 2SLS bigger than that of OLS?

We say a matrix $A$ is at least as large as $B$ if their difference $A-B$ is positive semidefinite (psd). An equivalent statement that turns out to be handier to check here is that $B^{-1}-A^{-1}$ is ...
Christoph Hanck's user avatar
6 votes
Accepted

Log transformation of binary explanatory variable in regression

You're right, and not just because log zero is not defined. Any one-to-one transformation of $0$ and $1$ to $a$ and $b$ would just be a linear rescaling. This is true with any rule or function: even ...
Nick Cox's user avatar
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6 votes
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Omitting a variable in IV estimation

The first thing to note is that whether you should consider $X$ or not cannot be answered without structural knowledge. For instance, consider the following model: In this case X is correlated with Z ...
Carlos Cinelli's user avatar
6 votes
Accepted

Does the Heckman correction with an exclusion restriction provide causal inference?

This indeed can be confusing, because the term "selection bias" pops up in two problems which are clearly different: People "select" a treatment $D$ based on a variable that influences an outcome $Y$,...
Julian Schuessler's user avatar
6 votes
Accepted

Does direction of causality between instrument and variable matter?

Yes, the direction matters. As pointed in this answer, to check whether $Z$ is an instrument for the causal effect of $X$ on $Y$ conditional on a set of covariates $S$, you have two simple graphical ...
Carlos Cinelli's user avatar
6 votes

What are the "moment conditions" in the GMM method? Also: GMM vs IV vs 2SLS?

The moment condition is the exogeneity condition $\mathbb{E}(u_i x_i) = 0$. ($\mathbb{E}(u_i | x_i)=0$ is not a moment condition. It is an equality of random variables.) OLS is a special case of ...
Michael's user avatar
  • 3,348
5 votes

Is the key assumption for instrumental variables not testable?

First, as others have said, the assumption as you have stated is not correct. The standard IV model is given by, And the key assumptions here are that $Z$ has no effect on $Y$ except through $X$ (...
Carlos Cinelli's user avatar
5 votes
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Regressing dependent variable on instruments

When you have an outcome $Y$, an endogenous explanatory variable $D$, a valid instrument $Z$, and controls $X$, then your two-stage least squares (2SLS) equation system would be $$ \begin{align} Y &...
Andy's user avatar
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